%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU743^1 : 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.osqknaPJDK true
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 2 04:56:04 PM UTC 2025
% Result : Theorem 86.64s 22.72s
% Output : Refutation 86.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/1.06 % Problem : SEU743^1 : TPTP v9.2.0. Released v3.7.0.
% 0.10/1.15 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.osqknaPJDK true
% 0.11/1.56 % Computer : n010.cluster.edu
% 0.11/1.56 % Model : x86_64 x86_64
% 0.11/1.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/1.56 % Memory : 8042.1875MB
% 0.11/1.56 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/1.56 % CPULimit : 300
% 0.11/1.56 % WCLimit : 300
% 0.11/1.56 % DateTime : Wed Oct 1 16:03:24 EDT 2025
% 0.11/1.57 % CPUTime :
% 0.11/1.57 % Running portfolio for 300 s
% 0.11/1.57 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/1.59 % Number of cores: 8
% 0.11/1.62 % Python version: Python 3.6.8
% 0.16/1.64 % Running in HO mode
% 0.30/2.09 % Total configuration time : 828
% 0.30/2.09 % Estimated wc time : 1656
% 0.30/2.09 % Estimated cpu time (8 cpus) : 207.0
% 0.31/2.17 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 1.62/2.47 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 1.74/2.50 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 1.74/2.51 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 1.76/2.52 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 1.76/2.54 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.76/2.56 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 1.76/2.57 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 86.64/22.72 % Solved by lams/40_c_ic.sh.
% 86.64/22.72 % done 2012 iterations in 19.840s
% 86.64/22.72 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 86.64/22.72 % SZS output start Refutation
% 86.64/22.72 thf(setadjoinAx_type, type, setadjoinAx: $o).
% 86.64/22.72 thf(notdexE_type, type, notdexE: $o).
% 86.64/22.72 thf(setukpairinjL2_type, type, setukpairinjL2: $o).
% 86.64/22.72 thf(doubleComplementI1_type, type, doubleComplementI1: $o).
% 86.64/22.72 thf(setunionAx_type, type, setunionAx: $o).
% 86.64/22.72 thf(setminusELneg_type, type, setminusELneg: $o).
% 86.64/22.72 thf(cartprodsndin_type, type, cartprodsndin: $o).
% 86.64/22.72 thf(ex1E1_type, type, ex1E1: $o).
% 86.64/22.72 thf(powersetE_type, type, powersetE: $o).
% 86.64/22.72 thf(omegaSAx_type, type, omegaSAx: $o).
% 86.64/22.72 thf(exuI1_type, type, exuI1: $o).
% 86.64/22.72 thf(exuI2_type, type, exuI2: $o).
% 86.64/22.72 thf(notequalI2_type, type, notequalI2: $o).
% 86.64/22.72 thf(setukpairinjL_type, type, setukpairinjL: $o).
% 86.64/22.72 thf(kpairiskpair_type, type, kpairiskpair: $o).
% 86.64/22.72 thf(upairsubunion_type, type, upairsubunion: $o).
% 86.64/22.72 thf(funcGraphProp3_type, type, funcGraphProp3: $o).
% 86.64/22.72 thf(cartprodmempaircEq_type, type, cartprodmempaircEq: $o).
% 86.64/22.72 thf(binintersectTERcontra_type, type, binintersectTERcontra: $o).
% 86.64/22.72 thf(powerset__Cong_type, type, powerset__Cong: $o).
% 86.64/22.72 thf(setminusILneg_type, type, setminusILneg: $o).
% 86.64/22.72 thf(wellorderingAx_type, type, wellorderingAx: $o).
% 86.64/22.72 thf(ksndpairEq_type, type, ksndpairEq: $o).
% 86.64/22.72 thf(funcGraphProp2_type, type, funcGraphProp2: $o).
% 86.64/22.72 thf(setadjoinSub2_type, type, setadjoinSub2: $o).
% 86.64/22.72 thf(binintersectSubset5_type, type, binintersectSubset5: $o).
% 86.64/22.72 thf(iftrue_type, type, iftrue: $o).
% 86.64/22.72 thf(upairinpowunion_type, type, upairinpowunion: $o).
% 86.64/22.72 thf(ifSingleton_type, type, ifSingleton: $o).
% 86.64/22.72 thf(doubleComplementSub2_type, type, doubleComplementSub2: $o).
% 86.64/22.72 thf(setoftrueEq_type, type, setoftrueEq: $o).
% 86.64/22.72 thf(funcImageSingleton_type, type, funcImageSingleton: $o).
% 86.64/22.72 thf(inIntersectImpInUnion2_type, type, inIntersectImpInUnion2: $o).
% 86.64/22.72 thf(dpsetconstrERa_type, type, dpsetconstrERa: $o).
% 86.64/22.72 thf(lamProp_type, type, lamProp: $o).
% 86.64/22.72 thf(cartprodpairmemEL_type, type, cartprodpairmemEL: $o).
% 86.64/22.72 thf(emptyset__Cong_type, type, emptyset__Cong: $o).
% 86.64/22.72 thf(sk__156_type, type, sk__156: $i).
% 86.64/22.72 thf(dpsetconstrER_type, type, dpsetconstrER: $o).
% 86.64/22.72 thf(sepInPowerset_type, type, sepInPowerset: $o).
% 86.64/22.72 thf(setukpairIR_type, type, setukpairIR: $o).
% 86.64/22.72 thf(setukpairinjR1_type, type, setukpairinjR1: $o).
% 86.64/22.72 thf(lam2p_type, type, lam2p: $o).
% 86.64/22.72 thf(kpair_type, type, kpair: $i > $i > $i).
% 86.64/22.72 thf(binunionE_type, type, binunionE: $o).
% 86.64/22.72 thf(setext_type, type, setext: $o).
% 86.64/22.72 thf(emptyinPowerset_type, type, emptyinPowerset: $o).
% 86.64/22.72 thf(ubforcartprodlem1_type, type, ubforcartprodlem1: $o).
% 86.64/22.72 thf(descr__Cong_type, type, descr__Cong: $o).
% 86.64/22.72 thf(kfstsingleton_type, type, kfstsingleton: $o).
% 86.64/22.72 thf(binintersectTELcontra_type, type, binintersectTELcontra: $o).
% 86.64/22.72 thf(doubleComplementEq_type, type, doubleComplementEq: $o).
% 86.64/22.72 thf(eqbreln_type, type, eqbreln: $o).
% 86.64/22.72 thf(binintersectSubset1_type, type, binintersectSubset1: $o).
% 86.64/22.72 thf(complementImpComplementIntersect_type, type, complementImpComplementIntersect:
% 86.64/22.72 $o).
% 86.64/22.72 thf(in_type, type, in: $i > $i > $o).
% 86.64/22.72 thf(binunionT_lem_type, type, binunionT_lem: $o).
% 86.64/22.72 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o).
% 86.64/22.72 thf(complementT_lem_type, type, complementT_lem: $o).
% 86.64/22.72 thf(binunion_type, type, binunion: $i > $i > $i).
% 86.64/22.72 thf(kpairsurjEq_type, type, kpairsurjEq: $o).
% 86.64/22.72 thf(setadjoinIR_type, type, setadjoinIR: $o).
% 86.64/22.72 thf(doubleComplementE1_type, type, doubleComplementE1: $o).
% 86.64/22.72 thf(beta1_type, type, beta1: $o).
% 86.64/22.72 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o).
% 86.64/22.72 thf(powersetTE1_type, type, powersetTE1: $o).
% 86.64/22.72 thf(symdiffI2_type, type, symdiffI2: $o).
% 86.64/22.72 thf(iftrueProp2_type, type, iftrueProp2: $o).
% 86.64/22.72 thf(upairset2IR_type, type, upairset2IR: $o).
% 86.64/22.72 thf(iffalseProp2_type, type, iffalseProp2: $o).
% 86.64/22.72 thf(subsetE_type, type, subsetE: $o).
% 86.64/22.72 thf(prop2set2propI_type, type, prop2set2propI: $o).
% 86.64/22.72 thf(dsetconstrEL_type, type, dsetconstrEL: $o).
% 86.64/22.72 thf(setbeta_type, type, setbeta: $o).
% 86.64/22.72 thf(eqinunit_type, type, eqinunit: $o).
% 86.64/22.72 thf(upairsetIL_type, type, upairsetIL: $o).
% 86.64/22.72 thf(powersetI1_type, type, powersetI1: $o).
% 86.64/22.72 thf(kfstpairEq_type, type, kfstpairEq: $o).
% 86.64/22.72 thf(binintersectSubset3_type, type, binintersectSubset3: $o).
% 86.64/22.72 thf(setminusIRneg_type, type, setminusIRneg: $o).
% 86.64/22.72 thf(ap2apEq1_type, type, ap2apEq1: $o).
% 86.64/22.72 thf(powersetAx_type, type, powersetAx: $o).
% 86.64/22.72 thf(binintersectSubset4_type, type, binintersectSubset4: $o).
% 86.64/22.72 thf(singletoninpowunion_type, type, singletoninpowunion: $o).
% 86.64/22.72 thf(binunionTIRcontra_type, type, binunionTIRcontra: $o).
% 86.64/22.72 thf(powersetI_type, type, powersetI: $o).
% 86.64/22.72 thf(cartprodmempair_type, type, cartprodmempair: $o).
% 86.64/22.72 thf(upairsetIR_type, type, upairsetIR: $o).
% 86.64/22.72 thf(lamp_type, type, lamp: $o).
% 86.64/22.72 thf(dpsetconstrEL1_type, type, dpsetconstrEL1: $o).
% 86.64/22.72 thf(inCongP_type, type, inCongP: $o).
% 86.64/22.72 thf(setadjoinSub_type, type, setadjoinSub: $o).
% 86.64/22.72 thf(exuE3e_type, type, exuE3e: $o).
% 86.64/22.72 thf(emptysetE_type, type, emptysetE: $o).
% 86.64/22.72 thf(binintersectSubset2_type, type, binintersectSubset2: $o).
% 86.64/22.72 thf(setunionI_type, type, setunionI: $o).
% 86.64/22.72 thf(sk__158_type, type, sk__158: $i).
% 86.64/22.72 thf(setunion__Cong_type, type, setunion__Cong: $o).
% 86.64/22.72 thf(prop2setI_type, type, prop2setI: $o).
% 86.64/22.72 thf(singletonsuniq_type, type, singletonsuniq: $o).
% 86.64/22.72 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o).
% 86.64/22.72 thf(setminusER_type, type, setminusER: $o).
% 86.64/22.72 thf(exuE2_type, type, exuE2: $o).
% 86.64/22.72 thf(emptyset_type, type, emptyset: $i).
% 86.64/22.72 thf(setukpairinjR11_type, type, setukpairinjR11: $o).
% 86.64/22.72 thf(ex1I_type, type, ex1I: $o).
% 86.64/22.72 thf(ex1E2_type, type, ex1E2: $o).
% 86.64/22.72 thf(setminus_type, type, setminus: $i > $i > $i).
% 86.64/22.72 thf(setukpairinjL1_type, type, setukpairinjL1: $o).
% 86.64/22.72 thf(powersetsubset_type, type, powersetsubset: $o).
% 86.64/22.72 thf(binunionTILcontra_type, type, binunionTILcontra: $o).
% 86.64/22.72 thf(subPowSU_type, type, subPowSU: $o).
% 86.64/22.72 thf(notequalI1_type, type, notequalI1: $o).
% 86.64/22.72 thf(contrasubsetT_type, type, contrasubsetT: $o).
% 86.64/22.72 thf(notinemptyset_type, type, notinemptyset: $o).
% 86.64/22.72 thf(lam2lamEq_type, type, lam2lamEq: $o).
% 86.64/22.72 thf(nonemptyI1_type, type, nonemptyI1: $o).
% 86.64/22.72 thf(subsetTrans_type, type, subsetTrans: $o).
% 86.64/22.72 thf(kpairp_type, type, kpairp: $o).
% 86.64/22.72 thf(setukpairinjR12_type, type, setukpairinjR12: $o).
% 86.64/22.72 thf(setminusI_type, type, setminusI: $o).
% 86.64/22.72 thf(binunionIL_type, type, binunionIL: $o).
% 86.64/22.72 thf(dpsetconstrSub_type, type, dpsetconstrSub: $o).
% 86.64/22.72 thf(setunionsingleton_type, type, setunionsingleton: $o).
% 86.64/22.72 thf(subsetE2_type, type, subsetE2: $o).
% 86.64/22.72 thf(singletonsswitch_type, type, singletonsswitch: $o).
% 86.64/22.72 thf(ubforcartprodlem3_type, type, ubforcartprodlem3: $o).
% 86.64/22.72 thf(beta2_type, type, beta2: $o).
% 86.64/22.72 thf(dpsetconstrI_type, type, dpsetconstrI: $o).
% 86.64/22.72 thf(setextsub_type, type, setextsub: $o).
% 86.64/22.72 thf(binunionLsub_type, type, binunionLsub: $o).
% 86.64/22.72 thf(setunionsingleton1_type, type, setunionsingleton1: $o).
% 86.64/22.72 thf(binintersect_type, type, binintersect: $i > $i > $i).
% 86.64/22.72 thf(iftrueorfalse_type, type, iftrueorfalse: $o).
% 86.64/22.72 thf(emptysetsubset_type, type, emptysetsubset: $o).
% 86.64/22.72 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o).
% 86.64/22.72 thf(cartprodpairsurjEq_type, type, cartprodpairsurjEq: $o).
% 86.64/22.72 thf(setOfPairsIsBReln_type, type, setOfPairsIsBReln: $o).
% 86.64/22.72 thf(setunionE_type, type, setunionE: $o).
% 86.64/22.72 thf(ksndsingleton_type, type, ksndsingleton: $o).
% 86.64/22.72 thf(setminusSubset1_type, type, setminusSubset1: $o).
% 86.64/22.72 thf(powersetT_lem_type, type, powersetT_lem: $o).
% 86.64/22.72 thf(emptyinunitempty_type, type, emptyinunitempty: $o).
% 86.64/22.72 thf(binunionIR_type, type, binunionIR: $o).
% 86.64/22.72 thf(theeq_type, type, theeq: $o).
% 86.64/22.72 thf(setadjoinE_type, type, setadjoinE: $o).
% 86.64/22.72 thf(doubleComplementSub1_type, type, doubleComplementSub1: $o).
% 86.64/22.72 thf(infuncsetfunc_type, type, infuncsetfunc: $o).
% 86.64/22.72 thf(ap2apEq2_type, type, ap2apEq2: $o).
% 86.64/22.72 thf(ap2p_type, type, ap2p: $o).
% 86.64/22.72 thf(setadjoinIL_type, type, setadjoinIL: $o).
% 86.64/22.72 thf(cartprodsndpairEq_type, type, cartprodsndpairEq: $o).
% 86.64/22.72 thf(exuE1_type, type, exuE1: $o).
% 86.64/22.72 thf(ubforcartprodlem2_type, type, ubforcartprodlem2: $o).
% 86.64/22.72 thf(binintersectRsub_type, type, binintersectRsub: $o).
% 86.64/22.72 thf(setminusLsub_type, type, setminusLsub: $o).
% 86.64/22.72 thf(funcextLem_type, type, funcextLem: $o).
% 86.64/22.72 thf(setukpairinjR_type, type, setukpairinjR: $o).
% 86.64/22.72 thf(notinsingleton_type, type, notinsingleton: $o).
% 86.64/22.72 thf(inIntersectImpInIntersectUnions_type, type, inIntersectImpInIntersectUnions:
% 86.64/22.72 $o).
% 86.64/22.72 thf(eqimpsubset2_type, type, eqimpsubset2: $o).
% 86.64/22.72 thf(exuEu_type, type, exuEu: $o).
% 86.64/22.72 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o).
% 86.64/22.72 thf(upairsetE_type, type, upairsetE: $o).
% 86.64/22.72 thf(omega0Ax_type, type, omega0Ax: $o).
% 86.64/22.72 thf(subsetTI_type, type, subsetTI: $o).
% 86.64/22.72 thf(notsubsetI_type, type, notsubsetI: $o).
% 86.64/22.72 thf(contraSubsetComplement_type, type, contraSubsetComplement: $o).
% 86.64/22.72 thf(iffalseProp1_type, type, iffalseProp1: $o).
% 86.64/22.72 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o).
% 86.64/22.72 thf(setextAx_type, type, setextAx: $o).
% 86.64/22.72 thf(cartprodpairmemER_type, type, cartprodpairmemER: $o).
% 86.64/22.72 thf(powersetE1_type, type, powersetE1: $o).
% 86.64/22.72 thf(bs114d_type, type, bs114d: $o).
% 86.64/22.72 thf(contrasubsetT3_type, type, contrasubsetT3: $o).
% 86.64/22.72 thf(noeltsimpempty_type, type, noeltsimpempty: $o).
% 86.64/22.72 thf(complementTcontraSubset_type, type, complementTcontraSubset: $o).
% 86.64/22.72 thf(ifp_type, type, ifp: $o).
% 86.64/22.72 thf(inIntersectImpInUnion_type, type, inIntersectImpInUnion: $o).
% 86.64/22.72 thf(powersetTI1_type, type, powersetTI1: $o).
% 86.64/22.72 thf(binintersectLsub_type, type, binintersectLsub: $o).
% 86.64/22.72 thf(subsetI1_type, type, subsetI1: $o).
% 86.64/22.72 thf(symdiffE_type, type, symdiffE: $o).
% 86.64/22.72 thf(descrp_type, type, descrp: $o).
% 86.64/22.72 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o).
% 86.64/22.72 thf(foundationAx_type, type, foundationAx: $o).
% 86.64/22.72 thf(emptysetAx_type, type, emptysetAx: $o).
% 86.64/22.72 thf(emptyI_type, type, emptyI: $o).
% 86.64/22.72 thf(setadjoinOr_type, type, setadjoinOr: $o).
% 86.64/22.72 thf(eta2_type, type, eta2: $o).
% 86.64/22.72 thf(binintersectEL_type, type, binintersectEL: $o).
% 86.64/22.72 thf(emptyE1_type, type, emptyE1: $o).
% 86.64/22.72 thf(emptyInPowerset_type, type, emptyInPowerset: $o).
% 86.64/22.72 thf(complementTI1_type, type, complementTI1: $o).
% 86.64/22.72 thf(vacuousDall_type, type, vacuousDall: $o).
% 86.64/22.72 thf(dsetconstrER_type, type, dsetconstrER: $o).
% 86.64/22.72 thf(binintersectI_type, type, binintersectI: $o).
% 86.64/22.72 thf(funcext_type, type, funcext: $o).
% 86.64/22.72 thf(funcGraphProp4_type, type, funcGraphProp4: $o).
% 86.64/22.72 thf(cartprodpairin_type, type, cartprodpairin: $o).
% 86.64/22.72 thf(cartprodmempair1_type, type, cartprodmempair1: $o).
% 86.64/22.72 thf(brelnall2_type, type, brelnall2: $o).
% 86.64/22.72 thf(setextT_type, type, setextT: $o).
% 86.64/22.72 thf(ex1I2_type, type, ex1I2: $o).
% 86.64/22.72 thf(symdiffI1_type, type, symdiffI1: $o).
% 86.64/22.72 thf(sk__160_type, type, sk__160: $i > $i > $i).
% 86.64/22.72 thf(setukpairinjR2_type, type, setukpairinjR2: $o).
% 86.64/22.72 thf(dpsetconstrEL2_type, type, dpsetconstrEL2: $o).
% 86.64/22.72 thf(theprop_type, type, theprop: $o).
% 86.64/22.72 thf(subsetI2_type, type, subsetI2: $o).
% 86.64/22.72 thf(complementInPowersetComplementIntersect_type, type, complementInPowersetComplementIntersect:
% 86.64/22.72 $o).
% 86.64/22.72 thf(setminusT_lem_type, type, setminusT_lem: $o).
% 86.64/22.72 thf(symdiffIneg1_type, type, symdiffIneg1: $o).
% 86.64/22.72 thf(zip_tseitin_0_type, type, zip_tseitin_0: $i > $i > $i > $o).
% 86.64/22.72 thf(setminusERneg_type, type, setminusERneg: $o).
% 86.64/22.72 thf(symdiffIneg2_type, type, symdiffIneg2: $o).
% 86.64/22.72 thf(omega__Cong_type, type, omega__Cong: $o).
% 86.64/22.72 thf(subsetRefl_type, type, subsetRefl: $o).
% 86.64/22.72 thf(uniqinunit_type, type, uniqinunit: $o).
% 86.64/22.72 thf(sk__157_type, type, sk__157: $i).
% 86.64/22.72 thf(complementSubsetComplementIntersect_type, type, complementSubsetComplementIntersect:
% 86.64/22.72 $o).
% 86.64/22.72 thf(setminusSubset2_type, type, setminusSubset2: $o).
% 86.64/22.72 thf(prop2setE_type, type, prop2setE: $o).
% 86.64/22.72 thf(binunionEcases_type, type, binunionEcases: $o).
% 86.64/22.72 thf(funcinfuncset_type, type, funcinfuncset: $o).
% 86.64/22.72 thf(complementTE1_type, type, complementTE1: $o).
% 86.64/22.72 thf(nonemptyI_type, type, nonemptyI: $o).
% 86.64/22.72 thf(app_type, type, app: $o).
% 86.64/22.72 thf(disjointsetsI1_type, type, disjointsetsI1: $o).
% 86.64/22.72 thf(exuE3u_type, type, exuE3u: $o).
% 86.64/22.72 thf(eta1_type, type, eta1: $o).
% 86.64/22.72 thf(setminusEL_type, type, setminusEL: $o).
% 86.64/22.72 thf(cartprodfstin_type, type, cartprodfstin: $o).
% 86.64/22.72 thf(setunionsingleton2_type, type, setunionsingleton2: $o).
% 86.64/22.72 thf(sepSubset_type, type, sepSubset: $o).
% 86.64/22.72 thf(complementTnotintersectT_type, type, complementTnotintersectT: $o).
% 86.64/22.72 thf(upairset2E_type, type, upairset2E: $o).
% 86.64/22.72 thf(eqimpsubset1_type, type, eqimpsubset1: $o).
% 86.64/22.72 thf(exuI3_type, type, exuI3: $o).
% 86.64/22.72 thf(cartprodfstpairEq_type, type, cartprodfstpairEq: $o).
% 86.64/22.72 thf(apProp_type, type, apProp: $o).
% 86.64/22.72 thf(notdallE_type, type, notdallE: $o).
% 86.64/22.72 thf(iftrueProp1_type, type, iftrueProp1: $o).
% 86.64/22.72 thf(binintersectER_type, type, binintersectER: $o).
% 86.64/22.72 thf(brelnall1_type, type, brelnall1: $o).
% 86.64/22.72 thf(powerset_type, type, powerset: $i > $i).
% 86.64/22.72 thf(dsetconstrI_type, type, dsetconstrI: $o).
% 86.64/22.72 thf(funcGraphProp1_type, type, funcGraphProp1: $o).
% 86.64/22.72 thf(binintersectT_lem_type, type, binintersectT_lem: $o).
% 86.64/22.72 thf(setadjoin_type, type, setadjoin: $i > $i > $i).
% 86.64/22.72 thf(exu__Cong_type, type, exu__Cong: $o).
% 86.64/22.72 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o).
% 86.64/22.72 thf(contrasubsetT2_type, type, contrasubsetT2: $o).
% 86.64/22.72 thf(secondinupair_type, type, secondinupair: $o).
% 86.64/22.72 thf(singletonprop_type, type, singletonprop: $o).
% 86.64/22.72 thf(singletonsubset_type, type, singletonsubset: $o).
% 86.64/22.72 thf(contrasubsetT1_type, type, contrasubsetT1: $o).
% 86.64/22.72 thf(singletoninpowerset_type, type, singletoninpowerset: $o).
% 86.64/22.72 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o).
% 86.64/22.72 thf(replAx_type, type, replAx: $o).
% 86.64/22.72 thf(upairequniteq_type, type, upairequniteq: $o).
% 86.64/22.72 thf(nonemptyE1_type, type, nonemptyE1: $o).
% 86.64/22.72 thf(omegaIndAx_type, type, omegaIndAx: $o).
% 86.64/22.72 thf(setukpairIL_type, type, setukpairIL: $o).
% 86.64/22.72 thf(setunionE2_type, type, setunionE2: $o).
% 86.64/22.72 thf(inPowerset_type, type, inPowerset: $o).
% 86.64/22.72 thf(iffalse_type, type, iffalse: $o).
% 86.64/22.72 thf(funcext2_type, type, funcext2: $o).
% 86.64/22.72 thf(subset_type, type, subset: $i > $i > $o).
% 86.64/22.72 thf(subbreln_type, type, subbreln: $o).
% 86.64/22.72 thf(in__Cong_type, type, in__Cong: $o).
% 86.64/22.72 thf(binunionRsub_type, type, binunionRsub: $o).
% 86.64/22.72 thf(subset2powerset_type, type, subset2powerset: $o).
% 86.64/22.72 thf(inIntersectImpInIntersectUnions, axiom, inIntersectImpInIntersectUnions =
% 86.64/22.72 (![A:$i,X:$i]:
% 86.64/22.72 ( ( in @ X @ ( powerset @ A ) ) =>
% 86.64/22.72 ( ![Y:$i]:
% 86.64/22.72 ( ( in @ Y @ ( powerset @ A ) ) =>
% 86.64/22.72 ( ![Z:$i]:
% 86.64/22.72 ( ( in @ Z @ ( powerset @ A ) ) =>
% 86.64/22.72 ( ![Xx:$i]:
% 86.64/22.72 ( ( in @ Xx @ A ) =>
% 86.64/22.72 ( ( in @ Xx @ ( binintersect @ X @ Y ) ) =>
% 86.64/22.72 ( in @
% 86.64/22.72 Xx @
% 86.64/22.72 ( binintersect @
% 86.64/22.72 ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ) ))).
% 86.64/22.72 thf('0', plain,
% 86.64/22.72 (( inIntersectImpInIntersectUnions ) =
% 86.64/22.72 ( ![X4:$i,X6:$i]:
% 86.64/22.72 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 86.64/22.72 ( ![X8:$i]:
% 86.64/22.72 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 86.64/22.72 ( ![X10:$i]:
% 86.64/22.72 ( ( in @ X10 @ ( powerset @ X4 ) ) =>
% 86.64/22.72 ( ![X12:$i]:
% 86.64/22.72 ( ( in @ X12 @ X4 ) =>
% 86.64/22.72 ( ( in @ X12 @ ( binintersect @ X6 @ X8 ) ) =>
% 86.64/22.72 ( in @
% 86.64/22.72 X12 @
% 86.64/22.72 ( binintersect @
% 86.64/22.72 ( binunion @ X6 @ X10 ) @ ( binunion @ X8 @ X10 ) ) ) ) ) ) ) ) ) ) ) )),
% 86.64/22.72 define([status(thm)])).
% 86.64/22.72 thf(inIntersectImpInUnion2, axiom, inIntersectImpInUnion2 =
% 86.64/22.72 (![A:$i,X:$i]:
% 86.64/22.72 ( ( in @ X @ ( powerset @ A ) ) =>
% 86.64/22.72 ( ![Y:$i]:
% 86.64/22.72 ( ( in @ Y @ ( powerset @ A ) ) =>
% 86.64/22.72 ( ![Z:$i]:
% 86.64/22.72 ( ( in @ Z @ ( powerset @ A ) ) =>
% 86.64/22.72 ( ![Xx:$i]:
% 86.64/22.72 ( ( in @ Xx @ A ) =>
% 86.64/22.72 ( ( in @ Xx @ ( binintersect @ X @ Y ) ) =>
% 86.64/22.72 ( in @ Xx @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ))).
% 86.64/22.72 thf('1', plain,
% 86.64/22.72 (( inIntersectImpInUnion2 ) =
% 86.64/22.72 ( ![X4:$i,X6:$i]:
% 86.64/22.72 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 86.64/22.72 ( ![X8:$i]:
% 86.64/22.72 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 86.64/22.72 ( ![X10:$i]:
% 86.64/22.72 ( ( in @ X10 @ ( powerset @ X4 ) ) =>
% 86.64/22.72 ( ![X12:$i]:
% 86.64/22.72 ( ( in @ X12 @ X4 ) =>
% 86.64/22.72 ( ( in @ X12 @ ( binintersect @ X6 @ X8 ) ) =>
% 86.64/22.72 ( in @ X12 @ ( binunion @ X8 @ X10 ) ) ) ) ) ) ) ) ) ) )),
% 86.64/22.72 define([status(thm)])).
% 86.64/22.72 thf(inIntersectImpInUnion, axiom, inIntersectImpInUnion =
% 86.64/22.72 (![A:$i,X:$i]:
% 86.64/22.72 ( ( in @ X @ ( powerset @ A ) ) =>
% 86.64/22.72 ( ![Y:$i]:
% 86.64/22.72 ( ( in @ Y @ ( powerset @ A ) ) =>
% 86.64/22.72 ( ![Z:$i]:
% 86.64/22.72 ( ( in @ Z @ ( powerset @ A ) ) =>
% 86.64/22.72 ( ![Xx:$i]:
% 86.64/22.72 ( ( in @ Xx @ A ) =>
% 86.64/22.72 ( ( in @ Xx @ ( binintersect @ X @ Y ) ) =>
% 86.64/22.72 ( in @ Xx @ ( binunion @ X @ Z ) ) ) ) ) ) ) ) ) ))).
% 86.64/22.72 thf('2', plain,
% 86.64/22.72 (( inIntersectImpInUnion ) =
% 86.64/22.72 ( ![X4:$i,X6:$i]:
% 86.64/22.72 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 86.64/22.72 ( ![X8:$i]:
% 86.64/22.72 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 86.64/22.72 ( ![X10:$i]:
% 86.64/22.72 ( ( in @ X10 @ ( powerset @ X4 ) ) =>
% 86.64/22.72 ( ![X12:$i]:
% 86.64/22.72 ( ( in @ X12 @ X4 ) =>
% 86.64/22.72 ( ( in @ X12 @ ( binintersect @ X6 @ X8 ) ) =>
% 86.64/22.72 ( in @ X12 @ ( binunion @ X6 @ X10 ) ) ) ) ) ) ) ) ) ) )),
% 86.64/22.72 define([status(thm)])).
% 86.64/22.72 thf(binunionTIRcontra, axiom, binunionTIRcontra =
% 86.64/22.72 (![A:$i,X:$i]:
% 86.64/22.72 ( ( in @ X @ ( powerset @ A ) ) =>
% 86.64/22.72 ( ![Y:$i]:
% 86.64/22.72 ( ( in @ Y @ ( powerset @ A ) ) =>
% 86.64/22.72 ( ![Xx:$i]:
% 86.64/22.72 ( ( in @ Xx @ A ) =>
% 86.64/22.72 ( ( ~( in @ Xx @ ( binunion @ X @ Y ) ) ) =>
% 86.64/22.72 ( ~( in @ Xx @ Y ) ) ) ) ) ) ) ))).
% 86.64/22.72 thf('3', plain,
% 86.64/22.72 (( binunionTIRcontra ) =
% 86.64/22.72 ( ![X4:$i,X6:$i]:
% 86.64/22.72 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 86.64/22.72 ( ![X8:$i]:
% 86.64/22.72 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 86.64/22.72 ( ![X10:$i]:
% 86.64/22.72 ( ( in @ X10 @ X4 ) =>
% 86.64/22.72 ( ( ~( in @ X10 @ ( binunion @ X6 @ X8 ) ) ) =>
% 86.64/22.72 ( ~( in @ X10 @ X8 ) ) ) ) ) ) ) ) )),
% 86.64/22.72 define([status(thm)])).
% 86.64/22.72 thf(binunionTILcontra, axiom, binunionTILcontra =
% 86.64/22.72 (![A:$i,X:$i]:
% 86.64/22.72 ( ( in @ X @ ( powerset @ A ) ) =>
% 86.64/22.72 ( ![Y:$i]:
% 86.64/22.72 ( ( in @ Y @ ( powerset @ A ) ) =>
% 86.64/22.72 ( ![Xx:$i]:
% 86.64/22.72 ( ( in @ Xx @ A ) =>
% 86.64/22.72 ( ( ~( in @ Xx @ ( binunion @ X @ Y ) ) ) =>
% 86.64/22.72 ( ~( in @ Xx @ X ) ) ) ) ) ) ) ))).
% 86.64/22.72 thf('4', plain,
% 86.64/22.72 (( binunionTILcontra ) =
% 86.64/22.72 ( ![X4:$i,X6:$i]:
% 86.64/22.72 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 86.64/22.72 ( ![X8:$i]:
% 86.64/22.72 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 86.64/22.72 ( ![X10:$i]:
% 86.64/22.72 ( ( in @ X10 @ X4 ) =>
% 86.64/22.72 ( ( ~( in @ X10 @ ( binunion @ X6 @ X8 ) ) ) =>
% 86.64/22.72 ( ~( in @ X10 @ X6 ) ) ) ) ) ) ) ) )),
% 86.64/22.72 define([status(thm)])).
% 86.64/22.72 thf(complementInPowersetComplementIntersect, axiom,
% 86.64/22.72 complementInPowersetComplementIntersect =
% 86.64/22.72 (![A:$i,X:$i]:
% 86.64/22.72 ( ( in @ X @ ( powerset @ A ) ) =>
% 86.64/22.72 ( ![Y:$i]:
% 86.64/22.72 ( ( in @ Y @ ( powerset @ A ) ) =>
% 86.64/22.72 ( in @
% 86.64/22.72 ( setminus @ A @ X ) @
% 86.64/22.72 ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ))).
% 86.64/22.72 thf('5', plain,
% 86.64/22.72 (( complementInPowersetComplementIntersect ) =
% 86.64/22.72 ( ![X4:$i,X6:$i]:
% 86.64/22.72 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 86.64/22.72 ( ![X8:$i]:
% 86.64/22.72 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 86.64/22.72 ( in @
% 86.64/22.72 ( setminus @ X4 @ X6 ) @
% 86.64/22.72 ( powerset @ ( setminus @ X4 @ ( binintersect @ X6 @ X8 ) ) ) ) ) ) ) )),
% 86.64/22.72 define([status(thm)])).
% 86.64/22.72 thf(complementSubsetComplementIntersect, axiom,
% 86.64/22.72 complementSubsetComplementIntersect =
% 86.64/22.72 (![A:$i,X:$i]:
% 86.64/22.72 ( ( in @ X @ ( powerset @ A ) ) =>
% 86.64/22.72 ( ![Y:$i]:
% 86.64/22.72 ( ( in @ Y @ ( powerset @ A ) ) =>
% 86.64/22.72 ( subset @
% 86.64/22.72 ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ))).
% 86.64/22.72 thf('6', plain,
% 86.64/22.72 (( complementSubsetComplementIntersect ) =
% 86.64/22.72 ( ![X4:$i,X6:$i]:
% 86.64/22.72 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 86.64/22.72 ( ![X8:$i]:
% 86.64/22.72 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 86.64/22.72 ( subset @
% 86.64/22.72 ( setminus @ X4 @ X6 ) @
% 86.64/22.72 ( setminus @ X4 @ ( binintersect @ X6 @ X8 ) ) ) ) ) ) )),
% 86.64/22.72 define([status(thm)])).
% 86.64/22.72 thf(complementImpComplementIntersect, axiom,
% 86.64/22.72 complementImpComplementIntersect =
% 86.64/22.72 (![A:$i,X:$i]:
% 86.64/22.72 ( ( in @ X @ ( powerset @ A ) ) =>
% 86.64/22.72 ( ![Y:$i]:
% 86.64/22.72 ( ( in @ Y @ ( powerset @ A ) ) =>
% 86.64/22.72 ( ![Xx:$i]:
% 86.64/22.72 ( ( in @ Xx @ A ) =>
% 86.64/22.72 ( ( in @ Xx @ ( setminus @ A @ X ) ) =>
% 86.64/22.72 ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ))).
% 86.64/22.72 thf('7', plain,
% 86.64/22.72 (( complementImpComplementIntersect ) =
% 86.64/22.72 ( ![X4:$i,X6:$i]:
% 86.64/22.72 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 86.64/22.72 ( ![X8:$i]:
% 86.64/22.72 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 86.64/22.72 ( ![X10:$i]:
% 86.64/22.72 ( ( in @ X10 @ X4 ) =>
% 86.64/22.72 ( ( in @ X10 @ ( setminus @ X4 @ X6 ) ) =>
% 86.64/22.72 ( in @
% 86.64/22.72 X10 @ ( setminus @ X4 @ ( binintersect @ X6 @ X8 ) ) ) ) ) ) ) ) ) )),
% 86.64/22.72 define([status(thm)])).
% 86.64/22.72 thf(complementTnotintersectT, axiom, complementTnotintersectT =
% 86.64/22.72 (![A:$i,X:$i]:
% 86.64/22.72 ( ( in @ X @ ( powerset @ A ) ) =>
% 86.64/22.72 ( ![Y:$i]:
% 86.64/22.72 ( ( in @ Y @ ( powerset @ A ) ) =>
% 86.64/22.72 ( ![Xx:$i]:
% 86.64/22.72 ( ( in @ Xx @ A ) =>
% 86.64/22.72 ( ( in @ Xx @ ( setminus @ A @ X ) ) =>
% 86.64/22.72 ( ~( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ))).
% 86.64/22.72 thf('8', plain,
% 86.64/22.72 (( complementTnotintersectT ) =
% 86.64/22.72 ( ![X4:$i,X6:$i]:
% 86.64/22.72 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 86.64/22.72 ( ![X8:$i]:
% 86.64/22.72 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 86.64/22.72 ( ![X10:$i]:
% 86.64/22.72 ( ( in @ X10 @ X4 ) =>
% 86.64/22.72 ( ( in @ X10 @ ( setminus @ X4 @ X6 ) ) =>
% 86.64/22.72 ( ~( in @ X10 @ ( binintersect @ X6 @ X8 ) ) ) ) ) ) ) ) ) )),
% 86.64/22.72 define([status(thm)])).
% 86.64/22.72 thf(binintersectTERcontra, axiom, binintersectTERcontra =
% 86.64/22.72 (![A:$i,X:$i]:
% 86.64/22.72 ( ( in @ X @ ( powerset @ A ) ) =>
% 86.64/22.72 ( ![Y:$i]:
% 86.64/22.72 ( ( in @ Y @ ( powerset @ A ) ) =>
% 86.64/22.72 ( ![Xx:$i]:
% 86.64/22.72 ( ( in @ Xx @ A ) =>
% 86.64/22.72 ( ( ~( in @ Xx @ Y ) ) =>
% 86.64/22.72 ( ~( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ))).
% 86.64/22.72 thf('9', plain,
% 86.64/22.72 (( binintersectTERcontra ) =
% 86.64/22.72 ( ![X4:$i,X6:$i]:
% 86.64/22.72 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 86.64/22.72 ( ![X8:$i]:
% 86.64/22.72 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 86.64/22.72 ( ![X10:$i]:
% 86.64/22.72 ( ( in @ X10 @ X4 ) =>
% 86.64/22.72 ( ( ~( in @ X10 @ X8 ) ) =>
% 86.64/22.72 ( ~( in @ X10 @ ( binintersect @ X6 @ X8 ) ) ) ) ) ) ) ) ) )),
% 86.64/22.72 define([status(thm)])).
% 86.64/22.72 thf(binintersectTELcontra, axiom, binintersectTELcontra =
% 86.64/22.72 (![A:$i,X:$i]:
% 86.64/22.72 ( ( in @ X @ ( powerset @ A ) ) =>
% 86.64/22.72 ( ![Y:$i]:
% 86.64/22.72 ( ( in @ Y @ ( powerset @ A ) ) =>
% 86.64/22.72 ( ![Xx:$i]:
% 86.64/22.72 ( ( in @ Xx @ A ) =>
% 86.64/22.72 ( ( ~( in @ Xx @ X ) ) =>
% 86.64/22.72 ( ~( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ))).
% 86.64/22.72 thf('10', plain,
% 86.64/22.72 (( binintersectTELcontra ) =
% 86.64/22.72 ( ![X4:$i,X6:$i]:
% 86.64/22.72 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 86.64/22.72 ( ![X8:$i]:
% 86.64/22.72 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 86.64/22.72 ( ![X10:$i]:
% 86.64/22.72 ( ( in @ X10 @ X4 ) =>
% 86.64/22.72 ( ( ~( in @ X10 @ X6 ) ) =>
% 86.64/22.72 ( ~( in @ X10 @ ( binintersect @ X6 @ X8 ) ) ) ) ) ) ) ) ) )),
% 86.64/22.72 define([status(thm)])).
% 86.64/22.72 thf(powersetTE1, axiom, powersetTE1 =
% 86.64/22.72 (![A:$i,X:$i]:
% 86.64/22.72 ( ( in @ X @ ( powerset @ A ) ) =>
% 86.64/22.72 ( ![Y:$i]:
% 86.64/22.72 ( ( in @ Y @ ( powerset @ A ) ) =>
% 86.64/22.72 ( ![Xx:$i]:
% 86.64/22.72 ( ( in @ Xx @ A ) =>
% 86.64/22.72 ( ( in @ X @ ( powerset @ Y ) ) =>
% 86.64/22.72 ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) ) ) ) ))).
% 86.64/22.72 thf('11', plain,
% 86.64/22.72 (( powersetTE1 ) =
% 86.64/22.72 ( ![X4:$i,X6:$i]:
% 86.64/22.72 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 86.64/22.72 ( ![X8:$i]:
% 86.64/22.72 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 86.64/22.72 ( ![X10:$i]:
% 86.64/22.72 ( ( in @ X10 @ X4 ) =>
% 86.64/22.72 ( ( in @ X6 @ ( powerset @ X8 ) ) =>
% 86.64/22.72 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) ) ) ) ) )),
% 86.64/22.72 define([status(thm)])).
% 86.64/22.72 thf(powersetTI1, axiom, powersetTI1 =
% 86.64/22.72 (![A:$i,X:$i]:
% 86.64/22.72 ( ( in @ X @ ( powerset @ A ) ) =>
% 86.64/22.72 ( ![Y:$i]:
% 86.64/22.72 ( ( in @ Y @ ( powerset @ A ) ) =>
% 86.64/22.72 ( ( ![Xx:$i]:
% 86.64/22.72 ( ( in @ Xx @ A ) => ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) =>
% 86.64/22.72 ( in @ X @ ( powerset @ Y ) ) ) ) ) ))).
% 86.64/22.72 thf('12', plain,
% 86.64/22.72 (( powersetTI1 ) =
% 86.64/22.72 ( ![X4:$i,X6:$i]:
% 86.64/22.72 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 86.64/22.72 ( ![X8:$i]:
% 86.64/22.72 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 86.64/22.72 ( ( ![X10:$i]:
% 86.64/22.72 ( ( in @ X10 @ X4 ) =>
% 86.64/22.72 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) =>
% 86.64/22.72 ( in @ X6 @ ( powerset @ X8 ) ) ) ) ) ) )),
% 86.64/22.72 define([status(thm)])).
% 86.64/22.72 thf(setextT, axiom, setextT =
% 86.64/22.72 (![A:$i,X:$i]:
% 86.64/22.72 ( ( in @ X @ ( powerset @ A ) ) =>
% 86.64/22.72 ( ![Y:$i]:
% 86.64/22.72 ( ( in @ Y @ ( powerset @ A ) ) =>
% 86.64/22.72 ( ( ![Xx:$i]:
% 86.64/22.72 ( ( in @ Xx @ A ) => ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) =>
% 86.64/22.72 ( ( ![Xx:$i]:
% 86.64/22.72 ( ( in @ Xx @ A ) => ( ( in @ Xx @ Y ) => ( in @ Xx @ X ) ) ) ) =>
% 86.64/22.72 ( ( X ) = ( Y ) ) ) ) ) ) ))).
% 86.64/22.72 thf('13', plain,
% 86.64/22.72 (( setextT ) =
% 86.64/22.72 ( ![X4:$i,X6:$i]:
% 86.64/22.72 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 86.64/22.72 ( ![X8:$i]:
% 86.64/22.72 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 86.64/22.72 ( ( ![X10:$i]:
% 86.64/22.72 ( ( in @ X10 @ X4 ) =>
% 86.64/22.72 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) =>
% 86.64/22.72 ( ( ![X12:$i]:
% 86.64/22.72 ( ( in @ X12 @ X4 ) =>
% 86.64/22.72 ( ( in @ X12 @ X8 ) => ( in @ X12 @ X6 ) ) ) ) =>
% 86.64/22.72 ( ( X6 ) = ( X8 ) ) ) ) ) ) ) )),
% 86.64/22.72 define([status(thm)])).
% 86.64/22.72 thf(powersetT_lem, axiom, powersetT_lem =
% 86.64/22.72 (![A:$i,X:$i]:
% 86.64/22.72 ( ( in @ X @ ( powerset @ A ) ) =>
% 86.64/22.72 ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ))).
% 86.64/22.72 thf('14', plain,
% 86.64/22.72 (( powersetT_lem ) =
% 86.64/22.72 ( ![X4:$i,X6:$i]:
% 86.64/22.72 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 86.64/22.72 ( in @ ( powerset @ X6 ) @ ( powerset @ ( powerset @ X4 ) ) ) ) )),
% 86.64/22.72 define([status(thm)])).
% 86.64/22.72 thf(binunionT_lem, axiom, binunionT_lem =
% 86.64/22.72 (![A:$i,X:$i]:
% 86.64/22.72 ( ( in @ X @ ( powerset @ A ) ) =>
% 86.64/22.72 ( ![Y:$i]:
% 86.64/22.72 ( ( in @ Y @ ( powerset @ A ) ) =>
% 86.64/22.72 ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ))).
% 86.64/22.72 thf('15', plain,
% 86.64/22.72 (( binunionT_lem ) =
% 86.64/22.72 ( ![X4:$i,X6:$i]:
% 86.64/22.72 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 86.64/22.72 ( ![X8:$i]:
% 86.64/22.72 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 86.64/22.72 ( in @ ( binunion @ X6 @ X8 ) @ ( powerset @ X4 ) ) ) ) ) )),
% 86.64/22.72 define([status(thm)])).
% 86.64/22.72 thf(binintersectT_lem, axiom, binintersectT_lem =
% 86.64/22.72 (![A:$i,X:$i]:
% 86.64/22.72 ( ( in @ X @ ( powerset @ A ) ) =>
% 86.64/22.72 ( ![Y:$i]:
% 86.64/22.72 ( ( in @ Y @ ( powerset @ A ) ) =>
% 86.64/22.72 ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ))).
% 86.64/22.72 thf('16', plain,
% 86.64/22.72 (( binintersectT_lem ) =
% 86.64/22.72 ( ![X4:$i,X6:$i]:
% 86.64/22.72 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 86.64/22.72 ( ![X8:$i]:
% 86.64/22.72 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 86.64/22.72 ( in @ ( binintersect @ X6 @ X8 ) @ ( powerset @ X4 ) ) ) ) ) )),
% 86.64/22.72 define([status(thm)])).
% 86.64/22.72 thf(ubforcartprodlem3, axiom, ubforcartprodlem3 =
% 86.64/22.72 (![A:$i,B:$i,Xx:$i]:
% 86.64/22.72 ( ( in @ Xx @ A ) =>
% 86.64/22.72 ( ![Xy:$i]:
% 86.64/22.72 ( ( in @ Xy @ B ) =>
% 86.64/22.72 ( in @
% 86.64/22.72 ( kpair @ Xx @ Xy ) @
% 86.64/22.72 ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ))).
% 86.64/22.72 thf('17', plain,
% 86.64/22.72 (( ubforcartprodlem3 ) =
% 86.64/22.72 ( ![X4:$i,X6:$i,X8:$i]:
% 86.64/22.72 ( ( in @ X8 @ X4 ) =>
% 86.64/22.72 ( ![X10:$i]:
% 86.64/22.72 ( ( in @ X10 @ X6 ) =>
% 86.64/22.72 ( in @
% 86.64/22.72 ( kpair @ X8 @ X10 ) @
% 86.64/22.72 ( powerset @ ( powerset @ ( binunion @ X4 @ X6 ) ) ) ) ) ) ) )),
% 86.64/22.72 define([status(thm)])).
% 86.64/22.72 thf(ubforcartprodlem2, axiom, ubforcartprodlem2 =
% 86.64/22.72 (![A:$i,B:$i,Xx:$i]:
% 86.64/22.72 ( ( in @ Xx @ A ) =>
% 86.64/22.72 ( ![Xy:$i]:
% 86.64/22.72 ( ( in @ Xy @ B ) =>
% 86.64/22.72 ( in @
% 86.64/22.72 ( setadjoin @
% 86.64/22.72 ( setadjoin @ Xx @ emptyset ) @
% 86.64/22.72 ( setadjoin @
% 86.64/22.72 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @
% 86.64/22.72 ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ))).
% 86.64/22.72 thf('18', plain,
% 86.64/22.72 (( ubforcartprodlem2 ) =
% 86.64/22.72 ( ![X4:$i,X6:$i,X8:$i]:
% 86.64/22.72 ( ( in @ X8 @ X4 ) =>
% 86.64/22.72 ( ![X10:$i]:
% 86.64/22.72 ( ( in @ X10 @ X6 ) =>
% 86.64/22.72 ( in @
% 86.64/22.72 ( setadjoin @
% 86.64/22.72 ( setadjoin @ X8 @ emptyset ) @
% 86.64/22.72 ( setadjoin @
% 86.64/22.72 ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @
% 86.64/22.72 emptyset ) ) @
% 86.64/22.72 ( powerset @ ( powerset @ ( binunion @ X4 @ X6 ) ) ) ) ) ) ) )),
% 86.64/22.72 define([status(thm)])).
% 86.64/22.72 thf(ubforcartprodlem1, axiom, ubforcartprodlem1 =
% 86.64/22.72 (![A:$i,B:$i,Xx:$i]:
% 86.64/22.72 ( ( in @ Xx @ A ) =>
% 86.64/22.72 ( ![Xy:$i]:
% 86.64/22.72 ( ( in @ Xy @ B ) =>
% 86.64/22.72 ( subset @
% 86.64/22.72 ( setadjoin @
% 86.64/22.72 ( setadjoin @ Xx @ emptyset ) @
% 86.64/22.72 ( setadjoin @
% 86.64/22.72 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @
% 86.64/22.72 ( powerset @ ( binunion @ A @ B ) ) ) ) ) ))).
% 86.64/22.72 thf('19', plain,
% 86.64/22.72 (( ubforcartprodlem1 ) =
% 86.64/22.72 ( ![X4:$i,X6:$i,X8:$i]:
% 86.64/22.72 ( ( in @ X8 @ X4 ) =>
% 86.64/22.72 ( ![X10:$i]:
% 86.64/22.72 ( ( in @ X10 @ X6 ) =>
% 86.64/22.72 ( subset @
% 86.64/22.72 ( setadjoin @
% 86.64/22.72 ( setadjoin @ X8 @ emptyset ) @
% 86.64/22.72 ( setadjoin @
% 86.64/22.72 ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @
% 86.64/22.72 emptyset ) ) @
% 86.64/22.72 ( powerset @ ( binunion @ X4 @ X6 ) ) ) ) ) ) )),
% 86.64/22.72 define([status(thm)])).
% 86.64/22.72 thf(upairinpowunion, axiom, upairinpowunion =
% 86.64/22.72 (![A:$i,B:$i,Xx:$i]:
% 86.64/22.72 ( ( in @ Xx @ A ) =>
% 86.64/22.72 ( ![Xy:$i]:
% 86.64/22.72 ( ( in @ Xy @ B ) =>
% 86.64/22.72 ( in @
% 86.64/22.72 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @
% 86.64/22.72 ( powerset @ ( binunion @ A @ B ) ) ) ) ) ))).
% 86.64/22.72 thf('20', plain,
% 86.64/22.72 (( upairinpowunion ) =
% 86.64/22.72 ( ![X4:$i,X6:$i,X8:$i]:
% 86.64/22.72 ( ( in @ X8 @ X4 ) =>
% 86.64/22.72 ( ![X10:$i]:
% 86.64/22.72 ( ( in @ X10 @ X6 ) =>
% 86.64/22.72 ( in @
% 86.64/22.72 ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @
% 86.64/22.72 ( powerset @ ( binunion @ X4 @ X6 ) ) ) ) ) ) )),
% 86.64/22.72 define([status(thm)])).
% 86.64/22.72 thf(upairsubunion, axiom, upairsubunion =
% 86.64/22.72 (![A:$i,B:$i,Xx:$i]:
% 86.64/22.72 ( ( in @ Xx @ A ) =>
% 86.64/22.72 ( ![Xy:$i]:
% 86.64/22.72 ( ( in @ Xy @ B ) =>
% 86.64/22.72 ( subset @
% 86.64/22.72 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @
% 86.64/22.72 ( binunion @ A @ B ) ) ) ) ))).
% 86.64/22.72 thf('21', plain,
% 86.64/22.72 (( upairsubunion ) =
% 86.64/22.72 ( ![X4:$i,X6:$i,X8:$i]:
% 86.64/22.72 ( ( in @ X8 @ X4 ) =>
% 86.64/22.72 ( ![X10:$i]:
% 86.64/22.72 ( ( in @ X10 @ X6 ) =>
% 86.64/22.72 ( subset @
% 86.64/22.72 ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @
% 86.64/22.72 ( binunion @ X4 @ X6 ) ) ) ) ) )),
% 86.64/22.72 define([status(thm)])).
% 86.64/22.72 thf(singletoninpowunion, axiom, singletoninpowunion =
% 86.64/22.72 (![A:$i,B:$i,Xx:$i]:
% 86.64/22.72 ( ( in @ Xx @ A ) =>
% 86.64/22.72 ( in @
% 86.64/22.72 ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ))).
% 86.64/22.72 thf('22', plain,
% 86.64/22.72 (( singletoninpowunion ) =
% 86.64/22.72 ( ![X4:$i,X6:$i,X8:$i]:
% 86.64/22.72 ( ( in @ X8 @ X4 ) =>
% 86.64/22.72 ( in @
% 86.64/22.72 ( setadjoin @ X8 @ emptyset ) @
% 86.64/22.72 ( powerset @ ( binunion @ X4 @ X6 ) ) ) ) )),
% 86.64/22.72 define([status(thm)])).
% 86.64/22.72 thf(bs114d, axiom, bs114d =
% 86.64/22.72 (![A:$i,B:$i,C:$i]:
% 86.64/22.72 ( ( binintersect @ A @ ( binunion @ B @ C ) ) =
% 86.64/22.72 ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ))).
% 86.64/22.72 thf('23', plain,
% 86.64/22.72 (( bs114d ) =
% 86.64/22.72 ( ![X4:$i,X6:$i,X8:$i]:
% 86.64/22.72 ( ( binintersect @ X4 @ ( binunion @ X6 @ X8 ) ) =
% 86.64/22.72 ( binunion @ ( binintersect @ X4 @ X6 ) @ ( binintersect @ X4 @ X8 ) ) ) )),
% 86.64/22.72 define([status(thm)])).
% 86.64/22.72 thf(binintersectSubset1, axiom, binintersectSubset1 =
% 86.64/22.72 (![A:$i,B:$i]:
% 86.64/22.72 ( ( ( binintersect @ A @ B ) = ( A ) ) => ( subset @ A @ B ) ))).
% 86.64/22.72 thf('24', plain,
% 86.64/22.72 (( binintersectSubset1 ) =
% 86.64/22.72 ( ![X4:$i,X6:$i]:
% 86.64/22.72 ( ( ( binintersect @ X4 @ X6 ) = ( X4 ) ) => ( subset @ X4 @ X6 ) ) )),
% 86.64/22.72 define([status(thm)])).
% 86.64/22.72 thf(binintersectSubset4, axiom, binintersectSubset4 =
% 86.64/22.72 (![A:$i,B:$i]:
% 86.64/22.72 ( ( subset @ B @ A ) => ( ( binintersect @ A @ B ) = ( B ) ) ))).
% 86.64/22.72 thf('25', plain,
% 86.64/22.72 (( binintersectSubset4 ) =
% 86.64/22.72 ( ![X4:$i,X6:$i]:
% 86.64/22.72 ( ( subset @ X6 @ X4 ) => ( ( binintersect @ X4 @ X6 ) = ( X6 ) ) ) )),
% 86.64/22.72 define([status(thm)])).
% 86.64/22.72 thf(binintersectRsub, axiom, binintersectRsub =
% 86.64/22.72 (![A:$i,B:$i]: ( subset @ ( binintersect @ A @ B ) @ B ))).
% 86.64/22.72 thf('26', plain,
% 86.64/22.72 (( binintersectRsub ) =
% 86.64/22.72 ( ![X4:$i,X6:$i]: ( subset @ ( binintersect @ X4 @ X6 ) @ X6 ) )),
% 86.64/22.72 define([status(thm)])).
% 86.64/22.72 thf(disjointsetsI1, axiom, disjointsetsI1 =
% 86.64/22.72 (![A:$i,B:$i]:
% 86.64/22.72 ( ( ~( ?[Xx:$i]: ( ( in @ Xx @ B ) & ( in @ Xx @ A ) ) ) ) =>
% 86.64/22.72 ( ( binintersect @ A @ B ) = ( emptyset ) ) ))).
% 86.64/22.72 thf('27', plain,
% 86.64/22.72 (( disjointsetsI1 ) =
% 86.64/22.72 ( ![X4:$i,X6:$i]:
% 86.64/22.72 ( ( ~( ?[X8:$i]: ( ( in @ X8 @ X6 ) & ( in @ X8 @ X4 ) ) ) ) =>
% 86.64/22.72 ( ( binintersect @ X4 @ X6 ) = ( emptyset ) ) ) )),
% 86.64/22.72 define([status(thm)])).
% 86.64/22.72 thf(binintersectER, axiom, binintersectER =
% 86.64/22.72 (![A:$i,B:$i,Xx:$i]:
% 86.64/22.72 ( ( in @ Xx @ ( binintersect @ A @ B ) ) => ( in @ Xx @ B ) ))).
% 86.64/22.72 thf('28', plain,
% 86.64/22.72 (( binintersectER ) =
% 86.64/22.72 ( ![X4:$i,X6:$i,X8:$i]:
% 86.64/22.72 ( ( in @ X8 @ ( binintersect @ X4 @ X6 ) ) => ( in @ X8 @ X6 ) ) )),
% 86.64/22.72 define([status(thm)])).
% 86.64/22.72 thf(binintersectSubset3, axiom, binintersectSubset3 =
% 86.64/22.72 (![A:$i,B:$i]:
% 86.64/22.72 ( ( ( binintersect @ A @ B ) = ( B ) ) => ( subset @ B @ A ) ))).
% 86.64/22.72 thf('29', plain,
% 86.64/22.72 (( binintersectSubset3 ) =
% 86.64/22.72 ( ![X4:$i,X6:$i]:
% 86.64/22.72 ( ( ( binintersect @ X4 @ X6 ) = ( X6 ) ) => ( subset @ X6 @ X4 ) ) )),
% 86.64/22.72 define([status(thm)])).
% 86.64/22.72 thf(binintersectSubset2, axiom, binintersectSubset2 =
% 86.64/22.72 (![A:$i,B:$i]:
% 86.64/22.72 ( ( subset @ A @ B ) => ( ( binintersect @ A @ B ) = ( A ) ) ))).
% 86.64/22.72 thf('30', plain,
% 86.64/22.72 (( binintersectSubset2 ) =
% 86.64/22.72 ( ![X4:$i,X6:$i]:
% 86.64/22.72 ( ( subset @ X4 @ X6 ) => ( ( binintersect @ X4 @ X6 ) = ( X4 ) ) ) )),
% 86.64/22.72 define([status(thm)])).
% 86.64/22.72 thf(binintersectLsub, axiom, binintersectLsub =
% 86.64/22.72 (![A:$i,B:$i]: ( subset @ ( binintersect @ A @ B ) @ A ))).
% 86.64/22.72 thf('31', plain,
% 86.64/22.72 (( binintersectLsub ) =
% 86.64/22.72 ( ![X4:$i,X6:$i]: ( subset @ ( binintersect @ X4 @ X6 ) @ X4 ) )),
% 86.64/22.72 define([status(thm)])).
% 86.64/22.72 thf(binintersectEL, axiom, binintersectEL =
% 86.64/22.72 (![A:$i,B:$i,Xx:$i]:
% 86.64/22.72 ( ( in @ Xx @ ( binintersect @ A @ B ) ) => ( in @ Xx @ A ) ))).
% 86.64/22.72 thf('32', plain,
% 86.64/22.72 (( binintersectEL ) =
% 86.64/22.72 ( ![X4:$i,X6:$i,X8:$i]:
% 86.64/22.72 ( ( in @ X8 @ ( binintersect @ X4 @ X6 ) ) => ( in @ X8 @ X4 ) ) )),
% 86.64/22.72 define([status(thm)])).
% 86.64/22.72 thf(binintersectSubset5, axiom, binintersectSubset5 =
% 86.64/22.72 (![A:$i,B:$i,C:$i]:
% 86.64/22.72 ( ( subset @ C @ A ) =>
% 86.64/22.72 ( ( subset @ C @ B ) => ( subset @ C @ ( binintersect @ A @ B ) ) ) ))).
% 86.64/22.72 thf('33', plain,
% 86.64/22.72 (( binintersectSubset5 ) =
% 86.64/22.72 ( ![X4:$i,X6:$i,X8:$i]:
% 86.64/22.72 ( ( subset @ X8 @ X4 ) =>
% 86.64/22.72 ( ( subset @ X8 @ X6 ) =>
% 86.64/22.72 ( subset @ X8 @ ( binintersect @ X4 @ X6 ) ) ) ) )),
% 86.64/22.72 define([status(thm)])).
% 86.64/22.72 thf(binintersectI, axiom, binintersectI =
% 86.64/22.72 (![A:$i,B:$i,Xx:$i]:
% 86.64/22.72 ( ( in @ Xx @ A ) =>
% 86.64/22.72 ( ( in @ Xx @ B ) => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ))).
% 86.64/22.72 thf('34', plain,
% 86.64/22.72 (( binintersectI ) =
% 86.64/22.72 ( ![X4:$i,X6:$i,X8:$i]:
% 86.64/22.72 ( ( in @ X8 @ X4 ) =>
% 86.64/22.72 ( ( in @ X8 @ X6 ) => ( in @ X8 @ ( binintersect @ X4 @ X6 ) ) ) ) )),
% 86.64/22.72 define([status(thm)])).
% 86.64/22.72 thf(binunionRsub, axiom, binunionRsub =
% 86.64/22.72 (![A:$i,B:$i]: ( subset @ B @ ( binunion @ A @ B ) ))).
% 86.64/22.72 thf('35', plain,
% 86.64/22.72 (( binunionRsub ) =
% 86.64/22.72 ( ![X4:$i,X6:$i]: ( subset @ X6 @ ( binunion @ X4 @ X6 ) ) )),
% 86.64/22.72 define([status(thm)])).
% 86.64/22.72 thf(binunionLsub, axiom, binunionLsub =
% 86.64/22.72 (![A:$i,B:$i]: ( subset @ A @ ( binunion @ A @ B ) ))).
% 86.64/22.72 thf('36', plain,
% 86.64/22.72 (( binunionLsub ) =
% 86.64/22.72 ( ![X4:$i,X6:$i]: ( subset @ X4 @ ( binunion @ X4 @ X6 ) ) )),
% 86.64/22.72 define([status(thm)])).
% 86.64/22.72 thf(binunionE, axiom, binunionE =
% 86.64/22.72 (![A:$i,B:$i,Xx:$i]:
% 86.64/22.72 ( ( in @ Xx @ ( binunion @ A @ B ) ) =>
% 86.64/22.72 ( ( in @ Xx @ A ) | ( in @ Xx @ B ) ) ))).
% 86.64/22.72 thf('37', plain,
% 86.64/22.72 (( binunionE ) =
% 86.64/22.72 ( ![X4:$i,X6:$i,X8:$i]:
% 86.64/22.72 ( ( in @ X8 @ ( binunion @ X4 @ X6 ) ) =>
% 86.64/22.72 ( ( in @ X8 @ X4 ) | ( in @ X8 @ X6 ) ) ) )),
% 86.64/22.72 define([status(thm)])).
% 86.64/22.72 thf(binunionEcases, axiom, binunionEcases =
% 86.64/22.72 (![A:$i,B:$i,Xx:$i,Xphi:$o]:
% 86.64/22.72 ( ( in @ Xx @ ( binunion @ A @ B ) ) =>
% 86.64/22.72 ( ( ( in @ Xx @ A ) => ( Xphi ) ) =>
% 86.64/22.72 ( ( ( in @ Xx @ B ) => ( Xphi ) ) => ( Xphi ) ) ) ))).
% 86.64/22.72 thf('38', plain,
% 86.64/22.72 (( binunionEcases ) =
% 86.64/22.72 ( ![X4:$i,X6:$i,X8:$i,X10:$o]:
% 86.64/22.72 ( ( in @ X8 @ ( binunion @ X4 @ X6 ) ) =>
% 86.64/22.72 ( ( ( in @ X8 @ X4 ) => ( X10 ) ) =>
% 86.64/22.72 ( ( ( in @ X8 @ X6 ) => ( X10 ) ) => ( X10 ) ) ) ) )),
% 86.64/22.72 define([status(thm)])).
% 86.64/22.72 thf(binunionIR, axiom, binunionIR =
% 86.64/22.72 (![A:$i,B:$i,Xx:$i]:
% 86.64/22.72 ( ( in @ Xx @ B ) => ( in @ Xx @ ( binunion @ A @ B ) ) ))).
% 86.64/22.72 thf('39', plain,
% 86.64/22.72 (( binunionIR ) =
% 86.64/22.72 ( ![X4:$i,X6:$i,X8:$i]:
% 86.64/22.72 ( ( in @ X8 @ X6 ) => ( in @ X8 @ ( binunion @ X4 @ X6 ) ) ) )),
% 86.64/22.72 define([status(thm)])).
% 86.64/22.72 thf(binunionIL, axiom, binunionIL =
% 86.64/22.72 (![A:$i,B:$i,Xx:$i]:
% 86.64/22.72 ( ( in @ Xx @ A ) => ( in @ Xx @ ( binunion @ A @ B ) ) ))).
% 86.64/22.72 thf('40', plain,
% 86.64/22.72 (( binunionIL ) =
% 86.64/22.72 ( ![X4:$i,X6:$i,X8:$i]:
% 86.64/22.72 ( ( in @ X8 @ X4 ) => ( in @ X8 @ ( binunion @ X4 @ X6 ) ) ) )),
% 86.64/22.72 define([status(thm)])).
% 86.64/22.72 thf(inPowerset, axiom, inPowerset = (![A:$i]: ( in @ A @ ( powerset @ A ) ))).
% 86.64/22.72 thf('41', plain,
% 86.64/22.72 (( inPowerset ) = ( ![X4:$i]: ( in @ X4 @ ( powerset @ X4 ) ) )),
% 86.64/22.72 define([status(thm)])).
% 86.64/22.72 thf(powerset__Cong, axiom, powerset__Cong =
% 86.64/22.72 (![A:$i,B:$i]:
% 86.64/22.72 ( ( ( A ) = ( B ) ) => ( ( powerset @ A ) = ( powerset @ B ) ) ))).
% 86.64/22.72 thf('42', plain,
% 86.64/22.72 (( powerset__Cong ) =
% 86.64/22.72 ( ![X4:$i,X6:$i]:
% 86.64/22.72 ( ( ( X4 ) = ( X6 ) ) => ( ( powerset @ X4 ) = ( powerset @ X6 ) ) ) )),
% 86.64/22.72 define([status(thm)])).
% 86.64/22.72 thf(powersetE, axiom, powersetE =
% 86.64/22.72 (![A:$i,B:$i,Xx:$i]:
% 86.64/22.72 ( ( in @ B @ ( powerset @ A ) ) => ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ))).
% 86.64/22.72 thf('43', plain,
% 86.64/22.72 (( powersetE ) =
% 86.64/22.72 ( ![X4:$i,X6:$i,X8:$i]:
% 86.64/22.72 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 86.64/22.72 ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) )),
% 86.64/22.72 define([status(thm)])).
% 86.64/22.72 thf(emptyInPowerset, axiom, emptyInPowerset =
% 86.64/22.72 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))).
% 86.64/22.72 thf('44', plain,
% 86.64/22.72 (( emptyInPowerset ) =
% 86.64/22.72 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )),
% 86.64/22.72 define([status(thm)])).
% 86.64/22.72 thf(emptyinPowerset, axiom, emptyinPowerset =
% 86.64/22.72 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))).
% 86.64/22.72 thf('45', plain,
% 86.64/22.72 (( emptyinPowerset ) =
% 86.64/22.72 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )),
% 86.64/22.72 define([status(thm)])).
% 86.64/22.72 thf(powersetI, axiom, powersetI =
% 86.64/22.72 (![A:$i,B:$i]:
% 86.64/22.72 ( ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) =>
% 86.64/22.72 ( in @ B @ ( powerset @ A ) ) ))).
% 86.64/22.72 thf('46', plain,
% 86.64/22.72 (( powersetI ) =
% 86.64/22.72 ( ![X4:$i,X6:$i]:
% 86.64/22.72 ( ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) =>
% 86.64/22.72 ( in @ X6 @ ( powerset @ X4 ) ) ) )),
% 86.64/22.72 define([status(thm)])).
% 86.64/22.72 thf(powersetAx, axiom, powersetAx =
% 86.64/22.72 (![A:$i,B:$i]:
% 86.64/22.72 ( ( in @ B @ ( powerset @ A ) ) <=>
% 86.64/22.72 ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) ))).
% 86.64/22.72 thf('47', plain,
% 86.64/22.72 (( powersetAx ) =
% 86.64/22.72 ( ![X4:$i,X6:$i]:
% 86.64/22.72 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 86.64/22.72 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) )),
% 86.64/22.72 define([status(thm)])).
% 86.64/22.72 thf(intersectInPowersetIntersectUnions, conjecture,
% 86.64/22.72 (( setextAx ) =>
% 86.64/22.72 ( ( emptysetAx ) =>
% 86.64/22.72 ( ( setadjoinAx ) =>
% 86.64/22.72 ( ( powersetAx ) =>
% 86.64/22.72 ( ( setunionAx ) =>
% 86.64/22.72 ( ( omega0Ax ) =>
% 86.64/22.72 ( ( omegaSAx ) =>
% 86.64/22.72 ( ( omegaIndAx ) =>
% 86.64/22.72 ( ( replAx ) =>
% 86.64/22.72 ( ( foundationAx ) =>
% 86.64/22.72 ( ( wellorderingAx ) =>
% 86.64/22.72 ( ( descrp ) =>
% 86.64/22.72 ( ( dsetconstrI ) =>
% 86.64/22.72 ( ( dsetconstrEL ) =>
% 86.64/22.72 ( ( dsetconstrER ) =>
% 86.64/22.72 ( ( exuE1 ) =>
% 86.64/22.72 ( ( prop2setE ) =>
% 86.64/22.72 ( ( emptysetE ) =>
% 86.64/22.72 ( ( emptysetimpfalse ) =>
% 86.64/22.72 ( ( notinemptyset ) =>
% 86.64/22.72 ( ( exuE3e ) =>
% 86.64/22.72 ( ( setext ) =>
% 86.64/22.72 ( ( emptyI ) =>
% 86.64/22.72 ( ( noeltsimpempty ) =>
% 86.64/22.72 ( ( setbeta ) =>
% 86.64/22.72 ( ( nonemptyE1 ) =>
% 86.64/22.72 ( ( nonemptyI ) =>
% 86.64/22.72 ( ( nonemptyI1 ) =>
% 86.64/22.72 ( ( setadjoinIL ) =>
% 86.64/22.72 ( ( emptyinunitempty ) =>
% 86.64/22.72 ( ( setadjoinIR ) =>
% 86.64/22.72 ( ( setadjoinE ) =>
% 86.64/22.72 ( (
% 86.64/22.72 setadjoinOr ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 setoftrueEq ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 powersetI ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 emptyinPowerset ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 emptyInPowerset ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 powersetE ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 setunionI ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 setunionE ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 subPowSU ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 exuE2 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 nonemptyImpWitness ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 uniqinunit ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 notinsingleton ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 eqinunit ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 singletonsswitch ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 upairsetE ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 upairsetIL ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 upairsetIR ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 emptyE1 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 vacuousDall ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 quantDeMorgan1 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 quantDeMorgan2 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 quantDeMorgan3 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 quantDeMorgan4 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 prop2setI ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 prop2set2propI ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 notdexE ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 notdallE ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 exuI1 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 exuI3 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 exuI2 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 inCongP ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 in__Cong ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 exuE3u ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 exu__Cong ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 emptyset__Cong ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 setadjoin__Cong ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 powerset__Cong ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 setunion__Cong ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 omega__Cong ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 exuEu ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 descr__Cong ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 dsetconstr__Cong ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 subsetI1 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 eqimpsubset2 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 eqimpsubset1 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 subsetI2 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 emptysetsubset ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 subsetE ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 subsetE2 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 notsubsetI ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 notequalI1 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 notequalI2 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 subsetRefl ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 subsetTrans ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 setadjoinSub ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 setadjoinSub2 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 subset2powerset ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 setextsub ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 subsetemptysetimpeq ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 powersetI1 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 powersetE1 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 inPowerset ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 powersetsubset ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 sepInPowerset ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 sepSubset ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 binunionIL ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 upairset2IR ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 binunionIR ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 binunionEcases ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 binunionE ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 binunionLsub ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 binunionRsub ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 binintersectI ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 binintersectSubset5 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 binintersectEL ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 binintersectLsub ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 binintersectSubset2 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 binintersectSubset3 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 binintersectER ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 disjointsetsI1 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 binintersectRsub ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 binintersectSubset4 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 binintersectSubset1 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 bs114d ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 setminusI ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 setminusEL ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 setminusER ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 setminusSubset2 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 setminusERneg ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 setminusELneg ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 setminusILneg ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 setminusIRneg ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 setminusLsub ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 setminusSubset1 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 symdiffE ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 symdiffI1 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 symdiffI2 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 symdiffIneg1 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 symdiffIneg2 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 secondinupair ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 setukpairIL ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 setukpairIR ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 kpairiskpair ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 kpairp ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 singletonsubset ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 singletoninpowerset ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 singletoninpowunion ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 upairset2E ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 upairsubunion ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 upairinpowunion ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 ubforcartprodlem1 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 ubforcartprodlem2 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 ubforcartprodlem3 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 cartprodpairin ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 cartprodmempair1 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 cartprodmempair ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 setunionE2 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 setunionsingleton1 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 setunionsingleton2 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 setunionsingleton ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 singletonprop ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 ex1E1 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 ex1I ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 ex1I2 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 singletonsuniq ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 setukpairinjL1 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 kfstsingleton ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 theprop ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 kfstpairEq ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 cartprodfstin ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 setukpairinjL2 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 setukpairinjL ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 setukpairinjR11 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 setukpairinjR12 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 setukpairinjR1 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 upairequniteq ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 setukpairinjR2 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 setukpairinjR ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 ksndsingleton ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 ksndpairEq ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 kpairsurjEq ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 cartprodsndin ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 cartprodpairmemEL ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 cartprodpairmemER ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 cartprodmempaircEq ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 cartprodfstpairEq ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 cartprodsndpairEq ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 cartprodpairsurjEq ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 dpsetconstrI ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 dpsetconstrSub ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 setOfPairsIsBReln ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 dpsetconstrERa ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 dpsetconstrEL1 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 dpsetconstrEL2 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 dpsetconstrER ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 funcImageSingleton ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 apProp ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 app ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 infuncsetfunc ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 ap2p ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 funcinfuncset ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 lamProp ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 lamp ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 lam2p ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 brelnall1 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 brelnall2 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 ex1E2 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 funcGraphProp1 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 funcGraphProp3 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 funcGraphProp2 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 funcextLem ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 funcGraphProp4 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 subbreln ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 eqbreln ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 funcext ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 funcext2 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 ap2apEq1 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 ap2apEq2 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 beta1 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 eta1 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 lam2lamEq ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 beta2 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 eta2 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 iffalseProp1 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 iffalseProp2 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 iftrueProp1 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 iftrueProp2 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 ifSingleton ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 ifp ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 theeq ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 iftrue ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 iffalse ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 iftrueorfalse ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 binintersectT_lem ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 binunionT_lem ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 powersetT_lem ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 setminusT_lem ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 complementT_lem ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 setextT ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 subsetTI ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 powersetTI1 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 powersetTE1 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 complementTI1 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 complementTE1 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 binintersectTELcontra ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 binintersectTERcontra ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 contrasubsetT ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 contrasubsetT1 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 contrasubsetT2 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 contrasubsetT3 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 doubleComplementI1 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 doubleComplementE1 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 doubleComplementSub1 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 doubleComplementSub2 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 doubleComplementEq ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 complementTnotintersectT ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 complementImpComplementIntersect ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 complementSubsetComplementIntersect ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 complementInPowersetComplementIntersect ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 contraSubsetComplement ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 complementTcontraSubset ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 binunionTILcontra ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 binunionTIRcontra ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 inIntersectImpInUnion ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 inIntersectImpInUnion2 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 inIntersectImpInIntersectUnions ) =>
% 86.64/22.72 (
% 86.64/22.72 ![
% 86.64/22.72 A:$i,X:$i]:
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 in @
% 86.64/22.72 X @
% 86.64/22.72 (
% 86.64/22.72 powerset @
% 86.64/22.72 A ) ) =>
% 86.64/22.72 (
% 86.64/22.72 ![
% 86.64/22.72 Y:$i]:
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 in @
% 86.64/22.72 Y @
% 86.64/22.72 (
% 86.64/22.72 powerset @
% 86.64/22.72 A ) ) =>
% 86.64/22.72 (
% 86.64/22.72 ![
% 86.64/22.72 Z:$i]:
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 in @
% 86.64/22.72 Z @
% 86.64/22.72 (
% 86.64/22.72 powerset @
% 86.64/22.72 A ) ) =>
% 86.64/22.72 (
% 86.64/22.72 in @
% 86.64/22.72 (
% 86.64/22.72 binintersect
% 86.64/22.72 @
% 86.64/22.72 X @ Y ) @
% 86.64/22.72 (
% 86.64/22.72 powerset @
% 86.64/22.72 (
% 86.64/22.72 binintersect
% 86.64/22.72 @
% 86.64/22.72 (
% 86.64/22.72 binunion @
% 86.64/22.72 X @ Z ) @
% 86.64/22.72 (
% 86.64/22.72 binunion @
% 86.64/22.72 Y @ Z ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 86.64/22.72 thf(zf_stmt_0, conjecture,
% 86.64/22.72 (( setextAx ) =>
% 86.64/22.72 ( ( emptysetAx ) =>
% 86.64/22.72 ( ( setadjoinAx ) =>
% 86.64/22.72 ( ( ![X4:$i,X6:$i]:
% 86.64/22.72 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 86.64/22.72 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) ) =>
% 86.64/22.72 ( ( setunionAx ) =>
% 86.64/22.72 ( ( omega0Ax ) =>
% 86.64/22.72 ( ( omegaSAx ) =>
% 86.64/22.72 ( ( omegaIndAx ) =>
% 86.64/22.72 ( ( replAx ) =>
% 86.64/22.72 ( ( foundationAx ) =>
% 86.64/22.72 ( ( wellorderingAx ) =>
% 86.64/22.72 ( ( descrp ) =>
% 86.64/22.72 ( ( dsetconstrI ) =>
% 86.64/22.72 ( ( dsetconstrEL ) =>
% 86.64/22.72 ( ( dsetconstrER ) =>
% 86.64/22.72 ( ( exuE1 ) =>
% 86.64/22.72 ( ( prop2setE ) =>
% 86.64/22.72 ( ( emptysetE ) =>
% 86.64/22.72 ( ( emptysetimpfalse ) =>
% 86.64/22.72 ( ( notinemptyset ) =>
% 86.64/22.72 ( ( exuE3e ) =>
% 86.64/22.72 ( ( setext ) =>
% 86.64/22.72 ( ( emptyI ) =>
% 86.64/22.72 ( ( noeltsimpempty ) =>
% 86.64/22.72 ( ( setbeta ) =>
% 86.64/22.72 ( ( nonemptyE1 ) =>
% 86.64/22.72 ( ( nonemptyI ) =>
% 86.64/22.72 ( ( nonemptyI1 ) =>
% 86.64/22.72 ( ( setadjoinIL ) =>
% 86.64/22.72 ( ( emptyinunitempty ) =>
% 86.64/22.72 ( ( setadjoinIR ) =>
% 86.64/22.72 ( ( setadjoinE ) =>
% 86.64/22.72 ( (
% 86.64/22.72 setadjoinOr ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 setoftrueEq ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 ![
% 86.64/22.72 X10:$i,
% 86.64/22.72 X12:$i]:
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 ![
% 86.64/22.72 X14:$i]:
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 in @
% 86.64/22.72 X14 @ X12 ) =>
% 86.64/22.72 (
% 86.64/22.72 in @
% 86.64/22.72 X14 @ X10 ) ) ) =>
% 86.64/22.72 (
% 86.64/22.72 in @
% 86.64/22.72 X12 @
% 86.64/22.72 (
% 86.64/22.72 powerset @
% 86.64/22.72 X10 ) ) ) ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 ![
% 86.64/22.72 X16:$i]:
% 86.64/22.72 (
% 86.64/22.72 in @
% 86.64/22.72 emptyset @
% 86.64/22.72 (
% 86.64/22.72 powerset @
% 86.64/22.72 X16 ) ) ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 ![
% 86.64/22.72 X18:$i]:
% 86.64/22.72 (
% 86.64/22.72 in @
% 86.64/22.72 emptyset @
% 86.64/22.72 (
% 86.64/22.72 powerset @
% 86.64/22.72 X18 ) ) ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 ![
% 86.64/22.72 X20:$i,
% 86.64/22.72 X22:$i,
% 86.64/22.72 X24:$i]:
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 in @
% 86.64/22.72 X22 @
% 86.64/22.72 (
% 86.64/22.72 powerset @
% 86.64/22.72 X20 ) ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 in @
% 86.64/22.72 X24 @ X22 ) =>
% 86.64/22.72 (
% 86.64/22.72 in @
% 86.64/22.72 X24 @ X20 ) ) ) ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 setunionI ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 setunionE ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 subPowSU ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 exuE2 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 nonemptyImpWitness ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 uniqinunit ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 notinsingleton ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 eqinunit ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 singletonsswitch ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 upairsetE ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 upairsetIL ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 upairsetIR ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 emptyE1 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 vacuousDall ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 quantDeMorgan1 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 quantDeMorgan2 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 quantDeMorgan3 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 quantDeMorgan4 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 prop2setI ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 prop2set2propI ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 notdexE ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 notdallE ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 exuI1 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 exuI3 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 exuI2 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 inCongP ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 in__Cong ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 exuE3u ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 exu__Cong ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 emptyset__Cong ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 setadjoin__Cong ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 ![
% 86.64/22.72 X26:$i,
% 86.64/22.72 X28:$i]:
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 X26 ) =
% 86.64/22.72 (
% 86.64/22.72 X28 ) ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 powerset @
% 86.64/22.72 X26 ) =
% 86.64/22.72 (
% 86.64/22.72 powerset @
% 86.64/22.72 X28 ) ) ) ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 setunion__Cong ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 omega__Cong ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 exuEu ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 descr__Cong ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 dsetconstr__Cong ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 subsetI1 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 eqimpsubset2 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 eqimpsubset1 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 subsetI2 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 emptysetsubset ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 subsetE ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 subsetE2 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 notsubsetI ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 notequalI1 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 notequalI2 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 subsetRefl ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 subsetTrans ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 setadjoinSub ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 setadjoinSub2 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 subset2powerset ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 setextsub ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 subsetemptysetimpeq ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 powersetI1 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 powersetE1 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 ![
% 86.64/22.72 X30:$i]:
% 86.64/22.72 (
% 86.64/22.72 in @
% 86.64/22.72 X30 @
% 86.64/22.72 (
% 86.64/22.72 powerset @
% 86.64/22.72 X30 ) ) ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 powersetsubset ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 sepInPowerset ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 sepSubset ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 ![
% 86.64/22.72 X32:$i,
% 86.64/22.72 X34:$i,
% 86.64/22.72 X36:$i]:
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 in @
% 86.64/22.72 X36 @ X32 ) =>
% 86.64/22.72 (
% 86.64/22.72 in @
% 86.64/22.72 X36 @
% 86.64/22.72 (
% 86.64/22.72 binunion @
% 86.64/22.72 X32 @ X34 ) ) ) ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 upairset2IR ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 ![
% 86.64/22.72 X38:$i,
% 86.64/22.72 X40:$i,
% 86.64/22.72 X42:$i]:
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 in @
% 86.64/22.72 X42 @ X40 ) =>
% 86.64/22.72 (
% 86.64/22.72 in @
% 86.64/22.72 X42 @
% 86.64/22.72 (
% 86.64/22.72 binunion @
% 86.64/22.72 X38 @ X40 ) ) ) ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 ![
% 86.64/22.72 X44:$i,
% 86.64/22.72 X46:$i,
% 86.64/22.72 X48:$i,
% 86.64/22.72 X50:$o]:
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 in @
% 86.64/22.72 X48 @
% 86.64/22.72 (
% 86.64/22.72 binunion @
% 86.64/22.72 X44 @ X46 ) ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 in @
% 86.64/22.72 X48 @ X44 ) =>
% 86.64/22.72 (
% 86.64/22.72 X50 ) ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 in @
% 86.64/22.72 X48 @ X46 ) =>
% 86.64/22.72 (
% 86.64/22.72 X50 ) ) =>
% 86.64/22.72 (
% 86.64/22.72 X50 ) ) ) ) ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 ![
% 86.64/22.72 X52:$i,
% 86.64/22.72 X54:$i,
% 86.64/22.72 X56:$i]:
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 in @
% 86.64/22.72 X56 @
% 86.64/22.72 (
% 86.64/22.72 binunion @
% 86.64/22.72 X52 @ X54 ) ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 in @
% 86.64/22.72 X56 @ X54 ) |
% 86.64/22.72 (
% 86.64/22.72 in @
% 86.64/22.72 X56 @ X52 ) ) ) ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 ![
% 86.64/22.72 X58:$i,
% 86.64/22.72 X60:$i]:
% 86.64/22.72 (
% 86.64/22.72 subset @
% 86.64/22.72 X58 @
% 86.64/22.72 (
% 86.64/22.72 binunion @
% 86.64/22.72 X58 @ X60 ) ) ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 ![
% 86.64/22.72 X62:$i,
% 86.64/22.72 X64:$i]:
% 86.64/22.72 (
% 86.64/22.72 subset @
% 86.64/22.72 X64 @
% 86.64/22.72 (
% 86.64/22.72 binunion @
% 86.64/22.72 X62 @ X64 ) ) ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 ![
% 86.64/22.72 X66:$i,
% 86.64/22.72 X68:$i,
% 86.64/22.72 X70:$i]:
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 in @
% 86.64/22.72 X70 @ X66 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 in @
% 86.64/22.72 X70 @ X68 ) =>
% 86.64/22.72 (
% 86.64/22.72 in @
% 86.64/22.72 X70 @
% 86.64/22.72 (
% 86.64/22.72 binintersect
% 86.64/22.72 @
% 86.64/22.72 X66 @ X68 ) ) ) ) ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 ![
% 86.64/22.72 X72:$i,
% 86.64/22.72 X74:$i,
% 86.64/22.72 X76:$i]:
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 subset @
% 86.64/22.72 X76 @ X72 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 subset @
% 86.64/22.72 X76 @ X74 ) =>
% 86.64/22.72 (
% 86.64/22.72 subset @
% 86.64/22.72 X76 @
% 86.64/22.72 (
% 86.64/22.72 binintersect
% 86.64/22.72 @
% 86.64/22.72 X72 @ X74 ) ) ) ) ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 ![
% 86.64/22.72 X78:$i,
% 86.64/22.72 X80:$i,
% 86.64/22.72 X82:$i]:
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 in @
% 86.64/22.72 X82 @
% 86.64/22.72 (
% 86.64/22.72 binintersect
% 86.64/22.72 @
% 86.64/22.72 X78 @ X80 ) ) =>
% 86.64/22.72 (
% 86.64/22.72 in @
% 86.64/22.72 X82 @ X78 ) ) ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 ![
% 86.64/22.72 X84:$i,
% 86.64/22.72 X86:$i]:
% 86.64/22.72 (
% 86.64/22.72 subset @
% 86.64/22.72 (
% 86.64/22.72 binintersect
% 86.64/22.72 @
% 86.64/22.72 X84 @ X86 ) @
% 86.64/22.72 X84 ) ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 ![
% 86.64/22.72 X88:$i,
% 86.64/22.72 X90:$i]:
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 subset @
% 86.64/22.72 X88 @ X90 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 binintersect
% 86.64/22.72 @
% 86.64/22.72 X88 @ X90 ) =
% 86.64/22.72 (
% 86.64/22.72 X88 ) ) ) ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 ![
% 86.64/22.72 X92:$i,
% 86.64/22.72 X94:$i]:
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 binintersect
% 86.64/22.72 @
% 86.64/22.72 X92 @ X94 ) =
% 86.64/22.72 (
% 86.64/22.72 X94 ) ) =>
% 86.64/22.72 (
% 86.64/22.72 subset @
% 86.64/22.72 X94 @ X92 ) ) ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 ![
% 86.64/22.72 X96:$i,
% 86.64/22.72 X98:$i,
% 86.64/22.72 X100:$i]:
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 in @
% 86.64/22.72 X100 @
% 86.64/22.72 (
% 86.64/22.72 binintersect
% 86.64/22.72 @
% 86.64/22.72 X96 @ X98 ) ) =>
% 86.64/22.72 (
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% 86.64/22.72 X100 @ X98 ) ) ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 ![
% 86.64/22.72 X102:$i,
% 86.64/22.72 X104:$i]:
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 ~(
% 86.64/22.72 ?[
% 86.64/22.72 X106:$i]:
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 in @
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% 86.64/22.72 X102 ) &
% 86.64/22.72 (
% 86.64/22.72 in @
% 86.64/22.72 X106 @
% 86.64/22.72 X104 ) ) ) ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 binintersect
% 86.64/22.72 @
% 86.64/22.72 X102 @
% 86.64/22.72 X104 ) =
% 86.64/22.72 (
% 86.64/22.72 emptyset ) ) ) ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 ![
% 86.64/22.72 X108:$i,
% 86.64/22.72 X110:$i]:
% 86.64/22.72 (
% 86.64/22.72 subset @
% 86.64/22.72 (
% 86.64/22.72 binintersect
% 86.64/22.72 @
% 86.64/22.72 X108 @
% 86.64/22.72 X110 ) @
% 86.64/22.72 X110 ) ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 ![
% 86.64/22.72 X112:$i,
% 86.64/22.72 X114:$i]:
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 subset @
% 86.64/22.72 X114 @
% 86.64/22.72 X112 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 binintersect
% 86.64/22.72 @
% 86.64/22.72 X112 @
% 86.64/22.72 X114 ) =
% 86.64/22.72 (
% 86.64/22.72 X114 ) ) ) ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 ![
% 86.64/22.72 X116:$i,
% 86.64/22.72 X118:$i]:
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 binintersect
% 86.64/22.72 @
% 86.64/22.72 X116 @
% 86.64/22.72 X118 ) =
% 86.64/22.72 (
% 86.64/22.72 X116 ) ) =>
% 86.64/22.72 (
% 86.64/22.72 subset @
% 86.64/22.72 X116 @
% 86.64/22.72 X118 ) ) ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 ![
% 86.64/22.72 X120:$i,
% 86.64/22.72 X122:$i,
% 86.64/22.72 X124:$i]:
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 binintersect
% 86.64/22.72 @
% 86.64/22.72 X120 @
% 86.64/22.72 (
% 86.64/22.72 binunion @
% 86.64/22.72 X122 @
% 86.64/22.72 X124 ) ) =
% 86.64/22.72 (
% 86.64/22.72 binunion @
% 86.64/22.72 (
% 86.64/22.72 binintersect
% 86.64/22.72 @
% 86.64/22.72 X120 @
% 86.64/22.72 X122 ) @
% 86.64/22.72 (
% 86.64/22.72 binintersect
% 86.64/22.72 @
% 86.64/22.72 X120 @
% 86.64/22.72 X124 ) ) ) ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 setminusI ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 setminusEL ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 setminusER ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 setminusSubset2 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 setminusERneg ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 setminusELneg ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 setminusILneg ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 setminusIRneg ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 setminusLsub ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 setminusSubset1 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 symdiffE ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 symdiffI1 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 symdiffI2 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 symdiffIneg1 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 symdiffIneg2 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 secondinupair ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 setukpairIL ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 setukpairIR ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 kpairiskpair ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 kpairp ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 singletonsubset ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 singletoninpowerset ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 ![
% 86.64/22.72 X126:$i,
% 86.64/22.72 X128:$i,
% 86.64/22.72 X130:$i]:
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 in @
% 86.64/22.72 X130 @
% 86.64/22.72 X126 ) =>
% 86.64/22.72 (
% 86.64/22.72 in @
% 86.64/22.72 (
% 86.64/22.72 setadjoin
% 86.64/22.72 @
% 86.64/22.72 X130 @
% 86.64/22.72 emptyset ) @
% 86.64/22.72 (
% 86.64/22.72 powerset @
% 86.64/22.72 (
% 86.64/22.72 binunion @
% 86.64/22.72 X126 @
% 86.64/22.72 X128 ) ) ) ) ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 upairset2E ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 ![
% 86.64/22.72 X132:$i,
% 86.64/22.72 X134:$i,
% 86.64/22.72 X136:$i]:
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 in @
% 86.64/22.72 X136 @
% 86.64/22.72 X132 ) =>
% 86.64/22.72 (
% 86.64/22.72 ![
% 86.64/22.72 X138:$i]:
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 in @
% 86.64/22.72 X138 @
% 86.64/22.72 X134 ) =>
% 86.64/22.72 (
% 86.64/22.72 subset @
% 86.64/22.72 (
% 86.64/22.72 setadjoin
% 86.64/22.72 @
% 86.64/22.72 X136 @
% 86.64/22.72 (
% 86.64/22.72 setadjoin
% 86.64/22.72 @
% 86.64/22.72 X138 @
% 86.64/22.72 emptyset ) ) @
% 86.64/22.72 (
% 86.64/22.72 binunion @
% 86.64/22.72 X132 @
% 86.64/22.72 X134 ) ) ) ) ) ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 ![
% 86.64/22.72 X140:$i,
% 86.64/22.72 X142:$i,
% 86.64/22.72 X144:$i]:
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 in @
% 86.64/22.72 X144 @
% 86.64/22.72 X140 ) =>
% 86.64/22.72 (
% 86.64/22.72 ![
% 86.64/22.72 X146:$i]:
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 in @
% 86.64/22.72 X146 @
% 86.64/22.72 X142 ) =>
% 86.64/22.72 (
% 86.64/22.72 in @
% 86.64/22.72 (
% 86.64/22.72 setadjoin
% 86.64/22.72 @
% 86.64/22.72 X144 @
% 86.64/22.72 (
% 86.64/22.72 setadjoin
% 86.64/22.72 @
% 86.64/22.72 X146 @
% 86.64/22.72 emptyset ) ) @
% 86.64/22.72 (
% 86.64/22.72 powerset @
% 86.64/22.72 (
% 86.64/22.72 binunion @
% 86.64/22.72 X140 @
% 86.64/22.72 X142 ) ) ) ) ) ) ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 ![
% 86.64/22.72 X148:$i,
% 86.64/22.72 X150:$i,
% 86.64/22.72 X152:$i]:
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 in @
% 86.64/22.72 X152 @
% 86.64/22.72 X148 ) =>
% 86.64/22.72 (
% 86.64/22.72 ![
% 86.64/22.72 X154:$i]:
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 in @
% 86.64/22.72 X154 @
% 86.64/22.72 X150 ) =>
% 86.64/22.72 (
% 86.64/22.72 subset @
% 86.64/22.72 (
% 86.64/22.72 setadjoin
% 86.64/22.72 @
% 86.64/22.72 (
% 86.64/22.72 setadjoin
% 86.64/22.72 @
% 86.64/22.72 X152 @
% 86.64/22.72 emptyset ) @
% 86.64/22.72 (
% 86.64/22.72 setadjoin
% 86.64/22.72 @
% 86.64/22.72 (
% 86.64/22.72 setadjoin
% 86.64/22.72 @
% 86.64/22.72 X152 @
% 86.64/22.72 (
% 86.64/22.72 setadjoin
% 86.64/22.72 @
% 86.64/22.72 X154 @
% 86.64/22.72 emptyset ) ) @
% 86.64/22.72 emptyset ) ) @
% 86.64/22.72 (
% 86.64/22.72 powerset @
% 86.64/22.72 (
% 86.64/22.72 binunion @
% 86.64/22.72 X148 @
% 86.64/22.72 X150 ) ) ) ) ) ) ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 ![
% 86.64/22.72 X156:$i,
% 86.64/22.72 X158:$i,
% 86.64/22.72 X160:$i]:
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 in @
% 86.64/22.72 X160 @
% 86.64/22.72 X156 ) =>
% 86.64/22.72 (
% 86.64/22.72 ![
% 86.64/22.72 X162:$i]:
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 in @
% 86.64/22.72 X162 @
% 86.64/22.72 X158 ) =>
% 86.64/22.72 (
% 86.64/22.72 in @
% 86.64/22.72 (
% 86.64/22.72 setadjoin
% 86.64/22.72 @
% 86.64/22.72 (
% 86.64/22.72 setadjoin
% 86.64/22.72 @
% 86.64/22.72 X160 @
% 86.64/22.72 emptyset ) @
% 86.64/22.72 (
% 86.64/22.72 setadjoin
% 86.64/22.72 @
% 86.64/22.72 (
% 86.64/22.72 setadjoin
% 86.64/22.72 @
% 86.64/22.72 X160 @
% 86.64/22.72 (
% 86.64/22.72 setadjoin
% 86.64/22.72 @
% 86.64/22.72 X162 @
% 86.64/22.72 emptyset ) ) @
% 86.64/22.72 emptyset ) ) @
% 86.64/22.72 (
% 86.64/22.72 powerset @
% 86.64/22.72 (
% 86.64/22.72 powerset @
% 86.64/22.72 (
% 86.64/22.72 binunion @
% 86.64/22.72 X156 @
% 86.64/22.72 X158 ) ) ) ) ) ) ) ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 ![
% 86.64/22.72 X164:$i,
% 86.64/22.72 X166:$i,
% 86.64/22.72 X168:$i]:
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 in @
% 86.64/22.72 X168 @
% 86.64/22.72 X164 ) =>
% 86.64/22.72 (
% 86.64/22.72 ![
% 86.64/22.72 X170:$i]:
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 in @
% 86.64/22.72 X170 @
% 86.64/22.72 X166 ) =>
% 86.64/22.72 (
% 86.64/22.72 in @
% 86.64/22.72 (
% 86.64/22.72 kpair @
% 86.64/22.72 X168 @
% 86.64/22.72 X170 ) @
% 86.64/22.72 (
% 86.64/22.72 powerset @
% 86.64/22.72 (
% 86.64/22.72 powerset @
% 86.64/22.72 (
% 86.64/22.72 binunion @
% 86.64/22.72 X164 @
% 86.64/22.72 X166 ) ) ) ) ) ) ) ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 cartprodpairin ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 cartprodmempair1 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 cartprodmempair ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 setunionE2 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 setunionsingleton1 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 setunionsingleton2 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 setunionsingleton ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 singletonprop ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 ex1E1 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 ex1I ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 ex1I2 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 singletonsuniq ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 setukpairinjL1 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 kfstsingleton ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 theprop ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 kfstpairEq ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 cartprodfstin ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 setukpairinjL2 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 setukpairinjL ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 setukpairinjR11 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 setukpairinjR12 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 setukpairinjR1 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 upairequniteq ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 setukpairinjR2 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 setukpairinjR ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 ksndsingleton ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 ksndpairEq ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 kpairsurjEq ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 cartprodsndin ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 cartprodpairmemEL ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 cartprodpairmemER ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 cartprodmempaircEq ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 cartprodfstpairEq ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 cartprodsndpairEq ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 cartprodpairsurjEq ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 dpsetconstrI ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 dpsetconstrSub ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 setOfPairsIsBReln ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 dpsetconstrERa ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 dpsetconstrEL1 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 dpsetconstrEL2 ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 dpsetconstrER ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 funcImageSingleton ) =>
% 86.64/22.72 (
% 86.64/22.72 (
% 86.64/22.72 apProp ) =>
% 86.64/22.72 (
% 86.64/22.72 (
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% 86.64/22.73 contraSubsetComplement ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 complementTcontraSubset ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 ![
% 86.64/22.73 X258:$i,
% 86.64/22.73 X260:$i]:
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 in @
% 86.64/22.73 X260 @
% 86.64/22.73 (
% 86.64/22.73 powerset @
% 86.64/22.73 X258 ) ) =>
% 86.64/22.73 (
% 86.64/22.73 ![
% 86.64/22.73 X262:$i]:
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 in @
% 86.64/22.73 X262 @
% 86.64/22.73 (
% 86.64/22.73 powerset @
% 86.64/22.73 X258 ) ) =>
% 86.64/22.73 (
% 86.64/22.73 ![
% 86.64/22.73 X264:$i]:
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 in @
% 86.64/22.73 X264 @
% 86.64/22.73 X258 ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 ~(
% 86.64/22.73 in @
% 86.64/22.73 X264 @
% 86.64/22.73 (
% 86.64/22.73 binunion
% 86.64/22.73 @
% 86.64/22.73 X260 @
% 86.64/22.73 X262 ) ) ) =>
% 86.64/22.73 (
% 86.64/22.73 ~(
% 86.64/22.73 in @
% 86.64/22.73 X264 @
% 86.64/22.73 X260 ) ) ) ) ) ) ) ) ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 ![
% 86.64/22.73 X266:$i,
% 86.64/22.73 X268:$i]:
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 in @
% 86.64/22.73 X268 @
% 86.64/22.73 (
% 86.64/22.73 powerset @
% 86.64/22.73 X266 ) ) =>
% 86.64/22.73 (
% 86.64/22.73 ![
% 86.64/22.73 X270:$i]:
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 in @
% 86.64/22.73 X270 @
% 86.64/22.73 (
% 86.64/22.73 powerset @
% 86.64/22.73 X266 ) ) =>
% 86.64/22.73 (
% 86.64/22.73 ![
% 86.64/22.73 X272:$i]:
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 in @
% 86.64/22.73 X272 @
% 86.64/22.73 X266 ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 ~(
% 86.64/22.73 in @
% 86.64/22.73 X272 @
% 86.64/22.73 (
% 86.64/22.73 binunion
% 86.64/22.73 @
% 86.64/22.73 X268 @
% 86.64/22.73 X270 ) ) ) =>
% 86.64/22.73 (
% 86.64/22.73 ~(
% 86.64/22.73 in @
% 86.64/22.73 X272 @
% 86.64/22.73 X270 ) ) ) ) ) ) ) ) ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 ![
% 86.64/22.73 X274:$i,
% 86.64/22.73 X276:$i]:
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 in @
% 86.64/22.73 X276 @
% 86.64/22.73 (
% 86.64/22.73 powerset @
% 86.64/22.73 X274 ) ) =>
% 86.64/22.73 (
% 86.64/22.73 ![
% 86.64/22.73 X278:$i]:
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 in @
% 86.64/22.73 X278 @
% 86.64/22.73 (
% 86.64/22.73 powerset @
% 86.64/22.73 X274 ) ) =>
% 86.64/22.73 (
% 86.64/22.73 ![
% 86.64/22.73 X280:$i]:
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 in @
% 86.64/22.73 X280 @
% 86.64/22.73 (
% 86.64/22.73 powerset @
% 86.64/22.73 X274 ) ) =>
% 86.64/22.73 (
% 86.64/22.73 ![
% 86.64/22.73 X282:$i]:
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 in @
% 86.64/22.73 X282 @
% 86.64/22.73 X274 ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 in @
% 86.64/22.73 X282 @
% 86.64/22.73 (
% 86.64/22.73 binintersect
% 86.64/22.73 @
% 86.64/22.73 X276 @
% 86.64/22.73 X278 ) ) =>
% 86.64/22.73 (
% 86.64/22.73 in @
% 86.64/22.73 X282 @
% 86.64/22.73 (
% 86.64/22.73 binunion @
% 86.64/22.73 X276 @
% 86.64/22.73 X280 ) ) ) ) ) ) ) ) ) ) ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 ![
% 86.64/22.73 X284:$i,
% 86.64/22.73 X286:$i]:
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 in @
% 86.64/22.73 X286 @
% 86.64/22.73 (
% 86.64/22.73 powerset @
% 86.64/22.73 X284 ) ) =>
% 86.64/22.73 (
% 86.64/22.73 ![
% 86.64/22.73 X288:$i]:
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 in @
% 86.64/22.73 X288 @
% 86.64/22.73 (
% 86.64/22.73 powerset @
% 86.64/22.73 X284 ) ) =>
% 86.64/22.73 (
% 86.64/22.73 ![
% 86.64/22.73 X290:$i]:
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 in @
% 86.64/22.73 X290 @
% 86.64/22.73 (
% 86.64/22.73 powerset @
% 86.64/22.73 X284 ) ) =>
% 86.64/22.73 (
% 86.64/22.73 ![
% 86.64/22.73 X292:$i]:
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 in @
% 86.64/22.73 X292 @
% 86.64/22.73 X284 ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 in @
% 86.64/22.73 X292 @
% 86.64/22.73 (
% 86.64/22.73 binintersect
% 86.64/22.73 @
% 86.64/22.73 X286 @
% 86.64/22.73 X288 ) ) =>
% 86.64/22.73 (
% 86.64/22.73 in @
% 86.64/22.73 X292 @
% 86.64/22.73 (
% 86.64/22.73 binunion @
% 86.64/22.73 X288 @
% 86.64/22.73 X290 ) ) ) ) ) ) ) ) ) ) ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 ![
% 86.64/22.73 X294:$i,
% 86.64/22.73 X296:$i]:
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 in @
% 86.64/22.73 X296 @
% 86.64/22.73 (
% 86.64/22.73 powerset @
% 86.64/22.73 X294 ) ) =>
% 86.64/22.73 (
% 86.64/22.73 ![
% 86.64/22.73 X298:$i]:
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 in @
% 86.64/22.73 X298 @
% 86.64/22.73 (
% 86.64/22.73 powerset @
% 86.64/22.73 X294 ) ) =>
% 86.64/22.73 (
% 86.64/22.73 ![
% 86.64/22.73 X300:$i]:
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 in @
% 86.64/22.73 X300 @
% 86.64/22.73 (
% 86.64/22.73 powerset @
% 86.64/22.73 X294 ) ) =>
% 86.64/22.73 (
% 86.64/22.73 ![
% 86.64/22.73 X302:$i]:
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 in @
% 86.64/22.73 X302 @
% 86.64/22.73 X294 ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 in @
% 86.64/22.73 X302 @
% 86.64/22.73 (
% 86.64/22.73 binintersect
% 86.64/22.73 @
% 86.64/22.73 X296 @
% 86.64/22.73 X298 ) ) =>
% 86.64/22.73 (
% 86.64/22.73 in @
% 86.64/22.73 X302 @
% 86.64/22.73 (
% 86.64/22.73 binintersect
% 86.64/22.73 @
% 86.64/22.73 (
% 86.64/22.73 binunion @
% 86.64/22.73 X296 @
% 86.64/22.73 X300 ) @
% 86.64/22.73 (
% 86.64/22.73 binunion @
% 86.64/22.73 X298 @
% 86.64/22.73 X300 ) ) ) ) ) ) ) ) ) ) ) ) =>
% 86.64/22.73 (
% 86.64/22.73 ![
% 86.64/22.73 X304:$i,
% 86.64/22.73 X306:$i]:
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 in @
% 86.64/22.73 X306 @
% 86.64/22.73 (
% 86.64/22.73 powerset @
% 86.64/22.73 X304 ) ) =>
% 86.64/22.73 (
% 86.64/22.73 ![
% 86.64/22.73 X308:$i]:
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 in @
% 86.64/22.73 X308 @
% 86.64/22.73 (
% 86.64/22.73 powerset @
% 86.64/22.73 X304 ) ) =>
% 86.64/22.73 (
% 86.64/22.73 ![
% 86.64/22.73 X310:$i]:
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 in @
% 86.64/22.73 X310 @
% 86.64/22.73 (
% 86.64/22.73 powerset @
% 86.64/22.73 X304 ) ) =>
% 86.64/22.73 (
% 86.64/22.73 in @
% 86.64/22.73 (
% 86.64/22.73 binintersect
% 86.64/22.73 @
% 86.64/22.73 X306 @
% 86.64/22.73 X308 ) @
% 86.64/22.73 (
% 86.64/22.73 powerset @
% 86.64/22.73 (
% 86.64/22.73 binintersect
% 86.64/22.73 @
% 86.64/22.73 (
% 86.64/22.73 binunion @
% 86.64/22.73 X306 @
% 86.64/22.73 X310 ) @
% 86.64/22.73 (
% 86.64/22.73 binunion @
% 86.64/22.73 X308 @
% 86.64/22.73 X310 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 86.64/22.73 thf(zf_stmt_1, type, zip_tseitin_0 : $i > $i > $i > $o).
% 86.64/22.73 thf(zf_stmt_2, axiom,
% 86.64/22.73 (![X8:$i,X6:$i,X4:$i]:
% 86.64/22.73 ( ( zip_tseitin_0 @ X8 @ X6 @ X4 ) <=>
% 86.64/22.73 ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ))).
% 86.64/22.73 thf(zf_stmt_3, conjecture,
% 86.64/22.73 (( setextAx ) =>
% 86.64/22.73 ( ( emptysetAx ) =>
% 86.64/22.73 ( ( setadjoinAx ) =>
% 86.64/22.73 ( ( ![X4:$i,X6:$i]:
% 86.64/22.73 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 86.64/22.73 ( ![X8:$i]: ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) ) =>
% 86.64/22.73 ( ( setunionAx ) =>
% 86.64/22.73 ( ( omega0Ax ) =>
% 86.64/22.73 ( ( omegaSAx ) =>
% 86.64/22.73 ( ( omegaIndAx ) =>
% 86.64/22.73 ( ( replAx ) =>
% 86.64/22.73 ( ( foundationAx ) =>
% 86.64/22.73 ( ( wellorderingAx ) =>
% 86.64/22.73 ( ( descrp ) =>
% 86.64/22.73 ( ( dsetconstrI ) =>
% 86.64/22.73 ( ( dsetconstrEL ) =>
% 86.64/22.73 ( ( dsetconstrER ) =>
% 86.64/22.73 ( ( exuE1 ) =>
% 86.64/22.73 ( ( prop2setE ) =>
% 86.64/22.73 ( ( emptysetE ) =>
% 86.64/22.73 ( ( emptysetimpfalse ) =>
% 86.64/22.73 ( ( notinemptyset ) =>
% 86.64/22.73 ( ( exuE3e ) =>
% 86.64/22.73 ( ( setext ) =>
% 86.64/22.73 ( ( emptyI ) =>
% 86.64/22.73 ( ( noeltsimpempty ) =>
% 86.64/22.73 ( ( setbeta ) =>
% 86.64/22.73 ( ( nonemptyE1 ) =>
% 86.64/22.73 ( ( nonemptyI ) =>
% 86.64/22.73 ( ( nonemptyI1 ) =>
% 86.64/22.73 ( ( setadjoinIL ) =>
% 86.64/22.73 ( ( emptyinunitempty ) =>
% 86.64/22.73 ( ( setadjoinIR ) =>
% 86.64/22.73 ( ( setadjoinE ) =>
% 86.64/22.73 ( (
% 86.64/22.73 setadjoinOr ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 setoftrueEq ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 ![
% 86.64/22.73 X10:$i,
% 86.64/22.73 X12:$i]:
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 ![
% 86.64/22.73 X14:$i]:
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 in @
% 86.64/22.73 X14 @ X12 ) =>
% 86.64/22.73 (
% 86.64/22.73 in @
% 86.64/22.73 X14 @ X10 ) ) ) =>
% 86.64/22.73 (
% 86.64/22.73 in @
% 86.64/22.73 X12 @
% 86.64/22.73 (
% 86.64/22.73 powerset @
% 86.64/22.73 X10 ) ) ) ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 ![
% 86.64/22.73 X16:$i]:
% 86.64/22.73 (
% 86.64/22.73 in @
% 86.64/22.73 emptyset @
% 86.64/22.73 (
% 86.64/22.73 powerset @
% 86.64/22.73 X16 ) ) ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 ![
% 86.64/22.73 X18:$i]:
% 86.64/22.73 (
% 86.64/22.73 in @
% 86.64/22.73 emptyset @
% 86.64/22.73 (
% 86.64/22.73 powerset @
% 86.64/22.73 X18 ) ) ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 ![
% 86.64/22.73 X20:$i,
% 86.64/22.73 X22:$i,
% 86.64/22.73 X24:$i]:
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 in @
% 86.64/22.73 X22 @
% 86.64/22.73 (
% 86.64/22.73 powerset @
% 86.64/22.73 X20 ) ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 in @
% 86.64/22.73 X24 @ X22 ) =>
% 86.64/22.73 (
% 86.64/22.73 in @
% 86.64/22.73 X24 @ X20 ) ) ) ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 setunionI ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 setunionE ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 subPowSU ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 exuE2 ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 nonemptyImpWitness ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 uniqinunit ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 notinsingleton ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 eqinunit ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 singletonsswitch ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 upairsetE ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 upairsetIL ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 upairsetIR ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 emptyE1 ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 vacuousDall ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 quantDeMorgan1 ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 quantDeMorgan2 ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 quantDeMorgan3 ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 quantDeMorgan4 ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 prop2setI ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 prop2set2propI ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 notdexE ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 notdallE ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 exuI1 ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 exuI3 ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 exuI2 ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 inCongP ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 in__Cong ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 exuE3u ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 exu__Cong ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 emptyset__Cong ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 setadjoin__Cong ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 ![
% 86.64/22.73 X26:$i,
% 86.64/22.73 X28:$i]:
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 X26 ) =
% 86.64/22.73 (
% 86.64/22.73 X28 ) ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 powerset @
% 86.64/22.73 X26 ) =
% 86.64/22.73 (
% 86.64/22.73 powerset @
% 86.64/22.73 X28 ) ) ) ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 setunion__Cong ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 omega__Cong ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 exuEu ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 descr__Cong ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 dsetconstr__Cong ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 subsetI1 ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 eqimpsubset2 ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 eqimpsubset1 ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 subsetI2 ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 emptysetsubset ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 subsetE ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 subsetE2 ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 notsubsetI ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 notequalI1 ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 notequalI2 ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 subsetRefl ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 subsetTrans ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 setadjoinSub ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 setadjoinSub2 ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 subset2powerset ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 setextsub ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 subsetemptysetimpeq ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 powersetI1 ) =>
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% 86.64/22.73 X30:$i]:
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% 86.64/22.73 X30 ) ) ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 powersetsubset ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 sepInPowerset ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 sepSubset ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 ![
% 86.64/22.73 X32:$i,
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% 86.64/22.73 (
% 86.64/22.73 (
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% 86.64/22.73 (
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% 86.64/22.73 (
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% 86.64/22.73 (
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% 86.64/22.73 (
% 86.64/22.73 binunion @
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% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 setminusI ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 setminusEL ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 setminusER ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 setminusSubset2 ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 setminusERneg ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 setminusELneg ) =>
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% 86.64/22.73 (
% 86.64/22.73 setminusILneg ) =>
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% 86.64/22.73 (
% 86.64/22.73 setminusIRneg ) =>
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% 86.64/22.73 (
% 86.64/22.73 setminusLsub ) =>
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% 86.64/22.73 (
% 86.64/22.73 setminusSubset1 ) =>
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% 86.64/22.73 (
% 86.64/22.73 symdiffE ) =>
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% 86.64/22.73 (
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% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 symdiffIneg1 ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 symdiffIneg2 ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 secondinupair ) =>
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% 86.64/22.73 (
% 86.64/22.73 setukpairIL ) =>
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% 86.64/22.73 (
% 86.64/22.73 setukpairIR ) =>
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% 86.64/22.73 (
% 86.64/22.73 kpairiskpair ) =>
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% 86.64/22.73 (
% 86.64/22.73 kpairp ) =>
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% 86.64/22.73 (
% 86.64/22.73 singletonsubset ) =>
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% 86.64/22.73 (
% 86.64/22.73 singletoninpowerset ) =>
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% 86.64/22.73 X126:$i,
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% 86.64/22.73 (
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% 86.64/22.73 ![
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% 86.64/22.73 kpair @
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% 86.64/22.73 (
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% 86.64/22.73 (
% 86.64/22.73 powerset @
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% 86.64/22.73 (
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% 86.64/22.73 (
% 86.64/22.73 (
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% 86.64/22.73 (
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% 86.64/22.73 (
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% 86.64/22.73 (
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% 86.64/22.73 (
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% 86.64/22.73 (
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% 86.64/22.73 (
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% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 dpsetconstrSub ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 setOfPairsIsBReln ) =>
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% 86.64/22.73 (
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% 86.64/22.73 (
% 86.64/22.73 dpsetconstrEL1 ) =>
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% 86.64/22.73 (
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% 86.64/22.73 (
% 86.64/22.73 dpsetconstrER ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 funcImageSingleton ) =>
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% 86.64/22.73 apProp ) =>
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% 86.64/22.73 app ) =>
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% 86.64/22.73 (
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% 86.64/22.73 (
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% 86.64/22.73 (
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% 86.64/22.73 (
% 86.64/22.73 ap2apEq2 ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 beta1 ) =>
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% 86.64/22.73 (
% 86.64/22.73 eta1 ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 lam2lamEq ) =>
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% 86.64/22.73 (
% 86.64/22.73 ifp ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 theeq ) =>
% 86.64/22.73 (
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% 86.64/22.73 iftrue ) =>
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% 86.64/22.73 iffalse ) =>
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% 86.64/22.73 (
% 86.64/22.73 powerset @
% 86.64/22.73 X172 ) ) ) ) ) ) =>
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% 86.64/22.73 X178 ) ) ) ) ) ) =>
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% 86.64/22.73 (
% 86.64/22.73 powerset @
% 86.64/22.73 X184 ) ) ) ) ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 setminusT_lem ) =>
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% 86.64/22.73 (
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% 86.64/22.73 in @
% 86.64/22.73 X194 @
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% 86.64/22.73 in @
% 86.64/22.73 X196 @
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% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 X190 ) =
% 86.64/22.73 (
% 86.64/22.73 X192 ) ) ) ) ) ) ) ) =>
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% 86.64/22.73 (
% 86.64/22.73 in @
% 86.64/22.73 X212 @
% 86.64/22.73 X210 ) ) ) ) ) ) ) ) ) =>
% 86.64/22.73 (
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% 86.64/22.73 complementTE1 ) =>
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% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 ~(
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% 86.64/22.73 (
% 86.64/22.73 ~(
% 86.64/22.73 in @
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% 86.64/22.73 (
% 86.64/22.73 binintersect
% 86.64/22.73 @
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% 86.64/22.73 X218 ) ) ) ) ) ) ) ) ) ) =>
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% 86.64/22.73 (
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% 86.64/22.73 @
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% 86.64/22.73 X226 ) ) ) ) ) ) ) ) ) ) =>
% 86.64/22.73 (
% 86.64/22.73 (
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% 86.64/22.73 (
% 86.64/22.73 contrasubsetT1 ) =>
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% 86.64/22.73 (
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% 86.64/22.73 (
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% 86.64/22.73 (
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% 86.64/22.73 (
% 86.64/22.73 (
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% 86.64/22.73 (
% 86.64/22.73 (
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% 86.64/22.73 (
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% 86.64/22.73 (
% 86.64/22.73 binunion @
% 86.64/22.73 X298 @
% 86.64/22.73 X300 ) ) ) ) ) ) ) ) ) ) ) ) =>
% 86.64/22.73 (
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% 86.64/22.73 (
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% 86.64/22.73 (
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% 86.64/22.73 X304 ) ) =>
% 86.64/22.73 (
% 86.64/22.73 in @
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% 86.64/22.73 binintersect
% 86.64/22.73 @
% 86.64/22.73 X306 @
% 86.64/22.73 X308 ) @
% 86.64/22.73 (
% 86.64/22.73 powerset @
% 86.64/22.73 (
% 86.64/22.73 binintersect
% 86.64/22.73 @
% 86.64/22.73 (
% 86.64/22.73 binunion @
% 86.64/22.73 X306 @
% 86.64/22.73 X310 ) @
% 86.64/22.73 (
% 86.64/22.73 binunion @
% 86.64/22.73 X308 @
% 86.64/22.73 X310 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 86.64/22.73 thf(zf_stmt_4, negated_conjecture,
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% 86.64/22.73 (
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% 86.64/22.73 (
% 86.64/22.73 powerset
% 86.64/22.73 @
% 86.64/22.73 X10 ) ) ) ) =>
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% 86.64/22.73 (
% 86.64/22.73 ![
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% 86.64/22.73 X16 ) ) ) =>
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% 86.64/22.73 powerset
% 86.64/22.73 @
% 86.64/22.73 X18 ) ) ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 ![
% 86.64/22.73 X20:$i,
% 86.64/22.73 X22:$i,
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% 86.64/22.73 in @
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% 86.64/22.73 (
% 86.64/22.73 powerset
% 86.64/22.73 @
% 86.64/22.73 X20 ) ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 in @
% 86.64/22.73 X24 @ X22 ) =>
% 86.64/22.73 (
% 86.64/22.73 in @
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% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 setunionI ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 setunionE ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 subPowSU ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 exuE2 ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 nonemptyImpWitness ) =>
% 86.64/22.73 (
% 86.64/22.73 (
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% 86.64/22.73 (
% 86.64/22.73 (
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% 86.64/22.73 (
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% 86.64/22.73 (
% 86.64/22.73 upairsetE ) =>
% 86.64/22.73 (
% 86.64/22.73 (
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% 86.64/22.73 (
% 86.64/22.73 (
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% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 emptyE1 ) =>
% 86.64/22.73 (
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% 86.64/22.73 vacuousDall ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 quantDeMorgan1 ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 quantDeMorgan2 ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 quantDeMorgan3 ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 quantDeMorgan4 ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 prop2setI ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 prop2set2propI ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 notdexE ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 notdallE ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 exuI1 ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 exuI3 ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 exuI2 ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 inCongP ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 in__Cong ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 exuE3u ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 exu__Cong ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 emptyset__Cong ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 setadjoin__Cong ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 ![
% 86.64/22.73 X26:$i,
% 86.64/22.73 X28:$i]:
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 X26 ) =
% 86.64/22.73 (
% 86.64/22.73 X28 ) ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 powerset
% 86.64/22.73 @
% 86.64/22.73 X26 ) =
% 86.64/22.73 (
% 86.64/22.73 powerset
% 86.64/22.73 @
% 86.64/22.73 X28 ) ) ) ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 setunion__Cong ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 omega__Cong ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 exuEu ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 descr__Cong ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 dsetconstr__Cong ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 subsetI1 ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 eqimpsubset2 ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 eqimpsubset1 ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 subsetI2 ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 emptysetsubset ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 subsetE ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 subsetE2 ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 notsubsetI ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 notequalI1 ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 notequalI2 ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 subsetRefl ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 subsetTrans ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 setadjoinSub ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 setadjoinSub2 ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 subset2powerset ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 setextsub ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 subsetemptysetimpeq ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 powersetI1 ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 powersetE1 ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 ![
% 86.64/22.73 X30:$i]:
% 86.64/22.73 (
% 86.64/22.73 in @
% 86.64/22.73 X30 @
% 86.64/22.73 (
% 86.64/22.73 powerset
% 86.64/22.73 @
% 86.64/22.73 X30 ) ) ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 powersetsubset ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 sepInPowerset ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 sepSubset ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 ![
% 86.64/22.73 X32:$i,
% 86.64/22.73 X34:$i,
% 86.64/22.73 X36:$i]:
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 in @
% 86.64/22.73 X36 @ X32 ) =>
% 86.64/22.73 (
% 86.64/22.73 in @
% 86.64/22.73 X36 @
% 86.64/22.73 (
% 86.64/22.73 binunion
% 86.64/22.73 @
% 86.64/22.73 X32 @ X34 ) ) ) ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 upairset2IR ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 ![
% 86.64/22.73 X38:$i,
% 86.64/22.73 X40:$i,
% 86.64/22.73 X42:$i]:
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 in @
% 86.64/22.73 X42 @ X40 ) =>
% 86.64/22.73 (
% 86.64/22.73 in @
% 86.64/22.73 X42 @
% 86.64/22.73 (
% 86.64/22.73 binunion
% 86.64/22.73 @
% 86.64/22.73 X38 @ X40 ) ) ) ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 ![
% 86.64/22.73 X44:$i,
% 86.64/22.73 X46:$i,
% 86.64/22.73 X48:$i,
% 86.64/22.73 X50:$o]:
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 in @
% 86.64/22.73 X48 @
% 86.64/22.73 (
% 86.64/22.73 binunion
% 86.64/22.73 @
% 86.64/22.73 X44 @ X46 ) ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 in @
% 86.64/22.73 X48 @ X44 ) =>
% 86.64/22.73 (
% 86.64/22.73 X50 ) ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 in @
% 86.64/22.73 X48 @ X46 ) =>
% 86.64/22.73 (
% 86.64/22.73 X50 ) ) =>
% 86.64/22.73 (
% 86.64/22.73 X50 ) ) ) ) ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 ![
% 86.64/22.73 X52:$i,
% 86.64/22.73 X54:$i,
% 86.64/22.73 X56:$i]:
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 in @
% 86.64/22.73 X56 @
% 86.64/22.73 (
% 86.64/22.73 binunion
% 86.64/22.73 @
% 86.64/22.73 X52 @ X54 ) ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 in @
% 86.64/22.73 X56 @ X52 ) |
% 86.64/22.73 (
% 86.64/22.73 in @
% 86.64/22.73 X56 @ X54 ) ) ) ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 ![
% 86.64/22.73 X58:$i,
% 86.64/22.73 X60:$i]:
% 86.64/22.73 (
% 86.64/22.73 subset @
% 86.64/22.73 X58 @
% 86.64/22.73 (
% 86.64/22.73 binunion
% 86.64/22.73 @
% 86.64/22.73 X58 @ X60 ) ) ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 ![
% 86.64/22.73 X62:$i,
% 86.64/22.73 X64:$i]:
% 86.64/22.73 (
% 86.64/22.73 subset @
% 86.64/22.73 X64 @
% 86.64/22.73 (
% 86.64/22.73 binunion
% 86.64/22.73 @
% 86.64/22.73 X62 @ X64 ) ) ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 ![
% 86.64/22.73 X66:$i,
% 86.64/22.73 X68:$i,
% 86.64/22.73 X70:$i]:
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 in @
% 86.64/22.73 X70 @ X66 ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 in @
% 86.64/22.73 X70 @ X68 ) =>
% 86.64/22.73 (
% 86.64/22.73 in @
% 86.64/22.73 X70 @
% 86.64/22.73 (
% 86.64/22.73 binintersect
% 86.64/22.73 @
% 86.64/22.73 X66 @ X68 ) ) ) ) ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 ![
% 86.64/22.73 X72:$i,
% 86.64/22.73 X74:$i,
% 86.64/22.73 X76:$i]:
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 subset @
% 86.64/22.73 X76 @ X72 ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 subset @
% 86.64/22.73 X76 @ X74 ) =>
% 86.64/22.73 (
% 86.64/22.73 subset @
% 86.64/22.73 X76 @
% 86.64/22.73 (
% 86.64/22.73 binintersect
% 86.64/22.73 @
% 86.64/22.73 X72 @ X74 ) ) ) ) ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 ![
% 86.64/22.73 X78:$i,
% 86.64/22.73 X80:$i,
% 86.64/22.73 X82:$i]:
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 in @
% 86.64/22.73 X82 @
% 86.64/22.73 (
% 86.64/22.73 binintersect
% 86.64/22.73 @
% 86.64/22.73 X78 @ X80 ) ) =>
% 86.64/22.73 (
% 86.64/22.73 in @
% 86.64/22.73 X82 @ X78 ) ) ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 ![
% 86.64/22.73 X84:$i,
% 86.64/22.73 X86:$i]:
% 86.64/22.73 (
% 86.64/22.73 subset @
% 86.64/22.73 (
% 86.64/22.73 binintersect
% 86.64/22.73 @
% 86.64/22.73 X84 @ X86 ) @
% 86.64/22.73 X84 ) ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 ![
% 86.64/22.73 X88:$i,
% 86.64/22.73 X90:$i]:
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 subset @
% 86.64/22.73 X88 @ X90 ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 binintersect
% 86.64/22.73 @
% 86.64/22.73 X88 @ X90 ) =
% 86.64/22.73 (
% 86.64/22.73 X88 ) ) ) ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 ![
% 86.64/22.73 X92:$i,
% 86.64/22.73 X94:$i]:
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 binintersect
% 86.64/22.73 @
% 86.64/22.73 X92 @ X94 ) =
% 86.64/22.73 (
% 86.64/22.73 X94 ) ) =>
% 86.64/22.73 (
% 86.64/22.73 subset @
% 86.64/22.73 X94 @ X92 ) ) ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 ![
% 86.64/22.73 X96:$i,
% 86.64/22.73 X98:$i,
% 86.64/22.73 X100:$i]:
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 in @
% 86.64/22.73 X100 @
% 86.64/22.73 (
% 86.64/22.73 binintersect
% 86.64/22.73 @
% 86.64/22.73 X96 @ X98 ) ) =>
% 86.64/22.73 (
% 86.64/22.73 in @
% 86.64/22.73 X100 @
% 86.64/22.73 X98 ) ) ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 ![
% 86.64/22.73 X102:$i,
% 86.64/22.73 X104:$i]:
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 ~
% 86.64/22.73 (
% 86.64/22.73 ?[
% 86.64/22.73 X106:$i]:
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 in @
% 86.64/22.73 X106 @
% 86.64/22.73 X104 ) &
% 86.64/22.73 (
% 86.64/22.73 in @
% 86.64/22.73 X106 @
% 86.64/22.73 X102 ) ) ) ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 binintersect
% 86.64/22.73 @
% 86.64/22.73 X102 @
% 86.64/22.73 X104 ) =
% 86.64/22.73 (
% 86.64/22.73 emptyset ) ) ) ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 ![
% 86.64/22.73 X108:$i,
% 86.64/22.73 X110:$i]:
% 86.64/22.73 (
% 86.64/22.73 subset @
% 86.64/22.73 (
% 86.64/22.73 binintersect
% 86.64/22.73 @
% 86.64/22.73 X108 @
% 86.64/22.73 X110 ) @
% 86.64/22.73 X110 ) ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 ![
% 86.64/22.73 X112:$i,
% 86.64/22.73 X114:$i]:
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 subset @
% 86.64/22.73 X114 @
% 86.64/22.73 X112 ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 binintersect
% 86.64/22.73 @
% 86.64/22.73 X112 @
% 86.64/22.73 X114 ) =
% 86.64/22.73 (
% 86.64/22.73 X114 ) ) ) ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 ![
% 86.64/22.73 X116:$i,
% 86.64/22.73 X118:$i]:
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 binintersect
% 86.64/22.73 @
% 86.64/22.73 X116 @
% 86.64/22.73 X118 ) =
% 86.64/22.73 (
% 86.64/22.73 X116 ) ) =>
% 86.64/22.73 (
% 86.64/22.73 subset @
% 86.64/22.73 X116 @
% 86.64/22.73 X118 ) ) ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 ![
% 86.64/22.73 X120:$i,
% 86.64/22.73 X122:$i,
% 86.64/22.73 X124:$i]:
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 binintersect
% 86.64/22.73 @
% 86.64/22.73 X120 @
% 86.64/22.73 (
% 86.64/22.73 binunion
% 86.64/22.73 @
% 86.64/22.73 X122 @
% 86.64/22.73 X124 ) ) =
% 86.64/22.73 (
% 86.64/22.73 binunion
% 86.64/22.73 @
% 86.64/22.73 (
% 86.64/22.73 binintersect
% 86.64/22.73 @
% 86.64/22.73 X120 @
% 86.64/22.73 X122 ) @
% 86.64/22.73 (
% 86.64/22.73 binintersect
% 86.64/22.73 @
% 86.64/22.73 X120 @
% 86.64/22.73 X124 ) ) ) ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 setminusI ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 setminusEL ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 setminusER ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 setminusSubset2 ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 setminusERneg ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 setminusELneg ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 setminusILneg ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 setminusIRneg ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 setminusLsub ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 setminusSubset1 ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 symdiffE ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 symdiffI1 ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.73 symdiffI2 ) =>
% 86.64/22.73 (
% 86.64/22.73 (
% 86.64/22.75 symdiffIneg1 ) =>
% 86.64/22.75 (
% 86.64/22.75 (
% 86.64/22.75 symdiffIneg2 ) =>
% 86.64/22.75 (
% 86.64/22.75 (
% 86.64/22.75 secondinupair ) =>
% 86.64/22.75 (
% 86.64/22.75 (
% 86.64/22.75 setukpairIL ) =>
% 86.64/22.75 (
% 86.64/22.75 (
% 86.64/22.75 setukpairIR ) =>
% 86.64/22.75 (
% 86.64/22.75 (
% 86.64/22.75 kpairiskpair ) =>
% 86.64/22.75 (
% 86.64/22.75 (
% 86.64/22.75 kpairp ) =>
% 86.64/22.75 (
% 86.64/22.75 (
% 86.64/22.75 singletonsubset ) =>
% 86.64/22.75 (
% 86.64/22.75 (
% 86.64/22.75 singletoninpowerset ) =>
% 86.64/22.75 (
% 86.64/22.75 (
% 86.64/22.75 ![
% 86.64/22.75 X126:$i,
% 86.64/22.75 X128:$i,
% 86.64/22.75 X130:$i]:
% 86.64/22.75 (
% 86.64/22.75 (
% 86.64/22.75 in @
% 86.64/22.75 X130 @
% 86.64/22.75 X126 ) =>
% 86.64/22.75 (
% 86.64/22.75 in @
% 86.64/22.75 (
% 86.64/22.75 setadjoin
% 86.64/22.75 @
% 86.64/22.75 X130 @
% 86.64/22.75 emptyset ) @
% 86.64/22.75 (
% 86.64/22.75 powerset
% 86.64/22.75 @
% 86.64/22.75 (
% 86.64/22.75 binunion
% 86.64/22.75 @
% 86.64/22.75 X126 @
% 86.64/22.75 X128 ) ) ) ) ) =>
% 86.64/22.75 (
% 86.64/22.75 (
% 86.64/22.75 upairset2E ) =>
% 86.64/22.75 (
% 86.64/22.75 (
% 86.64/22.75 ![
% 86.64/22.75 X132:$i,
% 86.64/22.75 X134:$i,
% 86.64/22.75 X136:$i]:
% 86.64/22.75 (
% 86.64/22.75 (
% 86.64/22.75 in @
% 86.64/22.75 X136 @
% 86.64/22.75 X132 ) =>
% 86.64/22.75 (
% 86.64/22.75 ![
% 86.64/22.75 X138:$i]:
% 86.64/22.75 (
% 86.64/22.75 (
% 86.64/22.75 in @
% 86.64/22.75 X138 @
% 86.64/22.75 X134 ) =>
% 86.64/22.75 (
% 86.64/22.75 subset @
% 86.64/22.75 (
% 86.64/22.75 setadjoin
% 86.64/22.75 @
% 86.64/22.75 X136 @
% 86.64/22.75 (
% 86.64/22.75 setadjoin
% 86.64/22.75 @
% 86.64/22.75 X138 @
% 86.64/22.75 emptyset ) ) @
% 86.64/22.75 (
% 86.64/22.75 binunion
% 86.64/22.75 @
% 86.64/22.75 X132 @
% 86.64/22.75 X134 ) ) ) ) ) ) =>
% 86.64/22.75 (
% 86.64/22.75 (
% 86.64/22.75 ![
% 86.64/22.75 X140:$i,
% 86.64/22.75 X142:$i,
% 86.64/22.75 X144:$i]:
% 86.64/22.75 (
% 86.64/22.75 (
% 86.64/22.75 in @
% 86.64/22.75 X144 @
% 86.64/22.75 X140 ) =>
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% 86.69/22.76 (
% 86.69/22.76 powerset
% 86.69/22.76 @
% 86.69/22.76 X304 ) ) =>
% 86.69/22.76 (
% 86.69/22.76 in @
% 86.69/22.76 (
% 86.69/22.76 binintersect
% 86.69/22.76 @
% 86.69/22.76 X306 @
% 86.69/22.76 X308 ) @
% 86.69/22.76 (
% 86.69/22.76 powerset
% 86.69/22.76 @
% 86.69/22.76 (
% 86.69/22.76 binintersect
% 86.69/22.76 @
% 86.69/22.76 (
% 86.69/22.76 binunion
% 86.69/22.76 @
% 86.69/22.76 X306 @
% 86.69/22.76 X310 ) @
% 86.69/22.76 (
% 86.69/22.76 binunion
% 86.69/22.76 @
% 86.69/22.76 X308 @
% 86.69/22.76 X310 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 86.69/22.76 inference('cnf.neg', [status(esa)], [zf_stmt_3])).
% 86.69/22.76 thf(zip_derived_cl223, plain,
% 86.69/22.76 (![X122 : $i, X123 : $i]:
% 86.69/22.76 (((binintersect @ X122 @ X123) = (X122)) | ~ (subset @ X122 @ X123))),
% 86.69/22.76 inference('cnf', [status(esa)], [zf_stmt_4])).
% 86.69/22.76 thf(zip_derived_cl58, plain,
% 86.69/22.76 (![X18 : $i, X19 : $i]: (subset @ (binintersect @ X18 @ X19) @ X18)),
% 86.69/22.76 inference('cnf', [status(esa)], [zf_stmt_4])).
% 86.69/22.76 thf(zip_derived_cl358, plain,
% 86.69/22.76 (![X0 : $i, X1 : $i]:
% 86.69/22.76 ((binintersect @ (binintersect @ X0 @ X1) @ X0)
% 86.69/22.76 = (binintersect @ X0 @ X1))),
% 86.69/22.76 inference('sup+', [status(thm)], [zip_derived_cl223, zip_derived_cl58])).
% 86.69/22.76 thf(zip_derived_cl221, plain,
% 86.69/22.76 (![X117 : $i, X118 : $i]: (subset @ (binintersect @ X117 @ X118) @ X118)),
% 86.69/22.76 inference('cnf', [status(esa)], [zf_stmt_4])).
% 86.69/22.76 thf(zip_derived_cl223, plain,
% 86.69/22.76 (![X122 : $i, X123 : $i]:
% 86.69/22.76 (((binintersect @ X122 @ X123) = (X122)) | ~ (subset @ X122 @ X123))),
% 86.69/22.76 inference('cnf', [status(esa)], [zf_stmt_4])).
% 86.69/22.76 thf(zip_derived_cl221, plain,
% 86.69/22.76 (![X117 : $i, X118 : $i]: (subset @ (binintersect @ X117 @ X118) @ X118)),
% 86.69/22.76 inference('cnf', [status(esa)], [zf_stmt_4])).
% 86.69/22.76 thf(zip_derived_cl357, plain,
% 86.69/22.76 (![X0 : $i, X1 : $i]:
% 86.69/22.76 ((binintersect @ (binintersect @ X1 @ X0) @ X0)
% 86.69/22.76 = (binintersect @ X1 @ X0))),
% 86.69/22.76 inference('sup+', [status(thm)], [zip_derived_cl223, zip_derived_cl221])).
% 86.69/22.76 thf(zip_derived_cl57, plain,
% 86.69/22.76 (![X15 : $i, X16 : $i, X17 : $i]:
% 86.69/22.76 (~ (subset @ X15 @ X16)
% 86.69/22.76 | (subset @ X15 @ (binintersect @ X17 @ X16))
% 86.69/22.76 | ~ (subset @ X15 @ X17))),
% 86.69/22.76 inference('cnf', [status(esa)], [zf_stmt_4])).
% 86.69/22.76 thf(zip_derived_cl136, plain,
% 86.69/22.76 (~ (in @ (binintersect @ sk__156 @ sk__157) @
% 86.69/22.76 (powerset @
% 86.69/22.76 (binintersect @ (binunion @ sk__156 @ sk__158) @
% 86.69/22.76 (binunion @ sk__157 @ sk__158))))),
% 86.69/22.76 inference('cnf', [status(esa)], [zf_stmt_4])).
% 86.69/22.76 thf(zip_derived_cl223, plain,
% 86.69/22.76 (![X122 : $i, X123 : $i]:
% 86.69/22.76 (((binintersect @ X122 @ X123) = (X122)) | ~ (subset @ X122 @ X123))),
% 86.69/22.76 inference('cnf', [status(esa)], [zf_stmt_4])).
% 86.69/22.76 thf(zip_derived_cl226, plain,
% 86.69/22.76 (![X130 : $i, X131 : $i]: (subset @ X130 @ (binunion @ X130 @ X131))),
% 86.69/22.76 inference('cnf', [status(esa)], [zf_stmt_4])).
% 86.69/22.76 thf(zip_derived_cl360, plain,
% 86.69/22.76 (![X0 : $i, X1 : $i]: ((binintersect @ X1 @ (binunion @ X1 @ X0)) = (X1))),
% 86.69/22.76 inference('sup+', [status(thm)], [zip_derived_cl223, zip_derived_cl226])).
% 86.69/22.76 thf(zip_derived_cl63, plain,
% 86.69/22.76 (![X26 : $i, X27 : $i, X28 : $i]:
% 86.69/22.76 ((binintersect @ X26 @ (binunion @ X27 @ X28))
% 86.69/22.76 = (binunion @ (binintersect @ X26 @ X27) @
% 86.69/22.76 (binintersect @ X26 @ X28)))),
% 86.69/22.76 inference('cnf', [status(esa)], [zf_stmt_4])).
% 86.69/22.76 thf(zip_derived_cl62, plain,
% 86.69/22.76 (![X24 : $i, X25 : $i]:
% 86.69/22.76 (((binintersect @ X25 @ X24) = (X24)) | ~ (subset @ X24 @ X25))),
% 86.69/22.76 inference('cnf', [status(esa)], [zf_stmt_4])).
% 86.69/22.76 thf(zip_derived_cl226, plain,
% 86.69/22.76 (![X130 : $i, X131 : $i]: (subset @ X130 @ (binunion @ X130 @ X131))),
% 86.69/22.76 inference('cnf', [status(esa)], [zf_stmt_4])).
% 86.69/22.76 thf(zip_derived_cl332, plain,
% 86.69/22.76 (![X0 : $i, X1 : $i]: ((binintersect @ (binunion @ X1 @ X0) @ X1) = (X1))),
% 86.69/22.76 inference('sup+', [status(thm)], [zip_derived_cl62, zip_derived_cl226])).
% 86.69/22.76 thf(zip_derived_cl62, plain,
% 86.69/22.76 (![X24 : $i, X25 : $i]:
% 86.69/22.76 (((binintersect @ X25 @ X24) = (X24)) | ~ (subset @ X24 @ X25))),
% 86.69/22.76 inference('cnf', [status(esa)], [zf_stmt_4])).
% 86.69/22.76 thf(zip_derived_cl221, plain,
% 86.69/22.76 (![X117 : $i, X118 : $i]: (subset @ (binintersect @ X117 @ X118) @ X118)),
% 86.69/22.76 inference('cnf', [status(esa)], [zf_stmt_4])).
% 86.69/22.76 thf(zip_derived_cl329, plain,
% 86.69/22.76 (![X0 : $i, X1 : $i]:
% 86.69/22.76 ((binintersect @ X0 @ (binintersect @ X1 @ X0))
% 86.69/22.76 = (binintersect @ X1 @ X0))),
% 86.69/22.76 inference('sup+', [status(thm)], [zip_derived_cl62, zip_derived_cl221])).
% 86.69/22.76 thf(zip_derived_cl223, plain,
% 86.69/22.76 (![X122 : $i, X123 : $i]:
% 86.69/22.76 (((binintersect @ X122 @ X123) = (X122)) | ~ (subset @ X122 @ X123))),
% 86.69/22.76 inference('cnf', [status(esa)], [zf_stmt_4])).
% 86.69/22.76 thf(zip_derived_cl21, plain,
% 86.69/22.76 (![X0 : $i, X1 : $i]:
% 86.69/22.76 ( (in @ X0 @ (powerset @ X1)) | (in @ (sk__160 @ X0 @ X1) @ X0))),
% 86.69/22.76 inference('cnf', [status(esa)], [zf_stmt_4])).
% 86.69/22.76 thf(zip_derived_cl222, plain,
% 86.69/22.76 (![X119 : $i, X120 : $i, X121 : $i]:
% 86.69/22.76 ( (in @ X119 @ X120) | ~ (in @ X119 @ (binintersect @ X121 @ X120)))),
% 86.69/22.76 inference('cnf', [status(esa)], [zf_stmt_4])).
% 86.69/22.76 thf(zip_derived_cl309, plain,
% 86.69/22.76 (![X0 : $i, X1 : $i, X2 : $i]:
% 86.69/22.76 ( (in @ (binintersect @ X1 @ X0) @ (powerset @ X2))
% 86.69/22.76 | (in @ (sk__160 @ (binintersect @ X1 @ X0) @ X2) @ X0))),
% 86.69/22.76 inference('sup-', [status(thm)], [zip_derived_cl21, zip_derived_cl222])).
% 86.69/22.76 thf(zip_derived_cl20, plain,
% 86.69/22.76 (![X0 : $i, X1 : $i]:
% 86.69/22.76 ( (in @ X0 @ (powerset @ X1)) | ~ (in @ (sk__160 @ X0 @ X1) @ X1))),
% 86.69/22.76 inference('cnf', [status(esa)], [zf_stmt_4])).
% 86.69/22.76 thf(zip_derived_cl8996, plain, ($false),
% 86.69/22.76 inference('eprover', [status(thm)],
% 86.69/22.76 [zip_derived_cl358, zip_derived_cl221, zip_derived_cl357,
% 86.69/22.76 zip_derived_cl57, zip_derived_cl136, zip_derived_cl360,
% 86.69/22.76 zip_derived_cl63, zip_derived_cl332, zip_derived_cl329,
% 86.69/22.76 zip_derived_cl223, zip_derived_cl309, zip_derived_cl20])).
% 86.69/22.76
% 86.69/22.76 % SZS output end Refutation
% 86.69/22.76
% 86.69/22.76
% 86.69/22.76 % Terminating...
% 86.90/22.95 % Runner terminated.
% 86.93/22.98 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------