%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU768^1 : TPTP v9.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.Bvc8uGUGwV true
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 2 04:56:14 PM UTC 2025
% Result : Theorem 139.73s 20.54s
% Output : Refutation 139.99s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU768^1 : TPTP v9.2.0. Released v3.7.0.
% 0.07/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.Bvc8uGUGwV true
% 0.14/0.34 % Computer : n009.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Oct 1 16:06:23 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % Running portfolio for 300 s
% 0.14/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.35 % Number of cores: 8
% 0.14/0.35 % Python version: Python 3.6.8
% 0.14/0.35 % Running in HO mode
% 0.58/0.69 % Total configuration time : 828
% 0.58/0.69 % Estimated wc time : 1656
% 0.58/0.69 % Estimated cpu time (8 cpus) : 207.0
% 0.58/0.74 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.58/0.76 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.58/0.78 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.58/0.80 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.58/0.81 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.59/0.88 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.59/0.88 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.59/0.89 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 139.73/20.54 % Solved by lams/40_noforms.sh.
% 139.73/20.54 % done 1140 iterations in 19.294s
% 139.73/20.54 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 139.73/20.54 % SZS output start Refutation
% 139.73/20.54 thf(setadjoinAx_type, type, setadjoinAx: $o).
% 139.73/20.54 thf(notdexE_type, type, notdexE: $o).
% 139.73/20.54 thf(demorgan1a_type, type, demorgan1a: $o).
% 139.73/20.54 thf(setukpairinjL2_type, type, setukpairinjL2: $o).
% 139.73/20.54 thf(doubleComplementI1_type, type, doubleComplementI1: $o).
% 139.73/20.54 thf(setunionAx_type, type, setunionAx: $o).
% 139.73/20.54 thf(setminusELneg_type, type, setminusELneg: $o).
% 139.73/20.54 thf(cartprodsndin_type, type, cartprodsndin: $o).
% 139.73/20.54 thf(ex1E1_type, type, ex1E1: $o).
% 139.73/20.54 thf(powersetE_type, type, powersetE: $o).
% 139.73/20.54 thf(woz13rule4_type, type, woz13rule4: $o).
% 139.73/20.54 thf(omegaSAx_type, type, omegaSAx: $o).
% 139.73/20.54 thf(exuI1_type, type, exuI1: $o).
% 139.73/20.54 thf(exuI2_type, type, exuI2: $o).
% 139.73/20.54 thf(notequalI2_type, type, notequalI2: $o).
% 139.73/20.54 thf(setukpairinjL_type, type, setukpairinjL: $o).
% 139.73/20.54 thf(woz13rule1_type, type, woz13rule1: $o).
% 139.73/20.54 thf(kpairiskpair_type, type, kpairiskpair: $o).
% 139.73/20.54 thf(upairsubunion_type, type, upairsubunion: $o).
% 139.73/20.54 thf(funcGraphProp3_type, type, funcGraphProp3: $o).
% 139.73/20.54 thf(binunionTE_type, type, binunionTE: $o).
% 139.73/20.54 thf(cartprodmempaircEq_type, type, cartprodmempaircEq: $o).
% 139.73/20.54 thf(binintersectTERcontra_type, type, binintersectTERcontra: $o).
% 139.73/20.54 thf(powerset__Cong_type, type, powerset__Cong: $o).
% 139.73/20.54 thf(setminusILneg_type, type, setminusILneg: $o).
% 139.73/20.54 thf(sk__956_type, type, sk__956: $i).
% 139.73/20.54 thf(wellorderingAx_type, type, wellorderingAx: $o).
% 139.73/20.54 thf(ksndpairEq_type, type, ksndpairEq: $o).
% 139.73/20.54 thf(funcGraphProp2_type, type, funcGraphProp2: $o).
% 139.73/20.54 thf(setadjoinSub2_type, type, setadjoinSub2: $o).
% 139.73/20.54 thf(binintersectSubset5_type, type, binintersectSubset5: $o).
% 139.73/20.54 thf(iftrue_type, type, iftrue: $o).
% 139.73/20.54 thf(upairinpowunion_type, type, upairinpowunion: $o).
% 139.73/20.54 thf(ifSingleton_type, type, ifSingleton: $o).
% 139.73/20.54 thf(doubleComplementSub2_type, type, doubleComplementSub2: $o).
% 139.73/20.54 thf(setoftrueEq_type, type, setoftrueEq: $o).
% 139.73/20.54 thf(funcImageSingleton_type, type, funcImageSingleton: $o).
% 139.73/20.54 thf(ksnd_type, type, ksnd: $i > $i).
% 139.73/20.54 thf(inIntersectImpInUnion2_type, type, inIntersectImpInUnion2: $o).
% 139.73/20.54 thf(dpsetconstrERa_type, type, dpsetconstrERa: $o).
% 139.73/20.54 thf(demorgan2b2_type, type, demorgan2b2: $o).
% 139.73/20.54 thf(lamProp_type, type, lamProp: $o).
% 139.73/20.54 thf(cartprodpairmemEL_type, type, cartprodpairmemEL: $o).
% 139.73/20.54 thf(emptyset__Cong_type, type, emptyset__Cong: $o).
% 139.73/20.54 thf(demorgan2_type, type, demorgan2: $o).
% 139.73/20.54 thf(dpsetconstrER_type, type, dpsetconstrER: $o).
% 139.73/20.54 thf(sepInPowerset_type, type, sepInPowerset: $o).
% 139.73/20.54 thf(setukpairIR_type, type, setukpairIR: $o).
% 139.73/20.54 thf(setukpairinjR1_type, type, setukpairinjR1: $o).
% 139.73/20.54 thf(lam2p_type, type, lam2p: $o).
% 139.73/20.54 thf(kpair_type, type, kpair: $i > $i > $i).
% 139.73/20.54 thf(binunionE_type, type, binunionE: $o).
% 139.73/20.54 thf(setext_type, type, setext: $o).
% 139.73/20.54 thf(emptyinPowerset_type, type, emptyinPowerset: $o).
% 139.73/20.54 thf(ubforcartprodlem1_type, type, ubforcartprodlem1: $o).
% 139.73/20.54 thf(zip_tseitin_5_type, type, zip_tseitin_5: $i > ($i > $o) > $o).
% 139.73/20.54 thf(descr__Cong_type, type, descr__Cong: $o).
% 139.73/20.54 thf(kfstsingleton_type, type, kfstsingleton: $o).
% 139.73/20.54 thf(binintersectTELcontra_type, type, binintersectTELcontra: $o).
% 139.73/20.54 thf(doubleComplementEq_type, type, doubleComplementEq: $o).
% 139.73/20.54 thf(eqbreln_type, type, eqbreln: $o).
% 139.73/20.54 thf(binintersectSubset1_type, type, binintersectSubset1: $o).
% 139.73/20.54 thf(inComplementUnionImpInComplement1_type, type, inComplementUnionImpInComplement1:
% 139.73/20.54 $o).
% 139.73/20.54 thf(complementImpComplementIntersect_type, type, complementImpComplementIntersect:
% 139.73/20.54 $o).
% 139.73/20.54 thf(in_type, type, in: $i > $i > $o).
% 139.73/20.54 thf(binunionT_lem_type, type, binunionT_lem: $o).
% 139.73/20.54 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o).
% 139.73/20.54 thf(complementT_lem_type, type, complementT_lem: $o).
% 139.73/20.54 thf(binunion_type, type, binunion: $i > $i > $i).
% 139.73/20.54 thf(kpairsurjEq_type, type, kpairsurjEq: $o).
% 139.73/20.54 thf(setadjoinIR_type, type, setadjoinIR: $o).
% 139.73/20.54 thf(doubleComplementE1_type, type, doubleComplementE1: $o).
% 139.73/20.54 thf(beta1_type, type, beta1: $o).
% 139.73/20.54 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o).
% 139.73/20.54 thf(powersetTE1_type, type, powersetTE1: $o).
% 139.73/20.54 thf(symdiffI2_type, type, symdiffI2: $o).
% 139.73/20.54 thf(iftrueProp2_type, type, iftrueProp2: $o).
% 139.73/20.54 thf(upairset2IR_type, type, upairset2IR: $o).
% 139.73/20.54 thf(iffalseProp2_type, type, iffalseProp2: $o).
% 139.73/20.54 thf(lam_type, type, lam: $i > $i > ($i > $i) > $i).
% 139.73/20.54 thf(subsetE_type, type, subsetE: $o).
% 139.73/20.54 thf(prop2set2propI_type, type, prop2set2propI: $o).
% 139.73/20.54 thf(demorgan2a_type, type, demorgan2a: $o).
% 139.73/20.54 thf(dsetconstrEL_type, type, dsetconstrEL: $o).
% 139.73/20.54 thf(setbeta_type, type, setbeta: $o).
% 139.73/20.54 thf(eqinunit_type, type, eqinunit: $o).
% 139.73/20.54 thf(upairsetIL_type, type, upairsetIL: $o).
% 139.73/20.54 thf(powersetI1_type, type, powersetI1: $o).
% 139.73/20.54 thf(kfstpairEq_type, type, kfstpairEq: $o).
% 139.73/20.54 thf(binintersectSubset3_type, type, binintersectSubset3: $o).
% 139.73/20.54 thf(inComplementUnionImpNotIn1_type, type, inComplementUnionImpNotIn1: $o).
% 139.73/20.54 thf(setminusIRneg_type, type, setminusIRneg: $o).
% 139.73/20.54 thf(ap2apEq1_type, type, ap2apEq1: $o).
% 139.73/20.54 thf(powersetAx_type, type, powersetAx: $o).
% 139.73/20.54 thf(binintersectSubset4_type, type, binintersectSubset4: $o).
% 139.73/20.54 thf(singletoninpowunion_type, type, singletoninpowunion: $o).
% 139.73/20.54 thf(binunionTIRcontra_type, type, binunionTIRcontra: $o).
% 139.73/20.54 thf(powersetI_type, type, powersetI: $o).
% 139.73/20.54 thf(cartprodmempair_type, type, cartprodmempair: $o).
% 139.73/20.54 thf(upairsetIR_type, type, upairsetIR: $o).
% 139.73/20.54 thf(lamp_type, type, lamp: $o).
% 139.73/20.54 thf(dpsetconstrEL1_type, type, dpsetconstrEL1: $o).
% 139.73/20.54 thf(inCongP_type, type, inCongP: $o).
% 139.73/20.54 thf(setadjoinSub_type, type, setadjoinSub: $o).
% 139.73/20.54 thf(exuE3e_type, type, exuE3e: $o).
% 139.73/20.54 thf(emptysetE_type, type, emptysetE: $o).
% 139.73/20.54 thf(binintersectSubset2_type, type, binintersectSubset2: $o).
% 139.73/20.54 thf(setunionI_type, type, setunionI: $o).
% 139.73/20.54 thf(symdiff_type, type, symdiff: $i > $i > $i).
% 139.73/20.54 thf(setunion__Cong_type, type, setunion__Cong: $o).
% 139.73/20.54 thf(prop2setI_type, type, prop2setI: $o).
% 139.73/20.54 thf(singletonsuniq_type, type, singletonsuniq: $o).
% 139.73/20.54 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o).
% 139.73/20.54 thf(setminusER_type, type, setminusER: $o).
% 139.73/20.54 thf(exuE2_type, type, exuE2: $o).
% 139.73/20.54 thf(emptyset_type, type, emptyset: $i).
% 139.73/20.54 thf(setukpairinjR11_type, type, setukpairinjR11: $o).
% 139.73/20.54 thf(ex1I_type, type, ex1I: $o).
% 139.73/20.54 thf(ex1E2_type, type, ex1E2: $o).
% 139.73/20.54 thf(setminus_type, type, setminus: $i > $i > $i).
% 139.73/20.54 thf(setukpairinjL1_type, type, setukpairinjL1: $o).
% 139.73/20.54 thf(powersetsubset_type, type, powersetsubset: $o).
% 139.73/20.54 thf(binunionTILcontra_type, type, binunionTILcontra: $o).
% 139.73/20.54 thf(subPowSU_type, type, subPowSU: $o).
% 139.73/20.54 thf(notequalI1_type, type, notequalI1: $o).
% 139.73/20.54 thf(contrasubsetT_type, type, contrasubsetT: $o).
% 139.73/20.54 thf(notinemptyset_type, type, notinemptyset: $o).
% 139.73/20.54 thf(lam2lamEq_type, type, lam2lamEq: $o).
% 139.73/20.54 thf(nonemptyI1_type, type, nonemptyI1: $o).
% 139.73/20.54 thf(subsetTrans_type, type, subsetTrans: $o).
% 139.73/20.54 thf(ap_type, type, ap: $i > $i > $i > $i > $i).
% 139.73/20.54 thf(kpairp_type, type, kpairp: $o).
% 139.73/20.54 thf(setukpairinjR12_type, type, setukpairinjR12: $o).
% 139.73/20.54 thf(setminusI_type, type, setminusI: $o).
% 139.73/20.54 thf(binunionIL_type, type, binunionIL: $o).
% 139.73/20.54 thf(dpsetconstrSub_type, type, dpsetconstrSub: $o).
% 139.73/20.54 thf(setunionsingleton_type, type, setunionsingleton: $o).
% 139.73/20.54 thf(subsetE2_type, type, subsetE2: $o).
% 139.73/20.54 thf(singletonsswitch_type, type, singletonsswitch: $o).
% 139.73/20.54 thf(ubforcartprodlem3_type, type, ubforcartprodlem3: $o).
% 139.73/20.54 thf(beta2_type, type, beta2: $o).
% 139.73/20.54 thf(dpsetconstrI_type, type, dpsetconstrI: $o).
% 139.73/20.54 thf(setextsub_type, type, setextsub: $o).
% 139.73/20.54 thf(binunionLsub_type, type, binunionLsub: $o).
% 139.73/20.54 thf(setunionsingleton1_type, type, setunionsingleton1: $o).
% 139.73/20.54 thf(binintersect_type, type, binintersect: $i > $i > $i).
% 139.73/20.54 thf(demorgan2a2_type, type, demorgan2a2: $o).
% 139.73/20.54 thf(complementUnionInPowersetComplement_type, type, complementUnionInPowersetComplement:
% 139.73/20.54 $o).
% 139.73/20.54 thf(iftrueorfalse_type, type, iftrueorfalse: $o).
% 139.73/20.54 thf(emptysetsubset_type, type, emptysetsubset: $o).
% 139.73/20.54 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o).
% 139.73/20.54 thf(cartprodpairsurjEq_type, type, cartprodpairsurjEq: $o).
% 139.73/20.54 thf(setOfPairsIsBReln_type, type, setOfPairsIsBReln: $o).
% 139.73/20.54 thf(setunionE_type, type, setunionE: $o).
% 139.73/20.54 thf(ksndsingleton_type, type, ksndsingleton: $o).
% 139.73/20.54 thf(setminusSubset1_type, type, setminusSubset1: $o).
% 139.73/20.54 thf(woz13rule0_type, type, woz13rule0: $o).
% 139.73/20.54 thf(powersetT_lem_type, type, powersetT_lem: $o).
% 139.73/20.54 thf(woz1_5_type, type, woz1_5: $o).
% 139.73/20.54 thf(funcSet_type, type, funcSet: $i > $i > $i).
% 139.73/20.54 thf(dpsetconstr_type, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 139.73/20.54 thf(emptyinunitempty_type, type, emptyinunitempty: $o).
% 139.73/20.54 thf(binunionIR_type, type, binunionIR: $o).
% 139.73/20.54 thf(theeq_type, type, theeq: $o).
% 139.73/20.54 thf(setadjoinE_type, type, setadjoinE: $o).
% 139.73/20.54 thf(doubleComplementSub1_type, type, doubleComplementSub1: $o).
% 139.73/20.54 thf(descr_type, type, descr: ($i > $o) > $i).
% 139.73/20.54 thf(ex1_type, type, ex1: $i > ($i > $o) > $o).
% 139.73/20.54 thf(infuncsetfunc_type, type, infuncsetfunc: $o).
% 139.73/20.54 thf(woz13rule3_type, type, woz13rule3: $o).
% 139.73/20.54 thf(zip_tseitin_2_type, type, zip_tseitin_2: $i > $i > $i > $o).
% 139.73/20.54 thf(ap2apEq2_type, type, ap2apEq2: $o).
% 139.73/20.54 thf(ap2p_type, type, ap2p: $o).
% 139.73/20.54 thf(zip_tseitin_3_type, type, zip_tseitin_3: $i > $i > $i > ($i > $i > $o) > $o).
% 139.73/20.54 thf(setadjoinIL_type, type, setadjoinIL: $o).
% 139.73/20.54 thf(cartprodsndpairEq_type, type, cartprodsndpairEq: $o).
% 139.73/20.54 thf(exuE1_type, type, exuE1: $o).
% 139.73/20.54 thf(ubforcartprodlem2_type, type, ubforcartprodlem2: $o).
% 139.73/20.54 thf(binintersectRsub_type, type, binintersectRsub: $o).
% 139.73/20.54 thf(setminusLsub_type, type, setminusLsub: $o).
% 139.73/20.54 thf(prop2set_type, type, prop2set: $o > $i).
% 139.73/20.54 thf(funcextLem_type, type, funcextLem: $o).
% 139.73/20.54 thf(setukpairinjR_type, type, setukpairinjR: $o).
% 139.73/20.54 thf(notinsingleton_type, type, notinsingleton: $o).
% 139.73/20.54 thf(inIntersectImpInIntersectUnions_type, type, inIntersectImpInIntersectUnions:
% 139.73/20.54 $o).
% 139.73/20.54 thf(eqimpsubset2_type, type, eqimpsubset2: $o).
% 139.73/20.54 thf(exuEu_type, type, exuEu: $o).
% 139.73/20.54 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o).
% 139.73/20.54 thf(upairsetE_type, type, upairsetE: $o).
% 139.73/20.54 thf(omega0Ax_type, type, omega0Ax: $o).
% 139.73/20.54 thf(subsetTI_type, type, subsetTI: $o).
% 139.73/20.54 thf(notsubsetI_type, type, notsubsetI: $o).
% 139.73/20.54 thf(contraSubsetComplement_type, type, contraSubsetComplement: $o).
% 139.73/20.54 thf(iffalseProp1_type, type, iffalseProp1: $o).
% 139.73/20.54 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o).
% 139.73/20.54 thf(setextAx_type, type, setextAx: $o).
% 139.73/20.54 thf(cartprodpairmemER_type, type, cartprodpairmemER: $o).
% 139.73/20.54 thf(powersetE1_type, type, powersetE1: $o).
% 139.73/20.54 thf(bs114d_type, type, bs114d: $o).
% 139.73/20.54 thf(breln1_type, type, breln1: $i > $i > $o).
% 139.73/20.54 thf(contrasubsetT3_type, type, contrasubsetT3: $o).
% 139.73/20.54 thf(noeltsimpempty_type, type, noeltsimpempty: $o).
% 139.73/20.54 thf(breln_type, type, breln: $i > $i > $i > $o).
% 139.73/20.54 thf(complementTcontraSubset_type, type, complementTcontraSubset: $o).
% 139.73/20.54 thf(setunion_type, type, setunion: $i > $i).
% 139.73/20.54 thf(woz1_3_type, type, woz1_3: $o).
% 139.73/20.54 thf(ifp_type, type, ifp: $o).
% 139.73/20.54 thf(iskpair_type, type, iskpair: $i > $o).
% 139.73/20.54 thf(inIntersectImpInUnion_type, type, inIntersectImpInUnion: $o).
% 139.73/20.54 thf(powersetTI1_type, type, powersetTI1: $o).
% 139.73/20.54 thf(binintersectLsub_type, type, binintersectLsub: $o).
% 139.73/20.54 thf(subsetI1_type, type, subsetI1: $o).
% 139.73/20.54 thf(symdiffE_type, type, symdiffE: $o).
% 139.73/20.54 thf(descrp_type, type, descrp: $o).
% 139.73/20.54 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o).
% 139.73/20.54 thf(foundationAx_type, type, foundationAx: $o).
% 139.73/20.54 thf(emptysetAx_type, type, emptysetAx: $o).
% 139.73/20.54 thf(emptyI_type, type, emptyI: $o).
% 139.73/20.54 thf(setadjoinOr_type, type, setadjoinOr: $o).
% 139.73/20.54 thf(eta2_type, type, eta2: $o).
% 139.73/20.54 thf(binintersectEL_type, type, binintersectEL: $o).
% 139.73/20.54 thf(emptyE1_type, type, emptyE1: $o).
% 139.73/20.54 thf(woz1_2_type, type, woz1_2: $o).
% 139.73/20.54 thf(emptyInPowerset_type, type, emptyInPowerset: $o).
% 139.73/20.54 thf(complementTI1_type, type, complementTI1: $o).
% 139.73/20.54 thf(vacuousDall_type, type, vacuousDall: $o).
% 139.73/20.54 thf(dsetconstr_type, type, dsetconstr: $i > ($i > $o) > $i).
% 139.73/20.54 thf(dsetconstrER_type, type, dsetconstrER: $o).
% 139.73/20.54 thf(exu_type, type, exu: ($i > $o) > $o).
% 139.73/20.54 thf(binintersectI_type, type, binintersectI: $o).
% 139.73/20.54 thf(woz1_4_type, type, woz1_4: $o).
% 139.73/20.54 thf(funcext_type, type, funcext: $o).
% 139.73/20.54 thf(funcGraphProp4_type, type, funcGraphProp4: $o).
% 139.73/20.54 thf(cartprodpairin_type, type, cartprodpairin: $o).
% 139.73/20.54 thf(func_type, type, func: $i > $i > $i > $o).
% 139.73/20.54 thf(cartprodmempair1_type, type, cartprodmempair1: $o).
% 139.73/20.54 thf(woz13rule2_type, type, woz13rule2: $o).
% 139.73/20.54 thf(brelnall2_type, type, brelnall2: $o).
% 139.73/20.54 thf(setextT_type, type, setextT: $o).
% 139.73/20.54 thf(singleton_type, type, singleton: $i > $o).
% 139.73/20.54 thf(ex1I2_type, type, ex1I2: $o).
% 139.73/20.54 thf(symdiffI1_type, type, symdiffI1: $o).
% 139.73/20.54 thf(setukpairinjR2_type, type, setukpairinjR2: $o).
% 139.73/20.54 thf(zip_tseitin_1_type, type, zip_tseitin_1: $i > $i > $i > $o).
% 139.73/20.54 thf(dpsetconstrEL2_type, type, dpsetconstrEL2: $o).
% 139.73/20.54 thf(theprop_type, type, theprop: $o).
% 139.73/20.54 thf(subsetI2_type, type, subsetI2: $o).
% 139.73/20.54 thf(complementInPowersetComplementIntersect_type, type, complementInPowersetComplementIntersect:
% 139.73/20.54 $o).
% 139.73/20.54 thf(demorgan1_type, type, demorgan1: $o).
% 139.73/20.54 thf(setminusT_lem_type, type, setminusT_lem: $o).
% 139.73/20.54 thf(symdiffIneg1_type, type, symdiffIneg1: $o).
% 139.73/20.54 thf(kfst_type, type, kfst: $i > $i).
% 139.73/20.54 thf(if_type, type, if: $i > $o > $i > $i > $i).
% 139.73/20.54 thf(setminusERneg_type, type, setminusERneg: $o).
% 139.73/20.54 thf(symdiffIneg2_type, type, symdiffIneg2: $o).
% 139.73/20.54 thf(omega__Cong_type, type, omega__Cong: $o).
% 139.73/20.54 thf(subsetRefl_type, type, subsetRefl: $o).
% 139.73/20.54 thf(uniqinunit_type, type, uniqinunit: $o).
% 139.73/20.54 thf(zip_tseitin_4_type, type, zip_tseitin_4: $i > $i > ($i > $o) > $o).
% 139.73/20.54 thf(sk__958_type, type, sk__958: $i > $o).
% 139.73/20.54 thf(complementSubsetComplementIntersect_type, type, complementSubsetComplementIntersect:
% 139.73/20.54 $o).
% 139.73/20.54 thf(demorgan2b_type, type, demorgan2b: $o).
% 139.73/20.54 thf(setminusSubset2_type, type, setminusSubset2: $o).
% 139.73/20.54 thf(prop2setE_type, type, prop2setE: $o).
% 139.73/20.54 thf(binunionEcases_type, type, binunionEcases: $o).
% 139.73/20.54 thf(funcinfuncset_type, type, funcinfuncset: $o).
% 139.73/20.54 thf(complementTE1_type, type, complementTE1: $o).
% 139.73/20.54 thf(omega_type, type, omega: $i).
% 139.73/20.54 thf(nonemptyI_type, type, nonemptyI: $o).
% 139.73/20.54 thf(app_type, type, app: $o).
% 139.73/20.54 thf(disjointsetsI1_type, type, disjointsetsI1: $o).
% 139.73/20.54 thf(sk__957_type, type, sk__957: $i).
% 139.73/20.54 thf(demorgan2a1_type, type, demorgan2a1: $o).
% 139.73/20.54 thf(exuE3u_type, type, exuE3u: $o).
% 139.73/20.54 thf(eta1_type, type, eta1: $o).
% 139.73/20.54 thf(setminusEL_type, type, setminusEL: $o).
% 139.73/20.54 thf(cartprodfstin_type, type, cartprodfstin: $o).
% 139.73/20.54 thf(zip_tseitin_0_type, type, zip_tseitin_0: $i > $i > $i > $o).
% 139.73/20.54 thf(setunionsingleton2_type, type, setunionsingleton2: $o).
% 139.73/20.54 thf(sepSubset_type, type, sepSubset: $o).
% 139.73/20.54 thf(complementTnotintersectT_type, type, complementTnotintersectT: $o).
% 139.73/20.54 thf(upairset2E_type, type, upairset2E: $o).
% 139.73/20.54 thf(eqimpsubset1_type, type, eqimpsubset1: $o).
% 139.73/20.54 thf(exuI3_type, type, exuI3: $o).
% 139.73/20.54 thf(cartprodfstpairEq_type, type, cartprodfstpairEq: $o).
% 139.73/20.54 thf(apProp_type, type, apProp: $o).
% 139.73/20.54 thf(notdallE_type, type, notdallE: $o).
% 139.73/20.54 thf(iftrueProp1_type, type, iftrueProp1: $o).
% 139.73/20.54 thf(binintersectER_type, type, binintersectER: $o).
% 139.73/20.54 thf(brelnall1_type, type, brelnall1: $o).
% 139.73/20.54 thf(powerset_type, type, powerset: $i > $i).
% 139.73/20.54 thf(binunionTEcontra_type, type, binunionTEcontra: $o).
% 139.73/20.54 thf(demorgan1b_type, type, demorgan1b: $o).
% 139.73/20.54 thf(dsetconstrI_type, type, dsetconstrI: $o).
% 139.73/20.54 thf(nonempty_type, type, nonempty: $i > $o).
% 139.73/20.54 thf(set2prop_type, type, set2prop: $i > $o).
% 139.73/20.54 thf(funcGraphProp1_type, type, funcGraphProp1: $o).
% 139.73/20.54 thf(binintersectT_lem_type, type, binintersectT_lem: $o).
% 139.73/20.54 thf(setadjoin_type, type, setadjoin: $i > $i > $i).
% 139.73/20.54 thf(exu__Cong_type, type, exu__Cong: $o).
% 139.73/20.54 thf(intersectInPowersetIntersectUnions_type, type, intersectInPowersetIntersectUnions:
% 139.73/20.54 $o).
% 139.73/20.54 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o).
% 139.73/20.54 thf(contrasubsetT2_type, type, contrasubsetT2: $o).
% 139.73/20.54 thf(secondinupair_type, type, secondinupair: $o).
% 139.73/20.54 thf(singletonprop_type, type, singletonprop: $o).
% 139.73/20.54 thf(singletonsubset_type, type, singletonsubset: $o).
% 139.73/20.54 thf(contrasubsetT1_type, type, contrasubsetT1: $o).
% 139.73/20.54 thf(singletoninpowerset_type, type, singletoninpowerset: $o).
% 139.73/20.54 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o).
% 139.73/20.54 thf(replAx_type, type, replAx: $o).
% 139.73/20.54 thf(upairequniteq_type, type, upairequniteq: $o).
% 139.73/20.54 thf(nonemptyE1_type, type, nonemptyE1: $o).
% 139.73/20.54 thf(omegaIndAx_type, type, omegaIndAx: $o).
% 139.73/20.54 thf(setukpairIL_type, type, setukpairIL: $o).
% 139.73/20.54 thf(setunionE2_type, type, setunionE2: $o).
% 139.73/20.54 thf(inPowerset_type, type, inPowerset: $o).
% 139.73/20.54 thf(iffalse_type, type, iffalse: $o).
% 139.73/20.54 thf(funcext2_type, type, funcext2: $o).
% 139.73/20.54 thf(cartprod_type, type, cartprod: $i > $i > $i).
% 139.73/20.54 thf(subset_type, type, subset: $i > $i > $o).
% 139.73/20.54 thf(woz1_1_type, type, woz1_1: $o).
% 139.73/20.54 thf(subbreln_type, type, subbreln: $o).
% 139.73/20.54 thf(in__Cong_type, type, in__Cong: $o).
% 139.73/20.54 thf(sk__959_type, type, sk__959: $i).
% 139.73/20.54 thf(binunionRsub_type, type, binunionRsub: $o).
% 139.73/20.54 thf(subset2powerset_type, type, subset2powerset: $o).
% 139.73/20.54 thf(breln1, axiom,(( breln1 ) = (^[A:$i,R:$i]: ( breln @ A @ A @ R )))).
% 139.73/20.54 thf(breln, axiom,(( breln ) =
% 139.73/20.54 (^[A:$i,B:$i,C:$i]: ( subset @ C @ ( cartprod @ A @ B ) )))).
% 139.73/20.54 thf('0', plain,
% 139.73/20.54 (( breln ) = ( ^[A:$i,B:$i,C:$i]: ( subset @ C @ ( cartprod @ A @ B ) ) )),
% 139.73/20.54 inference('simplify_rw_rule', [status(thm)], [breln])).
% 139.73/20.54 thf('1', plain,
% 139.73/20.54 (( breln ) =
% 139.73/20.54 ( ^[V_1:$i,V_2:$i,V_3:$i]: ( subset @ V_3 @ ( cartprod @ V_1 @ V_2 ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf('2', plain, (( breln1 ) = ( ^[A:$i,R:$i]: ( breln @ A @ A @ R ) )),
% 139.73/20.54 inference('simplify_rw_rule', [status(thm)], [breln1, '1'])).
% 139.73/20.54 thf('3', plain,
% 139.73/20.54 (( breln1 ) = ( ^[V_1:$i,V_2:$i]: ( breln @ V_1 @ V_1 @ V_2 ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(woz1_5, axiom, woz1_5 =
% 139.73/20.54 (![A:$i,X:$i]:
% 139.73/20.54 ( ( in @ X @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Y:$i]:
% 139.73/20.54 ( ( in @ Y @ ( powerset @ A ) ) =>
% 139.73/20.54 ( in @
% 139.73/20.54 ( setminus @ A @ ( binunion @ X @ Y ) ) @
% 139.73/20.54 ( powerset @ ( setminus @ A @ X ) ) ) ) ) ))).
% 139.73/20.54 thf('4', plain,
% 139.73/20.54 (( woz1_5 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( in @
% 139.73/20.54 ( setminus @ X4 @ ( binunion @ X6 @ X8 ) ) @
% 139.73/20.54 ( powerset @ ( setminus @ X4 @ X6 ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(woz1_4, axiom, woz1_4 =
% 139.73/20.54 (![A:$i,X:$i]:
% 139.73/20.54 ( ( in @ X @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Y:$i]:
% 139.73/20.54 ( ( in @ Y @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ( subset @ X @ ( setminus @ A @ Y ) ) =>
% 139.73/20.54 ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ))).
% 139.73/20.54 thf('5', plain,
% 139.73/20.54 (( woz1_4 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ( subset @ X6 @ ( setminus @ X4 @ X8 ) ) =>
% 139.73/20.54 ( subset @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(woz1_3, axiom, woz1_3 =
% 139.73/20.54 (![A:$i,X:$i]:
% 139.73/20.54 ( ( in @ X @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Y:$i]:
% 139.73/20.54 ( ( in @ Y @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Z:$i]:
% 139.73/20.54 ( ( in @ Z @ ( powerset @ A ) ) =>
% 139.73/20.54 ( in @
% 139.73/20.54 ( binintersect @ X @ Y ) @
% 139.73/20.54 ( powerset @
% 139.73/20.54 ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ))).
% 139.73/20.54 thf('6', plain,
% 139.73/20.54 (( woz1_3 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( in @
% 139.73/20.54 ( binintersect @ X6 @ X8 ) @
% 139.73/20.54 ( powerset @
% 139.73/20.54 ( binintersect @
% 139.73/20.54 ( binunion @ X6 @ X10 ) @ ( binunion @ X8 @ X10 ) ) ) ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(woz1_2, axiom, woz1_2 =
% 139.73/20.54 (![A:$i,X:$i]:
% 139.73/20.54 ( ( in @ X @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Y:$i]:
% 139.73/20.54 ( ( in @ Y @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Z:$i]:
% 139.73/20.54 ( ( in @ Z @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![W:$i]:
% 139.73/20.54 ( ( in @ W @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ( setminus @
% 139.73/20.54 A @
% 139.73/20.54 ( binintersect @
% 139.73/20.54 ( binunion @ X @ Y ) @ ( binunion @ Z @ W ) ) ) =
% 139.73/20.54 ( binunion @
% 139.73/20.54 ( binintersect @
% 139.73/20.54 ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) @
% 139.73/20.54 ( binintersect @
% 139.73/20.54 ( setminus @ A @ Z ) @ ( setminus @ A @ W ) ) ) ) ) ) ) ) ) ) ))).
% 139.73/20.54 thf('7', plain,
% 139.73/20.54 (( woz1_2 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X12:$i]:
% 139.73/20.54 ( ( in @ X12 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ( setminus @
% 139.73/20.54 X4 @
% 139.73/20.54 ( binintersect @
% 139.73/20.54 ( binunion @ X6 @ X8 ) @ ( binunion @ X10 @ X12 ) ) ) =
% 139.73/20.54 ( binunion @
% 139.73/20.54 ( binintersect @
% 139.73/20.54 ( setminus @ X4 @ X6 ) @ ( setminus @ X4 @ X8 ) ) @
% 139.73/20.54 ( binintersect @
% 139.73/20.54 ( setminus @ X4 @ X10 ) @ ( setminus @ X4 @ X12 ) ) ) ) ) ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(woz1_1, axiom, woz1_1 =
% 139.73/20.54 (![A:$i,X:$i]:
% 139.73/20.54 ( ( in @ X @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Y:$i]:
% 139.73/20.54 ( ( in @ Y @ ( powerset @ A ) ) =>
% 139.73/20.54 ( in @
% 139.73/20.54 ( setminus @ A @ X ) @
% 139.73/20.54 ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ))).
% 139.73/20.54 thf('8', plain,
% 139.73/20.54 (( woz1_1 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( in @
% 139.73/20.54 ( setminus @ X4 @ X6 ) @
% 139.73/20.54 ( powerset @ ( setminus @ X4 @ ( binintersect @ X6 @ X8 ) ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(woz13rule4, axiom, woz13rule4 =
% 139.73/20.54 (![A:$i,X:$i]:
% 139.73/20.54 ( ( in @ X @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Y:$i]:
% 139.73/20.54 ( ( in @ Y @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Z:$i]:
% 139.73/20.54 ( ( in @ Z @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![W:$i]:
% 139.73/20.54 ( ( in @ W @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ( subset @ X @ Z ) =>
% 139.73/20.54 ( ( subset @ Y @ W ) =>
% 139.73/20.54 ( subset @
% 139.73/20.54 ( binintersect @ X @ Y ) @ ( binintersect @ Z @ W ) ) ) ) ) ) ) ) ) ) ))).
% 139.73/20.54 thf('9', plain,
% 139.73/20.54 (( woz13rule4 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X12:$i]:
% 139.73/20.54 ( ( in @ X12 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ( subset @ X6 @ X10 ) =>
% 139.73/20.54 ( ( subset @ X8 @ X12 ) =>
% 139.73/20.54 ( subset @
% 139.73/20.54 ( binintersect @ X6 @ X8 ) @
% 139.73/20.54 ( binintersect @ X10 @ X12 ) ) ) ) ) ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(woz13rule3, axiom, woz13rule3 =
% 139.73/20.54 (![A:$i,X:$i]:
% 139.73/20.54 ( ( in @ X @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Y:$i]:
% 139.73/20.54 ( ( in @ Y @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Z:$i]:
% 139.73/20.54 ( ( in @ Z @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ( subset @ X @ Y ) =>
% 139.73/20.54 ( ( subset @ X @ Z ) =>
% 139.73/20.54 ( subset @ X @ ( binintersect @ Y @ Z ) ) ) ) ) ) ) ) ))).
% 139.73/20.54 thf('10', plain,
% 139.73/20.54 (( woz13rule3 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ( subset @ X6 @ X8 ) =>
% 139.73/20.54 ( ( subset @ X6 @ X10 ) =>
% 139.73/20.54 ( subset @ X6 @ ( binintersect @ X8 @ X10 ) ) ) ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(woz13rule2, axiom, woz13rule2 =
% 139.73/20.54 (![A:$i,X:$i]:
% 139.73/20.54 ( ( in @ X @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Y:$i]:
% 139.73/20.54 ( ( in @ Y @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Z:$i]:
% 139.73/20.54 ( ( in @ Z @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ( subset @ Y @ Z ) =>
% 139.73/20.54 ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ))).
% 139.73/20.54 thf('11', plain,
% 139.73/20.54 (( woz13rule2 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ( subset @ X8 @ X10 ) =>
% 139.73/20.54 ( subset @ ( binintersect @ X6 @ X8 ) @ X10 ) ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(woz13rule1, axiom, woz13rule1 =
% 139.73/20.54 (![A:$i,X:$i]:
% 139.73/20.54 ( ( in @ X @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Y:$i]:
% 139.73/20.54 ( ( in @ Y @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Z:$i]:
% 139.73/20.54 ( ( in @ Z @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ( subset @ X @ Z ) =>
% 139.73/20.54 ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ))).
% 139.73/20.54 thf('12', plain,
% 139.73/20.54 (( woz13rule1 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ( subset @ X6 @ X10 ) =>
% 139.73/20.54 ( subset @ ( binintersect @ X6 @ X8 ) @ X10 ) ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(woz13rule0, axiom, woz13rule0 =
% 139.73/20.54 (![A:$i,X:$i]:
% 139.73/20.54 ( ( in @ X @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Y:$i]:
% 139.73/20.54 ( ( in @ Y @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ ( binintersect @ X @ Y ) ) => ( in @ Xx @ A ) ) ) ) ) ))).
% 139.73/20.54 thf('13', plain,
% 139.73/20.54 (( woz13rule0 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ ( binintersect @ X6 @ X8 ) ) =>
% 139.73/20.54 ( in @ X10 @ X4 ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(demorgan2, axiom, demorgan2 =
% 139.73/20.54 (![A:$i,X:$i]:
% 139.73/20.54 ( ( in @ X @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Y:$i]:
% 139.73/20.54 ( ( in @ Y @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ( setminus @ A @ ( binunion @ X @ Y ) ) =
% 139.73/20.54 ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ))).
% 139.73/20.54 thf('14', plain,
% 139.73/20.54 (( demorgan2 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ( setminus @ X4 @ ( binunion @ X6 @ X8 ) ) =
% 139.73/20.54 ( binintersect @
% 139.73/20.54 ( setminus @ X4 @ X6 ) @ ( setminus @ X4 @ X8 ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(demorgan2b, axiom, demorgan2b =
% 139.73/20.54 (![A:$i,X:$i]:
% 139.73/20.54 ( ( in @ X @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Y:$i]:
% 139.73/20.54 ( ( in @ Y @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ( in @
% 139.73/20.54 Xx @
% 139.73/20.54 ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) =>
% 139.73/20.54 ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ))).
% 139.73/20.54 thf('15', plain,
% 139.73/20.54 (( demorgan2b ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ X4 ) =>
% 139.73/20.54 ( ( in @
% 139.73/20.54 X10 @
% 139.73/20.54 ( binintersect @
% 139.73/20.54 ( setminus @ X4 @ X6 ) @ ( setminus @ X4 @ X8 ) ) ) =>
% 139.73/20.54 ( in @ X10 @ ( setminus @ X4 @ ( binunion @ X6 @ X8 ) ) ) ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(demorgan2b2, axiom, demorgan2b2 =
% 139.73/20.54 (![A:$i,X:$i]:
% 139.73/20.54 ( ( in @ X @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Y:$i]:
% 139.73/20.54 ( ( in @ Y @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ( in @ Xx @ ( setminus @ A @ X ) ) =>
% 139.73/20.54 ( ( in @ Xx @ ( setminus @ A @ Y ) ) =>
% 139.73/20.54 ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ))).
% 139.73/20.54 thf('16', plain,
% 139.73/20.54 (( demorgan2b2 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ X4 ) =>
% 139.73/20.54 ( ( in @ X10 @ ( setminus @ X4 @ X6 ) ) =>
% 139.73/20.54 ( ( in @ X10 @ ( setminus @ X4 @ X8 ) ) =>
% 139.73/20.54 ( in @ X10 @ ( setminus @ X4 @ ( binunion @ X6 @ X8 ) ) ) ) ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(demorgan2a, axiom, demorgan2a =
% 139.73/20.54 (![A:$i,X:$i]:
% 139.73/20.54 ( ( in @ X @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Y:$i]:
% 139.73/20.54 ( ( in @ Y @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) =>
% 139.73/20.54 ( in @
% 139.73/20.54 Xx @
% 139.73/20.54 ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ))).
% 139.73/20.54 thf('17', plain,
% 139.73/20.54 (( demorgan2a ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ X4 ) =>
% 139.73/20.54 ( ( in @ X10 @ ( setminus @ X4 @ ( binunion @ X6 @ X8 ) ) ) =>
% 139.73/20.54 ( in @
% 139.73/20.54 X10 @
% 139.73/20.54 ( binintersect @
% 139.73/20.54 ( setminus @ X4 @ X6 ) @ ( setminus @ X4 @ X8 ) ) ) ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(demorgan1, axiom, demorgan1 =
% 139.73/20.54 (![A:$i,X:$i]:
% 139.73/20.54 ( ( in @ X @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Y:$i]:
% 139.73/20.54 ( ( in @ Y @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ( setminus @ A @ ( binintersect @ X @ Y ) ) =
% 139.73/20.54 ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ))).
% 139.73/20.54 thf('18', plain,
% 139.73/20.54 (( demorgan1 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ( setminus @ X4 @ ( binintersect @ X6 @ X8 ) ) =
% 139.73/20.54 ( binunion @ ( setminus @ X4 @ X6 ) @ ( setminus @ X4 @ X8 ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(demorgan1b, axiom, demorgan1b =
% 139.73/20.54 (![A:$i,X:$i]:
% 139.73/20.54 ( ( in @ X @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Y:$i]:
% 139.73/20.54 ( ( in @ Y @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ( in @
% 139.73/20.54 Xx @
% 139.73/20.54 ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) =>
% 139.73/20.54 ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ))).
% 139.73/20.54 thf('19', plain,
% 139.73/20.54 (( demorgan1b ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ X4 ) =>
% 139.73/20.54 ( ( in @
% 139.73/20.54 X10 @
% 139.73/20.54 ( binunion @
% 139.73/20.54 ( setminus @ X4 @ X6 ) @ ( setminus @ X4 @ X8 ) ) ) =>
% 139.73/20.54 ( in @
% 139.73/20.54 X10 @ ( setminus @ X4 @ ( binintersect @ X6 @ X8 ) ) ) ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(demorgan1a, axiom, demorgan1a =
% 139.73/20.54 (![A:$i,X:$i]:
% 139.73/20.54 ( ( in @ X @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Y:$i]:
% 139.73/20.54 ( ( in @ Y @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) =>
% 139.73/20.54 ( in @
% 139.73/20.54 Xx @
% 139.73/20.54 ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ))).
% 139.73/20.54 thf('20', plain,
% 139.73/20.54 (( demorgan1a ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ X4 ) =>
% 139.73/20.54 ( ( in @
% 139.73/20.54 X10 @ ( setminus @ X4 @ ( binintersect @ X6 @ X8 ) ) ) =>
% 139.73/20.54 ( in @
% 139.73/20.54 X10 @
% 139.73/20.54 ( binunion @
% 139.73/20.54 ( setminus @ X4 @ X6 ) @ ( setminus @ X4 @ X8 ) ) ) ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(demorgan2a2, axiom, demorgan2a2 =
% 139.73/20.54 (![A:$i,X:$i]:
% 139.73/20.54 ( ( in @ X @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Y:$i]:
% 139.73/20.54 ( ( in @ Y @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) =>
% 139.73/20.54 ( in @ Xx @ ( setminus @ A @ Y ) ) ) ) ) ) ) ))).
% 139.73/20.54 thf('21', plain,
% 139.73/20.54 (( demorgan2a2 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ X4 ) =>
% 139.73/20.54 ( ( in @ X10 @ ( setminus @ X4 @ ( binunion @ X6 @ X8 ) ) ) =>
% 139.73/20.54 ( in @ X10 @ ( setminus @ X4 @ X8 ) ) ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(complementUnionInPowersetComplement, axiom,
% 139.73/20.54 complementUnionInPowersetComplement =
% 139.73/20.54 (![A:$i,X:$i]:
% 139.73/20.54 ( ( in @ X @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Y:$i]:
% 139.73/20.54 ( ( in @ Y @ ( powerset @ A ) ) =>
% 139.73/20.54 ( in @
% 139.73/20.54 ( setminus @ A @ ( binunion @ X @ Y ) ) @
% 139.73/20.54 ( powerset @ ( setminus @ A @ X ) ) ) ) ) ))).
% 139.73/20.54 thf('22', plain,
% 139.73/20.54 (( complementUnionInPowersetComplement ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( in @
% 139.73/20.54 ( setminus @ X4 @ ( binunion @ X6 @ X8 ) ) @
% 139.73/20.54 ( powerset @ ( setminus @ X4 @ X6 ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(demorgan2a1, axiom, demorgan2a1 =
% 139.73/20.54 (![A:$i,X:$i]:
% 139.73/20.54 ( ( in @ X @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Y:$i]:
% 139.73/20.54 ( ( in @ Y @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) =>
% 139.73/20.54 ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ))).
% 139.73/20.54 thf('23', plain,
% 139.73/20.54 (( demorgan2a1 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ X4 ) =>
% 139.73/20.54 ( ( in @ X10 @ ( setminus @ X4 @ ( binunion @ X6 @ X8 ) ) ) =>
% 139.73/20.54 ( in @ X10 @ ( setminus @ X4 @ X6 ) ) ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(binunionTEcontra, axiom, binunionTEcontra =
% 139.73/20.54 (![A:$i,X:$i]:
% 139.73/20.54 ( ( in @ X @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Y:$i]:
% 139.73/20.54 ( ( in @ Y @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ( ~( in @ Xx @ X ) ) =>
% 139.73/20.54 ( ( ~( in @ Xx @ Y ) ) =>
% 139.73/20.54 ( ~( in @ Xx @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ))).
% 139.73/20.54 thf('24', plain,
% 139.73/20.54 (( binunionTEcontra ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ X4 ) =>
% 139.73/20.54 ( ( ~( in @ X10 @ X6 ) ) =>
% 139.73/20.54 ( ( ~( in @ X10 @ X8 ) ) =>
% 139.73/20.54 ( ~( in @ X10 @ ( binunion @ X6 @ X8 ) ) ) ) ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(binunionTE, axiom, binunionTE =
% 139.73/20.54 (![A:$i,X:$i]:
% 139.73/20.54 ( ( in @ X @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Y:$i]:
% 139.73/20.54 ( ( in @ Y @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Xphi:$o,Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ( in @ Xx @ ( binunion @ X @ Y ) ) =>
% 139.73/20.54 ( ( ( in @ Xx @ X ) => ( Xphi ) ) =>
% 139.73/20.54 ( ( ( in @ Xx @ Y ) => ( Xphi ) ) => ( Xphi ) ) ) ) ) ) ) ) ))).
% 139.73/20.54 thf('25', plain,
% 139.73/20.54 (( binunionTE ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X10:$o,X12:$i]:
% 139.73/20.54 ( ( in @ X12 @ X4 ) =>
% 139.73/20.54 ( ( in @ X12 @ ( binunion @ X6 @ X8 ) ) =>
% 139.73/20.54 ( ( ( in @ X12 @ X6 ) => ( X10 ) ) =>
% 139.73/20.54 ( ( ( in @ X12 @ X8 ) => ( X10 ) ) => ( X10 ) ) ) ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(inComplementUnionImpInComplement1, axiom,
% 139.73/20.54 inComplementUnionImpInComplement1 =
% 139.73/20.54 (![A:$i,X:$i]:
% 139.73/20.54 ( ( in @ X @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Y:$i]:
% 139.73/20.54 ( ( in @ Y @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) =>
% 139.73/20.54 ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ))).
% 139.73/20.54 thf('26', plain,
% 139.73/20.54 (( inComplementUnionImpInComplement1 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ X4 ) =>
% 139.73/20.54 ( ( in @ X10 @ ( setminus @ X4 @ ( binunion @ X6 @ X8 ) ) ) =>
% 139.73/20.54 ( in @ X10 @ ( setminus @ X4 @ X6 ) ) ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(inComplementUnionImpNotIn1, axiom, inComplementUnionImpNotIn1 =
% 139.73/20.54 (![A:$i,X:$i]:
% 139.73/20.54 ( ( in @ X @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Y:$i]:
% 139.73/20.54 ( ( in @ Y @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) =>
% 139.73/20.54 ( ~( in @ Xx @ X ) ) ) ) ) ) ) ))).
% 139.73/20.54 thf('27', plain,
% 139.73/20.54 (( inComplementUnionImpNotIn1 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ X4 ) =>
% 139.73/20.54 ( ( in @ X10 @ ( setminus @ X4 @ ( binunion @ X6 @ X8 ) ) ) =>
% 139.73/20.54 ( ~( in @ X10 @ X6 ) ) ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(intersectInPowersetIntersectUnions, axiom,
% 139.73/20.54 intersectInPowersetIntersectUnions =
% 139.73/20.54 (![A:$i,X:$i]:
% 139.73/20.54 ( ( in @ X @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Y:$i]:
% 139.73/20.54 ( ( in @ Y @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Z:$i]:
% 139.73/20.54 ( ( in @ Z @ ( powerset @ A ) ) =>
% 139.73/20.54 ( in @
% 139.73/20.54 ( binintersect @ X @ Y ) @
% 139.73/20.54 ( powerset @
% 139.73/20.54 ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ))).
% 139.73/20.54 thf('28', plain,
% 139.73/20.54 (( intersectInPowersetIntersectUnions ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( in @
% 139.73/20.54 ( binintersect @ X6 @ X8 ) @
% 139.73/20.54 ( powerset @
% 139.73/20.54 ( binintersect @
% 139.73/20.54 ( binunion @ X6 @ X10 ) @ ( binunion @ X8 @ X10 ) ) ) ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(inIntersectImpInIntersectUnions, axiom, inIntersectImpInIntersectUnions =
% 139.73/20.54 (![A:$i,X:$i]:
% 139.73/20.54 ( ( in @ X @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Y:$i]:
% 139.73/20.54 ( ( in @ Y @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Z:$i]:
% 139.73/20.54 ( ( in @ Z @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ( in @ Xx @ ( binintersect @ X @ Y ) ) =>
% 139.73/20.54 ( in @
% 139.73/20.54 Xx @
% 139.73/20.54 ( binintersect @
% 139.73/20.54 ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ) ))).
% 139.73/20.54 thf('29', plain,
% 139.73/20.54 (( inIntersectImpInIntersectUnions ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X12:$i]:
% 139.73/20.54 ( ( in @ X12 @ X4 ) =>
% 139.73/20.54 ( ( in @ X12 @ ( binintersect @ X6 @ X8 ) ) =>
% 139.73/20.54 ( in @
% 139.73/20.54 X12 @
% 139.73/20.54 ( binintersect @
% 139.73/20.54 ( binunion @ X6 @ X10 ) @ ( binunion @ X8 @ X10 ) ) ) ) ) ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(inIntersectImpInUnion2, axiom, inIntersectImpInUnion2 =
% 139.73/20.54 (![A:$i,X:$i]:
% 139.73/20.54 ( ( in @ X @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Y:$i]:
% 139.73/20.54 ( ( in @ Y @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Z:$i]:
% 139.73/20.54 ( ( in @ Z @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ( in @ Xx @ ( binintersect @ X @ Y ) ) =>
% 139.73/20.54 ( in @ Xx @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ))).
% 139.73/20.54 thf('30', plain,
% 139.73/20.54 (( inIntersectImpInUnion2 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X12:$i]:
% 139.73/20.54 ( ( in @ X12 @ X4 ) =>
% 139.73/20.54 ( ( in @ X12 @ ( binintersect @ X6 @ X8 ) ) =>
% 139.73/20.54 ( in @ X12 @ ( binunion @ X8 @ X10 ) ) ) ) ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(inIntersectImpInUnion, axiom, inIntersectImpInUnion =
% 139.73/20.54 (![A:$i,X:$i]:
% 139.73/20.54 ( ( in @ X @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Y:$i]:
% 139.73/20.54 ( ( in @ Y @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Z:$i]:
% 139.73/20.54 ( ( in @ Z @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ( in @ Xx @ ( binintersect @ X @ Y ) ) =>
% 139.73/20.54 ( in @ Xx @ ( binunion @ X @ Z ) ) ) ) ) ) ) ) ) ))).
% 139.73/20.54 thf('31', plain,
% 139.73/20.54 (( inIntersectImpInUnion ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X12:$i]:
% 139.73/20.54 ( ( in @ X12 @ X4 ) =>
% 139.73/20.54 ( ( in @ X12 @ ( binintersect @ X6 @ X8 ) ) =>
% 139.73/20.54 ( in @ X12 @ ( binunion @ X6 @ X10 ) ) ) ) ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(binunionTIRcontra, axiom, binunionTIRcontra =
% 139.73/20.54 (![A:$i,X:$i]:
% 139.73/20.54 ( ( in @ X @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Y:$i]:
% 139.73/20.54 ( ( in @ Y @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ( ~( in @ Xx @ ( binunion @ X @ Y ) ) ) =>
% 139.73/20.54 ( ~( in @ Xx @ Y ) ) ) ) ) ) ) ))).
% 139.73/20.54 thf('32', plain,
% 139.73/20.54 (( binunionTIRcontra ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ X4 ) =>
% 139.73/20.54 ( ( ~( in @ X10 @ ( binunion @ X6 @ X8 ) ) ) =>
% 139.73/20.54 ( ~( in @ X10 @ X8 ) ) ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(binunionTILcontra, axiom, binunionTILcontra =
% 139.73/20.54 (![A:$i,X:$i]:
% 139.73/20.54 ( ( in @ X @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Y:$i]:
% 139.73/20.54 ( ( in @ Y @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ( ~( in @ Xx @ ( binunion @ X @ Y ) ) ) =>
% 139.73/20.54 ( ~( in @ Xx @ X ) ) ) ) ) ) ) ))).
% 139.73/20.54 thf('33', plain,
% 139.73/20.54 (( binunionTILcontra ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ X4 ) =>
% 139.73/20.54 ( ( ~( in @ X10 @ ( binunion @ X6 @ X8 ) ) ) =>
% 139.73/20.54 ( ~( in @ X10 @ X6 ) ) ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(complementTcontraSubset, axiom, complementTcontraSubset =
% 139.73/20.54 (![A:$i,X:$i]:
% 139.73/20.54 ( ( in @ X @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Y:$i]:
% 139.73/20.54 ( ( in @ Y @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ( subset @ X @ ( setminus @ A @ Y ) ) =>
% 139.73/20.54 ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ))).
% 139.73/20.54 thf('34', plain,
% 139.73/20.54 (( complementTcontraSubset ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ( subset @ X6 @ ( setminus @ X4 @ X8 ) ) =>
% 139.73/20.54 ( subset @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(contraSubsetComplement, axiom, contraSubsetComplement =
% 139.73/20.54 (![A:$i,X:$i]:
% 139.73/20.54 ( ( in @ X @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Y:$i]:
% 139.73/20.54 ( ( in @ Y @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ( subset @ X @ ( setminus @ A @ Y ) ) =>
% 139.73/20.54 ( ![Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ( in @ Xx @ Y ) => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ))).
% 139.73/20.54 thf('35', plain,
% 139.73/20.54 (( contraSubsetComplement ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ( subset @ X6 @ ( setminus @ X4 @ X8 ) ) =>
% 139.73/20.54 ( ![X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ X4 ) =>
% 139.73/20.54 ( ( in @ X10 @ X8 ) =>
% 139.73/20.54 ( in @ X10 @ ( setminus @ X4 @ X6 ) ) ) ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(complementInPowersetComplementIntersect, axiom,
% 139.73/20.54 complementInPowersetComplementIntersect =
% 139.73/20.54 (![A:$i,X:$i]:
% 139.73/20.54 ( ( in @ X @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Y:$i]:
% 139.73/20.54 ( ( in @ Y @ ( powerset @ A ) ) =>
% 139.73/20.54 ( in @
% 139.73/20.54 ( setminus @ A @ X ) @
% 139.73/20.54 ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ))).
% 139.73/20.54 thf('36', plain,
% 139.73/20.54 (( complementInPowersetComplementIntersect ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( in @
% 139.73/20.54 ( setminus @ X4 @ X6 ) @
% 139.73/20.54 ( powerset @ ( setminus @ X4 @ ( binintersect @ X6 @ X8 ) ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(complementSubsetComplementIntersect, axiom,
% 139.73/20.54 complementSubsetComplementIntersect =
% 139.73/20.54 (![A:$i,X:$i]:
% 139.73/20.54 ( ( in @ X @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Y:$i]:
% 139.73/20.54 ( ( in @ Y @ ( powerset @ A ) ) =>
% 139.73/20.54 ( subset @
% 139.73/20.54 ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ))).
% 139.73/20.54 thf('37', plain,
% 139.73/20.54 (( complementSubsetComplementIntersect ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( subset @
% 139.73/20.54 ( setminus @ X4 @ X6 ) @
% 139.73/20.54 ( setminus @ X4 @ ( binintersect @ X6 @ X8 ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(complementImpComplementIntersect, axiom,
% 139.73/20.54 complementImpComplementIntersect =
% 139.73/20.54 (![A:$i,X:$i]:
% 139.73/20.54 ( ( in @ X @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Y:$i]:
% 139.73/20.54 ( ( in @ Y @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ( in @ Xx @ ( setminus @ A @ X ) ) =>
% 139.73/20.54 ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ))).
% 139.73/20.54 thf('38', plain,
% 139.73/20.54 (( complementImpComplementIntersect ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ X4 ) =>
% 139.73/20.54 ( ( in @ X10 @ ( setminus @ X4 @ X6 ) ) =>
% 139.73/20.54 ( in @
% 139.73/20.54 X10 @ ( setminus @ X4 @ ( binintersect @ X6 @ X8 ) ) ) ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(complementTnotintersectT, axiom, complementTnotintersectT =
% 139.73/20.54 (![A:$i,X:$i]:
% 139.73/20.54 ( ( in @ X @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Y:$i]:
% 139.73/20.54 ( ( in @ Y @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ( in @ Xx @ ( setminus @ A @ X ) ) =>
% 139.73/20.54 ( ~( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ))).
% 139.73/20.54 thf('39', plain,
% 139.73/20.54 (( complementTnotintersectT ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ X4 ) =>
% 139.73/20.54 ( ( in @ X10 @ ( setminus @ X4 @ X6 ) ) =>
% 139.73/20.54 ( ~( in @ X10 @ ( binintersect @ X6 @ X8 ) ) ) ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(doubleComplementEq, axiom, doubleComplementEq =
% 139.73/20.54 (![A:$i,X:$i]:
% 139.73/20.54 ( ( in @ X @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ( X ) = ( setminus @ A @ ( setminus @ A @ X ) ) ) ))).
% 139.73/20.54 thf('40', plain,
% 139.73/20.54 (( doubleComplementEq ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ( X6 ) = ( setminus @ X4 @ ( setminus @ X4 @ X6 ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(doubleComplementSub2, axiom, doubleComplementSub2 =
% 139.73/20.54 (![A:$i,X:$i]:
% 139.73/20.54 ( ( in @ X @ ( powerset @ A ) ) =>
% 139.73/20.54 ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ))).
% 139.73/20.54 thf('41', plain,
% 139.73/20.54 (( doubleComplementSub2 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( subset @ ( setminus @ X4 @ ( setminus @ X4 @ X6 ) ) @ X6 ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(doubleComplementSub1, axiom, doubleComplementSub1 =
% 139.73/20.54 (![A:$i,X:$i]:
% 139.73/20.54 ( ( in @ X @ ( powerset @ A ) ) =>
% 139.73/20.54 ( subset @ X @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ))).
% 139.73/20.54 thf('42', plain,
% 139.73/20.54 (( doubleComplementSub1 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( subset @ X6 @ ( setminus @ X4 @ ( setminus @ X4 @ X6 ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(doubleComplementE1, axiom, doubleComplementE1 =
% 139.73/20.54 (![A:$i,X:$i]:
% 139.73/20.54 ( ( in @ X @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) =>
% 139.73/20.54 ( in @ Xx @ X ) ) ) ) ))).
% 139.73/20.54 thf('43', plain,
% 139.73/20.54 (( doubleComplementE1 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ X4 ) =>
% 139.73/20.54 ( ( in @ X8 @ ( setminus @ X4 @ ( setminus @ X4 @ X6 ) ) ) =>
% 139.73/20.54 ( in @ X8 @ X6 ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(doubleComplementI1, axiom, doubleComplementI1 =
% 139.73/20.54 (![A:$i,X:$i]:
% 139.73/20.54 ( ( in @ X @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ( in @ Xx @ X ) =>
% 139.73/20.54 ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ))).
% 139.73/20.54 thf('44', plain,
% 139.73/20.54 (( doubleComplementI1 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ X4 ) =>
% 139.73/20.54 ( ( in @ X8 @ X6 ) =>
% 139.73/20.54 ( in @ X8 @ ( setminus @ X4 @ ( setminus @ X4 @ X6 ) ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(contrasubsetT3, axiom, contrasubsetT3 =
% 139.73/20.54 (![A:$i,X:$i]:
% 139.73/20.54 ( ( in @ X @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Y:$i]:
% 139.73/20.54 ( ( in @ Y @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) =>
% 139.73/20.54 ( subset @ X @ Y ) ) ) ) ))).
% 139.73/20.54 thf('45', plain,
% 139.73/20.54 (( contrasubsetT3 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ( subset @ ( setminus @ X4 @ X8 ) @ ( setminus @ X4 @ X6 ) ) =>
% 139.73/20.54 ( subset @ X6 @ X8 ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(contrasubsetT2, axiom, contrasubsetT2 =
% 139.73/20.54 (![A:$i,X:$i]:
% 139.73/20.54 ( ( in @ X @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Y:$i]:
% 139.73/20.54 ( ( in @ Y @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ( subset @ X @ Y ) =>
% 139.73/20.54 ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) ) ))).
% 139.73/20.54 thf('46', plain,
% 139.73/20.54 (( contrasubsetT2 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ( subset @ X6 @ X8 ) =>
% 139.73/20.54 ( subset @ ( setminus @ X4 @ X8 ) @ ( setminus @ X4 @ X6 ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(contrasubsetT1, axiom, contrasubsetT1 =
% 139.73/20.54 (![A:$i,X:$i]:
% 139.73/20.54 ( ( in @ X @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Y:$i]:
% 139.73/20.54 ( ( in @ Y @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ( subset @ X @ Y ) =>
% 139.73/20.54 ( ( ~( in @ Xx @ Y ) ) => ( ~( in @ Xx @ X ) ) ) ) ) ) ) ) ))).
% 139.73/20.54 thf('47', plain,
% 139.73/20.54 (( contrasubsetT1 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ X4 ) =>
% 139.73/20.54 ( ( subset @ X6 @ X8 ) =>
% 139.73/20.54 ( ( ~( in @ X10 @ X8 ) ) => ( ~( in @ X10 @ X6 ) ) ) ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(contrasubsetT, axiom, contrasubsetT =
% 139.73/20.54 (![A:$i,X:$i]:
% 139.73/20.54 ( ( in @ X @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Y:$i]:
% 139.73/20.54 ( ( in @ Y @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ( subset @ X @ ( setminus @ A @ Y ) ) =>
% 139.73/20.54 ( ( in @ Xx @ Y ) => ( ~( in @ Xx @ X ) ) ) ) ) ) ) ) ))).
% 139.73/20.54 thf('48', plain,
% 139.73/20.54 (( contrasubsetT ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ X4 ) =>
% 139.73/20.54 ( ( subset @ X6 @ ( setminus @ X4 @ X8 ) ) =>
% 139.73/20.54 ( ( in @ X10 @ X8 ) => ( ~( in @ X10 @ X6 ) ) ) ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(binintersectTERcontra, axiom, binintersectTERcontra =
% 139.73/20.54 (![A:$i,X:$i]:
% 139.73/20.54 ( ( in @ X @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Y:$i]:
% 139.73/20.54 ( ( in @ Y @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ( ~( in @ Xx @ Y ) ) =>
% 139.73/20.54 ( ~( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ))).
% 139.73/20.54 thf('49', plain,
% 139.73/20.54 (( binintersectTERcontra ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ X4 ) =>
% 139.73/20.54 ( ( ~( in @ X10 @ X8 ) ) =>
% 139.73/20.54 ( ~( in @ X10 @ ( binintersect @ X6 @ X8 ) ) ) ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(binintersectTELcontra, axiom, binintersectTELcontra =
% 139.73/20.54 (![A:$i,X:$i]:
% 139.73/20.54 ( ( in @ X @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Y:$i]:
% 139.73/20.54 ( ( in @ Y @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ( ~( in @ Xx @ X ) ) =>
% 139.73/20.54 ( ~( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ))).
% 139.73/20.54 thf('50', plain,
% 139.73/20.54 (( binintersectTELcontra ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ X4 ) =>
% 139.73/20.54 ( ( ~( in @ X10 @ X6 ) ) =>
% 139.73/20.54 ( ~( in @ X10 @ ( binintersect @ X6 @ X8 ) ) ) ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(complementTE1, axiom, complementTE1 =
% 139.73/20.54 (![A:$i,X:$i]:
% 139.73/20.54 ( ( in @ X @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ( ~( in @ Xx @ ( setminus @ A @ X ) ) ) => ( in @ Xx @ X ) ) ) ) ))).
% 139.73/20.54 thf('51', plain,
% 139.73/20.54 (( complementTE1 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ X4 ) =>
% 139.73/20.54 ( ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) => ( in @ X8 @ X6 ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(complementTI1, axiom, complementTI1 =
% 139.73/20.54 (![A:$i,X:$i]:
% 139.73/20.54 ( ( in @ X @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ( in @ Xx @ X ) => ( ~( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ))).
% 139.73/20.54 thf('52', plain,
% 139.73/20.54 (( complementTI1 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ X4 ) =>
% 139.73/20.54 ( ( in @ X8 @ X6 ) => ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(powersetTE1, axiom, powersetTE1 =
% 139.73/20.54 (![A:$i,X:$i]:
% 139.73/20.54 ( ( in @ X @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Y:$i]:
% 139.73/20.54 ( ( in @ Y @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ( in @ X @ ( powerset @ Y ) ) =>
% 139.73/20.54 ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) ) ) ) ))).
% 139.73/20.54 thf('53', plain,
% 139.73/20.54 (( powersetTE1 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ X4 ) =>
% 139.73/20.54 ( ( in @ X6 @ ( powerset @ X8 ) ) =>
% 139.73/20.54 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(powersetTI1, axiom, powersetTI1 =
% 139.73/20.54 (![A:$i,X:$i]:
% 139.73/20.54 ( ( in @ X @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Y:$i]:
% 139.73/20.54 ( ( in @ Y @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ( ![Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) => ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) =>
% 139.73/20.54 ( in @ X @ ( powerset @ Y ) ) ) ) ) ))).
% 139.73/20.54 thf('54', plain,
% 139.73/20.54 (( powersetTI1 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ( ![X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ X4 ) =>
% 139.73/20.54 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) =>
% 139.73/20.54 ( in @ X6 @ ( powerset @ X8 ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(subsetTI, axiom, subsetTI =
% 139.73/20.54 (![A:$i,X:$i]:
% 139.73/20.54 ( ( in @ X @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Y:$i]:
% 139.73/20.54 ( ( in @ Y @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ( ![Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) => ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) =>
% 139.73/20.54 ( subset @ X @ Y ) ) ) ) ))).
% 139.73/20.54 thf('55', plain,
% 139.73/20.54 (( subsetTI ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ( ![X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ X4 ) =>
% 139.73/20.54 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) =>
% 139.73/20.54 ( subset @ X6 @ X8 ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(setextT, axiom, setextT =
% 139.73/20.54 (![A:$i,X:$i]:
% 139.73/20.54 ( ( in @ X @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Y:$i]:
% 139.73/20.54 ( ( in @ Y @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ( ![Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) => ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) =>
% 139.73/20.54 ( ( ![Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) => ( ( in @ Xx @ Y ) => ( in @ Xx @ X ) ) ) ) =>
% 139.73/20.54 ( ( X ) = ( Y ) ) ) ) ) ) ))).
% 139.73/20.54 thf('56', plain,
% 139.73/20.54 (( setextT ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ( ![X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ X4 ) =>
% 139.73/20.54 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) =>
% 139.73/20.54 ( ( ![X12:$i]:
% 139.73/20.54 ( ( in @ X12 @ X4 ) =>
% 139.73/20.54 ( ( in @ X12 @ X8 ) => ( in @ X12 @ X6 ) ) ) ) =>
% 139.73/20.54 ( ( X6 ) = ( X8 ) ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(complementT_lem, axiom, complementT_lem =
% 139.73/20.54 (![A:$i,X:$i]:
% 139.73/20.54 ( ( in @ X @ ( powerset @ A ) ) =>
% 139.73/20.54 ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ))).
% 139.73/20.54 thf('57', plain,
% 139.73/20.54 (( complementT_lem ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( in @ ( setminus @ X4 @ X6 ) @ ( powerset @ X4 ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(setminusT_lem, axiom, setminusT_lem =
% 139.73/20.54 (![A:$i,X:$i]:
% 139.73/20.54 ( ( in @ X @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Y:$i]:
% 139.73/20.54 ( ( in @ Y @ ( powerset @ A ) ) =>
% 139.73/20.54 ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ))).
% 139.73/20.54 thf('58', plain,
% 139.73/20.54 (( setminusT_lem ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( in @ ( setminus @ X6 @ X8 ) @ ( powerset @ X4 ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(powersetT_lem, axiom, powersetT_lem =
% 139.73/20.54 (![A:$i,X:$i]:
% 139.73/20.54 ( ( in @ X @ ( powerset @ A ) ) =>
% 139.73/20.54 ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ))).
% 139.73/20.54 thf('59', plain,
% 139.73/20.54 (( powersetT_lem ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( in @ ( powerset @ X6 ) @ ( powerset @ ( powerset @ X4 ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(binunionT_lem, axiom, binunionT_lem =
% 139.73/20.54 (![A:$i,X:$i]:
% 139.73/20.54 ( ( in @ X @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Y:$i]:
% 139.73/20.54 ( ( in @ Y @ ( powerset @ A ) ) =>
% 139.73/20.54 ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ))).
% 139.73/20.54 thf('60', plain,
% 139.73/20.54 (( binunionT_lem ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( in @ ( binunion @ X6 @ X8 ) @ ( powerset @ X4 ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(binintersectT_lem, axiom, binintersectT_lem =
% 139.73/20.54 (![A:$i,X:$i]:
% 139.73/20.54 ( ( in @ X @ ( powerset @ A ) ) =>
% 139.73/20.54 ( ![Y:$i]:
% 139.73/20.54 ( ( in @ Y @ ( powerset @ A ) ) =>
% 139.73/20.54 ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ))).
% 139.73/20.54 thf('61', plain,
% 139.73/20.54 (( binintersectT_lem ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ![X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( in @ ( binintersect @ X6 @ X8 ) @ ( powerset @ X4 ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(iftrueorfalse, axiom, iftrueorfalse =
% 139.73/20.54 (![A:$i,Xphi:$o,Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ![Xy:$i]:
% 139.73/20.54 ( ( in @ Xy @ A ) =>
% 139.73/20.54 ( in @
% 139.73/20.54 ( if @ A @ Xphi @ Xx @ Xy ) @
% 139.73/20.54 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ))).
% 139.73/20.54 thf('62', plain,
% 139.73/20.54 (( iftrueorfalse ) =
% 139.73/20.54 ( ![X4:$i,X6:$o,X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ X4 ) =>
% 139.73/20.54 ( ![X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ X4 ) =>
% 139.73/20.54 ( in @
% 139.73/20.54 ( if @ X4 @ X6 @ X8 @ X10 ) @
% 139.73/20.54 ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(iffalse, axiom, iffalse =
% 139.73/20.54 (![A:$i,Xphi:$o,Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ![Xy:$i]:
% 139.73/20.54 ( ( in @ Xy @ A ) =>
% 139.73/20.54 ( ( ~( Xphi ) ) => ( ( if @ A @ Xphi @ Xx @ Xy ) = ( Xy ) ) ) ) ) ))).
% 139.73/20.54 thf('63', plain,
% 139.73/20.54 (( iffalse ) =
% 139.73/20.54 ( ![X4:$i,X6:$o,X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ X4 ) =>
% 139.73/20.54 ( ![X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ X4 ) =>
% 139.73/20.54 ( ( ~( X6 ) ) => ( ( if @ X4 @ X6 @ X8 @ X10 ) = ( X10 ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(iftrue, axiom, iftrue =
% 139.73/20.54 (![A:$i,Xphi:$o,Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ![Xy:$i]:
% 139.73/20.54 ( ( in @ Xy @ A ) =>
% 139.73/20.54 ( ( Xphi ) => ( ( if @ A @ Xphi @ Xx @ Xy ) = ( Xx ) ) ) ) ) ))).
% 139.73/20.54 thf('64', plain,
% 139.73/20.54 (( iftrue ) =
% 139.73/20.54 ( ![X4:$i,X6:$o,X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ X4 ) =>
% 139.73/20.54 ( ![X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ X4 ) =>
% 139.73/20.54 ( ( X6 ) => ( ( if @ X4 @ X6 @ X8 @ X10 ) = ( X8 ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(theeq, axiom, theeq =
% 139.73/20.54 (![X:$i]:
% 139.73/20.54 ( ( singleton @ X ) =>
% 139.73/20.54 ( ![Xx:$i]: ( ( in @ Xx @ X ) => ( ( setunion @ X ) = ( Xx ) ) ) ) ))).
% 139.73/20.54 thf('65', plain,
% 139.73/20.54 (( theeq ) =
% 139.73/20.54 ( ![X4:$i]:
% 139.73/20.54 ( ( singleton @ X4 ) =>
% 139.73/20.54 ( ![X6:$i]: ( ( in @ X6 @ X4 ) => ( ( setunion @ X4 ) = ( X6 ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(ifp, axiom, ifp =
% 139.73/20.54 (![A:$i,Xphi:$o,Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ![Xy:$i]:
% 139.73/20.54 ( ( in @ Xy @ A ) => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) ))).
% 139.73/20.54 thf('66', plain,
% 139.73/20.54 (( ifp ) =
% 139.73/20.54 ( ![X4:$i,X6:$o,X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ X4 ) =>
% 139.73/20.54 ( ![X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ X4 ) => ( in @ ( if @ X4 @ X6 @ X8 @ X10 ) @ X4 ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(ifSingleton, axiom, ifSingleton =
% 139.73/20.54 (![A:$i,Xphi:$o,Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ![Xy:$i]:
% 139.73/20.54 ( ( in @ Xy @ A ) =>
% 139.73/20.54 ( singleton @
% 139.73/20.54 ( dsetconstr @
% 139.73/20.54 A @
% 139.73/20.54 ( ^[Xz:$i]:
% 139.73/20.54 ( ( ( Xphi ) & ( ( Xz ) = ( Xx ) ) ) |
% 139.73/20.54 ( ( ~( Xphi ) ) & ( ( Xz ) = ( Xy ) ) ) ) ) ) ) ) ) ))).
% 139.73/20.54 thf('67', plain,
% 139.73/20.54 (( ifSingleton ) =
% 139.73/20.54 ( ![X4:$i,X6:$o,X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ X4 ) =>
% 139.73/20.54 ( ![X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ X4 ) =>
% 139.73/20.54 ( singleton @
% 139.73/20.54 ( dsetconstr @
% 139.73/20.54 X4 @
% 139.73/20.54 ( ^[V_1:$i]:
% 139.73/20.54 ( ( ( X6 ) & ( ( V_1 ) = ( X8 ) ) ) |
% 139.73/20.54 ( ( ~( X6 ) ) & ( ( V_1 ) = ( X10 ) ) ) ) ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(iftrueProp2, axiom, iftrueProp2 =
% 139.73/20.54 (![A:$i,Xphi:$o,Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ![Xy:$i]:
% 139.73/20.54 ( ( in @ Xy @ A ) =>
% 139.73/20.54 ( ( Xphi ) =>
% 139.73/20.54 ( ( dsetconstr @
% 139.73/20.54 A @
% 139.73/20.54 ( ^[Xz:$i]:
% 139.73/20.54 ( ( ( Xphi ) & ( ( Xz ) = ( Xx ) ) ) |
% 139.73/20.54 ( ( ~( Xphi ) ) & ( ( Xz ) = ( Xy ) ) ) ) ) ) =
% 139.73/20.54 ( setadjoin @ Xx @ emptyset ) ) ) ) ) ))).
% 139.73/20.54 thf('68', plain,
% 139.73/20.54 (( iftrueProp2 ) =
% 139.73/20.54 ( ![X4:$i,X6:$o,X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ X4 ) =>
% 139.73/20.54 ( ![X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ X4 ) =>
% 139.73/20.54 ( ( X6 ) =>
% 139.73/20.54 ( ( dsetconstr @
% 139.73/20.54 X4 @
% 139.73/20.54 ( ^[V_1:$i]:
% 139.73/20.54 ( ( ( X6 ) & ( ( V_1 ) = ( X8 ) ) ) |
% 139.73/20.54 ( ( ~( X6 ) ) & ( ( V_1 ) = ( X10 ) ) ) ) ) ) =
% 139.73/20.54 ( setadjoin @ X8 @ emptyset ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(iftrueProp1, axiom, iftrueProp1 =
% 139.73/20.54 (![A:$i,Xphi:$o,Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ![Xy:$i]:
% 139.73/20.54 ( ( in @ Xy @ A ) =>
% 139.73/20.54 ( ( Xphi ) =>
% 139.73/20.54 ( in @
% 139.73/20.54 Xx @
% 139.73/20.54 ( dsetconstr @
% 139.73/20.54 A @
% 139.73/20.54 ( ^[Xz:$i]:
% 139.73/20.54 ( ( ( Xphi ) & ( ( Xz ) = ( Xx ) ) ) |
% 139.73/20.54 ( ( ~( Xphi ) ) & ( ( Xz ) = ( Xy ) ) ) ) ) ) ) ) ) ) ))).
% 139.73/20.54 thf('69', plain,
% 139.73/20.54 (( iftrueProp1 ) =
% 139.73/20.54 ( ![X4:$i,X6:$o,X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ X4 ) =>
% 139.73/20.54 ( ![X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ X4 ) =>
% 139.73/20.54 ( ( X6 ) =>
% 139.73/20.54 ( in @
% 139.73/20.54 X8 @
% 139.73/20.54 ( dsetconstr @
% 139.73/20.54 X4 @
% 139.73/20.54 ( ^[V_1:$i]:
% 139.73/20.54 ( ( ( X6 ) & ( ( V_1 ) = ( X8 ) ) ) |
% 139.73/20.54 ( ( ~( X6 ) ) & ( ( V_1 ) = ( X10 ) ) ) ) ) ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(iffalseProp2, axiom, iffalseProp2 =
% 139.73/20.54 (![A:$i,Xphi:$o,Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ![Xy:$i]:
% 139.73/20.54 ( ( in @ Xy @ A ) =>
% 139.73/20.54 ( ( ~( Xphi ) ) =>
% 139.73/20.54 ( ( dsetconstr @
% 139.73/20.54 A @
% 139.73/20.54 ( ^[Xz:$i]:
% 139.73/20.54 ( ( ( Xphi ) & ( ( Xz ) = ( Xx ) ) ) |
% 139.73/20.54 ( ( ~( Xphi ) ) & ( ( Xz ) = ( Xy ) ) ) ) ) ) =
% 139.73/20.54 ( setadjoin @ Xy @ emptyset ) ) ) ) ) ))).
% 139.73/20.54 thf('70', plain,
% 139.73/20.54 (( iffalseProp2 ) =
% 139.73/20.54 ( ![X4:$i,X6:$o,X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ X4 ) =>
% 139.73/20.54 ( ![X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ X4 ) =>
% 139.73/20.54 ( ( ~( X6 ) ) =>
% 139.73/20.54 ( ( dsetconstr @
% 139.73/20.54 X4 @
% 139.73/20.54 ( ^[V_1:$i]:
% 139.73/20.54 ( ( ( X6 ) & ( ( V_1 ) = ( X8 ) ) ) |
% 139.73/20.54 ( ( ~( X6 ) ) & ( ( V_1 ) = ( X10 ) ) ) ) ) ) =
% 139.73/20.54 ( setadjoin @ X10 @ emptyset ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(iffalseProp1, axiom, iffalseProp1 =
% 139.73/20.54 (![A:$i,Xphi:$o,Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ![Xy:$i]:
% 139.73/20.54 ( ( in @ Xy @ A ) =>
% 139.73/20.54 ( ( ~( Xphi ) ) =>
% 139.73/20.54 ( in @
% 139.73/20.54 Xy @
% 139.73/20.54 ( dsetconstr @
% 139.73/20.54 A @
% 139.73/20.54 ( ^[Xz:$i]:
% 139.73/20.54 ( ( ( Xphi ) & ( ( Xz ) = ( Xx ) ) ) |
% 139.73/20.54 ( ( ~( Xphi ) ) & ( ( Xz ) = ( Xy ) ) ) ) ) ) ) ) ) ) ))).
% 139.73/20.54 thf('71', plain,
% 139.73/20.54 (( iffalseProp1 ) =
% 139.73/20.54 ( ![X4:$i,X6:$o,X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ X4 ) =>
% 139.73/20.54 ( ![X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ X4 ) =>
% 139.73/20.54 ( ( ~( X6 ) ) =>
% 139.73/20.54 ( in @
% 139.73/20.54 X10 @
% 139.73/20.54 ( dsetconstr @
% 139.73/20.54 X4 @
% 139.73/20.54 ( ^[V_1:$i]:
% 139.73/20.54 ( ( ( X6 ) & ( ( V_1 ) = ( X8 ) ) ) |
% 139.73/20.54 ( ( ~( X6 ) ) & ( ( V_1 ) = ( X10 ) ) ) ) ) ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(eta2, axiom, eta2 =
% 139.73/20.54 (![A:$i,B:$i,Xf:$i]:
% 139.73/20.54 ( ( in @ Xf @ ( funcSet @ A @ B ) ) =>
% 139.73/20.54 ( ( lam @ A @ B @ ( ^[Xx:$i]: ( ap @ A @ B @ Xf @ Xx ) ) ) = ( Xf ) ) ))).
% 139.73/20.54 thf('72', plain,
% 139.73/20.54 (( eta2 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( funcSet @ X4 @ X6 ) ) =>
% 139.73/20.54 ( ( lam @ X4 @ X6 @ ( ^[V_1:$i]: ( ap @ X4 @ X6 @ X8 @ V_1 ) ) ) =
% 139.73/20.54 ( X8 ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(beta2, axiom, beta2 =
% 139.73/20.54 (![A:$i,B:$i,Xf:( $i > $i )]:
% 139.73/20.54 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( in @ ( Xf @ Xx ) @ B ) ) ) =>
% 139.73/20.54 ( ![Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ( ap @ A @ B @ ( lam @ A @ B @ ( ^[Xy:$i]: ( Xf @ Xy ) ) ) @ Xx ) =
% 139.73/20.54 ( Xf @ Xx ) ) ) ) ))).
% 139.73/20.54 thf('73', plain,
% 139.73/20.54 (( beta2 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:( $i > $i )]:
% 139.73/20.54 ( ( ![X10:$i]: ( ( in @ X10 @ X4 ) => ( in @ ( X8 @ X10 ) @ X6 ) ) ) =>
% 139.73/20.54 ( ![X12:$i]:
% 139.73/20.54 ( ( in @ X12 @ X4 ) =>
% 139.73/20.54 ( ( ap @
% 139.73/20.54 X4 @ X6 @ ( lam @ X4 @ X6 @ ( ^[V_1:$i]: ( X8 @ V_1 ) ) ) @
% 139.73/20.54 X12 ) =
% 139.73/20.54 ( X8 @ X12 ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(lam2lamEq, axiom, lam2lamEq =
% 139.73/20.54 (![A:$i,B:$i,Xf:( $i > $i )]:
% 139.73/20.54 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( in @ ( Xf @ Xx ) @ B ) ) ) =>
% 139.73/20.54 ( ( lam @ A @ B @ ( ^[Xx:$i]: ( Xf @ Xx ) ) ) =
% 139.73/20.54 ( lam @ A @ B @ ( ^[Xx:$i]: ( Xf @ Xx ) ) ) ) ))).
% 139.73/20.54 thf('74', plain,
% 139.73/20.54 (( lam2lamEq ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:( $i > $i )]:
% 139.73/20.54 ( ( ![X10:$i]: ( ( in @ X10 @ X4 ) => ( in @ ( X8 @ X10 ) @ X6 ) ) ) =>
% 139.73/20.54 ( ( lam @ X4 @ X6 @ ( ^[V_1:$i]: ( X8 @ V_1 ) ) ) =
% 139.73/20.54 ( lam @ X4 @ X6 @ ( ^[V_2:$i]: ( X8 @ V_2 ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(eta1, axiom, eta1 =
% 139.73/20.54 (![A:$i,B:$i,Xf:$i]:
% 139.73/20.54 ( ( func @ A @ B @ Xf ) =>
% 139.73/20.54 ( ( lam @ A @ B @ ( ^[Xx:$i]: ( ap @ A @ B @ Xf @ Xx ) ) ) = ( Xf ) ) ))).
% 139.73/20.54 thf('75', plain,
% 139.73/20.54 (( eta1 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.54 ( ( func @ X4 @ X6 @ X8 ) =>
% 139.73/20.54 ( ( lam @ X4 @ X6 @ ( ^[V_1:$i]: ( ap @ X4 @ X6 @ X8 @ V_1 ) ) ) =
% 139.73/20.54 ( X8 ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(beta1, axiom, beta1 =
% 139.73/20.54 (![A:$i,B:$i,Xf:( $i > $i )]:
% 139.73/20.54 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( in @ ( Xf @ Xx ) @ B ) ) ) =>
% 139.73/20.54 ( ![Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ( ap @ A @ B @ ( lam @ A @ B @ ( ^[Xy:$i]: ( Xf @ Xy ) ) ) @ Xx ) =
% 139.73/20.54 ( Xf @ Xx ) ) ) ) ))).
% 139.73/20.54 thf('76', plain,
% 139.73/20.54 (( beta1 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:( $i > $i )]:
% 139.73/20.54 ( ( ![X10:$i]: ( ( in @ X10 @ X4 ) => ( in @ ( X8 @ X10 ) @ X6 ) ) ) =>
% 139.73/20.54 ( ![X12:$i]:
% 139.73/20.54 ( ( in @ X12 @ X4 ) =>
% 139.73/20.54 ( ( ap @
% 139.73/20.54 X4 @ X6 @ ( lam @ X4 @ X6 @ ( ^[V_1:$i]: ( X8 @ V_1 ) ) ) @
% 139.73/20.54 X12 ) =
% 139.73/20.54 ( X8 @ X12 ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(ap2apEq2, axiom, ap2apEq2 =
% 139.73/20.54 (![A:$i,B:$i,Xf:$i]:
% 139.73/20.54 ( ( func @ A @ B @ Xf ) =>
% 139.73/20.54 ( ![Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ( ap @ A @ B @ Xf @ Xx ) = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ))).
% 139.73/20.54 thf('77', plain,
% 139.73/20.54 (( ap2apEq2 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.54 ( ( func @ X4 @ X6 @ X8 ) =>
% 139.73/20.54 ( ![X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ X4 ) =>
% 139.73/20.54 ( ( ap @ X4 @ X6 @ X8 @ X10 ) = ( ap @ X4 @ X6 @ X8 @ X10 ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(ap2apEq1, axiom, ap2apEq1 =
% 139.73/20.54 (![A:$i,B:$i,Xf:$i]:
% 139.73/20.54 ( ( in @ Xf @ ( funcSet @ A @ B ) ) =>
% 139.73/20.54 ( ![Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ( ap @ A @ B @ Xf @ Xx ) = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ))).
% 139.73/20.54 thf('78', plain,
% 139.73/20.54 (( ap2apEq1 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( funcSet @ X4 @ X6 ) ) =>
% 139.73/20.54 ( ![X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ X4 ) =>
% 139.73/20.54 ( ( ap @ X4 @ X6 @ X8 @ X10 ) = ( ap @ X4 @ X6 @ X8 @ X10 ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(funcext2, axiom, funcext2 =
% 139.73/20.54 (![A:$i,B:$i,Xf:$i]:
% 139.73/20.54 ( ( in @ Xf @ ( funcSet @ A @ B ) ) =>
% 139.73/20.54 ( ![Xg:$i]:
% 139.73/20.54 ( ( in @ Xg @ ( funcSet @ A @ B ) ) =>
% 139.73/20.54 ( ( ![Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ( ap @ A @ B @ Xf @ Xx ) = ( ap @ A @ B @ Xg @ Xx ) ) ) ) =>
% 139.73/20.54 ( ( Xf ) = ( Xg ) ) ) ) ) ))).
% 139.73/20.54 thf('79', plain,
% 139.73/20.54 (( funcext2 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( funcSet @ X4 @ X6 ) ) =>
% 139.73/20.54 ( ![X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ ( funcSet @ X4 @ X6 ) ) =>
% 139.73/20.54 ( ( ![X12:$i]:
% 139.73/20.54 ( ( in @ X12 @ X4 ) =>
% 139.73/20.54 ( ( ap @ X4 @ X6 @ X8 @ X12 ) =
% 139.73/20.54 ( ap @ X4 @ X6 @ X10 @ X12 ) ) ) ) =>
% 139.73/20.54 ( ( X8 ) = ( X10 ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(funcext, axiom, funcext =
% 139.73/20.54 (![A:$i,B:$i,Xf:$i]:
% 139.73/20.54 ( ( func @ A @ B @ Xf ) =>
% 139.73/20.54 ( ![Xg:$i]:
% 139.73/20.54 ( ( func @ A @ B @ Xg ) =>
% 139.73/20.54 ( ( ![Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ( ap @ A @ B @ Xf @ Xx ) = ( ap @ A @ B @ Xg @ Xx ) ) ) ) =>
% 139.73/20.54 ( ( Xf ) = ( Xg ) ) ) ) ) ))).
% 139.73/20.54 thf('80', plain,
% 139.73/20.54 (( funcext ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.54 ( ( func @ X4 @ X6 @ X8 ) =>
% 139.73/20.54 ( ![X10:$i]:
% 139.73/20.54 ( ( func @ X4 @ X6 @ X10 ) =>
% 139.73/20.54 ( ( ![X12:$i]:
% 139.73/20.54 ( ( in @ X12 @ X4 ) =>
% 139.73/20.54 ( ( ap @ X4 @ X6 @ X8 @ X12 ) =
% 139.73/20.54 ( ap @ X4 @ X6 @ X10 @ X12 ) ) ) ) =>
% 139.73/20.54 ( ( X8 ) = ( X10 ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(eqbreln, axiom, eqbreln =
% 139.73/20.54 (![A:$i,B:$i,R:$i]:
% 139.73/20.54 ( ( breln @ A @ B @ R ) =>
% 139.73/20.54 ( ![S:$i]:
% 139.73/20.54 ( ( breln @ A @ B @ S ) =>
% 139.73/20.54 ( ( ![Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ![Xy:$i]:
% 139.73/20.54 ( ( in @ Xy @ B ) =>
% 139.73/20.54 ( ( in @ ( kpair @ Xx @ Xy ) @ R ) =>
% 139.73/20.54 ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) ) ) ) =>
% 139.73/20.54 ( ( ![Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ![Xy:$i]:
% 139.73/20.54 ( ( in @ Xy @ B ) =>
% 139.73/20.54 ( ( in @ ( kpair @ Xx @ Xy ) @ S ) =>
% 139.73/20.54 ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) =>
% 139.73/20.54 ( ( R ) = ( S ) ) ) ) ) ) ))).
% 139.73/20.54 thf('81', plain,
% 139.73/20.54 (( eqbreln ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.54 ( ( breln @ X4 @ X6 @ X8 ) =>
% 139.73/20.54 ( ![X10:$i]:
% 139.73/20.54 ( ( breln @ X4 @ X6 @ X10 ) =>
% 139.73/20.54 ( ( ![X12:$i]:
% 139.73/20.54 ( ( in @ X12 @ X4 ) =>
% 139.73/20.54 ( ![X14:$i]:
% 139.73/20.54 ( ( in @ X14 @ X6 ) =>
% 139.73/20.54 ( ( in @ ( kpair @ X12 @ X14 ) @ X8 ) =>
% 139.73/20.54 ( in @ ( kpair @ X12 @ X14 ) @ X10 ) ) ) ) ) ) =>
% 139.73/20.54 ( ( ![X16:$i]:
% 139.73/20.54 ( ( in @ X16 @ X4 ) =>
% 139.73/20.54 ( ![X18:$i]:
% 139.73/20.54 ( ( in @ X18 @ X6 ) =>
% 139.73/20.54 ( ( in @ ( kpair @ X16 @ X18 ) @ X10 ) =>
% 139.73/20.54 ( in @ ( kpair @ X16 @ X18 ) @ X8 ) ) ) ) ) ) =>
% 139.73/20.54 ( ( X8 ) = ( X10 ) ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(subbreln, axiom, subbreln =
% 139.73/20.54 (![A:$i,B:$i,R:$i]:
% 139.73/20.54 ( ( breln @ A @ B @ R ) =>
% 139.73/20.54 ( ![S:$i]:
% 139.73/20.54 ( ( breln @ A @ B @ S ) =>
% 139.73/20.54 ( ( ![Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ![Xy:$i]:
% 139.73/20.54 ( ( in @ Xy @ B ) =>
% 139.73/20.54 ( ( in @ ( kpair @ Xx @ Xy ) @ R ) =>
% 139.73/20.54 ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) ) ) ) =>
% 139.73/20.54 ( subset @ R @ S ) ) ) ) ))).
% 139.73/20.54 thf('82', plain,
% 139.73/20.54 (( subbreln ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.54 ( ( breln @ X4 @ X6 @ X8 ) =>
% 139.73/20.54 ( ![X10:$i]:
% 139.73/20.54 ( ( breln @ X4 @ X6 @ X10 ) =>
% 139.73/20.54 ( ( ![X12:$i]:
% 139.73/20.54 ( ( in @ X12 @ X4 ) =>
% 139.73/20.54 ( ![X14:$i]:
% 139.73/20.54 ( ( in @ X14 @ X6 ) =>
% 139.73/20.54 ( ( in @ ( kpair @ X12 @ X14 ) @ X8 ) =>
% 139.73/20.54 ( in @ ( kpair @ X12 @ X14 ) @ X10 ) ) ) ) ) ) =>
% 139.73/20.54 ( subset @ X8 @ X10 ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(funcGraphProp4, axiom, funcGraphProp4 =
% 139.73/20.54 (![A:$i,B:$i,Xf:$i]:
% 139.73/20.54 ( ( in @ Xf @ ( funcSet @ A @ B ) ) =>
% 139.73/20.54 ( ![Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ![Xy:$i]:
% 139.73/20.54 ( ( in @ Xy @ B ) =>
% 139.73/20.54 ( ( in @ ( kpair @ Xx @ Xy ) @ Xf ) =>
% 139.73/20.54 ( ( ap @ A @ B @ Xf @ Xx ) = ( Xy ) ) ) ) ) ) ) ))).
% 139.73/20.54 thf('83', plain,
% 139.73/20.54 (( funcGraphProp4 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( funcSet @ X4 @ X6 ) ) =>
% 139.73/20.54 ( ![X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ X4 ) =>
% 139.73/20.54 ( ![X12:$i]:
% 139.73/20.54 ( ( in @ X12 @ X6 ) =>
% 139.73/20.54 ( ( in @ ( kpair @ X10 @ X12 ) @ X8 ) =>
% 139.73/20.54 ( ( ap @ X4 @ X6 @ X8 @ X10 ) = ( X12 ) ) ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(funcextLem, axiom, funcextLem =
% 139.73/20.54 (![A:$i,B:$i,Xf:$i]:
% 139.73/20.54 ( ( func @ A @ B @ Xf ) =>
% 139.73/20.54 ( ![Xg:$i]:
% 139.73/20.54 ( ( func @ A @ B @ Xg ) =>
% 139.73/20.54 ( ( ![Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ( ap @ A @ B @ Xf @ Xx ) = ( ap @ A @ B @ Xg @ Xx ) ) ) ) =>
% 139.73/20.54 ( ![Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ![Xy:$i]:
% 139.73/20.54 ( ( in @ Xy @ B ) =>
% 139.73/20.54 ( ( in @ ( kpair @ Xx @ Xy ) @ Xg ) =>
% 139.73/20.54 ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ) ))).
% 139.73/20.54 thf('84', plain,
% 139.73/20.54 (( funcextLem ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.54 ( ( func @ X4 @ X6 @ X8 ) =>
% 139.73/20.54 ( ![X10:$i]:
% 139.73/20.54 ( ( func @ X4 @ X6 @ X10 ) =>
% 139.73/20.54 ( ( ![X12:$i]:
% 139.73/20.54 ( ( in @ X12 @ X4 ) =>
% 139.73/20.54 ( ( ap @ X4 @ X6 @ X8 @ X12 ) =
% 139.73/20.54 ( ap @ X4 @ X6 @ X10 @ X12 ) ) ) ) =>
% 139.73/20.54 ( ![X14:$i]:
% 139.73/20.54 ( ( in @ X14 @ X4 ) =>
% 139.73/20.54 ( ![X16:$i]:
% 139.73/20.54 ( ( in @ X16 @ X6 ) =>
% 139.73/20.54 ( ( in @ ( kpair @ X14 @ X16 ) @ X10 ) =>
% 139.73/20.54 ( in @ ( kpair @ X14 @ X16 ) @ X8 ) ) ) ) ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(funcGraphProp2, axiom, funcGraphProp2 =
% 139.73/20.54 (![A:$i,B:$i,Xf:$i]:
% 139.73/20.54 ( ( func @ A @ B @ Xf ) =>
% 139.73/20.54 ( ![Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ![Xy:$i]:
% 139.73/20.54 ( ( in @ Xy @ B ) =>
% 139.73/20.54 ( ( in @ ( kpair @ Xx @ Xy ) @ Xf ) =>
% 139.73/20.54 ( ( ap @ A @ B @ Xf @ Xx ) = ( Xy ) ) ) ) ) ) ) ))).
% 139.73/20.54 thf('85', plain,
% 139.73/20.54 (( funcGraphProp2 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.54 ( ( func @ X4 @ X6 @ X8 ) =>
% 139.73/20.54 ( ![X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ X4 ) =>
% 139.73/20.54 ( ![X12:$i]:
% 139.73/20.54 ( ( in @ X12 @ X6 ) =>
% 139.73/20.54 ( ( in @ ( kpair @ X10 @ X12 ) @ X8 ) =>
% 139.73/20.54 ( ( ap @ X4 @ X6 @ X8 @ X10 ) = ( X12 ) ) ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(funcGraphProp3, axiom, funcGraphProp3 =
% 139.73/20.54 (![A:$i,B:$i,Xf:$i]:
% 139.73/20.54 ( ( in @ Xf @ ( funcSet @ A @ B ) ) =>
% 139.73/20.54 ( ![Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ))).
% 139.73/20.54 thf('86', plain,
% 139.73/20.54 (( funcGraphProp3 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( funcSet @ X4 @ X6 ) ) =>
% 139.73/20.54 ( ![X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ X4 ) =>
% 139.73/20.54 ( in @ ( kpair @ X10 @ ( ap @ X4 @ X6 @ X8 @ X10 ) ) @ X8 ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(funcGraphProp1, axiom, funcGraphProp1 =
% 139.73/20.54 (![A:$i,B:$i,Xf:$i]:
% 139.73/20.54 ( ( func @ A @ B @ Xf ) =>
% 139.73/20.54 ( ![Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ))).
% 139.73/20.54 thf('87', plain,
% 139.73/20.54 (( funcGraphProp1 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.54 ( ( func @ X4 @ X6 @ X8 ) =>
% 139.73/20.54 ( ![X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ X4 ) =>
% 139.73/20.54 ( in @ ( kpair @ X10 @ ( ap @ X4 @ X6 @ X8 @ X10 ) ) @ X8 ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(ex1E2, axiom, ex1E2 =
% 139.73/20.54 (![A:$i,Xphi:( $i > $o )]:
% 139.73/20.54 ( ( ex1 @ A @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) =>
% 139.73/20.54 ( ![Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ![Xy:$i]:
% 139.73/20.54 ( ( in @ Xy @ A ) =>
% 139.73/20.54 ( ( Xphi @ Xx ) => ( ( Xphi @ Xy ) => ( ( Xx ) = ( Xy ) ) ) ) ) ) ) ) ))).
% 139.73/20.54 thf('88', plain,
% 139.73/20.54 (( ex1E2 ) =
% 139.73/20.54 ( ![X4:$i,X6:( $i > $o )]:
% 139.73/20.54 ( ( ex1 @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) =>
% 139.73/20.54 ( ![X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ X4 ) =>
% 139.73/20.54 ( ![X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ X4 ) =>
% 139.73/20.54 ( ( X6 @ X8 ) => ( ( X6 @ X10 ) => ( ( X8 ) = ( X10 ) ) ) ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(brelnall2, axiom, brelnall2 =
% 139.73/20.54 (![A:$i,B:$i,R:$i]:
% 139.73/20.54 ( ( breln @ A @ B @ R ) =>
% 139.73/20.54 ( ![Xphi:( $i > $o )]:
% 139.73/20.54 ( ( ![Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ![Xy:$i]:
% 139.73/20.54 ( ( in @ Xy @ B ) =>
% 139.73/20.54 ( ( in @ ( kpair @ Xx @ Xy ) @ R ) =>
% 139.73/20.54 ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) ) ) ) =>
% 139.73/20.54 ( ![Xx:$i]: ( ( in @ Xx @ R ) => ( Xphi @ Xx ) ) ) ) ) ))).
% 139.73/20.54 thf('89', plain,
% 139.73/20.54 (( brelnall2 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.54 ( ( breln @ X4 @ X6 @ X8 ) =>
% 139.73/20.54 ( ![X10:( $i > $o )]:
% 139.73/20.54 ( ( ![X12:$i]:
% 139.73/20.54 ( ( in @ X12 @ X4 ) =>
% 139.73/20.54 ( ![X14:$i]:
% 139.73/20.54 ( ( in @ X14 @ X6 ) =>
% 139.73/20.54 ( ( in @ ( kpair @ X12 @ X14 ) @ X8 ) =>
% 139.73/20.54 ( X10 @ ( kpair @ X12 @ X14 ) ) ) ) ) ) ) =>
% 139.73/20.54 ( ![X16:$i]: ( ( in @ X16 @ X8 ) => ( X10 @ X16 ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(brelnall1, axiom, brelnall1 =
% 139.73/20.54 (![A:$i,B:$i,R:$i]:
% 139.73/20.54 ( ( breln @ A @ B @ R ) =>
% 139.73/20.54 ( ![Xphi:( $i > $o )]:
% 139.73/20.54 ( ( ![Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ![Xy:$i]:
% 139.73/20.54 ( ( in @ Xy @ B ) =>
% 139.73/20.54 ( ( in @ ( kpair @ Xx @ Xy ) @ R ) =>
% 139.73/20.54 ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) ) ) ) =>
% 139.73/20.54 ( ![Xx:$i]: ( ( in @ Xx @ R ) => ( Xphi @ Xx ) ) ) ) ) ))).
% 139.73/20.54 thf('90', plain,
% 139.73/20.54 (( brelnall1 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.54 ( ( breln @ X4 @ X6 @ X8 ) =>
% 139.73/20.54 ( ![X10:( $i > $o )]:
% 139.73/20.54 ( ( ![X12:$i]:
% 139.73/20.54 ( ( in @ X12 @ X4 ) =>
% 139.73/20.54 ( ![X14:$i]:
% 139.73/20.54 ( ( in @ X14 @ X6 ) =>
% 139.73/20.54 ( ( in @ ( kpair @ X12 @ X14 ) @ X8 ) =>
% 139.73/20.54 ( X10 @ ( kpair @ X12 @ X14 ) ) ) ) ) ) ) =>
% 139.73/20.54 ( ![X16:$i]: ( ( in @ X16 @ X8 ) => ( X10 @ X16 ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(lam2p, axiom, lam2p =
% 139.73/20.54 (![A:$i,B:$i,Xf:( $i > $i )]:
% 139.73/20.54 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( in @ ( Xf @ Xx ) @ B ) ) ) =>
% 139.73/20.54 ( in @ ( lam @ A @ B @ ( ^[Xx:$i]: ( Xf @ Xx ) ) ) @ ( funcSet @ A @ B ) ) ))).
% 139.73/20.54 thf('91', plain,
% 139.73/20.54 (( lam2p ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:( $i > $i )]:
% 139.73/20.54 ( ( ![X10:$i]: ( ( in @ X10 @ X4 ) => ( in @ ( X8 @ X10 ) @ X6 ) ) ) =>
% 139.73/20.54 ( in @
% 139.73/20.54 ( lam @ X4 @ X6 @ ( ^[V_1:$i]: ( X8 @ V_1 ) ) ) @
% 139.73/20.54 ( funcSet @ X4 @ X6 ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(lamp, axiom, lamp =
% 139.73/20.54 (![A:$i,B:$i,Xf:( $i > $i )]:
% 139.73/20.54 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( in @ ( Xf @ Xx ) @ B ) ) ) =>
% 139.73/20.54 ( func @ A @ B @ ( lam @ A @ B @ ( ^[Xx:$i]: ( Xf @ Xx ) ) ) ) ))).
% 139.73/20.54 thf('92', plain,
% 139.73/20.54 (( lamp ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:( $i > $i )]:
% 139.73/20.54 ( ( ![X10:$i]: ( ( in @ X10 @ X4 ) => ( in @ ( X8 @ X10 ) @ X6 ) ) ) =>
% 139.73/20.54 ( func @ X4 @ X6 @ ( lam @ X4 @ X6 @ ( ^[V_1:$i]: ( X8 @ V_1 ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(lamProp, axiom, lamProp =
% 139.73/20.54 (![A:$i,B:$i,Xf:( $i > $i )]:
% 139.73/20.54 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( in @ ( Xf @ Xx ) @ B ) ) ) =>
% 139.73/20.54 ( func @
% 139.73/20.54 A @ B @
% 139.73/20.54 ( dpsetconstr @ A @ B @ ( ^[Xx:$i,Xy:$i]: ( ( Xf @ Xx ) = ( Xy ) ) ) ) ) ))).
% 139.73/20.54 thf('93', plain,
% 139.73/20.54 (( lamProp ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:( $i > $i )]:
% 139.73/20.54 ( ( ![X10:$i]: ( ( in @ X10 @ X4 ) => ( in @ ( X8 @ X10 ) @ X6 ) ) ) =>
% 139.73/20.54 ( func @
% 139.73/20.54 X4 @ X6 @
% 139.73/20.54 ( dpsetconstr @
% 139.73/20.54 X4 @ X6 @ ( ^[V_1:$i,V_2:$i]: ( ( X8 @ V_1 ) = ( V_2 ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(funcinfuncset, axiom, funcinfuncset =
% 139.73/20.54 (![A:$i,B:$i,Xf:$i]:
% 139.73/20.54 ( ( func @ A @ B @ Xf ) => ( in @ Xf @ ( funcSet @ A @ B ) ) ))).
% 139.73/20.54 thf('94', plain,
% 139.73/20.54 (( funcinfuncset ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.54 ( ( func @ X4 @ X6 @ X8 ) => ( in @ X8 @ ( funcSet @ X4 @ X6 ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(ap2p, axiom, ap2p =
% 139.73/20.54 (![A:$i,B:$i,Xf:$i]:
% 139.73/20.54 ( ( in @ Xf @ ( funcSet @ A @ B ) ) =>
% 139.73/20.54 ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ))).
% 139.73/20.54 thf('95', plain,
% 139.73/20.54 (( ap2p ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( funcSet @ X4 @ X6 ) ) =>
% 139.73/20.54 ( ![X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ X4 ) => ( in @ ( ap @ X4 @ X6 @ X8 @ X10 ) @ X6 ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(infuncsetfunc, axiom, infuncsetfunc =
% 139.73/20.54 (![A:$i,B:$i,Xf:$i]:
% 139.73/20.54 ( ( in @ Xf @ ( funcSet @ A @ B ) ) => ( func @ A @ B @ Xf ) ))).
% 139.73/20.54 thf('96', plain,
% 139.73/20.54 (( infuncsetfunc ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( funcSet @ X4 @ X6 ) ) => ( func @ X4 @ X6 @ X8 ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(app, axiom, app =
% 139.73/20.54 (![A:$i,B:$i,Xf:$i]:
% 139.73/20.54 ( ( func @ A @ B @ Xf ) =>
% 139.73/20.54 ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ))).
% 139.73/20.54 thf('97', plain,
% 139.73/20.54 (( app ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.54 ( ( func @ X4 @ X6 @ X8 ) =>
% 139.73/20.54 ( ![X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ X4 ) => ( in @ ( ap @ X4 @ X6 @ X8 @ X10 ) @ X6 ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(apProp, axiom, apProp =
% 139.73/20.54 (![A:$i,B:$i,Xf:$i]:
% 139.73/20.54 ( ( func @ A @ B @ Xf ) =>
% 139.73/20.54 ( ![Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( in @
% 139.73/20.54 ( setunion @
% 139.73/20.54 ( dsetconstr @
% 139.73/20.54 B @ ( ^[Xy:$i]: ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) @
% 139.73/20.54 B ) ) ) ))).
% 139.73/20.54 thf('98', plain,
% 139.73/20.54 (( apProp ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.54 ( ( func @ X4 @ X6 @ X8 ) =>
% 139.73/20.54 ( ![X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ X4 ) =>
% 139.73/20.54 ( in @
% 139.73/20.54 ( setunion @
% 139.73/20.54 ( dsetconstr @
% 139.73/20.54 X6 @ ( ^[V_1:$i]: ( in @ ( kpair @ X10 @ V_1 ) @ X8 ) ) ) ) @
% 139.73/20.54 X6 ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(funcImageSingleton, axiom, funcImageSingleton =
% 139.73/20.54 (![A:$i,B:$i,Xf:$i]:
% 139.73/20.54 ( ( func @ A @ B @ Xf ) =>
% 139.73/20.54 ( ![Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( singleton @
% 139.73/20.54 ( dsetconstr @ B @ ( ^[Xy:$i]: ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ))).
% 139.73/20.54 thf('99', plain,
% 139.73/20.54 (( funcImageSingleton ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.54 ( ( func @ X4 @ X6 @ X8 ) =>
% 139.73/20.54 ( ![X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ X4 ) =>
% 139.73/20.54 ( singleton @
% 139.73/20.54 ( dsetconstr @
% 139.73/20.54 X6 @ ( ^[V_1:$i]: ( in @ ( kpair @ X10 @ V_1 ) @ X8 ) ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(dpsetconstrER, axiom, dpsetconstrER =
% 139.73/20.54 (![A:$i,B:$i,Xphi:( $i > $i > $o ),Xx:$i,Xy:$i]:
% 139.73/20.54 ( ( in @
% 139.73/20.54 ( kpair @ Xx @ Xy ) @
% 139.73/20.54 ( dpsetconstr @ A @ B @ ( ^[Xz:$i,Xu:$i]: ( Xphi @ Xz @ Xu ) ) ) ) =>
% 139.73/20.54 ( Xphi @ Xx @ Xy ) ))).
% 139.73/20.54 thf('100', plain,
% 139.73/20.54 (( dpsetconstrER ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:( $i > $i > $o ),X10:$i,X12:$i]:
% 139.73/20.54 ( ( in @
% 139.73/20.54 ( kpair @ X10 @ X12 ) @
% 139.73/20.54 ( dpsetconstr @ X4 @ X6 @ ( ^[V_1:$i,V_2:$i]: ( X8 @ V_1 @ V_2 ) ) ) ) =>
% 139.73/20.54 ( X8 @ X10 @ X12 ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(dpsetconstrEL2, axiom, dpsetconstrEL2 =
% 139.73/20.54 (![A:$i,B:$i,Xphi:( $i > $i > $o ),Xx:$i,Xy:$i]:
% 139.73/20.54 ( ( in @
% 139.73/20.54 ( kpair @ Xx @ Xy ) @
% 139.73/20.54 ( dpsetconstr @ A @ B @ ( ^[Xz:$i,Xu:$i]: ( Xphi @ Xz @ Xu ) ) ) ) =>
% 139.73/20.54 ( in @ Xy @ B ) ))).
% 139.73/20.54 thf('101', plain,
% 139.73/20.54 (( dpsetconstrEL2 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:( $i > $i > $o ),X10:$i,X12:$i]:
% 139.73/20.54 ( ( in @
% 139.73/20.54 ( kpair @ X10 @ X12 ) @
% 139.73/20.54 ( dpsetconstr @ X4 @ X6 @ ( ^[V_1:$i,V_2:$i]: ( X8 @ V_1 @ V_2 ) ) ) ) =>
% 139.73/20.54 ( in @ X12 @ X6 ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(dpsetconstrEL1, axiom, dpsetconstrEL1 =
% 139.73/20.54 (![A:$i,B:$i,Xphi:( $i > $i > $o ),Xx:$i,Xy:$i]:
% 139.73/20.54 ( ( in @
% 139.73/20.54 ( kpair @ Xx @ Xy ) @
% 139.73/20.54 ( dpsetconstr @ A @ B @ ( ^[Xz:$i,Xu:$i]: ( Xphi @ Xz @ Xu ) ) ) ) =>
% 139.73/20.54 ( in @ Xx @ A ) ))).
% 139.73/20.54 thf('102', plain,
% 139.73/20.54 (( dpsetconstrEL1 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:( $i > $i > $o ),X10:$i,X12:$i]:
% 139.73/20.54 ( ( in @
% 139.73/20.54 ( kpair @ X10 @ X12 ) @
% 139.73/20.54 ( dpsetconstr @ X4 @ X6 @ ( ^[V_1:$i,V_2:$i]: ( X8 @ V_1 @ V_2 ) ) ) ) =>
% 139.73/20.54 ( in @ X10 @ X4 ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(dpsetconstrERa, axiom, dpsetconstrERa =
% 139.73/20.54 (![A:$i,B:$i,Xphi:( $i > $i > $o ),Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ![Xy:$i]:
% 139.73/20.54 ( ( in @ Xy @ B ) =>
% 139.73/20.54 ( ( in @
% 139.73/20.54 ( kpair @ Xx @ Xy ) @
% 139.73/20.54 ( dpsetconstr @ A @ B @ ( ^[Xz:$i,Xu:$i]: ( Xphi @ Xz @ Xu ) ) ) ) =>
% 139.73/20.54 ( Xphi @ Xx @ Xy ) ) ) ) ))).
% 139.73/20.54 thf('103', plain,
% 139.73/20.54 (( dpsetconstrERa ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:( $i > $i > $o ),X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ X4 ) =>
% 139.73/20.54 ( ![X12:$i]:
% 139.73/20.54 ( ( in @ X12 @ X6 ) =>
% 139.73/20.54 ( ( in @
% 139.73/20.54 ( kpair @ X10 @ X12 ) @
% 139.73/20.54 ( dpsetconstr @
% 139.73/20.54 X4 @ X6 @ ( ^[V_1:$i,V_2:$i]: ( X8 @ V_1 @ V_2 ) ) ) ) =>
% 139.73/20.54 ( X8 @ X10 @ X12 ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(setOfPairsIsBReln, axiom, setOfPairsIsBReln =
% 139.73/20.54 (![A:$i,B:$i,Xphi:( $i > $i > $o )]:
% 139.73/20.54 ( breln @
% 139.73/20.54 A @ B @ ( dpsetconstr @ A @ B @ ( ^[Xx:$i,Xy:$i]: ( Xphi @ Xx @ Xy ) ) ) ))).
% 139.73/20.54 thf('104', plain,
% 139.73/20.54 (( setOfPairsIsBReln ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:( $i > $i > $o )]:
% 139.73/20.54 ( breln @
% 139.73/20.54 X4 @ X6 @
% 139.73/20.54 ( dpsetconstr @ X4 @ X6 @ ( ^[V_1:$i,V_2:$i]: ( X8 @ V_1 @ V_2 ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(dpsetconstrSub, axiom, dpsetconstrSub =
% 139.73/20.54 (![A:$i,B:$i,Xphi:( $i > $i > $o )]:
% 139.73/20.54 ( subset @
% 139.73/20.54 ( dpsetconstr @ A @ B @ ( ^[Xx:$i,Xy:$i]: ( Xphi @ Xx @ Xy ) ) ) @
% 139.73/20.54 ( cartprod @ A @ B ) ))).
% 139.73/20.54 thf('105', plain,
% 139.73/20.54 (( dpsetconstrSub ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:( $i > $i > $o )]:
% 139.73/20.54 ( subset @
% 139.73/20.54 ( dpsetconstr @ X4 @ X6 @ ( ^[V_1:$i,V_2:$i]: ( X8 @ V_1 @ V_2 ) ) ) @
% 139.73/20.54 ( cartprod @ X4 @ X6 ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(dpsetconstrI, axiom, dpsetconstrI =
% 139.73/20.54 (![A:$i,B:$i,Xphi:( $i > $i > $o ),Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ![Xy:$i]:
% 139.73/20.54 ( ( in @ Xy @ B ) =>
% 139.73/20.54 ( ( Xphi @ Xx @ Xy ) =>
% 139.73/20.54 ( in @
% 139.73/20.54 ( kpair @ Xx @ Xy ) @
% 139.73/20.54 ( dpsetconstr @ A @ B @ ( ^[Xz:$i,Xu:$i]: ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ))).
% 139.73/20.54 thf('106', plain,
% 139.73/20.54 (( dpsetconstrI ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:( $i > $i > $o ),X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ X4 ) =>
% 139.73/20.54 ( ![X12:$i]:
% 139.73/20.54 ( ( in @ X12 @ X6 ) =>
% 139.73/20.54 ( ( X8 @ X10 @ X12 ) =>
% 139.73/20.54 ( in @
% 139.73/20.54 ( kpair @ X10 @ X12 ) @
% 139.73/20.54 ( dpsetconstr @
% 139.73/20.54 X4 @ X6 @ ( ^[V_1:$i,V_2:$i]: ( X8 @ V_1 @ V_2 ) ) ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(cartprodpairsurjEq, axiom, cartprodpairsurjEq =
% 139.73/20.54 (![A:$i,B:$i,Xu:$i]:
% 139.73/20.54 ( ( in @ Xu @ ( cartprod @ A @ B ) ) =>
% 139.73/20.54 ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) ) = ( Xu ) ) ))).
% 139.73/20.54 thf('107', plain,
% 139.73/20.54 (( cartprodpairsurjEq ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( cartprod @ X4 @ X6 ) ) =>
% 139.73/20.54 ( ( kpair @ ( kfst @ X8 ) @ ( ksnd @ X8 ) ) = ( X8 ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(cartprodsndpairEq, axiom, cartprodsndpairEq =
% 139.73/20.54 (![A:$i,B:$i,Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ![Xy:$i]:
% 139.73/20.54 ( ( in @ Xy @ B ) => ( ( ksnd @ ( kpair @ Xx @ Xy ) ) = ( Xy ) ) ) ) ))).
% 139.73/20.54 thf('108', plain,
% 139.73/20.54 (( cartprodsndpairEq ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ X4 ) =>
% 139.73/20.54 ( ![X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ X6 ) =>
% 139.73/20.54 ( ( ksnd @ ( kpair @ X8 @ X10 ) ) = ( X10 ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(cartprodfstpairEq, axiom, cartprodfstpairEq =
% 139.73/20.54 (![A:$i,B:$i,Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ![Xy:$i]:
% 139.73/20.54 ( ( in @ Xy @ B ) => ( ( kfst @ ( kpair @ Xx @ Xy ) ) = ( Xx ) ) ) ) ))).
% 139.73/20.54 thf('109', plain,
% 139.73/20.54 (( cartprodfstpairEq ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ X4 ) =>
% 139.73/20.54 ( ![X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ X6 ) =>
% 139.73/20.54 ( ( kfst @ ( kpair @ X8 @ X10 ) ) = ( X8 ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(cartprodmempaircEq, axiom, cartprodmempaircEq =
% 139.73/20.54 (![A:$i,B:$i,Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ![Xy:$i]:
% 139.73/20.54 ( ( in @ Xy @ B ) => ( ( kpair @ Xx @ Xy ) = ( kpair @ Xx @ Xy ) ) ) ) ))).
% 139.73/20.54 thf('110', plain,
% 139.73/20.54 (( cartprodmempaircEq ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ X4 ) =>
% 139.73/20.54 ( ![X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ X6 ) =>
% 139.73/20.54 ( ( kpair @ X8 @ X10 ) = ( kpair @ X8 @ X10 ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(cartprodpairmemER, axiom, cartprodpairmemER =
% 139.73/20.54 (![A:$i,B:$i,Xx:$i,Xy:$i]:
% 139.73/20.54 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) => ( in @ Xy @ B ) ))).
% 139.73/20.54 thf('111', plain,
% 139.73/20.54 (( cartprodpairmemER ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i,X10:$i]:
% 139.73/20.54 ( ( in @ ( kpair @ X8 @ X10 ) @ ( cartprod @ X4 @ X6 ) ) =>
% 139.73/20.54 ( in @ X10 @ X6 ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(cartprodpairmemEL, axiom, cartprodpairmemEL =
% 139.73/20.54 (![A:$i,B:$i,Xx:$i,Xy:$i]:
% 139.73/20.54 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) => ( in @ Xx @ A ) ))).
% 139.73/20.54 thf('112', plain,
% 139.73/20.54 (( cartprodpairmemEL ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i,X10:$i]:
% 139.73/20.54 ( ( in @ ( kpair @ X8 @ X10 ) @ ( cartprod @ X4 @ X6 ) ) =>
% 139.73/20.54 ( in @ X8 @ X4 ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(cartprodsndin, axiom, cartprodsndin =
% 139.73/20.54 (![A:$i,B:$i,Xu:$i]:
% 139.73/20.54 ( ( in @ Xu @ ( cartprod @ A @ B ) ) => ( in @ ( ksnd @ Xu ) @ B ) ))).
% 139.73/20.54 thf('113', plain,
% 139.73/20.54 (( cartprodsndin ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( cartprod @ X4 @ X6 ) ) => ( in @ ( ksnd @ X8 ) @ X6 ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(kpairsurjEq, axiom, kpairsurjEq =
% 139.73/20.54 (![Xu:$i]:
% 139.73/20.54 ( ( iskpair @ Xu ) =>
% 139.73/20.54 ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) ) = ( Xu ) ) ))).
% 139.73/20.54 thf('114', plain,
% 139.73/20.54 (( kpairsurjEq ) =
% 139.73/20.54 ( ![X4:$i]:
% 139.73/20.54 ( ( iskpair @ X4 ) =>
% 139.73/20.54 ( ( kpair @ ( kfst @ X4 ) @ ( ksnd @ X4 ) ) = ( X4 ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(ksndpairEq, axiom, ksndpairEq =
% 139.73/20.54 (![Xx:$i,Xy:$i]: ( ( ksnd @ ( kpair @ Xx @ Xy ) ) = ( Xy ) ))).
% 139.73/20.54 thf('115', plain,
% 139.73/20.54 (( ksndpairEq ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]: ( ( ksnd @ ( kpair @ X4 @ X6 ) ) = ( X6 ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(ksndsingleton, axiom, ksndsingleton =
% 139.73/20.54 (![Xu:$i]:
% 139.73/20.54 ( ( iskpair @ Xu ) =>
% 139.73/20.54 ( singleton @
% 139.73/20.54 ( dsetconstr @
% 139.73/20.54 ( setunion @ Xu ) @
% 139.73/20.54 ( ^[Xx:$i]: ( ( Xu ) = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ))).
% 139.73/20.54 thf('116', plain,
% 139.73/20.54 (( ksndsingleton ) =
% 139.73/20.54 ( ![X4:$i]:
% 139.73/20.54 ( ( iskpair @ X4 ) =>
% 139.73/20.54 ( singleton @
% 139.73/20.54 ( dsetconstr @
% 139.73/20.54 ( setunion @ X4 ) @
% 139.73/20.54 ( ^[V_1:$i]: ( ( X4 ) = ( kpair @ ( kfst @ X4 ) @ V_1 ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(setukpairinjR, axiom, setukpairinjR =
% 139.73/20.54 (![Xx:$i,Xy:$i,Xz:$i,Xu:$i]:
% 139.73/20.54 ( ( ( kpair @ Xx @ Xy ) = ( kpair @ Xz @ Xu ) ) => ( ( Xy ) = ( Xu ) ) ))).
% 139.73/20.54 thf('117', plain,
% 139.73/20.54 (( setukpairinjR ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i,X10:$i]:
% 139.73/20.54 ( ( ( kpair @ X4 @ X6 ) = ( kpair @ X8 @ X10 ) ) =>
% 139.73/20.54 ( ( X6 ) = ( X10 ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(setukpairinjR2, axiom, setukpairinjR2 =
% 139.73/20.54 (![Xx:$i,Xy:$i,Xz:$i,Xu:$i]:
% 139.73/20.54 ( ( ( setadjoin @
% 139.73/20.54 ( setadjoin @ Xx @ emptyset ) @
% 139.73/20.54 ( setadjoin @
% 139.73/20.54 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) =
% 139.73/20.54 ( setadjoin @
% 139.73/20.54 ( setadjoin @ Xz @ emptyset ) @
% 139.73/20.54 ( setadjoin @
% 139.73/20.54 ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) ) =>
% 139.73/20.54 ( ( Xy ) = ( Xu ) ) ))).
% 139.73/20.54 thf('118', plain,
% 139.73/20.54 (( setukpairinjR2 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i,X10:$i]:
% 139.73/20.54 ( ( ( setadjoin @
% 139.73/20.54 ( setadjoin @ X4 @ emptyset ) @
% 139.73/20.54 ( setadjoin @
% 139.73/20.54 ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) @ emptyset ) ) =
% 139.73/20.54 ( setadjoin @
% 139.73/20.54 ( setadjoin @ X8 @ emptyset ) @
% 139.73/20.54 ( setadjoin @
% 139.73/20.54 ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @ emptyset ) ) ) =>
% 139.73/20.54 ( ( X6 ) = ( X10 ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(upairequniteq, axiom, upairequniteq =
% 139.73/20.54 (![Xx:$i,Xy:$i,Xz:$i]:
% 139.73/20.54 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) =
% 139.73/20.54 ( setadjoin @ Xz @ emptyset ) ) =>
% 139.73/20.54 ( ( Xx ) = ( Xy ) ) ))).
% 139.73/20.54 thf('119', plain,
% 139.73/20.54 (( upairequniteq ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.54 ( ( ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) =
% 139.73/20.54 ( setadjoin @ X8 @ emptyset ) ) =>
% 139.73/20.54 ( ( X4 ) = ( X6 ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(setukpairinjR1, axiom, setukpairinjR1 =
% 139.73/20.54 (![Xx:$i,Xy:$i,Xz:$i,Xu:$i]:
% 139.73/20.54 ( ( ( setadjoin @
% 139.73/20.54 ( setadjoin @ Xx @ emptyset ) @
% 139.73/20.54 ( setadjoin @
% 139.73/20.54 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) =
% 139.73/20.54 ( setadjoin @
% 139.73/20.54 ( setadjoin @ Xz @ emptyset ) @
% 139.73/20.54 ( setadjoin @
% 139.73/20.54 ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) ) =>
% 139.73/20.54 ( ( ( Xz ) = ( Xu ) ) => ( ( Xy ) = ( Xu ) ) ) ))).
% 139.73/20.54 thf('120', plain,
% 139.73/20.54 (( setukpairinjR1 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i,X10:$i]:
% 139.73/20.54 ( ( ( setadjoin @
% 139.73/20.54 ( setadjoin @ X4 @ emptyset ) @
% 139.73/20.54 ( setadjoin @
% 139.73/20.54 ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) @ emptyset ) ) =
% 139.73/20.54 ( setadjoin @
% 139.73/20.54 ( setadjoin @ X8 @ emptyset ) @
% 139.73/20.54 ( setadjoin @
% 139.73/20.54 ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @ emptyset ) ) ) =>
% 139.73/20.54 ( ( ( X8 ) = ( X10 ) ) => ( ( X6 ) = ( X10 ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(setukpairinjR12, axiom, setukpairinjR12 =
% 139.73/20.54 (![Xx:$i,Xy:$i]:
% 139.73/20.54 ( ( ( Xx ) = ( Xy ) ) =>
% 139.73/20.54 ( ( setadjoin @
% 139.73/20.54 ( setadjoin @ Xx @ emptyset ) @
% 139.73/20.54 ( setadjoin @
% 139.73/20.54 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) =
% 139.73/20.54 ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ))).
% 139.73/20.54 thf('121', plain,
% 139.73/20.54 (( setukpairinjR12 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( ( X4 ) = ( X6 ) ) =>
% 139.73/20.54 ( ( setadjoin @
% 139.73/20.54 ( setadjoin @ X4 @ emptyset ) @
% 139.73/20.54 ( setadjoin @
% 139.73/20.54 ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) @ emptyset ) ) =
% 139.73/20.54 ( setadjoin @ ( setadjoin @ X4 @ emptyset ) @ emptyset ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(setukpairinjR11, axiom, setukpairinjR11 =
% 139.73/20.54 (![Xx:$i,Xy:$i]:
% 139.73/20.54 ( ( ( Xx ) = ( Xy ) ) =>
% 139.73/20.54 ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) =
% 139.73/20.54 ( setadjoin @ Xx @ emptyset ) ) ))).
% 139.73/20.54 thf('122', plain,
% 139.73/20.54 (( setukpairinjR11 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( ( X4 ) = ( X6 ) ) =>
% 139.73/20.54 ( ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) =
% 139.73/20.54 ( setadjoin @ X4 @ emptyset ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(setukpairinjL, axiom, setukpairinjL =
% 139.73/20.54 (![Xx:$i,Xy:$i,Xz:$i,Xu:$i]:
% 139.73/20.54 ( ( ( kpair @ Xx @ Xy ) = ( kpair @ Xz @ Xu ) ) => ( ( Xx ) = ( Xz ) ) ))).
% 139.73/20.54 thf('123', plain,
% 139.73/20.54 (( setukpairinjL ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i,X10:$i]:
% 139.73/20.54 ( ( ( kpair @ X4 @ X6 ) = ( kpair @ X8 @ X10 ) ) =>
% 139.73/20.54 ( ( X4 ) = ( X8 ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(setukpairinjL2, axiom, setukpairinjL2 =
% 139.73/20.54 (![Xx:$i,Xy:$i,Xz:$i,Xu:$i]:
% 139.73/20.54 ( ( ( setadjoin @
% 139.73/20.54 ( setadjoin @ Xx @ emptyset ) @
% 139.73/20.54 ( setadjoin @
% 139.73/20.54 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) =
% 139.73/20.54 ( setadjoin @
% 139.73/20.54 ( setadjoin @ Xz @ emptyset ) @
% 139.73/20.54 ( setadjoin @
% 139.73/20.54 ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) ) =>
% 139.73/20.54 ( ( Xx ) = ( Xz ) ) ))).
% 139.73/20.54 thf('124', plain,
% 139.73/20.54 (( setukpairinjL2 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i,X10:$i]:
% 139.73/20.54 ( ( ( setadjoin @
% 139.73/20.54 ( setadjoin @ X4 @ emptyset ) @
% 139.73/20.54 ( setadjoin @
% 139.73/20.54 ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) @ emptyset ) ) =
% 139.73/20.54 ( setadjoin @
% 139.73/20.54 ( setadjoin @ X8 @ emptyset ) @
% 139.73/20.54 ( setadjoin @
% 139.73/20.54 ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @ emptyset ) ) ) =>
% 139.73/20.54 ( ( X4 ) = ( X8 ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(cartprodfstin, axiom, cartprodfstin =
% 139.73/20.54 (![A:$i,B:$i,Xu:$i]:
% 139.73/20.54 ( ( in @ Xu @ ( cartprod @ A @ B ) ) => ( in @ ( kfst @ Xu ) @ A ) ))).
% 139.73/20.54 thf('125', plain,
% 139.73/20.54 (( cartprodfstin ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( cartprod @ X4 @ X6 ) ) => ( in @ ( kfst @ X8 ) @ X4 ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(kfstpairEq, axiom, kfstpairEq =
% 139.73/20.54 (![Xx:$i,Xy:$i]: ( ( kfst @ ( kpair @ Xx @ Xy ) ) = ( Xx ) ))).
% 139.73/20.54 thf('126', plain,
% 139.73/20.54 (( kfstpairEq ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]: ( ( kfst @ ( kpair @ X4 @ X6 ) ) = ( X4 ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(theprop, axiom, theprop =
% 139.73/20.54 (![X:$i]: ( ( singleton @ X ) => ( in @ ( setunion @ X ) @ X ) ))).
% 139.73/20.54 thf('127', plain,
% 139.73/20.54 (( theprop ) =
% 139.73/20.54 ( ![X4:$i]: ( ( singleton @ X4 ) => ( in @ ( setunion @ X4 ) @ X4 ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(kfstsingleton, axiom, kfstsingleton =
% 139.73/20.54 (![Xu:$i]:
% 139.73/20.54 ( ( iskpair @ Xu ) =>
% 139.73/20.54 ( singleton @
% 139.73/20.54 ( dsetconstr @
% 139.73/20.54 ( setunion @ Xu ) @
% 139.73/20.54 ( ^[Xx:$i]: ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ))).
% 139.73/20.54 thf('128', plain,
% 139.73/20.54 (( kfstsingleton ) =
% 139.73/20.54 ( ![X4:$i]:
% 139.73/20.54 ( ( iskpair @ X4 ) =>
% 139.73/20.54 ( singleton @
% 139.73/20.54 ( dsetconstr @
% 139.73/20.54 ( setunion @ X4 ) @
% 139.73/20.54 ( ^[V_1:$i]: ( in @ ( setadjoin @ V_1 @ emptyset ) @ X4 ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(setukpairinjL1, axiom, setukpairinjL1 =
% 139.73/20.54 (![Xx:$i,Xy:$i,Xz:$i]:
% 139.73/20.54 ( ( in @
% 139.73/20.54 ( setadjoin @ Xz @ emptyset ) @
% 139.73/20.54 ( setadjoin @
% 139.73/20.54 ( setadjoin @ Xx @ emptyset ) @
% 139.73/20.54 ( setadjoin @
% 139.73/20.54 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) =>
% 139.73/20.54 ( ( Xx ) = ( Xz ) ) ))).
% 139.73/20.54 thf('129', plain,
% 139.73/20.54 (( setukpairinjL1 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.54 ( ( in @
% 139.73/20.54 ( setadjoin @ X8 @ emptyset ) @
% 139.73/20.54 ( setadjoin @
% 139.73/20.54 ( setadjoin @ X4 @ emptyset ) @
% 139.73/20.54 ( setadjoin @
% 139.73/20.54 ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) @ emptyset ) ) ) =>
% 139.73/20.54 ( ( X4 ) = ( X8 ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(singletonsuniq, axiom, singletonsuniq =
% 139.73/20.54 (![Xx:$i,Xy:$i]:
% 139.73/20.54 ( ( ( setadjoin @ Xx @ emptyset ) = ( setadjoin @ Xy @ emptyset ) ) =>
% 139.73/20.54 ( ( Xx ) = ( Xy ) ) ))).
% 139.73/20.54 thf('130', plain,
% 139.73/20.54 (( singletonsuniq ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( ( setadjoin @ X4 @ emptyset ) = ( setadjoin @ X6 @ emptyset ) ) =>
% 139.73/20.54 ( ( X4 ) = ( X6 ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(ex1I2, axiom, ex1I2 =
% 139.73/20.54 (![A:$i,Xphi:( $i > $o )]:
% 139.73/20.54 ( ( ![Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ![Xy:$i]:
% 139.73/20.54 ( ( in @ Xy @ A ) =>
% 139.73/20.54 ( ( Xphi @ Xx ) => ( ( Xphi @ Xy ) => ( ( Xx ) = ( Xy ) ) ) ) ) ) ) ) =>
% 139.73/20.54 ( ( ?[Xx:$i]: ( ( Xphi @ Xx ) & ( in @ Xx @ A ) ) ) =>
% 139.73/20.54 ( ex1 @ A @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) ) ))).
% 139.73/20.54 thf('131', plain,
% 139.73/20.54 (( ex1I2 ) =
% 139.73/20.54 ( ![X4:$i,X6:( $i > $o )]:
% 139.73/20.54 ( ( ![X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ X4 ) =>
% 139.73/20.54 ( ![X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ X4 ) =>
% 139.73/20.54 ( ( X6 @ X8 ) => ( ( X6 @ X10 ) => ( ( X8 ) = ( X10 ) ) ) ) ) ) ) ) =>
% 139.73/20.54 ( ( ?[X12:$i]: ( ( X6 @ X12 ) & ( in @ X12 @ X4 ) ) ) =>
% 139.73/20.54 ( ex1 @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(ex1I, axiom, ex1I =
% 139.73/20.54 (![A:$i,Xphi:( $i > $o ),Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ( Xphi @ Xx ) =>
% 139.73/20.54 ( ( ![Xy:$i]:
% 139.73/20.54 ( ( in @ Xy @ A ) => ( ( Xphi @ Xy ) => ( ( Xy ) = ( Xx ) ) ) ) ) =>
% 139.73/20.54 ( ex1 @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) ) ))).
% 139.73/20.54 thf('132', plain,
% 139.73/20.54 (( ex1I ) =
% 139.73/20.54 ( ![X4:$i,X6:( $i > $o ),X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ X4 ) =>
% 139.73/20.54 ( ( X6 @ X8 ) =>
% 139.73/20.54 ( ( ![X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ X4 ) =>
% 139.73/20.54 ( ( X6 @ X10 ) => ( ( X10 ) = ( X8 ) ) ) ) ) =>
% 139.73/20.54 ( ex1 @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(ex1E1, axiom, ex1E1 =
% 139.73/20.54 (![A:$i,Xphi:( $i > $o )]:
% 139.73/20.54 ( ( ex1 @ A @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) =>
% 139.73/20.54 ( ?[Xx:$i]: ( ( Xphi @ Xx ) & ( in @ Xx @ A ) ) ) ))).
% 139.73/20.54 thf('133', plain,
% 139.73/20.54 (( ex1E1 ) =
% 139.73/20.54 ( ![X4:$i,X6:( $i > $o )]:
% 139.73/20.54 ( ( ex1 @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) =>
% 139.73/20.54 ( ?[X8:$i]: ( ( X6 @ X8 ) & ( in @ X8 @ X4 ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(ex1, axiom,(( ex1 ) =
% 139.73/20.54 (^[A:$i,Xphi:( $i > $o )]:
% 139.73/20.54 ( singleton @ ( dsetconstr @ A @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) )))).
% 139.73/20.54 thf('134', plain,
% 139.73/20.54 (( ex1 ) =
% 139.73/20.54 ( ^[A:$i,Xphi:( $i > $o )]:
% 139.73/20.54 ( singleton @ ( dsetconstr @ A @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) ) )),
% 139.73/20.54 inference('simplify_rw_rule', [status(thm)], [ex1])).
% 139.73/20.54 thf('135', plain,
% 139.73/20.54 (( ex1 ) =
% 139.73/20.54 ( ^[V_1:$i,V_2:( $i > $o )]:
% 139.73/20.54 ( singleton @ ( dsetconstr @ V_1 @ ( ^[V_3:$i]: ( V_2 @ V_3 ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(singletonprop, axiom, singletonprop =
% 139.73/20.54 (![A:$i,Xphi:( $i > $o )]:
% 139.73/20.54 ( ( ![Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ![Xy:$i]:
% 139.73/20.54 ( ( in @ Xy @ A ) =>
% 139.73/20.54 ( ( Xphi @ Xx ) => ( ( Xphi @ Xy ) => ( ( Xx ) = ( Xy ) ) ) ) ) ) ) ) =>
% 139.73/20.54 ( ( ?[Xx:$i]: ( ( Xphi @ Xx ) & ( in @ Xx @ A ) ) ) =>
% 139.73/20.54 ( singleton @ ( dsetconstr @ A @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) ) ) ))).
% 139.73/20.54 thf('136', plain,
% 139.73/20.54 (( singletonprop ) =
% 139.73/20.54 ( ![X4:$i,X6:( $i > $o )]:
% 139.73/20.54 ( ( ![X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ X4 ) =>
% 139.73/20.54 ( ![X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ X4 ) =>
% 139.73/20.54 ( ( X6 @ X8 ) => ( ( X6 @ X10 ) => ( ( X8 ) = ( X10 ) ) ) ) ) ) ) ) =>
% 139.73/20.54 ( ( ?[X12:$i]: ( ( X6 @ X12 ) & ( in @ X12 @ X4 ) ) ) =>
% 139.73/20.54 ( singleton @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(setunionsingleton, axiom, setunionsingleton =
% 139.73/20.54 (![Xx:$i]: ( ( setunion @ ( setadjoin @ Xx @ emptyset ) ) = ( Xx ) ))).
% 139.73/20.54 thf('137', plain,
% 139.73/20.54 (( setunionsingleton ) =
% 139.73/20.54 ( ![X4:$i]: ( ( setunion @ ( setadjoin @ X4 @ emptyset ) ) = ( X4 ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(setunionsingleton2, axiom, setunionsingleton2 =
% 139.73/20.54 (![A:$i]: ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ))).
% 139.73/20.54 thf('138', plain,
% 139.73/20.54 (( setunionsingleton2 ) =
% 139.73/20.54 ( ![X4:$i]:
% 139.73/20.54 ( subset @ X4 @ ( setunion @ ( setadjoin @ X4 @ emptyset ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(setunionsingleton1, axiom, setunionsingleton1 =
% 139.73/20.54 (![A:$i]: ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ))).
% 139.73/20.54 thf('139', plain,
% 139.73/20.54 (( setunionsingleton1 ) =
% 139.73/20.54 ( ![X4:$i]:
% 139.73/20.54 ( subset @ ( setunion @ ( setadjoin @ X4 @ emptyset ) ) @ X4 ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(setunionE2, axiom, setunionE2 =
% 139.73/20.54 (![A:$i,Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ ( setunion @ A ) ) =>
% 139.73/20.54 ( ?[X:$i]: ( ( in @ Xx @ X ) & ( in @ X @ A ) ) ) ))).
% 139.73/20.54 thf('140', plain,
% 139.73/20.54 (( setunionE2 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( in @ X6 @ ( setunion @ X4 ) ) =>
% 139.73/20.54 ( ?[X8:$i]: ( ( in @ X6 @ X8 ) & ( in @ X8 @ X4 ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(cartprodmempair, axiom, cartprodmempair =
% 139.73/20.54 (![A:$i,B:$i,Xu:$i]:
% 139.73/20.54 ( ( in @ Xu @ ( cartprod @ A @ B ) ) => ( iskpair @ Xu ) ))).
% 139.73/20.54 thf('141', plain,
% 139.73/20.54 (( cartprodmempair ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( cartprod @ X4 @ X6 ) ) => ( iskpair @ X8 ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(cartprodmempair1, axiom, cartprodmempair1 =
% 139.73/20.54 (![A:$i,B:$i,Xu:$i]:
% 139.73/20.54 ( ( in @ Xu @ ( cartprod @ A @ B ) ) =>
% 139.73/20.54 ( ?[Xx:$i]:
% 139.73/20.54 ( ( ?[Xy:$i]: ( ( ( Xu ) = ( kpair @ Xx @ Xy ) ) & ( in @ Xy @ B ) ) ) &
% 139.73/20.54 ( in @ Xx @ A ) ) ) ))).
% 139.73/20.54 thf('142', plain,
% 139.73/20.54 (( cartprodmempair1 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( cartprod @ X4 @ X6 ) ) =>
% 139.73/20.54 ( ?[X10:$i]:
% 139.73/20.54 ( ( ?[X12:$i]:
% 139.73/20.54 ( ( ( X8 ) = ( kpair @ X10 @ X12 ) ) & ( in @ X12 @ X6 ) ) ) &
% 139.73/20.54 ( in @ X10 @ X4 ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(cartprodpairin, axiom, cartprodpairin =
% 139.73/20.54 (![A:$i,B:$i,Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ![Xy:$i]:
% 139.73/20.54 ( ( in @ Xy @ B ) =>
% 139.73/20.54 ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ))).
% 139.73/20.54 thf('143', plain,
% 139.73/20.54 (( cartprodpairin ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ X4 ) =>
% 139.73/20.54 ( ![X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ X6 ) =>
% 139.73/20.54 ( in @ ( kpair @ X8 @ X10 ) @ ( cartprod @ X4 @ X6 ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(ubforcartprodlem3, axiom, ubforcartprodlem3 =
% 139.73/20.54 (![A:$i,B:$i,Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ![Xy:$i]:
% 139.73/20.54 ( ( in @ Xy @ B ) =>
% 139.73/20.54 ( in @
% 139.73/20.54 ( kpair @ Xx @ Xy ) @
% 139.73/20.54 ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ))).
% 139.73/20.54 thf('144', plain,
% 139.73/20.54 (( ubforcartprodlem3 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ X4 ) =>
% 139.73/20.54 ( ![X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ X6 ) =>
% 139.73/20.54 ( in @
% 139.73/20.54 ( kpair @ X8 @ X10 ) @
% 139.73/20.54 ( powerset @ ( powerset @ ( binunion @ X4 @ X6 ) ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(ubforcartprodlem2, axiom, ubforcartprodlem2 =
% 139.73/20.54 (![A:$i,B:$i,Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ![Xy:$i]:
% 139.73/20.54 ( ( in @ Xy @ B ) =>
% 139.73/20.54 ( in @
% 139.73/20.54 ( setadjoin @
% 139.73/20.54 ( setadjoin @ Xx @ emptyset ) @
% 139.73/20.54 ( setadjoin @
% 139.73/20.54 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @
% 139.73/20.54 ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ))).
% 139.73/20.54 thf('145', plain,
% 139.73/20.54 (( ubforcartprodlem2 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ X4 ) =>
% 139.73/20.54 ( ![X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ X6 ) =>
% 139.73/20.54 ( in @
% 139.73/20.54 ( setadjoin @
% 139.73/20.54 ( setadjoin @ X8 @ emptyset ) @
% 139.73/20.54 ( setadjoin @
% 139.73/20.54 ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @
% 139.73/20.54 emptyset ) ) @
% 139.73/20.54 ( powerset @ ( powerset @ ( binunion @ X4 @ X6 ) ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(ubforcartprodlem1, axiom, ubforcartprodlem1 =
% 139.73/20.54 (![A:$i,B:$i,Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ![Xy:$i]:
% 139.73/20.54 ( ( in @ Xy @ B ) =>
% 139.73/20.54 ( subset @
% 139.73/20.54 ( setadjoin @
% 139.73/20.54 ( setadjoin @ Xx @ emptyset ) @
% 139.73/20.54 ( setadjoin @
% 139.73/20.54 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @
% 139.73/20.54 ( powerset @ ( binunion @ A @ B ) ) ) ) ) ))).
% 139.73/20.54 thf('146', plain,
% 139.73/20.54 (( ubforcartprodlem1 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ X4 ) =>
% 139.73/20.54 ( ![X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ X6 ) =>
% 139.73/20.54 ( subset @
% 139.73/20.54 ( setadjoin @
% 139.73/20.54 ( setadjoin @ X8 @ emptyset ) @
% 139.73/20.54 ( setadjoin @
% 139.73/20.54 ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @
% 139.73/20.54 emptyset ) ) @
% 139.73/20.54 ( powerset @ ( binunion @ X4 @ X6 ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(upairinpowunion, axiom, upairinpowunion =
% 139.73/20.54 (![A:$i,B:$i,Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ![Xy:$i]:
% 139.73/20.54 ( ( in @ Xy @ B ) =>
% 139.73/20.54 ( in @
% 139.73/20.54 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @
% 139.73/20.54 ( powerset @ ( binunion @ A @ B ) ) ) ) ) ))).
% 139.73/20.54 thf('147', plain,
% 139.73/20.54 (( upairinpowunion ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ X4 ) =>
% 139.73/20.54 ( ![X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ X6 ) =>
% 139.73/20.54 ( in @
% 139.73/20.54 ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @
% 139.73/20.54 ( powerset @ ( binunion @ X4 @ X6 ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(upairsubunion, axiom, upairsubunion =
% 139.73/20.54 (![A:$i,B:$i,Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ![Xy:$i]:
% 139.73/20.54 ( ( in @ Xy @ B ) =>
% 139.73/20.54 ( subset @
% 139.73/20.54 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @
% 139.73/20.54 ( binunion @ A @ B ) ) ) ) ))).
% 139.73/20.54 thf('148', plain,
% 139.73/20.54 (( upairsubunion ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ X4 ) =>
% 139.73/20.54 ( ![X10:$i]:
% 139.73/20.54 ( ( in @ X10 @ X6 ) =>
% 139.73/20.54 ( subset @
% 139.73/20.54 ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @
% 139.73/20.54 ( binunion @ X4 @ X6 ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(upairset2E, axiom, upairset2E =
% 139.73/20.54 (![Xx:$i,Xy:$i,Xz:$i]:
% 139.73/20.54 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) =>
% 139.73/20.54 ( ( ( Xz ) = ( Xx ) ) | ( ( Xz ) = ( Xy ) ) ) ))).
% 139.73/20.54 thf('149', plain,
% 139.73/20.54 (( upairset2E ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) =>
% 139.73/20.54 ( ( ( X8 ) = ( X4 ) ) | ( ( X8 ) = ( X6 ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(singletoninpowunion, axiom, singletoninpowunion =
% 139.73/20.54 (![A:$i,B:$i,Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( in @
% 139.73/20.54 ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ))).
% 139.73/20.54 thf('150', plain,
% 139.73/20.54 (( singletoninpowunion ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ X4 ) =>
% 139.73/20.54 ( in @
% 139.73/20.54 ( setadjoin @ X8 @ emptyset ) @
% 139.73/20.54 ( powerset @ ( binunion @ X4 @ X6 ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(singletoninpowerset, axiom, singletoninpowerset =
% 139.73/20.54 (![A:$i,Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ))).
% 139.73/20.54 thf('151', plain,
% 139.73/20.54 (( singletoninpowerset ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( in @ X6 @ X4 ) =>
% 139.73/20.54 ( in @ ( setadjoin @ X6 @ emptyset ) @ ( powerset @ X4 ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(singletonsubset, axiom, singletonsubset =
% 139.73/20.54 (![A:$i,Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ))).
% 139.73/20.54 thf('152', plain,
% 139.73/20.54 (( singletonsubset ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( in @ X6 @ X4 ) => ( subset @ ( setadjoin @ X6 @ emptyset ) @ X4 ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(kpairp, axiom, kpairp =
% 139.73/20.54 (![Xx:$i,Xy:$i]: ( iskpair @ ( kpair @ Xx @ Xy ) ))).
% 139.73/20.54 thf('153', plain,
% 139.73/20.54 (( kpairp ) = ( ![X4:$i,X6:$i]: ( iskpair @ ( kpair @ X4 @ X6 ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(kpairiskpair, axiom, kpairiskpair =
% 139.73/20.54 (![Xx:$i,Xy:$i]:
% 139.73/20.54 ( iskpair @
% 139.73/20.54 ( setadjoin @
% 139.73/20.54 ( setadjoin @ Xx @ emptyset ) @
% 139.73/20.54 ( setadjoin @
% 139.73/20.54 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ))).
% 139.73/20.54 thf('154', plain,
% 139.73/20.54 (( kpairiskpair ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( iskpair @
% 139.73/20.54 ( setadjoin @
% 139.73/20.54 ( setadjoin @ X4 @ emptyset ) @
% 139.73/20.54 ( setadjoin @
% 139.73/20.54 ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) @ emptyset ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(setukpairIR, axiom, setukpairIR =
% 139.73/20.54 (![Xx:$i,Xy:$i]:
% 139.73/20.54 ( in @
% 139.73/20.54 Xy @
% 139.73/20.54 ( setunion @
% 139.73/20.54 ( setadjoin @
% 139.73/20.54 ( setadjoin @ Xx @ emptyset ) @
% 139.73/20.54 ( setadjoin @
% 139.73/20.54 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ))).
% 139.73/20.54 thf('155', plain,
% 139.73/20.54 (( setukpairIR ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( in @
% 139.73/20.54 X6 @
% 139.73/20.54 ( setunion @
% 139.73/20.54 ( setadjoin @
% 139.73/20.54 ( setadjoin @ X4 @ emptyset ) @
% 139.73/20.54 ( setadjoin @
% 139.73/20.54 ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) @ emptyset ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(setukpairIL, axiom, setukpairIL =
% 139.73/20.54 (![Xx:$i,Xy:$i]:
% 139.73/20.54 ( in @
% 139.73/20.54 Xx @
% 139.73/20.54 ( setunion @
% 139.73/20.54 ( setadjoin @
% 139.73/20.54 ( setadjoin @ Xx @ emptyset ) @
% 139.73/20.54 ( setadjoin @
% 139.73/20.54 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ))).
% 139.73/20.54 thf('156', plain,
% 139.73/20.54 (( setukpairIL ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( in @
% 139.73/20.54 X4 @
% 139.73/20.54 ( setunion @
% 139.73/20.54 ( setadjoin @
% 139.73/20.54 ( setadjoin @ X4 @ emptyset ) @
% 139.73/20.54 ( setadjoin @
% 139.73/20.54 ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) @ emptyset ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(secondinupair, axiom, secondinupair =
% 139.73/20.54 (![Xx:$i,Xy:$i]:
% 139.73/20.54 ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 139.73/20.54 thf('157', plain,
% 139.73/20.54 (( secondinupair ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( in @ X6 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(symdiffIneg2, axiom, symdiffIneg2 =
% 139.73/20.54 (![A:$i,B:$i,Xx:$i]:
% 139.73/20.54 ( ( ~( in @ Xx @ A ) ) =>
% 139.73/20.54 ( ( ~( in @ Xx @ B ) ) => ( ~( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ))).
% 139.73/20.54 thf('158', plain,
% 139.73/20.54 (( symdiffIneg2 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.54 ( ( ~( in @ X8 @ X4 ) ) =>
% 139.73/20.54 ( ( ~( in @ X8 @ X6 ) ) => ( ~( in @ X8 @ ( symdiff @ X4 @ X6 ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(symdiffIneg1, axiom, symdiffIneg1 =
% 139.73/20.54 (![A:$i,B:$i,Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ( in @ Xx @ B ) => ( ~( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ))).
% 139.73/20.54 thf('159', plain,
% 139.73/20.54 (( symdiffIneg1 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ X4 ) =>
% 139.73/20.54 ( ( in @ X8 @ X6 ) => ( ~( in @ X8 @ ( symdiff @ X4 @ X6 ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(symdiffI2, axiom, symdiffI2 =
% 139.73/20.54 (![A:$i,B:$i,Xx:$i]:
% 139.73/20.54 ( ( ~( in @ Xx @ A ) ) =>
% 139.73/20.54 ( ( in @ Xx @ B ) => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ))).
% 139.73/20.54 thf('160', plain,
% 139.73/20.54 (( symdiffI2 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.54 ( ( ~( in @ X8 @ X4 ) ) =>
% 139.73/20.54 ( ( in @ X8 @ X6 ) => ( in @ X8 @ ( symdiff @ X4 @ X6 ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(symdiffI1, axiom, symdiffI1 =
% 139.73/20.54 (![A:$i,B:$i,Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ( ~( in @ Xx @ B ) ) => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ))).
% 139.73/20.54 thf('161', plain,
% 139.73/20.54 (( symdiffI1 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ X4 ) =>
% 139.73/20.54 ( ( ~( in @ X8 @ X6 ) ) => ( in @ X8 @ ( symdiff @ X4 @ X6 ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(symdiffE, axiom, symdiffE =
% 139.73/20.54 (![A:$i,B:$i,Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ ( symdiff @ A @ B ) ) =>
% 139.73/20.54 ( ![Xphi:$o]:
% 139.73/20.54 ( ( ( in @ Xx @ A ) => ( ( ~( in @ Xx @ B ) ) => ( Xphi ) ) ) =>
% 139.73/20.54 ( ( ( ~( in @ Xx @ A ) ) => ( ( in @ Xx @ B ) => ( Xphi ) ) ) =>
% 139.73/20.54 ( Xphi ) ) ) ) ))).
% 139.73/20.54 thf('162', plain,
% 139.73/20.54 (( symdiffE ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( symdiff @ X4 @ X6 ) ) =>
% 139.73/20.54 ( ![X10:$o]:
% 139.73/20.54 ( ( ( in @ X8 @ X4 ) => ( ( ~( in @ X8 @ X6 ) ) => ( X10 ) ) ) =>
% 139.73/20.54 ( ( ( ~( in @ X8 @ X4 ) ) => ( ( in @ X8 @ X6 ) => ( X10 ) ) ) =>
% 139.73/20.54 ( X10 ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(setminusSubset1, axiom, setminusSubset1 =
% 139.73/20.54 (![A:$i,B:$i]:
% 139.73/20.54 ( ( ( setminus @ A @ B ) = ( emptyset ) ) => ( subset @ A @ B ) ))).
% 139.73/20.54 thf('163', plain,
% 139.73/20.54 (( setminusSubset1 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( ( setminus @ X4 @ X6 ) = ( emptyset ) ) => ( subset @ X4 @ X6 ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(setminusLsub, axiom, setminusLsub =
% 139.73/20.54 (![A:$i,B:$i]: ( subset @ ( setminus @ A @ B ) @ A ))).
% 139.73/20.54 thf('164', plain,
% 139.73/20.54 (( setminusLsub ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]: ( subset @ ( setminus @ X4 @ X6 ) @ X4 ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(setminusIRneg, axiom, setminusIRneg =
% 139.73/20.54 (![A:$i,B:$i,Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ B ) => ( ~( in @ Xx @ ( setminus @ A @ B ) ) ) ))).
% 139.73/20.54 thf('165', plain,
% 139.73/20.54 (( setminusIRneg ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ X6 ) => ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(setminusILneg, axiom, setminusILneg =
% 139.73/20.54 (![A:$i,B:$i,Xx:$i]:
% 139.73/20.54 ( ( ~( in @ Xx @ A ) ) => ( ~( in @ Xx @ ( setminus @ A @ B ) ) ) ))).
% 139.73/20.54 thf('166', plain,
% 139.73/20.54 (( setminusILneg ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.54 ( ( ~( in @ X8 @ X4 ) ) => ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(setminusELneg, axiom, setminusELneg =
% 139.73/20.54 (![A:$i,B:$i,Xx:$i]:
% 139.73/20.54 ( ( ~( in @ Xx @ ( setminus @ A @ B ) ) ) =>
% 139.73/20.54 ( ( ~( in @ Xx @ B ) ) => ( ~( in @ Xx @ A ) ) ) ))).
% 139.73/20.54 thf('167', plain,
% 139.73/20.54 (( setminusELneg ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.54 ( ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) =>
% 139.73/20.54 ( ( ~( in @ X8 @ X6 ) ) => ( ~( in @ X8 @ X4 ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(setminusERneg, axiom, setminusERneg =
% 139.73/20.54 (![A:$i,B:$i,Xx:$i]:
% 139.73/20.54 ( ( ~( in @ Xx @ ( setminus @ A @ B ) ) ) =>
% 139.73/20.54 ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ))).
% 139.73/20.54 thf('168', plain,
% 139.73/20.54 (( setminusERneg ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.54 ( ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) =>
% 139.73/20.54 ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(setminusSubset2, axiom, setminusSubset2 =
% 139.73/20.54 (![A:$i,B:$i]:
% 139.73/20.54 ( ( subset @ A @ B ) => ( ( setminus @ A @ B ) = ( emptyset ) ) ))).
% 139.73/20.54 thf('169', plain,
% 139.73/20.54 (( setminusSubset2 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( subset @ X4 @ X6 ) => ( ( setminus @ X4 @ X6 ) = ( emptyset ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(setminusER, axiom, setminusER =
% 139.73/20.54 (![A:$i,B:$i,Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ ( setminus @ A @ B ) ) => ( ~( in @ Xx @ B ) ) ))).
% 139.73/20.54 thf('170', plain,
% 139.73/20.54 (( setminusER ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( setminus @ X4 @ X6 ) ) => ( ~( in @ X8 @ X6 ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(setminusEL, axiom, setminusEL =
% 139.73/20.54 (![A:$i,B:$i,Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ ( setminus @ A @ B ) ) => ( in @ Xx @ A ) ))).
% 139.73/20.54 thf('171', plain,
% 139.73/20.54 (( setminusEL ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( setminus @ X4 @ X6 ) ) => ( in @ X8 @ X4 ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(setminusI, axiom, setminusI =
% 139.73/20.54 (![A:$i,B:$i,Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ( ~( in @ Xx @ B ) ) => ( in @ Xx @ ( setminus @ A @ B ) ) ) ))).
% 139.73/20.54 thf('172', plain,
% 139.73/20.54 (( setminusI ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ X4 ) =>
% 139.73/20.54 ( ( ~( in @ X8 @ X6 ) ) => ( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(bs114d, axiom, bs114d =
% 139.73/20.54 (![A:$i,B:$i,C:$i]:
% 139.73/20.54 ( ( binintersect @ A @ ( binunion @ B @ C ) ) =
% 139.73/20.54 ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ))).
% 139.73/20.54 thf('173', plain,
% 139.73/20.54 (( bs114d ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.54 ( ( binintersect @ X4 @ ( binunion @ X6 @ X8 ) ) =
% 139.73/20.54 ( binunion @ ( binintersect @ X4 @ X6 ) @ ( binintersect @ X4 @ X8 ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(binintersectSubset1, axiom, binintersectSubset1 =
% 139.73/20.54 (![A:$i,B:$i]:
% 139.73/20.54 ( ( ( binintersect @ A @ B ) = ( A ) ) => ( subset @ A @ B ) ))).
% 139.73/20.54 thf('174', plain,
% 139.73/20.54 (( binintersectSubset1 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( ( binintersect @ X4 @ X6 ) = ( X4 ) ) => ( subset @ X4 @ X6 ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(binintersectSubset4, axiom, binintersectSubset4 =
% 139.73/20.54 (![A:$i,B:$i]:
% 139.73/20.54 ( ( subset @ B @ A ) => ( ( binintersect @ A @ B ) = ( B ) ) ))).
% 139.73/20.54 thf('175', plain,
% 139.73/20.54 (( binintersectSubset4 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( subset @ X6 @ X4 ) => ( ( binintersect @ X4 @ X6 ) = ( X6 ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(binintersectRsub, axiom, binintersectRsub =
% 139.73/20.54 (![A:$i,B:$i]: ( subset @ ( binintersect @ A @ B ) @ B ))).
% 139.73/20.54 thf('176', plain,
% 139.73/20.54 (( binintersectRsub ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]: ( subset @ ( binintersect @ X4 @ X6 ) @ X6 ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(disjointsetsI1, axiom, disjointsetsI1 =
% 139.73/20.54 (![A:$i,B:$i]:
% 139.73/20.54 ( ( ~( ?[Xx:$i]: ( ( in @ Xx @ B ) & ( in @ Xx @ A ) ) ) ) =>
% 139.73/20.54 ( ( binintersect @ A @ B ) = ( emptyset ) ) ))).
% 139.73/20.54 thf('177', plain,
% 139.73/20.54 (( disjointsetsI1 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( ~( ?[X8:$i]: ( ( in @ X8 @ X6 ) & ( in @ X8 @ X4 ) ) ) ) =>
% 139.73/20.54 ( ( binintersect @ X4 @ X6 ) = ( emptyset ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(binintersectER, axiom, binintersectER =
% 139.73/20.54 (![A:$i,B:$i,Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ ( binintersect @ A @ B ) ) => ( in @ Xx @ B ) ))).
% 139.73/20.54 thf('178', plain,
% 139.73/20.54 (( binintersectER ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( binintersect @ X4 @ X6 ) ) => ( in @ X8 @ X6 ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(binintersectSubset3, axiom, binintersectSubset3 =
% 139.73/20.54 (![A:$i,B:$i]:
% 139.73/20.54 ( ( ( binintersect @ A @ B ) = ( B ) ) => ( subset @ B @ A ) ))).
% 139.73/20.54 thf('179', plain,
% 139.73/20.54 (( binintersectSubset3 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( ( binintersect @ X4 @ X6 ) = ( X6 ) ) => ( subset @ X6 @ X4 ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(binintersectSubset2, axiom, binintersectSubset2 =
% 139.73/20.54 (![A:$i,B:$i]:
% 139.73/20.54 ( ( subset @ A @ B ) => ( ( binintersect @ A @ B ) = ( A ) ) ))).
% 139.73/20.54 thf('180', plain,
% 139.73/20.54 (( binintersectSubset2 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( subset @ X4 @ X6 ) => ( ( binintersect @ X4 @ X6 ) = ( X4 ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(binintersectLsub, axiom, binintersectLsub =
% 139.73/20.54 (![A:$i,B:$i]: ( subset @ ( binintersect @ A @ B ) @ A ))).
% 139.73/20.54 thf('181', plain,
% 139.73/20.54 (( binintersectLsub ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]: ( subset @ ( binintersect @ X4 @ X6 ) @ X4 ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(binintersectEL, axiom, binintersectEL =
% 139.73/20.54 (![A:$i,B:$i,Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ ( binintersect @ A @ B ) ) => ( in @ Xx @ A ) ))).
% 139.73/20.54 thf('182', plain,
% 139.73/20.54 (( binintersectEL ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( binintersect @ X4 @ X6 ) ) => ( in @ X8 @ X4 ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(binintersectSubset5, axiom, binintersectSubset5 =
% 139.73/20.54 (![A:$i,B:$i,C:$i]:
% 139.73/20.54 ( ( subset @ C @ A ) =>
% 139.73/20.54 ( ( subset @ C @ B ) => ( subset @ C @ ( binintersect @ A @ B ) ) ) ))).
% 139.73/20.54 thf('183', plain,
% 139.73/20.54 (( binintersectSubset5 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.54 ( ( subset @ X8 @ X4 ) =>
% 139.73/20.54 ( ( subset @ X8 @ X6 ) =>
% 139.73/20.54 ( subset @ X8 @ ( binintersect @ X4 @ X6 ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(binintersectI, axiom, binintersectI =
% 139.73/20.54 (![A:$i,B:$i,Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ( in @ Xx @ B ) => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ))).
% 139.73/20.54 thf('184', plain,
% 139.73/20.54 (( binintersectI ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ X4 ) =>
% 139.73/20.54 ( ( in @ X8 @ X6 ) => ( in @ X8 @ ( binintersect @ X4 @ X6 ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(binunionRsub, axiom, binunionRsub =
% 139.73/20.54 (![A:$i,B:$i]: ( subset @ B @ ( binunion @ A @ B ) ))).
% 139.73/20.54 thf('185', plain,
% 139.73/20.54 (( binunionRsub ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]: ( subset @ X6 @ ( binunion @ X4 @ X6 ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(binunionLsub, axiom, binunionLsub =
% 139.73/20.54 (![A:$i,B:$i]: ( subset @ A @ ( binunion @ A @ B ) ))).
% 139.73/20.54 thf('186', plain,
% 139.73/20.54 (( binunionLsub ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]: ( subset @ X4 @ ( binunion @ X4 @ X6 ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(binunionE, axiom, binunionE =
% 139.73/20.54 (![A:$i,B:$i,Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ ( binunion @ A @ B ) ) =>
% 139.73/20.54 ( ( in @ Xx @ A ) | ( in @ Xx @ B ) ) ))).
% 139.73/20.54 thf('187', plain,
% 139.73/20.54 (( binunionE ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( binunion @ X4 @ X6 ) ) =>
% 139.73/20.54 ( ( in @ X8 @ X4 ) | ( in @ X8 @ X6 ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(binunionEcases, axiom, binunionEcases =
% 139.73/20.54 (![A:$i,B:$i,Xx:$i,Xphi:$o]:
% 139.73/20.54 ( ( in @ Xx @ ( binunion @ A @ B ) ) =>
% 139.73/20.54 ( ( ( in @ Xx @ A ) => ( Xphi ) ) =>
% 139.73/20.54 ( ( ( in @ Xx @ B ) => ( Xphi ) ) => ( Xphi ) ) ) ))).
% 139.73/20.54 thf('188', plain,
% 139.73/20.54 (( binunionEcases ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i,X10:$o]:
% 139.73/20.54 ( ( in @ X8 @ ( binunion @ X4 @ X6 ) ) =>
% 139.73/20.54 ( ( ( in @ X8 @ X4 ) => ( X10 ) ) =>
% 139.73/20.54 ( ( ( in @ X8 @ X6 ) => ( X10 ) ) => ( X10 ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(binunionIR, axiom, binunionIR =
% 139.73/20.54 (![A:$i,B:$i,Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ B ) => ( in @ Xx @ ( binunion @ A @ B ) ) ))).
% 139.73/20.54 thf('189', plain,
% 139.73/20.54 (( binunionIR ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ X6 ) => ( in @ X8 @ ( binunion @ X4 @ X6 ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(upairset2IR, axiom, upairset2IR =
% 139.73/20.54 (![Xx:$i,Xy:$i]:
% 139.73/20.54 ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 139.73/20.54 thf('190', plain,
% 139.73/20.54 (( upairset2IR ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( in @ X6 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(binunionIL, axiom, binunionIL =
% 139.73/20.54 (![A:$i,B:$i,Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) => ( in @ Xx @ ( binunion @ A @ B ) ) ))).
% 139.73/20.54 thf('191', plain,
% 139.73/20.54 (( binunionIL ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ X4 ) => ( in @ X8 @ ( binunion @ X4 @ X6 ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(sepSubset, axiom, sepSubset =
% 139.73/20.54 (![A:$i,Xphi:( $i > $o )]:
% 139.73/20.54 ( subset @ ( dsetconstr @ A @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) @ A ))).
% 139.73/20.54 thf('192', plain,
% 139.73/20.54 (( sepSubset ) =
% 139.73/20.54 ( ![X4:$i,X6:( $i > $o )]:
% 139.73/20.54 ( subset @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) @ X4 ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(sepInPowerset, axiom, sepInPowerset =
% 139.73/20.54 (![A:$i,Xphi:( $i > $o )]:
% 139.73/20.54 ( in @ ( dsetconstr @ A @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) @ ( powerset @ A ) ))).
% 139.73/20.54 thf('193', plain,
% 139.73/20.54 (( sepInPowerset ) =
% 139.73/20.54 ( ![X4:$i,X6:( $i > $o )]:
% 139.73/20.54 ( in @
% 139.73/20.54 ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) @
% 139.73/20.54 ( powerset @ X4 ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(powersetsubset, axiom, powersetsubset =
% 139.73/20.54 (![A:$i,B:$i]:
% 139.73/20.54 ( ( subset @ A @ B ) => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ))).
% 139.73/20.54 thf('194', plain,
% 139.73/20.54 (( powersetsubset ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( subset @ X4 @ X6 ) =>
% 139.73/20.54 ( subset @ ( powerset @ X4 ) @ ( powerset @ X6 ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(inPowerset, axiom, inPowerset = (![A:$i]: ( in @ A @ ( powerset @ A ) ))).
% 139.73/20.54 thf('195', plain,
% 139.73/20.54 (( inPowerset ) = ( ![X4:$i]: ( in @ X4 @ ( powerset @ X4 ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(powersetE1, axiom, powersetE1 =
% 139.73/20.54 (![A:$i,B:$i]: ( ( in @ B @ ( powerset @ A ) ) => ( subset @ B @ A ) ))).
% 139.73/20.54 thf('196', plain,
% 139.73/20.54 (( powersetE1 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( in @ X6 @ ( powerset @ X4 ) ) => ( subset @ X6 @ X4 ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(powersetI1, axiom, powersetI1 =
% 139.73/20.54 (![A:$i,B:$i]: ( ( subset @ B @ A ) => ( in @ B @ ( powerset @ A ) ) ))).
% 139.73/20.54 thf('197', plain,
% 139.73/20.54 (( powersetI1 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( subset @ X6 @ X4 ) => ( in @ X6 @ ( powerset @ X4 ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(subsetemptysetimpeq, axiom, subsetemptysetimpeq =
% 139.73/20.54 (![A:$i]: ( ( subset @ A @ emptyset ) => ( ( A ) = ( emptyset ) ) ))).
% 139.73/20.54 thf('198', plain,
% 139.73/20.54 (( subsetemptysetimpeq ) =
% 139.73/20.54 ( ![X4:$i]: ( ( subset @ X4 @ emptyset ) => ( ( X4 ) = ( emptyset ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(setextsub, axiom, setextsub =
% 139.73/20.54 (![A:$i,B:$i]:
% 139.73/20.54 ( ( subset @ A @ B ) => ( ( subset @ B @ A ) => ( ( A ) = ( B ) ) ) ))).
% 139.73/20.54 thf('199', plain,
% 139.73/20.54 (( setextsub ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( subset @ X4 @ X6 ) =>
% 139.73/20.54 ( ( subset @ X6 @ X4 ) => ( ( X4 ) = ( X6 ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(subset2powerset, axiom, subset2powerset =
% 139.73/20.54 (![A:$i,B:$i]: ( ( subset @ A @ B ) => ( in @ A @ ( powerset @ B ) ) ))).
% 139.73/20.54 thf('200', plain,
% 139.73/20.54 (( subset2powerset ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( subset @ X4 @ X6 ) => ( in @ X4 @ ( powerset @ X6 ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(setadjoinSub2, axiom, setadjoinSub2 =
% 139.73/20.54 (![A:$i,Xx:$i,B:$i]:
% 139.73/20.54 ( ( subset @ A @ B ) => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ))).
% 139.73/20.54 thf('201', plain,
% 139.73/20.54 (( setadjoinSub2 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.54 ( ( subset @ X4 @ X8 ) => ( subset @ X4 @ ( setadjoin @ X6 @ X8 ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(setadjoinSub, axiom, setadjoinSub =
% 139.73/20.54 (![Xx:$i,A:$i]: ( subset @ A @ ( setadjoin @ Xx @ A ) ))).
% 139.73/20.54 thf('202', plain,
% 139.73/20.54 (( setadjoinSub ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]: ( subset @ X6 @ ( setadjoin @ X4 @ X6 ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(subsetTrans, axiom, subsetTrans =
% 139.73/20.54 (![A:$i,B:$i,C:$i]:
% 139.73/20.54 ( ( subset @ A @ B ) => ( ( subset @ B @ C ) => ( subset @ A @ C ) ) ))).
% 139.73/20.54 thf('203', plain,
% 139.73/20.54 (( subsetTrans ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.54 ( ( subset @ X4 @ X6 ) =>
% 139.73/20.54 ( ( subset @ X6 @ X8 ) => ( subset @ X4 @ X8 ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(subsetRefl, axiom, subsetRefl = (![A:$i]: ( subset @ A @ A ))).
% 139.73/20.54 thf('204', plain, (( subsetRefl ) = ( ![X4:$i]: ( subset @ X4 @ X4 ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(notequalI2, axiom, notequalI2 =
% 139.73/20.54 (![A:$i,B:$i,Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) => ( ( ~( in @ Xx @ B ) ) => ( ( A ) != ( B ) ) ) ))).
% 139.73/20.54 thf('205', plain,
% 139.73/20.54 (( notequalI2 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ X4 ) =>
% 139.73/20.54 ( ( ~( in @ X8 @ X6 ) ) => ( ( X4 ) != ( X6 ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(notequalI1, axiom, notequalI1 =
% 139.73/20.54 (![A:$i,B:$i]: ( ( ~( subset @ A @ B ) ) => ( ( A ) != ( B ) ) ))).
% 139.73/20.54 thf('206', plain,
% 139.73/20.54 (( notequalI1 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]: ( ( ~( subset @ X4 @ X6 ) ) => ( ( X4 ) != ( X6 ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(notsubsetI, axiom, notsubsetI =
% 139.73/20.54 (![A:$i,B:$i,Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) => ( ( ~( in @ Xx @ B ) ) => ( ~( subset @ A @ B ) ) ) ))).
% 139.73/20.54 thf('207', plain,
% 139.73/20.54 (( notsubsetI ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ X4 ) =>
% 139.73/20.54 ( ( ~( in @ X8 @ X6 ) ) => ( ~( subset @ X4 @ X6 ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(subsetE2, axiom, subsetE2 =
% 139.73/20.54 (![A:$i,B:$i,Xx:$i]:
% 139.73/20.54 ( ( subset @ A @ B ) => ( ( ~( in @ Xx @ B ) ) => ( ~( in @ Xx @ A ) ) ) ))).
% 139.73/20.54 thf('208', plain,
% 139.73/20.54 (( subsetE2 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.54 ( ( subset @ X4 @ X6 ) =>
% 139.73/20.54 ( ( ~( in @ X8 @ X6 ) ) => ( ~( in @ X8 @ X4 ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(subsetE, axiom, subsetE =
% 139.73/20.54 (![A:$i,B:$i,Xx:$i]:
% 139.73/20.54 ( ( subset @ A @ B ) => ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ))).
% 139.73/20.54 thf('209', plain,
% 139.73/20.54 (( subsetE ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.54 ( ( subset @ X4 @ X6 ) => ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(emptysetsubset, axiom, emptysetsubset =
% 139.73/20.54 (![A:$i]: ( subset @ emptyset @ A ))).
% 139.73/20.54 thf('210', plain,
% 139.73/20.54 (( emptysetsubset ) = ( ![X4:$i]: ( subset @ emptyset @ X4 ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(subsetI2, axiom, subsetI2 =
% 139.73/20.54 (![A:$i,B:$i]:
% 139.73/20.54 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ) =>
% 139.73/20.54 ( subset @ A @ B ) ))).
% 139.73/20.54 thf('211', plain,
% 139.73/20.54 (( subsetI2 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) =>
% 139.73/20.54 ( subset @ X4 @ X6 ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(eqimpsubset1, axiom, eqimpsubset1 =
% 139.73/20.54 (![A:$i,B:$i]: ( ( ( A ) = ( B ) ) => ( subset @ A @ B ) ))).
% 139.73/20.54 thf('212', plain,
% 139.73/20.54 (( eqimpsubset1 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]: ( ( ( X4 ) = ( X6 ) ) => ( subset @ X4 @ X6 ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(eqimpsubset2, axiom, eqimpsubset2 =
% 139.73/20.54 (![A:$i,B:$i]: ( ( ( A ) = ( B ) ) => ( subset @ B @ A ) ))).
% 139.73/20.54 thf('213', plain,
% 139.73/20.54 (( eqimpsubset2 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]: ( ( ( X4 ) = ( X6 ) ) => ( subset @ X6 @ X4 ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(subsetI1, axiom, subsetI1 =
% 139.73/20.54 (![A:$i,B:$i]:
% 139.73/20.54 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ) =>
% 139.73/20.54 ( subset @ A @ B ) ))).
% 139.73/20.54 thf('214', plain,
% 139.73/20.54 (( subsetI1 ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) =>
% 139.73/20.54 ( subset @ X4 @ X6 ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(dsetconstr__Cong, axiom, dsetconstr__Cong =
% 139.73/20.54 (![A:$i,B:$i]:
% 139.73/20.54 ( ( ( A ) = ( B ) ) =>
% 139.73/20.54 ( ![Xphi:( $i > $o ),Xpsi:( $i > $o )]:
% 139.73/20.54 ( ( ![Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) =>
% 139.73/20.54 ( ![Xy:$i]:
% 139.73/20.54 ( ( in @ Xy @ B ) =>
% 139.73/20.54 ( ( ( Xx ) = ( Xy ) ) => ( ( Xphi @ Xx ) <=> ( Xpsi @ Xy ) ) ) ) ) ) ) =>
% 139.73/20.54 ( ( dsetconstr @ A @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) =
% 139.73/20.54 ( dsetconstr @ B @ ( ^[Xx:$i]: ( Xpsi @ Xx ) ) ) ) ) ) ))).
% 139.73/20.54 thf('215', plain,
% 139.73/20.54 (( dsetconstr__Cong ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( ( X4 ) = ( X6 ) ) =>
% 139.73/20.54 ( ![X8:( $i > $o ),X10:( $i > $o )]:
% 139.73/20.54 ( ( ![X12:$i]:
% 139.73/20.54 ( ( in @ X12 @ X4 ) =>
% 139.73/20.54 ( ![X14:$i]:
% 139.73/20.54 ( ( in @ X14 @ X6 ) =>
% 139.73/20.54 ( ( ( X12 ) = ( X14 ) ) =>
% 139.73/20.54 ( ( X8 @ X12 ) <=> ( X10 @ X14 ) ) ) ) ) ) ) =>
% 139.73/20.54 ( ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X8 @ V_1 ) ) ) =
% 139.73/20.54 ( dsetconstr @ X6 @ ( ^[V_2:$i]: ( X10 @ V_2 ) ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(descr__Cong, axiom, descr__Cong =
% 139.73/20.54 (![Xphi:( $i > $o ),Xpsi:( $i > $o )]:
% 139.73/20.54 ( ( ![Xx:$i,Xy:$i]:
% 139.73/20.54 ( ( ( Xx ) = ( Xy ) ) => ( ( Xphi @ Xx ) <=> ( Xpsi @ Xy ) ) ) ) =>
% 139.73/20.54 ( ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) =>
% 139.73/20.54 ( ( exu @ ( ^[Xx:$i]: ( Xpsi @ Xx ) ) ) =>
% 139.73/20.54 ( ( descr @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) =
% 139.73/20.54 ( descr @ ( ^[Xx:$i]: ( Xpsi @ Xx ) ) ) ) ) ) ))).
% 139.73/20.54 thf('216', plain,
% 139.73/20.54 (( descr__Cong ) =
% 139.73/20.54 ( ![X4:( $i > $o ),X6:( $i > $o )]:
% 139.73/20.54 ( ( ![X8:$i,X10:$i]:
% 139.73/20.54 ( ( ( X8 ) = ( X10 ) ) => ( ( X4 @ X8 ) <=> ( X6 @ X10 ) ) ) ) =>
% 139.73/20.54 ( ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) =>
% 139.73/20.54 ( ( exu @ ( ^[V_2:$i]: ( X6 @ V_2 ) ) ) =>
% 139.73/20.54 ( ( descr @ ( ^[V_3:$i]: ( X4 @ V_3 ) ) ) =
% 139.73/20.54 ( descr @ ( ^[V_4:$i]: ( X6 @ V_4 ) ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(exuEu, axiom, exuEu =
% 139.73/20.54 (![Xphi:( $i > $o )]:
% 139.73/20.54 ( ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) =>
% 139.73/20.54 ( ![Xx:$i,Xy:$i]:
% 139.73/20.54 ( ( Xphi @ Xx ) => ( ( Xphi @ Xy ) => ( ( Xx ) = ( Xy ) ) ) ) ) ))).
% 139.73/20.54 thf('217', plain,
% 139.73/20.54 (( exuEu ) =
% 139.73/20.54 ( ![X4:( $i > $o )]:
% 139.73/20.54 ( ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) =>
% 139.73/20.54 ( ![X6:$i,X8:$i]:
% 139.73/20.54 ( ( X4 @ X6 ) => ( ( X4 @ X8 ) => ( ( X6 ) = ( X8 ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(omega__Cong, axiom, omega__Cong = (( omega ) = ( omega ))).
% 139.73/20.54 thf('218', plain, (( omega__Cong ) = ( ( omega ) = ( omega ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(setunion__Cong, axiom, setunion__Cong =
% 139.73/20.54 (![A:$i,B:$i]:
% 139.73/20.54 ( ( ( A ) = ( B ) ) => ( ( setunion @ A ) = ( setunion @ B ) ) ))).
% 139.73/20.54 thf('219', plain,
% 139.73/20.54 (( setunion__Cong ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( ( X4 ) = ( X6 ) ) => ( ( setunion @ X4 ) = ( setunion @ X6 ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(powerset__Cong, axiom, powerset__Cong =
% 139.73/20.54 (![A:$i,B:$i]:
% 139.73/20.54 ( ( ( A ) = ( B ) ) => ( ( powerset @ A ) = ( powerset @ B ) ) ))).
% 139.73/20.54 thf('220', plain,
% 139.73/20.54 (( powerset__Cong ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( ( X4 ) = ( X6 ) ) => ( ( powerset @ X4 ) = ( powerset @ X6 ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(setadjoin__Cong, axiom, setadjoin__Cong =
% 139.73/20.54 (![Xx:$i,Xy:$i]:
% 139.73/20.54 ( ( ( Xx ) = ( Xy ) ) =>
% 139.73/20.54 ( ![Xz:$i,Xu:$i]:
% 139.73/20.54 ( ( ( Xz ) = ( Xu ) ) =>
% 139.73/20.54 ( ( setadjoin @ Xx @ Xz ) = ( setadjoin @ Xy @ Xu ) ) ) ) ))).
% 139.73/20.54 thf('221', plain,
% 139.73/20.54 (( setadjoin__Cong ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( ( X4 ) = ( X6 ) ) =>
% 139.73/20.54 ( ![X8:$i,X10:$i]:
% 139.73/20.54 ( ( ( X8 ) = ( X10 ) ) =>
% 139.73/20.54 ( ( setadjoin @ X4 @ X8 ) = ( setadjoin @ X6 @ X10 ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(emptyset__Cong, axiom, emptyset__Cong = (( emptyset ) = ( emptyset ))).
% 139.73/20.54 thf('222', plain, (( emptyset__Cong ) = ( ( emptyset ) = ( emptyset ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(exu__Cong, axiom, exu__Cong =
% 139.73/20.54 (![Xphi:( $i > $o ),Xpsi:( $i > $o )]:
% 139.73/20.54 ( ( ![Xx:$i,Xy:$i]:
% 139.73/20.54 ( ( ( Xx ) = ( Xy ) ) => ( ( Xphi @ Xx ) <=> ( Xpsi @ Xy ) ) ) ) =>
% 139.73/20.54 ( ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) <=>
% 139.73/20.54 ( exu @ ( ^[Xx:$i]: ( Xpsi @ Xx ) ) ) ) ))).
% 139.73/20.54 thf('223', plain,
% 139.73/20.54 (( exu__Cong ) =
% 139.73/20.54 ( ![X4:( $i > $o ),X6:( $i > $o )]:
% 139.73/20.54 ( ( ![X8:$i,X10:$i]:
% 139.73/20.54 ( ( ( X8 ) = ( X10 ) ) => ( ( X4 @ X8 ) <=> ( X6 @ X10 ) ) ) ) =>
% 139.73/20.54 ( ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) <=>
% 139.73/20.54 ( exu @ ( ^[V_2:$i]: ( X6 @ V_2 ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(exuE3u, axiom, exuE3u =
% 139.73/20.54 (![Xphi:( $i > $o )]:
% 139.73/20.54 ( ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) =>
% 139.73/20.54 ( ![Xx:$i,Xy:$i]:
% 139.73/20.54 ( ( Xphi @ Xx ) => ( ( Xphi @ Xy ) => ( ( Xx ) = ( Xy ) ) ) ) ) ))).
% 139.73/20.54 thf('224', plain,
% 139.73/20.54 (( exuE3u ) =
% 139.73/20.54 ( ![X4:( $i > $o )]:
% 139.73/20.54 ( ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) =>
% 139.73/20.54 ( ![X6:$i,X8:$i]:
% 139.73/20.54 ( ( X4 @ X6 ) => ( ( X4 @ X8 ) => ( ( X6 ) = ( X8 ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(in__Cong, axiom, in__Cong =
% 139.73/20.54 (![A:$i,B:$i]:
% 139.73/20.54 ( ( ( A ) = ( B ) ) =>
% 139.73/20.54 ( ![Xx:$i,Xy:$i]:
% 139.73/20.54 ( ( ( Xx ) = ( Xy ) ) => ( ( in @ Xx @ A ) <=> ( in @ Xy @ B ) ) ) ) ))).
% 139.73/20.54 thf('225', plain,
% 139.73/20.54 (( in__Cong ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( ( X4 ) = ( X6 ) ) =>
% 139.73/20.54 ( ![X8:$i,X10:$i]:
% 139.73/20.54 ( ( ( X8 ) = ( X10 ) ) =>
% 139.73/20.54 ( ( in @ X8 @ X4 ) <=> ( in @ X10 @ X6 ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(inCongP, axiom, inCongP =
% 139.73/20.54 (![A:$i,B:$i]:
% 139.73/20.54 ( ( ( A ) = ( B ) ) =>
% 139.73/20.54 ( ![Xx:$i,Xy:$i]:
% 139.73/20.54 ( ( ( Xx ) = ( Xy ) ) => ( ( in @ Xx @ A ) => ( in @ Xy @ B ) ) ) ) ))).
% 139.73/20.54 thf('226', plain,
% 139.73/20.54 (( inCongP ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( ( X4 ) = ( X6 ) ) =>
% 139.73/20.54 ( ![X8:$i,X10:$i]:
% 139.73/20.54 ( ( ( X8 ) = ( X10 ) ) =>
% 139.73/20.54 ( ( in @ X8 @ X4 ) => ( in @ X10 @ X6 ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(exuI2, axiom, exuI2 =
% 139.73/20.54 (![Xphi:( $i > $o )]:
% 139.73/20.54 ( ( ?[Xx:$i]: ( ![Xy:$i]: ( ( Xphi @ Xy ) <=> ( ( Xy ) = ( Xx ) ) ) ) ) =>
% 139.73/20.54 ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) ))).
% 139.73/20.54 thf('227', plain,
% 139.73/20.54 (( exuI2 ) =
% 139.73/20.54 ( ![X4:( $i > $o )]:
% 139.73/20.54 ( ( ?[X6:$i]: ( ![X8:$i]: ( ( X4 @ X8 ) <=> ( ( X8 ) = ( X6 ) ) ) ) ) =>
% 139.73/20.54 ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(exuI3, axiom, exuI3 =
% 139.73/20.54 (![Xphi:( $i > $o )]:
% 139.73/20.54 ( ( ?[Xx:$i]: ( Xphi @ Xx ) ) =>
% 139.73/20.54 ( ( ![Xx:$i,Xy:$i]:
% 139.73/20.54 ( ( Xphi @ Xx ) => ( ( Xphi @ Xy ) => ( ( Xx ) = ( Xy ) ) ) ) ) =>
% 139.73/20.54 ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) ) ))).
% 139.73/20.54 thf('228', plain,
% 139.73/20.54 (( exuI3 ) =
% 139.73/20.54 ( ![X4:( $i > $o )]:
% 139.73/20.54 ( ( ?[X6:$i]: ( X4 @ X6 ) ) =>
% 139.73/20.54 ( ( ![X8:$i,X10:$i]:
% 139.73/20.54 ( ( X4 @ X8 ) => ( ( X4 @ X10 ) => ( ( X8 ) = ( X10 ) ) ) ) ) =>
% 139.73/20.54 ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(exuI1, axiom, exuI1 =
% 139.73/20.54 (![Xphi:( $i > $o )]:
% 139.73/20.54 ( ( ?[Xx:$i]:
% 139.73/20.54 ( ( ![Xy:$i]: ( ( Xphi @ Xy ) => ( ( Xx ) = ( Xy ) ) ) ) &
% 139.73/20.54 ( Xphi @ Xx ) ) ) =>
% 139.73/20.54 ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) ))).
% 139.73/20.54 thf('229', plain,
% 139.73/20.54 (( exuI1 ) =
% 139.73/20.54 ( ![X4:( $i > $o )]:
% 139.73/20.54 ( ( ?[X6:$i]:
% 139.73/20.54 ( ( ![X8:$i]: ( ( X4 @ X8 ) => ( ( X6 ) = ( X8 ) ) ) ) &
% 139.73/20.54 ( X4 @ X6 ) ) ) =>
% 139.73/20.54 ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(notdallE, axiom, notdallE =
% 139.73/20.54 (![A:$i,Xphi:( $i > $o )]:
% 139.73/20.54 ( ( ~( ![Xx:$i]: ( ( in @ Xx @ A ) => ( Xphi @ Xx ) ) ) ) =>
% 139.73/20.54 ( ?[Xx:$i]: ( ( ~( Xphi @ Xx ) ) & ( in @ Xx @ A ) ) ) ))).
% 139.73/20.54 thf('230', plain,
% 139.73/20.54 (( notdallE ) =
% 139.73/20.54 ( ![X4:$i,X6:( $i > $o )]:
% 139.73/20.54 ( ( ~( ![X8:$i]: ( ( in @ X8 @ X4 ) => ( X6 @ X8 ) ) ) ) =>
% 139.73/20.54 ( ?[X10:$i]: ( ( ~( X6 @ X10 ) ) & ( in @ X10 @ X4 ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(notdexE, axiom, notdexE =
% 139.73/20.54 (![A:$i,Xphi:( $i > $o )]:
% 139.73/20.54 ( ( ~( ?[Xx:$i]: ( ( Xphi @ Xx ) & ( in @ Xx @ A ) ) ) ) =>
% 139.73/20.54 ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( ~( Xphi @ Xx ) ) ) ) ))).
% 139.73/20.54 thf('231', plain,
% 139.73/20.54 (( notdexE ) =
% 139.73/20.54 ( ![X4:$i,X6:( $i > $o )]:
% 139.73/20.54 ( ( ~( ?[X8:$i]: ( ( X6 @ X8 ) & ( in @ X8 @ X4 ) ) ) ) =>
% 139.73/20.54 ( ![X10:$i]: ( ( in @ X10 @ X4 ) => ( ~( X6 @ X10 ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(prop2set2propI, axiom, prop2set2propI =
% 139.73/20.54 (![Xphi:$o]: ( ( Xphi ) => ( set2prop @ ( prop2set @ Xphi ) ) ))).
% 139.73/20.54 thf('232', plain,
% 139.73/20.54 (( prop2set2propI ) =
% 139.73/20.54 ( ![X4:$o]: ( ( X4 ) => ( set2prop @ ( prop2set @ X4 ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(prop2setI, axiom, prop2setI =
% 139.73/20.54 (![Xphi:$o]: ( ( Xphi ) => ( in @ emptyset @ ( prop2set @ Xphi ) ) ))).
% 139.73/20.54 thf('233', plain,
% 139.73/20.54 (( prop2setI ) =
% 139.73/20.54 ( ![X4:$o]: ( ( X4 ) => ( in @ emptyset @ ( prop2set @ X4 ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(quantDeMorgan4, axiom, quantDeMorgan4 =
% 139.73/20.54 (![A:$i,Xphi:( $i > $o )]:
% 139.73/20.54 ( ( ?[Xx:$i]: ( ( ~( Xphi @ Xx ) ) & ( in @ Xx @ A ) ) ) =>
% 139.73/20.54 ( ~( ![Xx:$i]: ( ( in @ Xx @ A ) => ( Xphi @ Xx ) ) ) ) ))).
% 139.73/20.54 thf('234', plain,
% 139.73/20.54 (( quantDeMorgan4 ) =
% 139.73/20.54 ( ![X4:$i,X6:( $i > $o )]:
% 139.73/20.54 ( ( ?[X8:$i]: ( ( ~( X6 @ X8 ) ) & ( in @ X8 @ X4 ) ) ) =>
% 139.73/20.54 ( ~( ![X10:$i]: ( ( in @ X10 @ X4 ) => ( X6 @ X10 ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(quantDeMorgan3, axiom, quantDeMorgan3 =
% 139.73/20.54 (![A:$i,Xphi:( $i > $o )]:
% 139.73/20.54 ( ( ~( ?[Xx:$i]: ( ( Xphi @ Xx ) & ( in @ Xx @ A ) ) ) ) =>
% 139.73/20.54 ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( ~( Xphi @ Xx ) ) ) ) ))).
% 139.73/20.54 thf('235', plain,
% 139.73/20.54 (( quantDeMorgan3 ) =
% 139.73/20.54 ( ![X4:$i,X6:( $i > $o )]:
% 139.73/20.54 ( ( ~( ?[X8:$i]: ( ( X6 @ X8 ) & ( in @ X8 @ X4 ) ) ) ) =>
% 139.73/20.54 ( ![X10:$i]: ( ( in @ X10 @ X4 ) => ( ~( X6 @ X10 ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(quantDeMorgan2, axiom, quantDeMorgan2 =
% 139.73/20.54 (![A:$i,Xphi:( $i > $o )]:
% 139.73/20.54 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( ~( Xphi @ Xx ) ) ) ) =>
% 139.73/20.54 ( ~( ?[Xx:$i]: ( ( Xphi @ Xx ) & ( in @ Xx @ A ) ) ) ) ))).
% 139.73/20.54 thf('236', plain,
% 139.73/20.54 (( quantDeMorgan2 ) =
% 139.73/20.54 ( ![X4:$i,X6:( $i > $o )]:
% 139.73/20.54 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) => ( ~( X6 @ X8 ) ) ) ) =>
% 139.73/20.54 ( ~( ?[X10:$i]: ( ( X6 @ X10 ) & ( in @ X10 @ X4 ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(quantDeMorgan1, axiom, quantDeMorgan1 =
% 139.73/20.54 (![A:$i,Xphi:( $i > $o )]:
% 139.73/20.54 ( ( ~( ![Xx:$i]: ( ( in @ Xx @ A ) => ( Xphi @ Xx ) ) ) ) =>
% 139.73/20.54 ( ?[Xx:$i]: ( ( ~( Xphi @ Xx ) ) & ( in @ Xx @ A ) ) ) ))).
% 139.73/20.54 thf('237', plain,
% 139.73/20.54 (( quantDeMorgan1 ) =
% 139.73/20.54 ( ![X4:$i,X6:( $i > $o )]:
% 139.73/20.54 ( ( ~( ![X8:$i]: ( ( in @ X8 @ X4 ) => ( X6 @ X8 ) ) ) ) =>
% 139.73/20.54 ( ?[X10:$i]: ( ( ~( X6 @ X10 ) ) & ( in @ X10 @ X4 ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(vacuousDall, axiom, vacuousDall =
% 139.73/20.54 (![Xphi:( $i > $o ),Xx:$i]: ( ( in @ Xx @ emptyset ) => ( Xphi @ Xx ) ))).
% 139.73/20.54 thf('238', plain,
% 139.73/20.54 (( vacuousDall ) =
% 139.73/20.54 ( ![X4:( $i > $o ),X6:$i]: ( ( in @ X6 @ emptyset ) => ( X4 @ X6 ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(emptyE1, axiom, emptyE1 =
% 139.73/20.54 (![A:$i,Xphi:( $i > $o )]:
% 139.73/20.54 ( ( ?[Xx:$i]: ( ( Xphi @ Xx ) & ( in @ Xx @ A ) ) ) =>
% 139.73/20.54 ( ( ( dsetconstr @ A @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) = ( emptyset ) ) =>
% 139.73/20.54 ( $false ) ) ))).
% 139.73/20.54 thf('239', plain,
% 139.73/20.54 (( emptyE1 ) =
% 139.73/20.54 ( ![X4:$i,X6:( $i > $o )]:
% 139.73/20.54 ( ( ?[X8:$i]: ( ( X6 @ X8 ) & ( in @ X8 @ X4 ) ) ) =>
% 139.73/20.54 ( ( ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) = ( emptyset ) ) =>
% 139.73/20.54 ( $false ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(upairsetIR, axiom, upairsetIR =
% 139.73/20.54 (![Xx:$i,Xy:$i]:
% 139.73/20.54 ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 139.73/20.54 thf('240', plain,
% 139.73/20.54 (( upairsetIR ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( in @ X6 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(upairsetIL, axiom, upairsetIL =
% 139.73/20.54 (![Xx:$i,Xy:$i]:
% 139.73/20.54 ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 139.73/20.54 thf('241', plain,
% 139.73/20.54 (( upairsetIL ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( in @ X4 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(upairsetE, axiom, upairsetE =
% 139.73/20.54 (![Xx:$i,Xy:$i,Xz:$i]:
% 139.73/20.54 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) =>
% 139.73/20.54 ( ( ( Xz ) = ( Xx ) ) | ( ( Xz ) = ( Xy ) ) ) ))).
% 139.73/20.54 thf('242', plain,
% 139.73/20.54 (( upairsetE ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.54 ( ( in @ X8 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) =>
% 139.73/20.54 ( ( ( X8 ) = ( X4 ) ) | ( ( X8 ) = ( X6 ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(singletonsswitch, axiom, singletonsswitch =
% 139.73/20.54 (![Xx:$i,Xy:$i]:
% 139.73/20.54 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) =>
% 139.73/20.54 ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ))).
% 139.73/20.54 thf('243', plain,
% 139.73/20.54 (( singletonsswitch ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) =>
% 139.73/20.54 ( in @ X6 @ ( setadjoin @ X4 @ emptyset ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(eqinunit, axiom, eqinunit =
% 139.73/20.54 (![Xx:$i,Xy:$i]:
% 139.73/20.54 ( ( ( Xx ) = ( Xy ) ) => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 139.73/20.54 thf('244', plain,
% 139.73/20.54 (( eqinunit ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( ( X4 ) = ( X6 ) ) => ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(notinsingleton, axiom, notinsingleton =
% 139.73/20.54 (![Xx:$i,Xy:$i]:
% 139.73/20.54 ( ( ( Xx ) != ( Xy ) ) => ( ~( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ))).
% 139.73/20.54 thf('245', plain,
% 139.73/20.54 (( notinsingleton ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( ( X4 ) != ( X6 ) ) =>
% 139.73/20.54 ( ~( in @ X6 @ ( setadjoin @ X4 @ emptyset ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(uniqinunit, axiom, uniqinunit =
% 139.73/20.54 (![Xx:$i,Xy:$i]:
% 139.73/20.54 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) => ( ( Xx ) = ( Xy ) ) ))).
% 139.73/20.54 thf('246', plain,
% 139.73/20.54 (( uniqinunit ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) => ( ( X4 ) = ( X6 ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(nonemptyImpWitness, axiom, nonemptyImpWitness =
% 139.73/20.54 (![A:$i]: ( ( nonempty @ A ) => ( ?[Xx:$i]: ( in @ Xx @ A ) ) ))).
% 139.73/20.54 thf('247', plain,
% 139.73/20.54 (( nonemptyImpWitness ) =
% 139.73/20.54 ( ![X4:$i]: ( ( nonempty @ X4 ) => ( ?[X6:$i]: ( in @ X6 @ X4 ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(exuE2, axiom, exuE2 =
% 139.73/20.54 (![Xphi:( $i > $o )]:
% 139.73/20.54 ( ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) =>
% 139.73/20.54 ( ?[Xx:$i]: ( ![Xy:$i]: ( ( Xphi @ Xy ) <=> ( ( Xy ) = ( Xx ) ) ) ) ) ))).
% 139.73/20.54 thf('248', plain,
% 139.73/20.54 (( exuE2 ) =
% 139.73/20.54 ( ![X4:( $i > $o )]:
% 139.73/20.54 ( ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) =>
% 139.73/20.54 ( ?[X6:$i]: ( ![X8:$i]: ( ( X4 @ X8 ) <=> ( ( X8 ) = ( X6 ) ) ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(subPowSU, axiom, subPowSU =
% 139.73/20.54 (![A:$i,Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ A ) => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ))).
% 139.73/20.54 thf('249', plain,
% 139.73/20.54 (( subPowSU ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( in @ X6 @ X4 ) => ( in @ X6 @ ( powerset @ ( setunion @ X4 ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(setunionE, axiom, setunionE =
% 139.73/20.54 (![A:$i,Xx:$i]:
% 139.73/20.54 ( ( in @ Xx @ ( setunion @ A ) ) =>
% 139.73/20.54 ( ![Xphi:$o]:
% 139.73/20.54 ( ( ![B:$i]: ( ( in @ Xx @ B ) => ( ( in @ B @ A ) => ( Xphi ) ) ) ) =>
% 139.73/20.54 ( Xphi ) ) ) ))).
% 139.73/20.54 thf('250', plain,
% 139.73/20.54 (( setunionE ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( in @ X6 @ ( setunion @ X4 ) ) =>
% 139.73/20.54 ( ![X8:$o]:
% 139.73/20.54 ( ( ![X10:$i]:
% 139.73/20.54 ( ( in @ X6 @ X10 ) => ( ( in @ X10 @ X4 ) => ( X8 ) ) ) ) =>
% 139.73/20.54 ( X8 ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(setunionI, axiom, setunionI =
% 139.73/20.54 (![A:$i,Xx:$i,B:$i]:
% 139.73/20.54 ( ( in @ Xx @ B ) => ( ( in @ B @ A ) => ( in @ Xx @ ( setunion @ A ) ) ) ))).
% 139.73/20.54 thf('251', plain,
% 139.73/20.54 (( setunionI ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.54 ( ( in @ X6 @ X8 ) =>
% 139.73/20.54 ( ( in @ X8 @ X4 ) => ( in @ X6 @ ( setunion @ X4 ) ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(powersetE, axiom, powersetE =
% 139.73/20.54 (![A:$i,B:$i,Xx:$i]:
% 139.73/20.54 ( ( in @ B @ ( powerset @ A ) ) => ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ))).
% 139.73/20.54 thf('252', plain,
% 139.73/20.54 (( powersetE ) =
% 139.73/20.54 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.54 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 139.73/20.54 ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(emptyInPowerset, axiom, emptyInPowerset =
% 139.73/20.54 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))).
% 139.73/20.54 thf('253', plain,
% 139.73/20.54 (( emptyInPowerset ) =
% 139.73/20.54 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(emptyinPowerset, axiom, emptyinPowerset =
% 139.73/20.54 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))).
% 139.73/20.54 thf('254', plain,
% 139.73/20.54 (( emptyinPowerset ) =
% 139.73/20.54 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(powersetI, axiom, powersetI =
% 139.73/20.54 (![A:$i,B:$i]:
% 139.73/20.54 ( ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) =>
% 139.73/20.54 ( in @ B @ ( powerset @ A ) ) ))).
% 139.73/20.54 thf('255', plain,
% 139.73/20.54 (( powersetI ) =
% 139.73/20.54 ( ![X4:$i,X6:$i]:
% 139.73/20.54 ( ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) =>
% 139.73/20.54 ( in @ X6 @ ( powerset @ X4 ) ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(setoftrueEq, axiom, setoftrueEq =
% 139.73/20.54 (![A:$i]: ( ( dsetconstr @ A @ ( ^[Xx:$i]: ( $true ) ) ) = ( A ) ))).
% 139.73/20.54 thf('256', plain,
% 139.73/20.54 (( setoftrueEq ) =
% 139.73/20.54 ( ![X4:$i]: ( ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( $true ) ) ) = ( X4 ) ) )),
% 139.73/20.54 define([status(thm)])).
% 139.73/20.54 thf(setadjoinOr, axiom, setadjoinOr =
% 139.73/20.55 (![Xx:$i,A:$i,Xy:$i]:
% 139.73/20.55 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) =>
% 139.73/20.55 ( ( ( Xy ) = ( Xx ) ) | ( in @ Xy @ A ) ) ))).
% 139.73/20.55 thf('257', plain,
% 139.73/20.55 (( setadjoinOr ) =
% 139.73/20.55 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.55 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) =>
% 139.73/20.55 ( ( ( X8 ) = ( X4 ) ) | ( in @ X8 @ X6 ) ) ) )),
% 139.73/20.55 define([status(thm)])).
% 139.73/20.55 thf(setadjoinE, axiom, setadjoinE =
% 139.73/20.55 (![Xx:$i,A:$i,Xy:$i]:
% 139.73/20.55 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) =>
% 139.73/20.55 ( ![Xphi:$o]:
% 139.73/20.55 ( ( ( ( Xy ) = ( Xx ) ) => ( Xphi ) ) =>
% 139.73/20.55 ( ( ( in @ Xy @ A ) => ( Xphi ) ) => ( Xphi ) ) ) ) ))).
% 139.73/20.55 thf('258', plain,
% 139.73/20.55 (( setadjoinE ) =
% 139.73/20.55 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.55 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) =>
% 139.73/20.55 ( ![X10:$o]:
% 139.73/20.55 ( ( ( ( X8 ) = ( X4 ) ) => ( X10 ) ) =>
% 139.73/20.55 ( ( ( in @ X8 @ X6 ) => ( X10 ) ) => ( X10 ) ) ) ) ) )),
% 139.73/20.55 define([status(thm)])).
% 139.73/20.55 thf(setadjoinIR, axiom, setadjoinIR =
% 139.73/20.55 (![Xx:$i,A:$i,Xy:$i]:
% 139.73/20.55 ( ( in @ Xy @ A ) => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ))).
% 139.73/20.55 thf('259', plain,
% 139.73/20.55 (( setadjoinIR ) =
% 139.73/20.55 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.55 ( ( in @ X8 @ X6 ) => ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) ) )),
% 139.73/20.55 define([status(thm)])).
% 139.73/20.55 thf(emptyinunitempty, axiom,(( emptyinunitempty ) =
% 139.73/20.55 (in @ emptyset @ ( setadjoin @ emptyset @ emptyset )))).
% 139.73/20.55 thf('260', plain,
% 139.73/20.55 (( emptyinunitempty ) =
% 139.73/20.55 ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )),
% 139.73/20.55 inference('simplify_rw_rule', [status(thm)], [emptyinunitempty])).
% 139.73/20.55 thf('261', plain,
% 139.73/20.55 (( emptyinunitempty ) =
% 139.73/20.55 ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )),
% 139.73/20.55 define([status(thm)])).
% 139.73/20.55 thf(setadjoinIL, axiom, setadjoinIL =
% 139.73/20.55 (![Xx:$i,Xy:$i]: ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ))).
% 139.73/20.55 thf('262', plain,
% 139.73/20.55 (( setadjoinIL ) =
% 139.73/20.55 ( ![X4:$i,X6:$i]: ( in @ X4 @ ( setadjoin @ X4 @ X6 ) ) )),
% 139.73/20.55 define([status(thm)])).
% 139.73/20.55 thf(nonemptyI1, axiom, nonemptyI1 =
% 139.73/20.55 (![A:$i]: ( ( ?[Xx:$i]: ( in @ Xx @ A ) ) => ( nonempty @ A ) ))).
% 139.73/20.55 thf('263', plain,
% 139.73/20.55 (( nonemptyI1 ) =
% 139.73/20.55 ( ![X4:$i]: ( ( ?[X6:$i]: ( in @ X6 @ X4 ) ) => ( nonempty @ X4 ) ) )),
% 139.73/20.55 define([status(thm)])).
% 139.73/20.55 thf(nonemptyI, axiom, nonemptyI =
% 139.73/20.55 (![A:$i,Xphi:( $i > $o ),Xx:$i]:
% 139.73/20.55 ( ( in @ Xx @ A ) =>
% 139.73/20.55 ( ( Xphi @ Xx ) =>
% 139.73/20.55 ( nonempty @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) ) ))).
% 139.73/20.55 thf('264', plain,
% 139.73/20.55 (( nonemptyI ) =
% 139.73/20.55 ( ![X4:$i,X6:( $i > $o ),X8:$i]:
% 139.73/20.55 ( ( in @ X8 @ X4 ) =>
% 139.73/20.55 ( ( X6 @ X8 ) =>
% 139.73/20.55 ( nonempty @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) ) ) )),
% 139.73/20.55 define([status(thm)])).
% 139.73/20.55 thf(nonemptyE1, axiom, nonemptyE1 =
% 139.73/20.55 (![A:$i]: ( ( nonempty @ A ) => ( ?[Xx:$i]: ( in @ Xx @ A ) ) ))).
% 139.73/20.55 thf('265', plain,
% 139.73/20.55 (( nonemptyE1 ) =
% 139.73/20.55 ( ![X4:$i]: ( ( nonempty @ X4 ) => ( ?[X6:$i]: ( in @ X6 @ X4 ) ) ) )),
% 139.73/20.55 define([status(thm)])).
% 139.73/20.55 thf(nonempty, axiom,(( nonempty ) = (^[Xx:$i]: ( ( Xx ) != ( emptyset ) )))).
% 139.73/20.55 thf('266', plain, (( nonempty ) = ( ^[Xx:$i]: ( ( Xx ) != ( emptyset ) ) )),
% 139.73/20.55 inference('simplify_rw_rule', [status(thm)], [nonempty])).
% 139.73/20.55 thf('267', plain,
% 139.73/20.55 (( nonempty ) = ( ^[V_1:$i]: ( ( V_1 ) != ( emptyset ) ) )),
% 139.73/20.55 define([status(thm)])).
% 139.73/20.55 thf(setbeta, axiom, setbeta =
% 139.73/20.55 (![A:$i,Xphi:( $i > $o ),Xx:$i]:
% 139.73/20.55 ( ( in @ Xx @ A ) =>
% 139.73/20.55 ( ( in @ Xx @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) <=>
% 139.73/20.55 ( Xphi @ Xx ) ) ))).
% 139.73/20.55 thf('268', plain,
% 139.73/20.55 (( setbeta ) =
% 139.73/20.55 ( ![X4:$i,X6:( $i > $o ),X8:$i]:
% 139.73/20.55 ( ( in @ X8 @ X4 ) =>
% 139.73/20.55 ( ( in @ X8 @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) <=>
% 139.73/20.55 ( X6 @ X8 ) ) ) )),
% 139.73/20.55 define([status(thm)])).
% 139.73/20.55 thf(noeltsimpempty, axiom, noeltsimpempty =
% 139.73/20.55 (![A:$i]:
% 139.73/20.55 ( ( ![Xx:$i]: ( ~( in @ Xx @ A ) ) ) => ( ( A ) = ( emptyset ) ) ))).
% 139.73/20.55 thf('269', plain,
% 139.73/20.55 (( noeltsimpempty ) =
% 139.73/20.55 ( ![X4:$i]:
% 139.73/20.55 ( ( ![X6:$i]: ( ~( in @ X6 @ X4 ) ) ) => ( ( X4 ) = ( emptyset ) ) ) )),
% 139.73/20.55 define([status(thm)])).
% 139.73/20.55 thf(emptyI, axiom, emptyI =
% 139.73/20.55 (![A:$i]:
% 139.73/20.55 ( ( ![Xx:$i]: ( ~( in @ Xx @ A ) ) ) => ( ( A ) = ( emptyset ) ) ))).
% 139.73/20.55 thf('270', plain,
% 139.73/20.55 (( emptyI ) =
% 139.73/20.55 ( ![X4:$i]:
% 139.73/20.55 ( ( ![X6:$i]: ( ~( in @ X6 @ X4 ) ) ) => ( ( X4 ) = ( emptyset ) ) ) )),
% 139.73/20.55 define([status(thm)])).
% 139.73/20.55 thf(setext, axiom, setext =
% 139.73/20.55 (![A:$i,B:$i]:
% 139.73/20.55 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ) =>
% 139.73/20.55 ( ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) =>
% 139.73/20.55 ( ( A ) = ( B ) ) ) ))).
% 139.73/20.55 thf('271', plain,
% 139.73/20.55 (( setext ) =
% 139.73/20.55 ( ![X4:$i,X6:$i]:
% 139.73/20.55 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) =>
% 139.73/20.55 ( ( ![X10:$i]: ( ( in @ X10 @ X6 ) => ( in @ X10 @ X4 ) ) ) =>
% 139.73/20.55 ( ( X4 ) = ( X6 ) ) ) ) )),
% 139.73/20.55 define([status(thm)])).
% 139.73/20.55 thf(exuE3e, axiom, exuE3e =
% 139.73/20.55 (![Xphi:( $i > $o )]:
% 139.73/20.55 ( ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) => ( ?[Xx:$i]: ( Xphi @ Xx ) ) ))).
% 139.73/20.55 thf('272', plain,
% 139.73/20.55 (( exuE3e ) =
% 139.73/20.55 ( ![X4:( $i > $o )]:
% 139.73/20.55 ( ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) => ( ?[X6:$i]: ( X4 @ X6 ) ) ) )),
% 139.73/20.55 define([status(thm)])).
% 139.73/20.55 thf(notinemptyset, axiom, notinemptyset =
% 139.73/20.55 (![Xx:$i]: ( ~( in @ Xx @ emptyset ) ))).
% 139.73/20.55 thf('273', plain,
% 139.73/20.55 (( notinemptyset ) = ( ![X4:$i]: ( ~( in @ X4 @ emptyset ) ) )),
% 139.73/20.55 define([status(thm)])).
% 139.73/20.55 thf(emptysetimpfalse, axiom, emptysetimpfalse =
% 139.73/20.55 (![Xx:$i]: ( ( in @ Xx @ emptyset ) => ( $false ) ))).
% 139.73/20.55 thf('274', plain,
% 139.73/20.55 (( emptysetimpfalse ) =
% 139.73/20.55 ( ![X4:$i]: ( ( in @ X4 @ emptyset ) => ( $false ) ) )),
% 139.73/20.55 define([status(thm)])).
% 139.73/20.55 thf(emptysetE, axiom, emptysetE =
% 139.73/20.55 (![Xx:$i]: ( ( in @ Xx @ emptyset ) => ( ![Xphi:$o]: ( Xphi ) ) ))).
% 139.73/20.55 thf('275', plain,
% 139.73/20.55 (( emptysetE ) =
% 139.73/20.55 ( ![X4:$i]: ( ( in @ X4 @ emptyset ) => ( ![X6:$o]: ( X6 ) ) ) )),
% 139.73/20.55 define([status(thm)])).
% 139.73/20.55 thf(prop2setE, axiom, prop2setE =
% 139.73/20.55 (![Xphi:$o,Xx:$i]: ( ( in @ Xx @ ( prop2set @ Xphi ) ) => ( Xphi ) ))).
% 139.73/20.55 thf('276', plain,
% 139.73/20.55 (( prop2setE ) =
% 139.73/20.55 ( ![X4:$o,X6:$i]: ( ( in @ X6 @ ( prop2set @ X4 ) ) => ( X4 ) ) )),
% 139.73/20.55 define([status(thm)])).
% 139.73/20.55 thf(exuE1, axiom, exuE1 =
% 139.73/20.55 (![Xphi:( $i > $o )]:
% 139.73/20.55 ( ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) =>
% 139.73/20.55 ( ?[Xx:$i]:
% 139.73/20.55 ( ( ![Xy:$i]: ( ( Xphi @ Xy ) => ( ( Xx ) = ( Xy ) ) ) ) &
% 139.73/20.55 ( Xphi @ Xx ) ) ) ))).
% 139.73/20.55 thf('277', plain,
% 139.73/20.55 (( exuE1 ) =
% 139.73/20.55 ( ![X4:( $i > $o )]:
% 139.73/20.55 ( ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) =>
% 139.73/20.55 ( ?[X6:$i]:
% 139.73/20.55 ( ( ![X8:$i]: ( ( X4 @ X8 ) => ( ( X6 ) = ( X8 ) ) ) ) &
% 139.73/20.55 ( X4 @ X6 ) ) ) ) )),
% 139.73/20.55 define([status(thm)])).
% 139.73/20.55 thf(dsetconstrER, axiom, dsetconstrER =
% 139.73/20.55 (![A:$i,Xphi:( $i > $o ),Xx:$i]:
% 139.73/20.55 ( ( in @ Xx @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) =>
% 139.73/20.55 ( Xphi @ Xx ) ))).
% 139.73/20.55 thf('278', plain,
% 139.73/20.55 (( dsetconstrER ) =
% 139.73/20.55 ( ![X4:$i,X6:( $i > $o ),X8:$i]:
% 139.73/20.55 ( ( in @ X8 @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) =>
% 139.73/20.55 ( X6 @ X8 ) ) )),
% 139.73/20.55 define([status(thm)])).
% 139.73/20.55 thf(dsetconstrEL, axiom, dsetconstrEL =
% 139.73/20.55 (![A:$i,Xphi:( $i > $o ),Xx:$i]:
% 139.73/20.55 ( ( in @ Xx @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) =>
% 139.73/20.55 ( in @ Xx @ A ) ))).
% 139.73/20.55 thf('279', plain,
% 139.73/20.55 (( dsetconstrEL ) =
% 139.73/20.55 ( ![X4:$i,X6:( $i > $o ),X8:$i]:
% 139.73/20.55 ( ( in @ X8 @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) =>
% 139.73/20.55 ( in @ X8 @ X4 ) ) )),
% 139.73/20.55 define([status(thm)])).
% 139.73/20.55 thf(dsetconstrI, axiom, dsetconstrI =
% 139.73/20.55 (![A:$i,Xphi:( $i > $o ),Xx:$i]:
% 139.73/20.55 ( ( in @ Xx @ A ) =>
% 139.73/20.55 ( ( Xphi @ Xx ) =>
% 139.73/20.55 ( in @ Xx @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) ) ))).
% 139.73/20.55 thf('280', plain,
% 139.73/20.55 (( dsetconstrI ) =
% 139.73/20.55 ( ![X4:$i,X6:( $i > $o ),X8:$i]:
% 139.73/20.55 ( ( in @ X8 @ X4 ) =>
% 139.73/20.55 ( ( X6 @ X8 ) =>
% 139.73/20.55 ( in @ X8 @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) ) ) )),
% 139.73/20.55 define([status(thm)])).
% 139.73/20.55 thf(descrp, axiom, descrp =
% 139.73/20.55 (![Xphi:( $i > $o )]:
% 139.73/20.55 ( ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) =>
% 139.73/20.55 ( Xphi @ ( descr @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) ) ))).
% 139.73/20.55 thf('281', plain,
% 139.73/20.55 (( descrp ) =
% 139.73/20.55 ( ![X4:( $i > $o )]:
% 139.73/20.55 ( ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) =>
% 139.73/20.55 ( X4 @ ( descr @ ( ^[V_2:$i]: ( X4 @ V_2 ) ) ) ) ) )),
% 139.73/20.55 define([status(thm)])).
% 139.73/20.55 thf(wellorderingAx, axiom, wellorderingAx =
% 139.73/20.55 (![A:$i]:
% 139.73/20.55 ( ?[B:$i]:
% 139.73/20.55 ( ( ![C:$i]:
% 139.73/20.55 ( ( ( ![Xx:$i]: ( ( in @ Xx @ C ) => ( in @ Xx @ A ) ) ) &
% 139.73/20.55 ( ?[Xx:$i]: ( in @ Xx @ C ) ) ) =>
% 139.73/20.55 ( ?[D:$i,Xx:$i]:
% 139.73/20.55 ( ( ![E:$i]:
% 139.73/20.55 ( ( in @ E @ B ) =>
% 139.73/20.55 ( ( ![Xy:$i]: ( ( in @ Xy @ E ) => ( in @ Xy @ D ) ) ) |
% 139.73/20.55 ( in @ Xx @ E ) ) ) ) &
% 139.73/20.55 ( ~( ?[Xy:$i]: ( ( in @ Xy @ C ) & ( in @ Xy @ D ) ) ) ) &
% 139.73/20.55 ( in @ Xx @ C ) & ( in @ D @ B ) ) ) ) ) &
% 139.73/20.55 ( ![C:$i,D:$i]:
% 139.73/20.55 ( ( ( in @ C @ B ) & ( in @ D @ B ) ) =>
% 139.73/20.55 ( ( ![Xx:$i]: ( ( in @ Xx @ C ) => ( in @ Xx @ D ) ) ) |
% 139.73/20.55 ( ![Xx:$i]: ( ( in @ Xx @ D ) => ( in @ Xx @ C ) ) ) ) ) ) &
% 139.73/20.55 ( ![Xx:$i,Xy:$i]:
% 139.73/20.55 ( ( ( in @ Xx @ A ) & ( in @ Xy @ A ) ) =>
% 139.73/20.55 ( ( ![C:$i]:
% 139.73/20.55 ( ( in @ C @ B ) => ( ( in @ Xx @ C ) <=> ( in @ Xy @ C ) ) ) ) =>
% 139.73/20.55 ( ( Xx ) = ( Xy ) ) ) ) ) &
% 139.73/20.55 ( ![C:$i]:
% 139.73/20.55 ( ( in @ C @ B ) =>
% 139.73/20.55 ( ![Xx:$i]: ( ( in @ Xx @ C ) => ( in @ Xx @ A ) ) ) ) ) ) ))).
% 139.73/20.55 thf('282', plain,
% 139.73/20.55 (( wellorderingAx ) =
% 139.73/20.55 ( ![X4:$i]:
% 139.73/20.55 ( ?[X6:$i]:
% 139.73/20.55 ( ( ![X8:$i]:
% 139.73/20.55 ( ( ( ![X10:$i]: ( ( in @ X10 @ X8 ) => ( in @ X10 @ X4 ) ) ) &
% 139.73/20.55 ( ?[X12:$i]: ( in @ X12 @ X8 ) ) ) =>
% 139.73/20.55 ( ?[X14:$i,X16:$i]:
% 139.73/20.55 ( ( ![X18:$i]:
% 139.73/20.55 ( ( in @ X18 @ X6 ) =>
% 139.73/20.55 ( ( ![X20:$i]:
% 139.73/20.55 ( ( in @ X20 @ X18 ) => ( in @ X20 @ X14 ) ) ) |
% 139.73/20.55 ( in @ X16 @ X18 ) ) ) ) &
% 139.73/20.55 ( ~( ?[X22:$i]: ( ( in @ X22 @ X8 ) & ( in @ X22 @ X14 ) ) ) ) &
% 139.73/20.55 ( in @ X16 @ X8 ) & ( in @ X14 @ X6 ) ) ) ) ) &
% 139.73/20.55 ( ![X24:$i,X26:$i]:
% 139.73/20.55 ( ( ( in @ X24 @ X6 ) & ( in @ X26 @ X6 ) ) =>
% 139.73/20.55 ( ( ![X28:$i]: ( ( in @ X28 @ X24 ) => ( in @ X28 @ X26 ) ) ) |
% 139.73/20.55 ( ![X30:$i]: ( ( in @ X30 @ X26 ) => ( in @ X30 @ X24 ) ) ) ) ) ) &
% 139.73/20.55 ( ![X32:$i,X34:$i]:
% 139.73/20.55 ( ( ( in @ X32 @ X4 ) & ( in @ X34 @ X4 ) ) =>
% 139.73/20.55 ( ( ![X36:$i]:
% 139.73/20.55 ( ( in @ X36 @ X6 ) =>
% 139.73/20.55 ( ( in @ X32 @ X36 ) <=> ( in @ X34 @ X36 ) ) ) ) =>
% 139.73/20.55 ( ( X32 ) = ( X34 ) ) ) ) ) &
% 139.73/20.55 ( ![X38:$i]:
% 139.73/20.55 ( ( in @ X38 @ X6 ) =>
% 139.73/20.55 ( ![X40:$i]: ( ( in @ X40 @ X38 ) => ( in @ X40 @ X4 ) ) ) ) ) ) ) )),
% 139.73/20.55 define([status(thm)])).
% 139.73/20.55 thf(foundationAx, axiom, foundationAx =
% 139.73/20.55 (![A:$i]:
% 139.73/20.55 ( ( ?[Xx:$i]: ( in @ Xx @ A ) ) =>
% 139.73/20.55 ( ?[B:$i]:
% 139.73/20.55 ( ( ~( ?[Xx:$i]: ( ( in @ Xx @ A ) & ( in @ Xx @ B ) ) ) ) &
% 139.73/20.55 ( in @ B @ A ) ) ) ))).
% 139.73/20.55 thf('283', plain,
% 139.73/20.55 (( foundationAx ) =
% 139.73/20.55 ( ![X4:$i]:
% 139.73/20.55 ( ( ?[X6:$i]: ( in @ X6 @ X4 ) ) =>
% 139.73/20.55 ( ?[X8:$i]:
% 139.73/20.55 ( ( ~( ?[X10:$i]: ( ( in @ X10 @ X4 ) & ( in @ X10 @ X8 ) ) ) ) &
% 139.73/20.55 ( in @ X8 @ X4 ) ) ) ) )),
% 139.73/20.55 define([status(thm)])).
% 139.73/20.55 thf(replAx, axiom, replAx =
% 139.73/20.55 (![Xphi:( $i > $i > $o ),A:$i]:
% 139.73/20.55 ( ( ![Xx:$i]:
% 139.73/20.55 ( ( in @ Xx @ A ) => ( exu @ ( ^[Xy:$i]: ( Xphi @ Xx @ Xy ) ) ) ) ) =>
% 139.73/20.55 ( ?[B:$i]:
% 139.73/20.55 ( ![Xx:$i]:
% 139.73/20.55 ( ( in @ Xx @ B ) <=>
% 139.73/20.55 ( ?[Xy:$i]: ( ( Xphi @ Xy @ Xx ) & ( in @ Xy @ A ) ) ) ) ) ) ))).
% 139.73/20.55 thf('284', plain,
% 139.73/20.55 (( replAx ) =
% 139.73/20.55 ( ![X4:( $i > $i > $o ),X6:$i]:
% 139.73/20.55 ( ( ![X8:$i]:
% 139.73/20.55 ( ( in @ X8 @ X6 ) => ( exu @ ( ^[V_1:$i]: ( X4 @ X8 @ V_1 ) ) ) ) ) =>
% 139.73/20.55 ( ?[X10:$i]:
% 139.73/20.55 ( ![X12:$i]:
% 139.73/20.55 ( ( in @ X12 @ X10 ) <=>
% 139.73/20.55 ( ?[X14:$i]: ( ( X4 @ X14 @ X12 ) & ( in @ X14 @ X6 ) ) ) ) ) ) ) )),
% 139.73/20.55 define([status(thm)])).
% 139.73/20.55 thf(omegaIndAx, axiom, omegaIndAx =
% 139.73/20.55 (![A:$i]:
% 139.73/20.55 ( ( ( in @ emptyset @ A ) &
% 139.73/20.55 ( ![Xx:$i]:
% 139.73/20.55 ( ( ( in @ Xx @ omega ) & ( in @ Xx @ A ) ) =>
% 139.73/20.55 ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) ) ) =>
% 139.73/20.55 ( ![Xx:$i]: ( ( in @ Xx @ omega ) => ( in @ Xx @ A ) ) ) ))).
% 139.73/20.55 thf('285', plain,
% 139.73/20.55 (( omegaIndAx ) =
% 139.73/20.55 ( ![X4:$i]:
% 139.73/20.55 ( ( ( in @ emptyset @ X4 ) &
% 139.73/20.55 ( ![X6:$i]:
% 139.73/20.55 ( ( ( in @ X6 @ omega ) & ( in @ X6 @ X4 ) ) =>
% 139.73/20.55 ( in @ ( setadjoin @ X6 @ X6 ) @ X4 ) ) ) ) =>
% 139.73/20.55 ( ![X8:$i]: ( ( in @ X8 @ omega ) => ( in @ X8 @ X4 ) ) ) ) )),
% 139.73/20.55 define([status(thm)])).
% 139.73/20.55 thf(omegaSAx, axiom, omegaSAx =
% 139.73/20.55 (![Xx:$i]:
% 139.73/20.55 ( ( in @ Xx @ omega ) => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ))).
% 139.73/20.55 thf('286', plain,
% 139.73/20.55 (( omegaSAx ) =
% 139.73/20.55 ( ![X4:$i]:
% 139.73/20.55 ( ( in @ X4 @ omega ) => ( in @ ( setadjoin @ X4 @ X4 ) @ omega ) ) )),
% 139.73/20.55 define([status(thm)])).
% 139.73/20.55 thf(omega0Ax, axiom,(( omega0Ax ) = (in @ emptyset @ omega))).
% 139.73/20.55 thf('287', plain, (( omega0Ax ) = ( in @ emptyset @ omega )),
% 139.73/20.55 inference('simplify_rw_rule', [status(thm)], [omega0Ax])).
% 139.73/20.55 thf('288', plain, (( omega0Ax ) = ( in @ emptyset @ omega )),
% 139.73/20.55 define([status(thm)])).
% 139.73/20.55 thf(setunionAx, axiom, setunionAx =
% 139.73/20.55 (![A:$i,Xx:$i]:
% 139.73/20.55 ( ( in @ Xx @ ( setunion @ A ) ) <=>
% 139.73/20.55 ( ?[B:$i]: ( ( in @ B @ A ) & ( in @ Xx @ B ) ) ) ))).
% 139.73/20.55 thf('289', plain,
% 139.73/20.55 (( setunionAx ) =
% 139.73/20.55 ( ![X4:$i,X6:$i]:
% 139.73/20.55 ( ( in @ X6 @ ( setunion @ X4 ) ) <=>
% 139.73/20.55 ( ?[X8:$i]: ( ( in @ X8 @ X4 ) & ( in @ X6 @ X8 ) ) ) ) )),
% 139.73/20.55 define([status(thm)])).
% 139.73/20.55 thf(powersetAx, axiom, powersetAx =
% 139.73/20.55 (![A:$i,B:$i]:
% 139.73/20.55 ( ( in @ B @ ( powerset @ A ) ) <=>
% 139.73/20.55 ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) ))).
% 139.73/20.55 thf('290', plain,
% 139.73/20.55 (( powersetAx ) =
% 139.73/20.55 ( ![X4:$i,X6:$i]:
% 139.73/20.55 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 139.73/20.55 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) )),
% 139.73/20.55 define([status(thm)])).
% 139.73/20.55 thf(setadjoinAx, axiom, setadjoinAx =
% 139.73/20.55 (![Xx:$i,A:$i,Xy:$i]:
% 139.73/20.55 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) <=>
% 139.73/20.55 ( ( ( Xy ) = ( Xx ) ) | ( in @ Xy @ A ) ) ))).
% 139.73/20.55 thf('291', plain,
% 139.73/20.55 (( setadjoinAx ) =
% 139.73/20.55 ( ![X4:$i,X6:$i,X8:$i]:
% 139.73/20.55 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) <=>
% 139.73/20.55 ( ( ( X8 ) = ( X4 ) ) | ( in @ X8 @ X6 ) ) ) )),
% 139.73/20.55 define([status(thm)])).
% 139.73/20.55 thf(emptysetAx, axiom, emptysetAx = (![Xx:$i]: ( ~( in @ Xx @ emptyset ) ))).
% 139.73/20.55 thf('292', plain,
% 139.73/20.55 (( emptysetAx ) = ( ![X4:$i]: ( ~( in @ X4 @ emptyset ) ) )),
% 139.73/20.55 define([status(thm)])).
% 139.73/20.55 thf(setextAx, axiom, setextAx =
% 139.73/20.55 (![A:$i,B:$i]:
% 139.73/20.55 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) <=> ( in @ Xx @ B ) ) ) =>
% 139.73/20.55 ( ( A ) = ( B ) ) ))).
% 139.73/20.55 thf('293', plain,
% 139.73/20.55 (( setextAx ) =
% 139.73/20.55 ( ![X4:$i,X6:$i]:
% 139.73/20.55 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) <=> ( in @ X8 @ X6 ) ) ) =>
% 139.73/20.55 ( ( X4 ) = ( X6 ) ) ) )),
% 139.73/20.55 define([status(thm)])).
% 139.73/20.55 thf(exu, axiom,(( exu ) =
% 139.73/20.55 (^[Xphi:( $i > $o )]:
% 139.73/20.55 ( ?[Xx:$i]:
% 139.73/20.55 ( ( ![Xy:$i]: ( ( Xphi @ Xy ) => ( ( Xx ) = ( Xy ) ) ) ) & ( Xphi @ Xx ) ) )))).
% 139.73/20.55 thf('294', plain,
% 139.73/20.55 (( exu ) =
% 139.73/20.55 ( ^[Xphi:( $i > $o )]:
% 139.73/20.55 ( ?[Xx:$i]:
% 139.73/20.55 ( ( ![Xy:$i]: ( ( Xphi @ Xy ) => ( ( Xx ) = ( Xy ) ) ) ) &
% 139.73/20.55 ( Xphi @ Xx ) ) ) )),
% 139.73/20.55 inference('simplify_rw_rule', [status(thm)], [exu])).
% 139.73/20.55 thf('295', plain,
% 139.73/20.55 (( exu ) =
% 139.73/20.55 ( ^[V_1:( $i > $o )]:
% 139.73/20.55 ( ?[X4:$i]:
% 139.73/20.55 ( ( ![X6:$i]: ( ( V_1 @ X6 ) => ( ( X4 ) = ( X6 ) ) ) ) &
% 139.73/20.55 ( V_1 @ X4 ) ) ) )),
% 139.73/20.55 define([status(thm)])).
% 139.73/20.55 thf(breln1all2, conjecture,
% 139.73/20.55 (( setextAx ) =>
% 139.73/20.55 ( ( emptysetAx ) =>
% 139.73/20.55 ( ( setadjoinAx ) =>
% 139.73/20.55 ( ( powersetAx ) =>
% 139.73/20.55 ( ( setunionAx ) =>
% 139.73/20.55 ( ( omega0Ax ) =>
% 139.73/20.55 ( ( omegaSAx ) =>
% 139.73/20.55 ( ( omegaIndAx ) =>
% 139.73/20.55 ( ( replAx ) =>
% 139.73/20.55 ( ( foundationAx ) =>
% 139.73/20.55 ( ( wellorderingAx ) =>
% 139.73/20.55 ( ( descrp ) =>
% 139.73/20.55 ( ( dsetconstrI ) =>
% 139.73/20.55 ( ( dsetconstrEL ) =>
% 139.73/20.55 ( ( dsetconstrER ) =>
% 139.73/20.55 ( ( exuE1 ) =>
% 139.73/20.55 ( ( prop2setE ) =>
% 139.73/20.55 ( ( emptysetE ) =>
% 139.73/20.55 ( ( emptysetimpfalse ) =>
% 139.73/20.55 ( ( notinemptyset ) =>
% 139.73/20.55 ( ( exuE3e ) =>
% 139.73/20.55 ( ( setext ) =>
% 139.73/20.55 ( ( emptyI ) =>
% 139.73/20.55 ( ( noeltsimpempty ) =>
% 139.73/20.55 ( ( setbeta ) =>
% 139.73/20.55 ( ( nonemptyE1 ) =>
% 139.73/20.55 ( ( nonemptyI ) =>
% 139.73/20.55 ( ( nonemptyI1 ) =>
% 139.73/20.55 ( ( setadjoinIL ) =>
% 139.73/20.55 ( ( emptyinunitempty ) =>
% 139.73/20.55 ( ( setadjoinIR ) =>
% 139.73/20.55 ( ( setadjoinE ) =>
% 139.73/20.55 ( (
% 139.73/20.55 setadjoinOr ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 setoftrueEq ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 powersetI ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 emptyinPowerset ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 emptyInPowerset ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 powersetE ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 setunionI ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 setunionE ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 subPowSU ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 exuE2 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 nonemptyImpWitness ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 uniqinunit ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 notinsingleton ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 eqinunit ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 singletonsswitch ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 upairsetE ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 upairsetIL ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 upairsetIR ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 emptyE1 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 vacuousDall ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 quantDeMorgan1 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 quantDeMorgan2 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 quantDeMorgan3 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 quantDeMorgan4 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 prop2setI ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 prop2set2propI ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 notdexE ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 notdallE ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 exuI1 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 exuI3 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 exuI2 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 inCongP ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 in__Cong ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 exuE3u ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 exu__Cong ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 emptyset__Cong ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 setadjoin__Cong ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 powerset__Cong ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 setunion__Cong ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 omega__Cong ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 exuEu ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 descr__Cong ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 dsetconstr__Cong ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 subsetI1 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 eqimpsubset2 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 eqimpsubset1 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 subsetI2 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 emptysetsubset ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 subsetE ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 subsetE2 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 notsubsetI ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 notequalI1 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 notequalI2 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 subsetRefl ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 subsetTrans ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 setadjoinSub ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 setadjoinSub2 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 subset2powerset ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 setextsub ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 subsetemptysetimpeq ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 powersetI1 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 powersetE1 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 inPowerset ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 powersetsubset ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 sepInPowerset ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 sepSubset ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 binunionIL ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 upairset2IR ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 binunionIR ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 binunionEcases ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 binunionE ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 binunionLsub ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 binunionRsub ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 binintersectI ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 binintersectSubset5 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 binintersectEL ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 binintersectLsub ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 binintersectSubset2 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 binintersectSubset3 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 binintersectER ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 disjointsetsI1 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 binintersectRsub ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 binintersectSubset4 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 binintersectSubset1 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 bs114d ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 setminusI ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 setminusEL ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 setminusER ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 setminusSubset2 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 setminusERneg ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 setminusELneg ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 setminusILneg ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 setminusIRneg ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 setminusLsub ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 setminusSubset1 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 symdiffE ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 symdiffI1 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 symdiffI2 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 symdiffIneg1 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 symdiffIneg2 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 secondinupair ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 setukpairIL ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 setukpairIR ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 kpairiskpair ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 kpairp ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 singletonsubset ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 singletoninpowerset ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 singletoninpowunion ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 upairset2E ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 upairsubunion ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 upairinpowunion ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 ubforcartprodlem1 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 ubforcartprodlem2 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 ubforcartprodlem3 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 cartprodpairin ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 cartprodmempair1 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 cartprodmempair ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 setunionE2 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 setunionsingleton1 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 setunionsingleton2 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 setunionsingleton ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 singletonprop ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 ex1E1 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 ex1I ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 ex1I2 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 singletonsuniq ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 setukpairinjL1 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 kfstsingleton ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 theprop ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 kfstpairEq ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 cartprodfstin ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 setukpairinjL2 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 setukpairinjL ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 setukpairinjR11 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 setukpairinjR12 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 setukpairinjR1 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 upairequniteq ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 setukpairinjR2 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 setukpairinjR ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 ksndsingleton ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 ksndpairEq ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 kpairsurjEq ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 cartprodsndin ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 cartprodpairmemEL ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 cartprodpairmemER ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 cartprodmempaircEq ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 cartprodfstpairEq ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 cartprodsndpairEq ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 cartprodpairsurjEq ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 dpsetconstrI ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 dpsetconstrSub ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 setOfPairsIsBReln ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 dpsetconstrERa ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 dpsetconstrEL1 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 dpsetconstrEL2 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 dpsetconstrER ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 funcImageSingleton ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 apProp ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 app ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 infuncsetfunc ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 ap2p ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 funcinfuncset ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 lamProp ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 lamp ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 lam2p ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 brelnall1 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 brelnall2 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 ex1E2 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 funcGraphProp1 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 funcGraphProp3 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 funcGraphProp2 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 funcextLem ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 funcGraphProp4 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 subbreln ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 eqbreln ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 funcext ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 funcext2 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 ap2apEq1 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 ap2apEq2 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 beta1 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 eta1 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 lam2lamEq ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 beta2 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 eta2 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 iffalseProp1 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 iffalseProp2 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 iftrueProp1 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 iftrueProp2 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 ifSingleton ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 ifp ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 theeq ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 iftrue ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 iffalse ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 iftrueorfalse ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 binintersectT_lem ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 binunionT_lem ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 powersetT_lem ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 setminusT_lem ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 complementT_lem ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 setextT ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 subsetTI ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 powersetTI1 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 powersetTE1 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 complementTI1 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 complementTE1 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 binintersectTELcontra ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 binintersectTERcontra ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 contrasubsetT ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 contrasubsetT1 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 contrasubsetT2 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 contrasubsetT3 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 doubleComplementI1 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 doubleComplementE1 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 doubleComplementSub1 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 doubleComplementSub2 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 doubleComplementEq ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 complementTnotintersectT ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 complementImpComplementIntersect ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 complementSubsetComplementIntersect ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 complementInPowersetComplementIntersect ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 contraSubsetComplement ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 complementTcontraSubset ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 binunionTILcontra ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 binunionTIRcontra ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 inIntersectImpInUnion ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 inIntersectImpInUnion2 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 inIntersectImpInIntersectUnions ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 intersectInPowersetIntersectUnions ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 inComplementUnionImpNotIn1 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 inComplementUnionImpInComplement1 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 binunionTE ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 binunionTEcontra ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 demorgan2a1 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 complementUnionInPowersetComplement ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 demorgan2a2 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 demorgan1a ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 demorgan1b ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 demorgan1 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 demorgan2a ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 demorgan2b2 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 demorgan2b ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 demorgan2 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 woz13rule0 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 woz13rule1 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 woz13rule2 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 woz13rule3 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 woz13rule4 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 woz1_1 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 woz1_2 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 woz1_3 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 woz1_4 ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 woz1_5 ) =>
% 139.73/20.55 (
% 139.73/20.55 ![
% 139.73/20.55 A:$i,R:$i]:
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 breln1 @
% 139.73/20.55 A @ R ) =>
% 139.73/20.55 (
% 139.73/20.55 ![
% 139.73/20.55 Xphi:(
% 139.73/20.55 $i > $o )]:
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 ![
% 139.73/20.55 Xx:$i]:
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 in @
% 139.73/20.55 Xx @ A ) =>
% 139.73/20.55 (
% 139.73/20.55 ![
% 139.73/20.55 Xy:$i]:
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 in @
% 139.73/20.55 Xy @ A ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 in @
% 139.73/20.55 (
% 139.73/20.55 kpair @
% 139.73/20.55 Xx @ Xy ) @
% 139.73/20.55 R ) =>
% 139.73/20.55 (
% 139.73/20.55 Xphi @
% 139.73/20.55 (
% 139.73/20.55 kpair @
% 139.73/20.55 Xx @ Xy ) ) ) ) ) ) ) =>
% 139.73/20.55 (
% 139.73/20.55 ![
% 139.73/20.55 Xx:$i]:
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 in @
% 139.73/20.55 Xx @ R ) =>
% 139.73/20.55 (
% 139.73/20.55 Xphi @ Xx ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 139.73/20.55 thf(zf_stmt_0, conjecture,
% 139.73/20.55 (( ![X4:$i,X6:$i]:
% 139.73/20.55 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) <=> ( in @ X8 @ X6 ) ) ) =>
% 139.73/20.55 ( ( X4 ) = ( X6 ) ) ) ) =>
% 139.73/20.55 ( ( ![X10:$i]: ( ~( in @ X10 @ emptyset ) ) ) =>
% 139.73/20.55 ( ( ![X12:$i,X14:$i,X16:$i]:
% 139.73/20.55 ( ( in @ X16 @ ( setadjoin @ X12 @ X14 ) ) <=>
% 139.73/20.55 ( ( in @ X16 @ X14 ) | ( ( X16 ) = ( X12 ) ) ) ) ) =>
% 139.73/20.55 ( ( ![X18:$i,X20:$i]:
% 139.73/20.55 ( ( in @ X20 @ ( powerset @ X18 ) ) <=>
% 139.73/20.55 ( ![X22:$i]: ( ( in @ X22 @ X20 ) => ( in @ X22 @ X18 ) ) ) ) ) =>
% 139.73/20.55 ( ( ![X24:$i,X26:$i]:
% 139.73/20.55 ( ( in @ X26 @ ( setunion @ X24 ) ) <=>
% 139.73/20.55 ( ?[X28:$i]: ( ( in @ X26 @ X28 ) & ( in @ X28 @ X24 ) ) ) ) ) =>
% 139.73/20.55 ( ( in @ emptyset @ omega ) =>
% 139.73/20.55 ( ( ![X30:$i]:
% 139.73/20.55 ( ( in @ X30 @ omega ) =>
% 139.73/20.55 ( in @ ( setadjoin @ X30 @ X30 ) @ omega ) ) ) =>
% 139.73/20.55 ( ( ![X32:$i]:
% 139.73/20.55 ( ( ( ![X34:$i]:
% 139.73/20.55 ( ( ( in @ X34 @ X32 ) & ( in @ X34 @ omega ) ) =>
% 139.73/20.55 ( in @ ( setadjoin @ X34 @ X34 ) @ X32 ) ) ) &
% 139.73/20.55 ( in @ emptyset @ X32 ) ) =>
% 139.73/20.55 ( ![X36:$i]:
% 139.73/20.55 ( ( in @ X36 @ omega ) => ( in @ X36 @ X32 ) ) ) ) ) =>
% 139.73/20.55 ( ( ![X38:( $i > $i > $o ),X40:$i]:
% 139.73/20.55 ( ( ![X42:$i]:
% 139.73/20.55 ( ( in @ X42 @ X40 ) =>
% 139.73/20.55 ( ?[X44:$i]:
% 139.73/20.55 ( ( X38 @ X42 @ X44 ) &
% 139.73/20.55 ( ![X46:$i]:
% 139.73/20.55 ( ( X38 @ X42 @ X46 ) =>
% 139.73/20.55 ( ( X44 ) = ( X46 ) ) ) ) ) ) ) ) =>
% 139.73/20.55 ( ?[X48:$i]:
% 139.73/20.55 ( ![X50:$i]:
% 139.73/20.55 ( ( in @ X50 @ X48 ) <=>
% 139.73/20.55 ( ?[X52:$i]:
% 139.73/20.55 ( ( in @ X52 @ X40 ) & ( X38 @ X52 @ X50 ) ) ) ) ) ) ) ) =>
% 139.73/20.55 ( ( ![X54:$i]:
% 139.73/20.55 ( ( ?[X56:$i]: ( in @ X56 @ X54 ) ) =>
% 139.73/20.55 ( ?[X58:$i]:
% 139.73/20.55 ( ( in @ X58 @ X54 ) &
% 139.73/20.55 ( ~( ?[X60:$i]:
% 139.73/20.55 ( ( in @ X60 @ X58 ) & ( in @ X60 @ X54 ) ) ) ) ) ) ) ) =>
% 139.73/20.55 ( ( ![X62:$i]:
% 139.73/20.55 ( ?[X64:$i]:
% 139.73/20.55 ( ( ![X96:$i]:
% 139.73/20.55 ( ( in @ X96 @ X64 ) =>
% 139.73/20.55 ( ![X98:$i]:
% 139.73/20.55 ( ( in @ X98 @ X96 ) => ( in @ X98 @ X62 ) ) ) ) ) &
% 139.73/20.55 ( ![X90:$i,X92:$i]:
% 139.73/20.55 ( ( ( in @ X92 @ X62 ) & ( in @ X90 @ X62 ) ) =>
% 139.73/20.55 ( ( ![X94:$i]:
% 139.73/20.55 ( ( in @ X94 @ X64 ) =>
% 139.73/20.55 ( ( in @ X90 @ X94 ) <=>
% 139.73/20.55 ( in @ X92 @ X94 ) ) ) ) =>
% 139.73/20.55 ( ( X90 ) = ( X92 ) ) ) ) ) &
% 139.73/20.55 ( ![X82:$i,X84:$i]:
% 139.73/20.55 ( ( ( in @ X84 @ X64 ) & ( in @ X82 @ X64 ) ) =>
% 139.73/20.55 ( ( ![X88:$i]:
% 139.73/20.55 ( ( in @ X88 @ X84 ) =>
% 139.73/20.55 ( in @ X88 @ X82 ) ) ) |
% 139.73/20.55 ( ![X86:$i]:
% 139.73/20.55 ( ( in @ X86 @ X82 ) =>
% 139.73/20.55 ( in @ X86 @ X84 ) ) ) ) ) ) &
% 139.73/20.55 ( ![X66:$i]:
% 139.73/20.55 ( ( ( ?[X70:$i]: ( in @ X70 @ X66 ) ) &
% 139.73/20.55 ( ![X68:$i]:
% 139.73/20.55 ( ( in @ X68 @ X66 ) =>
% 139.73/20.55 ( in @ X68 @ X62 ) ) ) ) =>
% 139.73/20.55 ( ?[X72:$i,X74:$i]:
% 139.73/20.55 ( ( in @ X72 @ X64 ) &
% 139.73/20.55 ( in @ X74 @ X66 ) &
% 139.73/20.55 ( ~( ?[X80:$i]:
% 139.73/20.55 ( ( in @ X80 @ X72 ) &
% 139.73/20.55 ( in @ X80 @ X66 ) ) ) ) &
% 139.73/20.55 ( ![X76:$i]:
% 139.73/20.55 ( ( in @ X76 @ X64 ) =>
% 139.73/20.55 ( ( in @ X74 @ X76 ) |
% 139.73/20.55 ( ![X78:$i]:
% 139.73/20.55 ( ( in @ X78 @ X76 ) =>
% 139.73/20.55 ( in @ X78 @ X72 ) ) ) ) ) ) ) ) ) ) ) ) ) =>
% 139.73/20.55 ( ( ![X100:( $i > $o )]:
% 139.73/20.55 ( ( ?[X102:$i]:
% 139.73/20.55 ( ( X100 @ X102 ) &
% 139.73/20.55 ( ![X104:$i]:
% 139.73/20.55 ( ( X100 @ X104 ) =>
% 139.73/20.55 ( ( X102 ) = ( X104 ) ) ) ) ) ) =>
% 139.73/20.55 ( X100 @
% 139.73/20.55 ( descr @ ( ^[V_1:$i]: ( X100 @ V_1 ) ) ) ) ) ) =>
% 139.73/20.55 ( ( ![X106:$i,X108:( $i > $o ),X110:$i]:
% 139.73/20.55 ( ( in @ X110 @ X106 ) =>
% 139.73/20.55 ( ( X108 @ X110 ) =>
% 139.73/20.55 ( in @
% 139.73/20.55 X110 @
% 139.73/20.55 ( dsetconstr @
% 139.73/20.55 X106 @ ( ^[V_2:$i]: ( X108 @ V_2 ) ) ) ) ) ) ) =>
% 139.73/20.55 ( ( ![X112:$i,X114:( $i > $o ),X116:$i]:
% 139.73/20.55 ( ( in @
% 139.73/20.55 X116 @
% 139.73/20.55 ( dsetconstr @
% 139.73/20.55 X112 @ ( ^[V_3:$i]: ( X114 @ V_3 ) ) ) ) =>
% 139.73/20.55 ( in @ X116 @ X112 ) ) ) =>
% 139.73/20.55 ( ( ![X118:$i,X120:( $i > $o ),X122:$i]:
% 139.73/20.55 ( ( in @
% 139.73/20.55 X122 @
% 139.73/20.55 ( dsetconstr @
% 139.73/20.55 X118 @ ( ^[V_4:$i]: ( X120 @ V_4 ) ) ) ) =>
% 139.73/20.55 ( X120 @ X122 ) ) ) =>
% 139.73/20.55 ( ( ![X124:( $i > $o )]:
% 139.73/20.55 ( ( ?[X126:$i]:
% 139.73/20.55 ( ( X124 @ X126 ) &
% 139.73/20.55 ( ![X128:$i]:
% 139.73/20.55 ( ( X124 @ X128 ) =>
% 139.73/20.55 ( ( X126 ) = ( X128 ) ) ) ) ) ) =>
% 139.73/20.55 ( ?[X130:$i]:
% 139.73/20.55 ( ( X124 @ X130 ) &
% 139.73/20.55 ( ![X132:$i]:
% 139.73/20.55 ( ( X124 @ X132 ) =>
% 139.73/20.55 ( ( X130 ) = ( X132 ) ) ) ) ) ) ) ) =>
% 139.73/20.55 ( ( ![X134:$o,X136:$i]:
% 139.73/20.55 ( ( in @ X136 @ ( prop2set @ X134 ) ) =>
% 139.73/20.55 ( X134 ) ) ) =>
% 139.73/20.55 ( ( ![X138:$i]:
% 139.73/20.55 ( ( in @ X138 @ emptyset ) =>
% 139.73/20.55 ( ![X140:$o]: ( X140 ) ) ) ) =>
% 139.73/20.55 ( ( ![X142:$i]:
% 139.73/20.55 ( ( in @ X142 @ emptyset ) =>
% 139.73/20.55 ( $false ) ) ) =>
% 139.73/20.55 ( ( ![X144:$i]:
% 139.73/20.55 ( ~( in @ X144 @ emptyset ) ) ) =>
% 139.73/20.55 ( ( ![X146:( $i > $o )]:
% 139.73/20.55 ( ( ?[X148:$i]:
% 139.73/20.55 ( ( X146 @ X148 ) &
% 139.73/20.55 ( ![X150:$i]:
% 139.73/20.55 ( ( X146 @ X150 ) =>
% 139.73/20.55 ( ( X148 ) = ( X150 ) ) ) ) ) ) =>
% 139.73/20.55 ( ?[X152:$i]: ( X146 @ X152 ) ) ) ) =>
% 139.73/20.55 ( ( ![X154:$i,X156:$i]:
% 139.73/20.55 ( ( ![X158:$i]:
% 139.73/20.55 ( ( in @ X158 @ X154 ) =>
% 139.73/20.55 ( in @ X158 @ X156 ) ) ) =>
% 139.73/20.55 ( ( ![X160:$i]:
% 139.73/20.55 ( ( in @ X160 @ X156 ) =>
% 139.73/20.55 ( in @ X160 @ X154 ) ) ) =>
% 139.73/20.55 ( ( X154 ) = ( X156 ) ) ) ) ) =>
% 139.73/20.55 ( ( ![X162:$i]:
% 139.73/20.55 ( ( ![X164:$i]:
% 139.73/20.55 ( ~( in @ X164 @ X162 ) ) ) =>
% 139.73/20.55 ( ( X162 ) = ( emptyset ) ) ) ) =>
% 139.73/20.55 ( ( ![X166:$i]:
% 139.73/20.55 ( ( ![X168:$i]:
% 139.73/20.55 ( ~( in @ X168 @ X166 ) ) ) =>
% 139.73/20.55 ( ( X166 ) =
% 139.73/20.55 ( emptyset ) ) ) ) =>
% 139.73/20.55 ( ( ![X170:$i,
% 139.73/20.55 X172:( $i > $o ),
% 139.73/20.55 X174:$i]:
% 139.73/20.55 ( ( in @ X174 @ X170 ) =>
% 139.73/20.55 ( ( in @
% 139.73/20.55 X174 @
% 139.73/20.55 ( dsetconstr @
% 139.73/20.55 X170 @
% 139.73/20.55 ( ^[V_5:$i]:
% 139.73/20.55 ( X172 @ V_5 ) ) ) ) <=>
% 139.73/20.55 ( X172 @ X174 ) ) ) ) =>
% 139.73/20.55 ( ( ![X176:$i]:
% 139.73/20.55 ( ( ( X176 ) !=
% 139.73/20.55 ( emptyset ) ) =>
% 139.73/20.55 ( ?[X178:$i]:
% 139.73/20.55 ( in @ X178 @ X176 ) ) ) ) =>
% 139.73/20.55 ( ( ![X180:$i,
% 139.73/20.55 X182:( $i > $o ),
% 139.73/20.55 X184:$i]:
% 139.73/20.55 ( ( in @ X184 @ X180 ) =>
% 139.73/20.55 ( ( X182 @ X184 ) =>
% 139.73/20.55 ( ( dsetconstr @
% 139.73/20.55 X180 @
% 139.73/20.55 ( ^[
% 139.73/20.55 V_6:$i]:
% 139.73/20.55 (
% 139.73/20.55 X182 @ V_6 ) ) ) !=
% 139.73/20.55 ( emptyset ) ) ) ) ) =>
% 139.73/20.55 ( ( ![X186:$i]:
% 139.73/20.55 ( ( ?[X188:$i]:
% 139.73/20.55 ( in @
% 139.73/20.55 X188 @ X186 ) ) =>
% 139.73/20.55 ( ( X186 ) !=
% 139.73/20.55 ( emptyset ) ) ) ) =>
% 139.73/20.55 ( ( ![X190:$i,
% 139.73/20.55 X192:$i]:
% 139.73/20.55 ( in @
% 139.73/20.55 X190 @
% 139.73/20.55 ( setadjoin @
% 139.73/20.55 X190 @ X192 ) ) ) =>
% 139.73/20.55 ( ( in @
% 139.73/20.55 emptyset @
% 139.73/20.55 ( setadjoin @
% 139.73/20.55 emptyset @
% 139.73/20.55 emptyset ) ) =>
% 139.73/20.55 ( ( ![X194:$i,
% 139.73/20.55 X196:$i,
% 139.73/20.55 X198:$i]:
% 139.73/20.55 ( (
% 139.73/20.55 in @
% 139.73/20.55 X198 @
% 139.73/20.55 X196 ) =>
% 139.73/20.55 (
% 139.73/20.55 in @
% 139.73/20.55 X198 @
% 139.73/20.55 (
% 139.73/20.55 setadjoin
% 139.73/20.55 @
% 139.73/20.55 X194 @
% 139.73/20.55 X196 ) ) ) ) =>
% 139.73/20.55 ( ( ![
% 139.73/20.55 X200:$i,
% 139.73/20.55 X202:$i,
% 139.73/20.55 X204:$i]:
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 in @
% 139.73/20.55 X204 @
% 139.73/20.55 (
% 139.73/20.55 setadjoin
% 139.73/20.55 @
% 139.73/20.55 X200 @
% 139.73/20.55 X202 ) ) =>
% 139.73/20.55 (
% 139.73/20.55 ![
% 139.73/20.55 X206:$o]:
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 X204 ) =
% 139.73/20.55 (
% 139.73/20.55 X200 ) ) =>
% 139.73/20.55 (
% 139.73/20.55 X206 ) ) =>
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 in @
% 139.73/20.55 X204 @
% 139.73/20.55 X202 ) =>
% 139.73/20.55 (
% 139.73/20.55 X206 ) ) =>
% 139.73/20.55 (
% 139.73/20.55 X206 ) ) ) ) ) ) =>
% 139.73/20.55 ( (
% 139.73/20.55 ![
% 139.73/20.55 X208:$i,
% 139.73/20.55 X210:$i,
% 139.73/20.55 X212:$i]:
% 139.73/20.55 (
% 139.73/20.55 (
% 139.73/20.55 in @
% 139.73/20.55 X212 @
% 139.73/20.55 (
% 139.73/20.55 setadjoin
% 139.73/20.55 @
% 139.73/20.55 X208 @
% 139.73/20.55 X210 ) ) =>
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% 139.73/20.56 (
% 139.73/20.56 ![
% 139.73/20.56 X824:$i,
% 139.73/20.56 X826:$i,
% 139.73/20.56 X828:$i]:
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 in @
% 139.73/20.56 X828 @
% 139.73/20.56 X824 ) =>
% 139.73/20.56 (
% 139.73/20.56 ![
% 139.73/20.56 X830:$i]:
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 in @
% 139.73/20.56 X830 @
% 139.73/20.56 X826 ) =>
% 139.73/20.56 (
% 139.73/20.56 subset @
% 139.73/20.56 (
% 139.73/20.56 setadjoin
% 139.73/20.56 @
% 139.73/20.56 (
% 139.73/20.56 setadjoin
% 139.73/20.56 @
% 139.73/20.56 X828 @
% 139.73/20.56 emptyset ) @
% 139.73/20.56 (
% 139.73/20.56 setadjoin
% 139.73/20.56 @
% 139.73/20.56 (
% 139.73/20.56 setadjoin
% 139.73/20.56 @
% 139.73/20.56 X828 @
% 139.73/20.56 (
% 139.73/20.56 setadjoin
% 139.73/20.56 @
% 139.73/20.56 X830 @
% 139.73/20.56 emptyset ) ) @
% 139.73/20.56 emptyset ) ) @
% 139.73/20.56 (
% 139.73/20.56 powerset @
% 139.73/20.56 (
% 139.73/20.56 binunion @
% 139.73/20.56 X824 @
% 139.73/20.56 X826 ) ) ) ) ) ) ) =>
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 ![
% 139.73/20.56 X832:$i,
% 139.73/20.56 X834:$i,
% 139.73/20.56 X836:$i]:
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 in @
% 139.73/20.56 X836 @
% 139.73/20.56 X832 ) =>
% 139.73/20.56 (
% 139.73/20.56 ![
% 139.73/20.56 X838:$i]:
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 in @
% 139.73/20.56 X838 @
% 139.73/20.56 X834 ) =>
% 139.73/20.56 (
% 139.73/20.56 in @
% 139.73/20.56 (
% 139.73/20.56 setadjoin
% 139.73/20.56 @
% 139.73/20.56 (
% 139.73/20.56 setadjoin
% 139.73/20.56 @
% 139.73/20.56 X836 @
% 139.73/20.56 emptyset ) @
% 139.73/20.56 (
% 139.73/20.56 setadjoin
% 139.73/20.56 @
% 139.73/20.56 (
% 139.73/20.56 setadjoin
% 139.73/20.56 @
% 139.73/20.56 X836 @
% 139.73/20.56 (
% 139.73/20.56 setadjoin
% 139.73/20.56 @
% 139.73/20.56 X838 @
% 139.73/20.56 emptyset ) ) @
% 139.73/20.56 emptyset ) ) @
% 139.73/20.56 (
% 139.73/20.56 powerset @
% 139.73/20.56 (
% 139.73/20.56 powerset @
% 139.73/20.56 (
% 139.73/20.56 binunion @
% 139.73/20.56 X832 @
% 139.73/20.56 X834 ) ) ) ) ) ) ) ) =>
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 ![
% 139.73/20.56 X840:$i,
% 139.73/20.56 X842:$i,
% 139.73/20.56 X844:$i]:
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 in @
% 139.73/20.56 X844 @
% 139.73/20.56 X840 ) =>
% 139.73/20.56 (
% 139.73/20.56 ![
% 139.73/20.56 X846:$i]:
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 in @
% 139.73/20.56 X846 @
% 139.73/20.56 X842 ) =>
% 139.73/20.56 (
% 139.73/20.56 in @
% 139.73/20.56 (
% 139.73/20.56 kpair @
% 139.73/20.56 X844 @
% 139.73/20.56 X846 ) @
% 139.73/20.56 (
% 139.73/20.56 powerset @
% 139.73/20.56 (
% 139.73/20.56 powerset @
% 139.73/20.56 (
% 139.73/20.56 binunion @
% 139.73/20.56 X840 @
% 139.73/20.56 X842 ) ) ) ) ) ) ) ) =>
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 ![
% 139.73/20.56 X848:$i,
% 139.73/20.56 X850:$i,
% 139.73/20.56 X852:$i]:
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 in @
% 139.73/20.56 X852 @
% 139.73/20.56 X848 ) =>
% 139.73/20.56 (
% 139.73/20.56 ![
% 139.73/20.56 X854:$i]:
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 in @
% 139.73/20.56 X854 @
% 139.73/20.56 X850 ) =>
% 139.73/20.56 (
% 139.73/20.56 in @
% 139.73/20.56 (
% 139.73/20.56 kpair @
% 139.73/20.56 X852 @
% 139.73/20.56 X854 ) @
% 139.73/20.56 (
% 139.73/20.56 cartprod @
% 139.73/20.56 X848 @
% 139.73/20.56 X850 ) ) ) ) ) ) =>
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 ![
% 139.73/20.56 X856:$i,
% 139.73/20.56 X858:$i,
% 139.73/20.56 X860:$i]:
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 in @
% 139.73/20.56 X860 @
% 139.73/20.56 (
% 139.73/20.56 cartprod @
% 139.73/20.56 X856 @
% 139.73/20.56 X858 ) ) =>
% 139.73/20.56 (
% 139.73/20.56 ?[
% 139.73/20.56 X862:$i]:
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 in @
% 139.73/20.56 X862 @
% 139.73/20.56 X856 ) &
% 139.73/20.56 (
% 139.73/20.56 ?[
% 139.73/20.56 X864:$i]:
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 in @
% 139.73/20.56 X864 @
% 139.73/20.56 X858 ) &
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 X860 ) =
% 139.73/20.56 (
% 139.73/20.56 kpair @
% 139.73/20.56 X862 @
% 139.73/20.56 X864 ) ) ) ) ) ) ) ) =>
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 ![
% 139.73/20.56 X866:$i,
% 139.73/20.56 X868:$i,
% 139.73/20.56 X870:$i]:
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 in @
% 139.73/20.56 X870 @
% 139.73/20.56 (
% 139.73/20.56 cartprod @
% 139.73/20.56 X866 @
% 139.73/20.56 X868 ) ) =>
% 139.73/20.56 (
% 139.73/20.56 iskpair @
% 139.73/20.56 X870 ) ) ) =>
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 ![
% 139.73/20.56 X872:$i,
% 139.73/20.56 X874:$i]:
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 in @
% 139.73/20.56 X874 @
% 139.73/20.56 (
% 139.73/20.56 setunion @
% 139.73/20.56 X872 ) ) =>
% 139.73/20.56 (
% 139.73/20.56 ?[
% 139.73/20.56 X876:$i]:
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 in @
% 139.73/20.56 X876 @
% 139.73/20.56 X872 ) &
% 139.73/20.56 (
% 139.73/20.56 in @
% 139.73/20.56 X874 @
% 139.73/20.56 X876 ) ) ) ) ) =>
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 ![
% 139.73/20.56 X878:$i]:
% 139.73/20.56 (
% 139.73/20.56 subset @
% 139.73/20.56 (
% 139.73/20.56 setunion @
% 139.73/20.56 (
% 139.73/20.56 setadjoin
% 139.73/20.56 @
% 139.73/20.56 X878 @
% 139.73/20.56 emptyset ) ) @
% 139.73/20.56 X878 ) ) =>
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 ![
% 139.73/20.56 X880:$i]:
% 139.73/20.56 (
% 139.73/20.56 subset @
% 139.73/20.56 X880 @
% 139.73/20.56 (
% 139.73/20.56 setunion @
% 139.73/20.56 (
% 139.73/20.56 setadjoin
% 139.73/20.56 @
% 139.73/20.56 X880 @
% 139.73/20.56 emptyset ) ) ) ) =>
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 ![
% 139.73/20.56 X882:$i]:
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 setunion @
% 139.73/20.56 (
% 139.73/20.56 setadjoin
% 139.73/20.56 @
% 139.73/20.56 X882 @
% 139.73/20.56 emptyset ) ) =
% 139.73/20.56 (
% 139.73/20.56 X882 ) ) ) =>
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 ![
% 139.73/20.56 X884:$i,
% 139.73/20.56 X886:(
% 139.73/20.56 $i > $o )]:
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 ![
% 139.73/20.56 X888:$i]:
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 in @
% 139.73/20.56 X888 @
% 139.73/20.56 X884 ) =>
% 139.73/20.56 (
% 139.73/20.56 ![
% 139.73/20.56 X890:$i]:
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 in @
% 139.73/20.56 X890 @
% 139.73/20.56 X884 ) =>
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 X886 @
% 139.73/20.56 X888 ) =>
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 X886 @
% 139.73/20.56 X890 ) =>
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 X888 ) =
% 139.73/20.56 (
% 139.73/20.56 X890 ) ) ) ) ) ) ) ) =>
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 ?[
% 139.73/20.56 X892:$i]:
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 in @
% 139.73/20.56 X892 @
% 139.73/20.56 X884 ) &
% 139.73/20.56 (
% 139.73/20.56 X886 @
% 139.73/20.56 X892 ) ) ) =>
% 139.73/20.56 (
% 139.73/20.56 singleton
% 139.73/20.56 @
% 139.73/20.56 (
% 139.73/20.56 dsetconstr
% 139.73/20.56 @
% 139.73/20.56 X884 @
% 139.73/20.56 (
% 139.73/20.56 ^[
% 139.73/20.56 V_15:$i]:
% 139.73/20.56 (
% 139.73/20.56 X886 @
% 139.73/20.56 V_15 ) ) ) ) ) ) ) =>
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 ![
% 139.73/20.56 X894:$i,
% 139.73/20.56 X896:(
% 139.73/20.56 $i > $o )]:
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 singleton
% 139.73/20.56 @
% 139.73/20.56 (
% 139.73/20.56 dsetconstr
% 139.73/20.56 @
% 139.73/20.56 X894 @
% 139.73/20.56 (
% 139.73/20.56 ^[
% 139.73/20.56 V_16:$i]:
% 139.73/20.56 (
% 139.73/20.56 X896 @
% 139.73/20.56 V_16 ) ) ) ) =>
% 139.73/20.56 (
% 139.73/20.56 ?[
% 139.73/20.56 X898:$i]:
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 in @
% 139.73/20.56 X898 @
% 139.73/20.56 X894 ) &
% 139.73/20.56 (
% 139.73/20.56 X896 @
% 139.73/20.56 X898 ) ) ) ) ) =>
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 ![
% 139.73/20.56 X900:$i,
% 139.73/20.56 X902:(
% 139.73/20.56 $i > $o ),
% 139.73/20.56 X904:$i]:
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 in @
% 139.73/20.56 X904 @
% 139.73/20.56 X900 ) =>
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 X902 @
% 139.73/20.56 X904 ) =>
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 ![
% 139.73/20.56 X906:$i]:
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 in @
% 139.73/20.56 X906 @
% 139.73/20.56 X900 ) =>
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 X902 @
% 139.73/20.56 X906 ) =>
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 X906 ) =
% 139.73/20.56 (
% 139.73/20.56 X904 ) ) ) ) ) =>
% 139.73/20.56 (
% 139.73/20.56 singleton
% 139.73/20.56 @
% 139.73/20.56 (
% 139.73/20.56 dsetconstr
% 139.73/20.56 @
% 139.73/20.56 X900 @
% 139.73/20.56 (
% 139.73/20.56 ^[
% 139.73/20.56 V_17:$i]:
% 139.73/20.56 (
% 139.73/20.56 X902 @
% 139.73/20.56 V_17 ) ) ) ) ) ) ) ) =>
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 ![
% 139.73/20.56 X908:$i,
% 139.73/20.56 X910:(
% 139.73/20.56 $i > $o )]:
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 ![
% 139.73/20.56 X912:$i]:
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 in @
% 139.73/20.56 X912 @
% 139.73/20.56 X908 ) =>
% 139.73/20.56 (
% 139.73/20.56 ![
% 139.73/20.56 X914:$i]:
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 in @
% 139.73/20.56 X914 @
% 139.73/20.56 X908 ) =>
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 X910 @
% 139.73/20.56 X912 ) =>
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 X910 @
% 139.73/20.56 X914 ) =>
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 X912 ) =
% 139.73/20.56 (
% 139.73/20.56 X914 ) ) ) ) ) ) ) ) =>
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 ?[
% 139.73/20.56 X916:$i]:
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 in @
% 139.73/20.56 X916 @
% 139.73/20.56 X908 ) &
% 139.73/20.56 (
% 139.73/20.56 X910 @
% 139.73/20.56 X916 ) ) ) =>
% 139.73/20.56 (
% 139.73/20.56 singleton
% 139.73/20.56 @
% 139.73/20.56 (
% 139.73/20.56 dsetconstr
% 139.73/20.56 @
% 139.73/20.56 X908 @
% 139.73/20.56 (
% 139.73/20.56 ^[
% 139.73/20.56 V_18:$i]:
% 139.73/20.56 (
% 139.73/20.56 X910 @
% 139.73/20.56 V_18 ) ) ) ) ) ) ) =>
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 ![
% 139.73/20.56 X918:$i,
% 139.73/20.56 X920:$i]:
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 setadjoin
% 139.73/20.56 @
% 139.73/20.56 X918 @
% 139.73/20.56 emptyset ) =
% 139.73/20.56 (
% 139.73/20.56 setadjoin
% 139.73/20.56 @
% 139.73/20.56 X920 @
% 139.73/20.56 emptyset ) ) =>
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 X918 ) =
% 139.73/20.56 (
% 139.73/20.56 X920 ) ) ) ) =>
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 ![
% 139.73/20.56 X922:$i,
% 139.73/20.56 X924:$i,
% 139.73/20.56 X926:$i]:
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 in @
% 139.73/20.56 (
% 139.73/20.56 setadjoin
% 139.73/20.56 @
% 139.73/20.56 X926 @
% 139.73/20.56 emptyset ) @
% 139.73/20.56 (
% 139.73/20.56 setadjoin
% 139.73/20.56 @
% 139.73/20.56 (
% 139.73/20.56 setadjoin
% 139.73/20.56 @
% 139.73/20.56 X922 @
% 139.73/20.56 emptyset ) @
% 139.73/20.56 (
% 139.73/20.56 setadjoin
% 139.73/20.56 @
% 139.73/20.56 (
% 139.73/20.56 setadjoin
% 139.73/20.56 @
% 139.73/20.56 X922 @
% 139.73/20.56 (
% 139.73/20.56 setadjoin
% 139.73/20.56 @
% 139.73/20.56 X924 @
% 139.73/20.56 emptyset ) ) @
% 139.73/20.56 emptyset ) ) ) =>
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 X922 ) =
% 139.73/20.56 (
% 139.73/20.56 X926 ) ) ) ) =>
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 ![
% 139.73/20.56 X928:$i]:
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 iskpair @
% 139.73/20.56 X928 ) =>
% 139.73/20.56 (
% 139.73/20.56 singleton
% 139.73/20.56 @
% 139.73/20.56 (
% 139.73/20.56 dsetconstr
% 139.73/20.56 @
% 139.73/20.56 (
% 139.73/20.56 setunion @
% 139.73/20.56 X928 ) @
% 139.73/20.56 (
% 139.73/20.56 ^[
% 139.73/20.56 V_19:$i]:
% 139.73/20.56 (
% 139.73/20.56 in @
% 139.73/20.56 (
% 139.73/20.56 setadjoin
% 139.73/20.56 @
% 139.73/20.56 V_19 @
% 139.73/20.56 emptyset ) @
% 139.73/20.56 X928 ) ) ) ) ) ) =>
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 ![
% 139.73/20.56 X930:$i]:
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 singleton
% 139.73/20.56 @
% 139.73/20.56 X930 ) =>
% 139.73/20.56 (
% 139.73/20.56 in @
% 139.73/20.56 (
% 139.73/20.56 setunion @
% 139.73/20.56 X930 ) @
% 139.73/20.56 X930 ) ) ) =>
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 ![
% 139.73/20.56 X932:$i,
% 139.73/20.56 X934:$i]:
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 kfst @
% 139.73/20.56 (
% 139.73/20.56 kpair @
% 139.73/20.56 X932 @
% 139.73/20.56 X934 ) ) =
% 139.73/20.56 (
% 139.73/20.56 X932 ) ) ) =>
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 ![
% 139.73/20.56 X936:$i,
% 139.73/20.56 X938:$i,
% 139.73/20.56 X940:$i]:
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 in @
% 139.73/20.56 X940 @
% 139.73/20.56 (
% 139.73/20.56 cartprod @
% 139.73/20.56 X936 @
% 139.73/20.56 X938 ) ) =>
% 139.73/20.56 (
% 139.73/20.56 in @
% 139.73/20.56 (
% 139.73/20.56 kfst @
% 139.73/20.56 X940 ) @
% 139.73/20.56 X936 ) ) ) =>
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 ![
% 139.73/20.56 X942:$i,
% 139.73/20.56 X944:$i,
% 139.73/20.56 X946:$i,
% 139.73/20.56 X948:$i]:
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 setadjoin
% 139.73/20.56 @
% 139.73/20.56 (
% 139.73/20.56 setadjoin
% 139.73/20.56 @
% 139.73/20.56 X942 @
% 139.73/20.56 emptyset ) @
% 139.73/20.56 (
% 139.73/20.56 setadjoin
% 139.73/20.56 @
% 139.73/20.56 (
% 139.73/20.56 setadjoin
% 139.73/20.56 @
% 139.73/20.56 X942 @
% 139.73/20.56 (
% 139.73/20.56 setadjoin
% 139.73/20.56 @
% 139.73/20.56 X944 @
% 139.73/20.56 emptyset ) ) @
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% 139.73/20.56 X1012:$i,
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% 139.73/20.56 ![
% 139.73/20.56 X1086:$i]:
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 in @
% 139.73/20.56 X1086 @
% 139.73/20.56 X1080 ) =>
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 in @
% 139.73/20.56 (
% 139.73/20.56 kpair @
% 139.73/20.56 X1084 @
% 139.73/20.56 X1086 ) @
% 139.73/20.56 (
% 139.73/20.56 dpsetconstr
% 139.73/20.56 @
% 139.73/20.56 X1078 @
% 139.73/20.56 X1080 @
% 139.73/20.56 (
% 139.73/20.56 ^[
% 139.73/20.56 V_27:$i,
% 139.73/20.56 V_28:$i]:
% 139.73/20.56 (
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% 139.73/20.56 V_28 ) ) ) ) =>
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% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 ![
% 139.73/20.56 X1088:$i,
% 139.73/20.56 X1090:$i,
% 139.73/20.56 X1092:(
% 139.73/20.56 $i > $i >
% 139.73/20.56 $o ),
% 139.73/20.56 X1094:$i,
% 139.73/20.56 X1096:$i]:
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 in @
% 139.73/20.56 (
% 139.73/20.56 kpair @
% 139.73/20.56 X1094 @
% 139.73/20.56 X1096 ) @
% 139.73/20.56 (
% 139.73/20.56 dpsetconstr
% 139.73/20.56 @
% 139.73/20.56 X1088 @
% 139.73/20.56 X1090 @
% 139.73/20.56 (
% 139.73/20.56 ^[
% 139.73/20.56 V_29:$i,
% 139.73/20.56 V_30:$i]:
% 139.73/20.56 (
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% 139.73/20.56 V_29 @
% 139.73/20.56 V_30 ) ) ) ) =>
% 139.73/20.56 (
% 139.73/20.56 in @
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% 139.73/20.56 X1088 ) ) ) =>
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 ![
% 139.73/20.56 X1098:$i,
% 139.73/20.56 X1100:$i,
% 139.73/20.56 X1102:(
% 139.73/20.56 $i > $i >
% 139.73/20.56 $o ),
% 139.73/20.56 X1104:$i,
% 139.73/20.56 X1106:$i]:
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 in @
% 139.73/20.56 (
% 139.73/20.56 kpair @
% 139.73/20.56 X1104 @
% 139.73/20.56 X1106 ) @
% 139.73/20.56 (
% 139.73/20.56 dpsetconstr
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% 139.73/20.56 X1098 @
% 139.73/20.56 X1100 @
% 139.73/20.56 (
% 139.73/20.56 ^[
% 139.73/20.56 V_31:$i,
% 139.73/20.56 V_32:$i]:
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% 139.73/20.56 (
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% 139.73/20.56 X1100 ) ) ) =>
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 ![
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% 139.73/20.56 X1110:$i,
% 139.73/20.56 X1112:(
% 139.73/20.56 $i > $i >
% 139.73/20.56 $o ),
% 139.73/20.56 X1114:$i,
% 139.73/20.56 X1116:$i]:
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 in @
% 139.73/20.56 (
% 139.73/20.56 kpair @
% 139.73/20.56 X1114 @
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% 139.73/20.56 (
% 139.73/20.56 dpsetconstr
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% 139.73/20.56 X1108 @
% 139.73/20.56 X1110 @
% 139.73/20.56 (
% 139.73/20.56 ^[
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% 139.73/20.56 V_34:$i]:
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% 139.73/20.56 (
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% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 ![
% 139.73/20.56 X1118:$i,
% 139.73/20.56 X1120:$i,
% 139.73/20.56 X1122:$i]:
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 func @
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% 139.73/20.56 X1120 @
% 139.73/20.56 X1122 ) =>
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% 139.73/20.56 ![
% 139.73/20.56 X1124:$i]:
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% 139.73/20.56 X1118 ) =>
% 139.73/20.56 (
% 139.73/20.56 singleton
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% 139.73/20.56 (
% 139.73/20.56 dsetconstr
% 139.73/20.56 @
% 139.73/20.56 X1120 @
% 139.73/20.56 (
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% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 ![
% 139.73/20.56 X1126:$i,
% 139.73/20.56 X1128:$i,
% 139.73/20.56 X1130:$i]:
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% 139.73/20.56 (
% 139.73/20.56 func @
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% 139.73/20.56 X1128 @
% 139.73/20.56 X1130 ) =>
% 139.73/20.56 (
% 139.73/20.56 ![
% 139.73/20.56 X1132:$i]:
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% 139.73/20.56 (
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% 139.73/20.56 X1126 ) =>
% 139.73/20.56 (
% 139.73/20.56 in @
% 139.73/20.56 (
% 139.73/20.56 setunion @
% 139.73/20.56 (
% 139.73/20.56 dsetconstr
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% 139.73/20.56 (
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% 139.73/20.56 V_36:$i]:
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% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 ![
% 139.73/20.56 X1134:$i,
% 139.73/20.56 X1136:$i,
% 139.73/20.56 X1138:$i]:
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 func @
% 139.73/20.56 X1134 @
% 139.73/20.56 X1136 @
% 139.73/20.56 X1138 ) =>
% 139.73/20.56 (
% 139.73/20.56 ![
% 139.73/20.56 X1140:$i]:
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% 139.73/20.56 (
% 139.73/20.56 in @
% 139.73/20.56 X1140 @
% 139.73/20.56 X1134 ) =>
% 139.73/20.56 (
% 139.73/20.56 in @
% 139.73/20.56 (
% 139.73/20.56 ap @
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% 139.73/20.56 X1138 @
% 139.73/20.56 X1140 ) @
% 139.73/20.56 X1136 ) ) ) ) ) =>
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 ![
% 139.73/20.56 X1142:$i,
% 139.73/20.56 X1144:$i,
% 139.73/20.56 X1146:$i]:
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 in @
% 139.73/20.56 X1146 @
% 139.73/20.56 (
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% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 ![
% 139.73/20.56 X1148:$i,
% 139.73/20.56 X1150:$i,
% 139.73/20.56 X1152:$i]:
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% 139.73/20.56 (
% 139.73/20.56 in @
% 139.73/20.56 X1152 @
% 139.73/20.56 (
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% 139.73/20.56 X1150 ) ) =>
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% 139.73/20.56 ![
% 139.73/20.56 X1154:$i]:
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% 139.73/20.56 (
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% 139.73/20.56 X1148 ) =>
% 139.73/20.56 (
% 139.73/20.56 in @
% 139.73/20.56 (
% 139.73/20.56 ap @
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% 139.73/20.56 X1150 ) ) ) ) ) =>
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 ![
% 139.73/20.56 X1156:$i,
% 139.73/20.56 X1158:$i,
% 139.73/20.56 X1160:$i]:
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 func @
% 139.73/20.56 X1156 @
% 139.73/20.56 X1158 @
% 139.73/20.56 X1160 ) =>
% 139.73/20.56 (
% 139.73/20.56 in @
% 139.73/20.56 X1160 @
% 139.73/20.56 (
% 139.73/20.56 funcSet @
% 139.73/20.56 X1156 @
% 139.73/20.56 X1158 ) ) ) ) =>
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 ![
% 139.73/20.56 X1162:$i,
% 139.73/20.56 X1164:$i,
% 139.73/20.56 X1166:(
% 139.73/20.56 $i > $i )]:
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 ![
% 139.73/20.56 X1168:$i]:
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 in @
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% 139.73/20.56 X1162 ) =>
% 139.73/20.56 (
% 139.73/20.56 in @
% 139.73/20.56 (
% 139.73/20.56 X1166 @
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% 139.73/20.56 X1164 ) ) ) =>
% 139.73/20.56 (
% 139.73/20.56 func @
% 139.73/20.56 X1162 @
% 139.73/20.56 X1164 @
% 139.73/20.56 (
% 139.73/20.56 dpsetconstr
% 139.73/20.56 @
% 139.73/20.56 X1162 @
% 139.73/20.56 X1164 @
% 139.73/20.56 (
% 139.73/20.56 ^[
% 139.73/20.56 V_37:$i,
% 139.73/20.56 V_38:$i]:
% 139.73/20.56 (
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% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 ![
% 139.73/20.56 X1170:$i,
% 139.73/20.56 X1172:$i,
% 139.73/20.56 X1174:(
% 139.73/20.56 $i > $i )]:
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 ![
% 139.73/20.56 X1176:$i]:
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 in @
% 139.73/20.56 X1176 @
% 139.73/20.56 X1170 ) =>
% 139.73/20.56 (
% 139.73/20.56 in @
% 139.73/20.56 (
% 139.73/20.56 X1174 @
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% 139.73/20.56 X1172 ) ) ) =>
% 139.73/20.56 (
% 139.73/20.56 func @
% 139.73/20.56 X1170 @
% 139.73/20.56 X1172 @
% 139.73/20.56 (
% 139.73/20.56 lam @
% 139.73/20.56 X1170 @
% 139.73/20.56 X1172 @
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% 139.73/20.56 ^[
% 139.73/20.56 V_39:$i]:
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% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 ![
% 139.73/20.56 X1178:$i,
% 139.73/20.56 X1180:$i,
% 139.73/20.56 X1182:(
% 139.73/20.56 $i > $i )]:
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 ![
% 139.73/20.56 X1184:$i]:
% 139.73/20.56 (
% 139.73/20.56 (
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% 139.73/20.56 (
% 139.73/20.56 (
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% 139.73/20.56 X1186:$i,
% 139.73/20.56 X1188:$i,
% 139.73/20.56 X1190:$i]:
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% 139.73/20.56 subset @
% 139.73/20.56 X1190 @
% 139.73/20.56 (
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% 139.73/20.56 X1188 ) ) =>
% 139.73/20.56 (
% 139.73/20.56 ![
% 139.73/20.56 X1192:(
% 139.73/20.56 $i > $o )]:
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% 139.73/20.56 (
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% 139.73/20.56 (
% 139.73/20.56 kpair @
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% 139.73/20.56 (
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% 139.73/20.56 X1200:$i,
% 139.73/20.56 X1202:$i,
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% 139.73/20.56 $i > $o )]:
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% 139.73/20.56 X1216:(
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% 139.73/20.56 (
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% 139.73/20.56 X1240:$i,
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% 139.73/20.56 func @
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% 139.73/20.56 X1302:$i,
% 139.73/20.56 X1304:$i]:
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% 139.73/20.56 ![
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% 139.73/20.56 lam @
% 139.73/20.56 X1352 @
% 139.73/20.56 X1354 @
% 139.73/20.56 (
% 139.73/20.56 ^[
% 139.73/20.56 V_44:$i]:
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% 139.73/20.56 V_44 ) ) ) =
% 139.73/20.56 (
% 139.73/20.56 lam @
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% 139.73/20.56 X1354 @
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% 139.73/20.56 V_45 ) ) ) ) ) ) =>
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 ![
% 139.73/20.56 X1360:$i,
% 139.73/20.56 X1362:$i,
% 139.73/20.56 X1364:(
% 139.73/20.56 $i > $i )]:
% 139.73/20.56 (
% 139.73/20.56 (
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% 139.73/20.56 X1366:$i]:
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% 139.73/20.56 (
% 139.73/20.56 in @
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% 139.73/20.56 X1360 ) =>
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% 139.73/20.56 in @
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% 139.73/20.56 (
% 139.73/20.56 ![
% 139.73/20.56 X1368:$i]:
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% 139.73/20.56 in @
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% 139.73/20.56 X1360 ) =>
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 ap @
% 139.73/20.56 X1360 @
% 139.73/20.56 X1362 @
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% 139.73/20.56 lam @
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% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 ![
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% 139.73/20.56 X1372:$i,
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% 139.73/20.56 in @
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% 139.73/20.56 (
% 139.73/20.56 funcSet @
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% 139.73/20.56 X1372 ) ) =>
% 139.73/20.56 (
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% 139.73/20.56 lam @
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% 139.73/20.56 (
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% 139.73/20.56 (
% 139.73/20.56 ![
% 139.73/20.56 X1376:$i,
% 139.73/20.56 X1378:$o,
% 139.73/20.56 X1380:$i]:
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% 139.73/20.56 (
% 139.73/20.56 in @
% 139.73/20.56 X1380 @
% 139.73/20.56 X1376 ) =>
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% 139.73/20.56 ![
% 139.73/20.56 X1382:$i]:
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% 139.73/20.56 X1382 @
% 139.73/20.56 X1376 ) =>
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 ~( X1378 ) ) =>
% 139.73/20.56 (
% 139.73/20.56 in @
% 139.73/20.56 X1382 @
% 139.73/20.56 (
% 139.73/20.56 dsetconstr
% 139.73/20.56 @
% 139.73/20.56 X1376 @
% 139.73/20.56 (
% 139.73/20.56 ^[
% 139.73/20.56 V_48:$i]:
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% 139.73/20.56 (
% 139.73/20.56 V_48 ) =
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% 139.73/20.56 (
% 139.73/20.56 ~( X1378 ) ) ) |
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 V_48 ) =
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% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 ![
% 139.73/20.56 X1384:$i,
% 139.73/20.56 X1386:$o,
% 139.73/20.56 X1388:$i]:
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% 139.73/20.56 in @
% 139.73/20.56 X1388 @
% 139.73/20.56 X1384 ) =>
% 139.73/20.56 (
% 139.73/20.56 ![
% 139.73/20.56 X1390:$i]:
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% 139.73/20.56 X1390 @
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% 139.73/20.56 (
% 139.73/20.56 ~( X1386 ) ) =>
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 dsetconstr
% 139.73/20.56 @
% 139.73/20.56 X1384 @
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% 139.73/20.56 ^[
% 139.73/20.56 V_49:$i]:
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% 139.73/20.56 (
% 139.73/20.56 X1390 ) ) &
% 139.73/20.56 (
% 139.73/20.56 ~( X1386 ) ) ) |
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 V_49 ) =
% 139.73/20.56 (
% 139.73/20.56 X1388 ) ) &
% 139.73/20.56 (
% 139.73/20.56 X1386 ) ) ) ) ) =
% 139.73/20.56 (
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% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 ![
% 139.73/20.56 X1392:$i,
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% 139.73/20.56 X1396:$i]:
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% 139.73/20.56 in @
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% 139.73/20.56 X1392 ) =>
% 139.73/20.56 (
% 139.73/20.56 ![
% 139.73/20.56 X1398:$i]:
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% 139.73/20.56 (
% 139.73/20.56 in @
% 139.73/20.56 X1398 @
% 139.73/20.56 X1392 ) =>
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 X1394 ) =>
% 139.73/20.56 (
% 139.73/20.56 in @
% 139.73/20.56 X1396 @
% 139.73/20.56 (
% 139.73/20.56 dsetconstr
% 139.73/20.56 @
% 139.73/20.56 X1392 @
% 139.73/20.56 (
% 139.73/20.56 ^[
% 139.73/20.56 V_50:$i]:
% 139.73/20.56 (
% 139.73/20.56 (
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% 139.73/20.56 (
% 139.73/20.56 V_50 ) =
% 139.73/20.56 (
% 139.73/20.56 X1398 ) ) &
% 139.73/20.56 (
% 139.73/20.56 ~( X1394 ) ) ) |
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 V_50 ) =
% 139.73/20.56 (
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% 139.73/20.56 (
% 139.73/20.56 X1394 ) ) ) ) ) ) ) ) ) ) ) =>
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 ![
% 139.73/20.56 X1400:$i,
% 139.73/20.56 X1402:$o,
% 139.73/20.56 X1404:$i]:
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% 139.73/20.56 (
% 139.73/20.56 in @
% 139.73/20.56 X1404 @
% 139.73/20.56 X1400 ) =>
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% 139.73/20.56 ![
% 139.73/20.56 X1406:$i]:
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% 139.73/20.56 in @
% 139.73/20.56 X1406 @
% 139.73/20.56 X1400 ) =>
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% 139.73/20.56 (
% 139.73/20.56 X1402 ) =>
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 dsetconstr
% 139.73/20.56 @
% 139.73/20.56 X1400 @
% 139.73/20.56 (
% 139.73/20.56 ^[
% 139.73/20.56 V_51:$i]:
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% 139.73/20.56 (
% 139.73/20.56 V_51 ) =
% 139.73/20.56 (
% 139.73/20.56 X1406 ) ) &
% 139.73/20.56 (
% 139.73/20.56 ~( X1402 ) ) ) |
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 V_51 ) =
% 139.73/20.56 (
% 139.73/20.56 X1404 ) ) &
% 139.73/20.56 (
% 139.73/20.56 X1402 ) ) ) ) ) =
% 139.73/20.56 (
% 139.73/20.56 setadjoin
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% 139.73/20.56 emptyset ) ) ) ) ) ) ) =>
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 ![
% 139.73/20.56 X1408:$i,
% 139.73/20.56 X1410:$o,
% 139.73/20.56 X1412:$i]:
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 in @
% 139.73/20.56 X1412 @
% 139.73/20.56 X1408 ) =>
% 139.73/20.56 (
% 139.73/20.56 ![
% 139.73/20.56 X1414:$i]:
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 in @
% 139.73/20.56 X1414 @
% 139.73/20.56 X1408 ) =>
% 139.73/20.56 (
% 139.73/20.56 singleton
% 139.73/20.56 @
% 139.73/20.56 (
% 139.73/20.56 dsetconstr
% 139.73/20.56 @
% 139.73/20.56 X1408 @
% 139.73/20.56 (
% 139.73/20.56 ^[
% 139.73/20.56 V_52:$i]:
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 V_52 ) =
% 139.73/20.56 (
% 139.73/20.56 X1414 ) ) &
% 139.73/20.56 (
% 139.73/20.56 ~( X1410 ) ) ) |
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 V_52 ) =
% 139.73/20.56 (
% 139.73/20.56 X1412 ) ) &
% 139.73/20.56 (
% 139.73/20.56 X1410 ) ) ) ) ) ) ) ) ) ) =>
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 ![
% 139.73/20.56 X1416:$i,
% 139.73/20.56 X1418:$o,
% 139.73/20.56 X1420:$i]:
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 in @
% 139.73/20.56 X1420 @
% 139.73/20.56 X1416 ) =>
% 139.73/20.56 (
% 139.73/20.56 ![
% 139.73/20.56 X1422:$i]:
% 139.73/20.56 (
% 139.73/20.56 (
% 139.73/20.56 in @
% 139.73/20.56 X1422 @
% 139.73/20.56 X1416 ) =>
% 139.73/20.56 (
% 139.73/20.56 in @
% 139.73/20.56 (
% 139.73/20.56 if @
% 139.73/20.56 X1416 @
% 139.73/20.56 X1418 @
% 139.73/20.56 X1420 @
% 139.73/20.56 X1422 ) @
% 139.73/20.57 X1416 ) ) ) ) ) =>
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 ![
% 139.73/20.57 X1424:$i]:
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 singleton
% 139.73/20.57 @
% 139.73/20.57 X1424 ) =>
% 139.73/20.57 (
% 139.73/20.57 ![
% 139.73/20.57 X1426:$i]:
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 X1426 @
% 139.73/20.57 X1424 ) =>
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 setunion @
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% 139.73/20.57 (
% 139.73/20.57 X1426 ) ) ) ) ) ) =>
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 ![
% 139.73/20.57 X1428:$i,
% 139.73/20.57 X1430:$o,
% 139.73/20.57 X1432:$i]:
% 139.73/20.57 (
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% 139.73/20.57 in @
% 139.73/20.57 X1432 @
% 139.73/20.57 X1428 ) =>
% 139.73/20.57 (
% 139.73/20.57 ![
% 139.73/20.57 X1434:$i]:
% 139.73/20.57 (
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% 139.73/20.57 X1434 @
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% 139.73/20.57 (
% 139.73/20.57 X1430 ) =>
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 if @
% 139.73/20.57 X1428 @
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% 139.73/20.57 X1432 ) ) ) ) ) ) ) =>
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 ![
% 139.73/20.57 X1436:$i,
% 139.73/20.57 X1438:$o,
% 139.73/20.57 X1440:$i]:
% 139.73/20.57 (
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% 139.73/20.57 in @
% 139.73/20.57 X1440 @
% 139.73/20.57 X1436 ) =>
% 139.73/20.57 (
% 139.73/20.57 ![
% 139.73/20.57 X1442:$i]:
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 X1442 @
% 139.73/20.57 X1436 ) =>
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 ~( X1438 ) ) =>
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 if @
% 139.73/20.57 X1436 @
% 139.73/20.57 X1438 @
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% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 ![
% 139.73/20.57 X1444:$i,
% 139.73/20.57 X1446:$o,
% 139.73/20.57 X1448:$i]:
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 X1448 @
% 139.73/20.57 X1444 ) =>
% 139.73/20.57 (
% 139.73/20.57 ![
% 139.73/20.57 X1450:$i]:
% 139.73/20.57 (
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% 139.73/20.57 (
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% 139.73/20.57 if @
% 139.73/20.57 X1444 @
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% 139.73/20.57 X1448 @
% 139.73/20.57 X1450 ) @
% 139.73/20.57 (
% 139.73/20.57 setadjoin
% 139.73/20.57 @
% 139.73/20.57 X1448 @
% 139.73/20.57 (
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% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 ![
% 139.73/20.57 X1452:$i,
% 139.73/20.57 X1454:$i]:
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 X1454 @
% 139.73/20.57 (
% 139.73/20.57 powerset @
% 139.73/20.57 X1452 ) ) =>
% 139.73/20.57 (
% 139.73/20.57 ![
% 139.73/20.57 X1456:$i]:
% 139.73/20.57 (
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% 139.73/20.57 in @
% 139.73/20.57 X1456 @
% 139.73/20.57 (
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% 139.73/20.57 X1452 ) ) =>
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 (
% 139.73/20.57 binintersect
% 139.73/20.57 @
% 139.73/20.57 X1454 @
% 139.73/20.57 X1456 ) @
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% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 ![
% 139.73/20.57 X1458:$i,
% 139.73/20.57 X1460:$i]:
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 X1460 @
% 139.73/20.57 (
% 139.73/20.57 powerset @
% 139.73/20.57 X1458 ) ) =>
% 139.73/20.57 (
% 139.73/20.57 ![
% 139.73/20.57 X1462:$i]:
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 X1462 @
% 139.73/20.57 (
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% 139.73/20.57 X1458 ) ) =>
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 (
% 139.73/20.57 binunion @
% 139.73/20.57 X1460 @
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% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 ![
% 139.73/20.57 X1464:$i,
% 139.73/20.57 X1466:$i]:
% 139.73/20.57 (
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% 139.73/20.57 in @
% 139.73/20.57 X1466 @
% 139.73/20.57 (
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% 139.73/20.57 X1464 ) ) =>
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 (
% 139.73/20.57 powerset @
% 139.73/20.57 X1466 ) @
% 139.73/20.57 (
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% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 ![
% 139.73/20.57 X1468:$i,
% 139.73/20.57 X1470:$i]:
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 X1470 @
% 139.73/20.57 (
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% 139.73/20.57 X1468 ) ) =>
% 139.73/20.57 (
% 139.73/20.57 ![
% 139.73/20.57 X1472:$i]:
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 X1472 @
% 139.73/20.57 (
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% 139.73/20.57 X1468 ) ) =>
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 (
% 139.73/20.57 setminus @
% 139.73/20.57 X1470 @
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% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 ![
% 139.73/20.57 X1474:$i,
% 139.73/20.57 X1476:$i]:
% 139.73/20.57 (
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% 139.73/20.57 in @
% 139.73/20.57 X1476 @
% 139.73/20.57 (
% 139.73/20.57 powerset @
% 139.73/20.57 X1474 ) ) =>
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 (
% 139.73/20.57 setminus @
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% 139.73/20.57 ![
% 139.73/20.57 X1794:$i]:
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 X1794 @
% 139.73/20.57 (
% 139.73/20.57 powerset @
% 139.73/20.57 X1790 ) ) =>
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 setminus @
% 139.73/20.57 X1790 @
% 139.73/20.57 (
% 139.73/20.57 binunion @
% 139.73/20.57 X1792 @
% 139.73/20.57 X1794 ) ) =
% 139.73/20.57 (
% 139.73/20.57 binintersect
% 139.73/20.57 @
% 139.73/20.57 (
% 139.73/20.57 setminus @
% 139.73/20.57 X1790 @
% 139.73/20.57 X1792 ) @
% 139.73/20.57 (
% 139.73/20.57 setminus @
% 139.73/20.57 X1790 @
% 139.73/20.57 X1794 ) ) ) ) ) ) ) =>
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 ![
% 139.73/20.57 X1796:$i,
% 139.73/20.57 X1798:$i]:
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 X1798 @
% 139.73/20.57 (
% 139.73/20.57 powerset @
% 139.73/20.57 X1796 ) ) =>
% 139.73/20.57 (
% 139.73/20.57 ![
% 139.73/20.57 X1800:$i]:
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 X1800 @
% 139.73/20.57 (
% 139.73/20.57 powerset @
% 139.73/20.57 X1796 ) ) =>
% 139.73/20.57 (
% 139.73/20.57 ![
% 139.73/20.57 X1802:$i]:
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 X1802 @
% 139.73/20.57 (
% 139.73/20.57 binintersect
% 139.73/20.57 @
% 139.73/20.57 X1798 @
% 139.73/20.57 X1800 ) ) =>
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 X1802 @
% 139.73/20.57 X1796 ) ) ) ) ) ) ) =>
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 ![
% 139.73/20.57 X1804:$i,
% 139.73/20.57 X1806:$i]:
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 X1806 @
% 139.73/20.57 (
% 139.73/20.57 powerset @
% 139.73/20.57 X1804 ) ) =>
% 139.73/20.57 (
% 139.73/20.57 ![
% 139.73/20.57 X1808:$i]:
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 X1808 @
% 139.73/20.57 (
% 139.73/20.57 powerset @
% 139.73/20.57 X1804 ) ) =>
% 139.73/20.57 (
% 139.73/20.57 ![
% 139.73/20.57 X1810:$i]:
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 X1810 @
% 139.73/20.57 (
% 139.73/20.57 powerset @
% 139.73/20.57 X1804 ) ) =>
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 subset @
% 139.73/20.57 X1806 @
% 139.73/20.57 X1810 ) =>
% 139.73/20.57 (
% 139.73/20.57 subset @
% 139.73/20.57 (
% 139.73/20.57 binintersect
% 139.73/20.57 @
% 139.73/20.57 X1806 @
% 139.73/20.57 X1808 ) @
% 139.73/20.57 X1810 ) ) ) ) ) ) ) ) =>
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 ![
% 139.73/20.57 X1812:$i,
% 139.73/20.57 X1814:$i]:
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 X1814 @
% 139.73/20.57 (
% 139.73/20.57 powerset @
% 139.73/20.57 X1812 ) ) =>
% 139.73/20.57 (
% 139.73/20.57 ![
% 139.73/20.57 X1816:$i]:
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 X1816 @
% 139.73/20.57 (
% 139.73/20.57 powerset @
% 139.73/20.57 X1812 ) ) =>
% 139.73/20.57 (
% 139.73/20.57 ![
% 139.73/20.57 X1818:$i]:
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 X1818 @
% 139.73/20.57 (
% 139.73/20.57 powerset @
% 139.73/20.57 X1812 ) ) =>
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 subset @
% 139.73/20.57 X1816 @
% 139.73/20.57 X1818 ) =>
% 139.73/20.57 (
% 139.73/20.57 subset @
% 139.73/20.57 (
% 139.73/20.57 binintersect
% 139.73/20.57 @
% 139.73/20.57 X1814 @
% 139.73/20.57 X1816 ) @
% 139.73/20.57 X1818 ) ) ) ) ) ) ) ) =>
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 ![
% 139.73/20.57 X1820:$i,
% 139.73/20.57 X1822:$i]:
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 X1822 @
% 139.73/20.57 (
% 139.73/20.57 powerset @
% 139.73/20.57 X1820 ) ) =>
% 139.73/20.57 (
% 139.73/20.57 ![
% 139.73/20.57 X1824:$i]:
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 X1824 @
% 139.73/20.57 (
% 139.73/20.57 powerset @
% 139.73/20.57 X1820 ) ) =>
% 139.73/20.57 (
% 139.73/20.57 ![
% 139.73/20.57 X1826:$i]:
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 X1826 @
% 139.73/20.57 (
% 139.73/20.57 powerset @
% 139.73/20.57 X1820 ) ) =>
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 subset @
% 139.73/20.57 X1822 @
% 139.73/20.57 X1824 ) =>
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 subset @
% 139.73/20.57 X1822 @
% 139.73/20.57 X1826 ) =>
% 139.73/20.57 (
% 139.73/20.57 subset @
% 139.73/20.57 X1822 @
% 139.73/20.57 (
% 139.73/20.57 binintersect
% 139.73/20.57 @
% 139.73/20.57 X1824 @
% 139.73/20.57 X1826 ) ) ) ) ) ) ) ) ) ) =>
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 ![
% 139.73/20.57 X1828:$i,
% 139.73/20.57 X1830:$i]:
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 X1830 @
% 139.73/20.57 (
% 139.73/20.57 powerset @
% 139.73/20.57 X1828 ) ) =>
% 139.73/20.57 (
% 139.73/20.57 ![
% 139.73/20.57 X1832:$i]:
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 X1832 @
% 139.73/20.57 (
% 139.73/20.57 powerset @
% 139.73/20.57 X1828 ) ) =>
% 139.73/20.57 (
% 139.73/20.57 ![
% 139.73/20.57 X1834:$i]:
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 X1834 @
% 139.73/20.57 (
% 139.73/20.57 powerset @
% 139.73/20.57 X1828 ) ) =>
% 139.73/20.57 (
% 139.73/20.57 ![
% 139.73/20.57 X1836:$i]:
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 X1836 @
% 139.73/20.57 (
% 139.73/20.57 powerset @
% 139.73/20.57 X1828 ) ) =>
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 subset @
% 139.73/20.57 X1830 @
% 139.73/20.57 X1834 ) =>
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 subset @
% 139.73/20.57 X1832 @
% 139.73/20.57 X1836 ) =>
% 139.73/20.57 (
% 139.73/20.57 subset @
% 139.73/20.57 (
% 139.73/20.57 binintersect
% 139.73/20.57 @
% 139.73/20.57 X1830 @
% 139.73/20.57 X1832 ) @
% 139.73/20.57 (
% 139.73/20.57 binintersect
% 139.73/20.57 @
% 139.73/20.57 X1834 @
% 139.73/20.57 X1836 ) ) ) ) ) ) ) ) ) ) ) ) =>
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 ![
% 139.73/20.57 X1838:$i,
% 139.73/20.57 X1840:$i]:
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 X1840 @
% 139.73/20.57 (
% 139.73/20.57 powerset @
% 139.73/20.57 X1838 ) ) =>
% 139.73/20.57 (
% 139.73/20.57 ![
% 139.73/20.57 X1842:$i]:
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 X1842 @
% 139.73/20.57 (
% 139.73/20.57 powerset @
% 139.73/20.57 X1838 ) ) =>
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 (
% 139.73/20.57 setminus @
% 139.73/20.57 X1838 @
% 139.73/20.57 X1840 ) @
% 139.73/20.57 (
% 139.73/20.57 powerset @
% 139.73/20.57 (
% 139.73/20.57 setminus @
% 139.73/20.57 X1838 @
% 139.73/20.57 (
% 139.73/20.57 binintersect
% 139.73/20.57 @
% 139.73/20.57 X1840 @
% 139.73/20.57 X1842 ) ) ) ) ) ) ) ) =>
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 ![
% 139.73/20.57 X1844:$i,
% 139.73/20.57 X1846:$i]:
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 X1846 @
% 139.73/20.57 (
% 139.73/20.57 powerset @
% 139.73/20.57 X1844 ) ) =>
% 139.73/20.57 (
% 139.73/20.57 ![
% 139.73/20.57 X1848:$i]:
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 X1848 @
% 139.73/20.57 (
% 139.73/20.57 powerset @
% 139.73/20.57 X1844 ) ) =>
% 139.73/20.57 (
% 139.73/20.57 ![
% 139.73/20.57 X1850:$i]:
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 X1850 @
% 139.73/20.57 (
% 139.73/20.57 powerset @
% 139.73/20.57 X1844 ) ) =>
% 139.73/20.57 (
% 139.73/20.57 ![
% 139.73/20.57 X1852:$i]:
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 X1852 @
% 139.73/20.57 (
% 139.73/20.57 powerset @
% 139.73/20.57 X1844 ) ) =>
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 setminus @
% 139.73/20.57 X1844 @
% 139.73/20.57 (
% 139.73/20.57 binintersect
% 139.73/20.57 @
% 139.73/20.57 (
% 139.73/20.57 binunion @
% 139.73/20.57 X1846 @
% 139.73/20.57 X1848 ) @
% 139.73/20.57 (
% 139.73/20.57 binunion @
% 139.73/20.57 X1850 @
% 139.73/20.57 X1852 ) ) ) =
% 139.73/20.57 (
% 139.73/20.57 binunion @
% 139.73/20.57 (
% 139.73/20.57 binintersect
% 139.73/20.57 @
% 139.73/20.57 (
% 139.73/20.57 setminus @
% 139.73/20.57 X1844 @
% 139.73/20.57 X1846 ) @
% 139.73/20.57 (
% 139.73/20.57 setminus @
% 139.73/20.57 X1844 @
% 139.73/20.57 X1848 ) ) @
% 139.73/20.57 (
% 139.73/20.57 binintersect
% 139.73/20.57 @
% 139.73/20.57 (
% 139.73/20.57 setminus @
% 139.73/20.57 X1844 @
% 139.73/20.57 X1850 ) @
% 139.73/20.57 (
% 139.73/20.57 setminus @
% 139.73/20.57 X1844 @
% 139.73/20.57 X1852 ) ) ) ) ) ) ) ) ) ) ) ) =>
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 ![
% 139.73/20.57 X1854:$i,
% 139.73/20.57 X1856:$i]:
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 X1856 @
% 139.73/20.57 (
% 139.73/20.57 powerset @
% 139.73/20.57 X1854 ) ) =>
% 139.73/20.57 (
% 139.73/20.57 ![
% 139.73/20.57 X1858:$i]:
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 X1858 @
% 139.73/20.57 (
% 139.73/20.57 powerset @
% 139.73/20.57 X1854 ) ) =>
% 139.73/20.57 (
% 139.73/20.57 ![
% 139.73/20.57 X1860:$i]:
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 X1860 @
% 139.73/20.57 (
% 139.73/20.57 powerset @
% 139.73/20.57 X1854 ) ) =>
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 (
% 139.73/20.57 binintersect
% 139.73/20.57 @
% 139.73/20.57 X1856 @
% 139.73/20.57 X1858 ) @
% 139.73/20.57 (
% 139.73/20.57 powerset @
% 139.73/20.57 (
% 139.73/20.57 binintersect
% 139.73/20.57 @
% 139.73/20.57 (
% 139.73/20.57 binunion @
% 139.73/20.57 X1856 @
% 139.73/20.57 X1860 ) @
% 139.73/20.57 (
% 139.73/20.57 binunion @
% 139.73/20.57 X1858 @
% 139.73/20.57 X1860 ) ) ) ) ) ) ) ) ) ) =>
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 ![
% 139.73/20.57 X1862:$i,
% 139.73/20.57 X1864:$i]:
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 X1864 @
% 139.73/20.57 (
% 139.73/20.57 powerset @
% 139.73/20.57 X1862 ) ) =>
% 139.73/20.57 (
% 139.73/20.57 ![
% 139.73/20.57 X1866:$i]:
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 X1866 @
% 139.73/20.57 (
% 139.73/20.57 powerset @
% 139.73/20.57 X1862 ) ) =>
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 subset @
% 139.73/20.57 X1864 @
% 139.73/20.57 (
% 139.73/20.57 setminus @
% 139.73/20.57 X1862 @
% 139.73/20.57 X1866 ) ) =>
% 139.73/20.57 (
% 139.73/20.57 subset @
% 139.73/20.57 X1866 @
% 139.73/20.57 (
% 139.73/20.57 setminus @
% 139.73/20.57 X1862 @
% 139.73/20.57 X1864 ) ) ) ) ) ) ) =>
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 ![
% 139.73/20.57 X1868:$i,
% 139.73/20.57 X1870:$i]:
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 X1870 @
% 139.73/20.57 (
% 139.73/20.57 powerset @
% 139.73/20.57 X1868 ) ) =>
% 139.73/20.57 (
% 139.73/20.57 ![
% 139.73/20.57 X1872:$i]:
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 X1872 @
% 139.73/20.57 (
% 139.73/20.57 powerset @
% 139.73/20.57 X1868 ) ) =>
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 (
% 139.73/20.57 setminus @
% 139.73/20.57 X1868 @
% 139.73/20.57 (
% 139.73/20.57 binunion @
% 139.73/20.57 X1870 @
% 139.73/20.57 X1872 ) ) @
% 139.73/20.57 (
% 139.73/20.57 powerset @
% 139.73/20.57 (
% 139.73/20.57 setminus @
% 139.73/20.57 X1868 @
% 139.73/20.57 X1870 ) ) ) ) ) ) ) =>
% 139.73/20.57 (
% 139.73/20.57 ![
% 139.73/20.57 X1874:$i,
% 139.73/20.57 X1876:$i]:
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 subset @
% 139.73/20.57 X1876 @
% 139.73/20.57 (
% 139.73/20.57 cartprod @
% 139.73/20.57 X1874 @
% 139.73/20.57 X1874 ) ) =>
% 139.73/20.57 (
% 139.73/20.57 ![
% 139.73/20.57 X1878:(
% 139.73/20.57 $i > $o )]:
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 ![
% 139.73/20.57 X1880:$i]:
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 X1880 @
% 139.73/20.57 X1874 ) =>
% 139.73/20.57 (
% 139.73/20.57 ![
% 139.73/20.57 X1882:$i]:
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 X1882 @
% 139.73/20.57 X1874 ) =>
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 (
% 139.73/20.57 kpair @
% 139.73/20.57 X1880 @
% 139.73/20.57 X1882 ) @
% 139.73/20.57 X1876 ) =>
% 139.73/20.57 (
% 139.73/20.57 X1878 @
% 139.73/20.57 (
% 139.73/20.57 kpair @
% 139.73/20.57 X1880 @
% 139.73/20.57 X1882 ) ) ) ) ) ) ) =>
% 139.73/20.57 (
% 139.73/20.57 ![
% 139.73/20.57 X1884:$i]:
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 X1884 @
% 139.73/20.57 X1876 ) =>
% 139.73/20.57 (
% 139.73/20.57 X1878 @
% 139.73/20.57 X1884 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 139.73/20.57 thf(zf_stmt_1, type, zip_tseitin_5 : $i > ( $i > $o ) > $o).
% 139.73/20.57 thf(zf_stmt_2, axiom,
% 139.73/20.57 (![X422:$i,X414:( $i > $o )]:
% 139.73/20.57 ( ( zip_tseitin_5 @ X422 @ X414 ) <=>
% 139.73/20.57 ( ( ![X424:$i]: ( zip_tseitin_4 @ X424 @ X422 @ X414 ) ) &
% 139.73/20.57 ( X414 @ X422 ) ) ))).
% 139.73/20.57 thf(zf_stmt_3, type, zip_tseitin_4 : $i > $i > ( $i > $o ) > $o).
% 139.73/20.57 thf(zf_stmt_4, axiom,
% 139.73/20.57 (![X424:$i,X422:$i,X414:( $i > $o )]:
% 139.73/20.57 ( ( zip_tseitin_4 @ X424 @ X422 @ X414 ) <=>
% 139.73/20.57 ( ( X414 @ X424 ) => ( ( X422 ) = ( X424 ) ) ) ))).
% 139.73/20.57 thf(zf_stmt_5, type, zip_tseitin_3 : $i > $i > $i > ( $i > $i > $o ) > $o).
% 139.73/20.57 thf(zf_stmt_6, axiom,
% 139.73/20.57 (![X52:$i,X50:$i,X40:$i,X38:( $i > $i > $o )]:
% 139.73/20.57 ( ( zip_tseitin_3 @ X52 @ X50 @ X40 @ X38 ) <=>
% 139.73/20.57 ( ( X38 @ X52 @ X50 ) & ( in @ X52 @ X40 ) ) ))).
% 139.73/20.57 thf(zf_stmt_7, type, zip_tseitin_2 : $i > $i > $i > $o).
% 139.73/20.57 thf(zf_stmt_8, axiom,
% 139.73/20.57 (![X28:$i,X26:$i,X24:$i]:
% 139.73/20.57 ( ( zip_tseitin_2 @ X28 @ X26 @ X24 ) <=>
% 139.73/20.57 ( ( in @ X28 @ X24 ) & ( in @ X26 @ X28 ) ) ))).
% 139.73/20.57 thf(zf_stmt_9, type, zip_tseitin_1 : $i > $i > $i > $o).
% 139.73/20.57 thf(zf_stmt_10, axiom,
% 139.73/20.57 (![X22:$i,X20:$i,X18:$i]:
% 139.73/20.57 ( ( zip_tseitin_1 @ X22 @ X20 @ X18 ) <=>
% 139.73/20.57 ( ( in @ X22 @ X20 ) => ( in @ X22 @ X18 ) ) ))).
% 139.73/20.57 thf(zf_stmt_11, type, zip_tseitin_0 : $i > $i > $i > $o).
% 139.73/20.57 thf(zf_stmt_12, axiom,
% 139.73/20.57 (![X16:$i,X14:$i,X12:$i]:
% 139.73/20.57 ( ( zip_tseitin_0 @ X16 @ X14 @ X12 ) <=>
% 139.73/20.57 ( ( ( X16 ) = ( X12 ) ) | ( in @ X16 @ X14 ) ) ))).
% 139.73/20.57 thf(zf_stmt_13, conjecture,
% 139.73/20.57 (( ![X4:$i,X6:$i]:
% 139.73/20.57 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) <=> ( in @ X8 @ X6 ) ) ) =>
% 139.73/20.57 ( ( X4 ) = ( X6 ) ) ) ) =>
% 139.73/20.57 ( ( ![X10:$i]: ( ~( in @ X10 @ emptyset ) ) ) =>
% 139.73/20.57 ( ( ![X12:$i,X14:$i,X16:$i]:
% 139.73/20.57 ( ( in @ X16 @ ( setadjoin @ X12 @ X14 ) ) <=>
% 139.73/20.57 ( zip_tseitin_0 @ X16 @ X14 @ X12 ) ) ) =>
% 139.73/20.57 ( ( ![X18:$i,X20:$i]:
% 139.73/20.57 ( ( in @ X20 @ ( powerset @ X18 ) ) <=>
% 139.73/20.57 ( ![X22:$i]: ( zip_tseitin_1 @ X22 @ X20 @ X18 ) ) ) ) =>
% 139.73/20.57 ( ( ![X24:$i,X26:$i]:
% 139.73/20.57 ( ( in @ X26 @ ( setunion @ X24 ) ) <=>
% 139.73/20.57 ( ?[X28:$i]: ( zip_tseitin_2 @ X28 @ X26 @ X24 ) ) ) ) =>
% 139.73/20.57 ( ( in @ emptyset @ omega ) =>
% 139.73/20.57 ( ( ![X30:$i]:
% 139.73/20.57 ( ( in @ X30 @ omega ) =>
% 139.73/20.57 ( in @ ( setadjoin @ X30 @ X30 ) @ omega ) ) ) =>
% 139.73/20.57 ( ( ![X32:$i]:
% 139.73/20.57 ( ( ( in @ emptyset @ X32 ) &
% 139.73/20.57 ( ![X34:$i]:
% 139.73/20.57 ( ( ( in @ X34 @ omega ) & ( in @ X34 @ X32 ) ) =>
% 139.73/20.57 ( in @ ( setadjoin @ X34 @ X34 ) @ X32 ) ) ) ) =>
% 139.73/20.57 ( ![X36:$i]:
% 139.73/20.57 ( ( in @ X36 @ omega ) => ( in @ X36 @ X32 ) ) ) ) ) =>
% 139.73/20.57 ( ( ![X38:( $i > $i > $o ),X40:$i]:
% 139.73/20.57 ( ( ![X42:$i]:
% 139.73/20.57 ( ( in @ X42 @ X40 ) =>
% 139.73/20.57 ( ?[X44:$i]:
% 139.73/20.57 ( ( ![X46:$i]:
% 139.73/20.57 ( ( X38 @ X42 @ X46 ) =>
% 139.73/20.57 ( ( X44 ) = ( X46 ) ) ) ) &
% 139.73/20.57 ( X38 @ X42 @ X44 ) ) ) ) ) =>
% 139.73/20.57 ( ?[X48:$i]:
% 139.73/20.57 ( ![X50:$i]:
% 139.73/20.57 ( ( in @ X50 @ X48 ) <=>
% 139.73/20.57 ( ?[X52:$i]:
% 139.73/20.57 ( zip_tseitin_3 @ X52 @ X50 @ X40 @ X38 ) ) ) ) ) ) ) =>
% 139.73/20.57 ( ( ![X54:$i]:
% 139.73/20.57 ( ( ?[X56:$i]: ( in @ X56 @ X54 ) ) =>
% 139.73/20.57 ( ?[X58:$i]:
% 139.73/20.57 ( ( ~( ?[X60:$i]:
% 139.73/20.57 ( ( in @ X60 @ X54 ) & ( in @ X60 @ X58 ) ) ) ) &
% 139.73/20.57 ( in @ X58 @ X54 ) ) ) ) ) =>
% 139.73/20.57 ( ( ![X62:$i]:
% 139.73/20.57 ( ?[X64:$i]:
% 139.73/20.57 ( ( ![X66:$i]:
% 139.73/20.57 ( ( ( ![X68:$i]:
% 139.73/20.57 ( ( in @ X68 @ X66 ) =>
% 139.73/20.57 ( in @ X68 @ X62 ) ) ) &
% 139.73/20.57 ( ?[X70:$i]: ( in @ X70 @ X66 ) ) ) =>
% 139.73/20.57 ( ?[X72:$i,X74:$i]:
% 139.73/20.57 ( ( ![X76:$i]:
% 139.73/20.57 ( ( in @ X76 @ X64 ) =>
% 139.73/20.57 ( ( ![X78:$i]:
% 139.73/20.57 ( ( in @ X78 @ X76 ) =>
% 139.73/20.57 ( in @ X78 @ X72 ) ) ) |
% 139.73/20.57 ( in @ X74 @ X76 ) ) ) ) &
% 139.73/20.57 ( ~( ?[X80:$i]:
% 139.73/20.57 ( ( in @ X80 @ X66 ) &
% 139.73/20.57 ( in @ X80 @ X72 ) ) ) ) &
% 139.73/20.57 ( in @ X74 @ X66 ) & ( in @ X72 @ X64 ) ) ) ) ) &
% 139.73/20.57 ( ![X82:$i,X84:$i]:
% 139.73/20.57 ( ( ( in @ X82 @ X64 ) & ( in @ X84 @ X64 ) ) =>
% 139.73/20.57 ( ( ![X86:$i]:
% 139.73/20.57 ( ( in @ X86 @ X82 ) =>
% 139.73/20.57 ( in @ X86 @ X84 ) ) ) |
% 139.73/20.57 ( ![X88:$i]:
% 139.73/20.57 ( ( in @ X88 @ X84 ) =>
% 139.73/20.57 ( in @ X88 @ X82 ) ) ) ) ) ) &
% 139.73/20.57 ( ![X90:$i,X92:$i]:
% 139.73/20.57 ( ( ( in @ X90 @ X62 ) & ( in @ X92 @ X62 ) ) =>
% 139.73/20.57 ( ( ![X94:$i]:
% 139.73/20.57 ( ( in @ X94 @ X64 ) =>
% 139.73/20.57 ( ( in @ X90 @ X94 ) <=>
% 139.73/20.57 ( in @ X92 @ X94 ) ) ) ) =>
% 139.73/20.57 ( ( X90 ) = ( X92 ) ) ) ) ) &
% 139.73/20.57 ( ![X96:$i]:
% 139.73/20.57 ( ( in @ X96 @ X64 ) =>
% 139.73/20.57 ( ![X98:$i]:
% 139.73/20.57 ( ( in @ X98 @ X96 ) => ( in @ X98 @ X62 ) ) ) ) ) ) ) ) =>
% 139.73/20.57 ( ( ![X100:( $i > $o )]:
% 139.73/20.57 ( ( ?[X102:$i]:
% 139.73/20.57 ( ( ![X104:$i]:
% 139.73/20.57 ( ( X100 @ X104 ) =>
% 139.73/20.57 ( ( X102 ) = ( X104 ) ) ) ) &
% 139.73/20.57 ( X100 @ X102 ) ) ) =>
% 139.73/20.57 ( X100 @
% 139.73/20.57 ( descr @ ( ^[V_1:$i]: ( X100 @ V_1 ) ) ) ) ) ) =>
% 139.73/20.57 ( ( ![X106:$i,X108:( $i > $o ),X110:$i]:
% 139.73/20.57 ( ( in @ X110 @ X106 ) =>
% 139.73/20.57 ( ( X108 @ X110 ) =>
% 139.73/20.57 ( in @
% 139.73/20.57 X110 @
% 139.73/20.57 ( dsetconstr @
% 139.73/20.57 X106 @ ( ^[V_2:$i]: ( X108 @ V_2 ) ) ) ) ) ) ) =>
% 139.73/20.57 ( ( ![X112:$i,X114:( $i > $o ),X116:$i]:
% 139.73/20.57 ( ( in @
% 139.73/20.57 X116 @
% 139.73/20.57 ( dsetconstr @
% 139.73/20.57 X112 @ ( ^[V_3:$i]: ( X114 @ V_3 ) ) ) ) =>
% 139.73/20.57 ( in @ X116 @ X112 ) ) ) =>
% 139.73/20.57 ( ( ![X118:$i,X120:( $i > $o ),X122:$i]:
% 139.73/20.57 ( ( in @
% 139.73/20.57 X122 @
% 139.73/20.57 ( dsetconstr @
% 139.73/20.57 X118 @ ( ^[V_4:$i]: ( X120 @ V_4 ) ) ) ) =>
% 139.73/20.57 ( X120 @ X122 ) ) ) =>
% 139.73/20.57 ( ( ![X124:( $i > $o )]:
% 139.73/20.57 ( ( ?[X126:$i]:
% 139.73/20.57 ( ( ![X128:$i]:
% 139.73/20.57 ( ( X124 @ X128 ) =>
% 139.73/20.57 ( ( X126 ) = ( X128 ) ) ) ) &
% 139.73/20.57 ( X124 @ X126 ) ) ) =>
% 139.73/20.57 ( ?[X130:$i]:
% 139.73/20.57 ( ( ![X132:$i]:
% 139.73/20.57 ( ( X124 @ X132 ) =>
% 139.73/20.57 ( ( X130 ) = ( X132 ) ) ) ) &
% 139.73/20.57 ( X124 @ X130 ) ) ) ) ) =>
% 139.73/20.57 ( ( ![X134:$o,X136:$i]:
% 139.73/20.57 ( ( in @ X136 @ ( prop2set @ X134 ) ) =>
% 139.73/20.57 ( X134 ) ) ) =>
% 139.73/20.57 ( ( ![X138:$i]:
% 139.73/20.57 ( ( in @ X138 @ emptyset ) =>
% 139.73/20.57 ( ![X140:$o]: ( X140 ) ) ) ) =>
% 139.73/20.57 ( ( ![X142:$i]:
% 139.73/20.57 ( ~( in @ X142 @ emptyset ) ) ) =>
% 139.73/20.57 ( ( ![X144:$i]:
% 139.73/20.57 ( ~( in @ X144 @ emptyset ) ) ) =>
% 139.73/20.57 ( ( ![X146:( $i > $o )]:
% 139.73/20.57 ( ( ?[X148:$i]:
% 139.73/20.57 ( ( ![X150:$i]:
% 139.73/20.57 ( ( X146 @ X150 ) =>
% 139.73/20.57 ( ( X148 ) = ( X150 ) ) ) ) &
% 139.73/20.57 ( X146 @ X148 ) ) ) =>
% 139.73/20.57 ( ?[X152:$i]: ( X146 @ X152 ) ) ) ) =>
% 139.73/20.57 ( ( ![X154:$i,X156:$i]:
% 139.73/20.57 ( ( ![X158:$i]:
% 139.73/20.57 ( ( in @ X158 @ X154 ) =>
% 139.73/20.57 ( in @ X158 @ X156 ) ) ) =>
% 139.73/20.57 ( ( ![X160:$i]:
% 139.73/20.57 ( ( in @ X160 @ X156 ) =>
% 139.73/20.57 ( in @ X160 @ X154 ) ) ) =>
% 139.73/20.57 ( ( X154 ) = ( X156 ) ) ) ) ) =>
% 139.73/20.57 ( ( ![X162:$i]:
% 139.73/20.57 ( ( ![X164:$i]:
% 139.73/20.57 ( ~( in @ X164 @ X162 ) ) ) =>
% 139.73/20.57 ( ( X162 ) = ( emptyset ) ) ) ) =>
% 139.73/20.57 ( ( ![X166:$i]:
% 139.73/20.57 ( ( ![X168:$i]:
% 139.73/20.57 ( ~( in @ X168 @ X166 ) ) ) =>
% 139.73/20.57 ( ( X166 ) =
% 139.73/20.57 ( emptyset ) ) ) ) =>
% 139.73/20.57 ( ( ![X170:$i,
% 139.73/20.57 X172:( $i > $o ),
% 139.73/20.57 X174:$i]:
% 139.73/20.57 ( ( in @ X174 @ X170 ) =>
% 139.73/20.57 ( ( in @
% 139.73/20.57 X174 @
% 139.73/20.57 ( dsetconstr @
% 139.73/20.57 X170 @
% 139.73/20.57 ( ^[V_5:$i]:
% 139.73/20.57 ( X172 @ V_5 ) ) ) ) <=>
% 139.73/20.57 ( X172 @ X174 ) ) ) ) =>
% 139.73/20.57 ( ( ![X176:$i]:
% 139.73/20.57 ( ( ( X176 ) !=
% 139.73/20.57 ( emptyset ) ) =>
% 139.73/20.57 ( ?[X178:$i]:
% 139.73/20.57 ( in @ X178 @ X176 ) ) ) ) =>
% 139.73/20.57 ( ( ![X180:$i,
% 139.73/20.57 X182:( $i > $o ),
% 139.73/20.57 X184:$i]:
% 139.73/20.57 ( ( in @ X184 @ X180 ) =>
% 139.73/20.57 ( ( X182 @ X184 ) =>
% 139.73/20.57 ( ( dsetconstr @
% 139.73/20.57 X180 @
% 139.73/20.57 ( ^[
% 139.73/20.57 V_6:$i]:
% 139.73/20.57 (
% 139.73/20.57 X182 @ V_6 ) ) ) !=
% 139.73/20.57 ( emptyset ) ) ) ) ) =>
% 139.73/20.57 ( ( ![X186:$i]:
% 139.73/20.57 ( ( ?[X188:$i]:
% 139.73/20.57 ( in @
% 139.73/20.57 X188 @ X186 ) ) =>
% 139.73/20.57 ( ( X186 ) !=
% 139.73/20.57 ( emptyset ) ) ) ) =>
% 139.73/20.57 ( ( ![X190:$i,
% 139.73/20.57 X192:$i]:
% 139.73/20.57 ( in @
% 139.73/20.57 X190 @
% 139.73/20.57 ( setadjoin @
% 139.73/20.57 X190 @ X192 ) ) ) =>
% 139.73/20.57 ( ( in @
% 139.73/20.57 emptyset @
% 139.73/20.57 ( setadjoin @
% 139.73/20.57 emptyset @
% 139.73/20.57 emptyset ) ) =>
% 139.73/20.57 ( ( ![X194:$i,
% 139.73/20.57 X196:$i,
% 139.73/20.57 X198:$i]:
% 139.73/20.57 ( (
% 139.73/20.57 in @
% 139.73/20.57 X198 @
% 139.73/20.57 X196 ) =>
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 X198 @
% 139.73/20.57 (
% 139.73/20.57 setadjoin
% 139.73/20.57 @
% 139.73/20.57 X194 @
% 139.73/20.57 X196 ) ) ) ) =>
% 139.73/20.57 ( ( ![
% 139.73/20.57 X200:$i,
% 139.73/20.57 X202:$i,
% 139.73/20.57 X204:$i]:
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 X204 @
% 139.73/20.57 (
% 139.73/20.57 setadjoin
% 139.73/20.57 @
% 139.73/20.57 X200 @
% 139.73/20.57 X202 ) ) =>
% 139.73/20.57 (
% 139.73/20.57 ![
% 139.73/20.57 X206:$o]:
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 X204 ) =
% 139.73/20.57 (
% 139.73/20.57 X200 ) ) =>
% 139.73/20.57 (
% 139.73/20.57 X206 ) ) =>
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 X204 @
% 139.73/20.57 X202 ) =>
% 139.73/20.57 (
% 139.73/20.57 X206 ) ) =>
% 139.73/20.57 (
% 139.73/20.57 X206 ) ) ) ) ) ) =>
% 139.73/20.57 ( (
% 139.73/20.57 ![
% 139.73/20.57 X208:$i,
% 139.73/20.57 X210:$i,
% 139.73/20.57 X212:$i]:
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 X212 @
% 139.73/20.57 (
% 139.73/20.57 setadjoin
% 139.73/20.57 @
% 139.73/20.57 X208 @
% 139.73/20.57 X210 ) ) =>
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 X212 ) =
% 139.73/20.57 (
% 139.73/20.57 X208 ) ) |
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 X212 @
% 139.73/20.57 X210 ) ) ) ) =>
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 ![
% 139.73/20.57 X214:$i]:
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 dsetconstr
% 139.73/20.57 @
% 139.73/20.57 X214 @
% 139.73/20.57 (
% 139.73/20.57 ^[
% 139.73/20.57 V_7:$i]:
% 139.73/20.57 (
% 139.73/20.57 $true ) ) ) =
% 139.73/20.57 (
% 139.73/20.57 X214 ) ) ) =>
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 ![
% 139.73/20.57 X216:$i,
% 139.73/20.57 X218:$i]:
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 ![
% 139.73/20.57 X220:$i]:
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 X220 @
% 139.73/20.57 X218 ) =>
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 X220 @
% 139.73/20.57 X216 ) ) ) =>
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 X218 @
% 139.73/20.57 (
% 139.73/20.57 powerset @
% 139.73/20.57 X216 ) ) ) ) =>
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 ![
% 139.73/20.57 X222:$i]:
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 emptyset @
% 139.73/20.57 (
% 139.73/20.57 powerset @
% 139.73/20.57 X222 ) ) ) =>
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 ![
% 139.73/20.57 X224:$i]:
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 emptyset @
% 139.73/20.57 (
% 139.73/20.57 powerset @
% 139.73/20.57 X224 ) ) ) =>
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 ![
% 139.73/20.57 X226:$i,
% 139.73/20.57 X228:$i,
% 139.73/20.57 X230:$i]:
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 X228 @
% 139.73/20.57 (
% 139.73/20.57 powerset @
% 139.73/20.57 X226 ) ) =>
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 X230 @
% 139.73/20.57 X228 ) =>
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 X230 @
% 139.73/20.57 X226 ) ) ) ) =>
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 ![
% 139.73/20.57 X232:$i,
% 139.73/20.57 X234:$i,
% 139.73/20.57 X236:$i]:
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 X234 @
% 139.73/20.57 X236 ) =>
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 X236 @
% 139.73/20.57 X232 ) =>
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 X234 @
% 139.73/20.57 (
% 139.73/20.57 setunion @
% 139.73/20.57 X232 ) ) ) ) ) =>
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 ![
% 139.73/20.57 X238:$i,
% 139.73/20.57 X240:$i]:
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 X240 @
% 139.73/20.57 (
% 139.73/20.57 setunion @
% 139.73/20.57 X238 ) ) =>
% 139.73/20.57 (
% 139.73/20.57 ![
% 139.73/20.57 X242:$o]:
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 ![
% 139.73/20.57 X244:$i]:
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 X240 @
% 139.73/20.57 X244 ) =>
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 X244 @
% 139.73/20.57 X238 ) =>
% 139.73/20.57 (
% 139.73/20.57 X242 ) ) ) ) =>
% 139.73/20.57 (
% 139.73/20.57 X242 ) ) ) ) ) =>
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 ![
% 139.73/20.57 X246:$i,
% 139.73/20.57 X248:$i]:
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 X248 @
% 139.73/20.57 X246 ) =>
% 139.73/20.57 (
% 139.73/20.57 in @
% 139.73/20.57 X248 @
% 139.73/20.57 (
% 139.73/20.57 powerset @
% 139.73/20.57 (
% 139.73/20.57 setunion @
% 139.73/20.57 X246 ) ) ) ) ) =>
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 ![
% 139.73/20.57 X250:(
% 139.73/20.57 $i > $o )]:
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 ?[
% 139.73/20.57 X252:$i]:
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 ![
% 139.73/20.57 X254:$i]:
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 X250 @
% 139.73/20.57 X254 ) =>
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 X252 ) =
% 139.73/20.57 (
% 139.73/20.57 X254 ) ) ) ) &
% 139.73/20.57 (
% 139.73/20.57 X250 @
% 139.73/20.57 X252 ) ) ) =>
% 139.73/20.57 (
% 139.73/20.57 ?[
% 139.73/20.57 X256:$i]:
% 139.73/20.57 (
% 139.73/20.57 ![
% 139.73/20.57 X258:$i]:
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 X250 @
% 139.73/20.57 X258 ) <=>
% 139.73/20.57 (
% 139.73/20.57 (
% 139.73/20.57 X258 ) =
% 139.73/20.57 (
% 139.73/20.57 X256 ) ) ) ) ) ) ) =>
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% 139.73/20.58 (
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% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 X472 ) =
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% 139.73/20.58 X474 ) ) =>
% 139.73/20.58 (
% 139.73/20.58 ![
% 139.73/20.58 X476:(
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% 139.73/20.58 X478:(
% 139.73/20.58 $i > $o )]:
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 ![
% 139.73/20.58 X480:$i]:
% 139.73/20.58 (
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% 139.73/20.58 ![
% 139.73/20.58 X482:$i]:
% 139.73/20.58 (
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% 139.73/20.58 (
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% 139.73/20.58 dsetconstr
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% 139.73/20.58 (
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% 139.73/20.58 X484:$i,
% 139.73/20.58 X486:$i]:
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 ![
% 139.73/20.58 X488:$i]:
% 139.73/20.58 (
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% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 ![
% 139.73/20.58 X490:$i,
% 139.73/20.58 X492:$i]:
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 X490 ) =
% 139.73/20.58 (
% 139.73/20.58 X492 ) ) =>
% 139.73/20.58 (
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% 139.73/20.58 (
% 139.73/20.58 (
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% 139.73/20.58 X494:$i,
% 139.73/20.58 X496:$i]:
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% 139.73/20.58 (
% 139.73/20.58 (
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% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 ![
% 139.73/20.58 X498:$i,
% 139.73/20.58 X500:$i]:
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% 139.73/20.58 (
% 139.73/20.58 ![
% 139.73/20.58 X502:$i]:
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% 139.73/20.58 (
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% 139.73/20.58 (
% 139.73/20.58 ![
% 139.73/20.58 X506:$i,
% 139.73/20.58 X508:$i,
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% 139.73/20.58 X508 ) =>
% 139.73/20.58 (
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% 139.73/20.58 X512:$i,
% 139.73/20.58 X514:$i,
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% 139.73/20.58 X514 ) =>
% 139.73/20.58 (
% 139.73/20.58 (
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% 139.73/20.58 X518:$i,
% 139.73/20.58 X520:$i,
% 139.73/20.58 X522:$i]:
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% 139.73/20.58 X522 @
% 139.73/20.58 X518 ) =>
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% 139.73/20.58 (
% 139.73/20.58 (
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% 139.73/20.58 X528:$i,
% 139.73/20.58 X530:$i,
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% 139.73/20.58 X536:$i,
% 139.73/20.58 X538:$i,
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% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 in @
% 139.73/20.58 X874 @
% 139.73/20.58 X876 ) &
% 139.73/20.58 (
% 139.73/20.58 in @
% 139.73/20.58 X876 @
% 139.73/20.58 X872 ) ) ) ) ) =>
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 ![
% 139.73/20.58 X878:$i]:
% 139.73/20.58 (
% 139.73/20.58 subset @
% 139.73/20.58 (
% 139.73/20.58 setunion @
% 139.73/20.58 (
% 139.73/20.58 setadjoin
% 139.73/20.58 @
% 139.73/20.58 X878 @
% 139.73/20.58 emptyset ) ) @
% 139.73/20.58 X878 ) ) =>
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 ![
% 139.73/20.58 X880:$i]:
% 139.73/20.58 (
% 139.73/20.58 subset @
% 139.73/20.58 X880 @
% 139.73/20.58 (
% 139.73/20.58 setunion @
% 139.73/20.58 (
% 139.73/20.58 setadjoin
% 139.73/20.58 @
% 139.73/20.58 X880 @
% 139.73/20.58 emptyset ) ) ) ) =>
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 ![
% 139.73/20.58 X882:$i]:
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 setunion @
% 139.73/20.58 (
% 139.73/20.58 setadjoin
% 139.73/20.58 @
% 139.73/20.58 X882 @
% 139.73/20.58 emptyset ) ) =
% 139.73/20.58 (
% 139.73/20.58 X882 ) ) ) =>
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 ![
% 139.73/20.58 X884:$i,
% 139.73/20.58 X886:(
% 139.73/20.58 $i > $o )]:
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 ![
% 139.73/20.58 X888:$i]:
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 in @
% 139.73/20.58 X888 @
% 139.73/20.58 X884 ) =>
% 139.73/20.58 (
% 139.73/20.58 ![
% 139.73/20.58 X890:$i]:
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 in @
% 139.73/20.58 X890 @
% 139.73/20.58 X884 ) =>
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 X886 @
% 139.73/20.58 X888 ) =>
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 X886 @
% 139.73/20.58 X890 ) =>
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 X888 ) =
% 139.73/20.58 (
% 139.73/20.58 X890 ) ) ) ) ) ) ) ) =>
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 ?[
% 139.73/20.58 X892:$i]:
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 X886 @
% 139.73/20.58 X892 ) &
% 139.73/20.58 (
% 139.73/20.58 in @
% 139.73/20.58 X892 @
% 139.73/20.58 X884 ) ) ) =>
% 139.73/20.58 (
% 139.73/20.58 singleton
% 139.73/20.58 @
% 139.73/20.58 (
% 139.73/20.58 dsetconstr
% 139.73/20.58 @
% 139.73/20.58 X884 @
% 139.73/20.58 (
% 139.73/20.58 ^[
% 139.73/20.58 V_15:$i]:
% 139.73/20.58 (
% 139.73/20.58 X886 @
% 139.73/20.58 V_15 ) ) ) ) ) ) ) =>
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 ![
% 139.73/20.58 X894:$i,
% 139.73/20.58 X896:(
% 139.73/20.58 $i > $o )]:
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 singleton
% 139.73/20.58 @
% 139.73/20.58 (
% 139.73/20.58 dsetconstr
% 139.73/20.58 @
% 139.73/20.58 X894 @
% 139.73/20.58 (
% 139.73/20.58 ^[
% 139.73/20.58 V_16:$i]:
% 139.73/20.58 (
% 139.73/20.58 X896 @
% 139.73/20.58 V_16 ) ) ) ) =>
% 139.73/20.58 (
% 139.73/20.58 ?[
% 139.73/20.58 X898:$i]:
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 X896 @
% 139.73/20.58 X898 ) &
% 139.73/20.58 (
% 139.73/20.58 in @
% 139.73/20.58 X898 @
% 139.73/20.58 X894 ) ) ) ) ) =>
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 ![
% 139.73/20.58 X900:$i,
% 139.73/20.58 X902:(
% 139.73/20.58 $i > $o ),
% 139.73/20.58 X904:$i]:
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 in @
% 139.73/20.58 X904 @
% 139.73/20.58 X900 ) =>
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 X902 @
% 139.73/20.58 X904 ) =>
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 ![
% 139.73/20.58 X906:$i]:
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 in @
% 139.73/20.58 X906 @
% 139.73/20.58 X900 ) =>
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 X902 @
% 139.73/20.58 X906 ) =>
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 X906 ) =
% 139.73/20.58 (
% 139.73/20.58 X904 ) ) ) ) ) =>
% 139.73/20.58 (
% 139.73/20.58 singleton
% 139.73/20.58 @
% 139.73/20.58 (
% 139.73/20.58 dsetconstr
% 139.73/20.58 @
% 139.73/20.58 X900 @
% 139.73/20.58 (
% 139.73/20.58 ^[
% 139.73/20.58 V_17:$i]:
% 139.73/20.58 (
% 139.73/20.58 X902 @
% 139.73/20.58 V_17 ) ) ) ) ) ) ) ) =>
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 ![
% 139.73/20.58 X908:$i,
% 139.73/20.58 X910:(
% 139.73/20.58 $i > $o )]:
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 ![
% 139.73/20.58 X912:$i]:
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 in @
% 139.73/20.58 X912 @
% 139.73/20.58 X908 ) =>
% 139.73/20.58 (
% 139.73/20.58 ![
% 139.73/20.58 X914:$i]:
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 in @
% 139.73/20.58 X914 @
% 139.73/20.58 X908 ) =>
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 X910 @
% 139.73/20.58 X912 ) =>
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 X910 @
% 139.73/20.58 X914 ) =>
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 X912 ) =
% 139.73/20.58 (
% 139.73/20.58 X914 ) ) ) ) ) ) ) ) =>
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 ?[
% 139.73/20.58 X916:$i]:
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 X910 @
% 139.73/20.58 X916 ) &
% 139.73/20.58 (
% 139.73/20.58 in @
% 139.73/20.58 X916 @
% 139.73/20.58 X908 ) ) ) =>
% 139.73/20.58 (
% 139.73/20.58 singleton
% 139.73/20.58 @
% 139.73/20.58 (
% 139.73/20.58 dsetconstr
% 139.73/20.58 @
% 139.73/20.58 X908 @
% 139.73/20.58 (
% 139.73/20.58 ^[
% 139.73/20.58 V_18:$i]:
% 139.73/20.58 (
% 139.73/20.58 X910 @
% 139.73/20.58 V_18 ) ) ) ) ) ) ) =>
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 ![
% 139.73/20.58 X918:$i,
% 139.73/20.58 X920:$i]:
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 setadjoin
% 139.73/20.58 @
% 139.73/20.58 X918 @
% 139.73/20.58 emptyset ) =
% 139.73/20.58 (
% 139.73/20.58 setadjoin
% 139.73/20.58 @
% 139.73/20.58 X920 @
% 139.73/20.58 emptyset ) ) =>
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 X918 ) =
% 139.73/20.58 (
% 139.73/20.58 X920 ) ) ) ) =>
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 ![
% 139.73/20.58 X922:$i,
% 139.73/20.58 X924:$i,
% 139.73/20.58 X926:$i]:
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 in @
% 139.73/20.58 (
% 139.73/20.58 setadjoin
% 139.73/20.58 @
% 139.73/20.58 X926 @
% 139.73/20.58 emptyset ) @
% 139.73/20.58 (
% 139.73/20.58 setadjoin
% 139.73/20.58 @
% 139.73/20.58 (
% 139.73/20.58 setadjoin
% 139.73/20.58 @
% 139.73/20.58 X922 @
% 139.73/20.58 emptyset ) @
% 139.73/20.58 (
% 139.73/20.58 setadjoin
% 139.73/20.58 @
% 139.73/20.58 (
% 139.73/20.58 setadjoin
% 139.73/20.58 @
% 139.73/20.58 X922 @
% 139.73/20.58 (
% 139.73/20.58 setadjoin
% 139.73/20.58 @
% 139.73/20.58 X924 @
% 139.73/20.58 emptyset ) ) @
% 139.73/20.58 emptyset ) ) ) =>
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 X922 ) =
% 139.73/20.58 (
% 139.73/20.58 X926 ) ) ) ) =>
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 ![
% 139.73/20.58 X928:$i]:
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 iskpair @
% 139.73/20.58 X928 ) =>
% 139.73/20.58 (
% 139.73/20.58 singleton
% 139.73/20.58 @
% 139.73/20.58 (
% 139.73/20.58 dsetconstr
% 139.73/20.58 @
% 139.73/20.58 (
% 139.73/20.58 setunion @
% 139.73/20.58 X928 ) @
% 139.73/20.58 (
% 139.73/20.58 ^[
% 139.73/20.58 V_19:$i]:
% 139.73/20.58 (
% 139.73/20.58 in @
% 139.73/20.58 (
% 139.73/20.58 setadjoin
% 139.73/20.58 @
% 139.73/20.58 V_19 @
% 139.73/20.58 emptyset ) @
% 139.73/20.58 X928 ) ) ) ) ) ) =>
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 ![
% 139.73/20.58 X930:$i]:
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 singleton
% 139.73/20.58 @
% 139.73/20.58 X930 ) =>
% 139.73/20.58 (
% 139.73/20.58 in @
% 139.73/20.58 (
% 139.73/20.58 setunion @
% 139.73/20.58 X930 ) @
% 139.73/20.58 X930 ) ) ) =>
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 ![
% 139.73/20.58 X932:$i,
% 139.73/20.58 X934:$i]:
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 kfst @
% 139.73/20.58 (
% 139.73/20.58 kpair @
% 139.73/20.58 X932 @
% 139.73/20.58 X934 ) ) =
% 139.73/20.58 (
% 139.73/20.58 X932 ) ) ) =>
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 ![
% 139.73/20.58 X936:$i,
% 139.73/20.58 X938:$i,
% 139.73/20.58 X940:$i]:
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 in @
% 139.73/20.58 X940 @
% 139.73/20.58 (
% 139.73/20.58 cartprod @
% 139.73/20.58 X936 @
% 139.73/20.58 X938 ) ) =>
% 139.73/20.58 (
% 139.73/20.58 in @
% 139.73/20.58 (
% 139.73/20.58 kfst @
% 139.73/20.58 X940 ) @
% 139.73/20.58 X936 ) ) ) =>
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 ![
% 139.73/20.58 X942:$i,
% 139.73/20.58 X944:$i,
% 139.73/20.58 X946:$i,
% 139.73/20.58 X948:$i]:
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 setadjoin
% 139.73/20.58 @
% 139.73/20.58 (
% 139.73/20.58 setadjoin
% 139.73/20.58 @
% 139.73/20.58 X942 @
% 139.73/20.58 emptyset ) @
% 139.73/20.58 (
% 139.73/20.58 setadjoin
% 139.73/20.58 @
% 139.73/20.58 (
% 139.73/20.58 setadjoin
% 139.73/20.58 @
% 139.73/20.58 X942 @
% 139.73/20.58 (
% 139.73/20.58 setadjoin
% 139.73/20.58 @
% 139.73/20.58 X944 @
% 139.73/20.58 emptyset ) ) @
% 139.73/20.58 emptyset ) ) =
% 139.73/20.58 (
% 139.73/20.58 setadjoin
% 139.73/20.58 @
% 139.73/20.58 (
% 139.73/20.58 setadjoin
% 139.73/20.58 @
% 139.73/20.58 X946 @
% 139.73/20.58 emptyset ) @
% 139.73/20.58 (
% 139.73/20.58 setadjoin
% 139.73/20.58 @
% 139.73/20.58 (
% 139.73/20.58 setadjoin
% 139.73/20.58 @
% 139.73/20.58 X946 @
% 139.73/20.58 (
% 139.73/20.58 setadjoin
% 139.73/20.58 @
% 139.73/20.58 X948 @
% 139.73/20.58 emptyset ) ) @
% 139.73/20.58 emptyset ) ) ) =>
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 X942 ) =
% 139.73/20.58 (
% 139.73/20.58 X946 ) ) ) ) =>
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 ![
% 139.73/20.58 X950:$i,
% 139.73/20.58 X952:$i,
% 139.73/20.58 X954:$i,
% 139.73/20.58 X956:$i]:
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 kpair @
% 139.73/20.58 X950 @
% 139.73/20.58 X952 ) =
% 139.73/20.58 (
% 139.73/20.58 kpair @
% 139.73/20.58 X954 @
% 139.73/20.58 X956 ) ) =>
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 X950 ) =
% 139.73/20.58 (
% 139.73/20.58 X954 ) ) ) ) =>
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 ![
% 139.73/20.58 X958:$i,
% 139.73/20.58 X960:$i]:
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 X958 ) =
% 139.73/20.58 (
% 139.73/20.58 X960 ) ) =>
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 setadjoin
% 139.73/20.58 @
% 139.73/20.58 X958 @
% 139.73/20.58 (
% 139.73/20.58 setadjoin
% 139.73/20.58 @
% 139.73/20.58 X960 @
% 139.73/20.58 emptyset ) ) =
% 139.73/20.58 (
% 139.73/20.58 setadjoin
% 139.73/20.58 @
% 139.73/20.58 X958 @
% 139.73/20.58 emptyset ) ) ) ) =>
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 ![
% 139.73/20.58 X962:$i,
% 139.73/20.58 X964:$i]:
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 X962 ) =
% 139.73/20.58 (
% 139.73/20.58 X964 ) ) =>
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 setadjoin
% 139.73/20.58 @
% 139.73/20.58 (
% 139.73/20.58 setadjoin
% 139.73/20.58 @
% 139.73/20.58 X962 @
% 139.73/20.58 emptyset ) @
% 139.73/20.58 (
% 139.73/20.58 setadjoin
% 139.73/20.58 @
% 139.73/20.58 (
% 139.73/20.58 setadjoin
% 139.73/20.58 @
% 139.73/20.58 X962 @
% 139.73/20.58 (
% 139.73/20.58 setadjoin
% 139.73/20.58 @
% 139.73/20.58 X964 @
% 139.73/20.58 emptyset ) ) @
% 139.73/20.58 emptyset ) ) =
% 139.73/20.58 (
% 139.73/20.58 setadjoin
% 139.73/20.58 @
% 139.73/20.58 (
% 139.73/20.58 setadjoin
% 139.73/20.58 @
% 139.73/20.58 X962 @
% 139.73/20.58 emptyset ) @
% 139.73/20.58 emptyset ) ) ) ) =>
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 ![
% 139.73/20.58 X966:$i,
% 139.73/20.58 X968:$i,
% 139.73/20.58 X970:$i,
% 139.73/20.58 X972:$i]:
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 setadjoin
% 139.73/20.58 @
% 139.73/20.58 (
% 139.73/20.58 setadjoin
% 139.73/20.58 @
% 139.73/20.58 X966 @
% 139.73/20.58 emptyset ) @
% 139.73/20.58 (
% 139.73/20.58 setadjoin
% 139.73/20.58 @
% 139.73/20.58 (
% 139.73/20.58 setadjoin
% 139.73/20.58 @
% 139.73/20.58 X966 @
% 139.73/20.58 (
% 139.73/20.58 setadjoin
% 139.73/20.58 @
% 139.73/20.58 X968 @
% 139.73/20.58 emptyset ) ) @
% 139.73/20.58 emptyset ) ) =
% 139.73/20.58 (
% 139.73/20.58 setadjoin
% 139.73/20.58 @
% 139.73/20.58 (
% 139.73/20.58 setadjoin
% 139.73/20.58 @
% 139.73/20.58 X970 @
% 139.73/20.58 emptyset ) @
% 139.73/20.58 (
% 139.73/20.58 setadjoin
% 139.73/20.58 @
% 139.73/20.58 (
% 139.73/20.58 setadjoin
% 139.73/20.58 @
% 139.73/20.58 X970 @
% 139.73/20.58 (
% 139.73/20.58 setadjoin
% 139.73/20.58 @
% 139.73/20.58 X972 @
% 139.73/20.58 emptyset ) ) @
% 139.73/20.58 emptyset ) ) ) =>
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 X970 ) =
% 139.73/20.58 (
% 139.73/20.58 X972 ) ) =>
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 X968 ) =
% 139.73/20.58 (
% 139.73/20.58 X972 ) ) ) ) ) =>
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 ![
% 139.73/20.58 X974:$i,
% 139.73/20.58 X976:$i,
% 139.73/20.58 X978:$i]:
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 setadjoin
% 139.73/20.58 @
% 139.73/20.58 X974 @
% 139.73/20.58 (
% 139.73/20.58 setadjoin
% 139.73/20.58 @
% 139.73/20.58 X976 @
% 139.73/20.58 emptyset ) ) =
% 139.73/20.58 (
% 139.73/20.58 setadjoin
% 139.73/20.58 @
% 139.73/20.58 X978 @
% 139.73/20.58 emptyset ) ) =>
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 X974 ) =
% 139.73/20.58 (
% 139.73/20.58 X976 ) ) ) ) =>
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 ![
% 139.73/20.58 X980:$i,
% 139.73/20.58 X982:$i,
% 139.73/20.58 X984:$i,
% 139.73/20.58 X986:$i]:
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 setadjoin
% 139.73/20.58 @
% 139.73/20.58 (
% 139.73/20.58 setadjoin
% 139.73/20.58 @
% 139.73/20.58 X980 @
% 139.73/20.58 emptyset ) @
% 139.73/20.58 (
% 139.73/20.58 setadjoin
% 139.73/20.58 @
% 139.73/20.58 (
% 139.73/20.58 setadjoin
% 139.73/20.58 @
% 139.73/20.58 X980 @
% 139.73/20.58 (
% 139.73/20.58 setadjoin
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% 139.73/20.58 X982 @
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% 139.73/20.58 emptyset ) ) =
% 139.73/20.58 (
% 139.73/20.58 setadjoin
% 139.73/20.58 @
% 139.73/20.58 (
% 139.73/20.58 setadjoin
% 139.73/20.58 @
% 139.73/20.58 X984 @
% 139.73/20.58 emptyset ) @
% 139.73/20.58 (
% 139.73/20.58 setadjoin
% 139.73/20.58 @
% 139.73/20.58 (
% 139.73/20.58 setadjoin
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% 139.73/20.58 X984 @
% 139.73/20.58 (
% 139.73/20.58 setadjoin
% 139.73/20.58 @
% 139.73/20.58 X986 @
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% 139.73/20.58 (
% 139.73/20.58 (
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% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 ![
% 139.73/20.58 X988:$i,
% 139.73/20.58 X990:$i,
% 139.73/20.58 X992:$i,
% 139.73/20.58 X994:$i]:
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 kpair @
% 139.73/20.58 X988 @
% 139.73/20.58 X990 ) =
% 139.73/20.58 (
% 139.73/20.58 kpair @
% 139.73/20.58 X992 @
% 139.73/20.58 X994 ) ) =>
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 X990 ) =
% 139.73/20.58 (
% 139.73/20.58 X994 ) ) ) ) =>
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 ![
% 139.73/20.58 X996:$i]:
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 iskpair @
% 139.73/20.58 X996 ) =>
% 139.73/20.58 (
% 139.73/20.58 singleton
% 139.73/20.58 @
% 139.73/20.58 (
% 139.73/20.58 dsetconstr
% 139.73/20.58 @
% 139.73/20.58 (
% 139.73/20.58 setunion @
% 139.73/20.58 X996 ) @
% 139.73/20.58 (
% 139.73/20.58 ^[
% 139.73/20.58 V_20:$i]:
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 X996 ) =
% 139.73/20.58 (
% 139.73/20.58 kpair @
% 139.73/20.58 (
% 139.73/20.58 kfst @
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% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 ![
% 139.73/20.58 X998:$i,
% 139.73/20.58 X1000:$i]:
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 ksnd @
% 139.73/20.58 (
% 139.73/20.58 kpair @
% 139.73/20.58 X998 @
% 139.73/20.58 X1000 ) ) =
% 139.73/20.58 (
% 139.73/20.58 X1000 ) ) ) =>
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 ![
% 139.73/20.58 X1002:$i]:
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 iskpair @
% 139.73/20.58 X1002 ) =>
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 kpair @
% 139.73/20.58 (
% 139.73/20.58 kfst @
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% 139.73/20.58 ksnd @
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% 139.73/20.58 X1002 ) ) ) ) =>
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 ![
% 139.73/20.58 X1004:$i,
% 139.73/20.58 X1006:$i,
% 139.73/20.58 X1008:$i]:
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 in @
% 139.73/20.58 X1008 @
% 139.73/20.58 (
% 139.73/20.58 cartprod @
% 139.73/20.58 X1004 @
% 139.73/20.58 X1006 ) ) =>
% 139.73/20.58 (
% 139.73/20.58 in @
% 139.73/20.58 (
% 139.73/20.58 ksnd @
% 139.73/20.58 X1008 ) @
% 139.73/20.58 X1006 ) ) ) =>
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 ![
% 139.73/20.58 X1010:$i,
% 139.73/20.58 X1012:$i,
% 139.73/20.58 X1014:$i,
% 139.73/20.58 X1016:$i]:
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 in @
% 139.73/20.58 (
% 139.73/20.58 kpair @
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% 139.73/20.58 (
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% 139.73/20.58 (
% 139.73/20.58 in @
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% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 ![
% 139.73/20.58 X1018:$i,
% 139.73/20.58 X1020:$i,
% 139.73/20.58 X1022:$i,
% 139.73/20.58 X1024:$i]:
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 in @
% 139.73/20.58 (
% 139.73/20.58 kpair @
% 139.73/20.58 X1022 @
% 139.73/20.58 X1024 ) @
% 139.73/20.58 (
% 139.73/20.58 cartprod @
% 139.73/20.58 X1018 @
% 139.73/20.58 X1020 ) ) =>
% 139.73/20.58 (
% 139.73/20.58 in @
% 139.73/20.58 X1024 @
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% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 ![
% 139.73/20.58 X1026:$i,
% 139.73/20.58 X1028:$i,
% 139.73/20.58 X1030:$i]:
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 in @
% 139.73/20.58 X1030 @
% 139.73/20.58 X1026 ) =>
% 139.73/20.58 (
% 139.73/20.58 ![
% 139.73/20.58 X1032:$i]:
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 in @
% 139.73/20.58 X1032 @
% 139.73/20.58 X1028 ) =>
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 kpair @
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% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 ![
% 139.73/20.58 X1034:$i,
% 139.73/20.58 X1036:$i,
% 139.73/20.58 X1038:$i]:
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 in @
% 139.73/20.58 X1038 @
% 139.73/20.58 X1034 ) =>
% 139.73/20.58 (
% 139.73/20.58 ![
% 139.73/20.58 X1040:$i]:
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 in @
% 139.73/20.58 X1040 @
% 139.73/20.58 X1036 ) =>
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 kfst @
% 139.73/20.58 (
% 139.73/20.58 kpair @
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% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 ![
% 139.73/20.58 X1042:$i,
% 139.73/20.58 X1044:$i,
% 139.73/20.58 X1046:$i]:
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 in @
% 139.73/20.58 X1046 @
% 139.73/20.58 X1042 ) =>
% 139.73/20.58 (
% 139.73/20.58 ![
% 139.73/20.58 X1048:$i]:
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 in @
% 139.73/20.58 X1048 @
% 139.73/20.58 X1044 ) =>
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 ksnd @
% 139.73/20.58 (
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% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 ![
% 139.73/20.58 X1050:$i,
% 139.73/20.58 X1052:$i,
% 139.73/20.58 X1054:$i]:
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 in @
% 139.73/20.58 X1054 @
% 139.73/20.58 (
% 139.73/20.58 cartprod @
% 139.73/20.58 X1050 @
% 139.73/20.58 X1052 ) ) =>
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 kpair @
% 139.73/20.58 (
% 139.73/20.58 kfst @
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% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 ![
% 139.73/20.58 X1056:$i,
% 139.73/20.58 X1058:$i,
% 139.73/20.58 X1060:(
% 139.73/20.58 $i > $i >
% 139.73/20.58 $o ),
% 139.73/20.58 X1062:$i]:
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 in @
% 139.73/20.58 X1062 @
% 139.73/20.58 X1056 ) =>
% 139.73/20.58 (
% 139.73/20.58 ![
% 139.73/20.58 X1064:$i]:
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 in @
% 139.73/20.58 X1064 @
% 139.73/20.58 X1058 ) =>
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 X1060 @
% 139.73/20.58 X1062 @
% 139.73/20.58 X1064 ) =>
% 139.73/20.58 (
% 139.73/20.58 in @
% 139.73/20.58 (
% 139.73/20.58 kpair @
% 139.73/20.58 X1062 @
% 139.73/20.58 X1064 ) @
% 139.73/20.58 (
% 139.73/20.58 dpsetconstr
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% 139.73/20.58 X1056 @
% 139.73/20.58 X1058 @
% 139.73/20.58 (
% 139.73/20.58 ^[
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% 139.73/20.58 V_22:$i]:
% 139.73/20.58 (
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% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 ![
% 139.73/20.58 X1066:$i,
% 139.73/20.58 X1068:$i,
% 139.73/20.58 X1070:(
% 139.73/20.58 $i > $i >
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% 139.73/20.58 (
% 139.73/20.58 subset @
% 139.73/20.58 (
% 139.73/20.58 dpsetconstr
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% 139.73/20.58 X1066 @
% 139.73/20.58 X1068 @
% 139.73/20.58 (
% 139.73/20.58 ^[
% 139.73/20.58 V_23:$i,
% 139.73/20.58 V_24:$i]:
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% 139.73/20.58 (
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% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 ![
% 139.73/20.58 X1072:$i,
% 139.73/20.58 X1074:$i,
% 139.73/20.58 X1076:(
% 139.73/20.58 $i > $i >
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% 139.73/20.58 (
% 139.73/20.58 subset @
% 139.73/20.58 (
% 139.73/20.58 dpsetconstr
% 139.73/20.58 @
% 139.73/20.58 X1072 @
% 139.73/20.58 X1074 @
% 139.73/20.58 (
% 139.73/20.58 ^[
% 139.73/20.58 V_25:$i,
% 139.73/20.58 V_26:$i]:
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% 139.73/20.58 (
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% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 ![
% 139.73/20.58 X1078:$i,
% 139.73/20.58 X1080:$i,
% 139.73/20.58 X1082:(
% 139.73/20.58 $i > $i >
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% 139.73/20.58 X1084:$i]:
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 in @
% 139.73/20.58 X1084 @
% 139.73/20.58 X1078 ) =>
% 139.73/20.58 (
% 139.73/20.58 ![
% 139.73/20.58 X1086:$i]:
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 in @
% 139.73/20.58 X1086 @
% 139.73/20.58 X1080 ) =>
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 in @
% 139.73/20.58 (
% 139.73/20.58 kpair @
% 139.73/20.58 X1084 @
% 139.73/20.58 X1086 ) @
% 139.73/20.58 (
% 139.73/20.58 dpsetconstr
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% 139.73/20.58 X1078 @
% 139.73/20.58 X1080 @
% 139.73/20.58 (
% 139.73/20.58 ^[
% 139.73/20.58 V_27:$i,
% 139.73/20.58 V_28:$i]:
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% 139.73/20.58 (
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% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 ![
% 139.73/20.58 X1088:$i,
% 139.73/20.58 X1090:$i,
% 139.73/20.58 X1092:(
% 139.73/20.58 $i > $i >
% 139.73/20.58 $o ),
% 139.73/20.58 X1094:$i,
% 139.73/20.58 X1096:$i]:
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 in @
% 139.73/20.58 (
% 139.73/20.58 kpair @
% 139.73/20.58 X1094 @
% 139.73/20.58 X1096 ) @
% 139.73/20.58 (
% 139.73/20.58 dpsetconstr
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% 139.73/20.58 X1088 @
% 139.73/20.58 X1090 @
% 139.73/20.58 (
% 139.73/20.58 ^[
% 139.73/20.58 V_29:$i,
% 139.73/20.58 V_30:$i]:
% 139.73/20.58 (
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% 139.73/20.58 (
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% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 ![
% 139.73/20.58 X1098:$i,
% 139.73/20.58 X1100:$i,
% 139.73/20.58 X1102:(
% 139.73/20.58 $i > $i >
% 139.73/20.58 $o ),
% 139.73/20.58 X1104:$i,
% 139.73/20.58 X1106:$i]:
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 in @
% 139.73/20.58 (
% 139.73/20.58 kpair @
% 139.73/20.58 X1104 @
% 139.73/20.58 X1106 ) @
% 139.73/20.58 (
% 139.73/20.58 dpsetconstr
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% 139.73/20.58 X1098 @
% 139.73/20.58 X1100 @
% 139.73/20.58 (
% 139.73/20.58 ^[
% 139.73/20.58 V_31:$i,
% 139.73/20.58 V_32:$i]:
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% 139.73/20.58 (
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% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 ![
% 139.73/20.58 X1108:$i,
% 139.73/20.58 X1110:$i,
% 139.73/20.58 X1112:(
% 139.73/20.58 $i > $i >
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% 139.73/20.58 X1114:$i,
% 139.73/20.58 X1116:$i]:
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 in @
% 139.73/20.58 (
% 139.73/20.58 kpair @
% 139.73/20.58 X1114 @
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% 139.73/20.58 (
% 139.73/20.58 dpsetconstr
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% 139.73/20.58 X1108 @
% 139.73/20.58 X1110 @
% 139.73/20.58 (
% 139.73/20.58 ^[
% 139.73/20.58 V_33:$i,
% 139.73/20.58 V_34:$i]:
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% 139.73/20.58 (
% 139.73/20.58 X1112 @
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% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 ![
% 139.73/20.58 X1118:$i,
% 139.73/20.58 X1120:$i,
% 139.73/20.58 X1122:$i]:
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 func @
% 139.73/20.58 X1118 @
% 139.73/20.58 X1120 @
% 139.73/20.58 X1122 ) =>
% 139.73/20.58 (
% 139.73/20.58 ![
% 139.73/20.58 X1124:$i]:
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 in @
% 139.73/20.58 X1124 @
% 139.73/20.58 X1118 ) =>
% 139.73/20.58 (
% 139.73/20.58 singleton
% 139.73/20.58 @
% 139.73/20.58 (
% 139.73/20.58 dsetconstr
% 139.73/20.58 @
% 139.73/20.58 X1120 @
% 139.73/20.58 (
% 139.73/20.58 ^[
% 139.73/20.58 V_35:$i]:
% 139.73/20.58 (
% 139.73/20.58 in @
% 139.73/20.58 (
% 139.73/20.58 kpair @
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% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 ![
% 139.73/20.58 X1126:$i,
% 139.73/20.58 X1128:$i,
% 139.73/20.58 X1130:$i]:
% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 func @
% 139.73/20.58 X1126 @
% 139.73/20.58 X1128 @
% 139.73/20.58 X1130 ) =>
% 139.73/20.58 (
% 139.73/20.58 ![
% 139.73/20.58 X1132:$i]:
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% 139.73/20.58 X1132 @
% 139.73/20.58 X1126 ) =>
% 139.73/20.58 (
% 139.73/20.58 in @
% 139.73/20.58 (
% 139.73/20.58 setunion @
% 139.73/20.58 (
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% 139.73/20.58 (
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% 139.73/20.58 V_36:$i]:
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% 139.73/20.58 (
% 139.73/20.58 (
% 139.73/20.58 ![
% 139.73/20.58 X1134:$i,
% 139.73/20.58 X1136:$i,
% 139.73/20.58 X1138:$i]:
% 139.73/20.58 (
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% 139.73/20.59 X1216:(
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% 139.73/20.59 (
% 139.73/20.59 (
% 139.73/20.59 singleton
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% 139.73/20.59 X1224:$i,
% 139.73/20.59 X1226:$i]:
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% 139.73/20.59 X1340:(
% 139.73/20.59 $i > $i )]:
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% 139.73/20.59 X1832 @
% 139.73/20.59 (
% 139.73/20.59 powerset @
% 139.73/20.59 X1828 ) ) =>
% 139.73/20.59 (
% 139.73/20.59 ![
% 139.73/20.59 X1834:$i]:
% 139.73/20.59 (
% 139.73/20.59 (
% 139.73/20.59 in @
% 139.73/20.59 X1834 @
% 139.73/20.59 (
% 139.73/20.59 powerset @
% 139.73/20.59 X1828 ) ) =>
% 139.73/20.59 (
% 139.73/20.59 ![
% 139.73/20.59 X1836:$i]:
% 139.73/20.59 (
% 139.73/20.59 (
% 139.73/20.59 in @
% 139.73/20.59 X1836 @
% 139.73/20.59 (
% 139.73/20.59 powerset @
% 139.73/20.59 X1828 ) ) =>
% 139.73/20.59 (
% 139.73/20.59 (
% 139.73/20.59 subset @
% 139.73/20.59 X1830 @
% 139.73/20.59 X1834 ) =>
% 139.73/20.59 (
% 139.73/20.59 (
% 139.73/20.59 subset @
% 139.73/20.59 X1832 @
% 139.73/20.59 X1836 ) =>
% 139.73/20.59 (
% 139.73/20.59 subset @
% 139.73/20.59 (
% 139.73/20.59 binintersect
% 139.73/20.59 @
% 139.73/20.59 X1830 @
% 139.73/20.59 X1832 ) @
% 139.73/20.60 (
% 139.73/20.60 binintersect
% 139.73/20.60 @
% 139.73/20.60 X1834 @
% 139.73/20.60 X1836 ) ) ) ) ) ) ) ) ) ) ) ) =>
% 139.73/20.60 (
% 139.73/20.60 (
% 139.73/20.60 ![
% 139.73/20.60 X1838:$i,
% 139.73/20.60 X1840:$i]:
% 139.73/20.60 (
% 139.73/20.60 (
% 139.73/20.60 in @
% 139.73/20.60 X1840 @
% 139.73/20.60 (
% 139.73/20.60 powerset @
% 139.73/20.60 X1838 ) ) =>
% 139.73/20.60 (
% 139.73/20.60 ![
% 139.73/20.60 X1842:$i]:
% 139.73/20.60 (
% 139.73/20.60 (
% 139.73/20.60 in @
% 139.73/20.60 X1842 @
% 139.73/20.60 (
% 139.73/20.60 powerset @
% 139.73/20.60 X1838 ) ) =>
% 139.73/20.60 (
% 139.73/20.60 in @
% 139.73/20.60 (
% 139.73/20.60 setminus @
% 139.73/20.60 X1838 @
% 139.73/20.60 X1840 ) @
% 139.73/20.60 (
% 139.73/20.60 powerset @
% 139.73/20.60 (
% 139.73/20.60 setminus @
% 139.73/20.60 X1838 @
% 139.73/20.60 (
% 139.73/20.60 binintersect
% 139.73/20.60 @
% 139.73/20.60 X1840 @
% 139.73/20.60 X1842 ) ) ) ) ) ) ) ) =>
% 139.73/20.60 (
% 139.73/20.60 (
% 139.73/20.60 ![
% 139.73/20.60 X1844:$i,
% 139.73/20.60 X1846:$i]:
% 139.73/20.60 (
% 139.73/20.60 (
% 139.73/20.60 in @
% 139.73/20.60 X1846 @
% 139.73/20.60 (
% 139.73/20.60 powerset @
% 139.73/20.60 X1844 ) ) =>
% 139.73/20.60 (
% 139.73/20.60 ![
% 139.73/20.60 X1848:$i]:
% 139.73/20.60 (
% 139.73/20.60 (
% 139.73/20.60 in @
% 139.73/20.60 X1848 @
% 139.73/20.60 (
% 139.73/20.60 powerset @
% 139.73/20.60 X1844 ) ) =>
% 139.73/20.60 (
% 139.73/20.60 ![
% 139.73/20.60 X1850:$i]:
% 139.73/20.60 (
% 139.73/20.60 (
% 139.73/20.60 in @
% 139.73/20.60 X1850 @
% 139.73/20.60 (
% 139.73/20.60 powerset @
% 139.73/20.60 X1844 ) ) =>
% 139.73/20.60 (
% 139.73/20.60 ![
% 139.73/20.60 X1852:$i]:
% 139.73/20.60 (
% 139.73/20.60 (
% 139.73/20.60 in @
% 139.73/20.60 X1852 @
% 139.73/20.60 (
% 139.73/20.60 powerset @
% 139.73/20.60 X1844 ) ) =>
% 139.73/20.60 (
% 139.73/20.60 (
% 139.73/20.60 setminus @
% 139.73/20.60 X1844 @
% 139.73/20.60 (
% 139.73/20.60 binintersect
% 139.73/20.60 @
% 139.73/20.60 (
% 139.73/20.60 binunion @
% 139.73/20.60 X1846 @
% 139.73/20.60 X1848 ) @
% 139.73/20.60 (
% 139.73/20.60 binunion @
% 139.73/20.60 X1850 @
% 139.73/20.60 X1852 ) ) ) =
% 139.73/20.60 (
% 139.73/20.60 binunion @
% 139.73/20.60 (
% 139.73/20.60 binintersect
% 139.73/20.60 @
% 139.73/20.60 (
% 139.73/20.60 setminus @
% 139.73/20.60 X1844 @
% 139.73/20.60 X1846 ) @
% 139.73/20.60 (
% 139.73/20.60 setminus @
% 139.73/20.60 X1844 @
% 139.73/20.60 X1848 ) ) @
% 139.73/20.60 (
% 139.73/20.60 binintersect
% 139.73/20.60 @
% 139.73/20.60 (
% 139.73/20.60 setminus @
% 139.73/20.60 X1844 @
% 139.73/20.60 X1850 ) @
% 139.73/20.60 (
% 139.73/20.60 setminus @
% 139.73/20.60 X1844 @
% 139.73/20.60 X1852 ) ) ) ) ) ) ) ) ) ) ) ) =>
% 139.73/20.60 (
% 139.73/20.60 (
% 139.73/20.60 ![
% 139.73/20.60 X1854:$i,
% 139.73/20.60 X1856:$i]:
% 139.73/20.60 (
% 139.73/20.60 (
% 139.73/20.60 in @
% 139.73/20.60 X1856 @
% 139.73/20.60 (
% 139.73/20.60 powerset @
% 139.73/20.60 X1854 ) ) =>
% 139.73/20.60 (
% 139.73/20.60 ![
% 139.73/20.60 X1858:$i]:
% 139.73/20.60 (
% 139.73/20.60 (
% 139.73/20.60 in @
% 139.73/20.60 X1858 @
% 139.73/20.60 (
% 139.73/20.60 powerset @
% 139.73/20.60 X1854 ) ) =>
% 139.73/20.60 (
% 139.73/20.60 ![
% 139.73/20.60 X1860:$i]:
% 139.73/20.60 (
% 139.73/20.60 (
% 139.73/20.60 in @
% 139.73/20.60 X1860 @
% 139.73/20.60 (
% 139.73/20.60 powerset @
% 139.73/20.60 X1854 ) ) =>
% 139.73/20.60 (
% 139.73/20.60 in @
% 139.73/20.60 (
% 139.73/20.60 binintersect
% 139.73/20.60 @
% 139.73/20.60 X1856 @
% 139.73/20.60 X1858 ) @
% 139.73/20.60 (
% 139.73/20.60 powerset @
% 139.73/20.60 (
% 139.73/20.60 binintersect
% 139.73/20.60 @
% 139.73/20.60 (
% 139.73/20.60 binunion @
% 139.73/20.60 X1856 @
% 139.73/20.60 X1860 ) @
% 139.73/20.60 (
% 139.73/20.60 binunion @
% 139.73/20.60 X1858 @
% 139.73/20.60 X1860 ) ) ) ) ) ) ) ) ) ) =>
% 139.73/20.60 (
% 139.73/20.60 (
% 139.73/20.60 ![
% 139.73/20.60 X1862:$i,
% 139.73/20.60 X1864:$i]:
% 139.73/20.60 (
% 139.73/20.60 (
% 139.73/20.60 in @
% 139.73/20.60 X1864 @
% 139.73/20.60 (
% 139.73/20.60 powerset @
% 139.73/20.60 X1862 ) ) =>
% 139.73/20.60 (
% 139.73/20.60 ![
% 139.73/20.60 X1866:$i]:
% 139.73/20.60 (
% 139.73/20.60 (
% 139.73/20.60 in @
% 139.73/20.60 X1866 @
% 139.73/20.60 (
% 139.73/20.60 powerset @
% 139.73/20.60 X1862 ) ) =>
% 139.73/20.60 (
% 139.73/20.60 (
% 139.73/20.60 subset @
% 139.73/20.60 X1864 @
% 139.73/20.60 (
% 139.73/20.60 setminus @
% 139.73/20.60 X1862 @
% 139.73/20.60 X1866 ) ) =>
% 139.73/20.60 (
% 139.73/20.60 subset @
% 139.73/20.60 X1866 @
% 139.73/20.60 (
% 139.73/20.60 setminus @
% 139.73/20.60 X1862 @
% 139.73/20.60 X1864 ) ) ) ) ) ) ) =>
% 139.73/20.60 (
% 139.73/20.60 (
% 139.73/20.60 ![
% 139.73/20.60 X1868:$i,
% 139.73/20.60 X1870:$i]:
% 139.73/20.60 (
% 139.73/20.60 (
% 139.73/20.60 in @
% 139.73/20.60 X1870 @
% 139.73/20.60 (
% 139.73/20.60 powerset @
% 139.73/20.60 X1868 ) ) =>
% 139.73/20.60 (
% 139.73/20.60 ![
% 139.73/20.60 X1872:$i]:
% 139.73/20.60 (
% 139.73/20.60 (
% 139.73/20.60 in @
% 139.73/20.60 X1872 @
% 139.73/20.60 (
% 139.73/20.60 powerset @
% 139.73/20.60 X1868 ) ) =>
% 139.73/20.60 (
% 139.73/20.60 in @
% 139.73/20.60 (
% 139.73/20.60 setminus @
% 139.73/20.60 X1868 @
% 139.73/20.60 (
% 139.73/20.60 binunion @
% 139.73/20.60 X1870 @
% 139.73/20.60 X1872 ) ) @
% 139.73/20.60 (
% 139.73/20.60 powerset @
% 139.73/20.60 (
% 139.73/20.60 setminus @
% 139.73/20.60 X1868 @
% 139.73/20.60 X1870 ) ) ) ) ) ) ) =>
% 139.73/20.60 (
% 139.73/20.60 ![
% 139.73/20.60 X1874:$i,
% 139.73/20.60 X1876:$i]:
% 139.73/20.60 (
% 139.73/20.60 (
% 139.73/20.60 subset @
% 139.73/20.60 X1876 @
% 139.73/20.60 (
% 139.73/20.60 cartprod @
% 139.73/20.60 X1874 @
% 139.73/20.60 X1874 ) ) =>
% 139.73/20.60 (
% 139.73/20.60 ![
% 139.73/20.60 X1878:(
% 139.73/20.60 $i > $o )]:
% 139.73/20.60 (
% 139.73/20.60 (
% 139.73/20.60 ![
% 139.73/20.60 X1880:$i]:
% 139.73/20.60 (
% 139.73/20.60 (
% 139.73/20.60 in @
% 139.73/20.60 X1880 @
% 139.73/20.60 X1874 ) =>
% 139.73/20.60 (
% 139.73/20.60 ![
% 139.73/20.60 X1882:$i]:
% 139.73/20.60 (
% 139.73/20.60 (
% 139.73/20.60 in @
% 139.73/20.60 X1882 @
% 139.73/20.60 X1874 ) =>
% 139.73/20.60 (
% 139.73/20.60 (
% 139.73/20.60 in @
% 139.73/20.60 (
% 139.73/20.60 kpair @
% 139.73/20.60 X1880 @
% 139.73/20.60 X1882 ) @
% 139.73/20.60 X1876 ) =>
% 139.73/20.60 (
% 139.73/20.60 X1878 @
% 139.73/20.60 (
% 139.73/20.60 kpair @
% 139.73/20.60 X1880 @
% 139.73/20.60 X1882 ) ) ) ) ) ) ) =>
% 139.73/20.60 (
% 139.73/20.60 ![
% 139.73/20.60 X1884:$i]:
% 139.73/20.60 (
% 139.73/20.60 (
% 139.73/20.60 in @
% 139.73/20.60 X1884 @
% 139.73/20.60 X1876 ) =>
% 139.73/20.60 (
% 139.73/20.60 X1878 @
% 139.73/20.60 X1884 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 139.73/20.60 thf(zf_stmt_14, negated_conjecture,
% 139.73/20.60 (~( ( ![X4:$i,X6:$i]:
% 139.73/20.60 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) <=> ( in @ X8 @ X6 ) ) ) =>
% 139.73/20.60 ( ( X4 ) = ( X6 ) ) ) ) =>
% 139.73/20.60 ( ( ![X10:$i]: ( ~( in @ X10 @ emptyset ) ) ) =>
% 139.73/20.60 ( ( ![X12:$i,X14:$i,X16:$i]:
% 139.73/20.60 ( ( in @ X16 @ ( setadjoin @ X12 @ X14 ) ) <=>
% 139.73/20.60 ( zip_tseitin_0 @ X16 @ X14 @ X12 ) ) ) =>
% 139.73/20.60 ( ( ![X18:$i,X20:$i]:
% 139.73/20.60 ( ( in @ X20 @ ( powerset @ X18 ) ) <=>
% 139.73/20.60 ( ![X22:$i]: ( zip_tseitin_1 @ X22 @ X20 @ X18 ) ) ) ) =>
% 139.73/20.60 ( ( ![X24:$i,X26:$i]:
% 139.73/20.60 ( ( in @ X26 @ ( setunion @ X24 ) ) <=>
% 139.73/20.60 ( ?[X28:$i]: ( zip_tseitin_2 @ X28 @ X26 @ X24 ) ) ) ) =>
% 139.73/20.60 ( ( in @ emptyset @ omega ) =>
% 139.73/20.60 ( ( ![X30:$i]:
% 139.73/20.60 ( ( in @ X30 @ omega ) =>
% 139.73/20.60 ( in @ ( setadjoin @ X30 @ X30 ) @ omega ) ) ) =>
% 139.73/20.60 ( ( ![X32:$i]:
% 139.73/20.60 ( ( ( in @ emptyset @ X32 ) &
% 139.73/20.60 ( ![X34:$i]:
% 139.73/20.60 ( ( ( in @ X34 @ omega ) & ( in @ X34 @ X32 ) ) =>
% 139.73/20.60 ( in @ ( setadjoin @ X34 @ X34 ) @ X32 ) ) ) ) =>
% 139.73/20.60 ( ![X36:$i]:
% 139.73/20.60 ( ( in @ X36 @ omega ) => ( in @ X36 @ X32 ) ) ) ) ) =>
% 139.73/20.60 ( ( ![X38:( $i > $i > $o ),X40:$i]:
% 139.73/20.60 ( ( ![X42:$i]:
% 139.73/20.60 ( ( in @ X42 @ X40 ) =>
% 139.73/20.60 ( ?[X44:$i]:
% 139.73/20.60 ( ( ![X46:$i]:
% 139.73/20.60 ( ( X38 @ X42 @ X46 ) =>
% 139.73/20.60 ( ( X44 ) = ( X46 ) ) ) ) &
% 139.73/20.60 ( X38 @ X42 @ X44 ) ) ) ) ) =>
% 139.73/20.60 ( ?[X48:$i]:
% 139.73/20.60 ( ![X50:$i]:
% 139.73/20.60 ( ( in @ X50 @ X48 ) <=>
% 139.73/20.60 ( ?[X52:$i]:
% 139.73/20.60 ( zip_tseitin_3 @ X52 @ X50 @ X40 @ X38 ) ) ) ) ) ) ) =>
% 139.73/20.60 ( ( ![X54:$i]:
% 139.73/20.60 ( ( ?[X56:$i]: ( in @ X56 @ X54 ) ) =>
% 139.73/20.60 ( ?[X58:$i]:
% 139.73/20.60 ( ( ~( ?[X60:$i]:
% 139.73/20.60 ( ( in @ X60 @ X54 ) &
% 139.73/20.60 ( in @ X60 @ X58 ) ) ) ) &
% 139.73/20.60 ( in @ X58 @ X54 ) ) ) ) ) =>
% 139.73/20.60 ( ( ![X62:$i]:
% 139.73/20.60 ( ?[X64:$i]:
% 139.73/20.60 ( ( ![X66:$i]:
% 139.73/20.60 ( ( ( ![X68:$i]:
% 139.73/20.60 ( ( in @ X68 @ X66 ) =>
% 139.73/20.60 ( in @ X68 @ X62 ) ) ) &
% 139.73/20.60 ( ?[X70:$i]: ( in @ X70 @ X66 ) ) ) =>
% 139.73/20.60 ( ?[X72:$i,X74:$i]:
% 139.73/20.60 ( ( ![X76:$i]:
% 139.73/20.60 ( ( in @ X76 @ X64 ) =>
% 139.73/20.60 ( ( ![X78:$i]:
% 139.73/20.60 ( ( in @ X78 @ X76 ) =>
% 139.73/20.60 ( in @ X78 @ X72 ) ) ) |
% 139.73/20.60 ( in @ X74 @ X76 ) ) ) ) &
% 139.73/20.60 ( ~( ?[X80:$i]:
% 139.73/20.60 ( ( in @ X80 @ X66 ) &
% 139.73/20.60 ( in @ X80 @ X72 ) ) ) ) &
% 139.73/20.60 ( in @ X74 @ X66 ) &
% 139.73/20.60 ( in @ X72 @ X64 ) ) ) ) ) &
% 139.73/20.60 ( ![X82:$i,X84:$i]:
% 139.73/20.60 ( ( ( in @ X82 @ X64 ) & ( in @ X84 @ X64 ) ) =>
% 139.73/20.60 ( ( ![X86:$i]:
% 139.73/20.60 ( ( in @ X86 @ X82 ) =>
% 139.73/20.60 ( in @ X86 @ X84 ) ) ) |
% 139.73/20.60 ( ![X88:$i]:
% 139.73/20.60 ( ( in @ X88 @ X84 ) =>
% 139.73/20.60 ( in @ X88 @ X82 ) ) ) ) ) ) &
% 139.73/20.60 ( ![X90:$i,X92:$i]:
% 139.73/20.60 ( ( ( in @ X90 @ X62 ) & ( in @ X92 @ X62 ) ) =>
% 139.73/20.60 ( ( ![X94:$i]:
% 139.73/20.60 ( ( in @ X94 @ X64 ) =>
% 139.73/20.60 ( ( in @ X90 @ X94 ) <=>
% 139.73/20.60 ( in @ X92 @ X94 ) ) ) ) =>
% 139.73/20.60 ( ( X90 ) = ( X92 ) ) ) ) ) &
% 139.73/20.60 ( ![X96:$i]:
% 139.73/20.60 ( ( in @ X96 @ X64 ) =>
% 139.73/20.60 ( ![X98:$i]:
% 139.73/20.60 ( ( in @ X98 @ X96 ) =>
% 139.73/20.60 ( in @ X98 @ X62 ) ) ) ) ) ) ) ) =>
% 139.73/20.60 ( ( ![X100:( $i > $o )]:
% 139.73/20.60 ( ( ?[X102:$i]:
% 139.73/20.60 ( ( ![X104:$i]:
% 139.73/20.60 ( ( X100 @ X104 ) =>
% 139.73/20.60 ( ( X102 ) = ( X104 ) ) ) ) &
% 139.73/20.60 ( X100 @ X102 ) ) ) =>
% 139.73/20.60 ( X100 @
% 139.73/20.60 ( descr @ ( ^[V_1:$i]: ( X100 @ V_1 ) ) ) ) ) ) =>
% 139.73/20.60 ( ( ![X106:$i,X108:( $i > $o ),X110:$i]:
% 139.73/20.60 ( ( in @ X110 @ X106 ) =>
% 139.73/20.60 ( ( X108 @ X110 ) =>
% 139.73/20.60 ( in @
% 139.73/20.60 X110 @
% 139.73/20.60 ( dsetconstr @
% 139.73/20.60 X106 @ ( ^[V_2:$i]: ( X108 @ V_2 ) ) ) ) ) ) ) =>
% 139.73/20.60 ( ( ![X112:$i,X114:( $i > $o ),X116:$i]:
% 139.73/20.60 ( ( in @
% 139.73/20.60 X116 @
% 139.73/20.60 ( dsetconstr @
% 139.73/20.60 X112 @ ( ^[V_3:$i]: ( X114 @ V_3 ) ) ) ) =>
% 139.73/20.60 ( in @ X116 @ X112 ) ) ) =>
% 139.73/20.60 ( ( ![X118:$i,X120:( $i > $o ),X122:$i]:
% 139.73/20.60 ( ( in @
% 139.73/20.60 X122 @
% 139.73/20.60 ( dsetconstr @
% 139.73/20.60 X118 @
% 139.73/20.60 ( ^[V_4:$i]: ( X120 @ V_4 ) ) ) ) =>
% 139.73/20.60 ( X120 @ X122 ) ) ) =>
% 139.73/20.60 ( ( ![X124:( $i > $o )]:
% 139.73/20.60 ( ( ?[X126:$i]:
% 139.73/20.60 ( ( ![X128:$i]:
% 139.73/20.60 ( ( X124 @ X128 ) =>
% 139.73/20.60 ( ( X126 ) = ( X128 ) ) ) ) &
% 139.73/20.60 ( X124 @ X126 ) ) ) =>
% 139.73/20.60 ( ?[X130:$i]:
% 139.73/20.60 ( ( ![X132:$i]:
% 139.73/20.60 ( ( X124 @ X132 ) =>
% 139.73/20.60 ( ( X130 ) = ( X132 ) ) ) ) &
% 139.73/20.60 ( X124 @ X130 ) ) ) ) ) =>
% 139.73/20.60 ( ( ![X134:$o,X136:$i]:
% 139.73/20.60 ( ( in @ X136 @ ( prop2set @ X134 ) ) =>
% 139.73/20.60 ( X134 ) ) ) =>
% 139.73/20.60 ( ( ![X138:$i]:
% 139.73/20.60 ( ( in @ X138 @ emptyset ) =>
% 139.73/20.60 ( ![X140:$o]: ( X140 ) ) ) ) =>
% 139.73/20.60 ( ( ![X142:$i]:
% 139.73/20.60 ( ~( in @ X142 @ emptyset ) ) ) =>
% 139.73/20.60 ( ( ![X144:$i]:
% 139.73/20.60 ( ~( in @ X144 @ emptyset ) ) ) =>
% 139.73/20.60 ( ( ![X146:( $i > $o )]:
% 139.73/20.60 ( ( ?[X148:$i]:
% 139.73/20.60 ( ( ![X150:$i]:
% 139.73/20.60 ( ( X146 @ X150 ) =>
% 139.73/20.60 ( ( X148 ) =
% 139.73/20.60 ( X150 ) ) ) ) &
% 139.73/20.60 ( X146 @ X148 ) ) ) =>
% 139.73/20.60 ( ?[X152:$i]:
% 139.73/20.60 ( X146 @ X152 ) ) ) ) =>
% 139.73/20.60 ( ( ![X154:$i,X156:$i]:
% 139.73/20.60 ( ( ![X158:$i]:
% 139.73/20.60 ( ( in @ X158 @ X154 ) =>
% 139.73/20.60 ( in @ X158 @ X156 ) ) ) =>
% 139.73/20.60 ( ( ![X160:$i]:
% 139.73/20.60 ( ( in @ X160 @ X156 ) =>
% 139.73/20.60 ( in @ X160 @ X154 ) ) ) =>
% 139.73/20.60 ( ( X154 ) = ( X156 ) ) ) ) ) =>
% 139.73/20.60 ( ( ![X162:$i]:
% 139.73/20.60 ( ( ![X164:$i]:
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% 139.99/20.61 (
% 139.99/20.61 (
% 139.99/20.61 ![
% 139.99/20.61 X1034:$i,
% 139.99/20.61 X1036:$i,
% 139.99/20.61 X1038:$i]:
% 139.99/20.61 (
% 139.99/20.61 (
% 139.99/20.61 in @
% 139.99/20.61 X1038 @
% 139.99/20.61 X1034 ) =>
% 139.99/20.61 (
% 139.99/20.61 ![
% 139.99/20.61 X1040:$i]:
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% 139.99/20.61 (
% 139.99/20.61 in @
% 139.99/20.61 X1040 @
% 139.99/20.61 X1036 ) =>
% 139.99/20.61 (
% 139.99/20.61 (
% 139.99/20.61 kfst @
% 139.99/20.61 (
% 139.99/20.61 kpair @
% 139.99/20.61 X1038 @
% 139.99/20.61 X1040 ) ) =
% 139.99/20.61 (
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% 139.99/20.61 (
% 139.99/20.61 (
% 139.99/20.61 ![
% 139.99/20.61 X1042:$i,
% 139.99/20.61 X1044:$i,
% 139.99/20.61 X1046:$i]:
% 139.99/20.61 (
% 139.99/20.61 (
% 139.99/20.61 in @
% 139.99/20.61 X1046 @
% 139.99/20.61 X1042 ) =>
% 139.99/20.61 (
% 139.99/20.61 ![
% 139.99/20.61 X1048:$i]:
% 139.99/20.61 (
% 139.99/20.61 (
% 139.99/20.61 in @
% 139.99/20.61 X1048 @
% 139.99/20.61 X1044 ) =>
% 139.99/20.61 (
% 139.99/20.61 (
% 139.99/20.61 ksnd @
% 139.99/20.61 (
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% 139.99/20.61 (
% 139.99/20.61 (
% 139.99/20.61 ![
% 139.99/20.61 X1050:$i,
% 139.99/20.61 X1052:$i,
% 139.99/20.61 X1054:$i]:
% 139.99/20.61 (
% 139.99/20.61 (
% 139.99/20.61 in @
% 139.99/20.61 X1054 @
% 139.99/20.61 (
% 139.99/20.61 cartprod
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% 139.99/20.61 X1050 @
% 139.99/20.61 X1052 ) ) =>
% 139.99/20.61 (
% 139.99/20.61 (
% 139.99/20.61 kpair @
% 139.99/20.61 (
% 139.99/20.61 kfst @
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% 139.99/20.61 (
% 139.99/20.61 ksnd @
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% 139.99/20.61 (
% 139.99/20.61 (
% 139.99/20.61 ![
% 139.99/20.61 X1056:$i,
% 139.99/20.61 X1058:$i,
% 139.99/20.61 X1060:(
% 139.99/20.61 $i > $i >
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% 139.99/20.61 X1062:$i]:
% 139.99/20.61 (
% 139.99/20.61 (
% 139.99/20.61 in @
% 139.99/20.61 X1062 @
% 139.99/20.61 X1056 ) =>
% 139.99/20.61 (
% 139.99/20.61 ![
% 139.99/20.61 X1064:$i]:
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% 139.99/20.61 (
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% 139.99/20.61 X1058 ) =>
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% 139.99/20.61 (
% 139.99/20.61 X1060 @
% 139.99/20.61 X1062 @
% 139.99/20.61 X1064 ) =>
% 139.99/20.61 (
% 139.99/20.61 in @
% 139.99/20.61 (
% 139.99/20.61 kpair @
% 139.99/20.61 X1062 @
% 139.99/20.61 X1064 ) @
% 139.99/20.61 (
% 139.99/20.61 dpsetconstr
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% 139.99/20.61 X1056 @
% 139.99/20.61 X1058 @
% 139.99/20.61 (
% 139.99/20.61 ^[
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% 139.99/20.61 (
% 139.99/20.61 (
% 139.99/20.61 ![
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% 139.99/20.61 X1068:$i,
% 139.99/20.61 X1070:(
% 139.99/20.61 $i > $i >
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% 139.99/20.61 (
% 139.99/20.61 subset @
% 139.99/20.61 (
% 139.99/20.61 dpsetconstr
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% 139.99/20.61 X1066 @
% 139.99/20.61 X1068 @
% 139.99/20.61 (
% 139.99/20.61 ^[
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% 139.99/20.61 V_24:$i]:
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% 139.99/20.61 (
% 139.99/20.61 cartprod
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% 139.99/20.61 X1068 ) ) ) =>
% 139.99/20.61 (
% 139.99/20.61 (
% 139.99/20.61 ![
% 139.99/20.61 X1072:$i,
% 139.99/20.61 X1074:$i,
% 139.99/20.61 X1076:(
% 139.99/20.61 $i > $i >
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% 139.99/20.61 (
% 139.99/20.61 subset @
% 139.99/20.61 (
% 139.99/20.61 dpsetconstr
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% 139.99/20.61 X1072 @
% 139.99/20.61 X1074 @
% 139.99/20.61 (
% 139.99/20.61 ^[
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% 139.99/20.61 V_26:$i]:
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% 139.99/20.61 (
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% 139.99/20.61 (
% 139.99/20.61 (
% 139.99/20.61 ![
% 139.99/20.61 X1078:$i,
% 139.99/20.61 X1080:$i,
% 139.99/20.61 X1082:(
% 139.99/20.61 $i > $i >
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% 139.99/20.61 X1084:$i]:
% 139.99/20.61 (
% 139.99/20.61 (
% 139.99/20.61 in @
% 139.99/20.61 X1084 @
% 139.99/20.61 X1078 ) =>
% 139.99/20.61 (
% 139.99/20.61 ![
% 139.99/20.61 X1086:$i]:
% 139.99/20.61 (
% 139.99/20.61 (
% 139.99/20.61 in @
% 139.99/20.61 X1086 @
% 139.99/20.61 X1080 ) =>
% 139.99/20.61 (
% 139.99/20.61 (
% 139.99/20.61 in @
% 139.99/20.61 (
% 139.99/20.61 kpair @
% 139.99/20.61 X1084 @
% 139.99/20.61 X1086 ) @
% 139.99/20.61 (
% 139.99/20.61 dpsetconstr
% 139.99/20.61 @
% 139.99/20.61 X1078 @
% 139.99/20.61 X1080 @
% 139.99/20.61 (
% 139.99/20.61 ^[
% 139.99/20.61 V_27:$i,
% 139.99/20.61 V_28:$i]:
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% 139.99/20.61 V_28 ) ) ) ) =>
% 139.99/20.61 (
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% 139.99/20.61 X1084 @
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% 139.99/20.61 (
% 139.99/20.61 (
% 139.99/20.61 ![
% 139.99/20.61 X1088:$i,
% 139.99/20.61 X1090:$i,
% 139.99/20.61 X1092:(
% 139.99/20.61 $i > $i >
% 139.99/20.61 $o ),
% 139.99/20.61 X1094:$i,
% 139.99/20.61 X1096:$i]:
% 139.99/20.61 (
% 139.99/20.61 (
% 139.99/20.61 in @
% 139.99/20.61 (
% 139.99/20.61 kpair @
% 139.99/20.61 X1094 @
% 139.99/20.61 X1096 ) @
% 139.99/20.61 (
% 139.99/20.61 dpsetconstr
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% 139.99/20.61 X1088 @
% 139.99/20.61 X1090 @
% 139.99/20.61 (
% 139.99/20.61 ^[
% 139.99/20.61 V_29:$i,
% 139.99/20.61 V_30:$i]:
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% 139.99/20.61 V_30 ) ) ) ) =>
% 139.99/20.61 (
% 139.99/20.61 in @
% 139.99/20.61 X1094 @
% 139.99/20.61 X1088 ) ) ) =>
% 139.99/20.61 (
% 139.99/20.61 (
% 139.99/20.61 ![
% 139.99/20.61 X1098:$i,
% 139.99/20.61 X1100:$i,
% 139.99/20.61 X1102:(
% 139.99/20.61 $i > $i >
% 139.99/20.61 $o ),
% 139.99/20.61 X1104:$i,
% 139.99/20.61 X1106:$i]:
% 139.99/20.61 (
% 139.99/20.61 (
% 139.99/20.61 in @
% 139.99/20.61 (
% 139.99/20.61 kpair @
% 139.99/20.61 X1104 @
% 139.99/20.61 X1106 ) @
% 139.99/20.61 (
% 139.99/20.61 dpsetconstr
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% 139.99/20.61 X1098 @
% 139.99/20.61 X1100 @
% 139.99/20.61 (
% 139.99/20.61 ^[
% 139.99/20.61 V_31:$i,
% 139.99/20.61 V_32:$i]:
% 139.99/20.61 (
% 139.99/20.61 X1102 @
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% 139.99/20.61 V_32 ) ) ) ) =>
% 139.99/20.61 (
% 139.99/20.61 in @
% 139.99/20.61 X1106 @
% 139.99/20.61 X1100 ) ) ) =>
% 139.99/20.61 (
% 139.99/20.61 (
% 139.99/20.61 ![
% 139.99/20.61 X1108:$i,
% 139.99/20.61 X1110:$i,
% 139.99/20.61 X1112:(
% 139.99/20.61 $i > $i >
% 139.99/20.61 $o ),
% 139.99/20.61 X1114:$i,
% 139.99/20.61 X1116:$i]:
% 139.99/20.61 (
% 139.99/20.61 (
% 139.99/20.61 in @
% 139.99/20.61 (
% 139.99/20.61 kpair @
% 139.99/20.61 X1114 @
% 139.99/20.61 X1116 ) @
% 139.99/20.61 (
% 139.99/20.61 dpsetconstr
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% 139.99/20.61 X1108 @
% 139.99/20.61 X1110 @
% 139.99/20.61 (
% 139.99/20.61 ^[
% 139.99/20.61 V_33:$i,
% 139.99/20.61 V_34:$i]:
% 139.99/20.61 (
% 139.99/20.61 X1112 @
% 139.99/20.61 V_33 @
% 139.99/20.61 V_34 ) ) ) ) =>
% 139.99/20.61 (
% 139.99/20.61 X1112 @
% 139.99/20.61 X1114 @
% 139.99/20.61 X1116 ) ) ) =>
% 139.99/20.61 (
% 139.99/20.61 (
% 139.99/20.61 ![
% 139.99/20.61 X1118:$i,
% 139.99/20.61 X1120:$i,
% 139.99/20.61 X1122:$i]:
% 139.99/20.61 (
% 139.99/20.61 (
% 139.99/20.61 func @
% 139.99/20.61 X1118 @
% 139.99/20.61 X1120 @
% 139.99/20.61 X1122 ) =>
% 139.99/20.61 (
% 139.99/20.61 ![
% 139.99/20.61 X1124:$i]:
% 139.99/20.61 (
% 139.99/20.61 (
% 139.99/20.61 in @
% 139.99/20.61 X1124 @
% 139.99/20.61 X1118 ) =>
% 139.99/20.61 (
% 139.99/20.61 singleton
% 139.99/20.61 @
% 139.99/20.61 (
% 139.99/20.61 dsetconstr
% 139.99/20.61 @
% 139.99/20.61 X1120 @
% 139.99/20.61 (
% 139.99/20.61 ^[
% 139.99/20.61 V_35:$i]:
% 139.99/20.61 (
% 139.99/20.61 in @
% 139.99/20.61 (
% 139.99/20.61 kpair @
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% 139.99/20.61 (
% 139.99/20.61 (
% 139.99/20.61 ![
% 139.99/20.61 X1126:$i,
% 139.99/20.61 X1128:$i,
% 139.99/20.61 X1130:$i]:
% 139.99/20.61 (
% 139.99/20.61 (
% 139.99/20.61 func @
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% 139.99/20.61 X1128 @
% 139.99/20.61 X1130 ) =>
% 139.99/20.61 (
% 139.99/20.61 ![
% 139.99/20.61 X1132:$i]:
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% 139.99/20.61 (
% 139.99/20.61 in @
% 139.99/20.61 X1132 @
% 139.99/20.61 X1126 ) =>
% 139.99/20.61 (
% 139.99/20.61 in @
% 139.99/20.61 (
% 139.99/20.61 setunion
% 139.99/20.61 @
% 139.99/20.61 (
% 139.99/20.61 dsetconstr
% 139.99/20.61 @
% 139.99/20.61 X1128 @
% 139.99/20.61 (
% 139.99/20.61 ^[
% 139.99/20.61 V_36:$i]:
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% 139.99/20.61 (
% 139.99/20.61 ![
% 139.99/20.61 X1134:$i,
% 139.99/20.61 X1136:$i,
% 139.99/20.61 X1138:$i]:
% 139.99/20.61 (
% 139.99/20.61 (
% 139.99/20.61 func @
% 139.99/20.61 X1134 @
% 139.99/20.61 X1136 @
% 139.99/20.61 X1138 ) =>
% 139.99/20.61 (
% 139.99/20.61 ![
% 139.99/20.61 X1140:$i]:
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% 139.99/20.61 (
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% 139.99/20.61 X1140 @
% 139.99/20.61 X1134 ) =>
% 139.99/20.61 (
% 139.99/20.61 in @
% 139.99/20.61 (
% 139.99/20.61 ap @
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% 139.99/20.61 (
% 139.99/20.61 (
% 139.99/20.61 ![
% 139.99/20.61 X1142:$i,
% 139.99/20.61 X1144:$i,
% 139.99/20.61 X1146:$i]:
% 139.99/20.61 (
% 139.99/20.61 (
% 139.99/20.61 in @
% 139.99/20.61 X1146 @
% 139.99/20.61 (
% 139.99/20.61 funcSet @
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% 139.99/20.61 X1144 ) ) =>
% 139.99/20.61 (
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% 139.99/20.61 X1144 @
% 139.99/20.61 X1146 ) ) ) =>
% 139.99/20.61 (
% 139.99/20.61 (
% 139.99/20.61 ![
% 139.99/20.61 X1148:$i,
% 139.99/20.61 X1150:$i,
% 139.99/20.61 X1152:$i]:
% 139.99/20.61 (
% 139.99/20.61 (
% 139.99/20.61 in @
% 139.99/20.61 X1152 @
% 139.99/20.61 (
% 139.99/20.61 funcSet @
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% 139.99/20.61 X1150 ) ) =>
% 139.99/20.61 (
% 139.99/20.61 ![
% 139.99/20.61 X1154:$i]:
% 139.99/20.61 (
% 139.99/20.61 (
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% 139.99/20.61 (
% 139.99/20.61 in @
% 139.99/20.61 (
% 139.99/20.61 ap @
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% 139.99/20.61 (
% 139.99/20.61 (
% 139.99/20.61 ![
% 139.99/20.61 X1156:$i,
% 139.99/20.61 X1158:$i,
% 139.99/20.61 X1160:$i]:
% 139.99/20.61 (
% 139.99/20.61 (
% 139.99/20.61 func @
% 139.99/20.61 X1156 @
% 139.99/20.61 X1158 @
% 139.99/20.61 X1160 ) =>
% 139.99/20.61 (
% 139.99/20.61 in @
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% 139.99/20.61 (
% 139.99/20.61 (
% 139.99/20.61 ![
% 139.99/20.61 X1162:$i,
% 139.99/20.61 X1164:$i,
% 139.99/20.61 X1166:(
% 139.99/20.61 $i > $i )]:
% 139.99/20.61 (
% 139.99/20.61 (
% 139.99/20.61 ![
% 139.99/20.61 X1168:$i]:
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% 139.99/20.61 (
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% 139.99/20.61 (
% 139.99/20.61 func @
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% 139.99/20.61 X1164 @
% 139.99/20.61 (
% 139.99/20.61 dpsetconstr
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% 139.99/20.61 X1164 @
% 139.99/20.61 (
% 139.99/20.61 ^[
% 139.99/20.61 V_37:$i,
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% 139.99/20.61 (
% 139.99/20.61 ![
% 139.99/20.61 X1170:$i,
% 139.99/20.61 X1172:$i,
% 139.99/20.61 X1174:(
% 139.99/20.61 $i > $i )]:
% 139.99/20.61 (
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% 139.99/20.61 ![
% 139.99/20.61 X1176:$i]:
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% 139.99/20.61 (
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% 139.99/20.61 X1182:(
% 139.99/20.61 $i > $i )]:
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% 139.99/20.61 X1184:$i]:
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% 139.99/20.61 (
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% 139.99/20.61 (
% 139.99/20.61 (
% 139.99/20.61 ![
% 139.99/20.61 X1186:$i,
% 139.99/20.61 X1188:$i,
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% 139.99/20.61 subset @
% 139.99/20.61 X1190 @
% 139.99/20.61 (
% 139.99/20.61 cartprod
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% 139.99/20.61 X1186 @
% 139.99/20.61 X1188 ) ) =>
% 139.99/20.61 (
% 139.99/20.61 ![
% 139.99/20.61 X1192:(
% 139.99/20.61 $i > $o )]:
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% 139.99/20.61 ![
% 139.99/20.61 X1194:$i]:
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% 139.99/20.61 X1196:$i]:
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% 139.99/20.61 (
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% 139.99/20.61 (
% 139.99/20.61 kpair @
% 139.99/20.61 X1194 @
% 139.99/20.61 X1196 ) @
% 139.99/20.61 X1190 ) =>
% 139.99/20.61 (
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% 139.99/20.61 X1198:$i]:
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% 139.99/20.61 X1200:$i,
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% 139.99/20.61 subset @
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% 139.99/20.61 X1202 ) ) =>
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% 139.99/20.61 ![
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% 139.99/20.61 $i > $o )]:
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% 139.99/20.61 X1208:$i]:
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% 139.99/20.61 X1216:(
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% 139.99/20.61 (
% 139.99/20.61 singleton
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% 139.99/20.61 (
% 139.99/20.61 dsetconstr
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% 139.99/20.61 X1218:$i]:
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% 139.99/20.61 ![
% 139.99/20.61 X1222:$i,
% 139.99/20.61 X1224:$i,
% 139.99/20.61 X1226:$i]:
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% 139.99/20.61 func @
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% 139.99/20.61 X1224 @
% 139.99/20.61 X1226 ) =>
% 139.99/20.61 (
% 139.99/20.61 ![
% 139.99/20.61 X1228:$i]:
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% 139.99/20.61 in @
% 139.99/20.61 (
% 139.99/20.61 kpair @
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% 139.99/20.61 ap @
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% 139.99/20.61 (
% 139.99/20.61 ![
% 139.99/20.61 X1230:$i,
% 139.99/20.61 X1232:$i,
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% 139.99/20.61 X1232 ) ) =>
% 139.99/20.61 (
% 139.99/20.61 ![
% 139.99/20.61 X1236:$i]:
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% 139.99/20.61 (
% 139.99/20.61 kpair @
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% 139.99/20.61 (
% 139.99/20.61 ![
% 139.99/20.61 X1238:$i,
% 139.99/20.61 X1240:$i,
% 139.99/20.61 X1242:$i]:
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% 139.99/20.61 X1242 ) =>
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% 139.99/20.61 X1246:$i]:
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% 139.99/20.61 X1242 ) =>
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% 139.99/20.61 (
% 139.99/20.61 ap @
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% 139.99/20.61 (
% 139.99/20.61 (
% 139.99/20.61 ![
% 139.99/20.61 X1248:$i,
% 139.99/20.61 X1250:$i,
% 139.99/20.61 X1252:$i]:
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% 139.99/20.61 X1250 @
% 139.99/20.61 X1252 ) =>
% 139.99/20.61 (
% 139.99/20.61 ![
% 139.99/20.61 X1254:$i]:
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% 139.99/20.61 (
% 139.99/20.61 ![
% 139.99/20.61 X1256:$i]:
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% 139.99/20.61 (
% 139.99/20.61 ap @
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% 139.99/20.61 X1252 @
% 139.99/20.61 X1256 ) =
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% 139.99/20.61 ap @
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% 139.99/20.61 ![
% 139.99/20.61 X1258:$i]:
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% 139.99/20.61 ![
% 139.99/20.61 X1260:$i]:
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% 139.99/20.61 (
% 139.99/20.61 in @
% 139.99/20.61 (
% 139.99/20.61 kpair @
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% 139.99/20.61 X1254 ) =>
% 139.99/20.61 (
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% 139.99/20.61 (
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% 139.99/20.61 X1262:$i,
% 139.99/20.61 X1264:$i,
% 139.99/20.61 X1266:$i]:
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% 139.99/20.61 (
% 139.99/20.61 in @
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% 139.99/20.61 X1264 ) ) =>
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% 139.99/20.61 X1270:$i]:
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% 139.99/20.61 X1266 ) =>
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% 139.99/20.61 X1276:$i]:
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% 139.99/20.62 X1836 @
% 139.99/20.62 (
% 139.99/20.62 powerset
% 139.99/20.62 @
% 139.99/20.62 X1828 ) ) =>
% 139.99/20.62 (
% 139.99/20.62 (
% 139.99/20.62 subset @
% 139.99/20.62 X1830 @
% 139.99/20.62 X1834 ) =>
% 139.99/20.62 (
% 139.99/20.62 (
% 139.99/20.62 subset @
% 139.99/20.62 X1832 @
% 139.99/20.62 X1836 ) =>
% 139.99/20.62 (
% 139.99/20.62 subset @
% 139.99/20.62 (
% 139.99/20.62 binintersect
% 139.99/20.62 @
% 139.99/20.62 X1830 @
% 139.99/20.62 X1832 ) @
% 139.99/20.62 (
% 139.99/20.62 binintersect
% 139.99/20.62 @
% 139.99/20.62 X1834 @
% 139.99/20.62 X1836 ) ) ) ) ) ) ) ) ) ) ) ) =>
% 139.99/20.62 (
% 139.99/20.62 (
% 139.99/20.62 ![
% 139.99/20.62 X1838:$i,
% 139.99/20.62 X1840:$i]:
% 139.99/20.62 (
% 139.99/20.62 (
% 139.99/20.62 in @
% 139.99/20.62 X1840 @
% 139.99/20.62 (
% 139.99/20.62 powerset
% 139.99/20.62 @
% 139.99/20.62 X1838 ) ) =>
% 139.99/20.62 (
% 139.99/20.62 ![
% 139.99/20.62 X1842:$i]:
% 139.99/20.62 (
% 139.99/20.62 (
% 139.99/20.62 in @
% 139.99/20.62 X1842 @
% 139.99/20.62 (
% 139.99/20.62 powerset
% 139.99/20.62 @
% 139.99/20.62 X1838 ) ) =>
% 139.99/20.62 (
% 139.99/20.62 in @
% 139.99/20.62 (
% 139.99/20.62 setminus
% 139.99/20.62 @
% 139.99/20.62 X1838 @
% 139.99/20.62 X1840 ) @
% 139.99/20.62 (
% 139.99/20.62 powerset
% 139.99/20.62 @
% 139.99/20.62 (
% 139.99/20.62 setminus
% 139.99/20.62 @
% 139.99/20.62 X1838 @
% 139.99/20.62 (
% 139.99/20.62 binintersect
% 139.99/20.62 @
% 139.99/20.62 X1840 @
% 139.99/20.62 X1842 ) ) ) ) ) ) ) ) =>
% 139.99/20.62 (
% 139.99/20.62 (
% 139.99/20.62 ![
% 139.99/20.62 X1844:$i,
% 139.99/20.62 X1846:$i]:
% 139.99/20.62 (
% 139.99/20.62 (
% 139.99/20.62 in @
% 139.99/20.62 X1846 @
% 139.99/20.62 (
% 139.99/20.62 powerset
% 139.99/20.62 @
% 139.99/20.62 X1844 ) ) =>
% 139.99/20.62 (
% 139.99/20.62 ![
% 139.99/20.62 X1848:$i]:
% 139.99/20.62 (
% 139.99/20.62 (
% 139.99/20.62 in @
% 139.99/20.62 X1848 @
% 139.99/20.62 (
% 139.99/20.62 powerset
% 139.99/20.62 @
% 139.99/20.62 X1844 ) ) =>
% 139.99/20.62 (
% 139.99/20.62 ![
% 139.99/20.62 X1850:$i]:
% 139.99/20.62 (
% 139.99/20.62 (
% 139.99/20.62 in @
% 139.99/20.62 X1850 @
% 139.99/20.62 (
% 139.99/20.62 powerset
% 139.99/20.62 @
% 139.99/20.62 X1844 ) ) =>
% 139.99/20.62 (
% 139.99/20.62 ![
% 139.99/20.62 X1852:$i]:
% 139.99/20.62 (
% 139.99/20.62 (
% 139.99/20.62 in @
% 139.99/20.62 X1852 @
% 139.99/20.62 (
% 139.99/20.62 powerset
% 139.99/20.62 @
% 139.99/20.62 X1844 ) ) =>
% 139.99/20.62 (
% 139.99/20.62 (
% 139.99/20.62 setminus
% 139.99/20.62 @
% 139.99/20.62 X1844 @
% 139.99/20.62 (
% 139.99/20.62 binintersect
% 139.99/20.62 @
% 139.99/20.62 (
% 139.99/20.62 binunion
% 139.99/20.62 @
% 139.99/20.62 X1846 @
% 139.99/20.62 X1848 ) @
% 139.99/20.62 (
% 139.99/20.62 binunion
% 139.99/20.62 @
% 139.99/20.62 X1850 @
% 139.99/20.62 X1852 ) ) ) =
% 139.99/20.62 (
% 139.99/20.62 binunion
% 139.99/20.62 @
% 139.99/20.62 (
% 139.99/20.62 binintersect
% 139.99/20.62 @
% 139.99/20.62 (
% 139.99/20.62 setminus
% 139.99/20.62 @
% 139.99/20.62 X1844 @
% 139.99/20.62 X1846 ) @
% 139.99/20.62 (
% 139.99/20.62 setminus
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% 139.99/20.62 X1844 @
% 139.99/20.62 X1848 ) ) @
% 139.99/20.62 (
% 139.99/20.62 binintersect
% 139.99/20.62 @
% 139.99/20.62 (
% 139.99/20.62 setminus
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% 139.99/20.62 X1844 @
% 139.99/20.62 X1850 ) @
% 139.99/20.62 (
% 139.99/20.62 setminus
% 139.99/20.62 @
% 139.99/20.62 X1844 @
% 139.99/20.62 X1852 ) ) ) ) ) ) ) ) ) ) ) ) =>
% 139.99/20.62 (
% 139.99/20.62 (
% 139.99/20.62 ![
% 139.99/20.62 X1854:$i,
% 139.99/20.62 X1856:$i]:
% 139.99/20.62 (
% 139.99/20.62 (
% 139.99/20.62 in @
% 139.99/20.62 X1856 @
% 139.99/20.62 (
% 139.99/20.62 powerset
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% 139.99/20.62 X1854 ) ) =>
% 139.99/20.62 (
% 139.99/20.62 ![
% 139.99/20.62 X1858:$i]:
% 139.99/20.62 (
% 139.99/20.62 (
% 139.99/20.62 in @
% 139.99/20.62 X1858 @
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% 139.99/20.62 powerset
% 139.99/20.62 @
% 139.99/20.62 X1854 ) ) =>
% 139.99/20.62 (
% 139.99/20.62 ![
% 139.99/20.62 X1860:$i]:
% 139.99/20.62 (
% 139.99/20.62 (
% 139.99/20.62 in @
% 139.99/20.62 X1860 @
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% 139.99/20.62 powerset
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% 139.99/20.62 X1854 ) ) =>
% 139.99/20.62 (
% 139.99/20.62 in @
% 139.99/20.62 (
% 139.99/20.62 binintersect
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% 139.99/20.62 X1856 @
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% 139.99/20.62 (
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% 139.99/20.62 binintersect
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% 139.99/20.62 (
% 139.99/20.62 binunion
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% 139.99/20.62 X1856 @
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% 139.99/20.62 (
% 139.99/20.62 binunion
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% 139.99/20.62 X1858 @
% 139.99/20.62 X1860 ) ) ) ) ) ) ) ) ) ) =>
% 139.99/20.62 (
% 139.99/20.62 (
% 139.99/20.62 ![
% 139.99/20.62 X1862:$i,
% 139.99/20.62 X1864:$i]:
% 139.99/20.62 (
% 139.99/20.62 (
% 139.99/20.62 in @
% 139.99/20.62 X1864 @
% 139.99/20.62 (
% 139.99/20.62 powerset
% 139.99/20.62 @
% 139.99/20.62 X1862 ) ) =>
% 139.99/20.62 (
% 139.99/20.62 ![
% 139.99/20.62 X1866:$i]:
% 139.99/20.62 (
% 139.99/20.62 (
% 139.99/20.62 in @
% 139.99/20.62 X1866 @
% 139.99/20.62 (
% 139.99/20.62 powerset
% 139.99/20.62 @
% 139.99/20.62 X1862 ) ) =>
% 139.99/20.62 (
% 139.99/20.62 (
% 139.99/20.62 subset @
% 139.99/20.62 X1864 @
% 139.99/20.62 (
% 139.99/20.62 setminus
% 139.99/20.62 @
% 139.99/20.62 X1862 @
% 139.99/20.62 X1866 ) ) =>
% 139.99/20.62 (
% 139.99/20.62 subset @
% 139.99/20.62 X1866 @
% 139.99/20.62 (
% 139.99/20.62 setminus
% 139.99/20.62 @
% 139.99/20.62 X1862 @
% 139.99/20.62 X1864 ) ) ) ) ) ) ) =>
% 139.99/20.62 (
% 139.99/20.62 (
% 139.99/20.62 ![
% 139.99/20.62 X1868:$i,
% 139.99/20.62 X1870:$i]:
% 139.99/20.62 (
% 139.99/20.62 (
% 139.99/20.62 in @
% 139.99/20.62 X1870 @
% 139.99/20.62 (
% 139.99/20.62 powerset
% 139.99/20.62 @
% 139.99/20.62 X1868 ) ) =>
% 139.99/20.62 (
% 139.99/20.62 ![
% 139.99/20.62 X1872:$i]:
% 139.99/20.62 (
% 139.99/20.62 (
% 139.99/20.62 in @
% 139.99/20.62 X1872 @
% 139.99/20.62 (
% 139.99/20.62 powerset
% 139.99/20.62 @
% 139.99/20.62 X1868 ) ) =>
% 139.99/20.62 (
% 139.99/20.62 in @
% 139.99/20.62 (
% 139.99/20.62 setminus
% 139.99/20.62 @
% 139.99/20.62 X1868 @
% 139.99/20.62 (
% 139.99/20.62 binunion
% 139.99/20.62 @
% 139.99/20.62 X1870 @
% 139.99/20.62 X1872 ) ) @
% 139.99/20.62 (
% 139.99/20.62 powerset
% 139.99/20.62 @
% 139.99/20.62 (
% 139.99/20.62 setminus
% 139.99/20.62 @
% 139.99/20.62 X1868 @
% 139.99/20.62 X1870 ) ) ) ) ) ) ) =>
% 139.99/20.62 (
% 139.99/20.62 ![
% 139.99/20.62 X1874:$i,
% 139.99/20.62 X1876:$i]:
% 139.99/20.62 (
% 139.99/20.62 (
% 139.99/20.62 subset @
% 139.99/20.62 X1876 @
% 139.99/20.62 (
% 139.99/20.62 cartprod
% 139.99/20.62 @
% 139.99/20.62 X1874 @
% 139.99/20.62 X1874 ) ) =>
% 139.99/20.62 (
% 139.99/20.62 ![
% 139.99/20.62 X1878:(
% 139.99/20.62 $i > $o )]:
% 139.99/20.62 (
% 139.99/20.62 (
% 139.99/20.62 ![
% 139.99/20.62 X1880:$i]:
% 139.99/20.62 (
% 139.99/20.62 (
% 139.99/20.62 in @
% 139.99/20.62 X1880 @
% 139.99/20.62 X1874 ) =>
% 139.99/20.62 (
% 139.99/20.62 ![
% 139.99/20.62 X1882:$i]:
% 139.99/20.62 (
% 139.99/20.62 (
% 139.99/20.62 in @
% 139.99/20.62 X1882 @
% 139.99/20.62 X1874 ) =>
% 139.99/20.62 (
% 139.99/20.62 (
% 139.99/20.62 in @
% 139.99/20.62 (
% 139.99/20.62 kpair @
% 139.99/20.62 X1880 @
% 139.99/20.62 X1882 ) @
% 139.99/20.62 X1876 ) =>
% 139.99/20.62 (
% 139.99/20.62 X1878 @
% 139.99/20.62 (
% 139.99/20.62 kpair @
% 139.99/20.62 X1880 @
% 139.99/20.62 X1882 ) ) ) ) ) ) ) =>
% 139.99/20.62 (
% 139.99/20.62 ![
% 139.99/20.62 X1884:$i]:
% 139.99/20.62 (
% 139.99/20.62 (
% 139.99/20.62 in @
% 139.99/20.62 X1884 @
% 139.99/20.62 X1876 ) =>
% 139.99/20.62 (
% 139.99/20.62 X1878 @
% 139.99/20.62 X1884 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 139.99/20.62 inference('cnf.neg', [status(esa)], [zf_stmt_13])).
% 139.99/20.62 thf(zip_derived_cl238, plain, (~ (sk__958 @ sk__959)),
% 139.99/20.62 inference('cnf', [status(esa)], [zf_stmt_14])).
% 139.99/20.62 thf(zip_derived_cl240, plain,
% 139.99/20.62 ( (subset @ sk__957 @ (cartprod @ sk__956 @ sk__956))),
% 139.99/20.62 inference('cnf', [status(esa)], [zf_stmt_14])).
% 139.99/20.62 thf(zip_derived_cl237, plain,
% 139.99/20.62 (![X447 : $i, X448 : $i]:
% 139.99/20.62 (~ (in @ X447 @ sk__956)
% 139.99/20.62 | (sk__958 @ (kpair @ X448 @ X447))
% 139.99/20.62 | ~ (in @ (kpair @ X448 @ X447) @ sk__957)
% 139.99/20.62 | ~ (in @ X448 @ sk__956))),
% 139.99/20.62 inference('cnf', [status(esa)], [zf_stmt_14])).
% 139.99/20.62 thf(zip_derived_cl155, plain,
% 139.99/20.62 (![X238 : $i, X239 : $i, X240 : $i]:
% 139.99/20.62 ( (in @ (ksnd @ X238) @ X239)
% 139.99/20.62 | ~ (in @ X238 @ (cartprod @ X240 @ X239)))),
% 139.99/20.62 inference('cnf', [status(esa)], [zf_stmt_14])).
% 139.99/20.62 thf(zip_derived_cl149, plain,
% 139.99/20.62 (![X220 : $i, X221 : $i, X222 : $i]:
% 139.99/20.62 ( (in @ (kfst @ X220) @ X221)
% 139.99/20.62 | ~ (in @ X220 @ (cartprod @ X221 @ X222)))),
% 139.99/20.62 inference('cnf', [status(esa)], [zf_stmt_14])).
% 139.99/20.62 thf(zip_derived_cl239, plain, ( (in @ sk__959 @ sk__957)),
% 139.99/20.62 inference('cnf', [status(esa)], [zf_stmt_14])).
% 139.99/20.62 thf(zip_derived_cl158, plain,
% 139.99/20.62 (![X249 : $i, X250 : $i, X251 : $i]:
% 139.99/20.62 (((kpair @ (kfst @ X249) @ (ksnd @ X249)) = (X249))
% 139.99/20.62 | ~ (in @ X249 @ (cartprod @ X250 @ X251)))),
% 139.99/20.62 inference('cnf', [status(esa)], [zf_stmt_14])).
% 139.99/20.62 thf(zip_derived_cl383, plain,
% 139.99/20.62 (![X767 : $i, X768 : $i, X769 : $i]:
% 139.99/20.62 (~ (subset @ X767 @ X768) | ~ (in @ X769 @ X767) | (in @ X769 @ X768))),
% 139.99/20.62 inference('cnf', [status(esa)], [zf_stmt_14])).
% 139.99/20.62 thf(zip_derived_cl28005, plain, ($false),
% 139.99/20.62 inference('eprover', [status(thm)],
% 139.99/20.62 [zip_derived_cl238, zip_derived_cl240, zip_derived_cl237,
% 139.99/20.62 zip_derived_cl155, zip_derived_cl149, zip_derived_cl239,
% 139.99/20.62 zip_derived_cl158, zip_derived_cl383])).
% 139.99/20.62
% 139.99/20.62 % SZS output end Refutation
% 139.99/20.62
% 139.99/20.62
% 139.99/20.62 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s
% 139.99/20.62 % Terminating...
% 140.82/20.81 % Runner terminated.
% 140.82/20.84 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------