%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU800^1 : 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.J6LZUlPuMV true
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 2 04:56:27 PM UTC 2025
% Result : Theorem 95.34s 12.68s
% Output : Refutation 96.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEU800^1 : TPTP v9.2.0. Released v3.7.0.
% 0.12/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.J6LZUlPuMV true
% 0.14/0.35 % Computer : n028.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Oct 1 16:09:53 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % Running portfolio for 300 s
% 0.14/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.35 % Number of cores: 8
% 0.14/0.35 % Python version: Python 3.6.8
% 0.14/0.35 % Running in HO mode
% 0.53/0.64 % Total configuration time : 828
% 0.53/0.64 % Estimated wc time : 1656
% 0.53/0.64 % Estimated cpu time (8 cpus) : 207.0
% 0.56/0.72 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.56/0.75 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.56/0.76 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.56/0.76 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.56/0.77 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.56/0.77 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.56/0.78 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.57/0.83 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 0.57/0.97 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s
% 95.34/12.68 % Solved by lams/40_noforms.sh.
% 95.34/12.68 % done 653 iterations in 11.423s
% 95.34/12.68 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 95.34/12.68 % SZS output start Refutation
% 95.34/12.68 thf(setadjoinAx_type, type, setadjoinAx: $o).
% 95.34/12.68 thf(cartprodfstpairEq_type, type, cartprodfstpairEq: $o).
% 95.34/12.68 thf(notdexE_type, type, notdexE: $o).
% 95.34/12.68 thf(sk__1151_type, type, sk__1151: $i > $i).
% 95.34/12.68 thf(setunionAx_type, type, setunionAx: $o).
% 95.34/12.68 thf(setminusELneg_type, type, setminusELneg: $o).
% 95.34/12.68 thf(breln1unionEcases_type, type, breln1unionEcases: $o).
% 95.34/12.68 thf(zip_tseitin_1_type, type, zip_tseitin_1: $i > $i > $i > $o).
% 95.34/12.68 thf(powersetE_type, type, powersetE: $o).
% 95.34/12.68 thf(woz1_1_type, type, woz1_1: $o).
% 95.34/12.68 thf(omegaSAx_type, type, omegaSAx: $o).
% 95.34/12.68 thf(breln1unionI_type, type, breln1unionI: $o).
% 95.34/12.68 thf(complementSubsetComplementIntersect_type, type, complementSubsetComplementIntersect:
% 95.34/12.68 $o).
% 95.34/12.68 thf(exuI1_type, type, exuI1: $o).
% 95.34/12.68 thf(exuI2_type, type, exuI2: $o).
% 95.34/12.68 thf(notequalI2_type, type, notequalI2: $o).
% 95.34/12.68 thf(kfstsingleton_type, type, kfstsingleton: $o).
% 95.34/12.68 thf(kpairiskpair_type, type, kpairiskpair: $o).
% 95.34/12.68 thf(lam_type, type, lam: $i > $i > ($i > $i) > $i).
% 95.34/12.68 thf(upairsubunion_type, type, upairsubunion: $o).
% 95.34/12.68 thf(binunionTE_type, type, binunionTE: $o).
% 95.34/12.68 thf(injFuncSetFuncIn_type, type, injFuncSetFuncIn: $o).
% 95.34/12.68 thf(binunionTEcontra_type, type, binunionTEcontra: $o).
% 95.34/12.68 thf(powerset__Cong_type, type, powerset__Cong: $o).
% 95.34/12.68 thf(setukpairinjR2_type, type, setukpairinjR2: $o).
% 95.34/12.68 thf(singletonsuniq_type, type, singletonsuniq: $o).
% 95.34/12.68 thf(setminusILneg_type, type, setminusILneg: $o).
% 95.34/12.68 thf(wellorderingAx_type, type, wellorderingAx: $o).
% 95.34/12.68 thf(kpairsurjEq_type, type, kpairsurjEq: $o).
% 95.34/12.68 thf(funcextLem_type, type, funcextLem: $o).
% 95.34/12.68 thf(setadjoinSub2_type, type, setadjoinSub2: $o).
% 95.34/12.68 thf(binintersectSubset5_type, type, binintersectSubset5: $o).
% 95.34/12.68 thf(upairinpowunion_type, type, upairinpowunion: $o).
% 95.34/12.68 thf(if_type, type, if: $i > $o > $i > $i > $i).
% 95.34/12.68 thf(eta1_type, type, eta1: $o).
% 95.34/12.68 thf(complementTnotintersectT_type, type, complementTnotintersectT: $o).
% 95.34/12.68 thf(setoftrueEq_type, type, setoftrueEq: $o).
% 95.34/12.68 thf(apProp_type, type, apProp: $o).
% 95.34/12.68 thf(setextT_type, type, setextT: $o).
% 95.34/12.68 thf(inIntersectImpInIntersectUnions_type, type, inIntersectImpInIntersectUnions:
% 95.34/12.68 $o).
% 95.34/12.68 thf(emptyset__Cong_type, type, emptyset__Cong: $o).
% 95.34/12.68 thf(cartprodmempaircEq_type, type, cartprodmempaircEq: $o).
% 95.34/12.68 thf(breln1invprop_type, type, breln1invprop: $o).
% 95.34/12.68 thf(lamProp_type, type, lamProp: $o).
% 95.34/12.68 thf(dpsetconstrSub_type, type, dpsetconstrSub: $o).
% 95.34/12.68 thf(ex1E1_type, type, ex1E1: $o).
% 95.34/12.68 thf(func_type, type, func: $i > $i > $i > $o).
% 95.34/12.68 thf(sepInPowerset_type, type, sepInPowerset: $o).
% 95.34/12.68 thf(setukpairIR_type, type, setukpairIR: $o).
% 95.34/12.68 thf(brelnall1_type, type, brelnall1: $o).
% 95.34/12.68 thf(kpair_type, type, kpair: $i > $i > $i).
% 95.34/12.68 thf(binunionE_type, type, binunionE: $o).
% 95.34/12.68 thf(setext_type, type, setext: $o).
% 95.34/12.68 thf(complementTcontraSubset_type, type, complementTcontraSubset: $o).
% 95.34/12.68 thf(emptyinPowerset_type, type, emptyinPowerset: $o).
% 95.34/12.68 thf(binintersectTELcontra_type, type, binintersectTELcontra: $o).
% 95.34/12.68 thf(ubforcartprodlem1_type, type, ubforcartprodlem1: $o).
% 95.34/12.68 thf(iftrue_type, type, iftrue: $o).
% 95.34/12.68 thf(woz13rule4_type, type, woz13rule4: $o).
% 95.34/12.68 thf(descr__Cong_type, type, descr__Cong: $o).
% 95.34/12.68 thf(funcGraphProp2_type, type, funcGraphProp2: $o).
% 95.34/12.68 thf(theprop_type, type, theprop: $o).
% 95.34/12.68 thf(image1I_type, type, image1I: $o).
% 95.34/12.68 thf(binintersectSubset1_type, type, binintersectSubset1: $o).
% 95.34/12.68 thf(in_type, type, in: $i > $i > $o).
% 95.34/12.68 thf(cartprodsndpairEq_type, type, cartprodsndpairEq: $o).
% 95.34/12.68 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o).
% 95.34/12.68 thf(setukpairinjL2_type, type, setukpairinjL2: $o).
% 95.34/12.68 thf(binunion_type, type, binunion: $i > $i > $i).
% 95.34/12.68 thf(demorgan1_type, type, demorgan1: $o).
% 95.34/12.68 thf(setadjoinIR_type, type, setadjoinIR: $o).
% 95.34/12.68 thf(complementInPowersetComplementIntersect_type, type, complementInPowersetComplementIntersect:
% 95.34/12.68 $o).
% 95.34/12.68 thf(inIntersectImpInUnion_type, type, inIntersectImpInUnion: $o).
% 95.34/12.68 thf(breln1SetBreln1_type, type, breln1SetBreln1: $o).
% 95.34/12.68 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o).
% 95.34/12.68 thf(ksndpairEq_type, type, ksndpairEq: $o).
% 95.34/12.68 thf(ex1I2_type, type, ex1I2: $o).
% 95.34/12.68 thf(symdiffI2_type, type, symdiffI2: $o).
% 95.34/12.68 thf(ap2apEq2_type, type, ap2apEq2: $o).
% 95.34/12.68 thf(ifSingleton_type, type, ifSingleton: $o).
% 95.34/12.68 thf(upairset2IR_type, type, upairset2IR: $o).
% 95.34/12.68 thf(iftrueProp1_type, type, iftrueProp1: $o).
% 95.34/12.68 thf(complementTI1_type, type, complementTI1: $o).
% 95.34/12.68 thf(subsetE_type, type, subsetE: $o).
% 95.34/12.68 thf(prop2set2propI_type, type, prop2set2propI: $o).
% 95.34/12.68 thf(zip_tseitin_5_type, type, zip_tseitin_5: $i > ($i > $o) > $o).
% 95.34/12.68 thf(doubleComplementSub2_type, type, doubleComplementSub2: $o).
% 95.34/12.68 thf(complementUnionInPowersetComplement_type, type, complementUnionInPowersetComplement:
% 95.34/12.68 $o).
% 95.34/12.68 thf(iffalse_type, type, iffalse: $o).
% 95.34/12.68 thf(dsetconstrEL_type, type, dsetconstrEL: $o).
% 95.34/12.68 thf(setbeta_type, type, setbeta: $o).
% 95.34/12.68 thf(eqinunit_type, type, eqinunit: $o).
% 95.34/12.68 thf(upairsetIL_type, type, upairsetIL: $o).
% 95.34/12.68 thf(powersetI1_type, type, powersetI1: $o).
% 95.34/12.68 thf(cartprodfstin_type, type, cartprodfstin: $o).
% 95.34/12.68 thf(lamp_type, type, lamp: $o).
% 95.34/12.68 thf(iffalseProp1_type, type, iffalseProp1: $o).
% 95.34/12.68 thf(breln1invI_type, type, breln1invI: $o).
% 95.34/12.68 thf(binintersectSubset3_type, type, binintersectSubset3: $o).
% 95.34/12.68 thf(breln1unionE_type, type, breln1unionE: $o).
% 95.34/12.68 thf(ksndsingleton_type, type, ksndsingleton: $o).
% 95.34/12.68 thf(setminusIRneg_type, type, setminusIRneg: $o).
% 95.34/12.68 thf(zip_tseitin_3_type, type, zip_tseitin_3: $i > $i > $i > ($i > $i > $o) > $o).
% 95.34/12.68 thf(lam2lamEq_type, type, lam2lamEq: $o).
% 95.34/12.68 thf(powersetAx_type, type, powersetAx: $o).
% 95.34/12.68 thf(woz2Ex_type, type, woz2Ex: $o).
% 95.34/12.68 thf(eta2_type, type, eta2: $o).
% 95.34/12.68 thf(binintersectSubset4_type, type, binintersectSubset4: $o).
% 95.34/12.68 thf(singletoninpowunion_type, type, singletoninpowunion: $o).
% 95.34/12.68 thf(image1Ex_type, type, image1Ex: $o).
% 95.34/12.68 thf(powersetI_type, type, powersetI: $o).
% 95.34/12.68 thf(cartprodmempair_type, type, cartprodmempair: $o).
% 95.34/12.68 thf(powersetTE1_type, type, powersetTE1: $o).
% 95.34/12.68 thf(upairsetIR_type, type, upairsetIR: $o).
% 95.34/12.68 thf(cartprodpairsurjEq_type, type, cartprodpairsurjEq: $o).
% 95.34/12.68 thf(lam2p_type, type, lam2p: $o).
% 95.34/12.68 thf(contraSubsetComplement_type, type, contraSubsetComplement: $o).
% 95.34/12.68 thf(doubleComplementSub1_type, type, doubleComplementSub1: $o).
% 95.34/12.68 thf(cartprodpairmemEL_type, type, cartprodpairmemEL: $o).
% 95.34/12.68 thf(setOfPairsIsBReln1_type, type, setOfPairsIsBReln1: $o).
% 95.34/12.68 thf(inCongP_type, type, inCongP: $o).
% 95.34/12.68 thf(setukpairinjR11_type, type, setukpairinjR11: $o).
% 95.34/12.68 thf(setadjoinSub_type, type, setadjoinSub: $o).
% 95.34/12.68 thf(exuE3e_type, type, exuE3e: $o).
% 95.34/12.68 thf(emptysetE_type, type, emptysetE: $o).
% 95.34/12.68 thf(woz13rule2_type, type, woz13rule2: $o).
% 95.34/12.68 thf(binintersectSubset2_type, type, binintersectSubset2: $o).
% 95.34/12.68 thf(image1E_type, type, image1E: $o).
% 95.34/12.68 thf(setunionI_type, type, setunionI: $o).
% 95.34/12.68 thf(breln1unionIR_type, type, breln1unionIR: $o).
% 95.34/12.68 thf(symdiff_type, type, symdiff: $i > $i > $i).
% 95.34/12.68 thf(binintersectTERcontra_type, type, binintersectTERcontra: $o).
% 95.34/12.68 thf(setunion__Cong_type, type, setunion__Cong: $o).
% 95.34/12.68 thf(prop2setI_type, type, prop2setI: $o).
% 95.34/12.68 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o).
% 95.34/12.68 thf(setminusER_type, type, setminusER: $o).
% 95.34/12.68 thf(exuE2_type, type, exuE2: $o).
% 95.34/12.68 thf(woz1_2_type, type, woz1_2: $o).
% 95.34/12.68 thf(emptyset_type, type, emptyset: $i).
% 95.34/12.68 thf(setukpairinjR12_type, type, setukpairinjR12: $o).
% 95.34/12.68 thf(funcGraphProp1_type, type, funcGraphProp1: $o).
% 95.34/12.68 thf(breln_type, type, breln: $i > $i > $i > $o).
% 95.34/12.68 thf(setminus_type, type, setminus: $i > $i > $i).
% 95.34/12.68 thf(zip_tseitin_0_type, type, zip_tseitin_0: $i > $i > $i > $o).
% 95.34/12.68 thf(powersetsubset_type, type, powersetsubset: $o).
% 95.34/12.68 thf(upairequniteq_type, type, upairequniteq: $o).
% 95.34/12.68 thf(zip_tseitin_4_type, type, zip_tseitin_4: $i > $i > ($i > $o) > $o).
% 95.34/12.68 thf(dpsetconstrEL1_type, type, dpsetconstrEL1: $o).
% 95.34/12.68 thf(sk__1103_type, type, sk__1103: $i).
% 95.34/12.68 thf(subPowSU_type, type, subPowSU: $o).
% 95.34/12.68 thf(breln1compprop_type, type, breln1compprop: $o).
% 95.34/12.68 thf(woz2B_type, type, woz2B: $o).
% 95.34/12.68 thf(notequalI1_type, type, notequalI1: $o).
% 95.34/12.68 thf(demorgan2b_type, type, demorgan2b: $o).
% 95.34/12.68 thf(notinemptyset_type, type, notinemptyset: $o).
% 95.34/12.68 thf(nonemptyI1_type, type, nonemptyI1: $o).
% 95.34/12.68 thf(breln1unionIL_type, type, breln1unionIL: $o).
% 95.34/12.68 thf(subsetTrans_type, type, subsetTrans: $o).
% 95.34/12.68 thf(setukpairinjR_type, type, setukpairinjR: $o).
% 95.34/12.68 thf(infuncsetfunc_type, type, infuncsetfunc: $o).
% 95.34/12.68 thf(kpairp_type, type, kpairp: $o).
% 95.34/12.68 thf(setukpairinjR1_type, type, setukpairinjR1: $o).
% 95.34/12.68 thf(setminusI_type, type, setminusI: $o).
% 95.34/12.68 thf(binunionIL_type, type, binunionIL: $o).
% 95.34/12.68 thf(setOfPairsIsBReln_type, type, setOfPairsIsBReln: $o).
% 95.34/12.68 thf(setukpairinjL1_type, type, setukpairinjL1: $o).
% 95.34/12.68 thf(setunionsingleton_type, type, setunionsingleton: $o).
% 95.34/12.68 thf(powersetTI1_type, type, powersetTI1: $o).
% 95.34/12.68 thf(subsetE2_type, type, subsetE2: $o).
% 95.34/12.68 thf(image1Ex1_type, type, image1Ex1: $o).
% 95.34/12.68 thf(singletonsswitch_type, type, singletonsswitch: $o).
% 95.34/12.68 thf(ubforcartprodlem3_type, type, ubforcartprodlem3: $o).
% 95.34/12.68 thf(setextsub_type, type, setextsub: $o).
% 95.34/12.68 thf(binunionLsub_type, type, binunionLsub: $o).
% 95.34/12.68 thf(contrasubsetT1_type, type, contrasubsetT1: $o).
% 95.34/12.68 thf(setunionsingleton1_type, type, setunionsingleton1: $o).
% 95.34/12.68 thf(breln1compE_type, type, breln1compE: $o).
% 95.34/12.68 thf(binintersect_type, type, binintersect: $i > $i > $i).
% 95.34/12.68 thf(emptysetsubset_type, type, emptysetsubset: $o).
% 95.34/12.68 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o).
% 95.34/12.68 thf(dpsetconstrERa_type, type, dpsetconstrERa: $o).
% 95.34/12.68 thf(setunionE_type, type, setunionE: $o).
% 95.34/12.68 thf(ksnd_type, type, ksnd: $i > $i).
% 95.34/12.68 thf(setminusSubset1_type, type, setminusSubset1: $o).
% 95.34/12.68 thf(complementT_lem_type, type, complementT_lem: $o).
% 95.34/12.68 thf(binintersectT_lem_type, type, binintersectT_lem: $o).
% 95.34/12.68 thf(emptyinunitempty_type, type, emptyinunitempty: $o).
% 95.34/12.68 thf(binunionIR_type, type, binunionIR: $o).
% 95.34/12.68 thf(setadjoinE_type, type, setadjoinE: $o).
% 95.34/12.68 thf(doubleComplementEq_type, type, doubleComplementEq: $o).
% 95.34/12.68 thf(descr_type, type, descr: ($i > $o) > $i).
% 95.34/12.68 thf(eqbreln1_type, type, eqbreln1: $o).
% 95.34/12.68 thf(cartprodpairmemER_type, type, cartprodpairmemER: $o).
% 95.34/12.68 thf(ex1_type, type, ex1: $i > ($i > $o) > $o).
% 95.34/12.68 thf(sk__1148_type, type, sk__1148: ($i > $o) > $i > $i).
% 95.34/12.68 thf(dpsetconstrER_type, type, dpsetconstrER: $o).
% 95.34/12.68 thf(doubleComplementE1_type, type, doubleComplementE1: $o).
% 95.34/12.68 thf(setadjoinIL_type, type, setadjoinIL: $o).
% 95.34/12.68 thf(exuE1_type, type, exuE1: $o).
% 95.34/12.68 thf(ubforcartprodlem2_type, type, ubforcartprodlem2: $o).
% 95.34/12.68 thf(binintersectRsub_type, type, binintersectRsub: $o).
% 95.34/12.68 thf(setminusLsub_type, type, setminusLsub: $o).
% 95.34/12.68 thf(prop2set_type, type, prop2set: $o > $i).
% 95.34/12.68 thf(notinsingleton_type, type, notinsingleton: $o).
% 95.34/12.68 thf(intersectInPowersetIntersectUnions_type, type, intersectInPowersetIntersectUnions:
% 95.34/12.68 $o).
% 95.34/12.68 thf(dpsetconstrEL2_type, type, dpsetconstrEL2: $o).
% 95.34/12.68 thf(image1_type, type, image1: $i > ($i > $i) > $i).
% 95.34/12.68 thf(eqimpsubset2_type, type, eqimpsubset2: $o).
% 95.34/12.68 thf(exuEu_type, type, exuEu: $o).
% 95.34/12.68 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o).
% 95.34/12.68 thf(reflwellordering_type, type, reflwellordering: $i > $i > $o).
% 95.34/12.68 thf(upairsetE_type, type, upairsetE: $o).
% 95.34/12.68 thf(omega0Ax_type, type, omega0Ax: $o).
% 95.34/12.68 thf(breln1invE_type, type, breln1invE: $o).
% 95.34/12.68 thf(breln1unionCommutes_type, type, breln1unionCommutes: $o).
% 95.34/12.68 thf(funcGraphProp3_type, type, funcGraphProp3: $o).
% 95.34/12.68 thf(app_type, type, app: $o).
% 95.34/12.68 thf(zip_tseitin_6_type, type, zip_tseitin_6: $i > $i > ($i > $i) > $i > $o).
% 95.34/12.68 thf(funcImageSingleton_type, type, funcImageSingleton: $o).
% 95.34/12.68 thf(dpsetconstrI_type, type, dpsetconstrI: $o).
% 95.34/12.68 thf(notsubsetI_type, type, notsubsetI: $o).
% 95.34/12.68 thf(powersetT_lem_type, type, powersetT_lem: $o).
% 95.34/12.68 thf(woz2W_type, type, woz2W: $o).
% 95.34/12.68 thf(iffalseProp2_type, type, iffalseProp2: $o).
% 95.34/12.68 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o).
% 95.34/12.68 thf(setextAx_type, type, setextAx: $o).
% 95.34/12.68 thf(breln1all1_type, type, breln1all1: $o).
% 95.34/12.68 thf(choice2fnsingleton_type, type, choice2fnsingleton: $o).
% 95.34/12.68 thf(breln1compI_type, type, breln1compI: $o).
% 95.34/12.68 thf(demorgan2a1_type, type, demorgan2a1: $o).
% 95.34/12.68 thf(powersetE1_type, type, powersetE1: $o).
% 95.34/12.68 thf(bs114d_type, type, bs114d: $o).
% 95.34/12.68 thf(complementTE1_type, type, complementTE1: $o).
% 95.34/12.68 thf(noeltsimpempty_type, type, noeltsimpempty: $o).
% 95.34/12.68 thf(setunion_type, type, setunion: $i > $i).
% 95.34/12.68 thf(breln1all2_type, type, breln1all2: $o).
% 95.34/12.68 thf(contrasubsetT2_type, type, contrasubsetT2: $o).
% 95.34/12.68 thf(iskpair_type, type, iskpair: $i > $o).
% 95.34/12.68 thf(inIntersectImpInUnion2_type, type, inIntersectImpInUnion2: $o).
% 95.34/12.68 thf(demorgan2b2_type, type, demorgan2b2: $o).
% 95.34/12.68 thf(sk__1102_type, type, sk__1102: $i).
% 95.34/12.68 thf(binintersectLsub_type, type, binintersectLsub: $o).
% 95.34/12.68 thf(subsetI1_type, type, subsetI1: $o).
% 95.34/12.68 thf(symdiffE_type, type, symdiffE: $o).
% 95.34/12.68 thf(woz13rule1_type, type, woz13rule1: $o).
% 95.34/12.68 thf(breln1unionprop_type, type, breln1unionprop: $o).
% 95.34/12.68 thf(descrp_type, type, descrp: $o).
% 95.34/12.68 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o).
% 95.34/12.68 thf(foundationAx_type, type, foundationAx: $o).
% 95.34/12.68 thf(brelnall2_type, type, brelnall2: $o).
% 95.34/12.68 thf(emptysetAx_type, type, emptysetAx: $o).
% 95.34/12.68 thf(emptyI_type, type, emptyI: $o).
% 95.34/12.68 thf(setadjoinOr_type, type, setadjoinOr: $o).
% 95.34/12.68 thf(binintersectEL_type, type, binintersectEL: $o).
% 95.34/12.68 thf(emptyE1_type, type, emptyE1: $o).
% 95.34/12.68 thf(demorgan2a_type, type, demorgan2a: $o).
% 95.34/12.68 thf(woz1_3_type, type, woz1_3: $o).
% 95.34/12.68 thf(emptyInPowerset_type, type, emptyInPowerset: $o).
% 95.34/12.68 thf(vacuousDall_type, type, vacuousDall: $o).
% 95.34/12.68 thf(dsetconstr_type, type, dsetconstr: $i > ($i > $o) > $i).
% 95.34/12.68 thf(dsetconstrER_type, type, dsetconstrER: $o).
% 95.34/12.68 thf(demorgan1a_type, type, demorgan1a: $o).
% 95.34/12.68 thf(ifp_type, type, ifp: $o).
% 95.34/12.68 thf(funcSet_type, type, funcSet: $i > $i > $i).
% 95.34/12.68 thf(exu_type, type, exu: ($i > $o) > $o).
% 95.34/12.68 thf(binintersectI_type, type, binintersectI: $o).
% 95.34/12.68 thf(breln1_type, type, breln1: $i > $i > $o).
% 95.34/12.68 thf(beta1_type, type, beta1: $o).
% 95.34/12.68 thf(funcext2_type, type, funcext2: $o).
% 95.34/12.68 thf(subbreln_type, type, subbreln: $o).
% 95.34/12.68 thf(cartprodpairin_type, type, cartprodpairin: $o).
% 95.34/12.68 thf(breln1compset_type, type, breln1compset: $i > $i > $i > $i).
% 95.34/12.68 thf(cartprodmempair1_type, type, cartprodmempair1: $o).
% 95.34/12.68 thf(subbreln1_type, type, subbreln1: $o).
% 95.34/12.68 thf(demorgan2a2_type, type, demorgan2a2: $o).
% 95.34/12.68 thf(image1Equiv_type, type, image1Equiv: $o).
% 95.34/12.68 thf(subsetTI_type, type, subsetTI: $o).
% 95.34/12.68 thf(setminusT_lem_type, type, setminusT_lem: $o).
% 95.34/12.68 thf(ap2p_type, type, ap2p: $o).
% 95.34/12.68 thf(doubleComplementI1_type, type, doubleComplementI1: $o).
% 95.34/12.68 thf(singleton_type, type, singleton: $i > $o).
% 95.34/12.68 thf(breln1Set_type, type, breln1Set: $i > $i).
% 95.34/12.68 thf(binunionT_lem_type, type, binunionT_lem: $o).
% 95.34/12.68 thf(symdiffI1_type, type, symdiffI1: $o).
% 95.34/12.68 thf(woz1_4_type, type, woz1_4: $o).
% 95.34/12.68 thf(kfstpairEq_type, type, kfstpairEq: $o).
% 95.34/12.68 thf(subsetI2_type, type, subsetI2: $o).
% 95.34/12.68 thf(symdiffIneg1_type, type, symdiffIneg1: $o).
% 95.34/12.68 thf(theeq_type, type, theeq: $o).
% 95.34/12.68 thf(setminusERneg_type, type, setminusERneg: $o).
% 95.34/12.68 thf(symdiffIneg2_type, type, symdiffIneg2: $o).
% 95.34/12.68 thf(binunionTIRcontra_type, type, binunionTIRcontra: $o).
% 95.34/12.68 thf(omega__Cong_type, type, omega__Cong: $o).
% 95.34/12.68 thf(demorgan1b_type, type, demorgan1b: $o).
% 95.34/12.68 thf(subsetRefl_type, type, subsetRefl: $o).
% 95.34/12.68 thf(uniqinunit_type, type, uniqinunit: $o).
% 95.34/12.68 thf(eqbreln_type, type, eqbreln: $o).
% 95.34/12.68 thf(inComplementUnionImpNotIn1_type, type, inComplementUnionImpNotIn1: $o).
% 95.34/12.68 thf(funcinfuncset_type, type, funcinfuncset: $o).
% 95.34/12.68 thf(breln1compEex_type, type, breln1compEex: $o).
% 95.34/12.68 thf(contrasubsetT_type, type, contrasubsetT: $o).
% 95.34/12.68 thf(setminusSubset2_type, type, setminusSubset2: $o).
% 95.34/12.68 thf(prop2setE_type, type, prop2setE: $o).
% 95.34/12.68 thf(binunionEcases_type, type, binunionEcases: $o).
% 95.34/12.68 thf(breln1invset_type, type, breln1invset: $i > $i > $i).
% 95.34/12.68 thf(omega_type, type, omega: $i).
% 95.34/12.68 thf(nonemptyI_type, type, nonemptyI: $o).
% 95.34/12.68 thf(disjointsetsI1_type, type, disjointsetsI1: $o).
% 95.34/12.68 thf(woz2A_type, type, woz2A: $o).
% 95.34/12.68 thf(injective_type, type, injective: $i > $i > $i > $o).
% 95.34/12.68 thf(exuE3u_type, type, exuE3u: $o).
% 95.34/12.68 thf(setminusEL_type, type, setminusEL: $o).
% 95.34/12.68 thf(funcGraphProp4_type, type, funcGraphProp4: $o).
% 95.34/12.68 thf(woz1_5_type, type, woz1_5: $o).
% 95.34/12.68 thf(demorgan2_type, type, demorgan2: $o).
% 95.34/12.68 thf(setunionsingleton2_type, type, setunionsingleton2: $o).
% 95.34/12.68 thf(sepSubset_type, type, sepSubset: $o).
% 95.34/12.68 thf(inComplementUnionImpInComplement1_type, type, inComplementUnionImpInComplement1:
% 95.34/12.68 $o).
% 95.34/12.68 thf(funcext_type, type, funcext: $o).
% 95.34/12.68 thf(sk__1101_type, type, sk__1101: $i).
% 95.34/12.68 thf(upairset2E_type, type, upairset2E: $o).
% 95.34/12.68 thf(eqimpsubset1_type, type, eqimpsubset1: $o).
% 95.34/12.68 thf(exuI3_type, type, exuI3: $o).
% 95.34/12.68 thf(ap_type, type, ap: $i > $i > $i > $i > $i).
% 95.34/12.68 thf(notdallE_type, type, notdallE: $o).
% 95.34/12.68 thf(iftrueProp2_type, type, iftrueProp2: $o).
% 95.34/12.68 thf(binintersectER_type, type, binintersectER: $o).
% 95.34/12.68 thf(powerset_type, type, powerset: $i > $i).
% 95.34/12.68 thf(woz13rule0_type, type, woz13rule0: $o).
% 95.34/12.68 thf(kfst_type, type, kfst: $i > $i).
% 95.34/12.68 thf(dsetconstrI_type, type, dsetconstrI: $o).
% 95.34/12.68 thf(dpsetconstr_type, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 95.34/12.68 thf(nonempty_type, type, nonempty: $i > $o).
% 95.34/12.68 thf(set2prop_type, type, set2prop: $i > $o).
% 95.34/12.68 thf(beta2_type, type, beta2: $o).
% 95.34/12.68 thf(setadjoin_type, type, setadjoin: $i > $i > $i).
% 95.34/12.68 thf(exu__Cong_type, type, exu__Cong: $o).
% 95.34/12.68 thf(cartprodsndin_type, type, cartprodsndin: $o).
% 95.34/12.68 thf(iftrueorfalse_type, type, iftrueorfalse: $o).
% 95.34/12.68 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o).
% 95.34/12.68 thf(ex1I_type, type, ex1I: $o).
% 95.34/12.68 thf(secondinupair_type, type, secondinupair: $o).
% 95.34/12.68 thf(singletonprop_type, type, singletonprop: $o).
% 95.34/12.68 thf(singletonsubset_type, type, singletonsubset: $o).
% 95.34/12.68 thf(singletoninpowerset_type, type, singletoninpowerset: $o).
% 95.34/12.68 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o).
% 95.34/12.68 thf(injFuncInInjFuncSet_type, type, injFuncInInjFuncSet: $o).
% 95.34/12.68 thf(ex1E2_type, type, ex1E2: $o).
% 95.34/12.68 thf(replAx_type, type, replAx: $o).
% 95.34/12.68 thf(zip_tseitin_2_type, type, zip_tseitin_2: $i > $i > $i > $o).
% 95.34/12.68 thf(nonemptyE1_type, type, nonemptyE1: $o).
% 95.34/12.68 thf(omegaIndAx_type, type, omegaIndAx: $o).
% 95.34/12.68 thf(setukpairIL_type, type, setukpairIL: $o).
% 95.34/12.68 thf(setunionE2_type, type, setunionE2: $o).
% 95.34/12.68 thf(inPowerset_type, type, inPowerset: $o).
% 95.34/12.68 thf(injFuncSet_type, type, injFuncSet: $i > $i > $i).
% 95.34/12.68 thf(binunionTILcontra_type, type, binunionTILcontra: $o).
% 95.34/12.68 thf(ap2apEq1_type, type, ap2apEq1: $o).
% 95.34/12.68 thf(contrasubsetT3_type, type, contrasubsetT3: $o).
% 95.34/12.68 thf(cartprod_type, type, cartprod: $i > $i > $i).
% 95.34/12.68 thf(subset_type, type, subset: $i > $i > $o).
% 95.34/12.68 thf(woz13rule3_type, type, woz13rule3: $o).
% 95.34/12.68 thf(complementImpComplementIntersect_type, type, complementImpComplementIntersect:
% 95.34/12.68 $o).
% 95.34/12.68 thf(in__Cong_type, type, in__Cong: $o).
% 95.34/12.68 thf(setukpairinjL_type, type, setukpairinjL: $o).
% 95.34/12.68 thf(binunionRsub_type, type, binunionRsub: $o).
% 95.34/12.68 thf(subset2powerset_type, type, subset2powerset: $o).
% 95.34/12.68 thf(injFuncSetFuncIn, axiom, injFuncSetFuncIn =
% 95.34/12.68 (![A:$i,B:$i,Xf:$i]:
% 95.34/12.68 ( ( in @ Xf @ ( injFuncSet @ A @ B ) ) =>
% 95.34/12.68 ( in @ Xf @ ( funcSet @ A @ B ) ) ))).
% 95.34/12.68 thf('0', plain,
% 95.34/12.68 (( injFuncSetFuncIn ) =
% 95.34/12.68 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.68 ( ( in @ X8 @ ( injFuncSet @ X4 @ X6 ) ) =>
% 95.34/12.68 ( in @ X8 @ ( funcSet @ X4 @ X6 ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(injFuncInInjFuncSet, axiom, injFuncInInjFuncSet =
% 95.34/12.68 (![A:$i,B:$i,Xf:$i]:
% 95.34/12.68 ( ( in @ Xf @ ( funcSet @ A @ B ) ) =>
% 95.34/12.68 ( ( injective @ A @ B @ Xf ) => ( in @ Xf @ ( injFuncSet @ A @ B ) ) ) ))).
% 95.34/12.68 thf('1', plain,
% 95.34/12.68 (( injFuncInInjFuncSet ) =
% 95.34/12.68 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.68 ( ( in @ X8 @ ( funcSet @ X4 @ X6 ) ) =>
% 95.34/12.68 ( ( injective @ X4 @ X6 @ X8 ) =>
% 95.34/12.68 ( in @ X8 @ ( injFuncSet @ X4 @ X6 ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(image1I, axiom, image1I =
% 95.34/12.68 (![A:$i,Xf:( $i > $i ),Xx:$i]:
% 95.34/12.68 ( ( ?[Xy:$i]: ( ( ( Xx ) = ( Xf @ Xy ) ) & ( in @ Xy @ A ) ) ) =>
% 95.34/12.68 ( in @ Xx @ ( image1 @ A @ ( ^[Xy:$i]: ( Xf @ Xy ) ) ) ) ))).
% 95.34/12.68 thf('2', plain,
% 95.34/12.68 (( image1I ) =
% 95.34/12.68 ( ![X4:$i,X6:( $i > $i ),X8:$i]:
% 95.34/12.68 ( ( ?[X10:$i]: ( ( ( X8 ) = ( X6 @ X10 ) ) & ( in @ X10 @ X4 ) ) ) =>
% 95.34/12.68 ( in @ X8 @ ( image1 @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(image1E, axiom, image1E =
% 95.34/12.68 (![A:$i,Xf:( $i > $i ),Xx:$i]:
% 95.34/12.68 ( ( in @ Xx @ ( image1 @ A @ ( ^[Xy:$i]: ( Xf @ Xy ) ) ) ) =>
% 95.34/12.68 ( ?[Xy:$i]: ( ( ( Xx ) = ( Xf @ Xy ) ) & ( in @ Xy @ A ) ) ) ))).
% 95.34/12.68 thf('3', plain,
% 95.34/12.68 (( image1E ) =
% 95.34/12.68 ( ![X4:$i,X6:( $i > $i ),X8:$i]:
% 95.34/12.68 ( ( in @ X8 @ ( image1 @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) =>
% 95.34/12.68 ( ?[X10:$i]: ( ( ( X8 ) = ( X6 @ X10 ) ) & ( in @ X10 @ X4 ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(image1Equiv, axiom, image1Equiv =
% 95.34/12.68 (![A:$i,Xf:( $i > $i ),Xx:$i]:
% 95.34/12.68 ( ( in @ Xx @ ( image1 @ A @ ( ^[Xy:$i]: ( Xf @ Xy ) ) ) ) <=>
% 95.34/12.68 ( ?[Xy:$i]: ( ( ( Xx ) = ( Xf @ Xy ) ) & ( in @ Xy @ A ) ) ) ))).
% 95.34/12.68 thf('4', plain,
% 95.34/12.68 (( image1Equiv ) =
% 95.34/12.68 ( ![X4:$i,X6:( $i > $i ),X8:$i]:
% 95.34/12.68 ( ( in @ X8 @ ( image1 @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) <=>
% 95.34/12.68 ( ?[X10:$i]: ( ( ( X8 ) = ( X6 @ X10 ) ) & ( in @ X10 @ X4 ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(image1Ex1, axiom, image1Ex1 =
% 95.34/12.68 (![A:$i,Xf:( $i > $i )]:
% 95.34/12.68 ( exu @
% 95.34/12.68 ( ^[B:$i]:
% 95.34/12.68 ( ![Xx:$i]:
% 95.34/12.68 ( ( in @ Xx @ B ) <=>
% 95.34/12.68 ( ?[Xy:$i]: ( ( ( Xx ) = ( Xf @ Xy ) ) & ( in @ Xy @ A ) ) ) ) ) ) ))).
% 95.34/12.68 thf('5', plain,
% 95.34/12.68 (( image1Ex1 ) =
% 95.34/12.68 ( ![X4:$i,X6:( $i > $i )]:
% 95.34/12.68 ( exu @
% 95.34/12.68 ( ^[V_1:$i]:
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( in @ X8 @ V_1 ) <=>
% 95.34/12.68 ( ?[X10:$i]: ( ( ( X8 ) = ( X6 @ X10 ) ) & ( in @ X10 @ X4 ) ) ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(image1Ex, axiom, image1Ex =
% 95.34/12.68 (![A:$i,Xf:( $i > $i )]:
% 95.34/12.68 ( ?[B:$i]:
% 95.34/12.68 ( ![Xx:$i]:
% 95.34/12.68 ( ( in @ Xx @ B ) <=>
% 95.34/12.68 ( ?[Xy:$i]: ( ( ( Xx ) = ( Xf @ Xy ) ) & ( in @ Xy @ A ) ) ) ) ) ))).
% 95.34/12.68 thf('6', plain,
% 95.34/12.68 (( image1Ex ) =
% 95.34/12.68 ( ![X4:$i,X6:( $i > $i )]:
% 95.34/12.68 ( ?[X8:$i]:
% 95.34/12.68 ( ![X10:$i]:
% 95.34/12.68 ( ( in @ X10 @ X8 ) <=>
% 95.34/12.68 ( ?[X12:$i]: ( ( ( X10 ) = ( X6 @ X12 ) ) & ( in @ X12 @ X4 ) ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(woz2B, axiom, woz2B =
% 95.34/12.68 (![A:$i,R:$i]:
% 95.34/12.68 ( ( breln1 @ A @ R ) =>
% 95.34/12.68 ( ![S:$i]:
% 95.34/12.68 ( ( breln1 @ A @ S ) =>
% 95.34/12.68 ( ![T:$i]:
% 95.34/12.68 ( ( breln1 @ A @ T ) =>
% 95.34/12.68 ( ( breln1compset @ A @ ( binunion @ R @ S ) @ T ) =
% 95.34/12.68 ( binunion @
% 95.34/12.68 ( breln1invset @
% 95.34/12.68 A @
% 95.34/12.68 ( breln1compset @
% 95.34/12.68 A @ ( breln1invset @ A @ T ) @ ( breln1invset @ A @ S ) ) ) @
% 95.34/12.68 ( breln1invset @
% 95.34/12.68 A @
% 95.34/12.68 ( breln1compset @
% 95.34/12.68 A @ ( breln1invset @ A @ T ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ) ) ))).
% 95.34/12.68 thf('7', plain,
% 95.34/12.68 (( woz2B ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( breln1 @ X4 @ X6 ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( breln1 @ X4 @ X8 ) =>
% 95.34/12.68 ( ![X10:$i]:
% 95.34/12.68 ( ( breln1 @ X4 @ X10 ) =>
% 95.34/12.68 ( ( breln1compset @ X4 @ ( binunion @ X6 @ X8 ) @ X10 ) =
% 95.34/12.68 ( binunion @
% 95.34/12.68 ( breln1invset @
% 95.34/12.68 X4 @
% 95.34/12.68 ( breln1compset @
% 95.34/12.68 X4 @ ( breln1invset @ X4 @ X10 ) @
% 95.34/12.68 ( breln1invset @ X4 @ X8 ) ) ) @
% 95.34/12.68 ( breln1invset @
% 95.34/12.68 X4 @
% 95.34/12.68 ( breln1compset @
% 95.34/12.68 X4 @ ( breln1invset @ X4 @ X10 ) @
% 95.34/12.68 ( breln1invset @ X4 @ X6 ) ) ) ) ) ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(woz2A, axiom, woz2A =
% 95.34/12.68 (![A:$i,R:$i]:
% 95.34/12.68 ( ( breln1 @ A @ R ) =>
% 95.34/12.68 ( ![S:$i]:
% 95.34/12.68 ( ( breln1 @ A @ S ) =>
% 95.34/12.68 ( ![T:$i]:
% 95.34/12.68 ( ( breln1 @ A @ T ) =>
% 95.34/12.68 ( ( breln1compset @ A @ ( binunion @ R @ S ) @ T ) =
% 95.34/12.68 ( binunion @
% 95.34/12.68 ( breln1compset @ A @ R @ T ) @
% 95.34/12.68 ( breln1compset @ A @ S @ T ) ) ) ) ) ) ) ))).
% 95.34/12.68 thf('8', plain,
% 95.34/12.68 (( woz2A ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( breln1 @ X4 @ X6 ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( breln1 @ X4 @ X8 ) =>
% 95.34/12.68 ( ![X10:$i]:
% 95.34/12.68 ( ( breln1 @ X4 @ X10 ) =>
% 95.34/12.68 ( ( breln1compset @ X4 @ ( binunion @ X6 @ X8 ) @ X10 ) =
% 95.34/12.68 ( binunion @
% 95.34/12.68 ( breln1compset @ X4 @ X6 @ X10 ) @
% 95.34/12.68 ( breln1compset @ X4 @ X8 @ X10 ) ) ) ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(woz2W, axiom, woz2W =
% 95.34/12.68 (![A:$i,R:$i]:
% 95.34/12.68 ( ( breln1 @ A @ R ) =>
% 95.34/12.68 ( ![S:$i]:
% 95.34/12.68 ( ( breln1 @ A @ S ) =>
% 95.34/12.68 ( ( breln1invset @ A @ ( breln1compset @ A @ R @ S ) ) =
% 95.34/12.68 ( breln1compset @
% 95.34/12.68 A @ ( breln1invset @ A @ S ) @ ( breln1invset @ A @ R ) ) ) ) ) ))).
% 95.34/12.68 thf('9', plain,
% 95.34/12.68 (( woz2W ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( breln1 @ X4 @ X6 ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( breln1 @ X4 @ X8 ) =>
% 95.34/12.68 ( ( breln1invset @ X4 @ ( breln1compset @ X4 @ X6 @ X8 ) ) =
% 95.34/12.68 ( breln1compset @
% 95.34/12.68 X4 @ ( breln1invset @ X4 @ X8 ) @ ( breln1invset @ X4 @ X6 ) ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(woz2Ex, axiom, woz2Ex =
% 95.34/12.68 (![A:$i,R:$i]:
% 95.34/12.68 ( ( breln1 @ A @ R ) =>
% 95.34/12.68 ( ( R ) = ( breln1invset @ A @ ( breln1invset @ A @ R ) ) ) ))).
% 95.34/12.68 thf('10', plain,
% 95.34/12.68 (( woz2Ex ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( breln1 @ X4 @ X6 ) =>
% 95.34/12.68 ( ( X6 ) = ( breln1invset @ X4 @ ( breln1invset @ X4 @ X6 ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(breln1unionCommutes, axiom, breln1unionCommutes =
% 95.34/12.68 (![A:$i,R:$i]:
% 95.34/12.68 ( ( breln1 @ A @ R ) =>
% 95.34/12.68 ( ![S:$i]:
% 95.34/12.68 ( ( breln1 @ A @ S ) =>
% 95.34/12.68 ( ( binunion @ R @ S ) = ( binunion @ S @ R ) ) ) ) ))).
% 95.34/12.68 thf('11', plain,
% 95.34/12.68 (( breln1unionCommutes ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( breln1 @ X4 @ X6 ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( breln1 @ X4 @ X8 ) =>
% 95.34/12.68 ( ( binunion @ X6 @ X8 ) = ( binunion @ X8 @ X6 ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(breln1unionEcases, axiom, breln1unionEcases =
% 95.34/12.68 (![A:$i,R:$i]:
% 95.34/12.68 ( ( breln1 @ A @ R ) =>
% 95.34/12.68 ( ![S:$i]:
% 95.34/12.68 ( ( breln1 @ A @ S ) =>
% 95.34/12.68 ( ![Xx:$i]:
% 95.34/12.68 ( ( in @ Xx @ A ) =>
% 95.34/12.68 ( ![Xy:$i]:
% 95.34/12.68 ( ( in @ Xy @ A ) =>
% 95.34/12.68 ( ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) =>
% 95.34/12.68 ( ![Xphi:$o]:
% 95.34/12.68 ( ( ( in @ ( kpair @ Xx @ Xy ) @ R ) => ( Xphi ) ) =>
% 95.34/12.68 ( ( ( in @ ( kpair @ Xx @ Xy ) @ S ) => ( Xphi ) ) =>
% 95.34/12.68 ( Xphi ) ) ) ) ) ) ) ) ) ) ) ))).
% 95.34/12.68 thf('12', plain,
% 95.34/12.68 (( breln1unionEcases ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( breln1 @ X4 @ X6 ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( breln1 @ X4 @ X8 ) =>
% 95.34/12.68 ( ![X10:$i]:
% 95.34/12.68 ( ( in @ X10 @ X4 ) =>
% 95.34/12.68 ( ![X12:$i]:
% 95.34/12.68 ( ( in @ X12 @ X4 ) =>
% 95.34/12.68 ( ( in @ ( kpair @ X10 @ X12 ) @ ( binunion @ X6 @ X8 ) ) =>
% 95.34/12.68 ( ![X14:$o]:
% 95.34/12.68 ( ( ( in @ ( kpair @ X10 @ X12 ) @ X6 ) => ( X14 ) ) =>
% 95.34/12.68 ( ( ( in @ ( kpair @ X10 @ X12 ) @ X8 ) => ( X14 ) ) =>
% 95.34/12.68 ( X14 ) ) ) ) ) ) ) ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(breln1unionE, axiom, breln1unionE =
% 95.34/12.68 (![A:$i,R:$i]:
% 95.34/12.68 ( ( breln1 @ A @ R ) =>
% 95.34/12.68 ( ![S:$i]:
% 95.34/12.68 ( ( breln1 @ A @ S ) =>
% 95.34/12.68 ( ![Xx:$i]:
% 95.34/12.68 ( ( in @ Xx @ A ) =>
% 95.34/12.68 ( ![Xy:$i]:
% 95.34/12.68 ( ( in @ Xy @ A ) =>
% 95.34/12.68 ( ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) =>
% 95.34/12.68 ( ( in @ ( kpair @ Xx @ Xy ) @ R ) |
% 95.34/12.68 ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) ) ) ) ) ) ) ))).
% 95.34/12.68 thf('13', plain,
% 95.34/12.68 (( breln1unionE ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( breln1 @ X4 @ X6 ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( breln1 @ X4 @ X8 ) =>
% 95.34/12.68 ( ![X10:$i]:
% 95.34/12.68 ( ( in @ X10 @ X4 ) =>
% 95.34/12.68 ( ![X12:$i]:
% 95.34/12.68 ( ( in @ X12 @ X4 ) =>
% 95.34/12.68 ( ( in @ ( kpair @ X10 @ X12 ) @ ( binunion @ X6 @ X8 ) ) =>
% 95.34/12.68 ( ( in @ ( kpair @ X10 @ X12 ) @ X6 ) |
% 95.34/12.68 ( in @ ( kpair @ X10 @ X12 ) @ X8 ) ) ) ) ) ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(breln1unionI, axiom, breln1unionI =
% 95.34/12.68 (![A:$i,R:$i]:
% 95.34/12.68 ( ( breln1 @ A @ R ) =>
% 95.34/12.68 ( ![S:$i]:
% 95.34/12.68 ( ( breln1 @ A @ S ) =>
% 95.34/12.68 ( ![Xx:$i]:
% 95.34/12.68 ( ( in @ Xx @ A ) =>
% 95.34/12.68 ( ![Xy:$i]:
% 95.34/12.68 ( ( in @ Xy @ A ) =>
% 95.34/12.68 ( ( ( in @ ( kpair @ Xx @ Xy ) @ R ) |
% 95.34/12.68 ( in @ ( kpair @ Xx @ Xy ) @ S ) ) =>
% 95.34/12.68 ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ))).
% 95.34/12.68 thf('14', plain,
% 95.34/12.68 (( breln1unionI ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( breln1 @ X4 @ X6 ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( breln1 @ X4 @ X8 ) =>
% 95.34/12.68 ( ![X10:$i]:
% 95.34/12.68 ( ( in @ X10 @ X4 ) =>
% 95.34/12.68 ( ![X12:$i]:
% 95.34/12.68 ( ( in @ X12 @ X4 ) =>
% 95.34/12.68 ( ( ( in @ ( kpair @ X10 @ X12 ) @ X6 ) |
% 95.34/12.68 ( in @ ( kpair @ X10 @ X12 ) @ X8 ) ) =>
% 95.34/12.68 ( in @ ( kpair @ X10 @ X12 ) @ ( binunion @ X6 @ X8 ) ) ) ) ) ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(breln1unionIR, axiom, breln1unionIR =
% 95.34/12.68 (![A:$i,R:$i]:
% 95.34/12.68 ( ( breln1 @ A @ R ) =>
% 95.34/12.68 ( ![S:$i]:
% 95.34/12.68 ( ( breln1 @ A @ S ) =>
% 95.34/12.68 ( ![Xx:$i]:
% 95.34/12.68 ( ( in @ Xx @ A ) =>
% 95.34/12.68 ( ![Xy:$i]:
% 95.34/12.68 ( ( in @ Xy @ A ) =>
% 95.34/12.68 ( ( in @ ( kpair @ Xx @ Xy ) @ S ) =>
% 95.34/12.68 ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ))).
% 95.34/12.68 thf('15', plain,
% 95.34/12.68 (( breln1unionIR ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( breln1 @ X4 @ X6 ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( breln1 @ X4 @ X8 ) =>
% 95.34/12.68 ( ![X10:$i]:
% 95.34/12.68 ( ( in @ X10 @ X4 ) =>
% 95.34/12.68 ( ![X12:$i]:
% 95.34/12.68 ( ( in @ X12 @ X4 ) =>
% 95.34/12.68 ( ( in @ ( kpair @ X10 @ X12 ) @ X8 ) =>
% 95.34/12.68 ( in @ ( kpair @ X10 @ X12 ) @ ( binunion @ X6 @ X8 ) ) ) ) ) ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(breln1unionIL, axiom, breln1unionIL =
% 95.34/12.68 (![A:$i,R:$i]:
% 95.34/12.68 ( ( breln1 @ A @ R ) =>
% 95.34/12.68 ( ![S:$i]:
% 95.34/12.68 ( ( breln1 @ A @ S ) =>
% 95.34/12.68 ( ![Xx:$i]:
% 95.34/12.68 ( ( in @ Xx @ A ) =>
% 95.34/12.68 ( ![Xy:$i]:
% 95.34/12.68 ( ( in @ Xy @ A ) =>
% 95.34/12.68 ( ( in @ ( kpair @ Xx @ Xy ) @ R ) =>
% 95.34/12.68 ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ))).
% 95.34/12.68 thf('16', plain,
% 95.34/12.68 (( breln1unionIL ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( breln1 @ X4 @ X6 ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( breln1 @ X4 @ X8 ) =>
% 95.34/12.68 ( ![X10:$i]:
% 95.34/12.68 ( ( in @ X10 @ X4 ) =>
% 95.34/12.68 ( ![X12:$i]:
% 95.34/12.68 ( ( in @ X12 @ X4 ) =>
% 95.34/12.68 ( ( in @ ( kpair @ X10 @ X12 ) @ X6 ) =>
% 95.34/12.68 ( in @ ( kpair @ X10 @ X12 ) @ ( binunion @ X6 @ X8 ) ) ) ) ) ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(breln1unionprop, axiom, breln1unionprop =
% 95.34/12.68 (![A:$i,R:$i]:
% 95.34/12.68 ( ( breln1 @ A @ R ) =>
% 95.34/12.68 ( ![S:$i]:
% 95.34/12.68 ( ( breln1 @ A @ S ) => ( breln1 @ A @ ( binunion @ R @ S ) ) ) ) ))).
% 95.34/12.68 thf('17', plain,
% 95.34/12.68 (( breln1unionprop ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( breln1 @ X4 @ X6 ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( breln1 @ X4 @ X8 ) => ( breln1 @ X4 @ ( binunion @ X6 @ X8 ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(breln1compEex, axiom, breln1compEex =
% 95.34/12.68 (![A:$i,R:$i]:
% 95.34/12.68 ( ( breln1 @ A @ R ) =>
% 95.34/12.68 ( ![S:$i]:
% 95.34/12.68 ( ( breln1 @ A @ S ) =>
% 95.34/12.68 ( ![Xx:$i]:
% 95.34/12.68 ( ( in @ Xx @ A ) =>
% 95.34/12.68 ( ![Xy:$i]:
% 95.34/12.68 ( ( in @ Xy @ A ) =>
% 95.34/12.68 ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) ) =>
% 95.34/12.68 ( ![Xphi:$o]:
% 95.34/12.68 ( ( ![Xz:$i]:
% 95.34/12.68 ( ( in @ Xz @ A ) =>
% 95.34/12.68 ( ( in @ ( kpair @ Xx @ Xz ) @ R ) =>
% 95.34/12.68 ( ( in @ ( kpair @ Xz @ Xy ) @ S ) => ( Xphi ) ) ) ) ) =>
% 95.34/12.68 ( Xphi ) ) ) ) ) ) ) ) ) ) ))).
% 95.34/12.68 thf('18', plain,
% 95.34/12.68 (( breln1compEex ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( breln1 @ X4 @ X6 ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( breln1 @ X4 @ X8 ) =>
% 95.34/12.68 ( ![X10:$i]:
% 95.34/12.68 ( ( in @ X10 @ X4 ) =>
% 95.34/12.68 ( ![X12:$i]:
% 95.34/12.68 ( ( in @ X12 @ X4 ) =>
% 95.34/12.68 ( ( in @
% 95.34/12.68 ( kpair @ X10 @ X12 ) @
% 95.34/12.68 ( breln1compset @ X4 @ X6 @ X8 ) ) =>
% 95.34/12.68 ( ![X14:$o]:
% 95.34/12.68 ( ( ![X16:$i]:
% 95.34/12.68 ( ( in @ X16 @ X4 ) =>
% 95.34/12.68 ( ( in @ ( kpair @ X10 @ X16 ) @ X6 ) =>
% 95.34/12.68 ( ( in @ ( kpair @ X16 @ X12 ) @ X8 ) =>
% 95.34/12.68 ( X14 ) ) ) ) ) =>
% 95.34/12.68 ( X14 ) ) ) ) ) ) ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(breln1compE, axiom, breln1compE =
% 95.34/12.68 (![A:$i,R:$i]:
% 95.34/12.68 ( ( breln1 @ A @ R ) =>
% 95.34/12.68 ( ![S:$i]:
% 95.34/12.68 ( ( breln1 @ A @ S ) =>
% 95.34/12.68 ( ![Xx:$i]:
% 95.34/12.68 ( ( in @ Xx @ A ) =>
% 95.34/12.68 ( ![Xy:$i]:
% 95.34/12.68 ( ( in @ Xy @ A ) =>
% 95.34/12.68 ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) ) =>
% 95.34/12.68 ( ?[Xz:$i]:
% 95.34/12.68 ( ( in @ ( kpair @ Xz @ Xy ) @ S ) &
% 95.34/12.68 ( in @ ( kpair @ Xx @ Xz ) @ R ) & ( in @ Xz @ A ) ) ) ) ) ) ) ) ) ) ))).
% 95.34/12.68 thf('19', plain,
% 95.34/12.68 (( breln1compE ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( breln1 @ X4 @ X6 ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( breln1 @ X4 @ X8 ) =>
% 95.34/12.68 ( ![X10:$i]:
% 95.34/12.68 ( ( in @ X10 @ X4 ) =>
% 95.34/12.68 ( ![X12:$i]:
% 95.34/12.68 ( ( in @ X12 @ X4 ) =>
% 95.34/12.68 ( ( in @
% 95.34/12.68 ( kpair @ X10 @ X12 ) @
% 95.34/12.68 ( breln1compset @ X4 @ X6 @ X8 ) ) =>
% 95.34/12.68 ( ?[X14:$i]:
% 95.34/12.68 ( ( in @ ( kpair @ X14 @ X12 ) @ X8 ) &
% 95.34/12.68 ( in @ ( kpair @ X10 @ X14 ) @ X6 ) &
% 95.34/12.68 ( in @ X14 @ X4 ) ) ) ) ) ) ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(breln1compI, axiom, breln1compI =
% 95.34/12.68 (![A:$i,R:$i]:
% 95.34/12.68 ( ( breln1 @ A @ R ) =>
% 95.34/12.68 ( ![S:$i]:
% 95.34/12.68 ( ( breln1 @ A @ S ) =>
% 95.34/12.68 ( ![Xx:$i]:
% 95.34/12.68 ( ( in @ Xx @ A ) =>
% 95.34/12.68 ( ![Xy:$i]:
% 95.34/12.68 ( ( in @ Xy @ A ) =>
% 95.34/12.68 ( ![Xz:$i]:
% 95.34/12.68 ( ( in @ Xz @ A ) =>
% 95.34/12.68 ( ( in @ ( kpair @ Xx @ Xz ) @ R ) =>
% 95.34/12.68 ( ( in @ ( kpair @ Xz @ Xy ) @ S ) =>
% 95.34/12.68 ( in @
% 95.34/12.68 ( kpair @ Xx @ Xy ) @
% 95.34/12.68 ( breln1compset @ A @ R @ S ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 95.34/12.68 thf('20', plain,
% 95.34/12.68 (( breln1compI ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( breln1 @ X4 @ X6 ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( breln1 @ X4 @ X8 ) =>
% 95.34/12.68 ( ![X10:$i]:
% 95.34/12.68 ( ( in @ X10 @ X4 ) =>
% 95.34/12.68 ( ![X12:$i]:
% 95.34/12.68 ( ( in @ X12 @ X4 ) =>
% 95.34/12.68 ( ![X14:$i]:
% 95.34/12.68 ( ( in @ X14 @ X4 ) =>
% 95.34/12.68 ( ( in @ ( kpair @ X10 @ X14 ) @ X6 ) =>
% 95.34/12.68 ( ( in @ ( kpair @ X14 @ X12 ) @ X8 ) =>
% 95.34/12.68 ( in @
% 95.34/12.68 ( kpair @ X10 @ X12 ) @
% 95.34/12.68 ( breln1compset @ X4 @ X6 @ X8 ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(breln1compprop, axiom, breln1compprop =
% 95.34/12.68 (![A:$i,R:$i]:
% 95.34/12.68 ( ( breln1 @ A @ R ) =>
% 95.34/12.68 ( ![S:$i]:
% 95.34/12.68 ( ( breln1 @ A @ S ) => ( breln1 @ A @ ( breln1compset @ A @ R @ S ) ) ) ) ))).
% 95.34/12.68 thf('21', plain,
% 95.34/12.68 (( breln1compprop ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( breln1 @ X4 @ X6 ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( breln1 @ X4 @ X8 ) =>
% 95.34/12.68 ( breln1 @ X4 @ ( breln1compset @ X4 @ X6 @ X8 ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(breln1invE, axiom, breln1invE =
% 95.34/12.68 (![A:$i,R:$i]:
% 95.34/12.68 ( ( breln1 @ A @ R ) =>
% 95.34/12.68 ( ![Xx:$i]:
% 95.34/12.68 ( ( in @ Xx @ A ) =>
% 95.34/12.68 ( ![Xy:$i]:
% 95.34/12.68 ( ( in @ Xy @ A ) =>
% 95.34/12.68 ( ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) ) =>
% 95.34/12.68 ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ))).
% 95.34/12.68 thf('22', plain,
% 95.34/12.68 (( breln1invE ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( breln1 @ X4 @ X6 ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( in @ X8 @ X4 ) =>
% 95.34/12.68 ( ![X10:$i]:
% 95.34/12.68 ( ( in @ X10 @ X4 ) =>
% 95.34/12.68 ( ( in @ ( kpair @ X10 @ X8 ) @ ( breln1invset @ X4 @ X6 ) ) =>
% 95.34/12.68 ( in @ ( kpair @ X8 @ X10 ) @ X6 ) ) ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(breln1invI, axiom, breln1invI =
% 95.34/12.68 (![A:$i,R:$i]:
% 95.34/12.68 ( ( breln1 @ A @ R ) =>
% 95.34/12.68 ( ![Xx:$i]:
% 95.34/12.68 ( ( in @ Xx @ A ) =>
% 95.34/12.68 ( ![Xy:$i]:
% 95.34/12.68 ( ( in @ Xy @ A ) =>
% 95.34/12.68 ( ( in @ ( kpair @ Xx @ Xy ) @ R ) =>
% 95.34/12.68 ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ))).
% 95.34/12.68 thf('23', plain,
% 95.34/12.68 (( breln1invI ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( breln1 @ X4 @ X6 ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( in @ X8 @ X4 ) =>
% 95.34/12.68 ( ![X10:$i]:
% 95.34/12.68 ( ( in @ X10 @ X4 ) =>
% 95.34/12.68 ( ( in @ ( kpair @ X8 @ X10 ) @ X6 ) =>
% 95.34/12.68 ( in @ ( kpair @ X10 @ X8 ) @ ( breln1invset @ X4 @ X6 ) ) ) ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(breln1invprop, axiom, breln1invprop =
% 95.34/12.68 (![A:$i,R:$i]:
% 95.34/12.68 ( ( breln1 @ A @ R ) => ( breln1 @ A @ ( breln1invset @ A @ R ) ) ))).
% 95.34/12.68 thf('24', plain,
% 95.34/12.68 (( breln1invprop ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( breln1 @ X4 @ X6 ) => ( breln1 @ X4 @ ( breln1invset @ X4 @ X6 ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(eqbreln1, axiom, eqbreln1 =
% 95.34/12.68 (![A:$i,R:$i]:
% 95.34/12.68 ( ( breln1 @ A @ R ) =>
% 95.34/12.68 ( ![S:$i]:
% 95.34/12.68 ( ( breln1 @ A @ S ) =>
% 95.34/12.68 ( ( ![Xx:$i]:
% 95.34/12.68 ( ( in @ Xx @ A ) =>
% 95.34/12.68 ( ![Xy:$i]:
% 95.34/12.68 ( ( in @ Xy @ A ) =>
% 95.34/12.68 ( ( in @ ( kpair @ Xx @ Xy ) @ R ) =>
% 95.34/12.68 ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) ) ) ) =>
% 95.34/12.68 ( ( ![Xx:$i]:
% 95.34/12.68 ( ( in @ Xx @ A ) =>
% 95.34/12.68 ( ![Xy:$i]:
% 95.34/12.68 ( ( in @ Xy @ A ) =>
% 95.34/12.68 ( ( in @ ( kpair @ Xx @ Xy ) @ S ) =>
% 95.34/12.68 ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) =>
% 95.34/12.68 ( ( R ) = ( S ) ) ) ) ) ) ))).
% 95.34/12.68 thf('25', plain,
% 95.34/12.68 (( eqbreln1 ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( breln1 @ X4 @ X6 ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( breln1 @ X4 @ X8 ) =>
% 95.34/12.68 ( ( ![X10:$i]:
% 95.34/12.68 ( ( in @ X10 @ X4 ) =>
% 95.34/12.68 ( ![X12:$i]:
% 95.34/12.68 ( ( in @ X12 @ X4 ) =>
% 95.34/12.68 ( ( in @ ( kpair @ X10 @ X12 ) @ X6 ) =>
% 95.34/12.68 ( in @ ( kpair @ X10 @ X12 ) @ X8 ) ) ) ) ) ) =>
% 95.34/12.68 ( ( ![X14:$i]:
% 95.34/12.68 ( ( in @ X14 @ X4 ) =>
% 95.34/12.68 ( ![X16:$i]:
% 95.34/12.68 ( ( in @ X16 @ X4 ) =>
% 95.34/12.68 ( ( in @ ( kpair @ X14 @ X16 ) @ X8 ) =>
% 95.34/12.68 ( in @ ( kpair @ X14 @ X16 ) @ X6 ) ) ) ) ) ) =>
% 95.34/12.68 ( ( X6 ) = ( X8 ) ) ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(subbreln1, axiom, subbreln1 =
% 95.34/12.68 (![A:$i,R:$i]:
% 95.34/12.68 ( ( breln1 @ A @ R ) =>
% 95.34/12.68 ( ![S:$i]:
% 95.34/12.68 ( ( breln1 @ A @ S ) =>
% 95.34/12.68 ( ( ![Xx:$i]:
% 95.34/12.68 ( ( in @ Xx @ A ) =>
% 95.34/12.68 ( ![Xy:$i]:
% 95.34/12.68 ( ( in @ Xy @ A ) =>
% 95.34/12.68 ( ( in @ ( kpair @ Xx @ Xy ) @ R ) =>
% 95.34/12.68 ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) ) ) ) =>
% 95.34/12.68 ( subset @ R @ S ) ) ) ) ))).
% 95.34/12.68 thf('26', plain,
% 95.34/12.68 (( subbreln1 ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( breln1 @ X4 @ X6 ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( breln1 @ X4 @ X8 ) =>
% 95.34/12.68 ( ( ![X10:$i]:
% 95.34/12.68 ( ( in @ X10 @ X4 ) =>
% 95.34/12.68 ( ![X12:$i]:
% 95.34/12.68 ( ( in @ X12 @ X4 ) =>
% 95.34/12.68 ( ( in @ ( kpair @ X10 @ X12 ) @ X6 ) =>
% 95.34/12.68 ( in @ ( kpair @ X10 @ X12 ) @ X8 ) ) ) ) ) ) =>
% 95.34/12.68 ( subset @ X6 @ X8 ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(breln1all1, axiom, breln1all1 =
% 95.34/12.68 (![A:$i,R:$i]:
% 95.34/12.68 ( ( breln1 @ A @ R ) =>
% 95.34/12.68 ( ![Xphi:( $i > $o )]:
% 95.34/12.68 ( ( ![Xx:$i]:
% 95.34/12.68 ( ( in @ Xx @ A ) =>
% 95.34/12.68 ( ![Xy:$i]:
% 95.34/12.68 ( ( in @ Xy @ A ) =>
% 95.34/12.68 ( ( in @ ( kpair @ Xx @ Xy ) @ R ) =>
% 95.34/12.68 ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) ) ) ) =>
% 95.34/12.68 ( ![Xx:$i]: ( ( in @ Xx @ R ) => ( Xphi @ Xx ) ) ) ) ) ))).
% 95.34/12.68 thf('27', plain,
% 95.34/12.68 (( breln1all1 ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( breln1 @ X4 @ X6 ) =>
% 95.34/12.68 ( ![X8:( $i > $o )]:
% 95.34/12.68 ( ( ![X10:$i]:
% 95.34/12.68 ( ( in @ X10 @ X4 ) =>
% 95.34/12.68 ( ![X12:$i]:
% 95.34/12.68 ( ( in @ X12 @ X4 ) =>
% 95.34/12.68 ( ( in @ ( kpair @ X10 @ X12 ) @ X6 ) =>
% 95.34/12.68 ( X8 @ ( kpair @ X10 @ X12 ) ) ) ) ) ) ) =>
% 95.34/12.68 ( ![X14:$i]: ( ( in @ X14 @ X6 ) => ( X8 @ X14 ) ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(setOfPairsIsBReln1, axiom, setOfPairsIsBReln1 =
% 95.34/12.68 (![A:$i,Xphi:( $i > $i > $o )]:
% 95.34/12.68 ( breln1 @
% 95.34/12.68 A @ ( dpsetconstr @ A @ A @ ( ^[Xx:$i,Xy:$i]: ( Xphi @ Xx @ Xy ) ) ) ))).
% 95.34/12.68 thf('28', plain,
% 95.34/12.68 (( setOfPairsIsBReln1 ) =
% 95.34/12.68 ( ![X4:$i,X6:( $i > $i > $o )]:
% 95.34/12.68 ( breln1 @
% 95.34/12.68 X4 @
% 95.34/12.68 ( dpsetconstr @ X4 @ X4 @ ( ^[V_1:$i,V_2:$i]: ( X6 @ V_1 @ V_2 ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(choice2fnsingleton, axiom, choice2fnsingleton =
% 95.34/12.68 (![A:$i,B:$i,Xphi:( $i > $i > $o )]:
% 95.34/12.68 ( ( ![Xx:$i]:
% 95.34/12.68 ( ( in @ Xx @ A ) =>
% 95.34/12.68 ( ?[Xy:$i]: ( ( Xphi @ Xx @ Xy ) & ( in @ Xy @ B ) ) ) ) ) =>
% 95.34/12.68 ( ![R:$i]:
% 95.34/12.68 ( ( in @ R @ ( breln1Set @ B ) ) =>
% 95.34/12.68 ( ( reflwellordering @ B @ R ) =>
% 95.34/12.68 ( ![Xx:$i]:
% 95.34/12.68 ( ( in @ Xx @ A ) =>
% 95.34/12.68 ( singleton @
% 95.34/12.68 ( dsetconstr @
% 95.34/12.68 B @
% 95.34/12.68 ( ^[Xy:$i]:
% 95.34/12.68 ( ( Xphi @ Xx @ Xy ) &
% 95.34/12.68 ( ![Xz:$i]:
% 95.34/12.68 ( ( in @ Xz @ B ) =>
% 95.34/12.68 ( ( Xphi @ Xx @ Xz ) =>
% 95.34/12.68 ( in @ ( kpair @ Xy @ Xz ) @ R ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 95.34/12.68 thf('29', plain,
% 95.34/12.68 (( choice2fnsingleton ) =
% 95.34/12.68 ( ![X4:$i,X6:$i,X8:( $i > $i > $o )]:
% 95.34/12.68 ( ( ![X10:$i]:
% 95.34/12.68 ( ( in @ X10 @ X4 ) =>
% 95.34/12.68 ( ?[X12:$i]: ( ( X8 @ X10 @ X12 ) & ( in @ X12 @ X6 ) ) ) ) ) =>
% 95.34/12.68 ( ![X14:$i]:
% 95.34/12.68 ( ( in @ X14 @ ( breln1Set @ X6 ) ) =>
% 95.34/12.68 ( ( reflwellordering @ X6 @ X14 ) =>
% 95.34/12.68 ( ![X16:$i]:
% 95.34/12.68 ( ( in @ X16 @ X4 ) =>
% 95.34/12.68 ( singleton @
% 95.34/12.68 ( dsetconstr @
% 95.34/12.68 X6 @
% 95.34/12.68 ( ^[V_1:$i]:
% 95.34/12.68 ( ( X8 @ X16 @ V_1 ) &
% 95.34/12.68 ( ![X18:$i]:
% 95.34/12.68 ( ( in @ X18 @ X6 ) =>
% 95.34/12.68 ( ( X8 @ X16 @ X18 ) =>
% 95.34/12.68 ( in @ ( kpair @ V_1 @ X18 ) @ X14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(breln1SetBreln1, axiom, breln1SetBreln1 =
% 95.34/12.68 (![A:$i,R:$i]: ( ( in @ R @ ( breln1Set @ A ) ) => ( breln1 @ A @ R ) ))).
% 95.34/12.68 thf('30', plain,
% 95.34/12.68 (( breln1SetBreln1 ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( in @ X6 @ ( breln1Set @ X4 ) ) => ( breln1 @ X4 @ X6 ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(breln1all2, axiom, breln1all2 =
% 95.34/12.68 (![A:$i,R:$i]:
% 95.34/12.68 ( ( breln1 @ A @ R ) =>
% 95.34/12.68 ( ![Xphi:( $i > $o )]:
% 95.34/12.68 ( ( ![Xx:$i]:
% 95.34/12.68 ( ( in @ Xx @ A ) =>
% 95.34/12.68 ( ![Xy:$i]:
% 95.34/12.68 ( ( in @ Xy @ A ) =>
% 95.34/12.68 ( ( in @ ( kpair @ Xx @ Xy ) @ R ) =>
% 95.34/12.68 ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) ) ) ) =>
% 95.34/12.68 ( ![Xx:$i]: ( ( in @ Xx @ R ) => ( Xphi @ Xx ) ) ) ) ) ))).
% 95.34/12.68 thf('31', plain,
% 95.34/12.68 (( breln1all2 ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( breln1 @ X4 @ X6 ) =>
% 95.34/12.68 ( ![X8:( $i > $o )]:
% 95.34/12.68 ( ( ![X10:$i]:
% 95.34/12.68 ( ( in @ X10 @ X4 ) =>
% 95.34/12.68 ( ![X12:$i]:
% 95.34/12.68 ( ( in @ X12 @ X4 ) =>
% 95.34/12.68 ( ( in @ ( kpair @ X10 @ X12 ) @ X6 ) =>
% 95.34/12.68 ( X8 @ ( kpair @ X10 @ X12 ) ) ) ) ) ) ) =>
% 95.34/12.68 ( ![X14:$i]: ( ( in @ X14 @ X6 ) => ( X8 @ X14 ) ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(woz1_5, axiom, woz1_5 =
% 95.34/12.68 (![A:$i,X:$i]:
% 95.34/12.68 ( ( in @ X @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Y:$i]:
% 95.34/12.68 ( ( in @ Y @ ( powerset @ A ) ) =>
% 95.34/12.68 ( in @
% 95.34/12.68 ( setminus @ A @ ( binunion @ X @ Y ) ) @
% 95.34/12.68 ( powerset @ ( setminus @ A @ X ) ) ) ) ) ))).
% 95.34/12.68 thf('32', plain,
% 95.34/12.68 (( woz1_5 ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( in @
% 95.34/12.68 ( setminus @ X4 @ ( binunion @ X6 @ X8 ) ) @
% 95.34/12.68 ( powerset @ ( setminus @ X4 @ X6 ) ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(woz1_4, axiom, woz1_4 =
% 95.34/12.68 (![A:$i,X:$i]:
% 95.34/12.68 ( ( in @ X @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Y:$i]:
% 95.34/12.68 ( ( in @ Y @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ( subset @ X @ ( setminus @ A @ Y ) ) =>
% 95.34/12.68 ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ))).
% 95.34/12.68 thf('33', plain,
% 95.34/12.68 (( woz1_4 ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ( subset @ X6 @ ( setminus @ X4 @ X8 ) ) =>
% 95.34/12.68 ( subset @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(woz1_3, axiom, woz1_3 =
% 95.34/12.68 (![A:$i,X:$i]:
% 95.34/12.68 ( ( in @ X @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Y:$i]:
% 95.34/12.68 ( ( in @ Y @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Z:$i]:
% 95.34/12.68 ( ( in @ Z @ ( powerset @ A ) ) =>
% 95.34/12.68 ( in @
% 95.34/12.68 ( binintersect @ X @ Y ) @
% 95.34/12.68 ( powerset @
% 95.34/12.68 ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ))).
% 95.34/12.68 thf('34', plain,
% 95.34/12.68 (( woz1_3 ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X10:$i]:
% 95.34/12.68 ( ( in @ X10 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( in @
% 95.34/12.68 ( binintersect @ X6 @ X8 ) @
% 95.34/12.68 ( powerset @
% 95.34/12.68 ( binintersect @
% 95.34/12.68 ( binunion @ X6 @ X10 ) @ ( binunion @ X8 @ X10 ) ) ) ) ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(woz1_2, axiom, woz1_2 =
% 95.34/12.68 (![A:$i,X:$i]:
% 95.34/12.68 ( ( in @ X @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Y:$i]:
% 95.34/12.68 ( ( in @ Y @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Z:$i]:
% 95.34/12.68 ( ( in @ Z @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![W:$i]:
% 95.34/12.68 ( ( in @ W @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ( setminus @
% 95.34/12.68 A @
% 95.34/12.68 ( binintersect @
% 95.34/12.68 ( binunion @ X @ Y ) @ ( binunion @ Z @ W ) ) ) =
% 95.34/12.68 ( binunion @
% 95.34/12.68 ( binintersect @
% 95.34/12.68 ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) @
% 95.34/12.68 ( binintersect @
% 95.34/12.68 ( setminus @ A @ Z ) @ ( setminus @ A @ W ) ) ) ) ) ) ) ) ) ) ))).
% 95.34/12.68 thf('35', plain,
% 95.34/12.68 (( woz1_2 ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X10:$i]:
% 95.34/12.68 ( ( in @ X10 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X12:$i]:
% 95.34/12.68 ( ( in @ X12 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ( setminus @
% 95.34/12.68 X4 @
% 95.34/12.68 ( binintersect @
% 95.34/12.68 ( binunion @ X6 @ X8 ) @ ( binunion @ X10 @ X12 ) ) ) =
% 95.34/12.68 ( binunion @
% 95.34/12.68 ( binintersect @
% 95.34/12.68 ( setminus @ X4 @ X6 ) @ ( setminus @ X4 @ X8 ) ) @
% 95.34/12.68 ( binintersect @
% 95.34/12.68 ( setminus @ X4 @ X10 ) @ ( setminus @ X4 @ X12 ) ) ) ) ) ) ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(woz1_1, axiom, woz1_1 =
% 95.34/12.68 (![A:$i,X:$i]:
% 95.34/12.68 ( ( in @ X @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Y:$i]:
% 95.34/12.68 ( ( in @ Y @ ( powerset @ A ) ) =>
% 95.34/12.68 ( in @
% 95.34/12.68 ( setminus @ A @ X ) @
% 95.34/12.68 ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ))).
% 95.34/12.68 thf('36', plain,
% 95.34/12.68 (( woz1_1 ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( in @
% 95.34/12.68 ( setminus @ X4 @ X6 ) @
% 95.34/12.68 ( powerset @ ( setminus @ X4 @ ( binintersect @ X6 @ X8 ) ) ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(woz13rule4, axiom, woz13rule4 =
% 95.34/12.68 (![A:$i,X:$i]:
% 95.34/12.68 ( ( in @ X @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Y:$i]:
% 95.34/12.68 ( ( in @ Y @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Z:$i]:
% 95.34/12.68 ( ( in @ Z @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![W:$i]:
% 95.34/12.68 ( ( in @ W @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ( subset @ X @ Z ) =>
% 95.34/12.68 ( ( subset @ Y @ W ) =>
% 95.34/12.68 ( subset @
% 95.34/12.68 ( binintersect @ X @ Y ) @ ( binintersect @ Z @ W ) ) ) ) ) ) ) ) ) ) ))).
% 95.34/12.68 thf('37', plain,
% 95.34/12.68 (( woz13rule4 ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X10:$i]:
% 95.34/12.68 ( ( in @ X10 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X12:$i]:
% 95.34/12.68 ( ( in @ X12 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ( subset @ X6 @ X10 ) =>
% 95.34/12.68 ( ( subset @ X8 @ X12 ) =>
% 95.34/12.68 ( subset @
% 95.34/12.68 ( binintersect @ X6 @ X8 ) @
% 95.34/12.68 ( binintersect @ X10 @ X12 ) ) ) ) ) ) ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(woz13rule3, axiom, woz13rule3 =
% 95.34/12.68 (![A:$i,X:$i]:
% 95.34/12.68 ( ( in @ X @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Y:$i]:
% 95.34/12.68 ( ( in @ Y @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Z:$i]:
% 95.34/12.68 ( ( in @ Z @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ( subset @ X @ Y ) =>
% 95.34/12.68 ( ( subset @ X @ Z ) =>
% 95.34/12.68 ( subset @ X @ ( binintersect @ Y @ Z ) ) ) ) ) ) ) ) ))).
% 95.34/12.68 thf('38', plain,
% 95.34/12.68 (( woz13rule3 ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X10:$i]:
% 95.34/12.68 ( ( in @ X10 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ( subset @ X6 @ X8 ) =>
% 95.34/12.68 ( ( subset @ X6 @ X10 ) =>
% 95.34/12.68 ( subset @ X6 @ ( binintersect @ X8 @ X10 ) ) ) ) ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(woz13rule2, axiom, woz13rule2 =
% 95.34/12.68 (![A:$i,X:$i]:
% 95.34/12.68 ( ( in @ X @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Y:$i]:
% 95.34/12.68 ( ( in @ Y @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Z:$i]:
% 95.34/12.68 ( ( in @ Z @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ( subset @ Y @ Z ) =>
% 95.34/12.68 ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ))).
% 95.34/12.68 thf('39', plain,
% 95.34/12.68 (( woz13rule2 ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X10:$i]:
% 95.34/12.68 ( ( in @ X10 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ( subset @ X8 @ X10 ) =>
% 95.34/12.68 ( subset @ ( binintersect @ X6 @ X8 ) @ X10 ) ) ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(woz13rule1, axiom, woz13rule1 =
% 95.34/12.68 (![A:$i,X:$i]:
% 95.34/12.68 ( ( in @ X @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Y:$i]:
% 95.34/12.68 ( ( in @ Y @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Z:$i]:
% 95.34/12.68 ( ( in @ Z @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ( subset @ X @ Z ) =>
% 95.34/12.68 ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ))).
% 95.34/12.68 thf('40', plain,
% 95.34/12.68 (( woz13rule1 ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X10:$i]:
% 95.34/12.68 ( ( in @ X10 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ( subset @ X6 @ X10 ) =>
% 95.34/12.68 ( subset @ ( binintersect @ X6 @ X8 ) @ X10 ) ) ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(woz13rule0, axiom, woz13rule0 =
% 95.34/12.68 (![A:$i,X:$i]:
% 95.34/12.68 ( ( in @ X @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Y:$i]:
% 95.34/12.68 ( ( in @ Y @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Xx:$i]:
% 95.34/12.68 ( ( in @ Xx @ ( binintersect @ X @ Y ) ) => ( in @ Xx @ A ) ) ) ) ) ))).
% 95.34/12.68 thf('41', plain,
% 95.34/12.68 (( woz13rule0 ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X10:$i]:
% 95.34/12.68 ( ( in @ X10 @ ( binintersect @ X6 @ X8 ) ) =>
% 95.34/12.68 ( in @ X10 @ X4 ) ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(demorgan2, axiom, demorgan2 =
% 95.34/12.68 (![A:$i,X:$i]:
% 95.34/12.68 ( ( in @ X @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Y:$i]:
% 95.34/12.68 ( ( in @ Y @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ( setminus @ A @ ( binunion @ X @ Y ) ) =
% 95.34/12.68 ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ))).
% 95.34/12.68 thf('42', plain,
% 95.34/12.68 (( demorgan2 ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ( setminus @ X4 @ ( binunion @ X6 @ X8 ) ) =
% 95.34/12.68 ( binintersect @
% 95.34/12.68 ( setminus @ X4 @ X6 ) @ ( setminus @ X4 @ X8 ) ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(demorgan2b, axiom, demorgan2b =
% 95.34/12.68 (![A:$i,X:$i]:
% 95.34/12.68 ( ( in @ X @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Y:$i]:
% 95.34/12.68 ( ( in @ Y @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Xx:$i]:
% 95.34/12.68 ( ( in @ Xx @ A ) =>
% 95.34/12.68 ( ( in @
% 95.34/12.68 Xx @
% 95.34/12.68 ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) =>
% 95.34/12.68 ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ))).
% 95.34/12.68 thf('43', plain,
% 95.34/12.68 (( demorgan2b ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X10:$i]:
% 95.34/12.68 ( ( in @ X10 @ X4 ) =>
% 95.34/12.68 ( ( in @
% 95.34/12.68 X10 @
% 95.34/12.68 ( binintersect @
% 95.34/12.68 ( setminus @ X4 @ X6 ) @ ( setminus @ X4 @ X8 ) ) ) =>
% 95.34/12.68 ( in @ X10 @ ( setminus @ X4 @ ( binunion @ X6 @ X8 ) ) ) ) ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(demorgan2b2, axiom, demorgan2b2 =
% 95.34/12.68 (![A:$i,X:$i]:
% 95.34/12.68 ( ( in @ X @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Y:$i]:
% 95.34/12.68 ( ( in @ Y @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Xx:$i]:
% 95.34/12.68 ( ( in @ Xx @ A ) =>
% 95.34/12.68 ( ( in @ Xx @ ( setminus @ A @ X ) ) =>
% 95.34/12.68 ( ( in @ Xx @ ( setminus @ A @ Y ) ) =>
% 95.34/12.68 ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ))).
% 95.34/12.68 thf('44', plain,
% 95.34/12.68 (( demorgan2b2 ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X10:$i]:
% 95.34/12.68 ( ( in @ X10 @ X4 ) =>
% 95.34/12.68 ( ( in @ X10 @ ( setminus @ X4 @ X6 ) ) =>
% 95.34/12.68 ( ( in @ X10 @ ( setminus @ X4 @ X8 ) ) =>
% 95.34/12.68 ( in @ X10 @ ( setminus @ X4 @ ( binunion @ X6 @ X8 ) ) ) ) ) ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(demorgan2a, axiom, demorgan2a =
% 95.34/12.68 (![A:$i,X:$i]:
% 95.34/12.68 ( ( in @ X @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Y:$i]:
% 95.34/12.68 ( ( in @ Y @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Xx:$i]:
% 95.34/12.68 ( ( in @ Xx @ A ) =>
% 95.34/12.68 ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) =>
% 95.34/12.68 ( in @
% 95.34/12.68 Xx @
% 95.34/12.68 ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ))).
% 95.34/12.68 thf('45', plain,
% 95.34/12.68 (( demorgan2a ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X10:$i]:
% 95.34/12.68 ( ( in @ X10 @ X4 ) =>
% 95.34/12.68 ( ( in @ X10 @ ( setminus @ X4 @ ( binunion @ X6 @ X8 ) ) ) =>
% 95.34/12.68 ( in @
% 95.34/12.68 X10 @
% 95.34/12.68 ( binintersect @
% 95.34/12.68 ( setminus @ X4 @ X6 ) @ ( setminus @ X4 @ X8 ) ) ) ) ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(demorgan1, axiom, demorgan1 =
% 95.34/12.68 (![A:$i,X:$i]:
% 95.34/12.68 ( ( in @ X @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Y:$i]:
% 95.34/12.68 ( ( in @ Y @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ( setminus @ A @ ( binintersect @ X @ Y ) ) =
% 95.34/12.68 ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ))).
% 95.34/12.68 thf('46', plain,
% 95.34/12.68 (( demorgan1 ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ( setminus @ X4 @ ( binintersect @ X6 @ X8 ) ) =
% 95.34/12.68 ( binunion @ ( setminus @ X4 @ X6 ) @ ( setminus @ X4 @ X8 ) ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(demorgan1b, axiom, demorgan1b =
% 95.34/12.68 (![A:$i,X:$i]:
% 95.34/12.68 ( ( in @ X @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Y:$i]:
% 95.34/12.68 ( ( in @ Y @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Xx:$i]:
% 95.34/12.68 ( ( in @ Xx @ A ) =>
% 95.34/12.68 ( ( in @
% 95.34/12.68 Xx @
% 95.34/12.68 ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) =>
% 95.34/12.68 ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ))).
% 95.34/12.68 thf('47', plain,
% 95.34/12.68 (( demorgan1b ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X10:$i]:
% 95.34/12.68 ( ( in @ X10 @ X4 ) =>
% 95.34/12.68 ( ( in @
% 95.34/12.68 X10 @
% 95.34/12.68 ( binunion @
% 95.34/12.68 ( setminus @ X4 @ X6 ) @ ( setminus @ X4 @ X8 ) ) ) =>
% 95.34/12.68 ( in @
% 95.34/12.68 X10 @ ( setminus @ X4 @ ( binintersect @ X6 @ X8 ) ) ) ) ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(demorgan1a, axiom, demorgan1a =
% 95.34/12.68 (![A:$i,X:$i]:
% 95.34/12.68 ( ( in @ X @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Y:$i]:
% 95.34/12.68 ( ( in @ Y @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Xx:$i]:
% 95.34/12.68 ( ( in @ Xx @ A ) =>
% 95.34/12.68 ( ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) =>
% 95.34/12.68 ( in @
% 95.34/12.68 Xx @
% 95.34/12.68 ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ))).
% 95.34/12.68 thf('48', plain,
% 95.34/12.68 (( demorgan1a ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X10:$i]:
% 95.34/12.68 ( ( in @ X10 @ X4 ) =>
% 95.34/12.68 ( ( in @
% 95.34/12.68 X10 @ ( setminus @ X4 @ ( binintersect @ X6 @ X8 ) ) ) =>
% 95.34/12.68 ( in @
% 95.34/12.68 X10 @
% 95.34/12.68 ( binunion @
% 95.34/12.68 ( setminus @ X4 @ X6 ) @ ( setminus @ X4 @ X8 ) ) ) ) ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(demorgan2a2, axiom, demorgan2a2 =
% 95.34/12.68 (![A:$i,X:$i]:
% 95.34/12.68 ( ( in @ X @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Y:$i]:
% 95.34/12.68 ( ( in @ Y @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Xx:$i]:
% 95.34/12.68 ( ( in @ Xx @ A ) =>
% 95.34/12.68 ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) =>
% 95.34/12.68 ( in @ Xx @ ( setminus @ A @ Y ) ) ) ) ) ) ) ))).
% 95.34/12.68 thf('49', plain,
% 95.34/12.68 (( demorgan2a2 ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X10:$i]:
% 95.34/12.68 ( ( in @ X10 @ X4 ) =>
% 95.34/12.68 ( ( in @ X10 @ ( setminus @ X4 @ ( binunion @ X6 @ X8 ) ) ) =>
% 95.34/12.68 ( in @ X10 @ ( setminus @ X4 @ X8 ) ) ) ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(complementUnionInPowersetComplement, axiom,
% 95.34/12.68 complementUnionInPowersetComplement =
% 95.34/12.68 (![A:$i,X:$i]:
% 95.34/12.68 ( ( in @ X @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Y:$i]:
% 95.34/12.68 ( ( in @ Y @ ( powerset @ A ) ) =>
% 95.34/12.68 ( in @
% 95.34/12.68 ( setminus @ A @ ( binunion @ X @ Y ) ) @
% 95.34/12.68 ( powerset @ ( setminus @ A @ X ) ) ) ) ) ))).
% 95.34/12.68 thf('50', plain,
% 95.34/12.68 (( complementUnionInPowersetComplement ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( in @
% 95.34/12.68 ( setminus @ X4 @ ( binunion @ X6 @ X8 ) ) @
% 95.34/12.68 ( powerset @ ( setminus @ X4 @ X6 ) ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(demorgan2a1, axiom, demorgan2a1 =
% 95.34/12.68 (![A:$i,X:$i]:
% 95.34/12.68 ( ( in @ X @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Y:$i]:
% 95.34/12.68 ( ( in @ Y @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Xx:$i]:
% 95.34/12.68 ( ( in @ Xx @ A ) =>
% 95.34/12.68 ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) =>
% 95.34/12.68 ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ))).
% 95.34/12.68 thf('51', plain,
% 95.34/12.68 (( demorgan2a1 ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X10:$i]:
% 95.34/12.68 ( ( in @ X10 @ X4 ) =>
% 95.34/12.68 ( ( in @ X10 @ ( setminus @ X4 @ ( binunion @ X6 @ X8 ) ) ) =>
% 95.34/12.68 ( in @ X10 @ ( setminus @ X4 @ X6 ) ) ) ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(binunionTEcontra, axiom, binunionTEcontra =
% 95.34/12.68 (![A:$i,X:$i]:
% 95.34/12.68 ( ( in @ X @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Y:$i]:
% 95.34/12.68 ( ( in @ Y @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Xx:$i]:
% 95.34/12.68 ( ( in @ Xx @ A ) =>
% 95.34/12.68 ( ( ~( in @ Xx @ X ) ) =>
% 95.34/12.68 ( ( ~( in @ Xx @ Y ) ) =>
% 95.34/12.68 ( ~( in @ Xx @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ))).
% 95.34/12.68 thf('52', plain,
% 95.34/12.68 (( binunionTEcontra ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X10:$i]:
% 95.34/12.68 ( ( in @ X10 @ X4 ) =>
% 95.34/12.68 ( ( ~( in @ X10 @ X6 ) ) =>
% 95.34/12.68 ( ( ~( in @ X10 @ X8 ) ) =>
% 95.34/12.68 ( ~( in @ X10 @ ( binunion @ X6 @ X8 ) ) ) ) ) ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(binunionTE, axiom, binunionTE =
% 95.34/12.68 (![A:$i,X:$i]:
% 95.34/12.68 ( ( in @ X @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Y:$i]:
% 95.34/12.68 ( ( in @ Y @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Xphi:$o,Xx:$i]:
% 95.34/12.68 ( ( in @ Xx @ A ) =>
% 95.34/12.68 ( ( in @ Xx @ ( binunion @ X @ Y ) ) =>
% 95.34/12.68 ( ( ( in @ Xx @ X ) => ( Xphi ) ) =>
% 95.34/12.68 ( ( ( in @ Xx @ Y ) => ( Xphi ) ) => ( Xphi ) ) ) ) ) ) ) ) ))).
% 95.34/12.68 thf('53', plain,
% 95.34/12.68 (( binunionTE ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X10:$o,X12:$i]:
% 95.34/12.68 ( ( in @ X12 @ X4 ) =>
% 95.34/12.68 ( ( in @ X12 @ ( binunion @ X6 @ X8 ) ) =>
% 95.34/12.68 ( ( ( in @ X12 @ X6 ) => ( X10 ) ) =>
% 95.34/12.68 ( ( ( in @ X12 @ X8 ) => ( X10 ) ) => ( X10 ) ) ) ) ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(inComplementUnionImpInComplement1, axiom,
% 95.34/12.68 inComplementUnionImpInComplement1 =
% 95.34/12.68 (![A:$i,X:$i]:
% 95.34/12.68 ( ( in @ X @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Y:$i]:
% 95.34/12.68 ( ( in @ Y @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Xx:$i]:
% 95.34/12.68 ( ( in @ Xx @ A ) =>
% 95.34/12.68 ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) =>
% 95.34/12.68 ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ))).
% 95.34/12.68 thf('54', plain,
% 95.34/12.68 (( inComplementUnionImpInComplement1 ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X10:$i]:
% 95.34/12.68 ( ( in @ X10 @ X4 ) =>
% 95.34/12.68 ( ( in @ X10 @ ( setminus @ X4 @ ( binunion @ X6 @ X8 ) ) ) =>
% 95.34/12.68 ( in @ X10 @ ( setminus @ X4 @ X6 ) ) ) ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(inComplementUnionImpNotIn1, axiom, inComplementUnionImpNotIn1 =
% 95.34/12.68 (![A:$i,X:$i]:
% 95.34/12.68 ( ( in @ X @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Y:$i]:
% 95.34/12.68 ( ( in @ Y @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Xx:$i]:
% 95.34/12.68 ( ( in @ Xx @ A ) =>
% 95.34/12.68 ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) =>
% 95.34/12.68 ( ~( in @ Xx @ X ) ) ) ) ) ) ) ))).
% 95.34/12.68 thf('55', plain,
% 95.34/12.68 (( inComplementUnionImpNotIn1 ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X10:$i]:
% 95.34/12.68 ( ( in @ X10 @ X4 ) =>
% 95.34/12.68 ( ( in @ X10 @ ( setminus @ X4 @ ( binunion @ X6 @ X8 ) ) ) =>
% 95.34/12.68 ( ~( in @ X10 @ X6 ) ) ) ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(intersectInPowersetIntersectUnions, axiom,
% 95.34/12.68 intersectInPowersetIntersectUnions =
% 95.34/12.68 (![A:$i,X:$i]:
% 95.34/12.68 ( ( in @ X @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Y:$i]:
% 95.34/12.68 ( ( in @ Y @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Z:$i]:
% 95.34/12.68 ( ( in @ Z @ ( powerset @ A ) ) =>
% 95.34/12.68 ( in @
% 95.34/12.68 ( binintersect @ X @ Y ) @
% 95.34/12.68 ( powerset @
% 95.34/12.68 ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ))).
% 95.34/12.68 thf('56', plain,
% 95.34/12.68 (( intersectInPowersetIntersectUnions ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X10:$i]:
% 95.34/12.68 ( ( in @ X10 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( in @
% 95.34/12.68 ( binintersect @ X6 @ X8 ) @
% 95.34/12.68 ( powerset @
% 95.34/12.68 ( binintersect @
% 95.34/12.68 ( binunion @ X6 @ X10 ) @ ( binunion @ X8 @ X10 ) ) ) ) ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(inIntersectImpInIntersectUnions, axiom, inIntersectImpInIntersectUnions =
% 95.34/12.68 (![A:$i,X:$i]:
% 95.34/12.68 ( ( in @ X @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Y:$i]:
% 95.34/12.68 ( ( in @ Y @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Z:$i]:
% 95.34/12.68 ( ( in @ Z @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Xx:$i]:
% 95.34/12.68 ( ( in @ Xx @ A ) =>
% 95.34/12.68 ( ( in @ Xx @ ( binintersect @ X @ Y ) ) =>
% 95.34/12.68 ( in @
% 95.34/12.68 Xx @
% 95.34/12.68 ( binintersect @
% 95.34/12.68 ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ) ))).
% 95.34/12.68 thf('57', plain,
% 95.34/12.68 (( inIntersectImpInIntersectUnions ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X10:$i]:
% 95.34/12.68 ( ( in @ X10 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X12:$i]:
% 95.34/12.68 ( ( in @ X12 @ X4 ) =>
% 95.34/12.68 ( ( in @ X12 @ ( binintersect @ X6 @ X8 ) ) =>
% 95.34/12.68 ( in @
% 95.34/12.68 X12 @
% 95.34/12.68 ( binintersect @
% 95.34/12.68 ( binunion @ X6 @ X10 ) @ ( binunion @ X8 @ X10 ) ) ) ) ) ) ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(inIntersectImpInUnion2, axiom, inIntersectImpInUnion2 =
% 95.34/12.68 (![A:$i,X:$i]:
% 95.34/12.68 ( ( in @ X @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Y:$i]:
% 95.34/12.68 ( ( in @ Y @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Z:$i]:
% 95.34/12.68 ( ( in @ Z @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Xx:$i]:
% 95.34/12.68 ( ( in @ Xx @ A ) =>
% 95.34/12.68 ( ( in @ Xx @ ( binintersect @ X @ Y ) ) =>
% 95.34/12.68 ( in @ Xx @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ))).
% 95.34/12.68 thf('58', plain,
% 95.34/12.68 (( inIntersectImpInUnion2 ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X10:$i]:
% 95.34/12.68 ( ( in @ X10 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X12:$i]:
% 95.34/12.68 ( ( in @ X12 @ X4 ) =>
% 95.34/12.68 ( ( in @ X12 @ ( binintersect @ X6 @ X8 ) ) =>
% 95.34/12.68 ( in @ X12 @ ( binunion @ X8 @ X10 ) ) ) ) ) ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(inIntersectImpInUnion, axiom, inIntersectImpInUnion =
% 95.34/12.68 (![A:$i,X:$i]:
% 95.34/12.68 ( ( in @ X @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Y:$i]:
% 95.34/12.68 ( ( in @ Y @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Z:$i]:
% 95.34/12.68 ( ( in @ Z @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Xx:$i]:
% 95.34/12.68 ( ( in @ Xx @ A ) =>
% 95.34/12.68 ( ( in @ Xx @ ( binintersect @ X @ Y ) ) =>
% 95.34/12.68 ( in @ Xx @ ( binunion @ X @ Z ) ) ) ) ) ) ) ) ) ))).
% 95.34/12.68 thf('59', plain,
% 95.34/12.68 (( inIntersectImpInUnion ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X10:$i]:
% 95.34/12.68 ( ( in @ X10 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X12:$i]:
% 95.34/12.68 ( ( in @ X12 @ X4 ) =>
% 95.34/12.68 ( ( in @ X12 @ ( binintersect @ X6 @ X8 ) ) =>
% 95.34/12.68 ( in @ X12 @ ( binunion @ X6 @ X10 ) ) ) ) ) ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(binunionTIRcontra, axiom, binunionTIRcontra =
% 95.34/12.68 (![A:$i,X:$i]:
% 95.34/12.68 ( ( in @ X @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Y:$i]:
% 95.34/12.68 ( ( in @ Y @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Xx:$i]:
% 95.34/12.68 ( ( in @ Xx @ A ) =>
% 95.34/12.68 ( ( ~( in @ Xx @ ( binunion @ X @ Y ) ) ) =>
% 95.34/12.68 ( ~( in @ Xx @ Y ) ) ) ) ) ) ) ))).
% 95.34/12.68 thf('60', plain,
% 95.34/12.68 (( binunionTIRcontra ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X10:$i]:
% 95.34/12.68 ( ( in @ X10 @ X4 ) =>
% 95.34/12.68 ( ( ~( in @ X10 @ ( binunion @ X6 @ X8 ) ) ) =>
% 95.34/12.68 ( ~( in @ X10 @ X8 ) ) ) ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(binunionTILcontra, axiom, binunionTILcontra =
% 95.34/12.68 (![A:$i,X:$i]:
% 95.34/12.68 ( ( in @ X @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Y:$i]:
% 95.34/12.68 ( ( in @ Y @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Xx:$i]:
% 95.34/12.68 ( ( in @ Xx @ A ) =>
% 95.34/12.68 ( ( ~( in @ Xx @ ( binunion @ X @ Y ) ) ) =>
% 95.34/12.68 ( ~( in @ Xx @ X ) ) ) ) ) ) ) ))).
% 95.34/12.68 thf('61', plain,
% 95.34/12.68 (( binunionTILcontra ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X10:$i]:
% 95.34/12.68 ( ( in @ X10 @ X4 ) =>
% 95.34/12.68 ( ( ~( in @ X10 @ ( binunion @ X6 @ X8 ) ) ) =>
% 95.34/12.68 ( ~( in @ X10 @ X6 ) ) ) ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(complementTcontraSubset, axiom, complementTcontraSubset =
% 95.34/12.68 (![A:$i,X:$i]:
% 95.34/12.68 ( ( in @ X @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Y:$i]:
% 95.34/12.68 ( ( in @ Y @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ( subset @ X @ ( setminus @ A @ Y ) ) =>
% 95.34/12.68 ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ))).
% 95.34/12.68 thf('62', plain,
% 95.34/12.68 (( complementTcontraSubset ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ( subset @ X6 @ ( setminus @ X4 @ X8 ) ) =>
% 95.34/12.68 ( subset @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(contraSubsetComplement, axiom, contraSubsetComplement =
% 95.34/12.68 (![A:$i,X:$i]:
% 95.34/12.68 ( ( in @ X @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Y:$i]:
% 95.34/12.68 ( ( in @ Y @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ( subset @ X @ ( setminus @ A @ Y ) ) =>
% 95.34/12.68 ( ![Xx:$i]:
% 95.34/12.68 ( ( in @ Xx @ A ) =>
% 95.34/12.68 ( ( in @ Xx @ Y ) => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ))).
% 95.34/12.68 thf('63', plain,
% 95.34/12.68 (( contraSubsetComplement ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ( subset @ X6 @ ( setminus @ X4 @ X8 ) ) =>
% 95.34/12.68 ( ![X10:$i]:
% 95.34/12.68 ( ( in @ X10 @ X4 ) =>
% 95.34/12.68 ( ( in @ X10 @ X8 ) =>
% 95.34/12.68 ( in @ X10 @ ( setminus @ X4 @ X6 ) ) ) ) ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(complementInPowersetComplementIntersect, axiom,
% 95.34/12.68 complementInPowersetComplementIntersect =
% 95.34/12.68 (![A:$i,X:$i]:
% 95.34/12.68 ( ( in @ X @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Y:$i]:
% 95.34/12.68 ( ( in @ Y @ ( powerset @ A ) ) =>
% 95.34/12.68 ( in @
% 95.34/12.68 ( setminus @ A @ X ) @
% 95.34/12.68 ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ))).
% 95.34/12.68 thf('64', plain,
% 95.34/12.68 (( complementInPowersetComplementIntersect ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( in @
% 95.34/12.68 ( setminus @ X4 @ X6 ) @
% 95.34/12.68 ( powerset @ ( setminus @ X4 @ ( binintersect @ X6 @ X8 ) ) ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(complementSubsetComplementIntersect, axiom,
% 95.34/12.68 complementSubsetComplementIntersect =
% 95.34/12.68 (![A:$i,X:$i]:
% 95.34/12.68 ( ( in @ X @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Y:$i]:
% 95.34/12.68 ( ( in @ Y @ ( powerset @ A ) ) =>
% 95.34/12.68 ( subset @
% 95.34/12.68 ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ))).
% 95.34/12.68 thf('65', plain,
% 95.34/12.68 (( complementSubsetComplementIntersect ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( subset @
% 95.34/12.68 ( setminus @ X4 @ X6 ) @
% 95.34/12.68 ( setminus @ X4 @ ( binintersect @ X6 @ X8 ) ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(complementImpComplementIntersect, axiom,
% 95.34/12.68 complementImpComplementIntersect =
% 95.34/12.68 (![A:$i,X:$i]:
% 95.34/12.68 ( ( in @ X @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Y:$i]:
% 95.34/12.68 ( ( in @ Y @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Xx:$i]:
% 95.34/12.68 ( ( in @ Xx @ A ) =>
% 95.34/12.68 ( ( in @ Xx @ ( setminus @ A @ X ) ) =>
% 95.34/12.68 ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ))).
% 95.34/12.68 thf('66', plain,
% 95.34/12.68 (( complementImpComplementIntersect ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X10:$i]:
% 95.34/12.68 ( ( in @ X10 @ X4 ) =>
% 95.34/12.68 ( ( in @ X10 @ ( setminus @ X4 @ X6 ) ) =>
% 95.34/12.68 ( in @
% 95.34/12.68 X10 @ ( setminus @ X4 @ ( binintersect @ X6 @ X8 ) ) ) ) ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(complementTnotintersectT, axiom, complementTnotintersectT =
% 95.34/12.68 (![A:$i,X:$i]:
% 95.34/12.68 ( ( in @ X @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Y:$i]:
% 95.34/12.68 ( ( in @ Y @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Xx:$i]:
% 95.34/12.68 ( ( in @ Xx @ A ) =>
% 95.34/12.68 ( ( in @ Xx @ ( setminus @ A @ X ) ) =>
% 95.34/12.68 ( ~( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ))).
% 95.34/12.68 thf('67', plain,
% 95.34/12.68 (( complementTnotintersectT ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X10:$i]:
% 95.34/12.68 ( ( in @ X10 @ X4 ) =>
% 95.34/12.68 ( ( in @ X10 @ ( setminus @ X4 @ X6 ) ) =>
% 95.34/12.68 ( ~( in @ X10 @ ( binintersect @ X6 @ X8 ) ) ) ) ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(doubleComplementEq, axiom, doubleComplementEq =
% 95.34/12.68 (![A:$i,X:$i]:
% 95.34/12.68 ( ( in @ X @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ( X ) = ( setminus @ A @ ( setminus @ A @ X ) ) ) ))).
% 95.34/12.68 thf('68', plain,
% 95.34/12.68 (( doubleComplementEq ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ( X6 ) = ( setminus @ X4 @ ( setminus @ X4 @ X6 ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(doubleComplementSub2, axiom, doubleComplementSub2 =
% 95.34/12.68 (![A:$i,X:$i]:
% 95.34/12.68 ( ( in @ X @ ( powerset @ A ) ) =>
% 95.34/12.68 ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ))).
% 95.34/12.68 thf('69', plain,
% 95.34/12.68 (( doubleComplementSub2 ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( subset @ ( setminus @ X4 @ ( setminus @ X4 @ X6 ) ) @ X6 ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(doubleComplementSub1, axiom, doubleComplementSub1 =
% 95.34/12.68 (![A:$i,X:$i]:
% 95.34/12.68 ( ( in @ X @ ( powerset @ A ) ) =>
% 95.34/12.68 ( subset @ X @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ))).
% 95.34/12.68 thf('70', plain,
% 95.34/12.68 (( doubleComplementSub1 ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( subset @ X6 @ ( setminus @ X4 @ ( setminus @ X4 @ X6 ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(doubleComplementE1, axiom, doubleComplementE1 =
% 95.34/12.68 (![A:$i,X:$i]:
% 95.34/12.68 ( ( in @ X @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Xx:$i]:
% 95.34/12.68 ( ( in @ Xx @ A ) =>
% 95.34/12.68 ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) =>
% 95.34/12.68 ( in @ Xx @ X ) ) ) ) ))).
% 95.34/12.68 thf('71', plain,
% 95.34/12.68 (( doubleComplementE1 ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( in @ X8 @ X4 ) =>
% 95.34/12.68 ( ( in @ X8 @ ( setminus @ X4 @ ( setminus @ X4 @ X6 ) ) ) =>
% 95.34/12.68 ( in @ X8 @ X6 ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(doubleComplementI1, axiom, doubleComplementI1 =
% 95.34/12.68 (![A:$i,X:$i]:
% 95.34/12.68 ( ( in @ X @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Xx:$i]:
% 95.34/12.68 ( ( in @ Xx @ A ) =>
% 95.34/12.68 ( ( in @ Xx @ X ) =>
% 95.34/12.68 ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ))).
% 95.34/12.68 thf('72', plain,
% 95.34/12.68 (( doubleComplementI1 ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( in @ X8 @ X4 ) =>
% 95.34/12.68 ( ( in @ X8 @ X6 ) =>
% 95.34/12.68 ( in @ X8 @ ( setminus @ X4 @ ( setminus @ X4 @ X6 ) ) ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(contrasubsetT3, axiom, contrasubsetT3 =
% 95.34/12.68 (![A:$i,X:$i]:
% 95.34/12.68 ( ( in @ X @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Y:$i]:
% 95.34/12.68 ( ( in @ Y @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) =>
% 95.34/12.68 ( subset @ X @ Y ) ) ) ) ))).
% 95.34/12.68 thf('73', plain,
% 95.34/12.68 (( contrasubsetT3 ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ( subset @ ( setminus @ X4 @ X8 ) @ ( setminus @ X4 @ X6 ) ) =>
% 95.34/12.68 ( subset @ X6 @ X8 ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(contrasubsetT2, axiom, contrasubsetT2 =
% 95.34/12.68 (![A:$i,X:$i]:
% 95.34/12.68 ( ( in @ X @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Y:$i]:
% 95.34/12.68 ( ( in @ Y @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ( subset @ X @ Y ) =>
% 95.34/12.68 ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) ) ))).
% 95.34/12.68 thf('74', plain,
% 95.34/12.68 (( contrasubsetT2 ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ( subset @ X6 @ X8 ) =>
% 95.34/12.68 ( subset @ ( setminus @ X4 @ X8 ) @ ( setminus @ X4 @ X6 ) ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(contrasubsetT1, axiom, contrasubsetT1 =
% 95.34/12.68 (![A:$i,X:$i]:
% 95.34/12.68 ( ( in @ X @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Y:$i]:
% 95.34/12.68 ( ( in @ Y @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Xx:$i]:
% 95.34/12.68 ( ( in @ Xx @ A ) =>
% 95.34/12.68 ( ( subset @ X @ Y ) =>
% 95.34/12.68 ( ( ~( in @ Xx @ Y ) ) => ( ~( in @ Xx @ X ) ) ) ) ) ) ) ) ))).
% 95.34/12.68 thf('75', plain,
% 95.34/12.68 (( contrasubsetT1 ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X10:$i]:
% 95.34/12.68 ( ( in @ X10 @ X4 ) =>
% 95.34/12.68 ( ( subset @ X6 @ X8 ) =>
% 95.34/12.68 ( ( ~( in @ X10 @ X8 ) ) => ( ~( in @ X10 @ X6 ) ) ) ) ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(contrasubsetT, axiom, contrasubsetT =
% 95.34/12.68 (![A:$i,X:$i]:
% 95.34/12.68 ( ( in @ X @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Y:$i]:
% 95.34/12.68 ( ( in @ Y @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Xx:$i]:
% 95.34/12.68 ( ( in @ Xx @ A ) =>
% 95.34/12.68 ( ( subset @ X @ ( setminus @ A @ Y ) ) =>
% 95.34/12.68 ( ( in @ Xx @ Y ) => ( ~( in @ Xx @ X ) ) ) ) ) ) ) ) ))).
% 95.34/12.68 thf('76', plain,
% 95.34/12.68 (( contrasubsetT ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X10:$i]:
% 95.34/12.68 ( ( in @ X10 @ X4 ) =>
% 95.34/12.68 ( ( subset @ X6 @ ( setminus @ X4 @ X8 ) ) =>
% 95.34/12.68 ( ( in @ X10 @ X8 ) => ( ~( in @ X10 @ X6 ) ) ) ) ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(binintersectTERcontra, axiom, binintersectTERcontra =
% 95.34/12.68 (![A:$i,X:$i]:
% 95.34/12.68 ( ( in @ X @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Y:$i]:
% 95.34/12.68 ( ( in @ Y @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Xx:$i]:
% 95.34/12.68 ( ( in @ Xx @ A ) =>
% 95.34/12.68 ( ( ~( in @ Xx @ Y ) ) =>
% 95.34/12.68 ( ~( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ))).
% 95.34/12.68 thf('77', plain,
% 95.34/12.68 (( binintersectTERcontra ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X10:$i]:
% 95.34/12.68 ( ( in @ X10 @ X4 ) =>
% 95.34/12.68 ( ( ~( in @ X10 @ X8 ) ) =>
% 95.34/12.68 ( ~( in @ X10 @ ( binintersect @ X6 @ X8 ) ) ) ) ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(binintersectTELcontra, axiom, binintersectTELcontra =
% 95.34/12.68 (![A:$i,X:$i]:
% 95.34/12.68 ( ( in @ X @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Y:$i]:
% 95.34/12.68 ( ( in @ Y @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Xx:$i]:
% 95.34/12.68 ( ( in @ Xx @ A ) =>
% 95.34/12.68 ( ( ~( in @ Xx @ X ) ) =>
% 95.34/12.68 ( ~( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ))).
% 95.34/12.68 thf('78', plain,
% 95.34/12.68 (( binintersectTELcontra ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X10:$i]:
% 95.34/12.68 ( ( in @ X10 @ X4 ) =>
% 95.34/12.68 ( ( ~( in @ X10 @ X6 ) ) =>
% 95.34/12.68 ( ~( in @ X10 @ ( binintersect @ X6 @ X8 ) ) ) ) ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(complementTE1, axiom, complementTE1 =
% 95.34/12.68 (![A:$i,X:$i]:
% 95.34/12.68 ( ( in @ X @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Xx:$i]:
% 95.34/12.68 ( ( in @ Xx @ A ) =>
% 95.34/12.68 ( ( ~( in @ Xx @ ( setminus @ A @ X ) ) ) => ( in @ Xx @ X ) ) ) ) ))).
% 95.34/12.68 thf('79', plain,
% 95.34/12.68 (( complementTE1 ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( in @ X8 @ X4 ) =>
% 95.34/12.68 ( ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) => ( in @ X8 @ X6 ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(complementTI1, axiom, complementTI1 =
% 95.34/12.68 (![A:$i,X:$i]:
% 95.34/12.68 ( ( in @ X @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Xx:$i]:
% 95.34/12.68 ( ( in @ Xx @ A ) =>
% 95.34/12.68 ( ( in @ Xx @ X ) => ( ~( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ))).
% 95.34/12.68 thf('80', plain,
% 95.34/12.68 (( complementTI1 ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( in @ X8 @ X4 ) =>
% 95.34/12.68 ( ( in @ X8 @ X6 ) => ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(powersetTE1, axiom, powersetTE1 =
% 95.34/12.68 (![A:$i,X:$i]:
% 95.34/12.68 ( ( in @ X @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Y:$i]:
% 95.34/12.68 ( ( in @ Y @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Xx:$i]:
% 95.34/12.68 ( ( in @ Xx @ A ) =>
% 95.34/12.68 ( ( in @ X @ ( powerset @ Y ) ) =>
% 95.34/12.68 ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) ) ) ) ))).
% 95.34/12.68 thf('81', plain,
% 95.34/12.68 (( powersetTE1 ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X10:$i]:
% 95.34/12.68 ( ( in @ X10 @ X4 ) =>
% 95.34/12.68 ( ( in @ X6 @ ( powerset @ X8 ) ) =>
% 95.34/12.68 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(powersetTI1, axiom, powersetTI1 =
% 95.34/12.68 (![A:$i,X:$i]:
% 95.34/12.68 ( ( in @ X @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Y:$i]:
% 95.34/12.68 ( ( in @ Y @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ( ![Xx:$i]:
% 95.34/12.68 ( ( in @ Xx @ A ) => ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) =>
% 95.34/12.68 ( in @ X @ ( powerset @ Y ) ) ) ) ) ))).
% 95.34/12.68 thf('82', plain,
% 95.34/12.68 (( powersetTI1 ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ( ![X10:$i]:
% 95.34/12.68 ( ( in @ X10 @ X4 ) =>
% 95.34/12.68 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) =>
% 95.34/12.68 ( in @ X6 @ ( powerset @ X8 ) ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(subsetTI, axiom, subsetTI =
% 95.34/12.68 (![A:$i,X:$i]:
% 95.34/12.68 ( ( in @ X @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Y:$i]:
% 95.34/12.68 ( ( in @ Y @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ( ![Xx:$i]:
% 95.34/12.68 ( ( in @ Xx @ A ) => ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) =>
% 95.34/12.68 ( subset @ X @ Y ) ) ) ) ))).
% 95.34/12.68 thf('83', plain,
% 95.34/12.68 (( subsetTI ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ( ![X10:$i]:
% 95.34/12.68 ( ( in @ X10 @ X4 ) =>
% 95.34/12.68 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) =>
% 95.34/12.68 ( subset @ X6 @ X8 ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(setextT, axiom, setextT =
% 95.34/12.68 (![A:$i,X:$i]:
% 95.34/12.68 ( ( in @ X @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Y:$i]:
% 95.34/12.68 ( ( in @ Y @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ( ![Xx:$i]:
% 95.34/12.68 ( ( in @ Xx @ A ) => ( ( in @ Xx @ X ) => ( in @ Xx @ Y ) ) ) ) =>
% 95.34/12.68 ( ( ![Xx:$i]:
% 95.34/12.68 ( ( in @ Xx @ A ) => ( ( in @ Xx @ Y ) => ( in @ Xx @ X ) ) ) ) =>
% 95.34/12.68 ( ( X ) = ( Y ) ) ) ) ) ) ))).
% 95.34/12.68 thf('84', plain,
% 95.34/12.68 (( setextT ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ( ![X10:$i]:
% 95.34/12.68 ( ( in @ X10 @ X4 ) =>
% 95.34/12.68 ( ( in @ X10 @ X6 ) => ( in @ X10 @ X8 ) ) ) ) =>
% 95.34/12.68 ( ( ![X12:$i]:
% 95.34/12.68 ( ( in @ X12 @ X4 ) =>
% 95.34/12.68 ( ( in @ X12 @ X8 ) => ( in @ X12 @ X6 ) ) ) ) =>
% 95.34/12.68 ( ( X6 ) = ( X8 ) ) ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(complementT_lem, axiom, complementT_lem =
% 95.34/12.68 (![A:$i,X:$i]:
% 95.34/12.68 ( ( in @ X @ ( powerset @ A ) ) =>
% 95.34/12.68 ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ))).
% 95.34/12.68 thf('85', plain,
% 95.34/12.68 (( complementT_lem ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( in @ ( setminus @ X4 @ X6 ) @ ( powerset @ X4 ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(setminusT_lem, axiom, setminusT_lem =
% 95.34/12.68 (![A:$i,X:$i]:
% 95.34/12.68 ( ( in @ X @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Y:$i]:
% 95.34/12.68 ( ( in @ Y @ ( powerset @ A ) ) =>
% 95.34/12.68 ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ))).
% 95.34/12.68 thf('86', plain,
% 95.34/12.68 (( setminusT_lem ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( in @ ( setminus @ X6 @ X8 ) @ ( powerset @ X4 ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(powersetT_lem, axiom, powersetT_lem =
% 95.34/12.68 (![A:$i,X:$i]:
% 95.34/12.68 ( ( in @ X @ ( powerset @ A ) ) =>
% 95.34/12.68 ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ))).
% 95.34/12.68 thf('87', plain,
% 95.34/12.68 (( powersetT_lem ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( in @ ( powerset @ X6 ) @ ( powerset @ ( powerset @ X4 ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(binunionT_lem, axiom, binunionT_lem =
% 95.34/12.68 (![A:$i,X:$i]:
% 95.34/12.68 ( ( in @ X @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Y:$i]:
% 95.34/12.68 ( ( in @ Y @ ( powerset @ A ) ) =>
% 95.34/12.68 ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ))).
% 95.34/12.68 thf('88', plain,
% 95.34/12.68 (( binunionT_lem ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( in @ ( binunion @ X6 @ X8 ) @ ( powerset @ X4 ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(binintersectT_lem, axiom, binintersectT_lem =
% 95.34/12.68 (![A:$i,X:$i]:
% 95.34/12.68 ( ( in @ X @ ( powerset @ A ) ) =>
% 95.34/12.68 ( ![Y:$i]:
% 95.34/12.68 ( ( in @ Y @ ( powerset @ A ) ) =>
% 95.34/12.68 ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ))).
% 95.34/12.68 thf('89', plain,
% 95.34/12.68 (( binintersectT_lem ) =
% 95.34/12.68 ( ![X4:$i,X6:$i]:
% 95.34/12.68 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( ![X8:$i]:
% 95.34/12.68 ( ( in @ X8 @ ( powerset @ X4 ) ) =>
% 95.34/12.68 ( in @ ( binintersect @ X6 @ X8 ) @ ( powerset @ X4 ) ) ) ) ) )),
% 95.34/12.68 define([status(thm)])).
% 95.34/12.68 thf(iftrueorfalse, axiom, iftrueorfalse =
% 95.34/12.68 (![A:$i,Xphi:$o,Xx:$i]:
% 95.34/12.68 ( ( in @ Xx @ A ) =>
% 95.34/12.68 ( ![Xy:$i]:
% 95.34/12.69 ( ( in @ Xy @ A ) =>
% 95.34/12.69 ( in @
% 95.34/12.69 ( if @ A @ Xphi @ Xx @ Xy ) @
% 95.34/12.69 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ))).
% 95.34/12.69 thf('90', plain,
% 95.34/12.69 (( iftrueorfalse ) =
% 95.34/12.69 ( ![X4:$i,X6:$o,X8:$i]:
% 95.34/12.69 ( ( in @ X8 @ X4 ) =>
% 95.34/12.69 ( ![X10:$i]:
% 95.34/12.69 ( ( in @ X10 @ X4 ) =>
% 95.34/12.69 ( in @
% 95.34/12.69 ( if @ X4 @ X6 @ X8 @ X10 ) @
% 95.34/12.69 ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(iffalse, axiom, iffalse =
% 95.34/12.69 (![A:$i,Xphi:$o,Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ A ) =>
% 95.34/12.69 ( ![Xy:$i]:
% 95.34/12.69 ( ( in @ Xy @ A ) =>
% 95.34/12.69 ( ( ~( Xphi ) ) => ( ( if @ A @ Xphi @ Xx @ Xy ) = ( Xy ) ) ) ) ) ))).
% 95.34/12.69 thf('91', plain,
% 95.34/12.69 (( iffalse ) =
% 95.34/12.69 ( ![X4:$i,X6:$o,X8:$i]:
% 95.34/12.69 ( ( in @ X8 @ X4 ) =>
% 95.34/12.69 ( ![X10:$i]:
% 95.34/12.69 ( ( in @ X10 @ X4 ) =>
% 95.34/12.69 ( ( ~( X6 ) ) => ( ( if @ X4 @ X6 @ X8 @ X10 ) = ( X10 ) ) ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(iftrue, axiom, iftrue =
% 95.34/12.69 (![A:$i,Xphi:$o,Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ A ) =>
% 95.34/12.69 ( ![Xy:$i]:
% 95.34/12.69 ( ( in @ Xy @ A ) =>
% 95.34/12.69 ( ( Xphi ) => ( ( if @ A @ Xphi @ Xx @ Xy ) = ( Xx ) ) ) ) ) ))).
% 95.34/12.69 thf('92', plain,
% 95.34/12.69 (( iftrue ) =
% 95.34/12.69 ( ![X4:$i,X6:$o,X8:$i]:
% 95.34/12.69 ( ( in @ X8 @ X4 ) =>
% 95.34/12.69 ( ![X10:$i]:
% 95.34/12.69 ( ( in @ X10 @ X4 ) =>
% 95.34/12.69 ( ( X6 ) => ( ( if @ X4 @ X6 @ X8 @ X10 ) = ( X8 ) ) ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(theeq, axiom, theeq =
% 95.34/12.69 (![X:$i]:
% 95.34/12.69 ( ( singleton @ X ) =>
% 95.34/12.69 ( ![Xx:$i]: ( ( in @ Xx @ X ) => ( ( setunion @ X ) = ( Xx ) ) ) ) ))).
% 95.34/12.69 thf('93', plain,
% 95.34/12.69 (( theeq ) =
% 95.34/12.69 ( ![X4:$i]:
% 95.34/12.69 ( ( singleton @ X4 ) =>
% 95.34/12.69 ( ![X6:$i]: ( ( in @ X6 @ X4 ) => ( ( setunion @ X4 ) = ( X6 ) ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(ifp, axiom, ifp =
% 95.34/12.69 (![A:$i,Xphi:$o,Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ A ) =>
% 95.34/12.69 ( ![Xy:$i]:
% 95.34/12.69 ( ( in @ Xy @ A ) => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) ))).
% 95.34/12.69 thf('94', plain,
% 95.34/12.69 (( ifp ) =
% 95.34/12.69 ( ![X4:$i,X6:$o,X8:$i]:
% 95.34/12.69 ( ( in @ X8 @ X4 ) =>
% 95.34/12.69 ( ![X10:$i]:
% 95.34/12.69 ( ( in @ X10 @ X4 ) => ( in @ ( if @ X4 @ X6 @ X8 @ X10 ) @ X4 ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(ifSingleton, axiom, ifSingleton =
% 95.34/12.69 (![A:$i,Xphi:$o,Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ A ) =>
% 95.34/12.69 ( ![Xy:$i]:
% 95.34/12.69 ( ( in @ Xy @ A ) =>
% 95.34/12.69 ( singleton @
% 95.34/12.69 ( dsetconstr @
% 95.34/12.69 A @
% 95.34/12.69 ( ^[Xz:$i]:
% 95.34/12.69 ( ( ( Xphi ) & ( ( Xz ) = ( Xx ) ) ) |
% 95.34/12.69 ( ( ~( Xphi ) ) & ( ( Xz ) = ( Xy ) ) ) ) ) ) ) ) ) ))).
% 95.34/12.69 thf('95', plain,
% 95.34/12.69 (( ifSingleton ) =
% 95.34/12.69 ( ![X4:$i,X6:$o,X8:$i]:
% 95.34/12.69 ( ( in @ X8 @ X4 ) =>
% 95.34/12.69 ( ![X10:$i]:
% 95.34/12.69 ( ( in @ X10 @ X4 ) =>
% 95.34/12.69 ( singleton @
% 95.34/12.69 ( dsetconstr @
% 95.34/12.69 X4 @
% 95.34/12.69 ( ^[V_1:$i]:
% 95.34/12.69 ( ( ( X6 ) & ( ( V_1 ) = ( X8 ) ) ) |
% 95.34/12.69 ( ( ~( X6 ) ) & ( ( V_1 ) = ( X10 ) ) ) ) ) ) ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(iftrueProp2, axiom, iftrueProp2 =
% 95.34/12.69 (![A:$i,Xphi:$o,Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ A ) =>
% 95.34/12.69 ( ![Xy:$i]:
% 95.34/12.69 ( ( in @ Xy @ A ) =>
% 95.34/12.69 ( ( Xphi ) =>
% 95.34/12.69 ( ( dsetconstr @
% 95.34/12.69 A @
% 95.34/12.69 ( ^[Xz:$i]:
% 95.34/12.69 ( ( ( Xphi ) & ( ( Xz ) = ( Xx ) ) ) |
% 95.34/12.69 ( ( ~( Xphi ) ) & ( ( Xz ) = ( Xy ) ) ) ) ) ) =
% 95.34/12.69 ( setadjoin @ Xx @ emptyset ) ) ) ) ) ))).
% 95.34/12.69 thf('96', plain,
% 95.34/12.69 (( iftrueProp2 ) =
% 95.34/12.69 ( ![X4:$i,X6:$o,X8:$i]:
% 95.34/12.69 ( ( in @ X8 @ X4 ) =>
% 95.34/12.69 ( ![X10:$i]:
% 95.34/12.69 ( ( in @ X10 @ X4 ) =>
% 95.34/12.69 ( ( X6 ) =>
% 95.34/12.69 ( ( dsetconstr @
% 95.34/12.69 X4 @
% 95.34/12.69 ( ^[V_1:$i]:
% 95.34/12.69 ( ( ( X6 ) & ( ( V_1 ) = ( X8 ) ) ) |
% 95.34/12.69 ( ( ~( X6 ) ) & ( ( V_1 ) = ( X10 ) ) ) ) ) ) =
% 95.34/12.69 ( setadjoin @ X8 @ emptyset ) ) ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(iftrueProp1, axiom, iftrueProp1 =
% 95.34/12.69 (![A:$i,Xphi:$o,Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ A ) =>
% 95.34/12.69 ( ![Xy:$i]:
% 95.34/12.69 ( ( in @ Xy @ A ) =>
% 95.34/12.69 ( ( Xphi ) =>
% 95.34/12.69 ( in @
% 95.34/12.69 Xx @
% 95.34/12.69 ( dsetconstr @
% 95.34/12.69 A @
% 95.34/12.69 ( ^[Xz:$i]:
% 95.34/12.69 ( ( ( Xphi ) & ( ( Xz ) = ( Xx ) ) ) |
% 95.34/12.69 ( ( ~( Xphi ) ) & ( ( Xz ) = ( Xy ) ) ) ) ) ) ) ) ) ) ))).
% 95.34/12.69 thf('97', plain,
% 95.34/12.69 (( iftrueProp1 ) =
% 95.34/12.69 ( ![X4:$i,X6:$o,X8:$i]:
% 95.34/12.69 ( ( in @ X8 @ X4 ) =>
% 95.34/12.69 ( ![X10:$i]:
% 95.34/12.69 ( ( in @ X10 @ X4 ) =>
% 95.34/12.69 ( ( X6 ) =>
% 95.34/12.69 ( in @
% 95.34/12.69 X8 @
% 95.34/12.69 ( dsetconstr @
% 95.34/12.69 X4 @
% 95.34/12.69 ( ^[V_1:$i]:
% 95.34/12.69 ( ( ( X6 ) & ( ( V_1 ) = ( X8 ) ) ) |
% 95.34/12.69 ( ( ~( X6 ) ) & ( ( V_1 ) = ( X10 ) ) ) ) ) ) ) ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(iffalseProp2, axiom, iffalseProp2 =
% 95.34/12.69 (![A:$i,Xphi:$o,Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ A ) =>
% 95.34/12.69 ( ![Xy:$i]:
% 95.34/12.69 ( ( in @ Xy @ A ) =>
% 95.34/12.69 ( ( ~( Xphi ) ) =>
% 95.34/12.69 ( ( dsetconstr @
% 95.34/12.69 A @
% 95.34/12.69 ( ^[Xz:$i]:
% 95.34/12.69 ( ( ( Xphi ) & ( ( Xz ) = ( Xx ) ) ) |
% 95.34/12.69 ( ( ~( Xphi ) ) & ( ( Xz ) = ( Xy ) ) ) ) ) ) =
% 95.34/12.69 ( setadjoin @ Xy @ emptyset ) ) ) ) ) ))).
% 95.34/12.69 thf('98', plain,
% 95.34/12.69 (( iffalseProp2 ) =
% 95.34/12.69 ( ![X4:$i,X6:$o,X8:$i]:
% 95.34/12.69 ( ( in @ X8 @ X4 ) =>
% 95.34/12.69 ( ![X10:$i]:
% 95.34/12.69 ( ( in @ X10 @ X4 ) =>
% 95.34/12.69 ( ( ~( X6 ) ) =>
% 95.34/12.69 ( ( dsetconstr @
% 95.34/12.69 X4 @
% 95.34/12.69 ( ^[V_1:$i]:
% 95.34/12.69 ( ( ( X6 ) & ( ( V_1 ) = ( X8 ) ) ) |
% 95.34/12.69 ( ( ~( X6 ) ) & ( ( V_1 ) = ( X10 ) ) ) ) ) ) =
% 95.34/12.69 ( setadjoin @ X10 @ emptyset ) ) ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(iffalseProp1, axiom, iffalseProp1 =
% 95.34/12.69 (![A:$i,Xphi:$o,Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ A ) =>
% 95.34/12.69 ( ![Xy:$i]:
% 95.34/12.69 ( ( in @ Xy @ A ) =>
% 95.34/12.69 ( ( ~( Xphi ) ) =>
% 95.34/12.69 ( in @
% 95.34/12.69 Xy @
% 95.34/12.69 ( dsetconstr @
% 95.34/12.69 A @
% 95.34/12.69 ( ^[Xz:$i]:
% 95.34/12.69 ( ( ( Xphi ) & ( ( Xz ) = ( Xx ) ) ) |
% 95.34/12.69 ( ( ~( Xphi ) ) & ( ( Xz ) = ( Xy ) ) ) ) ) ) ) ) ) ) ))).
% 95.34/12.69 thf('99', plain,
% 95.34/12.69 (( iffalseProp1 ) =
% 95.34/12.69 ( ![X4:$i,X6:$o,X8:$i]:
% 95.34/12.69 ( ( in @ X8 @ X4 ) =>
% 95.34/12.69 ( ![X10:$i]:
% 95.34/12.69 ( ( in @ X10 @ X4 ) =>
% 95.34/12.69 ( ( ~( X6 ) ) =>
% 95.34/12.69 ( in @
% 95.34/12.69 X10 @
% 95.34/12.69 ( dsetconstr @
% 95.34/12.69 X4 @
% 95.34/12.69 ( ^[V_1:$i]:
% 95.34/12.69 ( ( ( X6 ) & ( ( V_1 ) = ( X8 ) ) ) |
% 95.34/12.69 ( ( ~( X6 ) ) & ( ( V_1 ) = ( X10 ) ) ) ) ) ) ) ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(eta2, axiom, eta2 =
% 95.34/12.69 (![A:$i,B:$i,Xf:$i]:
% 95.34/12.69 ( ( in @ Xf @ ( funcSet @ A @ B ) ) =>
% 95.34/12.69 ( ( lam @ A @ B @ ( ^[Xx:$i]: ( ap @ A @ B @ Xf @ Xx ) ) ) = ( Xf ) ) ))).
% 95.34/12.69 thf('100', plain,
% 95.34/12.69 (( eta2 ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( in @ X8 @ ( funcSet @ X4 @ X6 ) ) =>
% 95.34/12.69 ( ( lam @ X4 @ X6 @ ( ^[V_1:$i]: ( ap @ X4 @ X6 @ X8 @ V_1 ) ) ) =
% 95.34/12.69 ( X8 ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(beta2, axiom, beta2 =
% 95.34/12.69 (![A:$i,B:$i,Xf:( $i > $i )]:
% 95.34/12.69 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( in @ ( Xf @ Xx ) @ B ) ) ) =>
% 95.34/12.69 ( ![Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ A ) =>
% 95.34/12.69 ( ( ap @ A @ B @ ( lam @ A @ B @ ( ^[Xy:$i]: ( Xf @ Xy ) ) ) @ Xx ) =
% 95.34/12.69 ( Xf @ Xx ) ) ) ) ))).
% 95.34/12.69 thf('101', plain,
% 95.34/12.69 (( beta2 ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:( $i > $i )]:
% 95.34/12.69 ( ( ![X10:$i]: ( ( in @ X10 @ X4 ) => ( in @ ( X8 @ X10 ) @ X6 ) ) ) =>
% 95.34/12.69 ( ![X12:$i]:
% 95.34/12.69 ( ( in @ X12 @ X4 ) =>
% 95.34/12.69 ( ( ap @
% 95.34/12.69 X4 @ X6 @ ( lam @ X4 @ X6 @ ( ^[V_1:$i]: ( X8 @ V_1 ) ) ) @
% 95.34/12.69 X12 ) =
% 95.34/12.69 ( X8 @ X12 ) ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(lam2lamEq, axiom, lam2lamEq =
% 95.34/12.69 (![A:$i,B:$i,Xf:( $i > $i )]:
% 95.34/12.69 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( in @ ( Xf @ Xx ) @ B ) ) ) =>
% 95.34/12.69 ( ( lam @ A @ B @ ( ^[Xx:$i]: ( Xf @ Xx ) ) ) =
% 95.34/12.69 ( lam @ A @ B @ ( ^[Xx:$i]: ( Xf @ Xx ) ) ) ) ))).
% 95.34/12.69 thf('102', plain,
% 95.34/12.69 (( lam2lamEq ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:( $i > $i )]:
% 95.34/12.69 ( ( ![X10:$i]: ( ( in @ X10 @ X4 ) => ( in @ ( X8 @ X10 ) @ X6 ) ) ) =>
% 95.34/12.69 ( ( lam @ X4 @ X6 @ ( ^[V_1:$i]: ( X8 @ V_1 ) ) ) =
% 95.34/12.69 ( lam @ X4 @ X6 @ ( ^[V_2:$i]: ( X8 @ V_2 ) ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(eta1, axiom, eta1 =
% 95.34/12.69 (![A:$i,B:$i,Xf:$i]:
% 95.34/12.69 ( ( func @ A @ B @ Xf ) =>
% 95.34/12.69 ( ( lam @ A @ B @ ( ^[Xx:$i]: ( ap @ A @ B @ Xf @ Xx ) ) ) = ( Xf ) ) ))).
% 95.34/12.69 thf('103', plain,
% 95.34/12.69 (( eta1 ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( func @ X4 @ X6 @ X8 ) =>
% 95.34/12.69 ( ( lam @ X4 @ X6 @ ( ^[V_1:$i]: ( ap @ X4 @ X6 @ X8 @ V_1 ) ) ) =
% 95.34/12.69 ( X8 ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(beta1, axiom, beta1 =
% 95.34/12.69 (![A:$i,B:$i,Xf:( $i > $i )]:
% 95.34/12.69 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( in @ ( Xf @ Xx ) @ B ) ) ) =>
% 95.34/12.69 ( ![Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ A ) =>
% 95.34/12.69 ( ( ap @ A @ B @ ( lam @ A @ B @ ( ^[Xy:$i]: ( Xf @ Xy ) ) ) @ Xx ) =
% 95.34/12.69 ( Xf @ Xx ) ) ) ) ))).
% 95.34/12.69 thf('104', plain,
% 95.34/12.69 (( beta1 ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:( $i > $i )]:
% 95.34/12.69 ( ( ![X10:$i]: ( ( in @ X10 @ X4 ) => ( in @ ( X8 @ X10 ) @ X6 ) ) ) =>
% 95.34/12.69 ( ![X12:$i]:
% 95.34/12.69 ( ( in @ X12 @ X4 ) =>
% 95.34/12.69 ( ( ap @
% 95.34/12.69 X4 @ X6 @ ( lam @ X4 @ X6 @ ( ^[V_1:$i]: ( X8 @ V_1 ) ) ) @
% 95.34/12.69 X12 ) =
% 95.34/12.69 ( X8 @ X12 ) ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(ap2apEq2, axiom, ap2apEq2 =
% 95.34/12.69 (![A:$i,B:$i,Xf:$i]:
% 95.34/12.69 ( ( func @ A @ B @ Xf ) =>
% 95.34/12.69 ( ![Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ A ) =>
% 95.34/12.69 ( ( ap @ A @ B @ Xf @ Xx ) = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ))).
% 95.34/12.69 thf('105', plain,
% 95.34/12.69 (( ap2apEq2 ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( func @ X4 @ X6 @ X8 ) =>
% 95.34/12.69 ( ![X10:$i]:
% 95.34/12.69 ( ( in @ X10 @ X4 ) =>
% 95.34/12.69 ( ( ap @ X4 @ X6 @ X8 @ X10 ) = ( ap @ X4 @ X6 @ X8 @ X10 ) ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(ap2apEq1, axiom, ap2apEq1 =
% 95.34/12.69 (![A:$i,B:$i,Xf:$i]:
% 95.34/12.69 ( ( in @ Xf @ ( funcSet @ A @ B ) ) =>
% 95.34/12.69 ( ![Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ A ) =>
% 95.34/12.69 ( ( ap @ A @ B @ Xf @ Xx ) = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ))).
% 95.34/12.69 thf('106', plain,
% 95.34/12.69 (( ap2apEq1 ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( in @ X8 @ ( funcSet @ X4 @ X6 ) ) =>
% 95.34/12.69 ( ![X10:$i]:
% 95.34/12.69 ( ( in @ X10 @ X4 ) =>
% 95.34/12.69 ( ( ap @ X4 @ X6 @ X8 @ X10 ) = ( ap @ X4 @ X6 @ X8 @ X10 ) ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(funcext2, axiom, funcext2 =
% 95.34/12.69 (![A:$i,B:$i,Xf:$i]:
% 95.34/12.69 ( ( in @ Xf @ ( funcSet @ A @ B ) ) =>
% 95.34/12.69 ( ![Xg:$i]:
% 95.34/12.69 ( ( in @ Xg @ ( funcSet @ A @ B ) ) =>
% 95.34/12.69 ( ( ![Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ A ) =>
% 95.34/12.69 ( ( ap @ A @ B @ Xf @ Xx ) = ( ap @ A @ B @ Xg @ Xx ) ) ) ) =>
% 95.34/12.69 ( ( Xf ) = ( Xg ) ) ) ) ) ))).
% 95.34/12.69 thf('107', plain,
% 95.34/12.69 (( funcext2 ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( in @ X8 @ ( funcSet @ X4 @ X6 ) ) =>
% 95.34/12.69 ( ![X10:$i]:
% 95.34/12.69 ( ( in @ X10 @ ( funcSet @ X4 @ X6 ) ) =>
% 95.34/12.69 ( ( ![X12:$i]:
% 95.34/12.69 ( ( in @ X12 @ X4 ) =>
% 95.34/12.69 ( ( ap @ X4 @ X6 @ X8 @ X12 ) =
% 95.34/12.69 ( ap @ X4 @ X6 @ X10 @ X12 ) ) ) ) =>
% 95.34/12.69 ( ( X8 ) = ( X10 ) ) ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(funcext, axiom, funcext =
% 95.34/12.69 (![A:$i,B:$i,Xf:$i]:
% 95.34/12.69 ( ( func @ A @ B @ Xf ) =>
% 95.34/12.69 ( ![Xg:$i]:
% 95.34/12.69 ( ( func @ A @ B @ Xg ) =>
% 95.34/12.69 ( ( ![Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ A ) =>
% 95.34/12.69 ( ( ap @ A @ B @ Xf @ Xx ) = ( ap @ A @ B @ Xg @ Xx ) ) ) ) =>
% 95.34/12.69 ( ( Xf ) = ( Xg ) ) ) ) ) ))).
% 95.34/12.69 thf('108', plain,
% 95.34/12.69 (( funcext ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( func @ X4 @ X6 @ X8 ) =>
% 95.34/12.69 ( ![X10:$i]:
% 95.34/12.69 ( ( func @ X4 @ X6 @ X10 ) =>
% 95.34/12.69 ( ( ![X12:$i]:
% 95.34/12.69 ( ( in @ X12 @ X4 ) =>
% 95.34/12.69 ( ( ap @ X4 @ X6 @ X8 @ X12 ) =
% 95.34/12.69 ( ap @ X4 @ X6 @ X10 @ X12 ) ) ) ) =>
% 95.34/12.69 ( ( X8 ) = ( X10 ) ) ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(eqbreln, axiom, eqbreln =
% 95.34/12.69 (![A:$i,B:$i,R:$i]:
% 95.34/12.69 ( ( breln @ A @ B @ R ) =>
% 95.34/12.69 ( ![S:$i]:
% 95.34/12.69 ( ( breln @ A @ B @ S ) =>
% 95.34/12.69 ( ( ![Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ A ) =>
% 95.34/12.69 ( ![Xy:$i]:
% 95.34/12.69 ( ( in @ Xy @ B ) =>
% 95.34/12.69 ( ( in @ ( kpair @ Xx @ Xy ) @ R ) =>
% 95.34/12.69 ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) ) ) ) =>
% 95.34/12.69 ( ( ![Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ A ) =>
% 95.34/12.69 ( ![Xy:$i]:
% 95.34/12.69 ( ( in @ Xy @ B ) =>
% 95.34/12.69 ( ( in @ ( kpair @ Xx @ Xy ) @ S ) =>
% 95.34/12.69 ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) =>
% 95.34/12.69 ( ( R ) = ( S ) ) ) ) ) ) ))).
% 95.34/12.69 thf('109', plain,
% 95.34/12.69 (( eqbreln ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( breln @ X4 @ X6 @ X8 ) =>
% 95.34/12.69 ( ![X10:$i]:
% 95.34/12.69 ( ( breln @ X4 @ X6 @ X10 ) =>
% 95.34/12.69 ( ( ![X12:$i]:
% 95.34/12.69 ( ( in @ X12 @ X4 ) =>
% 95.34/12.69 ( ![X14:$i]:
% 95.34/12.69 ( ( in @ X14 @ X6 ) =>
% 95.34/12.69 ( ( in @ ( kpair @ X12 @ X14 ) @ X8 ) =>
% 95.34/12.69 ( in @ ( kpair @ X12 @ X14 ) @ X10 ) ) ) ) ) ) =>
% 95.34/12.69 ( ( ![X16:$i]:
% 95.34/12.69 ( ( in @ X16 @ X4 ) =>
% 95.34/12.69 ( ![X18:$i]:
% 95.34/12.69 ( ( in @ X18 @ X6 ) =>
% 95.34/12.69 ( ( in @ ( kpair @ X16 @ X18 ) @ X10 ) =>
% 95.34/12.69 ( in @ ( kpair @ X16 @ X18 ) @ X8 ) ) ) ) ) ) =>
% 95.34/12.69 ( ( X8 ) = ( X10 ) ) ) ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(subbreln, axiom, subbreln =
% 95.34/12.69 (![A:$i,B:$i,R:$i]:
% 95.34/12.69 ( ( breln @ A @ B @ R ) =>
% 95.34/12.69 ( ![S:$i]:
% 95.34/12.69 ( ( breln @ A @ B @ S ) =>
% 95.34/12.69 ( ( ![Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ A ) =>
% 95.34/12.69 ( ![Xy:$i]:
% 95.34/12.69 ( ( in @ Xy @ B ) =>
% 95.34/12.69 ( ( in @ ( kpair @ Xx @ Xy ) @ R ) =>
% 95.34/12.69 ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) ) ) ) =>
% 95.34/12.69 ( subset @ R @ S ) ) ) ) ))).
% 95.34/12.69 thf('110', plain,
% 95.34/12.69 (( subbreln ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( breln @ X4 @ X6 @ X8 ) =>
% 95.34/12.69 ( ![X10:$i]:
% 95.34/12.69 ( ( breln @ X4 @ X6 @ X10 ) =>
% 95.34/12.69 ( ( ![X12:$i]:
% 95.34/12.69 ( ( in @ X12 @ X4 ) =>
% 95.34/12.69 ( ![X14:$i]:
% 95.34/12.69 ( ( in @ X14 @ X6 ) =>
% 95.34/12.69 ( ( in @ ( kpair @ X12 @ X14 ) @ X8 ) =>
% 95.34/12.69 ( in @ ( kpair @ X12 @ X14 ) @ X10 ) ) ) ) ) ) =>
% 95.34/12.69 ( subset @ X8 @ X10 ) ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(funcGraphProp4, axiom, funcGraphProp4 =
% 95.34/12.69 (![A:$i,B:$i,Xf:$i]:
% 95.34/12.69 ( ( in @ Xf @ ( funcSet @ A @ B ) ) =>
% 95.34/12.69 ( ![Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ A ) =>
% 95.34/12.69 ( ![Xy:$i]:
% 95.34/12.69 ( ( in @ Xy @ B ) =>
% 95.34/12.69 ( ( in @ ( kpair @ Xx @ Xy ) @ Xf ) =>
% 95.34/12.69 ( ( ap @ A @ B @ Xf @ Xx ) = ( Xy ) ) ) ) ) ) ) ))).
% 95.34/12.69 thf('111', plain,
% 95.34/12.69 (( funcGraphProp4 ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( in @ X8 @ ( funcSet @ X4 @ X6 ) ) =>
% 95.34/12.69 ( ![X10:$i]:
% 95.34/12.69 ( ( in @ X10 @ X4 ) =>
% 95.34/12.69 ( ![X12:$i]:
% 95.34/12.69 ( ( in @ X12 @ X6 ) =>
% 95.34/12.69 ( ( in @ ( kpair @ X10 @ X12 ) @ X8 ) =>
% 95.34/12.69 ( ( ap @ X4 @ X6 @ X8 @ X10 ) = ( X12 ) ) ) ) ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(funcextLem, axiom, funcextLem =
% 95.34/12.69 (![A:$i,B:$i,Xf:$i]:
% 95.34/12.69 ( ( func @ A @ B @ Xf ) =>
% 95.34/12.69 ( ![Xg:$i]:
% 95.34/12.69 ( ( func @ A @ B @ Xg ) =>
% 95.34/12.69 ( ( ![Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ A ) =>
% 95.34/12.69 ( ( ap @ A @ B @ Xf @ Xx ) = ( ap @ A @ B @ Xg @ Xx ) ) ) ) =>
% 95.34/12.69 ( ![Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ A ) =>
% 95.34/12.69 ( ![Xy:$i]:
% 95.34/12.69 ( ( in @ Xy @ B ) =>
% 95.34/12.69 ( ( in @ ( kpair @ Xx @ Xy ) @ Xg ) =>
% 95.34/12.69 ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ) ))).
% 95.34/12.69 thf('112', plain,
% 95.34/12.69 (( funcextLem ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( func @ X4 @ X6 @ X8 ) =>
% 95.34/12.69 ( ![X10:$i]:
% 95.34/12.69 ( ( func @ X4 @ X6 @ X10 ) =>
% 95.34/12.69 ( ( ![X12:$i]:
% 95.34/12.69 ( ( in @ X12 @ X4 ) =>
% 95.34/12.69 ( ( ap @ X4 @ X6 @ X8 @ X12 ) =
% 95.34/12.69 ( ap @ X4 @ X6 @ X10 @ X12 ) ) ) ) =>
% 95.34/12.69 ( ![X14:$i]:
% 95.34/12.69 ( ( in @ X14 @ X4 ) =>
% 95.34/12.69 ( ![X16:$i]:
% 95.34/12.69 ( ( in @ X16 @ X6 ) =>
% 95.34/12.69 ( ( in @ ( kpair @ X14 @ X16 ) @ X10 ) =>
% 95.34/12.69 ( in @ ( kpair @ X14 @ X16 ) @ X8 ) ) ) ) ) ) ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(funcGraphProp2, axiom, funcGraphProp2 =
% 95.34/12.69 (![A:$i,B:$i,Xf:$i]:
% 95.34/12.69 ( ( func @ A @ B @ Xf ) =>
% 95.34/12.69 ( ![Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ A ) =>
% 95.34/12.69 ( ![Xy:$i]:
% 95.34/12.69 ( ( in @ Xy @ B ) =>
% 95.34/12.69 ( ( in @ ( kpair @ Xx @ Xy ) @ Xf ) =>
% 95.34/12.69 ( ( ap @ A @ B @ Xf @ Xx ) = ( Xy ) ) ) ) ) ) ) ))).
% 95.34/12.69 thf('113', plain,
% 95.34/12.69 (( funcGraphProp2 ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( func @ X4 @ X6 @ X8 ) =>
% 95.34/12.69 ( ![X10:$i]:
% 95.34/12.69 ( ( in @ X10 @ X4 ) =>
% 95.34/12.69 ( ![X12:$i]:
% 95.34/12.69 ( ( in @ X12 @ X6 ) =>
% 95.34/12.69 ( ( in @ ( kpair @ X10 @ X12 ) @ X8 ) =>
% 95.34/12.69 ( ( ap @ X4 @ X6 @ X8 @ X10 ) = ( X12 ) ) ) ) ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(funcGraphProp3, axiom, funcGraphProp3 =
% 95.34/12.69 (![A:$i,B:$i,Xf:$i]:
% 95.34/12.69 ( ( in @ Xf @ ( funcSet @ A @ B ) ) =>
% 95.34/12.69 ( ![Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ A ) =>
% 95.34/12.69 ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ))).
% 95.34/12.69 thf('114', plain,
% 95.34/12.69 (( funcGraphProp3 ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( in @ X8 @ ( funcSet @ X4 @ X6 ) ) =>
% 95.34/12.69 ( ![X10:$i]:
% 95.34/12.69 ( ( in @ X10 @ X4 ) =>
% 95.34/12.69 ( in @ ( kpair @ X10 @ ( ap @ X4 @ X6 @ X8 @ X10 ) ) @ X8 ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(funcGraphProp1, axiom, funcGraphProp1 =
% 95.34/12.69 (![A:$i,B:$i,Xf:$i]:
% 95.34/12.69 ( ( func @ A @ B @ Xf ) =>
% 95.34/12.69 ( ![Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ A ) =>
% 95.34/12.69 ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ))).
% 95.34/12.69 thf('115', plain,
% 95.34/12.69 (( funcGraphProp1 ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( func @ X4 @ X6 @ X8 ) =>
% 95.34/12.69 ( ![X10:$i]:
% 95.34/12.69 ( ( in @ X10 @ X4 ) =>
% 95.34/12.69 ( in @ ( kpair @ X10 @ ( ap @ X4 @ X6 @ X8 @ X10 ) ) @ X8 ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(ex1E2, axiom, ex1E2 =
% 95.34/12.69 (![A:$i,Xphi:( $i > $o )]:
% 95.34/12.69 ( ( ex1 @ A @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) =>
% 95.34/12.69 ( ![Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ A ) =>
% 95.34/12.69 ( ![Xy:$i]:
% 95.34/12.69 ( ( in @ Xy @ A ) =>
% 95.34/12.69 ( ( Xphi @ Xx ) => ( ( Xphi @ Xy ) => ( ( Xx ) = ( Xy ) ) ) ) ) ) ) ) ))).
% 95.34/12.69 thf('116', plain,
% 95.34/12.69 (( ex1E2 ) =
% 95.34/12.69 ( ![X4:$i,X6:( $i > $o )]:
% 95.34/12.69 ( ( ex1 @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) =>
% 95.34/12.69 ( ![X8:$i]:
% 95.34/12.69 ( ( in @ X8 @ X4 ) =>
% 95.34/12.69 ( ![X10:$i]:
% 95.34/12.69 ( ( in @ X10 @ X4 ) =>
% 95.34/12.69 ( ( X6 @ X8 ) => ( ( X6 @ X10 ) => ( ( X8 ) = ( X10 ) ) ) ) ) ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(brelnall2, axiom, brelnall2 =
% 95.34/12.69 (![A:$i,B:$i,R:$i]:
% 95.34/12.69 ( ( breln @ A @ B @ R ) =>
% 95.34/12.69 ( ![Xphi:( $i > $o )]:
% 95.34/12.69 ( ( ![Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ A ) =>
% 95.34/12.69 ( ![Xy:$i]:
% 95.34/12.69 ( ( in @ Xy @ B ) =>
% 95.34/12.69 ( ( in @ ( kpair @ Xx @ Xy ) @ R ) =>
% 95.34/12.69 ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) ) ) ) =>
% 95.34/12.69 ( ![Xx:$i]: ( ( in @ Xx @ R ) => ( Xphi @ Xx ) ) ) ) ) ))).
% 95.34/12.69 thf('117', plain,
% 95.34/12.69 (( brelnall2 ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( breln @ X4 @ X6 @ X8 ) =>
% 95.34/12.69 ( ![X10:( $i > $o )]:
% 95.34/12.69 ( ( ![X12:$i]:
% 95.34/12.69 ( ( in @ X12 @ X4 ) =>
% 95.34/12.69 ( ![X14:$i]:
% 95.34/12.69 ( ( in @ X14 @ X6 ) =>
% 95.34/12.69 ( ( in @ ( kpair @ X12 @ X14 ) @ X8 ) =>
% 95.34/12.69 ( X10 @ ( kpair @ X12 @ X14 ) ) ) ) ) ) ) =>
% 95.34/12.69 ( ![X16:$i]: ( ( in @ X16 @ X8 ) => ( X10 @ X16 ) ) ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(brelnall1, axiom, brelnall1 =
% 95.34/12.69 (![A:$i,B:$i,R:$i]:
% 95.34/12.69 ( ( breln @ A @ B @ R ) =>
% 95.34/12.69 ( ![Xphi:( $i > $o )]:
% 95.34/12.69 ( ( ![Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ A ) =>
% 95.34/12.69 ( ![Xy:$i]:
% 95.34/12.69 ( ( in @ Xy @ B ) =>
% 95.34/12.69 ( ( in @ ( kpair @ Xx @ Xy ) @ R ) =>
% 95.34/12.69 ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) ) ) ) =>
% 95.34/12.69 ( ![Xx:$i]: ( ( in @ Xx @ R ) => ( Xphi @ Xx ) ) ) ) ) ))).
% 95.34/12.69 thf('118', plain,
% 95.34/12.69 (( brelnall1 ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( breln @ X4 @ X6 @ X8 ) =>
% 95.34/12.69 ( ![X10:( $i > $o )]:
% 95.34/12.69 ( ( ![X12:$i]:
% 95.34/12.69 ( ( in @ X12 @ X4 ) =>
% 95.34/12.69 ( ![X14:$i]:
% 95.34/12.69 ( ( in @ X14 @ X6 ) =>
% 95.34/12.69 ( ( in @ ( kpair @ X12 @ X14 ) @ X8 ) =>
% 95.34/12.69 ( X10 @ ( kpair @ X12 @ X14 ) ) ) ) ) ) ) =>
% 95.34/12.69 ( ![X16:$i]: ( ( in @ X16 @ X8 ) => ( X10 @ X16 ) ) ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(lam2p, axiom, lam2p =
% 95.34/12.69 (![A:$i,B:$i,Xf:( $i > $i )]:
% 95.34/12.69 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( in @ ( Xf @ Xx ) @ B ) ) ) =>
% 95.34/12.69 ( in @ ( lam @ A @ B @ ( ^[Xx:$i]: ( Xf @ Xx ) ) ) @ ( funcSet @ A @ B ) ) ))).
% 95.34/12.69 thf('119', plain,
% 95.34/12.69 (( lam2p ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:( $i > $i )]:
% 95.34/12.69 ( ( ![X10:$i]: ( ( in @ X10 @ X4 ) => ( in @ ( X8 @ X10 ) @ X6 ) ) ) =>
% 95.34/12.69 ( in @
% 95.34/12.69 ( lam @ X4 @ X6 @ ( ^[V_1:$i]: ( X8 @ V_1 ) ) ) @
% 95.34/12.69 ( funcSet @ X4 @ X6 ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(lamp, axiom, lamp =
% 95.34/12.69 (![A:$i,B:$i,Xf:( $i > $i )]:
% 95.34/12.69 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( in @ ( Xf @ Xx ) @ B ) ) ) =>
% 95.34/12.69 ( func @ A @ B @ ( lam @ A @ B @ ( ^[Xx:$i]: ( Xf @ Xx ) ) ) ) ))).
% 95.34/12.69 thf('120', plain,
% 95.34/12.69 (( lamp ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:( $i > $i )]:
% 95.34/12.69 ( ( ![X10:$i]: ( ( in @ X10 @ X4 ) => ( in @ ( X8 @ X10 ) @ X6 ) ) ) =>
% 95.34/12.69 ( func @ X4 @ X6 @ ( lam @ X4 @ X6 @ ( ^[V_1:$i]: ( X8 @ V_1 ) ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(lamProp, axiom, lamProp =
% 95.34/12.69 (![A:$i,B:$i,Xf:( $i > $i )]:
% 95.34/12.69 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( in @ ( Xf @ Xx ) @ B ) ) ) =>
% 95.34/12.69 ( func @
% 95.34/12.69 A @ B @
% 95.34/12.69 ( dpsetconstr @ A @ B @ ( ^[Xx:$i,Xy:$i]: ( ( Xf @ Xx ) = ( Xy ) ) ) ) ) ))).
% 95.34/12.69 thf('121', plain,
% 95.34/12.69 (( lamProp ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:( $i > $i )]:
% 95.34/12.69 ( ( ![X10:$i]: ( ( in @ X10 @ X4 ) => ( in @ ( X8 @ X10 ) @ X6 ) ) ) =>
% 95.34/12.69 ( func @
% 95.34/12.69 X4 @ X6 @
% 95.34/12.69 ( dpsetconstr @
% 95.34/12.69 X4 @ X6 @ ( ^[V_1:$i,V_2:$i]: ( ( X8 @ V_1 ) = ( V_2 ) ) ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(funcinfuncset, axiom, funcinfuncset =
% 95.34/12.69 (![A:$i,B:$i,Xf:$i]:
% 95.34/12.69 ( ( func @ A @ B @ Xf ) => ( in @ Xf @ ( funcSet @ A @ B ) ) ))).
% 95.34/12.69 thf('122', plain,
% 95.34/12.69 (( funcinfuncset ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( func @ X4 @ X6 @ X8 ) => ( in @ X8 @ ( funcSet @ X4 @ X6 ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(ap2p, axiom, ap2p =
% 95.34/12.69 (![A:$i,B:$i,Xf:$i]:
% 95.34/12.69 ( ( in @ Xf @ ( funcSet @ A @ B ) ) =>
% 95.34/12.69 ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ))).
% 95.34/12.69 thf('123', plain,
% 95.34/12.69 (( ap2p ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( in @ X8 @ ( funcSet @ X4 @ X6 ) ) =>
% 95.34/12.69 ( ![X10:$i]:
% 95.34/12.69 ( ( in @ X10 @ X4 ) => ( in @ ( ap @ X4 @ X6 @ X8 @ X10 ) @ X6 ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(infuncsetfunc, axiom, infuncsetfunc =
% 95.34/12.69 (![A:$i,B:$i,Xf:$i]:
% 95.34/12.69 ( ( in @ Xf @ ( funcSet @ A @ B ) ) => ( func @ A @ B @ Xf ) ))).
% 95.34/12.69 thf('124', plain,
% 95.34/12.69 (( infuncsetfunc ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( in @ X8 @ ( funcSet @ X4 @ X6 ) ) => ( func @ X4 @ X6 @ X8 ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(app, axiom, app =
% 95.34/12.69 (![A:$i,B:$i,Xf:$i]:
% 95.34/12.69 ( ( func @ A @ B @ Xf ) =>
% 95.34/12.69 ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ))).
% 95.34/12.69 thf('125', plain,
% 95.34/12.69 (( app ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( func @ X4 @ X6 @ X8 ) =>
% 95.34/12.69 ( ![X10:$i]:
% 95.34/12.69 ( ( in @ X10 @ X4 ) => ( in @ ( ap @ X4 @ X6 @ X8 @ X10 ) @ X6 ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(apProp, axiom, apProp =
% 95.34/12.69 (![A:$i,B:$i,Xf:$i]:
% 95.34/12.69 ( ( func @ A @ B @ Xf ) =>
% 95.34/12.69 ( ![Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ A ) =>
% 95.34/12.69 ( in @
% 95.34/12.69 ( setunion @
% 95.34/12.69 ( dsetconstr @
% 95.34/12.69 B @ ( ^[Xy:$i]: ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) @
% 95.34/12.69 B ) ) ) ))).
% 95.34/12.69 thf('126', plain,
% 95.34/12.69 (( apProp ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( func @ X4 @ X6 @ X8 ) =>
% 95.34/12.69 ( ![X10:$i]:
% 95.34/12.69 ( ( in @ X10 @ X4 ) =>
% 95.34/12.69 ( in @
% 95.34/12.69 ( setunion @
% 95.34/12.69 ( dsetconstr @
% 95.34/12.69 X6 @ ( ^[V_1:$i]: ( in @ ( kpair @ X10 @ V_1 ) @ X8 ) ) ) ) @
% 95.34/12.69 X6 ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(funcImageSingleton, axiom, funcImageSingleton =
% 95.34/12.69 (![A:$i,B:$i,Xf:$i]:
% 95.34/12.69 ( ( func @ A @ B @ Xf ) =>
% 95.34/12.69 ( ![Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ A ) =>
% 95.34/12.69 ( singleton @
% 95.34/12.69 ( dsetconstr @ B @ ( ^[Xy:$i]: ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ))).
% 95.34/12.69 thf('127', plain,
% 95.34/12.69 (( funcImageSingleton ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( func @ X4 @ X6 @ X8 ) =>
% 95.34/12.69 ( ![X10:$i]:
% 95.34/12.69 ( ( in @ X10 @ X4 ) =>
% 95.34/12.69 ( singleton @
% 95.34/12.69 ( dsetconstr @
% 95.34/12.69 X6 @ ( ^[V_1:$i]: ( in @ ( kpair @ X10 @ V_1 ) @ X8 ) ) ) ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(dpsetconstrER, axiom, dpsetconstrER =
% 95.34/12.69 (![A:$i,B:$i,Xphi:( $i > $i > $o ),Xx:$i,Xy:$i]:
% 95.34/12.69 ( ( in @
% 95.34/12.69 ( kpair @ Xx @ Xy ) @
% 95.34/12.69 ( dpsetconstr @ A @ B @ ( ^[Xz:$i,Xu:$i]: ( Xphi @ Xz @ Xu ) ) ) ) =>
% 95.34/12.69 ( Xphi @ Xx @ Xy ) ))).
% 95.34/12.69 thf('128', plain,
% 95.34/12.69 (( dpsetconstrER ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:( $i > $i > $o ),X10:$i,X12:$i]:
% 95.34/12.69 ( ( in @
% 95.34/12.69 ( kpair @ X10 @ X12 ) @
% 95.34/12.69 ( dpsetconstr @ X4 @ X6 @ ( ^[V_1:$i,V_2:$i]: ( X8 @ V_1 @ V_2 ) ) ) ) =>
% 95.34/12.69 ( X8 @ X10 @ X12 ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(dpsetconstrEL2, axiom, dpsetconstrEL2 =
% 95.34/12.69 (![A:$i,B:$i,Xphi:( $i > $i > $o ),Xx:$i,Xy:$i]:
% 95.34/12.69 ( ( in @
% 95.34/12.69 ( kpair @ Xx @ Xy ) @
% 95.34/12.69 ( dpsetconstr @ A @ B @ ( ^[Xz:$i,Xu:$i]: ( Xphi @ Xz @ Xu ) ) ) ) =>
% 95.34/12.69 ( in @ Xy @ B ) ))).
% 95.34/12.69 thf('129', plain,
% 95.34/12.69 (( dpsetconstrEL2 ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:( $i > $i > $o ),X10:$i,X12:$i]:
% 95.34/12.69 ( ( in @
% 95.34/12.69 ( kpair @ X10 @ X12 ) @
% 95.34/12.69 ( dpsetconstr @ X4 @ X6 @ ( ^[V_1:$i,V_2:$i]: ( X8 @ V_1 @ V_2 ) ) ) ) =>
% 95.34/12.69 ( in @ X12 @ X6 ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(dpsetconstrEL1, axiom, dpsetconstrEL1 =
% 95.34/12.69 (![A:$i,B:$i,Xphi:( $i > $i > $o ),Xx:$i,Xy:$i]:
% 95.34/12.69 ( ( in @
% 95.34/12.69 ( kpair @ Xx @ Xy ) @
% 95.34/12.69 ( dpsetconstr @ A @ B @ ( ^[Xz:$i,Xu:$i]: ( Xphi @ Xz @ Xu ) ) ) ) =>
% 95.34/12.69 ( in @ Xx @ A ) ))).
% 95.34/12.69 thf('130', plain,
% 95.34/12.69 (( dpsetconstrEL1 ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:( $i > $i > $o ),X10:$i,X12:$i]:
% 95.34/12.69 ( ( in @
% 95.34/12.69 ( kpair @ X10 @ X12 ) @
% 95.34/12.69 ( dpsetconstr @ X4 @ X6 @ ( ^[V_1:$i,V_2:$i]: ( X8 @ V_1 @ V_2 ) ) ) ) =>
% 95.34/12.69 ( in @ X10 @ X4 ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(dpsetconstrERa, axiom, dpsetconstrERa =
% 95.34/12.69 (![A:$i,B:$i,Xphi:( $i > $i > $o ),Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ A ) =>
% 95.34/12.69 ( ![Xy:$i]:
% 95.34/12.69 ( ( in @ Xy @ B ) =>
% 95.34/12.69 ( ( in @
% 95.34/12.69 ( kpair @ Xx @ Xy ) @
% 95.34/12.69 ( dpsetconstr @ A @ B @ ( ^[Xz:$i,Xu:$i]: ( Xphi @ Xz @ Xu ) ) ) ) =>
% 95.34/12.69 ( Xphi @ Xx @ Xy ) ) ) ) ))).
% 95.34/12.69 thf('131', plain,
% 95.34/12.69 (( dpsetconstrERa ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:( $i > $i > $o ),X10:$i]:
% 95.34/12.69 ( ( in @ X10 @ X4 ) =>
% 95.34/12.69 ( ![X12:$i]:
% 95.34/12.69 ( ( in @ X12 @ X6 ) =>
% 95.34/12.69 ( ( in @
% 95.34/12.69 ( kpair @ X10 @ X12 ) @
% 95.34/12.69 ( dpsetconstr @
% 95.34/12.69 X4 @ X6 @ ( ^[V_1:$i,V_2:$i]: ( X8 @ V_1 @ V_2 ) ) ) ) =>
% 95.34/12.69 ( X8 @ X10 @ X12 ) ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(setOfPairsIsBReln, axiom, setOfPairsIsBReln =
% 95.34/12.69 (![A:$i,B:$i,Xphi:( $i > $i > $o )]:
% 95.34/12.69 ( breln @
% 95.34/12.69 A @ B @ ( dpsetconstr @ A @ B @ ( ^[Xx:$i,Xy:$i]: ( Xphi @ Xx @ Xy ) ) ) ))).
% 95.34/12.69 thf('132', plain,
% 95.34/12.69 (( setOfPairsIsBReln ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:( $i > $i > $o )]:
% 95.34/12.69 ( breln @
% 95.34/12.69 X4 @ X6 @
% 95.34/12.69 ( dpsetconstr @ X4 @ X6 @ ( ^[V_1:$i,V_2:$i]: ( X8 @ V_1 @ V_2 ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(dpsetconstrSub, axiom, dpsetconstrSub =
% 95.34/12.69 (![A:$i,B:$i,Xphi:( $i > $i > $o )]:
% 95.34/12.69 ( subset @
% 95.34/12.69 ( dpsetconstr @ A @ B @ ( ^[Xx:$i,Xy:$i]: ( Xphi @ Xx @ Xy ) ) ) @
% 95.34/12.69 ( cartprod @ A @ B ) ))).
% 95.34/12.69 thf('133', plain,
% 95.34/12.69 (( dpsetconstrSub ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:( $i > $i > $o )]:
% 95.34/12.69 ( subset @
% 95.34/12.69 ( dpsetconstr @ X4 @ X6 @ ( ^[V_1:$i,V_2:$i]: ( X8 @ V_1 @ V_2 ) ) ) @
% 95.34/12.69 ( cartprod @ X4 @ X6 ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(dpsetconstrI, axiom, dpsetconstrI =
% 95.34/12.69 (![A:$i,B:$i,Xphi:( $i > $i > $o ),Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ A ) =>
% 95.34/12.69 ( ![Xy:$i]:
% 95.34/12.69 ( ( in @ Xy @ B ) =>
% 95.34/12.69 ( ( Xphi @ Xx @ Xy ) =>
% 95.34/12.69 ( in @
% 95.34/12.69 ( kpair @ Xx @ Xy ) @
% 95.34/12.69 ( dpsetconstr @ A @ B @ ( ^[Xz:$i,Xu:$i]: ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ))).
% 95.34/12.69 thf('134', plain,
% 95.34/12.69 (( dpsetconstrI ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:( $i > $i > $o ),X10:$i]:
% 95.34/12.69 ( ( in @ X10 @ X4 ) =>
% 95.34/12.69 ( ![X12:$i]:
% 95.34/12.69 ( ( in @ X12 @ X6 ) =>
% 95.34/12.69 ( ( X8 @ X10 @ X12 ) =>
% 95.34/12.69 ( in @
% 95.34/12.69 ( kpair @ X10 @ X12 ) @
% 95.34/12.69 ( dpsetconstr @
% 95.34/12.69 X4 @ X6 @ ( ^[V_1:$i,V_2:$i]: ( X8 @ V_1 @ V_2 ) ) ) ) ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(cartprodpairsurjEq, axiom, cartprodpairsurjEq =
% 95.34/12.69 (![A:$i,B:$i,Xu:$i]:
% 95.34/12.69 ( ( in @ Xu @ ( cartprod @ A @ B ) ) =>
% 95.34/12.69 ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) ) = ( Xu ) ) ))).
% 95.34/12.69 thf('135', plain,
% 95.34/12.69 (( cartprodpairsurjEq ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( in @ X8 @ ( cartprod @ X4 @ X6 ) ) =>
% 95.34/12.69 ( ( kpair @ ( kfst @ X8 ) @ ( ksnd @ X8 ) ) = ( X8 ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(cartprodsndpairEq, axiom, cartprodsndpairEq =
% 95.34/12.69 (![A:$i,B:$i,Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ A ) =>
% 95.34/12.69 ( ![Xy:$i]:
% 95.34/12.69 ( ( in @ Xy @ B ) => ( ( ksnd @ ( kpair @ Xx @ Xy ) ) = ( Xy ) ) ) ) ))).
% 95.34/12.69 thf('136', plain,
% 95.34/12.69 (( cartprodsndpairEq ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( in @ X8 @ X4 ) =>
% 95.34/12.69 ( ![X10:$i]:
% 95.34/12.69 ( ( in @ X10 @ X6 ) =>
% 95.34/12.69 ( ( ksnd @ ( kpair @ X8 @ X10 ) ) = ( X10 ) ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(cartprodfstpairEq, axiom, cartprodfstpairEq =
% 95.34/12.69 (![A:$i,B:$i,Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ A ) =>
% 95.34/12.69 ( ![Xy:$i]:
% 95.34/12.69 ( ( in @ Xy @ B ) => ( ( kfst @ ( kpair @ Xx @ Xy ) ) = ( Xx ) ) ) ) ))).
% 95.34/12.69 thf('137', plain,
% 95.34/12.69 (( cartprodfstpairEq ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( in @ X8 @ X4 ) =>
% 95.34/12.69 ( ![X10:$i]:
% 95.34/12.69 ( ( in @ X10 @ X6 ) =>
% 95.34/12.69 ( ( kfst @ ( kpair @ X8 @ X10 ) ) = ( X8 ) ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(cartprodmempaircEq, axiom, cartprodmempaircEq =
% 95.34/12.69 (![A:$i,B:$i,Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ A ) =>
% 95.34/12.69 ( ![Xy:$i]:
% 95.34/12.69 ( ( in @ Xy @ B ) => ( ( kpair @ Xx @ Xy ) = ( kpair @ Xx @ Xy ) ) ) ) ))).
% 95.34/12.69 thf('138', plain,
% 95.34/12.69 (( cartprodmempaircEq ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( in @ X8 @ X4 ) =>
% 95.34/12.69 ( ![X10:$i]:
% 95.34/12.69 ( ( in @ X10 @ X6 ) =>
% 95.34/12.69 ( ( kpair @ X8 @ X10 ) = ( kpair @ X8 @ X10 ) ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(cartprodpairmemER, axiom, cartprodpairmemER =
% 95.34/12.69 (![A:$i,B:$i,Xx:$i,Xy:$i]:
% 95.34/12.69 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) => ( in @ Xy @ B ) ))).
% 95.34/12.69 thf('139', plain,
% 95.34/12.69 (( cartprodpairmemER ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i,X10:$i]:
% 95.34/12.69 ( ( in @ ( kpair @ X8 @ X10 ) @ ( cartprod @ X4 @ X6 ) ) =>
% 95.34/12.69 ( in @ X10 @ X6 ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(cartprodpairmemEL, axiom, cartprodpairmemEL =
% 95.34/12.69 (![A:$i,B:$i,Xx:$i,Xy:$i]:
% 95.34/12.69 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) => ( in @ Xx @ A ) ))).
% 95.34/12.69 thf('140', plain,
% 95.34/12.69 (( cartprodpairmemEL ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i,X10:$i]:
% 95.34/12.69 ( ( in @ ( kpair @ X8 @ X10 ) @ ( cartprod @ X4 @ X6 ) ) =>
% 95.34/12.69 ( in @ X8 @ X4 ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(cartprodsndin, axiom, cartprodsndin =
% 95.34/12.69 (![A:$i,B:$i,Xu:$i]:
% 95.34/12.69 ( ( in @ Xu @ ( cartprod @ A @ B ) ) => ( in @ ( ksnd @ Xu ) @ B ) ))).
% 95.34/12.69 thf('141', plain,
% 95.34/12.69 (( cartprodsndin ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( in @ X8 @ ( cartprod @ X4 @ X6 ) ) => ( in @ ( ksnd @ X8 ) @ X6 ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(kpairsurjEq, axiom, kpairsurjEq =
% 95.34/12.69 (![Xu:$i]:
% 95.34/12.69 ( ( iskpair @ Xu ) =>
% 95.34/12.69 ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) ) = ( Xu ) ) ))).
% 95.34/12.69 thf('142', plain,
% 95.34/12.69 (( kpairsurjEq ) =
% 95.34/12.69 ( ![X4:$i]:
% 95.34/12.69 ( ( iskpair @ X4 ) =>
% 95.34/12.69 ( ( kpair @ ( kfst @ X4 ) @ ( ksnd @ X4 ) ) = ( X4 ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(ksndpairEq, axiom, ksndpairEq =
% 95.34/12.69 (![Xx:$i,Xy:$i]: ( ( ksnd @ ( kpair @ Xx @ Xy ) ) = ( Xy ) ))).
% 95.34/12.69 thf('143', plain,
% 95.34/12.69 (( ksndpairEq ) =
% 95.34/12.69 ( ![X4:$i,X6:$i]: ( ( ksnd @ ( kpair @ X4 @ X6 ) ) = ( X6 ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(ksndsingleton, axiom, ksndsingleton =
% 95.34/12.69 (![Xu:$i]:
% 95.34/12.69 ( ( iskpair @ Xu ) =>
% 95.34/12.69 ( singleton @
% 95.34/12.69 ( dsetconstr @
% 95.34/12.69 ( setunion @ Xu ) @
% 95.34/12.69 ( ^[Xx:$i]: ( ( Xu ) = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ))).
% 95.34/12.69 thf('144', plain,
% 95.34/12.69 (( ksndsingleton ) =
% 95.34/12.69 ( ![X4:$i]:
% 95.34/12.69 ( ( iskpair @ X4 ) =>
% 95.34/12.69 ( singleton @
% 95.34/12.69 ( dsetconstr @
% 95.34/12.69 ( setunion @ X4 ) @
% 95.34/12.69 ( ^[V_1:$i]: ( ( X4 ) = ( kpair @ ( kfst @ X4 ) @ V_1 ) ) ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(setukpairinjR, axiom, setukpairinjR =
% 95.34/12.69 (![Xx:$i,Xy:$i,Xz:$i,Xu:$i]:
% 95.34/12.69 ( ( ( kpair @ Xx @ Xy ) = ( kpair @ Xz @ Xu ) ) => ( ( Xy ) = ( Xu ) ) ))).
% 95.34/12.69 thf('145', plain,
% 95.34/12.69 (( setukpairinjR ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i,X10:$i]:
% 95.34/12.69 ( ( ( kpair @ X4 @ X6 ) = ( kpair @ X8 @ X10 ) ) =>
% 95.34/12.69 ( ( X6 ) = ( X10 ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(setukpairinjR2, axiom, setukpairinjR2 =
% 95.34/12.69 (![Xx:$i,Xy:$i,Xz:$i,Xu:$i]:
% 95.34/12.69 ( ( ( setadjoin @
% 95.34/12.69 ( setadjoin @ Xx @ emptyset ) @
% 95.34/12.69 ( setadjoin @
% 95.34/12.69 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) =
% 95.34/12.69 ( setadjoin @
% 95.34/12.69 ( setadjoin @ Xz @ emptyset ) @
% 95.34/12.69 ( setadjoin @
% 95.34/12.69 ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) ) =>
% 95.34/12.69 ( ( Xy ) = ( Xu ) ) ))).
% 95.34/12.69 thf('146', plain,
% 95.34/12.69 (( setukpairinjR2 ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i,X10:$i]:
% 95.34/12.69 ( ( ( setadjoin @
% 95.34/12.69 ( setadjoin @ X4 @ emptyset ) @
% 95.34/12.69 ( setadjoin @
% 95.34/12.69 ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) @ emptyset ) ) =
% 95.34/12.69 ( setadjoin @
% 95.34/12.69 ( setadjoin @ X8 @ emptyset ) @
% 95.34/12.69 ( setadjoin @
% 95.34/12.69 ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @ emptyset ) ) ) =>
% 95.34/12.69 ( ( X6 ) = ( X10 ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(upairequniteq, axiom, upairequniteq =
% 95.34/12.69 (![Xx:$i,Xy:$i,Xz:$i]:
% 95.34/12.69 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) =
% 95.34/12.69 ( setadjoin @ Xz @ emptyset ) ) =>
% 95.34/12.69 ( ( Xx ) = ( Xy ) ) ))).
% 95.34/12.69 thf('147', plain,
% 95.34/12.69 (( upairequniteq ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) =
% 95.34/12.69 ( setadjoin @ X8 @ emptyset ) ) =>
% 95.34/12.69 ( ( X4 ) = ( X6 ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(setukpairinjR1, axiom, setukpairinjR1 =
% 95.34/12.69 (![Xx:$i,Xy:$i,Xz:$i,Xu:$i]:
% 95.34/12.69 ( ( ( setadjoin @
% 95.34/12.69 ( setadjoin @ Xx @ emptyset ) @
% 95.34/12.69 ( setadjoin @
% 95.34/12.69 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) =
% 95.34/12.69 ( setadjoin @
% 95.34/12.69 ( setadjoin @ Xz @ emptyset ) @
% 95.34/12.69 ( setadjoin @
% 95.34/12.69 ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) ) =>
% 95.34/12.69 ( ( ( Xz ) = ( Xu ) ) => ( ( Xy ) = ( Xu ) ) ) ))).
% 95.34/12.69 thf('148', plain,
% 95.34/12.69 (( setukpairinjR1 ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i,X10:$i]:
% 95.34/12.69 ( ( ( setadjoin @
% 95.34/12.69 ( setadjoin @ X4 @ emptyset ) @
% 95.34/12.69 ( setadjoin @
% 95.34/12.69 ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) @ emptyset ) ) =
% 95.34/12.69 ( setadjoin @
% 95.34/12.69 ( setadjoin @ X8 @ emptyset ) @
% 95.34/12.69 ( setadjoin @
% 95.34/12.69 ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @ emptyset ) ) ) =>
% 95.34/12.69 ( ( ( X8 ) = ( X10 ) ) => ( ( X6 ) = ( X10 ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(setukpairinjR12, axiom, setukpairinjR12 =
% 95.34/12.69 (![Xx:$i,Xy:$i]:
% 95.34/12.69 ( ( ( Xx ) = ( Xy ) ) =>
% 95.34/12.69 ( ( setadjoin @
% 95.34/12.69 ( setadjoin @ Xx @ emptyset ) @
% 95.34/12.69 ( setadjoin @
% 95.34/12.69 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) =
% 95.34/12.69 ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ))).
% 95.34/12.69 thf('149', plain,
% 95.34/12.69 (( setukpairinjR12 ) =
% 95.34/12.69 ( ![X4:$i,X6:$i]:
% 95.34/12.69 ( ( ( X4 ) = ( X6 ) ) =>
% 95.34/12.69 ( ( setadjoin @
% 95.34/12.69 ( setadjoin @ X4 @ emptyset ) @
% 95.34/12.69 ( setadjoin @
% 95.34/12.69 ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) @ emptyset ) ) =
% 95.34/12.69 ( setadjoin @ ( setadjoin @ X4 @ emptyset ) @ emptyset ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(setukpairinjR11, axiom, setukpairinjR11 =
% 95.34/12.69 (![Xx:$i,Xy:$i]:
% 95.34/12.69 ( ( ( Xx ) = ( Xy ) ) =>
% 95.34/12.69 ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) =
% 95.34/12.69 ( setadjoin @ Xx @ emptyset ) ) ))).
% 95.34/12.69 thf('150', plain,
% 95.34/12.69 (( setukpairinjR11 ) =
% 95.34/12.69 ( ![X4:$i,X6:$i]:
% 95.34/12.69 ( ( ( X4 ) = ( X6 ) ) =>
% 95.34/12.69 ( ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) =
% 95.34/12.69 ( setadjoin @ X4 @ emptyset ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(setukpairinjL, axiom, setukpairinjL =
% 95.34/12.69 (![Xx:$i,Xy:$i,Xz:$i,Xu:$i]:
% 95.34/12.69 ( ( ( kpair @ Xx @ Xy ) = ( kpair @ Xz @ Xu ) ) => ( ( Xx ) = ( Xz ) ) ))).
% 95.34/12.69 thf('151', plain,
% 95.34/12.69 (( setukpairinjL ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i,X10:$i]:
% 95.34/12.69 ( ( ( kpair @ X4 @ X6 ) = ( kpair @ X8 @ X10 ) ) =>
% 95.34/12.69 ( ( X4 ) = ( X8 ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(setukpairinjL2, axiom, setukpairinjL2 =
% 95.34/12.69 (![Xx:$i,Xy:$i,Xz:$i,Xu:$i]:
% 95.34/12.69 ( ( ( setadjoin @
% 95.34/12.69 ( setadjoin @ Xx @ emptyset ) @
% 95.34/12.69 ( setadjoin @
% 95.34/12.69 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) =
% 95.34/12.69 ( setadjoin @
% 95.34/12.69 ( setadjoin @ Xz @ emptyset ) @
% 95.34/12.69 ( setadjoin @
% 95.34/12.69 ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) ) =>
% 95.34/12.69 ( ( Xx ) = ( Xz ) ) ))).
% 95.34/12.69 thf('152', plain,
% 95.34/12.69 (( setukpairinjL2 ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i,X10:$i]:
% 95.34/12.69 ( ( ( setadjoin @
% 95.34/12.69 ( setadjoin @ X4 @ emptyset ) @
% 95.34/12.69 ( setadjoin @
% 95.34/12.69 ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) @ emptyset ) ) =
% 95.34/12.69 ( setadjoin @
% 95.34/12.69 ( setadjoin @ X8 @ emptyset ) @
% 95.34/12.69 ( setadjoin @
% 95.34/12.69 ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @ emptyset ) ) ) =>
% 95.34/12.69 ( ( X4 ) = ( X8 ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(cartprodfstin, axiom, cartprodfstin =
% 95.34/12.69 (![A:$i,B:$i,Xu:$i]:
% 95.34/12.69 ( ( in @ Xu @ ( cartprod @ A @ B ) ) => ( in @ ( kfst @ Xu ) @ A ) ))).
% 95.34/12.69 thf('153', plain,
% 95.34/12.69 (( cartprodfstin ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( in @ X8 @ ( cartprod @ X4 @ X6 ) ) => ( in @ ( kfst @ X8 ) @ X4 ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(kfstpairEq, axiom, kfstpairEq =
% 95.34/12.69 (![Xx:$i,Xy:$i]: ( ( kfst @ ( kpair @ Xx @ Xy ) ) = ( Xx ) ))).
% 95.34/12.69 thf('154', plain,
% 95.34/12.69 (( kfstpairEq ) =
% 95.34/12.69 ( ![X4:$i,X6:$i]: ( ( kfst @ ( kpair @ X4 @ X6 ) ) = ( X4 ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(theprop, axiom, theprop =
% 95.34/12.69 (![X:$i]: ( ( singleton @ X ) => ( in @ ( setunion @ X ) @ X ) ))).
% 95.34/12.69 thf('155', plain,
% 95.34/12.69 (( theprop ) =
% 95.34/12.69 ( ![X4:$i]: ( ( singleton @ X4 ) => ( in @ ( setunion @ X4 ) @ X4 ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(kfstsingleton, axiom, kfstsingleton =
% 95.34/12.69 (![Xu:$i]:
% 95.34/12.69 ( ( iskpair @ Xu ) =>
% 95.34/12.69 ( singleton @
% 95.34/12.69 ( dsetconstr @
% 95.34/12.69 ( setunion @ Xu ) @
% 95.34/12.69 ( ^[Xx:$i]: ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ))).
% 95.34/12.69 thf('156', plain,
% 95.34/12.69 (( kfstsingleton ) =
% 95.34/12.69 ( ![X4:$i]:
% 95.34/12.69 ( ( iskpair @ X4 ) =>
% 95.34/12.69 ( singleton @
% 95.34/12.69 ( dsetconstr @
% 95.34/12.69 ( setunion @ X4 ) @
% 95.34/12.69 ( ^[V_1:$i]: ( in @ ( setadjoin @ V_1 @ emptyset ) @ X4 ) ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(setukpairinjL1, axiom, setukpairinjL1 =
% 95.34/12.69 (![Xx:$i,Xy:$i,Xz:$i]:
% 95.34/12.69 ( ( in @
% 95.34/12.69 ( setadjoin @ Xz @ emptyset ) @
% 95.34/12.69 ( setadjoin @
% 95.34/12.69 ( setadjoin @ Xx @ emptyset ) @
% 95.34/12.69 ( setadjoin @
% 95.34/12.69 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) =>
% 95.34/12.69 ( ( Xx ) = ( Xz ) ) ))).
% 95.34/12.69 thf('157', plain,
% 95.34/12.69 (( setukpairinjL1 ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( in @
% 95.34/12.69 ( setadjoin @ X8 @ emptyset ) @
% 95.34/12.69 ( setadjoin @
% 95.34/12.69 ( setadjoin @ X4 @ emptyset ) @
% 95.34/12.69 ( setadjoin @
% 95.34/12.69 ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) @ emptyset ) ) ) =>
% 95.34/12.69 ( ( X4 ) = ( X8 ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(singletonsuniq, axiom, singletonsuniq =
% 95.34/12.69 (![Xx:$i,Xy:$i]:
% 95.34/12.69 ( ( ( setadjoin @ Xx @ emptyset ) = ( setadjoin @ Xy @ emptyset ) ) =>
% 95.34/12.69 ( ( Xx ) = ( Xy ) ) ))).
% 95.34/12.69 thf('158', plain,
% 95.34/12.69 (( singletonsuniq ) =
% 95.34/12.69 ( ![X4:$i,X6:$i]:
% 95.34/12.69 ( ( ( setadjoin @ X4 @ emptyset ) = ( setadjoin @ X6 @ emptyset ) ) =>
% 95.34/12.69 ( ( X4 ) = ( X6 ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(ex1I2, axiom, ex1I2 =
% 95.34/12.69 (![A:$i,Xphi:( $i > $o )]:
% 95.34/12.69 ( ( ![Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ A ) =>
% 95.34/12.69 ( ![Xy:$i]:
% 95.34/12.69 ( ( in @ Xy @ A ) =>
% 95.34/12.69 ( ( Xphi @ Xx ) => ( ( Xphi @ Xy ) => ( ( Xx ) = ( Xy ) ) ) ) ) ) ) ) =>
% 95.34/12.69 ( ( ?[Xx:$i]: ( ( Xphi @ Xx ) & ( in @ Xx @ A ) ) ) =>
% 95.34/12.69 ( ex1 @ A @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) ) ))).
% 95.34/12.69 thf('159', plain,
% 95.34/12.69 (( ex1I2 ) =
% 95.34/12.69 ( ![X4:$i,X6:( $i > $o )]:
% 95.34/12.69 ( ( ![X8:$i]:
% 95.34/12.69 ( ( in @ X8 @ X4 ) =>
% 95.34/12.69 ( ![X10:$i]:
% 95.34/12.69 ( ( in @ X10 @ X4 ) =>
% 95.34/12.69 ( ( X6 @ X8 ) => ( ( X6 @ X10 ) => ( ( X8 ) = ( X10 ) ) ) ) ) ) ) ) =>
% 95.34/12.69 ( ( ?[X12:$i]: ( ( X6 @ X12 ) & ( in @ X12 @ X4 ) ) ) =>
% 95.34/12.69 ( ex1 @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(ex1I, axiom, ex1I =
% 95.34/12.69 (![A:$i,Xphi:( $i > $o ),Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ A ) =>
% 95.34/12.69 ( ( Xphi @ Xx ) =>
% 95.34/12.69 ( ( ![Xy:$i]:
% 95.34/12.69 ( ( in @ Xy @ A ) => ( ( Xphi @ Xy ) => ( ( Xy ) = ( Xx ) ) ) ) ) =>
% 95.34/12.69 ( ex1 @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) ) ))).
% 95.34/12.69 thf('160', plain,
% 95.34/12.69 (( ex1I ) =
% 95.34/12.69 ( ![X4:$i,X6:( $i > $o ),X8:$i]:
% 95.34/12.69 ( ( in @ X8 @ X4 ) =>
% 95.34/12.69 ( ( X6 @ X8 ) =>
% 95.34/12.69 ( ( ![X10:$i]:
% 95.34/12.69 ( ( in @ X10 @ X4 ) =>
% 95.34/12.69 ( ( X6 @ X10 ) => ( ( X10 ) = ( X8 ) ) ) ) ) =>
% 95.34/12.69 ( ex1 @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(ex1E1, axiom, ex1E1 =
% 95.34/12.69 (![A:$i,Xphi:( $i > $o )]:
% 95.34/12.69 ( ( ex1 @ A @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) =>
% 95.34/12.69 ( ?[Xx:$i]: ( ( Xphi @ Xx ) & ( in @ Xx @ A ) ) ) ))).
% 95.34/12.69 thf('161', plain,
% 95.34/12.69 (( ex1E1 ) =
% 95.34/12.69 ( ![X4:$i,X6:( $i > $o )]:
% 95.34/12.69 ( ( ex1 @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) =>
% 95.34/12.69 ( ?[X8:$i]: ( ( X6 @ X8 ) & ( in @ X8 @ X4 ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(singletonprop, axiom, singletonprop =
% 95.34/12.69 (![A:$i,Xphi:( $i > $o )]:
% 95.34/12.69 ( ( ![Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ A ) =>
% 95.34/12.69 ( ![Xy:$i]:
% 95.34/12.69 ( ( in @ Xy @ A ) =>
% 95.34/12.69 ( ( Xphi @ Xx ) => ( ( Xphi @ Xy ) => ( ( Xx ) = ( Xy ) ) ) ) ) ) ) ) =>
% 95.34/12.69 ( ( ?[Xx:$i]: ( ( Xphi @ Xx ) & ( in @ Xx @ A ) ) ) =>
% 95.34/12.69 ( singleton @ ( dsetconstr @ A @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) ) ) ))).
% 95.34/12.69 thf('162', plain,
% 95.34/12.69 (( singletonprop ) =
% 95.34/12.69 ( ![X4:$i,X6:( $i > $o )]:
% 95.34/12.69 ( ( ![X8:$i]:
% 95.34/12.69 ( ( in @ X8 @ X4 ) =>
% 95.34/12.69 ( ![X10:$i]:
% 95.34/12.69 ( ( in @ X10 @ X4 ) =>
% 95.34/12.69 ( ( X6 @ X8 ) => ( ( X6 @ X10 ) => ( ( X8 ) = ( X10 ) ) ) ) ) ) ) ) =>
% 95.34/12.69 ( ( ?[X12:$i]: ( ( X6 @ X12 ) & ( in @ X12 @ X4 ) ) ) =>
% 95.34/12.69 ( singleton @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(setunionsingleton, axiom, setunionsingleton =
% 95.34/12.69 (![Xx:$i]: ( ( setunion @ ( setadjoin @ Xx @ emptyset ) ) = ( Xx ) ))).
% 95.34/12.69 thf('163', plain,
% 95.34/12.69 (( setunionsingleton ) =
% 95.34/12.69 ( ![X4:$i]: ( ( setunion @ ( setadjoin @ X4 @ emptyset ) ) = ( X4 ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(setunionsingleton2, axiom, setunionsingleton2 =
% 95.34/12.69 (![A:$i]: ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ))).
% 95.34/12.69 thf('164', plain,
% 95.34/12.69 (( setunionsingleton2 ) =
% 95.34/12.69 ( ![X4:$i]:
% 95.34/12.69 ( subset @ X4 @ ( setunion @ ( setadjoin @ X4 @ emptyset ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(setunionsingleton1, axiom, setunionsingleton1 =
% 95.34/12.69 (![A:$i]: ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ))).
% 95.34/12.69 thf('165', plain,
% 95.34/12.69 (( setunionsingleton1 ) =
% 95.34/12.69 ( ![X4:$i]:
% 95.34/12.69 ( subset @ ( setunion @ ( setadjoin @ X4 @ emptyset ) ) @ X4 ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(setunionE2, axiom, setunionE2 =
% 95.34/12.69 (![A:$i,Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ ( setunion @ A ) ) =>
% 95.34/12.69 ( ?[X:$i]: ( ( in @ Xx @ X ) & ( in @ X @ A ) ) ) ))).
% 95.34/12.69 thf('166', plain,
% 95.34/12.69 (( setunionE2 ) =
% 95.34/12.69 ( ![X4:$i,X6:$i]:
% 95.34/12.69 ( ( in @ X6 @ ( setunion @ X4 ) ) =>
% 95.34/12.69 ( ?[X8:$i]: ( ( in @ X6 @ X8 ) & ( in @ X8 @ X4 ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(cartprodmempair, axiom, cartprodmempair =
% 95.34/12.69 (![A:$i,B:$i,Xu:$i]:
% 95.34/12.69 ( ( in @ Xu @ ( cartprod @ A @ B ) ) => ( iskpair @ Xu ) ))).
% 95.34/12.69 thf('167', plain,
% 95.34/12.69 (( cartprodmempair ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( in @ X8 @ ( cartprod @ X4 @ X6 ) ) => ( iskpair @ X8 ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(cartprodmempair1, axiom, cartprodmempair1 =
% 95.34/12.69 (![A:$i,B:$i,Xu:$i]:
% 95.34/12.69 ( ( in @ Xu @ ( cartprod @ A @ B ) ) =>
% 95.34/12.69 ( ?[Xx:$i]:
% 95.34/12.69 ( ( ?[Xy:$i]: ( ( ( Xu ) = ( kpair @ Xx @ Xy ) ) & ( in @ Xy @ B ) ) ) &
% 95.34/12.69 ( in @ Xx @ A ) ) ) ))).
% 95.34/12.69 thf('168', plain,
% 95.34/12.69 (( cartprodmempair1 ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( in @ X8 @ ( cartprod @ X4 @ X6 ) ) =>
% 95.34/12.69 ( ?[X10:$i]:
% 95.34/12.69 ( ( ?[X12:$i]:
% 95.34/12.69 ( ( ( X8 ) = ( kpair @ X10 @ X12 ) ) & ( in @ X12 @ X6 ) ) ) &
% 95.34/12.69 ( in @ X10 @ X4 ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(cartprodpairin, axiom, cartprodpairin =
% 95.34/12.69 (![A:$i,B:$i,Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ A ) =>
% 95.34/12.69 ( ![Xy:$i]:
% 95.34/12.69 ( ( in @ Xy @ B ) =>
% 95.34/12.69 ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ))).
% 95.34/12.69 thf('169', plain,
% 95.34/12.69 (( cartprodpairin ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( in @ X8 @ X4 ) =>
% 95.34/12.69 ( ![X10:$i]:
% 95.34/12.69 ( ( in @ X10 @ X6 ) =>
% 95.34/12.69 ( in @ ( kpair @ X8 @ X10 ) @ ( cartprod @ X4 @ X6 ) ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(ubforcartprodlem3, axiom, ubforcartprodlem3 =
% 95.34/12.69 (![A:$i,B:$i,Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ A ) =>
% 95.34/12.69 ( ![Xy:$i]:
% 95.34/12.69 ( ( in @ Xy @ B ) =>
% 95.34/12.69 ( in @
% 95.34/12.69 ( kpair @ Xx @ Xy ) @
% 95.34/12.69 ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ))).
% 95.34/12.69 thf('170', plain,
% 95.34/12.69 (( ubforcartprodlem3 ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( in @ X8 @ X4 ) =>
% 95.34/12.69 ( ![X10:$i]:
% 95.34/12.69 ( ( in @ X10 @ X6 ) =>
% 95.34/12.69 ( in @
% 95.34/12.69 ( kpair @ X8 @ X10 ) @
% 95.34/12.69 ( powerset @ ( powerset @ ( binunion @ X4 @ X6 ) ) ) ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(ubforcartprodlem2, axiom, ubforcartprodlem2 =
% 95.34/12.69 (![A:$i,B:$i,Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ A ) =>
% 95.34/12.69 ( ![Xy:$i]:
% 95.34/12.69 ( ( in @ Xy @ B ) =>
% 95.34/12.69 ( in @
% 95.34/12.69 ( setadjoin @
% 95.34/12.69 ( setadjoin @ Xx @ emptyset ) @
% 95.34/12.69 ( setadjoin @
% 95.34/12.69 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @
% 95.34/12.69 ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ))).
% 95.34/12.69 thf('171', plain,
% 95.34/12.69 (( ubforcartprodlem2 ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( in @ X8 @ X4 ) =>
% 95.34/12.69 ( ![X10:$i]:
% 95.34/12.69 ( ( in @ X10 @ X6 ) =>
% 95.34/12.69 ( in @
% 95.34/12.69 ( setadjoin @
% 95.34/12.69 ( setadjoin @ X8 @ emptyset ) @
% 95.34/12.69 ( setadjoin @
% 95.34/12.69 ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @
% 95.34/12.69 emptyset ) ) @
% 95.34/12.69 ( powerset @ ( powerset @ ( binunion @ X4 @ X6 ) ) ) ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(ubforcartprodlem1, axiom, ubforcartprodlem1 =
% 95.34/12.69 (![A:$i,B:$i,Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ A ) =>
% 95.34/12.69 ( ![Xy:$i]:
% 95.34/12.69 ( ( in @ Xy @ B ) =>
% 95.34/12.69 ( subset @
% 95.34/12.69 ( setadjoin @
% 95.34/12.69 ( setadjoin @ Xx @ emptyset ) @
% 95.34/12.69 ( setadjoin @
% 95.34/12.69 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @
% 95.34/12.69 ( powerset @ ( binunion @ A @ B ) ) ) ) ) ))).
% 95.34/12.69 thf('172', plain,
% 95.34/12.69 (( ubforcartprodlem1 ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( in @ X8 @ X4 ) =>
% 95.34/12.69 ( ![X10:$i]:
% 95.34/12.69 ( ( in @ X10 @ X6 ) =>
% 95.34/12.69 ( subset @
% 95.34/12.69 ( setadjoin @
% 95.34/12.69 ( setadjoin @ X8 @ emptyset ) @
% 95.34/12.69 ( setadjoin @
% 95.34/12.69 ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @
% 95.34/12.69 emptyset ) ) @
% 95.34/12.69 ( powerset @ ( binunion @ X4 @ X6 ) ) ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(upairinpowunion, axiom, upairinpowunion =
% 95.34/12.69 (![A:$i,B:$i,Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ A ) =>
% 95.34/12.69 ( ![Xy:$i]:
% 95.34/12.69 ( ( in @ Xy @ B ) =>
% 95.34/12.69 ( in @
% 95.34/12.69 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @
% 95.34/12.69 ( powerset @ ( binunion @ A @ B ) ) ) ) ) ))).
% 95.34/12.69 thf('173', plain,
% 95.34/12.69 (( upairinpowunion ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( in @ X8 @ X4 ) =>
% 95.34/12.69 ( ![X10:$i]:
% 95.34/12.69 ( ( in @ X10 @ X6 ) =>
% 95.34/12.69 ( in @
% 95.34/12.69 ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @
% 95.34/12.69 ( powerset @ ( binunion @ X4 @ X6 ) ) ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(upairsubunion, axiom, upairsubunion =
% 95.34/12.69 (![A:$i,B:$i,Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ A ) =>
% 95.34/12.69 ( ![Xy:$i]:
% 95.34/12.69 ( ( in @ Xy @ B ) =>
% 95.34/12.69 ( subset @
% 95.34/12.69 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @
% 95.34/12.69 ( binunion @ A @ B ) ) ) ) ))).
% 95.34/12.69 thf('174', plain,
% 95.34/12.69 (( upairsubunion ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( in @ X8 @ X4 ) =>
% 95.34/12.69 ( ![X10:$i]:
% 95.34/12.69 ( ( in @ X10 @ X6 ) =>
% 95.34/12.69 ( subset @
% 95.34/12.69 ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @
% 95.34/12.69 ( binunion @ X4 @ X6 ) ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(upairset2E, axiom, upairset2E =
% 95.34/12.69 (![Xx:$i,Xy:$i,Xz:$i]:
% 95.34/12.69 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) =>
% 95.34/12.69 ( ( ( Xz ) = ( Xx ) ) | ( ( Xz ) = ( Xy ) ) ) ))).
% 95.34/12.69 thf('175', plain,
% 95.34/12.69 (( upairset2E ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( in @ X8 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) =>
% 95.34/12.69 ( ( ( X8 ) = ( X4 ) ) | ( ( X8 ) = ( X6 ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(singletoninpowunion, axiom, singletoninpowunion =
% 95.34/12.69 (![A:$i,B:$i,Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ A ) =>
% 95.34/12.69 ( in @
% 95.34/12.69 ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ))).
% 95.34/12.69 thf('176', plain,
% 95.34/12.69 (( singletoninpowunion ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( in @ X8 @ X4 ) =>
% 95.34/12.69 ( in @
% 95.34/12.69 ( setadjoin @ X8 @ emptyset ) @
% 95.34/12.69 ( powerset @ ( binunion @ X4 @ X6 ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(singletoninpowerset, axiom, singletoninpowerset =
% 95.34/12.69 (![A:$i,Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ A ) =>
% 95.34/12.69 ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ))).
% 95.34/12.69 thf('177', plain,
% 95.34/12.69 (( singletoninpowerset ) =
% 95.34/12.69 ( ![X4:$i,X6:$i]:
% 95.34/12.69 ( ( in @ X6 @ X4 ) =>
% 95.34/12.69 ( in @ ( setadjoin @ X6 @ emptyset ) @ ( powerset @ X4 ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(singletonsubset, axiom, singletonsubset =
% 95.34/12.69 (![A:$i,Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ A ) => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ))).
% 95.34/12.69 thf('178', plain,
% 95.34/12.69 (( singletonsubset ) =
% 95.34/12.69 ( ![X4:$i,X6:$i]:
% 95.34/12.69 ( ( in @ X6 @ X4 ) => ( subset @ ( setadjoin @ X6 @ emptyset ) @ X4 ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(kpairp, axiom, kpairp =
% 95.34/12.69 (![Xx:$i,Xy:$i]: ( iskpair @ ( kpair @ Xx @ Xy ) ))).
% 95.34/12.69 thf('179', plain,
% 95.34/12.69 (( kpairp ) = ( ![X4:$i,X6:$i]: ( iskpair @ ( kpair @ X4 @ X6 ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(kpairiskpair, axiom, kpairiskpair =
% 95.34/12.69 (![Xx:$i,Xy:$i]:
% 95.34/12.69 ( iskpair @
% 95.34/12.69 ( setadjoin @
% 95.34/12.69 ( setadjoin @ Xx @ emptyset ) @
% 95.34/12.69 ( setadjoin @
% 95.34/12.69 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ))).
% 95.34/12.69 thf('180', plain,
% 95.34/12.69 (( kpairiskpair ) =
% 95.34/12.69 ( ![X4:$i,X6:$i]:
% 95.34/12.69 ( iskpair @
% 95.34/12.69 ( setadjoin @
% 95.34/12.69 ( setadjoin @ X4 @ emptyset ) @
% 95.34/12.69 ( setadjoin @
% 95.34/12.69 ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) @ emptyset ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(setukpairIR, axiom, setukpairIR =
% 95.34/12.69 (![Xx:$i,Xy:$i]:
% 95.34/12.69 ( in @
% 95.34/12.69 Xy @
% 95.34/12.69 ( setunion @
% 95.34/12.69 ( setadjoin @
% 95.34/12.69 ( setadjoin @ Xx @ emptyset ) @
% 95.34/12.69 ( setadjoin @
% 95.34/12.69 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ))).
% 95.34/12.69 thf('181', plain,
% 95.34/12.69 (( setukpairIR ) =
% 95.34/12.69 ( ![X4:$i,X6:$i]:
% 95.34/12.69 ( in @
% 95.34/12.69 X6 @
% 95.34/12.69 ( setunion @
% 95.34/12.69 ( setadjoin @
% 95.34/12.69 ( setadjoin @ X4 @ emptyset ) @
% 95.34/12.69 ( setadjoin @
% 95.34/12.69 ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) @ emptyset ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(setukpairIL, axiom, setukpairIL =
% 95.34/12.69 (![Xx:$i,Xy:$i]:
% 95.34/12.69 ( in @
% 95.34/12.69 Xx @
% 95.34/12.69 ( setunion @
% 95.34/12.69 ( setadjoin @
% 95.34/12.69 ( setadjoin @ Xx @ emptyset ) @
% 95.34/12.69 ( setadjoin @
% 95.34/12.69 ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ))).
% 95.34/12.69 thf('182', plain,
% 95.34/12.69 (( setukpairIL ) =
% 95.34/12.69 ( ![X4:$i,X6:$i]:
% 95.34/12.69 ( in @
% 95.34/12.69 X4 @
% 95.34/12.69 ( setunion @
% 95.34/12.69 ( setadjoin @
% 95.34/12.69 ( setadjoin @ X4 @ emptyset ) @
% 95.34/12.69 ( setadjoin @
% 95.34/12.69 ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) @ emptyset ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(secondinupair, axiom, secondinupair =
% 95.34/12.69 (![Xx:$i,Xy:$i]:
% 95.34/12.69 ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 95.34/12.69 thf('183', plain,
% 95.34/12.69 (( secondinupair ) =
% 95.34/12.69 ( ![X4:$i,X6:$i]:
% 95.34/12.69 ( in @ X6 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(symdiffIneg2, axiom, symdiffIneg2 =
% 95.34/12.69 (![A:$i,B:$i,Xx:$i]:
% 95.34/12.69 ( ( ~( in @ Xx @ A ) ) =>
% 95.34/12.69 ( ( ~( in @ Xx @ B ) ) => ( ~( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ))).
% 95.34/12.69 thf('184', plain,
% 95.34/12.69 (( symdiffIneg2 ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( ~( in @ X8 @ X4 ) ) =>
% 95.34/12.69 ( ( ~( in @ X8 @ X6 ) ) => ( ~( in @ X8 @ ( symdiff @ X4 @ X6 ) ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(symdiffIneg1, axiom, symdiffIneg1 =
% 95.34/12.69 (![A:$i,B:$i,Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ A ) =>
% 95.34/12.69 ( ( in @ Xx @ B ) => ( ~( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ))).
% 95.34/12.69 thf('185', plain,
% 95.34/12.69 (( symdiffIneg1 ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( in @ X8 @ X4 ) =>
% 95.34/12.69 ( ( in @ X8 @ X6 ) => ( ~( in @ X8 @ ( symdiff @ X4 @ X6 ) ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(symdiffI2, axiom, symdiffI2 =
% 95.34/12.69 (![A:$i,B:$i,Xx:$i]:
% 95.34/12.69 ( ( ~( in @ Xx @ A ) ) =>
% 95.34/12.69 ( ( in @ Xx @ B ) => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ))).
% 95.34/12.69 thf('186', plain,
% 95.34/12.69 (( symdiffI2 ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( ~( in @ X8 @ X4 ) ) =>
% 95.34/12.69 ( ( in @ X8 @ X6 ) => ( in @ X8 @ ( symdiff @ X4 @ X6 ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(symdiffI1, axiom, symdiffI1 =
% 95.34/12.69 (![A:$i,B:$i,Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ A ) =>
% 95.34/12.69 ( ( ~( in @ Xx @ B ) ) => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ))).
% 95.34/12.69 thf('187', plain,
% 95.34/12.69 (( symdiffI1 ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( in @ X8 @ X4 ) =>
% 95.34/12.69 ( ( ~( in @ X8 @ X6 ) ) => ( in @ X8 @ ( symdiff @ X4 @ X6 ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(symdiffE, axiom, symdiffE =
% 95.34/12.69 (![A:$i,B:$i,Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ ( symdiff @ A @ B ) ) =>
% 95.34/12.69 ( ![Xphi:$o]:
% 95.34/12.69 ( ( ( in @ Xx @ A ) => ( ( ~( in @ Xx @ B ) ) => ( Xphi ) ) ) =>
% 95.34/12.69 ( ( ( ~( in @ Xx @ A ) ) => ( ( in @ Xx @ B ) => ( Xphi ) ) ) =>
% 95.34/12.69 ( Xphi ) ) ) ) ))).
% 95.34/12.69 thf('188', plain,
% 95.34/12.69 (( symdiffE ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( in @ X8 @ ( symdiff @ X4 @ X6 ) ) =>
% 95.34/12.69 ( ![X10:$o]:
% 95.34/12.69 ( ( ( in @ X8 @ X4 ) => ( ( ~( in @ X8 @ X6 ) ) => ( X10 ) ) ) =>
% 95.34/12.69 ( ( ( ~( in @ X8 @ X4 ) ) => ( ( in @ X8 @ X6 ) => ( X10 ) ) ) =>
% 95.34/12.69 ( X10 ) ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(setminusSubset1, axiom, setminusSubset1 =
% 95.34/12.69 (![A:$i,B:$i]:
% 95.34/12.69 ( ( ( setminus @ A @ B ) = ( emptyset ) ) => ( subset @ A @ B ) ))).
% 95.34/12.69 thf('189', plain,
% 95.34/12.69 (( setminusSubset1 ) =
% 95.34/12.69 ( ![X4:$i,X6:$i]:
% 95.34/12.69 ( ( ( setminus @ X4 @ X6 ) = ( emptyset ) ) => ( subset @ X4 @ X6 ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(setminusLsub, axiom, setminusLsub =
% 95.34/12.69 (![A:$i,B:$i]: ( subset @ ( setminus @ A @ B ) @ A ))).
% 95.34/12.69 thf('190', plain,
% 95.34/12.69 (( setminusLsub ) =
% 95.34/12.69 ( ![X4:$i,X6:$i]: ( subset @ ( setminus @ X4 @ X6 ) @ X4 ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(setminusIRneg, axiom, setminusIRneg =
% 95.34/12.69 (![A:$i,B:$i,Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ B ) => ( ~( in @ Xx @ ( setminus @ A @ B ) ) ) ))).
% 95.34/12.69 thf('191', plain,
% 95.34/12.69 (( setminusIRneg ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( in @ X8 @ X6 ) => ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(setminusILneg, axiom, setminusILneg =
% 95.34/12.69 (![A:$i,B:$i,Xx:$i]:
% 95.34/12.69 ( ( ~( in @ Xx @ A ) ) => ( ~( in @ Xx @ ( setminus @ A @ B ) ) ) ))).
% 95.34/12.69 thf('192', plain,
% 95.34/12.69 (( setminusILneg ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( ~( in @ X8 @ X4 ) ) => ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(setminusELneg, axiom, setminusELneg =
% 95.34/12.69 (![A:$i,B:$i,Xx:$i]:
% 95.34/12.69 ( ( ~( in @ Xx @ ( setminus @ A @ B ) ) ) =>
% 95.34/12.69 ( ( ~( in @ Xx @ B ) ) => ( ~( in @ Xx @ A ) ) ) ))).
% 95.34/12.69 thf('193', plain,
% 95.34/12.69 (( setminusELneg ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) =>
% 95.34/12.69 ( ( ~( in @ X8 @ X6 ) ) => ( ~( in @ X8 @ X4 ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(setminusERneg, axiom, setminusERneg =
% 95.34/12.69 (![A:$i,B:$i,Xx:$i]:
% 95.34/12.69 ( ( ~( in @ Xx @ ( setminus @ A @ B ) ) ) =>
% 95.34/12.69 ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ))).
% 95.34/12.69 thf('194', plain,
% 95.34/12.69 (( setminusERneg ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( ~( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) =>
% 95.34/12.69 ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(setminusSubset2, axiom, setminusSubset2 =
% 95.34/12.69 (![A:$i,B:$i]:
% 95.34/12.69 ( ( subset @ A @ B ) => ( ( setminus @ A @ B ) = ( emptyset ) ) ))).
% 95.34/12.69 thf('195', plain,
% 95.34/12.69 (( setminusSubset2 ) =
% 95.34/12.69 ( ![X4:$i,X6:$i]:
% 95.34/12.69 ( ( subset @ X4 @ X6 ) => ( ( setminus @ X4 @ X6 ) = ( emptyset ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(setminusER, axiom, setminusER =
% 95.34/12.69 (![A:$i,B:$i,Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ ( setminus @ A @ B ) ) => ( ~( in @ Xx @ B ) ) ))).
% 95.34/12.69 thf('196', plain,
% 95.34/12.69 (( setminusER ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( in @ X8 @ ( setminus @ X4 @ X6 ) ) => ( ~( in @ X8 @ X6 ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(setminusEL, axiom, setminusEL =
% 95.34/12.69 (![A:$i,B:$i,Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ ( setminus @ A @ B ) ) => ( in @ Xx @ A ) ))).
% 95.34/12.69 thf('197', plain,
% 95.34/12.69 (( setminusEL ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( in @ X8 @ ( setminus @ X4 @ X6 ) ) => ( in @ X8 @ X4 ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(setminusI, axiom, setminusI =
% 95.34/12.69 (![A:$i,B:$i,Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ A ) =>
% 95.34/12.69 ( ( ~( in @ Xx @ B ) ) => ( in @ Xx @ ( setminus @ A @ B ) ) ) ))).
% 95.34/12.69 thf('198', plain,
% 95.34/12.69 (( setminusI ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( in @ X8 @ X4 ) =>
% 95.34/12.69 ( ( ~( in @ X8 @ X6 ) ) => ( in @ X8 @ ( setminus @ X4 @ X6 ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(bs114d, axiom, bs114d =
% 95.34/12.69 (![A:$i,B:$i,C:$i]:
% 95.34/12.69 ( ( binintersect @ A @ ( binunion @ B @ C ) ) =
% 95.34/12.69 ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ))).
% 95.34/12.69 thf('199', plain,
% 95.34/12.69 (( bs114d ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( binintersect @ X4 @ ( binunion @ X6 @ X8 ) ) =
% 95.34/12.69 ( binunion @ ( binintersect @ X4 @ X6 ) @ ( binintersect @ X4 @ X8 ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(binintersectSubset1, axiom, binintersectSubset1 =
% 95.34/12.69 (![A:$i,B:$i]:
% 95.34/12.69 ( ( ( binintersect @ A @ B ) = ( A ) ) => ( subset @ A @ B ) ))).
% 95.34/12.69 thf('200', plain,
% 95.34/12.69 (( binintersectSubset1 ) =
% 95.34/12.69 ( ![X4:$i,X6:$i]:
% 95.34/12.69 ( ( ( binintersect @ X4 @ X6 ) = ( X4 ) ) => ( subset @ X4 @ X6 ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(binintersectSubset4, axiom, binintersectSubset4 =
% 95.34/12.69 (![A:$i,B:$i]:
% 95.34/12.69 ( ( subset @ B @ A ) => ( ( binintersect @ A @ B ) = ( B ) ) ))).
% 95.34/12.69 thf('201', plain,
% 95.34/12.69 (( binintersectSubset4 ) =
% 95.34/12.69 ( ![X4:$i,X6:$i]:
% 95.34/12.69 ( ( subset @ X6 @ X4 ) => ( ( binintersect @ X4 @ X6 ) = ( X6 ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(binintersectRsub, axiom, binintersectRsub =
% 95.34/12.69 (![A:$i,B:$i]: ( subset @ ( binintersect @ A @ B ) @ B ))).
% 95.34/12.69 thf('202', plain,
% 95.34/12.69 (( binintersectRsub ) =
% 95.34/12.69 ( ![X4:$i,X6:$i]: ( subset @ ( binintersect @ X4 @ X6 ) @ X6 ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(disjointsetsI1, axiom, disjointsetsI1 =
% 95.34/12.69 (![A:$i,B:$i]:
% 95.34/12.69 ( ( ~( ?[Xx:$i]: ( ( in @ Xx @ B ) & ( in @ Xx @ A ) ) ) ) =>
% 95.34/12.69 ( ( binintersect @ A @ B ) = ( emptyset ) ) ))).
% 95.34/12.69 thf('203', plain,
% 95.34/12.69 (( disjointsetsI1 ) =
% 95.34/12.69 ( ![X4:$i,X6:$i]:
% 95.34/12.69 ( ( ~( ?[X8:$i]: ( ( in @ X8 @ X6 ) & ( in @ X8 @ X4 ) ) ) ) =>
% 95.34/12.69 ( ( binintersect @ X4 @ X6 ) = ( emptyset ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(binintersectER, axiom, binintersectER =
% 95.34/12.69 (![A:$i,B:$i,Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ ( binintersect @ A @ B ) ) => ( in @ Xx @ B ) ))).
% 95.34/12.69 thf('204', plain,
% 95.34/12.69 (( binintersectER ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( in @ X8 @ ( binintersect @ X4 @ X6 ) ) => ( in @ X8 @ X6 ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(binintersectSubset3, axiom, binintersectSubset3 =
% 95.34/12.69 (![A:$i,B:$i]:
% 95.34/12.69 ( ( ( binintersect @ A @ B ) = ( B ) ) => ( subset @ B @ A ) ))).
% 95.34/12.69 thf('205', plain,
% 95.34/12.69 (( binintersectSubset3 ) =
% 95.34/12.69 ( ![X4:$i,X6:$i]:
% 95.34/12.69 ( ( ( binintersect @ X4 @ X6 ) = ( X6 ) ) => ( subset @ X6 @ X4 ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(binintersectSubset2, axiom, binintersectSubset2 =
% 95.34/12.69 (![A:$i,B:$i]:
% 95.34/12.69 ( ( subset @ A @ B ) => ( ( binintersect @ A @ B ) = ( A ) ) ))).
% 95.34/12.69 thf('206', plain,
% 95.34/12.69 (( binintersectSubset2 ) =
% 95.34/12.69 ( ![X4:$i,X6:$i]:
% 95.34/12.69 ( ( subset @ X4 @ X6 ) => ( ( binintersect @ X4 @ X6 ) = ( X4 ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(binintersectLsub, axiom, binintersectLsub =
% 95.34/12.69 (![A:$i,B:$i]: ( subset @ ( binintersect @ A @ B ) @ A ))).
% 95.34/12.69 thf('207', plain,
% 95.34/12.69 (( binintersectLsub ) =
% 95.34/12.69 ( ![X4:$i,X6:$i]: ( subset @ ( binintersect @ X4 @ X6 ) @ X4 ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(binintersectEL, axiom, binintersectEL =
% 95.34/12.69 (![A:$i,B:$i,Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ ( binintersect @ A @ B ) ) => ( in @ Xx @ A ) ))).
% 95.34/12.69 thf('208', plain,
% 95.34/12.69 (( binintersectEL ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( in @ X8 @ ( binintersect @ X4 @ X6 ) ) => ( in @ X8 @ X4 ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(binintersectSubset5, axiom, binintersectSubset5 =
% 95.34/12.69 (![A:$i,B:$i,C:$i]:
% 95.34/12.69 ( ( subset @ C @ A ) =>
% 95.34/12.69 ( ( subset @ C @ B ) => ( subset @ C @ ( binintersect @ A @ B ) ) ) ))).
% 95.34/12.69 thf('209', plain,
% 95.34/12.69 (( binintersectSubset5 ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( subset @ X8 @ X4 ) =>
% 95.34/12.69 ( ( subset @ X8 @ X6 ) =>
% 95.34/12.69 ( subset @ X8 @ ( binintersect @ X4 @ X6 ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(binintersectI, axiom, binintersectI =
% 95.34/12.69 (![A:$i,B:$i,Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ A ) =>
% 95.34/12.69 ( ( in @ Xx @ B ) => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ))).
% 95.34/12.69 thf('210', plain,
% 95.34/12.69 (( binintersectI ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( in @ X8 @ X4 ) =>
% 95.34/12.69 ( ( in @ X8 @ X6 ) => ( in @ X8 @ ( binintersect @ X4 @ X6 ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(binunionRsub, axiom, binunionRsub =
% 95.34/12.69 (![A:$i,B:$i]: ( subset @ B @ ( binunion @ A @ B ) ))).
% 95.34/12.69 thf('211', plain,
% 95.34/12.69 (( binunionRsub ) =
% 95.34/12.69 ( ![X4:$i,X6:$i]: ( subset @ X6 @ ( binunion @ X4 @ X6 ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(binunionLsub, axiom, binunionLsub =
% 95.34/12.69 (![A:$i,B:$i]: ( subset @ A @ ( binunion @ A @ B ) ))).
% 95.34/12.69 thf('212', plain,
% 95.34/12.69 (( binunionLsub ) =
% 95.34/12.69 ( ![X4:$i,X6:$i]: ( subset @ X4 @ ( binunion @ X4 @ X6 ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(binunionE, axiom, binunionE =
% 95.34/12.69 (![A:$i,B:$i,Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ ( binunion @ A @ B ) ) =>
% 95.34/12.69 ( ( in @ Xx @ A ) | ( in @ Xx @ B ) ) ))).
% 95.34/12.69 thf('213', plain,
% 95.34/12.69 (( binunionE ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( in @ X8 @ ( binunion @ X4 @ X6 ) ) =>
% 95.34/12.69 ( ( in @ X8 @ X4 ) | ( in @ X8 @ X6 ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(binunionEcases, axiom, binunionEcases =
% 95.34/12.69 (![A:$i,B:$i,Xx:$i,Xphi:$o]:
% 95.34/12.69 ( ( in @ Xx @ ( binunion @ A @ B ) ) =>
% 95.34/12.69 ( ( ( in @ Xx @ A ) => ( Xphi ) ) =>
% 95.34/12.69 ( ( ( in @ Xx @ B ) => ( Xphi ) ) => ( Xphi ) ) ) ))).
% 95.34/12.69 thf('214', plain,
% 95.34/12.69 (( binunionEcases ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i,X10:$o]:
% 95.34/12.69 ( ( in @ X8 @ ( binunion @ X4 @ X6 ) ) =>
% 95.34/12.69 ( ( ( in @ X8 @ X4 ) => ( X10 ) ) =>
% 95.34/12.69 ( ( ( in @ X8 @ X6 ) => ( X10 ) ) => ( X10 ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(binunionIR, axiom, binunionIR =
% 95.34/12.69 (![A:$i,B:$i,Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ B ) => ( in @ Xx @ ( binunion @ A @ B ) ) ))).
% 95.34/12.69 thf('215', plain,
% 95.34/12.69 (( binunionIR ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( in @ X8 @ X6 ) => ( in @ X8 @ ( binunion @ X4 @ X6 ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(upairset2IR, axiom, upairset2IR =
% 95.34/12.69 (![Xx:$i,Xy:$i]:
% 95.34/12.69 ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 95.34/12.69 thf('216', plain,
% 95.34/12.69 (( upairset2IR ) =
% 95.34/12.69 ( ![X4:$i,X6:$i]:
% 95.34/12.69 ( in @ X6 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(binunionIL, axiom, binunionIL =
% 95.34/12.69 (![A:$i,B:$i,Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ A ) => ( in @ Xx @ ( binunion @ A @ B ) ) ))).
% 95.34/12.69 thf('217', plain,
% 95.34/12.69 (( binunionIL ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( in @ X8 @ X4 ) => ( in @ X8 @ ( binunion @ X4 @ X6 ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(sepSubset, axiom, sepSubset =
% 95.34/12.69 (![A:$i,Xphi:( $i > $o )]:
% 95.34/12.69 ( subset @ ( dsetconstr @ A @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) @ A ))).
% 95.34/12.69 thf('218', plain,
% 95.34/12.69 (( sepSubset ) =
% 95.34/12.69 ( ![X4:$i,X6:( $i > $o )]:
% 95.34/12.69 ( subset @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) @ X4 ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(sepInPowerset, axiom, sepInPowerset =
% 95.34/12.69 (![A:$i,Xphi:( $i > $o )]:
% 95.34/12.69 ( in @ ( dsetconstr @ A @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) @ ( powerset @ A ) ))).
% 95.34/12.69 thf('219', plain,
% 95.34/12.69 (( sepInPowerset ) =
% 95.34/12.69 ( ![X4:$i,X6:( $i > $o )]:
% 95.34/12.69 ( in @
% 95.34/12.69 ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) @
% 95.34/12.69 ( powerset @ X4 ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(powersetsubset, axiom, powersetsubset =
% 95.34/12.69 (![A:$i,B:$i]:
% 95.34/12.69 ( ( subset @ A @ B ) => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ))).
% 95.34/12.69 thf('220', plain,
% 95.34/12.69 (( powersetsubset ) =
% 95.34/12.69 ( ![X4:$i,X6:$i]:
% 95.34/12.69 ( ( subset @ X4 @ X6 ) =>
% 95.34/12.69 ( subset @ ( powerset @ X4 ) @ ( powerset @ X6 ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(inPowerset, axiom, inPowerset = (![A:$i]: ( in @ A @ ( powerset @ A ) ))).
% 95.34/12.69 thf('221', plain,
% 95.34/12.69 (( inPowerset ) = ( ![X4:$i]: ( in @ X4 @ ( powerset @ X4 ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(powersetE1, axiom, powersetE1 =
% 95.34/12.69 (![A:$i,B:$i]: ( ( in @ B @ ( powerset @ A ) ) => ( subset @ B @ A ) ))).
% 95.34/12.69 thf('222', plain,
% 95.34/12.69 (( powersetE1 ) =
% 95.34/12.69 ( ![X4:$i,X6:$i]:
% 95.34/12.69 ( ( in @ X6 @ ( powerset @ X4 ) ) => ( subset @ X6 @ X4 ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(powersetI1, axiom, powersetI1 =
% 95.34/12.69 (![A:$i,B:$i]: ( ( subset @ B @ A ) => ( in @ B @ ( powerset @ A ) ) ))).
% 95.34/12.69 thf('223', plain,
% 95.34/12.69 (( powersetI1 ) =
% 95.34/12.69 ( ![X4:$i,X6:$i]:
% 95.34/12.69 ( ( subset @ X6 @ X4 ) => ( in @ X6 @ ( powerset @ X4 ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(subsetemptysetimpeq, axiom, subsetemptysetimpeq =
% 95.34/12.69 (![A:$i]: ( ( subset @ A @ emptyset ) => ( ( A ) = ( emptyset ) ) ))).
% 95.34/12.69 thf('224', plain,
% 95.34/12.69 (( subsetemptysetimpeq ) =
% 95.34/12.69 ( ![X4:$i]: ( ( subset @ X4 @ emptyset ) => ( ( X4 ) = ( emptyset ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(setextsub, axiom, setextsub =
% 95.34/12.69 (![A:$i,B:$i]:
% 95.34/12.69 ( ( subset @ A @ B ) => ( ( subset @ B @ A ) => ( ( A ) = ( B ) ) ) ))).
% 95.34/12.69 thf('225', plain,
% 95.34/12.69 (( setextsub ) =
% 95.34/12.69 ( ![X4:$i,X6:$i]:
% 95.34/12.69 ( ( subset @ X4 @ X6 ) =>
% 95.34/12.69 ( ( subset @ X6 @ X4 ) => ( ( X4 ) = ( X6 ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(subset2powerset, axiom, subset2powerset =
% 95.34/12.69 (![A:$i,B:$i]: ( ( subset @ A @ B ) => ( in @ A @ ( powerset @ B ) ) ))).
% 95.34/12.69 thf('226', plain,
% 95.34/12.69 (( subset2powerset ) =
% 95.34/12.69 ( ![X4:$i,X6:$i]:
% 95.34/12.69 ( ( subset @ X4 @ X6 ) => ( in @ X4 @ ( powerset @ X6 ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(setadjoinSub2, axiom, setadjoinSub2 =
% 95.34/12.69 (![A:$i,Xx:$i,B:$i]:
% 95.34/12.69 ( ( subset @ A @ B ) => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ))).
% 95.34/12.69 thf('227', plain,
% 95.34/12.69 (( setadjoinSub2 ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( subset @ X4 @ X8 ) => ( subset @ X4 @ ( setadjoin @ X6 @ X8 ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(setadjoinSub, axiom, setadjoinSub =
% 95.34/12.69 (![Xx:$i,A:$i]: ( subset @ A @ ( setadjoin @ Xx @ A ) ))).
% 95.34/12.69 thf('228', plain,
% 95.34/12.69 (( setadjoinSub ) =
% 95.34/12.69 ( ![X4:$i,X6:$i]: ( subset @ X6 @ ( setadjoin @ X4 @ X6 ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(subsetTrans, axiom, subsetTrans =
% 95.34/12.69 (![A:$i,B:$i,C:$i]:
% 95.34/12.69 ( ( subset @ A @ B ) => ( ( subset @ B @ C ) => ( subset @ A @ C ) ) ))).
% 95.34/12.69 thf('229', plain,
% 95.34/12.69 (( subsetTrans ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( subset @ X4 @ X6 ) =>
% 95.34/12.69 ( ( subset @ X6 @ X8 ) => ( subset @ X4 @ X8 ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(subsetRefl, axiom, subsetRefl = (![A:$i]: ( subset @ A @ A ))).
% 95.34/12.69 thf('230', plain, (( subsetRefl ) = ( ![X4:$i]: ( subset @ X4 @ X4 ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(notequalI2, axiom, notequalI2 =
% 95.34/12.69 (![A:$i,B:$i,Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ A ) => ( ( ~( in @ Xx @ B ) ) => ( ( A ) != ( B ) ) ) ))).
% 95.34/12.69 thf('231', plain,
% 95.34/12.69 (( notequalI2 ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( in @ X8 @ X4 ) =>
% 95.34/12.69 ( ( ~( in @ X8 @ X6 ) ) => ( ( X4 ) != ( X6 ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(notequalI1, axiom, notequalI1 =
% 95.34/12.69 (![A:$i,B:$i]: ( ( ~( subset @ A @ B ) ) => ( ( A ) != ( B ) ) ))).
% 95.34/12.69 thf('232', plain,
% 95.34/12.69 (( notequalI1 ) =
% 95.34/12.69 ( ![X4:$i,X6:$i]: ( ( ~( subset @ X4 @ X6 ) ) => ( ( X4 ) != ( X6 ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(notsubsetI, axiom, notsubsetI =
% 95.34/12.69 (![A:$i,B:$i,Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ A ) => ( ( ~( in @ Xx @ B ) ) => ( ~( subset @ A @ B ) ) ) ))).
% 95.34/12.69 thf('233', plain,
% 95.34/12.69 (( notsubsetI ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( in @ X8 @ X4 ) =>
% 95.34/12.69 ( ( ~( in @ X8 @ X6 ) ) => ( ~( subset @ X4 @ X6 ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(subsetE2, axiom, subsetE2 =
% 95.34/12.69 (![A:$i,B:$i,Xx:$i]:
% 95.34/12.69 ( ( subset @ A @ B ) => ( ( ~( in @ Xx @ B ) ) => ( ~( in @ Xx @ A ) ) ) ))).
% 95.34/12.69 thf('234', plain,
% 95.34/12.69 (( subsetE2 ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( subset @ X4 @ X6 ) =>
% 95.34/12.69 ( ( ~( in @ X8 @ X6 ) ) => ( ~( in @ X8 @ X4 ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(subsetE, axiom, subsetE =
% 95.34/12.69 (![A:$i,B:$i,Xx:$i]:
% 95.34/12.69 ( ( subset @ A @ B ) => ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ))).
% 95.34/12.69 thf('235', plain,
% 95.34/12.69 (( subsetE ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( subset @ X4 @ X6 ) => ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(emptysetsubset, axiom, emptysetsubset =
% 95.34/12.69 (![A:$i]: ( subset @ emptyset @ A ))).
% 95.34/12.69 thf('236', plain,
% 95.34/12.69 (( emptysetsubset ) = ( ![X4:$i]: ( subset @ emptyset @ X4 ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(subsetI2, axiom, subsetI2 =
% 95.34/12.69 (![A:$i,B:$i]:
% 95.34/12.69 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ) =>
% 95.34/12.69 ( subset @ A @ B ) ))).
% 95.34/12.69 thf('237', plain,
% 95.34/12.69 (( subsetI2 ) =
% 95.34/12.69 ( ![X4:$i,X6:$i]:
% 95.34/12.69 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) =>
% 95.34/12.69 ( subset @ X4 @ X6 ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(eqimpsubset1, axiom, eqimpsubset1 =
% 95.34/12.69 (![A:$i,B:$i]: ( ( ( A ) = ( B ) ) => ( subset @ A @ B ) ))).
% 95.34/12.69 thf('238', plain,
% 95.34/12.69 (( eqimpsubset1 ) =
% 95.34/12.69 ( ![X4:$i,X6:$i]: ( ( ( X4 ) = ( X6 ) ) => ( subset @ X4 @ X6 ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(eqimpsubset2, axiom, eqimpsubset2 =
% 95.34/12.69 (![A:$i,B:$i]: ( ( ( A ) = ( B ) ) => ( subset @ B @ A ) ))).
% 95.34/12.69 thf('239', plain,
% 95.34/12.69 (( eqimpsubset2 ) =
% 95.34/12.69 ( ![X4:$i,X6:$i]: ( ( ( X4 ) = ( X6 ) ) => ( subset @ X6 @ X4 ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(subsetI1, axiom, subsetI1 =
% 95.34/12.69 (![A:$i,B:$i]:
% 95.34/12.69 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ) =>
% 95.34/12.69 ( subset @ A @ B ) ))).
% 95.34/12.69 thf('240', plain,
% 95.34/12.69 (( subsetI1 ) =
% 95.34/12.69 ( ![X4:$i,X6:$i]:
% 95.34/12.69 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) =>
% 95.34/12.69 ( subset @ X4 @ X6 ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(dsetconstr__Cong, axiom, dsetconstr__Cong =
% 95.34/12.69 (![A:$i,B:$i]:
% 95.34/12.69 ( ( ( A ) = ( B ) ) =>
% 95.34/12.69 ( ![Xphi:( $i > $o ),Xpsi:( $i > $o )]:
% 95.34/12.69 ( ( ![Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ A ) =>
% 95.34/12.69 ( ![Xy:$i]:
% 95.34/12.69 ( ( in @ Xy @ B ) =>
% 95.34/12.69 ( ( ( Xx ) = ( Xy ) ) => ( ( Xphi @ Xx ) <=> ( Xpsi @ Xy ) ) ) ) ) ) ) =>
% 95.34/12.69 ( ( dsetconstr @ A @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) =
% 95.34/12.69 ( dsetconstr @ B @ ( ^[Xx:$i]: ( Xpsi @ Xx ) ) ) ) ) ) ))).
% 95.34/12.69 thf('241', plain,
% 95.34/12.69 (( dsetconstr__Cong ) =
% 95.34/12.69 ( ![X4:$i,X6:$i]:
% 95.34/12.69 ( ( ( X4 ) = ( X6 ) ) =>
% 95.34/12.69 ( ![X8:( $i > $o ),X10:( $i > $o )]:
% 95.34/12.69 ( ( ![X12:$i]:
% 95.34/12.69 ( ( in @ X12 @ X4 ) =>
% 95.34/12.69 ( ![X14:$i]:
% 95.34/12.69 ( ( in @ X14 @ X6 ) =>
% 95.34/12.69 ( ( ( X12 ) = ( X14 ) ) =>
% 95.34/12.69 ( ( X8 @ X12 ) <=> ( X10 @ X14 ) ) ) ) ) ) ) =>
% 95.34/12.69 ( ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X8 @ V_1 ) ) ) =
% 95.34/12.69 ( dsetconstr @ X6 @ ( ^[V_2:$i]: ( X10 @ V_2 ) ) ) ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(descr__Cong, axiom, descr__Cong =
% 95.34/12.69 (![Xphi:( $i > $o ),Xpsi:( $i > $o )]:
% 95.34/12.69 ( ( ![Xx:$i,Xy:$i]:
% 95.34/12.69 ( ( ( Xx ) = ( Xy ) ) => ( ( Xphi @ Xx ) <=> ( Xpsi @ Xy ) ) ) ) =>
% 95.34/12.69 ( ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) =>
% 95.34/12.69 ( ( exu @ ( ^[Xx:$i]: ( Xpsi @ Xx ) ) ) =>
% 95.34/12.69 ( ( descr @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) =
% 95.34/12.69 ( descr @ ( ^[Xx:$i]: ( Xpsi @ Xx ) ) ) ) ) ) ))).
% 95.34/12.69 thf('242', plain,
% 95.34/12.69 (( descr__Cong ) =
% 95.34/12.69 ( ![X4:( $i > $o ),X6:( $i > $o )]:
% 95.34/12.69 ( ( ![X8:$i,X10:$i]:
% 95.34/12.69 ( ( ( X8 ) = ( X10 ) ) => ( ( X4 @ X8 ) <=> ( X6 @ X10 ) ) ) ) =>
% 95.34/12.69 ( ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) =>
% 95.34/12.69 ( ( exu @ ( ^[V_2:$i]: ( X6 @ V_2 ) ) ) =>
% 95.34/12.69 ( ( descr @ ( ^[V_3:$i]: ( X4 @ V_3 ) ) ) =
% 95.34/12.69 ( descr @ ( ^[V_4:$i]: ( X6 @ V_4 ) ) ) ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(exuEu, axiom, exuEu =
% 95.34/12.69 (![Xphi:( $i > $o )]:
% 95.34/12.69 ( ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) =>
% 95.34/12.69 ( ![Xx:$i,Xy:$i]:
% 95.34/12.69 ( ( Xphi @ Xx ) => ( ( Xphi @ Xy ) => ( ( Xx ) = ( Xy ) ) ) ) ) ))).
% 95.34/12.69 thf('243', plain,
% 95.34/12.69 (( exuEu ) =
% 95.34/12.69 ( ![X4:( $i > $o )]:
% 95.34/12.69 ( ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) =>
% 95.34/12.69 ( ![X6:$i,X8:$i]:
% 95.34/12.69 ( ( X4 @ X6 ) => ( ( X4 @ X8 ) => ( ( X6 ) = ( X8 ) ) ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(omega__Cong, axiom, omega__Cong = (( omega ) = ( omega ))).
% 95.34/12.69 thf('244', plain, (( omega__Cong ) = ( ( omega ) = ( omega ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(setunion__Cong, axiom, setunion__Cong =
% 95.34/12.69 (![A:$i,B:$i]:
% 95.34/12.69 ( ( ( A ) = ( B ) ) => ( ( setunion @ A ) = ( setunion @ B ) ) ))).
% 95.34/12.69 thf('245', plain,
% 95.34/12.69 (( setunion__Cong ) =
% 95.34/12.69 ( ![X4:$i,X6:$i]:
% 95.34/12.69 ( ( ( X4 ) = ( X6 ) ) => ( ( setunion @ X4 ) = ( setunion @ X6 ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(powerset__Cong, axiom, powerset__Cong =
% 95.34/12.69 (![A:$i,B:$i]:
% 95.34/12.69 ( ( ( A ) = ( B ) ) => ( ( powerset @ A ) = ( powerset @ B ) ) ))).
% 95.34/12.69 thf('246', plain,
% 95.34/12.69 (( powerset__Cong ) =
% 95.34/12.69 ( ![X4:$i,X6:$i]:
% 95.34/12.69 ( ( ( X4 ) = ( X6 ) ) => ( ( powerset @ X4 ) = ( powerset @ X6 ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(setadjoin__Cong, axiom, setadjoin__Cong =
% 95.34/12.69 (![Xx:$i,Xy:$i]:
% 95.34/12.69 ( ( ( Xx ) = ( Xy ) ) =>
% 95.34/12.69 ( ![Xz:$i,Xu:$i]:
% 95.34/12.69 ( ( ( Xz ) = ( Xu ) ) =>
% 95.34/12.69 ( ( setadjoin @ Xx @ Xz ) = ( setadjoin @ Xy @ Xu ) ) ) ) ))).
% 95.34/12.69 thf('247', plain,
% 95.34/12.69 (( setadjoin__Cong ) =
% 95.34/12.69 ( ![X4:$i,X6:$i]:
% 95.34/12.69 ( ( ( X4 ) = ( X6 ) ) =>
% 95.34/12.69 ( ![X8:$i,X10:$i]:
% 95.34/12.69 ( ( ( X8 ) = ( X10 ) ) =>
% 95.34/12.69 ( ( setadjoin @ X4 @ X8 ) = ( setadjoin @ X6 @ X10 ) ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(emptyset__Cong, axiom, emptyset__Cong = (( emptyset ) = ( emptyset ))).
% 95.34/12.69 thf('248', plain, (( emptyset__Cong ) = ( ( emptyset ) = ( emptyset ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(exu__Cong, axiom, exu__Cong =
% 95.34/12.69 (![Xphi:( $i > $o ),Xpsi:( $i > $o )]:
% 95.34/12.69 ( ( ![Xx:$i,Xy:$i]:
% 95.34/12.69 ( ( ( Xx ) = ( Xy ) ) => ( ( Xphi @ Xx ) <=> ( Xpsi @ Xy ) ) ) ) =>
% 95.34/12.69 ( ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) <=>
% 95.34/12.69 ( exu @ ( ^[Xx:$i]: ( Xpsi @ Xx ) ) ) ) ))).
% 95.34/12.69 thf('249', plain,
% 95.34/12.69 (( exu__Cong ) =
% 95.34/12.69 ( ![X4:( $i > $o ),X6:( $i > $o )]:
% 95.34/12.69 ( ( ![X8:$i,X10:$i]:
% 95.34/12.69 ( ( ( X8 ) = ( X10 ) ) => ( ( X4 @ X8 ) <=> ( X6 @ X10 ) ) ) ) =>
% 95.34/12.69 ( ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) <=>
% 95.34/12.69 ( exu @ ( ^[V_2:$i]: ( X6 @ V_2 ) ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(exuE3u, axiom, exuE3u =
% 95.34/12.69 (![Xphi:( $i > $o )]:
% 95.34/12.69 ( ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) =>
% 95.34/12.69 ( ![Xx:$i,Xy:$i]:
% 95.34/12.69 ( ( Xphi @ Xx ) => ( ( Xphi @ Xy ) => ( ( Xx ) = ( Xy ) ) ) ) ) ))).
% 95.34/12.69 thf('250', plain,
% 95.34/12.69 (( exuE3u ) =
% 95.34/12.69 ( ![X4:( $i > $o )]:
% 95.34/12.69 ( ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) =>
% 95.34/12.69 ( ![X6:$i,X8:$i]:
% 95.34/12.69 ( ( X4 @ X6 ) => ( ( X4 @ X8 ) => ( ( X6 ) = ( X8 ) ) ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(in__Cong, axiom, in__Cong =
% 95.34/12.69 (![A:$i,B:$i]:
% 95.34/12.69 ( ( ( A ) = ( B ) ) =>
% 95.34/12.69 ( ![Xx:$i,Xy:$i]:
% 95.34/12.69 ( ( ( Xx ) = ( Xy ) ) => ( ( in @ Xx @ A ) <=> ( in @ Xy @ B ) ) ) ) ))).
% 95.34/12.69 thf('251', plain,
% 95.34/12.69 (( in__Cong ) =
% 95.34/12.69 ( ![X4:$i,X6:$i]:
% 95.34/12.69 ( ( ( X4 ) = ( X6 ) ) =>
% 95.34/12.69 ( ![X8:$i,X10:$i]:
% 95.34/12.69 ( ( ( X8 ) = ( X10 ) ) =>
% 95.34/12.69 ( ( in @ X8 @ X4 ) <=> ( in @ X10 @ X6 ) ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(inCongP, axiom, inCongP =
% 95.34/12.69 (![A:$i,B:$i]:
% 95.34/12.69 ( ( ( A ) = ( B ) ) =>
% 95.34/12.69 ( ![Xx:$i,Xy:$i]:
% 95.34/12.69 ( ( ( Xx ) = ( Xy ) ) => ( ( in @ Xx @ A ) => ( in @ Xy @ B ) ) ) ) ))).
% 95.34/12.69 thf('252', plain,
% 95.34/12.69 (( inCongP ) =
% 95.34/12.69 ( ![X4:$i,X6:$i]:
% 95.34/12.69 ( ( ( X4 ) = ( X6 ) ) =>
% 95.34/12.69 ( ![X8:$i,X10:$i]:
% 95.34/12.69 ( ( ( X8 ) = ( X10 ) ) =>
% 95.34/12.69 ( ( in @ X8 @ X4 ) => ( in @ X10 @ X6 ) ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(exuI2, axiom, exuI2 =
% 95.34/12.69 (![Xphi:( $i > $o )]:
% 95.34/12.69 ( ( ?[Xx:$i]: ( ![Xy:$i]: ( ( Xphi @ Xy ) <=> ( ( Xy ) = ( Xx ) ) ) ) ) =>
% 95.34/12.69 ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) ))).
% 95.34/12.69 thf('253', plain,
% 95.34/12.69 (( exuI2 ) =
% 95.34/12.69 ( ![X4:( $i > $o )]:
% 95.34/12.69 ( ( ?[X6:$i]: ( ![X8:$i]: ( ( X4 @ X8 ) <=> ( ( X8 ) = ( X6 ) ) ) ) ) =>
% 95.34/12.69 ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(exuI3, axiom, exuI3 =
% 95.34/12.69 (![Xphi:( $i > $o )]:
% 95.34/12.69 ( ( ?[Xx:$i]: ( Xphi @ Xx ) ) =>
% 95.34/12.69 ( ( ![Xx:$i,Xy:$i]:
% 95.34/12.69 ( ( Xphi @ Xx ) => ( ( Xphi @ Xy ) => ( ( Xx ) = ( Xy ) ) ) ) ) =>
% 95.34/12.69 ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) ) ))).
% 95.34/12.69 thf('254', plain,
% 95.34/12.69 (( exuI3 ) =
% 95.34/12.69 ( ![X4:( $i > $o )]:
% 95.34/12.69 ( ( ?[X6:$i]: ( X4 @ X6 ) ) =>
% 95.34/12.69 ( ( ![X8:$i,X10:$i]:
% 95.34/12.69 ( ( X4 @ X8 ) => ( ( X4 @ X10 ) => ( ( X8 ) = ( X10 ) ) ) ) ) =>
% 95.34/12.69 ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(exuI1, axiom, exuI1 =
% 95.34/12.69 (![Xphi:( $i > $o )]:
% 95.34/12.69 ( ( ?[Xx:$i]:
% 95.34/12.69 ( ( ![Xy:$i]: ( ( Xphi @ Xy ) => ( ( Xx ) = ( Xy ) ) ) ) &
% 95.34/12.69 ( Xphi @ Xx ) ) ) =>
% 95.34/12.69 ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) ))).
% 95.34/12.69 thf('255', plain,
% 95.34/12.69 (( exuI1 ) =
% 95.34/12.69 ( ![X4:( $i > $o )]:
% 95.34/12.69 ( ( ?[X6:$i]:
% 95.34/12.69 ( ( ![X8:$i]: ( ( X4 @ X8 ) => ( ( X6 ) = ( X8 ) ) ) ) &
% 95.34/12.69 ( X4 @ X6 ) ) ) =>
% 95.34/12.69 ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(notdallE, axiom, notdallE =
% 95.34/12.69 (![A:$i,Xphi:( $i > $o )]:
% 95.34/12.69 ( ( ~( ![Xx:$i]: ( ( in @ Xx @ A ) => ( Xphi @ Xx ) ) ) ) =>
% 95.34/12.69 ( ?[Xx:$i]: ( ( ~( Xphi @ Xx ) ) & ( in @ Xx @ A ) ) ) ))).
% 95.34/12.69 thf('256', plain,
% 95.34/12.69 (( notdallE ) =
% 95.34/12.69 ( ![X4:$i,X6:( $i > $o )]:
% 95.34/12.69 ( ( ~( ![X8:$i]: ( ( in @ X8 @ X4 ) => ( X6 @ X8 ) ) ) ) =>
% 95.34/12.69 ( ?[X10:$i]: ( ( ~( X6 @ X10 ) ) & ( in @ X10 @ X4 ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(notdexE, axiom, notdexE =
% 95.34/12.69 (![A:$i,Xphi:( $i > $o )]:
% 95.34/12.69 ( ( ~( ?[Xx:$i]: ( ( Xphi @ Xx ) & ( in @ Xx @ A ) ) ) ) =>
% 95.34/12.69 ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( ~( Xphi @ Xx ) ) ) ) ))).
% 95.34/12.69 thf('257', plain,
% 95.34/12.69 (( notdexE ) =
% 95.34/12.69 ( ![X4:$i,X6:( $i > $o )]:
% 95.34/12.69 ( ( ~( ?[X8:$i]: ( ( X6 @ X8 ) & ( in @ X8 @ X4 ) ) ) ) =>
% 95.34/12.69 ( ![X10:$i]: ( ( in @ X10 @ X4 ) => ( ~( X6 @ X10 ) ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(prop2set2propI, axiom, prop2set2propI =
% 95.34/12.69 (![Xphi:$o]: ( ( Xphi ) => ( set2prop @ ( prop2set @ Xphi ) ) ))).
% 95.34/12.69 thf('258', plain,
% 95.34/12.69 (( prop2set2propI ) =
% 95.34/12.69 ( ![X4:$o]: ( ( X4 ) => ( set2prop @ ( prop2set @ X4 ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(prop2setI, axiom, prop2setI =
% 95.34/12.69 (![Xphi:$o]: ( ( Xphi ) => ( in @ emptyset @ ( prop2set @ Xphi ) ) ))).
% 95.34/12.69 thf('259', plain,
% 95.34/12.69 (( prop2setI ) =
% 95.34/12.69 ( ![X4:$o]: ( ( X4 ) => ( in @ emptyset @ ( prop2set @ X4 ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(quantDeMorgan4, axiom, quantDeMorgan4 =
% 95.34/12.69 (![A:$i,Xphi:( $i > $o )]:
% 95.34/12.69 ( ( ?[Xx:$i]: ( ( ~( Xphi @ Xx ) ) & ( in @ Xx @ A ) ) ) =>
% 95.34/12.69 ( ~( ![Xx:$i]: ( ( in @ Xx @ A ) => ( Xphi @ Xx ) ) ) ) ))).
% 95.34/12.69 thf('260', plain,
% 95.34/12.69 (( quantDeMorgan4 ) =
% 95.34/12.69 ( ![X4:$i,X6:( $i > $o )]:
% 95.34/12.69 ( ( ?[X8:$i]: ( ( ~( X6 @ X8 ) ) & ( in @ X8 @ X4 ) ) ) =>
% 95.34/12.69 ( ~( ![X10:$i]: ( ( in @ X10 @ X4 ) => ( X6 @ X10 ) ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(quantDeMorgan3, axiom, quantDeMorgan3 =
% 95.34/12.69 (![A:$i,Xphi:( $i > $o )]:
% 95.34/12.69 ( ( ~( ?[Xx:$i]: ( ( Xphi @ Xx ) & ( in @ Xx @ A ) ) ) ) =>
% 95.34/12.69 ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( ~( Xphi @ Xx ) ) ) ) ))).
% 95.34/12.69 thf('261', plain,
% 95.34/12.69 (( quantDeMorgan3 ) =
% 95.34/12.69 ( ![X4:$i,X6:( $i > $o )]:
% 95.34/12.69 ( ( ~( ?[X8:$i]: ( ( X6 @ X8 ) & ( in @ X8 @ X4 ) ) ) ) =>
% 95.34/12.69 ( ![X10:$i]: ( ( in @ X10 @ X4 ) => ( ~( X6 @ X10 ) ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(quantDeMorgan2, axiom, quantDeMorgan2 =
% 95.34/12.69 (![A:$i,Xphi:( $i > $o )]:
% 95.34/12.69 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( ~( Xphi @ Xx ) ) ) ) =>
% 95.34/12.69 ( ~( ?[Xx:$i]: ( ( Xphi @ Xx ) & ( in @ Xx @ A ) ) ) ) ))).
% 95.34/12.69 thf('262', plain,
% 95.34/12.69 (( quantDeMorgan2 ) =
% 95.34/12.69 ( ![X4:$i,X6:( $i > $o )]:
% 95.34/12.69 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) => ( ~( X6 @ X8 ) ) ) ) =>
% 95.34/12.69 ( ~( ?[X10:$i]: ( ( X6 @ X10 ) & ( in @ X10 @ X4 ) ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(quantDeMorgan1, axiom, quantDeMorgan1 =
% 95.34/12.69 (![A:$i,Xphi:( $i > $o )]:
% 95.34/12.69 ( ( ~( ![Xx:$i]: ( ( in @ Xx @ A ) => ( Xphi @ Xx ) ) ) ) =>
% 95.34/12.69 ( ?[Xx:$i]: ( ( ~( Xphi @ Xx ) ) & ( in @ Xx @ A ) ) ) ))).
% 95.34/12.69 thf('263', plain,
% 95.34/12.69 (( quantDeMorgan1 ) =
% 95.34/12.69 ( ![X4:$i,X6:( $i > $o )]:
% 95.34/12.69 ( ( ~( ![X8:$i]: ( ( in @ X8 @ X4 ) => ( X6 @ X8 ) ) ) ) =>
% 95.34/12.69 ( ?[X10:$i]: ( ( ~( X6 @ X10 ) ) & ( in @ X10 @ X4 ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(vacuousDall, axiom, vacuousDall =
% 95.34/12.69 (![Xphi:( $i > $o ),Xx:$i]: ( ( in @ Xx @ emptyset ) => ( Xphi @ Xx ) ))).
% 95.34/12.69 thf('264', plain,
% 95.34/12.69 (( vacuousDall ) =
% 95.34/12.69 ( ![X4:( $i > $o ),X6:$i]: ( ( in @ X6 @ emptyset ) => ( X4 @ X6 ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(emptyE1, axiom, emptyE1 =
% 95.34/12.69 (![A:$i,Xphi:( $i > $o )]:
% 95.34/12.69 ( ( ?[Xx:$i]: ( ( Xphi @ Xx ) & ( in @ Xx @ A ) ) ) =>
% 95.34/12.69 ( ( ( dsetconstr @ A @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) = ( emptyset ) ) =>
% 95.34/12.69 ( $false ) ) ))).
% 95.34/12.69 thf('265', plain,
% 95.34/12.69 (( emptyE1 ) =
% 95.34/12.69 ( ![X4:$i,X6:( $i > $o )]:
% 95.34/12.69 ( ( ?[X8:$i]: ( ( X6 @ X8 ) & ( in @ X8 @ X4 ) ) ) =>
% 95.34/12.69 ( ( ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) = ( emptyset ) ) =>
% 95.34/12.69 ( $false ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(upairsetIR, axiom, upairsetIR =
% 95.34/12.69 (![Xx:$i,Xy:$i]:
% 95.34/12.69 ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 95.34/12.69 thf('266', plain,
% 95.34/12.69 (( upairsetIR ) =
% 95.34/12.69 ( ![X4:$i,X6:$i]:
% 95.34/12.69 ( in @ X6 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(upairsetIL, axiom, upairsetIL =
% 95.34/12.69 (![Xx:$i,Xy:$i]:
% 95.34/12.69 ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 95.34/12.69 thf('267', plain,
% 95.34/12.69 (( upairsetIL ) =
% 95.34/12.69 ( ![X4:$i,X6:$i]:
% 95.34/12.69 ( in @ X4 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(upairsetE, axiom, upairsetE =
% 95.34/12.69 (![Xx:$i,Xy:$i,Xz:$i]:
% 95.34/12.69 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) =>
% 95.34/12.69 ( ( ( Xz ) = ( Xx ) ) | ( ( Xz ) = ( Xy ) ) ) ))).
% 95.34/12.69 thf('268', plain,
% 95.34/12.69 (( upairsetE ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( in @ X8 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) =>
% 95.34/12.69 ( ( ( X8 ) = ( X4 ) ) | ( ( X8 ) = ( X6 ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(singletonsswitch, axiom, singletonsswitch =
% 95.34/12.69 (![Xx:$i,Xy:$i]:
% 95.34/12.69 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) =>
% 95.34/12.69 ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ))).
% 95.34/12.69 thf('269', plain,
% 95.34/12.69 (( singletonsswitch ) =
% 95.34/12.69 ( ![X4:$i,X6:$i]:
% 95.34/12.69 ( ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) =>
% 95.34/12.69 ( in @ X6 @ ( setadjoin @ X4 @ emptyset ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(eqinunit, axiom, eqinunit =
% 95.34/12.69 (![Xx:$i,Xy:$i]:
% 95.34/12.69 ( ( ( Xx ) = ( Xy ) ) => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ))).
% 95.34/12.69 thf('270', plain,
% 95.34/12.69 (( eqinunit ) =
% 95.34/12.69 ( ![X4:$i,X6:$i]:
% 95.34/12.69 ( ( ( X4 ) = ( X6 ) ) => ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(notinsingleton, axiom, notinsingleton =
% 95.34/12.69 (![Xx:$i,Xy:$i]:
% 95.34/12.69 ( ( ( Xx ) != ( Xy ) ) => ( ~( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ))).
% 95.34/12.69 thf('271', plain,
% 95.34/12.69 (( notinsingleton ) =
% 95.34/12.69 ( ![X4:$i,X6:$i]:
% 95.34/12.69 ( ( ( X4 ) != ( X6 ) ) =>
% 95.34/12.69 ( ~( in @ X6 @ ( setadjoin @ X4 @ emptyset ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(uniqinunit, axiom, uniqinunit =
% 95.34/12.69 (![Xx:$i,Xy:$i]:
% 95.34/12.69 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) => ( ( Xx ) = ( Xy ) ) ))).
% 95.34/12.69 thf('272', plain,
% 95.34/12.69 (( uniqinunit ) =
% 95.34/12.69 ( ![X4:$i,X6:$i]:
% 95.34/12.69 ( ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) => ( ( X4 ) = ( X6 ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(nonemptyImpWitness, axiom, nonemptyImpWitness =
% 95.34/12.69 (![A:$i]: ( ( nonempty @ A ) => ( ?[Xx:$i]: ( in @ Xx @ A ) ) ))).
% 95.34/12.69 thf('273', plain,
% 95.34/12.69 (( nonemptyImpWitness ) =
% 95.34/12.69 ( ![X4:$i]: ( ( nonempty @ X4 ) => ( ?[X6:$i]: ( in @ X6 @ X4 ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(exuE2, axiom, exuE2 =
% 95.34/12.69 (![Xphi:( $i > $o )]:
% 95.34/12.69 ( ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) =>
% 95.34/12.69 ( ?[Xx:$i]: ( ![Xy:$i]: ( ( Xphi @ Xy ) <=> ( ( Xy ) = ( Xx ) ) ) ) ) ))).
% 95.34/12.69 thf('274', plain,
% 95.34/12.69 (( exuE2 ) =
% 95.34/12.69 ( ![X4:( $i > $o )]:
% 95.34/12.69 ( ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) =>
% 95.34/12.69 ( ?[X6:$i]: ( ![X8:$i]: ( ( X4 @ X8 ) <=> ( ( X8 ) = ( X6 ) ) ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(subPowSU, axiom, subPowSU =
% 95.34/12.69 (![A:$i,Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ A ) => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ))).
% 95.34/12.69 thf('275', plain,
% 95.34/12.69 (( subPowSU ) =
% 95.34/12.69 ( ![X4:$i,X6:$i]:
% 95.34/12.69 ( ( in @ X6 @ X4 ) => ( in @ X6 @ ( powerset @ ( setunion @ X4 ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(setunionE, axiom, setunionE =
% 95.34/12.69 (![A:$i,Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ ( setunion @ A ) ) =>
% 95.34/12.69 ( ![Xphi:$o]:
% 95.34/12.69 ( ( ![B:$i]: ( ( in @ Xx @ B ) => ( ( in @ B @ A ) => ( Xphi ) ) ) ) =>
% 95.34/12.69 ( Xphi ) ) ) ))).
% 95.34/12.69 thf('276', plain,
% 95.34/12.69 (( setunionE ) =
% 95.34/12.69 ( ![X4:$i,X6:$i]:
% 95.34/12.69 ( ( in @ X6 @ ( setunion @ X4 ) ) =>
% 95.34/12.69 ( ![X8:$o]:
% 95.34/12.69 ( ( ![X10:$i]:
% 95.34/12.69 ( ( in @ X6 @ X10 ) => ( ( in @ X10 @ X4 ) => ( X8 ) ) ) ) =>
% 95.34/12.69 ( X8 ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(setunionI, axiom, setunionI =
% 95.34/12.69 (![A:$i,Xx:$i,B:$i]:
% 95.34/12.69 ( ( in @ Xx @ B ) => ( ( in @ B @ A ) => ( in @ Xx @ ( setunion @ A ) ) ) ))).
% 95.34/12.69 thf('277', plain,
% 95.34/12.69 (( setunionI ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( in @ X6 @ X8 ) =>
% 95.34/12.69 ( ( in @ X8 @ X4 ) => ( in @ X6 @ ( setunion @ X4 ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(powersetE, axiom, powersetE =
% 95.34/12.69 (![A:$i,B:$i,Xx:$i]:
% 95.34/12.69 ( ( in @ B @ ( powerset @ A ) ) => ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ))).
% 95.34/12.69 thf('278', plain,
% 95.34/12.69 (( powersetE ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( in @ X6 @ ( powerset @ X4 ) ) =>
% 95.34/12.69 ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(emptyInPowerset, axiom, emptyInPowerset =
% 95.34/12.69 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))).
% 95.34/12.69 thf('279', plain,
% 95.34/12.69 (( emptyInPowerset ) =
% 95.34/12.69 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(emptyinPowerset, axiom, emptyinPowerset =
% 95.34/12.69 (![A:$i]: ( in @ emptyset @ ( powerset @ A ) ))).
% 95.34/12.69 thf('280', plain,
% 95.34/12.69 (( emptyinPowerset ) =
% 95.34/12.69 ( ![X4:$i]: ( in @ emptyset @ ( powerset @ X4 ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(powersetI, axiom, powersetI =
% 95.34/12.69 (![A:$i,B:$i]:
% 95.34/12.69 ( ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) =>
% 95.34/12.69 ( in @ B @ ( powerset @ A ) ) ))).
% 95.34/12.69 thf('281', plain,
% 95.34/12.69 (( powersetI ) =
% 95.34/12.69 ( ![X4:$i,X6:$i]:
% 95.34/12.69 ( ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) =>
% 95.34/12.69 ( in @ X6 @ ( powerset @ X4 ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(setoftrueEq, axiom, setoftrueEq =
% 95.34/12.69 (![A:$i]: ( ( dsetconstr @ A @ ( ^[Xx:$i]: ( $true ) ) ) = ( A ) ))).
% 95.34/12.69 thf('282', plain,
% 95.34/12.69 (( setoftrueEq ) =
% 95.34/12.69 ( ![X4:$i]: ( ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( $true ) ) ) = ( X4 ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(setadjoinOr, axiom, setadjoinOr =
% 95.34/12.69 (![Xx:$i,A:$i,Xy:$i]:
% 95.34/12.69 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) =>
% 95.34/12.69 ( ( ( Xy ) = ( Xx ) ) | ( in @ Xy @ A ) ) ))).
% 95.34/12.69 thf('283', plain,
% 95.34/12.69 (( setadjoinOr ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) =>
% 95.34/12.69 ( ( ( X8 ) = ( X4 ) ) | ( in @ X8 @ X6 ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(setadjoinE, axiom, setadjoinE =
% 95.34/12.69 (![Xx:$i,A:$i,Xy:$i]:
% 95.34/12.69 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) =>
% 95.34/12.69 ( ![Xphi:$o]:
% 95.34/12.69 ( ( ( ( Xy ) = ( Xx ) ) => ( Xphi ) ) =>
% 95.34/12.69 ( ( ( in @ Xy @ A ) => ( Xphi ) ) => ( Xphi ) ) ) ) ))).
% 95.34/12.69 thf('284', plain,
% 95.34/12.69 (( setadjoinE ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) =>
% 95.34/12.69 ( ![X10:$o]:
% 95.34/12.69 ( ( ( ( X8 ) = ( X4 ) ) => ( X10 ) ) =>
% 95.34/12.69 ( ( ( in @ X8 @ X6 ) => ( X10 ) ) => ( X10 ) ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(setadjoinIR, axiom, setadjoinIR =
% 95.34/12.69 (![Xx:$i,A:$i,Xy:$i]:
% 95.34/12.69 ( ( in @ Xy @ A ) => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ))).
% 95.34/12.69 thf('285', plain,
% 95.34/12.69 (( setadjoinIR ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( in @ X8 @ X6 ) => ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(emptyinunitempty, axiom,(( emptyinunitempty ) =
% 95.34/12.69 (in @ emptyset @ ( setadjoin @ emptyset @ emptyset )))).
% 95.34/12.69 thf('286', plain,
% 95.34/12.69 (( emptyinunitempty ) =
% 95.34/12.69 ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )),
% 95.34/12.69 inference('simplify_rw_rule', [status(thm)], [emptyinunitempty])).
% 95.34/12.69 thf('287', plain,
% 95.34/12.69 (( emptyinunitempty ) =
% 95.34/12.69 ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(setadjoinIL, axiom, setadjoinIL =
% 95.34/12.69 (![Xx:$i,Xy:$i]: ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ))).
% 95.34/12.69 thf('288', plain,
% 95.34/12.69 (( setadjoinIL ) =
% 95.34/12.69 ( ![X4:$i,X6:$i]: ( in @ X4 @ ( setadjoin @ X4 @ X6 ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(nonemptyI1, axiom, nonemptyI1 =
% 95.34/12.69 (![A:$i]: ( ( ?[Xx:$i]: ( in @ Xx @ A ) ) => ( nonempty @ A ) ))).
% 95.34/12.69 thf('289', plain,
% 95.34/12.69 (( nonemptyI1 ) =
% 95.34/12.69 ( ![X4:$i]: ( ( ?[X6:$i]: ( in @ X6 @ X4 ) ) => ( nonempty @ X4 ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(nonemptyI, axiom, nonemptyI =
% 95.34/12.69 (![A:$i,Xphi:( $i > $o ),Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ A ) =>
% 95.34/12.69 ( ( Xphi @ Xx ) =>
% 95.34/12.69 ( nonempty @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) ) ))).
% 95.34/12.69 thf('290', plain,
% 95.34/12.69 (( nonemptyI ) =
% 95.34/12.69 ( ![X4:$i,X6:( $i > $o ),X8:$i]:
% 95.34/12.69 ( ( in @ X8 @ X4 ) =>
% 95.34/12.69 ( ( X6 @ X8 ) =>
% 95.34/12.69 ( nonempty @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(nonemptyE1, axiom, nonemptyE1 =
% 95.34/12.69 (![A:$i]: ( ( nonempty @ A ) => ( ?[Xx:$i]: ( in @ Xx @ A ) ) ))).
% 95.34/12.69 thf('291', plain,
% 95.34/12.69 (( nonemptyE1 ) =
% 95.34/12.69 ( ![X4:$i]: ( ( nonempty @ X4 ) => ( ?[X6:$i]: ( in @ X6 @ X4 ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(nonempty, axiom,(( nonempty ) = (^[Xx:$i]: ( ( Xx ) != ( emptyset ) )))).
% 95.34/12.69 thf('292', plain, (( nonempty ) = ( ^[Xx:$i]: ( ( Xx ) != ( emptyset ) ) )),
% 95.34/12.69 inference('simplify_rw_rule', [status(thm)], [nonempty])).
% 95.34/12.69 thf('293', plain,
% 95.34/12.69 (( nonempty ) = ( ^[V_1:$i]: ( ( V_1 ) != ( emptyset ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(setbeta, axiom, setbeta =
% 95.34/12.69 (![A:$i,Xphi:( $i > $o ),Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ A ) =>
% 95.34/12.69 ( ( in @ Xx @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) <=>
% 95.34/12.69 ( Xphi @ Xx ) ) ))).
% 95.34/12.69 thf('294', plain,
% 95.34/12.69 (( setbeta ) =
% 95.34/12.69 ( ![X4:$i,X6:( $i > $o ),X8:$i]:
% 95.34/12.69 ( ( in @ X8 @ X4 ) =>
% 95.34/12.69 ( ( in @ X8 @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) <=>
% 95.34/12.69 ( X6 @ X8 ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(noeltsimpempty, axiom, noeltsimpempty =
% 95.34/12.69 (![A:$i]:
% 95.34/12.69 ( ( ![Xx:$i]: ( ~( in @ Xx @ A ) ) ) => ( ( A ) = ( emptyset ) ) ))).
% 95.34/12.69 thf('295', plain,
% 95.34/12.69 (( noeltsimpempty ) =
% 95.34/12.69 ( ![X4:$i]:
% 95.34/12.69 ( ( ![X6:$i]: ( ~( in @ X6 @ X4 ) ) ) => ( ( X4 ) = ( emptyset ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(emptyI, axiom, emptyI =
% 95.34/12.69 (![A:$i]:
% 95.34/12.69 ( ( ![Xx:$i]: ( ~( in @ Xx @ A ) ) ) => ( ( A ) = ( emptyset ) ) ))).
% 95.34/12.69 thf('296', plain,
% 95.34/12.69 (( emptyI ) =
% 95.34/12.69 ( ![X4:$i]:
% 95.34/12.69 ( ( ![X6:$i]: ( ~( in @ X6 @ X4 ) ) ) => ( ( X4 ) = ( emptyset ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(setext, axiom, setext =
% 95.34/12.69 (![A:$i,B:$i]:
% 95.34/12.69 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) => ( in @ Xx @ B ) ) ) =>
% 95.34/12.69 ( ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) =>
% 95.34/12.69 ( ( A ) = ( B ) ) ) ))).
% 95.34/12.69 thf('297', plain,
% 95.34/12.69 (( setext ) =
% 95.34/12.69 ( ![X4:$i,X6:$i]:
% 95.34/12.69 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) => ( in @ X8 @ X6 ) ) ) =>
% 95.34/12.69 ( ( ![X10:$i]: ( ( in @ X10 @ X6 ) => ( in @ X10 @ X4 ) ) ) =>
% 95.34/12.69 ( ( X4 ) = ( X6 ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(exuE3e, axiom, exuE3e =
% 95.34/12.69 (![Xphi:( $i > $o )]:
% 95.34/12.69 ( ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) => ( ?[Xx:$i]: ( Xphi @ Xx ) ) ))).
% 95.34/12.69 thf('298', plain,
% 95.34/12.69 (( exuE3e ) =
% 95.34/12.69 ( ![X4:( $i > $o )]:
% 95.34/12.69 ( ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) => ( ?[X6:$i]: ( X4 @ X6 ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(notinemptyset, axiom, notinemptyset =
% 95.34/12.69 (![Xx:$i]: ( ~( in @ Xx @ emptyset ) ))).
% 95.34/12.69 thf('299', plain,
% 95.34/12.69 (( notinemptyset ) = ( ![X4:$i]: ( ~( in @ X4 @ emptyset ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(emptysetimpfalse, axiom, emptysetimpfalse =
% 95.34/12.69 (![Xx:$i]: ( ( in @ Xx @ emptyset ) => ( $false ) ))).
% 95.34/12.69 thf('300', plain,
% 95.34/12.69 (( emptysetimpfalse ) =
% 95.34/12.69 ( ![X4:$i]: ( ( in @ X4 @ emptyset ) => ( $false ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(emptysetE, axiom, emptysetE =
% 95.34/12.69 (![Xx:$i]: ( ( in @ Xx @ emptyset ) => ( ![Xphi:$o]: ( Xphi ) ) ))).
% 95.34/12.69 thf('301', plain,
% 95.34/12.69 (( emptysetE ) =
% 95.34/12.69 ( ![X4:$i]: ( ( in @ X4 @ emptyset ) => ( ![X6:$o]: ( X6 ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(prop2setE, axiom, prop2setE =
% 95.34/12.69 (![Xphi:$o,Xx:$i]: ( ( in @ Xx @ ( prop2set @ Xphi ) ) => ( Xphi ) ))).
% 95.34/12.69 thf('302', plain,
% 95.34/12.69 (( prop2setE ) =
% 95.34/12.69 ( ![X4:$o,X6:$i]: ( ( in @ X6 @ ( prop2set @ X4 ) ) => ( X4 ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(exuE1, axiom, exuE1 =
% 95.34/12.69 (![Xphi:( $i > $o )]:
% 95.34/12.69 ( ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) =>
% 95.34/12.69 ( ?[Xx:$i]:
% 95.34/12.69 ( ( ![Xy:$i]: ( ( Xphi @ Xy ) => ( ( Xx ) = ( Xy ) ) ) ) &
% 95.34/12.69 ( Xphi @ Xx ) ) ) ))).
% 95.34/12.69 thf('303', plain,
% 95.34/12.69 (( exuE1 ) =
% 95.34/12.69 ( ![X4:( $i > $o )]:
% 95.34/12.69 ( ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) =>
% 95.34/12.69 ( ?[X6:$i]:
% 95.34/12.69 ( ( ![X8:$i]: ( ( X4 @ X8 ) => ( ( X6 ) = ( X8 ) ) ) ) &
% 95.34/12.69 ( X4 @ X6 ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(dsetconstrER, axiom, dsetconstrER =
% 95.34/12.69 (![A:$i,Xphi:( $i > $o ),Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) =>
% 95.34/12.69 ( Xphi @ Xx ) ))).
% 95.34/12.69 thf('304', plain,
% 95.34/12.69 (( dsetconstrER ) =
% 95.34/12.69 ( ![X4:$i,X6:( $i > $o ),X8:$i]:
% 95.34/12.69 ( ( in @ X8 @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) =>
% 95.34/12.69 ( X6 @ X8 ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(dsetconstrEL, axiom, dsetconstrEL =
% 95.34/12.69 (![A:$i,Xphi:( $i > $o ),Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) =>
% 95.34/12.69 ( in @ Xx @ A ) ))).
% 95.34/12.69 thf('305', plain,
% 95.34/12.69 (( dsetconstrEL ) =
% 95.34/12.69 ( ![X4:$i,X6:( $i > $o ),X8:$i]:
% 95.34/12.69 ( ( in @ X8 @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) =>
% 95.34/12.69 ( in @ X8 @ X4 ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(dsetconstrI, axiom, dsetconstrI =
% 95.34/12.69 (![A:$i,Xphi:( $i > $o ),Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ A ) =>
% 95.34/12.69 ( ( Xphi @ Xx ) =>
% 95.34/12.69 ( in @ Xx @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) ) ))).
% 95.34/12.69 thf('306', plain,
% 95.34/12.69 (( dsetconstrI ) =
% 95.34/12.69 ( ![X4:$i,X6:( $i > $o ),X8:$i]:
% 95.34/12.69 ( ( in @ X8 @ X4 ) =>
% 95.34/12.69 ( ( X6 @ X8 ) =>
% 95.34/12.69 ( in @ X8 @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(descrp, axiom, descrp =
% 95.34/12.69 (![Xphi:( $i > $o )]:
% 95.34/12.69 ( ( exu @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) =>
% 95.34/12.69 ( Xphi @ ( descr @ ( ^[Xx:$i]: ( Xphi @ Xx ) ) ) ) ))).
% 95.34/12.69 thf('307', plain,
% 95.34/12.69 (( descrp ) =
% 95.34/12.69 ( ![X4:( $i > $o )]:
% 95.34/12.69 ( ( exu @ ( ^[V_1:$i]: ( X4 @ V_1 ) ) ) =>
% 95.34/12.69 ( X4 @ ( descr @ ( ^[V_2:$i]: ( X4 @ V_2 ) ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(wellorderingAx, axiom, wellorderingAx =
% 95.34/12.69 (![A:$i]:
% 95.34/12.69 ( ?[B:$i]:
% 95.34/12.69 ( ( ![C:$i]:
% 95.34/12.69 ( ( ( ![Xx:$i]: ( ( in @ Xx @ C ) => ( in @ Xx @ A ) ) ) &
% 95.34/12.69 ( ?[Xx:$i]: ( in @ Xx @ C ) ) ) =>
% 95.34/12.69 ( ?[D:$i,Xx:$i]:
% 95.34/12.69 ( ( ![E:$i]:
% 95.34/12.69 ( ( in @ E @ B ) =>
% 95.34/12.69 ( ( ![Xy:$i]: ( ( in @ Xy @ E ) => ( in @ Xy @ D ) ) ) |
% 95.34/12.69 ( in @ Xx @ E ) ) ) ) &
% 95.34/12.69 ( ~( ?[Xy:$i]: ( ( in @ Xy @ C ) & ( in @ Xy @ D ) ) ) ) &
% 95.34/12.69 ( in @ Xx @ C ) & ( in @ D @ B ) ) ) ) ) &
% 95.34/12.69 ( ![C:$i,D:$i]:
% 95.34/12.69 ( ( ( in @ C @ B ) & ( in @ D @ B ) ) =>
% 95.34/12.69 ( ( ![Xx:$i]: ( ( in @ Xx @ C ) => ( in @ Xx @ D ) ) ) |
% 95.34/12.69 ( ![Xx:$i]: ( ( in @ Xx @ D ) => ( in @ Xx @ C ) ) ) ) ) ) &
% 95.34/12.69 ( ![Xx:$i,Xy:$i]:
% 95.34/12.69 ( ( ( in @ Xx @ A ) & ( in @ Xy @ A ) ) =>
% 95.34/12.69 ( ( ![C:$i]:
% 95.34/12.69 ( ( in @ C @ B ) => ( ( in @ Xx @ C ) <=> ( in @ Xy @ C ) ) ) ) =>
% 95.34/12.69 ( ( Xx ) = ( Xy ) ) ) ) ) &
% 95.34/12.69 ( ![C:$i]:
% 95.34/12.69 ( ( in @ C @ B ) =>
% 95.34/12.69 ( ![Xx:$i]: ( ( in @ Xx @ C ) => ( in @ Xx @ A ) ) ) ) ) ) ))).
% 95.34/12.69 thf('308', plain,
% 95.34/12.69 (( wellorderingAx ) =
% 95.34/12.69 ( ![X4:$i]:
% 95.34/12.69 ( ?[X6:$i]:
% 95.34/12.69 ( ( ![X8:$i]:
% 95.34/12.69 ( ( ( ![X10:$i]: ( ( in @ X10 @ X8 ) => ( in @ X10 @ X4 ) ) ) &
% 95.34/12.69 ( ?[X12:$i]: ( in @ X12 @ X8 ) ) ) =>
% 95.34/12.69 ( ?[X14:$i,X16:$i]:
% 95.34/12.69 ( ( ![X18:$i]:
% 95.34/12.69 ( ( in @ X18 @ X6 ) =>
% 95.34/12.69 ( ( ![X20:$i]:
% 95.34/12.69 ( ( in @ X20 @ X18 ) => ( in @ X20 @ X14 ) ) ) |
% 95.34/12.69 ( in @ X16 @ X18 ) ) ) ) &
% 95.34/12.69 ( ~( ?[X22:$i]: ( ( in @ X22 @ X8 ) & ( in @ X22 @ X14 ) ) ) ) &
% 95.34/12.69 ( in @ X16 @ X8 ) & ( in @ X14 @ X6 ) ) ) ) ) &
% 95.34/12.69 ( ![X24:$i,X26:$i]:
% 95.34/12.69 ( ( ( in @ X24 @ X6 ) & ( in @ X26 @ X6 ) ) =>
% 95.34/12.69 ( ( ![X28:$i]: ( ( in @ X28 @ X24 ) => ( in @ X28 @ X26 ) ) ) |
% 95.34/12.69 ( ![X30:$i]: ( ( in @ X30 @ X26 ) => ( in @ X30 @ X24 ) ) ) ) ) ) &
% 95.34/12.69 ( ![X32:$i,X34:$i]:
% 95.34/12.69 ( ( ( in @ X32 @ X4 ) & ( in @ X34 @ X4 ) ) =>
% 95.34/12.69 ( ( ![X36:$i]:
% 95.34/12.69 ( ( in @ X36 @ X6 ) =>
% 95.34/12.69 ( ( in @ X32 @ X36 ) <=> ( in @ X34 @ X36 ) ) ) ) =>
% 95.34/12.69 ( ( X32 ) = ( X34 ) ) ) ) ) &
% 95.34/12.69 ( ![X38:$i]:
% 95.34/12.69 ( ( in @ X38 @ X6 ) =>
% 95.34/12.69 ( ![X40:$i]: ( ( in @ X40 @ X38 ) => ( in @ X40 @ X4 ) ) ) ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(foundationAx, axiom, foundationAx =
% 95.34/12.69 (![A:$i]:
% 95.34/12.69 ( ( ?[Xx:$i]: ( in @ Xx @ A ) ) =>
% 95.34/12.69 ( ?[B:$i]:
% 95.34/12.69 ( ( ~( ?[Xx:$i]: ( ( in @ Xx @ A ) & ( in @ Xx @ B ) ) ) ) &
% 95.34/12.69 ( in @ B @ A ) ) ) ))).
% 95.34/12.69 thf('309', plain,
% 95.34/12.69 (( foundationAx ) =
% 95.34/12.69 ( ![X4:$i]:
% 95.34/12.69 ( ( ?[X6:$i]: ( in @ X6 @ X4 ) ) =>
% 95.34/12.69 ( ?[X8:$i]:
% 95.34/12.69 ( ( ~( ?[X10:$i]: ( ( in @ X10 @ X4 ) & ( in @ X10 @ X8 ) ) ) ) &
% 95.34/12.69 ( in @ X8 @ X4 ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(replAx, axiom, replAx =
% 95.34/12.69 (![Xphi:( $i > $i > $o ),A:$i]:
% 95.34/12.69 ( ( ![Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ A ) => ( exu @ ( ^[Xy:$i]: ( Xphi @ Xx @ Xy ) ) ) ) ) =>
% 95.34/12.69 ( ?[B:$i]:
% 95.34/12.69 ( ![Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ B ) <=>
% 95.34/12.69 ( ?[Xy:$i]: ( ( Xphi @ Xy @ Xx ) & ( in @ Xy @ A ) ) ) ) ) ) ))).
% 95.34/12.69 thf('310', plain,
% 95.34/12.69 (( replAx ) =
% 95.34/12.69 ( ![X4:( $i > $i > $o ),X6:$i]:
% 95.34/12.69 ( ( ![X8:$i]:
% 95.34/12.69 ( ( in @ X8 @ X6 ) => ( exu @ ( ^[V_1:$i]: ( X4 @ X8 @ V_1 ) ) ) ) ) =>
% 95.34/12.69 ( ?[X10:$i]:
% 95.34/12.69 ( ![X12:$i]:
% 95.34/12.69 ( ( in @ X12 @ X10 ) <=>
% 95.34/12.69 ( ?[X14:$i]: ( ( X4 @ X14 @ X12 ) & ( in @ X14 @ X6 ) ) ) ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(omegaIndAx, axiom, omegaIndAx =
% 95.34/12.69 (![A:$i]:
% 95.34/12.69 ( ( ( in @ emptyset @ A ) &
% 95.34/12.69 ( ![Xx:$i]:
% 95.34/12.69 ( ( ( in @ Xx @ omega ) & ( in @ Xx @ A ) ) =>
% 95.34/12.69 ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) ) ) =>
% 95.34/12.69 ( ![Xx:$i]: ( ( in @ Xx @ omega ) => ( in @ Xx @ A ) ) ) ))).
% 95.34/12.69 thf('311', plain,
% 95.34/12.69 (( omegaIndAx ) =
% 95.34/12.69 ( ![X4:$i]:
% 95.34/12.69 ( ( ( in @ emptyset @ X4 ) &
% 95.34/12.69 ( ![X6:$i]:
% 95.34/12.69 ( ( ( in @ X6 @ omega ) & ( in @ X6 @ X4 ) ) =>
% 95.34/12.69 ( in @ ( setadjoin @ X6 @ X6 ) @ X4 ) ) ) ) =>
% 95.34/12.69 ( ![X8:$i]: ( ( in @ X8 @ omega ) => ( in @ X8 @ X4 ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(omegaSAx, axiom, omegaSAx =
% 95.34/12.69 (![Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ omega ) => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ))).
% 95.34/12.69 thf('312', plain,
% 95.34/12.69 (( omegaSAx ) =
% 95.34/12.69 ( ![X4:$i]:
% 95.34/12.69 ( ( in @ X4 @ omega ) => ( in @ ( setadjoin @ X4 @ X4 ) @ omega ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(omega0Ax, axiom,(( omega0Ax ) = (in @ emptyset @ omega))).
% 95.34/12.69 thf('313', plain, (( omega0Ax ) = ( in @ emptyset @ omega )),
% 95.34/12.69 inference('simplify_rw_rule', [status(thm)], [omega0Ax])).
% 95.34/12.69 thf('314', plain, (( omega0Ax ) = ( in @ emptyset @ omega )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(setunionAx, axiom, setunionAx =
% 95.34/12.69 (![A:$i,Xx:$i]:
% 95.34/12.69 ( ( in @ Xx @ ( setunion @ A ) ) <=>
% 95.34/12.69 ( ?[B:$i]: ( ( in @ B @ A ) & ( in @ Xx @ B ) ) ) ))).
% 95.34/12.69 thf('315', plain,
% 95.34/12.69 (( setunionAx ) =
% 95.34/12.69 ( ![X4:$i,X6:$i]:
% 95.34/12.69 ( ( in @ X6 @ ( setunion @ X4 ) ) <=>
% 95.34/12.69 ( ?[X8:$i]: ( ( in @ X8 @ X4 ) & ( in @ X6 @ X8 ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(powersetAx, axiom, powersetAx =
% 95.34/12.69 (![A:$i,B:$i]:
% 95.34/12.69 ( ( in @ B @ ( powerset @ A ) ) <=>
% 95.34/12.69 ( ![Xx:$i]: ( ( in @ Xx @ B ) => ( in @ Xx @ A ) ) ) ))).
% 95.34/12.69 thf('316', plain,
% 95.34/12.69 (( powersetAx ) =
% 95.34/12.69 ( ![X4:$i,X6:$i]:
% 95.34/12.69 ( ( in @ X6 @ ( powerset @ X4 ) ) <=>
% 95.34/12.69 ( ![X8:$i]: ( ( in @ X8 @ X6 ) => ( in @ X8 @ X4 ) ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(setadjoinAx, axiom, setadjoinAx =
% 95.34/12.69 (![Xx:$i,A:$i,Xy:$i]:
% 95.34/12.69 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) ) <=>
% 95.34/12.69 ( ( ( Xy ) = ( Xx ) ) | ( in @ Xy @ A ) ) ))).
% 95.34/12.69 thf('317', plain,
% 95.34/12.69 (( setadjoinAx ) =
% 95.34/12.69 ( ![X4:$i,X6:$i,X8:$i]:
% 95.34/12.69 ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) <=>
% 95.34/12.69 ( ( ( X8 ) = ( X4 ) ) | ( in @ X8 @ X6 ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(emptysetAx, axiom, emptysetAx = (![Xx:$i]: ( ~( in @ Xx @ emptyset ) ))).
% 95.34/12.69 thf('318', plain,
% 95.34/12.69 (( emptysetAx ) = ( ![X4:$i]: ( ~( in @ X4 @ emptyset ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(setextAx, axiom, setextAx =
% 95.34/12.69 (![A:$i,B:$i]:
% 95.34/12.69 ( ( ![Xx:$i]: ( ( in @ Xx @ A ) <=> ( in @ Xx @ B ) ) ) =>
% 95.34/12.69 ( ( A ) = ( B ) ) ))).
% 95.34/12.69 thf('319', plain,
% 95.34/12.69 (( setextAx ) =
% 95.34/12.69 ( ![X4:$i,X6:$i]:
% 95.34/12.69 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) <=> ( in @ X8 @ X6 ) ) ) =>
% 95.34/12.69 ( ( X4 ) = ( X6 ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(exu, axiom,(( exu ) =
% 95.34/12.69 (^[Xphi:( $i > $o )]:
% 95.34/12.69 ( ?[Xx:$i]:
% 95.34/12.69 ( ( ![Xy:$i]: ( ( Xphi @ Xy ) => ( ( Xx ) = ( Xy ) ) ) ) & ( Xphi @ Xx ) ) )))).
% 95.34/12.69 thf('320', plain,
% 95.34/12.69 (( exu ) =
% 95.34/12.69 ( ^[Xphi:( $i > $o )]:
% 95.34/12.69 ( ?[Xx:$i]:
% 95.34/12.69 ( ( ![Xy:$i]: ( ( Xphi @ Xy ) => ( ( Xx ) = ( Xy ) ) ) ) &
% 95.34/12.69 ( Xphi @ Xx ) ) ) )),
% 95.34/12.69 inference('simplify_rw_rule', [status(thm)], [exu])).
% 95.34/12.69 thf('321', plain,
% 95.34/12.69 (( exu ) =
% 95.34/12.69 ( ^[V_1:( $i > $o )]:
% 95.34/12.69 ( ?[X4:$i]:
% 95.34/12.69 ( ( ![X6:$i]: ( ( V_1 @ X6 ) => ( ( X4 ) = ( X6 ) ) ) ) &
% 95.34/12.69 ( V_1 @ X4 ) ) ) )),
% 95.34/12.69 define([status(thm)])).
% 95.34/12.69 thf(injFuncSetFuncInj, conjecture,
% 95.34/12.69 (( setextAx ) =>
% 95.34/12.69 ( ( emptysetAx ) =>
% 95.34/12.69 ( ( setadjoinAx ) =>
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% 95.34/12.69 setextT ) =>
% 95.34/12.69 (
% 95.34/12.69 (
% 95.34/12.69 subsetTI ) =>
% 95.34/12.69 (
% 95.34/12.69 (
% 95.34/12.69 powersetTI1 ) =>
% 95.34/12.69 (
% 95.34/12.69 (
% 95.34/12.69 powersetTE1 ) =>
% 95.34/12.69 (
% 95.34/12.69 (
% 95.34/12.69 complementTI1 ) =>
% 95.34/12.69 (
% 95.34/12.69 (
% 95.34/12.69 complementTE1 ) =>
% 95.34/12.69 (
% 95.34/12.69 (
% 95.34/12.69 binintersectTELcontra ) =>
% 95.34/12.69 (
% 95.34/12.69 (
% 95.34/12.69 binintersectTERcontra ) =>
% 95.34/12.69 (
% 95.34/12.69 (
% 95.34/12.69 contrasubsetT ) =>
% 95.34/12.69 (
% 95.34/12.69 (
% 95.34/12.69 contrasubsetT1 ) =>
% 95.34/12.69 (
% 95.34/12.69 (
% 95.34/12.69 contrasubsetT2 ) =>
% 95.34/12.69 (
% 95.34/12.69 (
% 95.34/12.69 contrasubsetT3 ) =>
% 95.34/12.69 (
% 95.34/12.69 (
% 95.34/12.69 doubleComplementI1 ) =>
% 95.34/12.69 (
% 95.34/12.69 (
% 95.34/12.69 doubleComplementE1 ) =>
% 95.34/12.69 (
% 95.34/12.69 (
% 95.34/12.69 doubleComplementSub1 ) =>
% 95.34/12.69 (
% 95.34/12.69 (
% 95.34/12.69 doubleComplementSub2 ) =>
% 95.34/12.69 (
% 95.34/12.69 (
% 95.34/12.69 doubleComplementEq ) =>
% 95.34/12.69 (
% 95.34/12.69 (
% 95.34/12.69 complementTnotintersectT ) =>
% 95.34/12.69 (
% 95.34/12.69 (
% 95.34/12.69 complementImpComplementIntersect ) =>
% 95.34/12.69 (
% 95.34/12.69 (
% 95.34/12.69 complementSubsetComplementIntersect ) =>
% 95.34/12.69 (
% 95.34/12.69 (
% 95.34/12.69 complementInPowersetComplementIntersect ) =>
% 95.34/12.69 (
% 95.34/12.69 (
% 95.34/12.69 contraSubsetComplement ) =>
% 95.34/12.69 (
% 95.34/12.69 (
% 95.34/12.69 complementTcontraSubset ) =>
% 95.34/12.69 (
% 95.34/12.69 (
% 95.34/12.69 binunionTILcontra ) =>
% 95.34/12.69 (
% 95.34/12.69 (
% 95.34/12.69 binunionTIRcontra ) =>
% 95.34/12.69 (
% 95.34/12.69 (
% 95.34/12.69 inIntersectImpInUnion ) =>
% 95.34/12.69 (
% 95.34/12.69 (
% 95.34/12.69 inIntersectImpInUnion2 ) =>
% 95.34/12.69 (
% 95.34/12.69 (
% 95.34/12.69 inIntersectImpInIntersectUnions ) =>
% 95.34/12.69 (
% 95.34/12.69 (
% 95.34/12.69 intersectInPowersetIntersectUnions ) =>
% 95.34/12.69 (
% 95.34/12.69 (
% 95.34/12.69 inComplementUnionImpNotIn1 ) =>
% 95.34/12.69 (
% 95.34/12.69 (
% 95.34/12.69 inComplementUnionImpInComplement1 ) =>
% 95.34/12.69 (
% 95.34/12.69 (
% 95.34/12.69 binunionTE ) =>
% 95.34/12.69 (
% 95.34/12.69 (
% 95.34/12.69 binunionTEcontra ) =>
% 95.34/12.69 (
% 95.34/12.69 (
% 95.34/12.69 demorgan2a1 ) =>
% 95.34/12.69 (
% 95.34/12.69 (
% 95.34/12.69 complementUnionInPowersetComplement ) =>
% 95.34/12.69 (
% 95.34/12.69 (
% 95.34/12.69 demorgan2a2 ) =>
% 95.34/12.69 (
% 95.34/12.69 (
% 95.34/12.69 demorgan1a ) =>
% 95.34/12.69 (
% 95.34/12.69 (
% 95.34/12.69 demorgan1b ) =>
% 95.34/12.69 (
% 95.34/12.69 (
% 95.34/12.69 demorgan1 ) =>
% 95.34/12.69 (
% 95.34/12.69 (
% 95.34/12.69 demorgan2a ) =>
% 95.34/12.69 (
% 95.34/12.69 (
% 95.34/12.69 demorgan2b2 ) =>
% 95.34/12.69 (
% 95.34/12.69 (
% 95.34/12.69 demorgan2b ) =>
% 95.34/12.69 (
% 95.34/12.69 (
% 95.34/12.69 demorgan2 ) =>
% 95.34/12.69 (
% 95.34/12.69 (
% 95.34/12.69 woz13rule0 ) =>
% 95.34/12.69 (
% 95.34/12.69 (
% 95.34/12.69 woz13rule1 ) =>
% 95.34/12.69 (
% 95.34/12.69 (
% 95.34/12.69 woz13rule2 ) =>
% 95.34/12.69 (
% 95.34/12.69 (
% 95.34/12.69 woz13rule3 ) =>
% 95.34/12.69 (
% 95.34/12.69 (
% 95.34/12.69 woz13rule4 ) =>
% 95.34/12.69 (
% 95.34/12.69 (
% 95.34/12.69 woz1_1 ) =>
% 95.34/12.69 (
% 95.34/12.69 (
% 95.34/12.69 woz1_2 ) =>
% 95.34/12.69 (
% 95.34/12.69 (
% 95.34/12.69 woz1_3 ) =>
% 95.34/12.69 (
% 95.34/12.69 (
% 95.34/12.69 woz1_4 ) =>
% 95.34/12.69 (
% 95.34/12.69 (
% 95.34/12.69 woz1_5 ) =>
% 95.34/12.69 (
% 95.34/12.69 (
% 95.34/12.69 breln1all2 ) =>
% 95.34/12.69 (
% 95.34/12.69 (
% 95.34/12.69 breln1SetBreln1 ) =>
% 95.34/12.69 (
% 95.34/12.69 (
% 95.34/12.69 choice2fnsingleton ) =>
% 95.34/12.69 (
% 95.34/12.69 (
% 95.34/12.69 setOfPairsIsBReln1 ) =>
% 95.34/12.69 (
% 95.34/12.69 (
% 95.34/12.69 breln1all1 ) =>
% 95.34/12.69 (
% 95.34/12.69 (
% 95.34/12.69 subbreln1 ) =>
% 95.34/12.69 (
% 95.34/12.69 (
% 95.34/12.69 eqbreln1 ) =>
% 95.34/12.69 (
% 95.34/12.69 (
% 95.34/12.69 breln1invprop ) =>
% 95.34/12.69 (
% 95.34/12.69 (
% 95.34/12.69 breln1invI ) =>
% 95.34/12.69 (
% 95.34/12.70 (
% 95.34/12.70 breln1invE ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 breln1compprop ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 breln1compI ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 breln1compE ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 breln1compEex ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 breln1unionprop ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 breln1unionIL ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 breln1unionIR ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 breln1unionI ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 breln1unionE ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 breln1unionEcases ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 breln1unionCommutes ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 woz2Ex ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 woz2W ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 woz2A ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 woz2B ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 image1Ex ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 image1Ex1 ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 image1Equiv ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 image1E ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 image1I ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 injFuncInInjFuncSet ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 injFuncSetFuncIn ) =>
% 95.34/12.70 (
% 95.34/12.70 ![
% 95.34/12.70 Xx:$i,
% 95.34/12.70 Xy:$i,
% 95.34/12.70 Xf:$i]:
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 in @
% 95.34/12.70 Xf @
% 95.34/12.70 (
% 95.34/12.70 injFuncSet
% 95.34/12.70 @
% 95.34/12.70 Xx @ Xy ) ) =>
% 95.34/12.70 (
% 95.34/12.70 injective
% 95.34/12.70 @
% 95.34/12.70 Xx @ Xy @
% 95.34/12.70 Xf ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 95.34/12.70 thf(zf_stmt_0, conjecture,
% 95.34/12.70 (( ![X4:$i,X6:$i]:
% 95.34/12.70 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) <=> ( in @ X8 @ X6 ) ) ) =>
% 95.34/12.70 ( ( X4 ) = ( X6 ) ) ) ) =>
% 95.34/12.70 ( ( ![X10:$i]: ( ~( in @ X10 @ emptyset ) ) ) =>
% 95.34/12.70 ( ( ![X12:$i,X14:$i,X16:$i]:
% 95.34/12.70 ( ( in @ X16 @ ( setadjoin @ X12 @ X14 ) ) <=>
% 95.34/12.70 ( ( in @ X16 @ X14 ) | ( ( X16 ) = ( X12 ) ) ) ) ) =>
% 95.34/12.70 ( ( ![X18:$i,X20:$i]:
% 95.34/12.70 ( ( in @ X20 @ ( powerset @ X18 ) ) <=>
% 95.34/12.70 ( ![X22:$i]: ( ( in @ X22 @ X20 ) => ( in @ X22 @ X18 ) ) ) ) ) =>
% 95.34/12.70 ( ( ![X24:$i,X26:$i]:
% 95.34/12.70 ( ( in @ X26 @ ( setunion @ X24 ) ) <=>
% 95.34/12.70 ( ?[X28:$i]: ( ( in @ X26 @ X28 ) & ( in @ X28 @ X24 ) ) ) ) ) =>
% 95.34/12.70 ( ( in @ emptyset @ omega ) =>
% 95.34/12.70 ( ( ![X30:$i]:
% 95.34/12.70 ( ( in @ X30 @ omega ) =>
% 95.34/12.70 ( in @ ( setadjoin @ X30 @ X30 ) @ omega ) ) ) =>
% 95.34/12.70 ( ( ![X32:$i]:
% 95.34/12.70 ( ( ( ![X34:$i]:
% 95.34/12.70 ( ( ( in @ X34 @ X32 ) & ( in @ X34 @ omega ) ) =>
% 95.34/12.70 ( in @ ( setadjoin @ X34 @ X34 ) @ X32 ) ) ) &
% 95.34/12.70 ( in @ emptyset @ X32 ) ) =>
% 95.34/12.70 ( ![X36:$i]:
% 95.34/12.70 ( ( in @ X36 @ omega ) => ( in @ X36 @ X32 ) ) ) ) ) =>
% 95.34/12.70 ( ( ![X38:( $i > $i > $o ),X40:$i]:
% 95.34/12.70 ( ( ![X42:$i]:
% 95.34/12.70 ( ( in @ X42 @ X40 ) =>
% 95.34/12.70 ( ?[X44:$i]:
% 95.34/12.70 ( ( X38 @ X42 @ X44 ) &
% 95.34/12.70 ( ![X46:$i]:
% 95.34/12.70 ( ( X38 @ X42 @ X46 ) =>
% 95.34/12.70 ( ( X44 ) = ( X46 ) ) ) ) ) ) ) ) =>
% 95.34/12.70 ( ?[X48:$i]:
% 95.34/12.70 ( ![X50:$i]:
% 95.34/12.70 ( ( in @ X50 @ X48 ) <=>
% 95.34/12.70 ( ?[X52:$i]:
% 95.34/12.70 ( ( in @ X52 @ X40 ) & ( X38 @ X52 @ X50 ) ) ) ) ) ) ) ) =>
% 95.34/12.70 ( ( ![X54:$i]:
% 95.34/12.70 ( ( ?[X56:$i]: ( in @ X56 @ X54 ) ) =>
% 95.34/12.70 ( ?[X58:$i]:
% 95.34/12.70 ( ( in @ X58 @ X54 ) &
% 95.34/12.70 ( ~( ?[X60:$i]:
% 95.34/12.70 ( ( in @ X60 @ X58 ) & ( in @ X60 @ X54 ) ) ) ) ) ) ) ) =>
% 95.34/12.70 ( ( ![X62:$i]:
% 95.34/12.70 ( ?[X64:$i]:
% 95.34/12.70 ( ( ![X96:$i]:
% 95.34/12.70 ( ( in @ X96 @ X64 ) =>
% 95.34/12.70 ( ![X98:$i]:
% 95.34/12.70 ( ( in @ X98 @ X96 ) => ( in @ X98 @ X62 ) ) ) ) ) &
% 95.34/12.70 ( ![X90:$i,X92:$i]:
% 95.34/12.70 ( ( ( in @ X92 @ X62 ) & ( in @ X90 @ X62 ) ) =>
% 95.34/12.70 ( ( ![X94:$i]:
% 95.34/12.70 ( ( in @ X94 @ X64 ) =>
% 95.34/12.70 ( ( in @ X90 @ X94 ) <=>
% 95.34/12.70 ( in @ X92 @ X94 ) ) ) ) =>
% 95.34/12.70 ( ( X90 ) = ( X92 ) ) ) ) ) &
% 95.34/12.70 ( ![X82:$i,X84:$i]:
% 95.34/12.70 ( ( ( in @ X84 @ X64 ) & ( in @ X82 @ X64 ) ) =>
% 95.34/12.70 ( ( ![X88:$i]:
% 95.34/12.70 ( ( in @ X88 @ X84 ) =>
% 95.34/12.70 ( in @ X88 @ X82 ) ) ) |
% 95.34/12.70 ( ![X86:$i]:
% 95.34/12.70 ( ( in @ X86 @ X82 ) =>
% 95.34/12.70 ( in @ X86 @ X84 ) ) ) ) ) ) &
% 95.34/12.70 ( ![X66:$i]:
% 95.34/12.70 ( ( ( ?[X70:$i]: ( in @ X70 @ X66 ) ) &
% 95.34/12.70 ( ![X68:$i]:
% 95.34/12.70 ( ( in @ X68 @ X66 ) =>
% 95.34/12.70 ( in @ X68 @ X62 ) ) ) ) =>
% 95.34/12.70 ( ?[X72:$i,X74:$i]:
% 95.34/12.70 ( ( in @ X72 @ X64 ) &
% 95.34/12.70 ( in @ X74 @ X66 ) &
% 95.34/12.70 ( ~( ?[X80:$i]:
% 95.34/12.70 ( ( in @ X80 @ X72 ) &
% 95.34/12.70 ( in @ X80 @ X66 ) ) ) ) &
% 95.34/12.70 ( ![X76:$i]:
% 95.34/12.70 ( ( in @ X76 @ X64 ) =>
% 95.34/12.70 ( ( in @ X74 @ X76 ) |
% 95.34/12.70 ( ![X78:$i]:
% 95.34/12.70 ( ( in @ X78 @ X76 ) =>
% 95.34/12.70 ( in @ X78 @ X72 ) ) ) ) ) ) ) ) ) ) ) ) ) =>
% 95.34/12.70 ( ( ![X100:( $i > $o )]:
% 95.34/12.70 ( ( ?[X102:$i]:
% 95.34/12.70 ( ( X100 @ X102 ) &
% 95.34/12.70 ( ![X104:$i]:
% 95.34/12.70 ( ( X100 @ X104 ) =>
% 95.34/12.70 ( ( X102 ) = ( X104 ) ) ) ) ) ) =>
% 95.34/12.70 ( X100 @
% 95.34/12.70 ( descr @ ( ^[V_1:$i]: ( X100 @ V_1 ) ) ) ) ) ) =>
% 95.34/12.70 ( ( ![X106:$i,X108:( $i > $o ),X110:$i]:
% 95.34/12.70 ( ( in @ X110 @ X106 ) =>
% 95.34/12.70 ( ( X108 @ X110 ) =>
% 95.34/12.70 ( in @
% 95.34/12.70 X110 @
% 95.34/12.70 ( dsetconstr @
% 95.34/12.70 X106 @ ( ^[V_2:$i]: ( X108 @ V_2 ) ) ) ) ) ) ) =>
% 95.34/12.70 ( ( ![X112:$i,X114:( $i > $o ),X116:$i]:
% 95.34/12.70 ( ( in @
% 95.34/12.70 X116 @
% 95.34/12.70 ( dsetconstr @
% 95.34/12.70 X112 @ ( ^[V_3:$i]: ( X114 @ V_3 ) ) ) ) =>
% 95.34/12.70 ( in @ X116 @ X112 ) ) ) =>
% 95.34/12.70 ( ( ![X118:$i,X120:( $i > $o ),X122:$i]:
% 95.34/12.70 ( ( in @
% 95.34/12.70 X122 @
% 95.34/12.70 ( dsetconstr @
% 95.34/12.70 X118 @ ( ^[V_4:$i]: ( X120 @ V_4 ) ) ) ) =>
% 95.34/12.70 ( X120 @ X122 ) ) ) =>
% 95.34/12.70 ( ( ![X124:( $i > $o )]:
% 95.34/12.70 ( ( ?[X126:$i]:
% 95.34/12.70 ( ( X124 @ X126 ) &
% 95.34/12.70 ( ![X128:$i]:
% 95.34/12.70 ( ( X124 @ X128 ) =>
% 95.34/12.70 ( ( X126 ) = ( X128 ) ) ) ) ) ) =>
% 95.34/12.70 ( ?[X130:$i]:
% 95.34/12.70 ( ( X124 @ X130 ) &
% 95.34/12.70 ( ![X132:$i]:
% 95.34/12.70 ( ( X124 @ X132 ) =>
% 95.34/12.70 ( ( X130 ) = ( X132 ) ) ) ) ) ) ) ) =>
% 95.34/12.70 ( ( ![X134:$o,X136:$i]:
% 95.34/12.70 ( ( in @ X136 @ ( prop2set @ X134 ) ) =>
% 95.34/12.70 ( X134 ) ) ) =>
% 95.34/12.70 ( ( ![X138:$i]:
% 95.34/12.70 ( ( in @ X138 @ emptyset ) =>
% 95.34/12.70 ( ![X140:$o]: ( X140 ) ) ) ) =>
% 95.34/12.70 ( ( ![X142:$i]:
% 95.34/12.70 ( ( in @ X142 @ emptyset ) =>
% 95.34/12.70 ( $false ) ) ) =>
% 95.34/12.70 ( ( ![X144:$i]:
% 95.34/12.70 ( ~( in @ X144 @ emptyset ) ) ) =>
% 95.34/12.70 ( ( ![X146:( $i > $o )]:
% 95.34/12.70 ( ( ?[X148:$i]:
% 95.34/12.70 ( ( X146 @ X148 ) &
% 95.34/12.70 ( ![X150:$i]:
% 95.34/12.70 ( ( X146 @ X150 ) =>
% 95.34/12.70 ( ( X148 ) = ( X150 ) ) ) ) ) ) =>
% 95.34/12.70 ( ?[X152:$i]: ( X146 @ X152 ) ) ) ) =>
% 95.34/12.70 ( ( ![X154:$i,X156:$i]:
% 95.34/12.70 ( ( ![X158:$i]:
% 95.34/12.70 ( ( in @ X158 @ X154 ) =>
% 95.34/12.70 ( in @ X158 @ X156 ) ) ) =>
% 95.34/12.70 ( ( ![X160:$i]:
% 95.34/12.70 ( ( in @ X160 @ X156 ) =>
% 95.34/12.70 ( in @ X160 @ X154 ) ) ) =>
% 95.34/12.70 ( ( X154 ) = ( X156 ) ) ) ) ) =>
% 95.34/12.70 ( ( ![X162:$i]:
% 95.34/12.70 ( ( ![X164:$i]:
% 95.34/12.70 ( ~( in @ X164 @ X162 ) ) ) =>
% 95.34/12.70 ( ( X162 ) = ( emptyset ) ) ) ) =>
% 95.34/12.70 ( ( ![X166:$i]:
% 95.34/12.70 ( ( ![X168:$i]:
% 95.34/12.70 ( ~( in @ X168 @ X166 ) ) ) =>
% 95.34/12.70 ( ( X166 ) =
% 95.34/12.70 ( emptyset ) ) ) ) =>
% 95.34/12.70 ( ( ![X170:$i,
% 95.34/12.70 X172:( $i > $o ),
% 95.34/12.70 X174:$i]:
% 95.34/12.70 ( ( in @ X174 @ X170 ) =>
% 95.34/12.70 ( ( in @
% 95.34/12.70 X174 @
% 95.34/12.70 ( dsetconstr @
% 95.34/12.70 X170 @
% 95.34/12.70 ( ^[V_5:$i]:
% 95.34/12.70 ( X172 @ V_5 ) ) ) ) <=>
% 95.34/12.70 ( X172 @ X174 ) ) ) ) =>
% 95.34/12.70 ( ( ![X176:$i]:
% 95.34/12.70 ( ( ( X176 ) !=
% 95.34/12.70 ( emptyset ) ) =>
% 95.34/12.70 ( ?[X178:$i]:
% 95.34/12.70 ( in @ X178 @ X176 ) ) ) ) =>
% 95.34/12.70 ( ( ![X180:$i,
% 95.34/12.70 X182:( $i > $o ),
% 95.34/12.70 X184:$i]:
% 95.34/12.70 ( ( in @ X184 @ X180 ) =>
% 95.34/12.70 ( ( X182 @ X184 ) =>
% 95.34/12.70 ( ( dsetconstr @
% 95.34/12.70 X180 @
% 95.34/12.70 ( ^[
% 95.34/12.70 V_6:$i]:
% 95.34/12.70 (
% 95.34/12.70 X182 @ V_6 ) ) ) !=
% 95.34/12.70 ( emptyset ) ) ) ) ) =>
% 95.34/12.70 ( ( ![X186:$i]:
% 95.34/12.70 ( ( ?[X188:$i]:
% 95.34/12.70 ( in @
% 95.34/12.70 X188 @ X186 ) ) =>
% 95.34/12.70 ( ( X186 ) !=
% 95.34/12.70 ( emptyset ) ) ) ) =>
% 95.34/12.70 ( ( ![X190:$i,
% 95.34/12.70 X192:$i]:
% 95.34/12.70 ( in @
% 95.34/12.70 X190 @
% 95.34/12.70 ( setadjoin @
% 95.34/12.70 X190 @ X192 ) ) ) =>
% 95.34/12.70 ( ( in @
% 95.34/12.70 emptyset @
% 95.34/12.70 ( setadjoin @
% 95.34/12.70 emptyset @
% 95.34/12.70 emptyset ) ) =>
% 95.34/12.70 ( ( ![X194:$i,
% 95.34/12.70 X196:$i,
% 95.34/12.70 X198:$i]:
% 95.34/12.70 ( (
% 95.34/12.70 in @
% 95.34/12.70 X198 @
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% 95.34/12.70 X388:$i,
% 95.34/12.70 X390:$i]:
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% 95.34/12.70 (
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% 95.34/12.70 X392:$i,
% 95.34/12.70 X394:$i]:
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% 95.34/12.70 X396:$i,
% 95.34/12.70 X398:$i]:
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% 95.34/12.70 (
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% 95.34/12.70 X400:$i,
% 95.34/12.70 X402:$i]:
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% 95.34/12.70 (
% 95.34/12.70 X400 ) =
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% 95.34/12.70 X404:(
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% 95.34/12.70 ![
% 95.34/12.70 X408:$i]:
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% 95.34/12.70 (
% 95.34/12.70 X408 ) ) ) ) ) ) =>
% 95.34/12.70 (
% 95.34/12.70 ![
% 95.34/12.70 X410:$i,
% 95.34/12.70 X412:$i]:
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 X404 @
% 95.34/12.70 X410 ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 X404 @
% 95.34/12.70 X412 ) =>
% 95.34/12.70 (
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% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 ![
% 95.34/12.70 X414:(
% 95.34/12.70 $i > $o ),
% 95.34/12.70 X416:(
% 95.34/12.70 $i > $o )]:
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 ![
% 95.34/12.70 X418:$i,
% 95.34/12.70 X420:$i]:
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 X418 ) =
% 95.34/12.70 (
% 95.34/12.70 X420 ) ) =>
% 95.34/12.70 (
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% 95.34/12.70 X414 @
% 95.34/12.70 X418 ) <=>
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% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 ?[
% 95.34/12.70 X422:$i]:
% 95.34/12.70 (
% 95.34/12.70 (
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% 95.34/12.70 (
% 95.34/12.70 ![
% 95.34/12.70 X424:$i]:
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% 95.34/12.70 X426:$i]:
% 95.34/12.70 (
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% 95.34/12.70 X416 @
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% 95.34/12.70 (
% 95.34/12.70 ![
% 95.34/12.70 X428:$i]:
% 95.34/12.70 (
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% 95.34/12.70 (
% 95.34/12.70 (
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% 95.34/12.70 X428 ) ) ) ) ) ) ) ) ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 emptyset ) =
% 95.34/12.70 (
% 95.34/12.70 emptyset ) ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 ![
% 95.34/12.70 X430:$i,
% 95.34/12.70 X432:$i]:
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 X430 ) =
% 95.34/12.70 (
% 95.34/12.70 X432 ) ) =>
% 95.34/12.70 (
% 95.34/12.70 ![
% 95.34/12.70 X434:$i,
% 95.34/12.70 X436:$i]:
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 X434 ) =
% 95.34/12.70 (
% 95.34/12.70 X436 ) ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 setadjoin
% 95.34/12.70 @
% 95.34/12.70 X430 @
% 95.34/12.70 X434 ) =
% 95.34/12.70 (
% 95.34/12.70 setadjoin
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% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 ![
% 95.34/12.70 X438:$i,
% 95.34/12.70 X440:$i]:
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 X438 ) =
% 95.34/12.70 (
% 95.34/12.70 X440 ) ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 powerset @
% 95.34/12.70 X438 ) =
% 95.34/12.70 (
% 95.34/12.70 powerset @
% 95.34/12.70 X440 ) ) ) ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 ![
% 95.34/12.70 X442:$i,
% 95.34/12.70 X444:$i]:
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 X442 ) =
% 95.34/12.70 (
% 95.34/12.70 X444 ) ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 setunion @
% 95.34/12.70 X442 ) =
% 95.34/12.70 (
% 95.34/12.70 setunion @
% 95.34/12.70 X444 ) ) ) ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 omega ) =
% 95.34/12.70 (
% 95.34/12.70 omega ) ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 ![
% 95.34/12.70 X446:(
% 95.34/12.70 $i > $o )]:
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 ?[
% 95.34/12.70 X448:$i]:
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 X446 @
% 95.34/12.70 X448 ) &
% 95.34/12.70 (
% 95.34/12.70 ![
% 95.34/12.70 X450:$i]:
% 95.34/12.70 (
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% 95.34/12.70 X446 @
% 95.34/12.70 X450 ) =>
% 95.34/12.70 (
% 95.34/12.70 (
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% 95.34/12.70 (
% 95.34/12.70 X450 ) ) ) ) ) ) =>
% 95.34/12.70 (
% 95.34/12.70 ![
% 95.34/12.70 X452:$i,
% 95.34/12.70 X454:$i]:
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 X446 @
% 95.34/12.70 X452 ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 X446 @
% 95.34/12.70 X454 ) =>
% 95.34/12.70 (
% 95.34/12.70 (
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% 95.34/12.70 X454 ) ) ) ) ) ) ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 ![
% 95.34/12.70 X456:(
% 95.34/12.70 $i > $o ),
% 95.34/12.70 X458:(
% 95.34/12.70 $i > $o )]:
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 ![
% 95.34/12.70 X460:$i,
% 95.34/12.70 X462:$i]:
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 X460 ) =
% 95.34/12.70 (
% 95.34/12.70 X462 ) ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 X456 @
% 95.34/12.70 X460 ) <=>
% 95.34/12.70 (
% 95.34/12.70 X458 @
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% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 ?[
% 95.34/12.70 X464:$i]:
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 X456 @
% 95.34/12.70 X464 ) &
% 95.34/12.70 (
% 95.34/12.70 ![
% 95.34/12.70 X466:$i]:
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 X456 @
% 95.34/12.70 X466 ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 X464 ) =
% 95.34/12.70 (
% 95.34/12.70 X466 ) ) ) ) ) ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 ?[
% 95.34/12.70 X468:$i]:
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 X458 @
% 95.34/12.70 X468 ) &
% 95.34/12.70 (
% 95.34/12.70 ![
% 95.34/12.70 X470:$i]:
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 X458 @
% 95.34/12.70 X470 ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 X468 ) =
% 95.34/12.70 (
% 95.34/12.70 X470 ) ) ) ) ) ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 descr @
% 95.34/12.70 (
% 95.34/12.70 ^[
% 95.34/12.70 V_9:$i]:
% 95.34/12.70 (
% 95.34/12.70 X456 @ V_9 ) ) ) =
% 95.34/12.70 (
% 95.34/12.70 descr @
% 95.34/12.70 (
% 95.34/12.70 ^[
% 95.34/12.70 V_10:$i]:
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% 95.34/12.70 X458 @
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% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 ![
% 95.34/12.70 X472:$i,
% 95.34/12.70 X474:$i]:
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 X472 ) =
% 95.34/12.70 (
% 95.34/12.70 X474 ) ) =>
% 95.34/12.70 (
% 95.34/12.70 ![
% 95.34/12.70 X476:(
% 95.34/12.70 $i > $o ),
% 95.34/12.70 X478:(
% 95.34/12.70 $i > $o )]:
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 ![
% 95.34/12.70 X480:$i]:
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 in @
% 95.34/12.70 X480 @
% 95.34/12.70 X472 ) =>
% 95.34/12.70 (
% 95.34/12.70 ![
% 95.34/12.70 X482:$i]:
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 in @
% 95.34/12.70 X482 @
% 95.34/12.70 X474 ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 X480 ) =
% 95.34/12.70 (
% 95.34/12.70 X482 ) ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 X476 @
% 95.34/12.70 X480 ) <=>
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% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 dsetconstr
% 95.34/12.70 @
% 95.34/12.70 X472 @
% 95.34/12.70 (
% 95.34/12.70 ^[
% 95.34/12.70 V_11:$i]:
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% 95.34/12.70 (
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% 95.34/12.70 @
% 95.34/12.70 X474 @
% 95.34/12.70 (
% 95.34/12.70 ^[
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% 95.34/12.70 (
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% 95.34/12.70 ![
% 95.34/12.70 X484:$i,
% 95.34/12.70 X486:$i]:
% 95.34/12.70 (
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% 95.34/12.70 X488:$i]:
% 95.34/12.70 (
% 95.34/12.70 (
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% 95.34/12.70 (
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% 95.34/12.70 (
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% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 ![
% 95.34/12.70 X490:$i,
% 95.34/12.70 X492:$i]:
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 X490 ) =
% 95.34/12.70 (
% 95.34/12.70 X492 ) ) =>
% 95.34/12.70 (
% 95.34/12.70 subset @
% 95.34/12.70 X492 @
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% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 ![
% 95.34/12.70 X494:$i,
% 95.34/12.70 X496:$i]:
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 X494 ) =
% 95.34/12.70 (
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% 95.34/12.70 (
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% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 ![
% 95.34/12.70 X498:$i,
% 95.34/12.70 X500:$i]:
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 ![
% 95.34/12.70 X502:$i]:
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 in @
% 95.34/12.70 X502 @
% 95.34/12.70 X498 ) =>
% 95.34/12.70 (
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% 95.34/12.70 X502 @
% 95.34/12.70 X500 ) ) ) =>
% 95.34/12.70 (
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% 95.34/12.70 X498 @
% 95.34/12.70 X500 ) ) ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 ![
% 95.34/12.70 X504:$i]:
% 95.34/12.70 (
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% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 ![
% 95.34/12.70 X506:$i,
% 95.34/12.70 X508:$i,
% 95.34/12.70 X510:$i]:
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 subset @
% 95.34/12.70 X506 @
% 95.34/12.70 X508 ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 in @
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% 95.34/12.70 (
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% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 ![
% 95.34/12.70 X512:$i,
% 95.34/12.70 X514:$i,
% 95.34/12.70 X516:$i]:
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 subset @
% 95.34/12.70 X512 @
% 95.34/12.70 X514 ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 ~(
% 95.34/12.70 in @
% 95.34/12.70 X516 @
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% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 ![
% 95.34/12.70 X518:$i,
% 95.34/12.70 X520:$i,
% 95.34/12.70 X522:$i]:
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 in @
% 95.34/12.70 X522 @
% 95.34/12.70 X518 ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 ~(
% 95.34/12.70 in @
% 95.34/12.70 X522 @
% 95.34/12.70 X520 ) ) =>
% 95.34/12.70 (
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% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 ![
% 95.34/12.70 X524:$i,
% 95.34/12.70 X526:$i]:
% 95.34/12.70 (
% 95.34/12.70 (
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% 95.34/12.70 subset @
% 95.34/12.70 X524 @
% 95.34/12.70 X526 ) ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 X524 ) !=
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% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 ![
% 95.34/12.70 X528:$i,
% 95.34/12.70 X530:$i,
% 95.34/12.70 X532:$i]:
% 95.34/12.70 (
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% 95.34/12.70 in @
% 95.34/12.70 X532 @
% 95.34/12.70 X528 ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 ~(
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% 95.34/12.70 X532 @
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% 95.34/12.70 (
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% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 ![
% 95.34/12.70 X534:$i]:
% 95.34/12.70 (
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% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 ![
% 95.34/12.70 X536:$i,
% 95.34/12.70 X538:$i,
% 95.34/12.70 X540:$i]:
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 subset @
% 95.34/12.70 X536 @
% 95.34/12.70 X538 ) =>
% 95.34/12.70 (
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% 95.34/12.70 subset @
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% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 ![
% 95.34/12.70 X542:$i,
% 95.34/12.70 X544:$i]:
% 95.34/12.70 (
% 95.34/12.70 subset @
% 95.34/12.70 X544 @
% 95.34/12.70 (
% 95.34/12.70 setadjoin
% 95.34/12.70 @
% 95.34/12.70 X542 @
% 95.34/12.70 X544 ) ) ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 ![
% 95.34/12.70 X546:$i,
% 95.34/12.70 X548:$i,
% 95.34/12.70 X550:$i]:
% 95.34/12.70 (
% 95.34/12.70 (
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% 95.34/12.70 (
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% 95.34/12.70 (
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% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 ![
% 95.34/12.70 X552:$i,
% 95.34/12.70 X554:$i]:
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 subset @
% 95.34/12.70 X552 @
% 95.34/12.70 X554 ) =>
% 95.34/12.70 (
% 95.34/12.70 in @
% 95.34/12.70 X552 @
% 95.34/12.70 (
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% 95.34/12.70 X554 ) ) ) ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 ![
% 95.34/12.70 X556:$i,
% 95.34/12.70 X558:$i]:
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 subset @
% 95.34/12.70 X556 @
% 95.34/12.70 X558 ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 subset @
% 95.34/12.70 X558 @
% 95.34/12.70 X556 ) =>
% 95.34/12.70 (
% 95.34/12.70 (
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% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 ![
% 95.34/12.70 X560:$i]:
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 subset @
% 95.34/12.70 X560 @
% 95.34/12.70 emptyset ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 X560 ) =
% 95.34/12.70 (
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% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 ![
% 95.34/12.70 X562:$i,
% 95.34/12.70 X564:$i]:
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 subset @
% 95.34/12.70 X564 @
% 95.34/12.70 X562 ) =>
% 95.34/12.70 (
% 95.34/12.70 in @
% 95.34/12.70 X564 @
% 95.34/12.70 (
% 95.34/12.70 powerset @
% 95.34/12.70 X562 ) ) ) ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 ![
% 95.34/12.70 X566:$i,
% 95.34/12.70 X568:$i]:
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 in @
% 95.34/12.70 X568 @
% 95.34/12.70 (
% 95.34/12.70 powerset @
% 95.34/12.70 X566 ) ) =>
% 95.34/12.70 (
% 95.34/12.70 subset @
% 95.34/12.70 X568 @
% 95.34/12.70 X566 ) ) ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 ![
% 95.34/12.70 X570:$i]:
% 95.34/12.70 (
% 95.34/12.70 in @
% 95.34/12.70 X570 @
% 95.34/12.70 (
% 95.34/12.70 powerset @
% 95.34/12.70 X570 ) ) ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 ![
% 95.34/12.70 X572:$i,
% 95.34/12.70 X574:$i]:
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 subset @
% 95.34/12.70 X572 @
% 95.34/12.70 X574 ) =>
% 95.34/12.70 (
% 95.34/12.70 subset @
% 95.34/12.70 (
% 95.34/12.70 powerset @
% 95.34/12.70 X572 ) @
% 95.34/12.70 (
% 95.34/12.70 powerset @
% 95.34/12.70 X574 ) ) ) ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 ![
% 95.34/12.70 X576:$i,
% 95.34/12.70 X578:(
% 95.34/12.70 $i > $o )]:
% 95.34/12.70 (
% 95.34/12.70 in @
% 95.34/12.70 (
% 95.34/12.70 dsetconstr
% 95.34/12.70 @
% 95.34/12.70 X576 @
% 95.34/12.70 (
% 95.34/12.70 ^[
% 95.34/12.70 V_13:$i]:
% 95.34/12.70 (
% 95.34/12.70 X578 @
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% 95.34/12.70 (
% 95.34/12.70 powerset @
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% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 ![
% 95.34/12.70 X580:$i,
% 95.34/12.70 X582:(
% 95.34/12.70 $i > $o )]:
% 95.34/12.70 (
% 95.34/12.70 subset @
% 95.34/12.70 (
% 95.34/12.70 dsetconstr
% 95.34/12.70 @
% 95.34/12.70 X580 @
% 95.34/12.70 (
% 95.34/12.70 ^[
% 95.34/12.70 V_14:$i]:
% 95.34/12.70 (
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% 95.34/12.70 X580 ) ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 ![
% 95.34/12.70 X584:$i,
% 95.34/12.70 X586:$i,
% 95.34/12.70 X588:$i]:
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 in @
% 95.34/12.70 X588 @
% 95.34/12.70 X584 ) =>
% 95.34/12.70 (
% 95.34/12.70 in @
% 95.34/12.70 X588 @
% 95.34/12.70 (
% 95.34/12.70 binunion @
% 95.34/12.70 X584 @
% 95.34/12.70 X586 ) ) ) ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 ![
% 95.34/12.70 X590:$i,
% 95.34/12.70 X592:$i]:
% 95.34/12.70 (
% 95.34/12.70 in @
% 95.34/12.70 X592 @
% 95.34/12.70 (
% 95.34/12.70 setadjoin
% 95.34/12.70 @
% 95.34/12.70 X590 @
% 95.34/12.70 (
% 95.34/12.70 setadjoin
% 95.34/12.70 @
% 95.34/12.70 X592 @
% 95.34/12.70 emptyset ) ) ) ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 ![
% 95.34/12.70 X594:$i,
% 95.34/12.70 X596:$i,
% 95.34/12.70 X598:$i]:
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 in @
% 95.34/12.70 X598 @
% 95.34/12.70 X596 ) =>
% 95.34/12.70 (
% 95.34/12.70 in @
% 95.34/12.70 X598 @
% 95.34/12.70 (
% 95.34/12.70 binunion @
% 95.34/12.70 X594 @
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% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 ![
% 95.34/12.70 X600:$i,
% 95.34/12.70 X602:$i,
% 95.34/12.70 X604:$i,
% 95.34/12.70 X606:$o]:
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 in @
% 95.34/12.70 X604 @
% 95.34/12.70 (
% 95.34/12.70 binunion @
% 95.34/12.70 X600 @
% 95.34/12.70 X602 ) ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 in @
% 95.34/12.70 X604 @
% 95.34/12.70 X600 ) =>
% 95.34/12.70 (
% 95.34/12.70 X606 ) ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 in @
% 95.34/12.70 X604 @
% 95.34/12.70 X602 ) =>
% 95.34/12.70 (
% 95.34/12.70 X606 ) ) =>
% 95.34/12.70 (
% 95.34/12.70 X606 ) ) ) ) ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 ![
% 95.34/12.70 X608:$i,
% 95.34/12.70 X610:$i,
% 95.34/12.70 X612:$i]:
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 in @
% 95.34/12.70 X612 @
% 95.34/12.70 (
% 95.34/12.70 binunion @
% 95.34/12.70 X608 @
% 95.34/12.70 X610 ) ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 in @
% 95.34/12.70 X612 @
% 95.34/12.70 X610 ) |
% 95.34/12.70 (
% 95.34/12.70 in @
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% 95.34/12.70 X608 ) ) ) ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 ![
% 95.34/12.70 X614:$i,
% 95.34/12.70 X616:$i]:
% 95.34/12.70 (
% 95.34/12.70 subset @
% 95.34/12.70 X614 @
% 95.34/12.70 (
% 95.34/12.70 binunion @
% 95.34/12.70 X614 @
% 95.34/12.70 X616 ) ) ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 ![
% 95.34/12.70 X618:$i,
% 95.34/12.70 X620:$i]:
% 95.34/12.70 (
% 95.34/12.70 subset @
% 95.34/12.70 X620 @
% 95.34/12.70 (
% 95.34/12.70 binunion @
% 95.34/12.70 X618 @
% 95.34/12.70 X620 ) ) ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 ![
% 95.34/12.70 X622:$i,
% 95.34/12.70 X624:$i,
% 95.34/12.70 X626:$i]:
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 in @
% 95.34/12.70 X626 @
% 95.34/12.70 X622 ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 in @
% 95.34/12.70 X626 @
% 95.34/12.70 X624 ) =>
% 95.34/12.70 (
% 95.34/12.70 in @
% 95.34/12.70 X626 @
% 95.34/12.70 (
% 95.34/12.70 binintersect
% 95.34/12.70 @
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% 95.34/12.70 X624 ) ) ) ) ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 ![
% 95.34/12.70 X628:$i,
% 95.34/12.70 X630:$i,
% 95.34/12.70 X632:$i]:
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 subset @
% 95.34/12.70 X632 @
% 95.34/12.70 X628 ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 subset @
% 95.34/12.70 X632 @
% 95.34/12.70 X630 ) =>
% 95.34/12.70 (
% 95.34/12.70 subset @
% 95.34/12.70 X632 @
% 95.34/12.70 (
% 95.34/12.70 binintersect
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% 95.34/12.70 X630 ) ) ) ) ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 ![
% 95.34/12.70 X634:$i,
% 95.34/12.70 X636:$i,
% 95.34/12.70 X638:$i]:
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 in @
% 95.34/12.70 X638 @
% 95.34/12.70 (
% 95.34/12.70 binintersect
% 95.34/12.70 @
% 95.34/12.70 X634 @
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% 95.34/12.70 (
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% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 ![
% 95.34/12.70 X640:$i,
% 95.34/12.70 X642:$i]:
% 95.34/12.70 (
% 95.34/12.70 subset @
% 95.34/12.70 (
% 95.34/12.70 binintersect
% 95.34/12.70 @
% 95.34/12.70 X640 @
% 95.34/12.70 X642 ) @
% 95.34/12.70 X640 ) ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 ![
% 95.34/12.70 X644:$i,
% 95.34/12.70 X646:$i]:
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 subset @
% 95.34/12.70 X644 @
% 95.34/12.70 X646 ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 binintersect
% 95.34/12.70 @
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% 95.34/12.70 (
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% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 ![
% 95.34/12.70 X648:$i,
% 95.34/12.70 X650:$i]:
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 binintersect
% 95.34/12.70 @
% 95.34/12.70 X648 @
% 95.34/12.70 X650 ) =
% 95.34/12.70 (
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% 95.34/12.70 (
% 95.34/12.70 subset @
% 95.34/12.70 X650 @
% 95.34/12.70 X648 ) ) ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 ![
% 95.34/12.70 X652:$i,
% 95.34/12.70 X654:$i,
% 95.34/12.70 X656:$i]:
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 in @
% 95.34/12.70 X656 @
% 95.34/12.70 (
% 95.34/12.70 binintersect
% 95.34/12.70 @
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% 95.34/12.70 (
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% 95.34/12.70 X656 @
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% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 ![
% 95.34/12.70 X658:$i,
% 95.34/12.70 X660:$i]:
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 ~(
% 95.34/12.70 ?[
% 95.34/12.70 X662:$i]:
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 in @
% 95.34/12.70 X662 @
% 95.34/12.70 X658 ) &
% 95.34/12.70 (
% 95.34/12.70 in @
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% 95.34/12.70 X660 ) ) ) ) =>
% 95.34/12.70 (
% 95.34/12.70 (
% 95.34/12.70 binintersect
% 95.34/12.70 @
% 95.34/12.70 X658 @
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% 95.81/12.70 X842:$i,
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% 95.81/12.70 (
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% 95.81/12.70 X848:$i,
% 95.81/12.70 X850:$i,
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% 95.81/12.70 X866:$i,
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% 95.81/12.70 (
% 95.81/12.70 (
% 95.81/12.70 ![
% 95.81/12.70 X872:$i,
% 95.81/12.70 X874:$i]:
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% 95.81/12.70 X874 @
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% 95.81/12.70 (
% 95.81/12.70 (
% 95.81/12.70 ![
% 95.81/12.70 X884:$i,
% 95.81/12.70 X886:(
% 95.81/12.70 $i > $o )]:
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% 95.81/12.70 (
% 95.81/12.70 ![
% 95.81/12.70 X888:$i]:
% 95.81/12.70 (
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% 95.81/12.70 X890:$i]:
% 95.81/12.70 (
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% 95.81/12.70 (
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% 95.81/12.70 X888 ) =>
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% 95.81/12.70 (
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% 95.81/12.70 (
% 95.81/12.70 (
% 95.81/12.70 ?[
% 95.81/12.70 X892:$i]:
% 95.81/12.70 (
% 95.81/12.70 (
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% 95.81/12.70 X892 @
% 95.81/12.70 X884 ) &
% 95.81/12.70 (
% 95.81/12.70 X886 @
% 95.81/12.70 X892 ) ) ) =>
% 95.81/12.70 (
% 95.81/12.70 singleton
% 95.81/12.70 @
% 95.81/12.70 (
% 95.81/12.70 dsetconstr
% 95.81/12.70 @
% 95.81/12.70 X884 @
% 95.81/12.70 (
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% 95.81/12.70 (
% 95.81/12.70 (
% 95.81/12.70 ![
% 95.81/12.70 X894:$i,
% 95.81/12.70 X896:(
% 95.81/12.70 $i > $o )]:
% 95.81/12.70 (
% 95.81/12.70 (
% 95.81/12.70 ex1 @
% 95.81/12.70 X894 @
% 95.81/12.70 (
% 95.81/12.70 ^[
% 95.81/12.70 V_16:$i]:
% 95.81/12.70 (
% 95.81/12.70 X896 @
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% 95.81/12.70 (
% 95.81/12.70 ?[
% 95.81/12.70 X898:$i]:
% 95.81/12.70 (
% 95.81/12.70 (
% 95.81/12.70 in @
% 95.81/12.70 X898 @
% 95.81/12.70 X894 ) &
% 95.81/12.70 (
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% 95.81/12.70 (
% 95.81/12.70 (
% 95.81/12.70 ![
% 95.81/12.70 X900:$i,
% 95.81/12.70 X902:(
% 95.81/12.70 $i > $o ),
% 95.81/12.70 X904:$i]:
% 95.81/12.70 (
% 95.81/12.70 (
% 95.81/12.70 in @
% 95.81/12.70 X904 @
% 95.81/12.70 X900 ) =>
% 95.81/12.70 (
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% 95.81/12.70 (
% 95.81/12.70 (
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% 95.81/12.70 X906:$i]:
% 95.81/12.70 (
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% 95.81/12.70 X906 @
% 95.81/12.70 X900 ) =>
% 95.81/12.70 (
% 95.81/12.70 (
% 95.81/12.70 X902 @
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% 95.81/12.70 (
% 95.81/12.70 (
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% 95.81/12.70 (
% 95.81/12.70 ex1 @
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% 95.81/12.70 V_17:$i]:
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% 95.81/12.70 (
% 95.81/12.70 (
% 95.81/12.70 ![
% 95.81/12.71 X908:$i,
% 95.81/12.71 X910:(
% 95.81/12.71 $i > $o )]:
% 95.81/12.71 (
% 95.81/12.71 (
% 95.81/12.71 ![
% 95.81/12.71 X912:$i]:
% 95.81/12.71 (
% 95.81/12.71 (
% 95.81/12.71 in @
% 95.81/12.71 X912 @
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% 95.81/12.71 (
% 95.81/12.71 ![
% 95.81/12.71 X914:$i]:
% 95.81/12.71 (
% 95.81/12.71 (
% 95.81/12.71 in @
% 95.81/12.71 X914 @
% 95.81/12.71 X908 ) =>
% 95.81/12.71 (
% 95.81/12.71 (
% 95.81/12.71 X910 @
% 95.81/12.71 X912 ) =>
% 95.81/12.71 (
% 95.81/12.71 (
% 95.81/12.71 X910 @
% 95.81/12.71 X914 ) =>
% 95.81/12.71 (
% 95.81/12.71 (
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% 95.81/12.71 (
% 95.81/12.71 (
% 95.81/12.71 ?[
% 95.81/12.71 X916:$i]:
% 95.81/12.71 (
% 95.81/12.71 (
% 95.81/12.71 in @
% 95.81/12.71 X916 @
% 95.81/12.71 X908 ) &
% 95.81/12.71 (
% 95.81/12.71 X910 @
% 95.81/12.71 X916 ) ) ) =>
% 95.81/12.71 (
% 95.81/12.71 ex1 @
% 95.81/12.71 X908 @
% 95.81/12.71 (
% 95.81/12.71 ^[
% 95.81/12.71 V_18:$i]:
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% 95.81/12.71 (
% 95.81/12.71 (
% 95.81/12.71 ![
% 95.81/12.71 X918:$i,
% 95.81/12.71 X920:$i]:
% 95.81/12.71 (
% 95.81/12.71 (
% 95.81/12.71 (
% 95.81/12.71 setadjoin
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% 95.81/12.71 X918 @
% 95.81/12.71 emptyset ) =
% 95.81/12.71 (
% 95.81/12.71 setadjoin
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% 95.81/12.71 (
% 95.81/12.71 (
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% 95.81/12.71 (
% 95.81/12.71 (
% 95.81/12.71 ![
% 95.81/12.71 X922:$i,
% 95.81/12.71 X924:$i,
% 95.81/12.71 X926:$i]:
% 95.81/12.71 (
% 95.81/12.71 (
% 95.81/12.71 in @
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% 95.81/12.71 @
% 95.81/12.71 X926 @
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% 95.81/12.71 (
% 95.81/12.71 (
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% 95.81/12.71 (
% 95.81/12.71 (
% 95.81/12.71 ![
% 95.81/12.71 X928:$i]:
% 95.81/12.71 (
% 95.81/12.71 (
% 95.81/12.71 iskpair @
% 95.81/12.71 X928 ) =>
% 95.81/12.71 (
% 95.81/12.71 singleton
% 95.81/12.71 @
% 95.81/12.71 (
% 95.81/12.71 dsetconstr
% 95.81/12.71 @
% 95.81/12.71 (
% 95.81/12.71 setunion @
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% 95.81/12.71 (
% 95.81/12.71 ^[
% 95.81/12.71 V_19:$i]:
% 95.81/12.71 (
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% 95.81/12.71 (
% 95.81/12.71 (
% 95.81/12.71 ![
% 95.81/12.71 X930:$i]:
% 95.81/12.71 (
% 95.81/12.71 (
% 95.81/12.71 singleton
% 95.81/12.71 @
% 95.81/12.71 X930 ) =>
% 95.81/12.71 (
% 95.81/12.71 in @
% 95.81/12.71 (
% 95.81/12.71 setunion @
% 95.81/12.71 X930 ) @
% 95.81/12.71 X930 ) ) ) =>
% 95.81/12.71 (
% 95.81/12.71 (
% 95.81/12.71 ![
% 95.81/12.71 X932:$i,
% 95.81/12.71 X934:$i]:
% 95.81/12.71 (
% 95.81/12.71 (
% 95.81/12.71 kfst @
% 95.81/12.71 (
% 95.81/12.71 kpair @
% 95.81/12.71 X932 @
% 95.81/12.71 X934 ) ) =
% 95.81/12.71 (
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% 95.81/12.71 (
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% 95.81/12.71 (
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% 95.81/12.72 in @
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% 95.81/12.72 X1890 ) =>
% 95.81/12.72 (
% 95.81/12.72 ?[
% 95.81/12.72 X1898:$i]:
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 in @
% 95.81/12.72 X1898 @
% 95.81/12.72 X1892 ) &
% 95.81/12.72 (
% 95.81/12.72 X1894 @
% 95.81/12.72 X1896 @
% 95.81/12.72 X1898 ) ) ) ) ) =>
% 95.81/12.72 (
% 95.81/12.72 ![
% 95.81/12.72 X1900:$i]:
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 in @
% 95.81/12.72 X1900 @
% 95.81/12.72 (
% 95.81/12.72 breln1Set
% 95.81/12.72 @
% 95.81/12.72 X1892 ) ) =>
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 reflwellordering
% 95.81/12.72 @
% 95.81/12.72 X1892 @
% 95.81/12.72 X1900 ) =>
% 95.81/12.72 (
% 95.81/12.72 ![
% 95.81/12.72 X1902:$i]:
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 in @
% 95.81/12.72 X1902 @
% 95.81/12.72 X1890 ) =>
% 95.81/12.72 (
% 95.81/12.72 singleton
% 95.81/12.72 @
% 95.81/12.72 (
% 95.81/12.72 dsetconstr
% 95.81/12.72 @
% 95.81/12.72 X1892 @
% 95.81/12.72 (
% 95.81/12.72 ^[
% 95.81/12.72 V_53:$i]:
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 ![
% 95.81/12.72 X1904:$i]:
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 in @
% 95.81/12.72 X1904 @
% 95.81/12.72 X1892 ) =>
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 X1894 @
% 95.81/12.72 X1902 @
% 95.81/12.72 X1904 ) =>
% 95.81/12.72 (
% 95.81/12.72 in @
% 95.81/12.72 (
% 95.81/12.72 kpair @
% 95.81/12.72 V_53 @
% 95.81/12.72 X1904 ) @
% 95.81/12.72 X1900 ) ) ) ) &
% 95.81/12.72 (
% 95.81/12.72 X1894 @
% 95.81/12.72 X1902 @
% 95.81/12.72 V_53 ) ) ) ) ) ) ) ) ) ) ) ) =>
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 ![
% 95.81/12.72 X1906:$i,
% 95.81/12.72 X1908:(
% 95.81/12.72 $i > $i >
% 95.81/12.72 $o )]:
% 95.81/12.72 (
% 95.81/12.72 breln1 @
% 95.81/12.72 X1906 @
% 95.81/12.72 (
% 95.81/12.72 dpsetconstr
% 95.81/12.72 @
% 95.81/12.72 X1906 @
% 95.81/12.72 X1906 @
% 95.81/12.72 (
% 95.81/12.72 ^[
% 95.81/12.72 V_54:$i,
% 95.81/12.72 V_55:$i]:
% 95.81/12.72 (
% 95.81/12.72 X1908 @
% 95.81/12.72 V_54 @
% 95.81/12.72 V_55 ) ) ) ) ) =>
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 ![
% 95.81/12.72 X1910:$i,
% 95.81/12.72 X1912:$i]:
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 breln1 @
% 95.81/12.72 X1910 @
% 95.81/12.72 X1912 ) =>
% 95.81/12.72 (
% 95.81/12.72 ![
% 95.81/12.72 X1914:(
% 95.81/12.72 $i > $o )]:
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 ![
% 95.81/12.72 X1916:$i]:
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 in @
% 95.81/12.72 X1916 @
% 95.81/12.72 X1910 ) =>
% 95.81/12.72 (
% 95.81/12.72 ![
% 95.81/12.72 X1918:$i]:
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 in @
% 95.81/12.72 X1918 @
% 95.81/12.72 X1910 ) =>
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 in @
% 95.81/12.72 (
% 95.81/12.72 kpair @
% 95.81/12.72 X1916 @
% 95.81/12.72 X1918 ) @
% 95.81/12.72 X1912 ) =>
% 95.81/12.72 (
% 95.81/12.72 X1914 @
% 95.81/12.72 (
% 95.81/12.72 kpair @
% 95.81/12.72 X1916 @
% 95.81/12.72 X1918 ) ) ) ) ) ) ) =>
% 95.81/12.72 (
% 95.81/12.72 ![
% 95.81/12.72 X1920:$i]:
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 in @
% 95.81/12.72 X1920 @
% 95.81/12.72 X1912 ) =>
% 95.81/12.72 (
% 95.81/12.72 X1914 @
% 95.81/12.72 X1920 ) ) ) ) ) ) ) =>
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 ![
% 95.81/12.72 X1922:$i,
% 95.81/12.72 X1924:$i]:
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 breln1 @
% 95.81/12.72 X1922 @
% 95.81/12.72 X1924 ) =>
% 95.81/12.72 (
% 95.81/12.72 ![
% 95.81/12.72 X1926:$i]:
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 breln1 @
% 95.81/12.72 X1922 @
% 95.81/12.72 X1926 ) =>
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 ![
% 95.81/12.72 X1928:$i]:
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 in @
% 95.81/12.72 X1928 @
% 95.81/12.72 X1922 ) =>
% 95.81/12.72 (
% 95.81/12.72 ![
% 95.81/12.72 X1930:$i]:
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 in @
% 95.81/12.72 X1930 @
% 95.81/12.72 X1922 ) =>
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 in @
% 95.81/12.72 (
% 95.81/12.72 kpair @
% 95.81/12.72 X1928 @
% 95.81/12.72 X1930 ) @
% 95.81/12.72 X1924 ) =>
% 95.81/12.72 (
% 95.81/12.72 in @
% 95.81/12.72 (
% 95.81/12.72 kpair @
% 95.81/12.72 X1928 @
% 95.81/12.72 X1930 ) @
% 95.81/12.72 X1926 ) ) ) ) ) ) =>
% 95.81/12.72 (
% 95.81/12.72 subset @
% 95.81/12.72 X1924 @
% 95.81/12.72 X1926 ) ) ) ) ) ) =>
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 ![
% 95.81/12.72 X1932:$i,
% 95.81/12.72 X1934:$i]:
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 breln1 @
% 95.81/12.72 X1932 @
% 95.81/12.72 X1934 ) =>
% 95.81/12.72 (
% 95.81/12.72 ![
% 95.81/12.72 X1936:$i]:
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 breln1 @
% 95.81/12.72 X1932 @
% 95.81/12.72 X1936 ) =>
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 ![
% 95.81/12.72 X1938:$i]:
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 in @
% 95.81/12.72 X1938 @
% 95.81/12.72 X1932 ) =>
% 95.81/12.72 (
% 95.81/12.72 ![
% 95.81/12.72 X1940:$i]:
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 in @
% 95.81/12.72 X1940 @
% 95.81/12.72 X1932 ) =>
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 in @
% 95.81/12.72 (
% 95.81/12.72 kpair @
% 95.81/12.72 X1938 @
% 95.81/12.72 X1940 ) @
% 95.81/12.72 X1934 ) =>
% 95.81/12.72 (
% 95.81/12.72 in @
% 95.81/12.72 (
% 95.81/12.72 kpair @
% 95.81/12.72 X1938 @
% 95.81/12.72 X1940 ) @
% 95.81/12.72 X1936 ) ) ) ) ) ) =>
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 ![
% 95.81/12.72 X1942:$i]:
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 in @
% 95.81/12.72 X1942 @
% 95.81/12.72 X1932 ) =>
% 95.81/12.72 (
% 95.81/12.72 ![
% 95.81/12.72 X1944:$i]:
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 in @
% 95.81/12.72 X1944 @
% 95.81/12.72 X1932 ) =>
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 in @
% 95.81/12.72 (
% 95.81/12.72 kpair @
% 95.81/12.72 X1942 @
% 95.81/12.72 X1944 ) @
% 95.81/12.72 X1936 ) =>
% 95.81/12.72 (
% 95.81/12.72 in @
% 95.81/12.72 (
% 95.81/12.72 kpair @
% 95.81/12.72 X1942 @
% 95.81/12.72 X1944 ) @
% 95.81/12.72 X1934 ) ) ) ) ) ) =>
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 X1934 ) =
% 95.81/12.72 (
% 95.81/12.72 X1936 ) ) ) ) ) ) ) ) =>
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 ![
% 95.81/12.72 X1946:$i,
% 95.81/12.72 X1948:$i]:
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 breln1 @
% 95.81/12.72 X1946 @
% 95.81/12.72 X1948 ) =>
% 95.81/12.72 (
% 95.81/12.72 breln1 @
% 95.81/12.72 X1946 @
% 95.81/12.72 (
% 95.81/12.72 breln1invset
% 95.81/12.72 @
% 95.81/12.72 X1946 @
% 95.81/12.72 X1948 ) ) ) ) =>
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 ![
% 95.81/12.72 X1950:$i,
% 95.81/12.72 X1952:$i]:
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 breln1 @
% 95.81/12.72 X1950 @
% 95.81/12.72 X1952 ) =>
% 95.81/12.72 (
% 95.81/12.72 ![
% 95.81/12.72 X1954:$i]:
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 in @
% 95.81/12.72 X1954 @
% 95.81/12.72 X1950 ) =>
% 95.81/12.72 (
% 95.81/12.72 ![
% 95.81/12.72 X1956:$i]:
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 in @
% 95.81/12.72 X1956 @
% 95.81/12.72 X1950 ) =>
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 in @
% 95.81/12.72 (
% 95.81/12.72 kpair @
% 95.81/12.72 X1954 @
% 95.81/12.72 X1956 ) @
% 95.81/12.72 X1952 ) =>
% 95.81/12.72 (
% 95.81/12.72 in @
% 95.81/12.72 (
% 95.81/12.72 kpair @
% 95.81/12.72 X1956 @
% 95.81/12.72 X1954 ) @
% 95.81/12.72 (
% 95.81/12.72 breln1invset
% 95.81/12.72 @
% 95.81/12.72 X1950 @
% 95.81/12.72 X1952 ) ) ) ) ) ) ) ) ) =>
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 ![
% 95.81/12.72 X1958:$i,
% 95.81/12.72 X1960:$i]:
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 breln1 @
% 95.81/12.72 X1958 @
% 95.81/12.72 X1960 ) =>
% 95.81/12.72 (
% 95.81/12.72 ![
% 95.81/12.72 X1962:$i]:
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 in @
% 95.81/12.72 X1962 @
% 95.81/12.72 X1958 ) =>
% 95.81/12.72 (
% 95.81/12.72 ![
% 95.81/12.72 X1964:$i]:
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 in @
% 95.81/12.72 X1964 @
% 95.81/12.72 X1958 ) =>
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 in @
% 95.81/12.72 (
% 95.81/12.72 kpair @
% 95.81/12.72 X1964 @
% 95.81/12.72 X1962 ) @
% 95.81/12.72 (
% 95.81/12.72 breln1invset
% 95.81/12.72 @
% 95.81/12.72 X1958 @
% 95.81/12.72 X1960 ) ) =>
% 95.81/12.72 (
% 95.81/12.72 in @
% 95.81/12.72 (
% 95.81/12.72 kpair @
% 95.81/12.72 X1962 @
% 95.81/12.72 X1964 ) @
% 95.81/12.72 X1960 ) ) ) ) ) ) ) ) =>
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 ![
% 95.81/12.72 X1966:$i,
% 95.81/12.72 X1968:$i]:
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 breln1 @
% 95.81/12.72 X1966 @
% 95.81/12.72 X1968 ) =>
% 95.81/12.72 (
% 95.81/12.72 ![
% 95.81/12.72 X1970:$i]:
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 breln1 @
% 95.81/12.72 X1966 @
% 95.81/12.72 X1970 ) =>
% 95.81/12.72 (
% 95.81/12.72 breln1 @
% 95.81/12.72 X1966 @
% 95.81/12.72 (
% 95.81/12.72 breln1compset
% 95.81/12.72 @
% 95.81/12.72 X1966 @
% 95.81/12.72 X1968 @
% 95.81/12.72 X1970 ) ) ) ) ) ) =>
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 ![
% 95.81/12.72 X1972:$i,
% 95.81/12.72 X1974:$i]:
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 breln1 @
% 95.81/12.72 X1972 @
% 95.81/12.72 X1974 ) =>
% 95.81/12.72 (
% 95.81/12.72 ![
% 95.81/12.72 X1976:$i]:
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 breln1 @
% 95.81/12.72 X1972 @
% 95.81/12.72 X1976 ) =>
% 95.81/12.72 (
% 95.81/12.72 ![
% 95.81/12.72 X1978:$i]:
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 in @
% 95.81/12.72 X1978 @
% 95.81/12.72 X1972 ) =>
% 95.81/12.72 (
% 95.81/12.72 ![
% 95.81/12.72 X1980:$i]:
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 in @
% 95.81/12.72 X1980 @
% 95.81/12.72 X1972 ) =>
% 95.81/12.72 (
% 95.81/12.72 ![
% 95.81/12.72 X1982:$i]:
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 in @
% 95.81/12.72 X1982 @
% 95.81/12.72 X1972 ) =>
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 in @
% 95.81/12.72 (
% 95.81/12.72 kpair @
% 95.81/12.72 X1978 @
% 95.81/12.72 X1982 ) @
% 95.81/12.72 X1974 ) =>
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 in @
% 95.81/12.72 (
% 95.81/12.72 kpair @
% 95.81/12.72 X1982 @
% 95.81/12.72 X1980 ) @
% 95.81/12.72 X1976 ) =>
% 95.81/12.72 (
% 95.81/12.72 in @
% 95.81/12.72 (
% 95.81/12.72 kpair @
% 95.81/12.72 X1978 @
% 95.81/12.72 X1980 ) @
% 95.81/12.72 (
% 95.81/12.72 breln1compset
% 95.81/12.72 @
% 95.81/12.72 X1972 @
% 95.81/12.72 X1974 @
% 95.81/12.72 X1976 ) ) ) ) ) ) ) ) ) ) ) ) ) ) =>
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 ![
% 95.81/12.72 X1984:$i,
% 95.81/12.72 X1986:$i]:
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 breln1 @
% 95.81/12.72 X1984 @
% 95.81/12.72 X1986 ) =>
% 95.81/12.72 (
% 95.81/12.72 ![
% 95.81/12.72 X1988:$i]:
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 breln1 @
% 95.81/12.72 X1984 @
% 95.81/12.72 X1988 ) =>
% 95.81/12.72 (
% 95.81/12.72 ![
% 95.81/12.72 X1990:$i]:
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 in @
% 95.81/12.72 X1990 @
% 95.81/12.72 X1984 ) =>
% 95.81/12.72 (
% 95.81/12.72 ![
% 95.81/12.72 X1992:$i]:
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 in @
% 95.81/12.72 X1992 @
% 95.81/12.72 X1984 ) =>
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 in @
% 95.81/12.72 (
% 95.81/12.72 kpair @
% 95.81/12.72 X1990 @
% 95.81/12.72 X1992 ) @
% 95.81/12.72 (
% 95.81/12.72 breln1compset
% 95.81/12.72 @
% 95.81/12.72 X1984 @
% 95.81/12.72 X1986 @
% 95.81/12.72 X1988 ) ) =>
% 95.81/12.72 (
% 95.81/12.72 ?[
% 95.81/12.72 X1994:$i]:
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 in @
% 95.81/12.72 X1994 @
% 95.81/12.72 X1984 ) &
% 95.81/12.72 (
% 95.81/12.72 in @
% 95.81/12.72 (
% 95.81/12.72 kpair @
% 95.81/12.72 X1990 @
% 95.81/12.72 X1994 ) @
% 95.81/12.72 X1986 ) &
% 95.81/12.72 (
% 95.81/12.72 in @
% 95.81/12.72 (
% 95.81/12.72 kpair @
% 95.81/12.72 X1994 @
% 95.81/12.72 X1992 ) @
% 95.81/12.72 X1988 ) ) ) ) ) ) ) ) ) ) ) ) =>
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 ![
% 95.81/12.72 X1996:$i,
% 95.81/12.72 X1998:$i]:
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 breln1 @
% 95.81/12.72 X1996 @
% 95.81/12.72 X1998 ) =>
% 95.81/12.72 (
% 95.81/12.72 ![
% 95.81/12.72 X2000:$i]:
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 breln1 @
% 95.81/12.72 X1996 @
% 95.81/12.72 X2000 ) =>
% 95.81/12.72 (
% 95.81/12.72 ![
% 95.81/12.72 X2002:$i]:
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 in @
% 95.81/12.72 X2002 @
% 95.81/12.72 X1996 ) =>
% 95.81/12.72 (
% 95.81/12.72 ![
% 95.81/12.72 X2004:$i]:
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 in @
% 95.81/12.72 X2004 @
% 95.81/12.72 X1996 ) =>
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 in @
% 95.81/12.72 (
% 95.81/12.72 kpair @
% 95.81/12.72 X2002 @
% 95.81/12.72 X2004 ) @
% 95.81/12.72 (
% 95.81/12.72 breln1compset
% 95.81/12.72 @
% 95.81/12.72 X1996 @
% 95.81/12.72 X1998 @
% 95.81/12.72 X2000 ) ) =>
% 95.81/12.72 (
% 95.81/12.72 ![
% 95.81/12.72 X2006:$o]:
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 ![
% 95.81/12.72 X2008:$i]:
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 in @
% 95.81/12.72 X2008 @
% 95.81/12.72 X1996 ) =>
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 in @
% 95.81/12.72 (
% 95.81/12.72 kpair @
% 95.81/12.72 X2002 @
% 95.81/12.72 X2008 ) @
% 95.81/12.72 X1998 ) =>
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 in @
% 95.81/12.72 (
% 95.81/12.72 kpair @
% 95.81/12.72 X2008 @
% 95.81/12.72 X2004 ) @
% 95.81/12.72 X2000 ) =>
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% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 X2118 ) =
% 95.81/12.72 (
% 95.81/12.72 X2112 @
% 95.81/12.72 X2120 ) ) ) ) ) ) =>
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 X2114 ) =
% 95.81/12.72 (
% 95.81/12.72 X2116 ) ) ) ) ) ) ) =>
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 ![
% 95.81/12.72 X2126:$i,
% 95.81/12.72 X2128:(
% 95.81/12.72 $i > $i ),
% 95.81/12.72 X2130:$i]:
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 in @
% 95.81/12.72 X2130 @
% 95.81/12.72 (
% 95.81/12.72 image1 @
% 95.81/12.72 X2126 @
% 95.81/12.72 (
% 95.81/12.72 ^[
% 95.81/12.72 V_56:$i]:
% 95.81/12.72 (
% 95.81/12.72 X2128 @
% 95.81/12.72 V_56 ) ) ) ) <=>
% 95.81/12.72 (
% 95.81/12.72 ?[
% 95.81/12.72 X2132:$i]:
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 in @
% 95.81/12.72 X2132 @
% 95.81/12.72 X2126 ) &
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 X2130 ) =
% 95.81/12.72 (
% 95.81/12.72 X2128 @
% 95.81/12.72 X2132 ) ) ) ) ) ) =>
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 ![
% 95.81/12.72 X2134:$i,
% 95.81/12.72 X2136:(
% 95.81/12.72 $i > $i ),
% 95.81/12.72 X2138:$i]:
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 in @
% 95.81/12.72 X2138 @
% 95.81/12.72 (
% 95.81/12.72 image1 @
% 95.81/12.72 X2134 @
% 95.81/12.72 (
% 95.81/12.72 ^[
% 95.81/12.72 V_57:$i]:
% 95.81/12.72 (
% 95.81/12.72 X2136 @
% 95.81/12.72 V_57 ) ) ) ) =>
% 95.81/12.72 (
% 95.81/12.72 ?[
% 95.81/12.72 X2140:$i]:
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 in @
% 95.81/12.72 X2140 @
% 95.81/12.72 X2134 ) &
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 X2138 ) =
% 95.81/12.72 (
% 95.81/12.72 X2136 @
% 95.81/12.72 X2140 ) ) ) ) ) ) =>
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 ![
% 95.81/12.72 X2142:$i,
% 95.81/12.72 X2144:(
% 95.81/12.72 $i > $i ),
% 95.81/12.72 X2146:$i]:
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 ?[
% 95.81/12.72 X2148:$i]:
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 in @
% 95.81/12.72 X2148 @
% 95.81/12.72 X2142 ) &
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 X2146 ) =
% 95.81/12.72 (
% 95.81/12.72 X2144 @
% 95.81/12.72 X2148 ) ) ) ) =>
% 95.81/12.72 (
% 95.81/12.72 in @
% 95.81/12.72 X2146 @
% 95.81/12.72 (
% 95.81/12.72 image1 @
% 95.81/12.72 X2142 @
% 95.81/12.72 (
% 95.81/12.72 ^[
% 95.81/12.72 V_58:$i]:
% 95.81/12.72 (
% 95.81/12.72 X2144 @
% 95.81/12.72 V_58 ) ) ) ) ) ) =>
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 ![
% 95.81/12.72 X2150:$i,
% 95.81/12.72 X2152:$i,
% 95.81/12.72 X2154:$i]:
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 in @
% 95.81/12.72 X2154 @
% 95.81/12.72 (
% 95.81/12.72 funcSet @
% 95.81/12.72 X2150 @
% 95.81/12.72 X2152 ) ) =>
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 injective
% 95.81/12.72 @
% 95.81/12.72 X2150 @
% 95.81/12.72 X2152 @
% 95.81/12.72 X2154 ) =>
% 95.81/12.72 (
% 95.81/12.72 in @
% 95.81/12.72 X2154 @
% 95.81/12.72 (
% 95.81/12.72 injFuncSet
% 95.81/12.72 @
% 95.81/12.72 X2150 @
% 95.81/12.72 X2152 ) ) ) ) ) =>
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 ![
% 95.81/12.72 X2156:$i,
% 95.81/12.72 X2158:$i,
% 95.81/12.72 X2160:$i]:
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 in @
% 95.81/12.72 X2160 @
% 95.81/12.72 (
% 95.81/12.72 injFuncSet
% 95.81/12.72 @
% 95.81/12.72 X2156 @
% 95.81/12.72 X2158 ) ) =>
% 95.81/12.72 (
% 95.81/12.72 in @
% 95.81/12.72 X2160 @
% 95.81/12.72 (
% 95.81/12.72 funcSet @
% 95.81/12.72 X2156 @
% 95.81/12.72 X2158 ) ) ) ) =>
% 95.81/12.72 (
% 95.81/12.72 ![
% 95.81/12.72 X2162:$i,
% 95.81/12.72 X2164:$i,
% 95.81/12.72 X2166:$i]:
% 95.81/12.72 (
% 95.81/12.72 (
% 95.81/12.72 in @
% 95.81/12.72 X2166 @
% 95.81/12.72 (
% 95.81/12.72 injFuncSet
% 95.81/12.72 @
% 95.81/12.72 X2162 @
% 95.81/12.72 X2164 ) ) =>
% 95.81/12.72 (
% 95.81/12.72 injective
% 95.81/12.72 @
% 95.81/12.72 X2162 @
% 95.81/12.72 X2164 @
% 95.81/12.72 X2166 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 95.81/12.72 thf(zf_stmt_1, type, zip_tseitin_6 : $i > $i > ( $i > $i ) > $i > $o).
% 95.81/12.72 thf(zf_stmt_2, axiom,
% 95.81/12.72 (![X2108:$i,X2106:$i,X2102:( $i > $i ),X2100:$i]:
% 95.81/12.72 ( ( zip_tseitin_6 @ X2108 @ X2106 @ X2102 @ X2100 ) <=>
% 95.81/12.72 ( ( ( X2106 ) = ( X2102 @ X2108 ) ) & ( in @ X2108 @ X2100 ) ) ))).
% 95.81/12.72 thf(zf_stmt_3, type, zip_tseitin_5 : $i > ( $i > $o ) > $o).
% 95.81/12.72 thf(zf_stmt_4, axiom,
% 95.81/12.72 (![X422:$i,X414:( $i > $o )]:
% 95.81/12.72 ( ( zip_tseitin_5 @ X422 @ X414 ) <=>
% 95.81/12.72 ( ( ![X424:$i]: ( zip_tseitin_4 @ X424 @ X422 @ X414 ) ) &
% 95.81/12.72 ( X414 @ X422 ) ) ))).
% 95.81/12.72 thf(zf_stmt_5, type, zip_tseitin_4 : $i > $i > ( $i > $o ) > $o).
% 95.81/12.72 thf(zf_stmt_6, axiom,
% 95.81/12.72 (![X424:$i,X422:$i,X414:( $i > $o )]:
% 95.81/12.72 ( ( zip_tseitin_4 @ X424 @ X422 @ X414 ) <=>
% 95.81/12.72 ( ( X414 @ X424 ) => ( ( X422 ) = ( X424 ) ) ) ))).
% 95.81/12.72 thf(zf_stmt_7, type, zip_tseitin_3 : $i > $i > $i > ( $i > $i > $o ) > $o).
% 95.81/12.72 thf(zf_stmt_8, axiom,
% 95.81/12.72 (![X52:$i,X50:$i,X40:$i,X38:( $i > $i > $o )]:
% 95.81/12.72 ( ( zip_tseitin_3 @ X52 @ X50 @ X40 @ X38 ) <=>
% 95.81/12.72 ( ( X38 @ X52 @ X50 ) & ( in @ X52 @ X40 ) ) ))).
% 95.81/12.72 thf(zf_stmt_9, type, zip_tseitin_2 : $i > $i > $i > $o).
% 95.81/12.72 thf(zf_stmt_10, axiom,
% 95.81/12.72 (![X28:$i,X26:$i,X24:$i]:
% 95.81/12.72 ( ( zip_tseitin_2 @ X28 @ X26 @ X24 ) <=>
% 95.81/12.72 ( ( in @ X28 @ X24 ) & ( in @ X26 @ X28 ) ) ))).
% 95.81/12.72 thf(zf_stmt_11, type, zip_tseitin_1 : $i > $i > $i > $o).
% 95.81/12.72 thf(zf_stmt_12, axiom,
% 95.81/12.72 (![X22:$i,X20:$i,X18:$i]:
% 95.81/12.72 ( ( zip_tseitin_1 @ X22 @ X20 @ X18 ) <=>
% 95.81/12.72 ( ( in @ X22 @ X20 ) => ( in @ X22 @ X18 ) ) ))).
% 95.81/12.72 thf(zf_stmt_13, type, zip_tseitin_0 : $i > $i > $i > $o).
% 95.81/12.72 thf(zf_stmt_14, axiom,
% 95.81/12.72 (![X16:$i,X14:$i,X12:$i]:
% 95.81/12.72 ( ( zip_tseitin_0 @ X16 @ X14 @ X12 ) <=>
% 95.81/12.72 ( ( ( X16 ) = ( X12 ) ) | ( in @ X16 @ X14 ) ) ))).
% 95.81/12.72 thf(zf_stmt_15, conjecture,
% 95.81/12.72 (( ![X4:$i,X6:$i]:
% 95.81/12.72 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) <=> ( in @ X8 @ X6 ) ) ) =>
% 95.81/12.72 ( ( X4 ) = ( X6 ) ) ) ) =>
% 95.81/12.72 ( ( ![X10:$i]: ( ~( in @ X10 @ emptyset ) ) ) =>
% 95.81/12.72 ( ( ![X12:$i,X14:$i,X16:$i]:
% 95.81/12.72 ( ( in @ X16 @ ( setadjoin @ X12 @ X14 ) ) <=>
% 95.81/12.72 ( zip_tseitin_0 @ X16 @ X14 @ X12 ) ) ) =>
% 95.81/12.72 ( ( ![X18:$i,X20:$i]:
% 95.81/12.72 ( ( in @ X20 @ ( powerset @ X18 ) ) <=>
% 95.81/12.72 ( ![X22:$i]: ( zip_tseitin_1 @ X22 @ X20 @ X18 ) ) ) ) =>
% 95.81/12.72 ( ( ![X24:$i,X26:$i]:
% 95.81/12.72 ( ( in @ X26 @ ( setunion @ X24 ) ) <=>
% 95.81/12.72 ( ?[X28:$i]: ( zip_tseitin_2 @ X28 @ X26 @ X24 ) ) ) ) =>
% 95.81/12.72 ( ( in @ emptyset @ omega ) =>
% 95.81/12.72 ( ( ![X30:$i]:
% 95.81/12.72 ( ( in @ X30 @ omega ) =>
% 95.81/12.72 ( in @ ( setadjoin @ X30 @ X30 ) @ omega ) ) ) =>
% 95.81/12.72 ( ( ![X32:$i]:
% 95.81/12.72 ( ( ( in @ emptyset @ X32 ) &
% 95.81/12.72 ( ![X34:$i]:
% 95.81/12.72 ( ( ( in @ X34 @ omega ) & ( in @ X34 @ X32 ) ) =>
% 95.81/12.72 ( in @ ( setadjoin @ X34 @ X34 ) @ X32 ) ) ) ) =>
% 95.81/12.72 ( ![X36:$i]:
% 95.81/12.72 ( ( in @ X36 @ omega ) => ( in @ X36 @ X32 ) ) ) ) ) =>
% 95.81/12.72 ( ( ![X38:( $i > $i > $o ),X40:$i]:
% 95.81/12.72 ( ( ![X42:$i]:
% 95.81/12.72 ( ( in @ X42 @ X40 ) =>
% 95.81/12.72 ( ?[X44:$i]:
% 95.81/12.72 ( ( ![X46:$i]:
% 95.81/12.72 ( ( X38 @ X42 @ X46 ) =>
% 95.81/12.72 ( ( X44 ) = ( X46 ) ) ) ) &
% 95.81/12.72 ( X38 @ X42 @ X44 ) ) ) ) ) =>
% 95.81/12.72 ( ?[X48:$i]:
% 95.81/12.72 ( ![X50:$i]:
% 95.81/12.72 ( ( in @ X50 @ X48 ) <=>
% 95.81/12.72 ( ?[X52:$i]:
% 95.81/12.72 ( zip_tseitin_3 @ X52 @ X50 @ X40 @ X38 ) ) ) ) ) ) ) =>
% 95.81/12.72 ( ( ![X54:$i]:
% 95.81/12.72 ( ( ?[X56:$i]: ( in @ X56 @ X54 ) ) =>
% 95.81/12.72 ( ?[X58:$i]:
% 95.81/12.72 ( ( ~( ?[X60:$i]:
% 95.81/12.72 ( ( in @ X60 @ X54 ) & ( in @ X60 @ X58 ) ) ) ) &
% 95.81/12.72 ( in @ X58 @ X54 ) ) ) ) ) =>
% 95.81/12.72 ( ( ![X62:$i]:
% 95.81/12.72 ( ?[X64:$i]:
% 95.81/12.72 ( ( ![X66:$i]:
% 95.81/12.72 ( ( ( ![X68:$i]:
% 95.81/12.72 ( ( in @ X68 @ X66 ) =>
% 95.81/12.72 ( in @ X68 @ X62 ) ) ) &
% 95.81/12.72 ( ?[X70:$i]: ( in @ X70 @ X66 ) ) ) =>
% 95.81/12.72 ( ?[X72:$i,X74:$i]:
% 95.81/12.72 ( ( ![X76:$i]:
% 95.81/12.72 ( ( in @ X76 @ X64 ) =>
% 95.81/12.72 ( ( ![X78:$i]:
% 95.81/12.72 ( ( in @ X78 @ X76 ) =>
% 95.81/12.72 ( in @ X78 @ X72 ) ) ) |
% 95.81/12.72 ( in @ X74 @ X76 ) ) ) ) &
% 95.81/12.72 ( ~( ?[X80:$i]:
% 95.81/12.72 ( ( in @ X80 @ X66 ) &
% 95.81/12.72 ( in @ X80 @ X72 ) ) ) ) &
% 95.81/12.72 ( in @ X74 @ X66 ) & ( in @ X72 @ X64 ) ) ) ) ) &
% 95.81/12.72 ( ![X82:$i,X84:$i]:
% 95.81/12.72 ( ( ( in @ X82 @ X64 ) & ( in @ X84 @ X64 ) ) =>
% 95.81/12.72 ( ( ![X86:$i]:
% 95.81/12.72 ( ( in @ X86 @ X82 ) =>
% 95.81/12.72 ( in @ X86 @ X84 ) ) ) |
% 95.81/12.72 ( ![X88:$i]:
% 95.81/12.72 ( ( in @ X88 @ X84 ) =>
% 95.81/12.72 ( in @ X88 @ X82 ) ) ) ) ) ) &
% 95.81/12.72 ( ![X90:$i,X92:$i]:
% 95.81/12.72 ( ( ( in @ X90 @ X62 ) & ( in @ X92 @ X62 ) ) =>
% 95.81/12.72 ( ( ![X94:$i]:
% 95.81/12.72 ( ( in @ X94 @ X64 ) =>
% 95.81/12.72 ( ( in @ X90 @ X94 ) <=>
% 95.81/12.72 ( in @ X92 @ X94 ) ) ) ) =>
% 95.81/12.72 ( ( X90 ) = ( X92 ) ) ) ) ) &
% 95.81/12.72 ( ![X96:$i]:
% 95.81/12.72 ( ( in @ X96 @ X64 ) =>
% 95.81/12.72 ( ![X98:$i]:
% 95.81/12.72 ( ( in @ X98 @ X96 ) => ( in @ X98 @ X62 ) ) ) ) ) ) ) ) =>
% 95.81/12.72 ( ( ![X100:( $i > $o )]:
% 95.81/12.72 ( ( ?[X102:$i]:
% 95.81/12.72 ( ( ![X104:$i]:
% 95.81/12.72 ( ( X100 @ X104 ) =>
% 95.81/12.72 ( ( X102 ) = ( X104 ) ) ) ) &
% 95.81/12.72 ( X100 @ X102 ) ) ) =>
% 95.81/12.72 ( X100 @
% 95.81/12.72 ( descr @ ( ^[V_1:$i]: ( X100 @ V_1 ) ) ) ) ) ) =>
% 95.81/12.72 ( ( ![X106:$i,X108:( $i > $o ),X110:$i]:
% 95.81/12.72 ( ( in @ X110 @ X106 ) =>
% 95.81/12.72 ( ( X108 @ X110 ) =>
% 95.81/12.72 ( in @
% 95.81/12.72 X110 @
% 95.81/12.72 ( dsetconstr @
% 95.81/12.72 X106 @ ( ^[V_2:$i]: ( X108 @ V_2 ) ) ) ) ) ) ) =>
% 95.81/12.72 ( ( ![X112:$i,X114:( $i > $o ),X116:$i]:
% 95.81/12.72 ( ( in @
% 95.81/12.72 X116 @
% 95.81/12.72 ( dsetconstr @
% 95.81/12.72 X112 @ ( ^[V_3:$i]: ( X114 @ V_3 ) ) ) ) =>
% 95.81/12.72 ( in @ X116 @ X112 ) ) ) =>
% 95.81/12.72 ( ( ![X118:$i,X120:( $i > $o ),X122:$i]:
% 95.81/12.72 ( ( in @
% 95.81/12.72 X122 @
% 95.81/12.72 ( dsetconstr @
% 95.81/12.72 X118 @ ( ^[V_4:$i]: ( X120 @ V_4 ) ) ) ) =>
% 95.81/12.72 ( X120 @ X122 ) ) ) =>
% 95.81/12.72 ( ( ![X124:( $i > $o )]:
% 95.81/12.72 ( ( ?[X126:$i]:
% 95.81/12.72 ( ( ![X128:$i]:
% 95.81/12.72 ( ( X124 @ X128 ) =>
% 95.81/12.72 ( ( X126 ) = ( X128 ) ) ) ) &
% 95.81/12.72 ( X124 @ X126 ) ) ) =>
% 95.81/12.72 ( ?[X130:$i]:
% 95.81/12.73 ( ( ![X132:$i]:
% 95.81/12.73 ( ( X124 @ X132 ) =>
% 95.81/12.73 ( ( X130 ) = ( X132 ) ) ) ) &
% 95.81/12.73 ( X124 @ X130 ) ) ) ) ) =>
% 95.81/12.73 ( ( ![X134:$o,X136:$i]:
% 95.81/12.73 ( ( in @ X136 @ ( prop2set @ X134 ) ) =>
% 95.81/12.73 ( X134 ) ) ) =>
% 95.81/12.73 ( ( ![X138:$i]:
% 95.81/12.73 ( ( in @ X138 @ emptyset ) =>
% 95.81/12.73 ( ![X140:$o]: ( X140 ) ) ) ) =>
% 95.81/12.73 ( ( ![X142:$i]:
% 95.81/12.73 ( ~( in @ X142 @ emptyset ) ) ) =>
% 95.81/12.73 ( ( ![X144:$i]:
% 95.81/12.73 ( ~( in @ X144 @ emptyset ) ) ) =>
% 95.81/12.73 ( ( ![X146:( $i > $o )]:
% 95.81/12.73 ( ( ?[X148:$i]:
% 95.81/12.73 ( ( ![X150:$i]:
% 95.81/12.73 ( ( X146 @ X150 ) =>
% 95.81/12.73 ( ( X148 ) = ( X150 ) ) ) ) &
% 95.81/12.73 ( X146 @ X148 ) ) ) =>
% 95.81/12.73 ( ?[X152:$i]: ( X146 @ X152 ) ) ) ) =>
% 95.81/12.73 ( ( ![X154:$i,X156:$i]:
% 95.81/12.73 ( ( ![X158:$i]:
% 95.81/12.73 ( ( in @ X158 @ X154 ) =>
% 95.81/12.73 ( in @ X158 @ X156 ) ) ) =>
% 95.81/12.73 ( ( ![X160:$i]:
% 95.81/12.73 ( ( in @ X160 @ X156 ) =>
% 95.81/12.73 ( in @ X160 @ X154 ) ) ) =>
% 95.81/12.73 ( ( X154 ) = ( X156 ) ) ) ) ) =>
% 95.81/12.73 ( ( ![X162:$i]:
% 95.81/12.73 ( ( ![X164:$i]:
% 95.81/12.73 ( ~( in @ X164 @ X162 ) ) ) =>
% 95.81/12.73 ( ( X162 ) = ( emptyset ) ) ) ) =>
% 95.81/12.73 ( ( ![X166:$i]:
% 95.81/12.73 ( ( ![X168:$i]:
% 95.81/12.73 ( ~( in @ X168 @ X166 ) ) ) =>
% 95.81/12.73 ( ( X166 ) =
% 95.81/12.73 ( emptyset ) ) ) ) =>
% 95.81/12.73 ( ( ![X170:$i,
% 95.81/12.73 X172:( $i > $o ),
% 95.81/12.73 X174:$i]:
% 95.81/12.73 ( ( in @ X174 @ X170 ) =>
% 95.81/12.73 ( ( in @
% 95.81/12.73 X174 @
% 95.81/12.73 ( dsetconstr @
% 95.81/12.73 X170 @
% 95.81/12.73 ( ^[V_5:$i]:
% 95.81/12.73 ( X172 @ V_5 ) ) ) ) <=>
% 95.81/12.73 ( X172 @ X174 ) ) ) ) =>
% 95.81/12.73 ( ( ![X176:$i]:
% 95.81/12.73 ( ( ( X176 ) !=
% 95.81/12.73 ( emptyset ) ) =>
% 95.81/12.73 ( ?[X178:$i]:
% 95.81/12.73 ( in @ X178 @ X176 ) ) ) ) =>
% 95.81/12.73 ( ( ![X180:$i,
% 95.81/12.73 X182:( $i > $o ),
% 95.81/12.73 X184:$i]:
% 95.81/12.73 ( ( in @ X184 @ X180 ) =>
% 95.81/12.73 ( ( X182 @ X184 ) =>
% 95.81/12.73 ( ( dsetconstr @
% 95.81/12.73 X180 @
% 95.81/12.73 ( ^[
% 95.81/12.73 V_6:$i]:
% 95.81/12.73 (
% 95.81/12.73 X182 @ V_6 ) ) ) !=
% 95.81/12.73 ( emptyset ) ) ) ) ) =>
% 95.81/12.73 ( ( ![X186:$i]:
% 95.81/12.73 ( ( ?[X188:$i]:
% 95.81/12.73 ( in @
% 95.81/12.73 X188 @ X186 ) ) =>
% 95.81/12.73 ( ( X186 ) !=
% 95.81/12.73 ( emptyset ) ) ) ) =>
% 95.81/12.73 ( ( ![X190:$i,
% 95.81/12.73 X192:$i]:
% 95.81/12.73 ( in @
% 95.81/12.73 X190 @
% 95.81/12.73 ( setadjoin @
% 95.81/12.73 X190 @ X192 ) ) ) =>
% 95.81/12.73 ( ( in @
% 95.81/12.73 emptyset @
% 95.81/12.73 ( setadjoin @
% 95.81/12.73 emptyset @
% 95.81/12.73 emptyset ) ) =>
% 95.81/12.73 ( ( ![X194:$i,
% 95.81/12.73 X196:$i,
% 95.81/12.73 X198:$i]:
% 95.81/12.73 ( (
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% 95.81/12.73 (
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% 95.81/12.73 (
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% 95.81/12.74 V_25:$i,
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% 95.81/12.74 X1080 ) =>
% 95.81/12.74 (
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% 95.81/12.74 (
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% 95.81/12.74 (
% 95.81/12.74 dpsetconstr
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% 95.81/12.74 X1078 @
% 95.81/12.74 X1080 @
% 95.81/12.74 (
% 95.81/12.74 ^[
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% 95.81/12.74 (
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% 95.81/12.74 X1090 @
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% 95.81/12.74 X1104:$i,
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% 95.81/12.74 (
% 95.81/12.74 dpsetconstr
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% 95.81/12.74 X1098 @
% 95.81/12.74 X1100 @
% 95.81/12.74 (
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% 95.81/12.74 (
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% 95.81/12.74 (
% 95.81/12.74 singleton
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% 95.81/12.74 (
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% 95.81/12.74 (
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% 95.81/12.74 (
% 95.81/12.74 (
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% 95.81/12.74 X1160 ) =>
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% 95.81/12.74 in @
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% 95.81/12.74 (
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% 95.81/12.74 X1166:(
% 95.81/12.74 $i > $i )]:
% 95.81/12.74 (
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% 95.81/12.74 (
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% 95.81/12.74 X1166 @
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% 95.81/12.74 (
% 95.81/12.74 dpsetconstr
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% 95.81/12.74 X1164 @
% 95.81/12.74 (
% 95.81/12.74 ^[
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% 95.81/12.74 (
% 95.81/12.74 (
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% 95.81/12.74 $i > $i )]:
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% 95.81/12.74 (
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% 95.81/12.74 $i > $i )]:
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% 95.81/12.74 (
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% 95.81/12.74 (
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% 95.81/12.74 X1192:(
% 95.81/12.74 $i > $o )]:
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% 95.81/12.74 (
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% 95.81/12.74 X1202:$i,
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% 95.81/12.74 X1204 ) =>
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% 95.81/12.74 ![
% 95.81/12.74 X1206:(
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% 95.81/12.75 breln1Set
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% 95.81/12.75 X1892 ) ) =>
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 reflwellordering
% 95.81/12.75 @
% 95.81/12.75 X1892 @
% 95.81/12.75 X1900 ) =>
% 95.81/12.75 (
% 95.81/12.75 ![
% 95.81/12.75 X1902:$i]:
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 in @
% 95.81/12.75 X1902 @
% 95.81/12.75 X1890 ) =>
% 95.81/12.75 (
% 95.81/12.75 singleton
% 95.81/12.75 @
% 95.81/12.75 (
% 95.81/12.75 dsetconstr
% 95.81/12.75 @
% 95.81/12.75 X1892 @
% 95.81/12.75 (
% 95.81/12.75 ^[
% 95.81/12.75 V_53:$i]:
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 ![
% 95.81/12.75 X1904:$i]:
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 in @
% 95.81/12.75 X1904 @
% 95.81/12.75 X1892 ) =>
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 X1894 @
% 95.81/12.75 X1902 @
% 95.81/12.75 X1904 ) =>
% 95.81/12.75 (
% 95.81/12.75 in @
% 95.81/12.75 (
% 95.81/12.75 kpair @
% 95.81/12.75 V_53 @
% 95.81/12.75 X1904 ) @
% 95.81/12.75 X1900 ) ) ) ) &
% 95.81/12.75 (
% 95.81/12.75 X1894 @
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% 95.81/12.75 V_53 ) ) ) ) ) ) ) ) ) ) ) ) =>
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 ![
% 95.81/12.75 X1906:$i,
% 95.81/12.75 X1908:(
% 95.81/12.75 $i > $i >
% 95.81/12.75 $o )]:
% 95.81/12.75 (
% 95.81/12.75 breln1 @
% 95.81/12.75 X1906 @
% 95.81/12.75 (
% 95.81/12.75 dpsetconstr
% 95.81/12.75 @
% 95.81/12.75 X1906 @
% 95.81/12.75 X1906 @
% 95.81/12.75 (
% 95.81/12.75 ^[
% 95.81/12.75 V_54:$i,
% 95.81/12.75 V_55:$i]:
% 95.81/12.75 (
% 95.81/12.75 X1908 @
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% 95.81/12.75 V_55 ) ) ) ) ) =>
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 ![
% 95.81/12.75 X1910:$i,
% 95.81/12.75 X1912:$i]:
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 breln1 @
% 95.81/12.75 X1910 @
% 95.81/12.75 X1912 ) =>
% 95.81/12.75 (
% 95.81/12.75 ![
% 95.81/12.75 X1914:(
% 95.81/12.75 $i > $o )]:
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 ![
% 95.81/12.75 X1916:$i]:
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 in @
% 95.81/12.75 X1916 @
% 95.81/12.75 X1910 ) =>
% 95.81/12.75 (
% 95.81/12.75 ![
% 95.81/12.75 X1918:$i]:
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 in @
% 95.81/12.75 X1918 @
% 95.81/12.75 X1910 ) =>
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 in @
% 95.81/12.75 (
% 95.81/12.75 kpair @
% 95.81/12.75 X1916 @
% 95.81/12.75 X1918 ) @
% 95.81/12.75 X1912 ) =>
% 95.81/12.75 (
% 95.81/12.75 X1914 @
% 95.81/12.75 (
% 95.81/12.75 kpair @
% 95.81/12.75 X1916 @
% 95.81/12.75 X1918 ) ) ) ) ) ) ) =>
% 95.81/12.75 (
% 95.81/12.75 ![
% 95.81/12.75 X1920:$i]:
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 in @
% 95.81/12.75 X1920 @
% 95.81/12.75 X1912 ) =>
% 95.81/12.75 (
% 95.81/12.75 X1914 @
% 95.81/12.75 X1920 ) ) ) ) ) ) ) =>
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 ![
% 95.81/12.75 X1922:$i,
% 95.81/12.75 X1924:$i]:
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 breln1 @
% 95.81/12.75 X1922 @
% 95.81/12.75 X1924 ) =>
% 95.81/12.75 (
% 95.81/12.75 ![
% 95.81/12.75 X1926:$i]:
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 breln1 @
% 95.81/12.75 X1922 @
% 95.81/12.75 X1926 ) =>
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 ![
% 95.81/12.75 X1928:$i]:
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 in @
% 95.81/12.75 X1928 @
% 95.81/12.75 X1922 ) =>
% 95.81/12.75 (
% 95.81/12.75 ![
% 95.81/12.75 X1930:$i]:
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 in @
% 95.81/12.75 X1930 @
% 95.81/12.75 X1922 ) =>
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 in @
% 95.81/12.75 (
% 95.81/12.75 kpair @
% 95.81/12.75 X1928 @
% 95.81/12.75 X1930 ) @
% 95.81/12.75 X1924 ) =>
% 95.81/12.75 (
% 95.81/12.75 in @
% 95.81/12.75 (
% 95.81/12.75 kpair @
% 95.81/12.75 X1928 @
% 95.81/12.75 X1930 ) @
% 95.81/12.75 X1926 ) ) ) ) ) ) =>
% 95.81/12.75 (
% 95.81/12.75 subset @
% 95.81/12.75 X1924 @
% 95.81/12.75 X1926 ) ) ) ) ) ) =>
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 ![
% 95.81/12.75 X1932:$i,
% 95.81/12.75 X1934:$i]:
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 breln1 @
% 95.81/12.75 X1932 @
% 95.81/12.75 X1934 ) =>
% 95.81/12.75 (
% 95.81/12.75 ![
% 95.81/12.75 X1936:$i]:
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 breln1 @
% 95.81/12.75 X1932 @
% 95.81/12.75 X1936 ) =>
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 ![
% 95.81/12.75 X1938:$i]:
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 in @
% 95.81/12.75 X1938 @
% 95.81/12.75 X1932 ) =>
% 95.81/12.75 (
% 95.81/12.75 ![
% 95.81/12.75 X1940:$i]:
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 in @
% 95.81/12.75 X1940 @
% 95.81/12.75 X1932 ) =>
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 in @
% 95.81/12.75 (
% 95.81/12.75 kpair @
% 95.81/12.75 X1938 @
% 95.81/12.75 X1940 ) @
% 95.81/12.75 X1934 ) =>
% 95.81/12.75 (
% 95.81/12.75 in @
% 95.81/12.75 (
% 95.81/12.75 kpair @
% 95.81/12.75 X1938 @
% 95.81/12.75 X1940 ) @
% 95.81/12.75 X1936 ) ) ) ) ) ) =>
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 ![
% 95.81/12.75 X1942:$i]:
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 in @
% 95.81/12.75 X1942 @
% 95.81/12.75 X1932 ) =>
% 95.81/12.75 (
% 95.81/12.75 ![
% 95.81/12.75 X1944:$i]:
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 in @
% 95.81/12.75 X1944 @
% 95.81/12.75 X1932 ) =>
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 in @
% 95.81/12.75 (
% 95.81/12.75 kpair @
% 95.81/12.75 X1942 @
% 95.81/12.75 X1944 ) @
% 95.81/12.75 X1936 ) =>
% 95.81/12.75 (
% 95.81/12.75 in @
% 95.81/12.75 (
% 95.81/12.75 kpair @
% 95.81/12.75 X1942 @
% 95.81/12.75 X1944 ) @
% 95.81/12.75 X1934 ) ) ) ) ) ) =>
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 X1934 ) =
% 95.81/12.75 (
% 95.81/12.75 X1936 ) ) ) ) ) ) ) ) =>
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 ![
% 95.81/12.75 X1946:$i,
% 95.81/12.75 X1948:$i]:
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 breln1 @
% 95.81/12.75 X1946 @
% 95.81/12.75 X1948 ) =>
% 95.81/12.75 (
% 95.81/12.75 breln1 @
% 95.81/12.75 X1946 @
% 95.81/12.75 (
% 95.81/12.75 breln1invset
% 95.81/12.75 @
% 95.81/12.75 X1946 @
% 95.81/12.75 X1948 ) ) ) ) =>
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 ![
% 95.81/12.75 X1950:$i,
% 95.81/12.75 X1952:$i]:
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 breln1 @
% 95.81/12.75 X1950 @
% 95.81/12.75 X1952 ) =>
% 95.81/12.75 (
% 95.81/12.75 ![
% 95.81/12.75 X1954:$i]:
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 in @
% 95.81/12.75 X1954 @
% 95.81/12.75 X1950 ) =>
% 95.81/12.75 (
% 95.81/12.75 ![
% 95.81/12.75 X1956:$i]:
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 in @
% 95.81/12.75 X1956 @
% 95.81/12.75 X1950 ) =>
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 in @
% 95.81/12.75 (
% 95.81/12.75 kpair @
% 95.81/12.75 X1954 @
% 95.81/12.75 X1956 ) @
% 95.81/12.75 X1952 ) =>
% 95.81/12.75 (
% 95.81/12.75 in @
% 95.81/12.75 (
% 95.81/12.75 kpair @
% 95.81/12.75 X1956 @
% 95.81/12.75 X1954 ) @
% 95.81/12.75 (
% 95.81/12.75 breln1invset
% 95.81/12.75 @
% 95.81/12.75 X1950 @
% 95.81/12.75 X1952 ) ) ) ) ) ) ) ) ) =>
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 ![
% 95.81/12.75 X1958:$i,
% 95.81/12.75 X1960:$i]:
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 breln1 @
% 95.81/12.75 X1958 @
% 95.81/12.75 X1960 ) =>
% 95.81/12.75 (
% 95.81/12.75 ![
% 95.81/12.75 X1962:$i]:
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 in @
% 95.81/12.75 X1962 @
% 95.81/12.75 X1958 ) =>
% 95.81/12.75 (
% 95.81/12.75 ![
% 95.81/12.75 X1964:$i]:
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 in @
% 95.81/12.75 X1964 @
% 95.81/12.75 X1958 ) =>
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 in @
% 95.81/12.75 (
% 95.81/12.75 kpair @
% 95.81/12.75 X1964 @
% 95.81/12.75 X1962 ) @
% 95.81/12.75 (
% 95.81/12.75 breln1invset
% 95.81/12.75 @
% 95.81/12.75 X1958 @
% 95.81/12.75 X1960 ) ) =>
% 95.81/12.75 (
% 95.81/12.75 in @
% 95.81/12.75 (
% 95.81/12.75 kpair @
% 95.81/12.75 X1962 @
% 95.81/12.75 X1964 ) @
% 95.81/12.75 X1960 ) ) ) ) ) ) ) ) =>
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 ![
% 95.81/12.75 X1966:$i,
% 95.81/12.75 X1968:$i]:
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 breln1 @
% 95.81/12.75 X1966 @
% 95.81/12.75 X1968 ) =>
% 95.81/12.75 (
% 95.81/12.75 ![
% 95.81/12.75 X1970:$i]:
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 breln1 @
% 95.81/12.75 X1966 @
% 95.81/12.75 X1970 ) =>
% 95.81/12.75 (
% 95.81/12.75 breln1 @
% 95.81/12.75 X1966 @
% 95.81/12.75 (
% 95.81/12.75 breln1compset
% 95.81/12.75 @
% 95.81/12.75 X1966 @
% 95.81/12.75 X1968 @
% 95.81/12.75 X1970 ) ) ) ) ) ) =>
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 ![
% 95.81/12.75 X1972:$i,
% 95.81/12.75 X1974:$i]:
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 breln1 @
% 95.81/12.75 X1972 @
% 95.81/12.75 X1974 ) =>
% 95.81/12.75 (
% 95.81/12.75 ![
% 95.81/12.75 X1976:$i]:
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 breln1 @
% 95.81/12.75 X1972 @
% 95.81/12.75 X1976 ) =>
% 95.81/12.75 (
% 95.81/12.75 ![
% 95.81/12.75 X1978:$i]:
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 in @
% 95.81/12.75 X1978 @
% 95.81/12.75 X1972 ) =>
% 95.81/12.75 (
% 95.81/12.75 ![
% 95.81/12.75 X1980:$i]:
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 in @
% 95.81/12.75 X1980 @
% 95.81/12.75 X1972 ) =>
% 95.81/12.75 (
% 95.81/12.75 ![
% 95.81/12.75 X1982:$i]:
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 in @
% 95.81/12.75 X1982 @
% 95.81/12.75 X1972 ) =>
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 in @
% 95.81/12.75 (
% 95.81/12.75 kpair @
% 95.81/12.75 X1978 @
% 95.81/12.75 X1982 ) @
% 95.81/12.75 X1974 ) =>
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 in @
% 95.81/12.75 (
% 95.81/12.75 kpair @
% 95.81/12.75 X1982 @
% 95.81/12.75 X1980 ) @
% 95.81/12.75 X1976 ) =>
% 95.81/12.75 (
% 95.81/12.75 in @
% 95.81/12.75 (
% 95.81/12.75 kpair @
% 95.81/12.75 X1978 @
% 95.81/12.75 X1980 ) @
% 95.81/12.75 (
% 95.81/12.75 breln1compset
% 95.81/12.75 @
% 95.81/12.75 X1972 @
% 95.81/12.75 X1974 @
% 95.81/12.75 X1976 ) ) ) ) ) ) ) ) ) ) ) ) ) ) =>
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 ![
% 95.81/12.75 X1984:$i,
% 95.81/12.75 X1986:$i]:
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 breln1 @
% 95.81/12.75 X1984 @
% 95.81/12.75 X1986 ) =>
% 95.81/12.75 (
% 95.81/12.75 ![
% 95.81/12.75 X1988:$i]:
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 breln1 @
% 95.81/12.75 X1984 @
% 95.81/12.75 X1988 ) =>
% 95.81/12.75 (
% 95.81/12.75 ![
% 95.81/12.75 X1990:$i]:
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 in @
% 95.81/12.75 X1990 @
% 95.81/12.75 X1984 ) =>
% 95.81/12.75 (
% 95.81/12.75 ![
% 95.81/12.75 X1992:$i]:
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 in @
% 95.81/12.75 X1992 @
% 95.81/12.75 X1984 ) =>
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 in @
% 95.81/12.75 (
% 95.81/12.75 kpair @
% 95.81/12.75 X1990 @
% 95.81/12.75 X1992 ) @
% 95.81/12.75 (
% 95.81/12.75 breln1compset
% 95.81/12.75 @
% 95.81/12.75 X1984 @
% 95.81/12.75 X1986 @
% 95.81/12.75 X1988 ) ) =>
% 95.81/12.75 (
% 95.81/12.75 ?[
% 95.81/12.75 X1994:$i]:
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 in @
% 95.81/12.75 (
% 95.81/12.75 kpair @
% 95.81/12.75 X1994 @
% 95.81/12.75 X1992 ) @
% 95.81/12.75 X1988 ) &
% 95.81/12.75 (
% 95.81/12.75 in @
% 95.81/12.75 (
% 95.81/12.75 kpair @
% 95.81/12.75 X1990 @
% 95.81/12.75 X1994 ) @
% 95.81/12.75 X1986 ) &
% 95.81/12.75 (
% 95.81/12.75 in @
% 95.81/12.75 X1994 @
% 95.81/12.75 X1984 ) ) ) ) ) ) ) ) ) ) ) ) =>
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 ![
% 95.81/12.75 X1996:$i,
% 95.81/12.75 X1998:$i]:
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 breln1 @
% 95.81/12.75 X1996 @
% 95.81/12.75 X1998 ) =>
% 95.81/12.75 (
% 95.81/12.75 ![
% 95.81/12.75 X2000:$i]:
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 breln1 @
% 95.81/12.75 X1996 @
% 95.81/12.75 X2000 ) =>
% 95.81/12.75 (
% 95.81/12.75 ![
% 95.81/12.75 X2002:$i]:
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 in @
% 95.81/12.75 X2002 @
% 95.81/12.75 X1996 ) =>
% 95.81/12.75 (
% 95.81/12.75 ![
% 95.81/12.75 X2004:$i]:
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 in @
% 95.81/12.75 X2004 @
% 95.81/12.75 X1996 ) =>
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 in @
% 95.81/12.75 (
% 95.81/12.75 kpair @
% 95.81/12.75 X2002 @
% 95.81/12.75 X2004 ) @
% 95.81/12.75 (
% 95.81/12.75 breln1compset
% 95.81/12.75 @
% 95.81/12.75 X1996 @
% 95.81/12.75 X1998 @
% 95.81/12.75 X2000 ) ) =>
% 95.81/12.75 (
% 95.81/12.75 ![
% 95.81/12.75 X2006:$o]:
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 ![
% 95.81/12.75 X2008:$i]:
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 in @
% 95.81/12.75 X2008 @
% 95.81/12.75 X1996 ) =>
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 in @
% 95.81/12.75 (
% 95.81/12.75 kpair @
% 95.81/12.75 X2002 @
% 95.81/12.75 X2008 ) @
% 95.81/12.75 X1998 ) =>
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 in @
% 95.81/12.75 (
% 95.81/12.75 kpair @
% 95.81/12.75 X2008 @
% 95.81/12.75 X2004 ) @
% 95.81/12.75 X2000 ) =>
% 95.81/12.75 (
% 95.81/12.75 X2006 ) ) ) ) ) =>
% 95.81/12.75 (
% 95.81/12.75 X2006 ) ) ) ) ) ) ) ) ) ) ) ) =>
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 ![
% 95.81/12.75 X2010:$i,
% 95.81/12.75 X2012:$i]:
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 breln1 @
% 95.81/12.75 X2010 @
% 95.81/12.75 X2012 ) =>
% 95.81/12.75 (
% 95.81/12.75 ![
% 95.81/12.75 X2014:$i]:
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 breln1 @
% 95.81/12.75 X2010 @
% 95.81/12.75 X2014 ) =>
% 95.81/12.75 (
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% 95.81/12.75 (
% 95.81/12.75 binunion @
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% 95.81/12.75 (
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% 95.81/12.75 X2132:$i]:
% 95.81/12.75 (
% 95.81/12.75 zip_tseitin_6
% 95.81/12.75 @
% 95.81/12.75 X2132 @
% 95.81/12.75 X2130 @
% 95.81/12.75 X2128 @
% 95.81/12.75 X2126 ) ) ) ) =>
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 ![
% 95.81/12.75 X2134:$i,
% 95.81/12.75 X2136:(
% 95.81/12.75 $i > $i ),
% 95.81/12.75 X2138:$i]:
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 in @
% 95.81/12.75 X2138 @
% 95.81/12.75 (
% 95.81/12.75 image1 @
% 95.81/12.75 X2134 @
% 95.81/12.75 (
% 95.81/12.75 ^[
% 95.81/12.75 V_57:$i]:
% 95.81/12.75 (
% 95.81/12.75 X2136 @
% 95.81/12.75 V_57 ) ) ) ) =>
% 95.81/12.75 (
% 95.81/12.75 ?[
% 95.81/12.75 X2140:$i]:
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 X2138 ) =
% 95.81/12.75 (
% 95.81/12.75 X2136 @
% 95.81/12.75 X2140 ) ) &
% 95.81/12.75 (
% 95.81/12.75 in @
% 95.81/12.75 X2140 @
% 95.81/12.75 X2134 ) ) ) ) ) =>
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 ![
% 95.81/12.75 X2142:$i,
% 95.81/12.75 X2144:(
% 95.81/12.75 $i > $i ),
% 95.81/12.75 X2146:$i]:
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 ?[
% 95.81/12.75 X2148:$i]:
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 X2146 ) =
% 95.81/12.75 (
% 95.81/12.75 X2144 @
% 95.81/12.75 X2148 ) ) &
% 95.81/12.75 (
% 95.81/12.75 in @
% 95.81/12.75 X2148 @
% 95.81/12.75 X2142 ) ) ) =>
% 95.81/12.75 (
% 95.81/12.75 in @
% 95.81/12.75 X2146 @
% 95.81/12.75 (
% 95.81/12.75 image1 @
% 95.81/12.75 X2142 @
% 95.81/12.75 (
% 95.81/12.75 ^[
% 95.81/12.75 V_58:$i]:
% 95.81/12.75 (
% 95.81/12.75 X2144 @
% 95.81/12.75 V_58 ) ) ) ) ) ) =>
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 ![
% 95.81/12.75 X2150:$i,
% 95.81/12.75 X2152:$i,
% 95.81/12.75 X2154:$i]:
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 in @
% 95.81/12.75 X2154 @
% 95.81/12.75 (
% 95.81/12.75 funcSet @
% 95.81/12.75 X2150 @
% 95.81/12.75 X2152 ) ) =>
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 injective
% 95.81/12.75 @
% 95.81/12.75 X2150 @
% 95.81/12.75 X2152 @
% 95.81/12.75 X2154 ) =>
% 95.81/12.75 (
% 95.81/12.75 in @
% 95.81/12.75 X2154 @
% 95.81/12.75 (
% 95.81/12.75 injFuncSet
% 95.81/12.75 @
% 95.81/12.75 X2150 @
% 95.81/12.75 X2152 ) ) ) ) ) =>
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 ![
% 95.81/12.75 X2156:$i,
% 95.81/12.75 X2158:$i,
% 95.81/12.75 X2160:$i]:
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 in @
% 95.81/12.75 X2160 @
% 95.81/12.75 (
% 95.81/12.75 injFuncSet
% 95.81/12.75 @
% 95.81/12.75 X2156 @
% 95.81/12.75 X2158 ) ) =>
% 95.81/12.75 (
% 95.81/12.75 in @
% 95.81/12.75 X2160 @
% 95.81/12.75 (
% 95.81/12.75 funcSet @
% 95.81/12.75 X2156 @
% 95.81/12.75 X2158 ) ) ) ) =>
% 95.81/12.75 (
% 95.81/12.75 ![
% 95.81/12.75 X2162:$i,
% 95.81/12.75 X2164:$i,
% 95.81/12.75 X2166:$i]:
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 in @
% 95.81/12.75 X2166 @
% 95.81/12.75 (
% 95.81/12.75 injFuncSet
% 95.81/12.75 @
% 95.81/12.75 X2162 @
% 95.81/12.75 X2164 ) ) =>
% 95.81/12.75 (
% 95.81/12.75 injective
% 95.81/12.75 @
% 95.81/12.75 X2162 @
% 95.81/12.75 X2164 @
% 95.81/12.75 X2166 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 95.81/12.75 thf(zf_stmt_16, negated_conjecture,
% 95.81/12.75 (~( ( ![X4:$i,X6:$i]:
% 95.81/12.75 ( ( ![X8:$i]: ( ( in @ X8 @ X4 ) <=> ( in @ X8 @ X6 ) ) ) =>
% 95.81/12.75 ( ( X4 ) = ( X6 ) ) ) ) =>
% 95.81/12.75 ( ( ![X10:$i]: ( ~( in @ X10 @ emptyset ) ) ) =>
% 95.81/12.75 ( ( ![X12:$i,X14:$i,X16:$i]:
% 95.81/12.75 ( ( in @ X16 @ ( setadjoin @ X12 @ X14 ) ) <=>
% 95.81/12.75 ( zip_tseitin_0 @ X16 @ X14 @ X12 ) ) ) =>
% 95.81/12.75 ( ( ![X18:$i,X20:$i]:
% 95.81/12.75 ( ( in @ X20 @ ( powerset @ X18 ) ) <=>
% 95.81/12.75 ( ![X22:$i]: ( zip_tseitin_1 @ X22 @ X20 @ X18 ) ) ) ) =>
% 95.81/12.75 ( ( ![X24:$i,X26:$i]:
% 95.81/12.75 ( ( in @ X26 @ ( setunion @ X24 ) ) <=>
% 95.81/12.75 ( ?[X28:$i]: ( zip_tseitin_2 @ X28 @ X26 @ X24 ) ) ) ) =>
% 95.81/12.75 ( ( in @ emptyset @ omega ) =>
% 95.81/12.75 ( ( ![X30:$i]:
% 95.81/12.75 ( ( in @ X30 @ omega ) =>
% 95.81/12.75 ( in @ ( setadjoin @ X30 @ X30 ) @ omega ) ) ) =>
% 95.81/12.75 ( ( ![X32:$i]:
% 95.81/12.75 ( ( ( in @ emptyset @ X32 ) &
% 95.81/12.75 ( ![X34:$i]:
% 95.81/12.75 ( ( ( in @ X34 @ omega ) & ( in @ X34 @ X32 ) ) =>
% 95.81/12.75 ( in @ ( setadjoin @ X34 @ X34 ) @ X32 ) ) ) ) =>
% 95.81/12.75 ( ![X36:$i]:
% 95.81/12.75 ( ( in @ X36 @ omega ) => ( in @ X36 @ X32 ) ) ) ) ) =>
% 95.81/12.75 ( ( ![X38:( $i > $i > $o ),X40:$i]:
% 95.81/12.75 ( ( ![X42:$i]:
% 95.81/12.75 ( ( in @ X42 @ X40 ) =>
% 95.81/12.75 ( ?[X44:$i]:
% 95.81/12.75 ( ( ![X46:$i]:
% 95.81/12.75 ( ( X38 @ X42 @ X46 ) =>
% 95.81/12.75 ( ( X44 ) = ( X46 ) ) ) ) &
% 95.81/12.75 ( X38 @ X42 @ X44 ) ) ) ) ) =>
% 95.81/12.75 ( ?[X48:$i]:
% 95.81/12.75 ( ![X50:$i]:
% 95.81/12.75 ( ( in @ X50 @ X48 ) <=>
% 95.81/12.75 ( ?[X52:$i]:
% 95.81/12.75 ( zip_tseitin_3 @ X52 @ X50 @ X40 @ X38 ) ) ) ) ) ) ) =>
% 95.81/12.75 ( ( ![X54:$i]:
% 95.81/12.75 ( ( ?[X56:$i]: ( in @ X56 @ X54 ) ) =>
% 95.81/12.75 ( ?[X58:$i]:
% 95.81/12.75 ( ( ~( ?[X60:$i]:
% 95.81/12.75 ( ( in @ X60 @ X54 ) &
% 95.81/12.75 ( in @ X60 @ X58 ) ) ) ) &
% 95.81/12.75 ( in @ X58 @ X54 ) ) ) ) ) =>
% 95.81/12.75 ( ( ![X62:$i]:
% 95.81/12.75 ( ?[X64:$i]:
% 95.81/12.75 ( ( ![X66:$i]:
% 95.81/12.75 ( ( ( ![X68:$i]:
% 95.81/12.75 ( ( in @ X68 @ X66 ) =>
% 95.81/12.75 ( in @ X68 @ X62 ) ) ) &
% 95.81/12.75 ( ?[X70:$i]: ( in @ X70 @ X66 ) ) ) =>
% 95.81/12.75 ( ?[X72:$i,X74:$i]:
% 95.81/12.75 ( ( ![X76:$i]:
% 95.81/12.75 ( ( in @ X76 @ X64 ) =>
% 95.81/12.75 ( ( ![X78:$i]:
% 95.81/12.75 ( ( in @ X78 @ X76 ) =>
% 95.81/12.75 ( in @ X78 @ X72 ) ) ) |
% 95.81/12.75 ( in @ X74 @ X76 ) ) ) ) &
% 95.81/12.75 ( ~( ?[X80:$i]:
% 95.81/12.75 ( ( in @ X80 @ X66 ) &
% 95.81/12.75 ( in @ X80 @ X72 ) ) ) ) &
% 95.81/12.75 ( in @ X74 @ X66 ) &
% 95.81/12.75 ( in @ X72 @ X64 ) ) ) ) ) &
% 95.81/12.75 ( ![X82:$i,X84:$i]:
% 95.81/12.75 ( ( ( in @ X82 @ X64 ) & ( in @ X84 @ X64 ) ) =>
% 95.81/12.75 ( ( ![X86:$i]:
% 95.81/12.75 ( ( in @ X86 @ X82 ) =>
% 95.81/12.75 ( in @ X86 @ X84 ) ) ) |
% 95.81/12.75 ( ![X88:$i]:
% 95.81/12.75 ( ( in @ X88 @ X84 ) =>
% 95.81/12.75 ( in @ X88 @ X82 ) ) ) ) ) ) &
% 95.81/12.75 ( ![X90:$i,X92:$i]:
% 95.81/12.75 ( ( ( in @ X90 @ X62 ) & ( in @ X92 @ X62 ) ) =>
% 95.81/12.75 ( ( ![X94:$i]:
% 95.81/12.75 ( ( in @ X94 @ X64 ) =>
% 95.81/12.75 ( ( in @ X90 @ X94 ) <=>
% 95.81/12.75 ( in @ X92 @ X94 ) ) ) ) =>
% 95.81/12.75 ( ( X90 ) = ( X92 ) ) ) ) ) &
% 95.81/12.75 ( ![X96:$i]:
% 95.81/12.75 ( ( in @ X96 @ X64 ) =>
% 95.81/12.75 ( ![X98:$i]:
% 95.81/12.75 ( ( in @ X98 @ X96 ) =>
% 95.81/12.75 ( in @ X98 @ X62 ) ) ) ) ) ) ) ) =>
% 95.81/12.75 ( ( ![X100:( $i > $o )]:
% 95.81/12.75 ( ( ?[X102:$i]:
% 95.81/12.75 ( ( ![X104:$i]:
% 95.81/12.75 ( ( X100 @ X104 ) =>
% 95.81/12.75 ( ( X102 ) = ( X104 ) ) ) ) &
% 95.81/12.75 ( X100 @ X102 ) ) ) =>
% 95.81/12.75 ( X100 @
% 95.81/12.75 ( descr @ ( ^[V_1:$i]: ( X100 @ V_1 ) ) ) ) ) ) =>
% 95.81/12.75 ( ( ![X106:$i,X108:( $i > $o ),X110:$i]:
% 95.81/12.75 ( ( in @ X110 @ X106 ) =>
% 95.81/12.75 ( ( X108 @ X110 ) =>
% 95.81/12.75 ( in @
% 95.81/12.75 X110 @
% 95.81/12.75 ( dsetconstr @
% 95.81/12.75 X106 @ ( ^[V_2:$i]: ( X108 @ V_2 ) ) ) ) ) ) ) =>
% 95.81/12.75 ( ( ![X112:$i,X114:( $i > $o ),X116:$i]:
% 95.81/12.75 ( ( in @
% 95.81/12.75 X116 @
% 95.81/12.75 ( dsetconstr @
% 95.81/12.75 X112 @ ( ^[V_3:$i]: ( X114 @ V_3 ) ) ) ) =>
% 95.81/12.75 ( in @ X116 @ X112 ) ) ) =>
% 95.81/12.75 ( ( ![X118:$i,X120:( $i > $o ),X122:$i]:
% 95.81/12.75 ( ( in @
% 95.81/12.75 X122 @
% 95.81/12.75 ( dsetconstr @
% 95.81/12.75 X118 @
% 95.81/12.75 ( ^[V_4:$i]: ( X120 @ V_4 ) ) ) ) =>
% 95.81/12.75 ( X120 @ X122 ) ) ) =>
% 95.81/12.75 ( ( ![X124:( $i > $o )]:
% 95.81/12.75 ( ( ?[X126:$i]:
% 95.81/12.75 ( ( ![X128:$i]:
% 95.81/12.75 ( ( X124 @ X128 ) =>
% 95.81/12.75 ( ( X126 ) = ( X128 ) ) ) ) &
% 95.81/12.75 ( X124 @ X126 ) ) ) =>
% 95.81/12.75 ( ?[X130:$i]:
% 95.81/12.75 ( ( ![X132:$i]:
% 95.81/12.75 ( ( X124 @ X132 ) =>
% 95.81/12.75 ( ( X130 ) = ( X132 ) ) ) ) &
% 95.81/12.75 ( X124 @ X130 ) ) ) ) ) =>
% 95.81/12.75 ( ( ![X134:$o,X136:$i]:
% 95.81/12.75 ( ( in @ X136 @ ( prop2set @ X134 ) ) =>
% 95.81/12.75 ( X134 ) ) ) =>
% 95.81/12.75 ( ( ![X138:$i]:
% 95.81/12.75 ( ( in @ X138 @ emptyset ) =>
% 95.81/12.75 ( ![X140:$o]: ( X140 ) ) ) ) =>
% 95.81/12.75 ( ( ![X142:$i]:
% 95.81/12.75 ( ~( in @ X142 @ emptyset ) ) ) =>
% 95.81/12.75 ( ( ![X144:$i]:
% 95.81/12.75 ( ~( in @ X144 @ emptyset ) ) ) =>
% 95.81/12.75 ( ( ![X146:( $i > $o )]:
% 95.81/12.75 ( ( ?[X148:$i]:
% 95.81/12.75 ( ( ![X150:$i]:
% 95.81/12.75 ( ( X146 @ X150 ) =>
% 95.81/12.75 ( ( X148 ) =
% 95.81/12.75 ( X150 ) ) ) ) &
% 95.81/12.75 ( X146 @ X148 ) ) ) =>
% 95.81/12.75 ( ?[X152:$i]:
% 95.81/12.75 ( X146 @ X152 ) ) ) ) =>
% 95.81/12.75 ( ( ![X154:$i,X156:$i]:
% 95.81/12.75 ( ( ![X158:$i]:
% 95.81/12.75 ( ( in @ X158 @ X154 ) =>
% 95.81/12.75 ( in @ X158 @ X156 ) ) ) =>
% 95.81/12.75 ( ( ![X160:$i]:
% 95.81/12.75 ( ( in @ X160 @ X156 ) =>
% 95.81/12.75 ( in @ X160 @ X154 ) ) ) =>
% 95.81/12.75 ( ( X154 ) = ( X156 ) ) ) ) ) =>
% 95.81/12.75 ( ( ![X162:$i]:
% 95.81/12.75 ( ( ![X164:$i]:
% 95.81/12.75 ( ~( in @ X164 @ X162 ) ) ) =>
% 95.81/12.75 ( ( X162 ) =
% 95.81/12.75 ( emptyset ) ) ) ) =>
% 95.81/12.75 ( ( ![X166:$i]:
% 95.81/12.75 ( ( ![X168:$i]:
% 95.81/12.75 ( ~( in @
% 95.81/12.75 X168 @ X166 ) ) ) =>
% 95.81/12.75 ( ( X166 ) =
% 95.81/12.75 ( emptyset ) ) ) ) =>
% 95.81/12.75 ( ( ![X170:$i,
% 95.81/12.75 X172:( $i > $o ),
% 95.81/12.75 X174:$i]:
% 95.81/12.75 ( ( in @ X174 @ X170 ) =>
% 95.81/12.75 ( ( in @
% 95.81/12.75 X174 @
% 95.81/12.75 ( dsetconstr @
% 95.81/12.75 X170 @
% 95.81/12.75 ( ^[V_5:$i]:
% 95.81/12.75 ( X172 @
% 95.81/12.75 V_5 ) ) ) ) <=>
% 95.81/12.75 ( X172 @ X174 ) ) ) ) =>
% 95.81/12.75 ( ( ![X176:$i]:
% 95.81/12.75 ( ( ( X176 ) !=
% 95.81/12.75 ( emptyset ) ) =>
% 95.81/12.75 ( ?[X178:$i]:
% 95.81/12.75 ( in @
% 95.81/12.75 X178 @ X176 ) ) ) ) =>
% 95.81/12.75 ( ( ![X180:$i,
% 95.81/12.75 X182:(
% 95.81/12.75 $i > $o ),
% 95.81/12.75 X184:$i]:
% 95.81/12.75 ( ( in @
% 95.81/12.75 X184 @ X180 ) =>
% 95.81/12.75 ( ( X182 @ X184 ) =>
% 95.81/12.75 ( ( dsetconstr
% 95.81/12.75 @
% 95.81/12.75 X180 @
% 95.81/12.75 (
% 95.81/12.75 ^[
% 95.81/12.75 V_6:$i]:
% 95.81/12.75 (
% 95.81/12.75 X182 @
% 95.81/12.75 V_6 ) ) ) !=
% 95.81/12.75 ( emptyset ) ) ) ) ) =>
% 95.81/12.75 ( ( ![X186:$i]:
% 95.81/12.75 ( ( ?[X188:$i]:
% 95.81/12.75 ( in @
% 95.81/12.75 X188 @
% 95.81/12.75 X186 ) ) =>
% 95.81/12.75 ( ( X186 ) !=
% 95.81/12.75 ( emptyset ) ) ) ) =>
% 95.81/12.75 ( ( ![X190:$i,
% 95.81/12.75 X192:$i]:
% 95.81/12.75 ( in @
% 95.81/12.75 X190 @
% 95.81/12.75 ( setadjoin
% 95.81/12.75 @
% 95.81/12.75 X190 @
% 95.81/12.75 X192 ) ) ) =>
% 95.81/12.75 ( ( in @
% 95.81/12.75 emptyset @
% 95.81/12.75 ( setadjoin
% 95.81/12.75 @
% 95.81/12.75 emptyset @
% 95.81/12.75 emptyset ) ) =>
% 95.81/12.75 ( ( ![
% 95.81/12.75 X194:$i,
% 95.81/12.75 X196:$i,
% 95.81/12.75 X198:$i]:
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 in @
% 95.81/12.75 X198 @
% 95.81/12.75 X196 ) =>
% 95.81/12.75 (
% 95.81/12.75 in @
% 95.81/12.75 X198 @
% 95.81/12.75 (
% 95.81/12.75 setadjoin
% 95.81/12.75 @
% 95.81/12.75 X194 @
% 95.81/12.75 X196 ) ) ) ) =>
% 95.81/12.75 ( (
% 95.81/12.75 ![
% 95.81/12.75 X200:$i,
% 95.81/12.75 X202:$i,
% 95.81/12.75 X204:$i]:
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 in @
% 95.81/12.75 X204 @
% 95.81/12.75 (
% 95.81/12.75 setadjoin
% 95.81/12.75 @
% 95.81/12.75 X200 @
% 95.81/12.75 X202 ) ) =>
% 95.81/12.75 (
% 95.81/12.75 ![
% 95.81/12.75 X206:$o]:
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 X204 ) =
% 95.81/12.75 (
% 95.81/12.75 X200 ) ) =>
% 95.81/12.75 (
% 95.81/12.75 X206 ) ) =>
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 in @
% 95.81/12.75 X204 @
% 95.81/12.75 X202 ) =>
% 95.81/12.75 (
% 95.81/12.75 X206 ) ) =>
% 95.81/12.75 (
% 95.81/12.75 X206 ) ) ) ) ) ) =>
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 ![
% 95.81/12.75 X208:$i,
% 95.81/12.75 X210:$i,
% 95.81/12.75 X212:$i]:
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 in @
% 95.81/12.75 X212 @
% 95.81/12.75 (
% 95.81/12.75 setadjoin
% 95.81/12.75 @
% 95.81/12.75 X208 @
% 95.81/12.75 X210 ) ) =>
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 (
% 95.81/12.75 X212 ) =
% 95.81/12.76 (
% 95.81/12.76 X208 ) ) |
% 95.81/12.76 (
% 95.81/12.76 in @
% 95.81/12.76 X212 @
% 95.81/12.76 X210 ) ) ) ) =>
% 95.81/12.76 (
% 95.81/12.76 (
% 95.81/12.76 ![
% 95.81/12.76 X214:$i]:
% 95.81/12.76 (
% 95.81/12.76 (
% 95.81/12.76 dsetconstr
% 95.81/12.76 @
% 95.81/12.76 X214 @
% 95.81/12.76 (
% 95.81/12.76 ^[
% 95.81/12.76 V_7:$i]:
% 95.81/12.76 (
% 95.81/12.76 $true ) ) ) =
% 95.81/12.76 (
% 95.81/12.76 X214 ) ) ) =>
% 95.81/12.76 (
% 95.81/12.76 (
% 95.81/12.76 ![
% 95.81/12.76 X216:$i,
% 95.81/12.76 X218:$i]:
% 95.81/12.76 (
% 95.81/12.76 (
% 95.81/12.76 ![
% 95.81/12.76 X220:$i]:
% 95.81/12.76 (
% 95.81/12.76 (
% 95.81/12.76 in @
% 95.81/12.76 X220 @
% 95.81/12.76 X218 ) =>
% 95.81/12.76 (
% 95.81/12.76 in @
% 95.81/12.76 X220 @
% 95.81/12.76 X216 ) ) ) =>
% 95.81/12.76 (
% 95.81/12.76 in @
% 95.81/12.76 X218 @
% 95.81/12.76 (
% 95.81/12.76 powerset
% 95.81/12.76 @
% 95.81/12.76 X216 ) ) ) ) =>
% 95.81/12.76 (
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% 96.22/12.76 X830:$i]:
% 96.22/12.76 (
% 96.22/12.76 (
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% 96.22/12.76 X826 ) =>
% 96.22/12.76 (
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% 96.22/12.76 (
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% 96.22/12.76 (
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% 96.22/12.76 (
% 96.22/12.76 powerset
% 96.22/12.76 @
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% 96.22/12.76 (
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% 96.22/12.76 (
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% 96.22/12.76 X872:$i,
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% 96.22/12.76 X876:$i]:
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% 96.22/12.76 (
% 96.22/12.76 (
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% 96.22/12.76 X884:$i,
% 96.22/12.76 X886:(
% 96.22/12.76 $i > $o )]:
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% 96.22/12.76 X888:$i]:
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% 96.22/12.76 X890:$i]:
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% 96.22/12.76 (
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% 96.22/12.76 X888 ) =>
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% 96.22/12.76 (
% 96.22/12.76 (
% 96.22/12.76 ?[
% 96.22/12.76 X892:$i]:
% 96.22/12.76 (
% 96.22/12.76 (
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% 96.22/12.76 X892 ) &
% 96.22/12.76 (
% 96.22/12.76 in @
% 96.22/12.76 X892 @
% 96.22/12.76 X884 ) ) ) =>
% 96.22/12.76 (
% 96.22/12.76 singleton
% 96.22/12.76 @
% 96.22/12.76 (
% 96.22/12.76 dsetconstr
% 96.22/12.76 @
% 96.22/12.76 X884 @
% 96.22/12.76 (
% 96.22/12.76 ^[
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% 96.22/12.76 (
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% 96.22/12.76 X894:$i,
% 96.22/12.76 X896:(
% 96.22/12.76 $i > $o )]:
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% 96.22/12.76 X898:$i]:
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% 96.22/12.76 (
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% 96.22/12.76 X900:$i,
% 96.22/12.76 X902:(
% 96.22/12.76 $i > $o ),
% 96.22/12.76 X904:$i]:
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% 96.22/12.76 X906:$i]:
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% 96.22/12.76 (
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% 96.22/12.76 (
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% 96.22/12.76 $i > $o )]:
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% 96.22/12.76 X912:$i]:
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% 96.22/12.76 X914:$i]:
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% 96.22/12.76 X912 ) =>
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% 96.22/12.76 (
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% 96.22/12.76 X914 ) =>
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% 96.22/12.76 (
% 96.22/12.76 (
% 96.22/12.76 ?[
% 96.22/12.76 X916:$i]:
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% 96.22/12.76 (
% 96.22/12.76 in @
% 96.22/12.76 X916 @
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% 96.22/12.76 (
% 96.22/12.76 ex1 @
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% 96.22/12.76 (
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% 96.22/12.76 X918:$i,
% 96.22/12.76 X920:$i]:
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% 96.22/12.76 (
% 96.22/12.76 (
% 96.22/12.76 ![
% 96.22/12.76 X922:$i,
% 96.22/12.76 X924:$i,
% 96.22/12.76 X926:$i]:
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% 96.22/12.76 (
% 96.22/12.76 (
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% 96.22/12.76 X926 ) ) ) ) =>
% 96.22/12.76 (
% 96.22/12.76 (
% 96.22/12.76 ![
% 96.22/12.76 X928:$i]:
% 96.22/12.76 (
% 96.22/12.76 (
% 96.22/12.76 iskpair @
% 96.22/12.76 X928 ) =>
% 96.22/12.76 (
% 96.22/12.76 singleton
% 96.22/12.76 @
% 96.22/12.76 (
% 96.22/12.76 dsetconstr
% 96.22/12.76 @
% 96.22/12.76 (
% 96.22/12.76 setunion
% 96.22/12.76 @
% 96.22/12.76 X928 ) @
% 96.22/12.76 (
% 96.22/12.76 ^[
% 96.22/12.76 V_19:$i]:
% 96.22/12.76 (
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% 96.22/12.76 (
% 96.22/12.76 (
% 96.22/12.76 ![
% 96.22/12.76 X930:$i]:
% 96.22/12.76 (
% 96.22/12.76 (
% 96.22/12.76 singleton
% 96.22/12.76 @
% 96.22/12.76 X930 ) =>
% 96.22/12.76 (
% 96.22/12.76 in @
% 96.22/12.76 (
% 96.22/12.76 setunion
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% 96.22/12.76 X930 ) ) ) =>
% 96.22/12.76 (
% 96.22/12.76 (
% 96.22/12.76 ![
% 96.22/12.76 X932:$i,
% 96.22/12.76 X934:$i]:
% 96.22/12.76 (
% 96.22/12.76 (
% 96.22/12.76 kfst @
% 96.22/12.76 (
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% 96.22/12.76 X932 @
% 96.22/12.76 X934 ) ) =
% 96.22/12.76 (
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% 96.22/12.76 (
% 96.22/12.76 (
% 96.22/12.76 ![
% 96.22/12.76 X936:$i,
% 96.22/12.76 X938:$i,
% 96.22/12.76 X940:$i]:
% 96.22/12.76 (
% 96.22/12.76 (
% 96.22/12.76 in @
% 96.22/12.76 X940 @
% 96.22/12.76 (
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% 96.22/12.76 (
% 96.22/12.76 (
% 96.22/12.76 ![
% 96.22/12.76 X942:$i,
% 96.22/12.76 X944:$i,
% 96.22/12.76 X946:$i,
% 96.22/12.76 X948:$i]:
% 96.22/12.76 (
% 96.22/12.76 (
% 96.22/12.76 (
% 96.22/12.76 setadjoin
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% 96.22/12.76 (
% 96.22/12.76 setadjoin
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% 96.22/12.77 V_28 ) ) ) ) =>
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% 96.22/12.77 $i > $i >
% 96.22/12.77 $o ),
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% 96.22/12.77 V_30 ) ) ) ) =>
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% 96.22/12.77 V_34 ) ) ) ) =>
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% 96.22/12.77 $i > $i )]:
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% 96.22/12.77 X1166 @
% 96.22/12.77 V_37 ) =
% 96.22/12.77 (
% 96.22/12.77 V_38 ) ) ) ) ) ) ) =>
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% 96.22/12.77 $i > $i )]:
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% 96.22/12.77 $i > $i )]:
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% 96.22/12.77 $i > $o )]:
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% 96.22/12.77 X1194 @
% 96.22/12.77 X1196 ) ) ) ) ) ) ) =>
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% 96.22/12.77 X1198 ) ) ) ) ) ) ) =>
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% 96.22/12.77 $i > $o )]:
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% 96.22/12.77 kpair @
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% 96.22/12.77 (
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% 96.22/12.77 X1228 ) ) @
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% 96.22/12.77 in @
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% 96.22/12.77 (
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% 96.22/12.77 (
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% 96.22/12.77 (
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% 96.22/12.77 X1264:$i,
% 96.22/12.77 X1266:$i]:
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% 96.22/12.77 X1274:$i,
% 96.22/12.77 X1276:$i]:
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% 96.22/12.77 X1276 ) =>
% 96.22/12.77 (
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% 96.22/12.77 (
% 96.22/12.77 (
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% 96.22/12.77 X1286:$i,
% 96.22/12.77 X1288:$i]:
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% 96.22/12.77 X1288 ) =>
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% 96.22/12.77 X1300:$i,
% 96.22/12.77 X1302:$i,
% 96.22/12.77 X1304:$i]:
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% 96.22/12.77 X1312:$i,
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% 96.22/12.77 (
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% 96.22/12.77 X1412:$i]:
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% 96.22/12.77 X1408 ) =>
% 96.22/12.77 (
% 96.22/12.77 singleton
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% 96.22/12.77 (
% 96.22/12.77 dsetconstr
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% 96.22/12.77 X1408 @
% 96.22/12.77 (
% 96.22/12.77 ^[
% 96.22/12.77 V_52:$i]:
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% 96.22/12.77 (
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% 96.22/12.77 ~
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% 96.22/12.77 X1410 ) ) ) |
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% 96.22/12.77 (
% 96.22/12.77 (
% 96.22/12.77 ![
% 96.22/12.77 X1416:$i,
% 96.22/12.77 X1418:$o,
% 96.22/12.77 X1420:$i]:
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% 96.22/12.77 X1422:$i]:
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% 96.22/12.77 ![
% 96.22/12.77 X1426:$i]:
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% 96.22/12.77 (
% 96.22/12.77 (
% 96.22/12.77 ![
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% 96.22/12.77 X1432:$i]:
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% 96.22/12.77 X1440:$i]:
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% 96.22/12.77 (
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% 96.22/12.77 (
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% 96.22/12.78 (
% 96.22/12.78 in @
% 96.22/12.78 X1866 @
% 96.22/12.78 (
% 96.22/12.78 powerset
% 96.22/12.78 @
% 96.22/12.78 X1862 ) ) =>
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 subset @
% 96.22/12.78 X1864 @
% 96.22/12.78 (
% 96.22/12.78 setminus
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% 96.22/12.78 (
% 96.22/12.78 subset @
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% 96.22/12.78 (
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% 96.22/12.78 X1870:$i]:
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 in @
% 96.22/12.78 X1870 @
% 96.22/12.78 (
% 96.22/12.78 powerset
% 96.22/12.78 @
% 96.22/12.78 X1868 ) ) =>
% 96.22/12.78 (
% 96.22/12.78 ![
% 96.22/12.78 X1872:$i]:
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 in @
% 96.22/12.78 X1872 @
% 96.22/12.78 (
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% 96.22/12.78 @
% 96.22/12.78 X1868 ) ) =>
% 96.22/12.78 (
% 96.22/12.78 in @
% 96.22/12.78 (
% 96.22/12.78 setminus
% 96.22/12.78 @
% 96.22/12.78 X1868 @
% 96.22/12.78 (
% 96.22/12.78 binunion
% 96.22/12.78 @
% 96.22/12.78 X1870 @
% 96.22/12.78 X1872 ) ) @
% 96.22/12.78 (
% 96.22/12.78 powerset
% 96.22/12.78 @
% 96.22/12.78 (
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% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 ![
% 96.22/12.78 X1874:$i,
% 96.22/12.78 X1876:$i]:
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 breln1 @
% 96.22/12.78 X1874 @
% 96.22/12.78 X1876 ) =>
% 96.22/12.78 (
% 96.22/12.78 ![
% 96.22/12.78 X1878:(
% 96.22/12.78 $i > $o )]:
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 ![
% 96.22/12.78 X1880:$i]:
% 96.22/12.78 (
% 96.22/12.78 (
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% 96.22/12.78 X1880 @
% 96.22/12.78 X1874 ) =>
% 96.22/12.78 (
% 96.22/12.78 ![
% 96.22/12.78 X1882:$i]:
% 96.22/12.78 (
% 96.22/12.78 (
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% 96.22/12.78 X1882 @
% 96.22/12.78 X1874 ) =>
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 in @
% 96.22/12.78 (
% 96.22/12.78 kpair @
% 96.22/12.78 X1880 @
% 96.22/12.78 X1882 ) @
% 96.22/12.78 X1876 ) =>
% 96.22/12.78 (
% 96.22/12.78 X1878 @
% 96.22/12.78 (
% 96.22/12.78 kpair @
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% 96.22/12.78 (
% 96.22/12.78 ![
% 96.22/12.78 X1884:$i]:
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 in @
% 96.22/12.78 X1884 @
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% 96.22/12.78 (
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% 96.22/12.78 ![
% 96.22/12.78 X1886:$i,
% 96.22/12.78 X1888:$i]:
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 in @
% 96.22/12.78 X1888 @
% 96.22/12.78 (
% 96.22/12.78 breln1Set
% 96.22/12.78 @
% 96.22/12.78 X1886 ) ) =>
% 96.22/12.78 (
% 96.22/12.78 breln1 @
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% 96.22/12.78 X1888 ) ) ) =>
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 ![
% 96.22/12.78 X1890:$i,
% 96.22/12.78 X1892:$i,
% 96.22/12.78 X1894:(
% 96.22/12.78 $i > $i >
% 96.22/12.78 $o )]:
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 ![
% 96.22/12.78 X1896:$i]:
% 96.22/12.78 (
% 96.22/12.78 (
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% 96.22/12.78 X1896 @
% 96.22/12.78 X1890 ) =>
% 96.22/12.78 (
% 96.22/12.78 ?[
% 96.22/12.78 X1898:$i]:
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 X1894 @
% 96.22/12.78 X1896 @
% 96.22/12.78 X1898 ) &
% 96.22/12.78 (
% 96.22/12.78 in @
% 96.22/12.78 X1898 @
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% 96.22/12.78 (
% 96.22/12.78 ![
% 96.22/12.78 X1900:$i]:
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 in @
% 96.22/12.78 X1900 @
% 96.22/12.78 (
% 96.22/12.78 breln1Set
% 96.22/12.78 @
% 96.22/12.78 X1892 ) ) =>
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 reflwellordering
% 96.22/12.78 @
% 96.22/12.78 X1892 @
% 96.22/12.78 X1900 ) =>
% 96.22/12.78 (
% 96.22/12.78 ![
% 96.22/12.78 X1902:$i]:
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 in @
% 96.22/12.78 X1902 @
% 96.22/12.78 X1890 ) =>
% 96.22/12.78 (
% 96.22/12.78 singleton
% 96.22/12.78 @
% 96.22/12.78 (
% 96.22/12.78 dsetconstr
% 96.22/12.78 @
% 96.22/12.78 X1892 @
% 96.22/12.78 (
% 96.22/12.78 ^[
% 96.22/12.78 V_53:$i]:
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 ![
% 96.22/12.78 X1904:$i]:
% 96.22/12.78 (
% 96.22/12.78 (
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% 96.22/12.78 X1892 ) =>
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 X1894 @
% 96.22/12.78 X1902 @
% 96.22/12.78 X1904 ) =>
% 96.22/12.78 (
% 96.22/12.78 in @
% 96.22/12.78 (
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% 96.22/12.78 X1900 ) ) ) ) &
% 96.22/12.78 (
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% 96.22/12.78 (
% 96.22/12.78 (
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% 96.22/12.78 X1906:$i,
% 96.22/12.78 X1908:(
% 96.22/12.78 $i > $i >
% 96.22/12.78 $o )]:
% 96.22/12.78 (
% 96.22/12.78 breln1 @
% 96.22/12.78 X1906 @
% 96.22/12.78 (
% 96.22/12.78 dpsetconstr
% 96.22/12.78 @
% 96.22/12.78 X1906 @
% 96.22/12.78 X1906 @
% 96.22/12.78 (
% 96.22/12.78 ^[
% 96.22/12.78 V_54:$i,
% 96.22/12.78 V_55:$i]:
% 96.22/12.78 (
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% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 ![
% 96.22/12.78 X1910:$i,
% 96.22/12.78 X1912:$i]:
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 breln1 @
% 96.22/12.78 X1910 @
% 96.22/12.78 X1912 ) =>
% 96.22/12.78 (
% 96.22/12.78 ![
% 96.22/12.78 X1914:(
% 96.22/12.78 $i > $o )]:
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 ![
% 96.22/12.78 X1916:$i]:
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 in @
% 96.22/12.78 X1916 @
% 96.22/12.78 X1910 ) =>
% 96.22/12.78 (
% 96.22/12.78 ![
% 96.22/12.78 X1918:$i]:
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 in @
% 96.22/12.78 X1918 @
% 96.22/12.78 X1910 ) =>
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 in @
% 96.22/12.78 (
% 96.22/12.78 kpair @
% 96.22/12.78 X1916 @
% 96.22/12.78 X1918 ) @
% 96.22/12.78 X1912 ) =>
% 96.22/12.78 (
% 96.22/12.78 X1914 @
% 96.22/12.78 (
% 96.22/12.78 kpair @
% 96.22/12.78 X1916 @
% 96.22/12.78 X1918 ) ) ) ) ) ) ) =>
% 96.22/12.78 (
% 96.22/12.78 ![
% 96.22/12.78 X1920:$i]:
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 in @
% 96.22/12.78 X1920 @
% 96.22/12.78 X1912 ) =>
% 96.22/12.78 (
% 96.22/12.78 X1914 @
% 96.22/12.78 X1920 ) ) ) ) ) ) ) =>
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 ![
% 96.22/12.78 X1922:$i,
% 96.22/12.78 X1924:$i]:
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 breln1 @
% 96.22/12.78 X1922 @
% 96.22/12.78 X1924 ) =>
% 96.22/12.78 (
% 96.22/12.78 ![
% 96.22/12.78 X1926:$i]:
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 breln1 @
% 96.22/12.78 X1922 @
% 96.22/12.78 X1926 ) =>
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 ![
% 96.22/12.78 X1928:$i]:
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 in @
% 96.22/12.78 X1928 @
% 96.22/12.78 X1922 ) =>
% 96.22/12.78 (
% 96.22/12.78 ![
% 96.22/12.78 X1930:$i]:
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 in @
% 96.22/12.78 X1930 @
% 96.22/12.78 X1922 ) =>
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 in @
% 96.22/12.78 (
% 96.22/12.78 kpair @
% 96.22/12.78 X1928 @
% 96.22/12.78 X1930 ) @
% 96.22/12.78 X1924 ) =>
% 96.22/12.78 (
% 96.22/12.78 in @
% 96.22/12.78 (
% 96.22/12.78 kpair @
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% 96.22/12.78 X1930 ) @
% 96.22/12.78 X1926 ) ) ) ) ) ) =>
% 96.22/12.78 (
% 96.22/12.78 subset @
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% 96.22/12.78 X1926 ) ) ) ) ) ) =>
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 ![
% 96.22/12.78 X1932:$i,
% 96.22/12.78 X1934:$i]:
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 breln1 @
% 96.22/12.78 X1932 @
% 96.22/12.78 X1934 ) =>
% 96.22/12.78 (
% 96.22/12.78 ![
% 96.22/12.78 X1936:$i]:
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 breln1 @
% 96.22/12.78 X1932 @
% 96.22/12.78 X1936 ) =>
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 ![
% 96.22/12.78 X1938:$i]:
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 in @
% 96.22/12.78 X1938 @
% 96.22/12.78 X1932 ) =>
% 96.22/12.78 (
% 96.22/12.78 ![
% 96.22/12.78 X1940:$i]:
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 in @
% 96.22/12.78 X1940 @
% 96.22/12.78 X1932 ) =>
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 in @
% 96.22/12.78 (
% 96.22/12.78 kpair @
% 96.22/12.78 X1938 @
% 96.22/12.78 X1940 ) @
% 96.22/12.78 X1934 ) =>
% 96.22/12.78 (
% 96.22/12.78 in @
% 96.22/12.78 (
% 96.22/12.78 kpair @
% 96.22/12.78 X1938 @
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% 96.22/12.78 X1936 ) ) ) ) ) ) =>
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 ![
% 96.22/12.78 X1942:$i]:
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 in @
% 96.22/12.78 X1942 @
% 96.22/12.78 X1932 ) =>
% 96.22/12.78 (
% 96.22/12.78 ![
% 96.22/12.78 X1944:$i]:
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 in @
% 96.22/12.78 X1944 @
% 96.22/12.78 X1932 ) =>
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 in @
% 96.22/12.78 (
% 96.22/12.78 kpair @
% 96.22/12.78 X1942 @
% 96.22/12.78 X1944 ) @
% 96.22/12.78 X1936 ) =>
% 96.22/12.78 (
% 96.22/12.78 in @
% 96.22/12.78 (
% 96.22/12.78 kpair @
% 96.22/12.78 X1942 @
% 96.22/12.78 X1944 ) @
% 96.22/12.78 X1934 ) ) ) ) ) ) =>
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 X1934 ) =
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% 96.22/12.78 X1936 ) ) ) ) ) ) ) ) =>
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 ![
% 96.22/12.78 X1946:$i,
% 96.22/12.78 X1948:$i]:
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 breln1 @
% 96.22/12.78 X1946 @
% 96.22/12.78 X1948 ) =>
% 96.22/12.78 (
% 96.22/12.78 breln1 @
% 96.22/12.78 X1946 @
% 96.22/12.78 (
% 96.22/12.78 breln1invset
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% 96.22/12.78 X1948 ) ) ) ) =>
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 ![
% 96.22/12.78 X1950:$i,
% 96.22/12.78 X1952:$i]:
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 breln1 @
% 96.22/12.78 X1950 @
% 96.22/12.78 X1952 ) =>
% 96.22/12.78 (
% 96.22/12.78 ![
% 96.22/12.78 X1954:$i]:
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 in @
% 96.22/12.78 X1954 @
% 96.22/12.78 X1950 ) =>
% 96.22/12.78 (
% 96.22/12.78 ![
% 96.22/12.78 X1956:$i]:
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 in @
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% 96.22/12.78 X1950 ) =>
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 in @
% 96.22/12.78 (
% 96.22/12.78 kpair @
% 96.22/12.78 X1954 @
% 96.22/12.78 X1956 ) @
% 96.22/12.78 X1952 ) =>
% 96.22/12.78 (
% 96.22/12.78 in @
% 96.22/12.78 (
% 96.22/12.78 kpair @
% 96.22/12.78 X1956 @
% 96.22/12.78 X1954 ) @
% 96.22/12.78 (
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% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 ![
% 96.22/12.78 X1958:$i,
% 96.22/12.78 X1960:$i]:
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 breln1 @
% 96.22/12.78 X1958 @
% 96.22/12.78 X1960 ) =>
% 96.22/12.78 (
% 96.22/12.78 ![
% 96.22/12.78 X1962:$i]:
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 in @
% 96.22/12.78 X1962 @
% 96.22/12.78 X1958 ) =>
% 96.22/12.78 (
% 96.22/12.78 ![
% 96.22/12.78 X1964:$i]:
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 in @
% 96.22/12.78 X1964 @
% 96.22/12.78 X1958 ) =>
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 in @
% 96.22/12.78 (
% 96.22/12.78 kpair @
% 96.22/12.78 X1964 @
% 96.22/12.78 X1962 ) @
% 96.22/12.78 (
% 96.22/12.78 breln1invset
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% 96.22/12.78 X1958 @
% 96.22/12.78 X1960 ) ) =>
% 96.22/12.78 (
% 96.22/12.78 in @
% 96.22/12.78 (
% 96.22/12.78 kpair @
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% 96.22/12.78 X1960 ) ) ) ) ) ) ) ) =>
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 ![
% 96.22/12.78 X1966:$i,
% 96.22/12.78 X1968:$i]:
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 breln1 @
% 96.22/12.78 X1966 @
% 96.22/12.78 X1968 ) =>
% 96.22/12.78 (
% 96.22/12.78 ![
% 96.22/12.78 X1970:$i]:
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 breln1 @
% 96.22/12.78 X1966 @
% 96.22/12.78 X1970 ) =>
% 96.22/12.78 (
% 96.22/12.78 breln1 @
% 96.22/12.78 X1966 @
% 96.22/12.78 (
% 96.22/12.78 breln1compset
% 96.22/12.78 @
% 96.22/12.78 X1966 @
% 96.22/12.78 X1968 @
% 96.22/12.78 X1970 ) ) ) ) ) ) =>
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 ![
% 96.22/12.78 X1972:$i,
% 96.22/12.78 X1974:$i]:
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 breln1 @
% 96.22/12.78 X1972 @
% 96.22/12.78 X1974 ) =>
% 96.22/12.78 (
% 96.22/12.78 ![
% 96.22/12.78 X1976:$i]:
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 breln1 @
% 96.22/12.78 X1972 @
% 96.22/12.78 X1976 ) =>
% 96.22/12.78 (
% 96.22/12.78 ![
% 96.22/12.78 X1978:$i]:
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 in @
% 96.22/12.78 X1978 @
% 96.22/12.78 X1972 ) =>
% 96.22/12.78 (
% 96.22/12.78 ![
% 96.22/12.78 X1980:$i]:
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 in @
% 96.22/12.78 X1980 @
% 96.22/12.78 X1972 ) =>
% 96.22/12.78 (
% 96.22/12.78 ![
% 96.22/12.78 X1982:$i]:
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 in @
% 96.22/12.78 X1982 @
% 96.22/12.78 X1972 ) =>
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 in @
% 96.22/12.78 (
% 96.22/12.78 kpair @
% 96.22/12.78 X1978 @
% 96.22/12.78 X1982 ) @
% 96.22/12.78 X1974 ) =>
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 in @
% 96.22/12.78 (
% 96.22/12.78 kpair @
% 96.22/12.78 X1982 @
% 96.22/12.78 X1980 ) @
% 96.22/12.78 X1976 ) =>
% 96.22/12.78 (
% 96.22/12.78 in @
% 96.22/12.78 (
% 96.22/12.78 kpair @
% 96.22/12.78 X1978 @
% 96.22/12.78 X1980 ) @
% 96.22/12.78 (
% 96.22/12.78 breln1compset
% 96.22/12.78 @
% 96.22/12.78 X1972 @
% 96.22/12.78 X1974 @
% 96.22/12.78 X1976 ) ) ) ) ) ) ) ) ) ) ) ) ) ) =>
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 ![
% 96.22/12.78 X1984:$i,
% 96.22/12.78 X1986:$i]:
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 breln1 @
% 96.22/12.78 X1984 @
% 96.22/12.78 X1986 ) =>
% 96.22/12.78 (
% 96.22/12.78 ![
% 96.22/12.78 X1988:$i]:
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 breln1 @
% 96.22/12.78 X1984 @
% 96.22/12.78 X1988 ) =>
% 96.22/12.78 (
% 96.22/12.78 ![
% 96.22/12.78 X1990:$i]:
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 in @
% 96.22/12.78 X1990 @
% 96.22/12.78 X1984 ) =>
% 96.22/12.78 (
% 96.22/12.78 ![
% 96.22/12.78 X1992:$i]:
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 in @
% 96.22/12.78 X1992 @
% 96.22/12.78 X1984 ) =>
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 in @
% 96.22/12.78 (
% 96.22/12.78 kpair @
% 96.22/12.78 X1990 @
% 96.22/12.78 X1992 ) @
% 96.22/12.78 (
% 96.22/12.78 breln1compset
% 96.22/12.78 @
% 96.22/12.78 X1984 @
% 96.22/12.78 X1986 @
% 96.22/12.78 X1988 ) ) =>
% 96.22/12.78 (
% 96.22/12.78 ?[
% 96.22/12.78 X1994:$i]:
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 in @
% 96.22/12.78 (
% 96.22/12.78 kpair @
% 96.22/12.78 X1994 @
% 96.22/12.78 X1992 ) @
% 96.22/12.78 X1988 ) &
% 96.22/12.78 (
% 96.22/12.78 in @
% 96.22/12.78 (
% 96.22/12.78 kpair @
% 96.22/12.78 X1990 @
% 96.22/12.78 X1994 ) @
% 96.22/12.78 X1986 ) &
% 96.22/12.78 (
% 96.22/12.78 in @
% 96.22/12.78 X1994 @
% 96.22/12.78 X1984 ) ) ) ) ) ) ) ) ) ) ) ) =>
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 ![
% 96.22/12.78 X1996:$i,
% 96.22/12.78 X1998:$i]:
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 breln1 @
% 96.22/12.78 X1996 @
% 96.22/12.78 X1998 ) =>
% 96.22/12.78 (
% 96.22/12.78 ![
% 96.22/12.78 X2000:$i]:
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 breln1 @
% 96.22/12.78 X1996 @
% 96.22/12.78 X2000 ) =>
% 96.22/12.78 (
% 96.22/12.78 ![
% 96.22/12.78 X2002:$i]:
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 in @
% 96.22/12.78 X2002 @
% 96.22/12.78 X1996 ) =>
% 96.22/12.78 (
% 96.22/12.78 ![
% 96.22/12.78 X2004:$i]:
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 in @
% 96.22/12.78 X2004 @
% 96.22/12.78 X1996 ) =>
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 in @
% 96.22/12.78 (
% 96.22/12.78 kpair @
% 96.22/12.78 X2002 @
% 96.22/12.78 X2004 ) @
% 96.22/12.78 (
% 96.22/12.78 breln1compset
% 96.22/12.78 @
% 96.22/12.78 X1996 @
% 96.22/12.78 X1998 @
% 96.22/12.78 X2000 ) ) =>
% 96.22/12.78 (
% 96.22/12.78 ![
% 96.22/12.78 X2006:$o]:
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 ![
% 96.22/12.78 X2008:$i]:
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 in @
% 96.22/12.78 X2008 @
% 96.22/12.78 X1996 ) =>
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 in @
% 96.22/12.78 (
% 96.22/12.78 kpair @
% 96.22/12.78 X2002 @
% 96.22/12.78 X2008 ) @
% 96.22/12.78 X1998 ) =>
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 in @
% 96.22/12.78 (
% 96.22/12.78 kpair @
% 96.22/12.78 X2008 @
% 96.22/12.78 X2004 ) @
% 96.22/12.78 X2000 ) =>
% 96.22/12.78 (
% 96.22/12.78 X2006 ) ) ) ) ) =>
% 96.22/12.78 (
% 96.22/12.78 X2006 ) ) ) ) ) ) ) ) ) ) ) ) =>
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 ![
% 96.22/12.78 X2010:$i,
% 96.22/12.78 X2012:$i]:
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 breln1 @
% 96.22/12.78 X2010 @
% 96.22/12.78 X2012 ) =>
% 96.22/12.78 (
% 96.22/12.78 ![
% 96.22/12.78 X2014:$i]:
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 breln1 @
% 96.22/12.78 X2010 @
% 96.22/12.78 X2014 ) =>
% 96.22/12.78 (
% 96.22/12.78 breln1 @
% 96.22/12.78 X2010 @
% 96.22/12.78 (
% 96.22/12.78 binunion
% 96.22/12.78 @
% 96.22/12.78 X2012 @
% 96.22/12.78 X2014 ) ) ) ) ) ) =>
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 ![
% 96.22/12.78 X2016:$i,
% 96.22/12.78 X2018:$i]:
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 breln1 @
% 96.22/12.78 X2016 @
% 96.22/12.78 X2018 ) =>
% 96.22/12.78 (
% 96.22/12.78 ![
% 96.22/12.78 X2020:$i]:
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 breln1 @
% 96.22/12.78 X2016 @
% 96.22/12.78 X2020 ) =>
% 96.22/12.78 (
% 96.22/12.78 ![
% 96.22/12.78 X2022:$i]:
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 in @
% 96.22/12.78 X2022 @
% 96.22/12.78 X2016 ) =>
% 96.22/12.78 (
% 96.22/12.78 ![
% 96.22/12.78 X2024:$i]:
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 in @
% 96.22/12.78 X2024 @
% 96.22/12.78 X2016 ) =>
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 in @
% 96.22/12.78 (
% 96.22/12.78 kpair @
% 96.22/12.78 X2022 @
% 96.22/12.78 X2024 ) @
% 96.22/12.78 X2018 ) =>
% 96.22/12.78 (
% 96.22/12.78 in @
% 96.22/12.78 (
% 96.22/12.78 kpair @
% 96.22/12.78 X2022 @
% 96.22/12.78 X2024 ) @
% 96.22/12.78 (
% 96.22/12.78 binunion
% 96.22/12.78 @
% 96.22/12.78 X2018 @
% 96.22/12.78 X2020 ) ) ) ) ) ) ) ) ) ) ) =>
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 ![
% 96.22/12.78 X2026:$i,
% 96.22/12.78 X2028:$i]:
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 breln1 @
% 96.22/12.78 X2026 @
% 96.22/12.78 X2028 ) =>
% 96.22/12.78 (
% 96.22/12.78 ![
% 96.22/12.78 X2030:$i]:
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 breln1 @
% 96.22/12.78 X2026 @
% 96.22/12.78 X2030 ) =>
% 96.22/12.78 (
% 96.22/12.78 ![
% 96.22/12.78 X2032:$i]:
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 in @
% 96.22/12.78 X2032 @
% 96.22/12.78 X2026 ) =>
% 96.22/12.78 (
% 96.22/12.78 ![
% 96.22/12.78 X2034:$i]:
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 in @
% 96.22/12.78 X2034 @
% 96.22/12.78 X2026 ) =>
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 in @
% 96.22/12.78 (
% 96.22/12.78 kpair @
% 96.22/12.78 X2032 @
% 96.22/12.78 X2034 ) @
% 96.22/12.78 X2030 ) =>
% 96.22/12.78 (
% 96.22/12.78 in @
% 96.22/12.78 (
% 96.22/12.78 kpair @
% 96.22/12.78 X2032 @
% 96.22/12.78 X2034 ) @
% 96.22/12.78 (
% 96.22/12.78 binunion
% 96.22/12.78 @
% 96.22/12.78 X2028 @
% 96.22/12.78 X2030 ) ) ) ) ) ) ) ) ) ) ) =>
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 ![
% 96.22/12.78 X2036:$i,
% 96.22/12.78 X2038:$i]:
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 breln1 @
% 96.22/12.78 X2036 @
% 96.22/12.78 X2038 ) =>
% 96.22/12.78 (
% 96.22/12.78 ![
% 96.22/12.78 X2040:$i]:
% 96.22/12.78 (
% 96.22/12.78 (
% 96.22/12.78 breln1 @
% 96.22/12.78 X2036 @
% 96.22/12.78 X2040 ) =>
% 96.22/12.78 (
% 96.22/12.79 ![
% 96.22/12.79 X2042:$i]:
% 96.22/12.79 (
% 96.22/12.79 (
% 96.22/12.79 in @
% 96.22/12.79 X2042 @
% 96.22/12.79 X2036 ) =>
% 96.22/12.79 (
% 96.22/12.79 ![
% 96.22/12.79 X2044:$i]:
% 96.22/12.79 (
% 96.22/12.79 (
% 96.22/12.79 in @
% 96.22/12.79 X2044 @
% 96.22/12.79 X2036 ) =>
% 96.22/12.79 (
% 96.22/12.79 (
% 96.22/12.79 (
% 96.22/12.79 in @
% 96.22/12.79 (
% 96.22/12.79 kpair @
% 96.22/12.79 X2042 @
% 96.22/12.79 X2044 ) @
% 96.22/12.79 X2038 ) |
% 96.22/12.79 (
% 96.22/12.79 in @
% 96.22/12.79 (
% 96.22/12.79 kpair @
% 96.22/12.79 X2042 @
% 96.22/12.79 X2044 ) @
% 96.22/12.79 X2040 ) ) =>
% 96.22/12.79 (
% 96.22/12.79 in @
% 96.22/12.79 (
% 96.22/12.79 kpair @
% 96.22/12.79 X2042 @
% 96.22/12.79 X2044 ) @
% 96.22/12.79 (
% 96.22/12.79 binunion
% 96.22/12.79 @
% 96.22/12.79 X2038 @
% 96.22/12.79 X2040 ) ) ) ) ) ) ) ) ) ) ) =>
% 96.22/12.79 (
% 96.22/12.79 (
% 96.22/12.79 ![
% 96.22/12.79 X2046:$i,
% 96.22/12.79 X2048:$i]:
% 96.22/12.79 (
% 96.22/12.79 (
% 96.22/12.79 breln1 @
% 96.22/12.79 X2046 @
% 96.22/12.79 X2048 ) =>
% 96.22/12.79 (
% 96.22/12.79 ![
% 96.22/12.79 X2050:$i]:
% 96.22/12.79 (
% 96.22/12.79 (
% 96.22/12.79 breln1 @
% 96.22/12.79 X2046 @
% 96.22/12.79 X2050 ) =>
% 96.22/12.79 (
% 96.22/12.79 ![
% 96.22/12.79 X2052:$i]:
% 96.22/12.79 (
% 96.22/12.79 (
% 96.22/12.79 in @
% 96.22/12.79 X2052 @
% 96.22/12.79 X2046 ) =>
% 96.22/12.79 (
% 96.22/12.79 ![
% 96.22/12.79 X2054:$i]:
% 96.22/12.79 (
% 96.22/12.79 (
% 96.22/12.79 in @
% 96.22/12.79 X2054 @
% 96.22/12.79 X2046 ) =>
% 96.22/12.79 (
% 96.22/12.79 (
% 96.22/12.79 in @
% 96.22/12.79 (
% 96.22/12.79 kpair @
% 96.22/12.79 X2052 @
% 96.22/12.79 X2054 ) @
% 96.22/12.79 (
% 96.22/12.79 binunion
% 96.22/12.79 @
% 96.22/12.79 X2048 @
% 96.22/12.79 X2050 ) ) =>
% 96.22/12.79 (
% 96.22/12.79 (
% 96.22/12.79 in @
% 96.22/12.79 (
% 96.22/12.79 kpair @
% 96.22/12.79 X2052 @
% 96.22/12.79 X2054 ) @
% 96.22/12.79 X2048 ) |
% 96.22/12.79 (
% 96.22/12.79 in @
% 96.22/12.79 (
% 96.22/12.79 kpair @
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% 96.22/12.79 X2054 ) @
% 96.22/12.79 X2050 ) ) ) ) ) ) ) ) ) ) ) =>
% 96.22/12.79 (
% 96.22/12.79 (
% 96.22/12.79 ![
% 96.22/12.79 X2056:$i,
% 96.22/12.79 X2058:$i]:
% 96.22/12.79 (
% 96.22/12.79 (
% 96.22/12.79 breln1 @
% 96.22/12.79 X2056 @
% 96.22/12.79 X2058 ) =>
% 96.22/12.79 (
% 96.22/12.79 ![
% 96.22/12.79 X2060:$i]:
% 96.22/12.79 (
% 96.22/12.79 (
% 96.22/12.79 breln1 @
% 96.22/12.79 X2056 @
% 96.22/12.79 X2060 ) =>
% 96.22/12.79 (
% 96.22/12.79 ![
% 96.22/12.79 X2062:$i]:
% 96.22/12.79 (
% 96.22/12.79 (
% 96.22/12.79 in @
% 96.22/12.79 X2062 @
% 96.22/12.79 X2056 ) =>
% 96.22/12.79 (
% 96.22/12.79 ![
% 96.22/12.79 X2064:$i]:
% 96.22/12.79 (
% 96.22/12.79 (
% 96.22/12.79 in @
% 96.22/12.79 X2064 @
% 96.22/12.79 X2056 ) =>
% 96.22/12.79 (
% 96.22/12.79 (
% 96.22/12.79 in @
% 96.22/12.79 (
% 96.22/12.79 kpair @
% 96.22/12.79 X2062 @
% 96.22/12.79 X2064 ) @
% 96.22/12.79 (
% 96.22/12.79 binunion
% 96.22/12.79 @
% 96.22/12.79 X2058 @
% 96.22/12.79 X2060 ) ) =>
% 96.22/12.79 (
% 96.22/12.79 ![
% 96.22/12.79 X2066:$o]:
% 96.22/12.79 (
% 96.22/12.79 (
% 96.22/12.79 (
% 96.22/12.79 in @
% 96.22/12.79 (
% 96.22/12.79 kpair @
% 96.22/12.79 X2062 @
% 96.22/12.79 X2064 ) @
% 96.22/12.79 X2058 ) =>
% 96.22/12.79 (
% 96.22/12.79 X2066 ) ) =>
% 96.22/12.79 (
% 96.22/12.79 (
% 96.22/12.79 (
% 96.22/12.79 in @
% 96.22/12.79 (
% 96.22/12.79 kpair @
% 96.22/12.79 X2062 @
% 96.22/12.79 X2064 ) @
% 96.22/12.79 X2060 ) =>
% 96.22/12.79 (
% 96.22/12.79 X2066 ) ) =>
% 96.22/12.79 (
% 96.22/12.79 X2066 ) ) ) ) ) ) ) ) ) ) ) ) ) =>
% 96.22/12.79 (
% 96.22/12.79 (
% 96.22/12.79 ![
% 96.22/12.79 X2068:$i,
% 96.22/12.79 X2070:$i]:
% 96.22/12.79 (
% 96.22/12.79 (
% 96.22/12.79 breln1 @
% 96.22/12.79 X2068 @
% 96.22/12.79 X2070 ) =>
% 96.22/12.79 (
% 96.22/12.79 ![
% 96.22/12.79 X2072:$i]:
% 96.22/12.79 (
% 96.22/12.79 (
% 96.22/12.79 breln1 @
% 96.22/12.79 X2068 @
% 96.22/12.79 X2072 ) =>
% 96.22/12.79 (
% 96.22/12.79 (
% 96.22/12.79 binunion
% 96.22/12.79 @
% 96.22/12.79 X2070 @
% 96.22/12.79 X2072 ) =
% 96.22/12.79 (
% 96.22/12.79 binunion
% 96.22/12.79 @
% 96.22/12.79 X2072 @
% 96.22/12.79 X2070 ) ) ) ) ) ) =>
% 96.22/12.79 (
% 96.22/12.79 (
% 96.22/12.79 ![
% 96.22/12.79 X2074:$i,
% 96.22/12.79 X2076:$i]:
% 96.22/12.79 (
% 96.22/12.79 (
% 96.22/12.79 breln1 @
% 96.22/12.79 X2074 @
% 96.22/12.79 X2076 ) =>
% 96.22/12.79 (
% 96.22/12.79 (
% 96.22/12.79 X2076 ) =
% 96.22/12.79 (
% 96.22/12.79 breln1invset
% 96.22/12.79 @
% 96.22/12.79 X2074 @
% 96.22/12.79 (
% 96.22/12.79 breln1invset
% 96.22/12.79 @
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% 96.22/12.79 X2076 ) ) ) ) ) =>
% 96.22/12.79 (
% 96.22/12.79 (
% 96.22/12.79 ![
% 96.22/12.79 X2078:$i,
% 96.22/12.79 X2080:$i]:
% 96.22/12.79 (
% 96.22/12.79 (
% 96.22/12.79 breln1 @
% 96.22/12.79 X2078 @
% 96.22/12.79 X2080 ) =>
% 96.22/12.79 (
% 96.22/12.79 ![
% 96.22/12.79 X2082:$i]:
% 96.22/12.79 (
% 96.22/12.79 (
% 96.22/12.79 breln1 @
% 96.22/12.79 X2078 @
% 96.22/12.79 X2082 ) =>
% 96.22/12.79 (
% 96.22/12.79 (
% 96.22/12.79 breln1invset
% 96.22/12.79 @
% 96.22/12.79 X2078 @
% 96.22/12.79 (
% 96.22/12.79 breln1compset
% 96.22/12.79 @
% 96.22/12.79 X2078 @
% 96.22/12.79 X2080 @
% 96.22/12.79 X2082 ) ) =
% 96.22/12.79 (
% 96.22/12.79 breln1compset
% 96.22/12.79 @
% 96.22/12.79 X2078 @
% 96.22/12.79 (
% 96.22/12.79 breln1invset
% 96.22/12.79 @
% 96.22/12.79 X2078 @
% 96.22/12.79 X2082 ) @
% 96.22/12.79 (
% 96.22/12.79 breln1invset
% 96.22/12.79 @
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% 96.22/12.79 X2080 ) ) ) ) ) ) ) =>
% 96.22/12.79 (
% 96.22/12.79 (
% 96.22/12.79 ![
% 96.22/12.79 X2084:$i,
% 96.22/12.79 X2086:$i]:
% 96.22/12.79 (
% 96.22/12.79 (
% 96.22/12.79 breln1 @
% 96.22/12.79 X2084 @
% 96.22/12.79 X2086 ) =>
% 96.22/12.79 (
% 96.22/12.79 ![
% 96.22/12.79 X2088:$i]:
% 96.22/12.79 (
% 96.22/12.79 (
% 96.22/12.79 breln1 @
% 96.22/12.79 X2084 @
% 96.22/12.79 X2088 ) =>
% 96.22/12.79 (
% 96.22/12.79 ![
% 96.22/12.79 X2090:$i]:
% 96.22/12.79 (
% 96.22/12.79 (
% 96.22/12.79 breln1 @
% 96.22/12.79 X2084 @
% 96.22/12.79 X2090 ) =>
% 96.22/12.79 (
% 96.22/12.79 (
% 96.22/12.79 breln1compset
% 96.22/12.79 @
% 96.22/12.79 X2084 @
% 96.22/12.79 (
% 96.22/12.79 binunion
% 96.22/12.79 @
% 96.22/12.79 X2086 @
% 96.22/12.79 X2088 ) @
% 96.22/12.79 X2090 ) =
% 96.22/12.79 (
% 96.22/12.79 binunion
% 96.22/12.79 @
% 96.22/12.79 (
% 96.22/12.79 breln1compset
% 96.22/12.79 @
% 96.22/12.79 X2084 @
% 96.22/12.79 X2086 @
% 96.22/12.79 X2090 ) @
% 96.22/12.79 (
% 96.22/12.79 breln1compset
% 96.22/12.79 @
% 96.22/12.79 X2084 @
% 96.22/12.79 X2088 @
% 96.22/12.79 X2090 ) ) ) ) ) ) ) ) ) =>
% 96.22/12.79 (
% 96.22/12.79 (
% 96.22/12.79 ![
% 96.22/12.79 X2092:$i,
% 96.22/12.79 X2094:$i]:
% 96.22/12.79 (
% 96.22/12.79 (
% 96.22/12.79 breln1 @
% 96.22/12.79 X2092 @
% 96.22/12.79 X2094 ) =>
% 96.22/12.79 (
% 96.22/12.79 ![
% 96.22/12.79 X2096:$i]:
% 96.22/12.79 (
% 96.22/12.79 (
% 96.22/12.79 breln1 @
% 96.22/12.79 X2092 @
% 96.22/12.79 X2096 ) =>
% 96.22/12.79 (
% 96.22/12.79 ![
% 96.22/12.79 X2098:$i]:
% 96.22/12.79 (
% 96.22/12.79 (
% 96.22/12.79 breln1 @
% 96.22/12.79 X2092 @
% 96.22/12.79 X2098 ) =>
% 96.22/12.79 (
% 96.22/12.79 (
% 96.22/12.79 breln1compset
% 96.22/12.79 @
% 96.22/12.79 X2092 @
% 96.22/12.79 (
% 96.22/12.79 binunion
% 96.22/12.79 @
% 96.22/12.79 X2094 @
% 96.22/12.79 X2096 ) @
% 96.22/12.79 X2098 ) =
% 96.22/12.79 (
% 96.22/12.79 binunion
% 96.22/12.79 @
% 96.22/12.79 (
% 96.22/12.79 breln1invset
% 96.22/12.79 @
% 96.22/12.79 X2092 @
% 96.22/12.79 (
% 96.22/12.79 breln1compset
% 96.22/12.79 @
% 96.22/12.79 X2092 @
% 96.22/12.79 (
% 96.22/12.79 breln1invset
% 96.22/12.79 @
% 96.22/12.79 X2092 @
% 96.22/12.79 X2098 ) @
% 96.22/12.79 (
% 96.22/12.79 breln1invset
% 96.22/12.79 @
% 96.22/12.79 X2092 @
% 96.22/12.79 X2096 ) ) ) @
% 96.22/12.79 (
% 96.22/12.79 breln1invset
% 96.22/12.79 @
% 96.22/12.79 X2092 @
% 96.22/12.79 (
% 96.22/12.79 breln1compset
% 96.22/12.79 @
% 96.22/12.79 X2092 @
% 96.22/12.79 (
% 96.22/12.79 breln1invset
% 96.22/12.79 @
% 96.22/12.79 X2092 @
% 96.22/12.79 X2098 ) @
% 96.22/12.79 (
% 96.22/12.79 breln1invset
% 96.22/12.79 @
% 96.22/12.79 X2092 @
% 96.22/12.79 X2094 ) ) ) ) ) ) ) ) ) ) ) =>
% 96.22/12.79 (
% 96.22/12.79 (
% 96.22/12.79 ![
% 96.22/12.79 X2100:$i,
% 96.22/12.79 X2102:(
% 96.22/12.79 $i > $i )]:
% 96.22/12.79 (
% 96.22/12.79 ?[
% 96.22/12.79 X2104:$i]:
% 96.22/12.79 (
% 96.22/12.79 ![
% 96.22/12.79 X2106:$i]:
% 96.22/12.79 (
% 96.22/12.79 (
% 96.22/12.79 in @
% 96.22/12.79 X2106 @
% 96.22/12.79 X2104 ) <=>
% 96.22/12.79 (
% 96.22/12.79 ?[
% 96.22/12.79 X2108:$i]:
% 96.22/12.79 (
% 96.22/12.79 zip_tseitin_6
% 96.22/12.79 @
% 96.22/12.79 X2108 @
% 96.22/12.79 X2106 @
% 96.22/12.79 X2102 @
% 96.22/12.79 X2100 ) ) ) ) ) ) =>
% 96.22/12.79 (
% 96.22/12.79 (
% 96.22/12.79 ![
% 96.22/12.79 X2110:$i,
% 96.22/12.79 X2112:(
% 96.22/12.79 $i > $i )]:
% 96.22/12.79 (
% 96.22/12.79 ?[
% 96.22/12.79 X2114:$i]:
% 96.22/12.79 (
% 96.22/12.79 (
% 96.22/12.79 ![
% 96.22/12.79 X2116:$i]:
% 96.22/12.79 (
% 96.22/12.79 (
% 96.22/12.79 ![
% 96.22/12.79 X2118:$i]:
% 96.22/12.79 (
% 96.22/12.79 (
% 96.22/12.79 in @
% 96.22/12.79 X2118 @
% 96.22/12.79 X2116 ) <=>
% 96.22/12.79 (
% 96.22/12.79 ?[
% 96.22/12.79 X2120:$i]:
% 96.22/12.79 (
% 96.22/12.79 zip_tseitin_6
% 96.22/12.79 @
% 96.22/12.79 X2120 @
% 96.22/12.79 X2118 @
% 96.22/12.79 X2112 @
% 96.22/12.79 X2110 ) ) ) ) =>
% 96.22/12.79 (
% 96.22/12.79 (
% 96.22/12.79 X2114 ) =
% 96.22/12.79 (
% 96.22/12.79 X2116 ) ) ) ) &
% 96.22/12.79 (
% 96.22/12.79 ![
% 96.22/12.79 X2122:$i]:
% 96.22/12.79 (
% 96.22/12.79 (
% 96.22/12.79 in @
% 96.22/12.79 X2122 @
% 96.22/12.79 X2114 ) <=>
% 96.22/12.79 (
% 96.22/12.79 ?[
% 96.22/12.79 X2124:$i]:
% 96.22/12.79 (
% 96.22/12.79 zip_tseitin_6
% 96.22/12.79 @
% 96.22/12.79 X2124 @
% 96.22/12.79 X2122 @
% 96.22/12.79 X2112 @
% 96.22/12.79 X2110 ) ) ) ) ) ) ) =>
% 96.22/12.79 (
% 96.22/12.79 (
% 96.22/12.79 ![
% 96.22/12.79 X2126:$i,
% 96.22/12.79 X2128:(
% 96.22/12.79 $i > $i ),
% 96.22/12.79 X2130:$i]:
% 96.22/12.79 (
% 96.22/12.79 (
% 96.22/12.79 in @
% 96.22/12.79 X2130 @
% 96.22/12.79 (
% 96.22/12.79 image1 @
% 96.22/12.79 X2126 @
% 96.22/12.79 (
% 96.22/12.79 ^[
% 96.22/12.79 V_56:$i]:
% 96.22/12.79 (
% 96.22/12.79 X2128 @
% 96.22/12.79 V_56 ) ) ) ) <=>
% 96.22/12.79 (
% 96.22/12.79 ?[
% 96.22/12.79 X2132:$i]:
% 96.22/12.79 (
% 96.22/12.79 zip_tseitin_6
% 96.22/12.79 @
% 96.22/12.79 X2132 @
% 96.22/12.79 X2130 @
% 96.22/12.79 X2128 @
% 96.22/12.79 X2126 ) ) ) ) =>
% 96.22/12.79 (
% 96.22/12.79 (
% 96.22/12.79 ![
% 96.22/12.79 X2134:$i,
% 96.22/12.79 X2136:(
% 96.22/12.79 $i > $i ),
% 96.22/12.79 X2138:$i]:
% 96.22/12.79 (
% 96.22/12.79 (
% 96.22/12.79 in @
% 96.22/12.79 X2138 @
% 96.22/12.79 (
% 96.22/12.79 image1 @
% 96.22/12.79 X2134 @
% 96.22/12.79 (
% 96.22/12.79 ^[
% 96.22/12.79 V_57:$i]:
% 96.22/12.79 (
% 96.22/12.79 X2136 @
% 96.22/12.79 V_57 ) ) ) ) =>
% 96.22/12.79 (
% 96.22/12.79 ?[
% 96.22/12.79 X2140:$i]:
% 96.22/12.79 (
% 96.22/12.79 (
% 96.22/12.79 (
% 96.22/12.79 X2138 ) =
% 96.22/12.79 (
% 96.22/12.79 X2136 @
% 96.22/12.79 X2140 ) ) &
% 96.22/12.79 (
% 96.22/12.79 in @
% 96.22/12.79 X2140 @
% 96.22/12.79 X2134 ) ) ) ) ) =>
% 96.22/12.79 (
% 96.22/12.79 (
% 96.22/12.79 ![
% 96.22/12.79 X2142:$i,
% 96.22/12.79 X2144:(
% 96.22/12.79 $i > $i ),
% 96.22/12.79 X2146:$i]:
% 96.22/12.79 (
% 96.22/12.79 (
% 96.22/12.79 ?[
% 96.22/12.79 X2148:$i]:
% 96.22/12.79 (
% 96.22/12.79 (
% 96.22/12.79 (
% 96.22/12.79 X2146 ) =
% 96.22/12.79 (
% 96.22/12.79 X2144 @
% 96.22/12.79 X2148 ) ) &
% 96.22/12.79 (
% 96.22/12.79 in @
% 96.22/12.79 X2148 @
% 96.22/12.79 X2142 ) ) ) =>
% 96.22/12.79 (
% 96.22/12.79 in @
% 96.22/12.79 X2146 @
% 96.22/12.79 (
% 96.22/12.79 image1 @
% 96.22/12.79 X2142 @
% 96.22/12.79 (
% 96.22/12.79 ^[
% 96.22/12.79 V_58:$i]:
% 96.22/12.79 (
% 96.22/12.79 X2144 @
% 96.22/12.79 V_58 ) ) ) ) ) ) =>
% 96.22/12.79 (
% 96.22/12.79 (
% 96.22/12.79 ![
% 96.22/12.79 X2150:$i,
% 96.22/12.79 X2152:$i,
% 96.22/12.79 X2154:$i]:
% 96.22/12.79 (
% 96.22/12.79 (
% 96.22/12.79 in @
% 96.22/12.79 X2154 @
% 96.22/12.79 (
% 96.22/12.79 funcSet @
% 96.22/12.79 X2150 @
% 96.22/12.79 X2152 ) ) =>
% 96.22/12.79 (
% 96.22/12.79 (
% 96.22/12.79 injective
% 96.22/12.79 @
% 96.22/12.79 X2150 @
% 96.22/12.79 X2152 @
% 96.22/12.79 X2154 ) =>
% 96.22/12.79 (
% 96.22/12.79 in @
% 96.22/12.79 X2154 @
% 96.22/12.79 (
% 96.22/12.79 injFuncSet
% 96.22/12.79 @
% 96.22/12.79 X2150 @
% 96.22/12.79 X2152 ) ) ) ) ) =>
% 96.22/12.79 (
% 96.22/12.79 (
% 96.22/12.79 ![
% 96.22/12.79 X2156:$i,
% 96.22/12.79 X2158:$i,
% 96.22/12.79 X2160:$i]:
% 96.22/12.79 (
% 96.22/12.79 (
% 96.22/12.79 in @
% 96.22/12.79 X2160 @
% 96.22/12.79 (
% 96.22/12.79 injFuncSet
% 96.22/12.79 @
% 96.22/12.79 X2156 @
% 96.22/12.79 X2158 ) ) =>
% 96.22/12.79 (
% 96.22/12.79 in @
% 96.22/12.79 X2160 @
% 96.22/12.79 (
% 96.22/12.79 funcSet @
% 96.22/12.79 X2156 @
% 96.22/12.79 X2158 ) ) ) ) =>
% 96.22/12.79 (
% 96.22/12.79 ![
% 96.22/12.79 X2162:$i,
% 96.22/12.79 X2164:$i,
% 96.22/12.79 X2166:$i]:
% 96.22/12.79 (
% 96.22/12.79 (
% 96.22/12.79 in @
% 96.22/12.79 X2166 @
% 96.22/12.79 (
% 96.22/12.79 injFuncSet
% 96.22/12.79 @
% 96.22/12.79 X2162 @
% 96.22/12.79 X2164 ) ) =>
% 96.22/12.79 (
% 96.22/12.79 injective
% 96.22/12.79 @
% 96.22/12.79 X2162 @
% 96.22/12.79 X2164 @
% 96.22/12.79 X2166 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 96.22/12.79 inference('cnf.neg', [status(esa)], [zf_stmt_15])).
% 96.22/12.79 thf(zip_derived_cl286, plain,
% 96.22/12.79 ( (in @ sk__1103 @ (injFuncSet @ sk__1101 @ sk__1102))),
% 96.22/12.79 inference('cnf', [status(esa)], [zf_stmt_16])).
% 96.22/12.79 thf(injFuncSet, axiom,
% 96.22/12.79 (![A:$i,B:$i]:
% 96.22/12.79 ( ( injFuncSet @ A @ B ) =
% 96.22/12.79 ( dsetconstr @
% 96.22/12.79 ( funcSet @ A @ B ) @ ( ^[Xf:$i]: ( injective @ A @ B @ Xf ) ) ) ))).
% 96.22/12.79 thf(zip_derived_cl0, plain,
% 96.22/12.79 (![X0 : $i, X1 : $i]:
% 96.22/12.79 ((injFuncSet @ X0 @ X1)
% 96.22/12.79 = (dsetconstr @ (funcSet @ X0 @ X1) @
% 96.22/12.79 (^[Y0 : $i]: (injective @ X0 @ X1 @ Y0))))),
% 96.22/12.79 inference('cnf', [status(esa)], [injFuncSet])).
% 96.22/12.79 thf(zip_derived_cl538, plain,
% 96.22/12.79 (![X0 : $i, X1 : $i]:
% 96.22/12.79 ((injFuncSet @ X0 @ X1)
% 96.22/12.79 = (dsetconstr @ (funcSet @ X0 @ X1) @ (injective @ X0 @ X1)))),
% 96.22/12.79 inference('ho_norm', [status(thm)], [zip_derived_cl0])).
% 96.22/12.79 thf(zip_derived_cl49, plain,
% 96.22/12.79 (![X34 : $i > $o, X35 : $i, X36 : $i]:
% 96.22/12.79 ( (X34 @ X35)
% 96.22/12.79 | ~ (in @ X35 @ (dsetconstr @ X36 @ (^[Y0 : $i]: (X34 @ Y0)))))),
% 96.22/12.79 inference('cnf', [status(esa)], [zf_stmt_16])).
% 96.22/12.79 thf(zip_derived_cl3501, plain,
% 96.22/12.79 (![X34 : $i > $o, X35 : $i, X36 : $i]:
% 96.22/12.79 ( (X34 @ X35) | ~ (in @ X35 @ (dsetconstr @ X36 @ X34)))),
% 96.22/12.79 inference('ho_norm', [status(thm)], [zip_derived_cl49])).
% 96.22/12.79 thf(zip_derived_cl505, plain,
% 96.22/12.79 (![X951 : $i]: ((dsetconstr @ X951 @ (^[Y0 : $i]: ($true))) = (X951))),
% 96.22/12.79 inference('cnf', [status(esa)], [zf_stmt_16])).
% 96.22/12.79 thf(zip_derived_cl532, plain, ( (in @ emptyset @ omega)),
% 96.22/12.79 inference('cnf', [status(esa)], [zf_stmt_16])).
% 96.22/12.79 thf(zip_derived_cl71, plain,
% 96.22/12.79 (![X75 : $i > $o, X76 : $i, X77 : $i]:
% 96.22/12.79 (~ (X75 @ (sk__1148 @ X75 @ X76)) | ~ (in @ X77 @ X76) | (X75 @ X77))),
% 96.22/12.79 inference('cnf', [status(esa)], [zf_stmt_16])).
% 96.22/12.79 thf(zip_derived_cl638, plain,
% 96.22/12.79 (![X0 : $i > $o]: ( (X0 @ emptyset) | ~ (X0 @ (sk__1148 @ X0 @ omega)))),
% 96.22/12.79 inference('sup-', [status(thm)], [zip_derived_cl532, zip_derived_cl71])).
% 96.22/12.79 thf(zip_derived_cl75, plain,
% 96.22/12.79 (![X81 : $o]: ( (in @ emptyset @ (prop2set @ X81)) | ~ (X81))),
% 96.22/12.79 inference('cnf', [status(esa)], [zf_stmt_16])).
% 96.22/12.79 thf(zip_derived_cl57, plain,
% 96.22/12.79 (![X46 : $i, X47 : $i > $o, X48 : $i]:
% 96.22/12.79 (((dsetconstr @ X46 @ (^[Y0 : $i]: (X47 @ Y0))) != (emptyset))
% 96.22/12.79 | ~ (in @ X48 @ X46)
% 96.22/12.79 | ~ (X47 @ X48))),
% 96.22/12.79 inference('cnf', [status(esa)], [zf_stmt_16])).
% 96.22/12.79 thf(zip_derived_cl729, plain,
% 96.22/12.79 (![X46 : $i, X47 : $i > $o, X48 : $i]:
% 96.22/12.79 (((dsetconstr @ X46 @ X47) != (emptyset))
% 96.22/12.79 | ~ (in @ X48 @ X46)
% 96.22/12.79 | ~ (X47 @ X48))),
% 96.22/12.79 inference('ho_norm', [status(thm)], [zip_derived_cl57])).
% 96.22/12.79 thf(zip_derived_cl1114, plain,
% 96.22/12.79 (![X0 : $o, X1 : $i > $o]:
% 96.22/12.79 (~ (X0)
% 96.22/12.79 | ~ (X1 @ emptyset)
% 96.22/12.79 | ((dsetconstr @ (prop2set @ X0) @ X1) != (emptyset)))),
% 96.22/12.79 inference('sup-', [status(thm)], [zip_derived_cl75, zip_derived_cl729])).
% 96.22/12.79 thf(zip_derived_cl1161, plain,
% 96.22/12.79 (![X0 : $i > $o]:
% 96.22/12.79 (~ (X0 @ emptyset)
% 96.22/12.79 | ((dsetconstr @ (prop2set @ ($true)) @ X0) != (emptyset)))),
% 96.22/12.79 inference('false_elim', [status(thm)], [zip_derived_cl1114])).
% 96.22/12.79 thf(zip_derived_cl6449, plain,
% 96.22/12.79 (![X0 : $o]:
% 96.22/12.79 (~ ((^[Y0 : $i]: (X0)) @ (sk__1148 @ (^[Y0 : $i]: (X0)) @ omega))
% 96.22/12.79 | ((dsetconstr @ (prop2set @ ($true)) @ (^[Y0 : $i]: (X0)))
% 96.22/12.79 != (emptyset)))),
% 96.22/12.79 inference('sup-', [status(thm)], [zip_derived_cl638, zip_derived_cl1161])).
% 96.22/12.79 thf(zip_derived_cl6591, plain,
% 96.22/12.79 (![X0 : $o]:
% 96.22/12.79 (~ (X0)
% 96.22/12.79 | ((dsetconstr @ (prop2set @ ($true)) @ (^[Y0 : $i]: (X0)))
% 96.22/12.79 != (emptyset)))),
% 96.22/12.79 inference('ho_norm', [status(thm)], [zip_derived_cl6449])).
% 96.22/12.79 thf(zip_derived_cl7271, plain, (((prop2set @ ($true)) != (emptyset))),
% 96.22/12.79 inference('sup-', [status(thm)], [zip_derived_cl505, zip_derived_cl6591])).
% 96.22/12.79 thf(zip_derived_cl7288, plain,
% 96.22/12.79 (![X0 : $i > $o, X1 : $i, X2 : $i]:
% 96.22/12.79 (((prop2set @ (X0 @ X1)) != (emptyset))
% 96.22/12.79 | ~ (in @ X1 @ (dsetconstr @ X2 @ X0)))),
% 96.22/12.79 inference('sup-', [status(thm)], [zip_derived_cl3501, zip_derived_cl7271])).
% 96.22/12.79 thf(zip_derived_cl7664, plain,
% 96.22/12.79 (![X0 : $i, X1 : $i, X2 : $i]:
% 96.22/12.79 (~ (in @ X2 @ (injFuncSet @ X1 @ X0))
% 96.22/12.79 | ((prop2set @ (injective @ X1 @ X0 @ X2)) != (emptyset)))),
% 96.22/12.79 inference('sup-', [status(thm)], [zip_derived_cl538, zip_derived_cl7288])).
% 96.22/12.79 thf(zip_derived_cl10225, plain,
% 96.22/12.79 (((prop2set @ (injective @ sk__1101 @ sk__1102 @ sk__1103)) != (emptyset))),
% 96.22/12.79 inference('sup-', [status(thm)], [zip_derived_cl286, zip_derived_cl7664])).
% 96.22/12.79 thf(zip_derived_cl285, plain,
% 96.22/12.79 (~ (injective @ sk__1101 @ sk__1102 @ sk__1103)),
% 96.22/12.79 inference('cnf', [status(esa)], [zf_stmt_16])).
% 96.22/12.79 thf(zip_derived_cl54, plain,
% 96.22/12.79 (![X42 : $i]: (((X42) = (emptyset)) | (in @ (sk__1151 @ X42) @ X42))),
% 96.22/12.79 inference('cnf', [status(esa)], [zf_stmt_16])).
% 96.22/12.79 thf(zip_derived_cl50, plain,
% 96.22/12.79 (![X37 : $o, X38 : $i]: ( (X37) | ~ (in @ X38 @ (prop2set @ X37)))),
% 96.22/12.79 inference('cnf', [status(esa)], [zf_stmt_16])).
% 96.22/12.79 thf(zip_derived_cl541, plain,
% 96.22/12.79 (![X0 : $i]: ~ (in @ X0 @ (prop2set @ ($false)))),
% 96.22/12.79 inference('ho.refine', [status(thm)], [zip_derived_cl50])).
% 96.22/12.79 thf(zip_derived_cl7521, plain, (((prop2set @ ($false)) = (emptyset))),
% 96.22/12.79 inference('sup-', [status(thm)], [zip_derived_cl54, zip_derived_cl541])).
% 96.22/12.79 thf(zip_derived_cl10238, plain, (((emptyset) != (emptyset))),
% 96.22/12.79 inference('demod', [status(thm)],
% 96.22/12.79 [zip_derived_cl10225, zip_derived_cl285, zip_derived_cl7521])).
% 96.22/12.79 thf(zip_derived_cl10239, plain, ($false),
% 96.22/12.79 inference('simplify', [status(thm)], [zip_derived_cl10238])).
% 96.22/12.79
% 96.22/12.79 % SZS output end Refutation
% 96.22/12.79
% 96.22/12.79
% 96.22/12.79 % /export/starexec/sandbox/solver/bin/lams/35_full_unif.sh running for 56s
% 96.22/12.79 % Terminating...
% 97.18/13.01 % Runner terminated.
% 97.18/13.03 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------