%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU736^1 : 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.nAj0S1LWoE true
% Computer : n026.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 04:56:02 PM UTC 2025
% Result : Theorem 7.11s 4.65s
% Output : Refutation 7.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/1.12 % Problem : SEU736^1 : TPTP v9.2.0. Released v3.7.0.
% 0.14/1.21 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.nAj0S1LWoE true
% 0.14/1.62 % Computer : n026.cluster.edu
% 0.14/1.62 % Model : x86_64 x86_64
% 0.14/1.62 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/1.62 % Memory : 8042.1875MB
% 0.14/1.62 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/1.62 % CPULimit : 300
% 0.14/1.62 % WCLimit : 300
% 0.14/1.62 % DateTime : Wed Oct 1 16:01:54 EDT 2025
% 0.14/1.63 % CPUTime :
% 0.14/1.63 % Running portfolio for 300 s
% 0.14/1.63 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/1.64 % Number of cores: 8
% 0.14/1.66 % Python version: Python 3.6.8
% 0.14/1.67 % Running in HO mode
% 0.55/2.42 % Total configuration time : 828
% 0.55/2.42 % Estimated wc time : 1656
% 0.55/2.42 % Estimated cpu time (8 cpus) : 207.0
% 0.58/2.74 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.58/2.77 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.58/2.80 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.58/2.85 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 1.50/2.90 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 1.50/2.91 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 1.50/2.94 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.54/2.96 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 7.11/4.65 % Solved by lams/40_c_ic.sh.
% 7.11/4.65 % done 608 iterations in 1.605s
% 7.11/4.65 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 7.11/4.65 % SZS output start Refutation
% 7.11/4.65 thf(setadjoinAx_type, type, setadjoinAx: $o).
% 7.11/4.65 thf(notdexE_type, type, notdexE: $o).
% 7.11/4.65 thf(setukpairinjL2_type, type, setukpairinjL2: $o).
% 7.11/4.65 thf(doubleComplementI1_type, type, doubleComplementI1: $o).
% 7.11/4.65 thf(setunionAx_type, type, setunionAx: $o).
% 7.11/4.65 thf(setminusELneg_type, type, setminusELneg: $o).
% 7.11/4.65 thf(cartprodsndin_type, type, cartprodsndin: $o).
% 7.11/4.65 thf(ex1E1_type, type, ex1E1: $o).
% 7.11/4.65 thf(powersetE_type, type, powersetE: $o).
% 7.11/4.65 thf(omegaSAx_type, type, omegaSAx: $o).
% 7.11/4.65 thf(exuI1_type, type, exuI1: $o).
% 7.11/4.65 thf(exuI2_type, type, exuI2: $o).
% 7.11/4.65 thf(notequalI2_type, type, notequalI2: $o).
% 7.11/4.65 thf(setukpairinjL_type, type, setukpairinjL: $o).
% 7.11/4.65 thf(kpairiskpair_type, type, kpairiskpair: $o).
% 7.11/4.65 thf(upairsubunion_type, type, upairsubunion: $o).
% 7.11/4.65 thf(funcGraphProp3_type, type, funcGraphProp3: $o).
% 7.11/4.65 thf(cartprodmempaircEq_type, type, cartprodmempaircEq: $o).
% 7.11/4.65 thf(binintersectTERcontra_type, type, binintersectTERcontra: $o).
% 7.11/4.65 thf(powerset__Cong_type, type, powerset__Cong: $o).
% 7.11/4.65 thf(sk__142_type, type, sk__142: $i).
% 7.11/4.65 thf(setminusILneg_type, type, setminusILneg: $o).
% 7.11/4.65 thf(wellorderingAx_type, type, wellorderingAx: $o).
% 7.11/4.65 thf(ksndpairEq_type, type, ksndpairEq: $o).
% 7.11/4.65 thf(funcGraphProp2_type, type, funcGraphProp2: $o).
% 7.11/4.65 thf(setadjoinSub2_type, type, setadjoinSub2: $o).
% 7.11/4.65 thf(binintersectSubset5_type, type, binintersectSubset5: $o).
% 7.11/4.65 thf(iftrue_type, type, iftrue: $o).
% 7.11/4.65 thf(upairinpowunion_type, type, upairinpowunion: $o).
% 7.11/4.65 thf(ifSingleton_type, type, ifSingleton: $o).
% 7.11/4.65 thf(doubleComplementSub2_type, type, doubleComplementSub2: $o).
% 7.11/4.65 thf(setoftrueEq_type, type, setoftrueEq: $o).
% 7.11/4.65 thf(funcImageSingleton_type, type, funcImageSingleton: $o).
% 7.11/4.65 thf(dpsetconstrERa_type, type, dpsetconstrERa: $o).
% 7.11/4.65 thf(lamProp_type, type, lamProp: $o).
% 7.11/4.65 thf(cartprodpairmemEL_type, type, cartprodpairmemEL: $o).
% 7.11/4.65 thf(emptyset__Cong_type, type, emptyset__Cong: $o).
% 7.11/4.65 thf(dpsetconstrER_type, type, dpsetconstrER: $o).
% 7.11/4.65 thf(sepInPowerset_type, type, sepInPowerset: $o).
% 7.11/4.65 thf(setukpairIR_type, type, setukpairIR: $o).
% 7.11/4.65 thf(setukpairinjR1_type, type, setukpairinjR1: $o).
% 7.11/4.65 thf(lam2p_type, type, lam2p: $o).
% 7.11/4.65 thf(binunionE_type, type, binunionE: $o).
% 7.11/4.65 thf(setext_type, type, setext: $o).
% 7.11/4.65 thf(emptyinPowerset_type, type, emptyinPowerset: $o).
% 7.11/4.65 thf(ubforcartprodlem1_type, type, ubforcartprodlem1: $o).
% 7.11/4.65 thf(descr__Cong_type, type, descr__Cong: $o).
% 7.11/4.65 thf(kfstsingleton_type, type, kfstsingleton: $o).
% 7.11/4.65 thf(binintersectTELcontra_type, type, binintersectTELcontra: $o).
% 7.11/4.65 thf(doubleComplementEq_type, type, doubleComplementEq: $o).
% 7.11/4.65 thf(eqbreln_type, type, eqbreln: $o).
% 7.11/4.65 thf(binintersectSubset1_type, type, binintersectSubset1: $o).
% 7.11/4.65 thf(complementImpComplementIntersect_type, type, complementImpComplementIntersect:
% 7.11/4.65 $o).
% 7.11/4.65 thf(in_type, type, in: $i > $i > $o).
% 7.11/4.65 thf(binunionT_lem_type, type, binunionT_lem: $o).
% 7.11/4.65 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o).
% 7.11/4.65 thf(complementT_lem_type, type, complementT_lem: $o).
% 7.11/4.65 thf(kpairsurjEq_type, type, kpairsurjEq: $o).
% 7.11/4.65 thf(setadjoinIR_type, type, setadjoinIR: $o).
% 7.11/4.65 thf(doubleComplementE1_type, type, doubleComplementE1: $o).
% 7.11/4.65 thf(beta1_type, type, beta1: $o).
% 7.11/4.65 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o).
% 7.11/4.65 thf(powersetTE1_type, type, powersetTE1: $o).
% 7.11/4.65 thf(symdiffI2_type, type, symdiffI2: $o).
% 7.11/4.65 thf(iftrueProp2_type, type, iftrueProp2: $o).
% 7.11/4.65 thf(upairset2IR_type, type, upairset2IR: $o).
% 7.11/4.65 thf(iffalseProp2_type, type, iffalseProp2: $o).
% 7.11/4.65 thf(subsetE_type, type, subsetE: $o).
% 7.11/4.65 thf(prop2set2propI_type, type, prop2set2propI: $o).
% 7.11/4.65 thf(dsetconstrEL_type, type, dsetconstrEL: $o).
% 7.11/4.65 thf(setbeta_type, type, setbeta: $o).
% 7.11/4.65 thf(eqinunit_type, type, eqinunit: $o).
% 7.11/4.65 thf(upairsetIL_type, type, upairsetIL: $o).
% 7.11/4.65 thf(powersetI1_type, type, powersetI1: $o).
% 7.11/4.65 thf(kfstpairEq_type, type, kfstpairEq: $o).
% 7.11/4.65 thf(binintersectSubset3_type, type, binintersectSubset3: $o).
% 7.11/4.65 thf(setminusIRneg_type, type, setminusIRneg: $o).
% 7.11/4.65 thf(ap2apEq1_type, type, ap2apEq1: $o).
% 7.11/4.65 thf(powersetAx_type, type, powersetAx: $o).
% 7.11/4.65 thf(binintersectSubset4_type, type, binintersectSubset4: $o).
% 7.11/4.65 thf(singletoninpowunion_type, type, singletoninpowunion: $o).
% 7.11/4.65 thf(powersetI_type, type, powersetI: $o).
% 7.11/4.65 thf(cartprodmempair_type, type, cartprodmempair: $o).
% 7.11/4.65 thf(upairsetIR_type, type, upairsetIR: $o).
% 7.11/4.65 thf(lamp_type, type, lamp: $o).
% 7.11/4.65 thf(dpsetconstrEL1_type, type, dpsetconstrEL1: $o).
% 7.11/4.65 thf(inCongP_type, type, inCongP: $o).
% 7.11/4.65 thf(setadjoinSub_type, type, setadjoinSub: $o).
% 7.11/4.65 thf(exuE3e_type, type, exuE3e: $o).
% 7.11/4.65 thf(emptysetE_type, type, emptysetE: $o).
% 7.11/4.65 thf(binintersectSubset2_type, type, binintersectSubset2: $o).
% 7.11/4.65 thf(setunionI_type, type, setunionI: $o).
% 7.11/4.65 thf(setunion__Cong_type, type, setunion__Cong: $o).
% 7.11/4.65 thf(prop2setI_type, type, prop2setI: $o).
% 7.11/4.65 thf(singletonsuniq_type, type, singletonsuniq: $o).
% 7.11/4.65 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o).
% 7.11/4.65 thf(zip_tseitin_0_type, type, zip_tseitin_0: $i > $i > $i > $o).
% 7.11/4.65 thf(setminusER_type, type, setminusER: $o).
% 7.11/4.65 thf(exuE2_type, type, exuE2: $o).
% 7.11/4.65 thf(emptyset_type, type, emptyset: $i).
% 7.11/4.65 thf(setukpairinjR11_type, type, setukpairinjR11: $o).
% 7.11/4.65 thf(ex1I_type, type, ex1I: $o).
% 7.11/4.65 thf(ex1E2_type, type, ex1E2: $o).
% 7.11/4.65 thf(setminus_type, type, setminus: $i > $i > $i).
% 7.11/4.65 thf(setukpairinjL1_type, type, setukpairinjL1: $o).
% 7.11/4.65 thf(powersetsubset_type, type, powersetsubset: $o).
% 7.11/4.65 thf(subPowSU_type, type, subPowSU: $o).
% 7.11/4.65 thf(notequalI1_type, type, notequalI1: $o).
% 7.11/4.65 thf(contrasubsetT_type, type, contrasubsetT: $o).
% 7.11/4.65 thf(notinemptyset_type, type, notinemptyset: $o).
% 7.11/4.65 thf(lam2lamEq_type, type, lam2lamEq: $o).
% 7.11/4.65 thf(nonemptyI1_type, type, nonemptyI1: $o).
% 7.11/4.65 thf(subsetTrans_type, type, subsetTrans: $o).
% 7.11/4.65 thf(kpairp_type, type, kpairp: $o).
% 7.11/4.65 thf(setukpairinjR12_type, type, setukpairinjR12: $o).
% 7.11/4.65 thf(setminusI_type, type, setminusI: $o).
% 7.11/4.65 thf(binunionIL_type, type, binunionIL: $o).
% 7.11/4.65 thf(dpsetconstrSub_type, type, dpsetconstrSub: $o).
% 7.11/4.65 thf(setunionsingleton_type, type, setunionsingleton: $o).
% 7.11/4.65 thf(subsetE2_type, type, subsetE2: $o).
% 7.11/4.65 thf(singletonsswitch_type, type, singletonsswitch: $o).
% 7.11/4.65 thf(ubforcartprodlem3_type, type, ubforcartprodlem3: $o).
% 7.11/4.65 thf(beta2_type, type, beta2: $o).
% 7.11/4.65 thf(dpsetconstrI_type, type, dpsetconstrI: $o).
% 7.11/4.65 thf(setextsub_type, type, setextsub: $o).
% 7.11/4.65 thf(binunionLsub_type, type, binunionLsub: $o).
% 7.11/4.65 thf(setunionsingleton1_type, type, setunionsingleton1: $o).
% 7.11/4.65 thf(iftrueorfalse_type, type, iftrueorfalse: $o).
% 7.11/4.65 thf(emptysetsubset_type, type, emptysetsubset: $o).
% 7.11/4.65 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o).
% 7.11/4.65 thf(cartprodpairsurjEq_type, type, cartprodpairsurjEq: $o).
% 7.11/4.65 thf(setOfPairsIsBReln_type, type, setOfPairsIsBReln: $o).
% 7.11/4.65 thf(setunionE_type, type, setunionE: $o).
% 7.11/4.65 thf(ksndsingleton_type, type, ksndsingleton: $o).
% 7.11/4.65 thf(setminusSubset1_type, type, setminusSubset1: $o).
% 7.11/4.65 thf(powersetT_lem_type, type, powersetT_lem: $o).
% 7.11/4.65 thf(emptyinunitempty_type, type, emptyinunitempty: $o).
% 7.11/4.65 thf(binunionIR_type, type, binunionIR: $o).
% 7.11/4.65 thf(theeq_type, type, theeq: $o).
% 7.11/4.65 thf(sk__143_type, type, sk__143: $i).
% 7.11/4.65 thf(setadjoinE_type, type, setadjoinE: $o).
% 7.11/4.65 thf(doubleComplementSub1_type, type, doubleComplementSub1: $o).
% 7.11/4.65 thf(infuncsetfunc_type, type, infuncsetfunc: $o).
% 7.11/4.65 thf(ap2apEq2_type, type, ap2apEq2: $o).
% 7.11/4.65 thf(ap2p_type, type, ap2p: $o).
% 7.11/4.65 thf(setadjoinIL_type, type, setadjoinIL: $o).
% 7.11/4.65 thf(cartprodsndpairEq_type, type, cartprodsndpairEq: $o).
% 7.11/4.65 thf(exuE1_type, type, exuE1: $o).
% 7.11/4.65 thf(ubforcartprodlem2_type, type, ubforcartprodlem2: $o).
% 7.11/4.65 thf(binintersectRsub_type, type, binintersectRsub: $o).
% 7.11/4.65 thf(setminusLsub_type, type, setminusLsub: $o).
% 7.11/4.65 thf(funcextLem_type, type, funcextLem: $o).
% 7.11/4.65 thf(setukpairinjR_type, type, setukpairinjR: $o).
% 7.11/4.65 thf(notinsingleton_type, type, notinsingleton: $o).
% 7.11/4.65 thf(eqimpsubset2_type, type, eqimpsubset2: $o).
% 7.11/4.65 thf(exuEu_type, type, exuEu: $o).
% 7.11/4.65 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o).
% 7.11/4.65 thf(upairsetE_type, type, upairsetE: $o).
% 7.11/4.65 thf(omega0Ax_type, type, omega0Ax: $o).
% 7.11/4.65 thf(subsetTI_type, type, subsetTI: $o).
% 7.11/4.65 thf(notsubsetI_type, type, notsubsetI: $o).
% 7.11/4.65 thf(iffalseProp1_type, type, iffalseProp1: $o).
% 7.11/4.65 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o).
% 7.11/4.65 thf(setextAx_type, type, setextAx: $o).
% 7.11/4.65 thf(cartprodpairmemER_type, type, cartprodpairmemER: $o).
% 7.11/4.65 thf(powersetE1_type, type, powersetE1: $o).
% 7.11/4.65 thf(bs114d_type, type, bs114d: $o).
% 7.11/4.65 thf(contrasubsetT3_type, type, contrasubsetT3: $o).
% 7.11/4.65 thf(noeltsimpempty_type, type, noeltsimpempty: $o).
% 7.11/4.65 thf(ifp_type, type, ifp: $o).
% 7.11/4.65 thf(powersetTI1_type, type, powersetTI1: $o).
% 7.11/4.65 thf(binintersectLsub_type, type, binintersectLsub: $o).
% 7.11/4.65 thf(subsetI1_type, type, subsetI1: $o).
% 7.11/4.65 thf(symdiffE_type, type, symdiffE: $o).
% 7.11/4.65 thf(descrp_type, type, descrp: $o).
% 7.11/4.65 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o).
% 7.11/4.65 thf(foundationAx_type, type, foundationAx: $o).
% 7.11/4.65 thf(emptysetAx_type, type, emptysetAx: $o).
% 7.11/4.65 thf(emptyI_type, type, emptyI: $o).
% 7.11/4.65 thf(setadjoinOr_type, type, setadjoinOr: $o).
% 7.11/4.65 thf(eta2_type, type, eta2: $o).
% 7.11/4.65 thf(binintersectEL_type, type, binintersectEL: $o).
% 7.11/4.65 thf(emptyE1_type, type, emptyE1: $o).
% 7.11/4.65 thf(emptyInPowerset_type, type, emptyInPowerset: $o).
% 7.11/4.65 thf(complementTI1_type, type, complementTI1: $o).
% 7.11/4.65 thf(vacuousDall_type, type, vacuousDall: $o).
% 7.11/4.65 thf(dsetconstrER_type, type, dsetconstrER: $o).
% 7.11/4.65 thf(binintersectI_type, type, binintersectI: $o).
% 7.11/4.65 thf(funcext_type, type, funcext: $o).
% 7.11/4.65 thf(funcGraphProp4_type, type, funcGraphProp4: $o).
% 7.11/4.65 thf(cartprodpairin_type, type, cartprodpairin: $o).
% 7.11/4.65 thf(cartprodmempair1_type, type, cartprodmempair1: $o).
% 7.11/4.65 thf(sk__145_type, type, sk__145: $i).
% 7.11/4.65 thf(brelnall2_type, type, brelnall2: $o).
% 7.11/4.65 thf(setextT_type, type, setextT: $o).
% 7.11/4.65 thf(ex1I2_type, type, ex1I2: $o).
% 7.11/4.65 thf(symdiffI1_type, type, symdiffI1: $o).
% 7.11/4.65 thf(setukpairinjR2_type, type, setukpairinjR2: $o).
% 7.11/4.65 thf(dpsetconstrEL2_type, type, dpsetconstrEL2: $o).
% 7.11/4.65 thf(theprop_type, type, theprop: $o).
% 7.11/4.65 thf(subsetI2_type, type, subsetI2: $o).
% 7.11/4.65 thf(complementInPowersetComplementIntersect_type, type, complementInPowersetComplementIntersect:
% 7.11/4.65 $o).
% 7.11/4.65 thf(setminusT_lem_type, type, setminusT_lem: $o).
% 7.11/4.65 thf(symdiffIneg1_type, type, symdiffIneg1: $o).
% 7.11/4.65 thf(sk__144_type, type, sk__144: $i).
% 7.11/4.65 thf(setminusERneg_type, type, setminusERneg: $o).
% 7.11/4.65 thf(symdiffIneg2_type, type, symdiffIneg2: $o).
% 7.11/4.65 thf(omega__Cong_type, type, omega__Cong: $o).
% 7.11/4.65 thf(subsetRefl_type, type, subsetRefl: $o).
% 7.11/4.65 thf(uniqinunit_type, type, uniqinunit: $o).
% 7.11/4.65 thf(complementSubsetComplementIntersect_type, type, complementSubsetComplementIntersect:
% 7.11/4.65 $o).
% 7.11/4.65 thf(setminusSubset2_type, type, setminusSubset2: $o).
% 7.11/4.65 thf(prop2setE_type, type, prop2setE: $o).
% 7.11/4.65 thf(binunionEcases_type, type, binunionEcases: $o).
% 7.11/4.65 thf(funcinfuncset_type, type, funcinfuncset: $o).
% 7.11/4.65 thf(complementTE1_type, type, complementTE1: $o).
% 7.11/4.65 thf(nonemptyI_type, type, nonemptyI: $o).
% 7.11/4.65 thf(app_type, type, app: $o).
% 7.11/4.65 thf(disjointsetsI1_type, type, disjointsetsI1: $o).
% 7.11/4.65 thf(exuE3u_type, type, exuE3u: $o).
% 7.11/4.65 thf(eta1_type, type, eta1: $o).
% 7.11/4.65 thf(setminusEL_type, type, setminusEL: $o).
% 7.11/4.65 thf(cartprodfstin_type, type, cartprodfstin: $o).
% 7.11/4.65 thf(setunionsingleton2_type, type, setunionsingleton2: $o).
% 7.11/4.65 thf(sepSubset_type, type, sepSubset: $o).
% 7.11/4.65 thf(complementTnotintersectT_type, type, complementTnotintersectT: $o).
% 7.11/4.65 thf(upairset2E_type, type, upairset2E: $o).
% 7.11/4.65 thf(eqimpsubset1_type, type, eqimpsubset1: $o).
% 7.11/4.65 thf(exuI3_type, type, exuI3: $o).
% 7.11/4.65 thf(cartprodfstpairEq_type, type, cartprodfstpairEq: $o).
% 7.11/4.65 thf(apProp_type, type, apProp: $o).
% 7.11/4.65 thf(notdallE_type, type, notdallE: $o).
% 7.11/4.65 thf(iftrueProp1_type, type, iftrueProp1: $o).
% 7.11/4.65 thf(binintersectER_type, type, binintersectER: $o).
% 7.11/4.65 thf(brelnall1_type, type, brelnall1: $o).
% 7.11/4.65 thf(powerset_type, type, powerset: $i > $i).
% 7.11/4.65 thf(dsetconstrI_type, type, dsetconstrI: $o).
% 7.11/4.65 thf(funcGraphProp1_type, type, funcGraphProp1: $o).
% 7.11/4.65 thf(binintersectT_lem_type, type, binintersectT_lem: $o).
% 7.11/4.65 thf(setadjoin_type, type, setadjoin: $i > $i > $i).
% 7.11/4.65 thf(exu__Cong_type, type, exu__Cong: $o).
% 7.11/4.65 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o).
% 7.11/4.65 thf(contrasubsetT2_type, type, contrasubsetT2: $o).
% 7.11/4.65 thf(secondinupair_type, type, secondinupair: $o).
% 7.11/4.65 thf(singletonprop_type, type, singletonprop: $o).
% 7.11/4.65 thf(singletonsubset_type, type, singletonsubset: $o).
% 7.11/4.65 thf(contrasubsetT1_type, type, contrasubsetT1: $o).
% 7.11/4.65 thf(singletoninpowerset_type, type, singletoninpowerset: $o).
% 7.11/4.65 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o).
% 7.11/4.65 thf(replAx_type, type, replAx: $o).
% 7.11/4.65 thf(upairequniteq_type, type, upairequniteq: $o).
% 7.11/4.65 thf(nonemptyE1_type, type, nonemptyE1: $o).
% 7.11/4.65 thf(omegaIndAx_type, type, omegaIndAx: $o).
% 7.11/4.65 thf(setukpairIL_type, type, setukpairIL: $o).
% 7.11/4.65 thf(setunionE2_type, type, setunionE2: $o).
% 7.11/4.65 thf(inPowerset_type, type, inPowerset: $o).
% 7.11/4.65 thf(iffalse_type, type, iffalse: $o).
% 7.11/4.65 thf(funcext2_type, type, funcext2: $o).
% 7.11/4.65 thf(subset_type, type, subset: $i > $i > $o).
% 7.11/4.65 thf(subbreln_type, type, subbreln: $o).
% 7.11/4.65 thf(in__Cong_type, type, in__Cong: $o).
% 7.11/4.65 thf(binunionRsub_type, type, binunionRsub: $o).
% 7.11/4.65 thf(subset2powerset_type, type, subset2powerset: $o).
% 7.11/4.65 thf(doubleComplementEq, axiom, doubleComplementEq =
% 7.11/4.65 (![A:$i,X:$i]:
% 7.11/4.65 ( ( in @ X @ ( powerset @ A ) ) =>
% 7.11/4.65 ( ( X ) = ( setminus @ A @ ( setminus @ A @ X ) ) ) ))).
% 7.11/4.65 thf('0', plain,
% 7.11/4.65 (( doubleComplementEq ) =
% 7.11/4.65 ( ![X4:$i,X6:$i]:
% 7.11/4.65 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 7.11/4.65 ( ( X6 ) = ( setminus @ X4 @ ( setminus @ X4 @ X6 ) ) ) ) )),
% 7.11/4.65 define([status(thm)])).
% 7.11/4.65 thf(doubleComplementSub2, axiom, doubleComplementSub2 =
% 7.11/4.65 (![A:$i,X:$i]:
% 7.11/4.65 ( ( in @ X @ ( powerset @ A ) ) =>
% 7.11/4.65 ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ))).
% 7.11/4.65 thf('1', plain,
% 7.11/4.65 (( doubleComplementSub2 ) =
% 7.11/4.65 ( ![X4:$i,X6:$i]:
% 7.11/4.65 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 7.11/4.65 ( subset @ ( setminus @ X4 @ ( setminus @ X4 @ X6 ) ) @ X6 ) ) )),
% 7.11/4.65 define([status(thm)])).
% 7.11/4.65 thf(doubleComplementSub1, axiom, doubleComplementSub1 =
% 7.11/4.65 (![A:$i,X:$i]:
% 7.11/4.65 ( ( in @ X @ ( powerset @ A ) ) =>
% 7.11/4.65 ( subset @ X @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ))).
% 7.11/4.65 thf('2', plain,
% 7.11/4.65 (( doubleComplementSub1 ) =
% 7.11/4.65 ( ![X4:$i,X6:$i]:
% 7.11/4.65 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 7.11/4.65 ( subset @ X6 @ ( setminus @ X4 @ ( setminus @ X4 @ X6 ) ) ) ) )),
% 7.11/4.65 define([status(thm)])).
% 7.11/4.65 thf(doubleComplementE1, axiom, doubleComplementE1 =
% 7.11/4.65 (![A:$i,X:$i]:
% 7.11/4.65 ( ( in @ X @ ( powerset @ A ) ) =>
% 7.11/4.65 ( ![Xx:$i]:
% 7.11/4.65 ( ( in @ Xx @ A ) =>
% 7.11/4.65 ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) =>
% 7.11/4.65 ( in @ Xx @ X ) ) ) ) ))).
% 7.11/4.65 thf('3', plain,
% 7.11/4.65 (( doubleComplementE1 ) =
% 7.11/4.65 ( ![X4:$i,X6:$i]:
% 7.11/4.65 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 7.11/4.65 ( ![X8:$i]:
% 7.11/4.65 ( ( in @ X8 @ X4 ) =>
% 7.11/4.65 ( ( in @ X8 @ ( setminus @ X4 @ ( setminus @ X4 @ X6 ) ) ) =>
% 7.11/4.65 ( in @ X8 @ X6 ) ) ) ) ) )),
% 7.11/4.65 define([status(thm)])).
% 7.11/4.65 thf(doubleComplementI1, axiom, doubleComplementI1 =
% 7.11/4.65 (![A:$i,X:$i]:
% 7.11/4.65 ( ( in @ X @ ( powerset @ A ) ) =>
% 7.11/4.65 ( ![Xx:$i]:
% 7.11/4.65 ( ( in @ Xx @ A ) =>
% 7.11/4.65 ( ( in @ Xx @ X ) =>
% 7.11/4.65 ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ))).
% 7.11/4.65 thf('4', plain,
% 7.11/4.65 (( doubleComplementI1 ) =
% 7.11/4.65 ( ![X4:$i,X6:$i]:
% 7.11/4.65 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 7.11/4.65 ( ![X8:$i]:
% 7.11/4.65 ( ( in @ X8 @ X4 ) =>
% 7.11/4.65 ( ( in @ X8 @ X6 ) =>
% 7.11/4.65 ( in @ X8 @ ( setminus @ X4 @ ( setminus @ X4 @ X6 ) ) ) ) ) ) ) )),
% 7.11/4.65 define([status(thm)])).
% 7.11/4.65 thf(contrasubsetT3, axiom, contrasubsetT3 =
% 7.11/4.65 (![A:$i,X:$i]:
% 7.11/4.65 ( ( in @ X @ ( powerset @ A ) ) =>
% 7.11/4.65 ( ![Y:$i]:
% 7.11/4.65 ( ( in @ Y @ ( powerset @ A ) ) =>
% 7.11/4.65 ( ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) =>
% 7.11/4.65 ( subset @ X @ Y ) ) ) ) ))).
% 7.11/4.65 thf('5', plain,
% 7.11/4.65 (( contrasubsetT3 ) =
% 7.11/4.65 ( ![X4:$i,X6:$i]:
% 7.11/4.65 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 7.11/4.65 ( ![X8:$i]:
% 7.11/4.65 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 7.11/4.65 ( ( subset @ ( setminus @ X4 @ X8 ) @ ( setminus @ X4 @ X6 ) ) =>
% 7.11/4.65 ( subset @ X6 @ X8 ) ) ) ) ) )),
% 7.11/4.65 define([status(thm)])).
% 7.11/4.65 thf(contrasubsetT2, axiom, contrasubsetT2 =
% 7.11/4.65 (![A:$i,X:$i]:
% 7.11/4.65 ( ( in @ X @ ( powerset @ A ) ) =>
% 7.11/4.65 ( ![Y:$i]:
% 7.11/4.65 ( ( in @ Y @ ( powerset @ A ) ) =>
% 7.11/4.65 ( ( subset @ X @ Y ) =>
% 7.11/4.65 ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) ) ))).
% 7.11/4.65 thf('6', plain,
% 7.11/4.65 (( contrasubsetT2 ) =
% 7.11/4.65 ( ![X4:$i,X6:$i]:
% 7.11/4.65 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 7.11/4.65 ( ![X8:$i]:
% 7.11/4.65 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 7.11/4.65 ( ( subset @ X6 @ X8 ) =>
% 7.11/4.65 ( subset @ ( setminus @ X4 @ X8 ) @ ( setminus @ X4 @ X6 ) ) ) ) ) ) )),
% 7.11/4.65 define([status(thm)])).
% 7.11/4.65 thf(contrasubsetT1, axiom, contrasubsetT1 =
% 7.11/4.65 (![A:$i,X:$i]:
% 7.11/4.65 ( ( in @ X @ ( powerset @ A ) ) =>
% 7.11/4.65 ( ![Y:$i]:
% 7.11/4.65 ( ( in @ Y @ ( powerset @ A ) ) =>
% 7.11/4.65 ( ![Xx:$i]:
% 7.11/4.65 ( ( in @ Xx @ A ) =>
% 7.11/4.65 ( ( subset @ X @ Y ) =>
% 7.11/4.65 ( ( ~( in @ Xx @ Y ) ) => ( ~( in @ Xx @ X ) ) ) ) ) ) ) ) ))).
% 7.11/4.65 thf('7', plain,
% 7.11/4.65 (( contrasubsetT1 ) =
% 7.11/4.65 ( ![X4:$i,X6:$i]:
% 7.11/4.65 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 7.11/4.65 ( ![X8:$i]:
% 7.11/4.65 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 7.11/4.65 ( ![X10:$i]:
% 7.11/4.65 ( ( in @ X10 @ X4 ) =>
% 7.11/4.65 ( ( subset @ X6 @ X8 ) =>
% 7.11/4.65 ( ( ~( in @ X10 @ X8 ) ) => ( ~( in @ X10 @ X6 ) ) ) ) ) ) ) ) ) )),
% 7.11/4.65 define([status(thm)])).
% 7.11/4.65 thf(contrasubsetT, axiom, contrasubsetT =
% 7.11/4.65 (![A:$i,X:$i]:
% 7.11/4.65 ( ( in @ X @ ( powerset @ A ) ) =>
% 7.11/4.65 ( ![Y:$i]:
% 7.11/4.65 ( ( in @ Y @ ( powerset @ A ) ) =>
% 7.11/4.65 ( ![Xx:$i]:
% 7.11/4.65 ( ( in @ Xx @ A ) =>
% 7.11/4.65 ( ( subset @ X @ ( setminus @ A @ Y ) ) =>
% 7.11/4.65 ( ( in @ Xx @ Y ) => ( ~( in @ Xx @ X ) ) ) ) ) ) ) ) ))).
% 7.11/4.65 thf('8', plain,
% 7.11/4.65 (( contrasubsetT ) =
% 7.11/4.65 ( ![X4:$i,X6:$i]:
% 7.11/4.65 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 7.11/4.65 ( ![X8:$i]:
% 7.11/4.65 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 7.11/4.65 ( ![X10:$i]:
% 7.11/4.65 ( ( in @ X10 @ X4 ) =>
% 7.11/4.65 ( ( subset @ X6 @ ( setminus @ X4 @ X8 ) ) =>
% 7.11/4.65 ( ( in @ X10 @ X8 ) => ( ~( in @ X10 @ X6 ) ) ) ) ) ) ) ) ) )),
% 7.11/4.65 define([status(thm)])).
% 7.11/4.65 thf(complementTE1, axiom, complementTE1 =
% 7.11/4.65 (![A:$i,X:$i]:
% 7.11/4.65 ( ( in @ X @ ( powerset @ A ) ) =>
% 7.11/4.65 ( ![Xx:$i]:
% 7.11/4.65 ( ( in @ Xx @ A ) =>
% 7.11/4.65 ( ( ~( in @ Xx @ ( setminus @ A @ X ) ) ) => ( in @ Xx @ X ) ) ) ) ))).
% 7.11/4.65 thf('9', plain,
% 7.11/4.65 (( complementTE1 ) =
% 7.11/4.65 ( ![X4:$i,X6:$i]:
% 7.11/4.65 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 7.11/4.65 ( ![X8:$i]:
% 7.11/4.65 ( ( in @ X8 @ X4 ) =>
% 7.11/4.65 ( ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) => ( in @ X8 @ X6 ) ) ) ) ) )),
% 7.11/4.65 define([status(thm)])).
% 7.11/4.65 thf(complementTI1, axiom, complementTI1 =
% 7.11/4.65 (![A:$i,X:$i]:
% 7.11/4.65 ( ( in @ X @ ( powerset @ A ) ) =>
% 7.11/4.65 ( ![Xx:$i]:
% 7.11/4.65 ( ( in @ Xx @ A ) =>
% 7.11/4.65 ( ( in @ Xx @ X ) => ( ~( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ))).
% 7.11/4.65 thf('10', plain,
% 7.11/4.65 (( complementTI1 ) =
% 7.11/4.65 ( ![X4:$i,X6:$i]:
% 7.11/4.65 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 7.11/4.65 ( ![X8:$i]:
% 7.11/4.65 ( ( in @ X8 @ X4 ) =>
% 7.11/4.65 ( ( in @ X8 @ X6 ) => ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) ) ) ) )),
% 7.11/4.65 define([status(thm)])).
% 7.11/4.65 thf(powersetTE1, axiom, powersetTE1 =
% 7.11/4.65 (![A:$i,X:$i]:
% 7.11/4.65 ( ( in @ X @ ( powerset @ A ) ) =>
% 7.11/4.65 ( ![Y:$i]:
% 7.11/4.65 ( ( in @ Y @ ( powerset @ A ) ) =>
% 7.11/4.65 ( ![Xx:$i]:
% 7.11/4.65 ( ( in @ Xx @ A ) =>
% 7.11/4.65 ( ( in @ X @ ( powerset @ Y ) ) =>
% 7.11/4.65 ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) ) ) ) ))).
% 7.11/4.65 thf('11', plain,
% 7.11/4.65 (( powersetTE1 ) =
% 7.11/4.65 ( ![X4:$i,X6:$i]:
% 7.11/4.65 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 7.11/4.65 ( ![X8:$i]:
% 7.11/4.65 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 7.11/4.65 ( ![X10:$i]:
% 7.11/4.65 ( ( in @ X10 @ X4 ) =>
% 7.11/4.65 ( ( in @ X6 @ ( powerset @ X8 ) ) =>
% 7.11/4.65 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) ) ) ) ) )),
% 7.11/4.65 define([status(thm)])).
% 7.11/4.65 thf(powersetTI1, axiom, powersetTI1 =
% 7.11/4.65 (![A:$i,X:$i]:
% 7.11/4.65 ( ( in @ X @ ( powerset @ A ) ) =>
% 7.11/4.65 ( ![Y:$i]:
% 7.11/4.65 ( ( in @ Y @ ( powerset @ A ) ) =>
% 7.11/4.65 ( ( ![Xx:$i]:
% 7.11/4.65 ( ( in @ Xx @ A ) => ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) =>
% 7.11/4.65 ( in @ X @ ( powerset @ Y ) ) ) ) ) ))).
% 7.11/4.65 thf('12', plain,
% 7.11/4.65 (( powersetTI1 ) =
% 7.11/4.65 ( ![X4:$i,X6:$i]:
% 7.11/4.65 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 7.11/4.65 ( ![X8:$i]:
% 7.11/4.65 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 7.11/4.65 ( ( ![X10:$i]:
% 7.11/4.65 ( ( in @ X10 @ X4 ) =>
% 7.11/4.65 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) =>
% 7.11/4.65 ( in @ X6 @ ( powerset @ X8 ) ) ) ) ) ) )),
% 7.11/4.65 define([status(thm)])).
% 7.11/4.65 thf(subsetTI, axiom, subsetTI =
% 7.11/4.65 (![A:$i,X:$i]:
% 7.11/4.65 ( ( in @ X @ ( powerset @ A ) ) =>
% 7.11/4.65 ( ![Y:$i]:
% 7.11/4.65 ( ( in @ Y @ ( powerset @ A ) ) =>
% 7.11/4.65 ( ( ![Xx:$i]:
% 7.11/4.65 ( ( in @ Xx @ A ) => ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) =>
% 7.11/4.65 ( subset @ X @ Y ) ) ) ) ))).
% 7.11/4.65 thf('13', plain,
% 7.11/4.65 (( subsetTI ) =
% 7.11/4.65 ( ![X4:$i,X6:$i]:
% 7.11/4.65 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 7.11/4.65 ( ![X8:$i]:
% 7.11/4.65 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 7.11/4.65 ( ( ![X10:$i]:
% 7.11/4.65 ( ( in @ X10 @ X4 ) =>
% 7.11/4.65 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) =>
% 7.11/4.65 ( subset @ X6 @ X8 ) ) ) ) ) )),
% 7.11/4.65 define([status(thm)])).
% 7.11/4.65 thf(setextT, axiom, setextT =
% 7.11/4.65 (![A:$i,X:$i]:
% 7.11/4.65 ( ( in @ X @ ( powerset @ A ) ) =>
% 7.11/4.65 ( ![Y:$i]:
% 7.11/4.65 ( ( in @ Y @ ( powerset @ A ) ) =>
% 7.11/4.65 ( ( ![Xx:$i]:
% 7.11/4.65 ( ( in @ Xx @ A ) => ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) =>
% 7.11/4.65 ( ( ![Xx:$i]:
% 7.11/4.65 ( ( in @ Xx @ A ) => ( ( in @ Xx @ Y ) => ( in @ Xx @ X ) ) ) ) =>
% 7.11/4.65 ( ( X ) = ( Y ) ) ) ) ) ) ))).
% 7.11/4.65 thf('14', plain,
% 7.11/4.65 (( setextT ) =
% 7.11/4.65 ( ![X4:$i,X6:$i]:
% 7.11/4.65 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 7.11/4.65 ( ![X8:$i]:
% 7.11/4.65 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 7.11/4.65 ( ( ![X10:$i]:
% 7.11/4.65 ( ( in @ X10 @ X4 ) =>
% 7.11/4.65 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) =>
% 7.11/4.65 ( ( ![X12:$i]:
% 7.11/4.65 ( ( in @ X12 @ X4 ) =>
% 7.11/4.65 ( ( in @ X12 @ X8 ) => ( in @ X12 @ X6 ) ) ) ) =>
% 7.11/4.65 ( ( X6 ) = ( X8 ) ) ) ) ) ) ) )),
% 7.11/4.65 define([status(thm)])).
% 7.11/4.65 thf(complementT_lem, axiom, complementT_lem =
% 7.11/4.65 (![A:$i,X:$i]:
% 7.11/4.65 ( ( in @ X @ ( powerset @ A ) ) =>
% 7.11/4.65 ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ))).
% 7.11/4.65 thf('15', plain,
% 7.11/4.65 (( complementT_lem ) =
% 7.11/4.65 ( ![X4:$i,X6:$i]:
% 7.11/4.65 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 7.11/4.65 ( in @ ( setminus @ X4 @ X6 ) @ ( powerset @ X4 ) ) ) )),
% 7.11/4.65 define([status(thm)])).
% 7.11/4.65 thf(setminusT_lem, axiom, setminusT_lem =
% 7.11/4.65 (![A:$i,X:$i]:
% 7.11/4.65 ( ( in @ X @ ( powerset @ A ) ) =>
% 7.11/4.65 ( ![Y:$i]:
% 7.11/4.65 ( ( in @ Y @ ( powerset @ A ) ) =>
% 7.11/4.65 ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ))).
% 7.11/4.65 thf('16', plain,
% 7.11/4.65 (( setminusT_lem ) =
% 7.11/4.65 ( ![X4:$i,X6:$i]:
% 7.11/4.65 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 7.11/4.65 ( ![X8:$i]:
% 7.11/4.65 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 7.11/4.65 ( in @ ( setminus @ X6 @ X8 ) @ ( powerset @ X4 ) ) ) ) ) )),
% 7.11/4.65 define([status(thm)])).
% 7.11/4.65 thf(powersetT_lem, axiom, powersetT_lem =
% 7.11/4.65 (![A:$i,X:$i]:
% 7.11/4.65 ( ( in @ X @ ( powerset @ A ) ) =>
% 7.11/4.65 ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ))).
% 7.11/4.65 thf('17', plain,
% 7.11/4.65 (( powersetT_lem ) =
% 7.11/4.65 ( ![X4:$i,X6:$i]:
% 7.11/4.65 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 7.11/4.65 ( in @ ( powerset @ X6 ) @ ( powerset @ ( powerset @ X4 ) ) ) ) )),
% 7.11/4.65 define([status(thm)])).
% 7.11/4.65 thf(singletoninpowerset, axiom, singletoninpowerset =
% 7.11/4.65 (![A:$i,Xx:$i]:
% 7.11/4.65 ( ( in @ Xx @ A ) =>
% 7.11/4.65 ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ))).
% 7.11/4.65 thf('18', plain,
% 7.11/4.65 (( singletoninpowerset ) =
% 7.11/4.65 ( ![X4:$i,X6:$i]:
% 7.11/4.65 ( ( in @ X6 @ X4 ) =>
% 7.11/4.65 ( in @ ( setadjoin @ X6 @ emptyset ) @ ( powerset @ X4 ) ) ) )),
% 7.11/4.65 define([status(thm)])).
% 7.11/4.65 thf(setminusSubset1, axiom, setminusSubset1 =
% 7.11/4.65 (![A:$i,B:$i]:
% 7.11/4.65 ( ( ( setminus @ A @ B ) = ( emptyset ) ) => ( subset @ A @ B ) ))).
% 7.11/4.65 thf('19', plain,
% 7.11/4.65 (( setminusSubset1 ) =
% 7.11/4.65 ( ![X4:$i,X6:$i]:
% 7.11/4.65 ( ( ( setminus @ X4 @ X6 ) = ( emptyset ) ) => ( subset @ X4 @ X6 ) ) )),
% 7.11/4.65 define([status(thm)])).
% 7.11/4.65 thf(setminusLsub, axiom, setminusLsub =
% 7.11/4.65 (![A:$i,B:$i]: ( subset @ ( setminus @ A @ B ) @ A ))).
% 7.11/4.65 thf('20', plain,
% 7.11/4.65 (( setminusLsub ) =
% 7.11/4.65 ( ![X4:$i,X6:$i]: ( subset @ ( setminus @ X4 @ X6 ) @ X4 ) )),
% 7.11/4.65 define([status(thm)])).
% 7.11/4.65 thf(setminusIRneg, axiom, setminusIRneg =
% 7.11/4.65 (![A:$i,B:$i,Xx:$i]:
% 7.11/4.65 ( ( in @ Xx @ B ) => ( ~( in @ Xx @ ( setminus @ A @ B ) ) ) ))).
% 7.11/4.65 thf('21', plain,
% 7.11/4.65 (( setminusIRneg ) =
% 7.11/4.65 ( ![X4:$i,X6:$i,X8:$i]:
% 7.11/4.65 ( ( in @ X8 @ X6 ) => ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) )),
% 7.11/4.65 define([status(thm)])).
% 7.11/4.65 thf(setminusILneg, axiom, setminusILneg =
% 7.11/4.65 (![A:$i,B:$i,Xx:$i]:
% 7.11/4.65 ( ( ~( in @ Xx @ A ) ) => ( ~( in @ Xx @ ( setminus @ A @ B ) ) ) ))).
% 7.11/4.65 thf('22', plain,
% 7.11/4.65 (( setminusILneg ) =
% 7.11/4.65 ( ![X4:$i,X6:$i,X8:$i]:
% 7.11/4.65 ( ( ~( in @ X8 @ X4 ) ) => ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) )),
% 7.11/4.65 define([status(thm)])).
% 7.11/4.65 thf(setminusELneg, axiom, setminusELneg =
% 7.11/4.65 (![A:$i,B:$i,Xx:$i]:
% 7.11/4.65 ( ( ~( in @ Xx @ ( setminus @ A @ B ) ) ) =>
% 7.11/4.65 ( ( ~( in @ Xx @ B ) ) => ( ~( in @ Xx @ A ) ) ) ))).
% 7.11/4.65 thf('23', plain,
% 7.11/4.65 (( setminusELneg ) =
% 7.11/4.65 ( ![X4:$i,X6:$i,X8:$i]:
% 7.11/4.65 ( ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) =>
% 7.11/4.65 ( ( ~( in @ X8 @ X6 ) ) => ( ~( in @ X8 @ X4 ) ) ) ) )),
% 7.11/4.65 define([status(thm)])).
% 7.11/4.65 thf(setminusERneg, axiom, setminusERneg =
% 7.11/4.65 (![A:$i,B:$i,Xx:$i]:
% 7.11/4.65 ( ( ~( in @ Xx @ ( setminus @ A @ B ) ) ) =>
% 7.11/4.65 ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ))).
% 7.11/4.65 thf('24', plain,
% 7.11/4.65 (( setminusERneg ) =
% 7.11/4.65 ( ![X4:$i,X6:$i,X8:$i]:
% 7.11/4.65 ( ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) =>
% 7.11/4.65 ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) )),
% 7.11/4.65 define([status(thm)])).
% 7.11/4.65 thf(setminusSubset2, axiom, setminusSubset2 =
% 7.11/4.65 (![A:$i,B:$i]:
% 7.11/4.65 ( ( subset @ A @ B ) => ( ( setminus @ A @ B ) = ( emptyset ) ) ))).
% 7.11/4.65 thf('25', plain,
% 7.11/4.65 (( setminusSubset2 ) =
% 7.11/4.65 ( ![X4:$i,X6:$i]:
% 7.11/4.65 ( ( subset @ X4 @ X6 ) => ( ( setminus @ X4 @ X6 ) = ( emptyset ) ) ) )),
% 7.11/4.65 define([status(thm)])).
% 7.11/4.65 thf(setminusER, axiom, setminusER =
% 7.11/4.65 (![A:$i,B:$i,Xx:$i]:
% 7.11/4.65 ( ( in @ Xx @ ( setminus @ A @ B ) ) => ( ~( in @ Xx @ B ) ) ))).
% 7.11/4.65 thf('26', plain,
% 7.11/4.65 (( setminusER ) =
% 7.11/4.65 ( ![X4:$i,X6:$i,X8:$i]:
% 7.11/4.65 ( ( in @ X8 @ ( setminus @ X4 @ X6 ) ) => ( ~( in @ X8 @ X6 ) ) ) )),
% 7.11/4.65 define([status(thm)])).
% 7.11/4.65 thf(setminusEL, axiom, setminusEL =
% 7.11/4.65 (![A:$i,B:$i,Xx:$i]:
% 7.11/4.65 ( ( in @ Xx @ ( setminus @ A @ B ) ) => ( in @ Xx @ A ) ))).
% 7.11/4.65 thf('27', plain,
% 7.11/4.65 (( setminusEL ) =
% 7.11/4.65 ( ![X4:$i,X6:$i,X8:$i]:
% 7.11/4.65 ( ( in @ X8 @ ( setminus @ X4 @ X6 ) ) => ( in @ X8 @ X4 ) ) )),
% 7.11/4.65 define([status(thm)])).
% 7.11/4.65 thf(setminusI, axiom, setminusI =
% 7.11/4.65 (![A:$i,B:$i,Xx:$i]:
% 7.11/4.65 ( ( in @ Xx @ A ) =>
% 7.11/4.65 ( ( ~( in @ Xx @ B ) ) => ( in @ Xx @ ( setminus @ A @ B ) ) ) ))).
% 7.11/4.65 thf('28', plain,
% 7.11/4.65 (( setminusI ) =
% 7.11/4.65 ( ![X4:$i,X6:$i,X8:$i]:
% 7.11/4.65 ( ( in @ X8 @ X4 ) =>
% 7.11/4.65 ( ( ~( in @ X8 @ X6 ) ) => ( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) )),
% 7.11/4.65 define([status(thm)])).
% 7.11/4.65 thf(powersetsubset, axiom, powersetsubset =
% 7.11/4.65 (![A:$i,B:$i]:
% 7.11/4.65 ( ( subset @ A @ B ) => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ))).
% 7.11/4.65 thf('29', plain,
% 7.11/4.65 (( powersetsubset ) =
% 7.11/4.65 ( ![X4:$i,X6:$i]:
% 7.11/4.65 ( ( subset @ X4 @ X6 ) =>
% 7.11/4.65 ( subset @ ( powerset @ X4 ) @ ( powerset @ X6 ) ) ) )),
% 7.11/4.65 define([status(thm)])).
% 7.11/4.65 thf(inPowerset, axiom, inPowerset = (![A:$i]: ( in @ A @ ( powerset @ A ) ))).
% 7.11/4.65 thf('30', plain,
% 7.11/4.65 (( inPowerset ) = ( ![X4:$i]: ( in @ X4 @ ( powerset @ X4 ) ) )),
% 7.11/4.65 define([status(thm)])).
% 7.11/4.65 thf(powersetE1, axiom, powersetE1 =
% 7.11/4.65 (![A:$i,B:$i]: ( ( in @ B @ ( powerset @ A ) ) => ( subset @ B @ A ) ))).
% 7.11/4.65 thf('31', plain,
% 7.11/4.65 (( powersetE1 ) =
% 7.11/4.65 ( ![X4:$i,X6:$i]:
% 7.11/4.65 ( ( in @ X6 @ ( powerset @ X4 ) ) => ( subset @ X6 @ X4 ) ) )),
% 7.11/4.65 define([status(thm)])).
% 7.11/4.65 thf(powersetI1, axiom, powersetI1 =
% 7.11/4.65 (![A:$i,B:$i]: ( ( subset @ B @ A ) => ( in @ B @ ( powerset @ A ) ) ))).
% 7.11/4.65 thf('32', plain,
% 7.11/4.65 (( powersetI1 ) =
% 7.11/4.65 ( ![X4:$i,X6:$i]:
% 7.11/4.65 ( ( subset @ X6 @ X4 ) => ( in @ X6 @ ( powerset @ X4 ) ) ) )),
% 7.11/4.65 define([status(thm)])).
% 7.11/4.65 thf(subsetemptysetimpeq, axiom, subsetemptysetimpeq =
% 7.11/4.65 (![A:$i]: ( ( subset @ A @ emptyset ) => ( ( A ) = ( emptyset ) ) ))).
% 7.11/4.65 thf('33', plain,
% 7.11/4.65 (( subsetemptysetimpeq ) =
% 7.11/4.65 ( ![X4:$i]: ( ( subset @ X4 @ emptyset ) => ( ( X4 ) = ( emptyset ) ) ) )),
% 7.11/4.65 define([status(thm)])).
% 7.11/4.65 thf(setextsub, axiom, setextsub =
% 7.11/4.65 (![A:$i,B:$i]:
% 7.11/4.65 ( ( subset @ A @ B ) => ( ( subset @ B @ A ) => ( ( A ) = ( B ) ) ) ))).
% 7.11/4.65 thf('34', plain,
% 7.11/4.65 (( setextsub ) =
% 7.11/4.65 ( ![X4:$i,X6:$i]:
% 7.11/4.65 ( ( subset @ X4 @ X6 ) =>
% 7.11/4.65 ( ( subset @ X6 @ X4 ) => ( ( X4 ) = ( X6 ) ) ) ) )),
% 7.11/4.65 define([status(thm)])).
% 7.11/4.65 thf(subset2powerset, axiom, subset2powerset =
% 7.11/4.65 (![A:$i,B:$i]: ( ( subset @ A @ B ) => ( in @ A @ ( powerset @ B ) ) ))).
% 7.11/4.65 thf('35', plain,
% 7.11/4.65 (( subset2powerset ) =
% 7.11/4.65 ( ![X4:$i,X6:$i]:
% 7.11/4.65 ( ( subset @ X4 @ X6 ) => ( in @ X4 @ ( powerset @ X6 ) ) ) )),
% 7.11/4.65 define([status(thm)])).
% 7.11/4.65 thf(subsetTrans, axiom, subsetTrans =
% 7.11/4.65 (![A:$i,B:$i,C:$i]:
% 7.11/4.65 ( ( subset @ A @ B ) => ( ( subset @ B @ C ) => ( subset @ A @ C ) ) ))).
% 7.11/4.65 thf('36', plain,
% 7.11/4.65 (( subsetTrans ) =
% 7.11/4.65 ( ![X4:$i,X6:$i,X8:$i]:
% 7.11/4.65 ( ( subset @ X4 @ X6 ) =>
% 7.11/4.65 ( ( subset @ X6 @ X8 ) => ( subset @ X4 @ X8 ) ) ) )),
% 7.11/4.65 define([status(thm)])).
% 7.11/4.65 thf(subsetRefl, axiom, subsetRefl = (![A:$i]: ( subset @ A @ A ))).
% 7.11/4.65 thf('37', plain, (( subsetRefl ) = ( ![X4:$i]: ( subset @ X4 @ X4 ) )),
% 7.11/4.65 define([status(thm)])).
% 7.11/4.65 thf(notequalI1, axiom, notequalI1 =
% 7.11/4.65 (![A:$i,B:$i]: ( ( ~( subset @ A @ B ) ) => ( ( A ) != ( B ) ) ))).
% 7.11/4.65 thf('38', plain,
% 7.11/4.65 (( notequalI1 ) =
% 7.11/4.65 ( ![X4:$i,X6:$i]: ( ( ~( subset @ X4 @ X6 ) ) => ( ( X4 ) != ( X6 ) ) ) )),
% 7.11/4.65 define([status(thm)])).
% 7.11/4.65 thf(notsubsetI, axiom, notsubsetI =
% 7.11/4.65 (![A:$i,B:$i,Xx:$i]:
% 7.11/4.65 ( ( in @ Xx @ A ) => ( ( ~( in @ Xx @ B ) ) => ( ~( subset @ A @ B ) ) ) ))).
% 7.11/4.65 thf('39', plain,
% 7.11/4.65 (( notsubsetI ) =
% 7.11/4.65 ( ![X4:$i,X6:$i,X8:$i]:
% 7.11/4.65 ( ( in @ X8 @ X4 ) =>
% 7.11/4.65 ( ( ~( in @ X8 @ X6 ) ) => ( ~( subset @ X4 @ X6 ) ) ) ) )),
% 7.11/4.65 define([status(thm)])).
% 7.11/4.65 thf(subsetE2, axiom, subsetE2 =
% 7.11/4.65 (![A:$i,B:$i,Xx:$i]:
% 7.11/4.65 ( ( subset @ A @ B ) => ( ( ~( in @ Xx @ B ) ) => ( ~( in @ Xx @ A ) ) ) ))).
% 7.11/4.65 thf('40', plain,
% 7.11/4.65 (( subsetE2 ) =
% 7.11/4.65 ( ![X4:$i,X6:$i,X8:$i]:
% 7.11/4.65 ( ( subset @ X4 @ X6 ) =>
% 7.11/4.65 ( ( ~( in @ X8 @ X6 ) ) => ( ~( in @ X8 @ X4 ) ) ) ) )),
% 7.11/4.65 define([status(thm)])).
% 7.11/4.65 thf(subsetE, axiom, subsetE =
% 7.11/4.65 (![A:$i,B:$i,Xx:$i]:
% 7.11/4.65 ( ( subset @ A @ B ) => ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ))).
% 7.11/4.65 thf('41', plain,
% 7.11/4.65 (( subsetE ) =
% 7.11/4.65 ( ![X4:$i,X6:$i,X8:$i]:
% 7.11/4.65 ( ( subset @ X4 @ X6 ) => ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) )),
% 7.11/4.65 define([status(thm)])).
% 7.11/4.65 thf(emptysetsubset, axiom, emptysetsubset =
% 7.11/4.65 (![A:$i]: ( subset @ emptyset @ A ))).
% 7.11/4.65 thf('42', plain,
% 7.11/4.65 (( emptysetsubset ) = ( ![X4:$i]: ( subset @ emptyset @ X4 ) )),
% 7.11/4.65 define([status(thm)])).
% 7.11/4.65 thf(subsetI2, axiom, subsetI2 =
% 7.11/4.65 (![A:$i,B:$i]:
% 7.11/4.65 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ) =>
% 7.11/4.65 ( subset @ A @ B ) ))).
% 7.11/4.65 thf('43', plain,
% 7.11/4.65 (( subsetI2 ) =
% 7.11/4.65 ( ![X4:$i,X6:$i]:
% 7.11/4.65 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) =>
% 7.11/4.65 ( subset @ X4 @ X6 ) ) )),
% 7.11/4.65 define([status(thm)])).
% 7.11/4.65 thf(eqimpsubset1, axiom, eqimpsubset1 =
% 7.11/4.65 (![A:$i,B:$i]: ( ( ( A ) = ( B ) ) => ( subset @ A @ B ) ))).
% 7.11/4.65 thf('44', plain,
% 7.11/4.65 (( eqimpsubset1 ) =
% 7.11/4.65 ( ![X4:$i,X6:$i]: ( ( ( X4 ) = ( X6 ) ) => ( subset @ X4 @ X6 ) ) )),
% 7.11/4.65 define([status(thm)])).
% 7.11/4.65 thf(eqimpsubset2, axiom, eqimpsubset2 =
% 7.11/4.65 (![A:$i,B:$i]: ( ( ( A ) = ( B ) ) => ( subset @ B @ A ) ))).
% 7.11/4.65 thf('45', plain,
% 7.11/4.65 (( eqimpsubset2 ) =
% 7.11/4.65 ( ![X4:$i,X6:$i]: ( ( ( X4 ) = ( X6 ) ) => ( subset @ X6 @ X4 ) ) )),
% 7.11/4.65 define([status(thm)])).
% 7.11/4.65 thf(subsetI1, axiom, subsetI1 =
% 7.11/4.65 (![A:$i,B:$i]:
% 7.11/4.65 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ) =>
% 7.11/4.65 ( subset @ A @ B ) ))).
% 7.11/4.65 thf('46', plain,
% 7.11/4.65 (( subsetI1 ) =
% 7.11/4.65 ( ![X4:$i,X6:$i]:
% 7.11/4.65 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) =>
% 7.11/4.65 ( subset @ X4 @ X6 ) ) )),
% 7.11/4.65 define([status(thm)])).
% 7.11/4.65 thf(powerset__Cong, axiom, powerset__Cong =
% 7.11/4.65 (![A:$i,B:$i]:
% 7.11/4.65 ( ( ( A ) = ( B ) ) => ( ( powerset @ A ) = ( powerset @ B ) ) ))).
% 7.11/4.65 thf('47', plain,
% 7.11/4.65 (( powerset__Cong ) =
% 7.11/4.65 ( ![X4:$i,X6:$i]:
% 7.11/4.65 ( ( ( X4 ) = ( X6 ) ) => ( ( powerset @ X4 ) = ( powerset @ X6 ) ) ) )),
% 7.11/4.65 define([status(thm)])).
% 7.11/4.65 thf(powersetE, axiom, powersetE =
% 7.11/4.65 (![A:$i,B:$i,Xx:$i]:
% 7.11/4.65 ( ( in @ B @ ( powerset @ A ) ) => ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ))).
% 7.11/4.65 thf('48', plain,
% 7.11/4.65 (( powersetE ) =
% 7.11/4.65 ( ![X4:$i,X6:$i,X8:$i]:
% 7.11/4.65 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 7.11/4.65 ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) )),
% 7.11/4.65 define([status(thm)])).
% 7.11/4.65 thf(emptyInPowerset, axiom, emptyInPowerset =
% 7.11/4.65 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))).
% 7.11/4.65 thf('49', plain,
% 7.11/4.65 (( emptyInPowerset ) =
% 7.11/4.65 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )),
% 7.11/4.65 define([status(thm)])).
% 7.11/4.65 thf(emptyinPowerset, axiom, emptyinPowerset =
% 7.11/4.65 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))).
% 7.11/4.65 thf('50', plain,
% 7.11/4.65 (( emptyinPowerset ) =
% 7.11/4.65 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )),
% 7.11/4.65 define([status(thm)])).
% 7.11/4.65 thf(powersetI, axiom, powersetI =
% 7.11/4.65 (![A:$i,B:$i]:
% 7.11/4.65 ( ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) =>
% 7.11/4.65 ( in @ B @ ( powerset @ A ) ) ))).
% 7.11/4.65 thf('51', plain,
% 7.11/4.65 (( powersetI ) =
% 7.11/4.65 ( ![X4:$i,X6:$i]:
% 7.11/4.65 ( ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) =>
% 7.11/4.65 ( in @ X6 @ ( powerset @ X4 ) ) ) )),
% 7.11/4.65 define([status(thm)])).
% 7.11/4.65 thf(powersetAx, axiom, powersetAx =
% 7.11/4.65 (![A:$i,B:$i]:
% 7.11/4.65 ( ( in @ B @ ( powerset @ A ) ) <=>
% 7.11/4.65 ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) ))).
% 7.11/4.65 thf('52', plain,
% 7.11/4.65 (( powersetAx ) =
% 7.11/4.65 ( ![X4:$i,X6:$i]:
% 7.11/4.65 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 7.11/4.65 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) )),
% 7.11/4.65 define([status(thm)])).
% 7.11/4.65 thf(contraSubsetComplement, conjecture,
% 7.11/4.65 (( setextAx ) =>
% 7.11/4.65 ( ( emptysetAx ) =>
% 7.11/4.65 ( ( setadjoinAx ) =>
% 7.11/4.65 ( ( powersetAx ) =>
% 7.11/4.65 ( ( setunionAx ) =>
% 7.11/4.65 ( ( omega0Ax ) =>
% 7.11/4.65 ( ( omegaSAx ) =>
% 7.11/4.65 ( ( omegaIndAx ) =>
% 7.11/4.65 ( ( replAx ) =>
% 7.11/4.65 ( ( foundationAx ) =>
% 7.11/4.65 ( ( wellorderingAx ) =>
% 7.11/4.65 ( ( descrp ) =>
% 7.11/4.65 ( ( dsetconstrI ) =>
% 7.11/4.65 ( ( dsetconstrEL ) =>
% 7.11/4.65 ( ( dsetconstrER ) =>
% 7.11/4.65 ( ( exuE1 ) =>
% 7.11/4.65 ( ( prop2setE ) =>
% 7.11/4.65 ( ( emptysetE ) =>
% 7.11/4.65 ( ( emptysetimpfalse ) =>
% 7.11/4.65 ( ( notinemptyset ) =>
% 7.11/4.65 ( ( exuE3e ) =>
% 7.11/4.65 ( ( setext ) =>
% 7.11/4.65 ( ( emptyI ) =>
% 7.11/4.65 ( ( noeltsimpempty ) =>
% 7.11/4.65 ( ( setbeta ) =>
% 7.11/4.65 ( ( nonemptyE1 ) =>
% 7.11/4.65 ( ( nonemptyI ) =>
% 7.11/4.65 ( ( nonemptyI1 ) =>
% 7.11/4.65 ( ( setadjoinIL ) =>
% 7.11/4.65 ( ( emptyinunitempty ) =>
% 7.11/4.65 ( ( setadjoinIR ) =>
% 7.11/4.65 ( ( setadjoinE ) =>
% 7.11/4.65 ( (
% 7.11/4.65 setadjoinOr ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 setoftrueEq ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 powersetI ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 emptyinPowerset ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 emptyInPowerset ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 powersetE ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 setunionI ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 setunionE ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 subPowSU ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 exuE2 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 nonemptyImpWitness ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 uniqinunit ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 notinsingleton ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 eqinunit ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 singletonsswitch ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 upairsetE ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 upairsetIL ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 upairsetIR ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 emptyE1 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 vacuousDall ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 quantDeMorgan1 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 quantDeMorgan2 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 quantDeMorgan3 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 quantDeMorgan4 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 prop2setI ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 prop2set2propI ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 notdexE ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 notdallE ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 exuI1 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 exuI3 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 exuI2 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 inCongP ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in__Cong ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 exuE3u ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 exu__Cong ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 emptyset__Cong ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 setadjoin__Cong ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 powerset__Cong ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 setunion__Cong ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 omega__Cong ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 exuEu ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 descr__Cong ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 dsetconstr__Cong ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 subsetI1 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 eqimpsubset2 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 eqimpsubset1 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 subsetI2 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 emptysetsubset ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 subsetE ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 subsetE2 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 notsubsetI ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 notequalI1 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 notequalI2 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 subsetRefl ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 subsetTrans ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 setadjoinSub ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 setadjoinSub2 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 subset2powerset ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 setextsub ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 subsetemptysetimpeq ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 powersetI1 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 powersetE1 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 inPowerset ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 powersetsubset ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 sepInPowerset ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 sepSubset ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 binunionIL ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 upairset2IR ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 binunionIR ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 binunionEcases ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 binunionE ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 binunionLsub ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 binunionRsub ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 binintersectI ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 binintersectSubset5 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 binintersectEL ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 binintersectLsub ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 binintersectSubset2 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 binintersectSubset3 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 binintersectER ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 disjointsetsI1 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 binintersectRsub ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 binintersectSubset4 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 binintersectSubset1 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 bs114d ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 setminusI ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 setminusEL ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 setminusER ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 setminusSubset2 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 setminusERneg ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 setminusELneg ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 setminusILneg ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 setminusIRneg ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 setminusLsub ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 setminusSubset1 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 symdiffE ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 symdiffI1 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 symdiffI2 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 symdiffIneg1 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 symdiffIneg2 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 secondinupair ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 setukpairIL ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 setukpairIR ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 kpairiskpair ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 kpairp ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 singletonsubset ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 singletoninpowerset ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 singletoninpowunion ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 upairset2E ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 upairsubunion ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 upairinpowunion ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ubforcartprodlem1 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ubforcartprodlem2 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ubforcartprodlem3 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 cartprodpairin ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 cartprodmempair1 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 cartprodmempair ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 setunionE2 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 setunionsingleton1 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 setunionsingleton2 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 setunionsingleton ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 singletonprop ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ex1E1 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ex1I ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ex1I2 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 singletonsuniq ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 setukpairinjL1 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 kfstsingleton ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 theprop ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 kfstpairEq ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 cartprodfstin ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 setukpairinjL2 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 setukpairinjL ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 setukpairinjR11 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 setukpairinjR12 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 setukpairinjR1 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 upairequniteq ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 setukpairinjR2 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 setukpairinjR ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ksndsingleton ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ksndpairEq ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 kpairsurjEq ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 cartprodsndin ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 cartprodpairmemEL ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 cartprodpairmemER ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 cartprodmempaircEq ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 cartprodfstpairEq ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 cartprodsndpairEq ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 cartprodpairsurjEq ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 dpsetconstrI ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 dpsetconstrSub ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 setOfPairsIsBReln ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 dpsetconstrERa ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 dpsetconstrEL1 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 dpsetconstrEL2 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 dpsetconstrER ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 funcImageSingleton ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 apProp ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 app ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 infuncsetfunc ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ap2p ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 funcinfuncset ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 lamProp ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 lamp ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 lam2p ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 brelnall1 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 brelnall2 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ex1E2 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 funcGraphProp1 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 funcGraphProp3 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 funcGraphProp2 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 funcextLem ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 funcGraphProp4 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 subbreln ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 eqbreln ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 funcext ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 funcext2 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ap2apEq1 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ap2apEq2 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 beta1 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 eta1 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 lam2lamEq ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 beta2 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 eta2 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 iffalseProp1 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 iffalseProp2 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 iftrueProp1 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 iftrueProp2 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ifSingleton ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ifp ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 theeq ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 iftrue ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 iffalse ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 iftrueorfalse ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 binintersectT_lem ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 binunionT_lem ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 powersetT_lem ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 setminusT_lem ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 complementT_lem ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 setextT ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 subsetTI ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 powersetTI1 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 powersetTE1 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 complementTI1 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 complementTE1 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 binintersectTELcontra ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 binintersectTERcontra ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 contrasubsetT ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 contrasubsetT1 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 contrasubsetT2 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 contrasubsetT3 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 doubleComplementI1 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 doubleComplementE1 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 doubleComplementSub1 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 doubleComplementSub2 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 doubleComplementEq ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 complementTnotintersectT ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 complementImpComplementIntersect ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 complementSubsetComplementIntersect ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 complementInPowersetComplementIntersect ) =>
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 A:$i,X:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X @
% 7.11/4.65 (
% 7.11/4.65 powerset @
% 7.11/4.65 A ) ) =>
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 Y:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 Y @
% 7.11/4.65 (
% 7.11/4.65 powerset @
% 7.11/4.65 A ) ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 subset @
% 7.11/4.65 X @
% 7.11/4.65 (
% 7.11/4.65 setminus @
% 7.11/4.65 A @ Y ) ) =>
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 Xx:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 Xx @ A ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 Xx @ Y ) =>
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 Xx @
% 7.11/4.65 (
% 7.11/4.65 setminus @
% 7.11/4.65 A @ X ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 7.11/4.65 thf(zf_stmt_0, conjecture,
% 7.11/4.65 (( setextAx ) =>
% 7.11/4.65 ( ( emptysetAx ) =>
% 7.11/4.65 ( ( setadjoinAx ) =>
% 7.11/4.65 ( ( ![X4:$i,X6:$i]:
% 7.11/4.65 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 7.11/4.65 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) ) =>
% 7.11/4.65 ( ( setunionAx ) =>
% 7.11/4.65 ( ( omega0Ax ) =>
% 7.11/4.65 ( ( omegaSAx ) =>
% 7.11/4.65 ( ( omegaIndAx ) =>
% 7.11/4.65 ( ( replAx ) =>
% 7.11/4.65 ( ( foundationAx ) =>
% 7.11/4.65 ( ( wellorderingAx ) =>
% 7.11/4.65 ( ( descrp ) =>
% 7.11/4.65 ( ( dsetconstrI ) =>
% 7.11/4.65 ( ( dsetconstrEL ) =>
% 7.11/4.65 ( ( dsetconstrER ) =>
% 7.11/4.65 ( ( exuE1 ) =>
% 7.11/4.65 ( ( prop2setE ) =>
% 7.11/4.65 ( ( emptysetE ) =>
% 7.11/4.65 ( ( emptysetimpfalse ) =>
% 7.11/4.65 ( ( notinemptyset ) =>
% 7.11/4.65 ( ( exuE3e ) =>
% 7.11/4.65 ( ( setext ) =>
% 7.11/4.65 ( ( emptyI ) =>
% 7.11/4.65 ( ( noeltsimpempty ) =>
% 7.11/4.65 ( ( setbeta ) =>
% 7.11/4.65 ( ( nonemptyE1 ) =>
% 7.11/4.65 ( ( nonemptyI ) =>
% 7.11/4.65 ( ( nonemptyI1 ) =>
% 7.11/4.65 ( ( setadjoinIL ) =>
% 7.11/4.65 ( ( emptyinunitempty ) =>
% 7.11/4.65 ( ( setadjoinIR ) =>
% 7.11/4.65 ( ( setadjoinE ) =>
% 7.11/4.65 ( (
% 7.11/4.65 setadjoinOr ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 setoftrueEq ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X10:$i,
% 7.11/4.65 X12:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X14:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X14 @ X12 ) =>
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X14 @ X10 ) ) ) =>
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X12 @
% 7.11/4.65 (
% 7.11/4.65 powerset @
% 7.11/4.65 X10 ) ) ) ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ![
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% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 emptyset @
% 7.11/4.65 (
% 7.11/4.65 powerset @
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% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ![
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% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 emptyset @
% 7.11/4.65 (
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% 7.11/4.65 X18 ) ) ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X20:$i,
% 7.11/4.65 X22:$i,
% 7.11/4.65 X24:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X22 @
% 7.11/4.65 (
% 7.11/4.65 powerset @
% 7.11/4.65 X20 ) ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X24 @ X22 ) =>
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X24 @ X20 ) ) ) ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 setunionI ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 setunionE ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 subPowSU ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 exuE2 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 nonemptyImpWitness ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 uniqinunit ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 notinsingleton ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 eqinunit ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 singletonsswitch ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 upairsetE ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 upairsetIL ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 upairsetIR ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 emptyE1 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 vacuousDall ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 quantDeMorgan1 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 quantDeMorgan2 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 quantDeMorgan3 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 quantDeMorgan4 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 prop2setI ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 prop2set2propI ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 notdexE ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 notdallE ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 exuI1 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 exuI3 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 exuI2 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 inCongP ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in__Cong ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 exuE3u ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 exu__Cong ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 emptyset__Cong ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 setadjoin__Cong ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X26:$i,
% 7.11/4.65 X28:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 X26 ) =
% 7.11/4.65 (
% 7.11/4.65 X28 ) ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 powerset @
% 7.11/4.65 X26 ) =
% 7.11/4.65 (
% 7.11/4.65 powerset @
% 7.11/4.65 X28 ) ) ) ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 setunion__Cong ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 omega__Cong ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 exuEu ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 descr__Cong ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 dsetconstr__Cong ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X30:$i,
% 7.11/4.65 X32:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X34:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X34 @ X30 ) =>
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X34 @ X32 ) ) ) =>
% 7.11/4.65 (
% 7.11/4.65 subset @
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% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X36:$i,
% 7.11/4.65 X38:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 X36 ) =
% 7.11/4.65 (
% 7.11/4.65 X38 ) ) =>
% 7.11/4.65 (
% 7.11/4.65 subset @
% 7.11/4.65 X38 @ X36 ) ) ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X40:$i,
% 7.11/4.65 X42:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 X40 ) =
% 7.11/4.65 (
% 7.11/4.65 X42 ) ) =>
% 7.11/4.65 (
% 7.11/4.65 subset @
% 7.11/4.65 X40 @ X42 ) ) ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X44:$i,
% 7.11/4.65 X46:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X48:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X48 @ X44 ) =>
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X48 @ X46 ) ) ) =>
% 7.11/4.65 (
% 7.11/4.65 subset @
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% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X50:$i]:
% 7.11/4.65 (
% 7.11/4.65 subset @
% 7.11/4.65 emptyset @
% 7.11/4.65 X50 ) ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X52:$i,
% 7.11/4.65 X54:$i,
% 7.11/4.65 X56:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 subset @
% 7.11/4.65 X52 @ X54 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X56 @ X52 ) =>
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X56 @ X54 ) ) ) ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X58:$i,
% 7.11/4.65 X60:$i,
% 7.11/4.65 X62:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 subset @
% 7.11/4.65 X58 @ X60 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ~(
% 7.11/4.65 in @
% 7.11/4.65 X62 @ X60 ) ) =>
% 7.11/4.65 (
% 7.11/4.65 ~(
% 7.11/4.65 in @
% 7.11/4.65 X62 @ X58 ) ) ) ) ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X64:$i,
% 7.11/4.65 X66:$i,
% 7.11/4.65 X68:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X68 @ X64 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ~(
% 7.11/4.65 in @
% 7.11/4.65 X68 @ X66 ) ) =>
% 7.11/4.65 (
% 7.11/4.65 ~(
% 7.11/4.65 subset @
% 7.11/4.65 X64 @ X66 ) ) ) ) ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X70:$i,
% 7.11/4.65 X72:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ~(
% 7.11/4.65 subset @
% 7.11/4.65 X70 @ X72 ) ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 X70 ) !=
% 7.11/4.65 (
% 7.11/4.65 X72 ) ) ) ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 notequalI2 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X74:$i]:
% 7.11/4.65 (
% 7.11/4.65 subset @
% 7.11/4.65 X74 @ X74 ) ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X76:$i,
% 7.11/4.65 X78:$i,
% 7.11/4.65 X80:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 subset @
% 7.11/4.65 X76 @ X78 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 subset @
% 7.11/4.65 X78 @ X80 ) =>
% 7.11/4.65 (
% 7.11/4.65 subset @
% 7.11/4.65 X76 @ X80 ) ) ) ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 setadjoinSub ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 setadjoinSub2 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X82:$i,
% 7.11/4.65 X84:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 subset @
% 7.11/4.65 X82 @ X84 ) =>
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X82 @
% 7.11/4.65 (
% 7.11/4.65 powerset @
% 7.11/4.65 X84 ) ) ) ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X86:$i,
% 7.11/4.65 X88:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 subset @
% 7.11/4.65 X86 @ X88 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 subset @
% 7.11/4.65 X88 @ X86 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 X86 ) =
% 7.11/4.65 (
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% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X90:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 subset @
% 7.11/4.65 X90 @
% 7.11/4.65 emptyset ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 X90 ) =
% 7.11/4.65 (
% 7.11/4.65 emptyset ) ) ) ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X92:$i,
% 7.11/4.65 X94:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 subset @
% 7.11/4.65 X94 @ X92 ) =>
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X94 @
% 7.11/4.65 (
% 7.11/4.65 powerset @
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% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X96:$i,
% 7.11/4.65 X98:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X98 @
% 7.11/4.65 (
% 7.11/4.65 powerset @
% 7.11/4.65 X96 ) ) =>
% 7.11/4.65 (
% 7.11/4.65 subset @
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% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X100:$i]:
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X100 @
% 7.11/4.65 (
% 7.11/4.65 powerset @
% 7.11/4.65 X100 ) ) ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X102:$i,
% 7.11/4.65 X104:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 subset @
% 7.11/4.65 X102 @
% 7.11/4.65 X104 ) =>
% 7.11/4.65 (
% 7.11/4.65 subset @
% 7.11/4.65 (
% 7.11/4.65 powerset @
% 7.11/4.65 X102 ) @
% 7.11/4.65 (
% 7.11/4.65 powerset @
% 7.11/4.65 X104 ) ) ) ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 sepInPowerset ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 sepSubset ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 binunionIL ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 upairset2IR ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 binunionIR ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 binunionEcases ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 binunionE ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 binunionLsub ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 binunionRsub ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 binintersectI ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 binintersectSubset5 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 binintersectEL ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 binintersectLsub ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 binintersectSubset2 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 binintersectSubset3 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 binintersectER ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 disjointsetsI1 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 binintersectRsub ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 binintersectSubset4 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 binintersectSubset1 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 bs114d ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X106:$i,
% 7.11/4.65 X108:$i,
% 7.11/4.65 X110:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X110 @
% 7.11/4.65 X106 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ~(
% 7.11/4.65 in @
% 7.11/4.65 X110 @
% 7.11/4.65 X108 ) ) =>
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X110 @
% 7.11/4.65 (
% 7.11/4.65 setminus @
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% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X112:$i,
% 7.11/4.65 X114:$i,
% 7.11/4.65 X116:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X116 @
% 7.11/4.65 (
% 7.11/4.65 setminus @
% 7.11/4.65 X112 @
% 7.11/4.65 X114 ) ) =>
% 7.11/4.65 (
% 7.11/4.65 in @
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% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X118:$i,
% 7.11/4.65 X120:$i,
% 7.11/4.65 X122:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X122 @
% 7.11/4.65 (
% 7.11/4.65 setminus @
% 7.11/4.65 X118 @
% 7.11/4.65 X120 ) ) =>
% 7.11/4.65 (
% 7.11/4.65 ~(
% 7.11/4.65 in @
% 7.11/4.65 X122 @
% 7.11/4.65 X120 ) ) ) ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X124:$i,
% 7.11/4.65 X126:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 subset @
% 7.11/4.65 X124 @
% 7.11/4.65 X126 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 setminus @
% 7.11/4.65 X124 @
% 7.11/4.65 X126 ) =
% 7.11/4.65 (
% 7.11/4.65 emptyset ) ) ) ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X128:$i,
% 7.11/4.65 X130:$i,
% 7.11/4.65 X132:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ~(
% 7.11/4.65 in @
% 7.11/4.65 X132 @
% 7.11/4.65 (
% 7.11/4.65 setminus
% 7.11/4.65 @
% 7.11/4.65 X128 @
% 7.11/4.65 X130 ) ) ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X132 @
% 7.11/4.65 X128 ) =>
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X132 @
% 7.11/4.65 X130 ) ) ) ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X134:$i,
% 7.11/4.65 X136:$i,
% 7.11/4.65 X138:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ~(
% 7.11/4.65 in @
% 7.11/4.65 X138 @
% 7.11/4.65 (
% 7.11/4.65 setminus
% 7.11/4.65 @
% 7.11/4.65 X134 @
% 7.11/4.65 X136 ) ) ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ~(
% 7.11/4.65 in @
% 7.11/4.65 X138 @
% 7.11/4.65 X136 ) ) =>
% 7.11/4.65 (
% 7.11/4.65 ~(
% 7.11/4.65 in @
% 7.11/4.65 X138 @
% 7.11/4.65 X134 ) ) ) ) ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X140:$i,
% 7.11/4.65 X142:$i,
% 7.11/4.65 X144:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ~(
% 7.11/4.65 in @
% 7.11/4.65 X144 @
% 7.11/4.65 X140 ) ) =>
% 7.11/4.65 (
% 7.11/4.65 ~(
% 7.11/4.65 in @
% 7.11/4.65 X144 @
% 7.11/4.65 (
% 7.11/4.65 setminus
% 7.11/4.65 @
% 7.11/4.65 X140 @
% 7.11/4.65 X142 ) ) ) ) ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X146:$i,
% 7.11/4.65 X148:$i,
% 7.11/4.65 X150:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X150 @
% 7.11/4.65 X148 ) =>
% 7.11/4.65 (
% 7.11/4.65 ~(
% 7.11/4.65 in @
% 7.11/4.65 X150 @
% 7.11/4.65 (
% 7.11/4.65 setminus
% 7.11/4.65 @
% 7.11/4.65 X146 @
% 7.11/4.65 X148 ) ) ) ) ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X152:$i,
% 7.11/4.65 X154:$i]:
% 7.11/4.65 (
% 7.11/4.65 subset @
% 7.11/4.65 (
% 7.11/4.65 setminus @
% 7.11/4.65 X152 @
% 7.11/4.65 X154 ) @
% 7.11/4.65 X152 ) ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X156:$i,
% 7.11/4.65 X158:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 setminus @
% 7.11/4.65 X156 @
% 7.11/4.65 X158 ) =
% 7.11/4.65 (
% 7.11/4.65 emptyset ) ) =>
% 7.11/4.65 (
% 7.11/4.65 subset @
% 7.11/4.65 X156 @
% 7.11/4.65 X158 ) ) ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 symdiffE ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 symdiffI1 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 symdiffI2 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 symdiffIneg1 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 symdiffIneg2 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 secondinupair ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 setukpairIL ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 setukpairIR ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 kpairiskpair ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 kpairp ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 singletonsubset ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X160:$i,
% 7.11/4.65 X162:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X162 @
% 7.11/4.65 X160 ) =>
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 (
% 7.11/4.65 setadjoin
% 7.11/4.65 @
% 7.11/4.65 X162 @
% 7.11/4.65 emptyset ) @
% 7.11/4.65 (
% 7.11/4.65 powerset @
% 7.11/4.65 X160 ) ) ) ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 singletoninpowunion ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 upairset2E ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 upairsubunion ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 upairinpowunion ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ubforcartprodlem1 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ubforcartprodlem2 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ubforcartprodlem3 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 cartprodpairin ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 cartprodmempair1 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 cartprodmempair ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 setunionE2 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 setunionsingleton1 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 setunionsingleton2 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 setunionsingleton ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 singletonprop ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ex1E1 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ex1I ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ex1I2 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 singletonsuniq ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 setukpairinjL1 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 kfstsingleton ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 theprop ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 kfstpairEq ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 cartprodfstin ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 setukpairinjL2 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 setukpairinjL ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 setukpairinjR11 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 setukpairinjR12 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 setukpairinjR1 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 upairequniteq ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 setukpairinjR2 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 setukpairinjR ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ksndsingleton ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ksndpairEq ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 kpairsurjEq ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 cartprodsndin ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 cartprodpairmemEL ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 cartprodpairmemER ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 cartprodmempaircEq ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 cartprodfstpairEq ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 cartprodsndpairEq ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 cartprodpairsurjEq ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 dpsetconstrI ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 dpsetconstrSub ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 setOfPairsIsBReln ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 dpsetconstrERa ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 dpsetconstrEL1 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 dpsetconstrEL2 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 dpsetconstrER ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 funcImageSingleton ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 apProp ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 app ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 infuncsetfunc ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ap2p ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 funcinfuncset ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 lamProp ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 lamp ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 lam2p ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 brelnall1 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 brelnall2 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ex1E2 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 funcGraphProp1 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 funcGraphProp3 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 funcGraphProp2 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 funcextLem ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 funcGraphProp4 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 subbreln ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 eqbreln ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 funcext ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 funcext2 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ap2apEq1 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ap2apEq2 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 beta1 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 eta1 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 lam2lamEq ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 beta2 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 eta2 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 iffalseProp1 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 iffalseProp2 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 iftrueProp1 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 iftrueProp2 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ifSingleton ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ifp ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 theeq ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 iftrue ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 iffalse ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 iftrueorfalse ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 binintersectT_lem ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 binunionT_lem ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X164:$i,
% 7.11/4.65 X166:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X166 @
% 7.11/4.65 (
% 7.11/4.65 powerset @
% 7.11/4.65 X164 ) ) =>
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 (
% 7.11/4.65 powerset @
% 7.11/4.65 X166 ) @
% 7.11/4.65 (
% 7.11/4.65 powerset @
% 7.11/4.65 (
% 7.11/4.65 powerset @
% 7.11/4.65 X164 ) ) ) ) ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X168:$i,
% 7.11/4.65 X170:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X170 @
% 7.11/4.65 (
% 7.11/4.65 powerset @
% 7.11/4.65 X168 ) ) =>
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X172:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X172 @
% 7.11/4.65 (
% 7.11/4.65 powerset @
% 7.11/4.65 X168 ) ) =>
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 (
% 7.11/4.65 setminus @
% 7.11/4.65 X170 @
% 7.11/4.65 X172 ) @
% 7.11/4.65 (
% 7.11/4.65 powerset @
% 7.11/4.65 X168 ) ) ) ) ) ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X174:$i,
% 7.11/4.65 X176:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X176 @
% 7.11/4.65 (
% 7.11/4.65 powerset @
% 7.11/4.65 X174 ) ) =>
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 (
% 7.11/4.65 setminus @
% 7.11/4.65 X174 @
% 7.11/4.65 X176 ) @
% 7.11/4.65 (
% 7.11/4.65 powerset @
% 7.11/4.65 X174 ) ) ) ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X178:$i,
% 7.11/4.65 X180:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X180 @
% 7.11/4.65 (
% 7.11/4.65 powerset @
% 7.11/4.65 X178 ) ) =>
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X182:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X182 @
% 7.11/4.65 (
% 7.11/4.65 powerset @
% 7.11/4.65 X178 ) ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X184:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X184 @
% 7.11/4.65 X178 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X184 @
% 7.11/4.65 X180 ) =>
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X184 @
% 7.11/4.65 X182 ) ) ) ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X186:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X186 @
% 7.11/4.65 X178 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X186 @
% 7.11/4.65 X182 ) =>
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X186 @
% 7.11/4.65 X180 ) ) ) ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 X180 ) =
% 7.11/4.65 (
% 7.11/4.65 X182 ) ) ) ) ) ) ) ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X188:$i,
% 7.11/4.65 X190:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X190 @
% 7.11/4.65 (
% 7.11/4.65 powerset @
% 7.11/4.65 X188 ) ) =>
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X192:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X192 @
% 7.11/4.65 (
% 7.11/4.65 powerset @
% 7.11/4.65 X188 ) ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X194:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X194 @
% 7.11/4.65 X188 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X194 @
% 7.11/4.65 X190 ) =>
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X194 @
% 7.11/4.65 X192 ) ) ) ) =>
% 7.11/4.65 (
% 7.11/4.65 subset @
% 7.11/4.65 X190 @
% 7.11/4.65 X192 ) ) ) ) ) ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X196:$i,
% 7.11/4.65 X198:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X198 @
% 7.11/4.65 (
% 7.11/4.65 powerset @
% 7.11/4.65 X196 ) ) =>
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X200:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X200 @
% 7.11/4.65 (
% 7.11/4.65 powerset @
% 7.11/4.65 X196 ) ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X202:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X202 @
% 7.11/4.65 X196 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X202 @
% 7.11/4.65 X198 ) =>
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X202 @
% 7.11/4.65 X200 ) ) ) ) =>
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X198 @
% 7.11/4.65 (
% 7.11/4.65 powerset @
% 7.11/4.65 X200 ) ) ) ) ) ) ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X204:$i,
% 7.11/4.65 X206:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X206 @
% 7.11/4.65 (
% 7.11/4.65 powerset @
% 7.11/4.65 X204 ) ) =>
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X208:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X208 @
% 7.11/4.65 (
% 7.11/4.65 powerset @
% 7.11/4.65 X204 ) ) =>
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X210:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X210 @
% 7.11/4.65 X204 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X206 @
% 7.11/4.65 (
% 7.11/4.65 powerset @
% 7.11/4.65 X208 ) ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X210 @
% 7.11/4.65 X206 ) =>
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X210 @
% 7.11/4.65 X208 ) ) ) ) ) ) ) ) ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X212:$i,
% 7.11/4.65 X214:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X214 @
% 7.11/4.65 (
% 7.11/4.65 powerset @
% 7.11/4.65 X212 ) ) =>
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X216:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X216 @
% 7.11/4.65 X212 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X216 @
% 7.11/4.65 X214 ) =>
% 7.11/4.65 (
% 7.11/4.65 ~(
% 7.11/4.65 in @
% 7.11/4.65 X216 @
% 7.11/4.65 (
% 7.11/4.65 setminus
% 7.11/4.65 @
% 7.11/4.65 X212 @
% 7.11/4.65 X214 ) ) ) ) ) ) ) ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X218:$i,
% 7.11/4.65 X220:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X220 @
% 7.11/4.65 (
% 7.11/4.65 powerset @
% 7.11/4.65 X218 ) ) =>
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X222:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X222 @
% 7.11/4.65 X218 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ~(
% 7.11/4.65 in @
% 7.11/4.65 X222 @
% 7.11/4.65 (
% 7.11/4.65 setminus
% 7.11/4.65 @
% 7.11/4.65 X218 @
% 7.11/4.65 X220 ) ) ) =>
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X222 @
% 7.11/4.65 X220 ) ) ) ) ) ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 binintersectTELcontra ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 binintersectTERcontra ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X224:$i,
% 7.11/4.65 X226:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X226 @
% 7.11/4.65 (
% 7.11/4.65 powerset @
% 7.11/4.65 X224 ) ) =>
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X228:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X228 @
% 7.11/4.65 (
% 7.11/4.65 powerset @
% 7.11/4.65 X224 ) ) =>
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X230:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X230 @
% 7.11/4.65 X224 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 subset @
% 7.11/4.65 X226 @
% 7.11/4.65 (
% 7.11/4.65 setminus @
% 7.11/4.65 X224 @
% 7.11/4.65 X228 ) ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X230 @
% 7.11/4.65 X228 ) =>
% 7.11/4.65 (
% 7.11/4.65 ~(
% 7.11/4.65 in @
% 7.11/4.65 X230 @
% 7.11/4.65 X226 ) ) ) ) ) ) ) ) ) ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X232:$i,
% 7.11/4.65 X234:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X234 @
% 7.11/4.65 (
% 7.11/4.65 powerset @
% 7.11/4.65 X232 ) ) =>
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X236:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X236 @
% 7.11/4.65 (
% 7.11/4.65 powerset @
% 7.11/4.65 X232 ) ) =>
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X238:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X238 @
% 7.11/4.65 X232 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 subset @
% 7.11/4.65 X234 @
% 7.11/4.65 X236 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ~(
% 7.11/4.65 in @
% 7.11/4.65 X238 @
% 7.11/4.65 X236 ) ) =>
% 7.11/4.65 (
% 7.11/4.65 ~(
% 7.11/4.65 in @
% 7.11/4.65 X238 @
% 7.11/4.65 X234 ) ) ) ) ) ) ) ) ) ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X240:$i,
% 7.11/4.65 X242:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X242 @
% 7.11/4.65 (
% 7.11/4.65 powerset @
% 7.11/4.65 X240 ) ) =>
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X244:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X244 @
% 7.11/4.65 (
% 7.11/4.65 powerset @
% 7.11/4.65 X240 ) ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 subset @
% 7.11/4.65 X242 @
% 7.11/4.65 X244 ) =>
% 7.11/4.65 (
% 7.11/4.65 subset @
% 7.11/4.65 (
% 7.11/4.65 setminus @
% 7.11/4.65 X240 @
% 7.11/4.65 X244 ) @
% 7.11/4.65 (
% 7.11/4.65 setminus @
% 7.11/4.65 X240 @
% 7.11/4.65 X242 ) ) ) ) ) ) ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X246:$i,
% 7.11/4.65 X248:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X248 @
% 7.11/4.65 (
% 7.11/4.65 powerset @
% 7.11/4.65 X246 ) ) =>
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X250:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X250 @
% 7.11/4.65 (
% 7.11/4.65 powerset @
% 7.11/4.65 X246 ) ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 subset @
% 7.11/4.65 (
% 7.11/4.65 setminus @
% 7.11/4.65 X246 @
% 7.11/4.65 X250 ) @
% 7.11/4.65 (
% 7.11/4.65 setminus @
% 7.11/4.65 X246 @
% 7.11/4.65 X248 ) ) =>
% 7.11/4.65 (
% 7.11/4.65 subset @
% 7.11/4.65 X248 @
% 7.11/4.65 X250 ) ) ) ) ) ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X252:$i,
% 7.11/4.65 X254:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X254 @
% 7.11/4.65 (
% 7.11/4.65 powerset @
% 7.11/4.65 X252 ) ) =>
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X256:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X256 @
% 7.11/4.65 X252 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X256 @
% 7.11/4.65 X254 ) =>
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X256 @
% 7.11/4.65 (
% 7.11/4.65 setminus @
% 7.11/4.65 X252 @
% 7.11/4.65 (
% 7.11/4.65 setminus @
% 7.11/4.65 X252 @
% 7.11/4.65 X254 ) ) ) ) ) ) ) ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X258:$i,
% 7.11/4.65 X260:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X260 @
% 7.11/4.65 (
% 7.11/4.65 powerset @
% 7.11/4.65 X258 ) ) =>
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X262:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X262 @
% 7.11/4.65 X258 ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X262 @
% 7.11/4.65 (
% 7.11/4.65 setminus @
% 7.11/4.65 X258 @
% 7.11/4.65 (
% 7.11/4.65 setminus @
% 7.11/4.65 X258 @
% 7.11/4.65 X260 ) ) ) =>
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X262 @
% 7.11/4.65 X260 ) ) ) ) ) ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X264:$i,
% 7.11/4.65 X266:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X266 @
% 7.11/4.65 (
% 7.11/4.65 powerset @
% 7.11/4.65 X264 ) ) =>
% 7.11/4.65 (
% 7.11/4.65 subset @
% 7.11/4.65 X266 @
% 7.11/4.65 (
% 7.11/4.65 setminus @
% 7.11/4.65 X264 @
% 7.11/4.65 (
% 7.11/4.65 setminus @
% 7.11/4.65 X264 @
% 7.11/4.65 X266 ) ) ) ) ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X268:$i,
% 7.11/4.65 X270:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X270 @
% 7.11/4.65 (
% 7.11/4.65 powerset @
% 7.11/4.65 X268 ) ) =>
% 7.11/4.65 (
% 7.11/4.65 subset @
% 7.11/4.65 (
% 7.11/4.65 setminus @
% 7.11/4.65 X268 @
% 7.11/4.65 (
% 7.11/4.65 setminus @
% 7.11/4.65 X268 @
% 7.11/4.65 X270 ) ) @
% 7.11/4.65 X270 ) ) ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X272:$i,
% 7.11/4.65 X274:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X274 @
% 7.11/4.65 (
% 7.11/4.65 powerset @
% 7.11/4.65 X272 ) ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 X274 ) =
% 7.11/4.65 (
% 7.11/4.65 setminus @
% 7.11/4.65 X272 @
% 7.11/4.65 (
% 7.11/4.65 setminus @
% 7.11/4.65 X272 @
% 7.11/4.65 X274 ) ) ) ) ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 complementTnotintersectT ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 complementImpComplementIntersect ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 complementSubsetComplementIntersect ) =>
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 complementInPowersetComplementIntersect ) =>
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X276:$i,
% 7.11/4.65 X278:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X278 @
% 7.11/4.65 (
% 7.11/4.65 powerset @
% 7.11/4.65 X276 ) ) =>
% 7.11/4.65 (
% 7.11/4.65 ![
% 7.11/4.65 X280:$i]:
% 7.11/4.65 (
% 7.11/4.65 (
% 7.11/4.65 in @
% 7.11/4.65 X280 @
% 7.11/4.65 (
% 7.11/4.65 powerset @
% 7.11/4.65 X276 ) ) =>
% 7.11/4.65 (
% 7.11/4.66 (
% 7.11/4.66 subset @
% 7.11/4.66 X278 @
% 7.11/4.66 (
% 7.11/4.66 setminus @
% 7.11/4.66 X276 @
% 7.11/4.66 X280 ) ) =>
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X282:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X282 @
% 7.11/4.66 X276 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X282 @
% 7.11/4.66 X280 ) =>
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X282 @
% 7.11/4.66 (
% 7.11/4.66 setminus @
% 7.11/4.66 X276 @
% 7.11/4.66 X278 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 7.11/4.66 thf(zf_stmt_1, type, zip_tseitin_0 : $i > $i > $i > $o).
% 7.11/4.66 thf(zf_stmt_2, axiom,
% 7.11/4.66 (![X8:$i,X6:$i,X4:$i]:
% 7.11/4.66 ( ( zip_tseitin_0 @ X8 @ X6 @ X4 ) <=>
% 7.11/4.66 ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ))).
% 7.11/4.66 thf(zf_stmt_3, conjecture,
% 7.11/4.66 (( setextAx ) =>
% 7.11/4.66 ( ( emptysetAx ) =>
% 7.11/4.66 ( ( setadjoinAx ) =>
% 7.11/4.66 ( ( ![X4:$i,X6:$i]:
% 7.11/4.66 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 7.11/4.66 ( ![X8:$i]: ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) ) =>
% 7.11/4.66 ( ( setunionAx ) =>
% 7.11/4.66 ( ( omega0Ax ) =>
% 7.11/4.66 ( ( omegaSAx ) =>
% 7.11/4.66 ( ( omegaIndAx ) =>
% 7.11/4.66 ( ( replAx ) =>
% 7.11/4.66 ( ( foundationAx ) =>
% 7.11/4.66 ( ( wellorderingAx ) =>
% 7.11/4.66 ( ( descrp ) =>
% 7.11/4.66 ( ( dsetconstrI ) =>
% 7.11/4.66 ( ( dsetconstrEL ) =>
% 7.11/4.66 ( ( dsetconstrER ) =>
% 7.11/4.66 ( ( exuE1 ) =>
% 7.11/4.66 ( ( prop2setE ) =>
% 7.11/4.66 ( ( emptysetE ) =>
% 7.11/4.66 ( ( emptysetimpfalse ) =>
% 7.11/4.66 ( ( notinemptyset ) =>
% 7.11/4.66 ( ( exuE3e ) =>
% 7.11/4.66 ( ( setext ) =>
% 7.11/4.66 ( ( emptyI ) =>
% 7.11/4.66 ( ( noeltsimpempty ) =>
% 7.11/4.66 ( ( setbeta ) =>
% 7.11/4.66 ( ( nonemptyE1 ) =>
% 7.11/4.66 ( ( nonemptyI ) =>
% 7.11/4.66 ( ( nonemptyI1 ) =>
% 7.11/4.66 ( ( setadjoinIL ) =>
% 7.11/4.66 ( ( emptyinunitempty ) =>
% 7.11/4.66 ( ( setadjoinIR ) =>
% 7.11/4.66 ( ( setadjoinE ) =>
% 7.11/4.66 ( (
% 7.11/4.66 setadjoinOr ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 setoftrueEq ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X10:$i,
% 7.11/4.66 X12:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X14:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X14 @ X12 ) =>
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X14 @ X10 ) ) ) =>
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X12 @
% 7.11/4.66 (
% 7.11/4.66 powerset @
% 7.11/4.66 X10 ) ) ) ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X16:$i]:
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 emptyset @
% 7.11/4.66 (
% 7.11/4.66 powerset @
% 7.11/4.66 X16 ) ) ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X18:$i]:
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 emptyset @
% 7.11/4.66 (
% 7.11/4.66 powerset @
% 7.11/4.66 X18 ) ) ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X20:$i,
% 7.11/4.66 X22:$i,
% 7.11/4.66 X24:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X22 @
% 7.11/4.66 (
% 7.11/4.66 powerset @
% 7.11/4.66 X20 ) ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X24 @ X22 ) =>
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X24 @ X20 ) ) ) ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 setunionI ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 setunionE ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 subPowSU ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 exuE2 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 nonemptyImpWitness ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 uniqinunit ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 notinsingleton ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 eqinunit ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 singletonsswitch ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 upairsetE ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 upairsetIL ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 upairsetIR ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 emptyE1 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 vacuousDall ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 quantDeMorgan1 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 quantDeMorgan2 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 quantDeMorgan3 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 quantDeMorgan4 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 prop2setI ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 prop2set2propI ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 notdexE ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 notdallE ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 exuI1 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 exuI3 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 exuI2 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 inCongP ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 in__Cong ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 exuE3u ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 exu__Cong ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 emptyset__Cong ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 setadjoin__Cong ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X26:$i,
% 7.11/4.66 X28:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 X26 ) =
% 7.11/4.66 (
% 7.11/4.66 X28 ) ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 powerset @
% 7.11/4.66 X26 ) =
% 7.11/4.66 (
% 7.11/4.66 powerset @
% 7.11/4.66 X28 ) ) ) ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 setunion__Cong ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 omega__Cong ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 exuEu ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 descr__Cong ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 dsetconstr__Cong ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X30:$i,
% 7.11/4.66 X32:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X34:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X34 @ X30 ) =>
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X34 @ X32 ) ) ) =>
% 7.11/4.66 (
% 7.11/4.66 subset @
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% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X36:$i,
% 7.11/4.66 X38:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 X36 ) =
% 7.11/4.66 (
% 7.11/4.66 X38 ) ) =>
% 7.11/4.66 (
% 7.11/4.66 subset @
% 7.11/4.66 X38 @ X36 ) ) ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X40:$i,
% 7.11/4.66 X42:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 X40 ) =
% 7.11/4.66 (
% 7.11/4.66 X42 ) ) =>
% 7.11/4.66 (
% 7.11/4.66 subset @
% 7.11/4.66 X40 @ X42 ) ) ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X44:$i,
% 7.11/4.66 X46:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X48:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X48 @ X44 ) =>
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X48 @ X46 ) ) ) =>
% 7.11/4.66 (
% 7.11/4.66 subset @
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% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X50:$i]:
% 7.11/4.66 (
% 7.11/4.66 subset @
% 7.11/4.66 emptyset @
% 7.11/4.66 X50 ) ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X52:$i,
% 7.11/4.66 X54:$i,
% 7.11/4.66 X56:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 subset @
% 7.11/4.66 X52 @ X54 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X56 @ X52 ) =>
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X56 @ X54 ) ) ) ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X58:$i,
% 7.11/4.66 X60:$i,
% 7.11/4.66 X62:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 subset @
% 7.11/4.66 X58 @ X60 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ~(
% 7.11/4.66 in @
% 7.11/4.66 X62 @ X60 ) ) =>
% 7.11/4.66 (
% 7.11/4.66 ~(
% 7.11/4.66 in @
% 7.11/4.66 X62 @ X58 ) ) ) ) ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X64:$i,
% 7.11/4.66 X66:$i,
% 7.11/4.66 X68:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X68 @ X64 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ~(
% 7.11/4.66 in @
% 7.11/4.66 X68 @ X66 ) ) =>
% 7.11/4.66 (
% 7.11/4.66 ~(
% 7.11/4.66 subset @
% 7.11/4.66 X64 @ X66 ) ) ) ) ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X70:$i,
% 7.11/4.66 X72:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ~(
% 7.11/4.66 subset @
% 7.11/4.66 X70 @ X72 ) ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 X70 ) !=
% 7.11/4.66 (
% 7.11/4.66 X72 ) ) ) ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 notequalI2 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X74:$i]:
% 7.11/4.66 (
% 7.11/4.66 subset @
% 7.11/4.66 X74 @ X74 ) ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X76:$i,
% 7.11/4.66 X78:$i,
% 7.11/4.66 X80:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 subset @
% 7.11/4.66 X76 @ X78 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 subset @
% 7.11/4.66 X78 @ X80 ) =>
% 7.11/4.66 (
% 7.11/4.66 subset @
% 7.11/4.66 X76 @ X80 ) ) ) ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 setadjoinSub ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 setadjoinSub2 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X82:$i,
% 7.11/4.66 X84:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 subset @
% 7.11/4.66 X82 @ X84 ) =>
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X82 @
% 7.11/4.66 (
% 7.11/4.66 powerset @
% 7.11/4.66 X84 ) ) ) ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X86:$i,
% 7.11/4.66 X88:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 subset @
% 7.11/4.66 X86 @ X88 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 subset @
% 7.11/4.66 X88 @ X86 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 X86 ) =
% 7.11/4.66 (
% 7.11/4.66 X88 ) ) ) ) ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X90:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 subset @
% 7.11/4.66 X90 @
% 7.11/4.66 emptyset ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 X90 ) =
% 7.11/4.66 (
% 7.11/4.66 emptyset ) ) ) ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X92:$i,
% 7.11/4.66 X94:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 subset @
% 7.11/4.66 X94 @ X92 ) =>
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X94 @
% 7.11/4.66 (
% 7.11/4.66 powerset @
% 7.11/4.66 X92 ) ) ) ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X96:$i,
% 7.11/4.66 X98:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X98 @
% 7.11/4.66 (
% 7.11/4.66 powerset @
% 7.11/4.66 X96 ) ) =>
% 7.11/4.66 (
% 7.11/4.66 subset @
% 7.11/4.66 X98 @ X96 ) ) ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X100:$i]:
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X100 @
% 7.11/4.66 (
% 7.11/4.66 powerset @
% 7.11/4.66 X100 ) ) ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X102:$i,
% 7.11/4.66 X104:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 subset @
% 7.11/4.66 X102 @
% 7.11/4.66 X104 ) =>
% 7.11/4.66 (
% 7.11/4.66 subset @
% 7.11/4.66 (
% 7.11/4.66 powerset @
% 7.11/4.66 X102 ) @
% 7.11/4.66 (
% 7.11/4.66 powerset @
% 7.11/4.66 X104 ) ) ) ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 sepInPowerset ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 sepSubset ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 binunionIL ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 upairset2IR ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 binunionIR ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 binunionEcases ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 binunionE ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 binunionLsub ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 binunionRsub ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 binintersectI ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 binintersectSubset5 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 binintersectEL ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 binintersectLsub ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 binintersectSubset2 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 binintersectSubset3 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 binintersectER ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 disjointsetsI1 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 binintersectRsub ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 binintersectSubset4 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 binintersectSubset1 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 bs114d ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X106:$i,
% 7.11/4.66 X108:$i,
% 7.11/4.66 X110:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X110 @
% 7.11/4.66 X106 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ~(
% 7.11/4.66 in @
% 7.11/4.66 X110 @
% 7.11/4.66 X108 ) ) =>
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X110 @
% 7.11/4.66 (
% 7.11/4.66 setminus @
% 7.11/4.66 X106 @
% 7.11/4.66 X108 ) ) ) ) ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X112:$i,
% 7.11/4.66 X114:$i,
% 7.11/4.66 X116:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X116 @
% 7.11/4.66 (
% 7.11/4.66 setminus @
% 7.11/4.66 X112 @
% 7.11/4.66 X114 ) ) =>
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X116 @
% 7.11/4.66 X112 ) ) ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X118:$i,
% 7.11/4.66 X120:$i,
% 7.11/4.66 X122:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X122 @
% 7.11/4.66 (
% 7.11/4.66 setminus @
% 7.11/4.66 X118 @
% 7.11/4.66 X120 ) ) =>
% 7.11/4.66 (
% 7.11/4.66 ~(
% 7.11/4.66 in @
% 7.11/4.66 X122 @
% 7.11/4.66 X120 ) ) ) ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X124:$i,
% 7.11/4.66 X126:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 subset @
% 7.11/4.66 X124 @
% 7.11/4.66 X126 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 setminus @
% 7.11/4.66 X124 @
% 7.11/4.66 X126 ) =
% 7.11/4.66 (
% 7.11/4.66 emptyset ) ) ) ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X128:$i,
% 7.11/4.66 X130:$i,
% 7.11/4.66 X132:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ~(
% 7.11/4.66 in @
% 7.11/4.66 X132 @
% 7.11/4.66 (
% 7.11/4.66 setminus
% 7.11/4.66 @
% 7.11/4.66 X128 @
% 7.11/4.66 X130 ) ) ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X132 @
% 7.11/4.66 X128 ) =>
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X132 @
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% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X134:$i,
% 7.11/4.66 X136:$i,
% 7.11/4.66 X138:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ~(
% 7.11/4.66 in @
% 7.11/4.66 X138 @
% 7.11/4.66 (
% 7.11/4.66 setminus
% 7.11/4.66 @
% 7.11/4.66 X134 @
% 7.11/4.66 X136 ) ) ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ~(
% 7.11/4.66 in @
% 7.11/4.66 X138 @
% 7.11/4.66 X136 ) ) =>
% 7.11/4.66 (
% 7.11/4.66 ~(
% 7.11/4.66 in @
% 7.11/4.66 X138 @
% 7.11/4.66 X134 ) ) ) ) ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X140:$i,
% 7.11/4.66 X142:$i,
% 7.11/4.66 X144:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ~(
% 7.11/4.66 in @
% 7.11/4.66 X144 @
% 7.11/4.66 X140 ) ) =>
% 7.11/4.66 (
% 7.11/4.66 ~(
% 7.11/4.66 in @
% 7.11/4.66 X144 @
% 7.11/4.66 (
% 7.11/4.66 setminus
% 7.11/4.66 @
% 7.11/4.66 X140 @
% 7.11/4.66 X142 ) ) ) ) ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X146:$i,
% 7.11/4.66 X148:$i,
% 7.11/4.66 X150:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X150 @
% 7.11/4.66 X148 ) =>
% 7.11/4.66 (
% 7.11/4.66 ~(
% 7.11/4.66 in @
% 7.11/4.66 X150 @
% 7.11/4.66 (
% 7.11/4.66 setminus
% 7.11/4.66 @
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% 7.11/4.66 X148 ) ) ) ) ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X152:$i,
% 7.11/4.66 X154:$i]:
% 7.11/4.66 (
% 7.11/4.66 subset @
% 7.11/4.66 (
% 7.11/4.66 setminus @
% 7.11/4.66 X152 @
% 7.11/4.66 X154 ) @
% 7.11/4.66 X152 ) ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X156:$i,
% 7.11/4.66 X158:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 setminus @
% 7.11/4.66 X156 @
% 7.11/4.66 X158 ) =
% 7.11/4.66 (
% 7.11/4.66 emptyset ) ) =>
% 7.11/4.66 (
% 7.11/4.66 subset @
% 7.11/4.66 X156 @
% 7.11/4.66 X158 ) ) ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 symdiffE ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 symdiffI1 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 symdiffI2 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 symdiffIneg1 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 symdiffIneg2 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 secondinupair ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 setukpairIL ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 setukpairIR ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 kpairiskpair ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 kpairp ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 singletonsubset ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X160:$i,
% 7.11/4.66 X162:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X162 @
% 7.11/4.66 X160 ) =>
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 (
% 7.11/4.66 setadjoin
% 7.11/4.66 @
% 7.11/4.66 X162 @
% 7.11/4.66 emptyset ) @
% 7.11/4.66 (
% 7.11/4.66 powerset @
% 7.11/4.66 X160 ) ) ) ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 singletoninpowunion ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 upairset2E ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 upairsubunion ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 upairinpowunion ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ubforcartprodlem1 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ubforcartprodlem2 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ubforcartprodlem3 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 cartprodpairin ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 cartprodmempair1 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 cartprodmempair ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 setunionE2 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 setunionsingleton1 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 setunionsingleton2 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 setunionsingleton ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 singletonprop ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ex1E1 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ex1I ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ex1I2 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 singletonsuniq ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 setukpairinjL1 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 kfstsingleton ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 theprop ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 kfstpairEq ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 cartprodfstin ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 setukpairinjL2 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 setukpairinjL ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 setukpairinjR11 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 setukpairinjR12 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 setukpairinjR1 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 upairequniteq ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 setukpairinjR2 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 setukpairinjR ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ksndsingleton ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ksndpairEq ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 kpairsurjEq ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 cartprodsndin ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 cartprodpairmemEL ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 cartprodpairmemER ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 cartprodmempaircEq ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 cartprodfstpairEq ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 cartprodsndpairEq ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 cartprodpairsurjEq ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 dpsetconstrI ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 dpsetconstrSub ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 setOfPairsIsBReln ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 dpsetconstrERa ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 dpsetconstrEL1 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 dpsetconstrEL2 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 dpsetconstrER ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 funcImageSingleton ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 apProp ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 app ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 infuncsetfunc ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ap2p ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 funcinfuncset ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 lamProp ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 lamp ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 lam2p ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 brelnall1 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 brelnall2 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ex1E2 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 funcGraphProp1 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 funcGraphProp3 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 funcGraphProp2 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 funcextLem ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 funcGraphProp4 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 subbreln ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 eqbreln ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 funcext ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 funcext2 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ap2apEq1 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ap2apEq2 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 beta1 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 eta1 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 lam2lamEq ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 beta2 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 eta2 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 iffalseProp1 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 iffalseProp2 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 iftrueProp1 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 iftrueProp2 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ifSingleton ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ifp ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 theeq ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 iftrue ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 iffalse ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 iftrueorfalse ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 binintersectT_lem ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 binunionT_lem ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X164:$i,
% 7.11/4.66 X166:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X166 @
% 7.11/4.66 (
% 7.11/4.66 powerset @
% 7.11/4.66 X164 ) ) =>
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 (
% 7.11/4.66 powerset @
% 7.11/4.66 X166 ) @
% 7.11/4.66 (
% 7.11/4.66 powerset @
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% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X168:$i,
% 7.11/4.66 X170:$i]:
% 7.11/4.66 (
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% 7.11/4.66 in @
% 7.11/4.66 X170 @
% 7.11/4.66 (
% 7.11/4.66 powerset @
% 7.11/4.66 X168 ) ) =>
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X172:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X172 @
% 7.11/4.66 (
% 7.11/4.66 powerset @
% 7.11/4.66 X168 ) ) =>
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 (
% 7.11/4.66 setminus @
% 7.11/4.66 X170 @
% 7.11/4.66 X172 ) @
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% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X174:$i,
% 7.11/4.66 X176:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X176 @
% 7.11/4.66 (
% 7.11/4.66 powerset @
% 7.11/4.66 X174 ) ) =>
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 (
% 7.11/4.66 setminus @
% 7.11/4.66 X174 @
% 7.11/4.66 X176 ) @
% 7.11/4.66 (
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% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X178:$i,
% 7.11/4.66 X180:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X180 @
% 7.11/4.66 (
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% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X182:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X182 @
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% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X184:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
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% 7.11/4.66 X184 @
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% 7.11/4.66 (
% 7.11/4.66 (
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% 7.11/4.66 X184 @
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% 7.11/4.66 (
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% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
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% 7.11/4.66 (
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% 7.11/4.66 X186 @
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% 7.11/4.66 (
% 7.11/4.66 (
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% 7.11/4.66 X186 @
% 7.11/4.66 X182 ) =>
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% 7.11/4.66 X186 @
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% 7.11/4.66 (
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% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X188:$i,
% 7.11/4.66 X190:$i]:
% 7.11/4.66 (
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% 7.11/4.66 in @
% 7.11/4.66 X190 @
% 7.11/4.66 (
% 7.11/4.66 powerset @
% 7.11/4.66 X188 ) ) =>
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X192:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X192 @
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% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X194:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
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% 7.11/4.66 X194 @
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% 7.11/4.66 (
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% 7.11/4.66 X194 @
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% 7.11/4.66 (
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% 7.11/4.66 (
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% 7.11/4.66 X198 @
% 7.11/4.66 (
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% 7.11/4.66 (
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% 7.11/4.66 X200:$i]:
% 7.11/4.66 (
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% 7.11/4.66 (
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% 7.11/4.66 ![
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% 7.11/4.66 (
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% 7.11/4.66 (
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% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
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% 7.11/4.66 X206:$i]:
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% 7.11/4.66 X206 @
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% 7.11/4.66 (
% 7.11/4.66 ![
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% 7.11/4.66 (
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% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X210:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
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% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X206 @
% 7.11/4.66 (
% 7.11/4.66 powerset @
% 7.11/4.66 X208 ) ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X210 @
% 7.11/4.66 X206 ) =>
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X210 @
% 7.11/4.66 X208 ) ) ) ) ) ) ) ) ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X212:$i,
% 7.11/4.66 X214:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X214 @
% 7.11/4.66 (
% 7.11/4.66 powerset @
% 7.11/4.66 X212 ) ) =>
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X216:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X216 @
% 7.11/4.66 X212 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X216 @
% 7.11/4.66 X214 ) =>
% 7.11/4.66 (
% 7.11/4.66 ~(
% 7.11/4.66 in @
% 7.11/4.66 X216 @
% 7.11/4.66 (
% 7.11/4.66 setminus
% 7.11/4.66 @
% 7.11/4.66 X212 @
% 7.11/4.66 X214 ) ) ) ) ) ) ) ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X218:$i,
% 7.11/4.66 X220:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X220 @
% 7.11/4.66 (
% 7.11/4.66 powerset @
% 7.11/4.66 X218 ) ) =>
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X222:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X222 @
% 7.11/4.66 X218 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ~(
% 7.11/4.66 in @
% 7.11/4.66 X222 @
% 7.11/4.66 (
% 7.11/4.66 setminus
% 7.11/4.66 @
% 7.11/4.66 X218 @
% 7.11/4.66 X220 ) ) ) =>
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X222 @
% 7.11/4.66 X220 ) ) ) ) ) ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 binintersectTELcontra ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 binintersectTERcontra ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X224:$i,
% 7.11/4.66 X226:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X226 @
% 7.11/4.66 (
% 7.11/4.66 powerset @
% 7.11/4.66 X224 ) ) =>
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X228:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X228 @
% 7.11/4.66 (
% 7.11/4.66 powerset @
% 7.11/4.66 X224 ) ) =>
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X230:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X230 @
% 7.11/4.66 X224 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 subset @
% 7.11/4.66 X226 @
% 7.11/4.66 (
% 7.11/4.66 setminus @
% 7.11/4.66 X224 @
% 7.11/4.66 X228 ) ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X230 @
% 7.11/4.66 X228 ) =>
% 7.11/4.66 (
% 7.11/4.66 ~(
% 7.11/4.66 in @
% 7.11/4.66 X230 @
% 7.11/4.66 X226 ) ) ) ) ) ) ) ) ) ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X232:$i,
% 7.11/4.66 X234:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X234 @
% 7.11/4.66 (
% 7.11/4.66 powerset @
% 7.11/4.66 X232 ) ) =>
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X236:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X236 @
% 7.11/4.66 (
% 7.11/4.66 powerset @
% 7.11/4.66 X232 ) ) =>
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X238:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X238 @
% 7.11/4.66 X232 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 subset @
% 7.11/4.66 X234 @
% 7.11/4.66 X236 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ~(
% 7.11/4.66 in @
% 7.11/4.66 X238 @
% 7.11/4.66 X236 ) ) =>
% 7.11/4.66 (
% 7.11/4.66 ~(
% 7.11/4.66 in @
% 7.11/4.66 X238 @
% 7.11/4.66 X234 ) ) ) ) ) ) ) ) ) ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X240:$i,
% 7.11/4.66 X242:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X242 @
% 7.11/4.66 (
% 7.11/4.66 powerset @
% 7.11/4.66 X240 ) ) =>
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X244:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X244 @
% 7.11/4.66 (
% 7.11/4.66 powerset @
% 7.11/4.66 X240 ) ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 subset @
% 7.11/4.66 X242 @
% 7.11/4.66 X244 ) =>
% 7.11/4.66 (
% 7.11/4.66 subset @
% 7.11/4.66 (
% 7.11/4.66 setminus @
% 7.11/4.66 X240 @
% 7.11/4.66 X244 ) @
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% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X246:$i,
% 7.11/4.66 X248:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X248 @
% 7.11/4.66 (
% 7.11/4.66 powerset @
% 7.11/4.66 X246 ) ) =>
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X250:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X250 @
% 7.11/4.66 (
% 7.11/4.66 powerset @
% 7.11/4.66 X246 ) ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 subset @
% 7.11/4.66 (
% 7.11/4.66 setminus @
% 7.11/4.66 X246 @
% 7.11/4.66 X250 ) @
% 7.11/4.66 (
% 7.11/4.66 setminus @
% 7.11/4.66 X246 @
% 7.11/4.66 X248 ) ) =>
% 7.11/4.66 (
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% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X252:$i,
% 7.11/4.66 X254:$i]:
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% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X254 @
% 7.11/4.66 (
% 7.11/4.66 powerset @
% 7.11/4.66 X252 ) ) =>
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X256:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X256 @
% 7.11/4.66 X252 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X256 @
% 7.11/4.66 X254 ) =>
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X256 @
% 7.11/4.66 (
% 7.11/4.66 setminus @
% 7.11/4.66 X252 @
% 7.11/4.66 (
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% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X258:$i,
% 7.11/4.66 X260:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X260 @
% 7.11/4.66 (
% 7.11/4.66 powerset @
% 7.11/4.66 X258 ) ) =>
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X262:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X262 @
% 7.11/4.66 X258 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X262 @
% 7.11/4.66 (
% 7.11/4.66 setminus @
% 7.11/4.66 X258 @
% 7.11/4.66 (
% 7.11/4.66 setminus @
% 7.11/4.66 X258 @
% 7.11/4.66 X260 ) ) ) =>
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X262 @
% 7.11/4.66 X260 ) ) ) ) ) ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X264:$i,
% 7.11/4.66 X266:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X266 @
% 7.11/4.66 (
% 7.11/4.66 powerset @
% 7.11/4.66 X264 ) ) =>
% 7.11/4.66 (
% 7.11/4.66 subset @
% 7.11/4.66 X266 @
% 7.11/4.66 (
% 7.11/4.66 setminus @
% 7.11/4.66 X264 @
% 7.11/4.66 (
% 7.11/4.66 setminus @
% 7.11/4.66 X264 @
% 7.11/4.66 X266 ) ) ) ) ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X268:$i,
% 7.11/4.66 X270:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X270 @
% 7.11/4.66 (
% 7.11/4.66 powerset @
% 7.11/4.66 X268 ) ) =>
% 7.11/4.66 (
% 7.11/4.66 subset @
% 7.11/4.66 (
% 7.11/4.66 setminus @
% 7.11/4.66 X268 @
% 7.11/4.66 (
% 7.11/4.66 setminus @
% 7.11/4.66 X268 @
% 7.11/4.66 X270 ) ) @
% 7.11/4.66 X270 ) ) ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X272:$i,
% 7.11/4.66 X274:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X274 @
% 7.11/4.66 (
% 7.11/4.66 powerset @
% 7.11/4.66 X272 ) ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 X274 ) =
% 7.11/4.66 (
% 7.11/4.66 setminus @
% 7.11/4.66 X272 @
% 7.11/4.66 (
% 7.11/4.66 setminus @
% 7.11/4.66 X272 @
% 7.11/4.66 X274 ) ) ) ) ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 complementTnotintersectT ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 complementImpComplementIntersect ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 complementSubsetComplementIntersect ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 complementInPowersetComplementIntersect ) =>
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X276:$i,
% 7.11/4.66 X278:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X278 @
% 7.11/4.66 (
% 7.11/4.66 powerset @
% 7.11/4.66 X276 ) ) =>
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X280:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X280 @
% 7.11/4.66 (
% 7.11/4.66 powerset @
% 7.11/4.66 X276 ) ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 subset @
% 7.11/4.66 X278 @
% 7.11/4.66 (
% 7.11/4.66 setminus @
% 7.11/4.66 X276 @
% 7.11/4.66 X280 ) ) =>
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X282:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X282 @
% 7.11/4.66 X276 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X282 @
% 7.11/4.66 X280 ) =>
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X282 @
% 7.11/4.66 (
% 7.11/4.66 setminus @
% 7.11/4.66 X276 @
% 7.11/4.66 X278 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 7.11/4.66 thf(zf_stmt_4, negated_conjecture,
% 7.11/4.66 (~( ( setextAx ) =>
% 7.11/4.66 ( ( emptysetAx ) =>
% 7.11/4.66 ( ( setadjoinAx ) =>
% 7.11/4.66 ( ( ![X4:$i,X6:$i]:
% 7.11/4.66 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 7.11/4.66 ( ![X8:$i]: ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) ) =>
% 7.11/4.66 ( ( setunionAx ) =>
% 7.11/4.66 ( ( omega0Ax ) =>
% 7.11/4.66 ( ( omegaSAx ) =>
% 7.11/4.66 ( ( omegaIndAx ) =>
% 7.11/4.66 ( ( replAx ) =>
% 7.11/4.66 ( ( foundationAx ) =>
% 7.11/4.66 ( ( wellorderingAx ) =>
% 7.11/4.66 ( ( descrp ) =>
% 7.11/4.66 ( ( dsetconstrI ) =>
% 7.11/4.66 ( ( dsetconstrEL ) =>
% 7.11/4.66 ( ( dsetconstrER ) =>
% 7.11/4.66 ( ( exuE1 ) =>
% 7.11/4.66 ( ( prop2setE ) =>
% 7.11/4.66 ( ( emptysetE ) =>
% 7.11/4.66 ( ( emptysetimpfalse ) =>
% 7.11/4.66 ( ( notinemptyset ) =>
% 7.11/4.66 ( ( exuE3e ) =>
% 7.11/4.66 ( ( setext ) =>
% 7.11/4.66 ( ( emptyI ) =>
% 7.11/4.66 ( ( noeltsimpempty ) =>
% 7.11/4.66 ( ( setbeta ) =>
% 7.11/4.66 ( ( nonemptyE1 ) =>
% 7.11/4.66 ( ( nonemptyI ) =>
% 7.11/4.66 ( ( nonemptyI1 ) =>
% 7.11/4.66 ( ( setadjoinIL ) =>
% 7.11/4.66 ( ( emptyinunitempty ) =>
% 7.11/4.66 ( ( setadjoinIR ) =>
% 7.11/4.66 ( (
% 7.11/4.66 setadjoinE ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 setadjoinOr ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 setoftrueEq ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X10:$i,
% 7.11/4.66 X12:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X14:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X14 @ X12 ) =>
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X14 @ X10 ) ) ) =>
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X12 @
% 7.11/4.66 (
% 7.11/4.66 powerset
% 7.11/4.66 @
% 7.11/4.66 X10 ) ) ) ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X16:$i]:
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 emptyset @
% 7.11/4.66 (
% 7.11/4.66 powerset
% 7.11/4.66 @
% 7.11/4.66 X16 ) ) ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X18:$i]:
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 emptyset @
% 7.11/4.66 (
% 7.11/4.66 powerset
% 7.11/4.66 @
% 7.11/4.66 X18 ) ) ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X20:$i,
% 7.11/4.66 X22:$i,
% 7.11/4.66 X24:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X22 @
% 7.11/4.66 (
% 7.11/4.66 powerset
% 7.11/4.66 @
% 7.11/4.66 X20 ) ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X24 @ X22 ) =>
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X24 @ X20 ) ) ) ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 setunionI ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 setunionE ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 subPowSU ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 exuE2 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 nonemptyImpWitness ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 uniqinunit ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 notinsingleton ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 eqinunit ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 singletonsswitch ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 upairsetE ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 upairsetIL ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 upairsetIR ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 emptyE1 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 vacuousDall ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 quantDeMorgan1 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 quantDeMorgan2 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 quantDeMorgan3 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 quantDeMorgan4 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 prop2setI ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 prop2set2propI ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 notdexE ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 notdallE ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 exuI1 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 exuI3 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 exuI2 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 inCongP ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 in__Cong ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 exuE3u ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 exu__Cong ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 emptyset__Cong ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 setadjoin__Cong ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X26:$i,
% 7.11/4.66 X28:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 X26 ) =
% 7.11/4.66 (
% 7.11/4.66 X28 ) ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 powerset
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% 7.11/4.66 (
% 7.11/4.66 powerset
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% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 setunion__Cong ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 omega__Cong ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 exuEu ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 descr__Cong ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 dsetconstr__Cong ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
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% 7.11/4.66 X32:$i]:
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% 7.11/4.66 (
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% 7.11/4.66 X34:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
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% 7.11/4.66 (
% 7.11/4.66 ![
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% 7.11/4.66 X38:$i]:
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% 7.11/4.66 (
% 7.11/4.66 (
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% 7.11/4.66 (
% 7.11/4.66 ![
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% 7.11/4.66 X42:$i]:
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% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 X40 ) =
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% 7.11/4.66 X42 ) ) =>
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% 7.11/4.66 (
% 7.11/4.66 ![
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% 7.11/4.66 X46:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X48:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
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% 7.11/4.66 (
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% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
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% 7.11/4.66 X54:$i,
% 7.11/4.66 X56:$i]:
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% 7.11/4.66 (
% 7.11/4.66 subset @
% 7.11/4.66 X52 @ X54 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 in @
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% 7.11/4.66 (
% 7.11/4.66 (
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% 7.11/4.66 X60:$i,
% 7.11/4.66 X62:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
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% 7.11/4.66 ~
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% 7.11/4.66 (
% 7.11/4.66 ![
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% 7.11/4.66 X66:$i,
% 7.11/4.66 X68:$i]:
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% 7.11/4.66 (
% 7.11/4.66 in @
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% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ~
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% 7.11/4.66 in @
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% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
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% 7.11/4.66 X72:$i]:
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% 7.11/4.66 (
% 7.11/4.66 ~
% 7.11/4.66 (
% 7.11/4.66 subset @
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% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 X70 ) !=
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% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 notequalI2 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X74:$i]:
% 7.11/4.66 (
% 7.11/4.66 subset @
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% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
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% 7.11/4.66 X78:$i,
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% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 subset @
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% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 subset @
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% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 setadjoinSub ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 setadjoinSub2 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X82:$i,
% 7.11/4.66 X84:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 subset @
% 7.11/4.66 X82 @ X84 ) =>
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X82 @
% 7.11/4.66 (
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% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
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% 7.11/4.66 X88:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 subset @
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% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 subset @
% 7.11/4.66 X88 @ X86 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
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% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X90:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 subset @
% 7.11/4.66 X90 @
% 7.11/4.66 emptyset ) =>
% 7.11/4.66 (
% 7.11/4.66 (
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% 7.11/4.66 (
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% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X92:$i,
% 7.11/4.66 X94:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 subset @
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% 7.11/4.66 (
% 7.11/4.66 in @
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% 7.11/4.66 (
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% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
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% 7.11/4.66 X98:$i]:
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% 7.11/4.66 (
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% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
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% 7.11/4.66 (
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% 7.11/4.66 (
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% 7.11/4.66 @
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% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X102:$i,
% 7.11/4.66 X104:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 subset @
% 7.11/4.66 X102 @
% 7.11/4.66 X104 ) =>
% 7.11/4.66 (
% 7.11/4.66 subset @
% 7.11/4.66 (
% 7.11/4.66 powerset
% 7.11/4.66 @
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% 7.11/4.66 (
% 7.11/4.66 powerset
% 7.11/4.66 @
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% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 sepInPowerset ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 sepSubset ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 binunionIL ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 upairset2IR ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 binunionIR ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 binunionEcases ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 binunionE ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 binunionLsub ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 binunionRsub ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 binintersectI ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 binintersectSubset5 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 binintersectEL ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 binintersectLsub ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 binintersectSubset2 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 binintersectSubset3 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 binintersectER ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 disjointsetsI1 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 binintersectRsub ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 binintersectSubset4 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 binintersectSubset1 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 bs114d ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X106:$i,
% 7.11/4.66 X108:$i,
% 7.11/4.66 X110:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 in @
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% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ~
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% 7.11/4.66 (
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% 7.11/4.66 X114:$i,
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% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
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% 7.11/4.66 X120:$i,
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% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
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% 7.11/4.66 X126:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
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% 7.11/4.66 X126 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
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% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
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% 7.11/4.66 X130:$i,
% 7.11/4.66 X132:$i]:
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% 7.11/4.66 (
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% 7.11/4.66 ![
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% 7.11/4.66 X136:$i,
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% 7.11/4.66 (
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% 7.11/4.66 (
% 7.11/4.66 subset @
% 7.11/4.66 X156 @
% 7.11/4.66 X158 ) ) ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 symdiffE ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 symdiffI1 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 symdiffI2 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 symdiffIneg1 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 symdiffIneg2 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 secondinupair ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 setukpairIL ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 setukpairIR ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 kpairiskpair ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 kpairp ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 singletonsubset ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X160:$i,
% 7.11/4.66 X162:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X162 @
% 7.11/4.66 X160 ) =>
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 (
% 7.11/4.66 setadjoin
% 7.11/4.66 @
% 7.11/4.66 X162 @
% 7.11/4.66 emptyset ) @
% 7.11/4.66 (
% 7.11/4.66 powerset
% 7.11/4.66 @
% 7.11/4.66 X160 ) ) ) ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 singletoninpowunion ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 upairset2E ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 upairsubunion ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 upairinpowunion ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ubforcartprodlem1 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ubforcartprodlem2 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ubforcartprodlem3 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 cartprodpairin ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 cartprodmempair1 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 cartprodmempair ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 setunionE2 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 setunionsingleton1 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 setunionsingleton2 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 setunionsingleton ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 singletonprop ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ex1E1 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ex1I ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ex1I2 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 singletonsuniq ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 setukpairinjL1 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 kfstsingleton ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 theprop ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 kfstpairEq ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 cartprodfstin ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 setukpairinjL2 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 setukpairinjL ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 setukpairinjR11 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 setukpairinjR12 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 setukpairinjR1 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 upairequniteq ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 setukpairinjR2 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 setukpairinjR ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ksndsingleton ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ksndpairEq ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 kpairsurjEq ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 cartprodsndin ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 cartprodpairmemEL ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 cartprodpairmemER ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 cartprodmempaircEq ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 cartprodfstpairEq ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 cartprodsndpairEq ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 cartprodpairsurjEq ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 dpsetconstrI ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 dpsetconstrSub ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 setOfPairsIsBReln ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 dpsetconstrERa ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 dpsetconstrEL1 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 dpsetconstrEL2 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 dpsetconstrER ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 funcImageSingleton ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 apProp ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 app ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 infuncsetfunc ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ap2p ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 funcinfuncset ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 lamProp ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 lamp ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 lam2p ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 brelnall1 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 brelnall2 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ex1E2 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 funcGraphProp1 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 funcGraphProp3 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 funcGraphProp2 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 funcextLem ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 funcGraphProp4 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 subbreln ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 eqbreln ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 funcext ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 funcext2 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ap2apEq1 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ap2apEq2 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 beta1 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 eta1 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 lam2lamEq ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 beta2 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 eta2 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 iffalseProp1 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 iffalseProp2 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 iftrueProp1 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 iftrueProp2 ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ifSingleton ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ifp ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 theeq ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 iftrue ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 iffalse ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 iftrueorfalse ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 binintersectT_lem ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 binunionT_lem ) =>
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X164:$i,
% 7.11/4.66 X166:$i]:
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% 7.11/4.66 (
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% 7.11/4.66 X166 @
% 7.11/4.66 (
% 7.11/4.66 powerset
% 7.11/4.66 @
% 7.11/4.66 X164 ) ) =>
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 (
% 7.11/4.66 powerset
% 7.11/4.66 @
% 7.11/4.66 X166 ) @
% 7.11/4.66 (
% 7.11/4.66 powerset
% 7.11/4.66 @
% 7.11/4.66 (
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% 7.11/4.66 @
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% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X168:$i,
% 7.11/4.66 X170:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X170 @
% 7.11/4.66 (
% 7.11/4.66 powerset
% 7.11/4.66 @
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% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X172:$i]:
% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 X172 @
% 7.11/4.66 (
% 7.11/4.66 powerset
% 7.11/4.66 @
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% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 (
% 7.11/4.66 setminus
% 7.11/4.66 @
% 7.11/4.66 X170 @
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% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X174:$i,
% 7.11/4.66 X176:$i]:
% 7.11/4.66 (
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% 7.11/4.66 X176 @
% 7.11/4.66 (
% 7.11/4.66 powerset
% 7.11/4.66 @
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% 7.11/4.66 (
% 7.11/4.66 in @
% 7.11/4.66 (
% 7.11/4.66 setminus
% 7.11/4.66 @
% 7.11/4.66 X174 @
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% 7.11/4.66 (
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% 7.11/4.66 (
% 7.11/4.66 (
% 7.11/4.66 ![
% 7.11/4.66 X178:$i,
% 7.11/4.66 X180:$i]:
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% 7.11/4.66 X180 @
% 7.11/4.66 (
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% 7.11/4.66 (
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% 7.11/4.66 (
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% 7.11/4.66 X190:$i]:
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% 7.11/4.66 (
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% 7.11/4.66 (
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% 7.11/4.66 (
% 7.11/4.66 (
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% 7.41/4.68 (
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% 7.41/4.68 X202 @
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% 7.41/4.68 setminus
% 7.41/4.68 @
% 7.41/4.68 X212 @
% 7.41/4.68 X214 ) ) ) ) ) ) ) ) =>
% 7.41/4.68 (
% 7.41/4.68 (
% 7.41/4.68 ![
% 7.41/4.68 X218:$i,
% 7.41/4.68 X220:$i]:
% 7.41/4.68 (
% 7.41/4.68 (
% 7.41/4.68 in @
% 7.41/4.68 X220 @
% 7.41/4.68 (
% 7.41/4.68 powerset
% 7.41/4.68 @
% 7.41/4.68 X218 ) ) =>
% 7.41/4.68 (
% 7.41/4.68 ![
% 7.41/4.68 X222:$i]:
% 7.41/4.68 (
% 7.41/4.68 (
% 7.41/4.68 in @
% 7.41/4.68 X222 @
% 7.41/4.68 X218 ) =>
% 7.41/4.68 (
% 7.41/4.68 (
% 7.41/4.68 ~
% 7.41/4.68 (
% 7.41/4.68 in @
% 7.41/4.68 X222 @
% 7.41/4.68 (
% 7.41/4.68 setminus
% 7.41/4.68 @
% 7.41/4.68 X218 @
% 7.41/4.68 X220 ) ) ) =>
% 7.41/4.68 (
% 7.41/4.68 in @
% 7.41/4.68 X222 @
% 7.41/4.68 X220 ) ) ) ) ) ) =>
% 7.41/4.68 (
% 7.41/4.68 (
% 7.41/4.68 binintersectTELcontra ) =>
% 7.41/4.68 (
% 7.41/4.68 (
% 7.41/4.68 binintersectTERcontra ) =>
% 7.41/4.68 (
% 7.41/4.68 (
% 7.41/4.68 ![
% 7.41/4.68 X224:$i,
% 7.41/4.68 X226:$i]:
% 7.41/4.68 (
% 7.41/4.68 (
% 7.41/4.68 in @
% 7.41/4.68 X226 @
% 7.41/4.68 (
% 7.41/4.68 powerset
% 7.41/4.68 @
% 7.41/4.68 X224 ) ) =>
% 7.41/4.68 (
% 7.41/4.68 ![
% 7.41/4.68 X228:$i]:
% 7.41/4.68 (
% 7.41/4.68 (
% 7.41/4.68 in @
% 7.41/4.68 X228 @
% 7.41/4.68 (
% 7.41/4.68 powerset
% 7.41/4.68 @
% 7.41/4.68 X224 ) ) =>
% 7.41/4.68 (
% 7.41/4.68 ![
% 7.41/4.68 X230:$i]:
% 7.41/4.68 (
% 7.41/4.68 (
% 7.41/4.68 in @
% 7.41/4.68 X230 @
% 7.41/4.68 X224 ) =>
% 7.41/4.68 (
% 7.41/4.68 (
% 7.41/4.68 subset @
% 7.41/4.68 X226 @
% 7.41/4.68 (
% 7.41/4.68 setminus
% 7.41/4.68 @
% 7.41/4.68 X224 @
% 7.41/4.68 X228 ) ) =>
% 7.41/4.68 (
% 7.41/4.68 (
% 7.41/4.68 in @
% 7.41/4.68 X230 @
% 7.41/4.68 X228 ) =>
% 7.41/4.68 (
% 7.41/4.68 ~
% 7.41/4.68 (
% 7.41/4.68 in @
% 7.41/4.68 X230 @
% 7.41/4.68 X226 ) ) ) ) ) ) ) ) ) ) =>
% 7.41/4.68 (
% 7.41/4.68 (
% 7.41/4.68 ![
% 7.41/4.68 X232:$i,
% 7.41/4.68 X234:$i]:
% 7.41/4.68 (
% 7.41/4.68 (
% 7.41/4.68 in @
% 7.41/4.68 X234 @
% 7.41/4.68 (
% 7.41/4.68 powerset
% 7.41/4.68 @
% 7.41/4.68 X232 ) ) =>
% 7.41/4.68 (
% 7.41/4.68 ![
% 7.41/4.68 X236:$i]:
% 7.41/4.68 (
% 7.41/4.68 (
% 7.41/4.68 in @
% 7.41/4.68 X236 @
% 7.41/4.68 (
% 7.41/4.68 powerset
% 7.41/4.68 @
% 7.41/4.68 X232 ) ) =>
% 7.41/4.68 (
% 7.41/4.68 ![
% 7.41/4.68 X238:$i]:
% 7.41/4.68 (
% 7.41/4.68 (
% 7.41/4.68 in @
% 7.41/4.68 X238 @
% 7.41/4.68 X232 ) =>
% 7.41/4.68 (
% 7.41/4.68 (
% 7.41/4.68 subset @
% 7.41/4.68 X234 @
% 7.41/4.68 X236 ) =>
% 7.41/4.68 (
% 7.41/4.68 (
% 7.41/4.68 ~
% 7.41/4.68 (
% 7.41/4.68 in @
% 7.41/4.68 X238 @
% 7.41/4.68 X236 ) ) =>
% 7.41/4.68 (
% 7.41/4.68 ~
% 7.41/4.68 (
% 7.41/4.68 in @
% 7.41/4.68 X238 @
% 7.41/4.68 X234 ) ) ) ) ) ) ) ) ) ) =>
% 7.41/4.68 (
% 7.41/4.68 (
% 7.41/4.68 ![
% 7.41/4.68 X240:$i,
% 7.41/4.68 X242:$i]:
% 7.41/4.68 (
% 7.41/4.68 (
% 7.41/4.68 in @
% 7.41/4.68 X242 @
% 7.41/4.68 (
% 7.41/4.68 powerset
% 7.41/4.68 @
% 7.41/4.68 X240 ) ) =>
% 7.41/4.68 (
% 7.41/4.68 ![
% 7.41/4.68 X244:$i]:
% 7.41/4.68 (
% 7.41/4.68 (
% 7.41/4.68 in @
% 7.41/4.68 X244 @
% 7.41/4.68 (
% 7.41/4.68 powerset
% 7.41/4.68 @
% 7.41/4.68 X240 ) ) =>
% 7.41/4.68 (
% 7.41/4.68 (
% 7.41/4.68 subset @
% 7.41/4.68 X242 @
% 7.41/4.68 X244 ) =>
% 7.41/4.68 (
% 7.41/4.68 subset @
% 7.41/4.68 (
% 7.41/4.68 setminus
% 7.41/4.68 @
% 7.41/4.68 X240 @
% 7.41/4.68 X244 ) @
% 7.41/4.68 (
% 7.41/4.68 setminus
% 7.41/4.68 @
% 7.41/4.68 X240 @
% 7.41/4.68 X242 ) ) ) ) ) ) ) =>
% 7.41/4.68 (
% 7.41/4.68 (
% 7.41/4.68 ![
% 7.41/4.68 X246:$i,
% 7.41/4.68 X248:$i]:
% 7.41/4.68 (
% 7.41/4.68 (
% 7.41/4.68 in @
% 7.41/4.68 X248 @
% 7.41/4.68 (
% 7.41/4.68 powerset
% 7.41/4.68 @
% 7.41/4.68 X246 ) ) =>
% 7.41/4.68 (
% 7.41/4.68 ![
% 7.41/4.68 X250:$i]:
% 7.41/4.68 (
% 7.41/4.68 (
% 7.41/4.68 in @
% 7.41/4.68 X250 @
% 7.41/4.68 (
% 7.41/4.68 powerset
% 7.41/4.68 @
% 7.41/4.68 X246 ) ) =>
% 7.41/4.68 (
% 7.41/4.68 (
% 7.41/4.68 subset @
% 7.41/4.68 (
% 7.41/4.68 setminus
% 7.41/4.68 @
% 7.41/4.68 X246 @
% 7.41/4.68 X250 ) @
% 7.41/4.68 (
% 7.41/4.68 setminus
% 7.41/4.68 @
% 7.41/4.68 X246 @
% 7.41/4.68 X248 ) ) =>
% 7.41/4.68 (
% 7.41/4.68 subset @
% 7.41/4.68 X248 @
% 7.41/4.68 X250 ) ) ) ) ) ) =>
% 7.41/4.68 (
% 7.41/4.68 (
% 7.41/4.68 ![
% 7.41/4.68 X252:$i,
% 7.41/4.68 X254:$i]:
% 7.41/4.68 (
% 7.41/4.68 (
% 7.41/4.68 in @
% 7.41/4.68 X254 @
% 7.41/4.68 (
% 7.41/4.68 powerset
% 7.41/4.68 @
% 7.41/4.68 X252 ) ) =>
% 7.41/4.68 (
% 7.41/4.68 ![
% 7.41/4.68 X256:$i]:
% 7.41/4.68 (
% 7.41/4.68 (
% 7.41/4.68 in @
% 7.41/4.68 X256 @
% 7.41/4.68 X252 ) =>
% 7.41/4.68 (
% 7.41/4.68 (
% 7.41/4.68 in @
% 7.41/4.68 X256 @
% 7.41/4.68 X254 ) =>
% 7.41/4.68 (
% 7.41/4.68 in @
% 7.41/4.68 X256 @
% 7.41/4.68 (
% 7.41/4.68 setminus
% 7.41/4.68 @
% 7.41/4.68 X252 @
% 7.41/4.68 (
% 7.41/4.68 setminus
% 7.41/4.68 @
% 7.41/4.68 X252 @
% 7.41/4.68 X254 ) ) ) ) ) ) ) ) =>
% 7.41/4.68 (
% 7.41/4.68 (
% 7.41/4.68 ![
% 7.41/4.68 X258:$i,
% 7.41/4.68 X260:$i]:
% 7.41/4.68 (
% 7.41/4.68 (
% 7.41/4.68 in @
% 7.41/4.68 X260 @
% 7.41/4.68 (
% 7.41/4.68 powerset
% 7.41/4.68 @
% 7.41/4.68 X258 ) ) =>
% 7.41/4.68 (
% 7.41/4.68 ![
% 7.41/4.68 X262:$i]:
% 7.41/4.68 (
% 7.41/4.68 (
% 7.41/4.68 in @
% 7.41/4.68 X262 @
% 7.41/4.68 X258 ) =>
% 7.41/4.68 (
% 7.41/4.68 (
% 7.41/4.68 in @
% 7.41/4.68 X262 @
% 7.41/4.68 (
% 7.41/4.68 setminus
% 7.41/4.68 @
% 7.41/4.68 X258 @
% 7.41/4.68 (
% 7.41/4.68 setminus
% 7.41/4.68 @
% 7.41/4.68 X258 @
% 7.41/4.68 X260 ) ) ) =>
% 7.41/4.68 (
% 7.41/4.68 in @
% 7.41/4.68 X262 @
% 7.41/4.68 X260 ) ) ) ) ) ) =>
% 7.41/4.68 (
% 7.41/4.68 (
% 7.41/4.68 ![
% 7.41/4.68 X264:$i,
% 7.41/4.68 X266:$i]:
% 7.41/4.68 (
% 7.41/4.68 (
% 7.41/4.68 in @
% 7.41/4.68 X266 @
% 7.41/4.68 (
% 7.41/4.68 powerset
% 7.41/4.68 @
% 7.41/4.68 X264 ) ) =>
% 7.41/4.68 (
% 7.41/4.68 subset @
% 7.41/4.68 X266 @
% 7.41/4.68 (
% 7.41/4.68 setminus
% 7.41/4.68 @
% 7.41/4.68 X264 @
% 7.41/4.68 (
% 7.41/4.68 setminus
% 7.41/4.68 @
% 7.41/4.68 X264 @
% 7.41/4.68 X266 ) ) ) ) ) =>
% 7.41/4.68 (
% 7.41/4.68 (
% 7.41/4.68 ![
% 7.41/4.68 X268:$i,
% 7.41/4.68 X270:$i]:
% 7.41/4.68 (
% 7.41/4.68 (
% 7.41/4.68 in @
% 7.41/4.68 X270 @
% 7.41/4.68 (
% 7.41/4.68 powerset
% 7.41/4.68 @
% 7.41/4.68 X268 ) ) =>
% 7.41/4.68 (
% 7.41/4.68 subset @
% 7.41/4.68 (
% 7.41/4.68 setminus
% 7.41/4.68 @
% 7.41/4.68 X268 @
% 7.41/4.68 (
% 7.41/4.68 setminus
% 7.41/4.68 @
% 7.41/4.68 X268 @
% 7.41/4.68 X270 ) ) @
% 7.41/4.68 X270 ) ) ) =>
% 7.41/4.68 (
% 7.41/4.68 (
% 7.41/4.68 ![
% 7.41/4.68 X272:$i,
% 7.41/4.68 X274:$i]:
% 7.41/4.68 (
% 7.41/4.68 (
% 7.41/4.68 in @
% 7.41/4.68 X274 @
% 7.41/4.68 (
% 7.41/4.68 powerset
% 7.41/4.68 @
% 7.41/4.68 X272 ) ) =>
% 7.41/4.68 (
% 7.41/4.68 (
% 7.41/4.68 X274 ) =
% 7.41/4.68 (
% 7.41/4.68 setminus
% 7.41/4.68 @
% 7.41/4.68 X272 @
% 7.41/4.68 (
% 7.41/4.68 setminus
% 7.41/4.68 @
% 7.41/4.68 X272 @
% 7.41/4.68 X274 ) ) ) ) ) =>
% 7.41/4.68 (
% 7.41/4.68 (
% 7.41/4.68 complementTnotintersectT ) =>
% 7.41/4.68 (
% 7.41/4.68 (
% 7.41/4.68 complementImpComplementIntersect ) =>
% 7.41/4.68 (
% 7.41/4.68 (
% 7.41/4.68 complementSubsetComplementIntersect ) =>
% 7.41/4.68 (
% 7.41/4.68 (
% 7.41/4.68 complementInPowersetComplementIntersect ) =>
% 7.41/4.68 (
% 7.41/4.68 ![
% 7.41/4.68 X276:$i,
% 7.41/4.68 X278:$i]:
% 7.41/4.68 (
% 7.41/4.68 (
% 7.41/4.68 in @
% 7.41/4.68 X278 @
% 7.41/4.68 (
% 7.41/4.68 powerset
% 7.41/4.68 @
% 7.41/4.68 X276 ) ) =>
% 7.41/4.68 (
% 7.41/4.68 ![
% 7.41/4.68 X280:$i]:
% 7.41/4.68 (
% 7.41/4.68 (
% 7.41/4.68 in @
% 7.41/4.68 X280 @
% 7.41/4.68 (
% 7.41/4.68 powerset
% 7.41/4.68 @
% 7.41/4.68 X276 ) ) =>
% 7.41/4.68 (
% 7.41/4.68 (
% 7.41/4.68 subset @
% 7.41/4.68 X278 @
% 7.41/4.68 (
% 7.41/4.68 setminus
% 7.41/4.68 @
% 7.41/4.68 X276 @
% 7.41/4.68 X280 ) ) =>
% 7.41/4.68 (
% 7.41/4.68 ![
% 7.41/4.68 X282:$i]:
% 7.41/4.68 (
% 7.41/4.68 (
% 7.41/4.68 in @
% 7.41/4.68 X282 @
% 7.41/4.68 X276 ) =>
% 7.41/4.68 (
% 7.41/4.68 (
% 7.41/4.68 in @
% 7.41/4.68 X282 @
% 7.41/4.68 X280 ) =>
% 7.41/4.68 (
% 7.41/4.68 in @
% 7.41/4.68 X282 @
% 7.41/4.68 (
% 7.41/4.68 setminus
% 7.41/4.68 @
% 7.41/4.68 X276 @
% 7.41/4.68 X278 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 7.41/4.68 inference('cnf.neg', [status(esa)], [zf_stmt_3])).
% 7.41/4.68 thf(zip_derived_cl136, plain, ( (in @ sk__145 @ sk__142)),
% 7.41/4.68 inference('cnf', [status(esa)], [zf_stmt_4])).
% 7.41/4.68 thf(zip_derived_cl66, plain,
% 7.41/4.68 (![X26 : $i, X27 : $i, X28 : $i]:
% 7.41/4.68 ( (in @ X26 @ X27)
% 7.41/4.68 | ~ (in @ X26 @ X28)
% 7.41/4.68 | (in @ X26 @ (setminus @ X28 @ X27)))),
% 7.41/4.68 inference('cnf', [status(esa)], [zf_stmt_4])).
% 7.41/4.68 thf(zip_derived_cl485, plain,
% 7.41/4.68 (![X0 : $i]:
% 7.41/4.68 ( (in @ sk__145 @ (setminus @ sk__142 @ X0)) | (in @ sk__145 @ X0))),
% 7.41/4.68 inference('sup-', [status(thm)], [zip_derived_cl136, zip_derived_cl66])).
% 7.41/4.68 thf(zip_derived_cl135, plain,
% 7.41/4.68 (~ (in @ sk__145 @ (setminus @ sk__142 @ sk__143))),
% 7.41/4.68 inference('cnf', [status(esa)], [zf_stmt_4])).
% 7.41/4.68 thf(zip_derived_cl598, plain, ( (in @ sk__145 @ sk__143)),
% 7.41/4.68 inference('sup-', [status(thm)], [zip_derived_cl485, zip_derived_cl135])).
% 7.41/4.68 thf(zip_derived_cl137, plain,
% 7.41/4.68 ( (subset @ sk__143 @ (setminus @ sk__142 @ sk__144))),
% 7.41/4.68 inference('cnf', [status(esa)], [zf_stmt_4])).
% 7.41/4.68 thf(zip_derived_cl145, plain,
% 7.41/4.68 (![X72 : $i, X73 : $i, X74 : $i, X75 : $i]:
% 7.41/4.68 (~ (in @ X72 @ (powerset @ X73))
% 7.41/4.68 | ~ (subset @ X74 @ (setminus @ X73 @ X72))
% 7.41/4.68 | ~ (in @ X75 @ X74)
% 7.41/4.68 | ~ (in @ X75 @ X72)
% 7.41/4.68 | ~ (in @ X75 @ X73)
% 7.41/4.68 | ~ (in @ X74 @ (powerset @ X73)))),
% 7.41/4.68 inference('cnf', [status(esa)], [zf_stmt_4])).
% 7.41/4.68 thf(zip_derived_cl257, plain,
% 7.41/4.68 (![X122 : $i, X123 : $i, X124 : $i]:
% 7.41/4.68 (~ (in @ X122 @ (powerset @ X123))
% 7.41/4.68 | (in @ X124 @ X123)
% 7.41/4.68 | ~ (in @ X124 @ X122))),
% 7.41/4.68 inference('cnf', [status(esa)], [zf_stmt_4])).
% 7.41/4.68 thf(zip_derived_cl1505, plain,
% 7.41/4.68 (![X72 : $i, X73 : $i, X74 : $i, X75 : $i]:
% 7.41/4.68 (~ (in @ X74 @ (powerset @ X73))
% 7.41/4.68 | ~ (in @ X75 @ X72)
% 7.41/4.68 | ~ (in @ X75 @ X74)
% 7.41/4.68 | ~ (subset @ X74 @ (setminus @ X73 @ X72))
% 7.41/4.68 | ~ (in @ X72 @ (powerset @ X73)))),
% 7.41/4.68 inference('clc', [status(thm)], [zip_derived_cl145, zip_derived_cl257])).
% 7.41/4.68 thf(zip_derived_cl1512, plain,
% 7.41/4.68 (![X0 : $i]:
% 7.41/4.68 (~ (in @ sk__144 @ (powerset @ sk__142))
% 7.41/4.68 | ~ (in @ X0 @ sk__143)
% 7.41/4.68 | ~ (in @ X0 @ sk__144)
% 7.41/4.68 | ~ (in @ sk__143 @ (powerset @ sk__142)))),
% 7.41/4.68 inference('sup-', [status(thm)], [zip_derived_cl137, zip_derived_cl1505])).
% 7.41/4.68 thf(zip_derived_cl133, plain, ( (in @ sk__144 @ (powerset @ sk__142))),
% 7.41/4.68 inference('cnf', [status(esa)], [zf_stmt_4])).
% 7.41/4.68 thf(zip_derived_cl138, plain, ( (in @ sk__143 @ (powerset @ sk__142))),
% 7.41/4.68 inference('cnf', [status(esa)], [zf_stmt_4])).
% 7.41/4.68 thf(zip_derived_cl1541, plain,
% 7.41/4.68 (![X0 : $i]: (~ (in @ X0 @ sk__143) | ~ (in @ X0 @ sk__144))),
% 7.41/4.68 inference('demod', [status(thm)],
% 7.41/4.68 [zip_derived_cl1512, zip_derived_cl133, zip_derived_cl138])).
% 7.41/4.68 thf(zip_derived_cl1560, plain, (~ (in @ sk__145 @ sk__144)),
% 7.41/4.68 inference('sup-', [status(thm)], [zip_derived_cl598, zip_derived_cl1541])).
% 7.41/4.68 thf(zip_derived_cl134, plain, ( (in @ sk__145 @ sk__144)),
% 7.41/4.68 inference('cnf', [status(esa)], [zf_stmt_4])).
% 7.41/4.68 thf(zip_derived_cl1566, plain, ($false),
% 7.41/4.68 inference('demod', [status(thm)], [zip_derived_cl1560, zip_derived_cl134])).
% 7.41/4.68
% 7.41/4.68 % SZS output end Refutation
% 7.41/4.68
% 7.41/4.68
% 7.41/4.68 % Terminating...
% 7.60/4.82 % Runner terminated.
% 7.60/4.85 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------