%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU722^1 : 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.d6hbDmV3YD true
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 2 04:55:57 PM UTC 2025
% Result : Theorem 1.26s 1.68s
% Output : Refutation 1.26s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.25 % Problem : SEU722^1 : TPTP v9.2.0. Released v3.7.0.
% 0.08/0.30 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.d6hbDmV3YD true
% 0.10/0.64 % Computer : n027.cluster.edu
% 0.10/0.64 % Model : x86_64 x86_64
% 0.10/0.64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.64 % Memory : 8042.1875MB
% 0.10/0.64 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.64 % CPULimit : 300
% 0.10/0.64 % WCLimit : 300
% 0.10/0.64 % DateTime : Wed Oct 1 16:04:23 EDT 2025
% 0.10/0.66 % CPUTime :
% 0.10/0.66 % Running portfolio for 300 s
% 0.10/0.66 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.67 % Number of cores: 8
% 0.10/0.68 % Python version: Python 3.6.8
% 0.10/0.70 % Running in HO mode
% 0.14/1.09 % Total configuration time : 828
% 0.14/1.09 % Estimated wc time : 1656
% 0.14/1.09 % Estimated cpu time (8 cpus) : 207.0
% 1.24/1.33 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 1.24/1.34 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 1.24/1.37 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 1.26/1.38 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 1.26/1.40 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 1.26/1.41 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 1.26/1.43 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 1.26/1.45 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.26/1.68 % Solved by lams/40_c_ic.sh.
% 1.26/1.68 % done 231 iterations in 0.204s
% 1.26/1.68 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 1.26/1.68 % SZS output start Refutation
% 1.26/1.68 thf(setadjoinAx_type, type, setadjoinAx: $o).
% 1.26/1.68 thf(notdexE_type, type, notdexE: $o).
% 1.26/1.68 thf(setukpairinjL2_type, type, setukpairinjL2: $o).
% 1.26/1.68 thf(setunionAx_type, type, setunionAx: $o).
% 1.26/1.68 thf(setminusELneg_type, type, setminusELneg: $o).
% 1.26/1.68 thf(cartprodsndin_type, type, cartprodsndin: $o).
% 1.26/1.68 thf(ex1E1_type, type, ex1E1: $o).
% 1.26/1.68 thf(powersetE_type, type, powersetE: $o).
% 1.26/1.68 thf(omegaSAx_type, type, omegaSAx: $o).
% 1.26/1.68 thf(exuI1_type, type, exuI1: $o).
% 1.26/1.68 thf(exuI2_type, type, exuI2: $o).
% 1.26/1.68 thf(notequalI2_type, type, notequalI2: $o).
% 1.26/1.68 thf(setukpairinjL_type, type, setukpairinjL: $o).
% 1.26/1.68 thf(kpairiskpair_type, type, kpairiskpair: $o).
% 1.26/1.68 thf(upairsubunion_type, type, upairsubunion: $o).
% 1.26/1.68 thf(funcGraphProp3_type, type, funcGraphProp3: $o).
% 1.26/1.68 thf(cartprodmempaircEq_type, type, cartprodmempaircEq: $o).
% 1.26/1.68 thf(powerset__Cong_type, type, powerset__Cong: $o).
% 1.26/1.68 thf(setminusILneg_type, type, setminusILneg: $o).
% 1.26/1.68 thf(wellorderingAx_type, type, wellorderingAx: $o).
% 1.26/1.68 thf(ksndpairEq_type, type, ksndpairEq: $o).
% 1.26/1.68 thf(funcGraphProp2_type, type, funcGraphProp2: $o).
% 1.26/1.68 thf(setadjoinSub2_type, type, setadjoinSub2: $o).
% 1.26/1.68 thf(binintersectSubset5_type, type, binintersectSubset5: $o).
% 1.26/1.68 thf(iftrue_type, type, iftrue: $o).
% 1.26/1.68 thf(upairinpowunion_type, type, upairinpowunion: $o).
% 1.26/1.68 thf(ifSingleton_type, type, ifSingleton: $o).
% 1.26/1.68 thf(setoftrueEq_type, type, setoftrueEq: $o).
% 1.26/1.68 thf(funcImageSingleton_type, type, funcImageSingleton: $o).
% 1.26/1.68 thf(dpsetconstrERa_type, type, dpsetconstrERa: $o).
% 1.26/1.68 thf(lamProp_type, type, lamProp: $o).
% 1.26/1.68 thf(cartprodpairmemEL_type, type, cartprodpairmemEL: $o).
% 1.26/1.68 thf(emptyset__Cong_type, type, emptyset__Cong: $o).
% 1.26/1.68 thf(dpsetconstrER_type, type, dpsetconstrER: $o).
% 1.26/1.68 thf(sepInPowerset_type, type, sepInPowerset: $o).
% 1.26/1.68 thf(setukpairIR_type, type, setukpairIR: $o).
% 1.26/1.68 thf(setukpairinjR1_type, type, setukpairinjR1: $o).
% 1.26/1.68 thf(lam2p_type, type, lam2p: $o).
% 1.26/1.68 thf(binunionE_type, type, binunionE: $o).
% 1.26/1.68 thf(setext_type, type, setext: $o).
% 1.26/1.68 thf(emptyinPowerset_type, type, emptyinPowerset: $o).
% 1.26/1.68 thf(ubforcartprodlem1_type, type, ubforcartprodlem1: $o).
% 1.26/1.68 thf(descr__Cong_type, type, descr__Cong: $o).
% 1.26/1.68 thf(kfstsingleton_type, type, kfstsingleton: $o).
% 1.26/1.68 thf(binintersectTELcontra_type, type, binintersectTELcontra: $o).
% 1.26/1.68 thf(eqbreln_type, type, eqbreln: $o).
% 1.26/1.68 thf(binintersectSubset1_type, type, binintersectSubset1: $o).
% 1.26/1.68 thf(in_type, type, in: $i > $i > $o).
% 1.26/1.68 thf(binunionT_lem_type, type, binunionT_lem: $o).
% 1.26/1.68 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o).
% 1.26/1.68 thf(complementT_lem_type, type, complementT_lem: $o).
% 1.26/1.68 thf(binunion_type, type, binunion: $i > $i > $i).
% 1.26/1.68 thf(kpairsurjEq_type, type, kpairsurjEq: $o).
% 1.26/1.68 thf(setadjoinIR_type, type, setadjoinIR: $o).
% 1.26/1.68 thf(beta1_type, type, beta1: $o).
% 1.26/1.68 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o).
% 1.26/1.68 thf(powersetTE1_type, type, powersetTE1: $o).
% 1.26/1.68 thf(symdiffI2_type, type, symdiffI2: $o).
% 1.26/1.68 thf(iftrueProp2_type, type, iftrueProp2: $o).
% 1.26/1.68 thf(upairset2IR_type, type, upairset2IR: $o).
% 1.26/1.68 thf(iffalseProp2_type, type, iffalseProp2: $o).
% 1.26/1.68 thf(subsetE_type, type, subsetE: $o).
% 1.26/1.68 thf(prop2set2propI_type, type, prop2set2propI: $o).
% 1.26/1.68 thf(dsetconstrEL_type, type, dsetconstrEL: $o).
% 1.26/1.68 thf(setbeta_type, type, setbeta: $o).
% 1.26/1.68 thf(eqinunit_type, type, eqinunit: $o).
% 1.26/1.68 thf(upairsetIL_type, type, upairsetIL: $o).
% 1.26/1.68 thf(powersetI1_type, type, powersetI1: $o).
% 1.26/1.68 thf(kfstpairEq_type, type, kfstpairEq: $o).
% 1.26/1.68 thf(binintersectSubset3_type, type, binintersectSubset3: $o).
% 1.26/1.68 thf(setminusIRneg_type, type, setminusIRneg: $o).
% 1.26/1.68 thf(zip_tseitin_0_type, type, zip_tseitin_0: $i > $i > $i > $o).
% 1.26/1.68 thf(ap2apEq1_type, type, ap2apEq1: $o).
% 1.26/1.68 thf(powersetAx_type, type, powersetAx: $o).
% 1.26/1.68 thf(binintersectSubset4_type, type, binintersectSubset4: $o).
% 1.26/1.68 thf(singletoninpowunion_type, type, singletoninpowunion: $o).
% 1.26/1.68 thf(powersetI_type, type, powersetI: $o).
% 1.26/1.68 thf(cartprodmempair_type, type, cartprodmempair: $o).
% 1.26/1.68 thf(upairsetIR_type, type, upairsetIR: $o).
% 1.26/1.68 thf(lamp_type, type, lamp: $o).
% 1.26/1.68 thf(dpsetconstrEL1_type, type, dpsetconstrEL1: $o).
% 1.26/1.68 thf(inCongP_type, type, inCongP: $o).
% 1.26/1.68 thf(setadjoinSub_type, type, setadjoinSub: $o).
% 1.26/1.68 thf(exuE3e_type, type, exuE3e: $o).
% 1.26/1.68 thf(emptysetE_type, type, emptysetE: $o).
% 1.26/1.68 thf(binintersectSubset2_type, type, binintersectSubset2: $o).
% 1.26/1.68 thf(setunionI_type, type, setunionI: $o).
% 1.26/1.68 thf(setunion__Cong_type, type, setunion__Cong: $o).
% 1.26/1.68 thf(prop2setI_type, type, prop2setI: $o).
% 1.26/1.68 thf(singletonsuniq_type, type, singletonsuniq: $o).
% 1.26/1.68 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o).
% 1.26/1.68 thf(setminusER_type, type, setminusER: $o).
% 1.26/1.68 thf(exuE2_type, type, exuE2: $o).
% 1.26/1.68 thf(emptyset_type, type, emptyset: $i).
% 1.26/1.68 thf(setukpairinjR11_type, type, setukpairinjR11: $o).
% 1.26/1.68 thf(ex1I_type, type, ex1I: $o).
% 1.26/1.68 thf(ex1E2_type, type, ex1E2: $o).
% 1.26/1.68 thf(setukpairinjL1_type, type, setukpairinjL1: $o).
% 1.26/1.68 thf(powersetsubset_type, type, powersetsubset: $o).
% 1.26/1.68 thf(subPowSU_type, type, subPowSU: $o).
% 1.26/1.68 thf(notequalI1_type, type, notequalI1: $o).
% 1.26/1.68 thf(notinemptyset_type, type, notinemptyset: $o).
% 1.26/1.68 thf(lam2lamEq_type, type, lam2lamEq: $o).
% 1.26/1.68 thf(nonemptyI1_type, type, nonemptyI1: $o).
% 1.26/1.68 thf(subsetTrans_type, type, subsetTrans: $o).
% 1.26/1.68 thf(kpairp_type, type, kpairp: $o).
% 1.26/1.68 thf(setukpairinjR12_type, type, setukpairinjR12: $o).
% 1.26/1.68 thf(setminusI_type, type, setminusI: $o).
% 1.26/1.68 thf(binunionIL_type, type, binunionIL: $o).
% 1.26/1.68 thf(dpsetconstrSub_type, type, dpsetconstrSub: $o).
% 1.26/1.68 thf(setunionsingleton_type, type, setunionsingleton: $o).
% 1.26/1.68 thf(subsetE2_type, type, subsetE2: $o).
% 1.26/1.68 thf(singletonsswitch_type, type, singletonsswitch: $o).
% 1.26/1.68 thf(ubforcartprodlem3_type, type, ubforcartprodlem3: $o).
% 1.26/1.68 thf(beta2_type, type, beta2: $o).
% 1.26/1.68 thf(dpsetconstrI_type, type, dpsetconstrI: $o).
% 1.26/1.68 thf(setextsub_type, type, setextsub: $o).
% 1.26/1.68 thf(binunionLsub_type, type, binunionLsub: $o).
% 1.26/1.68 thf(setunionsingleton1_type, type, setunionsingleton1: $o).
% 1.26/1.68 thf(binintersect_type, type, binintersect: $i > $i > $i).
% 1.26/1.68 thf(iftrueorfalse_type, type, iftrueorfalse: $o).
% 1.26/1.68 thf(emptysetsubset_type, type, emptysetsubset: $o).
% 1.26/1.68 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o).
% 1.26/1.68 thf(cartprodpairsurjEq_type, type, cartprodpairsurjEq: $o).
% 1.26/1.68 thf(setOfPairsIsBReln_type, type, setOfPairsIsBReln: $o).
% 1.26/1.68 thf(setunionE_type, type, setunionE: $o).
% 1.26/1.68 thf(ksndsingleton_type, type, ksndsingleton: $o).
% 1.26/1.68 thf(setminusSubset1_type, type, setminusSubset1: $o).
% 1.26/1.68 thf(powersetT_lem_type, type, powersetT_lem: $o).
% 1.26/1.68 thf(emptyinunitempty_type, type, emptyinunitempty: $o).
% 1.26/1.68 thf(binunionIR_type, type, binunionIR: $o).
% 1.26/1.68 thf(theeq_type, type, theeq: $o).
% 1.26/1.68 thf(setadjoinE_type, type, setadjoinE: $o).
% 1.26/1.68 thf(infuncsetfunc_type, type, infuncsetfunc: $o).
% 1.26/1.68 thf(ap2apEq2_type, type, ap2apEq2: $o).
% 1.26/1.68 thf(ap2p_type, type, ap2p: $o).
% 1.26/1.68 thf(setadjoinIL_type, type, setadjoinIL: $o).
% 1.26/1.68 thf(cartprodsndpairEq_type, type, cartprodsndpairEq: $o).
% 1.26/1.68 thf(exuE1_type, type, exuE1: $o).
% 1.26/1.68 thf(ubforcartprodlem2_type, type, ubforcartprodlem2: $o).
% 1.26/1.68 thf(binintersectRsub_type, type, binintersectRsub: $o).
% 1.26/1.68 thf(setminusLsub_type, type, setminusLsub: $o).
% 1.26/1.68 thf(funcextLem_type, type, funcextLem: $o).
% 1.26/1.68 thf(setukpairinjR_type, type, setukpairinjR: $o).
% 1.26/1.68 thf(notinsingleton_type, type, notinsingleton: $o).
% 1.26/1.68 thf(eqimpsubset2_type, type, eqimpsubset2: $o).
% 1.26/1.68 thf(exuEu_type, type, exuEu: $o).
% 1.26/1.68 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o).
% 1.26/1.68 thf(upairsetE_type, type, upairsetE: $o).
% 1.26/1.68 thf(omega0Ax_type, type, omega0Ax: $o).
% 1.26/1.68 thf(subsetTI_type, type, subsetTI: $o).
% 1.26/1.68 thf(notsubsetI_type, type, notsubsetI: $o).
% 1.26/1.68 thf(iffalseProp1_type, type, iffalseProp1: $o).
% 1.26/1.68 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o).
% 1.26/1.68 thf(setextAx_type, type, setextAx: $o).
% 1.26/1.68 thf(cartprodpairmemER_type, type, cartprodpairmemER: $o).
% 1.26/1.68 thf(powersetE1_type, type, powersetE1: $o).
% 1.26/1.68 thf(bs114d_type, type, bs114d: $o).
% 1.26/1.68 thf(noeltsimpempty_type, type, noeltsimpempty: $o).
% 1.26/1.68 thf(ifp_type, type, ifp: $o).
% 1.26/1.68 thf(powersetTI1_type, type, powersetTI1: $o).
% 1.26/1.68 thf(binintersectLsub_type, type, binintersectLsub: $o).
% 1.26/1.68 thf(subsetI1_type, type, subsetI1: $o).
% 1.26/1.68 thf(symdiffE_type, type, symdiffE: $o).
% 1.26/1.68 thf(descrp_type, type, descrp: $o).
% 1.26/1.68 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o).
% 1.26/1.68 thf(foundationAx_type, type, foundationAx: $o).
% 1.26/1.68 thf(emptysetAx_type, type, emptysetAx: $o).
% 1.26/1.68 thf(emptyI_type, type, emptyI: $o).
% 1.26/1.68 thf(setadjoinOr_type, type, setadjoinOr: $o).
% 1.26/1.68 thf(eta2_type, type, eta2: $o).
% 1.26/1.68 thf(binintersectEL_type, type, binintersectEL: $o).
% 1.26/1.68 thf(emptyE1_type, type, emptyE1: $o).
% 1.26/1.68 thf(emptyInPowerset_type, type, emptyInPowerset: $o).
% 1.26/1.68 thf(complementTI1_type, type, complementTI1: $o).
% 1.26/1.68 thf(vacuousDall_type, type, vacuousDall: $o).
% 1.26/1.68 thf(dsetconstrER_type, type, dsetconstrER: $o).
% 1.26/1.68 thf(binintersectI_type, type, binintersectI: $o).
% 1.26/1.68 thf(funcext_type, type, funcext: $o).
% 1.26/1.68 thf(funcGraphProp4_type, type, funcGraphProp4: $o).
% 1.26/1.68 thf(cartprodpairin_type, type, cartprodpairin: $o).
% 1.26/1.68 thf(cartprodmempair1_type, type, cartprodmempair1: $o).
% 1.26/1.68 thf(brelnall2_type, type, brelnall2: $o).
% 1.26/1.68 thf(setextT_type, type, setextT: $o).
% 1.26/1.68 thf(ex1I2_type, type, ex1I2: $o).
% 1.26/1.68 thf(symdiffI1_type, type, symdiffI1: $o).
% 1.26/1.68 thf(setukpairinjR2_type, type, setukpairinjR2: $o).
% 1.26/1.68 thf(dpsetconstrEL2_type, type, dpsetconstrEL2: $o).
% 1.26/1.68 thf(theprop_type, type, theprop: $o).
% 1.26/1.68 thf(subsetI2_type, type, subsetI2: $o).
% 1.26/1.68 thf(setminusT_lem_type, type, setminusT_lem: $o).
% 1.26/1.68 thf(sk__86_type, type, sk__86: $i).
% 1.26/1.68 thf(symdiffIneg1_type, type, symdiffIneg1: $o).
% 1.26/1.68 thf(setminusERneg_type, type, setminusERneg: $o).
% 1.26/1.68 thf(symdiffIneg2_type, type, symdiffIneg2: $o).
% 1.26/1.68 thf(omega__Cong_type, type, omega__Cong: $o).
% 1.26/1.68 thf(subsetRefl_type, type, subsetRefl: $o).
% 1.26/1.68 thf(uniqinunit_type, type, uniqinunit: $o).
% 1.26/1.68 thf(setminusSubset2_type, type, setminusSubset2: $o).
% 1.26/1.68 thf(prop2setE_type, type, prop2setE: $o).
% 1.26/1.68 thf(binunionEcases_type, type, binunionEcases: $o).
% 1.26/1.68 thf(funcinfuncset_type, type, funcinfuncset: $o).
% 1.26/1.68 thf(complementTE1_type, type, complementTE1: $o).
% 1.26/1.68 thf(nonemptyI_type, type, nonemptyI: $o).
% 1.26/1.68 thf(app_type, type, app: $o).
% 1.26/1.68 thf(disjointsetsI1_type, type, disjointsetsI1: $o).
% 1.26/1.68 thf(exuE3u_type, type, exuE3u: $o).
% 1.26/1.68 thf(eta1_type, type, eta1: $o).
% 1.26/1.68 thf(setminusEL_type, type, setminusEL: $o).
% 1.26/1.68 thf(sk__88_type, type, sk__88: $i).
% 1.26/1.68 thf(cartprodfstin_type, type, cartprodfstin: $o).
% 1.26/1.68 thf(sk__87_type, type, sk__87: $i).
% 1.26/1.68 thf(setunionsingleton2_type, type, setunionsingleton2: $o).
% 1.26/1.68 thf(sepSubset_type, type, sepSubset: $o).
% 1.26/1.68 thf(upairset2E_type, type, upairset2E: $o).
% 1.26/1.68 thf(eqimpsubset1_type, type, eqimpsubset1: $o).
% 1.26/1.68 thf(exuI3_type, type, exuI3: $o).
% 1.26/1.68 thf(cartprodfstpairEq_type, type, cartprodfstpairEq: $o).
% 1.26/1.68 thf(apProp_type, type, apProp: $o).
% 1.26/1.68 thf(notdallE_type, type, notdallE: $o).
% 1.26/1.68 thf(iftrueProp1_type, type, iftrueProp1: $o).
% 1.26/1.68 thf(binintersectER_type, type, binintersectER: $o).
% 1.26/1.68 thf(brelnall1_type, type, brelnall1: $o).
% 1.26/1.68 thf(powerset_type, type, powerset: $i > $i).
% 1.26/1.68 thf(dsetconstrI_type, type, dsetconstrI: $o).
% 1.26/1.68 thf(funcGraphProp1_type, type, funcGraphProp1: $o).
% 1.26/1.68 thf(binintersectT_lem_type, type, binintersectT_lem: $o).
% 1.26/1.68 thf(setadjoin_type, type, setadjoin: $i > $i > $i).
% 1.26/1.68 thf(exu__Cong_type, type, exu__Cong: $o).
% 1.26/1.68 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o).
% 1.26/1.68 thf(secondinupair_type, type, secondinupair: $o).
% 1.26/1.68 thf(singletonprop_type, type, singletonprop: $o).
% 1.26/1.68 thf(singletonsubset_type, type, singletonsubset: $o).
% 1.26/1.68 thf(singletoninpowerset_type, type, singletoninpowerset: $o).
% 1.26/1.68 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o).
% 1.26/1.68 thf(replAx_type, type, replAx: $o).
% 1.26/1.68 thf(upairequniteq_type, type, upairequniteq: $o).
% 1.26/1.68 thf(nonemptyE1_type, type, nonemptyE1: $o).
% 1.26/1.68 thf(omegaIndAx_type, type, omegaIndAx: $o).
% 1.26/1.68 thf(setukpairIL_type, type, setukpairIL: $o).
% 1.26/1.68 thf(setunionE2_type, type, setunionE2: $o).
% 1.26/1.68 thf(inPowerset_type, type, inPowerset: $o).
% 1.26/1.68 thf(iffalse_type, type, iffalse: $o).
% 1.26/1.68 thf(funcext2_type, type, funcext2: $o).
% 1.26/1.68 thf(subset_type, type, subset: $i > $i > $o).
% 1.26/1.68 thf(subbreln_type, type, subbreln: $o).
% 1.26/1.68 thf(in__Cong_type, type, in__Cong: $o).
% 1.26/1.68 thf(binunionRsub_type, type, binunionRsub: $o).
% 1.26/1.68 thf(subset2powerset_type, type, subset2powerset: $o).
% 1.26/1.68 thf(binintersectTELcontra, axiom, binintersectTELcontra =
% 1.26/1.68 (![A:$i,X:$i]:
% 1.26/1.68 ( ( in @ X @ ( powerset @ A ) ) =>
% 1.26/1.68 ( ![Y:$i]:
% 1.26/1.68 ( ( in @ Y @ ( powerset @ A ) ) =>
% 1.26/1.68 ( ![Xx:$i]:
% 1.26/1.68 ( ( in @ Xx @ A ) =>
% 1.26/1.68 ( ( ~( in @ Xx @ X ) ) =>
% 1.26/1.68 ( ~( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ))).
% 1.26/1.68 thf('0', plain,
% 1.26/1.68 (( binintersectTELcontra ) =
% 1.26/1.68 ( ![X4:$i,X6:$i]:
% 1.26/1.68 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 1.26/1.68 ( ![X8:$i]:
% 1.26/1.68 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 1.26/1.68 ( ![X10:$i]:
% 1.26/1.68 ( ( in @ X10 @ X4 ) =>
% 1.26/1.68 ( ( ~( in @ X10 @ X6 ) ) =>
% 1.26/1.68 ( ~( in @ X10 @ ( binintersect @ X6 @ X8 ) ) ) ) ) ) ) ) ) )),
% 1.26/1.68 define([status(thm)])).
% 1.26/1.68 thf(powersetTE1, axiom, powersetTE1 =
% 1.26/1.68 (![A:$i,X:$i]:
% 1.26/1.68 ( ( in @ X @ ( powerset @ A ) ) =>
% 1.26/1.68 ( ![Y:$i]:
% 1.26/1.68 ( ( in @ Y @ ( powerset @ A ) ) =>
% 1.26/1.68 ( ![Xx:$i]:
% 1.26/1.68 ( ( in @ Xx @ A ) =>
% 1.26/1.68 ( ( in @ X @ ( powerset @ Y ) ) =>
% 1.26/1.68 ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) ) ) ) ))).
% 1.26/1.68 thf('1', plain,
% 1.26/1.68 (( powersetTE1 ) =
% 1.26/1.68 ( ![X4:$i,X6:$i]:
% 1.26/1.68 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 1.26/1.68 ( ![X8:$i]:
% 1.26/1.68 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 1.26/1.68 ( ![X10:$i]:
% 1.26/1.68 ( ( in @ X10 @ X4 ) =>
% 1.26/1.68 ( ( in @ X6 @ ( powerset @ X8 ) ) =>
% 1.26/1.68 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) ) ) ) ) )),
% 1.26/1.68 define([status(thm)])).
% 1.26/1.68 thf(powersetTI1, axiom, powersetTI1 =
% 1.26/1.68 (![A:$i,X:$i]:
% 1.26/1.68 ( ( in @ X @ ( powerset @ A ) ) =>
% 1.26/1.68 ( ![Y:$i]:
% 1.26/1.68 ( ( in @ Y @ ( powerset @ A ) ) =>
% 1.26/1.68 ( ( ![Xx:$i]:
% 1.26/1.68 ( ( in @ Xx @ A ) => ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) =>
% 1.26/1.68 ( in @ X @ ( powerset @ Y ) ) ) ) ) ))).
% 1.26/1.68 thf('2', plain,
% 1.26/1.68 (( powersetTI1 ) =
% 1.26/1.68 ( ![X4:$i,X6:$i]:
% 1.26/1.68 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 1.26/1.68 ( ![X8:$i]:
% 1.26/1.68 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 1.26/1.68 ( ( ![X10:$i]:
% 1.26/1.68 ( ( in @ X10 @ X4 ) =>
% 1.26/1.68 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) =>
% 1.26/1.68 ( in @ X6 @ ( powerset @ X8 ) ) ) ) ) ) )),
% 1.26/1.68 define([status(thm)])).
% 1.26/1.68 thf(subsetTI, axiom, subsetTI =
% 1.26/1.68 (![A:$i,X:$i]:
% 1.26/1.68 ( ( in @ X @ ( powerset @ A ) ) =>
% 1.26/1.68 ( ![Y:$i]:
% 1.26/1.68 ( ( in @ Y @ ( powerset @ A ) ) =>
% 1.26/1.68 ( ( ![Xx:$i]:
% 1.26/1.68 ( ( in @ Xx @ A ) => ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) =>
% 1.26/1.68 ( subset @ X @ Y ) ) ) ) ))).
% 1.26/1.68 thf('3', plain,
% 1.26/1.68 (( subsetTI ) =
% 1.26/1.68 ( ![X4:$i,X6:$i]:
% 1.26/1.68 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 1.26/1.68 ( ![X8:$i]:
% 1.26/1.68 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 1.26/1.68 ( ( ![X10:$i]:
% 1.26/1.68 ( ( in @ X10 @ X4 ) =>
% 1.26/1.68 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) =>
% 1.26/1.68 ( subset @ X6 @ X8 ) ) ) ) ) )),
% 1.26/1.68 define([status(thm)])).
% 1.26/1.68 thf(setextT, axiom, setextT =
% 1.26/1.68 (![A:$i,X:$i]:
% 1.26/1.68 ( ( in @ X @ ( powerset @ A ) ) =>
% 1.26/1.68 ( ![Y:$i]:
% 1.26/1.68 ( ( in @ Y @ ( powerset @ A ) ) =>
% 1.26/1.68 ( ( ![Xx:$i]:
% 1.26/1.68 ( ( in @ Xx @ A ) => ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) =>
% 1.26/1.68 ( ( ![Xx:$i]:
% 1.26/1.68 ( ( in @ Xx @ A ) => ( ( in @ Xx @ Y ) => ( in @ Xx @ X ) ) ) ) =>
% 1.26/1.68 ( ( X ) = ( Y ) ) ) ) ) ) ))).
% 1.26/1.68 thf('4', plain,
% 1.26/1.68 (( setextT ) =
% 1.26/1.68 ( ![X4:$i,X6:$i]:
% 1.26/1.68 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 1.26/1.68 ( ![X8:$i]:
% 1.26/1.68 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 1.26/1.68 ( ( ![X10:$i]:
% 1.26/1.68 ( ( in @ X10 @ X4 ) =>
% 1.26/1.68 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) =>
% 1.26/1.68 ( ( ![X12:$i]:
% 1.26/1.68 ( ( in @ X12 @ X4 ) =>
% 1.26/1.68 ( ( in @ X12 @ X8 ) => ( in @ X12 @ X6 ) ) ) ) =>
% 1.26/1.68 ( ( X6 ) = ( X8 ) ) ) ) ) ) ) )),
% 1.26/1.68 define([status(thm)])).
% 1.26/1.68 thf(powersetT_lem, axiom, powersetT_lem =
% 1.26/1.68 (![A:$i,X:$i]:
% 1.26/1.68 ( ( in @ X @ ( powerset @ A ) ) =>
% 1.26/1.68 ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ))).
% 1.26/1.68 thf('5', plain,
% 1.26/1.68 (( powersetT_lem ) =
% 1.26/1.68 ( ![X4:$i,X6:$i]:
% 1.26/1.68 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 1.26/1.68 ( in @ ( powerset @ X6 ) @ ( powerset @ ( powerset @ X4 ) ) ) ) )),
% 1.26/1.68 define([status(thm)])).
% 1.26/1.68 thf(binintersectT_lem, axiom, binintersectT_lem =
% 1.26/1.68 (![A:$i,X:$i]:
% 1.26/1.68 ( ( in @ X @ ( powerset @ A ) ) =>
% 1.26/1.68 ( ![Y:$i]:
% 1.26/1.68 ( ( in @ Y @ ( powerset @ A ) ) =>
% 1.26/1.68 ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ))).
% 1.26/1.68 thf('6', plain,
% 1.26/1.68 (( binintersectT_lem ) =
% 1.26/1.68 ( ![X4:$i,X6:$i]:
% 1.26/1.68 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 1.26/1.68 ( ![X8:$i]:
% 1.26/1.68 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 1.26/1.68 ( in @ ( binintersect @ X6 @ X8 ) @ ( powerset @ X4 ) ) ) ) ) )),
% 1.26/1.68 define([status(thm)])).
% 1.26/1.68 thf(singletoninpowerset, axiom, singletoninpowerset =
% 1.26/1.68 (![A:$i,Xx:$i]:
% 1.26/1.68 ( ( in @ Xx @ A ) =>
% 1.26/1.68 ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ))).
% 1.26/1.68 thf('7', plain,
% 1.26/1.68 (( singletoninpowerset ) =
% 1.26/1.68 ( ![X4:$i,X6:$i]:
% 1.26/1.68 ( ( in @ X6 @ X4 ) =>
% 1.26/1.68 ( in @ ( setadjoin @ X6 @ emptyset ) @ ( powerset @ X4 ) ) ) )),
% 1.26/1.68 define([status(thm)])).
% 1.26/1.68 thf(bs114d, axiom, bs114d =
% 1.26/1.68 (![A:$i,B:$i,C:$i]:
% 1.26/1.68 ( ( binintersect @ A @ ( binunion @ B @ C ) ) =
% 1.26/1.68 ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ))).
% 1.26/1.68 thf('8', plain,
% 1.26/1.68 (( bs114d ) =
% 1.26/1.68 ( ![X4:$i,X6:$i,X8:$i]:
% 1.26/1.68 ( ( binintersect @ X4 @ ( binunion @ X6 @ X8 ) ) =
% 1.26/1.68 ( binunion @ ( binintersect @ X4 @ X6 ) @ ( binintersect @ X4 @ X8 ) ) ) )),
% 1.26/1.68 define([status(thm)])).
% 1.26/1.68 thf(binintersectSubset1, axiom, binintersectSubset1 =
% 1.26/1.68 (![A:$i,B:$i]:
% 1.26/1.68 ( ( ( binintersect @ A @ B ) = ( A ) ) => ( subset @ A @ B ) ))).
% 1.26/1.68 thf('9', plain,
% 1.26/1.68 (( binintersectSubset1 ) =
% 1.26/1.68 ( ![X4:$i,X6:$i]:
% 1.26/1.68 ( ( ( binintersect @ X4 @ X6 ) = ( X4 ) ) => ( subset @ X4 @ X6 ) ) )),
% 1.26/1.68 define([status(thm)])).
% 1.26/1.68 thf(binintersectSubset4, axiom, binintersectSubset4 =
% 1.26/1.68 (![A:$i,B:$i]:
% 1.26/1.68 ( ( subset @ B @ A ) => ( ( binintersect @ A @ B ) = ( B ) ) ))).
% 1.26/1.68 thf('10', plain,
% 1.26/1.68 (( binintersectSubset4 ) =
% 1.26/1.68 ( ![X4:$i,X6:$i]:
% 1.26/1.68 ( ( subset @ X6 @ X4 ) => ( ( binintersect @ X4 @ X6 ) = ( X6 ) ) ) )),
% 1.26/1.68 define([status(thm)])).
% 1.26/1.68 thf(binintersectRsub, axiom, binintersectRsub =
% 1.26/1.68 (![A:$i,B:$i]: ( subset @ ( binintersect @ A @ B ) @ B ))).
% 1.26/1.68 thf('11', plain,
% 1.26/1.68 (( binintersectRsub ) =
% 1.26/1.68 ( ![X4:$i,X6:$i]: ( subset @ ( binintersect @ X4 @ X6 ) @ X6 ) )),
% 1.26/1.68 define([status(thm)])).
% 1.26/1.68 thf(disjointsetsI1, axiom, disjointsetsI1 =
% 1.26/1.68 (![A:$i,B:$i]:
% 1.26/1.68 ( ( ~( ?[Xx:$i]: ( ( in @ Xx @ B ) & ( in @ Xx @ A ) ) ) ) =>
% 1.26/1.68 ( ( binintersect @ A @ B ) = ( emptyset ) ) ))).
% 1.26/1.68 thf('12', plain,
% 1.26/1.68 (( disjointsetsI1 ) =
% 1.26/1.68 ( ![X4:$i,X6:$i]:
% 1.26/1.68 ( ( ~( ?[X8:$i]: ( ( in @ X8 @ X6 ) & ( in @ X8 @ X4 ) ) ) ) =>
% 1.26/1.68 ( ( binintersect @ X4 @ X6 ) = ( emptyset ) ) ) )),
% 1.26/1.68 define([status(thm)])).
% 1.26/1.68 thf(binintersectER, axiom, binintersectER =
% 1.26/1.68 (![A:$i,B:$i,Xx:$i]:
% 1.26/1.68 ( ( in @ Xx @ ( binintersect @ A @ B ) ) => ( in @ Xx @ B ) ))).
% 1.26/1.68 thf('13', plain,
% 1.26/1.68 (( binintersectER ) =
% 1.26/1.68 ( ![X4:$i,X6:$i,X8:$i]:
% 1.26/1.68 ( ( in @ X8 @ ( binintersect @ X4 @ X6 ) ) => ( in @ X8 @ X6 ) ) )),
% 1.26/1.68 define([status(thm)])).
% 1.26/1.68 thf(binintersectSubset3, axiom, binintersectSubset3 =
% 1.26/1.68 (![A:$i,B:$i]:
% 1.26/1.68 ( ( ( binintersect @ A @ B ) = ( B ) ) => ( subset @ B @ A ) ))).
% 1.26/1.68 thf('14', plain,
% 1.26/1.68 (( binintersectSubset3 ) =
% 1.26/1.68 ( ![X4:$i,X6:$i]:
% 1.26/1.68 ( ( ( binintersect @ X4 @ X6 ) = ( X6 ) ) => ( subset @ X6 @ X4 ) ) )),
% 1.26/1.68 define([status(thm)])).
% 1.26/1.68 thf(binintersectSubset2, axiom, binintersectSubset2 =
% 1.26/1.68 (![A:$i,B:$i]:
% 1.26/1.68 ( ( subset @ A @ B ) => ( ( binintersect @ A @ B ) = ( A ) ) ))).
% 1.26/1.68 thf('15', plain,
% 1.26/1.68 (( binintersectSubset2 ) =
% 1.26/1.68 ( ![X4:$i,X6:$i]:
% 1.26/1.68 ( ( subset @ X4 @ X6 ) => ( ( binintersect @ X4 @ X6 ) = ( X4 ) ) ) )),
% 1.26/1.68 define([status(thm)])).
% 1.26/1.68 thf(binintersectLsub, axiom, binintersectLsub =
% 1.26/1.68 (![A:$i,B:$i]: ( subset @ ( binintersect @ A @ B ) @ A ))).
% 1.26/1.68 thf('16', plain,
% 1.26/1.68 (( binintersectLsub ) =
% 1.26/1.68 ( ![X4:$i,X6:$i]: ( subset @ ( binintersect @ X4 @ X6 ) @ X4 ) )),
% 1.26/1.68 define([status(thm)])).
% 1.26/1.68 thf(binintersectEL, axiom, binintersectEL =
% 1.26/1.68 (![A:$i,B:$i,Xx:$i]:
% 1.26/1.68 ( ( in @ Xx @ ( binintersect @ A @ B ) ) => ( in @ Xx @ A ) ))).
% 1.26/1.68 thf('17', plain,
% 1.26/1.68 (( binintersectEL ) =
% 1.26/1.68 ( ![X4:$i,X6:$i,X8:$i]:
% 1.26/1.68 ( ( in @ X8 @ ( binintersect @ X4 @ X6 ) ) => ( in @ X8 @ X4 ) ) )),
% 1.26/1.68 define([status(thm)])).
% 1.26/1.68 thf(binintersectSubset5, axiom, binintersectSubset5 =
% 1.26/1.68 (![A:$i,B:$i,C:$i]:
% 1.26/1.68 ( ( subset @ C @ A ) =>
% 1.26/1.68 ( ( subset @ C @ B ) => ( subset @ C @ ( binintersect @ A @ B ) ) ) ))).
% 1.26/1.68 thf('18', plain,
% 1.26/1.68 (( binintersectSubset5 ) =
% 1.26/1.68 ( ![X4:$i,X6:$i,X8:$i]:
% 1.26/1.68 ( ( subset @ X8 @ X4 ) =>
% 1.26/1.68 ( ( subset @ X8 @ X6 ) =>
% 1.26/1.68 ( subset @ X8 @ ( binintersect @ X4 @ X6 ) ) ) ) )),
% 1.26/1.68 define([status(thm)])).
% 1.26/1.68 thf(binintersectI, axiom, binintersectI =
% 1.26/1.68 (![A:$i,B:$i,Xx:$i]:
% 1.26/1.68 ( ( in @ Xx @ A ) =>
% 1.26/1.68 ( ( in @ Xx @ B ) => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ))).
% 1.26/1.68 thf('19', plain,
% 1.26/1.68 (( binintersectI ) =
% 1.26/1.68 ( ![X4:$i,X6:$i,X8:$i]:
% 1.26/1.68 ( ( in @ X8 @ X4 ) =>
% 1.26/1.68 ( ( in @ X8 @ X6 ) => ( in @ X8 @ ( binintersect @ X4 @ X6 ) ) ) ) )),
% 1.26/1.68 define([status(thm)])).
% 1.26/1.68 thf(powersetsubset, axiom, powersetsubset =
% 1.26/1.68 (![A:$i,B:$i]:
% 1.26/1.68 ( ( subset @ A @ B ) => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ))).
% 1.26/1.68 thf('20', plain,
% 1.26/1.68 (( powersetsubset ) =
% 1.26/1.68 ( ![X4:$i,X6:$i]:
% 1.26/1.68 ( ( subset @ X4 @ X6 ) =>
% 1.26/1.68 ( subset @ ( powerset @ X4 ) @ ( powerset @ X6 ) ) ) )),
% 1.26/1.68 define([status(thm)])).
% 1.26/1.68 thf(inPowerset, axiom, inPowerset = (![A:$i]: ( in @ A @ ( powerset @ A ) ))).
% 1.26/1.68 thf('21', plain,
% 1.26/1.68 (( inPowerset ) = ( ![X4:$i]: ( in @ X4 @ ( powerset @ X4 ) ) )),
% 1.26/1.68 define([status(thm)])).
% 1.26/1.68 thf(powersetE1, axiom, powersetE1 =
% 1.26/1.68 (![A:$i,B:$i]: ( ( in @ B @ ( powerset @ A ) ) => ( subset @ B @ A ) ))).
% 1.26/1.68 thf('22', plain,
% 1.26/1.68 (( powersetE1 ) =
% 1.26/1.68 ( ![X4:$i,X6:$i]:
% 1.26/1.68 ( ( in @ X6 @ ( powerset @ X4 ) ) => ( subset @ X6 @ X4 ) ) )),
% 1.26/1.68 define([status(thm)])).
% 1.26/1.68 thf(powersetI1, axiom, powersetI1 =
% 1.26/1.68 (![A:$i,B:$i]: ( ( subset @ B @ A ) => ( in @ B @ ( powerset @ A ) ) ))).
% 1.26/1.68 thf('23', plain,
% 1.26/1.68 (( powersetI1 ) =
% 1.26/1.68 ( ![X4:$i,X6:$i]:
% 1.26/1.68 ( ( subset @ X6 @ X4 ) => ( in @ X6 @ ( powerset @ X4 ) ) ) )),
% 1.26/1.68 define([status(thm)])).
% 1.26/1.68 thf(subset2powerset, axiom, subset2powerset =
% 1.26/1.68 (![A:$i,B:$i]: ( ( subset @ A @ B ) => ( in @ A @ ( powerset @ B ) ) ))).
% 1.26/1.68 thf('24', plain,
% 1.26/1.68 (( subset2powerset ) =
% 1.26/1.68 ( ![X4:$i,X6:$i]:
% 1.26/1.68 ( ( subset @ X4 @ X6 ) => ( in @ X4 @ ( powerset @ X6 ) ) ) )),
% 1.26/1.68 define([status(thm)])).
% 1.26/1.68 thf(powerset__Cong, axiom, powerset__Cong =
% 1.26/1.68 (![A:$i,B:$i]:
% 1.26/1.68 ( ( ( A ) = ( B ) ) => ( ( powerset @ A ) = ( powerset @ B ) ) ))).
% 1.26/1.68 thf('25', plain,
% 1.26/1.68 (( powerset__Cong ) =
% 1.26/1.68 ( ![X4:$i,X6:$i]:
% 1.26/1.68 ( ( ( X4 ) = ( X6 ) ) => ( ( powerset @ X4 ) = ( powerset @ X6 ) ) ) )),
% 1.26/1.68 define([status(thm)])).
% 1.26/1.68 thf(powersetE, axiom, powersetE =
% 1.26/1.68 (![A:$i,B:$i,Xx:$i]:
% 1.26/1.68 ( ( in @ B @ ( powerset @ A ) ) => ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ))).
% 1.26/1.68 thf('26', plain,
% 1.26/1.68 (( powersetE ) =
% 1.26/1.68 ( ![X4:$i,X6:$i,X8:$i]:
% 1.26/1.68 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 1.26/1.68 ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) )),
% 1.26/1.68 define([status(thm)])).
% 1.26/1.68 thf(emptyInPowerset, axiom, emptyInPowerset =
% 1.26/1.68 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))).
% 1.26/1.68 thf('27', plain,
% 1.26/1.68 (( emptyInPowerset ) =
% 1.26/1.68 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )),
% 1.26/1.68 define([status(thm)])).
% 1.26/1.68 thf(emptyinPowerset, axiom, emptyinPowerset =
% 1.26/1.68 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))).
% 1.26/1.68 thf('28', plain,
% 1.26/1.68 (( emptyinPowerset ) =
% 1.26/1.68 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )),
% 1.26/1.68 define([status(thm)])).
% 1.26/1.68 thf(powersetI, axiom, powersetI =
% 1.26/1.68 (![A:$i,B:$i]:
% 1.26/1.68 ( ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) =>
% 1.26/1.68 ( in @ B @ ( powerset @ A ) ) ))).
% 1.26/1.68 thf('29', plain,
% 1.26/1.68 (( powersetI ) =
% 1.26/1.68 ( ![X4:$i,X6:$i]:
% 1.26/1.68 ( ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) =>
% 1.26/1.68 ( in @ X6 @ ( powerset @ X4 ) ) ) )),
% 1.26/1.68 define([status(thm)])).
% 1.26/1.68 thf(powersetAx, axiom, powersetAx =
% 1.26/1.68 (![A:$i,B:$i]:
% 1.26/1.68 ( ( in @ B @ ( powerset @ A ) ) <=>
% 1.26/1.68 ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) ))).
% 1.26/1.68 thf('30', plain,
% 1.26/1.68 (( powersetAx ) =
% 1.26/1.68 ( ![X4:$i,X6:$i]:
% 1.26/1.68 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 1.26/1.68 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) )),
% 1.26/1.68 define([status(thm)])).
% 1.26/1.68 thf(binintersectTERcontra, conjecture,
% 1.26/1.68 (( setextAx ) =>
% 1.26/1.68 ( ( emptysetAx ) =>
% 1.26/1.68 ( ( setadjoinAx ) =>
% 1.26/1.68 ( ( powersetAx ) =>
% 1.26/1.68 ( ( setunionAx ) =>
% 1.26/1.68 ( ( omega0Ax ) =>
% 1.26/1.68 ( ( omegaSAx ) =>
% 1.26/1.68 ( ( omegaIndAx ) =>
% 1.26/1.68 ( ( replAx ) =>
% 1.26/1.68 ( ( foundationAx ) =>
% 1.26/1.68 ( ( wellorderingAx ) =>
% 1.26/1.68 ( ( descrp ) =>
% 1.26/1.68 ( ( dsetconstrI ) =>
% 1.26/1.68 ( ( dsetconstrEL ) =>
% 1.26/1.68 ( ( dsetconstrER ) =>
% 1.26/1.68 ( ( exuE1 ) =>
% 1.26/1.68 ( ( prop2setE ) =>
% 1.26/1.68 ( ( emptysetE ) =>
% 1.26/1.68 ( ( emptysetimpfalse ) =>
% 1.26/1.68 ( ( notinemptyset ) =>
% 1.26/1.68 ( ( exuE3e ) =>
% 1.26/1.68 ( ( setext ) =>
% 1.26/1.68 ( ( emptyI ) =>
% 1.26/1.68 ( ( noeltsimpempty ) =>
% 1.26/1.68 ( ( setbeta ) =>
% 1.26/1.68 ( ( nonemptyE1 ) =>
% 1.26/1.68 ( ( nonemptyI ) =>
% 1.26/1.68 ( ( nonemptyI1 ) =>
% 1.26/1.68 ( ( setadjoinIL ) =>
% 1.26/1.68 ( ( emptyinunitempty ) =>
% 1.26/1.68 ( ( setadjoinIR ) =>
% 1.26/1.68 ( ( setadjoinE ) =>
% 1.26/1.68 ( (
% 1.26/1.68 setadjoinOr ) =>
% 1.26/1.68 (
% 1.26/1.68 (
% 1.26/1.68 setoftrueEq ) =>
% 1.26/1.68 (
% 1.26/1.68 (
% 1.26/1.68 powersetI ) =>
% 1.26/1.68 (
% 1.26/1.68 (
% 1.26/1.68 emptyinPowerset ) =>
% 1.26/1.68 (
% 1.26/1.68 (
% 1.26/1.68 emptyInPowerset ) =>
% 1.26/1.68 (
% 1.26/1.68 (
% 1.26/1.68 powersetE ) =>
% 1.26/1.68 (
% 1.26/1.68 (
% 1.26/1.68 setunionI ) =>
% 1.26/1.68 (
% 1.26/1.68 (
% 1.26/1.68 setunionE ) =>
% 1.26/1.68 (
% 1.26/1.68 (
% 1.26/1.68 subPowSU ) =>
% 1.26/1.68 (
% 1.26/1.68 (
% 1.26/1.68 exuE2 ) =>
% 1.26/1.68 (
% 1.26/1.68 (
% 1.26/1.68 nonemptyImpWitness ) =>
% 1.26/1.68 (
% 1.26/1.68 (
% 1.26/1.68 uniqinunit ) =>
% 1.26/1.68 (
% 1.26/1.68 (
% 1.26/1.68 notinsingleton ) =>
% 1.26/1.68 (
% 1.26/1.68 (
% 1.26/1.68 eqinunit ) =>
% 1.26/1.68 (
% 1.26/1.68 (
% 1.26/1.68 singletonsswitch ) =>
% 1.26/1.68 (
% 1.26/1.68 (
% 1.26/1.68 upairsetE ) =>
% 1.26/1.68 (
% 1.26/1.68 (
% 1.26/1.68 upairsetIL ) =>
% 1.26/1.68 (
% 1.26/1.68 (
% 1.26/1.68 upairsetIR ) =>
% 1.26/1.68 (
% 1.26/1.68 (
% 1.26/1.68 emptyE1 ) =>
% 1.26/1.68 (
% 1.26/1.68 (
% 1.26/1.68 vacuousDall ) =>
% 1.26/1.68 (
% 1.26/1.68 (
% 1.26/1.68 quantDeMorgan1 ) =>
% 1.26/1.68 (
% 1.26/1.68 (
% 1.26/1.68 quantDeMorgan2 ) =>
% 1.26/1.68 (
% 1.26/1.68 (
% 1.26/1.68 quantDeMorgan3 ) =>
% 1.26/1.68 (
% 1.26/1.68 (
% 1.26/1.68 quantDeMorgan4 ) =>
% 1.26/1.68 (
% 1.26/1.68 (
% 1.26/1.68 prop2setI ) =>
% 1.26/1.68 (
% 1.26/1.68 (
% 1.26/1.68 prop2set2propI ) =>
% 1.26/1.68 (
% 1.26/1.68 (
% 1.26/1.68 notdexE ) =>
% 1.26/1.68 (
% 1.26/1.68 (
% 1.26/1.68 notdallE ) =>
% 1.26/1.68 (
% 1.26/1.68 (
% 1.26/1.68 exuI1 ) =>
% 1.26/1.68 (
% 1.26/1.68 (
% 1.26/1.68 exuI3 ) =>
% 1.26/1.68 (
% 1.26/1.68 (
% 1.26/1.68 exuI2 ) =>
% 1.26/1.68 (
% 1.26/1.68 (
% 1.26/1.68 inCongP ) =>
% 1.26/1.68 (
% 1.26/1.68 (
% 1.26/1.68 in__Cong ) =>
% 1.26/1.68 (
% 1.26/1.68 (
% 1.26/1.68 exuE3u ) =>
% 1.26/1.68 (
% 1.26/1.68 (
% 1.26/1.68 exu__Cong ) =>
% 1.26/1.68 (
% 1.26/1.68 (
% 1.26/1.68 emptyset__Cong ) =>
% 1.26/1.68 (
% 1.26/1.68 (
% 1.26/1.68 setadjoin__Cong ) =>
% 1.26/1.68 (
% 1.26/1.68 (
% 1.26/1.68 powerset__Cong ) =>
% 1.26/1.68 (
% 1.26/1.68 (
% 1.26/1.68 setunion__Cong ) =>
% 1.26/1.68 (
% 1.26/1.68 (
% 1.26/1.68 omega__Cong ) =>
% 1.26/1.68 (
% 1.26/1.68 (
% 1.26/1.68 exuEu ) =>
% 1.26/1.68 (
% 1.26/1.68 (
% 1.26/1.68 descr__Cong ) =>
% 1.26/1.68 (
% 1.26/1.68 (
% 1.26/1.68 dsetconstr__Cong ) =>
% 1.26/1.68 (
% 1.26/1.68 (
% 1.26/1.68 subsetI1 ) =>
% 1.26/1.68 (
% 1.26/1.68 (
% 1.26/1.68 eqimpsubset2 ) =>
% 1.26/1.68 (
% 1.26/1.68 (
% 1.26/1.68 eqimpsubset1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 subsetI2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 emptysetsubset ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 subsetE ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 subsetE2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 notsubsetI ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 notequalI1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 notequalI2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 subsetRefl ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 subsetTrans ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setadjoinSub ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setadjoinSub2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 subset2powerset ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setextsub ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 subsetemptysetimpeq ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 powersetI1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 powersetE1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 inPowerset ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 powersetsubset ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 sepInPowerset ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 sepSubset ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 binunionIL ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 upairset2IR ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 binunionIR ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 binunionEcases ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 binunionE ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 binunionLsub ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 binunionRsub ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 binintersectI ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 binintersectSubset5 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 binintersectEL ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 binintersectLsub ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 binintersectSubset2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 binintersectSubset3 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 binintersectER ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 disjointsetsI1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 binintersectRsub ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 binintersectSubset4 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 binintersectSubset1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 bs114d ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setminusI ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setminusEL ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setminusER ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setminusSubset2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setminusERneg ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setminusELneg ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setminusILneg ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setminusIRneg ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setminusLsub ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setminusSubset1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 symdiffE ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 symdiffI1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 symdiffI2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 symdiffIneg1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 symdiffIneg2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 secondinupair ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setukpairIL ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setukpairIR ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 kpairiskpair ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 kpairp ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 singletonsubset ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 singletoninpowerset ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 singletoninpowunion ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 upairset2E ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 upairsubunion ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 upairinpowunion ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ubforcartprodlem1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ubforcartprodlem2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ubforcartprodlem3 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 cartprodpairin ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 cartprodmempair1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 cartprodmempair ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setunionE2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setunionsingleton1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setunionsingleton2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setunionsingleton ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 singletonprop ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ex1E1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ex1I ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ex1I2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 singletonsuniq ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setukpairinjL1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 kfstsingleton ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 theprop ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 kfstpairEq ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 cartprodfstin ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setukpairinjL2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setukpairinjL ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setukpairinjR11 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setukpairinjR12 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setukpairinjR1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 upairequniteq ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setukpairinjR2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setukpairinjR ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ksndsingleton ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ksndpairEq ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 kpairsurjEq ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 cartprodsndin ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 cartprodpairmemEL ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 cartprodpairmemER ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 cartprodmempaircEq ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 cartprodfstpairEq ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 cartprodsndpairEq ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 cartprodpairsurjEq ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 dpsetconstrI ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 dpsetconstrSub ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setOfPairsIsBReln ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 dpsetconstrERa ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 dpsetconstrEL1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 dpsetconstrEL2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 dpsetconstrER ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 funcImageSingleton ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 apProp ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 app ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 infuncsetfunc ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ap2p ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 funcinfuncset ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 lamProp ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 lamp ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 lam2p ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 brelnall1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 brelnall2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ex1E2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 funcGraphProp1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 funcGraphProp3 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 funcGraphProp2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 funcextLem ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 funcGraphProp4 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 subbreln ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 eqbreln ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 funcext ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 funcext2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ap2apEq1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ap2apEq2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 beta1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 eta1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 lam2lamEq ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 beta2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 eta2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 iffalseProp1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 iffalseProp2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 iftrueProp1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 iftrueProp2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ifSingleton ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ifp ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 theeq ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 iftrue ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 iffalse ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 iftrueorfalse ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 binintersectT_lem ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 binunionT_lem ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 powersetT_lem ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setminusT_lem ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 complementT_lem ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setextT ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 subsetTI ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 powersetTI1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 powersetTE1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 complementTI1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 complementTE1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 binintersectTELcontra ) =>
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 A:$i,X:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X @
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 A ) ) =>
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 Y:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 Y @
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 A ) ) =>
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 Xx:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 Xx @ A ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ~(
% 1.26/1.69 in @
% 1.26/1.69 Xx @ Y ) ) =>
% 1.26/1.69 (
% 1.26/1.69 ~(
% 1.26/1.69 in @
% 1.26/1.69 Xx @
% 1.26/1.69 (
% 1.26/1.69 binintersect
% 1.26/1.69 @
% 1.26/1.69 X @ Y ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 1.26/1.69 thf(zf_stmt_0, conjecture,
% 1.26/1.69 (( setextAx ) =>
% 1.26/1.69 ( ( emptysetAx ) =>
% 1.26/1.69 ( ( setadjoinAx ) =>
% 1.26/1.69 ( ( ![X4:$i,X6:$i]:
% 1.26/1.69 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 1.26/1.69 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) ) =>
% 1.26/1.69 ( ( setunionAx ) =>
% 1.26/1.69 ( ( omega0Ax ) =>
% 1.26/1.69 ( ( omegaSAx ) =>
% 1.26/1.69 ( ( omegaIndAx ) =>
% 1.26/1.69 ( ( replAx ) =>
% 1.26/1.69 ( ( foundationAx ) =>
% 1.26/1.69 ( ( wellorderingAx ) =>
% 1.26/1.69 ( ( descrp ) =>
% 1.26/1.69 ( ( dsetconstrI ) =>
% 1.26/1.69 ( ( dsetconstrEL ) =>
% 1.26/1.69 ( ( dsetconstrER ) =>
% 1.26/1.69 ( ( exuE1 ) =>
% 1.26/1.69 ( ( prop2setE ) =>
% 1.26/1.69 ( ( emptysetE ) =>
% 1.26/1.69 ( ( emptysetimpfalse ) =>
% 1.26/1.69 ( ( notinemptyset ) =>
% 1.26/1.69 ( ( exuE3e ) =>
% 1.26/1.69 ( ( setext ) =>
% 1.26/1.69 ( ( emptyI ) =>
% 1.26/1.69 ( ( noeltsimpempty ) =>
% 1.26/1.69 ( ( setbeta ) =>
% 1.26/1.69 ( ( nonemptyE1 ) =>
% 1.26/1.69 ( ( nonemptyI ) =>
% 1.26/1.69 ( ( nonemptyI1 ) =>
% 1.26/1.69 ( ( setadjoinIL ) =>
% 1.26/1.69 ( ( emptyinunitempty ) =>
% 1.26/1.69 ( ( setadjoinIR ) =>
% 1.26/1.69 ( ( setadjoinE ) =>
% 1.26/1.69 ( (
% 1.26/1.69 setadjoinOr ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setoftrueEq ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X10:$i,
% 1.26/1.69 X12:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X14:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X14 @ X12 ) =>
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X14 @ X10 ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X12 @
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 X10 ) ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X16:$i]:
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 emptyset @
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 X16 ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X18:$i]:
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 emptyset @
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 X18 ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X20:$i,
% 1.26/1.69 X22:$i,
% 1.26/1.69 X24:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X22 @
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 X20 ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X24 @ X22 ) =>
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X24 @ X20 ) ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setunionI ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setunionE ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 subPowSU ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 exuE2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 nonemptyImpWitness ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 uniqinunit ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 notinsingleton ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 eqinunit ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 singletonsswitch ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 upairsetE ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 upairsetIL ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 upairsetIR ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 emptyE1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 vacuousDall ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 quantDeMorgan1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 quantDeMorgan2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 quantDeMorgan3 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 quantDeMorgan4 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 prop2setI ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 prop2set2propI ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 notdexE ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 notdallE ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 exuI1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 exuI3 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 exuI2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 inCongP ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in__Cong ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 exuE3u ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 exu__Cong ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 emptyset__Cong ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setadjoin__Cong ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X26:$i,
% 1.26/1.69 X28:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 X26 ) =
% 1.26/1.69 (
% 1.26/1.69 X28 ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 X26 ) =
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 X28 ) ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setunion__Cong ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 omega__Cong ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 exuEu ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 descr__Cong ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 dsetconstr__Cong ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 subsetI1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 eqimpsubset2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 eqimpsubset1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 subsetI2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 emptysetsubset ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 subsetE ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 subsetE2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 notsubsetI ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 notequalI1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 notequalI2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 subsetRefl ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 subsetTrans ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setadjoinSub ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setadjoinSub2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X30:$i,
% 1.26/1.69 X32:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 subset @
% 1.26/1.69 X30 @ X32 ) =>
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X30 @
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 X32 ) ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setextsub ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 subsetemptysetimpeq ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X34:$i,
% 1.26/1.69 X36:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 subset @
% 1.26/1.69 X36 @ X34 ) =>
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X36 @
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 X34 ) ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X38:$i,
% 1.26/1.69 X40:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X40 @
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 X38 ) ) =>
% 1.26/1.69 (
% 1.26/1.69 subset @
% 1.26/1.69 X40 @ X38 ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X42:$i]:
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X42 @
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 X42 ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X44:$i,
% 1.26/1.69 X46:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 subset @
% 1.26/1.69 X44 @ X46 ) =>
% 1.26/1.69 (
% 1.26/1.69 subset @
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 X44 ) @
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 X46 ) ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 sepInPowerset ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 sepSubset ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 binunionIL ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 upairset2IR ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 binunionIR ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 binunionEcases ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 binunionE ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 binunionLsub ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 binunionRsub ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X48:$i,
% 1.26/1.69 X50:$i,
% 1.26/1.69 X52:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X52 @ X48 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X52 @ X50 ) =>
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X52 @
% 1.26/1.69 (
% 1.26/1.69 binintersect
% 1.26/1.69 @
% 1.26/1.69 X48 @ X50 ) ) ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X54:$i,
% 1.26/1.69 X56:$i,
% 1.26/1.69 X58:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 subset @
% 1.26/1.69 X58 @ X54 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 subset @
% 1.26/1.69 X58 @ X56 ) =>
% 1.26/1.69 (
% 1.26/1.69 subset @
% 1.26/1.69 X58 @
% 1.26/1.69 (
% 1.26/1.69 binintersect
% 1.26/1.69 @
% 1.26/1.69 X54 @ X56 ) ) ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X60:$i,
% 1.26/1.69 X62:$i,
% 1.26/1.69 X64:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X64 @
% 1.26/1.69 (
% 1.26/1.69 binintersect
% 1.26/1.69 @
% 1.26/1.69 X60 @ X62 ) ) =>
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X64 @ X60 ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X66:$i,
% 1.26/1.69 X68:$i]:
% 1.26/1.69 (
% 1.26/1.69 subset @
% 1.26/1.69 (
% 1.26/1.69 binintersect
% 1.26/1.69 @
% 1.26/1.69 X66 @ X68 ) @
% 1.26/1.69 X66 ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X70:$i,
% 1.26/1.69 X72:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 subset @
% 1.26/1.69 X70 @ X72 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 binintersect
% 1.26/1.69 @
% 1.26/1.69 X70 @ X72 ) =
% 1.26/1.69 (
% 1.26/1.69 X70 ) ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X74:$i,
% 1.26/1.69 X76:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 binintersect
% 1.26/1.69 @
% 1.26/1.69 X74 @ X76 ) =
% 1.26/1.69 (
% 1.26/1.69 X76 ) ) =>
% 1.26/1.69 (
% 1.26/1.69 subset @
% 1.26/1.69 X76 @ X74 ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X78:$i,
% 1.26/1.69 X80:$i,
% 1.26/1.69 X82:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X82 @
% 1.26/1.69 (
% 1.26/1.69 binintersect
% 1.26/1.69 @
% 1.26/1.69 X78 @ X80 ) ) =>
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X82 @ X80 ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X84:$i,
% 1.26/1.69 X86:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ~(
% 1.26/1.69 ?[
% 1.26/1.69 X88:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X88 @ X84 ) &
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X88 @ X86 ) ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 binintersect
% 1.26/1.69 @
% 1.26/1.69 X84 @ X86 ) =
% 1.26/1.69 (
% 1.26/1.69 emptyset ) ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X90:$i,
% 1.26/1.69 X92:$i]:
% 1.26/1.69 (
% 1.26/1.69 subset @
% 1.26/1.69 (
% 1.26/1.69 binintersect
% 1.26/1.69 @
% 1.26/1.69 X90 @ X92 ) @
% 1.26/1.69 X92 ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X94:$i,
% 1.26/1.69 X96:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 subset @
% 1.26/1.69 X96 @ X94 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 binintersect
% 1.26/1.69 @
% 1.26/1.69 X94 @ X96 ) =
% 1.26/1.69 (
% 1.26/1.69 X96 ) ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X98:$i,
% 1.26/1.69 X100:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 binintersect
% 1.26/1.69 @
% 1.26/1.69 X98 @ X100 ) =
% 1.26/1.69 (
% 1.26/1.69 X98 ) ) =>
% 1.26/1.69 (
% 1.26/1.69 subset @
% 1.26/1.69 X98 @ X100 ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X102:$i,
% 1.26/1.69 X104:$i,
% 1.26/1.69 X106:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 binintersect
% 1.26/1.69 @
% 1.26/1.69 X102 @
% 1.26/1.69 (
% 1.26/1.69 binunion @
% 1.26/1.69 X104 @
% 1.26/1.69 X106 ) ) =
% 1.26/1.69 (
% 1.26/1.69 binunion @
% 1.26/1.69 (
% 1.26/1.69 binintersect
% 1.26/1.69 @
% 1.26/1.69 X102 @
% 1.26/1.69 X104 ) @
% 1.26/1.69 (
% 1.26/1.69 binintersect
% 1.26/1.69 @
% 1.26/1.69 X102 @
% 1.26/1.69 X106 ) ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setminusI ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setminusEL ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setminusER ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setminusSubset2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setminusERneg ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setminusELneg ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setminusILneg ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setminusIRneg ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setminusLsub ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setminusSubset1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 symdiffE ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 symdiffI1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 symdiffI2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 symdiffIneg1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 symdiffIneg2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 secondinupair ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setukpairIL ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setukpairIR ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 kpairiskpair ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 kpairp ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 singletonsubset ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X108:$i,
% 1.26/1.69 X110:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X110 @
% 1.26/1.69 X108 ) =>
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 (
% 1.26/1.69 setadjoin
% 1.26/1.69 @
% 1.26/1.69 X110 @
% 1.26/1.69 emptyset ) @
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 X108 ) ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 singletoninpowunion ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 upairset2E ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 upairsubunion ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 upairinpowunion ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ubforcartprodlem1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ubforcartprodlem2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ubforcartprodlem3 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 cartprodpairin ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 cartprodmempair1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 cartprodmempair ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setunionE2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setunionsingleton1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setunionsingleton2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setunionsingleton ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 singletonprop ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ex1E1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ex1I ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ex1I2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 singletonsuniq ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setukpairinjL1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 kfstsingleton ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 theprop ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 kfstpairEq ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 cartprodfstin ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setukpairinjL2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setukpairinjL ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setukpairinjR11 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setukpairinjR12 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setukpairinjR1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 upairequniteq ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setukpairinjR2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setukpairinjR ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ksndsingleton ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ksndpairEq ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 kpairsurjEq ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 cartprodsndin ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 cartprodpairmemEL ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 cartprodpairmemER ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 cartprodmempaircEq ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 cartprodfstpairEq ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 cartprodsndpairEq ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 cartprodpairsurjEq ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 dpsetconstrI ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 dpsetconstrSub ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setOfPairsIsBReln ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 dpsetconstrERa ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 dpsetconstrEL1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 dpsetconstrEL2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 dpsetconstrER ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 funcImageSingleton ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 apProp ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 app ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 infuncsetfunc ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ap2p ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 funcinfuncset ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 lamProp ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 lamp ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 lam2p ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 brelnall1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 brelnall2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ex1E2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 funcGraphProp1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 funcGraphProp3 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 funcGraphProp2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 funcextLem ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 funcGraphProp4 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 subbreln ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 eqbreln ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 funcext ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 funcext2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ap2apEq1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ap2apEq2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 beta1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 eta1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 lam2lamEq ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 beta2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 eta2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 iffalseProp1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 iffalseProp2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 iftrueProp1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 iftrueProp2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ifSingleton ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ifp ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 theeq ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 iftrue ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 iffalse ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 iftrueorfalse ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X112:$i,
% 1.26/1.69 X114:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X114 @
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 X112 ) ) =>
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X116:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X116 @
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 X112 ) ) =>
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 (
% 1.26/1.69 binintersect
% 1.26/1.69 @
% 1.26/1.69 X114 @
% 1.26/1.69 X116 ) @
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 X112 ) ) ) ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 binunionT_lem ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X118:$i,
% 1.26/1.69 X120:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X120 @
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 X118 ) ) =>
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 X120 ) @
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 X118 ) ) ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setminusT_lem ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 complementT_lem ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X122:$i,
% 1.26/1.69 X124:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X124 @
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 X122 ) ) =>
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X126:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X126 @
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 X122 ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X128:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X128 @
% 1.26/1.69 X122 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X128 @
% 1.26/1.69 X124 ) =>
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X128 @
% 1.26/1.69 X126 ) ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X130:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X130 @
% 1.26/1.69 X122 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X130 @
% 1.26/1.69 X126 ) =>
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X130 @
% 1.26/1.69 X124 ) ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 X124 ) =
% 1.26/1.69 (
% 1.26/1.69 X126 ) ) ) ) ) ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X132:$i,
% 1.26/1.69 X134:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X134 @
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 X132 ) ) =>
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X136:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X136 @
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 X132 ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X138:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X138 @
% 1.26/1.69 X132 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X138 @
% 1.26/1.69 X134 ) =>
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X138 @
% 1.26/1.69 X136 ) ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 subset @
% 1.26/1.69 X134 @
% 1.26/1.69 X136 ) ) ) ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X140:$i,
% 1.26/1.69 X142:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X142 @
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 X140 ) ) =>
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X144:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X144 @
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 X140 ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X146:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X146 @
% 1.26/1.69 X140 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X146 @
% 1.26/1.69 X142 ) =>
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X146 @
% 1.26/1.69 X144 ) ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X142 @
% 1.26/1.69 (
% 1.26/1.69 powerset @
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% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X148:$i,
% 1.26/1.69 X150:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X150 @
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 X148 ) ) =>
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X152:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X152 @
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 X148 ) ) =>
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X154:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X154 @
% 1.26/1.69 X148 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X150 @
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 X152 ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X154 @
% 1.26/1.69 X150 ) =>
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X154 @
% 1.26/1.69 X152 ) ) ) ) ) ) ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 complementTI1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 complementTE1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X156:$i,
% 1.26/1.69 X158:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X158 @
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 X156 ) ) =>
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X160:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X160 @
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 X156 ) ) =>
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X162:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X162 @
% 1.26/1.69 X156 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ~(
% 1.26/1.69 in @
% 1.26/1.69 X162 @
% 1.26/1.69 X158 ) ) =>
% 1.26/1.69 (
% 1.26/1.69 ~(
% 1.26/1.69 in @
% 1.26/1.69 X162 @
% 1.26/1.69 (
% 1.26/1.69 binintersect
% 1.26/1.69 @
% 1.26/1.69 X158 @
% 1.26/1.69 X160 ) ) ) ) ) ) ) ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X164:$i,
% 1.26/1.69 X166:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X166 @
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 X164 ) ) =>
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X168:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X168 @
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 X164 ) ) =>
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X170:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X170 @
% 1.26/1.69 X164 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ~(
% 1.26/1.69 in @
% 1.26/1.69 X170 @
% 1.26/1.69 X168 ) ) =>
% 1.26/1.69 (
% 1.26/1.69 ~(
% 1.26/1.69 in @
% 1.26/1.69 X170 @
% 1.26/1.69 (
% 1.26/1.69 binintersect
% 1.26/1.69 @
% 1.26/1.69 X166 @
% 1.26/1.69 X168 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 1.26/1.69 thf(zf_stmt_1, type, zip_tseitin_0 : $i > $i > $i > $o).
% 1.26/1.69 thf(zf_stmt_2, axiom,
% 1.26/1.69 (![X8:$i,X6:$i,X4:$i]:
% 1.26/1.69 ( ( zip_tseitin_0 @ X8 @ X6 @ X4 ) <=>
% 1.26/1.69 ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ))).
% 1.26/1.69 thf(zf_stmt_3, conjecture,
% 1.26/1.69 (( setextAx ) =>
% 1.26/1.69 ( ( emptysetAx ) =>
% 1.26/1.69 ( ( setadjoinAx ) =>
% 1.26/1.69 ( ( ![X4:$i,X6:$i]:
% 1.26/1.69 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 1.26/1.69 ( ![X8:$i]: ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) ) =>
% 1.26/1.69 ( ( setunionAx ) =>
% 1.26/1.69 ( ( omega0Ax ) =>
% 1.26/1.69 ( ( omegaSAx ) =>
% 1.26/1.69 ( ( omegaIndAx ) =>
% 1.26/1.69 ( ( replAx ) =>
% 1.26/1.69 ( ( foundationAx ) =>
% 1.26/1.69 ( ( wellorderingAx ) =>
% 1.26/1.69 ( ( descrp ) =>
% 1.26/1.69 ( ( dsetconstrI ) =>
% 1.26/1.69 ( ( dsetconstrEL ) =>
% 1.26/1.69 ( ( dsetconstrER ) =>
% 1.26/1.69 ( ( exuE1 ) =>
% 1.26/1.69 ( ( prop2setE ) =>
% 1.26/1.69 ( ( emptysetE ) =>
% 1.26/1.69 ( ( emptysetimpfalse ) =>
% 1.26/1.69 ( ( notinemptyset ) =>
% 1.26/1.69 ( ( exuE3e ) =>
% 1.26/1.69 ( ( setext ) =>
% 1.26/1.69 ( ( emptyI ) =>
% 1.26/1.69 ( ( noeltsimpempty ) =>
% 1.26/1.69 ( ( setbeta ) =>
% 1.26/1.69 ( ( nonemptyE1 ) =>
% 1.26/1.69 ( ( nonemptyI ) =>
% 1.26/1.69 ( ( nonemptyI1 ) =>
% 1.26/1.69 ( ( setadjoinIL ) =>
% 1.26/1.69 ( ( emptyinunitempty ) =>
% 1.26/1.69 ( ( setadjoinIR ) =>
% 1.26/1.69 ( ( setadjoinE ) =>
% 1.26/1.69 ( (
% 1.26/1.69 setadjoinOr ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setoftrueEq ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X10:$i,
% 1.26/1.69 X12:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X14:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X14 @ X12 ) =>
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X14 @ X10 ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X12 @
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 X10 ) ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X16:$i]:
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 emptyset @
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 X16 ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X18:$i]:
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 emptyset @
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 X18 ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X20:$i,
% 1.26/1.69 X22:$i,
% 1.26/1.69 X24:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X22 @
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 X20 ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X24 @ X22 ) =>
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X24 @ X20 ) ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setunionI ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setunionE ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 subPowSU ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 exuE2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 nonemptyImpWitness ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 uniqinunit ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 notinsingleton ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 eqinunit ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 singletonsswitch ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 upairsetE ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 upairsetIL ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 upairsetIR ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 emptyE1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 vacuousDall ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 quantDeMorgan1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 quantDeMorgan2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 quantDeMorgan3 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 quantDeMorgan4 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 prop2setI ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 prop2set2propI ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 notdexE ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 notdallE ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 exuI1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 exuI3 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 exuI2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 inCongP ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in__Cong ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 exuE3u ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 exu__Cong ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 emptyset__Cong ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setadjoin__Cong ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X26:$i,
% 1.26/1.69 X28:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 X26 ) =
% 1.26/1.69 (
% 1.26/1.69 X28 ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 X26 ) =
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 X28 ) ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setunion__Cong ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 omega__Cong ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 exuEu ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 descr__Cong ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 dsetconstr__Cong ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 subsetI1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 eqimpsubset2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 eqimpsubset1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 subsetI2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 emptysetsubset ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 subsetE ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 subsetE2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 notsubsetI ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 notequalI1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 notequalI2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 subsetRefl ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 subsetTrans ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setadjoinSub ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setadjoinSub2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X30:$i,
% 1.26/1.69 X32:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 subset @
% 1.26/1.69 X30 @ X32 ) =>
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X30 @
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 X32 ) ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setextsub ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 subsetemptysetimpeq ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X34:$i,
% 1.26/1.69 X36:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 subset @
% 1.26/1.69 X36 @ X34 ) =>
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X36 @
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 X34 ) ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X38:$i,
% 1.26/1.69 X40:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X40 @
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 X38 ) ) =>
% 1.26/1.69 (
% 1.26/1.69 subset @
% 1.26/1.69 X40 @ X38 ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X42:$i]:
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X42 @
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 X42 ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X44:$i,
% 1.26/1.69 X46:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 subset @
% 1.26/1.69 X44 @ X46 ) =>
% 1.26/1.69 (
% 1.26/1.69 subset @
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 X44 ) @
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 X46 ) ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 sepInPowerset ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 sepSubset ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 binunionIL ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 upairset2IR ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 binunionIR ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 binunionEcases ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 binunionE ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 binunionLsub ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 binunionRsub ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X48:$i,
% 1.26/1.69 X50:$i,
% 1.26/1.69 X52:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X52 @ X48 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X52 @ X50 ) =>
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X52 @
% 1.26/1.69 (
% 1.26/1.69 binintersect
% 1.26/1.69 @
% 1.26/1.69 X48 @ X50 ) ) ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X54:$i,
% 1.26/1.69 X56:$i,
% 1.26/1.69 X58:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 subset @
% 1.26/1.69 X58 @ X54 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 subset @
% 1.26/1.69 X58 @ X56 ) =>
% 1.26/1.69 (
% 1.26/1.69 subset @
% 1.26/1.69 X58 @
% 1.26/1.69 (
% 1.26/1.69 binintersect
% 1.26/1.69 @
% 1.26/1.69 X54 @ X56 ) ) ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X60:$i,
% 1.26/1.69 X62:$i,
% 1.26/1.69 X64:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X64 @
% 1.26/1.69 (
% 1.26/1.69 binintersect
% 1.26/1.69 @
% 1.26/1.69 X60 @ X62 ) ) =>
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X64 @ X60 ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X66:$i,
% 1.26/1.69 X68:$i]:
% 1.26/1.69 (
% 1.26/1.69 subset @
% 1.26/1.69 (
% 1.26/1.69 binintersect
% 1.26/1.69 @
% 1.26/1.69 X66 @ X68 ) @
% 1.26/1.69 X66 ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X70:$i,
% 1.26/1.69 X72:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 subset @
% 1.26/1.69 X70 @ X72 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 binintersect
% 1.26/1.69 @
% 1.26/1.69 X70 @ X72 ) =
% 1.26/1.69 (
% 1.26/1.69 X70 ) ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X74:$i,
% 1.26/1.69 X76:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 binintersect
% 1.26/1.69 @
% 1.26/1.69 X74 @ X76 ) =
% 1.26/1.69 (
% 1.26/1.69 X76 ) ) =>
% 1.26/1.69 (
% 1.26/1.69 subset @
% 1.26/1.69 X76 @ X74 ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X78:$i,
% 1.26/1.69 X80:$i,
% 1.26/1.69 X82:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X82 @
% 1.26/1.69 (
% 1.26/1.69 binintersect
% 1.26/1.69 @
% 1.26/1.69 X78 @ X80 ) ) =>
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X82 @ X80 ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X84:$i,
% 1.26/1.69 X86:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ~(
% 1.26/1.69 ?[
% 1.26/1.69 X88:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X88 @ X86 ) &
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X88 @ X84 ) ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 binintersect
% 1.26/1.69 @
% 1.26/1.69 X84 @ X86 ) =
% 1.26/1.69 (
% 1.26/1.69 emptyset ) ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X90:$i,
% 1.26/1.69 X92:$i]:
% 1.26/1.69 (
% 1.26/1.69 subset @
% 1.26/1.69 (
% 1.26/1.69 binintersect
% 1.26/1.69 @
% 1.26/1.69 X90 @ X92 ) @
% 1.26/1.69 X92 ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X94:$i,
% 1.26/1.69 X96:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 subset @
% 1.26/1.69 X96 @ X94 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 binintersect
% 1.26/1.69 @
% 1.26/1.69 X94 @ X96 ) =
% 1.26/1.69 (
% 1.26/1.69 X96 ) ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X98:$i,
% 1.26/1.69 X100:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 binintersect
% 1.26/1.69 @
% 1.26/1.69 X98 @ X100 ) =
% 1.26/1.69 (
% 1.26/1.69 X98 ) ) =>
% 1.26/1.69 (
% 1.26/1.69 subset @
% 1.26/1.69 X98 @ X100 ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X102:$i,
% 1.26/1.69 X104:$i,
% 1.26/1.69 X106:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 binintersect
% 1.26/1.69 @
% 1.26/1.69 X102 @
% 1.26/1.69 (
% 1.26/1.69 binunion @
% 1.26/1.69 X104 @
% 1.26/1.69 X106 ) ) =
% 1.26/1.69 (
% 1.26/1.69 binunion @
% 1.26/1.69 (
% 1.26/1.69 binintersect
% 1.26/1.69 @
% 1.26/1.69 X102 @
% 1.26/1.69 X104 ) @
% 1.26/1.69 (
% 1.26/1.69 binintersect
% 1.26/1.69 @
% 1.26/1.69 X102 @
% 1.26/1.69 X106 ) ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setminusI ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setminusEL ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setminusER ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setminusSubset2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setminusERneg ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setminusELneg ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setminusILneg ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setminusIRneg ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setminusLsub ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setminusSubset1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 symdiffE ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 symdiffI1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 symdiffI2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 symdiffIneg1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 symdiffIneg2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 secondinupair ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setukpairIL ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setukpairIR ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 kpairiskpair ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 kpairp ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 singletonsubset ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X108:$i,
% 1.26/1.69 X110:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X110 @
% 1.26/1.69 X108 ) =>
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 (
% 1.26/1.69 setadjoin
% 1.26/1.69 @
% 1.26/1.69 X110 @
% 1.26/1.69 emptyset ) @
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 X108 ) ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 singletoninpowunion ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 upairset2E ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 upairsubunion ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 upairinpowunion ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ubforcartprodlem1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ubforcartprodlem2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ubforcartprodlem3 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 cartprodpairin ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 cartprodmempair1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 cartprodmempair ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setunionE2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setunionsingleton1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setunionsingleton2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setunionsingleton ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 singletonprop ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ex1E1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ex1I ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ex1I2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 singletonsuniq ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setukpairinjL1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 kfstsingleton ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 theprop ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 kfstpairEq ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 cartprodfstin ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setukpairinjL2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setukpairinjL ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setukpairinjR11 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setukpairinjR12 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setukpairinjR1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 upairequniteq ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setukpairinjR2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setukpairinjR ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ksndsingleton ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ksndpairEq ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 kpairsurjEq ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 cartprodsndin ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 cartprodpairmemEL ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 cartprodpairmemER ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 cartprodmempaircEq ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 cartprodfstpairEq ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 cartprodsndpairEq ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 cartprodpairsurjEq ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 dpsetconstrI ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 dpsetconstrSub ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setOfPairsIsBReln ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 dpsetconstrERa ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 dpsetconstrEL1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 dpsetconstrEL2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 dpsetconstrER ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 funcImageSingleton ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 apProp ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 app ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 infuncsetfunc ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ap2p ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 funcinfuncset ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 lamProp ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 lamp ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 lam2p ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 brelnall1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 brelnall2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ex1E2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 funcGraphProp1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 funcGraphProp3 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 funcGraphProp2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 funcextLem ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 funcGraphProp4 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 subbreln ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 eqbreln ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 funcext ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 funcext2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ap2apEq1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ap2apEq2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 beta1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 eta1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 lam2lamEq ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 beta2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 eta2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 iffalseProp1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 iffalseProp2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 iftrueProp1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 iftrueProp2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ifSingleton ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ifp ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 theeq ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 iftrue ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 iffalse ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 iftrueorfalse ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X112:$i,
% 1.26/1.69 X114:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X114 @
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 X112 ) ) =>
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X116:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X116 @
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 X112 ) ) =>
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 (
% 1.26/1.69 binintersect
% 1.26/1.69 @
% 1.26/1.69 X114 @
% 1.26/1.69 X116 ) @
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 X112 ) ) ) ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 binunionT_lem ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X118:$i,
% 1.26/1.69 X120:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X120 @
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 X118 ) ) =>
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 X120 ) @
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 X118 ) ) ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setminusT_lem ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 complementT_lem ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X122:$i,
% 1.26/1.69 X124:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X124 @
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 X122 ) ) =>
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X126:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X126 @
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 X122 ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X128:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X128 @
% 1.26/1.69 X122 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X128 @
% 1.26/1.69 X124 ) =>
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X128 @
% 1.26/1.69 X126 ) ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X130:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X130 @
% 1.26/1.69 X122 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X130 @
% 1.26/1.69 X126 ) =>
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X130 @
% 1.26/1.69 X124 ) ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 X124 ) =
% 1.26/1.69 (
% 1.26/1.69 X126 ) ) ) ) ) ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X132:$i,
% 1.26/1.69 X134:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X134 @
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 X132 ) ) =>
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X136:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X136 @
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 X132 ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X138:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X138 @
% 1.26/1.69 X132 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X138 @
% 1.26/1.69 X134 ) =>
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X138 @
% 1.26/1.69 X136 ) ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 subset @
% 1.26/1.69 X134 @
% 1.26/1.69 X136 ) ) ) ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X140:$i,
% 1.26/1.69 X142:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X142 @
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 X140 ) ) =>
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X144:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X144 @
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 X140 ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X146:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X146 @
% 1.26/1.69 X140 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X146 @
% 1.26/1.69 X142 ) =>
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X146 @
% 1.26/1.69 X144 ) ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X142 @
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 X144 ) ) ) ) ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X148:$i,
% 1.26/1.69 X150:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X150 @
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 X148 ) ) =>
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X152:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X152 @
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 X148 ) ) =>
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X154:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X154 @
% 1.26/1.69 X148 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X150 @
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 X152 ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X154 @
% 1.26/1.69 X150 ) =>
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X154 @
% 1.26/1.69 X152 ) ) ) ) ) ) ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 complementTI1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 complementTE1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X156:$i,
% 1.26/1.69 X158:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X158 @
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 X156 ) ) =>
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X160:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X160 @
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 X156 ) ) =>
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X162:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X162 @
% 1.26/1.69 X156 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ~(
% 1.26/1.69 in @
% 1.26/1.69 X162 @
% 1.26/1.69 X158 ) ) =>
% 1.26/1.69 (
% 1.26/1.69 ~(
% 1.26/1.69 in @
% 1.26/1.69 X162 @
% 1.26/1.69 (
% 1.26/1.69 binintersect
% 1.26/1.69 @
% 1.26/1.69 X158 @
% 1.26/1.69 X160 ) ) ) ) ) ) ) ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X164:$i,
% 1.26/1.69 X166:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X166 @
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 X164 ) ) =>
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X168:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X168 @
% 1.26/1.69 (
% 1.26/1.69 powerset @
% 1.26/1.69 X164 ) ) =>
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X170:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X170 @
% 1.26/1.69 X164 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ~(
% 1.26/1.69 in @
% 1.26/1.69 X170 @
% 1.26/1.69 X168 ) ) =>
% 1.26/1.69 (
% 1.26/1.69 ~(
% 1.26/1.69 in @
% 1.26/1.69 X170 @
% 1.26/1.69 (
% 1.26/1.69 binintersect
% 1.26/1.69 @
% 1.26/1.69 X166 @
% 1.26/1.69 X168 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 1.26/1.69 thf(zf_stmt_4, negated_conjecture,
% 1.26/1.69 (~( ( setextAx ) =>
% 1.26/1.69 ( ( emptysetAx ) =>
% 1.26/1.69 ( ( setadjoinAx ) =>
% 1.26/1.69 ( ( ![X4:$i,X6:$i]:
% 1.26/1.69 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 1.26/1.69 ( ![X8:$i]: ( zip_tseitin_0 @ X8 @ X6 @ X4 ) ) ) ) =>
% 1.26/1.69 ( ( setunionAx ) =>
% 1.26/1.69 ( ( omega0Ax ) =>
% 1.26/1.69 ( ( omegaSAx ) =>
% 1.26/1.69 ( ( omegaIndAx ) =>
% 1.26/1.69 ( ( replAx ) =>
% 1.26/1.69 ( ( foundationAx ) =>
% 1.26/1.69 ( ( wellorderingAx ) =>
% 1.26/1.69 ( ( descrp ) =>
% 1.26/1.69 ( ( dsetconstrI ) =>
% 1.26/1.69 ( ( dsetconstrEL ) =>
% 1.26/1.69 ( ( dsetconstrER ) =>
% 1.26/1.69 ( ( exuE1 ) =>
% 1.26/1.69 ( ( prop2setE ) =>
% 1.26/1.69 ( ( emptysetE ) =>
% 1.26/1.69 ( ( emptysetimpfalse ) =>
% 1.26/1.69 ( ( notinemptyset ) =>
% 1.26/1.69 ( ( exuE3e ) =>
% 1.26/1.69 ( ( setext ) =>
% 1.26/1.69 ( ( emptyI ) =>
% 1.26/1.69 ( ( noeltsimpempty ) =>
% 1.26/1.69 ( ( setbeta ) =>
% 1.26/1.69 ( ( nonemptyE1 ) =>
% 1.26/1.69 ( ( nonemptyI ) =>
% 1.26/1.69 ( ( nonemptyI1 ) =>
% 1.26/1.69 ( ( setadjoinIL ) =>
% 1.26/1.69 ( ( emptyinunitempty ) =>
% 1.26/1.69 ( ( setadjoinIR ) =>
% 1.26/1.69 ( (
% 1.26/1.69 setadjoinE ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setadjoinOr ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setoftrueEq ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X10:$i,
% 1.26/1.69 X12:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X14:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X14 @ X12 ) =>
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X14 @ X10 ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X12 @
% 1.26/1.69 (
% 1.26/1.69 powerset
% 1.26/1.69 @
% 1.26/1.69 X10 ) ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X16:$i]:
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 emptyset @
% 1.26/1.69 (
% 1.26/1.69 powerset
% 1.26/1.69 @
% 1.26/1.69 X16 ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X18:$i]:
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 emptyset @
% 1.26/1.69 (
% 1.26/1.69 powerset
% 1.26/1.69 @
% 1.26/1.69 X18 ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X20:$i,
% 1.26/1.69 X22:$i,
% 1.26/1.69 X24:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X22 @
% 1.26/1.69 (
% 1.26/1.69 powerset
% 1.26/1.69 @
% 1.26/1.69 X20 ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X24 @ X22 ) =>
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X24 @ X20 ) ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setunionI ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setunionE ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 subPowSU ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 exuE2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 nonemptyImpWitness ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 uniqinunit ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 notinsingleton ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 eqinunit ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 singletonsswitch ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 upairsetE ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 upairsetIL ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 upairsetIR ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 emptyE1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 vacuousDall ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 quantDeMorgan1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 quantDeMorgan2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 quantDeMorgan3 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 quantDeMorgan4 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 prop2setI ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 prop2set2propI ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 notdexE ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 notdallE ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 exuI1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 exuI3 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 exuI2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 inCongP ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in__Cong ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 exuE3u ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 exu__Cong ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 emptyset__Cong ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setadjoin__Cong ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X26:$i,
% 1.26/1.69 X28:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 X26 ) =
% 1.26/1.69 (
% 1.26/1.69 X28 ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 powerset
% 1.26/1.69 @
% 1.26/1.69 X26 ) =
% 1.26/1.69 (
% 1.26/1.69 powerset
% 1.26/1.69 @
% 1.26/1.69 X28 ) ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setunion__Cong ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 omega__Cong ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 exuEu ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 descr__Cong ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 dsetconstr__Cong ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 subsetI1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 eqimpsubset2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 eqimpsubset1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 subsetI2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 emptysetsubset ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 subsetE ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 subsetE2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 notsubsetI ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 notequalI1 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 notequalI2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 subsetRefl ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 subsetTrans ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setadjoinSub ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setadjoinSub2 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X30:$i,
% 1.26/1.69 X32:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 subset @
% 1.26/1.69 X30 @ X32 ) =>
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X30 @
% 1.26/1.69 (
% 1.26/1.69 powerset
% 1.26/1.69 @
% 1.26/1.69 X32 ) ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 setextsub ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 subsetemptysetimpeq ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X34:$i,
% 1.26/1.69 X36:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 subset @
% 1.26/1.69 X36 @ X34 ) =>
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X36 @
% 1.26/1.69 (
% 1.26/1.69 powerset
% 1.26/1.69 @
% 1.26/1.69 X34 ) ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X38:$i,
% 1.26/1.69 X40:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X40 @
% 1.26/1.69 (
% 1.26/1.69 powerset
% 1.26/1.69 @
% 1.26/1.69 X38 ) ) =>
% 1.26/1.69 (
% 1.26/1.69 subset @
% 1.26/1.69 X40 @ X38 ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X42:$i]:
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X42 @
% 1.26/1.69 (
% 1.26/1.69 powerset
% 1.26/1.69 @
% 1.26/1.69 X42 ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X44:$i,
% 1.26/1.69 X46:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 subset @
% 1.26/1.69 X44 @ X46 ) =>
% 1.26/1.69 (
% 1.26/1.69 subset @
% 1.26/1.69 (
% 1.26/1.69 powerset
% 1.26/1.69 @
% 1.26/1.69 X44 ) @
% 1.26/1.69 (
% 1.26/1.69 powerset
% 1.26/1.69 @
% 1.26/1.69 X46 ) ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 sepInPowerset ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 sepSubset ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 binunionIL ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 upairset2IR ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 binunionIR ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 binunionEcases ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 binunionE ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 binunionLsub ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 binunionRsub ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X48:$i,
% 1.26/1.69 X50:$i,
% 1.26/1.69 X52:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X52 @ X48 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X52 @ X50 ) =>
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X52 @
% 1.26/1.69 (
% 1.26/1.69 binintersect
% 1.26/1.69 @
% 1.26/1.69 X48 @ X50 ) ) ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X54:$i,
% 1.26/1.69 X56:$i,
% 1.26/1.69 X58:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 subset @
% 1.26/1.69 X58 @ X54 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 subset @
% 1.26/1.69 X58 @ X56 ) =>
% 1.26/1.69 (
% 1.26/1.69 subset @
% 1.26/1.69 X58 @
% 1.26/1.69 (
% 1.26/1.69 binintersect
% 1.26/1.69 @
% 1.26/1.69 X54 @ X56 ) ) ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
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% 1.26/1.69 X62:$i,
% 1.26/1.69 X64:$i]:
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% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X64 @
% 1.26/1.69 (
% 1.26/1.69 binintersect
% 1.26/1.69 @
% 1.26/1.69 X60 @ X62 ) ) =>
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% 1.26/1.69 in @
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% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X66:$i,
% 1.26/1.69 X68:$i]:
% 1.26/1.69 (
% 1.26/1.69 subset @
% 1.26/1.69 (
% 1.26/1.69 binintersect
% 1.26/1.69 @
% 1.26/1.69 X66 @ X68 ) @
% 1.26/1.69 X66 ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X70:$i,
% 1.26/1.69 X72:$i]:
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% 1.26/1.69 (
% 1.26/1.69 subset @
% 1.26/1.69 X70 @ X72 ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 binintersect
% 1.26/1.69 @
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% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X74:$i,
% 1.26/1.69 X76:$i]:
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 binintersect
% 1.26/1.69 @
% 1.26/1.69 X74 @ X76 ) =
% 1.26/1.69 (
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% 1.26/1.69 (
% 1.26/1.69 subset @
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% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
% 1.26/1.69 X78:$i,
% 1.26/1.69 X80:$i,
% 1.26/1.69 X82:$i]:
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% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X82 @
% 1.26/1.69 (
% 1.26/1.69 binintersect
% 1.26/1.69 @
% 1.26/1.69 X78 @ X80 ) ) =>
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% 1.26/1.69 in @
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% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 ![
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% 1.26/1.69 ~
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% 1.26/1.69 (
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% 1.26/1.69 X88 @ X86 ) &
% 1.26/1.69 (
% 1.26/1.69 in @
% 1.26/1.69 X88 @ X84 ) ) ) ) =>
% 1.26/1.69 (
% 1.26/1.69 (
% 1.26/1.69 binintersect
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% 1.26/1.70 (
% 1.26/1.70 ![
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% 1.26/1.70 X92:$i]:
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% 1.26/1.70 subset @
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% 1.26/1.70 X90 @ X92 ) @
% 1.26/1.70 X92 ) ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 ![
% 1.26/1.70 X94:$i,
% 1.26/1.70 X96:$i]:
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 subset @
% 1.26/1.70 X96 @ X94 ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 binintersect
% 1.26/1.70 @
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% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 ![
% 1.26/1.70 X98:$i,
% 1.26/1.70 X100:$i]:
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 binintersect
% 1.26/1.70 @
% 1.26/1.70 X98 @
% 1.26/1.70 X100 ) =
% 1.26/1.70 (
% 1.26/1.70 X98 ) ) =>
% 1.26/1.70 (
% 1.26/1.70 subset @
% 1.26/1.70 X98 @
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% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 ![
% 1.26/1.70 X102:$i,
% 1.26/1.70 X104:$i,
% 1.26/1.70 X106:$i]:
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 binintersect
% 1.26/1.70 @
% 1.26/1.70 X102 @
% 1.26/1.70 (
% 1.26/1.70 binunion
% 1.26/1.70 @
% 1.26/1.70 X104 @
% 1.26/1.70 X106 ) ) =
% 1.26/1.70 (
% 1.26/1.70 binunion
% 1.26/1.70 @
% 1.26/1.70 (
% 1.26/1.70 binintersect
% 1.26/1.70 @
% 1.26/1.70 X102 @
% 1.26/1.70 X104 ) @
% 1.26/1.70 (
% 1.26/1.70 binintersect
% 1.26/1.70 @
% 1.26/1.70 X102 @
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% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 setminusI ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 setminusEL ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 setminusER ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 setminusSubset2 ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 setminusERneg ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 setminusELneg ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 setminusILneg ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 setminusIRneg ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 setminusLsub ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 setminusSubset1 ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 symdiffE ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 symdiffI1 ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 symdiffI2 ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 symdiffIneg1 ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 symdiffIneg2 ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 secondinupair ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 setukpairIL ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 setukpairIR ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 kpairiskpair ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 kpairp ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 singletonsubset ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 ![
% 1.26/1.70 X108:$i,
% 1.26/1.70 X110:$i]:
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 in @
% 1.26/1.70 X110 @
% 1.26/1.70 X108 ) =>
% 1.26/1.70 (
% 1.26/1.70 in @
% 1.26/1.70 (
% 1.26/1.70 setadjoin
% 1.26/1.70 @
% 1.26/1.70 X110 @
% 1.26/1.70 emptyset ) @
% 1.26/1.70 (
% 1.26/1.70 powerset
% 1.26/1.70 @
% 1.26/1.70 X108 ) ) ) ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 singletoninpowunion ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 upairset2E ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 upairsubunion ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 upairinpowunion ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 ubforcartprodlem1 ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 ubforcartprodlem2 ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 ubforcartprodlem3 ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 cartprodpairin ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 cartprodmempair1 ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 cartprodmempair ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 setunionE2 ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 setunionsingleton1 ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 setunionsingleton2 ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 setunionsingleton ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 singletonprop ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 ex1E1 ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 ex1I ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 ex1I2 ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 singletonsuniq ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 setukpairinjL1 ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 kfstsingleton ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 theprop ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 kfstpairEq ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 cartprodfstin ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 setukpairinjL2 ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 setukpairinjL ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 setukpairinjR11 ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 setukpairinjR12 ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 setukpairinjR1 ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 upairequniteq ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 setukpairinjR2 ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 setukpairinjR ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 ksndsingleton ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 ksndpairEq ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 kpairsurjEq ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 cartprodsndin ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 cartprodpairmemEL ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 cartprodpairmemER ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 cartprodmempaircEq ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 cartprodfstpairEq ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 cartprodsndpairEq ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 cartprodpairsurjEq ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 dpsetconstrI ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 dpsetconstrSub ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 setOfPairsIsBReln ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 dpsetconstrERa ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 dpsetconstrEL1 ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 dpsetconstrEL2 ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 dpsetconstrER ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 funcImageSingleton ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 apProp ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 app ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 infuncsetfunc ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 ap2p ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 funcinfuncset ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 lamProp ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 lamp ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 lam2p ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 brelnall1 ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 brelnall2 ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 ex1E2 ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 funcGraphProp1 ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 funcGraphProp3 ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 funcGraphProp2 ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 funcextLem ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 funcGraphProp4 ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 subbreln ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 eqbreln ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 funcext ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 funcext2 ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 ap2apEq1 ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 ap2apEq2 ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 beta1 ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 eta1 ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 lam2lamEq ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 beta2 ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 eta2 ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 iffalseProp1 ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 iffalseProp2 ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 iftrueProp1 ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 iftrueProp2 ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 ifSingleton ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 ifp ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 theeq ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 iftrue ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 iffalse ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 iftrueorfalse ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 ![
% 1.26/1.70 X112:$i,
% 1.26/1.70 X114:$i]:
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 in @
% 1.26/1.70 X114 @
% 1.26/1.70 (
% 1.26/1.70 powerset
% 1.26/1.70 @
% 1.26/1.70 X112 ) ) =>
% 1.26/1.70 (
% 1.26/1.70 ![
% 1.26/1.70 X116:$i]:
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 in @
% 1.26/1.70 X116 @
% 1.26/1.70 (
% 1.26/1.70 powerset
% 1.26/1.70 @
% 1.26/1.70 X112 ) ) =>
% 1.26/1.70 (
% 1.26/1.70 in @
% 1.26/1.70 (
% 1.26/1.70 binintersect
% 1.26/1.70 @
% 1.26/1.70 X114 @
% 1.26/1.70 X116 ) @
% 1.26/1.70 (
% 1.26/1.70 powerset
% 1.26/1.70 @
% 1.26/1.70 X112 ) ) ) ) ) ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 binunionT_lem ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 ![
% 1.26/1.70 X118:$i,
% 1.26/1.70 X120:$i]:
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 in @
% 1.26/1.70 X120 @
% 1.26/1.70 (
% 1.26/1.70 powerset
% 1.26/1.70 @
% 1.26/1.70 X118 ) ) =>
% 1.26/1.70 (
% 1.26/1.70 in @
% 1.26/1.70 (
% 1.26/1.70 powerset
% 1.26/1.70 @
% 1.26/1.70 X120 ) @
% 1.26/1.70 (
% 1.26/1.70 powerset
% 1.26/1.70 @
% 1.26/1.70 (
% 1.26/1.70 powerset
% 1.26/1.70 @
% 1.26/1.70 X118 ) ) ) ) ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 setminusT_lem ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 complementT_lem ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 ![
% 1.26/1.70 X122:$i,
% 1.26/1.70 X124:$i]:
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 in @
% 1.26/1.70 X124 @
% 1.26/1.70 (
% 1.26/1.70 powerset
% 1.26/1.70 @
% 1.26/1.70 X122 ) ) =>
% 1.26/1.70 (
% 1.26/1.70 ![
% 1.26/1.70 X126:$i]:
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 in @
% 1.26/1.70 X126 @
% 1.26/1.70 (
% 1.26/1.70 powerset
% 1.26/1.70 @
% 1.26/1.70 X122 ) ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 ![
% 1.26/1.70 X128:$i]:
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 in @
% 1.26/1.70 X128 @
% 1.26/1.70 X122 ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 in @
% 1.26/1.70 X128 @
% 1.26/1.70 X124 ) =>
% 1.26/1.70 (
% 1.26/1.70 in @
% 1.26/1.70 X128 @
% 1.26/1.70 X126 ) ) ) ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 ![
% 1.26/1.70 X130:$i]:
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 in @
% 1.26/1.70 X130 @
% 1.26/1.70 X122 ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 in @
% 1.26/1.70 X130 @
% 1.26/1.70 X126 ) =>
% 1.26/1.70 (
% 1.26/1.70 in @
% 1.26/1.70 X130 @
% 1.26/1.70 X124 ) ) ) ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 X124 ) =
% 1.26/1.70 (
% 1.26/1.70 X126 ) ) ) ) ) ) ) ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 ![
% 1.26/1.70 X132:$i,
% 1.26/1.70 X134:$i]:
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 in @
% 1.26/1.70 X134 @
% 1.26/1.70 (
% 1.26/1.70 powerset
% 1.26/1.70 @
% 1.26/1.70 X132 ) ) =>
% 1.26/1.70 (
% 1.26/1.70 ![
% 1.26/1.70 X136:$i]:
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 in @
% 1.26/1.70 X136 @
% 1.26/1.70 (
% 1.26/1.70 powerset
% 1.26/1.70 @
% 1.26/1.70 X132 ) ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 ![
% 1.26/1.70 X138:$i]:
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 in @
% 1.26/1.70 X138 @
% 1.26/1.70 X132 ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 in @
% 1.26/1.70 X138 @
% 1.26/1.70 X134 ) =>
% 1.26/1.70 (
% 1.26/1.70 in @
% 1.26/1.70 X138 @
% 1.26/1.70 X136 ) ) ) ) =>
% 1.26/1.70 (
% 1.26/1.70 subset @
% 1.26/1.70 X134 @
% 1.26/1.70 X136 ) ) ) ) ) ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 ![
% 1.26/1.70 X140:$i,
% 1.26/1.70 X142:$i]:
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 in @
% 1.26/1.70 X142 @
% 1.26/1.70 (
% 1.26/1.70 powerset
% 1.26/1.70 @
% 1.26/1.70 X140 ) ) =>
% 1.26/1.70 (
% 1.26/1.70 ![
% 1.26/1.70 X144:$i]:
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 in @
% 1.26/1.70 X144 @
% 1.26/1.70 (
% 1.26/1.70 powerset
% 1.26/1.70 @
% 1.26/1.70 X140 ) ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 ![
% 1.26/1.70 X146:$i]:
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 in @
% 1.26/1.70 X146 @
% 1.26/1.70 X140 ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 in @
% 1.26/1.70 X146 @
% 1.26/1.70 X142 ) =>
% 1.26/1.70 (
% 1.26/1.70 in @
% 1.26/1.70 X146 @
% 1.26/1.70 X144 ) ) ) ) =>
% 1.26/1.70 (
% 1.26/1.70 in @
% 1.26/1.70 X142 @
% 1.26/1.70 (
% 1.26/1.70 powerset
% 1.26/1.70 @
% 1.26/1.70 X144 ) ) ) ) ) ) ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 ![
% 1.26/1.70 X148:$i,
% 1.26/1.70 X150:$i]:
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 in @
% 1.26/1.70 X150 @
% 1.26/1.70 (
% 1.26/1.70 powerset
% 1.26/1.70 @
% 1.26/1.70 X148 ) ) =>
% 1.26/1.70 (
% 1.26/1.70 ![
% 1.26/1.70 X152:$i]:
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 in @
% 1.26/1.70 X152 @
% 1.26/1.70 (
% 1.26/1.70 powerset
% 1.26/1.70 @
% 1.26/1.70 X148 ) ) =>
% 1.26/1.70 (
% 1.26/1.70 ![
% 1.26/1.70 X154:$i]:
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 in @
% 1.26/1.70 X154 @
% 1.26/1.70 X148 ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 in @
% 1.26/1.70 X150 @
% 1.26/1.70 (
% 1.26/1.70 powerset
% 1.26/1.70 @
% 1.26/1.70 X152 ) ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 in @
% 1.26/1.70 X154 @
% 1.26/1.70 X150 ) =>
% 1.26/1.70 (
% 1.26/1.70 in @
% 1.26/1.70 X154 @
% 1.26/1.70 X152 ) ) ) ) ) ) ) ) ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 complementTI1 ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 complementTE1 ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 ![
% 1.26/1.70 X156:$i,
% 1.26/1.70 X158:$i]:
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 in @
% 1.26/1.70 X158 @
% 1.26/1.70 (
% 1.26/1.70 powerset
% 1.26/1.70 @
% 1.26/1.70 X156 ) ) =>
% 1.26/1.70 (
% 1.26/1.70 ![
% 1.26/1.70 X160:$i]:
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 in @
% 1.26/1.70 X160 @
% 1.26/1.70 (
% 1.26/1.70 powerset
% 1.26/1.70 @
% 1.26/1.70 X156 ) ) =>
% 1.26/1.70 (
% 1.26/1.70 ![
% 1.26/1.70 X162:$i]:
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 in @
% 1.26/1.70 X162 @
% 1.26/1.70 X156 ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 ~
% 1.26/1.70 (
% 1.26/1.70 in @
% 1.26/1.70 X162 @
% 1.26/1.70 X158 ) ) =>
% 1.26/1.70 (
% 1.26/1.70 ~
% 1.26/1.70 (
% 1.26/1.70 in @
% 1.26/1.70 X162 @
% 1.26/1.70 (
% 1.26/1.70 binintersect
% 1.26/1.70 @
% 1.26/1.70 X158 @
% 1.26/1.70 X160 ) ) ) ) ) ) ) ) ) ) =>
% 1.26/1.70 (
% 1.26/1.70 ![
% 1.26/1.70 X164:$i,
% 1.26/1.70 X166:$i]:
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 in @
% 1.26/1.70 X166 @
% 1.26/1.70 (
% 1.26/1.70 powerset
% 1.26/1.70 @
% 1.26/1.70 X164 ) ) =>
% 1.26/1.70 (
% 1.26/1.70 ![
% 1.26/1.70 X168:$i]:
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 in @
% 1.26/1.70 X168 @
% 1.26/1.70 (
% 1.26/1.70 powerset
% 1.26/1.70 @
% 1.26/1.70 X164 ) ) =>
% 1.26/1.70 (
% 1.26/1.70 ![
% 1.26/1.70 X170:$i]:
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 in @
% 1.26/1.70 X170 @
% 1.26/1.70 X164 ) =>
% 1.26/1.70 (
% 1.26/1.70 (
% 1.26/1.70 ~
% 1.26/1.70 (
% 1.26/1.70 in @
% 1.26/1.70 X170 @
% 1.26/1.70 X168 ) ) =>
% 1.26/1.70 (
% 1.26/1.70 ~
% 1.26/1.70 (
% 1.26/1.70 in @
% 1.26/1.70 X170 @
% 1.26/1.70 (
% 1.26/1.70 binintersect
% 1.26/1.70 @
% 1.26/1.70 X166 @
% 1.26/1.70 X168 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 1.26/1.70 inference('cnf.neg', [status(esa)], [zf_stmt_3])).
% 1.26/1.70 thf(zip_derived_cl127, plain, (~ (in @ sk__88 @ sk__87)),
% 1.26/1.70 inference('cnf', [status(esa)], [zf_stmt_4])).
% 1.26/1.70 thf(zip_derived_cl128, plain,
% 1.26/1.70 ( (in @ sk__88 @ (binintersect @ sk__86 @ sk__87))),
% 1.26/1.70 inference('cnf', [status(esa)], [zf_stmt_4])).
% 1.26/1.70 thf(zip_derived_cl204, plain,
% 1.26/1.70 (![X48 : $i, X49 : $i, X50 : $i]:
% 1.26/1.70 ( (in @ X48 @ X49) | ~ (in @ X48 @ (binintersect @ X50 @ X49)))),
% 1.26/1.70 inference('cnf', [status(esa)], [zf_stmt_4])).
% 1.26/1.70 thf(zip_derived_cl288, plain, ( (in @ sk__88 @ sk__87)),
% 1.26/1.70 inference('sup-', [status(thm)], [zip_derived_cl128, zip_derived_cl204])).
% 1.26/1.70 thf(zip_derived_cl293, plain, ($false),
% 1.26/1.70 inference('demod', [status(thm)], [zip_derived_cl127, zip_derived_cl288])).
% 1.26/1.70
% 1.26/1.70 % SZS output end Refutation
% 1.26/1.70
% 1.26/1.70
% 1.26/1.70 % Terminating...
% 2.59/1.93 % Runner terminated.
% 2.59/1.96 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------