%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU742^1 : TPTP v9.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.kgfJJzwMlX true
% Computer : n005.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 04:56:04 PM UTC 2025
% Result : Theorem 9.06s 1.76s
% Output : Refutation 9.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU742^1 : TPTP v9.2.0. Released v3.7.0.
% 0.03/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.kgfJJzwMlX true
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Oct 1 16:14:53 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % Running portfolio for 300 s
% 0.13/0.34 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.35 % Running in HO mode
% 0.59/0.69 % Total configuration time : 828
% 0.59/0.69 % Estimated wc time : 1656
% 0.59/0.69 % Estimated cpu time (8 cpus) : 207.0
% 0.59/0.78 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.59/0.78 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.59/0.79 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.59/0.80 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.59/0.80 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.59/0.81 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.59/0.81 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.59/0.81 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 9.06/1.76 % Solved by lams/40_c_ic.sh.
% 9.06/1.76 % done 843 iterations in 0.910s
% 9.06/1.76 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 9.06/1.76 % SZS output start Refutation
% 9.06/1.76 thf(setadjoinAx_type, type, setadjoinAx: $o).
% 9.06/1.76 thf(notdexE_type, type, notdexE: $o).
% 9.06/1.76 thf(setukpairinjL2_type, type, setukpairinjL2: $o).
% 9.06/1.76 thf(doubleComplementI1_type, type, doubleComplementI1: $o).
% 9.06/1.76 thf(setunionAx_type, type, setunionAx: $o).
% 9.06/1.76 thf(setminusELneg_type, type, setminusELneg: $o).
% 9.06/1.76 thf(cartprodsndin_type, type, cartprodsndin: $o).
% 9.06/1.76 thf(ex1E1_type, type, ex1E1: $o).
% 9.06/1.76 thf(powersetE_type, type, powersetE: $o).
% 9.06/1.76 thf(omegaSAx_type, type, omegaSAx: $o).
% 9.06/1.76 thf(exuI1_type, type, exuI1: $o).
% 9.06/1.76 thf(exuI2_type, type, exuI2: $o).
% 9.06/1.76 thf(notequalI2_type, type, notequalI2: $o).
% 9.06/1.76 thf(setukpairinjL_type, type, setukpairinjL: $o).
% 9.06/1.76 thf(kpairiskpair_type, type, kpairiskpair: $o).
% 9.06/1.76 thf(upairsubunion_type, type, upairsubunion: $o).
% 9.06/1.76 thf(funcGraphProp3_type, type, funcGraphProp3: $o).
% 9.06/1.76 thf(cartprodmempaircEq_type, type, cartprodmempaircEq: $o).
% 9.06/1.76 thf(binintersectTERcontra_type, type, binintersectTERcontra: $o).
% 9.06/1.76 thf(powerset__Cong_type, type, powerset__Cong: $o).
% 9.06/1.76 thf(setminusILneg_type, type, setminusILneg: $o).
% 9.06/1.76 thf(wellorderingAx_type, type, wellorderingAx: $o).
% 9.06/1.76 thf(ksndpairEq_type, type, ksndpairEq: $o).
% 9.06/1.76 thf(funcGraphProp2_type, type, funcGraphProp2: $o).
% 9.06/1.76 thf(setadjoinSub2_type, type, setadjoinSub2: $o).
% 9.06/1.76 thf(binintersectSubset5_type, type, binintersectSubset5: $o).
% 9.06/1.76 thf(iftrue_type, type, iftrue: $o).
% 9.06/1.76 thf(upairinpowunion_type, type, upairinpowunion: $o).
% 9.06/1.76 thf(ifSingleton_type, type, ifSingleton: $o).
% 9.06/1.76 thf(doubleComplementSub2_type, type, doubleComplementSub2: $o).
% 9.06/1.76 thf(setoftrueEq_type, type, setoftrueEq: $o).
% 9.06/1.76 thf(funcImageSingleton_type, type, funcImageSingleton: $o).
% 9.06/1.76 thf(inIntersectImpInUnion2_type, type, inIntersectImpInUnion2: $o).
% 9.06/1.76 thf(dpsetconstrERa_type, type, dpsetconstrERa: $o).
% 9.06/1.76 thf(lamProp_type, type, lamProp: $o).
% 9.06/1.76 thf(cartprodpairmemEL_type, type, cartprodpairmemEL: $o).
% 9.06/1.76 thf(emptyset__Cong_type, type, emptyset__Cong: $o).
% 9.06/1.76 thf(dpsetconstrER_type, type, dpsetconstrER: $o).
% 9.06/1.76 thf(sepInPowerset_type, type, sepInPowerset: $o).
% 9.06/1.76 thf(setukpairIR_type, type, setukpairIR: $o).
% 9.06/1.76 thf(setukpairinjR1_type, type, setukpairinjR1: $o).
% 9.06/1.76 thf(lam2p_type, type, lam2p: $o).
% 9.06/1.76 thf(kpair_type, type, kpair: $i > $i > $i).
% 9.06/1.76 thf(binunionE_type, type, binunionE: $o).
% 9.06/1.76 thf(setext_type, type, setext: $o).
% 9.06/1.76 thf(emptyinPowerset_type, type, emptyinPowerset: $o).
% 9.06/1.76 thf(ubforcartprodlem1_type, type, ubforcartprodlem1: $o).
% 9.06/1.76 thf(descr__Cong_type, type, descr__Cong: $o).
% 9.06/1.76 thf(kfstsingleton_type, type, kfstsingleton: $o).
% 9.06/1.76 thf(binintersectTELcontra_type, type, binintersectTELcontra: $o).
% 9.06/1.76 thf(doubleComplementEq_type, type, doubleComplementEq: $o).
% 9.06/1.76 thf(eqbreln_type, type, eqbreln: $o).
% 9.06/1.76 thf(binintersectSubset1_type, type, binintersectSubset1: $o).
% 9.06/1.76 thf(complementImpComplementIntersect_type, type, complementImpComplementIntersect:
% 9.06/1.76 $o).
% 9.06/1.76 thf(in_type, type, in: $i > $i > $o).
% 9.06/1.76 thf(binunionT_lem_type, type, binunionT_lem: $o).
% 9.06/1.76 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o).
% 9.06/1.76 thf(complementT_lem_type, type, complementT_lem: $o).
% 9.06/1.76 thf(binunion_type, type, binunion: $i > $i > $i).
% 9.06/1.76 thf(kpairsurjEq_type, type, kpairsurjEq: $o).
% 9.06/1.76 thf(setadjoinIR_type, type, setadjoinIR: $o).
% 9.06/1.76 thf(doubleComplementE1_type, type, doubleComplementE1: $o).
% 9.06/1.76 thf(beta1_type, type, beta1: $o).
% 9.06/1.76 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o).
% 9.06/1.76 thf(powersetTE1_type, type, powersetTE1: $o).
% 9.06/1.76 thf(symdiffI2_type, type, symdiffI2: $o).
% 9.06/1.76 thf(iftrueProp2_type, type, iftrueProp2: $o).
% 9.06/1.76 thf(upairset2IR_type, type, upairset2IR: $o).
% 9.06/1.76 thf(iffalseProp2_type, type, iffalseProp2: $o).
% 9.06/1.76 thf(subsetE_type, type, subsetE: $o).
% 9.06/1.76 thf(prop2set2propI_type, type, prop2set2propI: $o).
% 9.06/1.76 thf(dsetconstrEL_type, type, dsetconstrEL: $o).
% 9.06/1.76 thf(setbeta_type, type, setbeta: $o).
% 9.06/1.76 thf(eqinunit_type, type, eqinunit: $o).
% 9.06/1.76 thf(upairsetIL_type, type, upairsetIL: $o).
% 9.06/1.76 thf(powersetI1_type, type, powersetI1: $o).
% 9.06/1.76 thf(kfstpairEq_type, type, kfstpairEq: $o).
% 9.06/1.76 thf(binintersectSubset3_type, type, binintersectSubset3: $o).
% 9.06/1.76 thf(setminusIRneg_type, type, setminusIRneg: $o).
% 9.06/1.76 thf(ap2apEq1_type, type, ap2apEq1: $o).
% 9.06/1.76 thf(powersetAx_type, type, powersetAx: $o).
% 9.06/1.76 thf(binintersectSubset4_type, type, binintersectSubset4: $o).
% 9.06/1.76 thf(singletoninpowunion_type, type, singletoninpowunion: $o).
% 9.06/1.76 thf(binunionTIRcontra_type, type, binunionTIRcontra: $o).
% 9.06/1.76 thf(powersetI_type, type, powersetI: $o).
% 9.06/1.76 thf(cartprodmempair_type, type, cartprodmempair: $o).
% 9.06/1.76 thf(upairsetIR_type, type, upairsetIR: $o).
% 9.06/1.76 thf(lamp_type, type, lamp: $o).
% 9.06/1.76 thf(dpsetconstrEL1_type, type, dpsetconstrEL1: $o).
% 9.06/1.76 thf(inCongP_type, type, inCongP: $o).
% 9.06/1.76 thf(setadjoinSub_type, type, setadjoinSub: $o).
% 9.06/1.76 thf(exuE3e_type, type, exuE3e: $o).
% 9.06/1.76 thf(emptysetE_type, type, emptysetE: $o).
% 9.06/1.76 thf(binintersectSubset2_type, type, binintersectSubset2: $o).
% 9.06/1.76 thf(setunionI_type, type, setunionI: $o).
% 9.06/1.76 thf(setunion__Cong_type, type, setunion__Cong: $o).
% 9.06/1.76 thf(prop2setI_type, type, prop2setI: $o).
% 9.06/1.76 thf(singletonsuniq_type, type, singletonsuniq: $o).
% 9.06/1.76 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o).
% 9.06/1.76 thf(setminusER_type, type, setminusER: $o).
% 9.06/1.76 thf(exuE2_type, type, exuE2: $o).
% 9.06/1.76 thf(emptyset_type, type, emptyset: $i).
% 9.06/1.76 thf(setukpairinjR11_type, type, setukpairinjR11: $o).
% 9.06/1.76 thf(ex1I_type, type, ex1I: $o).
% 9.06/1.76 thf(ex1E2_type, type, ex1E2: $o).
% 9.06/1.76 thf(setminus_type, type, setminus: $i > $i > $i).
% 9.06/1.76 thf(setukpairinjL1_type, type, setukpairinjL1: $o).
% 9.06/1.76 thf(powersetsubset_type, type, powersetsubset: $o).
% 9.06/1.76 thf(binunionTILcontra_type, type, binunionTILcontra: $o).
% 9.06/1.76 thf(subPowSU_type, type, subPowSU: $o).
% 9.06/1.76 thf(notequalI1_type, type, notequalI1: $o).
% 9.06/1.76 thf(contrasubsetT_type, type, contrasubsetT: $o).
% 9.06/1.76 thf(notinemptyset_type, type, notinemptyset: $o).
% 9.06/1.76 thf(lam2lamEq_type, type, lam2lamEq: $o).
% 9.06/1.76 thf(nonemptyI1_type, type, nonemptyI1: $o).
% 9.06/1.76 thf(subsetTrans_type, type, subsetTrans: $o).
% 9.06/1.76 thf(kpairp_type, type, kpairp: $o).
% 9.06/1.76 thf(setukpairinjR12_type, type, setukpairinjR12: $o).
% 9.06/1.76 thf(setminusI_type, type, setminusI: $o).
% 9.06/1.76 thf(binunionIL_type, type, binunionIL: $o).
% 9.06/1.76 thf(dpsetconstrSub_type, type, dpsetconstrSub: $o).
% 9.06/1.76 thf(setunionsingleton_type, type, setunionsingleton: $o).
% 9.06/1.76 thf(subsetE2_type, type, subsetE2: $o).
% 9.06/1.76 thf(singletonsswitch_type, type, singletonsswitch: $o).
% 9.06/1.76 thf(ubforcartprodlem3_type, type, ubforcartprodlem3: $o).
% 9.06/1.76 thf(beta2_type, type, beta2: $o).
% 9.06/1.76 thf(dpsetconstrI_type, type, dpsetconstrI: $o).
% 9.06/1.76 thf(setextsub_type, type, setextsub: $o).
% 9.06/1.76 thf(binunionLsub_type, type, binunionLsub: $o).
% 9.06/1.76 thf(setunionsingleton1_type, type, setunionsingleton1: $o).
% 9.06/1.76 thf(binintersect_type, type, binintersect: $i > $i > $i).
% 9.06/1.76 thf(sk__153_type, type, sk__153: $i).
% 9.06/1.76 thf(iftrueorfalse_type, type, iftrueorfalse: $o).
% 9.06/1.76 thf(emptysetsubset_type, type, emptysetsubset: $o).
% 9.06/1.76 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o).
% 9.06/1.76 thf(cartprodpairsurjEq_type, type, cartprodpairsurjEq: $o).
% 9.06/1.76 thf(setOfPairsIsBReln_type, type, setOfPairsIsBReln: $o).
% 9.06/1.76 thf(setunionE_type, type, setunionE: $o).
% 9.06/1.76 thf(ksndsingleton_type, type, ksndsingleton: $o).
% 9.06/1.76 thf(setminusSubset1_type, type, setminusSubset1: $o).
% 9.06/1.76 thf(powersetT_lem_type, type, powersetT_lem: $o).
% 9.06/1.76 thf(emptyinunitempty_type, type, emptyinunitempty: $o).
% 9.06/1.76 thf(binunionIR_type, type, binunionIR: $o).
% 9.06/1.76 thf(theeq_type, type, theeq: $o).
% 9.06/1.76 thf(setadjoinE_type, type, setadjoinE: $o).
% 9.06/1.76 thf(doubleComplementSub1_type, type, doubleComplementSub1: $o).
% 9.06/1.76 thf(sk__154_type, type, sk__154: $i).
% 9.06/1.76 thf(infuncsetfunc_type, type, infuncsetfunc: $o).
% 9.06/1.76 thf(ap2apEq2_type, type, ap2apEq2: $o).
% 9.06/1.76 thf(ap2p_type, type, ap2p: $o).
% 9.06/1.76 thf(setadjoinIL_type, type, setadjoinIL: $o).
% 9.06/1.76 thf(cartprodsndpairEq_type, type, cartprodsndpairEq: $o).
% 9.06/1.76 thf(exuE1_type, type, exuE1: $o).
% 9.06/1.76 thf(ubforcartprodlem2_type, type, ubforcartprodlem2: $o).
% 9.06/1.76 thf(binintersectRsub_type, type, binintersectRsub: $o).
% 9.06/1.76 thf(setminusLsub_type, type, setminusLsub: $o).
% 9.06/1.76 thf(funcextLem_type, type, funcextLem: $o).
% 9.06/1.76 thf(setukpairinjR_type, type, setukpairinjR: $o).
% 9.06/1.76 thf(notinsingleton_type, type, notinsingleton: $o).
% 9.06/1.76 thf(eqimpsubset2_type, type, eqimpsubset2: $o).
% 9.06/1.76 thf(exuEu_type, type, exuEu: $o).
% 9.06/1.76 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o).
% 9.06/1.76 thf(upairsetE_type, type, upairsetE: $o).
% 9.06/1.76 thf(omega0Ax_type, type, omega0Ax: $o).
% 9.06/1.76 thf(subsetTI_type, type, subsetTI: $o).
% 9.06/1.76 thf(notsubsetI_type, type, notsubsetI: $o).
% 9.06/1.76 thf(contraSubsetComplement_type, type, contraSubsetComplement: $o).
% 9.06/1.76 thf(iffalseProp1_type, type, iffalseProp1: $o).
% 9.06/1.76 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o).
% 9.06/1.76 thf(setextAx_type, type, setextAx: $o).
% 9.06/1.76 thf(zip_tseitin_0_type, type, zip_tseitin_0: $i > $i > $i > $o).
% 9.06/1.76 thf(cartprodpairmemER_type, type, cartprodpairmemER: $o).
% 9.06/1.76 thf(powersetE1_type, type, powersetE1: $o).
% 9.06/1.76 thf(bs114d_type, type, bs114d: $o).
% 9.06/1.76 thf(contrasubsetT3_type, type, contrasubsetT3: $o).
% 9.06/1.76 thf(noeltsimpempty_type, type, noeltsimpempty: $o).
% 9.06/1.76 thf(complementTcontraSubset_type, type, complementTcontraSubset: $o).
% 9.06/1.76 thf(ifp_type, type, ifp: $o).
% 9.06/1.76 thf(sk__151_type, type, sk__151: $i).
% 9.06/1.76 thf(inIntersectImpInUnion_type, type, inIntersectImpInUnion: $o).
% 9.06/1.76 thf(powersetTI1_type, type, powersetTI1: $o).
% 9.06/1.76 thf(binintersectLsub_type, type, binintersectLsub: $o).
% 9.06/1.76 thf(subsetI1_type, type, subsetI1: $o).
% 9.06/1.76 thf(symdiffE_type, type, symdiffE: $o).
% 9.06/1.76 thf(descrp_type, type, descrp: $o).
% 9.06/1.76 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o).
% 9.06/1.76 thf(foundationAx_type, type, foundationAx: $o).
% 9.06/1.76 thf(emptysetAx_type, type, emptysetAx: $o).
% 9.06/1.76 thf(emptyI_type, type, emptyI: $o).
% 9.06/1.76 thf(setadjoinOr_type, type, setadjoinOr: $o).
% 9.06/1.76 thf(eta2_type, type, eta2: $o).
% 9.06/1.76 thf(binintersectEL_type, type, binintersectEL: $o).
% 9.06/1.76 thf(emptyE1_type, type, emptyE1: $o).
% 9.06/1.76 thf(emptyInPowerset_type, type, emptyInPowerset: $o).
% 9.06/1.76 thf(complementTI1_type, type, complementTI1: $o).
% 9.06/1.76 thf(sk__152_type, type, sk__152: $i).
% 9.06/1.76 thf(vacuousDall_type, type, vacuousDall: $o).
% 9.06/1.76 thf(dsetconstrER_type, type, dsetconstrER: $o).
% 9.06/1.76 thf(binintersectI_type, type, binintersectI: $o).
% 9.06/1.76 thf(funcext_type, type, funcext: $o).
% 9.06/1.76 thf(funcGraphProp4_type, type, funcGraphProp4: $o).
% 9.06/1.76 thf(cartprodpairin_type, type, cartprodpairin: $o).
% 9.06/1.76 thf(cartprodmempair1_type, type, cartprodmempair1: $o).
% 9.06/1.76 thf(brelnall2_type, type, brelnall2: $o).
% 9.06/1.76 thf(setextT_type, type, setextT: $o).
% 9.06/1.76 thf(ex1I2_type, type, ex1I2: $o).
% 9.06/1.76 thf(symdiffI1_type, type, symdiffI1: $o).
% 9.06/1.76 thf(setukpairinjR2_type, type, setukpairinjR2: $o).
% 9.06/1.76 thf(dpsetconstrEL2_type, type, dpsetconstrEL2: $o).
% 9.06/1.76 thf(theprop_type, type, theprop: $o).
% 9.06/1.76 thf(subsetI2_type, type, subsetI2: $o).
% 9.06/1.76 thf(complementInPowersetComplementIntersect_type, type, complementInPowersetComplementIntersect:
% 9.06/1.76 $o).
% 9.06/1.76 thf(setminusT_lem_type, type, setminusT_lem: $o).
% 9.06/1.76 thf(symdiffIneg1_type, type, symdiffIneg1: $o).
% 9.06/1.76 thf(setminusERneg_type, type, setminusERneg: $o).
% 9.06/1.76 thf(symdiffIneg2_type, type, symdiffIneg2: $o).
% 9.06/1.76 thf(omega__Cong_type, type, omega__Cong: $o).
% 9.06/1.76 thf(subsetRefl_type, type, subsetRefl: $o).
% 9.06/1.76 thf(uniqinunit_type, type, uniqinunit: $o).
% 9.06/1.76 thf(complementSubsetComplementIntersect_type, type, complementSubsetComplementIntersect:
% 9.06/1.76 $o).
% 9.06/1.76 thf(setminusSubset2_type, type, setminusSubset2: $o).
% 9.06/1.76 thf(prop2setE_type, type, prop2setE: $o).
% 9.06/1.76 thf(binunionEcases_type, type, binunionEcases: $o).
% 9.06/1.76 thf(funcinfuncset_type, type, funcinfuncset: $o).
% 9.06/1.76 thf(complementTE1_type, type, complementTE1: $o).
% 9.06/1.76 thf(nonemptyI_type, type, nonemptyI: $o).
% 9.06/1.76 thf(app_type, type, app: $o).
% 9.06/1.76 thf(disjointsetsI1_type, type, disjointsetsI1: $o).
% 9.06/1.76 thf(exuE3u_type, type, exuE3u: $o).
% 9.06/1.76 thf(eta1_type, type, eta1: $o).
% 9.06/1.76 thf(setminusEL_type, type, setminusEL: $o).
% 9.06/1.76 thf(cartprodfstin_type, type, cartprodfstin: $o).
% 9.06/1.76 thf(setunionsingleton2_type, type, setunionsingleton2: $o).
% 9.06/1.76 thf(sepSubset_type, type, sepSubset: $o).
% 9.06/1.76 thf(complementTnotintersectT_type, type, complementTnotintersectT: $o).
% 9.06/1.76 thf(upairset2E_type, type, upairset2E: $o).
% 9.06/1.76 thf(eqimpsubset1_type, type, eqimpsubset1: $o).
% 9.06/1.76 thf(exuI3_type, type, exuI3: $o).
% 9.06/1.76 thf(cartprodfstpairEq_type, type, cartprodfstpairEq: $o).
% 9.06/1.76 thf(apProp_type, type, apProp: $o).
% 9.06/1.76 thf(notdallE_type, type, notdallE: $o).
% 9.06/1.76 thf(iftrueProp1_type, type, iftrueProp1: $o).
% 9.06/1.76 thf(binintersectER_type, type, binintersectER: $o).
% 9.06/1.76 thf(brelnall1_type, type, brelnall1: $o).
% 9.06/1.76 thf(powerset_type, type, powerset: $i > $i).
% 9.06/1.76 thf(dsetconstrI_type, type, dsetconstrI: $o).
% 9.06/1.76 thf(funcGraphProp1_type, type, funcGraphProp1: $o).
% 9.06/1.76 thf(binintersectT_lem_type, type, binintersectT_lem: $o).
% 9.06/1.76 thf(setadjoin_type, type, setadjoin: $i > $i > $i).
% 9.06/1.76 thf(exu__Cong_type, type, exu__Cong: $o).
% 9.06/1.76 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o).
% 9.06/1.76 thf(contrasubsetT2_type, type, contrasubsetT2: $o).
% 9.06/1.76 thf(secondinupair_type, type, secondinupair: $o).
% 9.06/1.76 thf(singletonprop_type, type, singletonprop: $o).
% 9.06/1.76 thf(singletonsubset_type, type, singletonsubset: $o).
% 9.06/1.76 thf(contrasubsetT1_type, type, contrasubsetT1: $o).
% 9.06/1.76 thf(singletoninpowerset_type, type, singletoninpowerset: $o).
% 9.06/1.76 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o).
% 9.06/1.76 thf(replAx_type, type, replAx: $o).
% 9.06/1.76 thf(upairequniteq_type, type, upairequniteq: $o).
% 9.06/1.76 thf(nonemptyE1_type, type, nonemptyE1: $o).
% 9.06/1.76 thf(omegaIndAx_type, type, omegaIndAx: $o).
% 9.06/1.76 thf(setukpairIL_type, type, setukpairIL: $o).
% 9.06/1.76 thf(setunionE2_type, type, setunionE2: $o).
% 9.06/1.76 thf(inPowerset_type, type, inPowerset: $o).
% 9.06/1.76 thf(iffalse_type, type, iffalse: $o).
% 9.06/1.76 thf(funcext2_type, type, funcext2: $o).
% 9.06/1.76 thf(subset_type, type, subset: $i > $i > $o).
% 9.06/1.76 thf(subbreln_type, type, subbreln: $o).
% 9.06/1.76 thf(in__Cong_type, type, in__Cong: $o).
% 9.06/1.76 thf(binunionRsub_type, type, binunionRsub: $o).
% 9.06/1.76 thf(subset2powerset_type, type, subset2powerset: $o).
% 9.06/1.76 thf(inIntersectImpInUnion2, axiom, inIntersectImpInUnion2 =
% 9.06/1.76 (![A:$i,X:$i]:
% 9.06/1.76 ( ( in @ X @ ( powerset @ A ) ) =>
% 9.06/1.76 ( ![Y:$i]:
% 9.06/1.76 ( ( in @ Y @ ( powerset @ A ) ) =>
% 9.06/1.76 ( ![Z:$i]:
% 9.06/1.76 ( ( in @ Z @ ( powerset @ A ) ) =>
% 9.06/1.76 ( ![Xx:$i]:
% 9.06/1.76 ( ( in @ Xx @ A ) =>
% 9.06/1.76 ( ( in @ Xx @ ( binintersect @ X @ Y ) ) =>
% 9.06/1.76 ( in @ Xx @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ))).
% 9.06/1.76 thf('0', plain,
% 9.06/1.76 (( inIntersectImpInUnion2 ) =
% 9.06/1.76 ( ![X4:$i,X6:$i]:
% 9.06/1.76 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 9.06/1.76 ( ![X8:$i]:
% 9.06/1.76 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 9.06/1.76 ( ![X10:$i]:
% 9.06/1.76 ( ( in @ X10 @ ( powerset @ X4 ) ) =>
% 9.06/1.76 ( ![X12:$i]:
% 9.06/1.76 ( ( in @ X12 @ X4 ) =>
% 9.06/1.76 ( ( in @ X12 @ ( binintersect @ X6 @ X8 ) ) =>
% 9.06/1.76 ( in @ X12 @ ( binunion @ X8 @ X10 ) ) ) ) ) ) ) ) ) ) )),
% 9.06/1.76 define([status(thm)])).
% 9.06/1.76 thf(inIntersectImpInUnion, axiom, inIntersectImpInUnion =
% 9.06/1.76 (![A:$i,X:$i]:
% 9.06/1.76 ( ( in @ X @ ( powerset @ A ) ) =>
% 9.06/1.76 ( ![Y:$i]:
% 9.06/1.76 ( ( in @ Y @ ( powerset @ A ) ) =>
% 9.06/1.76 ( ![Z:$i]:
% 9.06/1.76 ( ( in @ Z @ ( powerset @ A ) ) =>
% 9.06/1.76 ( ![Xx:$i]:
% 9.06/1.76 ( ( in @ Xx @ A ) =>
% 9.06/1.76 ( ( in @ Xx @ ( binintersect @ X @ Y ) ) =>
% 9.06/1.76 ( in @ Xx @ ( binunion @ X @ Z ) ) ) ) ) ) ) ) ) ))).
% 9.06/1.76 thf('1', plain,
% 9.06/1.76 (( inIntersectImpInUnion ) =
% 9.06/1.76 ( ![X4:$i,X6:$i]:
% 9.06/1.76 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 9.06/1.76 ( ![X8:$i]:
% 9.06/1.76 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 9.06/1.76 ( ![X10:$i]:
% 9.06/1.76 ( ( in @ X10 @ ( powerset @ X4 ) ) =>
% 9.06/1.76 ( ![X12:$i]:
% 9.06/1.76 ( ( in @ X12 @ X4 ) =>
% 9.06/1.76 ( ( in @ X12 @ ( binintersect @ X6 @ X8 ) ) =>
% 9.06/1.76 ( in @ X12 @ ( binunion @ X6 @ X10 ) ) ) ) ) ) ) ) ) ) )),
% 9.06/1.76 define([status(thm)])).
% 9.06/1.76 thf(binunionTIRcontra, axiom, binunionTIRcontra =
% 9.06/1.76 (![A:$i,X:$i]:
% 9.06/1.76 ( ( in @ X @ ( powerset @ A ) ) =>
% 9.06/1.76 ( ![Y:$i]:
% 9.06/1.76 ( ( in @ Y @ ( powerset @ A ) ) =>
% 9.06/1.76 ( ![Xx:$i]:
% 9.06/1.76 ( ( in @ Xx @ A ) =>
% 9.06/1.76 ( ( ~( in @ Xx @ ( binunion @ X @ Y ) ) ) =>
% 9.06/1.76 ( ~( in @ Xx @ Y ) ) ) ) ) ) ) ))).
% 9.06/1.76 thf('2', plain,
% 9.06/1.76 (( binunionTIRcontra ) =
% 9.06/1.76 ( ![X4:$i,X6:$i]:
% 9.06/1.76 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 9.06/1.76 ( ![X8:$i]:
% 9.06/1.76 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 9.06/1.76 ( ![X10:$i]:
% 9.06/1.76 ( ( in @ X10 @ X4 ) =>
% 9.06/1.76 ( ( ~( in @ X10 @ ( binunion @ X6 @ X8 ) ) ) =>
% 9.06/1.76 ( ~( in @ X10 @ X8 ) ) ) ) ) ) ) ) )),
% 9.06/1.76 define([status(thm)])).
% 9.06/1.76 thf(binunionTILcontra, axiom, binunionTILcontra =
% 9.06/1.76 (![A:$i,X:$i]:
% 9.06/1.76 ( ( in @ X @ ( powerset @ A ) ) =>
% 9.06/1.76 ( ![Y:$i]:
% 9.06/1.76 ( ( in @ Y @ ( powerset @ A ) ) =>
% 9.06/1.76 ( ![Xx:$i]:
% 9.06/1.76 ( ( in @ Xx @ A ) =>
% 9.06/1.76 ( ( ~( in @ Xx @ ( binunion @ X @ Y ) ) ) =>
% 9.06/1.76 ( ~( in @ Xx @ X ) ) ) ) ) ) ) ))).
% 9.06/1.76 thf('3', plain,
% 9.06/1.76 (( binunionTILcontra ) =
% 9.06/1.76 ( ![X4:$i,X6:$i]:
% 9.06/1.76 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 9.06/1.76 ( ![X8:$i]:
% 9.06/1.76 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 9.06/1.76 ( ![X10:$i]:
% 9.06/1.76 ( ( in @ X10 @ X4 ) =>
% 9.06/1.76 ( ( ~( in @ X10 @ ( binunion @ X6 @ X8 ) ) ) =>
% 9.06/1.76 ( ~( in @ X10 @ X6 ) ) ) ) ) ) ) ) )),
% 9.06/1.76 define([status(thm)])).
% 9.06/1.76 thf(complementInPowersetComplementIntersect, axiom,
% 9.06/1.76 complementInPowersetComplementIntersect =
% 9.06/1.76 (![A:$i,X:$i]:
% 9.06/1.76 ( ( in @ X @ ( powerset @ A ) ) =>
% 9.06/1.76 ( ![Y:$i]:
% 9.06/1.76 ( ( in @ Y @ ( powerset @ A ) ) =>
% 9.06/1.76 ( in @
% 9.06/1.76 ( setminus @ A @ X ) @
% 9.06/1.76 ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ))).
% 9.06/1.76 thf('4', plain,
% 9.06/1.76 (( complementInPowersetComplementIntersect ) =
% 9.06/1.76 ( ![X4:$i,X6:$i]:
% 9.06/1.76 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 9.06/1.76 ( ![X8:$i]:
% 9.06/1.76 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 9.06/1.76 ( in @
% 9.06/1.76 ( setminus @ X4 @ X6 ) @
% 9.06/1.76 ( powerset @ ( setminus @ X4 @ ( binintersect @ X6 @ X8 ) ) ) ) ) ) ) )),
% 9.06/1.76 define([status(thm)])).
% 9.06/1.76 thf(complementSubsetComplementIntersect, axiom,
% 9.06/1.76 complementSubsetComplementIntersect =
% 9.06/1.76 (![A:$i,X:$i]:
% 9.06/1.76 ( ( in @ X @ ( powerset @ A ) ) =>
% 9.06/1.76 ( ![Y:$i]:
% 9.06/1.76 ( ( in @ Y @ ( powerset @ A ) ) =>
% 9.06/1.76 ( subset @
% 9.06/1.76 ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ))).
% 9.06/1.76 thf('5', plain,
% 9.06/1.76 (( complementSubsetComplementIntersect ) =
% 9.06/1.76 ( ![X4:$i,X6:$i]:
% 9.06/1.76 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 9.06/1.76 ( ![X8:$i]:
% 9.06/1.76 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 9.06/1.76 ( subset @
% 9.06/1.76 ( setminus @ X4 @ X6 ) @
% 9.06/1.76 ( setminus @ X4 @ ( binintersect @ X6 @ X8 ) ) ) ) ) ) )),
% 9.06/1.76 define([status(thm)])).
% 9.06/1.76 thf(complementImpComplementIntersect, axiom,
% 9.06/1.76 complementImpComplementIntersect =
% 9.06/1.76 (![A:$i,X:$i]:
% 9.06/1.76 ( ( in @ X @ ( powerset @ A ) ) =>
% 9.06/1.76 ( ![Y:$i]:
% 9.06/1.76 ( ( in @ Y @ ( powerset @ A ) ) =>
% 9.06/1.76 ( ![Xx:$i]:
% 9.06/1.76 ( ( in @ Xx @ A ) =>
% 9.06/1.76 ( ( in @ Xx @ ( setminus @ A @ X ) ) =>
% 9.06/1.76 ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ))).
% 9.06/1.76 thf('6', plain,
% 9.06/1.76 (( complementImpComplementIntersect ) =
% 9.06/1.76 ( ![X4:$i,X6:$i]:
% 9.06/1.76 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 9.06/1.76 ( ![X8:$i]:
% 9.06/1.76 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 9.06/1.76 ( ![X10:$i]:
% 9.06/1.76 ( ( in @ X10 @ X4 ) =>
% 9.06/1.76 ( ( in @ X10 @ ( setminus @ X4 @ X6 ) ) =>
% 9.06/1.76 ( in @
% 9.06/1.76 X10 @ ( setminus @ X4 @ ( binintersect @ X6 @ X8 ) ) ) ) ) ) ) ) ) )),
% 9.06/1.76 define([status(thm)])).
% 9.06/1.76 thf(complementTnotintersectT, axiom, complementTnotintersectT =
% 9.06/1.76 (![A:$i,X:$i]:
% 9.06/1.76 ( ( in @ X @ ( powerset @ A ) ) =>
% 9.06/1.76 ( ![Y:$i]:
% 9.06/1.76 ( ( in @ Y @ ( powerset @ A ) ) =>
% 9.06/1.76 ( ![Xx:$i]:
% 9.06/1.76 ( ( in @ Xx @ A ) =>
% 9.06/1.76 ( ( in @ Xx @ ( setminus @ A @ X ) ) =>
% 9.06/1.76 ( ~( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ))).
% 9.06/1.76 thf('7', plain,
% 9.06/1.76 (( complementTnotintersectT ) =
% 9.06/1.76 ( ![X4:$i,X6:$i]:
% 9.06/1.76 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 9.06/1.76 ( ![X8:$i]:
% 9.06/1.76 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 9.06/1.76 ( ![X10:$i]:
% 9.06/1.76 ( ( in @ X10 @ X4 ) =>
% 9.06/1.76 ( ( in @ X10 @ ( setminus @ X4 @ X6 ) ) =>
% 9.06/1.76 ( ~( in @ X10 @ ( binintersect @ X6 @ X8 ) ) ) ) ) ) ) ) ) )),
% 9.06/1.76 define([status(thm)])).
% 9.06/1.76 thf(binintersectTERcontra, axiom, binintersectTERcontra =
% 9.06/1.76 (![A:$i,X:$i]:
% 9.06/1.76 ( ( in @ X @ ( powerset @ A ) ) =>
% 9.06/1.76 ( ![Y:$i]:
% 9.06/1.76 ( ( in @ Y @ ( powerset @ A ) ) =>
% 9.06/1.76 ( ![Xx:$i]:
% 9.06/1.76 ( ( in @ Xx @ A ) =>
% 9.06/1.76 ( ( ~( in @ Xx @ Y ) ) =>
% 9.06/1.76 ( ~( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ))).
% 9.06/1.76 thf('8', plain,
% 9.06/1.76 (( binintersectTERcontra ) =
% 9.06/1.76 ( ![X4:$i,X6:$i]:
% 9.06/1.76 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 9.06/1.76 ( ![X8:$i]:
% 9.06/1.76 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 9.06/1.76 ( ![X10:$i]:
% 9.06/1.76 ( ( in @ X10 @ X4 ) =>
% 9.06/1.76 ( ( ~( in @ X10 @ X8 ) ) =>
% 9.06/1.76 ( ~( in @ X10 @ ( binintersect @ X6 @ X8 ) ) ) ) ) ) ) ) ) )),
% 9.06/1.76 define([status(thm)])).
% 9.06/1.76 thf(binintersectTELcontra, axiom, binintersectTELcontra =
% 9.06/1.76 (![A:$i,X:$i]:
% 9.06/1.76 ( ( in @ X @ ( powerset @ A ) ) =>
% 9.06/1.76 ( ![Y:$i]:
% 9.06/1.76 ( ( in @ Y @ ( powerset @ A ) ) =>
% 9.06/1.76 ( ![Xx:$i]:
% 9.06/1.76 ( ( in @ Xx @ A ) =>
% 9.06/1.76 ( ( ~( in @ Xx @ X ) ) =>
% 9.06/1.76 ( ~( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ))).
% 9.06/1.76 thf('9', plain,
% 9.06/1.76 (( binintersectTELcontra ) =
% 9.06/1.76 ( ![X4:$i,X6:$i]:
% 9.06/1.76 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 9.06/1.76 ( ![X8:$i]:
% 9.06/1.76 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 9.06/1.76 ( ![X10:$i]:
% 9.06/1.76 ( ( in @ X10 @ X4 ) =>
% 9.06/1.76 ( ( ~( in @ X10 @ X6 ) ) =>
% 9.06/1.76 ( ~( in @ X10 @ ( binintersect @ X6 @ X8 ) ) ) ) ) ) ) ) ) )),
% 9.06/1.76 define([status(thm)])).
% 9.06/1.76 thf(powersetTE1, axiom, powersetTE1 =
% 9.06/1.76 (![A:$i,X:$i]:
% 9.06/1.76 ( ( in @ X @ ( powerset @ A ) ) =>
% 9.06/1.76 ( ![Y:$i]:
% 9.06/1.76 ( ( in @ Y @ ( powerset @ A ) ) =>
% 9.06/1.76 ( ![Xx:$i]:
% 9.06/1.76 ( ( in @ Xx @ A ) =>
% 9.06/1.76 ( ( in @ X @ ( powerset @ Y ) ) =>
% 9.06/1.76 ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) ) ) ) ))).
% 9.06/1.76 thf('10', plain,
% 9.06/1.76 (( powersetTE1 ) =
% 9.06/1.76 ( ![X4:$i,X6:$i]:
% 9.06/1.76 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 9.06/1.76 ( ![X8:$i]:
% 9.06/1.76 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 9.06/1.76 ( ![X10:$i]:
% 9.06/1.76 ( ( in @ X10 @ X4 ) =>
% 9.06/1.76 ( ( in @ X6 @ ( powerset @ X8 ) ) =>
% 9.06/1.76 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) ) ) ) ) )),
% 9.06/1.76 define([status(thm)])).
% 9.06/1.76 thf(powersetTI1, axiom, powersetTI1 =
% 9.06/1.76 (![A:$i,X:$i]:
% 9.06/1.76 ( ( in @ X @ ( powerset @ A ) ) =>
% 9.06/1.76 ( ![Y:$i]:
% 9.06/1.76 ( ( in @ Y @ ( powerset @ A ) ) =>
% 9.06/1.76 ( ( ![Xx:$i]:
% 9.06/1.76 ( ( in @ Xx @ A ) => ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) =>
% 9.06/1.76 ( in @ X @ ( powerset @ Y ) ) ) ) ) ))).
% 9.06/1.76 thf('11', plain,
% 9.06/1.76 (( powersetTI1 ) =
% 9.06/1.76 ( ![X4:$i,X6:$i]:
% 9.06/1.76 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 9.06/1.76 ( ![X8:$i]:
% 9.06/1.76 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 9.06/1.76 ( ( ![X10:$i]:
% 9.06/1.76 ( ( in @ X10 @ X4 ) =>
% 9.06/1.76 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) =>
% 9.06/1.76 ( in @ X6 @ ( powerset @ X8 ) ) ) ) ) ) )),
% 9.06/1.76 define([status(thm)])).
% 9.06/1.76 thf(setextT, axiom, setextT =
% 9.06/1.76 (![A:$i,X:$i]:
% 9.06/1.76 ( ( in @ X @ ( powerset @ A ) ) =>
% 9.06/1.76 ( ![Y:$i]:
% 9.06/1.76 ( ( in @ Y @ ( powerset @ A ) ) =>
% 9.06/1.76 ( ( ![Xx:$i]:
% 9.06/1.76 ( ( in @ Xx @ A ) => ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) =>
% 9.06/1.76 ( ( ![Xx:$i]:
% 9.06/1.76 ( ( in @ Xx @ A ) => ( ( in @ Xx @ Y ) => ( in @ Xx @ X ) ) ) ) =>
% 9.06/1.76 ( ( X ) = ( Y ) ) ) ) ) ) ))).
% 9.06/1.76 thf('12', plain,
% 9.06/1.76 (( setextT ) =
% 9.06/1.76 ( ![X4:$i,X6:$i]:
% 9.06/1.76 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 9.06/1.76 ( ![X8:$i]:
% 9.06/1.76 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 9.06/1.76 ( ( ![X10:$i]:
% 9.06/1.76 ( ( in @ X10 @ X4 ) =>
% 9.06/1.76 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) =>
% 9.06/1.76 ( ( ![X12:$i]:
% 9.06/1.76 ( ( in @ X12 @ X4 ) =>
% 9.06/1.76 ( ( in @ X12 @ X8 ) => ( in @ X12 @ X6 ) ) ) ) =>
% 9.06/1.76 ( ( X6 ) = ( X8 ) ) ) ) ) ) ) )),
% 9.06/1.76 define([status(thm)])).
% 9.06/1.76 thf(powersetT_lem, axiom, powersetT_lem =
% 9.06/1.76 (![A:$i,X:$i]:
% 9.06/1.76 ( ( in @ X @ ( powerset @ A ) ) =>
% 9.06/1.76 ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ))).
% 9.06/1.76 thf('13', plain,
% 9.06/1.76 (( powersetT_lem ) =
% 9.06/1.76 ( ![X4:$i,X6:$i]:
% 9.06/1.76 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 9.06/1.76 ( in @ ( powerset @ X6 ) @ ( powerset @ ( powerset @ X4 ) ) ) ) )),
% 9.06/1.76 define([status(thm)])).
% 9.06/1.76 thf(binunionT_lem, axiom, binunionT_lem =
% 9.06/1.76 (![A:$i,X:$i]:
% 9.06/1.76 ( ( in @ X @ ( powerset @ A ) ) =>
% 9.06/1.76 ( ![Y:$i]:
% 9.06/1.76 ( ( in @ Y @ ( powerset @ A ) ) =>
% 9.06/1.76 ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ))).
% 9.06/1.76 thf('14', plain,
% 9.06/1.76 (( binunionT_lem ) =
% 9.06/1.76 ( ![X4:$i,X6:$i]:
% 9.06/1.76 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 9.06/1.76 ( ![X8:$i]:
% 9.06/1.76 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 9.06/1.76 ( in @ ( binunion @ X6 @ X8 ) @ ( powerset @ X4 ) ) ) ) ) )),
% 9.06/1.76 define([status(thm)])).
% 9.06/1.76 thf(binintersectT_lem, axiom, binintersectT_lem =
% 9.06/1.76 (![A:$i,X:$i]:
% 9.06/1.76 ( ( in @ X @ ( powerset @ A ) ) =>
% 9.06/1.76 ( ![Y:$i]:
% 9.06/1.76 ( ( in @ Y @ ( powerset @ A ) ) =>
% 9.06/1.76 ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ))).
% 9.06/1.76 thf('15', plain,
% 9.06/1.76 (( binintersectT_lem ) =
% 9.06/1.76 ( ![X4:$i,X6:$i]:
% 9.06/1.76 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 9.06/1.76 ( ![X8:$i]:
% 9.06/1.76 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 9.06/1.76 ( in @ ( binintersect @ X6 @ X8 ) @ ( powerset @ X4 ) ) ) ) ) )),
% 9.06/1.76 define([status(thm)])).
% 9.06/1.76 thf(ubforcartprodlem3, axiom, ubforcartprodlem3 =
% 9.06/1.76 (![A:$i,B:$i,Xx:$i]:
% 9.06/1.76 ( ( in @ Xx @ A ) =>
% 9.06/1.76 ( ![Xy:$i]:
% 9.06/1.76 ( ( in @ Xy @ B ) =>
% 9.06/1.76 ( in @
% 9.06/1.76 ( kpair @ Xx @ Xy ) @
% 9.06/1.76 ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ))).
% 9.06/1.76 thf('16', plain,
% 9.06/1.76 (( ubforcartprodlem3 ) =
% 9.06/1.76 ( ![X4:$i,X6:$i,X8:$i]:
% 9.06/1.76 ( ( in @ X8 @ X4 ) =>
% 9.06/1.76 ( ![X10:$i]:
% 9.06/1.76 ( ( in @ X10 @ X6 ) =>
% 9.06/1.76 ( in @
% 9.06/1.76 ( kpair @ X8 @ X10 ) @
% 9.06/1.76 ( powerset @ ( powerset @ ( binunion @ X4 @ X6 ) ) ) ) ) ) ) )),
% 9.06/1.76 define([status(thm)])).
% 9.06/1.76 thf(ubforcartprodlem2, axiom, ubforcartprodlem2 =
% 9.06/1.76 (![A:$i,B:$i,Xx:$i]:
% 9.06/1.76 ( ( in @ Xx @ A ) =>
% 9.06/1.76 ( ![Xy:$i]:
% 9.06/1.76 ( ( in @ Xy @ B ) =>
% 9.06/1.76 ( in @
% 9.06/1.76 ( setadjoin @
% 9.06/1.76 ( setadjoin @ Xx @ emptyset ) @
% 9.06/1.76 ( setadjoin @
% 9.06/1.76 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @
% 9.06/1.76 ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ))).
% 9.06/1.76 thf('17', plain,
% 9.06/1.76 (( ubforcartprodlem2 ) =
% 9.06/1.76 ( ![X4:$i,X6:$i,X8:$i]:
% 9.06/1.76 ( ( in @ X8 @ X4 ) =>
% 9.06/1.76 ( ![X10:$i]:
% 9.06/1.76 ( ( in @ X10 @ X6 ) =>
% 9.06/1.76 ( in @
% 9.06/1.76 ( setadjoin @
% 9.06/1.76 ( setadjoin @ X8 @ emptyset ) @
% 9.06/1.76 ( setadjoin @
% 9.06/1.76 ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @
% 9.06/1.76 emptyset ) ) @
% 9.06/1.76 ( powerset @ ( powerset @ ( binunion @ X4 @ X6 ) ) ) ) ) ) ) )),
% 9.06/1.76 define([status(thm)])).
% 9.06/1.76 thf(ubforcartprodlem1, axiom, ubforcartprodlem1 =
% 9.06/1.76 (![A:$i,B:$i,Xx:$i]:
% 9.06/1.76 ( ( in @ Xx @ A ) =>
% 9.06/1.76 ( ![Xy:$i]:
% 9.06/1.76 ( ( in @ Xy @ B ) =>
% 9.06/1.76 ( subset @
% 9.06/1.76 ( setadjoin @
% 9.06/1.76 ( setadjoin @ Xx @ emptyset ) @
% 9.06/1.76 ( setadjoin @
% 9.06/1.76 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @
% 9.06/1.76 ( powerset @ ( binunion @ A @ B ) ) ) ) ) ))).
% 9.06/1.76 thf('18', plain,
% 9.06/1.76 (( ubforcartprodlem1 ) =
% 9.06/1.76 ( ![X4:$i,X6:$i,X8:$i]:
% 9.06/1.76 ( ( in @ X8 @ X4 ) =>
% 9.06/1.76 ( ![X10:$i]:
% 9.06/1.76 ( ( in @ X10 @ X6 ) =>
% 9.06/1.76 ( subset @
% 9.06/1.76 ( setadjoin @
% 9.06/1.76 ( setadjoin @ X8 @ emptyset ) @
% 9.06/1.76 ( setadjoin @
% 9.06/1.76 ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @
% 9.06/1.76 emptyset ) ) @
% 9.06/1.76 ( powerset @ ( binunion @ X4 @ X6 ) ) ) ) ) ) )),
% 9.06/1.76 define([status(thm)])).
% 9.06/1.76 thf(upairinpowunion, axiom, upairinpowunion =
% 9.06/1.76 (![A:$i,B:$i,Xx:$i]:
% 9.06/1.76 ( ( in @ Xx @ A ) =>
% 9.06/1.76 ( ![Xy:$i]:
% 9.06/1.76 ( ( in @ Xy @ B ) =>
% 9.06/1.76 ( in @
% 9.06/1.76 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @
% 9.06/1.76 ( powerset @ ( binunion @ A @ B ) ) ) ) ) ))).
% 9.06/1.76 thf('19', plain,
% 9.06/1.76 (( upairinpowunion ) =
% 9.06/1.76 ( ![X4:$i,X6:$i,X8:$i]:
% 9.06/1.76 ( ( in @ X8 @ X4 ) =>
% 9.06/1.76 ( ![X10:$i]:
% 9.06/1.76 ( ( in @ X10 @ X6 ) =>
% 9.06/1.76 ( in @
% 9.06/1.76 ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @
% 9.06/1.76 ( powerset @ ( binunion @ X4 @ X6 ) ) ) ) ) ) )),
% 9.06/1.76 define([status(thm)])).
% 9.06/1.76 thf(upairsubunion, axiom, upairsubunion =
% 9.06/1.76 (![A:$i,B:$i,Xx:$i]:
% 9.06/1.76 ( ( in @ Xx @ A ) =>
% 9.06/1.76 ( ![Xy:$i]:
% 9.06/1.76 ( ( in @ Xy @ B ) =>
% 9.06/1.76 ( subset @
% 9.06/1.76 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @
% 9.06/1.76 ( binunion @ A @ B ) ) ) ) ))).
% 9.06/1.76 thf('20', plain,
% 9.06/1.76 (( upairsubunion ) =
% 9.06/1.76 ( ![X4:$i,X6:$i,X8:$i]:
% 9.06/1.76 ( ( in @ X8 @ X4 ) =>
% 9.06/1.76 ( ![X10:$i]:
% 9.06/1.76 ( ( in @ X10 @ X6 ) =>
% 9.06/1.76 ( subset @
% 9.06/1.76 ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @
% 9.06/1.76 ( binunion @ X4 @ X6 ) ) ) ) ) )),
% 9.06/1.76 define([status(thm)])).
% 9.06/1.76 thf(singletoninpowunion, axiom, singletoninpowunion =
% 9.06/1.76 (![A:$i,B:$i,Xx:$i]:
% 9.06/1.76 ( ( in @ Xx @ A ) =>
% 9.06/1.76 ( in @
% 9.06/1.76 ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ))).
% 9.06/1.76 thf('21', plain,
% 9.06/1.76 (( singletoninpowunion ) =
% 9.06/1.76 ( ![X4:$i,X6:$i,X8:$i]:
% 9.06/1.76 ( ( in @ X8 @ X4 ) =>
% 9.06/1.76 ( in @
% 9.06/1.76 ( setadjoin @ X8 @ emptyset ) @
% 9.06/1.76 ( powerset @ ( binunion @ X4 @ X6 ) ) ) ) )),
% 9.06/1.76 define([status(thm)])).
% 9.06/1.76 thf(bs114d, axiom, bs114d =
% 9.06/1.76 (![A:$i,B:$i,C:$i]:
% 9.06/1.76 ( ( binintersect @ A @ ( binunion @ B @ C ) ) =
% 9.06/1.76 ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ))).
% 9.06/1.76 thf('22', plain,
% 9.06/1.76 (( bs114d ) =
% 9.06/1.76 ( ![X4:$i,X6:$i,X8:$i]:
% 9.06/1.76 ( ( binintersect @ X4 @ ( binunion @ X6 @ X8 ) ) =
% 9.06/1.76 ( binunion @ ( binintersect @ X4 @ X6 ) @ ( binintersect @ X4 @ X8 ) ) ) )),
% 9.06/1.76 define([status(thm)])).
% 9.06/1.76 thf(binintersectSubset1, axiom, binintersectSubset1 =
% 9.06/1.76 (![A:$i,B:$i]:
% 9.06/1.76 ( ( ( binintersect @ A @ B ) = ( A ) ) => ( subset @ A @ B ) ))).
% 9.06/1.76 thf('23', plain,
% 9.06/1.76 (( binintersectSubset1 ) =
% 9.06/1.76 ( ![X4:$i,X6:$i]:
% 9.06/1.76 ( ( ( binintersect @ X4 @ X6 ) = ( X4 ) ) => ( subset @ X4 @ X6 ) ) )),
% 9.06/1.76 define([status(thm)])).
% 9.06/1.76 thf(binintersectSubset4, axiom, binintersectSubset4 =
% 9.06/1.76 (![A:$i,B:$i]:
% 9.06/1.76 ( ( subset @ B @ A ) => ( ( binintersect @ A @ B ) = ( B ) ) ))).
% 9.06/1.76 thf('24', plain,
% 9.06/1.76 (( binintersectSubset4 ) =
% 9.06/1.76 ( ![X4:$i,X6:$i]:
% 9.06/1.76 ( ( subset @ X6 @ X4 ) => ( ( binintersect @ X4 @ X6 ) = ( X6 ) ) ) )),
% 9.06/1.76 define([status(thm)])).
% 9.06/1.76 thf(binintersectRsub, axiom, binintersectRsub =
% 9.06/1.76 (![A:$i,B:$i]: ( subset @ ( binintersect @ A @ B ) @ B ))).
% 9.06/1.76 thf('25', plain,
% 9.06/1.76 (( binintersectRsub ) =
% 9.06/1.76 ( ![X4:$i,X6:$i]: ( subset @ ( binintersect @ X4 @ X6 ) @ X6 ) )),
% 9.06/1.76 define([status(thm)])).
% 9.06/1.76 thf(disjointsetsI1, axiom, disjointsetsI1 =
% 9.06/1.76 (![A:$i,B:$i]:
% 9.06/1.76 ( ( ~( ?[Xx:$i]: ( ( in @ Xx @ B ) & ( in @ Xx @ A ) ) ) ) =>
% 9.06/1.76 ( ( binintersect @ A @ B ) = ( emptyset ) ) ))).
% 9.06/1.76 thf('26', plain,
% 9.06/1.76 (( disjointsetsI1 ) =
% 9.06/1.76 ( ![X4:$i,X6:$i]:
% 9.06/1.76 ( ( ~( ?[X8:$i]: ( ( in @ X8 @ X6 ) & ( in @ X8 @ X4 ) ) ) ) =>
% 9.06/1.76 ( ( binintersect @ X4 @ X6 ) = ( emptyset ) ) ) )),
% 9.06/1.76 define([status(thm)])).
% 9.06/1.76 thf(binintersectER, axiom, binintersectER =
% 9.06/1.76 (![A:$i,B:$i,Xx:$i]:
% 9.06/1.76 ( ( in @ Xx @ ( binintersect @ A @ B ) ) => ( in @ Xx @ B ) ))).
% 9.06/1.76 thf('27', plain,
% 9.06/1.76 (( binintersectER ) =
% 9.06/1.76 ( ![X4:$i,X6:$i,X8:$i]:
% 9.06/1.76 ( ( in @ X8 @ ( binintersect @ X4 @ X6 ) ) => ( in @ X8 @ X6 ) ) )),
% 9.06/1.76 define([status(thm)])).
% 9.06/1.76 thf(binintersectSubset3, axiom, binintersectSubset3 =
% 9.06/1.76 (![A:$i,B:$i]:
% 9.06/1.76 ( ( ( binintersect @ A @ B ) = ( B ) ) => ( subset @ B @ A ) ))).
% 9.06/1.76 thf('28', plain,
% 9.06/1.76 (( binintersectSubset3 ) =
% 9.06/1.76 ( ![X4:$i,X6:$i]:
% 9.06/1.76 ( ( ( binintersect @ X4 @ X6 ) = ( X6 ) ) => ( subset @ X6 @ X4 ) ) )),
% 9.06/1.76 define([status(thm)])).
% 9.06/1.76 thf(binintersectSubset2, axiom, binintersectSubset2 =
% 9.06/1.76 (![A:$i,B:$i]:
% 9.06/1.76 ( ( subset @ A @ B ) => ( ( binintersect @ A @ B ) = ( A ) ) ))).
% 9.06/1.76 thf('29', plain,
% 9.06/1.76 (( binintersectSubset2 ) =
% 9.06/1.76 ( ![X4:$i,X6:$i]:
% 9.06/1.76 ( ( subset @ X4 @ X6 ) => ( ( binintersect @ X4 @ X6 ) = ( X4 ) ) ) )),
% 9.06/1.76 define([status(thm)])).
% 9.06/1.76 thf(binintersectLsub, axiom, binintersectLsub =
% 9.06/1.76 (![A:$i,B:$i]: ( subset @ ( binintersect @ A @ B ) @ A ))).
% 9.06/1.76 thf('30', plain,
% 9.06/1.76 (( binintersectLsub ) =
% 9.06/1.76 ( ![X4:$i,X6:$i]: ( subset @ ( binintersect @ X4 @ X6 ) @ X4 ) )),
% 9.06/1.76 define([status(thm)])).
% 9.06/1.76 thf(binintersectEL, axiom, binintersectEL =
% 9.06/1.76 (![A:$i,B:$i,Xx:$i]:
% 9.06/1.76 ( ( in @ Xx @ ( binintersect @ A @ B ) ) => ( in @ Xx @ A ) ))).
% 9.06/1.76 thf('31', plain,
% 9.06/1.76 (( binintersectEL ) =
% 9.06/1.76 ( ![X4:$i,X6:$i,X8:$i]:
% 9.06/1.76 ( ( in @ X8 @ ( binintersect @ X4 @ X6 ) ) => ( in @ X8 @ X4 ) ) )),
% 9.06/1.76 define([status(thm)])).
% 9.06/1.76 thf(binintersectSubset5, axiom, binintersectSubset5 =
% 9.06/1.76 (![A:$i,B:$i,C:$i]:
% 9.06/1.76 ( ( subset @ C @ A ) =>
% 9.06/1.76 ( ( subset @ C @ B ) => ( subset @ C @ ( binintersect @ A @ B ) ) ) ))).
% 9.06/1.76 thf('32', plain,
% 9.06/1.76 (( binintersectSubset5 ) =
% 9.06/1.76 ( ![X4:$i,X6:$i,X8:$i]:
% 9.06/1.76 ( ( subset @ X8 @ X4 ) =>
% 9.06/1.76 ( ( subset @ X8 @ X6 ) =>
% 9.06/1.76 ( subset @ X8 @ ( binintersect @ X4 @ X6 ) ) ) ) )),
% 9.06/1.76 define([status(thm)])).
% 9.06/1.76 thf(binintersectI, axiom, binintersectI =
% 9.06/1.76 (![A:$i,B:$i,Xx:$i]:
% 9.06/1.76 ( ( in @ Xx @ A ) =>
% 9.06/1.76 ( ( in @ Xx @ B ) => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ))).
% 9.06/1.76 thf('33', plain,
% 9.06/1.76 (( binintersectI ) =
% 9.06/1.76 ( ![X4:$i,X6:$i,X8:$i]:
% 9.06/1.76 ( ( in @ X8 @ X4 ) =>
% 9.06/1.76 ( ( in @ X8 @ X6 ) => ( in @ X8 @ ( binintersect @ X4 @ X6 ) ) ) ) )),
% 9.06/1.76 define([status(thm)])).
% 9.06/1.76 thf(binunionRsub, axiom, binunionRsub =
% 9.06/1.76 (![A:$i,B:$i]: ( subset @ B @ ( binunion @ A @ B ) ))).
% 9.06/1.76 thf('34', plain,
% 9.06/1.76 (( binunionRsub ) =
% 9.06/1.76 ( ![X4:$i,X6:$i]: ( subset @ X6 @ ( binunion @ X4 @ X6 ) ) )),
% 9.06/1.76 define([status(thm)])).
% 9.06/1.76 thf(binunionLsub, axiom, binunionLsub =
% 9.06/1.76 (![A:$i,B:$i]: ( subset @ A @ ( binunion @ A @ B ) ))).
% 9.06/1.76 thf('35', plain,
% 9.06/1.76 (( binunionLsub ) =
% 9.06/1.76 ( ![X4:$i,X6:$i]: ( subset @ X4 @ ( binunion @ X4 @ X6 ) ) )),
% 9.06/1.76 define([status(thm)])).
% 9.06/1.76 thf(binunionE, axiom, binunionE =
% 9.06/1.76 (![A:$i,B:$i,Xx:$i]:
% 9.06/1.76 ( ( in @ Xx @ ( binunion @ A @ B ) ) =>
% 9.06/1.76 ( ( in @ Xx @ A ) | ( in @ Xx @ B ) ) ))).
% 9.06/1.76 thf('36', plain,
% 9.06/1.76 (( binunionE ) =
% 9.06/1.76 ( ![X4:$i,X6:$i,X8:$i]:
% 9.06/1.76 ( ( in @ X8 @ ( binunion @ X4 @ X6 ) ) =>
% 9.06/1.76 ( ( in @ X8 @ X4 ) | ( in @ X8 @ X6 ) ) ) )),
% 9.06/1.76 define([status(thm)])).
% 9.06/1.76 thf(binunionEcases, axiom, binunionEcases =
% 9.06/1.76 (![A:$i,B:$i,Xx:$i,Xphi:$o]:
% 9.06/1.76 ( ( in @ Xx @ ( binunion @ A @ B ) ) =>
% 9.06/1.76 ( ( ( in @ Xx @ A ) => ( Xphi ) ) =>
% 9.06/1.76 ( ( ( in @ Xx @ B ) => ( Xphi ) ) => ( Xphi ) ) ) ))).
% 9.06/1.76 thf('37', plain,
% 9.06/1.76 (( binunionEcases ) =
% 9.06/1.76 ( ![X4:$i,X6:$i,X8:$i,X10:$o]:
% 9.06/1.76 ( ( in @ X8 @ ( binunion @ X4 @ X6 ) ) =>
% 9.06/1.76 ( ( ( in @ X8 @ X4 ) => ( X10 ) ) =>
% 9.06/1.76 ( ( ( in @ X8 @ X6 ) => ( X10 ) ) => ( X10 ) ) ) ) )),
% 9.06/1.76 define([status(thm)])).
% 9.06/1.76 thf(binunionIR, axiom, binunionIR =
% 9.06/1.76 (![A:$i,B:$i,Xx:$i]:
% 9.06/1.76 ( ( in @ Xx @ B ) => ( in @ Xx @ ( binunion @ A @ B ) ) ))).
% 9.06/1.76 thf('38', plain,
% 9.06/1.76 (( binunionIR ) =
% 9.06/1.76 ( ![X4:$i,X6:$i,X8:$i]:
% 9.06/1.76 ( ( in @ X8 @ X6 ) => ( in @ X8 @ ( binunion @ X4 @ X6 ) ) ) )),
% 9.06/1.76 define([status(thm)])).
% 9.06/1.76 thf(binunionIL, axiom, binunionIL =
% 9.06/1.76 (![A:$i,B:$i,Xx:$i]:
% 9.06/1.76 ( ( in @ Xx @ A ) => ( in @ Xx @ ( binunion @ A @ B ) ) ))).
% 9.06/1.76 thf('39', plain,
% 9.06/1.76 (( binunionIL ) =
% 9.06/1.76 ( ![X4:$i,X6:$i,X8:$i]:
% 9.06/1.76 ( ( in @ X8 @ X4 ) => ( in @ X8 @ ( binunion @ X4 @ X6 ) ) ) )),
% 9.06/1.77 define([status(thm)])).
% 9.06/1.77 thf(inPowerset, axiom, inPowerset = (![A:$i]: ( in @ A @ ( powerset @ A ) ))).
% 9.06/1.77 thf('40', plain,
% 9.06/1.77 (( inPowerset ) = ( ![X4:$i]: ( in @ X4 @ ( powerset @ X4 ) ) )),
% 9.06/1.77 define([status(thm)])).
% 9.06/1.77 thf(powerset__Cong, axiom, powerset__Cong =
% 9.06/1.77 (![A:$i,B:$i]:
% 9.06/1.77 ( ( ( A ) = ( B ) ) => ( ( powerset @ A ) = ( powerset @ B ) ) ))).
% 9.06/1.77 thf('41', plain,
% 9.06/1.77 (( powerset__Cong ) =
% 9.06/1.77 ( ![X4:$i,X6:$i]:
% 9.06/1.77 ( ( ( X4 ) = ( X6 ) ) => ( ( powerset @ X4 ) = ( powerset @ X6 ) ) ) )),
% 9.06/1.77 define([status(thm)])).
% 9.06/1.77 thf(powersetE, axiom, powersetE =
% 9.06/1.77 (![A:$i,B:$i,Xx:$i]:
% 9.06/1.77 ( ( in @ B @ ( powerset @ A ) ) => ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ))).
% 9.06/1.77 thf('42', plain,
% 9.06/1.77 (( powersetE ) =
% 9.06/1.77 ( ![X4:$i,X6:$i,X8:$i]:
% 9.06/1.77 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 9.06/1.77 ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) )),
% 9.06/1.77 define([status(thm)])).
% 9.06/1.77 thf(emptyInPowerset, axiom, emptyInPowerset =
% 9.06/1.77 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))).
% 9.06/1.77 thf('43', plain,
% 9.06/1.77 (( emptyInPowerset ) =
% 9.06/1.77 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )),
% 9.06/1.77 define([status(thm)])).
% 9.06/1.77 thf(emptyinPowerset, axiom, emptyinPowerset =
% 9.06/1.77 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))).
% 9.06/1.77 thf('44', plain,
% 9.06/1.77 (( emptyinPowerset ) =
% 9.06/1.77 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )),
% 9.06/1.77 define([status(thm)])).
% 9.06/1.77 thf(powersetI, axiom, powersetI =
% 9.06/1.77 (![A:$i,B:$i]:
% 9.06/1.77 ( ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) =>
% 9.06/1.77 ( in @ B @ ( powerset @ A ) ) ))).
% 9.06/1.77 thf('45', plain,
% 9.06/1.77 (( powersetI ) =
% 9.06/1.77 ( ![X4:$i,X6:$i]:
% 9.06/1.77 ( ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) =>
% 9.06/1.77 ( in @ X6 @ ( powerset @ X4 ) ) ) )),
% 9.06/1.77 define([status(thm)])).
% 9.06/1.77 thf(powersetAx, axiom, powersetAx =
% 9.06/1.77 (![A:$i,B:$i]:
% 9.06/1.77 ( ( in @ B @ ( powerset @ A ) ) <=>
% 9.06/1.77 ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) ))).
% 9.06/1.77 thf('46', plain,
% 9.06/1.77 (( powersetAx ) =
% 9.06/1.77 ( ![X4:$i,X6:$i]:
% 9.06/1.77 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 9.06/1.77 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) )),
% 9.06/1.77 define([status(thm)])).
% 9.06/1.77 thf(inIntersectImpInIntersectUnions, conjecture,
% 9.06/1.77 (( setextAx ) =>
% 9.06/1.77 ( ( emptysetAx ) =>
% 9.06/1.77 ( ( setadjoinAx ) =>
% 9.06/1.77 ( ( powersetAx ) =>
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% 9.06/1.77 ( (
% 9.06/1.77 setadjoinOr ) =>
% 9.06/1.77 (
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% 9.06/1.77 (
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% 9.06/1.77 (
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% 9.06/1.77 (
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% 9.06/1.77 (
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% 9.06/1.77 (
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% 9.06/1.77 (
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% 9.06/1.77 (
% 9.06/1.77 (
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% 9.06/1.77 (
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% 9.06/1.77 (
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% 9.06/1.77 (
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% 9.06/1.77 (
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% 9.06/1.77 (
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% 9.06/1.77 (
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% 9.06/1.77 (
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% 9.06/1.77 (
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% 9.06/1.77 (
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% 9.06/1.77 (
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% 9.06/1.77 (
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% 9.06/1.77 (
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% 9.06/1.77 (
% 9.06/1.77 (
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% 9.06/1.77 (
% 9.06/1.77 (
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% 9.06/1.77 (
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% 9.06/1.77 (
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% 9.06/1.77 (
% 9.06/1.77 (
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% 9.06/1.77 (
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% 9.06/1.77 (
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% 9.06/1.77 (
% 9.06/1.77 (
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% 9.06/1.77 (
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% 9.06/1.77 (
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% 9.06/1.77 (
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% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 subsetTI ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 powersetTI1 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 powersetTE1 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 complementTI1 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 complementTE1 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 binintersectTELcontra ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 binintersectTERcontra ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 contrasubsetT ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 contrasubsetT1 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 contrasubsetT2 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 contrasubsetT3 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 doubleComplementI1 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 doubleComplementE1 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 doubleComplementSub1 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 doubleComplementSub2 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 doubleComplementEq ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 complementTnotintersectT ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 complementImpComplementIntersect ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 complementSubsetComplementIntersect ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 complementInPowersetComplementIntersect ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 contraSubsetComplement ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 complementTcontraSubset ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 binunionTILcontra ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 binunionTIRcontra ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 inIntersectImpInUnion ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 inIntersectImpInUnion2 ) =>
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 A:$i,X:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X @
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 A ) ) =>
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 Y:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 Y @
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 A ) ) =>
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 Z:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 Z @
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 A ) ) =>
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 Xx:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 Xx @ A ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 Xx @
% 9.06/1.77 (
% 9.06/1.77 binintersect
% 9.06/1.77 @
% 9.06/1.77 X @ Y ) ) =>
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 Xx @
% 9.06/1.77 (
% 9.06/1.77 binintersect
% 9.06/1.77 @
% 9.06/1.77 (
% 9.06/1.77 binunion @
% 9.06/1.77 X @ Z ) @
% 9.06/1.77 (
% 9.06/1.77 binunion @
% 9.06/1.77 Y @ Z ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 9.06/1.77 thf(zf_stmt_0, conjecture,
% 9.06/1.77 (( setextAx ) =>
% 9.06/1.77 ( ( emptysetAx ) =>
% 9.06/1.77 ( ( setadjoinAx ) =>
% 9.06/1.77 ( ( ![X4:$i,X6:$i]:
% 9.06/1.77 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 9.06/1.77 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) ) =>
% 9.06/1.77 ( ( setunionAx ) =>
% 9.06/1.77 ( ( omega0Ax ) =>
% 9.06/1.77 ( ( omegaSAx ) =>
% 9.06/1.77 ( ( omegaIndAx ) =>
% 9.06/1.77 ( ( replAx ) =>
% 9.06/1.77 ( ( foundationAx ) =>
% 9.06/1.77 ( ( wellorderingAx ) =>
% 9.06/1.77 ( ( descrp ) =>
% 9.06/1.77 ( ( dsetconstrI ) =>
% 9.06/1.77 ( ( dsetconstrEL ) =>
% 9.06/1.77 ( ( dsetconstrER ) =>
% 9.06/1.77 ( ( exuE1 ) =>
% 9.06/1.77 ( ( prop2setE ) =>
% 9.06/1.77 ( ( emptysetE ) =>
% 9.06/1.77 ( ( emptysetimpfalse ) =>
% 9.06/1.77 ( ( notinemptyset ) =>
% 9.06/1.77 ( ( exuE3e ) =>
% 9.06/1.77 ( ( setext ) =>
% 9.06/1.77 ( ( emptyI ) =>
% 9.06/1.77 ( ( noeltsimpempty ) =>
% 9.06/1.77 ( ( setbeta ) =>
% 9.06/1.77 ( ( nonemptyE1 ) =>
% 9.06/1.77 ( ( nonemptyI ) =>
% 9.06/1.77 ( ( nonemptyI1 ) =>
% 9.06/1.77 ( ( setadjoinIL ) =>
% 9.06/1.77 ( ( emptyinunitempty ) =>
% 9.06/1.77 ( ( setadjoinIR ) =>
% 9.06/1.77 ( ( setadjoinE ) =>
% 9.06/1.77 ( (
% 9.06/1.77 setadjoinOr ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setoftrueEq ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X10:$i,
% 9.06/1.77 X12:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X14:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X14 @ X12 ) =>
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X14 @ X10 ) ) ) =>
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X12 @
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 X10 ) ) ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X16:$i]:
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 emptyset @
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 X16 ) ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X18:$i]:
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 emptyset @
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 X18 ) ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X20:$i,
% 9.06/1.77 X22:$i,
% 9.06/1.77 X24:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X22 @
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 X20 ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X24 @ X22 ) =>
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X24 @ X20 ) ) ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setunionI ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setunionE ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 subPowSU ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 exuE2 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 nonemptyImpWitness ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 uniqinunit ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 notinsingleton ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 eqinunit ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 singletonsswitch ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 upairsetE ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 upairsetIL ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 upairsetIR ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 emptyE1 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 vacuousDall ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 quantDeMorgan1 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 quantDeMorgan2 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 quantDeMorgan3 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 quantDeMorgan4 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 prop2setI ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 prop2set2propI ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 notdexE ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 notdallE ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 exuI1 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 exuI3 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 exuI2 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 inCongP ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in__Cong ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 exuE3u ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 exu__Cong ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 emptyset__Cong ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setadjoin__Cong ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X26:$i,
% 9.06/1.77 X28:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 X26 ) =
% 9.06/1.77 (
% 9.06/1.77 X28 ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 X26 ) =
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 X28 ) ) ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setunion__Cong ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 omega__Cong ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 exuEu ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 descr__Cong ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 dsetconstr__Cong ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 subsetI1 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 eqimpsubset2 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 eqimpsubset1 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 subsetI2 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 emptysetsubset ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 subsetE ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 subsetE2 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 notsubsetI ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 notequalI1 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 notequalI2 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 subsetRefl ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 subsetTrans ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setadjoinSub ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setadjoinSub2 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 subset2powerset ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setextsub ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 subsetemptysetimpeq ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 powersetI1 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 powersetE1 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X30:$i]:
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X30 @
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 X30 ) ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 powersetsubset ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 sepInPowerset ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 sepSubset ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X32:$i,
% 9.06/1.77 X34:$i,
% 9.06/1.77 X36:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X36 @ X32 ) =>
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X36 @
% 9.06/1.77 (
% 9.06/1.77 binunion @
% 9.06/1.77 X32 @ X34 ) ) ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 upairset2IR ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X38:$i,
% 9.06/1.77 X40:$i,
% 9.06/1.77 X42:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X42 @ X40 ) =>
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X42 @
% 9.06/1.77 (
% 9.06/1.77 binunion @
% 9.06/1.77 X38 @ X40 ) ) ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X44:$i,
% 9.06/1.77 X46:$i,
% 9.06/1.77 X48:$i,
% 9.06/1.77 X50:$o]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X48 @
% 9.06/1.77 (
% 9.06/1.77 binunion @
% 9.06/1.77 X44 @ X46 ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X48 @ X44 ) =>
% 9.06/1.77 (
% 9.06/1.77 X50 ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X48 @ X46 ) =>
% 9.06/1.77 (
% 9.06/1.77 X50 ) ) =>
% 9.06/1.77 (
% 9.06/1.77 X50 ) ) ) ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X52:$i,
% 9.06/1.77 X54:$i,
% 9.06/1.77 X56:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X56 @
% 9.06/1.77 (
% 9.06/1.77 binunion @
% 9.06/1.77 X52 @ X54 ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X56 @ X54 ) |
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X56 @ X52 ) ) ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X58:$i,
% 9.06/1.77 X60:$i]:
% 9.06/1.77 (
% 9.06/1.77 subset @
% 9.06/1.77 X58 @
% 9.06/1.77 (
% 9.06/1.77 binunion @
% 9.06/1.77 X58 @ X60 ) ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X62:$i,
% 9.06/1.77 X64:$i]:
% 9.06/1.77 (
% 9.06/1.77 subset @
% 9.06/1.77 X64 @
% 9.06/1.77 (
% 9.06/1.77 binunion @
% 9.06/1.77 X62 @ X64 ) ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X66:$i,
% 9.06/1.77 X68:$i,
% 9.06/1.77 X70:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X70 @ X66 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X70 @ X68 ) =>
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X70 @
% 9.06/1.77 (
% 9.06/1.77 binintersect
% 9.06/1.77 @
% 9.06/1.77 X66 @ X68 ) ) ) ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X72:$i,
% 9.06/1.77 X74:$i,
% 9.06/1.77 X76:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 subset @
% 9.06/1.77 X76 @ X72 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 subset @
% 9.06/1.77 X76 @ X74 ) =>
% 9.06/1.77 (
% 9.06/1.77 subset @
% 9.06/1.77 X76 @
% 9.06/1.77 (
% 9.06/1.77 binintersect
% 9.06/1.77 @
% 9.06/1.77 X72 @ X74 ) ) ) ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X78:$i,
% 9.06/1.77 X80:$i,
% 9.06/1.77 X82:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X82 @
% 9.06/1.77 (
% 9.06/1.77 binintersect
% 9.06/1.77 @
% 9.06/1.77 X78 @ X80 ) ) =>
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X82 @ X78 ) ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X84:$i,
% 9.06/1.77 X86:$i]:
% 9.06/1.77 (
% 9.06/1.77 subset @
% 9.06/1.77 (
% 9.06/1.77 binintersect
% 9.06/1.77 @
% 9.06/1.77 X84 @ X86 ) @
% 9.06/1.77 X84 ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X88:$i,
% 9.06/1.77 X90:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 subset @
% 9.06/1.77 X88 @ X90 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 binintersect
% 9.06/1.77 @
% 9.06/1.77 X88 @ X90 ) =
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% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X92:$i,
% 9.06/1.77 X94:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 binintersect
% 9.06/1.77 @
% 9.06/1.77 X92 @ X94 ) =
% 9.06/1.77 (
% 9.06/1.77 X94 ) ) =>
% 9.06/1.77 (
% 9.06/1.77 subset @
% 9.06/1.77 X94 @ X92 ) ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X96:$i,
% 9.06/1.77 X98:$i,
% 9.06/1.77 X100:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X100 @
% 9.06/1.77 (
% 9.06/1.77 binintersect
% 9.06/1.77 @
% 9.06/1.77 X96 @ X98 ) ) =>
% 9.06/1.77 (
% 9.06/1.77 in @
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% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X102:$i,
% 9.06/1.77 X104:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ~(
% 9.06/1.77 ?[
% 9.06/1.77 X106:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X106 @
% 9.06/1.77 X102 ) &
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X106 @
% 9.06/1.77 X104 ) ) ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 binintersect
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% 9.06/1.77 X102 @
% 9.06/1.77 X104 ) =
% 9.06/1.77 (
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% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X108:$i,
% 9.06/1.77 X110:$i]:
% 9.06/1.77 (
% 9.06/1.77 subset @
% 9.06/1.77 (
% 9.06/1.77 binintersect
% 9.06/1.77 @
% 9.06/1.77 X108 @
% 9.06/1.77 X110 ) @
% 9.06/1.77 X110 ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X112:$i,
% 9.06/1.77 X114:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 subset @
% 9.06/1.77 X114 @
% 9.06/1.77 X112 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 binintersect
% 9.06/1.77 @
% 9.06/1.77 X112 @
% 9.06/1.77 X114 ) =
% 9.06/1.77 (
% 9.06/1.77 X114 ) ) ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X116:$i,
% 9.06/1.77 X118:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 binintersect
% 9.06/1.77 @
% 9.06/1.77 X116 @
% 9.06/1.77 X118 ) =
% 9.06/1.77 (
% 9.06/1.77 X116 ) ) =>
% 9.06/1.77 (
% 9.06/1.77 subset @
% 9.06/1.77 X116 @
% 9.06/1.77 X118 ) ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X120:$i,
% 9.06/1.77 X122:$i,
% 9.06/1.77 X124:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 binintersect
% 9.06/1.77 @
% 9.06/1.77 X120 @
% 9.06/1.77 (
% 9.06/1.77 binunion @
% 9.06/1.77 X122 @
% 9.06/1.77 X124 ) ) =
% 9.06/1.77 (
% 9.06/1.77 binunion @
% 9.06/1.77 (
% 9.06/1.77 binintersect
% 9.06/1.77 @
% 9.06/1.77 X120 @
% 9.06/1.77 X122 ) @
% 9.06/1.77 (
% 9.06/1.77 binintersect
% 9.06/1.77 @
% 9.06/1.77 X120 @
% 9.06/1.77 X124 ) ) ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setminusI ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setminusEL ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setminusER ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setminusSubset2 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setminusERneg ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setminusELneg ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setminusILneg ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setminusIRneg ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setminusLsub ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setminusSubset1 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 symdiffE ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 symdiffI1 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 symdiffI2 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 symdiffIneg1 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 symdiffIneg2 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 secondinupair ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setukpairIL ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setukpairIR ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 kpairiskpair ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 kpairp ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 singletonsubset ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 singletoninpowerset ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X126:$i,
% 9.06/1.77 X128:$i,
% 9.06/1.77 X130:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X130 @
% 9.06/1.77 X126 ) =>
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 (
% 9.06/1.77 setadjoin
% 9.06/1.77 @
% 9.06/1.77 X130 @
% 9.06/1.77 emptyset ) @
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 (
% 9.06/1.77 binunion @
% 9.06/1.77 X126 @
% 9.06/1.77 X128 ) ) ) ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 upairset2E ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X132:$i,
% 9.06/1.77 X134:$i,
% 9.06/1.77 X136:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X136 @
% 9.06/1.77 X132 ) =>
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X138:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X138 @
% 9.06/1.77 X134 ) =>
% 9.06/1.77 (
% 9.06/1.77 subset @
% 9.06/1.77 (
% 9.06/1.77 setadjoin
% 9.06/1.77 @
% 9.06/1.77 X136 @
% 9.06/1.77 (
% 9.06/1.77 setadjoin
% 9.06/1.77 @
% 9.06/1.77 X138 @
% 9.06/1.77 emptyset ) ) @
% 9.06/1.77 (
% 9.06/1.77 binunion @
% 9.06/1.77 X132 @
% 9.06/1.77 X134 ) ) ) ) ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X140:$i,
% 9.06/1.77 X142:$i,
% 9.06/1.77 X144:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X144 @
% 9.06/1.77 X140 ) =>
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X146:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X146 @
% 9.06/1.77 X142 ) =>
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 (
% 9.06/1.77 setadjoin
% 9.06/1.77 @
% 9.06/1.77 X144 @
% 9.06/1.77 (
% 9.06/1.77 setadjoin
% 9.06/1.77 @
% 9.06/1.77 X146 @
% 9.06/1.77 emptyset ) ) @
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 (
% 9.06/1.77 binunion @
% 9.06/1.77 X140 @
% 9.06/1.77 X142 ) ) ) ) ) ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X148:$i,
% 9.06/1.77 X150:$i,
% 9.06/1.77 X152:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X152 @
% 9.06/1.77 X148 ) =>
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X154:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X154 @
% 9.06/1.77 X150 ) =>
% 9.06/1.77 (
% 9.06/1.77 subset @
% 9.06/1.77 (
% 9.06/1.77 setadjoin
% 9.06/1.77 @
% 9.06/1.77 (
% 9.06/1.77 setadjoin
% 9.06/1.77 @
% 9.06/1.77 X152 @
% 9.06/1.77 emptyset ) @
% 9.06/1.77 (
% 9.06/1.77 setadjoin
% 9.06/1.77 @
% 9.06/1.77 (
% 9.06/1.77 setadjoin
% 9.06/1.77 @
% 9.06/1.77 X152 @
% 9.06/1.77 (
% 9.06/1.77 setadjoin
% 9.06/1.77 @
% 9.06/1.77 X154 @
% 9.06/1.77 emptyset ) ) @
% 9.06/1.77 emptyset ) ) @
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 (
% 9.06/1.77 binunion @
% 9.06/1.77 X148 @
% 9.06/1.77 X150 ) ) ) ) ) ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X156:$i,
% 9.06/1.77 X158:$i,
% 9.06/1.77 X160:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X160 @
% 9.06/1.77 X156 ) =>
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X162:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X162 @
% 9.06/1.77 X158 ) =>
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 (
% 9.06/1.77 setadjoin
% 9.06/1.77 @
% 9.06/1.77 (
% 9.06/1.77 setadjoin
% 9.06/1.77 @
% 9.06/1.77 X160 @
% 9.06/1.77 emptyset ) @
% 9.06/1.77 (
% 9.06/1.77 setadjoin
% 9.06/1.77 @
% 9.06/1.77 (
% 9.06/1.77 setadjoin
% 9.06/1.77 @
% 9.06/1.77 X160 @
% 9.06/1.77 (
% 9.06/1.77 setadjoin
% 9.06/1.77 @
% 9.06/1.77 X162 @
% 9.06/1.77 emptyset ) ) @
% 9.06/1.77 emptyset ) ) @
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 (
% 9.06/1.77 binunion @
% 9.06/1.77 X156 @
% 9.06/1.77 X158 ) ) ) ) ) ) ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X164:$i,
% 9.06/1.77 X166:$i,
% 9.06/1.77 X168:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X168 @
% 9.06/1.77 X164 ) =>
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X170:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X170 @
% 9.06/1.77 X166 ) =>
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 (
% 9.06/1.77 kpair @
% 9.06/1.77 X168 @
% 9.06/1.77 X170 ) @
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 (
% 9.06/1.77 binunion @
% 9.06/1.77 X164 @
% 9.06/1.77 X166 ) ) ) ) ) ) ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 cartprodpairin ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 cartprodmempair1 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 cartprodmempair ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setunionE2 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setunionsingleton1 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setunionsingleton2 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setunionsingleton ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 singletonprop ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ex1E1 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ex1I ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ex1I2 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 singletonsuniq ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setukpairinjL1 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 kfstsingleton ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 theprop ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 kfstpairEq ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 cartprodfstin ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setukpairinjL2 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setukpairinjL ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setukpairinjR11 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setukpairinjR12 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setukpairinjR1 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 upairequniteq ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setukpairinjR2 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setukpairinjR ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ksndsingleton ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ksndpairEq ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 kpairsurjEq ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 cartprodsndin ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 cartprodpairmemEL ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 cartprodpairmemER ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 cartprodmempaircEq ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 cartprodfstpairEq ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 cartprodsndpairEq ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 cartprodpairsurjEq ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 dpsetconstrI ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 dpsetconstrSub ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setOfPairsIsBReln ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 dpsetconstrERa ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 dpsetconstrEL1 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 dpsetconstrEL2 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 dpsetconstrER ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 funcImageSingleton ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 apProp ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 app ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 infuncsetfunc ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ap2p ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 funcinfuncset ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 lamProp ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 lamp ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 lam2p ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 brelnall1 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 brelnall2 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ex1E2 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 funcGraphProp1 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 funcGraphProp3 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 funcGraphProp2 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 funcextLem ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 funcGraphProp4 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 subbreln ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 eqbreln ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 funcext ) =>
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% 9.06/1.77 (
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% 9.06/1.77 beta1 ) =>
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% 9.06/1.77 (
% 9.06/1.77 eta1 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 lam2lamEq ) =>
% 9.06/1.77 (
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% 9.06/1.77 beta2 ) =>
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% 9.06/1.77 (
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% 9.06/1.77 (
% 9.06/1.77 (
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% 9.06/1.77 (
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% 9.06/1.77 (
% 9.06/1.77 (
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% 9.06/1.77 (
% 9.06/1.77 ifSingleton ) =>
% 9.06/1.77 (
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% 9.06/1.77 ifp ) =>
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% 9.06/1.77 (
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% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 contrasubsetT2 ) =>
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% 9.06/1.77 (
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% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 doubleComplementI1 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 doubleComplementE1 ) =>
% 9.06/1.77 (
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% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X266:$i,
% 9.06/1.77 X268:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X268 @
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 X266 ) ) =>
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X270:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X270 @
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 X266 ) ) =>
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X272:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X272 @
% 9.06/1.77 X266 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ~(
% 9.06/1.77 in @
% 9.06/1.77 X272 @
% 9.06/1.77 (
% 9.06/1.77 binunion
% 9.06/1.77 @
% 9.06/1.77 X268 @
% 9.06/1.77 X270 ) ) ) =>
% 9.06/1.77 (
% 9.06/1.77 ~(
% 9.06/1.77 in @
% 9.06/1.77 X272 @
% 9.06/1.77 X270 ) ) ) ) ) ) ) ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X274:$i,
% 9.06/1.77 X276:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X276 @
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 X274 ) ) =>
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X278:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X278 @
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 X274 ) ) =>
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X280:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X280 @
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 X274 ) ) =>
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X282:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X282 @
% 9.06/1.77 X274 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X282 @
% 9.06/1.77 (
% 9.06/1.77 binintersect
% 9.06/1.77 @
% 9.06/1.77 X276 @
% 9.06/1.77 X278 ) ) =>
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X282 @
% 9.06/1.77 (
% 9.06/1.77 binunion @
% 9.06/1.77 X276 @
% 9.06/1.77 X280 ) ) ) ) ) ) ) ) ) ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X284:$i,
% 9.06/1.77 X286:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X286 @
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 X284 ) ) =>
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X288:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X288 @
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 X284 ) ) =>
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X290:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X290 @
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 X284 ) ) =>
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X292:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X292 @
% 9.06/1.77 X284 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X292 @
% 9.06/1.77 (
% 9.06/1.77 binintersect
% 9.06/1.77 @
% 9.06/1.77 X286 @
% 9.06/1.77 X288 ) ) =>
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X292 @
% 9.06/1.77 (
% 9.06/1.77 binunion @
% 9.06/1.77 X288 @
% 9.06/1.77 X290 ) ) ) ) ) ) ) ) ) ) ) =>
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X294:$i,
% 9.06/1.77 X296:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X296 @
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 X294 ) ) =>
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X298:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X298 @
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 X294 ) ) =>
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X300:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X300 @
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 X294 ) ) =>
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X302:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X302 @
% 9.06/1.77 X294 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X302 @
% 9.06/1.77 (
% 9.06/1.77 binintersect
% 9.06/1.77 @
% 9.06/1.77 X296 @
% 9.06/1.77 X298 ) ) =>
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X302 @
% 9.06/1.77 (
% 9.06/1.77 binintersect
% 9.06/1.77 @
% 9.06/1.77 (
% 9.06/1.77 binunion @
% 9.06/1.77 X296 @
% 9.06/1.77 X300 ) @
% 9.06/1.77 (
% 9.06/1.77 binunion @
% 9.06/1.77 X298 @
% 9.06/1.77 X300 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 9.06/1.77 thf(zf_stmt_1, type, zip_tseitin_0 : $i > $i > $i > $o).
% 9.06/1.77 thf(zf_stmt_2, axiom,
% 9.06/1.77 (![X8:$i,X6:$i,X4:$i]:
% 9.06/1.77 ( ( zip_tseitin_0 @ X8 @ X6 @ X4 ) <=>
% 9.06/1.77 ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ))).
% 9.06/1.77 thf(zf_stmt_3, conjecture,
% 9.06/1.77 (( setextAx ) =>
% 9.06/1.77 ( ( emptysetAx ) =>
% 9.06/1.77 ( ( setadjoinAx ) =>
% 9.06/1.77 ( ( ![X4:$i,X6:$i]:
% 9.06/1.77 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 9.06/1.77 ( ![X8:$i]: ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) ) =>
% 9.06/1.77 ( ( setunionAx ) =>
% 9.06/1.77 ( ( omega0Ax ) =>
% 9.06/1.77 ( ( omegaSAx ) =>
% 9.06/1.77 ( ( omegaIndAx ) =>
% 9.06/1.77 ( ( replAx ) =>
% 9.06/1.77 ( ( foundationAx ) =>
% 9.06/1.77 ( ( wellorderingAx ) =>
% 9.06/1.77 ( ( descrp ) =>
% 9.06/1.77 ( ( dsetconstrI ) =>
% 9.06/1.77 ( ( dsetconstrEL ) =>
% 9.06/1.77 ( ( dsetconstrER ) =>
% 9.06/1.77 ( ( exuE1 ) =>
% 9.06/1.77 ( ( prop2setE ) =>
% 9.06/1.77 ( ( emptysetE ) =>
% 9.06/1.77 ( ( emptysetimpfalse ) =>
% 9.06/1.77 ( ( notinemptyset ) =>
% 9.06/1.77 ( ( exuE3e ) =>
% 9.06/1.77 ( ( setext ) =>
% 9.06/1.77 ( ( emptyI ) =>
% 9.06/1.77 ( ( noeltsimpempty ) =>
% 9.06/1.77 ( ( setbeta ) =>
% 9.06/1.77 ( ( nonemptyE1 ) =>
% 9.06/1.77 ( ( nonemptyI ) =>
% 9.06/1.77 ( ( nonemptyI1 ) =>
% 9.06/1.77 ( ( setadjoinIL ) =>
% 9.06/1.77 ( ( emptyinunitempty ) =>
% 9.06/1.77 ( ( setadjoinIR ) =>
% 9.06/1.77 ( ( setadjoinE ) =>
% 9.06/1.77 ( (
% 9.06/1.77 setadjoinOr ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setoftrueEq ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X10:$i,
% 9.06/1.77 X12:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X14:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X14 @ X12 ) =>
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X14 @ X10 ) ) ) =>
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X12 @
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 X10 ) ) ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X16:$i]:
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 emptyset @
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 X16 ) ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X18:$i]:
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 emptyset @
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 X18 ) ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X20:$i,
% 9.06/1.77 X22:$i,
% 9.06/1.77 X24:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X22 @
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 X20 ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X24 @ X22 ) =>
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X24 @ X20 ) ) ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setunionI ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setunionE ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 subPowSU ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 exuE2 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 nonemptyImpWitness ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 uniqinunit ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 notinsingleton ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 eqinunit ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 singletonsswitch ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 upairsetE ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 upairsetIL ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 upairsetIR ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 emptyE1 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 vacuousDall ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 quantDeMorgan1 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 quantDeMorgan2 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 quantDeMorgan3 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 quantDeMorgan4 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 prop2setI ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 prop2set2propI ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 notdexE ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 notdallE ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 exuI1 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 exuI3 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 exuI2 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 inCongP ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in__Cong ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 exuE3u ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 exu__Cong ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 emptyset__Cong ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setadjoin__Cong ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X26:$i,
% 9.06/1.77 X28:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 X26 ) =
% 9.06/1.77 (
% 9.06/1.77 X28 ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 X26 ) =
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 X28 ) ) ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setunion__Cong ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 omega__Cong ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 exuEu ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 descr__Cong ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 dsetconstr__Cong ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 subsetI1 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 eqimpsubset2 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 eqimpsubset1 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 subsetI2 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 emptysetsubset ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 subsetE ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 subsetE2 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 notsubsetI ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 notequalI1 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 notequalI2 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 subsetRefl ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 subsetTrans ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setadjoinSub ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setadjoinSub2 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 subset2powerset ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setextsub ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 subsetemptysetimpeq ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 powersetI1 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 powersetE1 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X30:$i]:
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X30 @
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 X30 ) ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 powersetsubset ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 sepInPowerset ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 sepSubset ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X32:$i,
% 9.06/1.77 X34:$i,
% 9.06/1.77 X36:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X36 @ X32 ) =>
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X36 @
% 9.06/1.77 (
% 9.06/1.77 binunion @
% 9.06/1.77 X32 @ X34 ) ) ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 upairset2IR ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X38:$i,
% 9.06/1.77 X40:$i,
% 9.06/1.77 X42:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X42 @ X40 ) =>
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X42 @
% 9.06/1.77 (
% 9.06/1.77 binunion @
% 9.06/1.77 X38 @ X40 ) ) ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X44:$i,
% 9.06/1.77 X46:$i,
% 9.06/1.77 X48:$i,
% 9.06/1.77 X50:$o]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X48 @
% 9.06/1.77 (
% 9.06/1.77 binunion @
% 9.06/1.77 X44 @ X46 ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X48 @ X44 ) =>
% 9.06/1.77 (
% 9.06/1.77 X50 ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X48 @ X46 ) =>
% 9.06/1.77 (
% 9.06/1.77 X50 ) ) =>
% 9.06/1.77 (
% 9.06/1.77 X50 ) ) ) ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X52:$i,
% 9.06/1.77 X54:$i,
% 9.06/1.77 X56:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X56 @
% 9.06/1.77 (
% 9.06/1.77 binunion @
% 9.06/1.77 X52 @ X54 ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X56 @ X52 ) |
% 9.06/1.77 (
% 9.06/1.77 in @
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% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X58:$i,
% 9.06/1.77 X60:$i]:
% 9.06/1.77 (
% 9.06/1.77 subset @
% 9.06/1.77 X58 @
% 9.06/1.77 (
% 9.06/1.77 binunion @
% 9.06/1.77 X58 @ X60 ) ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X62:$i,
% 9.06/1.77 X64:$i]:
% 9.06/1.77 (
% 9.06/1.77 subset @
% 9.06/1.77 X64 @
% 9.06/1.77 (
% 9.06/1.77 binunion @
% 9.06/1.77 X62 @ X64 ) ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X66:$i,
% 9.06/1.77 X68:$i,
% 9.06/1.77 X70:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X70 @ X66 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X70 @ X68 ) =>
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X70 @
% 9.06/1.77 (
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% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X72:$i,
% 9.06/1.77 X74:$i,
% 9.06/1.77 X76:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 subset @
% 9.06/1.77 X76 @ X72 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 subset @
% 9.06/1.77 X76 @ X74 ) =>
% 9.06/1.77 (
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% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X78:$i,
% 9.06/1.77 X80:$i,
% 9.06/1.77 X82:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X82 @
% 9.06/1.77 (
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% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X84:$i,
% 9.06/1.77 X86:$i]:
% 9.06/1.77 (
% 9.06/1.77 subset @
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% 9.06/1.77 X84 @ X86 ) @
% 9.06/1.77 X84 ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X88:$i,
% 9.06/1.77 X90:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 subset @
% 9.06/1.77 X88 @ X90 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 binintersect
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% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X92:$i,
% 9.06/1.77 X94:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 binintersect
% 9.06/1.77 @
% 9.06/1.77 X92 @ X94 ) =
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% 9.06/1.77 (
% 9.06/1.77 subset @
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% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X96:$i,
% 9.06/1.77 X98:$i,
% 9.06/1.77 X100:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X100 @
% 9.06/1.77 (
% 9.06/1.77 binintersect
% 9.06/1.77 @
% 9.06/1.77 X96 @ X98 ) ) =>
% 9.06/1.77 (
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% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X102:$i,
% 9.06/1.77 X104:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ~(
% 9.06/1.77 ?[
% 9.06/1.77 X106:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X106 @
% 9.06/1.77 X104 ) &
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X106 @
% 9.06/1.77 X102 ) ) ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 binintersect
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% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X108:$i,
% 9.06/1.77 X110:$i]:
% 9.06/1.77 (
% 9.06/1.77 subset @
% 9.06/1.77 (
% 9.06/1.77 binintersect
% 9.06/1.77 @
% 9.06/1.77 X108 @
% 9.06/1.77 X110 ) @
% 9.06/1.77 X110 ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X112:$i,
% 9.06/1.77 X114:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 subset @
% 9.06/1.77 X114 @
% 9.06/1.77 X112 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 binintersect
% 9.06/1.77 @
% 9.06/1.77 X112 @
% 9.06/1.77 X114 ) =
% 9.06/1.77 (
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% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X116:$i,
% 9.06/1.77 X118:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 binintersect
% 9.06/1.77 @
% 9.06/1.77 X116 @
% 9.06/1.77 X118 ) =
% 9.06/1.77 (
% 9.06/1.77 X116 ) ) =>
% 9.06/1.77 (
% 9.06/1.77 subset @
% 9.06/1.77 X116 @
% 9.06/1.77 X118 ) ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X120:$i,
% 9.06/1.77 X122:$i,
% 9.06/1.77 X124:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 binintersect
% 9.06/1.77 @
% 9.06/1.77 X120 @
% 9.06/1.77 (
% 9.06/1.77 binunion @
% 9.06/1.77 X122 @
% 9.06/1.77 X124 ) ) =
% 9.06/1.77 (
% 9.06/1.77 binunion @
% 9.06/1.77 (
% 9.06/1.77 binintersect
% 9.06/1.77 @
% 9.06/1.77 X120 @
% 9.06/1.77 X122 ) @
% 9.06/1.77 (
% 9.06/1.77 binintersect
% 9.06/1.77 @
% 9.06/1.77 X120 @
% 9.06/1.77 X124 ) ) ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setminusI ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setminusEL ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setminusER ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setminusSubset2 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setminusERneg ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setminusELneg ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setminusILneg ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setminusIRneg ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setminusLsub ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setminusSubset1 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 symdiffE ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 symdiffI1 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 symdiffI2 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 symdiffIneg1 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 symdiffIneg2 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 secondinupair ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setukpairIL ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setukpairIR ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 kpairiskpair ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 kpairp ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 singletonsubset ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 singletoninpowerset ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X126:$i,
% 9.06/1.77 X128:$i,
% 9.06/1.77 X130:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X130 @
% 9.06/1.77 X126 ) =>
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 (
% 9.06/1.77 setadjoin
% 9.06/1.77 @
% 9.06/1.77 X130 @
% 9.06/1.77 emptyset ) @
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 (
% 9.06/1.77 binunion @
% 9.06/1.77 X126 @
% 9.06/1.77 X128 ) ) ) ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 upairset2E ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X132:$i,
% 9.06/1.77 X134:$i,
% 9.06/1.77 X136:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X136 @
% 9.06/1.77 X132 ) =>
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X138:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X138 @
% 9.06/1.77 X134 ) =>
% 9.06/1.77 (
% 9.06/1.77 subset @
% 9.06/1.77 (
% 9.06/1.77 setadjoin
% 9.06/1.77 @
% 9.06/1.77 X136 @
% 9.06/1.77 (
% 9.06/1.77 setadjoin
% 9.06/1.77 @
% 9.06/1.77 X138 @
% 9.06/1.77 emptyset ) ) @
% 9.06/1.77 (
% 9.06/1.77 binunion @
% 9.06/1.77 X132 @
% 9.06/1.77 X134 ) ) ) ) ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X140:$i,
% 9.06/1.77 X142:$i,
% 9.06/1.77 X144:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X144 @
% 9.06/1.77 X140 ) =>
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X146:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X146 @
% 9.06/1.77 X142 ) =>
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 (
% 9.06/1.77 setadjoin
% 9.06/1.77 @
% 9.06/1.77 X144 @
% 9.06/1.77 (
% 9.06/1.77 setadjoin
% 9.06/1.77 @
% 9.06/1.77 X146 @
% 9.06/1.77 emptyset ) ) @
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 (
% 9.06/1.77 binunion @
% 9.06/1.77 X140 @
% 9.06/1.77 X142 ) ) ) ) ) ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X148:$i,
% 9.06/1.77 X150:$i,
% 9.06/1.77 X152:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X152 @
% 9.06/1.77 X148 ) =>
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X154:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X154 @
% 9.06/1.77 X150 ) =>
% 9.06/1.77 (
% 9.06/1.77 subset @
% 9.06/1.77 (
% 9.06/1.77 setadjoin
% 9.06/1.77 @
% 9.06/1.77 (
% 9.06/1.77 setadjoin
% 9.06/1.77 @
% 9.06/1.77 X152 @
% 9.06/1.77 emptyset ) @
% 9.06/1.77 (
% 9.06/1.77 setadjoin
% 9.06/1.77 @
% 9.06/1.77 (
% 9.06/1.77 setadjoin
% 9.06/1.77 @
% 9.06/1.77 X152 @
% 9.06/1.77 (
% 9.06/1.77 setadjoin
% 9.06/1.77 @
% 9.06/1.77 X154 @
% 9.06/1.77 emptyset ) ) @
% 9.06/1.77 emptyset ) ) @
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 (
% 9.06/1.77 binunion @
% 9.06/1.77 X148 @
% 9.06/1.77 X150 ) ) ) ) ) ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X156:$i,
% 9.06/1.77 X158:$i,
% 9.06/1.77 X160:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X160 @
% 9.06/1.77 X156 ) =>
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X162:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X162 @
% 9.06/1.77 X158 ) =>
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 (
% 9.06/1.77 setadjoin
% 9.06/1.77 @
% 9.06/1.77 (
% 9.06/1.77 setadjoin
% 9.06/1.77 @
% 9.06/1.77 X160 @
% 9.06/1.77 emptyset ) @
% 9.06/1.77 (
% 9.06/1.77 setadjoin
% 9.06/1.77 @
% 9.06/1.77 (
% 9.06/1.77 setadjoin
% 9.06/1.77 @
% 9.06/1.77 X160 @
% 9.06/1.77 (
% 9.06/1.77 setadjoin
% 9.06/1.77 @
% 9.06/1.77 X162 @
% 9.06/1.77 emptyset ) ) @
% 9.06/1.77 emptyset ) ) @
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 (
% 9.06/1.77 binunion @
% 9.06/1.77 X156 @
% 9.06/1.77 X158 ) ) ) ) ) ) ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X164:$i,
% 9.06/1.77 X166:$i,
% 9.06/1.77 X168:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X168 @
% 9.06/1.77 X164 ) =>
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X170:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X170 @
% 9.06/1.77 X166 ) =>
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 (
% 9.06/1.77 kpair @
% 9.06/1.77 X168 @
% 9.06/1.77 X170 ) @
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 (
% 9.06/1.77 binunion @
% 9.06/1.77 X164 @
% 9.06/1.77 X166 ) ) ) ) ) ) ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 cartprodpairin ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 cartprodmempair1 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 cartprodmempair ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setunionE2 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setunionsingleton1 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setunionsingleton2 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setunionsingleton ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 singletonprop ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ex1E1 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ex1I ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ex1I2 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 singletonsuniq ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setukpairinjL1 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 kfstsingleton ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 theprop ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 kfstpairEq ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 cartprodfstin ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setukpairinjL2 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setukpairinjL ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setukpairinjR11 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setukpairinjR12 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setukpairinjR1 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 upairequniteq ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setukpairinjR2 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setukpairinjR ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ksndsingleton ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ksndpairEq ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 kpairsurjEq ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 cartprodsndin ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 cartprodpairmemEL ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 cartprodpairmemER ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 cartprodmempaircEq ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 cartprodfstpairEq ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 cartprodsndpairEq ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 cartprodpairsurjEq ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 dpsetconstrI ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 dpsetconstrSub ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setOfPairsIsBReln ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 dpsetconstrERa ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 dpsetconstrEL1 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 dpsetconstrEL2 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 dpsetconstrER ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 funcImageSingleton ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 apProp ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 app ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 infuncsetfunc ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ap2p ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 funcinfuncset ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 lamProp ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 lamp ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 lam2p ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 brelnall1 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 brelnall2 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ex1E2 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 funcGraphProp1 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 funcGraphProp3 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 funcGraphProp2 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 funcextLem ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 funcGraphProp4 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 subbreln ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 eqbreln ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 funcext ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 funcext2 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ap2apEq1 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ap2apEq2 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 beta1 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 eta1 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 lam2lamEq ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 beta2 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 eta2 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 iffalseProp1 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 iffalseProp2 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 iftrueProp1 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 iftrueProp2 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ifSingleton ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ifp ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 theeq ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 iftrue ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 iffalse ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 iftrueorfalse ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
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% 9.06/1.77 X174:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X174 @
% 9.06/1.77 (
% 9.06/1.77 powerset @
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% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X176:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X176 @
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 X172 ) ) =>
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 (
% 9.06/1.77 binintersect
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% 9.06/1.77 (
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% 9.06/1.77 ![
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% 9.06/1.77 X180:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X180 @
% 9.06/1.77 (
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% 9.06/1.77 (
% 9.06/1.77 ![
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% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X182 @
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 X178 ) ) =>
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 (
% 9.06/1.77 binunion @
% 9.06/1.77 X180 @
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% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
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% 9.06/1.77 X186:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X186 @
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 X184 ) ) =>
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 X186 ) @
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 (
% 9.06/1.77 powerset @
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% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setminusT_lem ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 complementT_lem ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X188:$i,
% 9.06/1.77 X190:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X190 @
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 X188 ) ) =>
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X192:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X192 @
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 X188 ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X194:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X194 @
% 9.06/1.77 X188 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X194 @
% 9.06/1.77 X190 ) =>
% 9.06/1.77 (
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% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X196:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X196 @
% 9.06/1.77 X188 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X196 @
% 9.06/1.77 X192 ) =>
% 9.06/1.77 (
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% 9.06/1.77 (
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% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 subsetTI ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X198:$i,
% 9.06/1.77 X200:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X200 @
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 X198 ) ) =>
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X202:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X202 @
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 X198 ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X204:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X204 @
% 9.06/1.77 X198 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X204 @
% 9.06/1.77 X200 ) =>
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X204 @
% 9.06/1.77 X202 ) ) ) ) =>
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X200 @
% 9.06/1.77 (
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% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X206:$i,
% 9.06/1.77 X208:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X208 @
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 X206 ) ) =>
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X210:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X210 @
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 X206 ) ) =>
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X212:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X212 @
% 9.06/1.77 X206 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X208 @
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 X210 ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X212 @
% 9.06/1.77 X208 ) =>
% 9.06/1.77 (
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% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 complementTI1 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 complementTE1 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X214:$i,
% 9.06/1.77 X216:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X216 @
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 X214 ) ) =>
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X218:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X218 @
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 X214 ) ) =>
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X220:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X220 @
% 9.06/1.77 X214 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ~(
% 9.06/1.77 in @
% 9.06/1.77 X220 @
% 9.06/1.77 X216 ) ) =>
% 9.06/1.77 (
% 9.06/1.77 ~(
% 9.06/1.77 in @
% 9.06/1.77 X220 @
% 9.06/1.77 (
% 9.06/1.77 binintersect
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% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X222:$i,
% 9.06/1.77 X224:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X224 @
% 9.06/1.77 (
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% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X226:$i]:
% 9.06/1.77 (
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% 9.06/1.77 X226 @
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% 9.06/1.77 (
% 9.06/1.77 ![
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% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X228 @
% 9.06/1.77 X222 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ~(
% 9.06/1.77 in @
% 9.06/1.77 X228 @
% 9.06/1.77 X226 ) ) =>
% 9.06/1.77 (
% 9.06/1.77 ~(
% 9.06/1.77 in @
% 9.06/1.77 X228 @
% 9.06/1.77 (
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% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 contrasubsetT ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 contrasubsetT1 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 contrasubsetT2 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 contrasubsetT3 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 doubleComplementI1 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 doubleComplementE1 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 doubleComplementSub1 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 doubleComplementSub2 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 doubleComplementEq ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X230:$i,
% 9.06/1.77 X232:$i]:
% 9.06/1.77 (
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% 9.06/1.77 X232 @
% 9.06/1.77 (
% 9.06/1.77 powerset @
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% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X234:$i]:
% 9.06/1.77 (
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% 9.06/1.77 (
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% 9.06/1.77 (
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% 9.06/1.77 (
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% 9.06/1.77 (
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% 9.06/1.77 @
% 9.06/1.77 X248 @
% 9.06/1.77 X250 ) ) ) ) ) ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X252:$i,
% 9.06/1.77 X254:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X254 @
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 X252 ) ) =>
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X256:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X256 @
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 X252 ) ) =>
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 (
% 9.06/1.77 setminus @
% 9.06/1.77 X252 @
% 9.06/1.77 X254 ) @
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 (
% 9.06/1.77 setminus @
% 9.06/1.77 X252 @
% 9.06/1.77 (
% 9.06/1.77 binintersect
% 9.06/1.77 @
% 9.06/1.77 X254 @
% 9.06/1.77 X256 ) ) ) ) ) ) ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 contraSubsetComplement ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 complementTcontraSubset ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X258:$i,
% 9.06/1.77 X260:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X260 @
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 X258 ) ) =>
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X262:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X262 @
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 X258 ) ) =>
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X264:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X264 @
% 9.06/1.77 X258 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ~(
% 9.06/1.77 in @
% 9.06/1.77 X264 @
% 9.06/1.77 (
% 9.06/1.77 binunion
% 9.06/1.77 @
% 9.06/1.77 X260 @
% 9.06/1.77 X262 ) ) ) =>
% 9.06/1.77 (
% 9.06/1.77 ~(
% 9.06/1.77 in @
% 9.06/1.77 X264 @
% 9.06/1.77 X260 ) ) ) ) ) ) ) ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X266:$i,
% 9.06/1.77 X268:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X268 @
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 X266 ) ) =>
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X270:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X270 @
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 X266 ) ) =>
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X272:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X272 @
% 9.06/1.77 X266 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ~(
% 9.06/1.77 in @
% 9.06/1.77 X272 @
% 9.06/1.77 (
% 9.06/1.77 binunion
% 9.06/1.77 @
% 9.06/1.77 X268 @
% 9.06/1.77 X270 ) ) ) =>
% 9.06/1.77 (
% 9.06/1.77 ~(
% 9.06/1.77 in @
% 9.06/1.77 X272 @
% 9.06/1.77 X270 ) ) ) ) ) ) ) ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X274:$i,
% 9.06/1.77 X276:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X276 @
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 X274 ) ) =>
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X278:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X278 @
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 X274 ) ) =>
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X280:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X280 @
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 X274 ) ) =>
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X282:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X282 @
% 9.06/1.77 X274 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X282 @
% 9.06/1.77 (
% 9.06/1.77 binintersect
% 9.06/1.77 @
% 9.06/1.77 X276 @
% 9.06/1.77 X278 ) ) =>
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X282 @
% 9.06/1.77 (
% 9.06/1.77 binunion @
% 9.06/1.77 X276 @
% 9.06/1.77 X280 ) ) ) ) ) ) ) ) ) ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X284:$i,
% 9.06/1.77 X286:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X286 @
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 X284 ) ) =>
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X288:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X288 @
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 X284 ) ) =>
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X290:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X290 @
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 X284 ) ) =>
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X292:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X292 @
% 9.06/1.77 X284 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X292 @
% 9.06/1.77 (
% 9.06/1.77 binintersect
% 9.06/1.77 @
% 9.06/1.77 X286 @
% 9.06/1.77 X288 ) ) =>
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X292 @
% 9.06/1.77 (
% 9.06/1.77 binunion @
% 9.06/1.77 X288 @
% 9.06/1.77 X290 ) ) ) ) ) ) ) ) ) ) ) =>
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X294:$i,
% 9.06/1.77 X296:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X296 @
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 X294 ) ) =>
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X298:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X298 @
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 X294 ) ) =>
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X300:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X300 @
% 9.06/1.77 (
% 9.06/1.77 powerset @
% 9.06/1.77 X294 ) ) =>
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X302:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X302 @
% 9.06/1.77 X294 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X302 @
% 9.06/1.77 (
% 9.06/1.77 binintersect
% 9.06/1.77 @
% 9.06/1.77 X296 @
% 9.06/1.77 X298 ) ) =>
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X302 @
% 9.06/1.77 (
% 9.06/1.77 binintersect
% 9.06/1.77 @
% 9.06/1.77 (
% 9.06/1.77 binunion @
% 9.06/1.77 X296 @
% 9.06/1.77 X300 ) @
% 9.06/1.77 (
% 9.06/1.77 binunion @
% 9.06/1.77 X298 @
% 9.06/1.77 X300 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 9.06/1.77 thf(zf_stmt_4, negated_conjecture,
% 9.06/1.77 (~( ( setextAx ) =>
% 9.06/1.77 ( ( emptysetAx ) =>
% 9.06/1.77 ( ( setadjoinAx ) =>
% 9.06/1.77 ( ( ![X4:$i,X6:$i]:
% 9.06/1.77 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 9.06/1.77 ( ![X8:$i]: ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) ) =>
% 9.06/1.77 ( ( setunionAx ) =>
% 9.06/1.77 ( ( omega0Ax ) =>
% 9.06/1.77 ( ( omegaSAx ) =>
% 9.06/1.77 ( ( omegaIndAx ) =>
% 9.06/1.77 ( ( replAx ) =>
% 9.06/1.77 ( ( foundationAx ) =>
% 9.06/1.77 ( ( wellorderingAx ) =>
% 9.06/1.77 ( ( descrp ) =>
% 9.06/1.77 ( ( dsetconstrI ) =>
% 9.06/1.77 ( ( dsetconstrEL ) =>
% 9.06/1.77 ( ( dsetconstrER ) =>
% 9.06/1.77 ( ( exuE1 ) =>
% 9.06/1.77 ( ( prop2setE ) =>
% 9.06/1.77 ( ( emptysetE ) =>
% 9.06/1.77 ( ( emptysetimpfalse ) =>
% 9.06/1.77 ( ( notinemptyset ) =>
% 9.06/1.77 ( ( exuE3e ) =>
% 9.06/1.77 ( ( setext ) =>
% 9.06/1.77 ( ( emptyI ) =>
% 9.06/1.77 ( ( noeltsimpempty ) =>
% 9.06/1.77 ( ( setbeta ) =>
% 9.06/1.77 ( ( nonemptyE1 ) =>
% 9.06/1.77 ( ( nonemptyI ) =>
% 9.06/1.77 ( ( nonemptyI1 ) =>
% 9.06/1.77 ( ( setadjoinIL ) =>
% 9.06/1.77 ( ( emptyinunitempty ) =>
% 9.06/1.77 ( ( setadjoinIR ) =>
% 9.06/1.77 ( (
% 9.06/1.77 setadjoinE ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setadjoinOr ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setoftrueEq ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X10:$i,
% 9.06/1.77 X12:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X14:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X14 @ X12 ) =>
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X14 @ X10 ) ) ) =>
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X12 @
% 9.06/1.77 (
% 9.06/1.77 powerset
% 9.06/1.77 @
% 9.06/1.77 X10 ) ) ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X16:$i]:
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 emptyset @
% 9.06/1.77 (
% 9.06/1.77 powerset
% 9.06/1.77 @
% 9.06/1.77 X16 ) ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X18:$i]:
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 emptyset @
% 9.06/1.77 (
% 9.06/1.77 powerset
% 9.06/1.77 @
% 9.06/1.77 X18 ) ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 ![
% 9.06/1.77 X20:$i,
% 9.06/1.77 X22:$i,
% 9.06/1.77 X24:$i]:
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X22 @
% 9.06/1.77 (
% 9.06/1.77 powerset
% 9.06/1.77 @
% 9.06/1.77 X20 ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X24 @ X22 ) =>
% 9.06/1.77 (
% 9.06/1.77 in @
% 9.06/1.77 X24 @ X20 ) ) ) ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setunionI ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 setunionE ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 subPowSU ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 exuE2 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 nonemptyImpWitness ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 uniqinunit ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 notinsingleton ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 eqinunit ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 singletonsswitch ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 upairsetE ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 upairsetIL ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 upairsetIR ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 emptyE1 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 vacuousDall ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 quantDeMorgan1 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 quantDeMorgan2 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 quantDeMorgan3 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 quantDeMorgan4 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 prop2setI ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 prop2set2propI ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 notdexE ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 notdallE ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 exuI1 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 exuI3 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 exuI2 ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 inCongP ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 in__Cong ) =>
% 9.06/1.77 (
% 9.06/1.77 (
% 9.06/1.77 exuE3u ) =>
% 9.27/1.77 (
% 9.27/1.77 (
% 9.27/1.77 exu__Cong ) =>
% 9.27/1.77 (
% 9.27/1.77 (
% 9.27/1.77 emptyset__Cong ) =>
% 9.27/1.77 (
% 9.27/1.77 (
% 9.27/1.77 setadjoin__Cong ) =>
% 9.27/1.77 (
% 9.27/1.77 (
% 9.27/1.77 ![
% 9.27/1.77 X26:$i,
% 9.27/1.77 X28:$i]:
% 9.27/1.77 (
% 9.27/1.77 (
% 9.27/1.77 (
% 9.27/1.77 X26 ) =
% 9.27/1.77 (
% 9.27/1.77 X28 ) ) =>
% 9.27/1.77 (
% 9.27/1.77 (
% 9.27/1.77 powerset
% 9.27/1.77 @
% 9.27/1.77 X26 ) =
% 9.27/1.77 (
% 9.27/1.77 powerset
% 9.27/1.77 @
% 9.27/1.77 X28 ) ) ) ) =>
% 9.27/1.77 (
% 9.27/1.77 (
% 9.27/1.77 setunion__Cong ) =>
% 9.27/1.77 (
% 9.27/1.77 (
% 9.27/1.77 omega__Cong ) =>
% 9.27/1.77 (
% 9.27/1.77 (
% 9.27/1.77 exuEu ) =>
% 9.27/1.77 (
% 9.27/1.77 (
% 9.27/1.77 descr__Cong ) =>
% 9.27/1.77 (
% 9.27/1.77 (
% 9.27/1.77 dsetconstr__Cong ) =>
% 9.27/1.77 (
% 9.27/1.77 (
% 9.27/1.77 subsetI1 ) =>
% 9.27/1.77 (
% 9.27/1.77 (
% 9.27/1.77 eqimpsubset2 ) =>
% 9.27/1.77 (
% 9.27/1.77 (
% 9.27/1.77 eqimpsubset1 ) =>
% 9.27/1.77 (
% 9.27/1.77 (
% 9.27/1.77 subsetI2 ) =>
% 9.27/1.77 (
% 9.27/1.77 (
% 9.27/1.77 emptysetsubset ) =>
% 9.27/1.77 (
% 9.27/1.77 (
% 9.27/1.77 subsetE ) =>
% 9.27/1.77 (
% 9.27/1.77 (
% 9.27/1.77 subsetE2 ) =>
% 9.27/1.77 (
% 9.27/1.77 (
% 9.27/1.77 notsubsetI ) =>
% 9.27/1.77 (
% 9.27/1.77 (
% 9.27/1.77 notequalI1 ) =>
% 9.27/1.77 (
% 9.27/1.77 (
% 9.27/1.77 notequalI2 ) =>
% 9.27/1.77 (
% 9.27/1.77 (
% 9.27/1.77 subsetRefl ) =>
% 9.27/1.77 (
% 9.27/1.77 (
% 9.27/1.77 subsetTrans ) =>
% 9.27/1.77 (
% 9.27/1.77 (
% 9.27/1.77 setadjoinSub ) =>
% 9.27/1.77 (
% 9.27/1.77 (
% 9.27/1.77 setadjoinSub2 ) =>
% 9.27/1.77 (
% 9.27/1.77 (
% 9.27/1.77 subset2powerset ) =>
% 9.27/1.77 (
% 9.27/1.77 (
% 9.27/1.77 setextsub ) =>
% 9.27/1.77 (
% 9.27/1.77 (
% 9.27/1.77 subsetemptysetimpeq ) =>
% 9.27/1.77 (
% 9.27/1.77 (
% 9.27/1.77 powersetI1 ) =>
% 9.27/1.77 (
% 9.27/1.77 (
% 9.27/1.77 powersetE1 ) =>
% 9.27/1.77 (
% 9.27/1.77 (
% 9.27/1.77 ![
% 9.27/1.77 X30:$i]:
% 9.27/1.77 (
% 9.27/1.77 in @
% 9.27/1.77 X30 @
% 9.27/1.77 (
% 9.27/1.77 powerset
% 9.27/1.77 @
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% 9.27/1.77 (
% 9.27/1.77 powersetsubset ) =>
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% 9.27/1.77 (
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% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 setminusER ) =>
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% 9.27/1.78 (
% 9.27/1.78 setminusSubset2 ) =>
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% 9.27/1.78 (
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% 9.27/1.78 (
% 9.27/1.78 setminusELneg ) =>
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% 9.27/1.78 (
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% 9.27/1.78 (
% 9.27/1.78 (
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% 9.27/1.78 (
% 9.27/1.78 (
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% 9.27/1.78 (
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% 9.27/1.78 (
% 9.27/1.78 (
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% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 symdiffI2 ) =>
% 9.27/1.78 (
% 9.27/1.78 (
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% 9.27/1.78 (
% 9.27/1.78 (
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% 9.27/1.78 (
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% 9.27/1.78 (
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% 9.27/1.78 X170 ) @
% 9.27/1.78 (
% 9.27/1.78 powerset
% 9.27/1.78 @
% 9.27/1.78 (
% 9.27/1.78 powerset
% 9.27/1.78 @
% 9.27/1.78 (
% 9.27/1.78 binunion
% 9.27/1.78 @
% 9.27/1.78 X164 @
% 9.27/1.78 X166 ) ) ) ) ) ) ) ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 cartprodpairin ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 cartprodmempair1 ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 cartprodmempair ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 setunionE2 ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 setunionsingleton1 ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 setunionsingleton2 ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 setunionsingleton ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 singletonprop ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 ex1E1 ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 ex1I ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 ex1I2 ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 singletonsuniq ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 setukpairinjL1 ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 kfstsingleton ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 theprop ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 kfstpairEq ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 cartprodfstin ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 setukpairinjL2 ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 setukpairinjL ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 setukpairinjR11 ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 setukpairinjR12 ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 setukpairinjR1 ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 upairequniteq ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 setukpairinjR2 ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 setukpairinjR ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 ksndsingleton ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 ksndpairEq ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 kpairsurjEq ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 cartprodsndin ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 cartprodpairmemEL ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 cartprodpairmemER ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 cartprodmempaircEq ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 cartprodfstpairEq ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 cartprodsndpairEq ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 cartprodpairsurjEq ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 dpsetconstrI ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 dpsetconstrSub ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 setOfPairsIsBReln ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 dpsetconstrERa ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 dpsetconstrEL1 ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 dpsetconstrEL2 ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 dpsetconstrER ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 funcImageSingleton ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 apProp ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 app ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 infuncsetfunc ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 ap2p ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 funcinfuncset ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 lamProp ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 lamp ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 lam2p ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 brelnall1 ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 brelnall2 ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 ex1E2 ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 funcGraphProp1 ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 funcGraphProp3 ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 funcGraphProp2 ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 funcextLem ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 funcGraphProp4 ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 subbreln ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 eqbreln ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 funcext ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 funcext2 ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 ap2apEq1 ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 ap2apEq2 ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 beta1 ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 eta1 ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 lam2lamEq ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 beta2 ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 eta2 ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 iffalseProp1 ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 iffalseProp2 ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 iftrueProp1 ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 iftrueProp2 ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 ifSingleton ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 ifp ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 theeq ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 iftrue ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 iffalse ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 iftrueorfalse ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 ![
% 9.27/1.78 X172:$i,
% 9.27/1.78 X174:$i]:
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X174 @
% 9.27/1.78 (
% 9.27/1.78 powerset
% 9.27/1.78 @
% 9.27/1.78 X172 ) ) =>
% 9.27/1.78 (
% 9.27/1.78 ![
% 9.27/1.78 X176:$i]:
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X176 @
% 9.27/1.78 (
% 9.27/1.78 powerset
% 9.27/1.78 @
% 9.27/1.78 X172 ) ) =>
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 (
% 9.27/1.78 binintersect
% 9.27/1.78 @
% 9.27/1.78 X174 @
% 9.27/1.78 X176 ) @
% 9.27/1.78 (
% 9.27/1.78 powerset
% 9.27/1.78 @
% 9.27/1.78 X172 ) ) ) ) ) ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 ![
% 9.27/1.78 X178:$i,
% 9.27/1.78 X180:$i]:
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X180 @
% 9.27/1.78 (
% 9.27/1.78 powerset
% 9.27/1.78 @
% 9.27/1.78 X178 ) ) =>
% 9.27/1.78 (
% 9.27/1.78 ![
% 9.27/1.78 X182:$i]:
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X182 @
% 9.27/1.78 (
% 9.27/1.78 powerset
% 9.27/1.78 @
% 9.27/1.78 X178 ) ) =>
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 (
% 9.27/1.78 binunion
% 9.27/1.78 @
% 9.27/1.78 X180 @
% 9.27/1.78 X182 ) @
% 9.27/1.78 (
% 9.27/1.78 powerset
% 9.27/1.78 @
% 9.27/1.78 X178 ) ) ) ) ) ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 ![
% 9.27/1.78 X184:$i,
% 9.27/1.78 X186:$i]:
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X186 @
% 9.27/1.78 (
% 9.27/1.78 powerset
% 9.27/1.78 @
% 9.27/1.78 X184 ) ) =>
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 (
% 9.27/1.78 powerset
% 9.27/1.78 @
% 9.27/1.78 X186 ) @
% 9.27/1.78 (
% 9.27/1.78 powerset
% 9.27/1.78 @
% 9.27/1.78 (
% 9.27/1.78 powerset
% 9.27/1.78 @
% 9.27/1.78 X184 ) ) ) ) ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 setminusT_lem ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 complementT_lem ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 ![
% 9.27/1.78 X188:$i,
% 9.27/1.78 X190:$i]:
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X190 @
% 9.27/1.78 (
% 9.27/1.78 powerset
% 9.27/1.78 @
% 9.27/1.78 X188 ) ) =>
% 9.27/1.78 (
% 9.27/1.78 ![
% 9.27/1.78 X192:$i]:
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X192 @
% 9.27/1.78 (
% 9.27/1.78 powerset
% 9.27/1.78 @
% 9.27/1.78 X188 ) ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 ![
% 9.27/1.78 X194:$i]:
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X194 @
% 9.27/1.78 X188 ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X194 @
% 9.27/1.78 X190 ) =>
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X194 @
% 9.27/1.78 X192 ) ) ) ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 ![
% 9.27/1.78 X196:$i]:
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X196 @
% 9.27/1.78 X188 ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X196 @
% 9.27/1.78 X192 ) =>
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X196 @
% 9.27/1.78 X190 ) ) ) ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 X190 ) =
% 9.27/1.78 (
% 9.27/1.78 X192 ) ) ) ) ) ) ) ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 subsetTI ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 ![
% 9.27/1.78 X198:$i,
% 9.27/1.78 X200:$i]:
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X200 @
% 9.27/1.78 (
% 9.27/1.78 powerset
% 9.27/1.78 @
% 9.27/1.78 X198 ) ) =>
% 9.27/1.78 (
% 9.27/1.78 ![
% 9.27/1.78 X202:$i]:
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X202 @
% 9.27/1.78 (
% 9.27/1.78 powerset
% 9.27/1.78 @
% 9.27/1.78 X198 ) ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 ![
% 9.27/1.78 X204:$i]:
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X204 @
% 9.27/1.78 X198 ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X204 @
% 9.27/1.78 X200 ) =>
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X204 @
% 9.27/1.78 X202 ) ) ) ) =>
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X200 @
% 9.27/1.78 (
% 9.27/1.78 powerset
% 9.27/1.78 @
% 9.27/1.78 X202 ) ) ) ) ) ) ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 ![
% 9.27/1.78 X206:$i,
% 9.27/1.78 X208:$i]:
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X208 @
% 9.27/1.78 (
% 9.27/1.78 powerset
% 9.27/1.78 @
% 9.27/1.78 X206 ) ) =>
% 9.27/1.78 (
% 9.27/1.78 ![
% 9.27/1.78 X210:$i]:
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X210 @
% 9.27/1.78 (
% 9.27/1.78 powerset
% 9.27/1.78 @
% 9.27/1.78 X206 ) ) =>
% 9.27/1.78 (
% 9.27/1.78 ![
% 9.27/1.78 X212:$i]:
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X212 @
% 9.27/1.78 X206 ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X208 @
% 9.27/1.78 (
% 9.27/1.78 powerset
% 9.27/1.78 @
% 9.27/1.78 X210 ) ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X212 @
% 9.27/1.78 X208 ) =>
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X212 @
% 9.27/1.78 X210 ) ) ) ) ) ) ) ) ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 complementTI1 ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 complementTE1 ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 ![
% 9.27/1.78 X214:$i,
% 9.27/1.78 X216:$i]:
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X216 @
% 9.27/1.78 (
% 9.27/1.78 powerset
% 9.27/1.78 @
% 9.27/1.78 X214 ) ) =>
% 9.27/1.78 (
% 9.27/1.78 ![
% 9.27/1.78 X218:$i]:
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X218 @
% 9.27/1.78 (
% 9.27/1.78 powerset
% 9.27/1.78 @
% 9.27/1.78 X214 ) ) =>
% 9.27/1.78 (
% 9.27/1.78 ![
% 9.27/1.78 X220:$i]:
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X220 @
% 9.27/1.78 X214 ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 ~
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X220 @
% 9.27/1.78 X216 ) ) =>
% 9.27/1.78 (
% 9.27/1.78 ~
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X220 @
% 9.27/1.78 (
% 9.27/1.78 binintersect
% 9.27/1.78 @
% 9.27/1.78 X216 @
% 9.27/1.78 X218 ) ) ) ) ) ) ) ) ) ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 ![
% 9.27/1.78 X222:$i,
% 9.27/1.78 X224:$i]:
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X224 @
% 9.27/1.78 (
% 9.27/1.78 powerset
% 9.27/1.78 @
% 9.27/1.78 X222 ) ) =>
% 9.27/1.78 (
% 9.27/1.78 ![
% 9.27/1.78 X226:$i]:
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X226 @
% 9.27/1.78 (
% 9.27/1.78 powerset
% 9.27/1.78 @
% 9.27/1.78 X222 ) ) =>
% 9.27/1.78 (
% 9.27/1.78 ![
% 9.27/1.78 X228:$i]:
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X228 @
% 9.27/1.78 X222 ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 ~
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X228 @
% 9.27/1.78 X226 ) ) =>
% 9.27/1.78 (
% 9.27/1.78 ~
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X228 @
% 9.27/1.78 (
% 9.27/1.78 binintersect
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% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 contrasubsetT ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 contrasubsetT1 ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 contrasubsetT2 ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 contrasubsetT3 ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 doubleComplementI1 ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 doubleComplementE1 ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 doubleComplementSub1 ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 doubleComplementSub2 ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 doubleComplementEq ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 ![
% 9.27/1.78 X230:$i,
% 9.27/1.78 X232:$i]:
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X232 @
% 9.27/1.78 (
% 9.27/1.78 powerset
% 9.27/1.78 @
% 9.27/1.78 X230 ) ) =>
% 9.27/1.78 (
% 9.27/1.78 ![
% 9.27/1.78 X234:$i]:
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X234 @
% 9.27/1.78 (
% 9.27/1.78 powerset
% 9.27/1.78 @
% 9.27/1.78 X230 ) ) =>
% 9.27/1.78 (
% 9.27/1.78 ![
% 9.27/1.78 X236:$i]:
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X236 @
% 9.27/1.78 X230 ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X236 @
% 9.27/1.78 (
% 9.27/1.78 setminus
% 9.27/1.78 @
% 9.27/1.78 X230 @
% 9.27/1.78 X232 ) ) =>
% 9.27/1.78 (
% 9.27/1.78 ~
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X236 @
% 9.27/1.78 (
% 9.27/1.78 binintersect
% 9.27/1.78 @
% 9.27/1.78 X232 @
% 9.27/1.78 X234 ) ) ) ) ) ) ) ) ) ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 ![
% 9.27/1.78 X238:$i,
% 9.27/1.78 X240:$i]:
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X240 @
% 9.27/1.78 (
% 9.27/1.78 powerset
% 9.27/1.78 @
% 9.27/1.78 X238 ) ) =>
% 9.27/1.78 (
% 9.27/1.78 ![
% 9.27/1.78 X242:$i]:
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X242 @
% 9.27/1.78 (
% 9.27/1.78 powerset
% 9.27/1.78 @
% 9.27/1.78 X238 ) ) =>
% 9.27/1.78 (
% 9.27/1.78 ![
% 9.27/1.78 X244:$i]:
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X244 @
% 9.27/1.78 X238 ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X244 @
% 9.27/1.78 (
% 9.27/1.78 setminus
% 9.27/1.78 @
% 9.27/1.78 X238 @
% 9.27/1.78 X240 ) ) =>
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X244 @
% 9.27/1.78 (
% 9.27/1.78 setminus
% 9.27/1.78 @
% 9.27/1.78 X238 @
% 9.27/1.78 (
% 9.27/1.78 binintersect
% 9.27/1.78 @
% 9.27/1.78 X240 @
% 9.27/1.78 X242 ) ) ) ) ) ) ) ) ) ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 ![
% 9.27/1.78 X246:$i,
% 9.27/1.78 X248:$i]:
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X248 @
% 9.27/1.78 (
% 9.27/1.78 powerset
% 9.27/1.78 @
% 9.27/1.78 X246 ) ) =>
% 9.27/1.78 (
% 9.27/1.78 ![
% 9.27/1.78 X250:$i]:
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X250 @
% 9.27/1.78 (
% 9.27/1.78 powerset
% 9.27/1.78 @
% 9.27/1.78 X246 ) ) =>
% 9.27/1.78 (
% 9.27/1.78 subset @
% 9.27/1.78 (
% 9.27/1.78 setminus
% 9.27/1.78 @
% 9.27/1.78 X246 @
% 9.27/1.78 X248 ) @
% 9.27/1.78 (
% 9.27/1.78 setminus
% 9.27/1.78 @
% 9.27/1.78 X246 @
% 9.27/1.78 (
% 9.27/1.78 binintersect
% 9.27/1.78 @
% 9.27/1.78 X248 @
% 9.27/1.78 X250 ) ) ) ) ) ) ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 ![
% 9.27/1.78 X252:$i,
% 9.27/1.78 X254:$i]:
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X254 @
% 9.27/1.78 (
% 9.27/1.78 powerset
% 9.27/1.78 @
% 9.27/1.78 X252 ) ) =>
% 9.27/1.78 (
% 9.27/1.78 ![
% 9.27/1.78 X256:$i]:
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X256 @
% 9.27/1.78 (
% 9.27/1.78 powerset
% 9.27/1.78 @
% 9.27/1.78 X252 ) ) =>
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 (
% 9.27/1.78 setminus
% 9.27/1.78 @
% 9.27/1.78 X252 @
% 9.27/1.78 X254 ) @
% 9.27/1.78 (
% 9.27/1.78 powerset
% 9.27/1.78 @
% 9.27/1.78 (
% 9.27/1.78 setminus
% 9.27/1.78 @
% 9.27/1.78 X252 @
% 9.27/1.78 (
% 9.27/1.78 binintersect
% 9.27/1.78 @
% 9.27/1.78 X254 @
% 9.27/1.78 X256 ) ) ) ) ) ) ) ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 contraSubsetComplement ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 complementTcontraSubset ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 ![
% 9.27/1.78 X258:$i,
% 9.27/1.78 X260:$i]:
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X260 @
% 9.27/1.78 (
% 9.27/1.78 powerset
% 9.27/1.78 @
% 9.27/1.78 X258 ) ) =>
% 9.27/1.78 (
% 9.27/1.78 ![
% 9.27/1.78 X262:$i]:
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X262 @
% 9.27/1.78 (
% 9.27/1.78 powerset
% 9.27/1.78 @
% 9.27/1.78 X258 ) ) =>
% 9.27/1.78 (
% 9.27/1.78 ![
% 9.27/1.78 X264:$i]:
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X264 @
% 9.27/1.78 X258 ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 ~
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X264 @
% 9.27/1.78 (
% 9.27/1.78 binunion
% 9.27/1.78 @
% 9.27/1.78 X260 @
% 9.27/1.78 X262 ) ) ) =>
% 9.27/1.78 (
% 9.27/1.78 ~
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X264 @
% 9.27/1.78 X260 ) ) ) ) ) ) ) ) ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 ![
% 9.27/1.78 X266:$i,
% 9.27/1.78 X268:$i]:
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X268 @
% 9.27/1.78 (
% 9.27/1.78 powerset
% 9.27/1.78 @
% 9.27/1.78 X266 ) ) =>
% 9.27/1.78 (
% 9.27/1.78 ![
% 9.27/1.78 X270:$i]:
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X270 @
% 9.27/1.78 (
% 9.27/1.78 powerset
% 9.27/1.78 @
% 9.27/1.78 X266 ) ) =>
% 9.27/1.78 (
% 9.27/1.78 ![
% 9.27/1.78 X272:$i]:
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X272 @
% 9.27/1.78 X266 ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 ~
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X272 @
% 9.27/1.78 (
% 9.27/1.78 binunion
% 9.27/1.78 @
% 9.27/1.78 X268 @
% 9.27/1.78 X270 ) ) ) =>
% 9.27/1.78 (
% 9.27/1.78 ~
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X272 @
% 9.27/1.78 X270 ) ) ) ) ) ) ) ) ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 ![
% 9.27/1.78 X274:$i,
% 9.27/1.78 X276:$i]:
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X276 @
% 9.27/1.78 (
% 9.27/1.78 powerset
% 9.27/1.78 @
% 9.27/1.78 X274 ) ) =>
% 9.27/1.78 (
% 9.27/1.78 ![
% 9.27/1.78 X278:$i]:
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X278 @
% 9.27/1.78 (
% 9.27/1.78 powerset
% 9.27/1.78 @
% 9.27/1.78 X274 ) ) =>
% 9.27/1.78 (
% 9.27/1.78 ![
% 9.27/1.78 X280:$i]:
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X280 @
% 9.27/1.78 (
% 9.27/1.78 powerset
% 9.27/1.78 @
% 9.27/1.78 X274 ) ) =>
% 9.27/1.78 (
% 9.27/1.78 ![
% 9.27/1.78 X282:$i]:
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X282 @
% 9.27/1.78 X274 ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X282 @
% 9.27/1.78 (
% 9.27/1.78 binintersect
% 9.27/1.78 @
% 9.27/1.78 X276 @
% 9.27/1.78 X278 ) ) =>
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X282 @
% 9.27/1.78 (
% 9.27/1.78 binunion
% 9.27/1.78 @
% 9.27/1.78 X276 @
% 9.27/1.78 X280 ) ) ) ) ) ) ) ) ) ) ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 ![
% 9.27/1.78 X284:$i,
% 9.27/1.78 X286:$i]:
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X286 @
% 9.27/1.78 (
% 9.27/1.78 powerset
% 9.27/1.78 @
% 9.27/1.78 X284 ) ) =>
% 9.27/1.78 (
% 9.27/1.78 ![
% 9.27/1.78 X288:$i]:
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X288 @
% 9.27/1.78 (
% 9.27/1.78 powerset
% 9.27/1.78 @
% 9.27/1.78 X284 ) ) =>
% 9.27/1.78 (
% 9.27/1.78 ![
% 9.27/1.78 X290:$i]:
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X290 @
% 9.27/1.78 (
% 9.27/1.78 powerset
% 9.27/1.78 @
% 9.27/1.78 X284 ) ) =>
% 9.27/1.78 (
% 9.27/1.78 ![
% 9.27/1.78 X292:$i]:
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X292 @
% 9.27/1.78 X284 ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X292 @
% 9.27/1.78 (
% 9.27/1.78 binintersect
% 9.27/1.78 @
% 9.27/1.78 X286 @
% 9.27/1.78 X288 ) ) =>
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X292 @
% 9.27/1.78 (
% 9.27/1.78 binunion
% 9.27/1.78 @
% 9.27/1.78 X288 @
% 9.27/1.78 X290 ) ) ) ) ) ) ) ) ) ) ) =>
% 9.27/1.78 (
% 9.27/1.78 ![
% 9.27/1.78 X294:$i,
% 9.27/1.78 X296:$i]:
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X296 @
% 9.27/1.78 (
% 9.27/1.78 powerset
% 9.27/1.78 @
% 9.27/1.78 X294 ) ) =>
% 9.27/1.78 (
% 9.27/1.78 ![
% 9.27/1.78 X298:$i]:
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X298 @
% 9.27/1.78 (
% 9.27/1.78 powerset
% 9.27/1.78 @
% 9.27/1.78 X294 ) ) =>
% 9.27/1.78 (
% 9.27/1.78 ![
% 9.27/1.78 X300:$i]:
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X300 @
% 9.27/1.78 (
% 9.27/1.78 powerset
% 9.27/1.78 @
% 9.27/1.78 X294 ) ) =>
% 9.27/1.78 (
% 9.27/1.78 ![
% 9.27/1.78 X302:$i]:
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X302 @
% 9.27/1.78 X294 ) =>
% 9.27/1.78 (
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X302 @
% 9.27/1.78 (
% 9.27/1.78 binintersect
% 9.27/1.78 @
% 9.27/1.78 X296 @
% 9.27/1.78 X298 ) ) =>
% 9.27/1.78 (
% 9.27/1.78 in @
% 9.27/1.78 X302 @
% 9.27/1.78 (
% 9.27/1.78 binintersect
% 9.27/1.78 @
% 9.27/1.78 (
% 9.27/1.78 binunion
% 9.27/1.78 @
% 9.27/1.78 X296 @
% 9.27/1.78 X300 ) @
% 9.27/1.78 (
% 9.27/1.78 binunion
% 9.27/1.78 @
% 9.27/1.78 X298 @
% 9.27/1.78 X300 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 9.27/1.78 inference('cnf.neg', [status(esa)], [zf_stmt_3])).
% 9.27/1.78 thf(zip_derived_cl53, plain,
% 9.27/1.78 (![X4 : $i, X5 : $i, X6 : $i]:
% 9.27/1.78 ( (in @ X4 @ (binunion @ X5 @ X6)) | ~ (in @ X4 @ X5))),
% 9.27/1.78 inference('cnf', [status(esa)], [zf_stmt_4])).
% 9.27/1.78 thf(zip_derived_cl53, plain,
% 9.27/1.78 (![X4 : $i, X5 : $i, X6 : $i]:
% 9.27/1.78 ( (in @ X4 @ (binunion @ X5 @ X6)) | ~ (in @ X4 @ X5))),
% 9.27/1.78 inference('cnf', [status(esa)], [zf_stmt_4])).
% 9.27/1.78 thf(zip_derived_cl226, plain,
% 9.27/1.78 (![X122 : $i, X123 : $i, X124 : $i]:
% 9.27/1.78 (~ (in @ X122 @ X123)
% 9.27/1.78 | (in @ X122 @ (binintersect @ X124 @ X123))
% 9.27/1.78 | ~ (in @ X122 @ X124))),
% 9.27/1.78 inference('cnf', [status(esa)], [zf_stmt_4])).
% 9.27/1.78 thf(zip_derived_cl136, plain,
% 9.27/1.78 (~ (in @ sk__154 @
% 9.27/1.78 (binintersect @ (binunion @ sk__151 @ sk__153) @
% 9.27/1.78 (binunion @ sk__152 @ sk__153)))),
% 9.27/1.78 inference('cnf', [status(esa)], [zf_stmt_4])).
% 9.27/1.78 thf(zip_derived_cl2556, plain,
% 9.27/1.78 ((~ (in @ sk__154 @ (binunion @ sk__151 @ sk__153))
% 9.27/1.78 | ~ (in @ sk__154 @ (binunion @ sk__152 @ sk__153)))),
% 9.27/1.78 inference('sup-', [status(thm)], [zip_derived_cl226, zip_derived_cl136])).
% 9.27/1.78 thf(zip_derived_cl2602, plain,
% 9.27/1.78 ((~ (in @ sk__154 @ sk__151)
% 9.27/1.78 | ~ (in @ sk__154 @ (binunion @ sk__152 @ sk__153)))),
% 9.27/1.78 inference('sup-', [status(thm)], [zip_derived_cl53, zip_derived_cl2556])).
% 9.27/1.78 thf(zip_derived_cl137, plain,
% 9.27/1.78 ( (in @ sk__154 @ (binintersect @ sk__151 @ sk__152))),
% 9.27/1.78 inference('cnf', [status(esa)], [zf_stmt_4])).
% 9.27/1.78 thf(zip_derived_cl225, plain,
% 9.27/1.78 (![X119 : $i, X120 : $i, X121 : $i]:
% 9.27/1.78 ( (in @ X119 @ X120) | ~ (in @ X119 @ (binintersect @ X120 @ X121)))),
% 9.27/1.78 inference('cnf', [status(esa)], [zf_stmt_4])).
% 9.27/1.78 thf(zip_derived_cl388, plain, ( (in @ sk__154 @ sk__151)),
% 9.27/1.78 inference('sup-', [status(thm)], [zip_derived_cl137, zip_derived_cl225])).
% 9.27/1.78 thf(zip_derived_cl2607, plain,
% 9.27/1.78 (~ (in @ sk__154 @ (binunion @ sk__152 @ sk__153))),
% 9.27/1.78 inference('demod', [status(thm)], [zip_derived_cl2602, zip_derived_cl388])).
% 9.27/1.78 thf(zip_derived_cl2612, plain, (~ (in @ sk__154 @ sk__152)),
% 9.27/1.78 inference('sup-', [status(thm)], [zip_derived_cl53, zip_derived_cl2607])).
% 9.27/1.78 thf(zip_derived_cl137, plain,
% 9.27/1.78 ( (in @ sk__154 @ (binintersect @ sk__151 @ sk__152))),
% 9.27/1.78 inference('cnf', [status(esa)], [zf_stmt_4])).
% 9.27/1.78 thf(zip_derived_cl223, plain,
% 9.27/1.78 (![X114 : $i, X115 : $i, X116 : $i]:
% 9.27/1.78 ( (in @ X114 @ X115) | ~ (in @ X114 @ (binintersect @ X116 @ X115)))),
% 9.27/1.78 inference('cnf', [status(esa)], [zf_stmt_4])).
% 9.27/1.78 thf(zip_derived_cl370, plain, ( (in @ sk__154 @ sk__152)),
% 9.27/1.78 inference('sup-', [status(thm)], [zip_derived_cl137, zip_derived_cl223])).
% 9.27/1.78 thf(zip_derived_cl2617, plain, ($false),
% 9.27/1.78 inference('demod', [status(thm)], [zip_derived_cl2612, zip_derived_cl370])).
% 9.27/1.78
% 9.27/1.78 % SZS output end Refutation
% 9.27/1.78
% 9.27/1.78
% 9.27/1.78 % Terminating...
% 9.27/1.78 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s
% 10.30/2.01 % Runner terminated.
% 10.30/2.03 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------