%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU771^1 : 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.S4u8yUtyLO true
% Computer : n001.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 04:56:15 PM UTC 2025
% Result : Theorem 97.29s 12.83s
% Output : Refutation 99.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SEU771^1 : TPTP v9.2.0. Released v3.7.0.
% 0.10/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.S4u8yUtyLO true
% 0.12/0.34 % Computer : n001.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Oct 1 16:06:53 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.34 % Running portfolio for 300 s
% 0.12/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.34 % Number of cores: 8
% 0.12/0.34 % Python version: Python 3.6.8
% 0.12/0.35 % Running in HO mode
% 0.68/0.64 % Total configuration time : 828
% 0.68/0.64 % Estimated wc time : 1656
% 0.68/0.64 % Estimated cpu time (8 cpus) : 207.0
% 0.68/0.70 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 1.31/0.70 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 1.31/0.70 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 1.31/0.70 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 1.31/0.70 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 1.31/0.71 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 1.31/0.71 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.31/0.71 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 97.29/12.83 % Solved by lams/40_b.comb.sh.
% 97.29/12.83 % done 0 iterations in 11.676s
% 97.29/12.83 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 97.29/12.83 % SZS output start Refutation
% 97.29/12.83 thf(setadjoinAx_type, type, setadjoinAx: $o).
% 97.29/12.83 thf(cartprodfstpairEq_type, type, cartprodfstpairEq: $o).
% 97.29/12.83 thf(notdexE_type, type, notdexE: $o).
% 97.29/12.83 thf(setunionAx_type, type, setunionAx: $o).
% 97.29/12.83 thf(setminusELneg_type, type, setminusELneg: $o).
% 97.29/12.83 thf(funcGraphProp1_type, type, funcGraphProp1: $o).
% 97.29/12.83 thf(beta1_type, type, beta1: $o).
% 97.29/12.83 thf(powersetE_type, type, powersetE: $o).
% 97.29/12.83 thf(doubleComplementE1_type, type, doubleComplementE1: $o).
% 97.29/12.83 thf(omegaSAx_type, type, omegaSAx: $o).
% 97.29/12.83 thf(doubleComplementI1_type, type, doubleComplementI1: $o).
% 97.29/12.83 thf(exuI1_type, type, exuI1: $o).
% 97.29/12.83 thf(binunionTEcontra_type, type, binunionTEcontra: $o).
% 97.29/12.83 thf(exuI2_type, type, exuI2: $o).
% 97.29/12.83 thf(notequalI2_type, type, notequalI2: $o).
% 97.29/12.83 thf(kfstsingleton_type, type, kfstsingleton: $o).
% 97.29/12.83 thf(demorgan1b_type, type, demorgan1b: $o).
% 97.29/12.83 thf(kpairiskpair_type, type, kpairiskpair: $o).
% 97.29/12.83 thf(demorgan2a_type, type, demorgan2a: $o).
% 97.29/12.83 thf(subsetTI_type, type, subsetTI: $o).
% 97.29/12.83 thf(upairsubunion_type, type, upairsubunion: $o).
% 97.29/12.83 thf(binintersectT_lem_type, type, binintersectT_lem: $o).
% 97.29/12.83 thf(funcGraphProp4_type, type, funcGraphProp4: $o).
% 97.29/12.83 thf(powerset__Cong_type, type, powerset__Cong: $o).
% 97.29/12.83 thf(complementImpComplementIntersect_type, type, complementImpComplementIntersect:
% 97.29/12.83 $o).
% 97.29/12.83 thf(setukpairinjR2_type, type, setukpairinjR2: $o).
% 97.29/12.83 thf(singletonsuniq_type, type, singletonsuniq: $o).
% 97.29/12.83 thf(binunionT_lem_type, type, binunionT_lem: $o).
% 97.29/12.83 thf(inIntersectImpInUnion2_type, type, inIntersectImpInUnion2: $o).
% 97.29/12.83 thf(setminusILneg_type, type, setminusILneg: $o).
% 97.29/12.83 thf(complementTcontraSubset_type, type, complementTcontraSubset: $o).
% 97.29/12.83 thf(funcinfuncset_type, type, funcinfuncset: $o).
% 97.29/12.83 thf(wellorderingAx_type, type, wellorderingAx: $o).
% 97.29/12.83 thf(kpairsurjEq_type, type, kpairsurjEq: $o).
% 97.29/12.83 thf(setadjoinSub2_type, type, setadjoinSub2: $o).
% 97.29/12.83 thf(binintersectSubset5_type, type, binintersectSubset5: $o).
% 97.29/12.83 thf(brelnall1_type, type, brelnall1: $o).
% 97.29/12.83 thf(upairinpowunion_type, type, upairinpowunion: $o).
% 97.29/12.83 thf(doubleComplementEq_type, type, doubleComplementEq: $o).
% 97.29/12.83 thf(setoftrueEq_type, type, setoftrueEq: $o).
% 97.29/12.83 thf(complementT_lem_type, type, complementT_lem: $o).
% 97.29/12.83 thf(funcextLem_type, type, funcextLem: $o).
% 97.29/12.83 thf(iftrueorfalse_type, type, iftrueorfalse: $o).
% 97.29/12.83 thf(emptyset__Cong_type, type, emptyset__Cong: $o).
% 97.29/12.83 thf(funcImageSingleton_type, type, funcImageSingleton: $o).
% 97.29/12.83 thf(cartprodmempaircEq_type, type, cartprodmempaircEq: $o).
% 97.29/12.83 thf(demorgan2b2_type, type, demorgan2b2: $o).
% 97.29/12.83 thf(demorgan2b_type, type, demorgan2b: $o).
% 97.29/12.83 thf(dpsetconstrI_type, type, dpsetconstrI: $o).
% 97.29/12.83 thf('#sk43_type', type, '#sk43': $i > $i > $o).
% 97.29/12.83 thf(ex1E1_type, type, ex1E1: $o).
% 97.29/12.83 thf(sepInPowerset_type, type, sepInPowerset: $o).
% 97.29/12.83 thf(setukpairIR_type, type, setukpairIR: $o).
% 97.29/12.83 thf(binunionE_type, type, binunionE: $o).
% 97.29/12.83 thf(setext_type, type, setext: $o).
% 97.29/12.83 thf(lam2p_type, type, lam2p: $o).
% 97.29/12.83 thf(emptyinPowerset_type, type, emptyinPowerset: $o).
% 97.29/12.83 thf(breln1_type, type, breln1: $i > $i > $o).
% 97.29/12.83 thf(ubforcartprodlem1_type, type, ubforcartprodlem1: $o).
% 97.29/12.83 thf(binintersectTERcontra_type, type, binintersectTERcontra: $o).
% 97.29/12.83 thf(theeq_type, type, theeq: $o).
% 97.29/12.83 thf(descr__Cong_type, type, descr__Cong: $o).
% 97.29/12.83 thf(theprop_type, type, theprop: $o).
% 97.29/12.83 thf(complementInPowersetComplementIntersect_type, type, complementInPowersetComplementIntersect:
% 97.29/12.83 $o).
% 97.29/12.83 thf(complementTnotintersectT_type, type, complementTnotintersectT: $o).
% 97.29/12.83 thf(binintersectSubset1_type, type, binintersectSubset1: $o).
% 97.29/12.83 thf(infuncsetfunc_type, type, infuncsetfunc: $o).
% 97.29/12.83 thf(in_type, type, in: $i > $i > $o).
% 97.29/12.83 thf(lamProp_type, type, lamProp: $o).
% 97.29/12.83 thf(cartprodsndpairEq_type, type, cartprodsndpairEq: $o).
% 97.29/12.83 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o).
% 97.29/12.83 thf(setextT_type, type, setextT: $o).
% 97.29/12.83 thf(setukpairinjL2_type, type, setukpairinjL2: $o).
% 97.29/12.83 thf(setOfPairsIsBReln_type, type, setOfPairsIsBReln: $o).
% 97.29/12.83 thf(setadjoinIR_type, type, setadjoinIR: $o).
% 97.29/12.83 thf(funcGraphProp3_type, type, funcGraphProp3: $o).
% 97.29/12.83 thf(ap2p_type, type, ap2p: $o).
% 97.29/12.83 thf(eqbreln_type, type, eqbreln: $o).
% 97.29/12.83 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o).
% 97.29/12.83 thf(ksndpairEq_type, type, ksndpairEq: $o).
% 97.29/12.83 thf(ex1I2_type, type, ex1I2: $o).
% 97.29/12.83 thf(dpsetconstrEL2_type, type, dpsetconstrEL2: $o).
% 97.29/12.83 thf(woz1_1_type, type, woz1_1: $o).
% 97.29/12.83 thf(demorgan1_type, type, demorgan1: $o).
% 97.29/12.83 thf(binintersectTELcontra_type, type, binintersectTELcontra: $o).
% 97.29/12.83 thf(symdiffI2_type, type, symdiffI2: $o).
% 97.29/12.83 thf(upairset2IR_type, type, upairset2IR: $o).
% 97.29/12.83 thf(subsetE_type, type, subsetE: $o).
% 97.29/12.83 thf(prop2set2propI_type, type, prop2set2propI: $o).
% 97.29/12.83 thf(doubleComplementSub1_type, type, doubleComplementSub1: $o).
% 97.29/12.83 thf(dsetconstrEL_type, type, dsetconstrEL: $o).
% 97.29/12.83 thf(setbeta_type, type, setbeta: $o).
% 97.29/12.83 thf(binunionTE_type, type, binunionTE: $o).
% 97.29/12.83 thf(eqinunit_type, type, eqinunit: $o).
% 97.29/12.83 thf(upairsetIL_type, type, upairsetIL: $o).
% 97.29/12.83 thf(powersetI1_type, type, powersetI1: $o).
% 97.29/12.83 thf(cartprodfstin_type, type, cartprodfstin: $o).
% 97.29/12.83 thf(iftrueProp1_type, type, iftrueProp1: $o).
% 97.29/12.83 thf(powersetTE1_type, type, powersetTE1: $o).
% 97.29/12.83 thf(binintersectSubset3_type, type, binintersectSubset3: $o).
% 97.29/12.83 thf(app_type, type, app: $o).
% 97.29/12.83 thf(ksndsingleton_type, type, ksndsingleton: $o).
% 97.29/12.83 thf(setminusIRneg_type, type, setminusIRneg: $o).
% 97.29/12.83 thf(inComplementUnionImpInComplement1_type, type, inComplementUnionImpInComplement1:
% 97.29/12.83 $o).
% 97.29/12.83 thf(powersetAx_type, type, powersetAx: $o).
% 97.29/12.83 thf(lamp_type, type, lamp: $o).
% 97.29/12.83 thf(binintersectSubset4_type, type, binintersectSubset4: $o).
% 97.29/12.83 thf(ifSingleton_type, type, ifSingleton: $o).
% 97.29/12.83 thf(iffalse_type, type, iffalse: $o).
% 97.29/12.83 thf(singletoninpowunion_type, type, singletoninpowunion: $o).
% 97.29/12.83 thf(inIntersectImpInUnion_type, type, inIntersectImpInUnion: $o).
% 97.29/12.83 thf(powersetI_type, type, powersetI: $o).
% 97.29/12.83 thf(cartprodmempair_type, type, cartprodmempair: $o).
% 97.29/12.83 thf(upairsetIR_type, type, upairsetIR: $o).
% 97.29/12.83 thf(cartprodpairsurjEq_type, type, cartprodpairsurjEq: $o).
% 97.29/12.83 thf(cartprodpairmemEL_type, type, cartprodpairmemEL: $o).
% 97.29/12.83 thf(funcext2_type, type, funcext2: $o).
% 97.29/12.83 thf(inCongP_type, type, inCongP: $o).
% 97.29/12.83 thf(setukpairinjR11_type, type, setukpairinjR11: $o).
% 97.29/12.83 thf(setadjoinSub_type, type, setadjoinSub: $o).
% 97.29/12.83 thf(exuE3e_type, type, exuE3e: $o).
% 97.29/12.83 thf(emptysetE_type, type, emptysetE: $o).
% 97.29/12.83 thf(binintersectSubset2_type, type, binintersectSubset2: $o).
% 97.29/12.83 thf(setunionI_type, type, setunionI: $o).
% 97.29/12.83 thf(setunion__Cong_type, type, setunion__Cong: $o).
% 97.29/12.83 thf(prop2setI_type, type, prop2setI: $o).
% 97.29/12.83 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o).
% 97.29/12.83 thf(setminusER_type, type, setminusER: $o).
% 97.29/12.83 thf(exuE2_type, type, exuE2: $o).
% 97.29/12.83 thf(dpsetconstrEL1_type, type, dpsetconstrEL1: $o).
% 97.29/12.83 thf(emptyset_type, type, emptyset: $i).
% 97.29/12.83 thf(setukpairinjR12_type, type, setukpairinjR12: $o).
% 97.29/12.83 thf(binunionTILcontra_type, type, binunionTILcontra: $o).
% 97.29/12.83 thf(complementTI1_type, type, complementTI1: $o).
% 97.29/12.83 thf(inComplementUnionImpNotIn1_type, type, inComplementUnionImpNotIn1: $o).
% 97.29/12.83 thf(breln_type, type, breln: $i > $i > $i > $o).
% 97.29/12.83 thf(dpsetconstrER_type, type, dpsetconstrER: $o).
% 97.29/12.83 thf(powersetsubset_type, type, powersetsubset: $o).
% 97.29/12.83 thf(upairequniteq_type, type, upairequniteq: $o).
% 97.29/12.83 thf(woz1_4_type, type, woz1_4: $o).
% 97.29/12.83 thf(subPowSU_type, type, subPowSU: $o).
% 97.29/12.83 thf(notequalI1_type, type, notequalI1: $o).
% 97.29/12.83 thf(notinemptyset_type, type, notinemptyset: $o).
% 97.29/12.83 thf(nonemptyI1_type, type, nonemptyI1: $o).
% 97.29/12.83 thf(subsetTrans_type, type, subsetTrans: $o).
% 97.29/12.83 thf(setukpairinjR_type, type, setukpairinjR: $o).
% 97.29/12.83 thf(kpairp_type, type, kpairp: $o).
% 97.29/12.83 thf(setukpairinjR1_type, type, setukpairinjR1: $o).
% 97.29/12.83 thf(setminusI_type, type, setminusI: $o).
% 97.29/12.83 thf(eta1_type, type, eta1: $o).
% 97.29/12.83 thf(binunionIL_type, type, binunionIL: $o).
% 97.29/12.83 thf(setukpairinjL1_type, type, setukpairinjL1: $o).
% 97.29/12.83 thf(setunionsingleton_type, type, setunionsingleton: $o).
% 97.29/12.83 thf(contrasubsetT1_type, type, contrasubsetT1: $o).
% 97.29/12.83 thf(subsetE2_type, type, subsetE2: $o).
% 97.29/12.83 thf(singletonsswitch_type, type, singletonsswitch: $o).
% 97.29/12.83 thf(ubforcartprodlem3_type, type, ubforcartprodlem3: $o).
% 97.29/12.83 thf(eta2_type, type, eta2: $o).
% 97.29/12.83 thf(contrasubsetT3_type, type, contrasubsetT3: $o).
% 97.29/12.83 thf(setextsub_type, type, setextsub: $o).
% 97.29/12.83 thf(binunionLsub_type, type, binunionLsub: $o).
% 97.29/12.83 thf(setunionsingleton1_type, type, setunionsingleton1: $o).
% 97.29/12.83 thf(emptysetsubset_type, type, emptysetsubset: $o).
% 97.29/12.83 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o).
% 97.29/12.83 thf(setunionE_type, type, setunionE: $o).
% 97.29/12.83 thf(setminusSubset1_type, type, setminusSubset1: $o).
% 97.29/12.83 thf(setminusT_lem_type, type, setminusT_lem: $o).
% 97.29/12.83 thf(emptyinunitempty_type, type, emptyinunitempty: $o).
% 97.29/12.83 thf(binunionIR_type, type, binunionIR: $o).
% 97.29/12.83 thf(iftrue_type, type, iftrue: $o).
% 97.29/12.83 thf(setadjoinE_type, type, setadjoinE: $o).
% 97.29/12.83 thf(doubleComplementSub2_type, type, doubleComplementSub2: $o).
% 97.29/12.83 thf(woz1_5_type, type, woz1_5: $o).
% 97.29/12.83 thf(cartprodpairmemER_type, type, cartprodpairmemER: $o).
% 97.29/12.83 thf(beta2_type, type, beta2: $o).
% 97.29/12.83 thf(complementSubsetComplementIntersect_type, type, complementSubsetComplementIntersect:
% 97.29/12.83 $o).
% 97.29/12.83 thf(brelnall2_type, type, brelnall2: $o).
% 97.29/12.83 thf(setadjoinIL_type, type, setadjoinIL: $o).
% 97.29/12.83 thf(exuE1_type, type, exuE1: $o).
% 97.29/12.83 thf(ubforcartprodlem2_type, type, ubforcartprodlem2: $o).
% 97.29/12.83 thf(binintersectRsub_type, type, binintersectRsub: $o).
% 97.29/12.83 thf(ifp_type, type, ifp: $o).
% 97.29/12.83 thf(setminusLsub_type, type, setminusLsub: $o).
% 97.29/12.83 thf(woz1_3_type, type, woz1_3: $o).
% 97.29/12.83 thf(notinsingleton_type, type, notinsingleton: $o).
% 97.29/12.83 thf(dpsetconstr_type, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 97.29/12.83 thf(eqimpsubset2_type, type, eqimpsubset2: $o).
% 97.29/12.83 thf(exuEu_type, type, exuEu: $o).
% 97.29/12.83 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o).
% 97.29/12.83 thf(upairsetE_type, type, upairsetE: $o).
% 97.29/12.83 thf(omega0Ax_type, type, omega0Ax: $o).
% 97.29/12.83 thf(complementTE1_type, type, complementTE1: $o).
% 97.29/12.83 thf(contrasubsetT2_type, type, contrasubsetT2: $o).
% 97.29/12.83 thf(notsubsetI_type, type, notsubsetI: $o).
% 97.29/12.83 thf(intersectInPowersetIntersectUnions_type, type, intersectInPowersetIntersectUnions:
% 97.29/12.83 $o).
% 97.29/12.83 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o).
% 97.29/12.83 thf(setextAx_type, type, setextAx: $o).
% 97.29/12.83 thf(breln1SetBreln1_type, type, breln1SetBreln1: $o).
% 97.29/12.83 thf(powersetE1_type, type, powersetE1: $o).
% 97.29/12.83 thf(bs114d_type, type, bs114d: $o).
% 97.29/12.83 thf(breln1all2_type, type, breln1all2: $o).
% 97.29/12.83 thf(woz13rule0_type, type, woz13rule0: $o).
% 97.29/12.83 thf(noeltsimpempty_type, type, noeltsimpempty: $o).
% 97.29/12.83 thf(contraSubsetComplement_type, type, contraSubsetComplement: $o).
% 97.29/12.83 thf(woz1_2_type, type, woz1_2: $o).
% 97.29/12.83 thf(binintersectLsub_type, type, binintersectLsub: $o).
% 97.29/12.83 thf(subsetI1_type, type, subsetI1: $o).
% 97.29/12.83 thf(symdiffE_type, type, symdiffE: $o).
% 97.29/12.83 thf(descrp_type, type, descrp: $o).
% 97.29/12.83 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o).
% 97.29/12.83 thf(foundationAx_type, type, foundationAx: $o).
% 97.29/12.83 thf(emptysetAx_type, type, emptysetAx: $o).
% 97.29/12.83 thf(emptyI_type, type, emptyI: $o).
% 97.29/12.83 thf(setadjoinOr_type, type, setadjoinOr: $o).
% 97.29/12.83 thf(binintersectEL_type, type, binintersectEL: $o).
% 97.29/12.83 thf(emptyE1_type, type, emptyE1: $o).
% 97.29/12.83 thf(emptyInPowerset_type, type, emptyInPowerset: $o).
% 97.29/12.83 thf(demorgan2_type, type, demorgan2: $o).
% 97.29/12.83 thf(vacuousDall_type, type, vacuousDall: $o).
% 97.29/12.83 thf(dsetconstrER_type, type, dsetconstrER: $o).
% 97.29/12.83 thf(funcGraphProp2_type, type, funcGraphProp2: $o).
% 97.29/12.83 thf(ex1E2_type, type, ex1E2: $o).
% 97.29/12.83 thf(binintersectI_type, type, binintersectI: $o).
% 97.29/12.83 thf(woz13rule3_type, type, woz13rule3: $o).
% 97.29/12.83 thf(iffalseProp2_type, type, iffalseProp2: $o).
% 97.29/12.83 thf(woz13rule2_type, type, woz13rule2: $o).
% 97.29/12.83 thf(cartprodpairin_type, type, cartprodpairin: $o).
% 97.29/12.83 thf(lam2lamEq_type, type, lam2lamEq: $o).
% 97.29/12.83 thf(choice2fnsingleton_type, type, choice2fnsingleton: $o).
% 97.29/12.83 thf(apProp_type, type, apProp: $o).
% 97.29/12.83 thf(dpsetconstrSub_type, type, dpsetconstrSub: $o).
% 97.29/12.83 thf(cartprodmempair1_type, type, cartprodmempair1: $o).
% 97.29/12.83 thf(iffalseProp1_type, type, iffalseProp1: $o).
% 97.29/12.83 thf(demorgan2a2_type, type, demorgan2a2: $o).
% 97.29/12.83 thf(powersetT_lem_type, type, powersetT_lem: $o).
% 97.29/12.83 thf(symdiffI1_type, type, symdiffI1: $o).
% 97.29/12.83 thf(kfstpairEq_type, type, kfstpairEq: $o).
% 97.29/12.83 thf(subsetI2_type, type, subsetI2: $o).
% 97.29/12.83 thf(symdiffIneg1_type, type, symdiffIneg1: $o).
% 97.29/12.83 thf(setminusERneg_type, type, setminusERneg: $o).
% 97.29/12.83 thf(symdiffIneg2_type, type, symdiffIneg2: $o).
% 97.29/12.83 thf(omega__Cong_type, type, omega__Cong: $o).
% 97.29/12.83 thf(subsetRefl_type, type, subsetRefl: $o).
% 97.29/12.83 thf(uniqinunit_type, type, uniqinunit: $o).
% 97.29/12.83 thf(setminusSubset2_type, type, setminusSubset2: $o).
% 97.29/12.83 thf(prop2setE_type, type, prop2setE: $o).
% 97.29/12.83 thf(binunionEcases_type, type, binunionEcases: $o).
% 97.29/12.83 thf(omega_type, type, omega: $i).
% 97.29/12.83 thf(inIntersectImpInIntersectUnions_type, type, inIntersectImpInIntersectUnions:
% 97.29/12.83 $o).
% 97.29/12.83 thf(nonemptyI_type, type, nonemptyI: $o).
% 97.29/12.83 thf(binunionTIRcontra_type, type, binunionTIRcontra: $o).
% 97.29/12.83 thf(disjointsetsI1_type, type, disjointsetsI1: $o).
% 97.29/12.83 thf(exuE3u_type, type, exuE3u: $o).
% 97.29/12.83 thf(setminusEL_type, type, setminusEL: $o).
% 97.29/12.83 thf(woz13rule4_type, type, woz13rule4: $o).
% 97.29/12.83 thf('#sk42_type', type, '#sk42': $i).
% 97.29/12.83 thf(setunionsingleton2_type, type, setunionsingleton2: $o).
% 97.29/12.83 thf(sepSubset_type, type, sepSubset: $o).
% 97.29/12.83 thf(upairset2E_type, type, upairset2E: $o).
% 97.29/12.83 thf(eqimpsubset1_type, type, eqimpsubset1: $o).
% 97.29/12.83 thf(woz13rule1_type, type, woz13rule1: $o).
% 97.29/12.83 thf(exuI3_type, type, exuI3: $o).
% 97.29/12.83 thf(notdallE_type, type, notdallE: $o).
% 97.29/12.83 thf(demorgan1a_type, type, demorgan1a: $o).
% 97.29/12.83 thf(binintersectER_type, type, binintersectER: $o).
% 97.29/12.83 thf(ap2apEq2_type, type, ap2apEq2: $o).
% 97.29/12.83 thf(dsetconstrI_type, type, dsetconstrI: $o).
% 97.29/12.83 thf(subbreln_type, type, subbreln: $o).
% 97.29/12.83 thf(setadjoin_type, type, setadjoin: $i > $i > $i).
% 97.29/12.83 thf(exu__Cong_type, type, exu__Cong: $o).
% 97.29/12.83 thf(iftrueProp2_type, type, iftrueProp2: $o).
% 97.29/12.83 thf(cartprodsndin_type, type, cartprodsndin: $o).
% 97.29/12.83 thf(contrasubsetT_type, type, contrasubsetT: $o).
% 97.29/12.83 thf(powersetTI1_type, type, powersetTI1: $o).
% 97.29/12.83 thf(funcext_type, type, funcext: $o).
% 97.29/12.83 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o).
% 97.29/12.83 thf(ex1I_type, type, ex1I: $o).
% 97.29/12.83 thf(secondinupair_type, type, secondinupair: $o).
% 97.29/12.83 thf(singletonprop_type, type, singletonprop: $o).
% 97.29/12.83 thf(singletonsubset_type, type, singletonsubset: $o).
% 97.29/12.83 thf(singletoninpowerset_type, type, singletoninpowerset: $o).
% 97.29/12.83 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o).
% 97.29/12.83 thf(replAx_type, type, replAx: $o).
% 97.29/12.83 thf(nonemptyE1_type, type, nonemptyE1: $o).
% 97.29/12.83 thf(omegaIndAx_type, type, omegaIndAx: $o).
% 97.29/12.83 thf(setukpairIL_type, type, setukpairIL: $o).
% 97.29/12.83 thf(setunionE2_type, type, setunionE2: $o).
% 97.29/12.83 thf(inPowerset_type, type, inPowerset: $o).
% 97.29/12.83 thf(demorgan2a1_type, type, demorgan2a1: $o).
% 97.29/12.83 thf(cartprod_type, type, cartprod: $i > $i > $i).
% 97.29/12.83 thf(subset_type, type, subset: $i > $i > $o).
% 97.29/12.83 thf(complementUnionInPowersetComplement_type, type, complementUnionInPowersetComplement:
% 97.29/12.83 $o).
% 97.29/12.83 thf(in__Cong_type, type, in__Cong: $o).
% 97.29/12.83 thf(dpsetconstrERa_type, type, dpsetconstrERa: $o).
% 97.29/12.83 thf(setukpairinjL_type, type, setukpairinjL: $o).
% 97.29/12.83 thf(binunionRsub_type, type, binunionRsub: $o).
% 97.29/12.83 thf(subset2powerset_type, type, subset2powerset: $o).
% 97.29/12.83 thf(ap2apEq1_type, type, ap2apEq1: $o).
% 97.29/12.83 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)).
% 97.29/12.83 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)).
% 97.29/12.83 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)).
% 97.29/12.83 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)).
% 97.29/12.83 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)).
% 97.29/12.83 thf(setOfPairsIsBReln1, conjecture,
% 97.29/12.83 (( setextAx ) =>
% 97.29/12.83 ( ( emptysetAx ) =>
% 97.29/12.83 ( ( setadjoinAx ) =>
% 97.29/12.83 ( ( powersetAx ) =>
% 97.29/12.83 ( ( setunionAx ) =>
% 97.29/12.83 ( ( omega0Ax ) =>
% 97.29/12.83 ( ( omegaSAx ) =>
% 97.29/12.83 ( ( omegaIndAx ) =>
% 97.29/12.83 ( ( replAx ) =>
% 97.29/12.83 ( ( foundationAx ) =>
% 97.29/12.83 ( ( wellorderingAx ) =>
% 97.29/12.83 ( ( descrp ) =>
% 97.29/12.83 ( ( dsetconstrI ) =>
% 97.29/12.83 ( ( dsetconstrEL ) =>
% 97.29/12.83 ( ( dsetconstrER ) =>
% 97.29/12.83 ( ( exuE1 ) =>
% 97.29/12.83 ( ( prop2setE ) =>
% 97.29/12.83 ( ( emptysetE ) =>
% 97.29/12.83 ( ( emptysetimpfalse ) =>
% 97.29/12.83 ( ( notinemptyset ) =>
% 97.29/12.83 ( ( exuE3e ) =>
% 97.29/12.83 ( ( setext ) =>
% 97.29/12.83 ( ( emptyI ) =>
% 97.29/12.83 ( ( noeltsimpempty ) =>
% 97.29/12.83 ( ( setbeta ) =>
% 97.29/12.83 ( ( nonemptyE1 ) =>
% 97.29/12.83 ( ( nonemptyI ) =>
% 97.29/12.83 ( ( nonemptyI1 ) =>
% 97.29/12.83 ( ( setadjoinIL ) =>
% 97.29/12.83 ( ( emptyinunitempty ) =>
% 97.29/12.83 ( ( setadjoinIR ) =>
% 97.29/12.83 ( ( setadjoinE ) =>
% 97.29/12.83 ( (
% 97.29/12.83 setadjoinOr ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setoftrueEq ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 powersetI ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 emptyinPowerset ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 emptyInPowerset ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 powersetE ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setunionI ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setunionE ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 subPowSU ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 exuE2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 nonemptyImpWitness ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 uniqinunit ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 notinsingleton ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 eqinunit ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 singletonsswitch ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 upairsetE ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 upairsetIL ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 upairsetIR ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 emptyE1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 vacuousDall ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 quantDeMorgan1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 quantDeMorgan2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 quantDeMorgan3 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 quantDeMorgan4 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 prop2setI ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 prop2set2propI ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 notdexE ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 notdallE ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 exuI1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 exuI3 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 exuI2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 inCongP ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 in__Cong ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 exuE3u ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 exu__Cong ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 emptyset__Cong ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setadjoin__Cong ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 powerset__Cong ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setunion__Cong ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 omega__Cong ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 exuEu ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 descr__Cong ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 dsetconstr__Cong ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 subsetI1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 eqimpsubset2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 eqimpsubset1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 subsetI2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 emptysetsubset ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 subsetE ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 subsetE2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 notsubsetI ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 notequalI1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 notequalI2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 subsetRefl ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 subsetTrans ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setadjoinSub ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setadjoinSub2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 subset2powerset ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setextsub ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 subsetemptysetimpeq ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 powersetI1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 powersetE1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 inPowerset ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 powersetsubset ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 sepInPowerset ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 sepSubset ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 binunionIL ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 upairset2IR ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 binunionIR ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 binunionEcases ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 binunionE ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 binunionLsub ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 binunionRsub ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 binintersectI ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 binintersectSubset5 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 binintersectEL ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 binintersectLsub ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 binintersectSubset2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 binintersectSubset3 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 binintersectER ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 disjointsetsI1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 binintersectRsub ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 binintersectSubset4 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 binintersectSubset1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 bs114d ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setminusI ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setminusEL ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setminusER ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setminusSubset2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setminusERneg ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setminusELneg ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setminusILneg ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setminusIRneg ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setminusLsub ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setminusSubset1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 symdiffE ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 symdiffI1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 symdiffI2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 symdiffIneg1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 symdiffIneg2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 secondinupair ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setukpairIL ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setukpairIR ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 kpairiskpair ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 kpairp ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 singletonsubset ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 singletoninpowerset ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 singletoninpowunion ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 upairset2E ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 upairsubunion ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 upairinpowunion ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 ubforcartprodlem1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 ubforcartprodlem2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 ubforcartprodlem3 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 cartprodpairin ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 cartprodmempair1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 cartprodmempair ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setunionE2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setunionsingleton1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setunionsingleton2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setunionsingleton ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 singletonprop ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 ex1E1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 ex1I ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 ex1I2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 singletonsuniq ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setukpairinjL1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 kfstsingleton ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 theprop ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 kfstpairEq ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 cartprodfstin ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setukpairinjL2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setukpairinjL ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setukpairinjR11 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setukpairinjR12 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setukpairinjR1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 upairequniteq ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setukpairinjR2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setukpairinjR ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 ksndsingleton ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 ksndpairEq ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 kpairsurjEq ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 cartprodsndin ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 cartprodpairmemEL ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 cartprodpairmemER ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 cartprodmempaircEq ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 cartprodfstpairEq ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 cartprodsndpairEq ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 cartprodpairsurjEq ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 dpsetconstrI ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 dpsetconstrSub ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setOfPairsIsBReln ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 dpsetconstrERa ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 dpsetconstrEL1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 dpsetconstrEL2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 dpsetconstrER ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 funcImageSingleton ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 apProp ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 app ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 infuncsetfunc ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 ap2p ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 funcinfuncset ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 lamProp ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 lamp ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 lam2p ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 brelnall1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 brelnall2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 ex1E2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 funcGraphProp1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 funcGraphProp3 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 funcGraphProp2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 funcextLem ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 funcGraphProp4 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 subbreln ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 eqbreln ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 funcext ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 funcext2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 ap2apEq1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 ap2apEq2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 beta1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 eta1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 lam2lamEq ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 beta2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 eta2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 iffalseProp1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 iffalseProp2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 iftrueProp1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 iftrueProp2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 ifSingleton ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 ifp ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 theeq ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 iftrue ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 iffalse ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 iftrueorfalse ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 binintersectT_lem ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 binunionT_lem ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 powersetT_lem ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setminusT_lem ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 complementT_lem ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setextT ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 subsetTI ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 powersetTI1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 powersetTE1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 complementTI1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 complementTE1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 binintersectTELcontra ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 binintersectTERcontra ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 contrasubsetT ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 contrasubsetT1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 contrasubsetT2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 contrasubsetT3 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 doubleComplementI1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 doubleComplementE1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 doubleComplementSub1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 doubleComplementSub2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 doubleComplementEq ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 complementTnotintersectT ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 complementImpComplementIntersect ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 complementSubsetComplementIntersect ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 complementInPowersetComplementIntersect ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 contraSubsetComplement ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 complementTcontraSubset ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 binunionTILcontra ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 binunionTIRcontra ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 inIntersectImpInUnion ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 inIntersectImpInUnion2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 inIntersectImpInIntersectUnions ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 intersectInPowersetIntersectUnions ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 inComplementUnionImpNotIn1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 inComplementUnionImpInComplement1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 binunionTE ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 binunionTEcontra ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 demorgan2a1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 complementUnionInPowersetComplement ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 demorgan2a2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 demorgan1a ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 demorgan1b ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 demorgan1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 demorgan2a ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 demorgan2b2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 demorgan2b ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 demorgan2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 woz13rule0 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 woz13rule1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 woz13rule2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 woz13rule3 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 woz13rule4 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 woz1_1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 woz1_2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 woz1_3 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 woz1_4 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 woz1_5 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 breln1all2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 breln1SetBreln1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 choice2fnsingleton ) =>
% 97.29/12.83 (
% 97.29/12.83 ![
% 97.29/12.83 A:$i,
% 97.29/12.83 Xphi:(
% 97.29/12.83 $i > $i >
% 97.29/12.83 $o )]:
% 97.29/12.83 (
% 97.29/12.83 breln1 @
% 97.29/12.83 A @
% 97.29/12.83 (
% 97.29/12.83 dpsetconstr
% 97.29/12.83 @
% 97.29/12.83 A @ A @
% 97.29/12.83 (
% 97.29/12.83 ^[
% 97.29/12.83 Xx:$i,
% 97.29/12.83 Xy:$i]:
% 97.29/12.83 (
% 97.29/12.83 Xphi @
% 97.29/12.83 Xx @ Xy ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 97.29/12.83 thf(zf_stmt_0, negated_conjecture,
% 97.29/12.83 (~( ( setextAx ) =>
% 97.29/12.83 ( ( emptysetAx ) =>
% 97.29/12.83 ( ( setadjoinAx ) =>
% 97.29/12.83 ( ( powersetAx ) =>
% 97.29/12.83 ( ( setunionAx ) =>
% 97.29/12.83 ( ( omega0Ax ) =>
% 97.29/12.83 ( ( omegaSAx ) =>
% 97.29/12.83 ( ( omegaIndAx ) =>
% 97.29/12.83 ( ( replAx ) =>
% 97.29/12.83 ( ( foundationAx ) =>
% 97.29/12.83 ( ( wellorderingAx ) =>
% 97.29/12.83 ( ( descrp ) =>
% 97.29/12.83 ( ( dsetconstrI ) =>
% 97.29/12.83 ( ( dsetconstrEL ) =>
% 97.29/12.83 ( ( dsetconstrER ) =>
% 97.29/12.83 ( ( exuE1 ) =>
% 97.29/12.83 ( ( prop2setE ) =>
% 97.29/12.83 ( ( emptysetE ) =>
% 97.29/12.83 ( ( emptysetimpfalse ) =>
% 97.29/12.83 ( ( notinemptyset ) =>
% 97.29/12.83 ( ( exuE3e ) =>
% 97.29/12.83 ( ( setext ) =>
% 97.29/12.83 ( ( emptyI ) =>
% 97.29/12.83 ( ( noeltsimpempty ) =>
% 97.29/12.83 ( ( setbeta ) =>
% 97.29/12.83 ( ( nonemptyE1 ) =>
% 97.29/12.83 ( ( nonemptyI ) =>
% 97.29/12.83 ( ( nonemptyI1 ) =>
% 97.29/12.83 ( ( setadjoinIL ) =>
% 97.29/12.83 ( ( emptyinunitempty ) =>
% 97.29/12.83 ( ( setadjoinIR ) =>
% 97.29/12.83 ( (
% 97.29/12.83 setadjoinE ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setadjoinOr ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setoftrueEq ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 powersetI ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 emptyinPowerset ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 emptyInPowerset ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 powersetE ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setunionI ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setunionE ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 subPowSU ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 exuE2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 nonemptyImpWitness ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 uniqinunit ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 notinsingleton ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 eqinunit ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 singletonsswitch ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 upairsetE ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 upairsetIL ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 upairsetIR ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 emptyE1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 vacuousDall ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 quantDeMorgan1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 quantDeMorgan2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 quantDeMorgan3 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 quantDeMorgan4 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 prop2setI ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 prop2set2propI ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 notdexE ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 notdallE ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 exuI1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 exuI3 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 exuI2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 inCongP ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 in__Cong ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 exuE3u ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 exu__Cong ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 emptyset__Cong ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setadjoin__Cong ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 powerset__Cong ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setunion__Cong ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 omega__Cong ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 exuEu ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 descr__Cong ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 dsetconstr__Cong ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 subsetI1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 eqimpsubset2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 eqimpsubset1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 subsetI2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 emptysetsubset ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 subsetE ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 subsetE2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 notsubsetI ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 notequalI1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 notequalI2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 subsetRefl ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 subsetTrans ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setadjoinSub ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setadjoinSub2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 subset2powerset ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setextsub ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 subsetemptysetimpeq ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 powersetI1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 powersetE1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 inPowerset ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 powersetsubset ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 sepInPowerset ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 sepSubset ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 binunionIL ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 upairset2IR ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 binunionIR ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 binunionEcases ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 binunionE ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 binunionLsub ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 binunionRsub ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 binintersectI ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 binintersectSubset5 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 binintersectEL ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 binintersectLsub ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 binintersectSubset2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 binintersectSubset3 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 binintersectER ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 disjointsetsI1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 binintersectRsub ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 binintersectSubset4 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 binintersectSubset1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 bs114d ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setminusI ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setminusEL ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setminusER ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setminusSubset2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setminusERneg ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setminusELneg ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setminusILneg ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setminusIRneg ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setminusLsub ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setminusSubset1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 symdiffE ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 symdiffI1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 symdiffI2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 symdiffIneg1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 symdiffIneg2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 secondinupair ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setukpairIL ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setukpairIR ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 kpairiskpair ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 kpairp ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 singletonsubset ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 singletoninpowerset ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 singletoninpowunion ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 upairset2E ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 upairsubunion ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 upairinpowunion ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 ubforcartprodlem1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 ubforcartprodlem2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 ubforcartprodlem3 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 cartprodpairin ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 cartprodmempair1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 cartprodmempair ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setunionE2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setunionsingleton1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setunionsingleton2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setunionsingleton ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 singletonprop ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 ex1E1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 ex1I ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 ex1I2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 singletonsuniq ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setukpairinjL1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 kfstsingleton ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 theprop ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 kfstpairEq ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 cartprodfstin ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setukpairinjL2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setukpairinjL ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setukpairinjR11 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setukpairinjR12 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setukpairinjR1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 upairequniteq ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setukpairinjR2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setukpairinjR ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 ksndsingleton ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 ksndpairEq ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 kpairsurjEq ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 cartprodsndin ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 cartprodpairmemEL ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 cartprodpairmemER ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 cartprodmempaircEq ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 cartprodfstpairEq ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 cartprodsndpairEq ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 cartprodpairsurjEq ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 dpsetconstrI ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 dpsetconstrSub ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setOfPairsIsBReln ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 dpsetconstrERa ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 dpsetconstrEL1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 dpsetconstrEL2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 dpsetconstrER ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 funcImageSingleton ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 apProp ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 app ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 infuncsetfunc ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 ap2p ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 funcinfuncset ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 lamProp ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 lamp ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 lam2p ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 brelnall1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 brelnall2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 ex1E2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 funcGraphProp1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 funcGraphProp3 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 funcGraphProp2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 funcextLem ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 funcGraphProp4 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 subbreln ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 eqbreln ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 funcext ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 funcext2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 ap2apEq1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 ap2apEq2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 beta1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 eta1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 lam2lamEq ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 beta2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 eta2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 iffalseProp1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 iffalseProp2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 iftrueProp1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 iftrueProp2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 ifSingleton ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 ifp ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 theeq ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 iftrue ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 iffalse ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 iftrueorfalse ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 binintersectT_lem ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 binunionT_lem ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 powersetT_lem ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setminusT_lem ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 complementT_lem ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 setextT ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 subsetTI ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 powersetTI1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 powersetTE1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 complementTI1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 complementTE1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 binintersectTELcontra ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 binintersectTERcontra ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 contrasubsetT ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 contrasubsetT1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 contrasubsetT2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 contrasubsetT3 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 doubleComplementI1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 doubleComplementE1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 doubleComplementSub1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 doubleComplementSub2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 doubleComplementEq ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 complementTnotintersectT ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 complementImpComplementIntersect ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 complementSubsetComplementIntersect ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 complementInPowersetComplementIntersect ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 contraSubsetComplement ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 complementTcontraSubset ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 binunionTILcontra ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 binunionTIRcontra ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 inIntersectImpInUnion ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 inIntersectImpInUnion2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 inIntersectImpInIntersectUnions ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 intersectInPowersetIntersectUnions ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 inComplementUnionImpNotIn1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 inComplementUnionImpInComplement1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 binunionTE ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 binunionTEcontra ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 demorgan2a1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 complementUnionInPowersetComplement ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 demorgan2a2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 demorgan1a ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 demorgan1b ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 demorgan1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 demorgan2a ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 demorgan2b2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 demorgan2b ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 demorgan2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 woz13rule0 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 woz13rule1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 woz13rule2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 woz13rule3 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 woz13rule4 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 woz1_1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 woz1_2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 woz1_3 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 woz1_4 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 woz1_5 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 breln1all2 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 breln1SetBreln1 ) =>
% 97.29/12.83 (
% 97.29/12.83 (
% 97.29/12.83 choice2fnsingleton ) =>
% 97.29/12.83 (
% 97.29/12.83 ![
% 97.29/12.83 A:$i,
% 97.29/12.83 Xphi:(
% 97.29/12.83 $i > $i >
% 97.29/12.83 $o )]:
% 97.29/12.83 (
% 97.29/12.83 breln1 @
% 97.29/12.83 A @
% 97.29/12.83 (
% 97.29/12.83 dpsetconstr
% 97.29/12.83 @
% 97.29/12.83 A @ A @
% 97.29/12.83 (
% 97.29/12.83 ^[
% 97.29/12.83 Xx:$i,
% 97.29/12.83 Xy:$i]:
% 97.29/12.83 (
% 97.29/12.83 Xphi @
% 97.29/12.83 Xx @ Xy ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 97.29/12.83 inference('cnf.neg', [status(esa)], [setOfPairsIsBReln1])).
% 97.29/12.83 thf(zip_derived_cl0, plain,
% 97.29/12.83 (~ (((setextAx) =>
% 97.29/12.83 (((emptysetAx) =>
% 97.29/12.83 (((setadjoinAx) =>
% 97.29/12.83 (((powersetAx) =>
% 97.29/12.83 (((setunionAx) =>
% 97.29/12.83 (((omega0Ax) =>
% 97.29/12.83 (((omegaSAx) =>
% 97.29/12.83 (((omegaIndAx) =>
% 97.29/12.83 (((replAx) =>
% 97.29/12.83 (((foundationAx) =>
% 97.29/12.83 (((wellorderingAx) =>
% 97.29/12.83 (((descrp) =>
% 97.29/12.83 (((dsetconstrI) =>
% 97.29/12.83 (((dsetconstrEL) =>
% 97.29/12.83 (((dsetconstrER) =>
% 97.29/12.83 (((exuE1) =>
% 97.29/12.83 (((prop2setE) =>
% 97.29/12.83 (((emptysetE) =>
% 97.29/12.83 (((emptysetimpfalse) =>
% 97.29/12.83 (((notinemptyset) =>
% 97.29/12.83 (((exuE3e) =>
% 97.29/12.83 (((setext) =>
% 97.29/12.83 (((emptyI) =>
% 97.29/12.83 (((noeltsimpempty) =>
% 97.29/12.83 (((setbeta) =>
% 97.29/12.83 (((nonemptyE1) =>
% 97.29/12.83 (((nonemptyI) =>
% 97.29/12.83 (((nonemptyI1) =>
% 97.29/12.83 (((setadjoinIL) =>
% 97.29/12.83 (((emptyinunitempty) =>
% 97.29/12.83 ((
% 97.29/12.83 (setadjoinIR) =>
% 97.29/12.83 ((
% 97.29/12.83 (setadjoinE) =>
% 97.29/12.83 ((
% 97.29/12.83 (setadjoinOr) =>
% 97.29/12.83 ((
% 97.29/12.83 (setoftrueEq) =>
% 97.29/12.83 ((
% 97.29/12.83 (powersetI) =>
% 97.29/12.83 ((
% 97.29/12.83 (emptyinPowerset) =>
% 97.29/12.83 ((
% 97.29/12.83 (emptyInPowerset) =>
% 97.29/12.83 ((
% 97.29/12.83 (powersetE) =>
% 97.29/12.83 ((
% 97.29/12.83 (setunionI) =>
% 97.29/12.83 ((
% 97.29/12.83 (setunionE) =>
% 97.29/12.83 ((
% 97.29/12.83 (subPowSU) =>
% 97.29/12.83 ((
% 97.29/12.83 (exuE2) =>
% 97.29/12.83 ((
% 97.29/12.83 (nonemptyImpWitness) =>
% 97.29/12.83 ((
% 97.29/12.83 (uniqinunit) =>
% 97.29/12.83 ((
% 97.29/12.83 (notinsingleton) =>
% 97.29/12.83 ((
% 97.29/12.83 (eqinunit) =>
% 97.29/12.83 ((
% 97.29/12.83 (singletonsswitch) =>
% 97.29/12.83 ((
% 97.29/12.83 (upairsetE) =>
% 97.29/12.83 ((
% 97.29/12.83 (upairsetIL) =>
% 97.29/12.83 ((
% 97.29/12.83 (upairsetIR) =>
% 97.29/12.83 ((
% 97.29/12.83 (emptyE1) =>
% 97.29/12.83 ((
% 97.29/12.83 (vacuousDall) =>
% 97.29/12.83 ((
% 97.29/12.83 (quantDeMorgan1) =>
% 97.29/12.83 ((
% 97.29/12.83 (quantDeMorgan2) =>
% 97.29/12.83 ((
% 97.29/12.83 (quantDeMorgan3) =>
% 97.29/12.83 ((
% 97.29/12.83 (quantDeMorgan4) =>
% 97.29/12.83 ((
% 97.29/12.83 (prop2setI) =>
% 97.29/12.83 ((
% 97.29/12.83 (prop2set2propI) =>
% 97.29/12.83 ((
% 97.29/12.83 (notdexE) =>
% 97.29/12.83 ((
% 97.29/12.83 (notdallE) =>
% 97.29/12.83 ((
% 97.29/12.83 (exuI1) =>
% 97.29/12.83 ((
% 97.29/12.83 (exuI3) =>
% 97.29/12.83 ((
% 97.29/12.83 (exuI2) =>
% 97.29/12.83 ((
% 97.29/12.83 (inCongP) =>
% 97.29/12.83 ((
% 97.29/12.83 (in__Cong) =>
% 97.29/12.83 ((
% 97.29/12.83 (exuE3u) =>
% 97.29/12.83 ((
% 97.29/12.83 (exu__Cong) =>
% 97.29/12.83 ((
% 97.29/12.83 (emptyset__Cong) =>
% 97.29/12.83 ((
% 97.29/12.83 (setadjoin__Cong) =>
% 97.29/12.83 ((
% 97.29/12.83 (powerset__Cong) =>
% 97.29/12.83 ((
% 97.29/12.83 (setunion__Cong) =>
% 97.29/12.83 ((
% 97.29/12.83 (omega__Cong) =>
% 97.29/12.83 ((
% 97.29/12.83 (exuEu) =>
% 97.29/12.83 ((
% 97.29/12.83 (descr__Cong) =>
% 97.29/12.83 ((
% 97.29/12.83 (dsetconstr__Cong) =>
% 97.29/12.83 ((
% 97.29/12.83 (subsetI1) =>
% 97.29/12.83 ((
% 97.29/12.83 (eqimpsubset2) =>
% 97.29/12.83 ((
% 97.29/12.83 (eqimpsubset1) =>
% 97.29/12.83 ((
% 97.29/12.83 (subsetI2) =>
% 97.29/12.83 ((
% 97.29/12.83 (emptysetsubset) =>
% 97.29/12.83 ((
% 97.29/12.83 (subsetE) =>
% 97.29/12.83 ((
% 97.29/12.83 (subsetE2) =>
% 97.29/12.83 ((
% 97.29/12.83 (notsubsetI) =>
% 97.29/12.83 ((
% 97.29/12.83 (notequalI1) =>
% 97.29/12.83 ((
% 97.29/12.83 (notequalI2) =>
% 97.29/12.83 ((
% 97.29/12.83 (subsetRefl) =>
% 97.29/12.83 ((
% 97.29/12.83 (subsetTrans) =>
% 97.29/12.83 ((
% 97.29/12.83 (setadjoinSub) =>
% 97.29/12.83 ((
% 97.29/12.83 (setadjoinSub2) =>
% 97.29/12.83 ((
% 97.29/12.83 (subset2powerset) =>
% 97.29/12.83 ((
% 97.29/12.83 (setextsub) =>
% 97.29/12.83 ((
% 97.29/12.83 (subsetemptysetimpeq) =>
% 97.29/12.83 ((
% 97.29/12.83 (powersetI1) =>
% 97.29/12.83 ((
% 97.29/12.83 (powersetE1) =>
% 97.29/12.83 ((
% 97.29/12.83 (inPowerset) =>
% 97.29/12.83 ((
% 97.29/12.83 (powersetsubset) =>
% 97.29/12.83 ((
% 97.29/12.83 (sepInPowerset) =>
% 97.29/12.83 ((
% 97.29/12.83 (sepSubset) =>
% 97.29/12.83 ((
% 97.29/12.83 (binunionIL) =>
% 97.29/12.83 ((
% 97.29/12.83 (upairset2IR) =>
% 97.29/12.83 ((
% 97.29/12.83 (binunionIR) =>
% 97.29/12.83 ((
% 97.29/12.83 (binunionEcases) =>
% 97.29/12.83 ((
% 97.29/12.83 (binunionE) =>
% 97.29/12.83 ((
% 97.29/12.83 (binunionLsub) =>
% 97.29/12.83 ((
% 97.29/12.83 (binunionRsub) =>
% 97.29/12.83 ((
% 97.29/12.83 (binintersectI) =>
% 97.29/12.83 ((
% 97.29/12.83 (binintersectSubset5) =>
% 97.29/12.83 ((
% 97.29/12.83 (binintersectEL) =>
% 97.29/12.83 ((
% 97.29/12.83 (binintersectLsub) =>
% 97.29/12.83 ((
% 97.29/12.83 (binintersectSubset2) =>
% 97.29/12.83 ((
% 97.29/12.83 (binintersectSubset3) =>
% 97.29/12.83 ((
% 97.29/12.83 (binintersectER) =>
% 97.29/12.83 ((
% 97.29/12.83 (disjointsetsI1) =>
% 97.29/12.83 ((
% 97.29/12.83 (binintersectRsub) =>
% 97.29/12.83 ((
% 97.29/12.83 (binintersectSubset4) =>
% 97.29/12.83 ((
% 97.29/12.83 (binintersectSubset1) =>
% 97.29/12.83 ((
% 97.29/12.83 (bs114d) =>
% 97.29/12.83 ((
% 97.29/12.83 (setminusI) =>
% 97.29/12.83 ((
% 97.29/12.83 (setminusEL) =>
% 97.29/12.83 ((
% 97.29/12.83 (setminusER) =>
% 97.29/12.83 ((
% 97.29/12.83 (setminusSubset2) =>
% 97.29/12.83 ((
% 97.29/12.83 (setminusERneg) =>
% 97.29/12.83 ((
% 97.29/12.83 (setminusELneg) =>
% 97.29/12.83 ((
% 97.29/12.83 (setminusILneg) =>
% 97.29/12.83 ((
% 97.29/12.83 (setminusIRneg) =>
% 97.29/12.83 ((
% 97.29/12.83 (setminusLsub) =>
% 97.29/12.83 ((
% 97.29/12.83 (setminusSubset1) =>
% 97.29/12.83 ((
% 97.29/12.83 (symdiffE) =>
% 97.29/12.83 ((
% 97.29/12.83 (symdiffI1) =>
% 97.29/12.83 ((
% 97.29/12.83 (symdiffI2) =>
% 97.29/12.83 ((
% 97.29/12.83 (symdiffIneg1) =>
% 97.29/12.83 ((
% 97.29/12.83 (symdiffIneg2) =>
% 97.29/12.83 ((
% 97.29/12.83 (secondinupair) =>
% 97.29/12.83 ((
% 97.29/12.83 (setukpairIL) =>
% 97.29/12.83 ((
% 97.29/12.83 (setukpairIR) =>
% 97.29/12.83 ((
% 97.29/12.83 (kpairiskpair) =>
% 97.29/12.83 ((
% 97.29/12.83 (kpairp) =>
% 97.29/12.83 ((
% 97.29/12.83 (singletonsubset) =>
% 97.29/12.83 ((
% 97.29/12.83 (singletoninpowerset) =>
% 97.29/12.83 ((
% 97.29/12.83 (singletoninpowunion) =>
% 97.29/12.83 ((
% 97.29/12.83 (upairset2E) =>
% 97.29/12.83 ((
% 97.29/12.83 (upairsubunion) =>
% 97.29/12.83 ((
% 97.29/12.83 (upairinpowunion) =>
% 97.29/12.83 ((
% 97.29/12.83 (ubforcartprodlem1) =>
% 97.29/12.83 ((
% 97.29/12.83 (ubforcartprodlem2) =>
% 97.29/12.83 ((
% 97.29/12.83 (ubforcartprodlem3) =>
% 97.29/12.83 ((
% 97.29/12.83 (cartprodpairin) =>
% 97.29/12.83 ((
% 97.29/12.83 (cartprodmempair1) =>
% 97.29/12.83 ((
% 97.29/12.83 (cartprodmempair) =>
% 97.29/12.83 ((
% 97.29/12.83 (setunionE2) =>
% 97.29/12.83 ((
% 97.29/12.83 (setunionsingleton1) =>
% 97.29/12.83 ((
% 97.29/12.83 (setunionsingleton2) =>
% 97.29/12.83 ((
% 97.29/12.83 (setunionsingleton) =>
% 97.29/12.83 ((
% 97.29/12.83 (singletonprop) =>
% 97.29/12.83 ((
% 97.29/12.83 (ex1E1) =>
% 97.29/12.83 ((
% 97.29/12.83 (ex1I) =>
% 97.29/12.83 ((
% 97.29/12.83 (ex1I2) =>
% 97.29/12.83 ((
% 97.29/12.83 (singletonsuniq) =>
% 97.29/12.83 ((
% 97.29/12.83 (setukpairinjL1) =>
% 97.29/12.83 ((
% 97.29/12.83 (kfstsingleton) =>
% 97.29/12.83 ((
% 97.29/12.83 (theprop) =>
% 97.29/12.83 ((
% 97.29/12.83 (kfstpairEq) =>
% 97.29/12.83 ((
% 97.29/12.83 (cartprodfstin) =>
% 97.29/12.83 ((
% 97.29/12.83 (setukpairinjL2) =>
% 97.29/12.83 ((
% 97.29/12.83 (setukpairinjL) =>
% 97.29/12.83 ((
% 97.29/12.83 (setukpairinjR11) =>
% 97.29/12.83 ((
% 97.29/12.83 (setukpairinjR12) =>
% 97.29/12.83 ((
% 97.29/12.83 (setukpairinjR1) =>
% 97.29/12.83 ((
% 97.29/12.83 (upairequniteq) =>
% 97.29/12.83 ((
% 97.29/12.83 (setukpairinjR2) =>
% 97.29/12.83 ((
% 97.29/12.83 (setukpairinjR) =>
% 97.29/12.83 ((
% 97.29/12.83 (ksndsingleton) =>
% 97.29/12.83 ((
% 97.29/12.83 (ksndpairEq) =>
% 97.29/12.83 ((
% 97.29/12.83 (kpairsurjEq) =>
% 97.29/12.83 ((
% 97.29/12.83 (cartprodsndin) =>
% 97.29/12.83 ((
% 97.29/12.83 (cartprodpairmemEL) =>
% 97.29/12.83 ((
% 97.29/12.83 (cartprodpairmemER) =>
% 97.29/12.83 ((
% 97.29/12.83 (cartprodmempaircEq) =>
% 97.29/12.83 ((
% 97.29/12.83 (cartprodfstpairEq) =>
% 97.29/12.83 ((
% 97.29/12.83 (cartprodsndpairEq) =>
% 97.29/12.83 ((
% 97.29/12.83 (cartprodpairsurjEq) =>
% 97.29/12.83 ((
% 97.29/12.83 (dpsetconstrI) =>
% 97.29/12.83 ((
% 97.29/12.83 (dpsetconstrSub) =>
% 97.29/12.83 ((
% 97.29/12.83 (setOfPairsIsBReln) =>
% 97.29/12.83 ((
% 97.29/12.83 (dpsetconstrERa) =>
% 97.29/12.83 ((
% 97.29/12.83 (dpsetconstrEL1) =>
% 97.29/12.83 ((
% 97.29/12.83 (dpsetconstrEL2) =>
% 97.29/12.83 ((
% 97.29/12.83 (dpsetconstrER) =>
% 97.29/12.83 ((
% 97.29/12.83 (funcImageSingleton) =>
% 97.29/12.83 ((
% 97.29/12.83 (apProp) =>
% 97.29/12.83 ((
% 97.29/12.83 (app) =>
% 97.29/12.83 ((
% 97.29/12.83 (infuncsetfunc) =>
% 97.29/12.83 ((
% 97.29/12.83 (ap2p) =>
% 97.29/12.83 ((
% 97.29/12.83 (funcinfuncset) =>
% 97.29/12.83 ((
% 97.29/12.83 (lamProp) =>
% 97.29/12.83 ((
% 97.29/12.83 (lamp) =>
% 97.29/12.83 ((
% 97.29/12.83 (lam2p) =>
% 97.29/12.83 ((
% 97.29/12.83 (brelnall1) =>
% 97.29/12.83 ((
% 97.29/12.83 (brelnall2) =>
% 97.29/12.83 ((
% 97.29/12.83 (ex1E2) =>
% 97.29/12.83 ((
% 97.29/12.83 (funcGraphProp1) =>
% 97.29/12.83 ((
% 97.29/12.83 (funcGraphProp3) =>
% 97.29/12.83 ((
% 97.29/12.83 (funcGraphProp2) =>
% 97.29/12.83 ((
% 97.29/12.83 (funcextLem) =>
% 97.29/12.83 ((
% 97.29/12.83 (funcGraphProp4) =>
% 97.29/12.83 ((
% 97.29/12.83 (subbreln) =>
% 97.29/12.83 ((
% 97.29/12.83 (eqbreln) =>
% 97.29/12.83 ((
% 97.29/12.83 (funcext) =>
% 97.29/12.83 ((
% 97.29/12.83 (funcext2) =>
% 97.29/12.83 ((
% 97.29/12.83 (ap2apEq1) =>
% 97.29/12.83 ((
% 97.29/12.83 (ap2apEq2) =>
% 97.29/12.83 ((
% 97.29/12.83 (beta1) =>
% 97.29/12.83 ((
% 97.29/12.83 (eta1) =>
% 97.29/12.83 ((
% 97.29/12.83 (lam2lamEq) =>
% 97.29/12.83 ((
% 97.29/12.83 (beta2) =>
% 97.29/12.83 ((
% 97.29/12.83 (eta2) =>
% 97.29/12.83 ((
% 97.29/12.83 (iffalseProp1) =>
% 97.29/12.83 ((
% 97.29/12.83 (iffalseProp2) =>
% 97.29/12.83 ((
% 97.29/12.83 (iftrueProp1) =>
% 97.29/12.83 ((
% 97.29/12.83 (iftrueProp2) =>
% 97.29/12.83 ((
% 97.29/12.83 (ifSingleton) =>
% 97.29/12.83 ((
% 97.29/12.83 (ifp) =>
% 97.29/12.83 ((
% 97.29/12.83 (theeq) =>
% 97.29/12.83 ((
% 97.29/12.83 (iftrue) =>
% 97.29/12.83 ((
% 97.29/12.83 (iffalse) =>
% 97.29/12.83 ((
% 97.29/12.83 (iftrueorfalse) =>
% 97.29/12.83 ((
% 97.29/12.83 (binintersectT_lem) =>
% 97.29/12.83 ((
% 97.29/12.83 (binunionT_lem) =>
% 97.29/12.83 ((
% 97.29/12.83 (powersetT_lem) =>
% 97.29/12.83 ((
% 97.29/12.83 (setminusT_lem) =>
% 97.29/12.83 ((
% 97.29/12.83 (complementT_lem) =>
% 97.29/12.83 ((
% 97.29/12.83 (setextT) =>
% 97.29/12.83 ((
% 97.29/12.83 (subsetTI) =>
% 97.29/12.83 ((
% 97.29/12.83 (powersetTI1) =>
% 97.29/12.83 ((
% 97.29/12.83 (powersetTE1) =>
% 97.29/12.83 ((
% 97.29/12.83 (complementTI1) =>
% 97.29/12.83 ((
% 97.29/12.83 (complementTE1) =>
% 97.29/12.83 ((
% 97.29/12.83 (binintersectTELcontra) =>
% 97.29/12.83 ((
% 97.29/12.83 (binintersectTERcontra) =>
% 97.29/12.83 ((
% 97.29/12.83 (contrasubsetT) =>
% 97.29/12.83 ((
% 97.29/12.83 (contrasubsetT1) =>
% 97.29/12.83 ((
% 97.29/12.83 (contrasubsetT2) =>
% 97.29/12.83 ((
% 97.29/12.83 (contrasubsetT3) =>
% 97.29/12.83 ((
% 97.29/12.83 (doubleComplementI1) =>
% 97.29/12.83 ((
% 97.29/12.83 (doubleComplementE1) =>
% 97.29/12.83 ((
% 97.29/12.83 (doubleComplementSub1) =>
% 97.29/12.83 ((
% 97.29/12.83 (doubleComplementSub2) =>
% 97.29/12.83 ((
% 97.29/12.83 (doubleComplementEq) =>
% 97.29/12.83 ((
% 97.29/12.83 (complementTnotintersectT) =>
% 97.29/12.83 ((
% 97.29/12.83 (complementImpComplementIntersect) =>
% 97.29/12.83 ((
% 97.29/12.83 (complementSubsetComplementIntersect) =>
% 97.29/12.83 ((
% 97.29/12.83 (complementInPowersetComplementIntersect) =>
% 97.29/12.83 ((
% 97.29/12.83 (contraSubsetComplement) =>
% 97.29/12.83 ((
% 97.29/12.83 (complementTcontraSubset) =>
% 97.29/12.83 ((
% 97.29/12.83 (binunionTILcontra) =>
% 97.29/12.83 ((
% 97.29/12.83 (binunionTIRcontra) =>
% 97.29/12.83 ((
% 97.29/12.83 (inIntersectImpInUnion) =>
% 97.29/12.83 ((
% 97.29/12.83 (inIntersectImpInUnion2) =>
% 97.29/12.83 ((
% 97.29/12.83 (inIntersectImpInIntersectUnions) =>
% 97.29/12.83 ((
% 97.29/12.83 (intersectInPowersetIntersectUnions) =>
% 97.29/12.83 ((
% 97.29/12.83 (inComplementUnionImpNotIn1) =>
% 97.29/12.83 ((
% 97.29/12.83 (inComplementUnionImpInComplement1) =>
% 97.29/12.83 ((
% 97.29/12.83 (binunionTE) =>
% 97.29/12.83 ((
% 97.29/12.83 (binunionTEcontra) =>
% 97.29/12.83 ((
% 97.29/12.83 (demorgan2a1) =>
% 97.29/12.83 ((
% 97.29/12.83 (complementUnionInPowersetComplement) =>
% 97.29/12.83 ((
% 97.29/12.83 (demorgan2a2) =>
% 97.29/12.83 ((
% 97.29/12.83 (demorgan1a) =>
% 97.29/12.83 ((
% 97.29/12.83 (demorgan1b) =>
% 97.29/12.83 ((
% 97.29/12.83 (demorgan1) =>
% 97.29/12.83 ((
% 97.29/12.83 (demorgan2a) =>
% 97.29/12.83 ((
% 97.29/12.83 (demorgan2b2) =>
% 97.29/12.83 ((
% 97.29/12.83 (demorgan2b) =>
% 97.29/12.83 ((
% 97.29/12.83 (demorgan2) =>
% 97.29/12.83 ((
% 97.29/12.83 (woz13rule0) =>
% 97.29/12.83 ((
% 97.29/12.83 (woz13rule1) =>
% 97.29/12.83 ((
% 97.29/12.83 (woz13rule2) =>
% 97.29/12.83 ((
% 97.29/12.83 (woz13rule3) =>
% 97.29/12.83 ((
% 97.29/12.83 (woz13rule4) =>
% 97.29/12.83 ((
% 97.29/12.83 (woz1_1) =>
% 97.29/12.83 ((
% 97.29/12.83 (woz1_2) =>
% 97.29/12.83 ((
% 97.29/12.83 (woz1_3) =>
% 97.29/12.83 ((
% 97.29/12.83 (woz1_4) =>
% 97.29/12.83 ((
% 97.29/12.83 (woz1_5) =>
% 97.29/12.83 ((
% 97.29/12.83 (breln1all2) =>
% 97.29/12.83 ((
% 97.29/12.83 (breln1SetBreln1) =>
% 97.29/12.83 ((
% 97.29/12.83 (choice2fnsingleton) =>
% 97.29/12.83 ((
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% 97.29/12.83 (Y1 @
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% 97.29/12.83 inference('cnf', [status(esa)], [zf_stmt_0])).
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% 97.29/12.83 ((
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% 97.29/12.83 ((
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% 97.29/12.83 ((
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% 97.29/12.83 ((
% 97.29/12.83 (exu__Cong) =>
% 97.29/12.83 ((
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% 97.29/12.83 ((
% 97.29/12.83 (setunion__Cong) =>
% 97.29/12.83 ((
% 97.29/12.83 (omega__Cong) =>
% 97.29/12.83 ((
% 97.29/12.83 (exuEu) =>
% 97.29/12.83 ((
% 97.29/12.83 (descr__Cong) =>
% 97.29/12.83 ((
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% 97.29/12.83 ((
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% 97.29/12.83 ((
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% 97.29/12.83 ((
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% 97.29/12.83 ((
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% 97.29/12.83 ((
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% 97.29/12.83 ((
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% 97.29/12.83 ((
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% 97.29/12.83 ((
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% 97.29/12.83 ((
% 97.29/12.83 (upairset2IR) =>
% 97.29/12.83 ((
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% 97.29/12.83 ((
% 97.29/12.83 (binunionEcases) =>
% 97.29/12.83 ((
% 97.29/12.83 (binunionE) =>
% 97.29/12.83 ((
% 97.29/12.83 (binunionLsub) =>
% 97.29/12.83 ((
% 97.29/12.83 (binunionRsub) =>
% 97.29/12.83 ((
% 97.29/12.83 (binintersectI) =>
% 97.29/12.83 ((
% 97.29/12.83 (binintersectSubset5) =>
% 97.29/12.83 ((
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% 97.29/12.83 ((
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% 97.29/12.83 ((
% 97.29/12.83 (binintersectSubset3) =>
% 97.29/12.83 ((
% 97.29/12.83 (binintersectER) =>
% 97.29/12.83 ((
% 97.29/12.83 (disjointsetsI1) =>
% 97.29/12.83 ((
% 97.29/12.83 (binintersectRsub) =>
% 97.29/12.83 ((
% 97.29/12.83 (binintersectSubset4) =>
% 97.29/12.83 ((
% 97.29/12.83 (binintersectSubset1) =>
% 97.29/12.83 ((
% 97.29/12.83 (bs114d) =>
% 97.29/12.83 ((
% 97.29/12.83 (setminusI) =>
% 97.29/12.83 ((
% 97.29/12.83 (setminusEL) =>
% 97.29/12.83 ((
% 97.29/12.83 (setminusER) =>
% 97.29/12.83 ((
% 97.29/12.83 (setminusSubset2) =>
% 97.29/12.83 ((
% 97.29/12.83 (setminusERneg) =>
% 97.29/12.83 ((
% 97.29/12.83 (setminusELneg) =>
% 97.29/12.83 ((
% 97.29/12.83 (setminusILneg) =>
% 97.29/12.83 ((
% 97.29/12.83 (setminusIRneg) =>
% 97.29/12.83 ((
% 97.29/12.83 (setminusLsub) =>
% 97.29/12.83 ((
% 97.29/12.83 (setminusSubset1) =>
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% 97.29/12.83 ((
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% 97.29/12.83 ((
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% 97.29/12.83 ((
% 97.29/12.83 (symdiffIneg2) =>
% 97.29/12.83 ((
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% 97.29/12.83 ((
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% 97.29/12.83 ((
% 97.29/12.83 (singletoninpowunion) =>
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% 97.29/12.83 ((
% 97.29/12.83 (upairsubunion) =>
% 97.29/12.83 ((
% 97.29/12.83 (upairinpowunion) =>
% 97.29/12.83 ((
% 97.29/12.83 (ubforcartprodlem1) =>
% 97.29/12.83 ((
% 97.29/12.83 (ubforcartprodlem2) =>
% 97.29/12.83 ((
% 97.29/12.83 (ubforcartprodlem3) =>
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% 97.29/12.83 ((
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% 97.29/12.83 ((
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% 97.29/12.83 ((
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% 97.29/12.83 (kpairsurjEq) =>
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% 97.29/12.83 ((
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% 97.29/12.83 ((
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% 97.29/12.84 (breln1all2) =>
% 97.29/12.84 ((
% 97.29/12.84 (breln1SetBreln1) =>
% 97.29/12.84 ((
% 97.29/12.84 (choice2fnsingleton) =>
% 97.29/12.84 ((
% 97.29/12.84 (!!) @ (
% 97.29/12.84 (('#B') @ (
% 97.29/12.84 !!) @
% 97.29/12.84 (
% 97.29/12.84 (
% 97.29/12.84 ('#S') @ (
% 97.29/12.84 (
% 97.29/12.84 ('#B') @ (
% 97.29/12.84 '#B') @
% 97.29/12.84 breln1)) @
% 97.29/12.84 (
% 97.29/12.84 (
% 97.29/12.84 ('#S') @ dpsetconstr @
% 97.29/12.84 (
% 97.29/12.84 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.29/12.84 inference('lams2combs', [status(thm)], [zip_derived_cl0])).
% 97.29/12.84 thf(omega0Ax, axiom,(( omega0Ax ) = ((in @ emptyset @ omega)))).
% 97.29/12.84 thf('0', plain, (( omega0Ax ) = ( in @ emptyset @ omega )),
% 97.29/12.84 define([status(thm)])).
% 97.29/12.84 thf(emptyinunitempty, axiom,(( emptyinunitempty ) =
% 97.29/12.84 ((in @ emptyset @ (setadjoin @ emptyset @ emptyset))))).
% 97.29/12.84 thf('1', plain,
% 97.29/12.84 (( emptyinunitempty ) =
% 97.29/12.84 ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )),
% 97.29/12.84 define([status(thm)])).
% 97.29/12.84 thf(emptyset__Cong, axiom,(( emptyset__Cong ) =
% 97.29/12.84 ((((emptyset) = (emptyset)))))).
% 97.29/12.84 thf('2', plain, (( emptyset__Cong ) = ( ( emptyset ) = ( emptyset ) )),
% 97.29/12.84 define([status(thm)])).
% 97.29/12.84 thf(omega__Cong, axiom,(( omega__Cong ) = ((((omega) = (omega)))))).
% 97.29/12.84 thf('3', plain, (( omega__Cong ) = ( ( omega ) = ( omega ) )),
% 97.29/12.84 define([status(thm)])).
% 97.29/12.84 thf(zip_derived_cl2, plain,
% 97.29/12.84 (~ (((setextAx) =>
% 97.29/12.84 (((emptysetAx) =>
% 97.29/12.84 (((setadjoinAx) =>
% 97.29/12.84 (((powersetAx) =>
% 97.29/12.84 (((setunionAx) =>
% 97.29/12.84 (((in @ emptyset @ omega) =>
% 97.29/12.84 (((omegaSAx) =>
% 97.29/12.84 (((omegaIndAx) =>
% 97.29/12.84 (((replAx) =>
% 97.29/12.84 (((foundationAx) =>
% 97.29/12.84 (((wellorderingAx) =>
% 97.29/12.84 (((descrp) =>
% 97.29/12.84 (((dsetconstrI) =>
% 97.29/12.84 (((dsetconstrEL) =>
% 97.29/12.84 (((dsetconstrER) =>
% 97.29/12.84 (((exuE1) =>
% 97.29/12.84 (((prop2setE) =>
% 97.29/12.84 (((emptysetE) =>
% 97.29/12.84 (((emptysetimpfalse) =>
% 97.29/12.84 (((notinemptyset) =>
% 97.29/12.84 (((exuE3e) =>
% 97.29/12.84 (((setext) =>
% 97.29/12.84 (((emptyI) =>
% 97.29/12.84 (((noeltsimpempty) =>
% 97.29/12.84 (((setbeta) =>
% 97.29/12.84 (((nonemptyE1) =>
% 97.29/12.84 (((nonemptyI) =>
% 97.29/12.84 (((nonemptyI1) =>
% 97.29/12.84 (((setadjoinIL) =>
% 97.29/12.84 (((in @
% 97.29/12.84 emptyset @
% 97.29/12.84 (setadjoin @
% 97.29/12.84 emptyset @
% 97.29/12.84 emptyset)) =>
% 97.29/12.84 ((
% 97.29/12.84 (setadjoinIR) =>
% 97.29/12.84 ((
% 97.29/12.84 (setadjoinE) =>
% 97.29/12.84 ((
% 97.29/12.84 (setadjoinOr) =>
% 97.29/12.84 ((
% 97.29/12.84 (setoftrueEq) =>
% 97.29/12.84 ((
% 97.29/12.84 (powersetI) =>
% 97.29/12.84 ((
% 97.29/12.84 (emptyinPowerset) =>
% 97.29/12.84 ((
% 97.29/12.84 (emptyInPowerset) =>
% 97.29/12.84 ((
% 97.29/12.84 (powersetE) =>
% 97.29/12.84 ((
% 97.29/12.84 (setunionI) =>
% 97.29/12.84 ((
% 97.29/12.84 (setunionE) =>
% 97.29/12.84 ((
% 97.29/12.84 (subPowSU) =>
% 97.29/12.84 ((
% 97.29/12.84 (exuE2) =>
% 97.29/12.84 ((
% 97.29/12.84 (nonemptyImpWitness) =>
% 97.29/12.84 ((
% 97.29/12.84 (uniqinunit) =>
% 97.29/12.84 ((
% 97.29/12.84 (notinsingleton) =>
% 97.29/12.84 ((
% 97.29/12.84 (eqinunit) =>
% 97.29/12.84 ((
% 97.29/12.84 (singletonsswitch) =>
% 97.29/12.84 ((
% 97.29/12.84 (upairsetE) =>
% 97.29/12.84 ((
% 97.29/12.84 (upairsetIL) =>
% 97.29/12.84 ((
% 97.29/12.84 (upairsetIR) =>
% 97.29/12.84 ((
% 97.29/12.84 (emptyE1) =>
% 97.29/12.84 ((
% 97.29/12.84 (vacuousDall) =>
% 97.29/12.84 ((
% 97.29/12.84 (quantDeMorgan1) =>
% 97.29/12.84 ((
% 97.29/12.84 (quantDeMorgan2) =>
% 97.29/12.84 ((
% 97.29/12.84 (quantDeMorgan3) =>
% 97.29/12.84 ((
% 97.29/12.84 (quantDeMorgan4) =>
% 97.29/12.84 ((
% 97.29/12.84 (prop2setI) =>
% 97.29/12.84 ((
% 97.29/12.84 (prop2set2propI) =>
% 97.29/12.84 ((
% 97.29/12.84 (notdexE) =>
% 97.29/12.84 ((
% 97.29/12.84 (notdallE) =>
% 97.29/12.84 ((
% 97.29/12.84 (exuI1) =>
% 97.29/12.84 ((
% 97.29/12.84 (exuI3) =>
% 97.29/12.84 ((
% 97.29/12.84 (exuI2) =>
% 97.29/12.84 ((
% 97.29/12.84 (inCongP) =>
% 97.29/12.84 ((
% 97.29/12.84 (in__Cong) =>
% 97.29/12.84 ((
% 97.29/12.84 (exuE3u) =>
% 97.29/12.84 ((
% 97.29/12.84 (exu__Cong) =>
% 97.29/12.84 ((
% 97.29/12.84 ((
% 97.29/12.84 (emptyset) =
% 97.29/12.84 (emptyset))) =>
% 97.29/12.84 ((
% 97.29/12.84 (setadjoin__Cong) =>
% 97.29/12.84 ((
% 97.29/12.84 (powerset__Cong) =>
% 97.29/12.84 ((
% 97.29/12.84 (setunion__Cong) =>
% 97.29/12.84 ((
% 97.29/12.84 ((
% 97.29/12.84 (omega) =
% 97.29/12.84 (omega))) =>
% 97.29/12.84 ((
% 97.29/12.84 (exuEu) =>
% 97.29/12.84 ((
% 97.29/12.84 (descr__Cong) =>
% 97.29/12.84 ((
% 97.29/12.84 (dsetconstr__Cong) =>
% 97.29/12.84 ((
% 97.29/12.84 (subsetI1) =>
% 97.29/12.84 ((
% 97.29/12.84 (eqimpsubset2) =>
% 97.29/12.84 ((
% 97.29/12.84 (eqimpsubset1) =>
% 97.29/12.84 ((
% 97.29/12.84 (subsetI2) =>
% 97.29/12.84 ((
% 97.29/12.84 (emptysetsubset) =>
% 97.29/12.84 ((
% 97.29/12.84 (subsetE) =>
% 97.29/12.84 ((
% 97.29/12.84 (subsetE2) =>
% 97.29/12.84 ((
% 97.29/12.84 (notsubsetI) =>
% 97.29/12.84 ((
% 97.29/12.84 (notequalI1) =>
% 97.29/12.84 ((
% 97.29/12.84 (notequalI2) =>
% 97.29/12.84 ((
% 97.29/12.84 (subsetRefl) =>
% 97.29/12.84 ((
% 97.29/12.84 (subsetTrans) =>
% 97.29/12.84 ((
% 97.29/12.84 (setadjoinSub) =>
% 97.29/12.84 ((
% 97.29/12.84 (setadjoinSub2) =>
% 97.29/12.84 ((
% 97.29/12.84 (subset2powerset) =>
% 97.29/12.84 ((
% 97.29/12.84 (setextsub) =>
% 97.29/12.84 ((
% 97.29/12.84 (subsetemptysetimpeq) =>
% 97.29/12.84 ((
% 97.29/12.84 (powersetI1) =>
% 97.29/12.84 ((
% 97.29/12.84 (powersetE1) =>
% 97.29/12.84 ((
% 97.29/12.84 (inPowerset) =>
% 97.29/12.84 ((
% 97.29/12.84 (powersetsubset) =>
% 97.29/12.84 ((
% 97.29/12.84 (sepInPowerset) =>
% 97.29/12.84 ((
% 97.29/12.84 (sepSubset) =>
% 97.29/12.84 ((
% 97.29/12.84 (binunionIL) =>
% 97.29/12.84 ((
% 97.29/12.84 (upairset2IR) =>
% 97.29/12.84 ((
% 97.29/12.84 (binunionIR) =>
% 97.29/12.84 ((
% 97.29/12.84 (binunionEcases) =>
% 97.29/12.84 ((
% 97.29/12.84 (binunionE) =>
% 97.29/12.84 ((
% 97.29/12.84 (binunionLsub) =>
% 97.29/12.84 ((
% 97.29/12.84 (binunionRsub) =>
% 97.29/12.84 ((
% 97.29/12.84 (binintersectI) =>
% 97.29/12.84 ((
% 97.29/12.84 (binintersectSubset5) =>
% 97.29/12.84 ((
% 97.29/12.84 (binintersectEL) =>
% 97.29/12.84 ((
% 97.29/12.84 (binintersectLsub) =>
% 97.29/12.84 ((
% 97.29/12.84 (binintersectSubset2) =>
% 97.29/12.84 ((
% 97.29/12.84 (binintersectSubset3) =>
% 97.29/12.84 ((
% 97.29/12.84 (binintersectER) =>
% 97.29/12.84 ((
% 97.29/12.84 (disjointsetsI1) =>
% 97.29/12.84 ((
% 97.29/12.84 (binintersectRsub) =>
% 97.29/12.84 ((
% 97.29/12.84 (binintersectSubset4) =>
% 97.29/12.84 ((
% 97.29/12.84 (binintersectSubset1) =>
% 97.29/12.84 ((
% 97.29/12.84 (bs114d) =>
% 97.29/12.84 ((
% 97.29/12.84 (setminusI) =>
% 97.29/12.84 ((
% 97.29/12.84 (setminusEL) =>
% 97.29/12.84 ((
% 97.29/12.84 (setminusER) =>
% 97.29/12.84 ((
% 97.29/12.84 (setminusSubset2) =>
% 97.29/12.84 ((
% 97.29/12.84 (setminusERneg) =>
% 97.29/12.84 ((
% 97.29/12.84 (setminusELneg) =>
% 97.29/12.84 ((
% 97.29/12.84 (setminusILneg) =>
% 97.29/12.84 ((
% 97.29/12.84 (setminusIRneg) =>
% 97.29/12.84 ((
% 97.29/12.84 (setminusLsub) =>
% 97.29/12.84 ((
% 97.29/12.84 (setminusSubset1) =>
% 97.29/12.84 ((
% 97.29/12.84 (symdiffE) =>
% 97.29/12.84 ((
% 97.29/12.84 (symdiffI1) =>
% 97.29/12.84 ((
% 97.29/12.84 (symdiffI2) =>
% 97.29/12.84 ((
% 97.29/12.84 (symdiffIneg1) =>
% 97.29/12.84 ((
% 97.29/12.84 (symdiffIneg2) =>
% 97.29/12.84 ((
% 97.29/12.84 (secondinupair) =>
% 97.29/12.84 ((
% 97.29/12.84 (setukpairIL) =>
% 97.29/12.84 ((
% 97.29/12.84 (setukpairIR) =>
% 97.29/12.84 ((
% 97.29/12.84 (kpairiskpair) =>
% 97.29/12.84 ((
% 97.29/12.84 (kpairp) =>
% 97.29/12.84 ((
% 97.29/12.84 (singletonsubset) =>
% 97.29/12.84 ((
% 97.29/12.84 (singletoninpowerset) =>
% 97.29/12.84 ((
% 97.29/12.84 (singletoninpowunion) =>
% 97.29/12.84 ((
% 97.29/12.84 (upairset2E) =>
% 97.29/12.84 ((
% 97.29/12.84 (upairsubunion) =>
% 97.29/12.84 ((
% 97.29/12.84 (upairinpowunion) =>
% 97.29/12.84 ((
% 97.29/12.84 (ubforcartprodlem1) =>
% 97.29/12.84 ((
% 97.29/12.84 (ubforcartprodlem2) =>
% 97.29/12.84 ((
% 97.29/12.84 (ubforcartprodlem3) =>
% 97.29/12.84 ((
% 97.29/12.84 (cartprodpairin) =>
% 97.29/12.84 ((
% 97.29/12.84 (cartprodmempair1) =>
% 97.29/12.84 ((
% 97.29/12.84 (cartprodmempair) =>
% 97.29/12.84 ((
% 97.29/12.84 (setunionE2) =>
% 97.29/12.84 ((
% 97.29/12.84 (setunionsingleton1) =>
% 97.29/12.84 ((
% 97.29/12.84 (setunionsingleton2) =>
% 97.29/12.84 ((
% 97.29/12.84 (setunionsingleton) =>
% 97.29/12.84 ((
% 97.29/12.84 (singletonprop) =>
% 97.29/12.84 ((
% 97.29/12.84 (ex1E1) =>
% 97.29/12.84 ((
% 97.29/12.84 (ex1I) =>
% 97.29/12.84 ((
% 97.29/12.84 (ex1I2) =>
% 97.29/12.84 ((
% 97.29/12.84 (singletonsuniq) =>
% 97.29/12.84 ((
% 97.29/12.84 (setukpairinjL1) =>
% 97.29/12.84 ((
% 97.29/12.84 (kfstsingleton) =>
% 97.29/12.84 ((
% 97.29/12.84 (theprop) =>
% 97.29/12.84 ((
% 97.29/12.84 (kfstpairEq) =>
% 97.29/12.84 ((
% 97.29/12.84 (cartprodfstin) =>
% 97.29/12.84 ((
% 97.29/12.84 (setukpairinjL2) =>
% 97.29/12.84 ((
% 97.29/12.84 (setukpairinjL) =>
% 97.29/12.84 ((
% 97.29/12.84 (setukpairinjR11) =>
% 97.29/12.84 ((
% 97.29/12.84 (setukpairinjR12) =>
% 97.29/12.84 ((
% 97.29/12.84 (setukpairinjR1) =>
% 97.29/12.84 ((
% 97.29/12.84 (upairequniteq) =>
% 97.29/12.84 ((
% 97.29/12.84 (setukpairinjR2) =>
% 97.29/12.84 ((
% 97.29/12.84 (setukpairinjR) =>
% 97.29/12.84 ((
% 97.29/12.84 (ksndsingleton) =>
% 97.29/12.84 ((
% 97.29/12.84 (ksndpairEq) =>
% 97.29/12.84 ((
% 97.29/12.84 (kpairsurjEq) =>
% 97.29/12.84 ((
% 97.29/12.84 (cartprodsndin) =>
% 97.29/12.84 ((
% 97.29/12.84 (cartprodpairmemEL) =>
% 97.29/12.84 ((
% 97.29/12.84 (cartprodpairmemER) =>
% 97.29/12.84 ((
% 97.29/12.84 (cartprodmempaircEq) =>
% 97.29/12.84 ((
% 97.29/12.84 (cartprodfstpairEq) =>
% 97.29/12.84 ((
% 97.29/12.84 (cartprodsndpairEq) =>
% 97.29/12.84 ((
% 97.29/12.84 (cartprodpairsurjEq) =>
% 97.29/12.84 ((
% 97.29/12.84 (dpsetconstrI) =>
% 97.29/12.84 ((
% 97.29/12.84 (dpsetconstrSub) =>
% 97.29/12.84 ((
% 97.29/12.84 (setOfPairsIsBReln) =>
% 97.29/12.84 ((
% 97.29/12.84 (dpsetconstrERa) =>
% 97.29/12.84 ((
% 97.29/12.84 (dpsetconstrEL1) =>
% 97.29/12.84 ((
% 97.29/12.84 (dpsetconstrEL2) =>
% 97.29/12.84 ((
% 97.29/12.84 (dpsetconstrER) =>
% 97.29/12.84 ((
% 97.29/12.84 (funcImageSingleton) =>
% 97.29/12.84 ((
% 97.29/12.84 (apProp) =>
% 97.29/12.84 ((
% 97.29/12.84 (app) =>
% 97.29/12.84 ((
% 97.29/12.84 (infuncsetfunc) =>
% 97.29/12.84 ((
% 97.29/12.84 (ap2p) =>
% 97.29/12.84 ((
% 97.29/12.84 (funcinfuncset) =>
% 97.29/12.84 ((
% 97.29/12.84 (lamProp) =>
% 97.29/12.84 ((
% 97.29/12.84 (lamp) =>
% 97.29/12.84 ((
% 97.29/12.84 (lam2p) =>
% 97.29/12.84 ((
% 97.29/12.84 (brelnall1) =>
% 97.29/12.84 ((
% 97.29/12.84 (brelnall2) =>
% 97.29/12.84 ((
% 97.29/12.84 (ex1E2) =>
% 97.29/12.84 ((
% 97.29/12.84 (funcGraphProp1) =>
% 97.29/12.84 ((
% 97.29/12.84 (funcGraphProp3) =>
% 97.29/12.84 ((
% 97.29/12.84 (funcGraphProp2) =>
% 97.29/12.84 ((
% 97.29/12.84 (funcextLem) =>
% 97.29/12.84 ((
% 97.29/12.84 (funcGraphProp4) =>
% 97.29/12.84 ((
% 97.29/12.84 (subbreln) =>
% 97.29/12.84 ((
% 97.29/12.84 (eqbreln) =>
% 97.29/12.84 ((
% 97.29/12.84 (funcext) =>
% 97.29/12.84 ((
% 97.29/12.84 (funcext2) =>
% 97.29/12.84 ((
% 97.29/12.84 (ap2apEq1) =>
% 97.29/12.84 ((
% 97.29/12.84 (ap2apEq2) =>
% 97.29/12.84 ((
% 97.29/12.84 (beta1) =>
% 97.29/12.84 ((
% 97.29/12.84 (eta1) =>
% 97.29/12.84 ((
% 97.29/12.84 (lam2lamEq) =>
% 97.29/12.84 ((
% 97.29/12.84 (beta2) =>
% 97.29/12.84 ((
% 97.29/12.84 (eta2) =>
% 97.29/12.84 ((
% 97.29/12.84 (iffalseProp1) =>
% 97.29/12.84 ((
% 97.29/12.84 (iffalseProp2) =>
% 97.29/12.84 ((
% 97.29/12.84 (iftrueProp1) =>
% 97.29/12.84 ((
% 97.29/12.84 (iftrueProp2) =>
% 97.29/12.84 ((
% 97.29/12.84 (ifSingleton) =>
% 97.29/12.84 ((
% 97.29/12.84 (ifp) =>
% 97.29/12.84 ((
% 97.29/12.84 (theeq) =>
% 97.29/12.84 ((
% 97.29/12.84 (iftrue) =>
% 97.29/12.84 ((
% 97.29/12.84 (iffalse) =>
% 97.29/12.84 ((
% 97.29/12.84 (iftrueorfalse) =>
% 97.29/12.84 ((
% 97.29/12.84 (binintersectT_lem) =>
% 97.29/12.84 ((
% 97.29/12.84 (binunionT_lem) =>
% 97.29/12.84 ((
% 97.29/12.84 (powersetT_lem) =>
% 97.29/12.84 ((
% 97.29/12.84 (setminusT_lem) =>
% 97.29/12.84 ((
% 97.29/12.84 (complementT_lem) =>
% 97.29/12.84 ((
% 97.29/12.84 (setextT) =>
% 97.29/12.84 ((
% 97.29/12.84 (subsetTI) =>
% 97.29/12.84 ((
% 97.29/12.84 (powersetTI1) =>
% 97.29/12.84 ((
% 97.29/12.84 (powersetTE1) =>
% 97.29/12.84 ((
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% 97.29/12.84 ((
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% 97.29/12.84 ((
% 97.29/12.84 (binintersectTERcontra) =>
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% 97.29/12.84 ((
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% 97.29/12.84 ((
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% 97.29/12.84 ((
% 97.29/12.84 (contrasubsetT3) =>
% 97.29/12.84 ((
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% 97.29/12.84 ((
% 97.29/12.84 (doubleComplementE1) =>
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% 97.29/12.84 ((
% 97.29/12.84 (doubleComplementSub2) =>
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% 97.29/12.84 (complementTnotintersectT) =>
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% 97.29/12.84 (complementInPowersetComplementIntersect) =>
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% 97.29/12.84 ((
% 97.29/12.84 (complementTcontraSubset) =>
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% 97.29/12.84 ((
% 97.29/12.84 (binunionTIRcontra) =>
% 97.29/12.84 ((
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% 97.29/12.84 ((
% 97.29/12.84 (inIntersectImpInUnion2) =>
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% 97.29/12.84 (inIntersectImpInIntersectUnions) =>
% 97.29/12.84 ((
% 97.29/12.84 (intersectInPowersetIntersectUnions) =>
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% 97.29/12.84 (inComplementUnionImpNotIn1) =>
% 97.29/12.84 ((
% 97.29/12.84 (inComplementUnionImpInComplement1) =>
% 97.29/12.84 ((
% 97.29/12.84 (binunionTE) =>
% 97.29/12.84 ((
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% 97.29/12.84 (inComplementUnionImpInComplement1) =>
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% 97.29/12.84 ((
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% 97.29/12.84 ((
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% 97.29/12.84 ((
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% 97.29/12.84 ((
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% 97.29/12.84 ((
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% 97.29/12.84 ((
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% 97.29/12.84 ((
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% 97.29/12.84 ((
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% 97.29/12.84 ((
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% 97.29/12.84 ((
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% 97.29/12.84 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
% 97.29/12.85 (demorgan2a2) =>
% 97.29/12.85 ((
% 97.29/12.85 (demorgan1a) =>
% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
% 97.29/12.85 (demorgan2b) =>
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% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
% 97.29/12.85 (exu__Cong) =>
% 97.29/12.85 ((
% 97.29/12.85 (setadjoin__Cong) =>
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% 97.29/12.85 ((
% 97.29/12.85 (setunion__Cong) =>
% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
% 97.29/12.85 (binintersectSubset2) =>
% 97.29/12.85 ((
% 97.29/12.85 (binintersectSubset3) =>
% 97.29/12.85 ((
% 97.29/12.85 (binintersectER) =>
% 97.29/12.85 ((
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% 97.29/12.85 ((
% 97.29/12.85 (binintersectRsub) =>
% 97.29/12.85 ((
% 97.29/12.85 (binintersectSubset4) =>
% 97.29/12.85 ((
% 97.29/12.85 (binintersectSubset1) =>
% 97.29/12.85 ((
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% 97.29/12.85 ((
% 97.29/12.85 (setminusI) =>
% 97.29/12.85 ((
% 97.29/12.85 (setminusEL) =>
% 97.29/12.85 ((
% 97.29/12.85 (setminusER) =>
% 97.29/12.85 ((
% 97.29/12.85 (setminusSubset2) =>
% 97.29/12.85 ((
% 97.29/12.85 (setminusERneg) =>
% 97.29/12.85 ((
% 97.29/12.85 (setminusELneg) =>
% 97.29/12.85 ((
% 97.29/12.85 (setminusILneg) =>
% 97.29/12.85 ((
% 97.29/12.85 (setminusIRneg) =>
% 97.29/12.85 ((
% 97.29/12.85 (setminusLsub) =>
% 97.29/12.85 ((
% 97.29/12.85 (setminusSubset1) =>
% 97.29/12.85 ((
% 97.29/12.85 (symdiffE) =>
% 97.29/12.85 ((
% 97.29/12.85 (symdiffI1) =>
% 97.29/12.85 ((
% 97.29/12.85 (symdiffI2) =>
% 97.29/12.85 ((
% 97.29/12.85 (symdiffIneg1) =>
% 97.29/12.85 ((
% 97.29/12.85 (symdiffIneg2) =>
% 97.29/12.85 ((
% 97.29/12.85 (secondinupair) =>
% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
% 97.29/12.85 (ubforcartprodlem3) =>
% 97.29/12.85 ((
% 97.29/12.85 (cartprodpairin) =>
% 97.29/12.85 ((
% 97.29/12.85 (cartprodmempair1) =>
% 97.29/12.85 ((
% 97.29/12.85 (cartprodmempair) =>
% 97.29/12.85 ((
% 97.29/12.85 (setunionE2) =>
% 97.29/12.85 ((
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% 97.29/12.85 ((
% 97.29/12.85 (setunionsingleton2) =>
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% 97.29/12.85 ((
% 97.29/12.85 (demorgan1a) =>
% 97.29/12.85 ((
% 97.29/12.85 (demorgan1b) =>
% 97.29/12.85 ((
% 97.29/12.85 (demorgan1) =>
% 97.29/12.85 ((
% 97.29/12.85 (demorgan2a) =>
% 97.29/12.85 ((
% 97.29/12.85 (demorgan2b2) =>
% 97.29/12.85 ((
% 97.29/12.85 (demorgan2b) =>
% 97.29/12.85 ((
% 97.29/12.85 (demorgan2) =>
% 97.29/12.85 ((
% 97.29/12.85 (woz13rule0) =>
% 97.29/12.85 ((
% 97.29/12.85 (woz13rule1) =>
% 97.29/12.85 ((
% 97.29/12.85 (woz13rule2) =>
% 97.29/12.85 ((
% 97.29/12.85 (woz13rule3) =>
% 97.29/12.85 ((
% 97.29/12.85 (woz13rule4) =>
% 97.29/12.85 ((
% 97.29/12.85 (woz1_1) =>
% 97.29/12.85 ((
% 97.29/12.85 (woz1_2) =>
% 97.29/12.85 ((
% 97.29/12.85 (woz1_3) =>
% 97.29/12.85 ((
% 97.29/12.85 (woz1_4) =>
% 97.29/12.85 ((
% 97.29/12.85 (woz1_5) =>
% 97.29/12.85 ((
% 97.29/12.85 (breln1all2) =>
% 97.29/12.85 ((
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% 97.29/12.85 (
% 97.29/12.85 (
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% 97.29/12.85 (
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% 97.29/12.85 (
% 97.29/12.85 (
% 97.29/12.85 ('#S') @ dpsetconstr @
% 97.29/12.85 (
% 97.29/12.85 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.29/12.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl25])).
% 97.29/12.85 thf(zip_derived_cl40, plain,
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% 97.29/12.85 (setadjoin @ emptyset @
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% 97.29/12.85 (((setadjoinIR) =>
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% 97.29/12.85 (((setoftrueEq) =>
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% 97.29/12.85 (((emptyinPowerset) =>
% 97.29/12.85 (((emptyInPowerset) =>
% 97.29/12.85 ((
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% 97.29/12.85 ((
% 97.29/12.85 (setunionE) =>
% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
% 97.29/12.85 (upairsetIR) =>
% 97.29/12.85 ((
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% 97.29/12.85 ((
% 97.29/12.85 (vacuousDall) =>
% 97.29/12.85 ((
% 97.29/12.85 (quantDeMorgan1) =>
% 97.29/12.85 ((
% 97.29/12.85 (quantDeMorgan2) =>
% 97.29/12.85 ((
% 97.29/12.85 (quantDeMorgan3) =>
% 97.29/12.85 ((
% 97.29/12.85 (quantDeMorgan4) =>
% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
% 97.29/12.85 (exuI3) =>
% 97.29/12.85 ((
% 97.29/12.85 (exuI2) =>
% 97.29/12.85 ((
% 97.29/12.85 (inCongP) =>
% 97.29/12.85 ((
% 97.29/12.85 (in__Cong) =>
% 97.29/12.85 ((
% 97.29/12.85 (exuE3u) =>
% 97.29/12.85 ((
% 97.29/12.85 (exu__Cong) =>
% 97.29/12.85 ((
% 97.29/12.85 (setadjoin__Cong) =>
% 97.29/12.85 ((
% 97.29/12.85 (powerset__Cong) =>
% 97.29/12.85 ((
% 97.29/12.85 (setunion__Cong) =>
% 97.29/12.85 ((
% 97.29/12.85 (exuEu) =>
% 97.29/12.85 ((
% 97.29/12.85 (descr__Cong) =>
% 97.29/12.85 ((
% 97.29/12.85 (dsetconstr__Cong) =>
% 97.29/12.85 ((
% 97.29/12.85 (subsetI1) =>
% 97.29/12.85 ((
% 97.29/12.85 (eqimpsubset2) =>
% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
% 97.29/12.85 (subsetE2) =>
% 97.29/12.85 ((
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% 97.29/12.85 ((
% 97.29/12.85 (notequalI1) =>
% 97.29/12.85 ((
% 97.29/12.85 (notequalI2) =>
% 97.29/12.85 ((
% 97.29/12.85 (subsetRefl) =>
% 97.29/12.85 ((
% 97.29/12.85 (subsetTrans) =>
% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
% 97.29/12.85 (powersetE1) =>
% 97.29/12.85 ((
% 97.29/12.85 (inPowerset) =>
% 97.29/12.85 ((
% 97.29/12.85 (powersetsubset) =>
% 97.29/12.85 ((
% 97.29/12.85 (sepInPowerset) =>
% 97.29/12.85 ((
% 97.29/12.85 (sepSubset) =>
% 97.29/12.85 ((
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% 97.29/12.85 ((
% 97.29/12.85 (upairset2IR) =>
% 97.29/12.85 ((
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% 97.29/12.85 ((
% 97.29/12.85 (binunionEcases) =>
% 97.29/12.85 ((
% 97.29/12.85 (binunionE) =>
% 97.29/12.85 ((
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% 97.29/12.85 ((
% 97.29/12.85 (binunionRsub) =>
% 97.29/12.85 ((
% 97.29/12.85 (binintersectI) =>
% 97.29/12.85 ((
% 97.29/12.85 (binintersectSubset5) =>
% 97.29/12.85 ((
% 97.29/12.85 (binintersectEL) =>
% 97.29/12.85 ((
% 97.29/12.85 (binintersectLsub) =>
% 97.29/12.85 ((
% 97.29/12.85 (binintersectSubset2) =>
% 97.29/12.85 ((
% 97.29/12.85 (binintersectSubset3) =>
% 97.29/12.85 ((
% 97.29/12.85 (binintersectER) =>
% 97.29/12.85 ((
% 97.29/12.85 (disjointsetsI1) =>
% 97.29/12.85 ((
% 97.29/12.85 (binintersectRsub) =>
% 97.29/12.85 ((
% 97.29/12.85 (binintersectSubset4) =>
% 97.29/12.85 ((
% 97.29/12.85 (binintersectSubset1) =>
% 97.29/12.85 ((
% 97.29/12.85 (bs114d) =>
% 97.29/12.85 ((
% 97.29/12.85 (setminusI) =>
% 97.29/12.85 ((
% 97.29/12.85 (setminusEL) =>
% 97.29/12.85 ((
% 97.29/12.85 (setminusER) =>
% 97.29/12.85 ((
% 97.29/12.85 (setminusSubset2) =>
% 97.29/12.85 ((
% 97.29/12.85 (setminusERneg) =>
% 97.29/12.85 ((
% 97.29/12.85 (setminusELneg) =>
% 97.29/12.85 ((
% 97.29/12.85 (setminusILneg) =>
% 97.29/12.85 ((
% 97.29/12.85 (setminusIRneg) =>
% 97.29/12.85 ((
% 97.29/12.85 (setminusLsub) =>
% 97.29/12.85 ((
% 97.29/12.85 (setminusSubset1) =>
% 97.29/12.85 ((
% 97.29/12.85 (symdiffE) =>
% 97.29/12.85 ((
% 97.29/12.85 (symdiffI1) =>
% 97.29/12.85 ((
% 97.29/12.85 (symdiffI2) =>
% 97.29/12.85 ((
% 97.29/12.85 (symdiffIneg1) =>
% 97.29/12.85 ((
% 97.29/12.85 (symdiffIneg2) =>
% 97.29/12.85 ((
% 97.29/12.85 (secondinupair) =>
% 97.29/12.85 ((
% 97.29/12.85 (setukpairIL) =>
% 97.29/12.85 ((
% 97.29/12.85 (setukpairIR) =>
% 97.29/12.85 ((
% 97.29/12.85 (kpairiskpair) =>
% 97.29/12.85 ((
% 97.29/12.85 (kpairp) =>
% 97.29/12.85 ((
% 97.29/12.85 (singletonsubset) =>
% 97.29/12.85 ((
% 97.29/12.85 (singletoninpowerset) =>
% 97.29/12.85 ((
% 97.29/12.85 (singletoninpowunion) =>
% 97.29/12.85 ((
% 97.29/12.85 (upairset2E) =>
% 97.29/12.85 ((
% 97.29/12.85 (upairsubunion) =>
% 97.29/12.85 ((
% 97.29/12.85 (upairinpowunion) =>
% 97.29/12.85 ((
% 97.29/12.85 (ubforcartprodlem1) =>
% 97.29/12.85 ((
% 97.29/12.85 (ubforcartprodlem2) =>
% 97.29/12.85 ((
% 97.29/12.85 (ubforcartprodlem3) =>
% 97.29/12.85 ((
% 97.29/12.85 (cartprodpairin) =>
% 97.29/12.85 ((
% 97.29/12.85 (cartprodmempair1) =>
% 97.29/12.85 ((
% 97.29/12.85 (cartprodmempair) =>
% 97.29/12.85 ((
% 97.29/12.85 (setunionE2) =>
% 97.29/12.85 ((
% 97.29/12.85 (setunionsingleton1) =>
% 97.29/12.85 ((
% 97.29/12.85 (setunionsingleton2) =>
% 97.29/12.85 ((
% 97.29/12.85 (setunionsingleton) =>
% 97.29/12.85 ((
% 97.29/12.85 (singletonprop) =>
% 97.29/12.85 ((
% 97.29/12.85 (ex1E1) =>
% 97.29/12.85 ((
% 97.29/12.85 (ex1I) =>
% 97.29/12.85 ((
% 97.29/12.85 (ex1I2) =>
% 97.29/12.85 ((
% 97.29/12.85 (singletonsuniq) =>
% 97.29/12.85 ((
% 97.29/12.85 (setukpairinjL1) =>
% 97.29/12.85 ((
% 97.29/12.85 (kfstsingleton) =>
% 97.29/12.85 ((
% 97.29/12.85 (theprop) =>
% 97.29/12.85 ((
% 97.29/12.85 (kfstpairEq) =>
% 97.29/12.85 ((
% 97.29/12.85 (cartprodfstin) =>
% 97.29/12.85 ((
% 97.29/12.85 (setukpairinjL2) =>
% 97.29/12.85 ((
% 97.29/12.85 (setukpairinjL) =>
% 97.29/12.85 ((
% 97.29/12.85 (setukpairinjR11) =>
% 97.29/12.85 ((
% 97.29/12.85 (setukpairinjR12) =>
% 97.29/12.85 ((
% 97.29/12.85 (setukpairinjR1) =>
% 97.29/12.85 ((
% 97.29/12.85 (upairequniteq) =>
% 97.29/12.85 ((
% 97.29/12.85 (setukpairinjR2) =>
% 97.29/12.85 ((
% 97.29/12.85 (setukpairinjR) =>
% 97.29/12.85 ((
% 97.29/12.85 (ksndsingleton) =>
% 97.29/12.85 ((
% 97.29/12.85 (ksndpairEq) =>
% 97.29/12.85 ((
% 97.29/12.85 (kpairsurjEq) =>
% 97.29/12.85 ((
% 97.29/12.85 (cartprodsndin) =>
% 97.29/12.85 ((
% 97.29/12.85 (cartprodpairmemEL) =>
% 97.29/12.85 ((
% 97.29/12.85 (cartprodpairmemER) =>
% 97.29/12.85 ((
% 97.29/12.85 (cartprodmempaircEq) =>
% 97.29/12.85 ((
% 97.29/12.85 (cartprodfstpairEq) =>
% 97.29/12.85 ((
% 97.29/12.85 (cartprodsndpairEq) =>
% 97.29/12.85 ((
% 97.29/12.85 (cartprodpairsurjEq) =>
% 97.29/12.85 ((
% 97.29/12.85 (dpsetconstrI) =>
% 97.29/12.85 ((
% 97.29/12.85 (dpsetconstrSub) =>
% 97.29/12.85 ((
% 97.29/12.85 (setOfPairsIsBReln) =>
% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
% 97.29/12.85 (dpsetconstrEL2) =>
% 97.29/12.85 ((
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% 97.29/12.85 ((
% 97.29/12.85 (funcImageSingleton) =>
% 97.29/12.85 ((
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% 97.29/12.85 ((
% 97.29/12.85 (app) =>
% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl46])).
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% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
% 97.29/12.85 (setminusILneg) =>
% 97.29/12.85 ((
% 97.29/12.85 (setminusIRneg) =>
% 97.29/12.85 ((
% 97.29/12.85 (setminusLsub) =>
% 97.29/12.85 ((
% 97.29/12.85 (setminusSubset1) =>
% 97.29/12.85 ((
% 97.29/12.85 (symdiffE) =>
% 97.29/12.85 ((
% 97.29/12.85 (symdiffI1) =>
% 97.29/12.85 ((
% 97.29/12.85 (symdiffI2) =>
% 97.29/12.85 ((
% 97.29/12.85 (symdiffIneg1) =>
% 97.29/12.85 ((
% 97.29/12.85 (symdiffIneg2) =>
% 97.29/12.85 ((
% 97.29/12.85 (secondinupair) =>
% 97.29/12.85 ((
% 97.29/12.85 (setukpairIL) =>
% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
% 97.29/12.85 (kpairp) =>
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% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 (cartprodmempair) =>
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% 97.29/12.85 ((
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% 97.29/12.85 breln1)) @
% 97.29/12.85 (
% 97.29/12.85 (
% 97.29/12.85 ('#S') @ dpsetconstr @
% 97.29/12.85 (
% 97.29/12.85 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.29/12.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl52])).
% 97.29/12.85 thf(zip_derived_cl64, plain,
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% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
% 97.29/12.85 (descr__Cong) =>
% 97.29/12.85 ((
% 97.29/12.85 (dsetconstr__Cong) =>
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% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
% 97.29/12.85 (binintersectSubset3) =>
% 97.29/12.85 ((
% 97.29/12.85 (binintersectER) =>
% 97.29/12.85 ((
% 97.29/12.85 (disjointsetsI1) =>
% 97.29/12.85 ((
% 97.29/12.85 (binintersectRsub) =>
% 97.29/12.85 ((
% 97.29/12.85 (binintersectSubset4) =>
% 97.29/12.85 ((
% 97.29/12.85 (binintersectSubset1) =>
% 97.29/12.85 ((
% 97.29/12.85 (bs114d) =>
% 97.29/12.85 ((
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% 97.29/12.85 ((
% 97.29/12.85 (setminusEL) =>
% 97.29/12.85 ((
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% 97.29/12.85 ((
% 97.29/12.85 (setminusSubset2) =>
% 97.29/12.85 ((
% 97.29/12.85 (setminusERneg) =>
% 97.29/12.85 ((
% 97.29/12.85 (setminusELneg) =>
% 97.29/12.85 ((
% 97.29/12.85 (setminusILneg) =>
% 97.29/12.85 ((
% 97.29/12.85 (setminusIRneg) =>
% 97.29/12.85 ((
% 97.29/12.85 (setminusLsub) =>
% 97.29/12.85 ((
% 97.29/12.85 (setminusSubset1) =>
% 97.29/12.85 ((
% 97.29/12.85 (symdiffE) =>
% 97.29/12.85 ((
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% 97.29/12.85 ((
% 97.29/12.85 (symdiffI2) =>
% 97.29/12.85 ((
% 97.29/12.85 (symdiffIneg1) =>
% 97.29/12.85 ((
% 97.29/12.85 (symdiffIneg2) =>
% 97.29/12.85 ((
% 97.29/12.85 (secondinupair) =>
% 97.29/12.85 ((
% 97.29/12.85 (setukpairIL) =>
% 97.29/12.85 ((
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% 97.29/12.85 ((
% 97.29/12.85 (kpairiskpair) =>
% 97.29/12.85 ((
% 97.29/12.85 (kpairp) =>
% 97.29/12.85 ((
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% 97.29/12.85 ((
% 97.29/12.85 (singletoninpowerset) =>
% 97.29/12.85 ((
% 97.29/12.85 (singletoninpowunion) =>
% 97.29/12.85 ((
% 97.29/12.85 (upairset2E) =>
% 97.29/12.85 ((
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% 97.29/12.85 ((
% 97.29/12.85 (upairinpowunion) =>
% 97.29/12.85 ((
% 97.29/12.85 (ubforcartprodlem1) =>
% 97.29/12.85 ((
% 97.29/12.85 (ubforcartprodlem2) =>
% 97.29/12.85 ((
% 97.29/12.85 (ubforcartprodlem3) =>
% 97.29/12.85 ((
% 97.29/12.85 (cartprodpairin) =>
% 97.29/12.85 ((
% 97.29/12.85 (cartprodmempair1) =>
% 97.29/12.85 ((
% 97.29/12.85 (cartprodmempair) =>
% 97.29/12.85 ((
% 97.29/12.85 (setunionE2) =>
% 97.29/12.85 ((
% 97.29/12.85 (setunionsingleton1) =>
% 97.29/12.85 ((
% 97.29/12.85 (setunionsingleton2) =>
% 97.29/12.85 ((
% 97.29/12.85 (setunionsingleton) =>
% 97.29/12.85 ((
% 97.29/12.85 (singletonprop) =>
% 97.29/12.85 ((
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% 97.29/12.85 ((
% 97.29/12.85 (ex1I) =>
% 97.29/12.85 ((
% 97.29/12.85 (ex1I2) =>
% 97.29/12.85 ((
% 97.29/12.85 (singletonsuniq) =>
% 97.29/12.85 ((
% 97.29/12.85 (setukpairinjL1) =>
% 97.29/12.85 ((
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% 97.29/12.85 ((
% 97.29/12.85 (theprop) =>
% 97.29/12.85 ((
% 97.29/12.85 (kfstpairEq) =>
% 97.29/12.85 ((
% 97.29/12.85 (cartprodfstin) =>
% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 (setukpairinjR12) =>
% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 (setukpairinjR) =>
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% 97.29/12.85 ((
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% 97.29/12.85 ((
% 97.29/12.85 (kpairsurjEq) =>
% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.85 ((
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% 97.29/12.86 ((
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% 97.29/12.86 ((
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% 97.29/12.86 ((
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% 97.29/12.86 ((
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% 97.29/12.86 ((
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% 97.29/12.86 ((
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% 97.29/12.86 ((
% 97.29/12.86 (doubleComplementSub2) =>
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% 97.29/12.86 ((
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% 97.29/12.86 (complementInPowersetComplementIntersect) =>
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% 97.29/12.86 ((
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% 97.29/12.86 ((
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% 97.29/12.86 ((
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% 97.29/12.86 ((
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% 97.29/12.86 ((
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% 97.29/12.86 ((
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% 97.29/12.86 ((
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% 97.29/12.86 ((
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% 97.29/12.86 (
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% 97.29/12.87 (quantDeMorgan2) =>
% 97.29/12.87 ((
% 97.29/12.87 (quantDeMorgan3) =>
% 97.29/12.87 ((
% 97.29/12.87 (quantDeMorgan4) =>
% 97.29/12.87 ((
% 97.29/12.87 (prop2setI) =>
% 97.29/12.87 ((
% 97.29/12.87 (prop2set2propI) =>
% 97.29/12.87 ((
% 97.29/12.87 (notdexE) =>
% 97.29/12.87 ((
% 97.29/12.87 (notdallE) =>
% 97.29/12.87 ((
% 97.29/12.87 (exuI1) =>
% 97.29/12.87 ((
% 97.29/12.87 (exuI3) =>
% 97.29/12.87 ((
% 97.29/12.87 (exuI2) =>
% 97.29/12.87 ((
% 97.29/12.87 (inCongP) =>
% 97.29/12.87 ((
% 97.29/12.87 (in__Cong) =>
% 97.29/12.87 ((
% 97.29/12.87 (exuE3u) =>
% 97.29/12.87 ((
% 97.29/12.87 (exu__Cong) =>
% 97.29/12.87 ((
% 97.29/12.87 (setadjoin__Cong) =>
% 97.29/12.87 ((
% 97.29/12.87 (powerset__Cong) =>
% 97.29/12.87 ((
% 97.29/12.87 (setunion__Cong) =>
% 97.29/12.87 ((
% 97.29/12.87 (exuEu) =>
% 97.29/12.87 ((
% 97.29/12.87 (descr__Cong) =>
% 97.29/12.87 ((
% 97.29/12.87 (dsetconstr__Cong) =>
% 97.29/12.87 ((
% 97.29/12.87 (subsetI1) =>
% 97.29/12.87 ((
% 97.29/12.87 (eqimpsubset2) =>
% 97.29/12.87 ((
% 97.29/12.87 (eqimpsubset1) =>
% 97.29/12.87 ((
% 97.29/12.87 (subsetI2) =>
% 97.29/12.87 ((
% 97.29/12.87 (emptysetsubset) =>
% 97.29/12.87 ((
% 97.29/12.87 (subsetE) =>
% 97.29/12.87 ((
% 97.29/12.87 (subsetE2) =>
% 97.29/12.87 ((
% 97.29/12.87 (notsubsetI) =>
% 97.29/12.87 ((
% 97.29/12.87 (notequalI1) =>
% 97.29/12.87 ((
% 97.29/12.87 (notequalI2) =>
% 97.29/12.87 ((
% 97.29/12.87 (subsetRefl) =>
% 97.29/12.87 ((
% 97.29/12.87 (subsetTrans) =>
% 97.29/12.87 ((
% 97.29/12.87 (setadjoinSub) =>
% 97.29/12.87 ((
% 97.29/12.87 (setadjoinSub2) =>
% 97.29/12.87 ((
% 97.29/12.87 (subset2powerset) =>
% 97.29/12.87 ((
% 97.29/12.87 (setextsub) =>
% 97.29/12.87 ((
% 97.29/12.87 (subsetemptysetimpeq) =>
% 97.29/12.87 ((
% 97.29/12.87 (powersetI1) =>
% 97.29/12.87 ((
% 97.29/12.87 (powersetE1) =>
% 97.29/12.87 ((
% 97.29/12.87 (inPowerset) =>
% 97.29/12.87 ((
% 97.29/12.87 (powersetsubset) =>
% 97.29/12.87 ((
% 97.29/12.87 (sepInPowerset) =>
% 97.29/12.87 ((
% 97.29/12.87 (sepSubset) =>
% 97.29/12.87 ((
% 97.29/12.87 (binunionIL) =>
% 97.29/12.87 ((
% 97.29/12.87 (upairset2IR) =>
% 97.29/12.87 ((
% 97.29/12.87 (binunionIR) =>
% 97.29/12.87 ((
% 97.29/12.87 (binunionEcases) =>
% 97.29/12.87 ((
% 97.29/12.87 (binunionE) =>
% 97.29/12.87 ((
% 97.29/12.87 (binunionLsub) =>
% 97.29/12.87 ((
% 97.29/12.87 (binunionRsub) =>
% 97.29/12.87 ((
% 97.29/12.87 (binintersectI) =>
% 97.29/12.87 ((
% 97.29/12.87 (binintersectSubset5) =>
% 97.29/12.87 ((
% 97.29/12.87 (binintersectEL) =>
% 97.29/12.87 ((
% 97.29/12.87 (binintersectLsub) =>
% 97.29/12.87 ((
% 97.29/12.87 (binintersectSubset2) =>
% 97.29/12.87 ((
% 97.29/12.87 (binintersectSubset3) =>
% 97.29/12.87 ((
% 97.29/12.87 (binintersectER) =>
% 97.29/12.87 ((
% 97.29/12.87 (disjointsetsI1) =>
% 97.29/12.87 ((
% 97.29/12.87 (binintersectRsub) =>
% 97.29/12.87 ((
% 97.29/12.87 (binintersectSubset4) =>
% 97.29/12.87 ((
% 97.29/12.87 (binintersectSubset1) =>
% 97.29/12.87 ((
% 97.29/12.87 (bs114d) =>
% 97.29/12.87 ((
% 97.29/12.87 (setminusI) =>
% 97.29/12.87 ((
% 97.29/12.87 (setminusEL) =>
% 97.29/12.87 ((
% 97.29/12.87 (setminusER) =>
% 97.29/12.87 ((
% 97.29/12.87 (setminusSubset2) =>
% 97.29/12.87 ((
% 97.29/12.87 (setminusERneg) =>
% 97.29/12.87 ((
% 97.29/12.87 (setminusELneg) =>
% 97.29/12.87 ((
% 97.29/12.87 (setminusILneg) =>
% 97.29/12.87 ((
% 97.29/12.87 (setminusIRneg) =>
% 97.29/12.87 ((
% 97.29/12.87 (setminusLsub) =>
% 97.29/12.87 ((
% 97.29/12.87 (setminusSubset1) =>
% 97.29/12.87 ((
% 97.29/12.87 (symdiffE) =>
% 97.29/12.87 ((
% 97.29/12.87 (symdiffI1) =>
% 97.29/12.87 ((
% 97.29/12.87 (symdiffI2) =>
% 97.29/12.87 ((
% 97.29/12.87 (symdiffIneg1) =>
% 97.29/12.87 ((
% 97.29/12.87 (symdiffIneg2) =>
% 97.29/12.87 ((
% 97.29/12.87 (secondinupair) =>
% 97.29/12.87 ((
% 97.29/12.87 (setukpairIL) =>
% 97.29/12.87 ((
% 97.29/12.87 (setukpairIR) =>
% 97.29/12.87 ((
% 97.29/12.87 (kpairiskpair) =>
% 97.29/12.87 ((
% 97.29/12.87 (kpairp) =>
% 97.29/12.87 ((
% 97.29/12.87 (singletonsubset) =>
% 97.29/12.87 ((
% 97.29/12.87 (singletoninpowerset) =>
% 97.29/12.87 ((
% 97.29/12.87 (singletoninpowunion) =>
% 97.29/12.87 ((
% 97.29/12.87 (upairset2E) =>
% 97.29/12.87 ((
% 97.29/12.87 (upairsubunion) =>
% 97.29/12.87 ((
% 97.29/12.87 (upairinpowunion) =>
% 97.29/12.87 ((
% 97.29/12.87 (ubforcartprodlem1) =>
% 97.29/12.87 ((
% 97.29/12.87 (ubforcartprodlem2) =>
% 97.29/12.87 ((
% 97.29/12.87 (ubforcartprodlem3) =>
% 97.29/12.87 ((
% 97.29/12.87 (cartprodpairin) =>
% 97.29/12.87 ((
% 97.29/12.87 (cartprodmempair1) =>
% 97.29/12.87 ((
% 97.29/12.87 (cartprodmempair) =>
% 97.29/12.87 ((
% 97.29/12.87 (setunionE2) =>
% 97.29/12.87 ((
% 97.29/12.87 (setunionsingleton1) =>
% 97.29/12.87 ((
% 97.29/12.87 (setunionsingleton2) =>
% 97.29/12.87 ((
% 97.29/12.87 (setunionsingleton) =>
% 97.29/12.87 ((
% 97.29/12.87 (singletonprop) =>
% 97.29/12.87 ((
% 97.29/12.87 (ex1E1) =>
% 97.29/12.87 ((
% 97.29/12.87 (ex1I) =>
% 97.29/12.87 ((
% 97.29/12.87 (ex1I2) =>
% 97.29/12.87 ((
% 97.29/12.87 (singletonsuniq) =>
% 97.29/12.87 ((
% 97.29/12.87 (setukpairinjL1) =>
% 97.29/12.87 ((
% 97.29/12.87 (kfstsingleton) =>
% 97.29/12.87 ((
% 97.29/12.87 (theprop) =>
% 97.29/12.87 ((
% 97.29/12.87 (kfstpairEq) =>
% 97.29/12.87 ((
% 97.29/12.87 (cartprodfstin) =>
% 97.29/12.87 ((
% 97.29/12.87 (setukpairinjL2) =>
% 97.29/12.87 ((
% 97.29/12.87 (setukpairinjL) =>
% 97.29/12.87 ((
% 97.29/12.87 (setukpairinjR11) =>
% 97.29/12.87 ((
% 97.29/12.87 (setukpairinjR12) =>
% 97.29/12.87 ((
% 97.29/12.87 (setukpairinjR1) =>
% 97.29/12.87 ((
% 97.29/12.87 (upairequniteq) =>
% 97.29/12.87 ((
% 97.29/12.87 (setukpairinjR2) =>
% 97.29/12.87 ((
% 97.29/12.87 (setukpairinjR) =>
% 97.29/12.87 ((
% 97.29/12.87 (ksndsingleton) =>
% 97.29/12.87 ((
% 97.29/12.87 (ksndpairEq) =>
% 97.29/12.87 ((
% 97.29/12.87 (kpairsurjEq) =>
% 97.29/12.87 ((
% 97.29/12.87 (cartprodsndin) =>
% 97.29/12.87 ((
% 97.29/12.87 (cartprodpairmemEL) =>
% 97.29/12.87 ((
% 97.29/12.87 (cartprodpairmemER) =>
% 97.29/12.87 ((
% 97.29/12.87 (cartprodmempaircEq) =>
% 97.29/12.87 ((
% 97.29/12.87 (cartprodfstpairEq) =>
% 97.29/12.87 ((
% 97.29/12.87 (cartprodsndpairEq) =>
% 97.29/12.87 ((
% 97.29/12.87 (cartprodpairsurjEq) =>
% 97.29/12.87 ((
% 97.29/12.87 (dpsetconstrI) =>
% 97.29/12.87 ((
% 97.29/12.87 (dpsetconstrSub) =>
% 97.29/12.87 ((
% 97.29/12.87 (setOfPairsIsBReln) =>
% 97.29/12.87 ((
% 97.29/12.87 (dpsetconstrERa) =>
% 97.29/12.87 ((
% 97.29/12.87 (dpsetconstrEL1) =>
% 97.29/12.87 ((
% 97.29/12.87 (dpsetconstrEL2) =>
% 97.29/12.87 ((
% 97.29/12.87 (dpsetconstrER) =>
% 97.29/12.87 ((
% 97.29/12.87 (funcImageSingleton) =>
% 97.29/12.87 ((
% 97.29/12.87 (apProp) =>
% 97.29/12.87 ((
% 97.29/12.87 (app) =>
% 97.29/12.87 ((
% 97.29/12.87 (infuncsetfunc) =>
% 97.29/12.87 ((
% 97.29/12.87 (ap2p) =>
% 97.29/12.87 ((
% 97.29/12.87 (funcinfuncset) =>
% 97.29/12.87 ((
% 97.29/12.87 (lamProp) =>
% 97.29/12.87 ((
% 97.29/12.87 (lamp) =>
% 97.29/12.87 ((
% 97.29/12.87 (lam2p) =>
% 97.29/12.87 ((
% 97.29/12.87 (brelnall1) =>
% 97.29/12.87 ((
% 97.29/12.87 (brelnall2) =>
% 97.29/12.87 ((
% 97.29/12.87 (ex1E2) =>
% 97.29/12.87 ((
% 97.29/12.87 (funcGraphProp1) =>
% 97.29/12.87 ((
% 97.29/12.87 (funcGraphProp3) =>
% 97.29/12.87 ((
% 97.29/12.87 (funcGraphProp2) =>
% 97.29/12.87 ((
% 97.29/12.87 (funcextLem) =>
% 97.29/12.87 ((
% 97.29/12.87 (funcGraphProp4) =>
% 97.29/12.87 ((
% 97.29/12.87 (subbreln) =>
% 97.29/12.87 ((
% 97.29/12.87 (eqbreln) =>
% 97.29/12.87 ((
% 97.29/12.87 (funcext) =>
% 97.29/12.87 ((
% 97.29/12.87 (funcext2) =>
% 97.29/12.87 ((
% 97.29/12.87 (ap2apEq1) =>
% 97.29/12.87 ((
% 97.29/12.87 (ap2apEq2) =>
% 97.29/12.87 ((
% 97.29/12.87 (beta1) =>
% 97.29/12.87 ((
% 97.29/12.87 (eta1) =>
% 97.29/12.87 ((
% 97.29/12.87 (lam2lamEq) =>
% 97.29/12.87 ((
% 97.29/12.87 (beta2) =>
% 97.29/12.87 ((
% 97.29/12.87 (eta2) =>
% 97.29/12.87 ((
% 97.29/12.87 (iffalseProp1) =>
% 97.29/12.87 ((
% 97.29/12.87 (iffalseProp2) =>
% 97.29/12.87 ((
% 97.29/12.87 (iftrueProp1) =>
% 97.29/12.87 ((
% 97.29/12.87 (iftrueProp2) =>
% 97.29/12.87 ((
% 97.29/12.87 (ifSingleton) =>
% 97.29/12.87 ((
% 97.29/12.87 (ifp) =>
% 97.29/12.87 ((
% 97.29/12.87 (theeq) =>
% 97.29/12.87 ((
% 97.29/12.87 (iftrue) =>
% 97.29/12.87 ((
% 97.29/12.87 (iffalse) =>
% 97.29/12.87 ((
% 97.29/12.87 (iftrueorfalse) =>
% 97.29/12.87 ((
% 97.29/12.87 (binintersectT_lem) =>
% 97.29/12.87 ((
% 97.29/12.87 (binunionT_lem) =>
% 97.29/12.87 ((
% 97.29/12.87 (powersetT_lem) =>
% 97.29/12.87 ((
% 97.29/12.87 (setminusT_lem) =>
% 97.29/12.87 ((
% 97.29/12.87 (complementT_lem) =>
% 97.29/12.87 ((
% 97.29/12.87 (setextT) =>
% 97.29/12.87 ((
% 97.29/12.87 (subsetTI) =>
% 97.29/12.87 ((
% 97.29/12.87 (powersetTI1) =>
% 97.29/12.87 ((
% 97.29/12.87 (powersetTE1) =>
% 97.29/12.87 ((
% 97.29/12.87 (complementTI1) =>
% 97.29/12.87 ((
% 97.29/12.87 (complementTE1) =>
% 97.29/12.87 ((
% 97.29/12.87 (binintersectTELcontra) =>
% 97.29/12.87 ((
% 97.29/12.87 (binintersectTERcontra) =>
% 97.29/12.87 ((
% 97.29/12.87 (contrasubsetT) =>
% 97.29/12.87 ((
% 97.29/12.87 (contrasubsetT1) =>
% 97.29/12.87 ((
% 97.29/12.87 (contrasubsetT2) =>
% 97.29/12.87 ((
% 97.29/12.87 (contrasubsetT3) =>
% 97.29/12.87 ((
% 97.29/12.87 (doubleComplementI1) =>
% 97.29/12.87 ((
% 97.29/12.87 (doubleComplementE1) =>
% 97.29/12.87 ((
% 97.29/12.87 (doubleComplementSub1) =>
% 97.29/12.87 ((
% 97.29/12.87 (doubleComplementSub2) =>
% 97.29/12.87 ((
% 97.29/12.87 (doubleComplementEq) =>
% 97.29/12.87 ((
% 97.29/12.87 (complementTnotintersectT) =>
% 97.29/12.87 ((
% 97.29/12.87 (complementImpComplementIntersect) =>
% 97.29/12.87 ((
% 97.29/12.87 (complementSubsetComplementIntersect) =>
% 97.29/12.87 ((
% 97.29/12.87 (complementInPowersetComplementIntersect) =>
% 97.29/12.87 ((
% 97.29/12.87 (contraSubsetComplement) =>
% 97.29/12.87 ((
% 97.29/12.87 (complementTcontraSubset) =>
% 97.29/12.87 ((
% 97.29/12.87 (binunionTILcontra) =>
% 97.29/12.87 ((
% 97.29/12.87 (binunionTIRcontra) =>
% 97.29/12.87 ((
% 97.29/12.87 (inIntersectImpInUnion) =>
% 97.29/12.87 ((
% 97.29/12.87 (inIntersectImpInUnion2) =>
% 97.29/12.87 ((
% 97.29/12.87 (inIntersectImpInIntersectUnions) =>
% 97.29/12.87 ((
% 97.29/12.87 (intersectInPowersetIntersectUnions) =>
% 97.29/12.87 ((
% 97.29/12.87 (inComplementUnionImpNotIn1) =>
% 97.29/12.87 ((
% 97.29/12.87 (inComplementUnionImpInComplement1) =>
% 97.29/12.87 ((
% 97.29/12.87 (binunionTE) =>
% 97.29/12.87 ((
% 97.29/12.87 (binunionTEcontra) =>
% 97.29/12.87 ((
% 97.29/12.87 (demorgan2a1) =>
% 97.29/12.87 ((
% 97.29/12.87 (complementUnionInPowersetComplement) =>
% 97.29/12.87 ((
% 97.29/12.87 (demorgan2a2) =>
% 97.29/12.87 ((
% 97.29/12.87 (demorgan1a) =>
% 97.29/12.87 ((
% 97.29/12.87 (demorgan1b) =>
% 97.29/12.87 ((
% 97.29/12.87 (demorgan1) =>
% 97.29/12.87 ((
% 97.29/12.87 (demorgan2a) =>
% 97.29/12.87 ((
% 97.29/12.87 (demorgan2b2) =>
% 97.29/12.87 ((
% 97.29/12.87 (demorgan2b) =>
% 97.29/12.87 ((
% 97.29/12.87 (demorgan2) =>
% 97.29/12.87 ((
% 97.29/12.87 (woz13rule0) =>
% 97.29/12.87 ((
% 97.29/12.87 (woz13rule1) =>
% 97.29/12.87 ((
% 97.29/12.87 (woz13rule2) =>
% 97.29/12.87 ((
% 97.29/12.87 (woz13rule3) =>
% 97.29/12.87 ((
% 97.29/12.87 (woz13rule4) =>
% 97.29/12.87 ((
% 97.29/12.87 (woz1_1) =>
% 97.29/12.87 ((
% 97.29/12.87 (woz1_2) =>
% 97.29/12.87 ((
% 97.29/12.87 (woz1_3) =>
% 97.29/12.87 ((
% 97.29/12.87 (woz1_4) =>
% 97.29/12.87 ((
% 97.29/12.87 (woz1_5) =>
% 97.29/12.87 ((
% 97.29/12.87 (breln1all2) =>
% 97.29/12.87 ((
% 97.29/12.87 (breln1SetBreln1) =>
% 97.29/12.87 ((
% 97.29/12.87 (choice2fnsingleton) =>
% 97.29/12.87 ((
% 97.29/12.87 (!!) @ (
% 97.29/12.87 (('#B') @ (
% 97.29/12.87 !!) @
% 97.29/12.87 (
% 97.29/12.87 (
% 97.29/12.87 ('#S') @ (
% 97.29/12.87 (
% 97.29/12.87 ('#B') @ (
% 97.29/12.87 '#B') @
% 97.29/12.87 breln1)) @
% 97.29/12.87 (
% 97.29/12.87 (
% 97.29/12.87 ('#S') @ dpsetconstr @
% 97.29/12.87 (
% 97.29/12.87 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.29/12.87 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl89])).
% 97.29/12.87 thf(zip_derived_cl123, plain,
% 97.29/12.87 (~ (((prop2setE) =>
% 97.29/12.87 (((emptysetE) =>
% 97.29/12.87 (((emptysetimpfalse) =>
% 97.29/12.87 (((notinemptyset) =>
% 97.29/12.87 (((exuE3e) =>
% 97.29/12.87 (((setext) =>
% 97.29/12.87 (((emptyI) =>
% 97.29/12.87 (((noeltsimpempty) =>
% 97.29/12.87 (((setbeta) =>
% 97.29/12.87 (((nonemptyE1) =>
% 97.29/12.87 (((nonemptyI) =>
% 97.29/12.87 (((nonemptyI1) =>
% 97.29/12.87 (((setadjoinIL) =>
% 97.29/12.87 (((in @ emptyset @
% 97.29/12.87 (setadjoin @ emptyset @ emptyset)) =>
% 97.29/12.87 (((setadjoinIR) =>
% 97.29/12.87 (((setadjoinE) =>
% 97.29/12.87 (((setadjoinOr) =>
% 97.29/12.87 (((setoftrueEq) =>
% 97.29/12.87 (((powersetI) =>
% 97.29/12.87 (((emptyinPowerset) =>
% 97.29/12.87 (((emptyInPowerset) =>
% 97.29/12.87 (((powersetE) =>
% 97.29/12.87 (((setunionI) =>
% 97.29/12.87 (((setunionE) =>
% 97.29/12.87 (((subPowSU) =>
% 97.29/12.87 (((exuE2) =>
% 97.29/12.87 (((nonemptyImpWitness) =>
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% 97.29/12.87 (((notinsingleton) =>
% 97.29/12.87 (((eqinunit) =>
% 97.29/12.87 ((
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% 97.29/12.87 ((
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% 97.29/12.87 ((
% 97.29/12.87 (upairsetIL) =>
% 97.29/12.87 ((
% 97.29/12.87 (upairsetIR) =>
% 97.29/12.87 ((
% 97.29/12.87 (emptyE1) =>
% 97.29/12.87 ((
% 97.29/12.87 (vacuousDall) =>
% 97.29/12.87 ((
% 97.29/12.87 (quantDeMorgan1) =>
% 97.29/12.87 ((
% 97.29/12.87 (quantDeMorgan2) =>
% 97.29/12.87 ((
% 97.29/12.87 (quantDeMorgan3) =>
% 97.29/12.87 ((
% 97.29/12.87 (quantDeMorgan4) =>
% 97.29/12.87 ((
% 97.29/12.87 (prop2setI) =>
% 97.29/12.87 ((
% 97.29/12.87 (prop2set2propI) =>
% 97.29/12.87 ((
% 97.29/12.87 (notdexE) =>
% 97.29/12.87 ((
% 97.29/12.87 (notdallE) =>
% 97.29/12.87 ((
% 97.29/12.87 (exuI1) =>
% 97.29/12.87 ((
% 97.29/12.87 (exuI3) =>
% 97.29/12.87 ((
% 97.29/12.87 (exuI2) =>
% 97.29/12.87 ((
% 97.29/12.87 (inCongP) =>
% 97.29/12.87 ((
% 97.29/12.87 (in__Cong) =>
% 97.29/12.87 ((
% 97.29/12.87 (exuE3u) =>
% 97.29/12.87 ((
% 97.29/12.87 (exu__Cong) =>
% 97.29/12.87 ((
% 97.29/12.87 (setadjoin__Cong) =>
% 97.29/12.87 ((
% 97.29/12.87 (powerset__Cong) =>
% 97.29/12.87 ((
% 97.29/12.87 (setunion__Cong) =>
% 97.29/12.87 ((
% 97.29/12.87 (exuEu) =>
% 97.29/12.87 ((
% 97.29/12.87 (descr__Cong) =>
% 97.29/12.87 ((
% 97.29/12.87 (dsetconstr__Cong) =>
% 97.29/12.87 ((
% 97.29/12.87 (subsetI1) =>
% 97.29/12.87 ((
% 97.29/12.87 (eqimpsubset2) =>
% 97.29/12.87 ((
% 97.29/12.87 (eqimpsubset1) =>
% 97.29/12.87 ((
% 97.29/12.87 (subsetI2) =>
% 97.29/12.87 ((
% 97.29/12.87 (emptysetsubset) =>
% 97.29/12.87 ((
% 97.29/12.87 (subsetE) =>
% 97.29/12.87 ((
% 97.29/12.87 (subsetE2) =>
% 97.29/12.87 ((
% 97.29/12.87 (notsubsetI) =>
% 97.29/12.87 ((
% 97.29/12.87 (notequalI1) =>
% 97.29/12.87 ((
% 97.29/12.87 (notequalI2) =>
% 97.29/12.87 ((
% 97.29/12.87 (subsetRefl) =>
% 97.29/12.87 ((
% 97.29/12.87 (subsetTrans) =>
% 97.29/12.87 ((
% 97.29/12.87 (setadjoinSub) =>
% 97.29/12.87 ((
% 97.29/12.87 (setadjoinSub2) =>
% 97.29/12.87 ((
% 97.29/12.87 (subset2powerset) =>
% 97.29/12.87 ((
% 97.29/12.87 (setextsub) =>
% 97.29/12.87 ((
% 97.29/12.87 (subsetemptysetimpeq) =>
% 97.29/12.87 ((
% 97.29/12.87 (powersetI1) =>
% 97.29/12.87 ((
% 97.29/12.87 (powersetE1) =>
% 97.29/12.87 ((
% 97.29/12.87 (inPowerset) =>
% 97.29/12.87 ((
% 97.29/12.87 (powersetsubset) =>
% 97.29/12.87 ((
% 97.29/12.87 (sepInPowerset) =>
% 97.29/12.87 ((
% 97.29/12.87 (sepSubset) =>
% 97.29/12.87 ((
% 97.29/12.87 (binunionIL) =>
% 97.29/12.87 ((
% 97.29/12.87 (upairset2IR) =>
% 97.29/12.87 ((
% 97.29/12.87 (binunionIR) =>
% 97.29/12.87 ((
% 97.29/12.87 (binunionEcases) =>
% 97.29/12.87 ((
% 97.29/12.87 (binunionE) =>
% 97.29/12.87 ((
% 97.29/12.87 (binunionLsub) =>
% 97.29/12.87 ((
% 97.29/12.87 (binunionRsub) =>
% 97.29/12.87 ((
% 97.29/12.87 (binintersectI) =>
% 97.29/12.87 ((
% 97.29/12.87 (binintersectSubset5) =>
% 97.29/12.87 ((
% 97.29/12.87 (binintersectEL) =>
% 97.29/12.87 ((
% 97.29/12.87 (binintersectLsub) =>
% 97.29/12.87 ((
% 97.29/12.87 (binintersectSubset2) =>
% 97.29/12.87 ((
% 97.29/12.87 (binintersectSubset3) =>
% 97.29/12.87 ((
% 97.29/12.87 (binintersectER) =>
% 97.29/12.87 ((
% 97.29/12.87 (disjointsetsI1) =>
% 97.29/12.87 ((
% 97.29/12.87 (binintersectRsub) =>
% 97.29/12.87 ((
% 97.29/12.87 (binintersectSubset4) =>
% 97.29/12.87 ((
% 97.29/12.87 (binintersectSubset1) =>
% 97.29/12.87 ((
% 97.29/12.87 (bs114d) =>
% 97.29/12.87 ((
% 97.29/12.87 (setminusI) =>
% 97.29/12.87 ((
% 97.29/12.87 (setminusEL) =>
% 97.29/12.87 ((
% 97.29/12.87 (setminusER) =>
% 97.29/12.87 ((
% 97.29/12.87 (setminusSubset2) =>
% 97.29/12.87 ((
% 97.29/12.87 (setminusERneg) =>
% 97.29/12.87 ((
% 97.29/12.87 (setminusELneg) =>
% 97.29/12.87 ((
% 97.29/12.87 (setminusILneg) =>
% 97.29/12.87 ((
% 97.29/12.87 (setminusIRneg) =>
% 97.29/12.87 ((
% 97.29/12.87 (setminusLsub) =>
% 97.29/12.87 ((
% 97.29/12.87 (setminusSubset1) =>
% 97.29/12.87 ((
% 97.29/12.87 (symdiffE) =>
% 97.29/12.87 ((
% 97.29/12.87 (symdiffI1) =>
% 97.29/12.87 ((
% 97.29/12.87 (symdiffI2) =>
% 97.29/12.87 ((
% 97.29/12.87 (symdiffIneg1) =>
% 97.29/12.87 ((
% 97.29/12.87 (symdiffIneg2) =>
% 97.29/12.87 ((
% 97.29/12.87 (secondinupair) =>
% 97.29/12.87 ((
% 97.29/12.87 (setukpairIL) =>
% 97.29/12.87 ((
% 97.29/12.87 (setukpairIR) =>
% 97.29/12.87 ((
% 97.29/12.87 (kpairiskpair) =>
% 97.29/12.87 ((
% 97.29/12.87 (kpairp) =>
% 97.29/12.87 ((
% 97.29/12.87 (singletonsubset) =>
% 97.29/12.87 ((
% 97.29/12.87 (singletoninpowerset) =>
% 97.29/12.87 ((
% 97.29/12.87 (singletoninpowunion) =>
% 97.29/12.87 ((
% 97.29/12.87 (upairset2E) =>
% 97.29/12.87 ((
% 97.29/12.87 (upairsubunion) =>
% 97.29/12.87 ((
% 97.29/12.87 (upairinpowunion) =>
% 97.29/12.87 ((
% 97.29/12.87 (ubforcartprodlem1) =>
% 97.29/12.87 ((
% 97.29/12.87 (ubforcartprodlem2) =>
% 97.29/12.87 ((
% 97.29/12.87 (ubforcartprodlem3) =>
% 97.29/12.87 ((
% 97.29/12.87 (cartprodpairin) =>
% 97.29/12.87 ((
% 97.29/12.87 (cartprodmempair1) =>
% 97.29/12.87 ((
% 97.29/12.87 (cartprodmempair) =>
% 97.29/12.87 ((
% 97.29/12.87 (setunionE2) =>
% 97.29/12.87 ((
% 97.29/12.87 (setunionsingleton1) =>
% 97.29/12.87 ((
% 97.29/12.87 (setunionsingleton2) =>
% 97.29/12.87 ((
% 97.29/12.87 (setunionsingleton) =>
% 97.29/12.87 ((
% 97.29/12.87 (singletonprop) =>
% 97.29/12.87 ((
% 97.29/12.87 (ex1E1) =>
% 97.29/12.87 ((
% 97.29/12.87 (ex1I) =>
% 97.29/12.87 ((
% 97.29/12.87 (ex1I2) =>
% 97.29/12.87 ((
% 97.29/12.87 (singletonsuniq) =>
% 97.29/12.87 ((
% 97.29/12.87 (setukpairinjL1) =>
% 97.29/12.87 ((
% 97.29/12.87 (kfstsingleton) =>
% 97.29/12.87 ((
% 97.29/12.87 (theprop) =>
% 97.29/12.87 ((
% 97.29/12.87 (kfstpairEq) =>
% 97.29/12.87 ((
% 97.29/12.87 (cartprodfstin) =>
% 97.29/12.87 ((
% 97.29/12.87 (setukpairinjL2) =>
% 97.29/12.87 ((
% 97.29/12.87 (setukpairinjL) =>
% 97.29/12.87 ((
% 97.29/12.87 (setukpairinjR11) =>
% 97.29/12.87 ((
% 97.29/12.87 (setukpairinjR12) =>
% 97.29/12.87 ((
% 97.29/12.87 (setukpairinjR1) =>
% 97.29/12.87 ((
% 97.29/12.87 (upairequniteq) =>
% 97.29/12.87 ((
% 97.29/12.87 (setukpairinjR2) =>
% 97.29/12.87 ((
% 97.29/12.87 (setukpairinjR) =>
% 97.29/12.87 ((
% 97.29/12.87 (ksndsingleton) =>
% 97.29/12.87 ((
% 97.29/12.87 (ksndpairEq) =>
% 97.29/12.87 ((
% 97.29/12.87 (kpairsurjEq) =>
% 97.29/12.87 ((
% 97.29/12.87 (cartprodsndin) =>
% 97.29/12.87 ((
% 97.29/12.87 (cartprodpairmemEL) =>
% 97.29/12.87 ((
% 97.29/12.87 (cartprodpairmemER) =>
% 97.29/12.87 ((
% 97.29/12.87 (cartprodmempaircEq) =>
% 97.29/12.87 ((
% 97.29/12.87 (cartprodfstpairEq) =>
% 97.29/12.87 ((
% 97.29/12.87 (cartprodsndpairEq) =>
% 97.29/12.87 ((
% 97.29/12.87 (cartprodpairsurjEq) =>
% 97.29/12.87 ((
% 97.29/12.87 (dpsetconstrI) =>
% 97.29/12.87 ((
% 97.29/12.87 (dpsetconstrSub) =>
% 97.29/12.87 ((
% 97.29/12.87 (setOfPairsIsBReln) =>
% 97.29/12.87 ((
% 97.29/12.87 (dpsetconstrERa) =>
% 97.29/12.87 ((
% 97.29/12.87 (dpsetconstrEL1) =>
% 97.29/12.87 ((
% 97.29/12.87 (dpsetconstrEL2) =>
% 97.29/12.87 ((
% 97.29/12.87 (dpsetconstrER) =>
% 97.29/12.87 ((
% 97.29/12.87 (funcImageSingleton) =>
% 97.29/12.87 ((
% 97.29/12.87 (apProp) =>
% 97.29/12.87 ((
% 97.29/12.87 (app) =>
% 97.29/12.87 ((
% 97.29/12.87 (infuncsetfunc) =>
% 97.29/12.87 ((
% 97.29/12.87 (ap2p) =>
% 97.29/12.87 ((
% 97.29/12.87 (funcinfuncset) =>
% 97.29/12.87 ((
% 97.29/12.87 (lamProp) =>
% 97.29/12.87 ((
% 97.29/12.87 (lamp) =>
% 97.29/12.87 ((
% 97.29/12.87 (lam2p) =>
% 97.29/12.87 ((
% 97.29/12.87 (brelnall1) =>
% 97.29/12.87 ((
% 97.29/12.87 (brelnall2) =>
% 97.29/12.87 ((
% 97.29/12.87 (ex1E2) =>
% 97.29/12.87 ((
% 97.29/12.87 (funcGraphProp1) =>
% 97.29/12.87 ((
% 97.29/12.87 (funcGraphProp3) =>
% 97.29/12.87 ((
% 97.29/12.87 (funcGraphProp2) =>
% 97.29/12.87 ((
% 97.29/12.87 (funcextLem) =>
% 97.29/12.87 ((
% 97.29/12.87 (funcGraphProp4) =>
% 97.29/12.87 ((
% 97.29/12.87 (subbreln) =>
% 97.29/12.87 ((
% 97.29/12.87 (eqbreln) =>
% 97.29/12.87 ((
% 97.29/12.87 (funcext) =>
% 97.29/12.87 ((
% 97.29/12.87 (funcext2) =>
% 97.29/12.87 ((
% 97.29/12.87 (ap2apEq1) =>
% 97.29/12.87 ((
% 97.29/12.87 (ap2apEq2) =>
% 97.29/12.87 ((
% 97.29/12.87 (beta1) =>
% 97.29/12.87 ((
% 97.29/12.87 (eta1) =>
% 97.29/12.87 ((
% 97.29/12.87 (lam2lamEq) =>
% 97.29/12.87 ((
% 97.29/12.87 (beta2) =>
% 97.29/12.87 ((
% 97.29/12.87 (eta2) =>
% 97.29/12.87 ((
% 97.29/12.87 (iffalseProp1) =>
% 97.29/12.87 ((
% 97.29/12.87 (iffalseProp2) =>
% 97.29/12.87 ((
% 97.29/12.87 (iftrueProp1) =>
% 97.29/12.87 ((
% 97.29/12.87 (iftrueProp2) =>
% 97.29/12.87 ((
% 97.29/12.87 (ifSingleton) =>
% 97.29/12.87 ((
% 97.29/12.87 (ifp) =>
% 97.29/12.87 ((
% 97.29/12.87 (theeq) =>
% 97.29/12.87 ((
% 97.29/12.87 (iftrue) =>
% 97.29/12.87 ((
% 97.29/12.87 (iffalse) =>
% 97.29/12.87 ((
% 97.29/12.87 (iftrueorfalse) =>
% 97.29/12.87 ((
% 97.29/12.87 (binintersectT_lem) =>
% 97.29/12.87 ((
% 97.29/12.87 (binunionT_lem) =>
% 97.29/12.87 ((
% 97.29/12.87 (powersetT_lem) =>
% 97.29/12.87 ((
% 97.29/12.87 (setminusT_lem) =>
% 97.29/12.87 ((
% 97.29/12.87 (complementT_lem) =>
% 97.29/12.87 ((
% 97.29/12.87 (setextT) =>
% 97.29/12.87 ((
% 97.29/12.87 (subsetTI) =>
% 97.29/12.87 ((
% 97.29/12.87 (powersetTI1) =>
% 97.29/12.87 ((
% 97.29/12.87 (powersetTE1) =>
% 97.29/12.87 ((
% 97.29/12.87 (complementTI1) =>
% 97.29/12.87 ((
% 97.29/12.87 (complementTE1) =>
% 97.29/12.87 ((
% 97.29/12.87 (binintersectTELcontra) =>
% 97.29/12.87 ((
% 97.29/12.87 (binintersectTERcontra) =>
% 97.29/12.87 ((
% 97.29/12.87 (contrasubsetT) =>
% 97.29/12.87 ((
% 97.29/12.87 (contrasubsetT1) =>
% 97.29/12.87 ((
% 97.29/12.87 (contrasubsetT2) =>
% 97.29/12.87 ((
% 97.29/12.87 (contrasubsetT3) =>
% 97.29/12.87 ((
% 97.29/12.87 (doubleComplementI1) =>
% 97.29/12.87 ((
% 97.29/12.87 (doubleComplementE1) =>
% 97.29/12.87 ((
% 97.29/12.87 (doubleComplementSub1) =>
% 97.29/12.87 ((
% 97.29/12.87 (doubleComplementSub2) =>
% 97.29/12.87 ((
% 97.29/12.87 (doubleComplementEq) =>
% 97.29/12.87 ((
% 97.29/12.87 (complementTnotintersectT) =>
% 97.29/12.87 ((
% 97.29/12.87 (complementImpComplementIntersect) =>
% 97.29/12.87 ((
% 97.29/12.87 (complementSubsetComplementIntersect) =>
% 97.29/12.87 ((
% 97.29/12.87 (complementInPowersetComplementIntersect) =>
% 97.29/12.87 ((
% 97.29/12.87 (contraSubsetComplement) =>
% 97.29/12.87 ((
% 97.29/12.87 (complementTcontraSubset) =>
% 97.29/12.87 ((
% 97.29/12.87 (binunionTILcontra) =>
% 97.29/12.87 ((
% 97.29/12.87 (binunionTIRcontra) =>
% 97.29/12.87 ((
% 97.29/12.87 (inIntersectImpInUnion) =>
% 97.29/12.87 ((
% 97.29/12.87 (inIntersectImpInUnion2) =>
% 97.29/12.87 ((
% 97.29/12.87 (inIntersectImpInIntersectUnions) =>
% 97.29/12.87 ((
% 97.29/12.87 (intersectInPowersetIntersectUnions) =>
% 97.29/12.87 ((
% 97.29/12.87 (inComplementUnionImpNotIn1) =>
% 97.29/12.87 ((
% 97.29/12.87 (inComplementUnionImpInComplement1) =>
% 97.29/12.87 ((
% 97.29/12.87 (binunionTE) =>
% 97.29/12.87 ((
% 97.29/12.87 (binunionTEcontra) =>
% 97.29/12.87 ((
% 97.29/12.87 (demorgan2a1) =>
% 97.29/12.87 ((
% 97.29/12.87 (complementUnionInPowersetComplement) =>
% 97.29/12.87 ((
% 97.29/12.87 (demorgan2a2) =>
% 97.29/12.87 ((
% 97.29/12.87 (demorgan1a) =>
% 97.29/12.87 ((
% 97.29/12.87 (demorgan1b) =>
% 97.29/12.87 ((
% 97.29/12.87 (demorgan1) =>
% 97.29/12.87 ((
% 97.29/12.87 (demorgan2a) =>
% 97.29/12.87 ((
% 97.29/12.87 (demorgan2b2) =>
% 97.29/12.87 ((
% 97.29/12.87 (demorgan2b) =>
% 97.29/12.87 ((
% 97.29/12.87 (demorgan2) =>
% 97.29/12.87 ((
% 97.29/12.87 (woz13rule0) =>
% 97.29/12.87 ((
% 97.29/12.87 (woz13rule1) =>
% 97.29/12.87 ((
% 97.29/12.87 (woz13rule2) =>
% 97.29/12.87 ((
% 97.29/12.87 (woz13rule3) =>
% 97.29/12.87 ((
% 97.29/12.87 (woz13rule4) =>
% 97.29/12.87 ((
% 97.29/12.87 (woz1_1) =>
% 97.29/12.87 ((
% 97.29/12.87 (woz1_2) =>
% 97.29/12.87 ((
% 97.29/12.87 (woz1_3) =>
% 97.29/12.87 ((
% 97.29/12.87 (woz1_4) =>
% 97.29/12.87 ((
% 97.29/12.87 (woz1_5) =>
% 97.29/12.87 ((
% 97.29/12.87 (breln1all2) =>
% 97.29/12.87 ((
% 97.29/12.87 (breln1SetBreln1) =>
% 97.29/12.87 ((
% 97.29/12.87 (choice2fnsingleton) =>
% 97.29/12.87 ((
% 97.29/12.87 (!!) @ (
% 97.29/12.87 (('#B') @ (
% 97.29/12.87 !!) @
% 97.29/12.87 (
% 97.29/12.87 (
% 97.29/12.87 ('#S') @ (
% 97.29/12.87 (
% 97.29/12.87 ('#B') @ (
% 97.29/12.87 '#B') @
% 97.29/12.87 breln1)) @
% 97.29/12.87 (
% 97.29/12.87 (
% 97.29/12.87 ('#S') @ dpsetconstr @
% 97.29/12.87 (
% 97.29/12.87 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.29/12.87 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl105])).
% 97.29/12.87 thf(zip_derived_cl142, plain,
% 97.29/12.87 (~ (((emptysetE) =>
% 97.29/12.87 (((emptysetimpfalse) =>
% 97.29/12.87 (((notinemptyset) =>
% 97.29/12.87 (((exuE3e) =>
% 97.29/12.87 (((setext) =>
% 97.29/12.87 (((emptyI) =>
% 97.29/12.87 (((noeltsimpempty) =>
% 97.29/12.87 (((setbeta) =>
% 97.29/12.87 (((nonemptyE1) =>
% 97.29/12.87 (((nonemptyI) =>
% 97.29/12.87 (((nonemptyI1) =>
% 97.29/12.87 (((setadjoinIL) =>
% 97.29/12.87 (((in @ emptyset @
% 97.29/12.87 (setadjoin @ emptyset @ emptyset)) =>
% 97.29/12.87 (((setadjoinIR) =>
% 97.29/12.87 (((setadjoinE) =>
% 97.29/12.87 (((setadjoinOr) =>
% 97.29/12.87 (((setoftrueEq) =>
% 97.29/12.87 (((powersetI) =>
% 97.29/12.87 (((emptyinPowerset) =>
% 97.29/12.87 (((emptyInPowerset) =>
% 97.29/12.87 (((powersetE) =>
% 97.29/12.87 (((setunionI) =>
% 97.29/12.87 (((setunionE) =>
% 97.29/12.87 (((subPowSU) =>
% 97.29/12.87 (((exuE2) =>
% 97.29/12.87 (((nonemptyImpWitness) =>
% 97.29/12.87 (((uniqinunit) =>
% 97.29/12.87 (((notinsingleton) =>
% 97.29/12.87 (((eqinunit) =>
% 97.29/12.87 (((singletonsswitch) =>
% 97.29/12.87 ((
% 97.29/12.87 (upairsetE) =>
% 97.29/12.87 ((
% 97.29/12.87 (upairsetIL) =>
% 97.29/12.87 ((
% 97.29/12.87 (upairsetIR) =>
% 97.29/12.87 ((
% 97.29/12.87 (emptyE1) =>
% 97.29/12.87 ((
% 97.29/12.87 (vacuousDall) =>
% 97.29/12.87 ((
% 97.29/12.87 (quantDeMorgan1) =>
% 97.29/12.87 ((
% 97.29/12.87 (quantDeMorgan2) =>
% 97.29/12.87 ((
% 97.29/12.87 (quantDeMorgan3) =>
% 97.29/12.87 ((
% 97.29/12.87 (quantDeMorgan4) =>
% 97.29/12.87 ((
% 97.29/12.87 (prop2setI) =>
% 97.29/12.87 ((
% 97.29/12.87 (prop2set2propI) =>
% 97.29/12.87 ((
% 97.29/12.87 (notdexE) =>
% 97.29/12.87 ((
% 97.29/12.87 (notdallE) =>
% 97.29/12.87 ((
% 97.29/12.87 (exuI1) =>
% 97.29/12.87 ((
% 97.29/12.87 (exuI3) =>
% 97.29/12.87 ((
% 97.29/12.87 (exuI2) =>
% 97.29/12.87 ((
% 97.29/12.87 (inCongP) =>
% 97.29/12.87 ((
% 97.29/12.87 (in__Cong) =>
% 97.29/12.87 ((
% 97.29/12.87 (exuE3u) =>
% 97.29/12.87 ((
% 97.29/12.87 (exu__Cong) =>
% 97.29/12.87 ((
% 97.29/12.87 (setadjoin__Cong) =>
% 97.29/12.87 ((
% 97.29/12.87 (powerset__Cong) =>
% 97.29/12.87 ((
% 97.29/12.87 (setunion__Cong) =>
% 97.29/12.87 ((
% 97.29/12.87 (exuEu) =>
% 97.29/12.87 ((
% 97.29/12.87 (descr__Cong) =>
% 97.29/12.87 ((
% 97.29/12.87 (dsetconstr__Cong) =>
% 97.29/12.87 ((
% 97.29/12.87 (subsetI1) =>
% 97.29/12.87 ((
% 97.29/12.87 (eqimpsubset2) =>
% 97.29/12.87 ((
% 97.29/12.87 (eqimpsubset1) =>
% 97.29/12.87 ((
% 97.29/12.87 (subsetI2) =>
% 97.29/12.87 ((
% 97.29/12.87 (emptysetsubset) =>
% 97.29/12.87 ((
% 97.29/12.87 (subsetE) =>
% 97.29/12.87 ((
% 97.29/12.87 (subsetE2) =>
% 97.29/12.87 ((
% 97.29/12.87 (notsubsetI) =>
% 97.29/12.87 ((
% 97.29/12.87 (notequalI1) =>
% 97.29/12.87 ((
% 97.29/12.87 (notequalI2) =>
% 97.29/12.87 ((
% 97.29/12.87 (subsetRefl) =>
% 97.29/12.87 ((
% 97.29/12.87 (subsetTrans) =>
% 97.29/12.87 ((
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% 97.29/12.87 ((
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% 97.29/12.87 ((
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% 97.29/12.87 ((
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% 97.29/12.87 ((
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% 97.29/12.87 ((
% 97.29/12.87 (powersetE1) =>
% 97.29/12.87 ((
% 97.29/12.87 (inPowerset) =>
% 97.29/12.87 ((
% 97.29/12.87 (powersetsubset) =>
% 97.29/12.87 ((
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% 97.29/12.87 ((
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% 97.29/12.87 ((
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% 97.29/12.87 ((
% 97.29/12.87 (upairset2IR) =>
% 97.29/12.87 ((
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% 97.29/12.87 ((
% 97.29/12.87 (binunionEcases) =>
% 97.29/12.87 ((
% 97.29/12.87 (binunionE) =>
% 97.29/12.87 ((
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% 97.29/12.87 ((
% 97.29/12.87 (binunionRsub) =>
% 97.29/12.87 ((
% 97.29/12.87 (binintersectI) =>
% 97.29/12.87 ((
% 97.29/12.87 (binintersectSubset5) =>
% 97.29/12.87 ((
% 97.29/12.87 (binintersectEL) =>
% 97.29/12.87 ((
% 97.29/12.87 (binintersectLsub) =>
% 97.29/12.87 ((
% 97.29/12.87 (binintersectSubset2) =>
% 97.29/12.87 ((
% 97.29/12.87 (binintersectSubset3) =>
% 97.29/12.87 ((
% 97.29/12.87 (binintersectER) =>
% 97.29/12.87 ((
% 97.29/12.87 (disjointsetsI1) =>
% 97.29/12.87 ((
% 97.29/12.87 (binintersectRsub) =>
% 97.29/12.87 ((
% 97.29/12.87 (binintersectSubset4) =>
% 97.29/12.87 ((
% 97.29/12.87 (binintersectSubset1) =>
% 97.29/12.87 ((
% 97.29/12.87 (bs114d) =>
% 97.29/12.87 ((
% 97.29/12.87 (setminusI) =>
% 97.29/12.87 ((
% 97.29/12.87 (setminusEL) =>
% 97.29/12.87 ((
% 97.29/12.87 (setminusER) =>
% 97.29/12.87 ((
% 97.29/12.87 (setminusSubset2) =>
% 97.29/12.87 ((
% 97.29/12.87 (setminusERneg) =>
% 97.29/12.87 ((
% 97.29/12.87 (setminusELneg) =>
% 97.29/12.87 ((
% 97.29/12.87 (setminusILneg) =>
% 97.29/12.87 ((
% 97.29/12.87 (setminusIRneg) =>
% 97.29/12.87 ((
% 97.29/12.87 (setminusLsub) =>
% 97.29/12.87 ((
% 97.29/12.87 (setminusSubset1) =>
% 97.29/12.87 ((
% 97.29/12.87 (symdiffE) =>
% 97.29/12.87 ((
% 97.29/12.87 (symdiffI1) =>
% 97.29/12.87 ((
% 97.29/12.87 (symdiffI2) =>
% 97.29/12.87 ((
% 97.29/12.87 (symdiffIneg1) =>
% 97.29/12.87 ((
% 97.29/12.87 (symdiffIneg2) =>
% 97.29/12.87 ((
% 97.29/12.87 (secondinupair) =>
% 97.29/12.87 ((
% 97.29/12.87 (setukpairIL) =>
% 97.29/12.87 ((
% 97.29/12.87 (setukpairIR) =>
% 97.29/12.87 ((
% 97.29/12.87 (kpairiskpair) =>
% 97.29/12.87 ((
% 97.29/12.87 (kpairp) =>
% 97.29/12.87 ((
% 97.29/12.87 (singletonsubset) =>
% 97.29/12.87 ((
% 97.29/12.87 (singletoninpowerset) =>
% 97.29/12.87 ((
% 97.29/12.87 (singletoninpowunion) =>
% 97.29/12.87 ((
% 97.29/12.87 (upairset2E) =>
% 97.29/12.87 ((
% 97.29/12.87 (upairsubunion) =>
% 97.29/12.87 ((
% 97.29/12.87 (upairinpowunion) =>
% 97.29/12.87 ((
% 97.29/12.87 (ubforcartprodlem1) =>
% 97.29/12.87 ((
% 97.29/12.87 (ubforcartprodlem2) =>
% 97.29/12.87 ((
% 97.29/12.87 (ubforcartprodlem3) =>
% 97.29/12.87 ((
% 97.29/12.87 (cartprodpairin) =>
% 97.29/12.87 ((
% 97.29/12.87 (cartprodmempair1) =>
% 97.29/12.87 ((
% 97.29/12.87 (cartprodmempair) =>
% 97.29/12.87 ((
% 97.29/12.87 (setunionE2) =>
% 97.29/12.87 ((
% 97.29/12.87 (setunionsingleton1) =>
% 97.29/12.87 ((
% 97.29/12.87 (setunionsingleton2) =>
% 97.29/12.87 ((
% 97.29/12.87 (setunionsingleton) =>
% 97.29/12.87 ((
% 97.29/12.87 (singletonprop) =>
% 97.29/12.87 ((
% 97.29/12.87 (ex1E1) =>
% 97.29/12.87 ((
% 97.29/12.87 (ex1I) =>
% 97.29/12.87 ((
% 97.29/12.87 (ex1I2) =>
% 97.29/12.87 ((
% 97.29/12.87 (singletonsuniq) =>
% 97.29/12.87 ((
% 97.29/12.87 (setukpairinjL1) =>
% 97.29/12.87 ((
% 97.29/12.87 (kfstsingleton) =>
% 97.29/12.87 ((
% 97.29/12.87 (theprop) =>
% 97.29/12.87 ((
% 97.29/12.87 (kfstpairEq) =>
% 97.29/12.87 ((
% 97.29/12.87 (cartprodfstin) =>
% 97.29/12.87 ((
% 97.29/12.87 (setukpairinjL2) =>
% 97.29/12.87 ((
% 97.29/12.87 (setukpairinjL) =>
% 97.29/12.87 ((
% 97.29/12.87 (setukpairinjR11) =>
% 97.29/12.87 ((
% 97.29/12.87 (setukpairinjR12) =>
% 97.29/12.87 ((
% 97.29/12.87 (setukpairinjR1) =>
% 97.29/12.87 ((
% 97.29/12.87 (upairequniteq) =>
% 97.29/12.87 ((
% 97.29/12.87 (setukpairinjR2) =>
% 97.29/12.87 ((
% 97.29/12.87 (setukpairinjR) =>
% 97.29/12.87 ((
% 97.29/12.87 (ksndsingleton) =>
% 97.29/12.87 ((
% 97.29/12.87 (ksndpairEq) =>
% 97.29/12.87 ((
% 97.29/12.87 (kpairsurjEq) =>
% 97.29/12.87 ((
% 97.29/12.87 (cartprodsndin) =>
% 97.29/12.87 ((
% 97.29/12.87 (cartprodpairmemEL) =>
% 97.29/12.87 ((
% 97.29/12.87 (cartprodpairmemER) =>
% 97.29/12.87 ((
% 97.29/12.87 (cartprodmempaircEq) =>
% 97.29/12.87 ((
% 97.29/12.87 (cartprodfstpairEq) =>
% 97.29/12.87 ((
% 97.29/12.87 (cartprodsndpairEq) =>
% 97.29/12.87 ((
% 97.29/12.87 (cartprodpairsurjEq) =>
% 97.29/12.87 ((
% 97.29/12.87 (dpsetconstrI) =>
% 97.29/12.87 ((
% 97.29/12.87 (dpsetconstrSub) =>
% 97.29/12.87 ((
% 97.29/12.87 (setOfPairsIsBReln) =>
% 97.29/12.87 ((
% 97.29/12.87 (dpsetconstrERa) =>
% 97.29/12.87 ((
% 97.29/12.87 (dpsetconstrEL1) =>
% 97.29/12.87 ((
% 97.29/12.87 (dpsetconstrEL2) =>
% 97.29/12.87 ((
% 97.29/12.87 (dpsetconstrER) =>
% 97.29/12.87 ((
% 97.29/12.87 (funcImageSingleton) =>
% 97.29/12.87 ((
% 97.29/12.87 (apProp) =>
% 97.29/12.87 ((
% 97.29/12.87 (app) =>
% 97.29/12.87 ((
% 97.29/12.87 (infuncsetfunc) =>
% 97.29/12.87 ((
% 97.29/12.87 (ap2p) =>
% 97.29/12.87 ((
% 97.29/12.87 (funcinfuncset) =>
% 97.29/12.87 ((
% 97.29/12.87 (lamProp) =>
% 97.29/12.87 ((
% 97.29/12.87 (lamp) =>
% 97.29/12.87 ((
% 97.29/12.87 (lam2p) =>
% 97.29/12.87 ((
% 97.29/12.87 (brelnall1) =>
% 97.29/12.87 ((
% 97.29/12.87 (brelnall2) =>
% 97.29/12.87 ((
% 97.29/12.87 (ex1E2) =>
% 97.29/12.87 ((
% 97.29/12.87 (funcGraphProp1) =>
% 97.29/12.87 ((
% 97.29/12.87 (funcGraphProp3) =>
% 97.29/12.87 ((
% 97.29/12.87 (funcGraphProp2) =>
% 97.29/12.87 ((
% 97.29/12.87 (funcextLem) =>
% 97.29/12.87 ((
% 97.29/12.87 (funcGraphProp4) =>
% 97.29/12.87 ((
% 97.29/12.87 (subbreln) =>
% 97.29/12.87 ((
% 97.29/12.87 (eqbreln) =>
% 97.29/12.87 ((
% 97.29/12.87 (funcext) =>
% 97.29/12.87 ((
% 97.29/12.87 (funcext2) =>
% 97.29/12.87 ((
% 97.29/12.87 (ap2apEq1) =>
% 97.29/12.87 ((
% 97.29/12.87 (ap2apEq2) =>
% 97.29/12.87 ((
% 97.29/12.87 (beta1) =>
% 97.29/12.87 ((
% 97.29/12.87 (eta1) =>
% 97.29/12.87 ((
% 97.29/12.87 (lam2lamEq) =>
% 97.29/12.87 ((
% 97.29/12.87 (beta2) =>
% 97.29/12.87 ((
% 97.29/12.87 (eta2) =>
% 97.29/12.87 ((
% 97.29/12.87 (iffalseProp1) =>
% 97.29/12.87 ((
% 97.29/12.87 (iffalseProp2) =>
% 97.29/12.87 ((
% 97.29/12.87 (iftrueProp1) =>
% 97.29/12.87 ((
% 97.29/12.87 (iftrueProp2) =>
% 97.29/12.87 ((
% 97.29/12.87 (ifSingleton) =>
% 97.29/12.87 ((
% 97.29/12.87 (ifp) =>
% 97.29/12.87 ((
% 97.29/12.87 (theeq) =>
% 97.29/12.87 ((
% 97.29/12.87 (iftrue) =>
% 97.29/12.87 ((
% 97.29/12.87 (iffalse) =>
% 97.29/12.87 ((
% 97.29/12.87 (iftrueorfalse) =>
% 97.29/12.87 ((
% 97.29/12.87 (binintersectT_lem) =>
% 97.29/12.87 ((
% 97.29/12.87 (binunionT_lem) =>
% 97.29/12.87 ((
% 97.29/12.87 (powersetT_lem) =>
% 97.29/12.87 ((
% 97.29/12.87 (setminusT_lem) =>
% 97.29/12.87 ((
% 97.29/12.87 (complementT_lem) =>
% 97.29/12.87 ((
% 97.29/12.87 (setextT) =>
% 97.29/12.87 ((
% 97.29/12.87 (subsetTI) =>
% 97.29/12.87 ((
% 97.29/12.87 (powersetTI1) =>
% 97.29/12.87 ((
% 97.29/12.87 (powersetTE1) =>
% 97.29/12.87 ((
% 97.29/12.87 (complementTI1) =>
% 97.29/12.87 ((
% 97.29/12.87 (complementTE1) =>
% 97.29/12.87 ((
% 97.29/12.87 (binintersectTELcontra) =>
% 97.29/12.87 ((
% 97.29/12.87 (binintersectTERcontra) =>
% 97.29/12.87 ((
% 97.29/12.87 (contrasubsetT) =>
% 97.29/12.87 ((
% 97.29/12.87 (contrasubsetT1) =>
% 97.29/12.87 ((
% 97.29/12.87 (contrasubsetT2) =>
% 97.29/12.87 ((
% 97.29/12.87 (contrasubsetT3) =>
% 97.29/12.87 ((
% 97.29/12.87 (doubleComplementI1) =>
% 97.29/12.87 ((
% 97.29/12.87 (doubleComplementE1) =>
% 97.29/12.87 ((
% 97.29/12.87 (doubleComplementSub1) =>
% 97.29/12.87 ((
% 97.29/12.87 (doubleComplementSub2) =>
% 97.29/12.87 ((
% 97.29/12.87 (doubleComplementEq) =>
% 97.29/12.87 ((
% 97.29/12.87 (complementTnotintersectT) =>
% 97.29/12.87 ((
% 97.29/12.87 (complementImpComplementIntersect) =>
% 97.29/12.87 ((
% 97.29/12.87 (complementSubsetComplementIntersect) =>
% 97.29/12.87 ((
% 97.29/12.87 (complementInPowersetComplementIntersect) =>
% 97.29/12.87 ((
% 97.29/12.87 (contraSubsetComplement) =>
% 97.29/12.87 ((
% 97.29/12.87 (complementTcontraSubset) =>
% 97.29/12.87 ((
% 97.29/12.87 (binunionTILcontra) =>
% 97.29/12.87 ((
% 97.29/12.87 (binunionTIRcontra) =>
% 97.29/12.87 ((
% 97.29/12.87 (inIntersectImpInUnion) =>
% 97.29/12.87 ((
% 97.29/12.87 (inIntersectImpInUnion2) =>
% 97.29/12.87 ((
% 97.29/12.87 (inIntersectImpInIntersectUnions) =>
% 97.29/12.87 ((
% 97.29/12.87 (intersectInPowersetIntersectUnions) =>
% 97.29/12.87 ((
% 97.29/12.87 (inComplementUnionImpNotIn1) =>
% 97.29/12.87 ((
% 97.29/12.87 (inComplementUnionImpInComplement1) =>
% 97.29/12.87 ((
% 97.29/12.87 (binunionTE) =>
% 97.29/12.87 ((
% 97.29/12.87 (binunionTEcontra) =>
% 97.29/12.87 ((
% 97.29/12.87 (demorgan2a1) =>
% 97.29/12.87 ((
% 97.29/12.87 (complementUnionInPowersetComplement) =>
% 97.29/12.87 ((
% 97.29/12.87 (demorgan2a2) =>
% 97.29/12.87 ((
% 97.29/12.87 (demorgan1a) =>
% 97.29/12.87 ((
% 97.29/12.87 (demorgan1b) =>
% 97.29/12.87 ((
% 97.29/12.87 (demorgan1) =>
% 97.29/12.87 ((
% 97.29/12.87 (demorgan2a) =>
% 97.29/12.87 ((
% 97.29/12.87 (demorgan2b2) =>
% 97.29/12.87 ((
% 97.29/12.87 (demorgan2b) =>
% 97.29/12.87 ((
% 97.29/12.87 (demorgan2) =>
% 97.29/12.87 ((
% 97.29/12.87 (woz13rule0) =>
% 97.29/12.87 ((
% 97.29/12.87 (woz13rule1) =>
% 97.29/12.87 ((
% 97.29/12.87 (woz13rule2) =>
% 97.29/12.87 ((
% 97.29/12.87 (woz13rule3) =>
% 97.29/12.87 ((
% 97.29/12.87 (woz13rule4) =>
% 97.29/12.87 ((
% 97.29/12.87 (woz1_1) =>
% 97.29/12.87 ((
% 97.29/12.87 (woz1_2) =>
% 97.29/12.87 ((
% 97.29/12.87 (woz1_3) =>
% 97.29/12.87 ((
% 97.29/12.87 (woz1_4) =>
% 97.29/12.87 ((
% 97.29/12.87 (woz1_5) =>
% 97.29/12.87 ((
% 97.29/12.87 (breln1all2) =>
% 97.29/12.87 ((
% 97.29/12.87 (breln1SetBreln1) =>
% 97.29/12.87 ((
% 97.29/12.87 (choice2fnsingleton) =>
% 97.29/12.87 ((
% 97.29/12.87 (!!) @ (
% 97.29/12.87 (('#B') @ (
% 97.29/12.87 !!) @
% 97.29/12.87 (
% 97.29/12.87 (
% 97.29/12.87 ('#S') @ (
% 97.29/12.87 (
% 97.29/12.87 ('#B') @ (
% 97.29/12.87 '#B') @
% 97.29/12.87 breln1)) @
% 97.29/12.87 (
% 97.29/12.87 (
% 97.29/12.87 ('#S') @ dpsetconstr @
% 97.29/12.87 (
% 97.29/12.87 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.29/12.87 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl123])).
% 97.29/12.87 thf(zip_derived_cl158, plain,
% 97.29/12.87 (~ (((emptysetimpfalse) =>
% 97.29/12.87 (((notinemptyset) =>
% 97.29/12.87 (((exuE3e) =>
% 97.29/12.87 (((setext) =>
% 97.29/12.87 (((emptyI) =>
% 97.29/12.87 (((noeltsimpempty) =>
% 97.29/12.87 (((setbeta) =>
% 97.29/12.87 (((nonemptyE1) =>
% 97.29/12.87 (((nonemptyI) =>
% 97.29/12.87 (((nonemptyI1) =>
% 97.29/12.87 (((setadjoinIL) =>
% 97.29/12.87 (((in @ emptyset @
% 97.29/12.87 (setadjoin @ emptyset @ emptyset)) =>
% 97.29/12.87 (((setadjoinIR) =>
% 97.29/12.87 (((setadjoinE) =>
% 97.29/12.87 (((setadjoinOr) =>
% 97.29/12.87 (((setoftrueEq) =>
% 97.29/12.87 (((powersetI) =>
% 97.29/12.87 (((emptyinPowerset) =>
% 97.29/12.87 (((emptyInPowerset) =>
% 97.29/12.87 (((powersetE) =>
% 97.29/12.87 (((setunionI) =>
% 97.29/12.87 (((setunionE) =>
% 97.29/12.87 (((subPowSU) =>
% 97.29/12.87 (((exuE2) =>
% 97.29/12.87 (((nonemptyImpWitness) =>
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% 97.29/12.87 (((notinsingleton) =>
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% 97.29/12.87 ((
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% 97.29/12.87 ((
% 97.29/12.87 (upairsetIR) =>
% 97.29/12.87 ((
% 97.29/12.87 (emptyE1) =>
% 97.29/12.87 ((
% 97.29/12.87 (vacuousDall) =>
% 97.29/12.87 ((
% 97.29/12.87 (quantDeMorgan1) =>
% 97.29/12.87 ((
% 97.29/12.87 (quantDeMorgan2) =>
% 97.29/12.87 ((
% 97.29/12.87 (quantDeMorgan3) =>
% 97.29/12.87 ((
% 97.29/12.87 (quantDeMorgan4) =>
% 97.29/12.87 ((
% 97.29/12.87 (prop2setI) =>
% 97.29/12.87 ((
% 97.29/12.87 (prop2set2propI) =>
% 97.29/12.87 ((
% 97.29/12.87 (notdexE) =>
% 97.29/12.87 ((
% 97.29/12.87 (notdallE) =>
% 97.29/12.87 ((
% 97.29/12.87 (exuI1) =>
% 97.29/12.87 ((
% 97.29/12.87 (exuI3) =>
% 97.29/12.87 ((
% 97.29/12.87 (exuI2) =>
% 97.29/12.87 ((
% 97.29/12.87 (inCongP) =>
% 97.29/12.87 ((
% 97.29/12.87 (in__Cong) =>
% 97.29/12.87 ((
% 97.29/12.87 (exuE3u) =>
% 97.29/12.87 ((
% 97.29/12.87 (exu__Cong) =>
% 97.29/12.87 ((
% 97.29/12.87 (setadjoin__Cong) =>
% 97.29/12.87 ((
% 97.29/12.87 (powerset__Cong) =>
% 97.29/12.87 ((
% 97.29/12.87 (setunion__Cong) =>
% 97.29/12.87 ((
% 97.29/12.87 (exuEu) =>
% 97.29/12.87 ((
% 97.29/12.87 (descr__Cong) =>
% 97.29/12.87 ((
% 97.29/12.87 (dsetconstr__Cong) =>
% 97.29/12.87 ((
% 97.29/12.87 (subsetI1) =>
% 97.29/12.87 ((
% 97.29/12.87 (eqimpsubset2) =>
% 97.29/12.87 ((
% 97.29/12.87 (eqimpsubset1) =>
% 97.29/12.87 ((
% 97.29/12.87 (subsetI2) =>
% 97.29/12.87 ((
% 97.29/12.87 (emptysetsubset) =>
% 97.29/12.87 ((
% 97.29/12.87 (subsetE) =>
% 97.29/12.87 ((
% 97.29/12.87 (subsetE2) =>
% 97.29/12.87 ((
% 97.29/12.87 (notsubsetI) =>
% 97.29/12.87 ((
% 97.29/12.87 (notequalI1) =>
% 97.29/12.87 ((
% 97.29/12.87 (notequalI2) =>
% 97.29/12.87 ((
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% 97.29/12.87 ((
% 97.29/12.87 (subsetTrans) =>
% 97.29/12.87 ((
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% 97.29/12.87 ((
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% 97.29/12.87 ((
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% 97.29/12.87 ((
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% 97.29/12.87 ((
% 97.29/12.87 (powersetE1) =>
% 97.29/12.87 ((
% 97.29/12.87 (inPowerset) =>
% 97.29/12.87 ((
% 97.29/12.87 (powersetsubset) =>
% 97.29/12.87 ((
% 97.29/12.87 (sepInPowerset) =>
% 97.29/12.87 ((
% 97.29/12.87 (sepSubset) =>
% 97.29/12.87 ((
% 97.29/12.87 (binunionIL) =>
% 97.29/12.87 ((
% 97.29/12.87 (upairset2IR) =>
% 97.29/12.87 ((
% 97.29/12.87 (binunionIR) =>
% 97.29/12.87 ((
% 97.29/12.87 (binunionEcases) =>
% 97.29/12.87 ((
% 97.29/12.87 (binunionE) =>
% 97.29/12.87 ((
% 97.29/12.87 (binunionLsub) =>
% 97.29/12.87 ((
% 97.29/12.87 (binunionRsub) =>
% 97.29/12.87 ((
% 97.29/12.87 (binintersectI) =>
% 97.29/12.87 ((
% 97.29/12.87 (binintersectSubset5) =>
% 97.29/12.87 ((
% 97.29/12.87 (binintersectEL) =>
% 97.29/12.87 ((
% 97.29/12.87 (binintersectLsub) =>
% 97.29/12.87 ((
% 97.29/12.87 (binintersectSubset2) =>
% 97.29/12.87 ((
% 97.29/12.87 (binintersectSubset3) =>
% 97.29/12.87 ((
% 97.29/12.87 (binintersectER) =>
% 97.29/12.87 ((
% 97.29/12.87 (disjointsetsI1) =>
% 97.29/12.87 ((
% 97.29/12.87 (binintersectRsub) =>
% 97.29/12.87 ((
% 97.29/12.87 (binintersectSubset4) =>
% 97.29/12.87 ((
% 97.29/12.87 (binintersectSubset1) =>
% 97.29/12.87 ((
% 97.29/12.87 (bs114d) =>
% 97.29/12.87 ((
% 97.29/12.87 (setminusI) =>
% 97.29/12.87 ((
% 97.29/12.87 (setminusEL) =>
% 97.29/12.87 ((
% 97.29/12.87 (setminusER) =>
% 97.29/12.87 ((
% 97.29/12.87 (setminusSubset2) =>
% 97.29/12.87 ((
% 97.29/12.87 (setminusERneg) =>
% 97.29/12.87 ((
% 97.29/12.87 (setminusELneg) =>
% 97.29/12.87 ((
% 97.29/12.87 (setminusILneg) =>
% 97.29/12.87 ((
% 97.29/12.87 (setminusIRneg) =>
% 97.29/12.87 ((
% 97.29/12.87 (setminusLsub) =>
% 97.29/12.87 ((
% 97.29/12.87 (setminusSubset1) =>
% 97.29/12.87 ((
% 97.29/12.87 (symdiffE) =>
% 97.29/12.87 ((
% 97.29/12.87 (symdiffI1) =>
% 97.29/12.87 ((
% 97.29/12.87 (symdiffI2) =>
% 97.29/12.87 ((
% 97.29/12.87 (symdiffIneg1) =>
% 97.29/12.87 ((
% 97.29/12.87 (symdiffIneg2) =>
% 97.29/12.87 ((
% 97.29/12.87 (secondinupair) =>
% 97.29/12.87 ((
% 97.29/12.87 (setukpairIL) =>
% 97.29/12.87 ((
% 97.29/12.87 (setukpairIR) =>
% 97.29/12.87 ((
% 97.29/12.87 (kpairiskpair) =>
% 97.29/12.87 ((
% 97.29/12.87 (kpairp) =>
% 97.29/12.87 ((
% 97.29/12.87 (singletonsubset) =>
% 97.29/12.87 ((
% 97.29/12.87 (singletoninpowerset) =>
% 97.29/12.87 ((
% 97.29/12.87 (singletoninpowunion) =>
% 97.29/12.87 ((
% 97.29/12.87 (upairset2E) =>
% 97.29/12.87 ((
% 97.29/12.87 (upairsubunion) =>
% 97.29/12.87 ((
% 97.29/12.87 (upairinpowunion) =>
% 97.29/12.87 ((
% 97.29/12.87 (ubforcartprodlem1) =>
% 97.29/12.87 ((
% 97.29/12.87 (ubforcartprodlem2) =>
% 97.29/12.87 ((
% 97.29/12.87 (ubforcartprodlem3) =>
% 97.29/12.87 ((
% 97.29/12.87 (cartprodpairin) =>
% 97.29/12.87 ((
% 97.29/12.87 (cartprodmempair1) =>
% 97.29/12.87 ((
% 97.29/12.87 (cartprodmempair) =>
% 97.29/12.87 ((
% 97.29/12.87 (setunionE2) =>
% 97.29/12.87 ((
% 97.29/12.87 (setunionsingleton1) =>
% 97.29/12.87 ((
% 97.29/12.87 (setunionsingleton2) =>
% 97.29/12.87 ((
% 97.29/12.87 (setunionsingleton) =>
% 97.29/12.87 ((
% 97.29/12.87 (singletonprop) =>
% 97.29/12.87 ((
% 97.29/12.87 (ex1E1) =>
% 97.29/12.87 ((
% 97.29/12.87 (ex1I) =>
% 97.29/12.87 ((
% 97.29/12.87 (ex1I2) =>
% 97.29/12.87 ((
% 97.29/12.87 (singletonsuniq) =>
% 97.29/12.87 ((
% 97.29/12.87 (setukpairinjL1) =>
% 97.29/12.87 ((
% 97.29/12.87 (kfstsingleton) =>
% 97.29/12.87 ((
% 97.29/12.87 (theprop) =>
% 97.29/12.87 ((
% 97.29/12.87 (kfstpairEq) =>
% 97.29/12.87 ((
% 97.29/12.87 (cartprodfstin) =>
% 97.29/12.87 ((
% 97.29/12.87 (setukpairinjL2) =>
% 97.29/12.87 ((
% 97.29/12.87 (setukpairinjL) =>
% 97.29/12.87 ((
% 97.29/12.87 (setukpairinjR11) =>
% 97.29/12.87 ((
% 97.29/12.87 (setukpairinjR12) =>
% 97.29/12.87 ((
% 97.29/12.87 (setukpairinjR1) =>
% 97.29/12.87 ((
% 97.29/12.87 (upairequniteq) =>
% 97.29/12.87 ((
% 97.29/12.87 (setukpairinjR2) =>
% 97.29/12.87 ((
% 97.29/12.87 (setukpairinjR) =>
% 97.29/12.87 ((
% 97.29/12.87 (ksndsingleton) =>
% 97.29/12.87 ((
% 97.29/12.87 (ksndpairEq) =>
% 97.29/12.87 ((
% 97.29/12.87 (kpairsurjEq) =>
% 97.29/12.87 ((
% 97.29/12.87 (cartprodsndin) =>
% 97.29/12.87 ((
% 97.29/12.87 (cartprodpairmemEL) =>
% 97.29/12.87 ((
% 97.29/12.87 (cartprodpairmemER) =>
% 97.29/12.87 ((
% 97.29/12.87 (cartprodmempaircEq) =>
% 97.29/12.87 ((
% 97.29/12.87 (cartprodfstpairEq) =>
% 97.29/12.87 ((
% 97.29/12.87 (cartprodsndpairEq) =>
% 97.29/12.87 ((
% 97.29/12.87 (cartprodpairsurjEq) =>
% 97.29/12.87 ((
% 97.29/12.87 (dpsetconstrI) =>
% 97.29/12.87 ((
% 97.29/12.87 (dpsetconstrSub) =>
% 97.29/12.87 ((
% 97.29/12.87 (setOfPairsIsBReln) =>
% 97.29/12.87 ((
% 97.29/12.87 (dpsetconstrERa) =>
% 97.29/12.87 ((
% 97.29/12.87 (dpsetconstrEL1) =>
% 97.29/12.87 ((
% 97.29/12.87 (dpsetconstrEL2) =>
% 97.29/12.87 ((
% 97.29/12.87 (dpsetconstrER) =>
% 97.29/12.87 ((
% 97.29/12.87 (funcImageSingleton) =>
% 97.29/12.87 ((
% 97.29/12.87 (apProp) =>
% 97.29/12.87 ((
% 97.29/12.87 (app) =>
% 97.29/12.87 ((
% 97.29/12.87 (infuncsetfunc) =>
% 97.29/12.87 ((
% 97.29/12.87 (ap2p) =>
% 97.29/12.87 ((
% 97.29/12.87 (funcinfuncset) =>
% 97.29/12.87 ((
% 97.29/12.87 (lamProp) =>
% 97.29/12.87 ((
% 97.29/12.87 (lamp) =>
% 97.29/12.87 ((
% 97.29/12.87 (lam2p) =>
% 97.29/12.87 ((
% 97.29/12.87 (brelnall1) =>
% 97.29/12.87 ((
% 97.29/12.87 (brelnall2) =>
% 97.29/12.87 ((
% 97.29/12.87 (ex1E2) =>
% 97.29/12.87 ((
% 97.29/12.87 (funcGraphProp1) =>
% 97.29/12.87 ((
% 97.29/12.87 (funcGraphProp3) =>
% 97.29/12.87 ((
% 97.29/12.87 (funcGraphProp2) =>
% 97.29/12.87 ((
% 97.29/12.87 (funcextLem) =>
% 97.29/12.87 ((
% 97.29/12.87 (funcGraphProp4) =>
% 97.29/12.87 ((
% 97.29/12.87 (subbreln) =>
% 97.29/12.87 ((
% 97.29/12.87 (eqbreln) =>
% 97.29/12.87 ((
% 97.29/12.87 (funcext) =>
% 97.29/12.87 ((
% 97.29/12.87 (funcext2) =>
% 97.29/12.87 ((
% 97.29/12.87 (ap2apEq1) =>
% 97.29/12.87 ((
% 97.29/12.87 (ap2apEq2) =>
% 97.29/12.87 ((
% 97.29/12.87 (beta1) =>
% 97.29/12.87 ((
% 97.29/12.87 (eta1) =>
% 97.29/12.87 ((
% 97.29/12.87 (lam2lamEq) =>
% 97.29/12.87 ((
% 97.29/12.87 (beta2) =>
% 97.29/12.87 ((
% 97.29/12.87 (eta2) =>
% 97.29/12.87 ((
% 97.29/12.87 (iffalseProp1) =>
% 97.29/12.87 ((
% 97.29/12.87 (iffalseProp2) =>
% 97.29/12.87 ((
% 97.29/12.87 (iftrueProp1) =>
% 97.29/12.87 ((
% 97.29/12.87 (iftrueProp2) =>
% 97.29/12.87 ((
% 97.29/12.87 (ifSingleton) =>
% 97.29/12.87 ((
% 97.29/12.87 (ifp) =>
% 97.29/12.87 ((
% 97.29/12.87 (theeq) =>
% 97.29/12.87 ((
% 97.29/12.87 (iftrue) =>
% 97.29/12.87 ((
% 97.29/12.87 (iffalse) =>
% 97.29/12.87 ((
% 97.29/12.87 (iftrueorfalse) =>
% 97.29/12.87 ((
% 97.29/12.87 (binintersectT_lem) =>
% 97.29/12.87 ((
% 97.29/12.87 (binunionT_lem) =>
% 97.29/12.87 ((
% 97.29/12.87 (powersetT_lem) =>
% 97.29/12.87 ((
% 97.29/12.87 (setminusT_lem) =>
% 97.29/12.87 ((
% 97.29/12.87 (complementT_lem) =>
% 97.29/12.87 ((
% 97.29/12.87 (setextT) =>
% 97.29/12.87 ((
% 97.29/12.87 (subsetTI) =>
% 97.29/12.87 ((
% 97.29/12.87 (powersetTI1) =>
% 97.29/12.87 ((
% 97.29/12.87 (powersetTE1) =>
% 97.29/12.87 ((
% 97.29/12.87 (complementTI1) =>
% 97.29/12.87 ((
% 97.29/12.87 (complementTE1) =>
% 97.29/12.87 ((
% 97.29/12.87 (binintersectTELcontra) =>
% 97.29/12.87 ((
% 97.29/12.87 (binintersectTERcontra) =>
% 97.29/12.87 ((
% 97.29/12.87 (contrasubsetT) =>
% 97.29/12.87 ((
% 97.29/12.87 (contrasubsetT1) =>
% 97.29/12.87 ((
% 97.29/12.87 (contrasubsetT2) =>
% 97.29/12.87 ((
% 97.29/12.87 (contrasubsetT3) =>
% 97.29/12.87 ((
% 97.29/12.87 (doubleComplementI1) =>
% 97.29/12.87 ((
% 97.29/12.87 (doubleComplementE1) =>
% 97.29/12.87 ((
% 97.29/12.87 (doubleComplementSub1) =>
% 97.29/12.87 ((
% 97.29/12.87 (doubleComplementSub2) =>
% 97.29/12.87 ((
% 97.29/12.87 (doubleComplementEq) =>
% 97.29/12.87 ((
% 97.29/12.87 (complementTnotintersectT) =>
% 97.29/12.87 ((
% 97.29/12.87 (complementImpComplementIntersect) =>
% 97.29/12.87 ((
% 97.29/12.87 (complementSubsetComplementIntersect) =>
% 97.29/12.87 ((
% 97.29/12.87 (complementInPowersetComplementIntersect) =>
% 97.29/12.87 ((
% 97.29/12.87 (contraSubsetComplement) =>
% 97.29/12.87 ((
% 97.29/12.87 (complementTcontraSubset) =>
% 97.29/12.87 ((
% 97.29/12.87 (binunionTILcontra) =>
% 97.29/12.87 ((
% 97.29/12.87 (binunionTIRcontra) =>
% 97.29/12.87 ((
% 97.29/12.87 (inIntersectImpInUnion) =>
% 97.29/12.87 ((
% 97.29/12.87 (inIntersectImpInUnion2) =>
% 97.29/12.87 ((
% 97.29/12.87 (inIntersectImpInIntersectUnions) =>
% 97.29/12.87 ((
% 97.29/12.87 (intersectInPowersetIntersectUnions) =>
% 97.29/12.87 ((
% 97.29/12.87 (inComplementUnionImpNotIn1) =>
% 97.29/12.87 ((
% 97.29/12.87 (inComplementUnionImpInComplement1) =>
% 97.29/12.87 ((
% 97.29/12.87 (binunionTE) =>
% 97.29/12.87 ((
% 97.29/12.87 (binunionTEcontra) =>
% 97.29/12.87 ((
% 97.29/12.87 (demorgan2a1) =>
% 97.29/12.87 ((
% 97.29/12.87 (complementUnionInPowersetComplement) =>
% 97.29/12.87 ((
% 97.29/12.87 (demorgan2a2) =>
% 97.29/12.87 ((
% 97.29/12.87 (demorgan1a) =>
% 97.29/12.87 ((
% 97.29/12.87 (demorgan1b) =>
% 97.29/12.87 ((
% 97.29/12.87 (demorgan1) =>
% 97.29/12.87 ((
% 97.29/12.87 (demorgan2a) =>
% 97.29/12.87 ((
% 97.29/12.87 (demorgan2b2) =>
% 97.29/12.87 ((
% 97.29/12.87 (demorgan2b) =>
% 97.29/12.87 ((
% 97.29/12.87 (demorgan2) =>
% 97.29/12.87 ((
% 97.29/12.87 (woz13rule0) =>
% 97.29/12.87 ((
% 97.29/12.87 (woz13rule1) =>
% 97.29/12.87 ((
% 97.29/12.87 (woz13rule2) =>
% 97.29/12.87 ((
% 97.29/12.87 (woz13rule3) =>
% 97.29/12.87 ((
% 97.29/12.87 (woz13rule4) =>
% 97.29/12.87 ((
% 97.29/12.87 (woz1_1) =>
% 97.29/12.87 ((
% 97.29/12.87 (woz1_2) =>
% 97.29/12.87 ((
% 97.29/12.87 (woz1_3) =>
% 97.29/12.87 ((
% 97.29/12.87 (woz1_4) =>
% 97.29/12.87 ((
% 97.29/12.87 (woz1_5) =>
% 97.29/12.87 ((
% 97.29/12.87 (breln1all2) =>
% 97.29/12.87 ((
% 97.29/12.87 (breln1SetBreln1) =>
% 97.29/12.87 ((
% 97.29/12.87 (choice2fnsingleton) =>
% 97.29/12.87 ((
% 97.29/12.87 (!!) @ (
% 97.29/12.87 (('#B') @ (
% 97.29/12.87 !!) @
% 97.29/12.87 (
% 97.29/12.87 (
% 97.29/12.87 ('#S') @ (
% 97.29/12.87 (
% 97.29/12.87 ('#B') @ (
% 97.29/12.87 '#B') @
% 97.29/12.87 breln1)) @
% 97.29/12.87 (
% 97.29/12.87 (
% 97.29/12.87 ('#S') @ dpsetconstr @
% 97.29/12.87 (
% 97.29/12.87 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.29/12.87 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl142])).
% 97.29/12.87 thf(zip_derived_cl174, plain,
% 97.29/12.87 (~ (((notinemptyset) =>
% 97.29/12.87 (((exuE3e) =>
% 97.29/12.87 (((setext) =>
% 97.29/12.87 (((emptyI) =>
% 97.29/12.87 (((noeltsimpempty) =>
% 97.29/12.87 (((setbeta) =>
% 97.29/12.87 (((nonemptyE1) =>
% 97.29/12.87 (((nonemptyI) =>
% 97.29/12.87 (((nonemptyI1) =>
% 97.29/12.87 (((setadjoinIL) =>
% 97.29/12.87 (((in @ emptyset @
% 97.29/12.87 (setadjoin @ emptyset @ emptyset)) =>
% 97.29/12.87 (((setadjoinIR) =>
% 97.29/12.87 (((setadjoinE) =>
% 97.29/12.87 (((setadjoinOr) =>
% 97.29/12.87 (((setoftrueEq) =>
% 97.29/12.87 (((powersetI) =>
% 97.29/12.87 (((emptyinPowerset) =>
% 97.29/12.87 (((emptyInPowerset) =>
% 97.29/12.87 (((powersetE) =>
% 97.29/12.87 (((setunionI) =>
% 97.29/12.87 (((setunionE) =>
% 97.29/12.87 (((subPowSU) =>
% 97.29/12.87 (((exuE2) =>
% 97.29/12.87 (((nonemptyImpWitness) =>
% 97.29/12.87 (((uniqinunit) =>
% 97.29/12.87 (((notinsingleton) =>
% 97.29/12.87 (((eqinunit) =>
% 97.29/12.87 (((singletonsswitch) =>
% 97.29/12.87 (((upairsetE) =>
% 97.29/12.87 (((upairsetIL) =>
% 97.29/12.87 ((
% 97.29/12.87 (upairsetIR) =>
% 97.29/12.87 ((
% 97.29/12.87 (emptyE1) =>
% 97.29/12.87 ((
% 97.29/12.87 (vacuousDall) =>
% 97.29/12.87 ((
% 97.29/12.87 (quantDeMorgan1) =>
% 97.29/12.87 ((
% 97.29/12.87 (quantDeMorgan2) =>
% 97.29/12.87 ((
% 97.29/12.87 (quantDeMorgan3) =>
% 97.29/12.87 ((
% 97.29/12.87 (quantDeMorgan4) =>
% 97.29/12.87 ((
% 97.29/12.87 (prop2setI) =>
% 97.29/12.87 ((
% 97.29/12.87 (prop2set2propI) =>
% 97.29/12.87 ((
% 97.29/12.87 (notdexE) =>
% 97.29/12.87 ((
% 97.29/12.87 (notdallE) =>
% 97.29/12.87 ((
% 97.29/12.87 (exuI1) =>
% 97.29/12.87 ((
% 97.29/12.87 (exuI3) =>
% 97.29/12.87 ((
% 97.29/12.87 (exuI2) =>
% 97.29/12.87 ((
% 97.29/12.87 (inCongP) =>
% 97.29/12.87 ((
% 97.29/12.87 (in__Cong) =>
% 97.29/12.87 ((
% 97.29/12.87 (exuE3u) =>
% 97.29/12.87 ((
% 97.29/12.87 (exu__Cong) =>
% 97.29/12.87 ((
% 97.29/12.87 (setadjoin__Cong) =>
% 97.29/12.87 ((
% 97.29/12.87 (powerset__Cong) =>
% 97.29/12.87 ((
% 97.29/12.87 (setunion__Cong) =>
% 97.29/12.87 ((
% 97.29/12.87 (exuEu) =>
% 97.29/12.87 ((
% 97.29/12.87 (descr__Cong) =>
% 97.29/12.87 ((
% 97.29/12.87 (dsetconstr__Cong) =>
% 97.29/12.87 ((
% 97.29/12.87 (subsetI1) =>
% 97.29/12.87 ((
% 97.29/12.87 (eqimpsubset2) =>
% 97.29/12.87 ((
% 97.29/12.87 (eqimpsubset1) =>
% 97.29/12.87 ((
% 97.29/12.87 (subsetI2) =>
% 97.29/12.87 ((
% 97.29/12.87 (emptysetsubset) =>
% 97.29/12.87 ((
% 97.29/12.87 (subsetE) =>
% 97.29/12.87 ((
% 97.29/12.87 (subsetE2) =>
% 97.29/12.87 ((
% 97.29/12.87 (notsubsetI) =>
% 97.29/12.87 ((
% 97.29/12.87 (notequalI1) =>
% 97.29/12.87 ((
% 97.29/12.87 (notequalI2) =>
% 97.29/12.87 ((
% 97.29/12.87 (subsetRefl) =>
% 97.29/12.87 ((
% 97.29/12.87 (subsetTrans) =>
% 97.29/12.87 ((
% 97.29/12.87 (setadjoinSub) =>
% 97.29/12.87 ((
% 97.29/12.87 (setadjoinSub2) =>
% 97.29/12.87 ((
% 97.29/12.87 (subset2powerset) =>
% 97.29/12.87 ((
% 97.29/12.87 (setextsub) =>
% 97.29/12.87 ((
% 97.29/12.87 (subsetemptysetimpeq) =>
% 97.29/12.87 ((
% 97.29/12.87 (powersetI1) =>
% 97.29/12.87 ((
% 97.29/12.87 (powersetE1) =>
% 97.29/12.87 ((
% 97.29/12.87 (inPowerset) =>
% 97.29/12.87 ((
% 97.29/12.87 (powersetsubset) =>
% 97.29/12.87 ((
% 97.29/12.87 (sepInPowerset) =>
% 97.29/12.87 ((
% 97.29/12.87 (sepSubset) =>
% 97.29/12.87 ((
% 97.29/12.87 (binunionIL) =>
% 97.29/12.87 ((
% 97.29/12.87 (upairset2IR) =>
% 97.29/12.87 ((
% 97.29/12.87 (binunionIR) =>
% 97.29/12.87 ((
% 97.29/12.87 (binunionEcases) =>
% 97.29/12.87 ((
% 97.29/12.87 (binunionE) =>
% 97.29/12.87 ((
% 97.29/12.87 (binunionLsub) =>
% 97.29/12.87 ((
% 97.29/12.87 (binunionRsub) =>
% 97.29/12.87 ((
% 97.29/12.87 (binintersectI) =>
% 97.29/12.87 ((
% 97.29/12.87 (binintersectSubset5) =>
% 97.29/12.87 ((
% 97.29/12.87 (binintersectEL) =>
% 97.29/12.87 ((
% 97.29/12.87 (binintersectLsub) =>
% 97.29/12.87 ((
% 97.29/12.87 (binintersectSubset2) =>
% 97.29/12.87 ((
% 97.29/12.87 (binintersectSubset3) =>
% 97.29/12.87 ((
% 97.29/12.87 (binintersectER) =>
% 97.29/12.87 ((
% 97.29/12.87 (disjointsetsI1) =>
% 97.29/12.87 ((
% 97.29/12.87 (binintersectRsub) =>
% 97.29/12.87 ((
% 97.29/12.87 (binintersectSubset4) =>
% 97.29/12.87 ((
% 97.29/12.87 (binintersectSubset1) =>
% 97.29/12.87 ((
% 97.29/12.87 (bs114d) =>
% 97.29/12.87 ((
% 97.29/12.87 (setminusI) =>
% 97.29/12.87 ((
% 97.29/12.87 (setminusEL) =>
% 97.29/12.87 ((
% 97.29/12.87 (setminusER) =>
% 97.29/12.87 ((
% 97.29/12.87 (setminusSubset2) =>
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% 97.29/12.87 ((
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% 97.29/12.87 (setminusIRneg) =>
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% 97.29/12.87 ((
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% 97.29/12.87 ((
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% 97.29/12.87 ((
% 97.29/12.87 (symdiffI2) =>
% 97.29/12.87 ((
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% 97.29/12.87 ((
% 97.29/12.87 (symdiffIneg2) =>
% 97.29/12.87 ((
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% 97.29/12.87 ((
% 97.29/12.87 (setukpairIL) =>
% 97.29/12.87 ((
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% 97.29/12.87 ((
% 97.29/12.87 (kpairiskpair) =>
% 97.29/12.87 ((
% 97.29/12.87 (kpairp) =>
% 97.29/12.87 ((
% 97.29/12.87 (singletonsubset) =>
% 97.29/12.87 ((
% 97.29/12.87 (singletoninpowerset) =>
% 97.29/12.87 ((
% 97.29/12.87 (singletoninpowunion) =>
% 97.29/12.87 ((
% 97.29/12.87 (upairset2E) =>
% 97.29/12.87 ((
% 97.29/12.87 (upairsubunion) =>
% 97.29/12.87 ((
% 97.29/12.87 (upairinpowunion) =>
% 97.29/12.87 ((
% 97.29/12.87 (ubforcartprodlem1) =>
% 97.29/12.87 ((
% 97.29/12.87 (ubforcartprodlem2) =>
% 97.29/12.87 ((
% 97.29/12.87 (ubforcartprodlem3) =>
% 97.29/12.87 ((
% 97.29/12.87 (cartprodpairin) =>
% 97.29/12.87 ((
% 97.29/12.87 (cartprodmempair1) =>
% 97.29/12.87 ((
% 97.29/12.87 (cartprodmempair) =>
% 97.29/12.87 ((
% 97.29/12.87 (setunionE2) =>
% 97.29/12.87 ((
% 97.29/12.87 (setunionsingleton1) =>
% 97.29/12.87 ((
% 97.29/12.87 (setunionsingleton2) =>
% 97.29/12.87 ((
% 97.29/12.87 (setunionsingleton) =>
% 97.29/12.87 ((
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% 97.29/12.87 ((
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% 97.29/12.87 ((
% 97.29/12.87 (ex1I) =>
% 97.29/12.87 ((
% 97.29/12.87 (ex1I2) =>
% 97.29/12.87 ((
% 97.29/12.87 (singletonsuniq) =>
% 97.29/12.87 ((
% 97.29/12.87 (setukpairinjL1) =>
% 97.29/12.87 ((
% 97.93/12.87 (kfstsingleton) =>
% 97.93/12.87 ((
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% 97.93/12.87 ((
% 97.93/12.87 (kfstpairEq) =>
% 97.93/12.87 ((
% 97.93/12.87 (cartprodfstin) =>
% 97.93/12.87 ((
% 97.93/12.87 (setukpairinjL2) =>
% 97.93/12.87 ((
% 97.93/12.87 (setukpairinjL) =>
% 97.93/12.87 ((
% 97.93/12.87 (setukpairinjR11) =>
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% 97.93/12.87 (setukpairinjR12) =>
% 97.93/12.87 ((
% 97.93/12.87 (setukpairinjR1) =>
% 97.93/12.87 ((
% 97.93/12.87 (upairequniteq) =>
% 97.93/12.87 ((
% 97.93/12.87 (setukpairinjR2) =>
% 97.93/12.87 ((
% 97.93/12.87 (setukpairinjR) =>
% 97.93/12.87 ((
% 97.93/12.87 (ksndsingleton) =>
% 97.93/12.87 ((
% 97.93/12.87 (ksndpairEq) =>
% 97.93/12.87 ((
% 97.93/12.87 (kpairsurjEq) =>
% 97.93/12.87 ((
% 97.93/12.87 (cartprodsndin) =>
% 97.93/12.87 ((
% 97.93/12.87 (cartprodpairmemEL) =>
% 97.93/12.87 ((
% 97.93/12.87 (cartprodpairmemER) =>
% 97.93/12.87 ((
% 97.93/12.87 (cartprodmempaircEq) =>
% 97.93/12.87 ((
% 97.93/12.87 (cartprodfstpairEq) =>
% 97.93/12.87 ((
% 97.93/12.87 (cartprodsndpairEq) =>
% 97.93/12.87 ((
% 97.93/12.87 (cartprodpairsurjEq) =>
% 97.93/12.87 ((
% 97.93/12.87 (dpsetconstrI) =>
% 97.93/12.87 ((
% 97.93/12.87 (dpsetconstrSub) =>
% 97.93/12.87 ((
% 97.93/12.87 (setOfPairsIsBReln) =>
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% 97.93/12.87 (dpsetconstrEL2) =>
% 97.93/12.87 ((
% 97.93/12.87 (dpsetconstrER) =>
% 97.93/12.87 ((
% 97.93/12.87 (funcImageSingleton) =>
% 97.93/12.87 ((
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% 97.93/12.87 ((
% 97.93/12.87 (app) =>
% 97.93/12.87 ((
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% 97.93/12.87 ((
% 97.93/12.87 (ap2p) =>
% 97.93/12.87 ((
% 97.93/12.87 (funcinfuncset) =>
% 97.93/12.87 ((
% 97.93/12.87 (lamProp) =>
% 97.93/12.87 ((
% 97.93/12.87 (lamp) =>
% 97.93/12.87 ((
% 97.93/12.87 (lam2p) =>
% 97.93/12.87 ((
% 97.93/12.87 (brelnall1) =>
% 97.93/12.87 ((
% 97.93/12.87 (brelnall2) =>
% 97.93/12.87 ((
% 97.93/12.87 (ex1E2) =>
% 97.93/12.87 ((
% 97.93/12.87 (funcGraphProp1) =>
% 97.93/12.87 ((
% 97.93/12.87 (funcGraphProp3) =>
% 97.93/12.87 ((
% 97.93/12.87 (funcGraphProp2) =>
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% 97.93/12.87 ((
% 97.93/12.87 (funcGraphProp4) =>
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% 97.93/12.87 (funcext) =>
% 97.93/12.87 ((
% 97.93/12.87 (funcext2) =>
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% 97.93/12.87 (ap2apEq2) =>
% 97.93/12.87 ((
% 97.93/12.87 (beta1) =>
% 97.93/12.87 ((
% 97.93/12.87 (eta1) =>
% 97.93/12.87 ((
% 97.93/12.87 (lam2lamEq) =>
% 97.93/12.87 ((
% 97.93/12.87 (beta2) =>
% 97.93/12.87 ((
% 97.93/12.87 (eta2) =>
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% 97.93/12.87 (iffalseProp1) =>
% 97.93/12.87 ((
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% 97.93/12.87 (ifp) =>
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% 97.93/12.87 (iftrue) =>
% 97.93/12.87 ((
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% 97.93/12.87 ((
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% 97.93/12.87 ((
% 97.93/12.87 (binunionT_lem) =>
% 97.93/12.87 ((
% 97.93/12.87 (powersetT_lem) =>
% 97.93/12.87 ((
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% 97.93/12.87 ((
% 97.93/12.87 (complementT_lem) =>
% 97.93/12.87 ((
% 97.93/12.87 (setextT) =>
% 97.93/12.87 ((
% 97.93/12.87 (subsetTI) =>
% 97.93/12.87 ((
% 97.93/12.87 (powersetTI1) =>
% 97.93/12.87 ((
% 97.93/12.87 (powersetTE1) =>
% 97.93/12.87 ((
% 97.93/12.87 (complementTI1) =>
% 97.93/12.87 ((
% 97.93/12.87 (complementTE1) =>
% 97.93/12.87 ((
% 97.93/12.87 (binintersectTELcontra) =>
% 97.93/12.87 ((
% 97.93/12.87 (binintersectTERcontra) =>
% 97.93/12.87 ((
% 97.93/12.87 (contrasubsetT) =>
% 97.93/12.87 ((
% 97.93/12.87 (contrasubsetT1) =>
% 97.93/12.87 ((
% 97.93/12.87 (contrasubsetT2) =>
% 97.93/12.87 ((
% 97.93/12.87 (contrasubsetT3) =>
% 97.93/12.87 ((
% 97.93/12.87 (doubleComplementI1) =>
% 97.93/12.87 ((
% 97.93/12.87 (doubleComplementE1) =>
% 97.93/12.87 ((
% 97.93/12.87 (doubleComplementSub1) =>
% 97.93/12.87 ((
% 97.93/12.87 (doubleComplementSub2) =>
% 97.93/12.87 ((
% 97.93/12.87 (doubleComplementEq) =>
% 97.93/12.87 ((
% 97.93/12.87 (complementTnotintersectT) =>
% 97.93/12.87 ((
% 97.93/12.87 (complementImpComplementIntersect) =>
% 97.93/12.87 ((
% 97.93/12.87 (complementSubsetComplementIntersect) =>
% 97.93/12.87 ((
% 97.93/12.87 (complementInPowersetComplementIntersect) =>
% 97.93/12.87 ((
% 97.93/12.87 (contraSubsetComplement) =>
% 97.93/12.87 ((
% 97.93/12.87 (complementTcontraSubset) =>
% 97.93/12.87 ((
% 97.93/12.87 (binunionTILcontra) =>
% 97.93/12.87 ((
% 97.93/12.87 (binunionTIRcontra) =>
% 97.93/12.87 ((
% 97.93/12.87 (inIntersectImpInUnion) =>
% 97.93/12.87 ((
% 97.93/12.87 (inIntersectImpInUnion2) =>
% 97.93/12.87 ((
% 97.93/12.87 (inIntersectImpInIntersectUnions) =>
% 97.93/12.87 ((
% 97.93/12.87 (intersectInPowersetIntersectUnions) =>
% 97.93/12.87 ((
% 97.93/12.87 (inComplementUnionImpNotIn1) =>
% 97.93/12.87 ((
% 97.93/12.87 (inComplementUnionImpInComplement1) =>
% 97.93/12.87 ((
% 97.93/12.87 (binunionTE) =>
% 97.93/12.87 ((
% 97.93/12.87 (binunionTEcontra) =>
% 97.93/12.87 ((
% 97.93/12.87 (demorgan2a1) =>
% 97.93/12.87 ((
% 97.93/12.87 (complementUnionInPowersetComplement) =>
% 97.93/12.87 ((
% 97.93/12.87 (demorgan2a2) =>
% 97.93/12.87 ((
% 97.93/12.87 (demorgan1a) =>
% 97.93/12.87 ((
% 97.93/12.87 (demorgan1b) =>
% 97.93/12.87 ((
% 97.93/12.87 (demorgan1) =>
% 97.93/12.87 ((
% 97.93/12.87 (demorgan2a) =>
% 97.93/12.87 ((
% 97.93/12.87 (demorgan2b2) =>
% 97.93/12.87 ((
% 97.93/12.87 (demorgan2b) =>
% 97.93/12.87 ((
% 97.93/12.87 (demorgan2) =>
% 97.93/12.87 ((
% 97.93/12.87 (woz13rule0) =>
% 97.93/12.87 ((
% 97.93/12.87 (woz13rule1) =>
% 97.93/12.87 ((
% 97.93/12.87 (woz13rule2) =>
% 97.93/12.87 ((
% 97.93/12.87 (woz13rule3) =>
% 97.93/12.87 ((
% 97.93/12.87 (woz13rule4) =>
% 97.93/12.87 ((
% 97.93/12.87 (woz1_1) =>
% 97.93/12.87 ((
% 97.93/12.87 (woz1_2) =>
% 97.93/12.87 ((
% 97.93/12.87 (woz1_3) =>
% 97.93/12.87 ((
% 97.93/12.87 (woz1_4) =>
% 97.93/12.87 ((
% 97.93/12.87 (woz1_5) =>
% 97.93/12.87 ((
% 97.93/12.87 (breln1all2) =>
% 97.93/12.87 ((
% 97.93/12.87 (breln1SetBreln1) =>
% 97.93/12.87 ((
% 97.93/12.87 (choice2fnsingleton) =>
% 97.93/12.87 ((
% 97.93/12.87 (!!) @ (
% 97.93/12.87 (('#B') @ (
% 97.93/12.87 !!) @
% 97.93/12.87 (
% 97.93/12.87 (
% 97.93/12.87 ('#S') @ (
% 97.93/12.87 (
% 97.93/12.87 ('#B') @ (
% 97.93/12.87 '#B') @
% 97.93/12.87 breln1)) @
% 97.93/12.87 (
% 97.93/12.87 (
% 97.93/12.87 ('#S') @ dpsetconstr @
% 97.93/12.87 (
% 97.93/12.87 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.93/12.87 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl158])).
% 97.93/12.87 thf(zip_derived_cl189, plain,
% 97.93/12.87 (~ (((exuE3e) =>
% 97.93/12.87 (((setext) =>
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% 97.93/12.87 (((noeltsimpempty) =>
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% 97.93/12.87 (((nonemptyI) =>
% 97.93/12.87 (((nonemptyI1) =>
% 97.93/12.87 (((setadjoinIL) =>
% 97.93/12.87 (((in @ emptyset @
% 97.93/12.87 (setadjoin @ emptyset @ emptyset)) =>
% 97.93/12.87 (((setadjoinIR) =>
% 97.93/12.87 (((setadjoinE) =>
% 97.93/12.87 (((setadjoinOr) =>
% 97.93/12.87 (((setoftrueEq) =>
% 97.93/12.87 (((powersetI) =>
% 97.93/12.87 (((emptyinPowerset) =>
% 97.93/12.87 (((emptyInPowerset) =>
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% 97.93/12.87 (((setunionE) =>
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% 97.93/12.87 (((upairsetIR) =>
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% 97.93/12.87 ((
% 97.93/12.87 (vacuousDall) =>
% 97.93/12.87 ((
% 97.93/12.87 (quantDeMorgan1) =>
% 97.93/12.87 ((
% 97.93/12.87 (quantDeMorgan2) =>
% 97.93/12.87 ((
% 97.93/12.87 (quantDeMorgan3) =>
% 97.93/12.87 ((
% 97.93/12.87 (quantDeMorgan4) =>
% 97.93/12.87 ((
% 97.93/12.87 (prop2setI) =>
% 97.93/12.87 ((
% 97.93/12.87 (prop2set2propI) =>
% 97.93/12.87 ((
% 97.93/12.87 (notdexE) =>
% 97.93/12.87 ((
% 97.93/12.87 (notdallE) =>
% 97.93/12.87 ((
% 97.93/12.87 (exuI1) =>
% 97.93/12.87 ((
% 97.93/12.87 (exuI3) =>
% 97.93/12.87 ((
% 97.93/12.87 (exuI2) =>
% 97.93/12.87 ((
% 97.93/12.87 (inCongP) =>
% 97.93/12.87 ((
% 97.93/12.87 (in__Cong) =>
% 97.93/12.87 ((
% 97.93/12.87 (exuE3u) =>
% 97.93/12.87 ((
% 97.93/12.87 (exu__Cong) =>
% 97.93/12.87 ((
% 97.93/12.87 (setadjoin__Cong) =>
% 97.93/12.87 ((
% 97.93/12.87 (powerset__Cong) =>
% 97.93/12.87 ((
% 97.93/12.87 (setunion__Cong) =>
% 97.93/12.87 ((
% 97.93/12.87 (exuEu) =>
% 97.93/12.87 ((
% 97.93/12.87 (descr__Cong) =>
% 97.93/12.87 ((
% 97.93/12.87 (dsetconstr__Cong) =>
% 97.93/12.87 ((
% 97.93/12.87 (subsetI1) =>
% 97.93/12.87 ((
% 97.93/12.87 (eqimpsubset2) =>
% 97.93/12.87 ((
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% 97.93/12.87 (subsetE2) =>
% 97.93/12.87 ((
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% 97.93/12.87 ((
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% 97.93/12.87 ((
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% 97.93/12.87 ((
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% 97.93/12.87 ((
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% 97.93/12.87 ((
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% 97.93/12.87 ((
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% 97.93/12.87 ((
% 97.93/12.87 (binunionEcases) =>
% 97.93/12.87 ((
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% 97.93/12.87 ((
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% 97.93/12.87 ((
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% 97.93/12.87 ((
% 97.93/12.87 (binintersectSubset5) =>
% 97.93/12.87 ((
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% 97.93/12.87 ((
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% 97.93/12.87 ((
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% 97.93/12.87 (binintersectSubset4) =>
% 97.93/12.87 ((
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% 97.93/12.87 ((
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% 97.93/12.87 ((
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% 97.93/12.87 (setminusERneg) =>
% 97.93/12.87 ((
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% 97.93/12.87 ((
% 97.93/12.87 (setminusILneg) =>
% 97.93/12.87 ((
% 97.93/12.87 (setminusIRneg) =>
% 97.93/12.87 ((
% 97.93/12.87 (setminusLsub) =>
% 97.93/12.87 ((
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% 97.93/12.87 ((
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% 97.93/12.87 ((
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% 97.93/12.87 ((
% 97.93/12.87 (symdiffI2) =>
% 97.93/12.87 ((
% 97.93/12.87 (symdiffIneg1) =>
% 97.93/12.87 ((
% 97.93/12.87 (symdiffIneg2) =>
% 97.93/12.87 ((
% 97.93/12.87 (secondinupair) =>
% 97.93/12.87 ((
% 97.93/12.87 (setukpairIL) =>
% 97.93/12.87 ((
% 97.93/12.87 (setukpairIR) =>
% 97.93/12.87 ((
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% 97.93/12.87 ((
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% 97.93/12.87 (cartprodsndpairEq) =>
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% 97.93/12.87 (cartprodpairsurjEq) =>
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% 97.93/12.87 ((
% 97.93/12.87 (binintersectTERcontra) =>
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% 97.93/12.87 (contrasubsetT3) =>
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% 97.93/12.87 (doubleComplementSub2) =>
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% 97.93/12.87 (complementTnotintersectT) =>
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% 97.93/12.87 (complementImpComplementIntersect) =>
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% 97.93/12.87 (complementSubsetComplementIntersect) =>
% 97.93/12.87 ((
% 97.93/12.87 (complementInPowersetComplementIntersect) =>
% 97.93/12.87 ((
% 97.93/12.87 (contraSubsetComplement) =>
% 97.93/12.87 ((
% 97.93/12.87 (complementTcontraSubset) =>
% 97.93/12.87 ((
% 97.93/12.87 (binunionTILcontra) =>
% 97.93/12.87 ((
% 97.93/12.87 (binunionTIRcontra) =>
% 97.93/12.87 ((
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% 97.93/12.87 ((
% 97.93/12.87 (inIntersectImpInUnion2) =>
% 97.93/12.87 ((
% 97.93/12.87 (inIntersectImpInIntersectUnions) =>
% 97.93/12.87 ((
% 97.93/12.87 (intersectInPowersetIntersectUnions) =>
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% 97.93/12.87 (inComplementUnionImpInComplement1) =>
% 97.93/12.87 ((
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% 97.93/12.87 ((
% 97.93/12.87 (binunionTEcontra) =>
% 97.93/12.87 ((
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% 97.93/12.87 ((
% 97.93/12.87 (complementUnionInPowersetComplement) =>
% 97.93/12.87 ((
% 97.93/12.87 (demorgan2a2) =>
% 97.93/12.87 ((
% 97.93/12.87 (demorgan1a) =>
% 97.93/12.87 ((
% 97.93/12.87 (demorgan1b) =>
% 97.93/12.87 ((
% 97.93/12.87 (demorgan1) =>
% 97.93/12.87 ((
% 97.93/12.87 (demorgan2a) =>
% 97.93/12.87 ((
% 97.93/12.87 (demorgan2b2) =>
% 97.93/12.87 ((
% 97.93/12.87 (demorgan2b) =>
% 97.93/12.87 ((
% 97.93/12.87 (demorgan2) =>
% 97.93/12.87 ((
% 97.93/12.87 (woz13rule0) =>
% 97.93/12.87 ((
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% 97.93/12.87 ((
% 97.93/12.87 (woz13rule2) =>
% 97.93/12.87 ((
% 97.93/12.87 (woz13rule3) =>
% 97.93/12.87 ((
% 97.93/12.87 (woz13rule4) =>
% 97.93/12.87 ((
% 97.93/12.87 (woz1_1) =>
% 97.93/12.87 ((
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% 97.93/12.87 ((
% 97.93/12.87 (woz1_5) =>
% 97.93/12.87 ((
% 97.93/12.87 (breln1all2) =>
% 97.93/12.87 ((
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% 97.93/12.87 (
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% 97.93/12.87 (exu__Cong) =>
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% 97.93/12.87 (powerset__Cong) =>
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% 97.93/12.87 ((
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% 97.93/12.87 ((
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% 97.93/12.87 (complementUnionInPowersetComplement) =>
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% 97.93/12.87 (demorgan1a) =>
% 97.93/12.87 ((
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% 97.93/12.87 ((
% 97.93/12.87 (demorgan2a) =>
% 97.93/12.87 ((
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% 97.93/12.88 (contraSubsetComplement) =>
% 97.93/12.88 ((
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% 97.93/12.88 ((
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% 97.93/12.88 ((
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% 97.93/12.88 ((
% 97.93/12.88 (demorgan2b2) =>
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% 98.01/12.89 (doubleComplementI1) =>
% 98.01/12.89 ((
% 98.01/12.89 (doubleComplementE1) =>
% 98.01/12.89 ((
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% 98.01/12.89 ((
% 98.01/12.89 (doubleComplementSub2) =>
% 98.01/12.89 ((
% 98.01/12.89 (doubleComplementEq) =>
% 98.01/12.89 ((
% 98.01/12.89 (complementTnotintersectT) =>
% 98.01/12.89 ((
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% 98.01/12.89 ((
% 98.01/12.89 (complementSubsetComplementIntersect) =>
% 98.01/12.89 ((
% 98.01/12.89 (complementInPowersetComplementIntersect) =>
% 98.01/12.89 ((
% 98.01/12.89 (contraSubsetComplement) =>
% 98.01/12.89 ((
% 98.01/12.89 (complementTcontraSubset) =>
% 98.01/12.89 ((
% 98.01/12.89 (binunionTILcontra) =>
% 98.01/12.89 ((
% 98.01/12.89 (binunionTIRcontra) =>
% 98.01/12.89 ((
% 98.01/12.89 (inIntersectImpInUnion) =>
% 98.01/12.89 ((
% 98.01/12.89 (inIntersectImpInUnion2) =>
% 98.01/12.89 ((
% 98.01/12.89 (inIntersectImpInIntersectUnions) =>
% 98.01/12.89 ((
% 98.01/12.89 (intersectInPowersetIntersectUnions) =>
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% 98.01/12.89 (inComplementUnionImpNotIn1) =>
% 98.01/12.89 ((
% 98.01/12.89 (inComplementUnionImpInComplement1) =>
% 98.01/12.89 ((
% 98.01/12.89 (binunionTE) =>
% 98.01/12.89 ((
% 98.01/12.89 (binunionTEcontra) =>
% 98.01/12.89 ((
% 98.01/12.89 (demorgan2a1) =>
% 98.01/12.89 ((
% 98.01/12.89 (complementUnionInPowersetComplement) =>
% 98.01/12.89 ((
% 98.01/12.89 (demorgan2a2) =>
% 98.01/12.89 ((
% 98.01/12.89 (demorgan1a) =>
% 98.01/12.89 ((
% 98.01/12.89 (demorgan1b) =>
% 98.01/12.89 ((
% 98.01/12.89 (demorgan1) =>
% 98.01/12.89 ((
% 98.01/12.89 (demorgan2a) =>
% 98.01/12.89 ((
% 98.01/12.89 (demorgan2b2) =>
% 98.01/12.89 ((
% 98.01/12.89 (demorgan2b) =>
% 98.01/12.89 ((
% 98.01/12.89 (demorgan2) =>
% 98.01/12.89 ((
% 98.01/12.89 (woz13rule0) =>
% 98.01/12.89 ((
% 98.01/12.89 (woz13rule1) =>
% 98.01/12.89 ((
% 98.01/12.89 (woz13rule2) =>
% 98.01/12.89 ((
% 98.01/12.89 (woz13rule3) =>
% 98.01/12.89 ((
% 98.01/12.89 (woz13rule4) =>
% 98.01/12.89 ((
% 98.01/12.89 (woz1_1) =>
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% 98.01/12.89 ((
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% 98.01/12.89 ((
% 98.01/12.89 (woz1_5) =>
% 98.01/12.89 ((
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% 98.01/12.89 breln1)) @
% 98.01/12.89 (
% 98.01/12.89 (
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% 98.01/12.89 (
% 98.01/12.89 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.01/12.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl251])).
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% 98.01/12.89 (((quantDeMorgan4) =>
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% 98.01/12.89 ((
% 98.01/12.89 (prop2set2propI) =>
% 98.01/12.89 ((
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% 98.01/12.89 ((
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% 98.01/12.89 ((
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% 98.01/12.89 ((
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% 98.01/12.89 ((
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% 98.01/12.89 ((
% 98.01/12.89 (in__Cong) =>
% 98.01/12.89 ((
% 98.01/12.89 (exuE3u) =>
% 98.01/12.89 ((
% 98.01/12.89 (exu__Cong) =>
% 98.01/12.89 ((
% 98.01/12.89 (setadjoin__Cong) =>
% 98.01/12.89 ((
% 98.01/12.89 (powerset__Cong) =>
% 98.01/12.89 ((
% 98.01/12.89 (setunion__Cong) =>
% 98.01/12.89 ((
% 98.01/12.89 (exuEu) =>
% 98.01/12.89 ((
% 98.01/12.89 (descr__Cong) =>
% 98.01/12.89 ((
% 98.01/12.89 (dsetconstr__Cong) =>
% 98.01/12.89 ((
% 98.01/12.89 (subsetI1) =>
% 98.01/12.89 ((
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% 98.01/12.89 ((
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% 98.01/12.89 ((
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% 98.01/12.89 ((
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% 98.01/12.89 ((
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% 98.01/12.89 ((
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% 98.01/12.89 ((
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% 98.01/12.89 ((
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% 98.01/12.89 ((
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% 98.01/12.89 ((
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% 98.01/12.89 ((
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% 98.01/12.89 ((
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% 98.01/12.89 ((
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% 98.01/12.89 ((
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% 98.01/12.89 ((
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% 98.01/12.89 ((
% 98.01/12.89 (binunionLsub) =>
% 98.01/12.89 ((
% 98.01/12.89 (binunionRsub) =>
% 98.01/12.89 ((
% 98.01/12.89 (binintersectI) =>
% 98.01/12.89 ((
% 98.01/12.89 (binintersectSubset5) =>
% 98.01/12.89 ((
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% 98.01/12.89 ((
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% 98.01/12.89 ((
% 98.01/12.89 (binintersectSubset2) =>
% 98.01/12.89 ((
% 98.01/12.89 (binintersectSubset3) =>
% 98.01/12.89 ((
% 98.01/12.89 (binintersectER) =>
% 98.01/12.89 ((
% 98.01/12.89 (disjointsetsI1) =>
% 98.01/12.89 ((
% 98.01/12.89 (binintersectRsub) =>
% 98.01/12.89 ((
% 98.01/12.89 (binintersectSubset4) =>
% 98.01/12.89 ((
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% 98.01/12.89 ((
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% 98.01/12.89 ((
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% 98.01/12.89 ((
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% 98.01/12.89 ((
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% 98.01/12.89 ((
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% 98.01/12.89 ((
% 98.01/12.89 (symdiffI2) =>
% 98.01/12.89 ((
% 98.01/12.89 (symdiffIneg1) =>
% 98.01/12.89 ((
% 98.01/12.89 (symdiffIneg2) =>
% 98.01/12.89 ((
% 98.01/12.89 (secondinupair) =>
% 98.01/12.89 ((
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% 98.01/12.89 ((
% 98.01/12.89 (setukpairIR) =>
% 98.01/12.89 ((
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% 98.01/12.89 ((
% 98.01/12.89 (kpairp) =>
% 98.01/12.89 ((
% 98.01/12.89 (singletonsubset) =>
% 98.01/12.89 ((
% 98.01/12.89 (singletoninpowerset) =>
% 98.01/12.89 ((
% 98.01/12.89 (singletoninpowunion) =>
% 98.01/12.89 ((
% 98.01/12.89 (upairset2E) =>
% 98.01/12.89 ((
% 98.01/12.89 (upairsubunion) =>
% 98.01/12.89 ((
% 98.01/12.89 (upairinpowunion) =>
% 98.01/12.89 ((
% 98.01/12.89 (ubforcartprodlem1) =>
% 98.01/12.89 ((
% 98.01/12.89 (ubforcartprodlem2) =>
% 98.01/12.89 ((
% 98.01/12.89 (ubforcartprodlem3) =>
% 98.01/12.89 ((
% 98.01/12.89 (cartprodpairin) =>
% 98.01/12.89 ((
% 98.01/12.89 (cartprodmempair1) =>
% 98.01/12.89 ((
% 98.01/12.89 (cartprodmempair) =>
% 98.01/12.89 ((
% 98.01/12.89 (setunionE2) =>
% 98.01/12.89 ((
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% 98.01/12.89 ((
% 98.01/12.89 (setunionsingleton2) =>
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% 98.01/12.89 ((
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% 98.01/12.89 ((
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% 98.01/12.89 ((
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% 98.01/12.89 ((
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% 98.01/12.89 ((
% 98.01/12.89 (kpairsurjEq) =>
% 98.01/12.89 ((
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% 98.01/12.89 ((
% 98.01/12.89 (cartprodpairmemEL) =>
% 98.01/12.89 ((
% 98.01/12.89 (cartprodpairmemER) =>
% 98.01/12.89 ((
% 98.01/12.89 (cartprodmempaircEq) =>
% 98.01/12.89 ((
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% 98.01/12.89 ((
% 98.01/12.89 (cartprodsndpairEq) =>
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% 98.01/12.89 ((
% 98.01/12.89 (demorgan2a2) =>
% 98.01/12.89 ((
% 98.01/12.89 (demorgan1a) =>
% 98.01/12.89 ((
% 98.01/12.89 (demorgan1b) =>
% 98.01/12.89 ((
% 98.01/12.89 (demorgan1) =>
% 98.01/12.89 ((
% 98.01/12.89 (demorgan2a) =>
% 98.01/12.89 ((
% 98.01/12.89 (demorgan2b2) =>
% 98.01/12.89 ((
% 98.01/12.89 (demorgan2b) =>
% 98.01/12.89 ((
% 98.01/12.89 (demorgan2) =>
% 98.01/12.89 ((
% 98.01/12.89 (woz13rule0) =>
% 98.01/12.89 ((
% 98.01/12.89 (woz13rule1) =>
% 98.01/12.89 ((
% 98.01/12.89 (woz13rule2) =>
% 98.01/12.89 ((
% 98.01/12.89 (woz13rule3) =>
% 98.01/12.89 ((
% 98.01/12.89 (woz13rule4) =>
% 98.01/12.89 ((
% 98.01/12.89 (woz1_1) =>
% 98.01/12.89 ((
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% 98.01/12.89 ((
% 98.01/12.89 (woz1_5) =>
% 98.01/12.89 ((
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% 98.01/12.89 ((
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% 98.01/12.89 (
% 98.01/12.89 (
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% 98.01/12.89 (
% 98.01/12.89 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.01/12.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl264])).
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% 98.01/12.89 ((
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% 98.01/12.89 ((
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% 98.01/12.89 ((
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% 98.01/12.89 ((
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% 98.01/12.89 ((
% 98.01/12.89 (powerset__Cong) =>
% 98.01/12.89 ((
% 98.01/12.89 (setunion__Cong) =>
% 98.01/12.89 ((
% 98.01/12.89 (exuEu) =>
% 98.01/12.89 ((
% 98.01/12.89 (descr__Cong) =>
% 98.01/12.89 ((
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% 98.01/12.89 ((
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% 98.01/12.89 ((
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% 98.01/12.89 ((
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% 98.01/12.89 ((
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% 98.01/12.89 ((
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% 98.01/12.89 ((
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% 98.01/12.89 ((
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% 98.01/12.89 ((
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% 98.01/12.89 ((
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% 98.01/12.89 ((
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% 98.01/12.89 ((
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% 98.01/12.89 ((
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% 98.01/12.89 ((
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% 98.01/12.89 ((
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% 98.01/12.89 ((
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% 98.01/12.89 ((
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% 98.01/12.89 ((
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% 98.01/12.89 ((
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% 98.01/12.89 ((
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% 98.01/12.89 ((
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% 98.01/12.89 ((
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% 98.01/12.89 ((
% 98.01/12.89 (symdiffI2) =>
% 98.01/12.89 ((
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% 98.01/12.89 ((
% 98.01/12.89 (symdiffIneg2) =>
% 98.01/12.89 ((
% 98.01/12.89 (secondinupair) =>
% 98.01/12.89 ((
% 98.01/12.89 (setukpairIL) =>
% 98.01/12.89 ((
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% 98.01/12.89 ((
% 98.01/12.89 (kpairiskpair) =>
% 98.01/12.89 ((
% 98.01/12.89 (kpairp) =>
% 98.01/12.89 ((
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% 98.01/12.89 ((
% 98.01/12.89 (singletoninpowerset) =>
% 98.01/12.89 ((
% 98.01/12.89 (singletoninpowunion) =>
% 98.01/12.89 ((
% 98.01/12.89 (upairset2E) =>
% 98.01/12.89 ((
% 98.01/12.89 (upairsubunion) =>
% 98.01/12.89 ((
% 98.01/12.89 (upairinpowunion) =>
% 98.01/12.89 ((
% 98.01/12.89 (ubforcartprodlem1) =>
% 98.01/12.89 ((
% 98.01/12.89 (ubforcartprodlem2) =>
% 98.01/12.89 ((
% 98.01/12.89 (ubforcartprodlem3) =>
% 98.01/12.89 ((
% 98.01/12.89 (cartprodpairin) =>
% 98.01/12.89 ((
% 98.01/12.89 (cartprodmempair1) =>
% 98.01/12.89 ((
% 98.01/12.89 (cartprodmempair) =>
% 98.01/12.89 ((
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% 98.01/12.89 ((
% 98.01/12.89 (setunionsingleton1) =>
% 98.01/12.89 ((
% 98.01/12.89 (setunionsingleton2) =>
% 98.01/12.89 ((
% 98.01/12.89 (setunionsingleton) =>
% 98.01/12.89 ((
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% 98.01/12.89 ((
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% 98.01/12.89 ((
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% 98.01/12.89 ((
% 98.01/12.89 (setukpairinjR12) =>
% 98.01/12.89 ((
% 98.01/12.89 (setukpairinjR1) =>
% 98.01/12.89 ((
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% 98.01/12.89 ((
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% 98.01/12.89 ((
% 98.01/12.89 (setukpairinjR) =>
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% 98.01/12.89 ((
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% 98.01/12.89 ((
% 98.01/12.89 (kpairsurjEq) =>
% 98.01/12.89 ((
% 98.01/12.89 (cartprodsndin) =>
% 98.01/12.89 ((
% 98.01/12.89 (cartprodpairmemEL) =>
% 98.01/12.89 ((
% 98.01/12.89 (cartprodpairmemER) =>
% 98.01/12.89 ((
% 98.01/12.89 (cartprodmempaircEq) =>
% 98.01/12.89 ((
% 98.01/12.89 (cartprodfstpairEq) =>
% 98.01/12.89 ((
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% 98.01/12.89 (
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% 98.01/12.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl280])).
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% 98.01/12.89 ((
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% 98.01/12.89 ((
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% 98.01/12.89 ((
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% 98.01/12.89 ((
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% 98.01/12.89 ((
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% 98.01/12.89 ((
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% 98.01/12.89 ((
% 98.01/12.89 (upairinpowunion) =>
% 98.01/12.89 ((
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% 98.01/12.89 ((
% 98.01/12.89 (ubforcartprodlem2) =>
% 98.01/12.89 ((
% 98.01/12.89 (ubforcartprodlem3) =>
% 98.01/12.89 ((
% 98.01/12.89 (cartprodpairin) =>
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% 98.01/12.89 ((
% 98.01/12.89 (cartprodmempair) =>
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% 98.01/12.89 ((
% 98.01/12.89 (cartprodpairmemEL) =>
% 98.01/12.89 ((
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% 98.01/12.89 ((
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% 98.01/12.89 ((
% 98.01/12.89 (cartprodsndpairEq) =>
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% 98.01/12.89 ((
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% 98.01/12.89 ((
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% 98.01/12.90 (cartprodsndpairEq) =>
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% 98.01/12.90 (binintersectTERcontra) =>
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% 98.01/12.90 (contrasubsetT2) =>
% 98.01/12.90 ((
% 98.01/12.90 (contrasubsetT3) =>
% 98.01/12.90 ((
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% 98.01/12.90 ((
% 98.01/12.90 (doubleComplementE1) =>
% 98.01/12.90 ((
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% 98.01/12.90 ((
% 98.01/12.90 (doubleComplementSub2) =>
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% 98.01/12.90 (complementTnotintersectT) =>
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% 98.01/12.90 (complementSubsetComplementIntersect) =>
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% 98.01/12.90 (complementInPowersetComplementIntersect) =>
% 98.01/12.90 ((
% 98.01/12.90 (contraSubsetComplement) =>
% 98.01/12.90 ((
% 98.01/12.90 (complementTcontraSubset) =>
% 98.01/12.90 ((
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% 98.01/12.90 ((
% 98.01/12.90 (binunionTIRcontra) =>
% 98.01/12.90 ((
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% 98.01/12.90 (inIntersectImpInIntersectUnions) =>
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% 98.01/12.90 (intersectInPowersetIntersectUnions) =>
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% 98.01/12.90 (inComplementUnionImpInComplement1) =>
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% 98.01/12.90 ((
% 98.01/12.90 (complementUnionInPowersetComplement) =>
% 98.01/12.90 ((
% 98.01/12.90 (demorgan2a2) =>
% 98.01/12.90 ((
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% 98.01/12.90 ((
% 98.01/12.90 (demorgan1b) =>
% 98.01/12.90 ((
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% 98.01/12.90 ((
% 98.01/12.90 (demorgan2a) =>
% 98.01/12.90 ((
% 98.01/12.90 (demorgan2b2) =>
% 98.01/12.90 ((
% 98.01/12.90 (demorgan2b) =>
% 98.01/12.90 ((
% 98.01/12.90 (demorgan2) =>
% 98.01/12.90 ((
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% 98.01/12.90 ((
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% 98.01/12.90 ((
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% 98.01/12.90 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl337])).
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% 98.01/12.90 (complementSubsetComplementIntersect) =>
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% 98.01/12.90 (complementInPowersetComplementIntersect) =>
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% 98.01/12.90 (contraSubsetComplement) =>
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% 98.01/12.90 (complementTcontraSubset) =>
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% 98.01/12.90 ((
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% 98.01/12.90 ((
% 98.01/12.90 (demorgan2a) =>
% 98.01/12.90 ((
% 98.01/12.90 (demorgan2b2) =>
% 98.01/12.90 ((
% 98.01/12.90 (demorgan2b) =>
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% 98.01/12.90 (contrasubsetT3) =>
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% 98.01/12.90 (contraSubsetComplement) =>
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% 98.01/12.90 ((
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% 98.01/12.90 ((
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% 98.01/12.90 ((
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% 98.01/12.90 ((
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% 98.01/12.90 ((
% 98.01/12.90 (demorgan2a) =>
% 98.01/12.90 ((
% 98.01/12.90 (demorgan2b2) =>
% 98.01/12.90 ((
% 98.01/12.90 (demorgan2b) =>
% 98.01/12.90 ((
% 98.01/12.90 (demorgan2) =>
% 98.01/12.90 ((
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% 98.01/12.90 ((
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% 98.01/12.90 ((
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% 98.01/12.90 ((
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% 98.01/12.90 (exu__Cong) =>
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% 98.01/12.90 (setadjoin__Cong) =>
% 98.01/12.90 ((
% 98.01/12.90 (powerset__Cong) =>
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% 98.01/12.90 (descr__Cong) =>
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% 98.01/12.90 (doubleComplementSub2) =>
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% 98.01/12.90 ((
% 98.01/12.90 (complementSubsetComplementIntersect) =>
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% 98.01/12.90 (complementInPowersetComplementIntersect) =>
% 98.01/12.90 ((
% 98.01/12.90 (contraSubsetComplement) =>
% 98.01/12.90 ((
% 98.01/12.90 (complementTcontraSubset) =>
% 98.01/12.90 ((
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% 98.01/12.90 (inComplementUnionImpInComplement1) =>
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% 98.01/12.90 ((
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% 98.01/12.90 ((
% 98.01/12.90 (complementUnionInPowersetComplement) =>
% 98.01/12.90 ((
% 98.01/12.90 (demorgan2a2) =>
% 98.01/12.90 ((
% 98.01/12.90 (demorgan1a) =>
% 98.01/12.90 ((
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% 98.01/12.90 ((
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% 98.01/12.90 ((
% 98.01/12.90 (demorgan2a) =>
% 98.01/12.90 ((
% 98.01/12.90 (demorgan2b2) =>
% 98.01/12.90 ((
% 98.01/12.90 (demorgan2b) =>
% 98.01/12.90 ((
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% 98.01/12.90 ((
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% 98.01/12.90 (
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% 98.01/12.90 (
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% 98.01/12.90 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl369])).
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% 98.01/12.90 ((
% 98.01/12.90 (exuEu) =>
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% 98.01/12.90 (descr__Cong) =>
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% 98.01/12.90 ((
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% 98.01/12.90 ((
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% 98.01/12.90 ((
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% 98.01/12.90 ((
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% 98.01/12.90 (ubforcartprodlem3) =>
% 98.01/12.90 ((
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% 98.01/12.90 ((
% 98.01/12.90 (cartprodmempair) =>
% 98.01/12.90 ((
% 98.01/12.90 (setunionE2) =>
% 98.01/12.90 ((
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% 98.01/12.90 (setunionsingleton2) =>
% 98.01/12.90 ((
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% 98.01/12.90 ((
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% 98.01/12.90 ((
% 98.01/12.90 (cartprodmempaircEq) =>
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% 98.01/12.90 (cartprodmempaircEq) =>
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% 98.01/12.90 (contraSubsetComplement) =>
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% 98.01/12.90 ((
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% 98.01/12.90 ((
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% 98.01/12.90 ((
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% 98.01/12.90 ((
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% 98.01/12.90 ((
% 98.01/12.90 (demorgan2a) =>
% 98.01/12.90 ((
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% 98.01/12.90 ((
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% 98.01/12.90 ((
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% 98.01/12.90 ((
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% 98.01/12.90 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl392])).
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% 98.01/12.92 ((
% 98.01/12.92 (ubforcartprodlem2) =>
% 98.01/12.92 ((
% 98.01/12.92 (ubforcartprodlem3) =>
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% 98.01/12.92 (cartprodpairin) =>
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% 98.01/12.92 ((
% 98.01/12.92 (cartprodmempair) =>
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% 98.01/12.92 (cartprodsndpairEq) =>
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% 98.01/12.92 ((
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% 98.01/12.92 ((
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% 98.01/12.92 ((
% 98.01/12.92 (complementTE1) =>
% 98.01/12.92 ((
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% 98.01/12.92 ((
% 98.01/12.92 (binintersectTERcontra) =>
% 98.01/12.92 ((
% 98.01/12.92 (contrasubsetT) =>
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% 98.01/12.92 (contrasubsetT1) =>
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% 98.01/12.92 (contrasubsetT2) =>
% 98.01/12.92 ((
% 98.01/12.92 (contrasubsetT3) =>
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% 98.01/12.92 ((
% 98.01/12.92 (doubleComplementE1) =>
% 98.01/12.92 ((
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% 98.01/12.92 ((
% 98.01/12.92 (doubleComplementSub2) =>
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% 98.01/12.92 ((
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% 98.01/12.92 ((
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% 98.01/12.92 ((
% 98.01/12.92 (complementSubsetComplementIntersect) =>
% 98.01/12.92 ((
% 98.01/12.92 (complementInPowersetComplementIntersect) =>
% 98.01/12.92 ((
% 98.01/12.92 (contraSubsetComplement) =>
% 98.01/12.92 ((
% 98.01/12.92 (complementTcontraSubset) =>
% 98.01/12.92 ((
% 98.01/12.92 (binunionTILcontra) =>
% 98.01/12.92 ((
% 98.01/12.92 (binunionTIRcontra) =>
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% 98.01/12.92 ((
% 98.01/12.92 (inIntersectImpInUnion2) =>
% 98.01/12.92 ((
% 98.01/12.92 (inIntersectImpInIntersectUnions) =>
% 98.01/12.92 ((
% 98.01/12.92 (intersectInPowersetIntersectUnions) =>
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% 98.01/12.92 ((
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% 98.01/12.92 (demorgan2a1) =>
% 98.01/12.92 ((
% 98.01/12.92 (complementUnionInPowersetComplement) =>
% 98.01/12.92 ((
% 98.01/12.92 (demorgan2a2) =>
% 98.01/12.92 ((
% 98.01/12.92 (demorgan1a) =>
% 98.01/12.92 ((
% 98.01/12.92 (demorgan1b) =>
% 98.01/12.92 ((
% 98.01/12.92 (demorgan1) =>
% 98.01/12.92 ((
% 98.01/12.92 (demorgan2a) =>
% 98.01/12.92 ((
% 98.01/12.92 (demorgan2b2) =>
% 98.01/12.92 ((
% 98.01/12.92 (demorgan2b) =>
% 98.01/12.92 ((
% 98.01/12.92 (demorgan2) =>
% 98.01/12.92 ((
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% 98.01/12.92 ((
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% 98.01/12.92 ((
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% 98.01/12.92 ((
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% 98.01/12.92 ((
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% 98.01/12.92 ((
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% 98.01/12.92 (
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% 98.01/12.92 (
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% 98.01/12.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl400])).
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% 98.01/12.92 ((
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% 98.01/12.92 (contrasubsetT3) =>
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% 98.01/12.92 (complementInPowersetComplementIntersect) =>
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% 98.01/12.92 (contraSubsetComplement) =>
% 98.01/12.92 ((
% 98.01/12.92 (complementTcontraSubset) =>
% 98.01/12.92 ((
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% 98.01/12.92 ((
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% 98.01/12.92 ((
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% 98.01/12.92 ((
% 98.01/12.92 (demorgan1a) =>
% 98.01/12.92 ((
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% 98.01/12.92 ((
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% 98.01/12.92 ((
% 98.01/12.92 (demorgan2a) =>
% 98.01/12.92 ((
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% 98.01/12.92 ((
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% 98.01/12.92 ((
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% 98.01/12.92 ((
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% 98.01/12.92 ((
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% 98.01/12.92 ((
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% 98.01/12.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl417])).
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% 98.01/12.92 ((
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% 98.01/12.92 ((
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% 98.01/12.92 ((
% 98.01/12.92 (ubforcartprodlem2) =>
% 98.01/12.92 ((
% 98.01/12.92 (ubforcartprodlem3) =>
% 98.01/12.92 ((
% 98.01/12.92 (cartprodpairin) =>
% 98.01/12.92 ((
% 98.01/12.92 (cartprodmempair1) =>
% 98.01/12.92 ((
% 98.01/12.92 (cartprodmempair) =>
% 98.01/12.92 ((
% 98.01/12.92 (setunionE2) =>
% 98.01/12.92 ((
% 98.01/12.92 (setunionsingleton1) =>
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% 98.01/12.92 (setunionsingleton2) =>
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% 98.01/12.92 (cartprodsndpairEq) =>
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% 98.01/12.92 ((
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% 98.01/12.92 ((
% 98.01/12.92 (powersetTI1) =>
% 98.01/12.92 ((
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% 98.01/12.92 ((
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% 98.01/12.92 ((
% 98.01/12.92 (complementTE1) =>
% 98.01/12.92 ((
% 98.01/12.92 (binintersectTELcontra) =>
% 98.01/12.92 ((
% 98.01/12.92 (binintersectTERcontra) =>
% 98.01/12.92 ((
% 98.01/12.92 (contrasubsetT) =>
% 98.01/12.92 ((
% 98.01/12.92 (contrasubsetT1) =>
% 98.01/12.92 ((
% 98.01/12.92 (contrasubsetT2) =>
% 98.01/12.92 ((
% 98.01/12.92 (contrasubsetT3) =>
% 98.01/12.92 ((
% 98.01/12.92 (doubleComplementI1) =>
% 98.01/12.92 ((
% 98.01/12.92 (doubleComplementE1) =>
% 98.01/12.92 ((
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% 98.01/12.92 ((
% 98.01/12.92 (doubleComplementSub2) =>
% 98.01/12.92 ((
% 98.01/12.92 (doubleComplementEq) =>
% 98.01/12.92 ((
% 98.01/12.92 (complementTnotintersectT) =>
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% 98.01/12.92 ((
% 98.01/12.92 (complementSubsetComplementIntersect) =>
% 98.01/12.92 ((
% 98.01/12.92 (complementInPowersetComplementIntersect) =>
% 98.01/12.92 ((
% 98.01/12.92 (contraSubsetComplement) =>
% 98.01/12.92 ((
% 98.01/12.92 (complementTcontraSubset) =>
% 98.01/12.92 ((
% 98.01/12.92 (binunionTILcontra) =>
% 98.01/12.92 ((
% 98.01/12.92 (binunionTIRcontra) =>
% 98.01/12.92 ((
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% 98.01/12.92 ((
% 98.01/12.92 (inIntersectImpInUnion2) =>
% 98.01/12.92 ((
% 98.01/12.92 (inIntersectImpInIntersectUnions) =>
% 98.01/12.92 ((
% 98.01/12.92 (intersectInPowersetIntersectUnions) =>
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% 98.01/12.92 ((
% 98.01/12.92 (inComplementUnionImpInComplement1) =>
% 98.01/12.92 ((
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% 98.01/12.92 ((
% 98.01/12.92 (binunionTEcontra) =>
% 98.01/12.92 ((
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% 98.01/12.92 ((
% 98.01/12.92 (complementUnionInPowersetComplement) =>
% 98.01/12.92 ((
% 98.01/12.92 (demorgan2a2) =>
% 98.01/12.92 ((
% 98.01/12.92 (demorgan1a) =>
% 98.01/12.92 ((
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% 98.01/12.92 ((
% 98.01/12.92 (demorgan1) =>
% 98.01/12.92 ((
% 98.01/12.92 (demorgan2a) =>
% 98.01/12.92 ((
% 98.01/12.92 (demorgan2b2) =>
% 98.01/12.92 ((
% 98.01/12.92 (demorgan2b) =>
% 98.01/12.92 ((
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% 98.01/12.92 ((
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% 98.01/12.92 ((
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% 98.01/12.92 ((
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% 98.01/12.92 ((
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% 98.01/12.92 ((
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% 98.01/12.92 ((
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% 98.01/12.92 (
% 98.01/12.92 (
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% 98.01/12.92 (
% 98.01/12.92 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.01/12.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl467])).
% 98.01/12.92 thf(zip_derived_cl485, plain,
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% 98.01/12.93 ((
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% 98.01/12.93 ((
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% 98.01/12.93 ((
% 98.01/12.93 (contraSubsetComplement) =>
% 98.01/12.93 ((
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% 98.01/12.93 (intersectInPowersetIntersectUnions) =>
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% 98.01/12.93 (inComplementUnionImpInComplement1) =>
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% 98.01/12.93 ((
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% 98.01/12.93 ((
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% 98.01/12.93 ((
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% 98.01/12.93 ((
% 98.01/12.93 (demorgan2b) =>
% 98.01/12.93 ((
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% 98.01/12.93 ((
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% 98.01/12.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl485])).
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% 98.01/12.93 (doubleComplementEq) =>
% 98.01/12.93 ((
% 98.01/12.93 (complementTnotintersectT) =>
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% 98.01/12.93 ((
% 98.01/12.93 (complementSubsetComplementIntersect) =>
% 98.01/12.93 ((
% 98.01/12.93 (complementInPowersetComplementIntersect) =>
% 98.01/12.93 ((
% 98.01/12.93 (contraSubsetComplement) =>
% 98.01/12.93 ((
% 98.01/12.93 (complementTcontraSubset) =>
% 98.01/12.93 ((
% 98.01/12.93 (binunionTILcontra) =>
% 98.01/12.93 ((
% 98.01/12.93 (binunionTIRcontra) =>
% 98.01/12.93 ((
% 98.01/12.93 (inIntersectImpInUnion) =>
% 98.01/12.93 ((
% 98.01/12.93 (inIntersectImpInUnion2) =>
% 98.01/12.93 ((
% 98.01/12.93 (inIntersectImpInIntersectUnions) =>
% 98.01/12.93 ((
% 98.01/12.93 (intersectInPowersetIntersectUnions) =>
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% 98.01/12.93 (inComplementUnionImpNotIn1) =>
% 98.01/12.93 ((
% 98.01/12.93 (inComplementUnionImpInComplement1) =>
% 98.01/12.93 ((
% 98.01/12.93 (binunionTE) =>
% 98.01/12.93 ((
% 98.01/12.93 (binunionTEcontra) =>
% 98.01/12.93 ((
% 98.01/12.93 (demorgan2a1) =>
% 98.01/12.93 ((
% 98.01/12.93 (complementUnionInPowersetComplement) =>
% 98.01/12.93 ((
% 98.01/12.93 (demorgan2a2) =>
% 98.01/12.93 ((
% 98.01/12.93 (demorgan1a) =>
% 98.28/12.93 ((
% 98.28/12.93 (demorgan1b) =>
% 98.28/12.93 ((
% 98.28/12.93 (demorgan1) =>
% 98.28/12.93 ((
% 98.28/12.93 (demorgan2a) =>
% 98.28/12.93 ((
% 98.28/12.93 (demorgan2b2) =>
% 98.28/12.93 ((
% 98.28/12.93 (demorgan2b) =>
% 98.28/12.93 ((
% 98.28/12.93 (demorgan2) =>
% 98.28/12.93 ((
% 98.28/12.93 (woz13rule0) =>
% 98.28/12.93 ((
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% 98.28/12.93 ((
% 98.28/12.93 (woz13rule2) =>
% 98.28/12.93 ((
% 98.28/12.93 (woz13rule3) =>
% 98.28/12.93 ((
% 98.28/12.93 (woz13rule4) =>
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% 98.28/12.93 (
% 98.28/12.93 (
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% 98.28/12.93 (
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% 98.28/12.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl496])).
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% 98.28/12.93 (((exuE3u) =>
% 98.28/12.93 (((exu__Cong) =>
% 98.28/12.93 (((setadjoin__Cong) =>
% 98.28/12.93 (((powerset__Cong) =>
% 98.28/12.93 (((setunion__Cong) =>
% 98.28/12.93 (((exuEu) =>
% 98.28/12.93 (((descr__Cong) =>
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% 98.28/12.93 ((
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% 98.28/12.93 ((
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% 98.28/12.93 ((
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% 98.28/12.93 ((
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% 98.28/12.93 ((
% 98.28/12.93 (sepSubset) =>
% 98.28/12.93 ((
% 98.28/12.93 (binunionIL) =>
% 98.28/12.93 ((
% 98.28/12.93 (upairset2IR) =>
% 98.28/12.93 ((
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% 98.28/12.93 ((
% 98.28/12.93 (binunionEcases) =>
% 98.28/12.93 ((
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% 98.28/12.93 ((
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% 98.28/12.93 ((
% 98.28/12.93 (binintersectI) =>
% 98.28/12.93 ((
% 98.28/12.93 (binintersectSubset5) =>
% 98.28/12.93 ((
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% 98.28/12.93 ((
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% 98.28/12.93 ((
% 98.28/12.93 (binintersectSubset2) =>
% 98.28/12.93 ((
% 98.28/12.93 (binintersectSubset3) =>
% 98.28/12.93 ((
% 98.28/12.93 (binintersectER) =>
% 98.28/12.93 ((
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% 98.28/12.93 ((
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% 98.28/12.93 ((
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% 98.28/12.93 ((
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% 98.28/12.93 ((
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% 98.28/12.93 ((
% 98.28/12.93 (kpairp) =>
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% 98.28/12.93 ((
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% 98.28/12.93 ((
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% 98.28/12.93 ((
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% 98.28/12.93 (ubforcartprodlem3) =>
% 98.28/12.93 ((
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% 98.28/12.93 ((
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% 98.28/12.93 ((
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% 98.28/12.93 ((
% 98.28/12.93 (kfstpairEq) =>
% 98.28/12.93 ((
% 98.28/12.93 (cartprodfstin) =>
% 98.28/12.93 ((
% 98.28/12.93 (setukpairinjL2) =>
% 98.28/12.93 ((
% 98.28/12.93 (setukpairinjL) =>
% 98.28/12.93 ((
% 98.28/12.93 (setukpairinjR11) =>
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% 98.28/12.93 (setukpairinjR12) =>
% 98.28/12.93 ((
% 98.28/12.93 (setukpairinjR1) =>
% 98.28/12.93 ((
% 98.28/12.93 (upairequniteq) =>
% 98.28/12.93 ((
% 98.28/12.93 (setukpairinjR2) =>
% 98.28/12.93 ((
% 98.28/12.93 (setukpairinjR) =>
% 98.28/12.93 ((
% 98.28/12.93 (ksndsingleton) =>
% 98.28/12.93 ((
% 98.28/12.93 (ksndpairEq) =>
% 98.28/12.93 ((
% 98.28/12.93 (kpairsurjEq) =>
% 98.28/12.93 ((
% 98.28/12.93 (cartprodsndin) =>
% 98.28/12.93 ((
% 98.28/12.93 (cartprodpairmemEL) =>
% 98.28/12.93 ((
% 98.28/12.93 (cartprodpairmemER) =>
% 98.28/12.93 ((
% 98.28/12.93 (cartprodmempaircEq) =>
% 98.28/12.93 ((
% 98.28/12.93 (cartprodfstpairEq) =>
% 98.28/12.93 ((
% 98.28/12.93 (cartprodsndpairEq) =>
% 98.28/12.93 ((
% 98.28/12.93 (cartprodpairsurjEq) =>
% 98.28/12.93 ((
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% 98.28/12.93 (dpsetconstrEL2) =>
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% 98.28/12.93 (dpsetconstrER) =>
% 98.28/12.93 ((
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% 98.28/12.93 ((
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% 98.28/12.93 ((
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% 98.28/12.93 ((
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% 98.28/12.93 ((
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% 98.28/12.93 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.28/12.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl507])).
% 98.28/12.93 thf(zip_derived_cl528, plain,
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% 98.28/12.93 (((quantDeMorgan2) =>
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% 98.28/12.93 (((exuI3) =>
% 98.28/12.93 (((exuI2) =>
% 98.28/12.93 (((inCongP) =>
% 98.28/12.93 (((in__Cong) =>
% 98.28/12.93 (((exuE3u) =>
% 98.28/12.93 (((exu__Cong) =>
% 98.28/12.93 (((setadjoin__Cong) =>
% 98.28/12.93 (((powerset__Cong) =>
% 98.28/12.93 (((setunion__Cong) =>
% 98.28/12.93 (((exuEu) =>
% 98.28/12.93 (((descr__Cong) =>
% 98.28/12.93 (((dsetconstr__Cong) =>
% 98.28/12.93 (((subsetI1) =>
% 98.28/12.93 (((eqimpsubset2) =>
% 98.28/12.93 (((eqimpsubset1) =>
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% 98.28/12.93 ((
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% 98.28/12.93 ((
% 98.28/12.93 (notequalI2) =>
% 98.28/12.93 ((
% 98.28/12.93 (subsetRefl) =>
% 98.28/12.93 ((
% 98.28/12.93 (subsetTrans) =>
% 98.28/12.93 ((
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% 98.28/12.93 ((
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% 98.28/12.93 ((
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% 98.28/12.93 ((
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% 98.28/12.93 ((
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% 98.28/12.93 ((
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% 98.28/12.93 ((
% 98.28/12.93 (powersetE1) =>
% 98.28/12.93 ((
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% 98.28/12.93 ((
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% 98.28/12.93 ((
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% 98.28/12.93 ((
% 98.28/12.93 (sepSubset) =>
% 98.28/12.93 ((
% 98.28/12.93 (binunionIL) =>
% 98.28/12.93 ((
% 98.28/12.93 (upairset2IR) =>
% 98.28/12.93 ((
% 98.28/12.93 (binunionIR) =>
% 98.28/12.93 ((
% 98.28/12.93 (binunionEcases) =>
% 98.28/12.93 ((
% 98.28/12.93 (binunionE) =>
% 98.28/12.93 ((
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% 98.28/12.93 ((
% 98.28/12.93 (binunionRsub) =>
% 98.28/12.93 ((
% 98.28/12.93 (binintersectI) =>
% 98.28/12.93 ((
% 98.28/12.93 (binintersectSubset5) =>
% 98.28/12.93 ((
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% 98.28/12.93 ((
% 98.28/12.93 (binintersectLsub) =>
% 98.28/12.93 ((
% 98.28/12.93 (binintersectSubset2) =>
% 98.28/12.93 ((
% 98.28/12.93 (binintersectSubset3) =>
% 98.28/12.93 ((
% 98.28/12.93 (binintersectER) =>
% 98.28/12.93 ((
% 98.28/12.93 (disjointsetsI1) =>
% 98.28/12.93 ((
% 98.28/12.93 (binintersectRsub) =>
% 98.28/12.93 ((
% 98.28/12.93 (binintersectSubset4) =>
% 98.28/12.93 ((
% 98.28/12.93 (binintersectSubset1) =>
% 98.28/12.93 ((
% 98.28/12.93 (bs114d) =>
% 98.28/12.93 ((
% 98.28/12.93 (setminusI) =>
% 98.28/12.93 ((
% 98.28/12.93 (setminusEL) =>
% 98.28/12.93 ((
% 98.28/12.93 (setminusER) =>
% 98.28/12.93 ((
% 98.28/12.93 (setminusSubset2) =>
% 98.28/12.93 ((
% 98.28/12.93 (setminusERneg) =>
% 98.28/12.93 ((
% 98.28/12.93 (setminusELneg) =>
% 98.28/12.93 ((
% 98.28/12.93 (setminusILneg) =>
% 98.28/12.93 ((
% 98.28/12.93 (setminusIRneg) =>
% 98.28/12.93 ((
% 98.28/12.93 (setminusLsub) =>
% 98.28/12.93 ((
% 98.28/12.93 (setminusSubset1) =>
% 98.28/12.93 ((
% 98.28/12.93 (symdiffE) =>
% 98.28/12.93 ((
% 98.28/12.93 (symdiffI1) =>
% 98.28/12.93 ((
% 98.28/12.93 (symdiffI2) =>
% 98.28/12.93 ((
% 98.28/12.93 (symdiffIneg1) =>
% 98.28/12.93 ((
% 98.28/12.93 (symdiffIneg2) =>
% 98.28/12.93 ((
% 98.28/12.93 (secondinupair) =>
% 98.28/12.93 ((
% 98.28/12.93 (setukpairIL) =>
% 98.28/12.93 ((
% 98.28/12.93 (setukpairIR) =>
% 98.28/12.93 ((
% 98.28/12.93 (kpairiskpair) =>
% 98.28/12.93 ((
% 98.28/12.93 (kpairp) =>
% 98.28/12.93 ((
% 98.28/12.93 (singletonsubset) =>
% 98.28/12.93 ((
% 98.28/12.93 (singletoninpowerset) =>
% 98.28/12.93 ((
% 98.28/12.93 (singletoninpowunion) =>
% 98.28/12.93 ((
% 98.28/12.93 (upairset2E) =>
% 98.28/12.93 ((
% 98.28/12.93 (upairsubunion) =>
% 98.28/12.93 ((
% 98.28/12.93 (upairinpowunion) =>
% 98.28/12.93 ((
% 98.28/12.93 (ubforcartprodlem1) =>
% 98.28/12.94 ((
% 98.28/12.94 (ubforcartprodlem2) =>
% 98.28/12.94 ((
% 98.28/12.94 (ubforcartprodlem3) =>
% 98.28/12.94 ((
% 98.28/12.94 (cartprodpairin) =>
% 98.28/12.94 ((
% 98.28/12.94 (cartprodmempair1) =>
% 98.28/12.94 ((
% 98.28/12.94 (cartprodmempair) =>
% 98.28/12.94 ((
% 98.28/12.94 (setunionE2) =>
% 98.28/12.94 ((
% 98.28/12.94 (setunionsingleton1) =>
% 98.28/12.94 ((
% 98.28/12.94 (setunionsingleton2) =>
% 98.28/12.94 ((
% 98.28/12.94 (setunionsingleton) =>
% 98.28/12.94 ((
% 98.28/12.94 (singletonprop) =>
% 98.28/12.94 ((
% 98.28/12.94 (ex1E1) =>
% 98.28/12.94 ((
% 98.28/12.94 (ex1I) =>
% 98.28/12.94 ((
% 98.28/12.94 (ex1I2) =>
% 98.28/12.94 ((
% 98.28/12.94 (singletonsuniq) =>
% 98.28/12.94 ((
% 98.28/12.94 (setukpairinjL1) =>
% 98.28/12.94 ((
% 98.28/12.94 (kfstsingleton) =>
% 98.28/12.94 ((
% 98.28/12.94 (theprop) =>
% 98.28/12.94 ((
% 98.28/12.94 (kfstpairEq) =>
% 98.28/12.94 ((
% 98.28/12.94 (cartprodfstin) =>
% 98.28/12.94 ((
% 98.28/12.94 (setukpairinjL2) =>
% 98.28/12.94 ((
% 98.28/12.94 (setukpairinjL) =>
% 98.28/12.94 ((
% 98.28/12.94 (setukpairinjR11) =>
% 98.28/12.94 ((
% 98.28/12.94 (setukpairinjR12) =>
% 98.28/12.94 ((
% 98.28/12.94 (setukpairinjR1) =>
% 98.28/12.94 ((
% 98.28/12.94 (upairequniteq) =>
% 98.28/12.94 ((
% 98.28/12.94 (setukpairinjR2) =>
% 98.28/12.94 ((
% 98.28/12.94 (setukpairinjR) =>
% 98.28/12.94 ((
% 98.28/12.94 (ksndsingleton) =>
% 98.28/12.94 ((
% 98.28/12.94 (ksndpairEq) =>
% 98.28/12.94 ((
% 98.28/12.94 (kpairsurjEq) =>
% 98.28/12.94 ((
% 98.28/12.94 (cartprodsndin) =>
% 98.28/12.94 ((
% 98.28/12.94 (cartprodpairmemEL) =>
% 98.28/12.94 ((
% 98.28/12.94 (cartprodpairmemER) =>
% 98.28/12.94 ((
% 98.28/12.94 (cartprodmempaircEq) =>
% 98.28/12.94 ((
% 98.28/12.94 (cartprodfstpairEq) =>
% 98.28/12.94 ((
% 98.28/12.94 (cartprodsndpairEq) =>
% 98.28/12.94 ((
% 98.28/12.94 (cartprodpairsurjEq) =>
% 98.28/12.94 ((
% 98.28/12.94 (dpsetconstrI) =>
% 98.28/12.94 ((
% 98.28/12.94 (dpsetconstrSub) =>
% 98.28/12.94 ((
% 98.28/12.94 (setOfPairsIsBReln) =>
% 98.28/12.94 ((
% 98.28/12.94 (dpsetconstrERa) =>
% 98.28/12.94 ((
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% 98.28/12.94 ((
% 98.28/12.94 (dpsetconstrEL2) =>
% 98.28/12.94 ((
% 98.28/12.94 (dpsetconstrER) =>
% 98.28/12.94 ((
% 98.28/12.94 (funcImageSingleton) =>
% 98.28/12.94 ((
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% 98.28/12.94 ((
% 98.28/12.94 (app) =>
% 98.28/12.94 ((
% 98.28/12.94 (infuncsetfunc) =>
% 98.28/12.94 ((
% 98.28/12.94 (ap2p) =>
% 98.28/12.94 ((
% 98.28/12.94 (funcinfuncset) =>
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% 98.28/12.94 ((
% 98.28/12.94 (lamp) =>
% 98.28/12.94 ((
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% 98.28/12.94 ((
% 98.28/12.94 (brelnall1) =>
% 98.28/12.94 ((
% 98.28/12.94 (brelnall2) =>
% 98.28/12.94 ((
% 98.28/12.94 (ex1E2) =>
% 98.28/12.94 ((
% 98.28/12.94 (funcGraphProp1) =>
% 98.28/12.94 ((
% 98.28/12.94 (funcGraphProp3) =>
% 98.28/12.94 ((
% 98.28/12.94 (funcGraphProp2) =>
% 98.28/12.94 ((
% 98.28/12.94 (funcextLem) =>
% 98.28/12.94 ((
% 98.28/12.94 (funcGraphProp4) =>
% 98.28/12.94 ((
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% 98.28/12.94 ((
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% 98.28/12.94 ((
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% 98.28/12.94 ((
% 98.28/12.94 (funcext2) =>
% 98.28/12.94 ((
% 98.28/12.94 (ap2apEq1) =>
% 98.28/12.94 ((
% 98.28/12.94 (ap2apEq2) =>
% 98.28/12.94 ((
% 98.28/12.94 (beta1) =>
% 98.28/12.94 ((
% 98.28/12.94 (eta1) =>
% 98.28/12.94 ((
% 98.28/12.94 (lam2lamEq) =>
% 98.28/12.94 ((
% 98.28/12.94 (beta2) =>
% 98.28/12.94 ((
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% 98.28/12.94 ((
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% 98.28/12.94 ((
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% 98.28/12.94 ((
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% 98.28/12.94 ((
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% 98.28/12.94 ((
% 98.28/12.94 (powersetT_lem) =>
% 98.28/12.94 ((
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% 98.28/12.94 ((
% 98.28/12.94 (complementT_lem) =>
% 98.28/12.94 ((
% 98.28/12.94 (setextT) =>
% 98.28/12.94 ((
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% 98.28/12.94 ((
% 98.28/12.94 (powersetTI1) =>
% 98.28/12.94 ((
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% 98.28/12.94 ((
% 98.28/12.94 (complementTI1) =>
% 98.28/12.94 ((
% 98.28/12.94 (complementTE1) =>
% 98.28/12.94 ((
% 98.28/12.94 (binintersectTELcontra) =>
% 98.28/12.94 ((
% 98.28/12.94 (binintersectTERcontra) =>
% 98.28/12.94 ((
% 98.28/12.94 (contrasubsetT) =>
% 98.28/12.94 ((
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% 98.28/12.94 ((
% 98.28/12.94 (contrasubsetT2) =>
% 98.28/12.94 ((
% 98.28/12.94 (contrasubsetT3) =>
% 98.28/12.94 ((
% 98.28/12.94 (doubleComplementI1) =>
% 98.28/12.94 ((
% 98.28/12.94 (doubleComplementE1) =>
% 98.28/12.94 ((
% 98.28/12.94 (doubleComplementSub1) =>
% 98.28/12.94 ((
% 98.28/12.94 (doubleComplementSub2) =>
% 98.28/12.94 ((
% 98.28/12.94 (doubleComplementEq) =>
% 98.28/12.94 ((
% 98.28/12.94 (complementTnotintersectT) =>
% 98.28/12.94 ((
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% 98.28/12.94 ((
% 98.28/12.94 (complementSubsetComplementIntersect) =>
% 98.28/12.94 ((
% 98.28/12.94 (complementInPowersetComplementIntersect) =>
% 98.28/12.94 ((
% 98.28/12.94 (contraSubsetComplement) =>
% 98.28/12.94 ((
% 98.28/12.94 (complementTcontraSubset) =>
% 98.28/12.94 ((
% 98.28/12.94 (binunionTILcontra) =>
% 98.28/12.94 ((
% 98.28/12.94 (binunionTIRcontra) =>
% 98.28/12.94 ((
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% 98.28/12.94 ((
% 98.28/12.94 (inIntersectImpInUnion2) =>
% 98.28/12.94 ((
% 98.28/12.94 (inIntersectImpInIntersectUnions) =>
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% 98.28/12.94 (intersectInPowersetIntersectUnions) =>
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% 98.28/12.94 (inComplementUnionImpNotIn1) =>
% 98.28/12.94 ((
% 98.28/12.94 (inComplementUnionImpInComplement1) =>
% 98.28/12.94 ((
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% 98.28/12.94 ((
% 98.28/12.94 (binunionTEcontra) =>
% 98.28/12.94 ((
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% 98.28/12.94 ((
% 98.28/12.94 (complementUnionInPowersetComplement) =>
% 98.28/12.94 ((
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% 98.28/12.94 ((
% 98.28/12.94 (demorgan1a) =>
% 98.28/12.94 ((
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% 98.28/12.94 ((
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% 98.28/12.94 ((
% 98.28/12.94 (demorgan2a) =>
% 98.28/12.94 ((
% 98.28/12.94 (demorgan2b2) =>
% 98.28/12.94 ((
% 98.28/12.94 (demorgan2b) =>
% 98.28/12.94 ((
% 98.28/12.94 (demorgan2) =>
% 98.28/12.94 ((
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% 98.28/12.94 ((
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% 98.28/12.94 ((
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% 98.28/12.94 ((
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% 98.28/12.94 ((
% 98.28/12.94 (woz13rule4) =>
% 98.28/12.94 ((
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% 98.28/12.94 ((
% 98.28/12.94 (woz1_2) =>
% 98.28/12.94 ((
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% 98.28/12.94 ((
% 98.28/12.94 (woz1_4) =>
% 98.28/12.94 ((
% 98.28/12.94 (woz1_5) =>
% 98.28/12.94 ((
% 98.28/12.94 (breln1all2) =>
% 98.28/12.94 ((
% 98.28/12.94 (breln1SetBreln1) =>
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% 98.28/12.94 (
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% 98.28/12.94 breln1)) @
% 98.28/12.94 (
% 98.28/12.94 (
% 98.28/12.94 ('#S') @ dpsetconstr @
% 98.28/12.94 (
% 98.28/12.94 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.28/12.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl517])).
% 98.28/12.94 thf(zip_derived_cl537, plain,
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% 98.28/12.94 (((exuI2) =>
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% 98.28/12.94 (((exuE3u) =>
% 98.28/12.94 (((exu__Cong) =>
% 98.28/12.94 (((setadjoin__Cong) =>
% 98.28/12.94 (((powerset__Cong) =>
% 98.28/12.94 (((setunion__Cong) =>
% 98.28/12.94 (((exuEu) =>
% 98.28/12.94 (((descr__Cong) =>
% 98.28/12.94 (((dsetconstr__Cong) =>
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% 98.28/12.94 ((
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% 98.28/12.94 ((
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% 98.28/12.94 ((
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% 98.28/12.94 ((
% 98.28/12.94 (binintersectSubset2) =>
% 98.28/12.94 ((
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% 98.28/12.94 ((
% 98.28/12.94 (binintersectRsub) =>
% 98.28/12.94 ((
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% 98.28/12.94 ((
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% 98.28/12.94 ((
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% 98.28/12.94 ((
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% 98.28/12.94 ((
% 98.28/12.94 (singletoninpowunion) =>
% 98.28/12.94 ((
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% 98.28/12.94 ((
% 98.28/12.94 (upairsubunion) =>
% 98.28/12.94 ((
% 98.28/12.94 (upairinpowunion) =>
% 98.28/12.94 ((
% 98.28/12.94 (ubforcartprodlem1) =>
% 98.28/12.94 ((
% 98.28/12.94 (ubforcartprodlem2) =>
% 98.28/12.94 ((
% 98.28/12.94 (ubforcartprodlem3) =>
% 98.28/12.94 ((
% 98.28/12.94 (cartprodpairin) =>
% 98.28/12.94 ((
% 98.28/12.94 (cartprodmempair1) =>
% 98.28/12.94 ((
% 98.28/12.94 (cartprodmempair) =>
% 98.28/12.94 ((
% 98.28/12.94 (setunionE2) =>
% 98.28/12.94 ((
% 98.28/12.94 (setunionsingleton1) =>
% 98.28/12.94 ((
% 98.28/12.94 (setunionsingleton2) =>
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% 98.28/12.94 ((
% 98.28/12.94 (ex1I2) =>
% 98.28/12.94 ((
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% 98.28/12.94 ((
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% 98.28/12.94 ((
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% 98.28/12.94 ((
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% 98.28/12.94 ((
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% 98.28/12.94 (setukpairinjR1) =>
% 98.28/12.94 ((
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% 98.28/12.94 (cartprodsndin) =>
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% 98.28/12.94 (cartprodmempaircEq) =>
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% 98.28/12.94 (cartprodfstpairEq) =>
% 98.28/12.94 ((
% 98.28/12.94 (cartprodsndpairEq) =>
% 98.28/12.94 ((
% 98.28/12.94 (cartprodpairsurjEq) =>
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% 98.28/12.94 ((
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% 98.28/12.94 (ex1E2) =>
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% 98.28/12.94 ((
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% 98.28/12.94 ((
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% 98.28/12.94 (lam2lamEq) =>
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% 98.28/12.94 ((
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% 98.28/12.94 ((
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% 98.28/12.94 ((
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% 98.28/12.94 ((
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% 98.28/12.94 ((
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% 98.28/12.94 ((
% 98.28/12.94 (complementTE1) =>
% 98.28/12.94 ((
% 98.28/12.94 (binintersectTELcontra) =>
% 98.28/12.94 ((
% 98.28/12.94 (binintersectTERcontra) =>
% 98.28/12.94 ((
% 98.28/12.94 (contrasubsetT) =>
% 98.28/12.94 ((
% 98.28/12.94 (contrasubsetT1) =>
% 98.28/12.94 ((
% 98.28/12.94 (contrasubsetT2) =>
% 98.28/12.94 ((
% 98.28/12.94 (contrasubsetT3) =>
% 98.28/12.94 ((
% 98.28/12.94 (doubleComplementI1) =>
% 98.28/12.94 ((
% 98.28/12.94 (doubleComplementE1) =>
% 98.28/12.94 ((
% 98.28/12.94 (doubleComplementSub1) =>
% 98.28/12.94 ((
% 98.28/12.94 (doubleComplementSub2) =>
% 98.28/12.94 ((
% 98.28/12.94 (doubleComplementEq) =>
% 98.28/12.94 ((
% 98.28/12.94 (complementTnotintersectT) =>
% 98.28/12.94 ((
% 98.28/12.94 (complementImpComplementIntersect) =>
% 98.28/12.94 ((
% 98.28/12.94 (complementSubsetComplementIntersect) =>
% 98.28/12.94 ((
% 98.28/12.94 (complementInPowersetComplementIntersect) =>
% 98.28/12.94 ((
% 98.28/12.94 (contraSubsetComplement) =>
% 98.28/12.94 ((
% 98.28/12.94 (complementTcontraSubset) =>
% 98.28/12.94 ((
% 98.28/12.94 (binunionTILcontra) =>
% 98.28/12.94 ((
% 98.28/12.94 (binunionTIRcontra) =>
% 98.28/12.94 ((
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% 98.28/12.94 ((
% 98.28/12.94 (inIntersectImpInUnion2) =>
% 98.28/12.94 ((
% 98.28/12.94 (inIntersectImpInIntersectUnions) =>
% 98.28/12.94 ((
% 98.28/12.94 (intersectInPowersetIntersectUnions) =>
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% 98.28/12.94 (inComplementUnionImpNotIn1) =>
% 98.28/12.94 ((
% 98.28/12.94 (inComplementUnionImpInComplement1) =>
% 98.28/12.94 ((
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% 98.28/12.94 ((
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% 98.28/12.94 ((
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% 98.28/12.94 ((
% 98.28/12.94 (complementUnionInPowersetComplement) =>
% 98.28/12.94 ((
% 98.28/12.94 (demorgan2a2) =>
% 98.28/12.94 ((
% 98.28/12.94 (demorgan1a) =>
% 98.28/12.94 ((
% 98.28/12.94 (demorgan1b) =>
% 98.28/12.94 ((
% 98.28/12.94 (demorgan1) =>
% 98.28/12.94 ((
% 98.28/12.94 (demorgan2a) =>
% 98.28/12.94 ((
% 98.28/12.94 (demorgan2b2) =>
% 98.28/12.94 ((
% 98.28/12.94 (demorgan2b) =>
% 98.28/12.94 ((
% 98.28/12.94 (demorgan2) =>
% 98.28/12.94 ((
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% 98.28/12.94 ((
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% 98.28/12.94 ((
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% 98.28/12.94 ((
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% 98.28/12.94 ((
% 98.28/12.94 (woz13rule4) =>
% 98.28/12.94 ((
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% 98.28/12.94 ((
% 98.28/12.94 (woz1_5) =>
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% 98.28/12.94 (
% 98.28/12.94 (
% 98.28/12.94 ('#S') @ (
% 98.28/12.94 (
% 98.28/12.94 ('#B') @ (
% 98.28/12.94 '#B') @
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% 98.28/12.94 (
% 98.28/12.94 (
% 98.28/12.94 ('#S') @ dpsetconstr @
% 98.28/12.94 (
% 98.28/12.94 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.28/12.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl528])).
% 98.28/12.94 thf(zip_derived_cl546, plain,
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% 98.28/12.94 ((
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% 98.28/12.94 ((
% 98.28/12.94 (binintersectTERcontra) =>
% 98.28/12.94 ((
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% 98.28/12.94 ((
% 98.28/12.94 (contrasubsetT2) =>
% 98.28/12.94 ((
% 98.28/12.94 (contrasubsetT3) =>
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% 98.28/12.94 ((
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% 98.28/12.94 ((
% 98.28/12.94 (complementSubsetComplementIntersect) =>
% 98.28/12.94 ((
% 98.28/12.94 (complementInPowersetComplementIntersect) =>
% 98.28/12.94 ((
% 98.28/12.94 (contraSubsetComplement) =>
% 98.28/12.94 ((
% 98.28/12.94 (complementTcontraSubset) =>
% 98.28/12.94 ((
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% 98.28/12.94 ((
% 98.28/12.94 (binunionTIRcontra) =>
% 98.28/12.94 ((
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% 98.28/12.94 ((
% 98.28/12.94 (inIntersectImpInUnion2) =>
% 98.28/12.94 ((
% 98.28/12.94 (inIntersectImpInIntersectUnions) =>
% 98.28/12.94 ((
% 98.28/12.94 (intersectInPowersetIntersectUnions) =>
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% 98.28/12.94 ((
% 98.28/12.94 (inComplementUnionImpInComplement1) =>
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% 98.28/12.94 ((
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% 98.28/12.94 ((
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% 98.28/12.94 ((
% 98.28/12.94 (complementUnionInPowersetComplement) =>
% 98.28/12.94 ((
% 98.28/12.94 (demorgan2a2) =>
% 98.28/12.94 ((
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% 98.28/12.94 ((
% 98.28/12.94 (demorgan1b) =>
% 98.28/12.94 ((
% 98.28/12.94 (demorgan1) =>
% 98.28/12.94 ((
% 98.28/12.94 (demorgan2a) =>
% 98.28/12.94 ((
% 98.28/12.94 (demorgan2b2) =>
% 98.28/12.94 ((
% 98.28/12.94 (demorgan2b) =>
% 98.28/12.94 ((
% 98.28/12.94 (demorgan2) =>
% 98.28/12.94 ((
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% 98.28/12.94 ((
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% 98.28/12.94 ((
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% 98.28/12.94 ((
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% 98.28/12.94 (
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% 98.28/12.94 (
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% 98.28/12.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl537])).
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% 98.40/12.94 (cartprodpairmemER) =>
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% 98.40/12.94 (cartprodmempaircEq) =>
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% 98.40/12.94 ((
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% 98.40/12.94 ((
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% 98.40/12.94 ((
% 98.40/12.94 (complementTE1) =>
% 98.40/12.94 ((
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% 98.40/12.94 ((
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% 98.40/12.94 ((
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% 98.40/12.94 ((
% 98.40/12.94 (contraSubsetComplement) =>
% 98.40/12.94 ((
% 98.40/12.94 (complementTcontraSubset) =>
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% 98.40/12.94 ((
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% 98.40/12.94 (inIntersectImpInUnion2) =>
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% 98.40/12.94 (inIntersectImpInIntersectUnions) =>
% 98.40/12.94 ((
% 98.40/12.94 (intersectInPowersetIntersectUnions) =>
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% 98.40/12.94 (inComplementUnionImpNotIn1) =>
% 98.40/12.94 ((
% 98.40/12.94 (inComplementUnionImpInComplement1) =>
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% 98.40/12.94 ((
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% 98.40/12.94 ((
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% 98.40/12.94 ((
% 98.40/12.94 (complementUnionInPowersetComplement) =>
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% 98.40/12.94 ((
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% 98.40/12.94 ((
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% 98.40/12.94 ((
% 98.40/12.94 (demorgan1) =>
% 98.40/12.94 ((
% 98.40/12.94 (demorgan2a) =>
% 98.40/12.94 ((
% 98.40/12.94 (demorgan2b2) =>
% 98.40/12.94 ((
% 98.40/12.94 (demorgan2b) =>
% 98.40/12.94 ((
% 98.40/12.94 (demorgan2) =>
% 98.40/12.94 ((
% 98.40/12.94 (woz13rule0) =>
% 98.40/12.94 ((
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% 98.40/12.94 ((
% 98.40/12.94 (woz13rule2) =>
% 98.40/12.94 ((
% 98.40/12.94 (woz13rule3) =>
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% 98.40/12.94 (
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% 98.40/12.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl546])).
% 98.40/12.94 thf(zip_derived_cl561, plain,
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% 98.40/12.94 (((powerset__Cong) =>
% 98.40/12.94 (((setunion__Cong) =>
% 98.40/12.94 (((exuEu) =>
% 98.40/12.94 (((descr__Cong) =>
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% 98.40/12.94 ((
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% 98.40/12.94 ((
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% 98.40/12.94 ((
% 98.40/12.94 (upairset2IR) =>
% 98.40/12.94 ((
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% 98.40/12.94 ((
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% 98.40/12.94 ((
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% 98.40/12.94 (binunionRsub) =>
% 98.40/12.94 ((
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% 98.40/12.94 ((
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% 98.40/12.94 ((
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% 98.40/12.94 ((
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% 98.40/12.94 ((
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% 98.40/12.94 (cartprodpairmemER) =>
% 98.40/12.94 ((
% 98.40/12.94 (cartprodmempaircEq) =>
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% 98.40/12.94 (cartprodfstpairEq) =>
% 98.40/12.94 ((
% 98.40/12.94 (cartprodsndpairEq) =>
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% 98.40/12.94 (cartprodpairsurjEq) =>
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% 98.40/12.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl595])).
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% 98.40/12.95 ((
% 98.40/12.95 (cartprodsndin) =>
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% 98.40/12.95 ((
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% 98.40/12.95 ((
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% 98.40/12.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl606])).
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% 98.40/12.95 (contraSubsetComplement) =>
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% 98.40/12.95 ((
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% 98.40/12.95 ((
% 98.40/12.95 (demorgan2a) =>
% 98.40/12.95 ((
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% 98.40/12.96 (woz1_5) =>
% 98.40/12.96 ((
% 98.40/12.96 (breln1all2) =>
% 98.40/12.96 ((
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% 98.40/12.96 ((
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% 98.40/12.96 ((
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% 98.40/12.96 '#B') @
% 98.40/12.96 breln1)) @
% 98.40/12.96 (
% 98.40/12.96 (
% 98.40/12.96 ('#S') @ dpsetconstr @
% 98.40/12.96 (
% 98.40/12.96 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.40/12.96 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl650])).
% 98.40/12.96 thf(zip_derived_cl672, plain,
% 98.40/12.96 (~ (((exu__Cong) =>
% 98.40/12.96 (((setadjoin__Cong) =>
% 98.40/12.96 (((powerset__Cong) =>
% 98.40/12.96 (((setunion__Cong) =>
% 98.40/12.96 (((exuEu) =>
% 98.40/12.96 (((descr__Cong) =>
% 98.40/12.96 (((dsetconstr__Cong) =>
% 98.40/12.96 (((subsetI1) =>
% 98.40/12.96 (((eqimpsubset2) =>
% 98.40/12.96 (((eqimpsubset1) =>
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% 98.40/12.96 (((subsetE) =>
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% 98.40/12.96 (((subsetemptysetimpeq) =>
% 98.40/12.96 (((powersetI1) =>
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% 98.40/12.96 (((sepSubset) =>
% 98.40/12.96 ((
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% 98.40/12.96 ((
% 98.40/12.96 (upairset2IR) =>
% 98.40/12.96 ((
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% 98.40/12.96 ((
% 98.40/12.96 (binunionEcases) =>
% 98.40/12.96 ((
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% 98.40/12.96 ((
% 98.40/12.96 (binunionLsub) =>
% 98.40/12.96 ((
% 98.40/12.96 (binunionRsub) =>
% 98.40/12.96 ((
% 98.40/12.96 (binintersectI) =>
% 98.40/12.96 ((
% 98.40/12.96 (binintersectSubset5) =>
% 98.40/12.96 ((
% 98.40/12.96 (binintersectEL) =>
% 98.40/12.96 ((
% 98.40/12.96 (binintersectLsub) =>
% 98.40/12.96 ((
% 98.40/12.96 (binintersectSubset2) =>
% 98.40/12.96 ((
% 98.40/12.96 (binintersectSubset3) =>
% 98.40/12.96 ((
% 98.40/12.96 (binintersectER) =>
% 98.40/12.96 ((
% 98.40/12.96 (disjointsetsI1) =>
% 98.40/12.96 ((
% 98.40/12.96 (binintersectRsub) =>
% 98.40/12.96 ((
% 98.40/12.96 (binintersectSubset4) =>
% 98.40/12.96 ((
% 98.40/12.96 (binintersectSubset1) =>
% 98.40/12.96 ((
% 98.40/12.96 (bs114d) =>
% 98.40/12.96 ((
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% 98.40/12.96 ((
% 98.40/12.96 (setminusEL) =>
% 98.40/12.96 ((
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% 98.40/12.96 ((
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% 98.40/12.96 ((
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% 98.40/12.96 ((
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% 98.40/12.96 ((
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% 98.40/12.96 ((
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% 98.40/12.96 ((
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% 98.40/12.96 ((
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% 98.40/12.96 ((
% 98.40/12.96 (symdiffE) =>
% 98.40/12.96 ((
% 98.40/12.96 (symdiffI1) =>
% 98.40/12.96 ((
% 98.40/12.96 (symdiffI2) =>
% 98.40/12.96 ((
% 98.40/12.96 (symdiffIneg1) =>
% 98.40/12.96 ((
% 98.40/12.96 (symdiffIneg2) =>
% 98.40/12.96 ((
% 98.40/12.96 (secondinupair) =>
% 98.40/12.96 ((
% 98.40/12.96 (setukpairIL) =>
% 98.40/12.96 ((
% 98.40/12.96 (setukpairIR) =>
% 98.40/12.96 ((
% 98.40/12.96 (kpairiskpair) =>
% 98.40/12.96 ((
% 98.40/12.96 (kpairp) =>
% 98.40/12.96 ((
% 98.40/12.96 (singletonsubset) =>
% 98.40/12.96 ((
% 98.40/12.96 (singletoninpowerset) =>
% 98.40/12.96 ((
% 98.40/12.96 (singletoninpowunion) =>
% 98.40/12.96 ((
% 98.40/12.96 (upairset2E) =>
% 98.40/12.96 ((
% 98.40/12.96 (upairsubunion) =>
% 98.40/12.96 ((
% 98.40/12.96 (upairinpowunion) =>
% 98.40/12.96 ((
% 98.40/12.96 (ubforcartprodlem1) =>
% 98.40/12.96 ((
% 98.40/12.96 (ubforcartprodlem2) =>
% 98.40/12.96 ((
% 98.40/12.96 (ubforcartprodlem3) =>
% 98.40/12.96 ((
% 98.40/12.96 (cartprodpairin) =>
% 98.40/12.96 ((
% 98.40/12.96 (cartprodmempair1) =>
% 98.40/12.96 ((
% 98.40/12.96 (cartprodmempair) =>
% 98.40/12.96 ((
% 98.40/12.96 (setunionE2) =>
% 98.40/12.96 ((
% 98.40/12.96 (setunionsingleton1) =>
% 98.40/12.96 ((
% 98.40/12.96 (setunionsingleton2) =>
% 98.40/12.96 ((
% 98.40/12.96 (setunionsingleton) =>
% 98.40/12.96 ((
% 98.40/12.96 (singletonprop) =>
% 98.40/12.96 ((
% 98.40/12.96 (ex1E1) =>
% 98.40/12.96 ((
% 98.40/12.96 (ex1I) =>
% 98.40/12.96 ((
% 98.40/12.96 (ex1I2) =>
% 98.40/12.96 ((
% 98.40/12.96 (singletonsuniq) =>
% 98.40/12.96 ((
% 98.40/12.96 (setukpairinjL1) =>
% 98.40/12.96 ((
% 98.40/12.96 (kfstsingleton) =>
% 98.40/12.96 ((
% 98.40/12.96 (theprop) =>
% 98.40/12.96 ((
% 98.40/12.96 (kfstpairEq) =>
% 98.40/12.96 ((
% 98.40/12.96 (cartprodfstin) =>
% 98.40/12.96 ((
% 98.40/12.96 (setukpairinjL2) =>
% 98.40/12.96 ((
% 98.40/12.96 (setukpairinjL) =>
% 98.40/12.96 ((
% 98.40/12.96 (setukpairinjR11) =>
% 98.40/12.96 ((
% 98.40/12.96 (setukpairinjR12) =>
% 98.40/12.96 ((
% 98.40/12.96 (setukpairinjR1) =>
% 98.40/12.96 ((
% 98.40/12.96 (upairequniteq) =>
% 98.40/12.96 ((
% 98.40/12.96 (setukpairinjR2) =>
% 98.40/12.96 ((
% 98.40/12.96 (setukpairinjR) =>
% 98.40/12.96 ((
% 98.40/12.96 (ksndsingleton) =>
% 98.40/12.96 ((
% 98.40/12.96 (ksndpairEq) =>
% 98.40/12.96 ((
% 98.40/12.96 (kpairsurjEq) =>
% 98.40/12.96 ((
% 98.40/12.96 (cartprodsndin) =>
% 98.40/12.96 ((
% 98.40/12.96 (cartprodpairmemEL) =>
% 98.40/12.96 ((
% 98.40/12.96 (cartprodpairmemER) =>
% 98.40/12.96 ((
% 98.40/12.96 (cartprodmempaircEq) =>
% 98.40/12.96 ((
% 98.40/12.96 (cartprodfstpairEq) =>
% 98.40/12.96 ((
% 98.40/12.96 (cartprodsndpairEq) =>
% 98.40/12.96 ((
% 98.40/12.96 (cartprodpairsurjEq) =>
% 98.40/12.96 ((
% 98.40/12.96 (dpsetconstrI) =>
% 98.40/12.96 ((
% 98.40/12.96 (dpsetconstrSub) =>
% 98.40/12.96 ((
% 98.40/12.96 (setOfPairsIsBReln) =>
% 98.40/12.96 ((
% 98.40/12.96 (dpsetconstrERa) =>
% 98.40/12.96 ((
% 98.40/12.96 (dpsetconstrEL1) =>
% 98.40/12.96 ((
% 98.40/12.96 (dpsetconstrEL2) =>
% 98.40/12.96 ((
% 98.40/12.96 (dpsetconstrER) =>
% 98.40/12.96 ((
% 98.40/12.96 (funcImageSingleton) =>
% 98.40/12.96 ((
% 98.40/12.96 (apProp) =>
% 98.40/12.96 ((
% 98.40/12.96 (app) =>
% 98.40/12.96 ((
% 98.40/12.96 (infuncsetfunc) =>
% 98.40/12.96 ((
% 98.40/12.96 (ap2p) =>
% 98.40/12.96 ((
% 98.40/12.96 (funcinfuncset) =>
% 98.40/12.96 ((
% 98.40/12.96 (lamProp) =>
% 98.40/12.96 ((
% 98.40/12.96 (lamp) =>
% 98.40/12.96 ((
% 98.40/12.96 (lam2p) =>
% 98.40/12.96 ((
% 98.40/12.96 (brelnall1) =>
% 98.40/12.96 ((
% 98.40/12.96 (brelnall2) =>
% 98.40/12.96 ((
% 98.40/12.96 (ex1E2) =>
% 98.40/12.96 ((
% 98.40/12.96 (funcGraphProp1) =>
% 98.40/12.96 ((
% 98.40/12.96 (funcGraphProp3) =>
% 98.40/12.96 ((
% 98.40/12.96 (funcGraphProp2) =>
% 98.40/12.96 ((
% 98.40/12.96 (funcextLem) =>
% 98.40/12.96 ((
% 98.40/12.96 (funcGraphProp4) =>
% 98.40/12.96 ((
% 98.40/12.96 (subbreln) =>
% 98.40/12.96 ((
% 98.40/12.96 (eqbreln) =>
% 98.40/12.96 ((
% 98.40/12.96 (funcext) =>
% 98.40/12.96 ((
% 98.40/12.96 (funcext2) =>
% 98.40/12.96 ((
% 98.40/12.96 (ap2apEq1) =>
% 98.40/12.96 ((
% 98.40/12.96 (ap2apEq2) =>
% 98.40/12.96 ((
% 98.40/12.96 (beta1) =>
% 98.40/12.96 ((
% 98.40/12.96 (eta1) =>
% 98.40/12.96 ((
% 98.40/12.96 (lam2lamEq) =>
% 98.40/12.96 ((
% 98.40/12.96 (beta2) =>
% 98.40/12.96 ((
% 98.40/12.96 (eta2) =>
% 98.40/12.96 ((
% 98.40/12.96 (iffalseProp1) =>
% 98.40/12.96 ((
% 98.40/12.96 (iffalseProp2) =>
% 98.40/12.96 ((
% 98.40/12.96 (iftrueProp1) =>
% 98.40/12.96 ((
% 98.40/12.96 (iftrueProp2) =>
% 98.40/12.96 ((
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% 98.40/12.96 ((
% 98.40/12.96 (ifp) =>
% 98.40/12.96 ((
% 98.40/12.96 (theeq) =>
% 98.40/12.96 ((
% 98.40/12.96 (iftrue) =>
% 98.40/12.96 ((
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% 98.40/12.96 ((
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% 98.40/12.96 ((
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% 98.40/12.96 ((
% 98.40/12.96 (binunionT_lem) =>
% 98.40/12.96 ((
% 98.40/12.96 (powersetT_lem) =>
% 98.40/12.96 ((
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% 98.40/12.96 ((
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% 98.40/12.96 ((
% 98.40/12.96 (setextT) =>
% 98.40/12.96 ((
% 98.40/12.96 (subsetTI) =>
% 98.40/12.96 ((
% 98.40/12.96 (powersetTI1) =>
% 98.40/12.96 ((
% 98.40/12.96 (powersetTE1) =>
% 98.40/12.96 ((
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% 98.40/12.96 ((
% 98.40/12.96 (complementTE1) =>
% 98.40/12.96 ((
% 98.40/12.96 (binintersectTELcontra) =>
% 98.40/12.96 ((
% 98.40/12.96 (binintersectTERcontra) =>
% 98.40/12.96 ((
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% 98.40/12.96 ((
% 98.40/12.96 (contrasubsetT1) =>
% 98.40/12.96 ((
% 98.40/12.96 (contrasubsetT2) =>
% 98.40/12.96 ((
% 98.40/12.96 (contrasubsetT3) =>
% 98.40/12.96 ((
% 98.40/12.96 (doubleComplementI1) =>
% 98.40/12.96 ((
% 98.40/12.96 (doubleComplementE1) =>
% 98.40/12.96 ((
% 98.40/12.96 (doubleComplementSub1) =>
% 98.40/12.96 ((
% 98.40/12.96 (doubleComplementSub2) =>
% 98.40/12.96 ((
% 98.40/12.96 (doubleComplementEq) =>
% 98.40/12.96 ((
% 98.40/12.96 (complementTnotintersectT) =>
% 98.40/12.96 ((
% 98.40/12.96 (complementImpComplementIntersect) =>
% 98.40/12.96 ((
% 98.40/12.96 (complementSubsetComplementIntersect) =>
% 98.40/12.96 ((
% 98.40/12.96 (complementInPowersetComplementIntersect) =>
% 98.40/12.96 ((
% 98.40/12.96 (contraSubsetComplement) =>
% 98.40/12.96 ((
% 98.40/12.96 (complementTcontraSubset) =>
% 98.40/12.96 ((
% 98.40/12.96 (binunionTILcontra) =>
% 98.40/12.96 ((
% 98.40/12.96 (binunionTIRcontra) =>
% 98.40/12.96 ((
% 98.40/12.96 (inIntersectImpInUnion) =>
% 98.40/12.96 ((
% 98.40/12.96 (inIntersectImpInUnion2) =>
% 98.40/12.96 ((
% 98.40/12.96 (inIntersectImpInIntersectUnions) =>
% 98.40/12.96 ((
% 98.40/12.96 (intersectInPowersetIntersectUnions) =>
% 98.40/12.96 ((
% 98.40/12.96 (inComplementUnionImpNotIn1) =>
% 98.40/12.96 ((
% 98.40/12.96 (inComplementUnionImpInComplement1) =>
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% 98.40/12.96 ((
% 98.40/12.96 (binunionTEcontra) =>
% 98.40/12.96 ((
% 98.40/12.96 (demorgan2a1) =>
% 98.40/12.96 ((
% 98.40/12.96 (complementUnionInPowersetComplement) =>
% 98.40/12.96 ((
% 98.40/12.96 (demorgan2a2) =>
% 98.40/12.96 ((
% 98.40/12.96 (demorgan1a) =>
% 98.40/12.96 ((
% 98.40/12.96 (demorgan1b) =>
% 98.40/12.96 ((
% 98.40/12.96 (demorgan1) =>
% 98.40/12.96 ((
% 98.40/12.96 (demorgan2a) =>
% 98.40/12.96 ((
% 98.40/12.96 (demorgan2b2) =>
% 98.40/12.96 ((
% 98.40/12.96 (demorgan2b) =>
% 98.40/12.96 ((
% 98.40/12.96 (demorgan2) =>
% 98.40/12.96 ((
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% 98.40/12.96 ((
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% 98.40/12.96 ((
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% 98.40/12.96 ((
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% 98.40/12.96 ((
% 98.40/12.96 (woz13rule4) =>
% 98.40/12.96 ((
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% 98.40/12.96 ((
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% 98.40/12.96 ((
% 98.40/12.96 (woz1_3) =>
% 98.40/12.96 ((
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% 98.40/12.96 ((
% 98.40/12.96 (woz1_5) =>
% 98.40/12.96 ((
% 98.40/12.96 (breln1all2) =>
% 98.40/12.96 ((
% 98.40/12.96 (breln1SetBreln1) =>
% 98.40/12.96 ((
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% 98.40/12.96 ((
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% 98.40/12.96 (
% 98.40/12.96 (
% 98.40/12.96 ('#S') @ (
% 98.40/12.96 (
% 98.40/12.96 ('#B') @ (
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% 98.40/12.96 breln1)) @
% 98.40/12.96 (
% 98.40/12.96 (
% 98.40/12.96 ('#S') @ dpsetconstr @
% 98.40/12.96 (
% 98.40/12.96 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.40/12.96 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl660])).
% 98.40/12.96 thf(zip_derived_cl685, plain,
% 98.40/12.96 (~ (((setadjoin__Cong) =>
% 98.40/12.96 (((powerset__Cong) =>
% 98.40/12.96 (((setunion__Cong) =>
% 98.40/12.96 (((exuEu) =>
% 98.40/12.96 (((descr__Cong) =>
% 98.40/12.96 (((dsetconstr__Cong) =>
% 98.40/12.96 (((subsetI1) =>
% 98.40/12.96 (((eqimpsubset2) =>
% 98.40/12.96 (((eqimpsubset1) =>
% 98.40/12.96 (((subsetI2) =>
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% 98.40/12.96 (((notequalI1) =>
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% 98.40/12.96 ((
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% 98.40/12.96 ((
% 98.40/12.96 (binintersectI) =>
% 98.40/12.96 ((
% 98.40/12.96 (binintersectSubset5) =>
% 98.40/12.96 ((
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% 98.40/12.96 ((
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% 98.40/12.96 ((
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% 98.40/12.96 ((
% 98.40/12.96 (binintersectSubset3) =>
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% 98.40/12.96 (binintersectER) =>
% 98.40/12.96 ((
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% 98.40/12.96 ((
% 98.40/12.96 (binintersectRsub) =>
% 98.40/12.96 ((
% 98.40/12.96 (binintersectSubset4) =>
% 98.40/12.96 ((
% 98.40/12.96 (binintersectSubset1) =>
% 98.40/12.96 ((
% 98.40/12.96 (bs114d) =>
% 98.40/12.96 ((
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% 98.40/12.96 ((
% 98.40/12.96 (setminusEL) =>
% 98.40/12.96 ((
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% 98.40/12.96 ((
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% 98.40/12.96 ((
% 98.40/12.96 (ubforcartprodlem2) =>
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% 98.40/12.96 (ubforcartprodlem3) =>
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% 98.40/12.96 (cartprodmempair) =>
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% 98.40/12.96 ((
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% 98.40/12.96 (cartprodfstpairEq) =>
% 98.40/12.96 ((
% 98.40/12.96 (cartprodsndpairEq) =>
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% 98.40/12.96 (binunionT_lem) =>
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% 98.40/12.96 (powersetT_lem) =>
% 98.40/12.96 ((
% 98.40/12.96 (setminusT_lem) =>
% 98.40/12.96 ((
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% 98.40/12.96 ((
% 98.40/12.96 (setextT) =>
% 98.40/12.96 ((
% 98.40/12.96 (subsetTI) =>
% 98.40/12.96 ((
% 98.40/12.96 (powersetTI1) =>
% 98.40/12.96 ((
% 98.40/12.96 (powersetTE1) =>
% 98.40/12.96 ((
% 98.40/12.96 (complementTI1) =>
% 98.40/12.96 ((
% 98.40/12.96 (complementTE1) =>
% 98.40/12.96 ((
% 98.40/12.96 (binintersectTELcontra) =>
% 98.40/12.96 ((
% 98.40/12.96 (binintersectTERcontra) =>
% 98.40/12.96 ((
% 98.40/12.96 (contrasubsetT) =>
% 98.40/12.96 ((
% 98.40/12.96 (contrasubsetT1) =>
% 98.40/12.96 ((
% 98.40/12.96 (contrasubsetT2) =>
% 98.40/12.96 ((
% 98.40/12.96 (contrasubsetT3) =>
% 98.40/12.96 ((
% 98.40/12.96 (doubleComplementI1) =>
% 98.40/12.96 ((
% 98.40/12.96 (doubleComplementE1) =>
% 98.40/12.96 ((
% 98.40/12.96 (doubleComplementSub1) =>
% 98.40/12.96 ((
% 98.40/12.96 (doubleComplementSub2) =>
% 98.40/12.96 ((
% 98.40/12.96 (doubleComplementEq) =>
% 98.40/12.96 ((
% 98.40/12.96 (complementTnotintersectT) =>
% 98.40/12.96 ((
% 98.40/12.96 (complementImpComplementIntersect) =>
% 98.40/12.96 ((
% 98.40/12.96 (complementSubsetComplementIntersect) =>
% 98.40/12.96 ((
% 98.40/12.96 (complementInPowersetComplementIntersect) =>
% 98.40/12.96 ((
% 98.40/12.96 (contraSubsetComplement) =>
% 98.40/12.96 ((
% 98.40/12.96 (complementTcontraSubset) =>
% 98.40/12.96 ((
% 98.40/12.96 (binunionTILcontra) =>
% 98.40/12.96 ((
% 98.40/12.96 (binunionTIRcontra) =>
% 98.40/12.96 ((
% 98.40/12.96 (inIntersectImpInUnion) =>
% 98.40/12.96 ((
% 98.40/12.96 (inIntersectImpInUnion2) =>
% 98.40/12.96 ((
% 98.40/12.96 (inIntersectImpInIntersectUnions) =>
% 98.40/12.96 ((
% 98.40/12.96 (intersectInPowersetIntersectUnions) =>
% 98.40/12.96 ((
% 98.40/12.96 (inComplementUnionImpNotIn1) =>
% 98.40/12.96 ((
% 98.40/12.96 (inComplementUnionImpInComplement1) =>
% 98.40/12.96 ((
% 98.40/12.96 (binunionTE) =>
% 98.40/12.96 ((
% 98.40/12.96 (binunionTEcontra) =>
% 98.40/12.96 ((
% 98.40/12.96 (demorgan2a1) =>
% 98.40/12.96 ((
% 98.40/12.96 (complementUnionInPowersetComplement) =>
% 98.40/12.96 ((
% 98.40/12.96 (demorgan2a2) =>
% 98.40/12.96 ((
% 98.40/12.96 (demorgan1a) =>
% 98.40/12.96 ((
% 98.40/12.96 (demorgan1b) =>
% 98.40/12.96 ((
% 98.40/12.96 (demorgan1) =>
% 98.40/12.96 ((
% 98.40/12.96 (demorgan2a) =>
% 98.40/12.96 ((
% 98.40/12.96 (demorgan2b2) =>
% 98.40/12.96 ((
% 98.40/12.96 (demorgan2b) =>
% 98.40/12.96 ((
% 98.40/12.96 (demorgan2) =>
% 98.40/12.96 ((
% 98.40/12.96 (woz13rule0) =>
% 98.40/12.96 ((
% 98.40/12.96 (woz13rule1) =>
% 98.40/12.96 ((
% 98.40/12.96 (woz13rule2) =>
% 98.40/12.96 ((
% 98.40/12.96 (woz13rule3) =>
% 98.40/12.96 ((
% 98.40/12.96 (woz13rule4) =>
% 98.40/12.96 ((
% 98.40/12.96 (woz1_1) =>
% 98.40/12.96 ((
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% 98.40/12.96 ((
% 98.40/12.96 (woz1_3) =>
% 98.40/12.96 ((
% 98.40/12.96 (woz1_4) =>
% 98.40/12.96 ((
% 98.40/12.96 (woz1_5) =>
% 98.40/12.96 ((
% 98.40/12.96 (breln1all2) =>
% 98.40/12.96 ((
% 98.40/12.96 (breln1SetBreln1) =>
% 98.40/12.96 ((
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% 98.40/12.96 ((
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% 98.40/12.96 (
% 98.40/12.96 (
% 98.40/12.96 ('#S') @ (
% 98.40/12.96 (
% 98.40/12.96 ('#B') @ (
% 98.40/12.96 '#B') @
% 98.40/12.96 breln1)) @
% 98.40/12.96 (
% 98.40/12.96 (
% 98.40/12.96 ('#S') @ dpsetconstr @
% 98.40/12.96 (
% 98.40/12.96 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.40/12.96 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl672])).
% 98.40/12.96 thf(zip_derived_cl699, plain,
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% 98.40/12.96 (((eqimpsubset2) =>
% 98.40/12.96 (((eqimpsubset1) =>
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% 98.40/12.96 (((notequalI1) =>
% 98.40/12.96 (((notequalI2) =>
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% 98.40/12.96 ((
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% 98.40/12.96 ((
% 98.40/12.96 (binintersectSubset4) =>
% 98.40/12.96 ((
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% 98.40/12.96 (upairinpowunion) =>
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% 98.40/12.96 (ubforcartprodlem3) =>
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% 98.40/12.96 (cartprodsndpairEq) =>
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% 98.40/12.96 (cartprodpairsurjEq) =>
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% 98.40/12.96 (contrasubsetT3) =>
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% 98.40/12.96 (doubleComplementE1) =>
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% 98.40/12.96 ((
% 98.40/12.96 (doubleComplementEq) =>
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% 98.40/12.96 (complementTnotintersectT) =>
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% 98.40/12.96 (complementSubsetComplementIntersect) =>
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% 98.40/12.96 (complementInPowersetComplementIntersect) =>
% 98.40/12.96 ((
% 98.40/12.96 (contraSubsetComplement) =>
% 98.40/12.96 ((
% 98.40/12.96 (complementTcontraSubset) =>
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% 98.40/12.96 ((
% 98.40/12.96 (binunionTIRcontra) =>
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% 98.40/12.96 ((
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% 98.40/12.96 (inIntersectImpInIntersectUnions) =>
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% 98.40/12.96 (inComplementUnionImpInComplement1) =>
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% 98.40/12.96 (demorgan2a2) =>
% 98.40/12.96 ((
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% 98.40/12.96 ((
% 98.40/12.96 (demorgan1b) =>
% 98.40/12.96 ((
% 98.40/12.96 (demorgan1) =>
% 98.40/12.96 ((
% 98.40/12.96 (demorgan2a) =>
% 98.40/12.96 ((
% 98.40/12.96 (demorgan2b2) =>
% 98.40/12.96 ((
% 98.40/12.96 (demorgan2b) =>
% 98.40/12.96 ((
% 98.40/12.96 (demorgan2) =>
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% 98.40/12.97 ((
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% 98.40/12.97 ((
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% 98.40/12.97 ((
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% 98.40/12.97 ((
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% 98.40/12.97 ((
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% 98.40/12.97 ((
% 98.40/12.97 (binintersectTERcontra) =>
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% 98.40/12.97 (contrasubsetT) =>
% 98.40/12.97 ((
% 98.40/12.97 (contrasubsetT1) =>
% 98.40/12.97 ((
% 98.40/12.97 (contrasubsetT2) =>
% 98.40/12.97 ((
% 98.40/12.97 (contrasubsetT3) =>
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% 98.40/12.97 (doubleComplementI1) =>
% 98.40/12.97 ((
% 98.40/12.97 (doubleComplementE1) =>
% 98.40/12.97 ((
% 98.40/12.97 (doubleComplementSub1) =>
% 98.40/12.97 ((
% 98.40/12.97 (doubleComplementSub2) =>
% 98.40/12.97 ((
% 98.40/12.97 (doubleComplementEq) =>
% 98.40/12.97 ((
% 98.40/12.97 (complementTnotintersectT) =>
% 98.40/12.97 ((
% 98.40/12.97 (complementImpComplementIntersect) =>
% 98.40/12.97 ((
% 98.40/12.97 (complementSubsetComplementIntersect) =>
% 98.40/12.97 ((
% 98.40/12.97 (complementInPowersetComplementIntersect) =>
% 98.40/12.97 ((
% 98.40/12.97 (contraSubsetComplement) =>
% 98.40/12.97 ((
% 98.40/12.97 (complementTcontraSubset) =>
% 98.40/12.97 ((
% 98.40/12.97 (binunionTILcontra) =>
% 98.40/12.97 ((
% 98.40/12.97 (binunionTIRcontra) =>
% 98.40/12.97 ((
% 98.40/12.97 (inIntersectImpInUnion) =>
% 98.40/12.97 ((
% 98.40/12.97 (inIntersectImpInUnion2) =>
% 98.40/12.97 ((
% 98.40/12.97 (inIntersectImpInIntersectUnions) =>
% 98.40/12.97 ((
% 98.40/12.97 (intersectInPowersetIntersectUnions) =>
% 98.40/12.97 ((
% 98.40/12.97 (inComplementUnionImpNotIn1) =>
% 98.40/12.97 ((
% 98.40/12.97 (inComplementUnionImpInComplement1) =>
% 98.40/12.97 ((
% 98.40/12.97 (binunionTE) =>
% 98.40/12.97 ((
% 98.40/12.97 (binunionTEcontra) =>
% 98.40/12.97 ((
% 98.40/12.97 (demorgan2a1) =>
% 98.40/12.97 ((
% 98.40/12.97 (complementUnionInPowersetComplement) =>
% 98.40/12.97 ((
% 98.40/12.97 (demorgan2a2) =>
% 98.40/12.97 ((
% 98.40/12.97 (demorgan1a) =>
% 98.40/12.97 ((
% 98.40/12.97 (demorgan1b) =>
% 98.40/12.97 ((
% 98.40/12.97 (demorgan1) =>
% 98.40/12.97 ((
% 98.40/12.97 (demorgan2a) =>
% 98.40/12.97 ((
% 98.40/12.97 (demorgan2b2) =>
% 98.40/12.97 ((
% 98.40/12.97 (demorgan2b) =>
% 98.40/12.97 ((
% 98.40/12.97 (demorgan2) =>
% 98.40/12.97 ((
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% 98.40/12.97 ((
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% 98.40/12.97 (woz13rule2) =>
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% 98.40/12.97 (woz13rule3) =>
% 98.40/12.97 ((
% 98.40/12.97 (woz13rule4) =>
% 98.40/12.97 ((
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% 98.40/12.97 ((
% 98.40/12.97 (woz1_5) =>
% 98.40/12.97 ((
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% 98.40/12.97 (
% 98.40/12.97 (
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% 98.40/12.97 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl807])).
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% 98.40/12.98 ((
% 98.40/12.98 (ubforcartprodlem2) =>
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% 98.40/12.98 (ubforcartprodlem3) =>
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% 98.40/12.98 (cartprodmempair) =>
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% 98.40/12.98 ((
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% 98.40/12.98 ((
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% 98.40/12.98 ((
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% 98.40/12.98 (cartprodsndpairEq) =>
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% 98.40/12.98 ((
% 98.40/12.98 (complementTE1) =>
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% 98.40/12.98 (binintersectTELcontra) =>
% 98.40/12.98 ((
% 98.40/12.98 (binintersectTERcontra) =>
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% 98.40/12.98 ((
% 98.40/12.98 (contrasubsetT2) =>
% 98.40/12.98 ((
% 98.40/12.98 (contrasubsetT3) =>
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% 98.40/12.98 (doubleComplementI1) =>
% 98.40/12.98 ((
% 98.40/12.98 (doubleComplementE1) =>
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% 98.40/12.98 (doubleComplementSub1) =>
% 98.40/12.98 ((
% 98.40/12.98 (doubleComplementSub2) =>
% 98.40/12.98 ((
% 98.40/12.98 (doubleComplementEq) =>
% 98.40/12.98 ((
% 98.40/12.98 (complementTnotintersectT) =>
% 98.40/12.98 ((
% 98.40/12.98 (complementImpComplementIntersect) =>
% 98.40/12.98 ((
% 98.40/12.98 (complementSubsetComplementIntersect) =>
% 98.40/12.98 ((
% 98.40/12.98 (complementInPowersetComplementIntersect) =>
% 98.40/12.98 ((
% 98.40/12.98 (contraSubsetComplement) =>
% 98.40/12.98 ((
% 98.40/12.98 (complementTcontraSubset) =>
% 98.40/12.98 ((
% 98.40/12.98 (binunionTILcontra) =>
% 98.40/12.98 ((
% 98.40/12.98 (binunionTIRcontra) =>
% 98.40/12.98 ((
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% 98.40/12.98 (inIntersectImpInUnion2) =>
% 98.40/12.98 ((
% 98.40/12.98 (inIntersectImpInIntersectUnions) =>
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% 98.40/12.98 (intersectInPowersetIntersectUnions) =>
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% 98.40/12.98 (inComplementUnionImpNotIn1) =>
% 98.40/12.98 ((
% 98.40/12.98 (inComplementUnionImpInComplement1) =>
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% 98.40/12.98 ((
% 98.40/12.98 (binunionTEcontra) =>
% 98.40/12.98 ((
% 98.40/12.98 (demorgan2a1) =>
% 98.40/12.98 ((
% 98.40/12.98 (complementUnionInPowersetComplement) =>
% 98.40/12.98 ((
% 98.40/12.98 (demorgan2a2) =>
% 98.40/12.98 ((
% 98.40/12.98 (demorgan1a) =>
% 98.40/12.98 ((
% 98.40/12.98 (demorgan1b) =>
% 98.40/12.98 ((
% 98.40/12.98 (demorgan1) =>
% 98.40/12.98 ((
% 98.40/12.98 (demorgan2a) =>
% 98.40/12.98 ((
% 98.40/12.98 (demorgan2b2) =>
% 98.40/12.98 ((
% 98.40/12.98 (demorgan2b) =>
% 98.40/12.98 ((
% 98.40/12.98 (demorgan2) =>
% 98.40/12.98 ((
% 98.40/12.98 (woz13rule0) =>
% 98.40/12.98 ((
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% 98.40/12.98 ((
% 98.40/12.98 (woz13rule2) =>
% 98.40/12.98 ((
% 98.40/12.98 (woz13rule3) =>
% 98.40/12.98 ((
% 98.40/12.98 (woz13rule4) =>
% 98.40/12.98 ((
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% 98.40/12.98 ((
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% 98.40/12.98 ((
% 98.40/12.98 (woz1_4) =>
% 98.40/12.98 ((
% 98.40/12.98 (woz1_5) =>
% 98.40/12.98 ((
% 98.40/12.98 (breln1all2) =>
% 98.40/12.98 ((
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% 98.40/12.98 (
% 98.40/12.98 (
% 98.40/12.98 ('#S') @ (
% 98.40/12.98 (
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% 98.40/12.98 (
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% 98.40/12.98 (
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% 98.40/12.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl967])).
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% 98.40/12.98 (((sepInPowerset) =>
% 98.40/12.98 (((sepSubset) =>
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% 98.40/12.98 (((upairset2IR) =>
% 98.40/12.98 (((binunionIR) =>
% 98.40/12.98 (((binunionEcases) =>
% 98.40/12.98 (((binunionE) =>
% 98.40/12.98 (((binunionLsub) =>
% 98.40/12.98 (((binunionRsub) =>
% 98.40/12.98 (((binintersectI) =>
% 98.40/12.98 (((binintersectSubset5) =>
% 98.40/12.98 (((binintersectEL) =>
% 98.40/12.98 (((binintersectLsub) =>
% 98.40/12.98 (((binintersectSubset2) =>
% 98.40/12.98 (((binintersectSubset3) =>
% 98.40/12.98 (((binintersectER) =>
% 98.40/12.98 (((disjointsetsI1) =>
% 98.40/12.98 (((binintersectRsub) =>
% 98.40/12.98 (((binintersectSubset4) =>
% 98.40/12.98 (((binintersectSubset1) =>
% 98.40/12.98 (((bs114d) =>
% 98.40/12.98 (((setminusI) =>
% 98.40/12.98 (((setminusEL) =>
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% 98.40/12.98 (((setminusSubset2) =>
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% 98.40/12.98 (setminusIRneg) =>
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% 98.40/12.98 (setminusLsub) =>
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% 98.40/12.98 (symdiffE) =>
% 98.40/12.98 ((
% 98.40/12.98 (symdiffI1) =>
% 98.40/12.98 ((
% 98.40/12.98 (symdiffI2) =>
% 98.40/12.98 ((
% 98.40/12.98 (symdiffIneg1) =>
% 98.40/12.98 ((
% 98.40/12.98 (symdiffIneg2) =>
% 98.40/12.98 ((
% 98.40/12.98 (secondinupair) =>
% 98.40/12.98 ((
% 98.40/12.98 (setukpairIL) =>
% 98.40/12.98 ((
% 98.40/12.98 (setukpairIR) =>
% 98.40/12.98 ((
% 98.40/12.98 (kpairiskpair) =>
% 98.40/12.98 ((
% 98.40/12.98 (kpairp) =>
% 98.40/12.98 ((
% 98.40/12.98 (singletonsubset) =>
% 98.40/12.98 ((
% 98.40/12.98 (singletoninpowerset) =>
% 98.40/12.98 ((
% 98.40/12.98 (singletoninpowunion) =>
% 98.40/12.98 ((
% 98.40/12.98 (upairset2E) =>
% 98.40/12.98 ((
% 98.40/12.98 (upairsubunion) =>
% 98.40/12.98 ((
% 98.40/12.98 (upairinpowunion) =>
% 98.40/12.98 ((
% 98.40/12.98 (ubforcartprodlem1) =>
% 98.40/12.98 ((
% 98.40/12.98 (ubforcartprodlem2) =>
% 98.40/12.98 ((
% 98.40/12.98 (ubforcartprodlem3) =>
% 98.40/12.98 ((
% 98.40/12.98 (cartprodpairin) =>
% 98.40/12.98 ((
% 98.40/12.98 (cartprodmempair1) =>
% 98.40/12.98 ((
% 98.40/12.98 (cartprodmempair) =>
% 98.40/12.98 ((
% 98.40/12.98 (setunionE2) =>
% 98.40/12.98 ((
% 98.40/12.98 (setunionsingleton1) =>
% 98.40/12.98 ((
% 98.40/12.98 (setunionsingleton2) =>
% 98.40/12.98 ((
% 98.40/12.98 (setunionsingleton) =>
% 98.40/12.98 ((
% 98.40/12.98 (singletonprop) =>
% 98.40/12.98 ((
% 98.40/12.98 (ex1E1) =>
% 98.40/12.98 ((
% 98.40/12.98 (ex1I) =>
% 98.40/12.98 ((
% 98.40/12.98 (ex1I2) =>
% 98.40/12.98 ((
% 98.40/12.98 (singletonsuniq) =>
% 98.40/12.98 ((
% 98.40/12.98 (setukpairinjL1) =>
% 98.40/12.98 ((
% 98.40/12.98 (kfstsingleton) =>
% 98.40/12.98 ((
% 98.40/12.98 (theprop) =>
% 98.40/12.98 ((
% 98.40/12.98 (kfstpairEq) =>
% 98.40/12.98 ((
% 98.40/12.98 (cartprodfstin) =>
% 98.40/12.98 ((
% 98.40/12.98 (setukpairinjL2) =>
% 98.40/12.98 ((
% 98.40/12.98 (setukpairinjL) =>
% 98.40/12.98 ((
% 98.40/12.98 (setukpairinjR11) =>
% 98.40/12.98 ((
% 98.40/12.98 (setukpairinjR12) =>
% 98.40/12.98 ((
% 98.40/12.98 (setukpairinjR1) =>
% 98.40/12.98 ((
% 98.40/12.98 (upairequniteq) =>
% 98.40/12.98 ((
% 98.40/12.98 (setukpairinjR2) =>
% 98.40/12.98 ((
% 98.40/12.98 (setukpairinjR) =>
% 98.40/12.98 ((
% 98.40/12.98 (ksndsingleton) =>
% 98.40/12.98 ((
% 98.40/12.98 (ksndpairEq) =>
% 98.40/12.98 ((
% 98.40/12.98 (kpairsurjEq) =>
% 98.40/12.98 ((
% 98.40/12.98 (cartprodsndin) =>
% 98.40/12.98 ((
% 98.40/12.98 (cartprodpairmemEL) =>
% 98.40/12.98 ((
% 98.40/12.98 (cartprodpairmemER) =>
% 98.40/12.98 ((
% 98.40/12.98 (cartprodmempaircEq) =>
% 98.40/12.98 ((
% 98.40/12.98 (cartprodfstpairEq) =>
% 98.40/12.98 ((
% 98.40/12.98 (cartprodsndpairEq) =>
% 98.40/12.98 ((
% 98.40/12.98 (cartprodpairsurjEq) =>
% 98.40/12.98 ((
% 98.40/12.98 (dpsetconstrI) =>
% 98.40/12.98 ((
% 98.40/12.98 (dpsetconstrSub) =>
% 98.40/12.98 ((
% 98.40/12.98 (setOfPairsIsBReln) =>
% 98.40/12.98 ((
% 98.40/12.98 (dpsetconstrERa) =>
% 98.40/12.98 ((
% 98.40/12.98 (dpsetconstrEL1) =>
% 98.40/12.98 ((
% 98.40/12.98 (dpsetconstrEL2) =>
% 98.40/12.98 ((
% 98.40/12.98 (dpsetconstrER) =>
% 98.40/12.98 ((
% 98.40/12.98 (funcImageSingleton) =>
% 98.40/12.98 ((
% 98.40/12.98 (apProp) =>
% 98.40/12.98 ((
% 98.40/12.98 (app) =>
% 98.40/12.98 ((
% 98.40/12.98 (infuncsetfunc) =>
% 98.40/12.98 ((
% 98.40/12.98 (ap2p) =>
% 98.40/12.98 ((
% 98.40/12.98 (funcinfuncset) =>
% 98.40/12.98 ((
% 98.40/12.98 (lamProp) =>
% 98.40/12.98 ((
% 98.40/12.98 (lamp) =>
% 98.40/12.98 ((
% 98.40/12.98 (lam2p) =>
% 98.40/12.98 ((
% 98.40/12.98 (brelnall1) =>
% 98.40/12.98 ((
% 98.40/12.98 (brelnall2) =>
% 98.40/12.98 ((
% 98.40/12.98 (ex1E2) =>
% 98.40/12.98 ((
% 98.40/12.98 (funcGraphProp1) =>
% 98.40/12.98 ((
% 98.40/12.98 (funcGraphProp3) =>
% 98.40/12.98 ((
% 98.40/12.98 (funcGraphProp2) =>
% 98.40/12.98 ((
% 98.40/12.98 (funcextLem) =>
% 98.40/12.98 ((
% 98.40/12.98 (funcGraphProp4) =>
% 98.40/12.98 ((
% 98.40/12.98 (subbreln) =>
% 98.40/12.98 ((
% 98.40/12.98 (eqbreln) =>
% 98.40/12.98 ((
% 98.40/12.98 (funcext) =>
% 98.40/12.98 ((
% 98.40/12.98 (funcext2) =>
% 98.40/12.98 ((
% 98.40/12.98 (ap2apEq1) =>
% 98.40/12.98 ((
% 98.40/12.98 (ap2apEq2) =>
% 98.40/12.98 ((
% 98.40/12.98 (beta1) =>
% 98.40/12.98 ((
% 98.40/12.98 (eta1) =>
% 98.40/12.98 ((
% 98.40/12.98 (lam2lamEq) =>
% 98.40/12.98 ((
% 98.40/12.98 (beta2) =>
% 98.40/12.98 ((
% 98.40/12.98 (eta2) =>
% 98.40/12.98 ((
% 98.40/12.98 (iffalseProp1) =>
% 98.40/12.98 ((
% 98.40/12.98 (iffalseProp2) =>
% 98.40/12.98 ((
% 98.40/12.98 (iftrueProp1) =>
% 98.40/12.98 ((
% 98.40/12.98 (iftrueProp2) =>
% 98.40/12.98 ((
% 98.40/12.98 (ifSingleton) =>
% 98.40/12.98 ((
% 98.40/12.98 (ifp) =>
% 98.40/12.98 ((
% 98.40/12.98 (theeq) =>
% 98.40/12.98 ((
% 98.40/12.98 (iftrue) =>
% 98.40/12.98 ((
% 98.40/12.98 (iffalse) =>
% 98.40/12.98 ((
% 98.40/12.98 (iftrueorfalse) =>
% 98.40/12.98 ((
% 98.40/12.98 (binintersectT_lem) =>
% 98.40/12.98 ((
% 98.40/12.98 (binunionT_lem) =>
% 98.40/12.98 ((
% 98.40/12.98 (powersetT_lem) =>
% 98.40/12.98 ((
% 98.40/12.98 (setminusT_lem) =>
% 98.40/12.98 ((
% 98.40/12.98 (complementT_lem) =>
% 98.40/12.98 ((
% 98.40/12.98 (setextT) =>
% 98.40/12.98 ((
% 98.40/12.98 (subsetTI) =>
% 98.40/12.98 ((
% 98.40/12.98 (powersetTI1) =>
% 98.40/12.98 ((
% 98.40/12.98 (powersetTE1) =>
% 98.40/12.98 ((
% 98.40/12.98 (complementTI1) =>
% 98.40/12.98 ((
% 98.40/12.98 (complementTE1) =>
% 98.40/12.98 ((
% 98.40/12.98 (binintersectTELcontra) =>
% 98.40/12.98 ((
% 98.40/12.98 (binintersectTERcontra) =>
% 98.40/12.98 ((
% 98.40/12.98 (contrasubsetT) =>
% 98.40/12.98 ((
% 98.40/12.98 (contrasubsetT1) =>
% 98.40/12.98 ((
% 98.40/12.98 (contrasubsetT2) =>
% 98.40/12.98 ((
% 98.40/12.98 (contrasubsetT3) =>
% 98.40/12.98 ((
% 98.40/12.98 (doubleComplementI1) =>
% 98.40/12.98 ((
% 98.40/12.98 (doubleComplementE1) =>
% 98.40/12.98 ((
% 98.40/12.98 (doubleComplementSub1) =>
% 98.40/12.98 ((
% 98.40/12.98 (doubleComplementSub2) =>
% 98.40/12.98 ((
% 98.40/12.98 (doubleComplementEq) =>
% 98.40/12.98 ((
% 98.40/12.98 (complementTnotintersectT) =>
% 98.40/12.98 ((
% 98.40/12.98 (complementImpComplementIntersect) =>
% 98.40/12.98 ((
% 98.40/12.98 (complementSubsetComplementIntersect) =>
% 98.40/12.98 ((
% 98.40/12.98 (complementInPowersetComplementIntersect) =>
% 98.40/12.98 ((
% 98.40/12.98 (contraSubsetComplement) =>
% 98.40/12.98 ((
% 98.40/12.98 (complementTcontraSubset) =>
% 98.40/12.98 ((
% 98.40/12.98 (binunionTILcontra) =>
% 98.40/12.98 ((
% 98.40/12.98 (binunionTIRcontra) =>
% 98.40/12.98 ((
% 98.40/12.98 (inIntersectImpInUnion) =>
% 98.40/12.98 ((
% 98.40/12.98 (inIntersectImpInUnion2) =>
% 98.40/12.98 ((
% 98.40/12.98 (inIntersectImpInIntersectUnions) =>
% 98.40/12.98 ((
% 98.40/12.98 (intersectInPowersetIntersectUnions) =>
% 98.40/12.98 ((
% 98.40/12.98 (inComplementUnionImpNotIn1) =>
% 98.40/12.98 ((
% 98.40/12.98 (inComplementUnionImpInComplement1) =>
% 98.40/12.98 ((
% 98.40/12.98 (binunionTE) =>
% 98.40/12.98 ((
% 98.40/12.98 (binunionTEcontra) =>
% 98.40/12.98 ((
% 98.40/12.98 (demorgan2a1) =>
% 98.40/12.98 ((
% 98.40/12.98 (complementUnionInPowersetComplement) =>
% 98.40/12.98 ((
% 98.40/12.98 (demorgan2a2) =>
% 98.40/12.98 ((
% 98.40/12.98 (demorgan1a) =>
% 98.40/12.98 ((
% 98.40/12.98 (demorgan1b) =>
% 98.40/12.98 ((
% 98.40/12.98 (demorgan1) =>
% 98.40/12.98 ((
% 98.40/12.98 (demorgan2a) =>
% 98.40/12.98 ((
% 98.40/12.98 (demorgan2b2) =>
% 98.40/12.98 ((
% 98.40/12.98 (demorgan2b) =>
% 98.40/12.98 ((
% 98.40/12.98 (demorgan2) =>
% 98.40/12.98 ((
% 98.40/12.98 (woz13rule0) =>
% 98.40/12.98 ((
% 98.40/12.98 (woz13rule1) =>
% 98.40/12.98 ((
% 98.40/12.98 (woz13rule2) =>
% 98.40/12.98 ((
% 98.40/12.98 (woz13rule3) =>
% 98.40/12.98 ((
% 98.40/12.98 (woz13rule4) =>
% 98.40/12.98 ((
% 98.40/12.98 (woz1_1) =>
% 98.40/12.98 ((
% 98.40/12.98 (woz1_2) =>
% 98.40/12.98 ((
% 98.40/12.98 (woz1_3) =>
% 98.40/12.98 ((
% 98.40/12.98 (woz1_4) =>
% 98.40/12.98 ((
% 98.40/12.98 (woz1_5) =>
% 98.40/12.98 ((
% 98.40/12.98 (breln1all2) =>
% 98.40/12.98 ((
% 98.40/12.98 (breln1SetBreln1) =>
% 98.40/12.98 ((
% 98.40/12.98 (choice2fnsingleton) =>
% 98.40/12.98 ((
% 98.40/12.98 (!!) @ (
% 98.40/12.98 (('#B') @ (
% 98.40/12.98 !!) @
% 98.40/12.98 (
% 98.40/12.98 (
% 98.40/12.98 ('#S') @ (
% 98.40/12.98 (
% 98.40/12.98 ('#B') @ (
% 98.40/12.98 '#B') @
% 98.40/12.98 breln1)) @
% 98.40/12.98 (
% 98.40/12.98 (
% 98.40/12.98 ('#S') @ dpsetconstr @
% 98.40/12.98 (
% 98.40/12.98 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.40/12.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1015])).
% 98.40/12.98 thf(zip_derived_cl1039, plain,
% 98.40/12.98 (~ (((powersetI1) =>
% 98.40/12.98 (((powersetE1) =>
% 98.40/12.98 (((inPowerset) =>
% 98.40/12.98 (((powersetsubset) =>
% 98.40/12.98 (((sepInPowerset) =>
% 98.40/12.98 (((sepSubset) =>
% 98.40/12.98 (((binunionIL) =>
% 98.40/12.98 (((upairset2IR) =>
% 98.40/12.98 (((binunionIR) =>
% 98.40/12.98 (((binunionEcases) =>
% 98.40/12.98 (((binunionE) =>
% 98.40/12.98 (((binunionLsub) =>
% 98.40/12.98 (((binunionRsub) =>
% 98.40/12.98 (((binintersectI) =>
% 98.40/12.98 (((binintersectSubset5) =>
% 98.40/12.98 (((binintersectEL) =>
% 98.40/12.98 (((binintersectLsub) =>
% 98.40/12.98 (((binintersectSubset2) =>
% 98.40/12.98 (((binintersectSubset3) =>
% 98.40/12.98 (((binintersectER) =>
% 98.40/12.98 (((disjointsetsI1) =>
% 98.40/12.98 (((binintersectRsub) =>
% 98.40/12.98 (((binintersectSubset4) =>
% 98.40/12.98 (((binintersectSubset1) =>
% 98.40/12.98 (((bs114d) =>
% 98.40/12.98 (((setminusI) =>
% 98.40/12.98 (((setminusEL) =>
% 98.40/12.98 (((setminusER) =>
% 98.40/12.98 (((setminusSubset2) =>
% 98.40/12.98 (((setminusERneg) =>
% 98.40/12.98 ((
% 98.40/12.98 (setminusELneg) =>
% 98.40/12.98 ((
% 98.40/12.98 (setminusILneg) =>
% 98.40/12.98 ((
% 98.40/12.98 (setminusIRneg) =>
% 98.40/12.98 ((
% 98.40/12.98 (setminusLsub) =>
% 98.40/12.98 ((
% 98.40/12.98 (setminusSubset1) =>
% 98.40/12.98 ((
% 98.40/12.98 (symdiffE) =>
% 98.40/12.98 ((
% 98.40/12.98 (symdiffI1) =>
% 98.40/12.98 ((
% 98.40/12.98 (symdiffI2) =>
% 98.40/12.98 ((
% 98.40/12.98 (symdiffIneg1) =>
% 98.40/12.98 ((
% 98.40/12.98 (symdiffIneg2) =>
% 98.40/12.98 ((
% 98.40/12.98 (secondinupair) =>
% 98.40/12.98 ((
% 98.40/12.98 (setukpairIL) =>
% 98.40/12.98 ((
% 98.40/12.98 (setukpairIR) =>
% 98.40/12.98 ((
% 98.40/12.98 (kpairiskpair) =>
% 98.40/12.98 ((
% 98.40/12.98 (kpairp) =>
% 98.40/12.98 ((
% 98.40/12.98 (singletonsubset) =>
% 98.40/12.98 ((
% 98.40/12.98 (singletoninpowerset) =>
% 98.40/12.98 ((
% 98.40/12.98 (singletoninpowunion) =>
% 98.40/12.98 ((
% 98.40/12.98 (upairset2E) =>
% 98.40/12.98 ((
% 98.40/12.98 (upairsubunion) =>
% 98.40/12.98 ((
% 98.40/12.98 (upairinpowunion) =>
% 98.40/12.98 ((
% 98.40/12.98 (ubforcartprodlem1) =>
% 98.40/12.98 ((
% 98.40/12.98 (ubforcartprodlem2) =>
% 98.40/12.98 ((
% 98.40/12.98 (ubforcartprodlem3) =>
% 98.40/12.98 ((
% 98.40/12.98 (cartprodpairin) =>
% 98.40/12.98 ((
% 98.40/12.98 (cartprodmempair1) =>
% 98.40/12.98 ((
% 98.40/12.98 (cartprodmempair) =>
% 98.40/12.98 ((
% 98.40/12.98 (setunionE2) =>
% 98.40/12.98 ((
% 98.40/12.98 (setunionsingleton1) =>
% 98.40/12.98 ((
% 98.40/12.98 (setunionsingleton2) =>
% 98.40/12.98 ((
% 98.40/12.98 (setunionsingleton) =>
% 98.40/12.98 ((
% 98.40/12.98 (singletonprop) =>
% 98.40/12.98 ((
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% 98.40/12.98 ((
% 98.40/12.98 (ex1I) =>
% 98.40/12.98 ((
% 98.40/12.98 (ex1I2) =>
% 98.40/12.98 ((
% 98.40/12.98 (singletonsuniq) =>
% 98.40/12.98 ((
% 98.40/12.98 (setukpairinjL1) =>
% 98.40/12.98 ((
% 98.40/12.98 (kfstsingleton) =>
% 98.40/12.98 ((
% 98.40/12.98 (theprop) =>
% 98.40/12.98 ((
% 98.40/12.98 (kfstpairEq) =>
% 98.40/12.98 ((
% 98.40/12.98 (cartprodfstin) =>
% 98.40/12.98 ((
% 98.40/12.98 (setukpairinjL2) =>
% 98.40/12.98 ((
% 98.40/12.98 (setukpairinjL) =>
% 98.40/12.98 ((
% 98.40/12.98 (setukpairinjR11) =>
% 98.40/12.98 ((
% 98.40/12.98 (setukpairinjR12) =>
% 98.40/12.98 ((
% 98.40/12.98 (setukpairinjR1) =>
% 98.40/12.98 ((
% 98.40/12.98 (upairequniteq) =>
% 98.40/12.98 ((
% 98.40/12.98 (setukpairinjR2) =>
% 98.40/12.98 ((
% 98.40/12.98 (setukpairinjR) =>
% 98.40/12.98 ((
% 98.40/12.98 (ksndsingleton) =>
% 98.40/12.98 ((
% 98.40/12.98 (ksndpairEq) =>
% 98.40/12.98 ((
% 98.40/12.98 (kpairsurjEq) =>
% 98.40/12.98 ((
% 98.40/12.98 (cartprodsndin) =>
% 98.40/12.98 ((
% 98.40/12.98 (cartprodpairmemEL) =>
% 98.40/12.98 ((
% 98.40/12.98 (cartprodpairmemER) =>
% 98.40/12.98 ((
% 98.40/12.98 (cartprodmempaircEq) =>
% 98.40/12.98 ((
% 98.40/12.98 (cartprodfstpairEq) =>
% 98.40/12.98 ((
% 98.40/12.98 (cartprodsndpairEq) =>
% 98.40/12.98 ((
% 98.40/12.98 (cartprodpairsurjEq) =>
% 98.40/12.98 ((
% 98.40/12.98 (dpsetconstrI) =>
% 98.40/12.98 ((
% 98.40/12.98 (dpsetconstrSub) =>
% 98.40/12.98 ((
% 98.40/12.98 (setOfPairsIsBReln) =>
% 98.40/12.98 ((
% 98.40/12.98 (dpsetconstrERa) =>
% 98.40/12.98 ((
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% 98.40/12.98 ((
% 98.40/12.98 (dpsetconstrEL2) =>
% 98.40/12.98 ((
% 98.40/12.98 (dpsetconstrER) =>
% 98.40/12.98 ((
% 98.40/12.98 (funcImageSingleton) =>
% 98.40/12.98 ((
% 98.40/12.98 (apProp) =>
% 98.40/12.98 ((
% 98.40/12.98 (app) =>
% 98.40/12.98 ((
% 98.40/12.98 (infuncsetfunc) =>
% 98.40/12.98 ((
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% 98.40/12.99 (demorgan2a) =>
% 98.40/12.99 ((
% 98.40/12.99 (demorgan2b2) =>
% 98.40/12.99 ((
% 98.40/12.99 (demorgan2b) =>
% 98.40/12.99 ((
% 98.40/12.99 (demorgan2) =>
% 98.40/12.99 ((
% 98.40/12.99 (woz13rule0) =>
% 98.40/12.99 ((
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% 98.40/12.99 ((
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% 98.40/12.99 ((
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% 98.40/12.99 ((
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% 98.40/12.99 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1074])).
% 98.40/12.99 thf(zip_derived_cl1090, plain,
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% 98.40/12.99 ((
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% 98.40/12.99 ((
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% 98.40/12.99 ((
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% 98.40/12.99 ((
% 98.40/12.99 (cartprodsndpairEq) =>
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% 98.40/12.99 ((
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% 98.40/12.99 ((
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% 98.40/12.99 ((
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% 98.40/12.99 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1082])).
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% 98.40/12.99 (kpairsurjEq) =>
% 98.40/12.99 ((
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% 98.40/12.99 ((
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% 98.40/12.99 ((
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% 98.40/12.99 (cartprodmempaircEq) =>
% 98.40/12.99 ((
% 98.40/12.99 (cartprodfstpairEq) =>
% 98.40/12.99 ((
% 98.40/12.99 (cartprodsndpairEq) =>
% 98.40/12.99 ((
% 98.40/12.99 (cartprodpairsurjEq) =>
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% 98.40/12.99 (dpsetconstrSub) =>
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% 98.40/12.99 (dpsetconstrER) =>
% 98.40/12.99 ((
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% 98.40/12.99 ((
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% 98.40/12.99 ((
% 98.40/12.99 (infuncsetfunc) =>
% 98.40/12.99 ((
% 98.40/12.99 (ap2p) =>
% 98.40/12.99 ((
% 98.40/12.99 (funcinfuncset) =>
% 98.40/12.99 ((
% 98.40/12.99 (lamProp) =>
% 98.40/12.99 ((
% 98.40/12.99 (lamp) =>
% 98.40/12.99 ((
% 98.40/12.99 (lam2p) =>
% 98.40/12.99 ((
% 98.40/12.99 (brelnall1) =>
% 98.40/12.99 ((
% 98.40/12.99 (brelnall2) =>
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% 98.40/12.99 (ex1E2) =>
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% 98.40/12.99 ((
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% 98.40/12.99 ((
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% 98.40/12.99 ((
% 98.40/12.99 (lam2lamEq) =>
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% 98.40/12.99 ((
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% 98.40/12.99 ((
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% 98.40/12.99 ((
% 98.40/12.99 (setextT) =>
% 98.40/12.99 ((
% 98.40/12.99 (subsetTI) =>
% 98.40/12.99 ((
% 98.40/12.99 (powersetTI1) =>
% 98.40/12.99 ((
% 98.40/12.99 (powersetTE1) =>
% 98.40/12.99 ((
% 98.40/12.99 (complementTI1) =>
% 98.40/12.99 ((
% 98.40/12.99 (complementTE1) =>
% 98.40/12.99 ((
% 98.40/12.99 (binintersectTELcontra) =>
% 98.40/12.99 ((
% 98.40/12.99 (binintersectTERcontra) =>
% 98.40/12.99 ((
% 98.40/12.99 (contrasubsetT) =>
% 98.40/12.99 ((
% 98.40/12.99 (contrasubsetT1) =>
% 98.40/12.99 ((
% 98.40/12.99 (contrasubsetT2) =>
% 98.40/12.99 ((
% 98.40/12.99 (contrasubsetT3) =>
% 98.40/12.99 ((
% 98.40/12.99 (doubleComplementI1) =>
% 98.40/12.99 ((
% 98.40/12.99 (doubleComplementE1) =>
% 98.40/12.99 ((
% 98.40/12.99 (doubleComplementSub1) =>
% 98.40/12.99 ((
% 98.40/12.99 (doubleComplementSub2) =>
% 98.40/12.99 ((
% 98.40/12.99 (doubleComplementEq) =>
% 98.40/12.99 ((
% 98.40/12.99 (complementTnotintersectT) =>
% 98.40/12.99 ((
% 98.40/12.99 (complementImpComplementIntersect) =>
% 98.40/12.99 ((
% 98.40/12.99 (complementSubsetComplementIntersect) =>
% 98.40/12.99 ((
% 98.40/12.99 (complementInPowersetComplementIntersect) =>
% 98.40/12.99 ((
% 98.40/12.99 (contraSubsetComplement) =>
% 98.40/12.99 ((
% 98.40/12.99 (complementTcontraSubset) =>
% 98.40/12.99 ((
% 98.40/12.99 (binunionTILcontra) =>
% 98.40/12.99 ((
% 98.40/12.99 (binunionTIRcontra) =>
% 98.40/12.99 ((
% 98.40/12.99 (inIntersectImpInUnion) =>
% 98.40/12.99 ((
% 98.40/12.99 (inIntersectImpInUnion2) =>
% 98.40/12.99 ((
% 98.40/12.99 (inIntersectImpInIntersectUnions) =>
% 98.40/12.99 ((
% 98.40/12.99 (intersectInPowersetIntersectUnions) =>
% 98.40/12.99 ((
% 98.40/12.99 (inComplementUnionImpNotIn1) =>
% 98.40/12.99 ((
% 98.40/12.99 (inComplementUnionImpInComplement1) =>
% 98.40/12.99 ((
% 98.40/12.99 (binunionTE) =>
% 98.40/12.99 ((
% 98.40/12.99 (binunionTEcontra) =>
% 98.40/12.99 ((
% 98.40/12.99 (demorgan2a1) =>
% 98.40/12.99 ((
% 98.40/12.99 (complementUnionInPowersetComplement) =>
% 98.40/12.99 ((
% 98.40/12.99 (demorgan2a2) =>
% 98.40/12.99 ((
% 98.40/12.99 (demorgan1a) =>
% 98.40/12.99 ((
% 98.40/12.99 (demorgan1b) =>
% 98.40/12.99 ((
% 98.40/12.99 (demorgan1) =>
% 98.40/12.99 ((
% 98.40/12.99 (demorgan2a) =>
% 98.40/12.99 ((
% 98.40/12.99 (demorgan2b2) =>
% 98.40/12.99 ((
% 98.40/12.99 (demorgan2b) =>
% 98.40/12.99 ((
% 98.40/12.99 (demorgan2) =>
% 98.40/12.99 ((
% 98.40/12.99 (woz13rule0) =>
% 98.40/12.99 ((
% 98.40/12.99 (woz13rule1) =>
% 98.40/12.99 ((
% 98.40/12.99 (woz13rule2) =>
% 98.40/12.99 ((
% 98.40/12.99 (woz13rule3) =>
% 98.40/12.99 ((
% 98.40/12.99 (woz13rule4) =>
% 98.40/12.99 ((
% 98.40/12.99 (woz1_1) =>
% 98.40/12.99 ((
% 98.40/12.99 (woz1_2) =>
% 98.40/12.99 ((
% 98.40/12.99 (woz1_3) =>
% 98.40/12.99 ((
% 98.40/12.99 (woz1_4) =>
% 98.40/12.99 ((
% 98.40/12.99 (woz1_5) =>
% 98.40/12.99 ((
% 98.40/12.99 (breln1all2) =>
% 98.40/12.99 ((
% 98.40/12.99 (breln1SetBreln1) =>
% 98.40/12.99 ((
% 98.40/12.99 (choice2fnsingleton) =>
% 98.40/12.99 ((
% 98.40/12.99 (!!) @ (
% 98.40/12.99 (('#B') @ (
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% 98.40/12.99 (
% 98.40/12.99 (
% 98.40/12.99 ('#S') @ (
% 98.40/12.99 (
% 98.40/12.99 ('#B') @ (
% 98.40/12.99 '#B') @
% 98.40/12.99 breln1)) @
% 98.40/12.99 (
% 98.40/12.99 (
% 98.40/12.99 ('#S') @ dpsetconstr @
% 98.40/12.99 (
% 98.40/12.99 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.40/12.99 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1090])).
% 98.40/12.99 thf(zip_derived_cl1102, plain,
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% 98.40/12.99 (((binunionEcases) =>
% 98.40/12.99 (((binunionE) =>
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% 98.40/12.99 (((binunionRsub) =>
% 98.40/12.99 (((binintersectI) =>
% 98.40/12.99 (((binintersectSubset5) =>
% 98.40/12.99 (((binintersectEL) =>
% 98.40/12.99 (((binintersectLsub) =>
% 98.40/12.99 (((binintersectSubset2) =>
% 98.40/12.99 (((binintersectSubset3) =>
% 98.40/12.99 (((binintersectER) =>
% 98.40/12.99 (((disjointsetsI1) =>
% 98.40/12.99 (((binintersectRsub) =>
% 98.40/12.99 (((binintersectSubset4) =>
% 98.40/12.99 (((binintersectSubset1) =>
% 98.40/12.99 (((bs114d) =>
% 98.40/12.99 (((setminusI) =>
% 98.40/12.99 (((setminusEL) =>
% 98.40/12.99 (((setminusER) =>
% 98.40/12.99 (((setminusSubset2) =>
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% 98.40/12.99 (((setminusELneg) =>
% 98.40/12.99 (((setminusILneg) =>
% 98.40/12.99 (((setminusIRneg) =>
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% 98.40/12.99 (((setminusSubset1) =>
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% 98.40/12.99 ((
% 98.40/12.99 (symdiffI2) =>
% 98.40/12.99 ((
% 98.40/12.99 (symdiffIneg1) =>
% 98.40/12.99 ((
% 98.40/12.99 (symdiffIneg2) =>
% 98.40/12.99 ((
% 98.40/12.99 (secondinupair) =>
% 98.40/12.99 ((
% 98.40/12.99 (setukpairIL) =>
% 98.40/12.99 ((
% 98.40/12.99 (setukpairIR) =>
% 98.40/12.99 ((
% 98.40/12.99 (kpairiskpair) =>
% 98.40/12.99 ((
% 98.40/12.99 (kpairp) =>
% 98.40/12.99 ((
% 98.40/12.99 (singletonsubset) =>
% 98.40/12.99 ((
% 98.40/12.99 (singletoninpowerset) =>
% 98.40/12.99 ((
% 98.40/12.99 (singletoninpowunion) =>
% 98.40/12.99 ((
% 98.40/12.99 (upairset2E) =>
% 98.40/12.99 ((
% 98.40/12.99 (upairsubunion) =>
% 98.40/12.99 ((
% 98.40/12.99 (upairinpowunion) =>
% 98.40/12.99 ((
% 98.40/12.99 (ubforcartprodlem1) =>
% 98.40/12.99 ((
% 98.40/12.99 (ubforcartprodlem2) =>
% 98.40/12.99 ((
% 98.40/12.99 (ubforcartprodlem3) =>
% 98.40/12.99 ((
% 98.40/12.99 (cartprodpairin) =>
% 98.40/12.99 ((
% 98.40/12.99 (cartprodmempair1) =>
% 98.40/12.99 ((
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% 98.40/12.99 ((
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% 98.40/12.99 ((
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% 98.40/12.99 ((
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% 98.40/12.99 ((
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% 98.40/12.99 ((
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% 98.40/12.99 ((
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% 98.40/12.99 ((
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% 98.40/12.99 ((
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% 98.40/12.99 ((
% 98.40/12.99 (cartprodfstin) =>
% 98.40/12.99 ((
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% 98.40/12.99 ((
% 98.40/12.99 (setukpairinjL) =>
% 98.40/12.99 ((
% 98.40/12.99 (setukpairinjR11) =>
% 98.40/12.99 ((
% 98.40/12.99 (setukpairinjR12) =>
% 98.40/12.99 ((
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% 98.40/12.99 ((
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% 98.40/12.99 ((
% 98.40/12.99 (setukpairinjR) =>
% 98.40/12.99 ((
% 98.40/12.99 (ksndsingleton) =>
% 98.40/12.99 ((
% 98.40/12.99 (ksndpairEq) =>
% 98.40/12.99 ((
% 98.40/12.99 (kpairsurjEq) =>
% 98.40/12.99 ((
% 98.40/12.99 (cartprodsndin) =>
% 98.40/12.99 ((
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% 98.40/12.99 ((
% 98.40/12.99 (cartprodpairmemER) =>
% 98.40/12.99 ((
% 98.40/12.99 (cartprodmempaircEq) =>
% 98.40/12.99 ((
% 98.40/12.99 (cartprodfstpairEq) =>
% 98.40/12.99 ((
% 98.40/12.99 (cartprodsndpairEq) =>
% 98.40/12.99 ((
% 98.40/12.99 (cartprodpairsurjEq) =>
% 98.40/12.99 ((
% 98.40/12.99 (dpsetconstrI) =>
% 98.40/12.99 ((
% 98.40/12.99 (dpsetconstrSub) =>
% 98.40/12.99 ((
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% 98.40/12.99 ((
% 98.40/12.99 (brelnall1) =>
% 98.40/12.99 ((
% 98.40/12.99 (brelnall2) =>
% 98.40/12.99 ((
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% 98.40/12.99 ((
% 98.40/12.99 (funcGraphProp1) =>
% 98.40/12.99 ((
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% 98.40/12.99 ((
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% 98.40/12.99 ((
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% 98.40/12.99 (funcext) =>
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% 98.40/12.99 (funcext2) =>
% 98.40/12.99 ((
% 98.40/12.99 (ap2apEq1) =>
% 98.40/12.99 ((
% 98.40/12.99 (ap2apEq2) =>
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% 98.40/12.99 (beta1) =>
% 98.40/12.99 ((
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% 98.40/12.99 ((
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% 98.40/12.99 (beta2) =>
% 98.40/12.99 ((
% 98.40/12.99 (eta2) =>
% 98.40/12.99 ((
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% 98.40/12.99 ((
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% 98.40/12.99 ((
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% 98.40/12.99 ((
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% 98.40/12.99 ((
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% 98.40/12.99 ((
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% 98.40/12.99 ((
% 98.40/12.99 (binintersectTERcontra) =>
% 98.40/12.99 ((
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% 98.40/12.99 ((
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% 98.40/12.99 ((
% 98.40/12.99 (contrasubsetT2) =>
% 98.40/12.99 ((
% 98.40/12.99 (contrasubsetT3) =>
% 98.40/12.99 ((
% 98.40/12.99 (doubleComplementI1) =>
% 98.40/12.99 ((
% 98.40/12.99 (doubleComplementE1) =>
% 98.40/12.99 ((
% 98.40/12.99 (doubleComplementSub1) =>
% 98.40/12.99 ((
% 98.40/12.99 (doubleComplementSub2) =>
% 98.40/12.99 ((
% 98.40/12.99 (doubleComplementEq) =>
% 98.40/12.99 ((
% 98.40/12.99 (complementTnotintersectT) =>
% 98.40/12.99 ((
% 98.40/12.99 (complementImpComplementIntersect) =>
% 98.40/12.99 ((
% 98.40/12.99 (complementSubsetComplementIntersect) =>
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% 98.40/12.99 (complementInPowersetComplementIntersect) =>
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% 98.40/12.99 (contraSubsetComplement) =>
% 98.40/12.99 ((
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% 98.40/12.99 ((
% 98.40/12.99 (binunionTIRcontra) =>
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% 98.40/12.99 (intersectInPowersetIntersectUnions) =>
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% 98.40/12.99 (inComplementUnionImpNotIn1) =>
% 98.40/12.99 ((
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% 98.40/12.99 ((
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% 98.40/12.99 (complementUnionInPowersetComplement) =>
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% 98.40/12.99 (demorgan2a2) =>
% 98.40/12.99 ((
% 98.40/12.99 (demorgan1a) =>
% 98.40/12.99 ((
% 98.40/12.99 (demorgan1b) =>
% 98.40/12.99 ((
% 98.40/12.99 (demorgan1) =>
% 98.40/12.99 ((
% 98.40/12.99 (demorgan2a) =>
% 98.40/12.99 ((
% 98.40/12.99 (demorgan2b2) =>
% 98.40/12.99 ((
% 98.40/12.99 (demorgan2b) =>
% 98.40/12.99 ((
% 98.40/12.99 (demorgan2) =>
% 98.40/12.99 ((
% 98.40/12.99 (woz13rule0) =>
% 98.40/12.99 ((
% 98.40/12.99 (woz13rule1) =>
% 98.40/12.99 ((
% 98.40/12.99 (woz13rule2) =>
% 98.40/12.99 ((
% 98.40/12.99 (woz13rule3) =>
% 98.40/12.99 ((
% 98.40/12.99 (woz13rule4) =>
% 98.40/12.99 ((
% 98.40/12.99 (woz1_1) =>
% 98.40/12.99 ((
% 98.40/12.99 (woz1_2) =>
% 98.40/12.99 ((
% 98.40/12.99 (woz1_3) =>
% 98.40/12.99 ((
% 98.40/12.99 (woz1_4) =>
% 98.40/12.99 ((
% 98.40/12.99 (woz1_5) =>
% 98.40/12.99 ((
% 98.40/12.99 (breln1all2) =>
% 98.40/12.99 ((
% 98.40/12.99 (breln1SetBreln1) =>
% 98.40/12.99 ((
% 98.40/12.99 (choice2fnsingleton) =>
% 98.40/12.99 ((
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% 98.40/12.99 (
% 98.40/12.99 (
% 98.40/12.99 ('#S') @ (
% 98.40/12.99 (
% 98.40/12.99 ('#B') @ (
% 98.40/12.99 '#B') @
% 98.40/12.99 breln1)) @
% 98.40/12.99 (
% 98.40/12.99 (
% 98.40/12.99 ('#S') @ dpsetconstr @
% 98.40/12.99 (
% 98.40/12.99 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.40/12.99 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1096])).
% 98.40/12.99 thf(zip_derived_cl1109, plain,
% 98.40/12.99 (~ (((binunionIR) =>
% 98.40/12.99 (((binunionEcases) =>
% 98.40/12.99 (((binunionE) =>
% 98.40/12.99 (((binunionLsub) =>
% 98.40/12.99 (((binunionRsub) =>
% 98.40/12.99 (((binintersectI) =>
% 98.40/12.99 (((binintersectSubset5) =>
% 98.40/12.99 (((binintersectEL) =>
% 98.40/12.99 (((binintersectLsub) =>
% 98.40/12.99 (((binintersectSubset2) =>
% 98.40/12.99 (((binintersectSubset3) =>
% 98.40/12.99 (((binintersectER) =>
% 98.40/12.99 (((disjointsetsI1) =>
% 98.40/12.99 (((binintersectRsub) =>
% 98.40/12.99 (((binintersectSubset4) =>
% 98.40/12.99 (((binintersectSubset1) =>
% 98.40/12.99 (((bs114d) =>
% 98.40/12.99 (((setminusI) =>
% 98.40/12.99 (((setminusEL) =>
% 98.40/12.99 (((setminusER) =>
% 98.40/12.99 (((setminusSubset2) =>
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% 98.40/12.99 (((setminusELneg) =>
% 98.40/12.99 (((setminusILneg) =>
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% 98.40/12.99 (((setminusLsub) =>
% 98.40/12.99 (((setminusSubset1) =>
% 98.40/12.99 (((symdiffE) =>
% 98.40/12.99 (((symdiffI1) =>
% 98.40/12.99 (((symdiffI2) =>
% 98.40/12.99 ((
% 98.40/12.99 (symdiffIneg1) =>
% 98.40/12.99 ((
% 98.40/12.99 (symdiffIneg2) =>
% 98.40/12.99 ((
% 98.40/12.99 (secondinupair) =>
% 98.40/12.99 ((
% 98.40/12.99 (setukpairIL) =>
% 98.40/12.99 ((
% 98.40/12.99 (setukpairIR) =>
% 98.40/12.99 ((
% 98.40/12.99 (kpairiskpair) =>
% 98.40/12.99 ((
% 98.40/12.99 (kpairp) =>
% 98.40/12.99 ((
% 98.40/12.99 (singletonsubset) =>
% 98.40/12.99 ((
% 98.40/12.99 (singletoninpowerset) =>
% 98.40/12.99 ((
% 98.40/12.99 (singletoninpowunion) =>
% 98.40/12.99 ((
% 98.40/12.99 (upairset2E) =>
% 98.40/12.99 ((
% 98.40/12.99 (upairsubunion) =>
% 98.40/12.99 ((
% 98.40/12.99 (upairinpowunion) =>
% 98.40/12.99 ((
% 98.40/12.99 (ubforcartprodlem1) =>
% 98.40/12.99 ((
% 98.40/12.99 (ubforcartprodlem2) =>
% 98.40/12.99 ((
% 98.40/12.99 (ubforcartprodlem3) =>
% 98.40/12.99 ((
% 98.40/12.99 (cartprodpairin) =>
% 98.40/12.99 ((
% 98.40/12.99 (cartprodmempair1) =>
% 98.40/12.99 ((
% 98.40/12.99 (cartprodmempair) =>
% 98.40/12.99 ((
% 98.40/12.99 (setunionE2) =>
% 98.40/12.99 ((
% 98.40/12.99 (setunionsingleton1) =>
% 98.40/12.99 ((
% 98.40/12.99 (setunionsingleton2) =>
% 98.40/12.99 ((
% 98.40/12.99 (setunionsingleton) =>
% 98.40/12.99 ((
% 98.40/12.99 (singletonprop) =>
% 98.40/12.99 ((
% 98.40/12.99 (ex1E1) =>
% 98.40/12.99 ((
% 98.40/12.99 (ex1I) =>
% 98.40/12.99 ((
% 98.40/12.99 (ex1I2) =>
% 98.40/12.99 ((
% 98.40/12.99 (singletonsuniq) =>
% 98.40/12.99 ((
% 98.40/12.99 (setukpairinjL1) =>
% 98.40/12.99 ((
% 98.40/12.99 (kfstsingleton) =>
% 98.40/12.99 ((
% 98.40/12.99 (theprop) =>
% 98.40/12.99 ((
% 98.40/12.99 (kfstpairEq) =>
% 98.40/12.99 ((
% 98.40/12.99 (cartprodfstin) =>
% 98.40/12.99 ((
% 98.40/12.99 (setukpairinjL2) =>
% 98.40/12.99 ((
% 98.40/12.99 (setukpairinjL) =>
% 98.40/12.99 ((
% 98.40/12.99 (setukpairinjR11) =>
% 98.40/12.99 ((
% 98.40/12.99 (setukpairinjR12) =>
% 98.40/12.99 ((
% 98.40/12.99 (setukpairinjR1) =>
% 98.40/12.99 ((
% 98.40/12.99 (upairequniteq) =>
% 98.40/12.99 ((
% 98.40/12.99 (setukpairinjR2) =>
% 98.40/12.99 ((
% 98.40/12.99 (setukpairinjR) =>
% 98.40/12.99 ((
% 98.40/12.99 (ksndsingleton) =>
% 98.40/12.99 ((
% 98.40/12.99 (ksndpairEq) =>
% 98.40/12.99 ((
% 98.40/12.99 (kpairsurjEq) =>
% 98.40/12.99 ((
% 98.40/12.99 (cartprodsndin) =>
% 98.40/12.99 ((
% 98.40/12.99 (cartprodpairmemEL) =>
% 98.40/12.99 ((
% 98.40/12.99 (cartprodpairmemER) =>
% 98.40/12.99 ((
% 98.40/12.99 (cartprodmempaircEq) =>
% 98.40/12.99 ((
% 98.40/12.99 (cartprodfstpairEq) =>
% 98.40/12.99 ((
% 98.40/12.99 (cartprodsndpairEq) =>
% 98.40/12.99 ((
% 98.40/12.99 (cartprodpairsurjEq) =>
% 98.40/12.99 ((
% 98.40/12.99 (dpsetconstrI) =>
% 98.40/12.99 ((
% 98.40/12.99 (dpsetconstrSub) =>
% 98.40/12.99 ((
% 98.40/12.99 (setOfPairsIsBReln) =>
% 98.40/12.99 ((
% 98.40/12.99 (dpsetconstrERa) =>
% 98.40/12.99 ((
% 98.40/12.99 (dpsetconstrEL1) =>
% 98.40/12.99 ((
% 98.40/12.99 (dpsetconstrEL2) =>
% 98.40/12.99 ((
% 98.40/12.99 (dpsetconstrER) =>
% 98.40/12.99 ((
% 98.40/12.99 (funcImageSingleton) =>
% 98.40/12.99 ((
% 98.40/12.99 (apProp) =>
% 98.40/12.99 ((
% 98.40/12.99 (app) =>
% 98.40/12.99 ((
% 98.40/12.99 (infuncsetfunc) =>
% 98.40/12.99 ((
% 98.40/12.99 (ap2p) =>
% 98.40/12.99 ((
% 98.40/12.99 (funcinfuncset) =>
% 98.40/12.99 ((
% 98.40/12.99 (lamProp) =>
% 98.40/12.99 ((
% 98.40/12.99 (lamp) =>
% 98.40/12.99 ((
% 98.40/12.99 (lam2p) =>
% 98.40/12.99 ((
% 98.40/12.99 (brelnall1) =>
% 98.40/12.99 ((
% 98.40/12.99 (brelnall2) =>
% 98.40/12.99 ((
% 98.40/12.99 (ex1E2) =>
% 98.40/12.99 ((
% 98.40/12.99 (funcGraphProp1) =>
% 98.40/12.99 ((
% 98.40/12.99 (funcGraphProp3) =>
% 98.40/12.99 ((
% 98.40/12.99 (funcGraphProp2) =>
% 98.40/12.99 ((
% 98.40/12.99 (funcextLem) =>
% 98.40/12.99 ((
% 98.40/12.99 (funcGraphProp4) =>
% 98.40/12.99 ((
% 98.40/12.99 (subbreln) =>
% 98.40/12.99 ((
% 98.40/12.99 (eqbreln) =>
% 98.40/12.99 ((
% 98.40/12.99 (funcext) =>
% 98.40/12.99 ((
% 98.40/12.99 (funcext2) =>
% 98.40/12.99 ((
% 98.40/12.99 (ap2apEq1) =>
% 98.40/12.99 ((
% 98.40/12.99 (ap2apEq2) =>
% 98.40/12.99 ((
% 98.40/12.99 (beta1) =>
% 98.40/12.99 ((
% 98.40/12.99 (eta1) =>
% 98.40/12.99 ((
% 98.40/12.99 (lam2lamEq) =>
% 98.40/12.99 ((
% 98.40/12.99 (beta2) =>
% 98.40/12.99 ((
% 98.40/12.99 (eta2) =>
% 98.40/12.99 ((
% 98.40/12.99 (iffalseProp1) =>
% 98.40/12.99 ((
% 98.40/12.99 (iffalseProp2) =>
% 98.40/12.99 ((
% 98.40/12.99 (iftrueProp1) =>
% 98.40/12.99 ((
% 98.40/12.99 (iftrueProp2) =>
% 98.40/12.99 ((
% 98.40/12.99 (ifSingleton) =>
% 98.40/12.99 ((
% 98.40/12.99 (ifp) =>
% 98.40/12.99 ((
% 98.40/12.99 (theeq) =>
% 98.40/12.99 ((
% 98.40/12.99 (iftrue) =>
% 98.40/12.99 ((
% 98.40/12.99 (iffalse) =>
% 98.40/12.99 ((
% 98.40/12.99 (iftrueorfalse) =>
% 98.40/12.99 ((
% 98.40/12.99 (binintersectT_lem) =>
% 98.40/12.99 ((
% 98.40/12.99 (binunionT_lem) =>
% 98.40/12.99 ((
% 98.40/12.99 (powersetT_lem) =>
% 98.40/12.99 ((
% 98.40/12.99 (setminusT_lem) =>
% 98.40/12.99 ((
% 98.40/12.99 (complementT_lem) =>
% 98.40/12.99 ((
% 98.40/12.99 (setextT) =>
% 98.40/12.99 ((
% 98.40/12.99 (subsetTI) =>
% 98.40/12.99 ((
% 98.40/12.99 (powersetTI1) =>
% 98.40/12.99 ((
% 98.40/12.99 (powersetTE1) =>
% 98.40/12.99 ((
% 98.40/12.99 (complementTI1) =>
% 98.40/12.99 ((
% 98.40/12.99 (complementTE1) =>
% 98.40/12.99 ((
% 98.40/12.99 (binintersectTELcontra) =>
% 98.40/12.99 ((
% 98.40/12.99 (binintersectTERcontra) =>
% 98.40/12.99 ((
% 98.40/12.99 (contrasubsetT) =>
% 98.40/12.99 ((
% 98.40/12.99 (contrasubsetT1) =>
% 98.40/12.99 ((
% 98.40/12.99 (contrasubsetT2) =>
% 98.40/12.99 ((
% 98.40/12.99 (contrasubsetT3) =>
% 98.40/12.99 ((
% 98.40/12.99 (doubleComplementI1) =>
% 98.40/12.99 ((
% 98.40/12.99 (doubleComplementE1) =>
% 98.40/12.99 ((
% 98.40/12.99 (doubleComplementSub1) =>
% 98.40/12.99 ((
% 98.40/12.99 (doubleComplementSub2) =>
% 98.40/12.99 ((
% 98.40/12.99 (doubleComplementEq) =>
% 98.40/12.99 ((
% 98.40/12.99 (complementTnotintersectT) =>
% 98.40/12.99 ((
% 98.40/12.99 (complementImpComplementIntersect) =>
% 98.40/12.99 ((
% 98.40/12.99 (complementSubsetComplementIntersect) =>
% 98.40/12.99 ((
% 98.40/12.99 (complementInPowersetComplementIntersect) =>
% 98.40/12.99 ((
% 98.40/12.99 (contraSubsetComplement) =>
% 98.40/12.99 ((
% 98.40/12.99 (complementTcontraSubset) =>
% 98.40/12.99 ((
% 98.40/12.99 (binunionTILcontra) =>
% 98.40/12.99 ((
% 98.40/12.99 (binunionTIRcontra) =>
% 98.40/12.99 ((
% 98.40/12.99 (inIntersectImpInUnion) =>
% 98.40/12.99 ((
% 98.40/12.99 (inIntersectImpInUnion2) =>
% 98.40/12.99 ((
% 98.40/12.99 (inIntersectImpInIntersectUnions) =>
% 98.40/12.99 ((
% 98.40/12.99 (intersectInPowersetIntersectUnions) =>
% 98.40/12.99 ((
% 98.40/12.99 (inComplementUnionImpNotIn1) =>
% 98.40/12.99 ((
% 98.40/12.99 (inComplementUnionImpInComplement1) =>
% 98.40/12.99 ((
% 98.40/12.99 (binunionTE) =>
% 98.40/12.99 ((
% 98.40/12.99 (binunionTEcontra) =>
% 98.40/12.99 ((
% 98.40/12.99 (demorgan2a1) =>
% 98.40/12.99 ((
% 98.40/12.99 (complementUnionInPowersetComplement) =>
% 98.40/12.99 ((
% 98.40/12.99 (demorgan2a2) =>
% 98.40/12.99 ((
% 98.40/12.99 (demorgan1a) =>
% 98.40/12.99 ((
% 98.40/12.99 (demorgan1b) =>
% 98.40/12.99 ((
% 98.40/12.99 (demorgan1) =>
% 98.40/12.99 ((
% 98.40/12.99 (demorgan2a) =>
% 98.40/12.99 ((
% 98.40/12.99 (demorgan2b2) =>
% 98.40/12.99 ((
% 98.40/12.99 (demorgan2b) =>
% 98.40/12.99 ((
% 98.40/12.99 (demorgan2) =>
% 98.40/12.99 ((
% 98.40/12.99 (woz13rule0) =>
% 98.40/12.99 ((
% 98.40/12.99 (woz13rule1) =>
% 98.40/12.99 ((
% 98.40/12.99 (woz13rule2) =>
% 98.40/12.99 ((
% 98.40/12.99 (woz13rule3) =>
% 98.40/12.99 ((
% 98.40/12.99 (woz13rule4) =>
% 98.40/12.99 ((
% 98.40/12.99 (woz1_1) =>
% 98.40/12.99 ((
% 98.40/12.99 (woz1_2) =>
% 98.40/12.99 ((
% 98.40/12.99 (woz1_3) =>
% 98.40/12.99 ((
% 98.40/12.99 (woz1_4) =>
% 98.40/12.99 ((
% 98.40/12.99 (woz1_5) =>
% 98.40/12.99 ((
% 98.40/12.99 (breln1all2) =>
% 98.40/12.99 ((
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% 98.40/12.99 ((
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% 98.40/12.99 ((
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% 98.40/12.99 (
% 98.40/12.99 (
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% 98.40/12.99 (
% 98.40/12.99 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.40/12.99 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1102])).
% 98.40/12.99 thf(zip_derived_cl1115, plain,
% 98.40/12.99 (~ (((binunionEcases) =>
% 98.40/12.99 (((binunionE) =>
% 98.40/12.99 (((binunionLsub) =>
% 98.40/12.99 (((binunionRsub) =>
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% 98.40/12.99 (((binintersectSubset5) =>
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% 98.40/12.99 (((binintersectSubset2) =>
% 98.40/12.99 (((binintersectSubset3) =>
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% 98.40/12.99 (((binintersectSubset1) =>
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% 98.40/12.99 (((setminusER) =>
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% 98.40/12.99 (symdiffIneg2) =>
% 98.40/12.99 ((
% 98.40/12.99 (secondinupair) =>
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% 98.40/12.99 (setukpairIL) =>
% 98.40/12.99 ((
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% 98.40/12.99 ((
% 98.40/12.99 (kpairp) =>
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% 98.40/12.99 (singletonsubset) =>
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% 98.40/12.99 (singletoninpowunion) =>
% 98.40/12.99 ((
% 98.40/12.99 (upairset2E) =>
% 98.40/12.99 ((
% 98.40/12.99 (upairsubunion) =>
% 98.40/12.99 ((
% 98.40/12.99 (upairinpowunion) =>
% 98.40/12.99 ((
% 98.40/12.99 (ubforcartprodlem1) =>
% 98.40/12.99 ((
% 98.40/12.99 (ubforcartprodlem2) =>
% 98.40/12.99 ((
% 98.40/12.99 (ubforcartprodlem3) =>
% 98.40/12.99 ((
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% 98.40/12.99 (contraSubsetComplement) =>
% 98.40/12.99 ((
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% 98.40/12.99 (complementUnionInPowersetComplement) =>
% 98.40/12.99 ((
% 98.40/12.99 (demorgan2a2) =>
% 98.40/12.99 ((
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% 98.40/12.99 ((
% 98.40/12.99 (demorgan1b) =>
% 98.40/12.99 ((
% 98.40/12.99 (demorgan1) =>
% 98.40/12.99 ((
% 98.40/12.99 (demorgan2a) =>
% 98.40/12.99 ((
% 98.40/12.99 (demorgan2b2) =>
% 98.40/12.99 ((
% 98.40/12.99 (demorgan2b) =>
% 98.40/12.99 ((
% 98.40/12.99 (demorgan2) =>
% 98.40/12.99 ((
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% 98.40/12.99 ((
% 98.40/12.99 (woz13rule1) =>
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% 98.40/12.99 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1109])).
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% 98.40/12.99 (demorgan2b) =>
% 98.40/12.99 ((
% 98.40/12.99 (demorgan2) =>
% 98.40/12.99 ((
% 98.40/12.99 (woz13rule0) =>
% 98.40/12.99 ((
% 98.40/12.99 (woz13rule1) =>
% 98.40/12.99 ((
% 98.40/12.99 (woz13rule2) =>
% 98.40/12.99 ((
% 98.40/12.99 (woz13rule3) =>
% 98.40/12.99 ((
% 98.40/12.99 (woz13rule4) =>
% 98.40/12.99 ((
% 98.40/12.99 (woz1_1) =>
% 98.40/12.99 ((
% 98.40/12.99 (woz1_2) =>
% 98.40/12.99 ((
% 98.40/12.99 (woz1_3) =>
% 98.40/12.99 ((
% 98.40/12.99 (woz1_4) =>
% 98.40/12.99 ((
% 98.40/12.99 (woz1_5) =>
% 98.40/12.99 ((
% 98.40/12.99 (breln1all2) =>
% 98.40/12.99 ((
% 98.40/12.99 (breln1SetBreln1) =>
% 98.40/12.99 ((
% 98.40/12.99 (choice2fnsingleton) =>
% 98.40/12.99 ((
% 98.40/12.99 (!!) @ (
% 98.40/12.99 (('#B') @ (
% 98.40/12.99 !!) @
% 98.40/12.99 (
% 98.40/12.99 (
% 98.40/12.99 ('#S') @ (
% 98.40/12.99 (
% 98.40/12.99 ('#B') @ (
% 98.40/12.99 '#B') @
% 98.40/12.99 breln1)) @
% 98.40/12.99 (
% 98.40/12.99 (
% 98.40/12.99 ('#S') @ dpsetconstr @
% 98.40/13.00 (
% 98.40/13.00 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.40/13.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1115])).
% 98.40/13.00 thf(zip_derived_cl1128, plain,
% 98.40/13.00 (~ (((binunionLsub) =>
% 98.40/13.00 (((binunionRsub) =>
% 98.40/13.00 (((binintersectI) =>
% 98.40/13.00 (((binintersectSubset5) =>
% 98.40/13.00 (((binintersectEL) =>
% 98.40/13.00 (((binintersectLsub) =>
% 98.40/13.00 (((binintersectSubset2) =>
% 98.40/13.00 (((binintersectSubset3) =>
% 98.40/13.00 (((binintersectER) =>
% 98.40/13.00 (((disjointsetsI1) =>
% 98.40/13.00 (((binintersectRsub) =>
% 98.40/13.00 (((binintersectSubset4) =>
% 98.40/13.00 (((binintersectSubset1) =>
% 98.40/13.00 (((bs114d) =>
% 98.40/13.00 (((setminusI) =>
% 98.40/13.00 (((setminusEL) =>
% 98.40/13.00 (((setminusER) =>
% 98.40/13.00 (((setminusSubset2) =>
% 98.40/13.00 (((setminusERneg) =>
% 98.40/13.00 (((setminusELneg) =>
% 98.40/13.00 (((setminusILneg) =>
% 98.40/13.00 (((setminusIRneg) =>
% 98.40/13.00 (((setminusLsub) =>
% 98.40/13.00 (((setminusSubset1) =>
% 98.40/13.00 (((symdiffE) =>
% 98.40/13.00 (((symdiffI1) =>
% 98.40/13.00 (((symdiffI2) =>
% 98.40/13.00 (((symdiffIneg1) =>
% 98.40/13.00 (((symdiffIneg2) =>
% 98.40/13.00 (((secondinupair) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairIL) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairIR) =>
% 98.40/13.00 ((
% 98.40/13.00 (kpairiskpair) =>
% 98.40/13.00 ((
% 98.40/13.00 (kpairp) =>
% 98.40/13.00 ((
% 98.40/13.00 (singletonsubset) =>
% 98.40/13.00 ((
% 98.40/13.00 (singletoninpowerset) =>
% 98.40/13.00 ((
% 98.40/13.00 (singletoninpowunion) =>
% 98.40/13.00 ((
% 98.40/13.00 (upairset2E) =>
% 98.40/13.00 ((
% 98.40/13.00 (upairsubunion) =>
% 98.40/13.00 ((
% 98.40/13.00 (upairinpowunion) =>
% 98.40/13.00 ((
% 98.40/13.00 (ubforcartprodlem1) =>
% 98.40/13.00 ((
% 98.40/13.00 (ubforcartprodlem2) =>
% 98.40/13.00 ((
% 98.40/13.00 (ubforcartprodlem3) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodpairin) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodmempair1) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodmempair) =>
% 98.40/13.00 ((
% 98.40/13.00 (setunionE2) =>
% 98.40/13.00 ((
% 98.40/13.00 (setunionsingleton1) =>
% 98.40/13.00 ((
% 98.40/13.00 (setunionsingleton2) =>
% 98.40/13.00 ((
% 98.40/13.00 (setunionsingleton) =>
% 98.40/13.00 ((
% 98.40/13.00 (singletonprop) =>
% 98.40/13.00 ((
% 98.40/13.00 (ex1E1) =>
% 98.40/13.00 ((
% 98.40/13.00 (ex1I) =>
% 98.40/13.00 ((
% 98.40/13.00 (ex1I2) =>
% 98.40/13.00 ((
% 98.40/13.00 (singletonsuniq) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjL1) =>
% 98.40/13.00 ((
% 98.40/13.00 (kfstsingleton) =>
% 98.40/13.00 ((
% 98.40/13.00 (theprop) =>
% 98.40/13.00 ((
% 98.40/13.00 (kfstpairEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodfstin) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjL2) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjL) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjR11) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjR12) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjR1) =>
% 98.40/13.00 ((
% 98.40/13.00 (upairequniteq) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjR2) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjR) =>
% 98.40/13.00 ((
% 98.40/13.00 (ksndsingleton) =>
% 98.40/13.00 ((
% 98.40/13.00 (ksndpairEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (kpairsurjEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodsndin) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodpairmemEL) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodpairmemER) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodmempaircEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodfstpairEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodsndpairEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodpairsurjEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (dpsetconstrI) =>
% 98.40/13.00 ((
% 98.40/13.00 (dpsetconstrSub) =>
% 98.40/13.00 ((
% 98.40/13.00 (setOfPairsIsBReln) =>
% 98.40/13.00 ((
% 98.40/13.00 (dpsetconstrERa) =>
% 98.40/13.00 ((
% 98.40/13.00 (dpsetconstrEL1) =>
% 98.40/13.00 ((
% 98.40/13.00 (dpsetconstrEL2) =>
% 98.40/13.00 ((
% 98.40/13.00 (dpsetconstrER) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcImageSingleton) =>
% 98.40/13.00 ((
% 98.40/13.00 (apProp) =>
% 98.40/13.00 ((
% 98.40/13.00 (app) =>
% 98.40/13.00 ((
% 98.40/13.00 (infuncsetfunc) =>
% 98.40/13.00 ((
% 98.40/13.00 (ap2p) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcinfuncset) =>
% 98.40/13.00 ((
% 98.40/13.00 (lamProp) =>
% 98.40/13.00 ((
% 98.40/13.00 (lamp) =>
% 98.40/13.00 ((
% 98.40/13.00 (lam2p) =>
% 98.40/13.00 ((
% 98.40/13.00 (brelnall1) =>
% 98.40/13.00 ((
% 98.40/13.00 (brelnall2) =>
% 98.40/13.00 ((
% 98.40/13.00 (ex1E2) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcGraphProp1) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcGraphProp3) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcGraphProp2) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcextLem) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcGraphProp4) =>
% 98.40/13.00 ((
% 98.40/13.00 (subbreln) =>
% 98.40/13.00 ((
% 98.40/13.00 (eqbreln) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcext) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcext2) =>
% 98.40/13.00 ((
% 98.40/13.00 (ap2apEq1) =>
% 98.40/13.00 ((
% 98.40/13.00 (ap2apEq2) =>
% 98.40/13.00 ((
% 98.40/13.00 (beta1) =>
% 98.40/13.00 ((
% 98.40/13.00 (eta1) =>
% 98.40/13.00 ((
% 98.40/13.00 (lam2lamEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (beta2) =>
% 98.40/13.00 ((
% 98.40/13.00 (eta2) =>
% 98.40/13.00 ((
% 98.40/13.00 (iffalseProp1) =>
% 98.40/13.00 ((
% 98.40/13.00 (iffalseProp2) =>
% 98.40/13.00 ((
% 98.40/13.00 (iftrueProp1) =>
% 98.40/13.00 ((
% 98.40/13.00 (iftrueProp2) =>
% 98.40/13.00 ((
% 98.40/13.00 (ifSingleton) =>
% 98.40/13.00 ((
% 98.40/13.00 (ifp) =>
% 98.40/13.00 ((
% 98.40/13.00 (theeq) =>
% 98.40/13.00 ((
% 98.40/13.00 (iftrue) =>
% 98.40/13.00 ((
% 98.40/13.00 (iffalse) =>
% 98.40/13.00 ((
% 98.40/13.00 (iftrueorfalse) =>
% 98.40/13.00 ((
% 98.40/13.00 (binintersectT_lem) =>
% 98.40/13.00 ((
% 98.40/13.00 (binunionT_lem) =>
% 98.40/13.00 ((
% 98.40/13.00 (powersetT_lem) =>
% 98.40/13.00 ((
% 98.40/13.00 (setminusT_lem) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementT_lem) =>
% 98.40/13.00 ((
% 98.40/13.00 (setextT) =>
% 98.40/13.00 ((
% 98.40/13.00 (subsetTI) =>
% 98.40/13.00 ((
% 98.40/13.00 (powersetTI1) =>
% 98.40/13.00 ((
% 98.40/13.00 (powersetTE1) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementTI1) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementTE1) =>
% 98.40/13.00 ((
% 98.40/13.00 (binintersectTELcontra) =>
% 98.40/13.00 ((
% 98.40/13.00 (binintersectTERcontra) =>
% 98.40/13.00 ((
% 98.40/13.00 (contrasubsetT) =>
% 98.40/13.00 ((
% 98.40/13.00 (contrasubsetT1) =>
% 98.40/13.00 ((
% 98.40/13.00 (contrasubsetT2) =>
% 98.40/13.00 ((
% 98.40/13.00 (contrasubsetT3) =>
% 98.40/13.00 ((
% 98.40/13.00 (doubleComplementI1) =>
% 98.40/13.00 ((
% 98.40/13.00 (doubleComplementE1) =>
% 98.40/13.00 ((
% 98.40/13.00 (doubleComplementSub1) =>
% 98.40/13.00 ((
% 98.40/13.00 (doubleComplementSub2) =>
% 98.40/13.00 ((
% 98.40/13.00 (doubleComplementEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementTnotintersectT) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementImpComplementIntersect) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementSubsetComplementIntersect) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementInPowersetComplementIntersect) =>
% 98.40/13.00 ((
% 98.40/13.00 (contraSubsetComplement) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementTcontraSubset) =>
% 98.40/13.00 ((
% 98.40/13.00 (binunionTILcontra) =>
% 98.40/13.00 ((
% 98.40/13.00 (binunionTIRcontra) =>
% 98.40/13.00 ((
% 98.40/13.00 (inIntersectImpInUnion) =>
% 98.40/13.00 ((
% 98.40/13.00 (inIntersectImpInUnion2) =>
% 98.40/13.00 ((
% 98.40/13.00 (inIntersectImpInIntersectUnions) =>
% 98.40/13.00 ((
% 98.40/13.00 (intersectInPowersetIntersectUnions) =>
% 98.40/13.00 ((
% 98.40/13.00 (inComplementUnionImpNotIn1) =>
% 98.40/13.00 ((
% 98.40/13.00 (inComplementUnionImpInComplement1) =>
% 98.40/13.00 ((
% 98.40/13.00 (binunionTE) =>
% 98.40/13.00 ((
% 98.40/13.00 (binunionTEcontra) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan2a1) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementUnionInPowersetComplement) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan2a2) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan1a) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan1b) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan1) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan2a) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan2b2) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan2b) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan2) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz13rule0) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz13rule1) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz13rule2) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz13rule3) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz13rule4) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz1_1) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz1_2) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz1_3) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz1_4) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz1_5) =>
% 98.40/13.00 ((
% 98.40/13.00 (breln1all2) =>
% 98.40/13.00 ((
% 98.40/13.00 (breln1SetBreln1) =>
% 98.40/13.00 ((
% 98.40/13.00 (choice2fnsingleton) =>
% 98.40/13.00 ((
% 98.40/13.00 (!!) @ (
% 98.40/13.00 (('#B') @ (
% 98.40/13.00 !!) @
% 98.40/13.00 (
% 98.40/13.00 (
% 98.40/13.00 ('#S') @ (
% 98.40/13.00 (
% 98.40/13.00 ('#B') @ (
% 98.40/13.00 '#B') @
% 98.40/13.00 breln1)) @
% 98.40/13.00 (
% 98.40/13.00 (
% 98.40/13.00 ('#S') @ dpsetconstr @
% 98.40/13.00 (
% 98.40/13.00 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.40/13.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1121])).
% 98.40/13.00 thf(zip_derived_cl1135, plain,
% 98.40/13.00 (~ (((binunionRsub) =>
% 98.40/13.00 (((binintersectI) =>
% 98.40/13.00 (((binintersectSubset5) =>
% 98.40/13.00 (((binintersectEL) =>
% 98.40/13.00 (((binintersectLsub) =>
% 98.40/13.00 (((binintersectSubset2) =>
% 98.40/13.00 (((binintersectSubset3) =>
% 98.40/13.00 (((binintersectER) =>
% 98.40/13.00 (((disjointsetsI1) =>
% 98.40/13.00 (((binintersectRsub) =>
% 98.40/13.00 (((binintersectSubset4) =>
% 98.40/13.00 (((binintersectSubset1) =>
% 98.40/13.00 (((bs114d) =>
% 98.40/13.00 (((setminusI) =>
% 98.40/13.00 (((setminusEL) =>
% 98.40/13.00 (((setminusER) =>
% 98.40/13.00 (((setminusSubset2) =>
% 98.40/13.00 (((setminusERneg) =>
% 98.40/13.00 (((setminusELneg) =>
% 98.40/13.00 (((setminusILneg) =>
% 98.40/13.00 (((setminusIRneg) =>
% 98.40/13.00 (((setminusLsub) =>
% 98.40/13.00 (((setminusSubset1) =>
% 98.40/13.00 (((symdiffE) =>
% 98.40/13.00 (((symdiffI1) =>
% 98.40/13.00 (((symdiffI2) =>
% 98.40/13.00 (((symdiffIneg1) =>
% 98.40/13.00 (((symdiffIneg2) =>
% 98.40/13.00 (((secondinupair) =>
% 98.40/13.00 (((setukpairIL) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairIR) =>
% 98.40/13.00 ((
% 98.40/13.00 (kpairiskpair) =>
% 98.40/13.00 ((
% 98.40/13.00 (kpairp) =>
% 98.40/13.00 ((
% 98.40/13.00 (singletonsubset) =>
% 98.40/13.00 ((
% 98.40/13.00 (singletoninpowerset) =>
% 98.40/13.00 ((
% 98.40/13.00 (singletoninpowunion) =>
% 98.40/13.00 ((
% 98.40/13.00 (upairset2E) =>
% 98.40/13.00 ((
% 98.40/13.00 (upairsubunion) =>
% 98.40/13.00 ((
% 98.40/13.00 (upairinpowunion) =>
% 98.40/13.00 ((
% 98.40/13.00 (ubforcartprodlem1) =>
% 98.40/13.00 ((
% 98.40/13.00 (ubforcartprodlem2) =>
% 98.40/13.00 ((
% 98.40/13.00 (ubforcartprodlem3) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodpairin) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodmempair1) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodmempair) =>
% 98.40/13.00 ((
% 98.40/13.00 (setunionE2) =>
% 98.40/13.00 ((
% 98.40/13.00 (setunionsingleton1) =>
% 98.40/13.00 ((
% 98.40/13.00 (setunionsingleton2) =>
% 98.40/13.00 ((
% 98.40/13.00 (setunionsingleton) =>
% 98.40/13.00 ((
% 98.40/13.00 (singletonprop) =>
% 98.40/13.00 ((
% 98.40/13.00 (ex1E1) =>
% 98.40/13.00 ((
% 98.40/13.00 (ex1I) =>
% 98.40/13.00 ((
% 98.40/13.00 (ex1I2) =>
% 98.40/13.00 ((
% 98.40/13.00 (singletonsuniq) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjL1) =>
% 98.40/13.00 ((
% 98.40/13.00 (kfstsingleton) =>
% 98.40/13.00 ((
% 98.40/13.00 (theprop) =>
% 98.40/13.00 ((
% 98.40/13.00 (kfstpairEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodfstin) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjL2) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjL) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjR11) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjR12) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjR1) =>
% 98.40/13.00 ((
% 98.40/13.00 (upairequniteq) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjR2) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjR) =>
% 98.40/13.00 ((
% 98.40/13.00 (ksndsingleton) =>
% 98.40/13.00 ((
% 98.40/13.00 (ksndpairEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (kpairsurjEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodsndin) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodpairmemEL) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodpairmemER) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodmempaircEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodfstpairEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodsndpairEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodpairsurjEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (dpsetconstrI) =>
% 98.40/13.00 ((
% 98.40/13.00 (dpsetconstrSub) =>
% 98.40/13.00 ((
% 98.40/13.00 (setOfPairsIsBReln) =>
% 98.40/13.00 ((
% 98.40/13.00 (dpsetconstrERa) =>
% 98.40/13.00 ((
% 98.40/13.00 (dpsetconstrEL1) =>
% 98.40/13.00 ((
% 98.40/13.00 (dpsetconstrEL2) =>
% 98.40/13.00 ((
% 98.40/13.00 (dpsetconstrER) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcImageSingleton) =>
% 98.40/13.00 ((
% 98.40/13.00 (apProp) =>
% 98.40/13.00 ((
% 98.40/13.00 (app) =>
% 98.40/13.00 ((
% 98.40/13.00 (infuncsetfunc) =>
% 98.40/13.00 ((
% 98.40/13.00 (ap2p) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcinfuncset) =>
% 98.40/13.00 ((
% 98.40/13.00 (lamProp) =>
% 98.40/13.00 ((
% 98.40/13.00 (lamp) =>
% 98.40/13.00 ((
% 98.40/13.00 (lam2p) =>
% 98.40/13.00 ((
% 98.40/13.00 (brelnall1) =>
% 98.40/13.00 ((
% 98.40/13.00 (brelnall2) =>
% 98.40/13.00 ((
% 98.40/13.00 (ex1E2) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcGraphProp1) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcGraphProp3) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcGraphProp2) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcextLem) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcGraphProp4) =>
% 98.40/13.00 ((
% 98.40/13.00 (subbreln) =>
% 98.40/13.00 ((
% 98.40/13.00 (eqbreln) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcext) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcext2) =>
% 98.40/13.00 ((
% 98.40/13.00 (ap2apEq1) =>
% 98.40/13.00 ((
% 98.40/13.00 (ap2apEq2) =>
% 98.40/13.00 ((
% 98.40/13.00 (beta1) =>
% 98.40/13.00 ((
% 98.40/13.00 (eta1) =>
% 98.40/13.00 ((
% 98.40/13.00 (lam2lamEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (beta2) =>
% 98.40/13.00 ((
% 98.40/13.00 (eta2) =>
% 98.40/13.00 ((
% 98.40/13.00 (iffalseProp1) =>
% 98.40/13.00 ((
% 98.40/13.00 (iffalseProp2) =>
% 98.40/13.00 ((
% 98.40/13.00 (iftrueProp1) =>
% 98.40/13.00 ((
% 98.40/13.00 (iftrueProp2) =>
% 98.40/13.00 ((
% 98.40/13.00 (ifSingleton) =>
% 98.40/13.00 ((
% 98.40/13.00 (ifp) =>
% 98.40/13.00 ((
% 98.40/13.00 (theeq) =>
% 98.40/13.00 ((
% 98.40/13.00 (iftrue) =>
% 98.40/13.00 ((
% 98.40/13.00 (iffalse) =>
% 98.40/13.00 ((
% 98.40/13.00 (iftrueorfalse) =>
% 98.40/13.00 ((
% 98.40/13.00 (binintersectT_lem) =>
% 98.40/13.00 ((
% 98.40/13.00 (binunionT_lem) =>
% 98.40/13.00 ((
% 98.40/13.00 (powersetT_lem) =>
% 98.40/13.00 ((
% 98.40/13.00 (setminusT_lem) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementT_lem) =>
% 98.40/13.00 ((
% 98.40/13.00 (setextT) =>
% 98.40/13.00 ((
% 98.40/13.00 (subsetTI) =>
% 98.40/13.00 ((
% 98.40/13.00 (powersetTI1) =>
% 98.40/13.00 ((
% 98.40/13.00 (powersetTE1) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementTI1) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementTE1) =>
% 98.40/13.00 ((
% 98.40/13.00 (binintersectTELcontra) =>
% 98.40/13.00 ((
% 98.40/13.00 (binintersectTERcontra) =>
% 98.40/13.00 ((
% 98.40/13.00 (contrasubsetT) =>
% 98.40/13.00 ((
% 98.40/13.00 (contrasubsetT1) =>
% 98.40/13.00 ((
% 98.40/13.00 (contrasubsetT2) =>
% 98.40/13.00 ((
% 98.40/13.00 (contrasubsetT3) =>
% 98.40/13.00 ((
% 98.40/13.00 (doubleComplementI1) =>
% 98.40/13.00 ((
% 98.40/13.00 (doubleComplementE1) =>
% 98.40/13.00 ((
% 98.40/13.00 (doubleComplementSub1) =>
% 98.40/13.00 ((
% 98.40/13.00 (doubleComplementSub2) =>
% 98.40/13.00 ((
% 98.40/13.00 (doubleComplementEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementTnotintersectT) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementImpComplementIntersect) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementSubsetComplementIntersect) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementInPowersetComplementIntersect) =>
% 98.40/13.00 ((
% 98.40/13.00 (contraSubsetComplement) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementTcontraSubset) =>
% 98.40/13.00 ((
% 98.40/13.00 (binunionTILcontra) =>
% 98.40/13.00 ((
% 98.40/13.00 (binunionTIRcontra) =>
% 98.40/13.00 ((
% 98.40/13.00 (inIntersectImpInUnion) =>
% 98.40/13.00 ((
% 98.40/13.00 (inIntersectImpInUnion2) =>
% 98.40/13.00 ((
% 98.40/13.00 (inIntersectImpInIntersectUnions) =>
% 98.40/13.00 ((
% 98.40/13.00 (intersectInPowersetIntersectUnions) =>
% 98.40/13.00 ((
% 98.40/13.00 (inComplementUnionImpNotIn1) =>
% 98.40/13.00 ((
% 98.40/13.00 (inComplementUnionImpInComplement1) =>
% 98.40/13.00 ((
% 98.40/13.00 (binunionTE) =>
% 98.40/13.00 ((
% 98.40/13.00 (binunionTEcontra) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan2a1) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementUnionInPowersetComplement) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan2a2) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan1a) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan1b) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan1) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan2a) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan2b2) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan2b) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan2) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz13rule0) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz13rule1) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz13rule2) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz13rule3) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz13rule4) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz1_1) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz1_2) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz1_3) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz1_4) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz1_5) =>
% 98.40/13.00 ((
% 98.40/13.00 (breln1all2) =>
% 98.40/13.00 ((
% 98.40/13.00 (breln1SetBreln1) =>
% 98.40/13.00 ((
% 98.40/13.00 (choice2fnsingleton) =>
% 98.40/13.00 ((
% 98.40/13.00 (!!) @ (
% 98.40/13.00 (('#B') @ (
% 98.40/13.00 !!) @
% 98.40/13.00 (
% 98.40/13.00 (
% 98.40/13.00 ('#S') @ (
% 98.40/13.00 (
% 98.40/13.00 ('#B') @ (
% 98.40/13.00 '#B') @
% 98.40/13.00 breln1)) @
% 98.40/13.00 (
% 98.40/13.00 (
% 98.40/13.00 ('#S') @ dpsetconstr @
% 98.40/13.00 (
% 98.40/13.00 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.40/13.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1128])).
% 98.40/13.00 thf(zip_derived_cl1142, plain,
% 98.40/13.00 (~ (((binintersectI) =>
% 98.40/13.00 (((binintersectSubset5) =>
% 98.40/13.00 (((binintersectEL) =>
% 98.40/13.00 (((binintersectLsub) =>
% 98.40/13.00 (((binintersectSubset2) =>
% 98.40/13.00 (((binintersectSubset3) =>
% 98.40/13.00 (((binintersectER) =>
% 98.40/13.00 (((disjointsetsI1) =>
% 98.40/13.00 (((binintersectRsub) =>
% 98.40/13.00 (((binintersectSubset4) =>
% 98.40/13.00 (((binintersectSubset1) =>
% 98.40/13.00 (((bs114d) =>
% 98.40/13.00 (((setminusI) =>
% 98.40/13.00 (((setminusEL) =>
% 98.40/13.00 (((setminusER) =>
% 98.40/13.00 (((setminusSubset2) =>
% 98.40/13.00 (((setminusERneg) =>
% 98.40/13.00 (((setminusELneg) =>
% 98.40/13.00 (((setminusILneg) =>
% 98.40/13.00 (((setminusIRneg) =>
% 98.40/13.00 (((setminusLsub) =>
% 98.40/13.00 (((setminusSubset1) =>
% 98.40/13.00 (((symdiffE) =>
% 98.40/13.00 (((symdiffI1) =>
% 98.40/13.00 (((symdiffI2) =>
% 98.40/13.00 (((symdiffIneg1) =>
% 98.40/13.00 (((symdiffIneg2) =>
% 98.40/13.00 (((secondinupair) =>
% 98.40/13.00 (((setukpairIL) =>
% 98.40/13.00 (((setukpairIR) =>
% 98.40/13.00 ((
% 98.40/13.00 (kpairiskpair) =>
% 98.40/13.00 ((
% 98.40/13.00 (kpairp) =>
% 98.40/13.00 ((
% 98.40/13.00 (singletonsubset) =>
% 98.40/13.00 ((
% 98.40/13.00 (singletoninpowerset) =>
% 98.40/13.00 ((
% 98.40/13.00 (singletoninpowunion) =>
% 98.40/13.00 ((
% 98.40/13.00 (upairset2E) =>
% 98.40/13.00 ((
% 98.40/13.00 (upairsubunion) =>
% 98.40/13.00 ((
% 98.40/13.00 (upairinpowunion) =>
% 98.40/13.00 ((
% 98.40/13.00 (ubforcartprodlem1) =>
% 98.40/13.00 ((
% 98.40/13.00 (ubforcartprodlem2) =>
% 98.40/13.00 ((
% 98.40/13.00 (ubforcartprodlem3) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodpairin) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodmempair1) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodmempair) =>
% 98.40/13.00 ((
% 98.40/13.00 (setunionE2) =>
% 98.40/13.00 ((
% 98.40/13.00 (setunionsingleton1) =>
% 98.40/13.00 ((
% 98.40/13.00 (setunionsingleton2) =>
% 98.40/13.00 ((
% 98.40/13.00 (setunionsingleton) =>
% 98.40/13.00 ((
% 98.40/13.00 (singletonprop) =>
% 98.40/13.00 ((
% 98.40/13.00 (ex1E1) =>
% 98.40/13.00 ((
% 98.40/13.00 (ex1I) =>
% 98.40/13.00 ((
% 98.40/13.00 (ex1I2) =>
% 98.40/13.00 ((
% 98.40/13.00 (singletonsuniq) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjL1) =>
% 98.40/13.00 ((
% 98.40/13.00 (kfstsingleton) =>
% 98.40/13.00 ((
% 98.40/13.00 (theprop) =>
% 98.40/13.00 ((
% 98.40/13.00 (kfstpairEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodfstin) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjL2) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjL) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjR11) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjR12) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjR1) =>
% 98.40/13.00 ((
% 98.40/13.00 (upairequniteq) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjR2) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjR) =>
% 98.40/13.00 ((
% 98.40/13.00 (ksndsingleton) =>
% 98.40/13.00 ((
% 98.40/13.00 (ksndpairEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (kpairsurjEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodsndin) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodpairmemEL) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodpairmemER) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodmempaircEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodfstpairEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodsndpairEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodpairsurjEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (dpsetconstrI) =>
% 98.40/13.00 ((
% 98.40/13.00 (dpsetconstrSub) =>
% 98.40/13.00 ((
% 98.40/13.00 (setOfPairsIsBReln) =>
% 98.40/13.00 ((
% 98.40/13.00 (dpsetconstrERa) =>
% 98.40/13.00 ((
% 98.40/13.00 (dpsetconstrEL1) =>
% 98.40/13.00 ((
% 98.40/13.00 (dpsetconstrEL2) =>
% 98.40/13.00 ((
% 98.40/13.00 (dpsetconstrER) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcImageSingleton) =>
% 98.40/13.00 ((
% 98.40/13.00 (apProp) =>
% 98.40/13.00 ((
% 98.40/13.00 (app) =>
% 98.40/13.00 ((
% 98.40/13.00 (infuncsetfunc) =>
% 98.40/13.00 ((
% 98.40/13.00 (ap2p) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcinfuncset) =>
% 98.40/13.00 ((
% 98.40/13.00 (lamProp) =>
% 98.40/13.00 ((
% 98.40/13.00 (lamp) =>
% 98.40/13.00 ((
% 98.40/13.00 (lam2p) =>
% 98.40/13.00 ((
% 98.40/13.00 (brelnall1) =>
% 98.40/13.00 ((
% 98.40/13.00 (brelnall2) =>
% 98.40/13.00 ((
% 98.40/13.00 (ex1E2) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcGraphProp1) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcGraphProp3) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcGraphProp2) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcextLem) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcGraphProp4) =>
% 98.40/13.00 ((
% 98.40/13.00 (subbreln) =>
% 98.40/13.00 ((
% 98.40/13.00 (eqbreln) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcext) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcext2) =>
% 98.40/13.00 ((
% 98.40/13.00 (ap2apEq1) =>
% 98.40/13.00 ((
% 98.40/13.00 (ap2apEq2) =>
% 98.40/13.00 ((
% 98.40/13.00 (beta1) =>
% 98.40/13.00 ((
% 98.40/13.00 (eta1) =>
% 98.40/13.00 ((
% 98.40/13.00 (lam2lamEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (beta2) =>
% 98.40/13.00 ((
% 98.40/13.00 (eta2) =>
% 98.40/13.00 ((
% 98.40/13.00 (iffalseProp1) =>
% 98.40/13.00 ((
% 98.40/13.00 (iffalseProp2) =>
% 98.40/13.00 ((
% 98.40/13.00 (iftrueProp1) =>
% 98.40/13.00 ((
% 98.40/13.00 (iftrueProp2) =>
% 98.40/13.00 ((
% 98.40/13.00 (ifSingleton) =>
% 98.40/13.00 ((
% 98.40/13.00 (ifp) =>
% 98.40/13.00 ((
% 98.40/13.00 (theeq) =>
% 98.40/13.00 ((
% 98.40/13.00 (iftrue) =>
% 98.40/13.00 ((
% 98.40/13.00 (iffalse) =>
% 98.40/13.00 ((
% 98.40/13.00 (iftrueorfalse) =>
% 98.40/13.00 ((
% 98.40/13.00 (binintersectT_lem) =>
% 98.40/13.00 ((
% 98.40/13.00 (binunionT_lem) =>
% 98.40/13.00 ((
% 98.40/13.00 (powersetT_lem) =>
% 98.40/13.00 ((
% 98.40/13.00 (setminusT_lem) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementT_lem) =>
% 98.40/13.00 ((
% 98.40/13.00 (setextT) =>
% 98.40/13.00 ((
% 98.40/13.00 (subsetTI) =>
% 98.40/13.00 ((
% 98.40/13.00 (powersetTI1) =>
% 98.40/13.00 ((
% 98.40/13.00 (powersetTE1) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementTI1) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementTE1) =>
% 98.40/13.00 ((
% 98.40/13.00 (binintersectTELcontra) =>
% 98.40/13.00 ((
% 98.40/13.00 (binintersectTERcontra) =>
% 98.40/13.00 ((
% 98.40/13.00 (contrasubsetT) =>
% 98.40/13.00 ((
% 98.40/13.00 (contrasubsetT1) =>
% 98.40/13.00 ((
% 98.40/13.00 (contrasubsetT2) =>
% 98.40/13.00 ((
% 98.40/13.00 (contrasubsetT3) =>
% 98.40/13.00 ((
% 98.40/13.00 (doubleComplementI1) =>
% 98.40/13.00 ((
% 98.40/13.00 (doubleComplementE1) =>
% 98.40/13.00 ((
% 98.40/13.00 (doubleComplementSub1) =>
% 98.40/13.00 ((
% 98.40/13.00 (doubleComplementSub2) =>
% 98.40/13.00 ((
% 98.40/13.00 (doubleComplementEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementTnotintersectT) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementImpComplementIntersect) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementSubsetComplementIntersect) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementInPowersetComplementIntersect) =>
% 98.40/13.00 ((
% 98.40/13.00 (contraSubsetComplement) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementTcontraSubset) =>
% 98.40/13.00 ((
% 98.40/13.00 (binunionTILcontra) =>
% 98.40/13.00 ((
% 98.40/13.00 (binunionTIRcontra) =>
% 98.40/13.00 ((
% 98.40/13.00 (inIntersectImpInUnion) =>
% 98.40/13.00 ((
% 98.40/13.00 (inIntersectImpInUnion2) =>
% 98.40/13.00 ((
% 98.40/13.00 (inIntersectImpInIntersectUnions) =>
% 98.40/13.00 ((
% 98.40/13.00 (intersectInPowersetIntersectUnions) =>
% 98.40/13.00 ((
% 98.40/13.00 (inComplementUnionImpNotIn1) =>
% 98.40/13.00 ((
% 98.40/13.00 (inComplementUnionImpInComplement1) =>
% 98.40/13.00 ((
% 98.40/13.00 (binunionTE) =>
% 98.40/13.00 ((
% 98.40/13.00 (binunionTEcontra) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan2a1) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementUnionInPowersetComplement) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan2a2) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan1a) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan1b) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan1) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan2a) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan2b2) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan2b) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan2) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz13rule0) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz13rule1) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz13rule2) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz13rule3) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz13rule4) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz1_1) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz1_2) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz1_3) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz1_4) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz1_5) =>
% 98.40/13.00 ((
% 98.40/13.00 (breln1all2) =>
% 98.40/13.00 ((
% 98.40/13.00 (breln1SetBreln1) =>
% 98.40/13.00 ((
% 98.40/13.00 (choice2fnsingleton) =>
% 98.40/13.00 ((
% 98.40/13.00 (!!) @ (
% 98.40/13.00 (('#B') @ (
% 98.40/13.00 !!) @
% 98.40/13.00 (
% 98.40/13.00 (
% 98.40/13.00 ('#S') @ (
% 98.40/13.00 (
% 98.40/13.00 ('#B') @ (
% 98.40/13.00 '#B') @
% 98.40/13.00 breln1)) @
% 98.40/13.00 (
% 98.40/13.00 (
% 98.40/13.00 ('#S') @ dpsetconstr @
% 98.40/13.00 (
% 98.40/13.00 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.40/13.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1135])).
% 98.40/13.00 thf(zip_derived_cl1150, plain,
% 98.40/13.00 (~ (((binintersectSubset5) =>
% 98.40/13.00 (((binintersectEL) =>
% 98.40/13.00 (((binintersectLsub) =>
% 98.40/13.00 (((binintersectSubset2) =>
% 98.40/13.00 (((binintersectSubset3) =>
% 98.40/13.00 (((binintersectER) =>
% 98.40/13.00 (((disjointsetsI1) =>
% 98.40/13.00 (((binintersectRsub) =>
% 98.40/13.00 (((binintersectSubset4) =>
% 98.40/13.00 (((binintersectSubset1) =>
% 98.40/13.00 (((bs114d) =>
% 98.40/13.00 (((setminusI) =>
% 98.40/13.00 (((setminusEL) =>
% 98.40/13.00 (((setminusER) =>
% 98.40/13.00 (((setminusSubset2) =>
% 98.40/13.00 (((setminusERneg) =>
% 98.40/13.00 (((setminusELneg) =>
% 98.40/13.00 (((setminusILneg) =>
% 98.40/13.00 (((setminusIRneg) =>
% 98.40/13.00 (((setminusLsub) =>
% 98.40/13.00 (((setminusSubset1) =>
% 98.40/13.00 (((symdiffE) =>
% 98.40/13.00 (((symdiffI1) =>
% 98.40/13.00 (((symdiffI2) =>
% 98.40/13.00 (((symdiffIneg1) =>
% 98.40/13.00 (((symdiffIneg2) =>
% 98.40/13.00 (((secondinupair) =>
% 98.40/13.00 (((setukpairIL) =>
% 98.40/13.00 (((setukpairIR) =>
% 98.40/13.00 (((kpairiskpair) =>
% 98.40/13.00 ((
% 98.40/13.00 (kpairp) =>
% 98.40/13.00 ((
% 98.40/13.00 (singletonsubset) =>
% 98.40/13.00 ((
% 98.40/13.00 (singletoninpowerset) =>
% 98.40/13.00 ((
% 98.40/13.00 (singletoninpowunion) =>
% 98.40/13.00 ((
% 98.40/13.00 (upairset2E) =>
% 98.40/13.00 ((
% 98.40/13.00 (upairsubunion) =>
% 98.40/13.00 ((
% 98.40/13.00 (upairinpowunion) =>
% 98.40/13.00 ((
% 98.40/13.00 (ubforcartprodlem1) =>
% 98.40/13.00 ((
% 98.40/13.00 (ubforcartprodlem2) =>
% 98.40/13.00 ((
% 98.40/13.00 (ubforcartprodlem3) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodpairin) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodmempair1) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodmempair) =>
% 98.40/13.00 ((
% 98.40/13.00 (setunionE2) =>
% 98.40/13.00 ((
% 98.40/13.00 (setunionsingleton1) =>
% 98.40/13.00 ((
% 98.40/13.00 (setunionsingleton2) =>
% 98.40/13.00 ((
% 98.40/13.00 (setunionsingleton) =>
% 98.40/13.00 ((
% 98.40/13.00 (singletonprop) =>
% 98.40/13.00 ((
% 98.40/13.00 (ex1E1) =>
% 98.40/13.00 ((
% 98.40/13.00 (ex1I) =>
% 98.40/13.00 ((
% 98.40/13.00 (ex1I2) =>
% 98.40/13.00 ((
% 98.40/13.00 (singletonsuniq) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjL1) =>
% 98.40/13.00 ((
% 98.40/13.00 (kfstsingleton) =>
% 98.40/13.00 ((
% 98.40/13.00 (theprop) =>
% 98.40/13.00 ((
% 98.40/13.00 (kfstpairEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodfstin) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjL2) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjL) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjR11) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjR12) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjR1) =>
% 98.40/13.00 ((
% 98.40/13.00 (upairequniteq) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjR2) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjR) =>
% 98.40/13.00 ((
% 98.40/13.00 (ksndsingleton) =>
% 98.40/13.00 ((
% 98.40/13.00 (ksndpairEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (kpairsurjEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodsndin) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodpairmemEL) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodpairmemER) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodmempaircEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodfstpairEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodsndpairEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodpairsurjEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (dpsetconstrI) =>
% 98.40/13.00 ((
% 98.40/13.00 (dpsetconstrSub) =>
% 98.40/13.00 ((
% 98.40/13.00 (setOfPairsIsBReln) =>
% 98.40/13.00 ((
% 98.40/13.00 (dpsetconstrERa) =>
% 98.40/13.00 ((
% 98.40/13.00 (dpsetconstrEL1) =>
% 98.40/13.00 ((
% 98.40/13.00 (dpsetconstrEL2) =>
% 98.40/13.00 ((
% 98.40/13.00 (dpsetconstrER) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcImageSingleton) =>
% 98.40/13.00 ((
% 98.40/13.00 (apProp) =>
% 98.40/13.00 ((
% 98.40/13.00 (app) =>
% 98.40/13.00 ((
% 98.40/13.00 (infuncsetfunc) =>
% 98.40/13.00 ((
% 98.40/13.00 (ap2p) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcinfuncset) =>
% 98.40/13.00 ((
% 98.40/13.00 (lamProp) =>
% 98.40/13.00 ((
% 98.40/13.00 (lamp) =>
% 98.40/13.00 ((
% 98.40/13.00 (lam2p) =>
% 98.40/13.00 ((
% 98.40/13.00 (brelnall1) =>
% 98.40/13.00 ((
% 98.40/13.00 (brelnall2) =>
% 98.40/13.00 ((
% 98.40/13.00 (ex1E2) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcGraphProp1) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcGraphProp3) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcGraphProp2) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcextLem) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcGraphProp4) =>
% 98.40/13.00 ((
% 98.40/13.00 (subbreln) =>
% 98.40/13.00 ((
% 98.40/13.00 (eqbreln) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcext) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcext2) =>
% 98.40/13.00 ((
% 98.40/13.00 (ap2apEq1) =>
% 98.40/13.00 ((
% 98.40/13.00 (ap2apEq2) =>
% 98.40/13.00 ((
% 98.40/13.00 (beta1) =>
% 98.40/13.00 ((
% 98.40/13.00 (eta1) =>
% 98.40/13.00 ((
% 98.40/13.00 (lam2lamEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (beta2) =>
% 98.40/13.00 ((
% 98.40/13.00 (eta2) =>
% 98.40/13.00 ((
% 98.40/13.00 (iffalseProp1) =>
% 98.40/13.00 ((
% 98.40/13.00 (iffalseProp2) =>
% 98.40/13.00 ((
% 98.40/13.00 (iftrueProp1) =>
% 98.40/13.00 ((
% 98.40/13.00 (iftrueProp2) =>
% 98.40/13.00 ((
% 98.40/13.00 (ifSingleton) =>
% 98.40/13.00 ((
% 98.40/13.00 (ifp) =>
% 98.40/13.00 ((
% 98.40/13.00 (theeq) =>
% 98.40/13.00 ((
% 98.40/13.00 (iftrue) =>
% 98.40/13.00 ((
% 98.40/13.00 (iffalse) =>
% 98.40/13.00 ((
% 98.40/13.00 (iftrueorfalse) =>
% 98.40/13.00 ((
% 98.40/13.00 (binintersectT_lem) =>
% 98.40/13.00 ((
% 98.40/13.00 (binunionT_lem) =>
% 98.40/13.00 ((
% 98.40/13.00 (powersetT_lem) =>
% 98.40/13.00 ((
% 98.40/13.00 (setminusT_lem) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementT_lem) =>
% 98.40/13.00 ((
% 98.40/13.00 (setextT) =>
% 98.40/13.00 ((
% 98.40/13.00 (subsetTI) =>
% 98.40/13.00 ((
% 98.40/13.00 (powersetTI1) =>
% 98.40/13.00 ((
% 98.40/13.00 (powersetTE1) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementTI1) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementTE1) =>
% 98.40/13.00 ((
% 98.40/13.00 (binintersectTELcontra) =>
% 98.40/13.00 ((
% 98.40/13.00 (binintersectTERcontra) =>
% 98.40/13.00 ((
% 98.40/13.00 (contrasubsetT) =>
% 98.40/13.00 ((
% 98.40/13.00 (contrasubsetT1) =>
% 98.40/13.00 ((
% 98.40/13.00 (contrasubsetT2) =>
% 98.40/13.00 ((
% 98.40/13.00 (contrasubsetT3) =>
% 98.40/13.00 ((
% 98.40/13.00 (doubleComplementI1) =>
% 98.40/13.00 ((
% 98.40/13.00 (doubleComplementE1) =>
% 98.40/13.00 ((
% 98.40/13.00 (doubleComplementSub1) =>
% 98.40/13.00 ((
% 98.40/13.00 (doubleComplementSub2) =>
% 98.40/13.00 ((
% 98.40/13.00 (doubleComplementEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementTnotintersectT) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementImpComplementIntersect) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementSubsetComplementIntersect) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementInPowersetComplementIntersect) =>
% 98.40/13.00 ((
% 98.40/13.00 (contraSubsetComplement) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementTcontraSubset) =>
% 98.40/13.00 ((
% 98.40/13.00 (binunionTILcontra) =>
% 98.40/13.00 ((
% 98.40/13.00 (binunionTIRcontra) =>
% 98.40/13.00 ((
% 98.40/13.00 (inIntersectImpInUnion) =>
% 98.40/13.00 ((
% 98.40/13.00 (inIntersectImpInUnion2) =>
% 98.40/13.00 ((
% 98.40/13.00 (inIntersectImpInIntersectUnions) =>
% 98.40/13.00 ((
% 98.40/13.00 (intersectInPowersetIntersectUnions) =>
% 98.40/13.00 ((
% 98.40/13.00 (inComplementUnionImpNotIn1) =>
% 98.40/13.00 ((
% 98.40/13.00 (inComplementUnionImpInComplement1) =>
% 98.40/13.00 ((
% 98.40/13.00 (binunionTE) =>
% 98.40/13.00 ((
% 98.40/13.00 (binunionTEcontra) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan2a1) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementUnionInPowersetComplement) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan2a2) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan1a) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan1b) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan1) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan2a) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan2b2) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan2b) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan2) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz13rule0) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz13rule1) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz13rule2) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz13rule3) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz13rule4) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz1_1) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz1_2) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz1_3) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz1_4) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz1_5) =>
% 98.40/13.00 ((
% 98.40/13.00 (breln1all2) =>
% 98.40/13.00 ((
% 98.40/13.00 (breln1SetBreln1) =>
% 98.40/13.00 ((
% 98.40/13.00 (choice2fnsingleton) =>
% 98.40/13.00 ((
% 98.40/13.00 (!!) @ (
% 98.40/13.00 (('#B') @ (
% 98.40/13.00 !!) @
% 98.40/13.00 (
% 98.40/13.00 (
% 98.40/13.00 ('#S') @ (
% 98.40/13.00 (
% 98.40/13.00 ('#B') @ (
% 98.40/13.00 '#B') @
% 98.40/13.00 breln1)) @
% 98.40/13.00 (
% 98.40/13.00 (
% 98.40/13.00 ('#S') @ dpsetconstr @
% 98.40/13.00 (
% 98.40/13.00 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.40/13.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1142])).
% 98.40/13.00 thf(zip_derived_cl1158, plain,
% 98.40/13.00 (~ (((binintersectEL) =>
% 98.40/13.00 (((binintersectLsub) =>
% 98.40/13.00 (((binintersectSubset2) =>
% 98.40/13.00 (((binintersectSubset3) =>
% 98.40/13.00 (((binintersectER) =>
% 98.40/13.00 (((disjointsetsI1) =>
% 98.40/13.00 (((binintersectRsub) =>
% 98.40/13.00 (((binintersectSubset4) =>
% 98.40/13.00 (((binintersectSubset1) =>
% 98.40/13.00 (((bs114d) =>
% 98.40/13.00 (((setminusI) =>
% 98.40/13.00 (((setminusEL) =>
% 98.40/13.00 (((setminusER) =>
% 98.40/13.00 (((setminusSubset2) =>
% 98.40/13.00 (((setminusERneg) =>
% 98.40/13.00 (((setminusELneg) =>
% 98.40/13.00 (((setminusILneg) =>
% 98.40/13.00 (((setminusIRneg) =>
% 98.40/13.00 (((setminusLsub) =>
% 98.40/13.00 (((setminusSubset1) =>
% 98.40/13.00 (((symdiffE) =>
% 98.40/13.00 (((symdiffI1) =>
% 98.40/13.00 (((symdiffI2) =>
% 98.40/13.00 (((symdiffIneg1) =>
% 98.40/13.00 (((symdiffIneg2) =>
% 98.40/13.00 (((secondinupair) =>
% 98.40/13.00 (((setukpairIL) =>
% 98.40/13.00 (((setukpairIR) =>
% 98.40/13.00 (((kpairiskpair) =>
% 98.40/13.00 (((kpairp) =>
% 98.40/13.00 ((
% 98.40/13.00 (singletonsubset) =>
% 98.40/13.00 ((
% 98.40/13.00 (singletoninpowerset) =>
% 98.40/13.00 ((
% 98.40/13.00 (singletoninpowunion) =>
% 98.40/13.00 ((
% 98.40/13.00 (upairset2E) =>
% 98.40/13.00 ((
% 98.40/13.00 (upairsubunion) =>
% 98.40/13.00 ((
% 98.40/13.00 (upairinpowunion) =>
% 98.40/13.00 ((
% 98.40/13.00 (ubforcartprodlem1) =>
% 98.40/13.00 ((
% 98.40/13.00 (ubforcartprodlem2) =>
% 98.40/13.00 ((
% 98.40/13.00 (ubforcartprodlem3) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodpairin) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodmempair1) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodmempair) =>
% 98.40/13.00 ((
% 98.40/13.00 (setunionE2) =>
% 98.40/13.00 ((
% 98.40/13.00 (setunionsingleton1) =>
% 98.40/13.00 ((
% 98.40/13.00 (setunionsingleton2) =>
% 98.40/13.00 ((
% 98.40/13.00 (setunionsingleton) =>
% 98.40/13.00 ((
% 98.40/13.00 (singletonprop) =>
% 98.40/13.00 ((
% 98.40/13.00 (ex1E1) =>
% 98.40/13.00 ((
% 98.40/13.00 (ex1I) =>
% 98.40/13.00 ((
% 98.40/13.00 (ex1I2) =>
% 98.40/13.00 ((
% 98.40/13.00 (singletonsuniq) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjL1) =>
% 98.40/13.00 ((
% 98.40/13.00 (kfstsingleton) =>
% 98.40/13.00 ((
% 98.40/13.00 (theprop) =>
% 98.40/13.00 ((
% 98.40/13.00 (kfstpairEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodfstin) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjL2) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjL) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjR11) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjR12) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjR1) =>
% 98.40/13.00 ((
% 98.40/13.00 (upairequniteq) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjR2) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjR) =>
% 98.40/13.00 ((
% 98.40/13.00 (ksndsingleton) =>
% 98.40/13.00 ((
% 98.40/13.00 (ksndpairEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (kpairsurjEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodsndin) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodpairmemEL) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodpairmemER) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodmempaircEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodfstpairEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodsndpairEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodpairsurjEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (dpsetconstrI) =>
% 98.40/13.00 ((
% 98.40/13.00 (dpsetconstrSub) =>
% 98.40/13.00 ((
% 98.40/13.00 (setOfPairsIsBReln) =>
% 98.40/13.00 ((
% 98.40/13.00 (dpsetconstrERa) =>
% 98.40/13.00 ((
% 98.40/13.00 (dpsetconstrEL1) =>
% 98.40/13.00 ((
% 98.40/13.00 (dpsetconstrEL2) =>
% 98.40/13.00 ((
% 98.40/13.00 (dpsetconstrER) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcImageSingleton) =>
% 98.40/13.00 ((
% 98.40/13.00 (apProp) =>
% 98.40/13.00 ((
% 98.40/13.00 (app) =>
% 98.40/13.00 ((
% 98.40/13.00 (infuncsetfunc) =>
% 98.40/13.00 ((
% 98.40/13.00 (ap2p) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcinfuncset) =>
% 98.40/13.00 ((
% 98.40/13.00 (lamProp) =>
% 98.40/13.00 ((
% 98.40/13.00 (lamp) =>
% 98.40/13.00 ((
% 98.40/13.00 (lam2p) =>
% 98.40/13.00 ((
% 98.40/13.00 (brelnall1) =>
% 98.40/13.00 ((
% 98.40/13.00 (brelnall2) =>
% 98.40/13.00 ((
% 98.40/13.00 (ex1E2) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcGraphProp1) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcGraphProp3) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcGraphProp2) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcextLem) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcGraphProp4) =>
% 98.40/13.00 ((
% 98.40/13.00 (subbreln) =>
% 98.40/13.00 ((
% 98.40/13.00 (eqbreln) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcext) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcext2) =>
% 98.40/13.00 ((
% 98.40/13.00 (ap2apEq1) =>
% 98.40/13.00 ((
% 98.40/13.00 (ap2apEq2) =>
% 98.40/13.00 ((
% 98.40/13.00 (beta1) =>
% 98.40/13.00 ((
% 98.40/13.00 (eta1) =>
% 98.40/13.00 ((
% 98.40/13.00 (lam2lamEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (beta2) =>
% 98.40/13.00 ((
% 98.40/13.00 (eta2) =>
% 98.40/13.00 ((
% 98.40/13.00 (iffalseProp1) =>
% 98.40/13.00 ((
% 98.40/13.00 (iffalseProp2) =>
% 98.40/13.00 ((
% 98.40/13.00 (iftrueProp1) =>
% 98.40/13.00 ((
% 98.40/13.00 (iftrueProp2) =>
% 98.40/13.00 ((
% 98.40/13.00 (ifSingleton) =>
% 98.40/13.00 ((
% 98.40/13.00 (ifp) =>
% 98.40/13.00 ((
% 98.40/13.00 (theeq) =>
% 98.40/13.00 ((
% 98.40/13.00 (iftrue) =>
% 98.40/13.00 ((
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% 98.40/13.00 ((
% 98.40/13.00 (iftrueorfalse) =>
% 98.40/13.00 ((
% 98.40/13.00 (binintersectT_lem) =>
% 98.40/13.00 ((
% 98.40/13.00 (binunionT_lem) =>
% 98.40/13.00 ((
% 98.40/13.00 (powersetT_lem) =>
% 98.40/13.00 ((
% 98.40/13.00 (setminusT_lem) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementT_lem) =>
% 98.40/13.00 ((
% 98.40/13.00 (setextT) =>
% 98.40/13.00 ((
% 98.40/13.00 (subsetTI) =>
% 98.40/13.00 ((
% 98.40/13.00 (powersetTI1) =>
% 98.40/13.00 ((
% 98.40/13.00 (powersetTE1) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementTI1) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementTE1) =>
% 98.40/13.00 ((
% 98.40/13.00 (binintersectTELcontra) =>
% 98.40/13.00 ((
% 98.40/13.00 (binintersectTERcontra) =>
% 98.40/13.00 ((
% 98.40/13.00 (contrasubsetT) =>
% 98.40/13.00 ((
% 98.40/13.00 (contrasubsetT1) =>
% 98.40/13.00 ((
% 98.40/13.00 (contrasubsetT2) =>
% 98.40/13.00 ((
% 98.40/13.00 (contrasubsetT3) =>
% 98.40/13.00 ((
% 98.40/13.00 (doubleComplementI1) =>
% 98.40/13.00 ((
% 98.40/13.00 (doubleComplementE1) =>
% 98.40/13.00 ((
% 98.40/13.00 (doubleComplementSub1) =>
% 98.40/13.00 ((
% 98.40/13.00 (doubleComplementSub2) =>
% 98.40/13.00 ((
% 98.40/13.00 (doubleComplementEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementTnotintersectT) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementImpComplementIntersect) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementSubsetComplementIntersect) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementInPowersetComplementIntersect) =>
% 98.40/13.00 ((
% 98.40/13.00 (contraSubsetComplement) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementTcontraSubset) =>
% 98.40/13.00 ((
% 98.40/13.00 (binunionTILcontra) =>
% 98.40/13.00 ((
% 98.40/13.00 (binunionTIRcontra) =>
% 98.40/13.00 ((
% 98.40/13.00 (inIntersectImpInUnion) =>
% 98.40/13.00 ((
% 98.40/13.00 (inIntersectImpInUnion2) =>
% 98.40/13.00 ((
% 98.40/13.00 (inIntersectImpInIntersectUnions) =>
% 98.40/13.00 ((
% 98.40/13.00 (intersectInPowersetIntersectUnions) =>
% 98.40/13.00 ((
% 98.40/13.00 (inComplementUnionImpNotIn1) =>
% 98.40/13.00 ((
% 98.40/13.00 (inComplementUnionImpInComplement1) =>
% 98.40/13.00 ((
% 98.40/13.00 (binunionTE) =>
% 98.40/13.00 ((
% 98.40/13.00 (binunionTEcontra) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan2a1) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementUnionInPowersetComplement) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan2a2) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan1a) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan1b) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan1) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan2a) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan2b2) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan2b) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan2) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz13rule0) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz13rule1) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz13rule2) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz13rule3) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz13rule4) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz1_1) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz1_2) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz1_3) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz1_4) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz1_5) =>
% 98.40/13.00 ((
% 98.40/13.00 (breln1all2) =>
% 98.40/13.00 ((
% 98.40/13.00 (breln1SetBreln1) =>
% 98.40/13.00 ((
% 98.40/13.00 (choice2fnsingleton) =>
% 98.40/13.00 ((
% 98.40/13.00 (!!) @ (
% 98.40/13.00 (('#B') @ (
% 98.40/13.00 !!) @
% 98.40/13.00 (
% 98.40/13.00 (
% 98.40/13.00 ('#S') @ (
% 98.40/13.00 (
% 98.40/13.00 ('#B') @ (
% 98.40/13.00 '#B') @
% 98.40/13.00 breln1)) @
% 98.40/13.00 (
% 98.40/13.00 (
% 98.40/13.00 ('#S') @ dpsetconstr @
% 98.40/13.00 (
% 98.40/13.00 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.40/13.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1150])).
% 98.40/13.00 thf(zip_derived_cl1166, plain,
% 98.40/13.00 (~ (((binintersectLsub) =>
% 98.40/13.00 (((binintersectSubset2) =>
% 98.40/13.00 (((binintersectSubset3) =>
% 98.40/13.00 (((binintersectER) =>
% 98.40/13.00 (((disjointsetsI1) =>
% 98.40/13.00 (((binintersectRsub) =>
% 98.40/13.00 (((binintersectSubset4) =>
% 98.40/13.00 (((binintersectSubset1) =>
% 98.40/13.00 (((bs114d) =>
% 98.40/13.00 (((setminusI) =>
% 98.40/13.00 (((setminusEL) =>
% 98.40/13.00 (((setminusER) =>
% 98.40/13.00 (((setminusSubset2) =>
% 98.40/13.00 (((setminusERneg) =>
% 98.40/13.00 (((setminusELneg) =>
% 98.40/13.00 (((setminusILneg) =>
% 98.40/13.00 (((setminusIRneg) =>
% 98.40/13.00 (((setminusLsub) =>
% 98.40/13.00 (((setminusSubset1) =>
% 98.40/13.00 (((symdiffE) =>
% 98.40/13.00 (((symdiffI1) =>
% 98.40/13.00 (((symdiffI2) =>
% 98.40/13.00 (((symdiffIneg1) =>
% 98.40/13.00 (((symdiffIneg2) =>
% 98.40/13.00 (((secondinupair) =>
% 98.40/13.00 (((setukpairIL) =>
% 98.40/13.00 (((setukpairIR) =>
% 98.40/13.00 (((kpairiskpair) =>
% 98.40/13.00 (((kpairp) =>
% 98.40/13.00 (((singletonsubset) =>
% 98.40/13.00 ((
% 98.40/13.00 (singletoninpowerset) =>
% 98.40/13.00 ((
% 98.40/13.00 (singletoninpowunion) =>
% 98.40/13.00 ((
% 98.40/13.00 (upairset2E) =>
% 98.40/13.00 ((
% 98.40/13.00 (upairsubunion) =>
% 98.40/13.00 ((
% 98.40/13.00 (upairinpowunion) =>
% 98.40/13.00 ((
% 98.40/13.00 (ubforcartprodlem1) =>
% 98.40/13.00 ((
% 98.40/13.00 (ubforcartprodlem2) =>
% 98.40/13.00 ((
% 98.40/13.00 (ubforcartprodlem3) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodpairin) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodmempair1) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodmempair) =>
% 98.40/13.00 ((
% 98.40/13.00 (setunionE2) =>
% 98.40/13.00 ((
% 98.40/13.00 (setunionsingleton1) =>
% 98.40/13.00 ((
% 98.40/13.00 (setunionsingleton2) =>
% 98.40/13.00 ((
% 98.40/13.00 (setunionsingleton) =>
% 98.40/13.00 ((
% 98.40/13.00 (singletonprop) =>
% 98.40/13.00 ((
% 98.40/13.00 (ex1E1) =>
% 98.40/13.00 ((
% 98.40/13.00 (ex1I) =>
% 98.40/13.00 ((
% 98.40/13.00 (ex1I2) =>
% 98.40/13.00 ((
% 98.40/13.00 (singletonsuniq) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjL1) =>
% 98.40/13.00 ((
% 98.40/13.00 (kfstsingleton) =>
% 98.40/13.00 ((
% 98.40/13.00 (theprop) =>
% 98.40/13.00 ((
% 98.40/13.00 (kfstpairEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodfstin) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjL2) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjL) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjR11) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjR12) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjR1) =>
% 98.40/13.00 ((
% 98.40/13.00 (upairequniteq) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjR2) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjR) =>
% 98.40/13.00 ((
% 98.40/13.00 (ksndsingleton) =>
% 98.40/13.00 ((
% 98.40/13.00 (ksndpairEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (kpairsurjEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodsndin) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodpairmemEL) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodpairmemER) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodmempaircEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodfstpairEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodsndpairEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodpairsurjEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (dpsetconstrI) =>
% 98.40/13.00 ((
% 98.40/13.00 (dpsetconstrSub) =>
% 98.40/13.00 ((
% 98.40/13.00 (setOfPairsIsBReln) =>
% 98.40/13.00 ((
% 98.40/13.00 (dpsetconstrERa) =>
% 98.40/13.00 ((
% 98.40/13.00 (dpsetconstrEL1) =>
% 98.40/13.00 ((
% 98.40/13.00 (dpsetconstrEL2) =>
% 98.40/13.00 ((
% 98.40/13.00 (dpsetconstrER) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcImageSingleton) =>
% 98.40/13.00 ((
% 98.40/13.00 (apProp) =>
% 98.40/13.00 ((
% 98.40/13.00 (app) =>
% 98.40/13.00 ((
% 98.40/13.00 (infuncsetfunc) =>
% 98.40/13.00 ((
% 98.40/13.00 (ap2p) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcinfuncset) =>
% 98.40/13.00 ((
% 98.40/13.00 (lamProp) =>
% 98.40/13.00 ((
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% 98.40/13.00 ((
% 98.40/13.00 (lam2p) =>
% 98.40/13.00 ((
% 98.40/13.00 (brelnall1) =>
% 98.40/13.00 ((
% 98.40/13.00 (brelnall2) =>
% 98.40/13.00 ((
% 98.40/13.00 (ex1E2) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcGraphProp1) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcGraphProp3) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcGraphProp2) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcextLem) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcGraphProp4) =>
% 98.40/13.00 ((
% 98.40/13.00 (subbreln) =>
% 98.40/13.00 ((
% 98.40/13.00 (eqbreln) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcext) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcext2) =>
% 98.40/13.00 ((
% 98.40/13.00 (ap2apEq1) =>
% 98.40/13.00 ((
% 98.40/13.00 (ap2apEq2) =>
% 98.40/13.00 ((
% 98.40/13.00 (beta1) =>
% 98.40/13.00 ((
% 98.40/13.00 (eta1) =>
% 98.40/13.00 ((
% 98.40/13.00 (lam2lamEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (beta2) =>
% 98.40/13.00 ((
% 98.40/13.00 (eta2) =>
% 98.40/13.00 ((
% 98.40/13.00 (iffalseProp1) =>
% 98.40/13.00 ((
% 98.40/13.00 (iffalseProp2) =>
% 98.40/13.00 ((
% 98.40/13.00 (iftrueProp1) =>
% 98.40/13.00 ((
% 98.40/13.00 (iftrueProp2) =>
% 98.40/13.00 ((
% 98.40/13.00 (ifSingleton) =>
% 98.40/13.00 ((
% 98.40/13.00 (ifp) =>
% 98.40/13.00 ((
% 98.40/13.00 (theeq) =>
% 98.40/13.00 ((
% 98.40/13.00 (iftrue) =>
% 98.40/13.00 ((
% 98.40/13.00 (iffalse) =>
% 98.40/13.00 ((
% 98.40/13.00 (iftrueorfalse) =>
% 98.40/13.00 ((
% 98.40/13.00 (binintersectT_lem) =>
% 98.40/13.00 ((
% 98.40/13.00 (binunionT_lem) =>
% 98.40/13.00 ((
% 98.40/13.00 (powersetT_lem) =>
% 98.40/13.00 ((
% 98.40/13.00 (setminusT_lem) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementT_lem) =>
% 98.40/13.00 ((
% 98.40/13.00 (setextT) =>
% 98.40/13.00 ((
% 98.40/13.00 (subsetTI) =>
% 98.40/13.00 ((
% 98.40/13.00 (powersetTI1) =>
% 98.40/13.00 ((
% 98.40/13.00 (powersetTE1) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementTI1) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementTE1) =>
% 98.40/13.00 ((
% 98.40/13.00 (binintersectTELcontra) =>
% 98.40/13.00 ((
% 98.40/13.00 (binintersectTERcontra) =>
% 98.40/13.00 ((
% 98.40/13.00 (contrasubsetT) =>
% 98.40/13.00 ((
% 98.40/13.00 (contrasubsetT1) =>
% 98.40/13.00 ((
% 98.40/13.00 (contrasubsetT2) =>
% 98.40/13.00 ((
% 98.40/13.00 (contrasubsetT3) =>
% 98.40/13.00 ((
% 98.40/13.00 (doubleComplementI1) =>
% 98.40/13.00 ((
% 98.40/13.00 (doubleComplementE1) =>
% 98.40/13.00 ((
% 98.40/13.00 (doubleComplementSub1) =>
% 98.40/13.00 ((
% 98.40/13.00 (doubleComplementSub2) =>
% 98.40/13.00 ((
% 98.40/13.00 (doubleComplementEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementTnotintersectT) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementImpComplementIntersect) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementSubsetComplementIntersect) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementInPowersetComplementIntersect) =>
% 98.40/13.00 ((
% 98.40/13.00 (contraSubsetComplement) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementTcontraSubset) =>
% 98.40/13.00 ((
% 98.40/13.00 (binunionTILcontra) =>
% 98.40/13.00 ((
% 98.40/13.00 (binunionTIRcontra) =>
% 98.40/13.00 ((
% 98.40/13.00 (inIntersectImpInUnion) =>
% 98.40/13.00 ((
% 98.40/13.00 (inIntersectImpInUnion2) =>
% 98.40/13.00 ((
% 98.40/13.00 (inIntersectImpInIntersectUnions) =>
% 98.40/13.00 ((
% 98.40/13.00 (intersectInPowersetIntersectUnions) =>
% 98.40/13.00 ((
% 98.40/13.00 (inComplementUnionImpNotIn1) =>
% 98.40/13.00 ((
% 98.40/13.00 (inComplementUnionImpInComplement1) =>
% 98.40/13.00 ((
% 98.40/13.00 (binunionTE) =>
% 98.40/13.00 ((
% 98.40/13.00 (binunionTEcontra) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan2a1) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementUnionInPowersetComplement) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan2a2) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan1a) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan1b) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan1) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan2a) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan2b2) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan2b) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan2) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz13rule0) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz13rule1) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz13rule2) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz13rule3) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz13rule4) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz1_1) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz1_2) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz1_3) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz1_4) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz1_5) =>
% 98.40/13.00 ((
% 98.40/13.00 (breln1all2) =>
% 98.40/13.00 ((
% 98.40/13.00 (breln1SetBreln1) =>
% 98.40/13.00 ((
% 98.40/13.00 (choice2fnsingleton) =>
% 98.40/13.00 ((
% 98.40/13.00 (!!) @ (
% 98.40/13.00 (('#B') @ (
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% 98.40/13.00 (
% 98.40/13.00 (
% 98.40/13.00 ('#S') @ (
% 98.40/13.00 (
% 98.40/13.00 ('#B') @ (
% 98.40/13.00 '#B') @
% 98.40/13.00 breln1)) @
% 98.40/13.00 (
% 98.40/13.00 (
% 98.40/13.00 ('#S') @ dpsetconstr @
% 98.40/13.00 (
% 98.40/13.00 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.40/13.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1158])).
% 98.40/13.00 thf(zip_derived_cl1174, plain,
% 98.40/13.00 (~ (((binintersectSubset2) =>
% 98.40/13.00 (((binintersectSubset3) =>
% 98.40/13.00 (((binintersectER) =>
% 98.40/13.00 (((disjointsetsI1) =>
% 98.40/13.00 (((binintersectRsub) =>
% 98.40/13.00 (((binintersectSubset4) =>
% 98.40/13.00 (((binintersectSubset1) =>
% 98.40/13.00 (((bs114d) =>
% 98.40/13.00 (((setminusI) =>
% 98.40/13.00 (((setminusEL) =>
% 98.40/13.00 (((setminusER) =>
% 98.40/13.00 (((setminusSubset2) =>
% 98.40/13.00 (((setminusERneg) =>
% 98.40/13.00 (((setminusELneg) =>
% 98.40/13.00 (((setminusILneg) =>
% 98.40/13.00 (((setminusIRneg) =>
% 98.40/13.00 (((setminusLsub) =>
% 98.40/13.00 (((setminusSubset1) =>
% 98.40/13.00 (((symdiffE) =>
% 98.40/13.00 (((symdiffI1) =>
% 98.40/13.00 (((symdiffI2) =>
% 98.40/13.00 (((symdiffIneg1) =>
% 98.40/13.00 (((symdiffIneg2) =>
% 98.40/13.00 (((secondinupair) =>
% 98.40/13.00 (((setukpairIL) =>
% 98.40/13.00 (((setukpairIR) =>
% 98.40/13.00 (((kpairiskpair) =>
% 98.40/13.00 (((kpairp) =>
% 98.40/13.00 (((singletonsubset) =>
% 98.40/13.00 (((singletoninpowerset) =>
% 98.40/13.00 ((
% 98.40/13.00 (singletoninpowunion) =>
% 98.40/13.00 ((
% 98.40/13.00 (upairset2E) =>
% 98.40/13.00 ((
% 98.40/13.00 (upairsubunion) =>
% 98.40/13.00 ((
% 98.40/13.00 (upairinpowunion) =>
% 98.40/13.00 ((
% 98.40/13.00 (ubforcartprodlem1) =>
% 98.40/13.00 ((
% 98.40/13.00 (ubforcartprodlem2) =>
% 98.40/13.00 ((
% 98.40/13.00 (ubforcartprodlem3) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodpairin) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodmempair1) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodmempair) =>
% 98.40/13.00 ((
% 98.40/13.00 (setunionE2) =>
% 98.40/13.00 ((
% 98.40/13.00 (setunionsingleton1) =>
% 98.40/13.00 ((
% 98.40/13.00 (setunionsingleton2) =>
% 98.40/13.00 ((
% 98.40/13.00 (setunionsingleton) =>
% 98.40/13.00 ((
% 98.40/13.00 (singletonprop) =>
% 98.40/13.00 ((
% 98.40/13.00 (ex1E1) =>
% 98.40/13.00 ((
% 98.40/13.00 (ex1I) =>
% 98.40/13.00 ((
% 98.40/13.00 (ex1I2) =>
% 98.40/13.00 ((
% 98.40/13.00 (singletonsuniq) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjL1) =>
% 98.40/13.00 ((
% 98.40/13.00 (kfstsingleton) =>
% 98.40/13.00 ((
% 98.40/13.00 (theprop) =>
% 98.40/13.00 ((
% 98.40/13.00 (kfstpairEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodfstin) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjL2) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjL) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjR11) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjR12) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjR1) =>
% 98.40/13.00 ((
% 98.40/13.00 (upairequniteq) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjR2) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjR) =>
% 98.40/13.00 ((
% 98.40/13.00 (ksndsingleton) =>
% 98.40/13.00 ((
% 98.40/13.00 (ksndpairEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (kpairsurjEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodsndin) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodpairmemEL) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodpairmemER) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodmempaircEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodfstpairEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodsndpairEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodpairsurjEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (dpsetconstrI) =>
% 98.40/13.00 ((
% 98.40/13.00 (dpsetconstrSub) =>
% 98.40/13.00 ((
% 98.40/13.00 (setOfPairsIsBReln) =>
% 98.40/13.00 ((
% 98.40/13.00 (dpsetconstrERa) =>
% 98.40/13.00 ((
% 98.40/13.00 (dpsetconstrEL1) =>
% 98.40/13.00 ((
% 98.40/13.00 (dpsetconstrEL2) =>
% 98.40/13.00 ((
% 98.40/13.00 (dpsetconstrER) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcImageSingleton) =>
% 98.40/13.00 ((
% 98.40/13.00 (apProp) =>
% 98.40/13.00 ((
% 98.40/13.00 (app) =>
% 98.40/13.00 ((
% 98.40/13.00 (infuncsetfunc) =>
% 98.40/13.00 ((
% 98.40/13.00 (ap2p) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcinfuncset) =>
% 98.40/13.00 ((
% 98.40/13.00 (lamProp) =>
% 98.40/13.00 ((
% 98.40/13.00 (lamp) =>
% 98.40/13.00 ((
% 98.40/13.00 (lam2p) =>
% 98.40/13.00 ((
% 98.40/13.00 (brelnall1) =>
% 98.40/13.00 ((
% 98.40/13.00 (brelnall2) =>
% 98.40/13.00 ((
% 98.40/13.00 (ex1E2) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcGraphProp1) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcGraphProp3) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcGraphProp2) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcextLem) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcGraphProp4) =>
% 98.40/13.00 ((
% 98.40/13.00 (subbreln) =>
% 98.40/13.00 ((
% 98.40/13.00 (eqbreln) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcext) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcext2) =>
% 98.40/13.00 ((
% 98.40/13.00 (ap2apEq1) =>
% 98.40/13.00 ((
% 98.40/13.00 (ap2apEq2) =>
% 98.40/13.00 ((
% 98.40/13.00 (beta1) =>
% 98.40/13.00 ((
% 98.40/13.00 (eta1) =>
% 98.40/13.00 ((
% 98.40/13.00 (lam2lamEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (beta2) =>
% 98.40/13.00 ((
% 98.40/13.00 (eta2) =>
% 98.40/13.00 ((
% 98.40/13.00 (iffalseProp1) =>
% 98.40/13.00 ((
% 98.40/13.00 (iffalseProp2) =>
% 98.40/13.00 ((
% 98.40/13.00 (iftrueProp1) =>
% 98.40/13.00 ((
% 98.40/13.00 (iftrueProp2) =>
% 98.40/13.00 ((
% 98.40/13.00 (ifSingleton) =>
% 98.40/13.00 ((
% 98.40/13.00 (ifp) =>
% 98.40/13.00 ((
% 98.40/13.00 (theeq) =>
% 98.40/13.00 ((
% 98.40/13.00 (iftrue) =>
% 98.40/13.00 ((
% 98.40/13.00 (iffalse) =>
% 98.40/13.00 ((
% 98.40/13.00 (iftrueorfalse) =>
% 98.40/13.00 ((
% 98.40/13.00 (binintersectT_lem) =>
% 98.40/13.00 ((
% 98.40/13.00 (binunionT_lem) =>
% 98.40/13.00 ((
% 98.40/13.00 (powersetT_lem) =>
% 98.40/13.00 ((
% 98.40/13.00 (setminusT_lem) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementT_lem) =>
% 98.40/13.00 ((
% 98.40/13.00 (setextT) =>
% 98.40/13.00 ((
% 98.40/13.00 (subsetTI) =>
% 98.40/13.00 ((
% 98.40/13.00 (powersetTI1) =>
% 98.40/13.00 ((
% 98.40/13.00 (powersetTE1) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementTI1) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementTE1) =>
% 98.40/13.00 ((
% 98.40/13.00 (binintersectTELcontra) =>
% 98.40/13.00 ((
% 98.40/13.00 (binintersectTERcontra) =>
% 98.40/13.00 ((
% 98.40/13.00 (contrasubsetT) =>
% 98.40/13.00 ((
% 98.40/13.00 (contrasubsetT1) =>
% 98.40/13.00 ((
% 98.40/13.00 (contrasubsetT2) =>
% 98.40/13.00 ((
% 98.40/13.00 (contrasubsetT3) =>
% 98.40/13.00 ((
% 98.40/13.00 (doubleComplementI1) =>
% 98.40/13.00 ((
% 98.40/13.00 (doubleComplementE1) =>
% 98.40/13.00 ((
% 98.40/13.00 (doubleComplementSub1) =>
% 98.40/13.00 ((
% 98.40/13.00 (doubleComplementSub2) =>
% 98.40/13.00 ((
% 98.40/13.00 (doubleComplementEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementTnotintersectT) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementImpComplementIntersect) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementSubsetComplementIntersect) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementInPowersetComplementIntersect) =>
% 98.40/13.00 ((
% 98.40/13.00 (contraSubsetComplement) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementTcontraSubset) =>
% 98.40/13.00 ((
% 98.40/13.00 (binunionTILcontra) =>
% 98.40/13.00 ((
% 98.40/13.00 (binunionTIRcontra) =>
% 98.40/13.00 ((
% 98.40/13.00 (inIntersectImpInUnion) =>
% 98.40/13.00 ((
% 98.40/13.00 (inIntersectImpInUnion2) =>
% 98.40/13.00 ((
% 98.40/13.00 (inIntersectImpInIntersectUnions) =>
% 98.40/13.00 ((
% 98.40/13.00 (intersectInPowersetIntersectUnions) =>
% 98.40/13.00 ((
% 98.40/13.00 (inComplementUnionImpNotIn1) =>
% 98.40/13.00 ((
% 98.40/13.00 (inComplementUnionImpInComplement1) =>
% 98.40/13.00 ((
% 98.40/13.00 (binunionTE) =>
% 98.40/13.00 ((
% 98.40/13.00 (binunionTEcontra) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan2a1) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementUnionInPowersetComplement) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan2a2) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan1a) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan1b) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan1) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan2a) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan2b2) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan2b) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan2) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz13rule0) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz13rule1) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz13rule2) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz13rule3) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz13rule4) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz1_1) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz1_2) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz1_3) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz1_4) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz1_5) =>
% 98.40/13.00 ((
% 98.40/13.00 (breln1all2) =>
% 98.40/13.00 ((
% 98.40/13.00 (breln1SetBreln1) =>
% 98.40/13.00 ((
% 98.40/13.00 (choice2fnsingleton) =>
% 98.40/13.00 ((
% 98.40/13.00 (!!) @ (
% 98.40/13.00 (('#B') @ (
% 98.40/13.00 !!) @
% 98.40/13.00 (
% 98.40/13.00 (
% 98.40/13.00 ('#S') @ (
% 98.40/13.00 (
% 98.40/13.00 ('#B') @ (
% 98.40/13.00 '#B') @
% 98.40/13.00 breln1)) @
% 98.40/13.00 (
% 98.40/13.00 (
% 98.40/13.00 ('#S') @ dpsetconstr @
% 98.40/13.00 (
% 98.40/13.00 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.40/13.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1166])).
% 98.40/13.00 thf(zip_derived_cl1183, plain,
% 98.40/13.00 (~ (((binintersectSubset3) =>
% 98.40/13.00 (((binintersectER) =>
% 98.40/13.00 (((disjointsetsI1) =>
% 98.40/13.00 (((binintersectRsub) =>
% 98.40/13.00 (((binintersectSubset4) =>
% 98.40/13.00 (((binintersectSubset1) =>
% 98.40/13.00 (((bs114d) =>
% 98.40/13.00 (((setminusI) =>
% 98.40/13.00 (((setminusEL) =>
% 98.40/13.00 (((setminusER) =>
% 98.40/13.00 (((setminusSubset2) =>
% 98.40/13.00 (((setminusERneg) =>
% 98.40/13.00 (((setminusELneg) =>
% 98.40/13.00 (((setminusILneg) =>
% 98.40/13.00 (((setminusIRneg) =>
% 98.40/13.00 (((setminusLsub) =>
% 98.40/13.00 (((setminusSubset1) =>
% 98.40/13.00 (((symdiffE) =>
% 98.40/13.00 (((symdiffI1) =>
% 98.40/13.00 (((symdiffI2) =>
% 98.40/13.00 (((symdiffIneg1) =>
% 98.40/13.00 (((symdiffIneg2) =>
% 98.40/13.00 (((secondinupair) =>
% 98.40/13.00 (((setukpairIL) =>
% 98.40/13.00 (((setukpairIR) =>
% 98.40/13.00 (((kpairiskpair) =>
% 98.40/13.00 (((kpairp) =>
% 98.40/13.00 (((singletonsubset) =>
% 98.40/13.00 (((singletoninpowerset) =>
% 98.40/13.00 (((singletoninpowunion) =>
% 98.40/13.00 ((
% 98.40/13.00 (upairset2E) =>
% 98.40/13.00 ((
% 98.40/13.00 (upairsubunion) =>
% 98.40/13.00 ((
% 98.40/13.00 (upairinpowunion) =>
% 98.40/13.00 ((
% 98.40/13.00 (ubforcartprodlem1) =>
% 98.40/13.00 ((
% 98.40/13.00 (ubforcartprodlem2) =>
% 98.40/13.00 ((
% 98.40/13.00 (ubforcartprodlem3) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodpairin) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodmempair1) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodmempair) =>
% 98.40/13.00 ((
% 98.40/13.00 (setunionE2) =>
% 98.40/13.00 ((
% 98.40/13.00 (setunionsingleton1) =>
% 98.40/13.00 ((
% 98.40/13.00 (setunionsingleton2) =>
% 98.40/13.00 ((
% 98.40/13.00 (setunionsingleton) =>
% 98.40/13.00 ((
% 98.40/13.00 (singletonprop) =>
% 98.40/13.00 ((
% 98.40/13.00 (ex1E1) =>
% 98.40/13.00 ((
% 98.40/13.00 (ex1I) =>
% 98.40/13.00 ((
% 98.40/13.00 (ex1I2) =>
% 98.40/13.00 ((
% 98.40/13.00 (singletonsuniq) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjL1) =>
% 98.40/13.00 ((
% 98.40/13.00 (kfstsingleton) =>
% 98.40/13.00 ((
% 98.40/13.00 (theprop) =>
% 98.40/13.00 ((
% 98.40/13.00 (kfstpairEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodfstin) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjL2) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjL) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjR11) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjR12) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjR1) =>
% 98.40/13.00 ((
% 98.40/13.00 (upairequniteq) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjR2) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjR) =>
% 98.40/13.00 ((
% 98.40/13.00 (ksndsingleton) =>
% 98.40/13.00 ((
% 98.40/13.00 (ksndpairEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (kpairsurjEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodsndin) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodpairmemEL) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodpairmemER) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodmempaircEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodfstpairEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodsndpairEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodpairsurjEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (dpsetconstrI) =>
% 98.40/13.00 ((
% 98.40/13.00 (dpsetconstrSub) =>
% 98.40/13.00 ((
% 98.40/13.00 (setOfPairsIsBReln) =>
% 98.40/13.00 ((
% 98.40/13.00 (dpsetconstrERa) =>
% 98.40/13.00 ((
% 98.40/13.00 (dpsetconstrEL1) =>
% 98.40/13.00 ((
% 98.40/13.00 (dpsetconstrEL2) =>
% 98.40/13.00 ((
% 98.40/13.00 (dpsetconstrER) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcImageSingleton) =>
% 98.40/13.00 ((
% 98.40/13.00 (apProp) =>
% 98.40/13.00 ((
% 98.40/13.00 (app) =>
% 98.40/13.00 ((
% 98.40/13.00 (infuncsetfunc) =>
% 98.40/13.00 ((
% 98.40/13.00 (ap2p) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcinfuncset) =>
% 98.40/13.00 ((
% 98.40/13.00 (lamProp) =>
% 98.40/13.00 ((
% 98.40/13.00 (lamp) =>
% 98.40/13.00 ((
% 98.40/13.00 (lam2p) =>
% 98.40/13.00 ((
% 98.40/13.00 (brelnall1) =>
% 98.40/13.00 ((
% 98.40/13.00 (brelnall2) =>
% 98.40/13.00 ((
% 98.40/13.00 (ex1E2) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcGraphProp1) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcGraphProp3) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcGraphProp2) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcextLem) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcGraphProp4) =>
% 98.40/13.00 ((
% 98.40/13.00 (subbreln) =>
% 98.40/13.00 ((
% 98.40/13.00 (eqbreln) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcext) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcext2) =>
% 98.40/13.00 ((
% 98.40/13.00 (ap2apEq1) =>
% 98.40/13.00 ((
% 98.40/13.00 (ap2apEq2) =>
% 98.40/13.00 ((
% 98.40/13.00 (beta1) =>
% 98.40/13.00 ((
% 98.40/13.00 (eta1) =>
% 98.40/13.00 ((
% 98.40/13.00 (lam2lamEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (beta2) =>
% 98.40/13.00 ((
% 98.40/13.00 (eta2) =>
% 98.40/13.00 ((
% 98.40/13.00 (iffalseProp1) =>
% 98.40/13.00 ((
% 98.40/13.00 (iffalseProp2) =>
% 98.40/13.00 ((
% 98.40/13.00 (iftrueProp1) =>
% 98.40/13.00 ((
% 98.40/13.00 (iftrueProp2) =>
% 98.40/13.00 ((
% 98.40/13.00 (ifSingleton) =>
% 98.40/13.00 ((
% 98.40/13.00 (ifp) =>
% 98.40/13.00 ((
% 98.40/13.00 (theeq) =>
% 98.40/13.00 ((
% 98.40/13.00 (iftrue) =>
% 98.40/13.00 ((
% 98.40/13.00 (iffalse) =>
% 98.40/13.00 ((
% 98.40/13.00 (iftrueorfalse) =>
% 98.40/13.00 ((
% 98.40/13.00 (binintersectT_lem) =>
% 98.40/13.00 ((
% 98.40/13.00 (binunionT_lem) =>
% 98.40/13.00 ((
% 98.40/13.00 (powersetT_lem) =>
% 98.40/13.00 ((
% 98.40/13.00 (setminusT_lem) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementT_lem) =>
% 98.40/13.00 ((
% 98.40/13.00 (setextT) =>
% 98.40/13.00 ((
% 98.40/13.00 (subsetTI) =>
% 98.40/13.00 ((
% 98.40/13.00 (powersetTI1) =>
% 98.40/13.00 ((
% 98.40/13.00 (powersetTE1) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementTI1) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementTE1) =>
% 98.40/13.00 ((
% 98.40/13.00 (binintersectTELcontra) =>
% 98.40/13.00 ((
% 98.40/13.00 (binintersectTERcontra) =>
% 98.40/13.00 ((
% 98.40/13.00 (contrasubsetT) =>
% 98.40/13.00 ((
% 98.40/13.00 (contrasubsetT1) =>
% 98.40/13.00 ((
% 98.40/13.00 (contrasubsetT2) =>
% 98.40/13.00 ((
% 98.40/13.00 (contrasubsetT3) =>
% 98.40/13.00 ((
% 98.40/13.00 (doubleComplementI1) =>
% 98.40/13.00 ((
% 98.40/13.00 (doubleComplementE1) =>
% 98.40/13.00 ((
% 98.40/13.00 (doubleComplementSub1) =>
% 98.40/13.00 ((
% 98.40/13.00 (doubleComplementSub2) =>
% 98.40/13.00 ((
% 98.40/13.00 (doubleComplementEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementTnotintersectT) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementImpComplementIntersect) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementSubsetComplementIntersect) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementInPowersetComplementIntersect) =>
% 98.40/13.00 ((
% 98.40/13.00 (contraSubsetComplement) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementTcontraSubset) =>
% 98.40/13.00 ((
% 98.40/13.00 (binunionTILcontra) =>
% 98.40/13.00 ((
% 98.40/13.00 (binunionTIRcontra) =>
% 98.40/13.00 ((
% 98.40/13.00 (inIntersectImpInUnion) =>
% 98.40/13.00 ((
% 98.40/13.00 (inIntersectImpInUnion2) =>
% 98.40/13.00 ((
% 98.40/13.00 (inIntersectImpInIntersectUnions) =>
% 98.40/13.00 ((
% 98.40/13.00 (intersectInPowersetIntersectUnions) =>
% 98.40/13.00 ((
% 98.40/13.00 (inComplementUnionImpNotIn1) =>
% 98.40/13.00 ((
% 98.40/13.00 (inComplementUnionImpInComplement1) =>
% 98.40/13.00 ((
% 98.40/13.00 (binunionTE) =>
% 98.40/13.00 ((
% 98.40/13.00 (binunionTEcontra) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan2a1) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementUnionInPowersetComplement) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan2a2) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan1a) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan1b) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan1) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan2a) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan2b2) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan2b) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan2) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz13rule0) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz13rule1) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz13rule2) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz13rule3) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz13rule4) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz1_1) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz1_2) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz1_3) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz1_4) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz1_5) =>
% 98.40/13.00 ((
% 98.40/13.00 (breln1all2) =>
% 98.40/13.00 ((
% 98.40/13.00 (breln1SetBreln1) =>
% 98.40/13.00 ((
% 98.40/13.00 (choice2fnsingleton) =>
% 98.40/13.00 ((
% 98.40/13.00 (!!) @ (
% 98.40/13.00 (('#B') @ (
% 98.40/13.00 !!) @
% 98.40/13.00 (
% 98.40/13.00 (
% 98.40/13.00 ('#S') @ (
% 98.40/13.00 (
% 98.40/13.00 ('#B') @ (
% 98.40/13.00 '#B') @
% 98.40/13.00 breln1)) @
% 98.40/13.00 (
% 98.40/13.00 (
% 98.40/13.00 ('#S') @ dpsetconstr @
% 98.40/13.00 (
% 98.40/13.00 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.40/13.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1174])).
% 98.40/13.00 thf(zip_derived_cl1193, plain,
% 98.40/13.00 (~ (((binintersectER) =>
% 98.40/13.00 (((disjointsetsI1) =>
% 98.40/13.00 (((binintersectRsub) =>
% 98.40/13.00 (((binintersectSubset4) =>
% 98.40/13.00 (((binintersectSubset1) =>
% 98.40/13.00 (((bs114d) =>
% 98.40/13.00 (((setminusI) =>
% 98.40/13.00 (((setminusEL) =>
% 98.40/13.00 (((setminusER) =>
% 98.40/13.00 (((setminusSubset2) =>
% 98.40/13.00 (((setminusERneg) =>
% 98.40/13.00 (((setminusELneg) =>
% 98.40/13.00 (((setminusILneg) =>
% 98.40/13.00 (((setminusIRneg) =>
% 98.40/13.00 (((setminusLsub) =>
% 98.40/13.00 (((setminusSubset1) =>
% 98.40/13.00 (((symdiffE) =>
% 98.40/13.00 (((symdiffI1) =>
% 98.40/13.00 (((symdiffI2) =>
% 98.40/13.00 (((symdiffIneg1) =>
% 98.40/13.00 (((symdiffIneg2) =>
% 98.40/13.00 (((secondinupair) =>
% 98.40/13.00 (((setukpairIL) =>
% 98.40/13.00 (((setukpairIR) =>
% 98.40/13.00 (((kpairiskpair) =>
% 98.40/13.00 (((kpairp) =>
% 98.40/13.00 (((singletonsubset) =>
% 98.40/13.00 (((singletoninpowerset) =>
% 98.40/13.00 (((singletoninpowunion) =>
% 98.40/13.00 (((upairset2E) =>
% 98.40/13.00 ((
% 98.40/13.00 (upairsubunion) =>
% 98.40/13.00 ((
% 98.40/13.00 (upairinpowunion) =>
% 98.40/13.00 ((
% 98.40/13.00 (ubforcartprodlem1) =>
% 98.40/13.00 ((
% 98.40/13.00 (ubforcartprodlem2) =>
% 98.40/13.00 ((
% 98.40/13.00 (ubforcartprodlem3) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodpairin) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodmempair1) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodmempair) =>
% 98.40/13.00 ((
% 98.40/13.00 (setunionE2) =>
% 98.40/13.00 ((
% 98.40/13.00 (setunionsingleton1) =>
% 98.40/13.00 ((
% 98.40/13.00 (setunionsingleton2) =>
% 98.40/13.00 ((
% 98.40/13.00 (setunionsingleton) =>
% 98.40/13.00 ((
% 98.40/13.00 (singletonprop) =>
% 98.40/13.00 ((
% 98.40/13.00 (ex1E1) =>
% 98.40/13.00 ((
% 98.40/13.00 (ex1I) =>
% 98.40/13.00 ((
% 98.40/13.00 (ex1I2) =>
% 98.40/13.00 ((
% 98.40/13.00 (singletonsuniq) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjL1) =>
% 98.40/13.00 ((
% 98.40/13.00 (kfstsingleton) =>
% 98.40/13.00 ((
% 98.40/13.00 (theprop) =>
% 98.40/13.00 ((
% 98.40/13.00 (kfstpairEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodfstin) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjL2) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjL) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjR11) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjR12) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjR1) =>
% 98.40/13.00 ((
% 98.40/13.00 (upairequniteq) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjR2) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjR) =>
% 98.40/13.00 ((
% 98.40/13.00 (ksndsingleton) =>
% 98.40/13.00 ((
% 98.40/13.00 (ksndpairEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (kpairsurjEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodsndin) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodpairmemEL) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodpairmemER) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodmempaircEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodfstpairEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodsndpairEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodpairsurjEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (dpsetconstrI) =>
% 98.40/13.00 ((
% 98.40/13.00 (dpsetconstrSub) =>
% 98.40/13.00 ((
% 98.40/13.00 (setOfPairsIsBReln) =>
% 98.40/13.00 ((
% 98.40/13.00 (dpsetconstrERa) =>
% 98.40/13.00 ((
% 98.40/13.00 (dpsetconstrEL1) =>
% 98.40/13.00 ((
% 98.40/13.00 (dpsetconstrEL2) =>
% 98.40/13.00 ((
% 98.40/13.00 (dpsetconstrER) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcImageSingleton) =>
% 98.40/13.00 ((
% 98.40/13.00 (apProp) =>
% 98.40/13.00 ((
% 98.40/13.00 (app) =>
% 98.40/13.00 ((
% 98.40/13.00 (infuncsetfunc) =>
% 98.40/13.00 ((
% 98.40/13.00 (ap2p) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcinfuncset) =>
% 98.40/13.00 ((
% 98.40/13.00 (lamProp) =>
% 98.40/13.00 ((
% 98.40/13.00 (lamp) =>
% 98.40/13.00 ((
% 98.40/13.00 (lam2p) =>
% 98.40/13.00 ((
% 98.40/13.00 (brelnall1) =>
% 98.40/13.00 ((
% 98.40/13.00 (brelnall2) =>
% 98.40/13.00 ((
% 98.40/13.00 (ex1E2) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcGraphProp1) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcGraphProp3) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcGraphProp2) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcextLem) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcGraphProp4) =>
% 98.40/13.00 ((
% 98.40/13.00 (subbreln) =>
% 98.40/13.00 ((
% 98.40/13.00 (eqbreln) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcext) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcext2) =>
% 98.40/13.00 ((
% 98.40/13.00 (ap2apEq1) =>
% 98.40/13.00 ((
% 98.40/13.00 (ap2apEq2) =>
% 98.40/13.00 ((
% 98.40/13.00 (beta1) =>
% 98.40/13.00 ((
% 98.40/13.00 (eta1) =>
% 98.40/13.00 ((
% 98.40/13.00 (lam2lamEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (beta2) =>
% 98.40/13.00 ((
% 98.40/13.00 (eta2) =>
% 98.40/13.00 ((
% 98.40/13.00 (iffalseProp1) =>
% 98.40/13.00 ((
% 98.40/13.00 (iffalseProp2) =>
% 98.40/13.00 ((
% 98.40/13.00 (iftrueProp1) =>
% 98.40/13.00 ((
% 98.40/13.00 (iftrueProp2) =>
% 98.40/13.00 ((
% 98.40/13.00 (ifSingleton) =>
% 98.40/13.00 ((
% 98.40/13.00 (ifp) =>
% 98.40/13.00 ((
% 98.40/13.00 (theeq) =>
% 98.40/13.00 ((
% 98.40/13.00 (iftrue) =>
% 98.40/13.00 ((
% 98.40/13.00 (iffalse) =>
% 98.40/13.00 ((
% 98.40/13.00 (iftrueorfalse) =>
% 98.40/13.00 ((
% 98.40/13.00 (binintersectT_lem) =>
% 98.40/13.00 ((
% 98.40/13.00 (binunionT_lem) =>
% 98.40/13.00 ((
% 98.40/13.00 (powersetT_lem) =>
% 98.40/13.00 ((
% 98.40/13.00 (setminusT_lem) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementT_lem) =>
% 98.40/13.00 ((
% 98.40/13.00 (setextT) =>
% 98.40/13.00 ((
% 98.40/13.00 (subsetTI) =>
% 98.40/13.00 ((
% 98.40/13.00 (powersetTI1) =>
% 98.40/13.00 ((
% 98.40/13.00 (powersetTE1) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementTI1) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementTE1) =>
% 98.40/13.00 ((
% 98.40/13.00 (binintersectTELcontra) =>
% 98.40/13.00 ((
% 98.40/13.00 (binintersectTERcontra) =>
% 98.40/13.00 ((
% 98.40/13.00 (contrasubsetT) =>
% 98.40/13.00 ((
% 98.40/13.00 (contrasubsetT1) =>
% 98.40/13.00 ((
% 98.40/13.00 (contrasubsetT2) =>
% 98.40/13.00 ((
% 98.40/13.00 (contrasubsetT3) =>
% 98.40/13.00 ((
% 98.40/13.00 (doubleComplementI1) =>
% 98.40/13.00 ((
% 98.40/13.00 (doubleComplementE1) =>
% 98.40/13.00 ((
% 98.40/13.00 (doubleComplementSub1) =>
% 98.40/13.00 ((
% 98.40/13.00 (doubleComplementSub2) =>
% 98.40/13.00 ((
% 98.40/13.00 (doubleComplementEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementTnotintersectT) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementImpComplementIntersect) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementSubsetComplementIntersect) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementInPowersetComplementIntersect) =>
% 98.40/13.00 ((
% 98.40/13.00 (contraSubsetComplement) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementTcontraSubset) =>
% 98.40/13.00 ((
% 98.40/13.00 (binunionTILcontra) =>
% 98.40/13.00 ((
% 98.40/13.00 (binunionTIRcontra) =>
% 98.40/13.00 ((
% 98.40/13.00 (inIntersectImpInUnion) =>
% 98.40/13.00 ((
% 98.40/13.00 (inIntersectImpInUnion2) =>
% 98.40/13.00 ((
% 98.40/13.00 (inIntersectImpInIntersectUnions) =>
% 98.40/13.00 ((
% 98.40/13.00 (intersectInPowersetIntersectUnions) =>
% 98.40/13.00 ((
% 98.40/13.00 (inComplementUnionImpNotIn1) =>
% 98.40/13.00 ((
% 98.40/13.00 (inComplementUnionImpInComplement1) =>
% 98.40/13.00 ((
% 98.40/13.00 (binunionTE) =>
% 98.40/13.00 ((
% 98.40/13.00 (binunionTEcontra) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan2a1) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementUnionInPowersetComplement) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan2a2) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan1a) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan1b) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan1) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan2a) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan2b2) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan2b) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan2) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz13rule0) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz13rule1) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz13rule2) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz13rule3) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz13rule4) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz1_1) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz1_2) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz1_3) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz1_4) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz1_5) =>
% 98.40/13.00 ((
% 98.40/13.00 (breln1all2) =>
% 98.40/13.00 ((
% 98.40/13.00 (breln1SetBreln1) =>
% 98.40/13.00 ((
% 98.40/13.00 (choice2fnsingleton) =>
% 98.40/13.00 ((
% 98.40/13.00 (!!) @ (
% 98.40/13.00 (('#B') @ (
% 98.40/13.00 !!) @
% 98.40/13.00 (
% 98.40/13.00 (
% 98.40/13.00 ('#S') @ (
% 98.40/13.00 (
% 98.40/13.00 ('#B') @ (
% 98.40/13.00 '#B') @
% 98.40/13.00 breln1)) @
% 98.40/13.00 (
% 98.40/13.00 (
% 98.40/13.00 ('#S') @ dpsetconstr @
% 98.40/13.00 (
% 98.40/13.00 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.40/13.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1183])).
% 98.40/13.00 thf(zip_derived_cl1206, plain,
% 98.40/13.00 (~ (((disjointsetsI1) =>
% 98.40/13.00 (((binintersectRsub) =>
% 98.40/13.00 (((binintersectSubset4) =>
% 98.40/13.00 (((binintersectSubset1) =>
% 98.40/13.00 (((bs114d) =>
% 98.40/13.00 (((setminusI) =>
% 98.40/13.00 (((setminusEL) =>
% 98.40/13.00 (((setminusER) =>
% 98.40/13.00 (((setminusSubset2) =>
% 98.40/13.00 (((setminusERneg) =>
% 98.40/13.00 (((setminusELneg) =>
% 98.40/13.00 (((setminusILneg) =>
% 98.40/13.00 (((setminusIRneg) =>
% 98.40/13.00 (((setminusLsub) =>
% 98.40/13.00 (((setminusSubset1) =>
% 98.40/13.00 (((symdiffE) =>
% 98.40/13.00 (((symdiffI1) =>
% 98.40/13.00 (((symdiffI2) =>
% 98.40/13.00 (((symdiffIneg1) =>
% 98.40/13.00 (((symdiffIneg2) =>
% 98.40/13.00 (((secondinupair) =>
% 98.40/13.00 (((setukpairIL) =>
% 98.40/13.00 (((setukpairIR) =>
% 98.40/13.00 (((kpairiskpair) =>
% 98.40/13.00 (((kpairp) =>
% 98.40/13.00 (((singletonsubset) =>
% 98.40/13.00 (((singletoninpowerset) =>
% 98.40/13.00 (((singletoninpowunion) =>
% 98.40/13.00 (((upairset2E) =>
% 98.40/13.00 (((upairsubunion) =>
% 98.40/13.00 ((
% 98.40/13.00 (upairinpowunion) =>
% 98.40/13.00 ((
% 98.40/13.00 (ubforcartprodlem1) =>
% 98.40/13.00 ((
% 98.40/13.00 (ubforcartprodlem2) =>
% 98.40/13.00 ((
% 98.40/13.00 (ubforcartprodlem3) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodpairin) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodmempair1) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodmempair) =>
% 98.40/13.00 ((
% 98.40/13.00 (setunionE2) =>
% 98.40/13.00 ((
% 98.40/13.00 (setunionsingleton1) =>
% 98.40/13.00 ((
% 98.40/13.00 (setunionsingleton2) =>
% 98.40/13.00 ((
% 98.40/13.00 (setunionsingleton) =>
% 98.40/13.00 ((
% 98.40/13.00 (singletonprop) =>
% 98.40/13.00 ((
% 98.40/13.00 (ex1E1) =>
% 98.40/13.00 ((
% 98.40/13.00 (ex1I) =>
% 98.40/13.00 ((
% 98.40/13.00 (ex1I2) =>
% 98.40/13.00 ((
% 98.40/13.00 (singletonsuniq) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjL1) =>
% 98.40/13.00 ((
% 98.40/13.00 (kfstsingleton) =>
% 98.40/13.00 ((
% 98.40/13.00 (theprop) =>
% 98.40/13.00 ((
% 98.40/13.00 (kfstpairEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodfstin) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjL2) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjL) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjR11) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjR12) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjR1) =>
% 98.40/13.00 ((
% 98.40/13.00 (upairequniteq) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjR2) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjR) =>
% 98.40/13.00 ((
% 98.40/13.00 (ksndsingleton) =>
% 98.40/13.00 ((
% 98.40/13.00 (ksndpairEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (kpairsurjEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodsndin) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodpairmemEL) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodpairmemER) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodmempaircEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodfstpairEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodsndpairEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodpairsurjEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (dpsetconstrI) =>
% 98.40/13.00 ((
% 98.40/13.00 (dpsetconstrSub) =>
% 98.40/13.00 ((
% 98.40/13.00 (setOfPairsIsBReln) =>
% 98.40/13.00 ((
% 98.40/13.00 (dpsetconstrERa) =>
% 98.40/13.00 ((
% 98.40/13.00 (dpsetconstrEL1) =>
% 98.40/13.00 ((
% 98.40/13.00 (dpsetconstrEL2) =>
% 98.40/13.00 ((
% 98.40/13.00 (dpsetconstrER) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcImageSingleton) =>
% 98.40/13.00 ((
% 98.40/13.00 (apProp) =>
% 98.40/13.00 ((
% 98.40/13.00 (app) =>
% 98.40/13.00 ((
% 98.40/13.00 (infuncsetfunc) =>
% 98.40/13.00 ((
% 98.40/13.00 (ap2p) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcinfuncset) =>
% 98.40/13.00 ((
% 98.40/13.00 (lamProp) =>
% 98.40/13.00 ((
% 98.40/13.00 (lamp) =>
% 98.40/13.00 ((
% 98.40/13.00 (lam2p) =>
% 98.40/13.00 ((
% 98.40/13.00 (brelnall1) =>
% 98.40/13.00 ((
% 98.40/13.00 (brelnall2) =>
% 98.40/13.00 ((
% 98.40/13.00 (ex1E2) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcGraphProp1) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcGraphProp3) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcGraphProp2) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcextLem) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcGraphProp4) =>
% 98.40/13.00 ((
% 98.40/13.00 (subbreln) =>
% 98.40/13.00 ((
% 98.40/13.00 (eqbreln) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcext) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcext2) =>
% 98.40/13.00 ((
% 98.40/13.00 (ap2apEq1) =>
% 98.40/13.00 ((
% 98.40/13.00 (ap2apEq2) =>
% 98.40/13.00 ((
% 98.40/13.00 (beta1) =>
% 98.40/13.00 ((
% 98.40/13.00 (eta1) =>
% 98.40/13.00 ((
% 98.40/13.00 (lam2lamEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (beta2) =>
% 98.40/13.00 ((
% 98.40/13.00 (eta2) =>
% 98.40/13.00 ((
% 98.40/13.00 (iffalseProp1) =>
% 98.40/13.00 ((
% 98.40/13.00 (iffalseProp2) =>
% 98.40/13.00 ((
% 98.40/13.00 (iftrueProp1) =>
% 98.40/13.00 ((
% 98.40/13.00 (iftrueProp2) =>
% 98.40/13.00 ((
% 98.40/13.00 (ifSingleton) =>
% 98.40/13.00 ((
% 98.40/13.00 (ifp) =>
% 98.40/13.00 ((
% 98.40/13.00 (theeq) =>
% 98.40/13.00 ((
% 98.40/13.00 (iftrue) =>
% 98.40/13.00 ((
% 98.40/13.00 (iffalse) =>
% 98.40/13.00 ((
% 98.40/13.00 (iftrueorfalse) =>
% 98.40/13.00 ((
% 98.40/13.00 (binintersectT_lem) =>
% 98.40/13.00 ((
% 98.40/13.00 (binunionT_lem) =>
% 98.40/13.00 ((
% 98.40/13.00 (powersetT_lem) =>
% 98.40/13.00 ((
% 98.40/13.00 (setminusT_lem) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementT_lem) =>
% 98.40/13.00 ((
% 98.40/13.00 (setextT) =>
% 98.40/13.00 ((
% 98.40/13.00 (subsetTI) =>
% 98.40/13.00 ((
% 98.40/13.00 (powersetTI1) =>
% 98.40/13.00 ((
% 98.40/13.00 (powersetTE1) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementTI1) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementTE1) =>
% 98.40/13.00 ((
% 98.40/13.00 (binintersectTELcontra) =>
% 98.40/13.00 ((
% 98.40/13.00 (binintersectTERcontra) =>
% 98.40/13.00 ((
% 98.40/13.00 (contrasubsetT) =>
% 98.40/13.00 ((
% 98.40/13.00 (contrasubsetT1) =>
% 98.40/13.00 ((
% 98.40/13.00 (contrasubsetT2) =>
% 98.40/13.00 ((
% 98.40/13.00 (contrasubsetT3) =>
% 98.40/13.00 ((
% 98.40/13.00 (doubleComplementI1) =>
% 98.40/13.00 ((
% 98.40/13.00 (doubleComplementE1) =>
% 98.40/13.00 ((
% 98.40/13.00 (doubleComplementSub1) =>
% 98.40/13.00 ((
% 98.40/13.00 (doubleComplementSub2) =>
% 98.40/13.00 ((
% 98.40/13.00 (doubleComplementEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementTnotintersectT) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementImpComplementIntersect) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementSubsetComplementIntersect) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementInPowersetComplementIntersect) =>
% 98.40/13.00 ((
% 98.40/13.00 (contraSubsetComplement) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementTcontraSubset) =>
% 98.40/13.00 ((
% 98.40/13.00 (binunionTILcontra) =>
% 98.40/13.00 ((
% 98.40/13.00 (binunionTIRcontra) =>
% 98.40/13.00 ((
% 98.40/13.00 (inIntersectImpInUnion) =>
% 98.40/13.00 ((
% 98.40/13.00 (inIntersectImpInUnion2) =>
% 98.40/13.00 ((
% 98.40/13.00 (inIntersectImpInIntersectUnions) =>
% 98.40/13.00 ((
% 98.40/13.00 (intersectInPowersetIntersectUnions) =>
% 98.40/13.00 ((
% 98.40/13.00 (inComplementUnionImpNotIn1) =>
% 98.40/13.00 ((
% 98.40/13.00 (inComplementUnionImpInComplement1) =>
% 98.40/13.00 ((
% 98.40/13.00 (binunionTE) =>
% 98.40/13.00 ((
% 98.40/13.00 (binunionTEcontra) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan2a1) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementUnionInPowersetComplement) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan2a2) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan1a) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan1b) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan1) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan2a) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan2b2) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan2b) =>
% 98.40/13.00 ((
% 98.40/13.00 (demorgan2) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz13rule0) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz13rule1) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz13rule2) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz13rule3) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz13rule4) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz1_1) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz1_2) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz1_3) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz1_4) =>
% 98.40/13.00 ((
% 98.40/13.00 (woz1_5) =>
% 98.40/13.00 ((
% 98.40/13.00 (breln1all2) =>
% 98.40/13.00 ((
% 98.40/13.00 (breln1SetBreln1) =>
% 98.40/13.00 ((
% 98.40/13.00 (choice2fnsingleton) =>
% 98.40/13.00 ((
% 98.40/13.00 (!!) @ (
% 98.40/13.00 (('#B') @ (
% 98.40/13.00 !!) @
% 98.40/13.00 (
% 98.40/13.00 (
% 98.40/13.00 ('#S') @ (
% 98.40/13.00 (
% 98.40/13.00 ('#B') @ (
% 98.40/13.00 '#B') @
% 98.40/13.00 breln1)) @
% 98.40/13.00 (
% 98.40/13.00 (
% 98.40/13.00 ('#S') @ dpsetconstr @
% 98.40/13.00 (
% 98.40/13.00 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.40/13.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1193])).
% 98.40/13.00 thf(zip_derived_cl1216, plain,
% 98.40/13.00 (~ (((binintersectRsub) =>
% 98.40/13.00 (((binintersectSubset4) =>
% 98.40/13.00 (((binintersectSubset1) =>
% 98.40/13.00 (((bs114d) =>
% 98.40/13.00 (((setminusI) =>
% 98.40/13.00 (((setminusEL) =>
% 98.40/13.00 (((setminusER) =>
% 98.40/13.00 (((setminusSubset2) =>
% 98.40/13.00 (((setminusERneg) =>
% 98.40/13.00 (((setminusELneg) =>
% 98.40/13.00 (((setminusILneg) =>
% 98.40/13.00 (((setminusIRneg) =>
% 98.40/13.00 (((setminusLsub) =>
% 98.40/13.00 (((setminusSubset1) =>
% 98.40/13.00 (((symdiffE) =>
% 98.40/13.00 (((symdiffI1) =>
% 98.40/13.00 (((symdiffI2) =>
% 98.40/13.00 (((symdiffIneg1) =>
% 98.40/13.00 (((symdiffIneg2) =>
% 98.40/13.00 (((secondinupair) =>
% 98.40/13.00 (((setukpairIL) =>
% 98.40/13.00 (((setukpairIR) =>
% 98.40/13.00 (((kpairiskpair) =>
% 98.40/13.00 (((kpairp) =>
% 98.40/13.00 (((singletonsubset) =>
% 98.40/13.00 (((singletoninpowerset) =>
% 98.40/13.00 (((singletoninpowunion) =>
% 98.40/13.00 (((upairset2E) =>
% 98.40/13.00 (((upairsubunion) =>
% 98.40/13.00 (((upairinpowunion) =>
% 98.40/13.00 ((
% 98.40/13.00 (ubforcartprodlem1) =>
% 98.40/13.00 ((
% 98.40/13.00 (ubforcartprodlem2) =>
% 98.40/13.00 ((
% 98.40/13.00 (ubforcartprodlem3) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodpairin) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodmempair1) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodmempair) =>
% 98.40/13.00 ((
% 98.40/13.00 (setunionE2) =>
% 98.40/13.00 ((
% 98.40/13.00 (setunionsingleton1) =>
% 98.40/13.00 ((
% 98.40/13.00 (setunionsingleton2) =>
% 98.40/13.00 ((
% 98.40/13.00 (setunionsingleton) =>
% 98.40/13.00 ((
% 98.40/13.00 (singletonprop) =>
% 98.40/13.00 ((
% 98.40/13.00 (ex1E1) =>
% 98.40/13.00 ((
% 98.40/13.00 (ex1I) =>
% 98.40/13.00 ((
% 98.40/13.00 (ex1I2) =>
% 98.40/13.00 ((
% 98.40/13.00 (singletonsuniq) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjL1) =>
% 98.40/13.00 ((
% 98.40/13.00 (kfstsingleton) =>
% 98.40/13.00 ((
% 98.40/13.00 (theprop) =>
% 98.40/13.00 ((
% 98.40/13.00 (kfstpairEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodfstin) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjL2) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjL) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjR11) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjR12) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjR1) =>
% 98.40/13.00 ((
% 98.40/13.00 (upairequniteq) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjR2) =>
% 98.40/13.00 ((
% 98.40/13.00 (setukpairinjR) =>
% 98.40/13.00 ((
% 98.40/13.00 (ksndsingleton) =>
% 98.40/13.00 ((
% 98.40/13.00 (ksndpairEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (kpairsurjEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodsndin) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodpairmemEL) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodpairmemER) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodmempaircEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodfstpairEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodsndpairEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (cartprodpairsurjEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (dpsetconstrI) =>
% 98.40/13.00 ((
% 98.40/13.00 (dpsetconstrSub) =>
% 98.40/13.00 ((
% 98.40/13.00 (setOfPairsIsBReln) =>
% 98.40/13.00 ((
% 98.40/13.00 (dpsetconstrERa) =>
% 98.40/13.00 ((
% 98.40/13.00 (dpsetconstrEL1) =>
% 98.40/13.00 ((
% 98.40/13.00 (dpsetconstrEL2) =>
% 98.40/13.00 ((
% 98.40/13.00 (dpsetconstrER) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcImageSingleton) =>
% 98.40/13.00 ((
% 98.40/13.00 (apProp) =>
% 98.40/13.00 ((
% 98.40/13.00 (app) =>
% 98.40/13.00 ((
% 98.40/13.00 (infuncsetfunc) =>
% 98.40/13.00 ((
% 98.40/13.00 (ap2p) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcinfuncset) =>
% 98.40/13.00 ((
% 98.40/13.00 (lamProp) =>
% 98.40/13.00 ((
% 98.40/13.00 (lamp) =>
% 98.40/13.00 ((
% 98.40/13.00 (lam2p) =>
% 98.40/13.00 ((
% 98.40/13.00 (brelnall1) =>
% 98.40/13.00 ((
% 98.40/13.00 (brelnall2) =>
% 98.40/13.00 ((
% 98.40/13.00 (ex1E2) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcGraphProp1) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcGraphProp3) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcGraphProp2) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcextLem) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcGraphProp4) =>
% 98.40/13.00 ((
% 98.40/13.00 (subbreln) =>
% 98.40/13.00 ((
% 98.40/13.00 (eqbreln) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcext) =>
% 98.40/13.00 ((
% 98.40/13.00 (funcext2) =>
% 98.40/13.00 ((
% 98.40/13.00 (ap2apEq1) =>
% 98.40/13.00 ((
% 98.40/13.00 (ap2apEq2) =>
% 98.40/13.00 ((
% 98.40/13.00 (beta1) =>
% 98.40/13.00 ((
% 98.40/13.00 (eta1) =>
% 98.40/13.00 ((
% 98.40/13.00 (lam2lamEq) =>
% 98.40/13.00 ((
% 98.40/13.00 (beta2) =>
% 98.40/13.00 ((
% 98.40/13.00 (eta2) =>
% 98.40/13.00 ((
% 98.40/13.00 (iffalseProp1) =>
% 98.40/13.00 ((
% 98.40/13.00 (iffalseProp2) =>
% 98.40/13.00 ((
% 98.40/13.00 (iftrueProp1) =>
% 98.40/13.00 ((
% 98.40/13.00 (iftrueProp2) =>
% 98.40/13.00 ((
% 98.40/13.00 (ifSingleton) =>
% 98.40/13.00 ((
% 98.40/13.00 (ifp) =>
% 98.40/13.00 ((
% 98.40/13.00 (theeq) =>
% 98.40/13.00 ((
% 98.40/13.00 (iftrue) =>
% 98.40/13.00 ((
% 98.40/13.00 (iffalse) =>
% 98.40/13.00 ((
% 98.40/13.00 (iftrueorfalse) =>
% 98.40/13.00 ((
% 98.40/13.00 (binintersectT_lem) =>
% 98.40/13.00 ((
% 98.40/13.00 (binunionT_lem) =>
% 98.40/13.00 ((
% 98.40/13.00 (powersetT_lem) =>
% 98.40/13.00 ((
% 98.40/13.00 (setminusT_lem) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementT_lem) =>
% 98.40/13.00 ((
% 98.40/13.00 (setextT) =>
% 98.40/13.00 ((
% 98.40/13.00 (subsetTI) =>
% 98.40/13.00 ((
% 98.40/13.00 (powersetTI1) =>
% 98.40/13.00 ((
% 98.40/13.00 (powersetTE1) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementTI1) =>
% 98.40/13.00 ((
% 98.40/13.00 (complementTE1) =>
% 98.40/13.00 ((
% 98.40/13.00 (binintersectTELcontra) =>
% 98.40/13.00 ((
% 98.40/13.00 (binintersectTERcontra) =>
% 98.40/13.01 ((
% 98.40/13.01 (contrasubsetT) =>
% 98.40/13.01 ((
% 98.40/13.01 (contrasubsetT1) =>
% 98.40/13.01 ((
% 98.40/13.01 (contrasubsetT2) =>
% 98.40/13.01 ((
% 98.40/13.01 (contrasubsetT3) =>
% 98.40/13.01 ((
% 98.40/13.01 (doubleComplementI1) =>
% 98.40/13.01 ((
% 98.40/13.01 (doubleComplementE1) =>
% 98.40/13.01 ((
% 98.40/13.01 (doubleComplementSub1) =>
% 98.40/13.01 ((
% 98.40/13.01 (doubleComplementSub2) =>
% 98.40/13.01 ((
% 98.40/13.01 (doubleComplementEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementTnotintersectT) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementImpComplementIntersect) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementSubsetComplementIntersect) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementInPowersetComplementIntersect) =>
% 98.40/13.01 ((
% 98.40/13.01 (contraSubsetComplement) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementTcontraSubset) =>
% 98.40/13.01 ((
% 98.40/13.01 (binunionTILcontra) =>
% 98.40/13.01 ((
% 98.40/13.01 (binunionTIRcontra) =>
% 98.40/13.01 ((
% 98.40/13.01 (inIntersectImpInUnion) =>
% 98.40/13.01 ((
% 98.40/13.01 (inIntersectImpInUnion2) =>
% 98.40/13.01 ((
% 98.40/13.01 (inIntersectImpInIntersectUnions) =>
% 98.40/13.01 ((
% 98.40/13.01 (intersectInPowersetIntersectUnions) =>
% 98.40/13.01 ((
% 98.40/13.01 (inComplementUnionImpNotIn1) =>
% 98.40/13.01 ((
% 98.40/13.01 (inComplementUnionImpInComplement1) =>
% 98.40/13.01 ((
% 98.40/13.01 (binunionTE) =>
% 98.40/13.01 ((
% 98.40/13.01 (binunionTEcontra) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan2a1) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementUnionInPowersetComplement) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan2a2) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan1a) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan1b) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan1) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan2a) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan2b2) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan2b) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan2) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz13rule0) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz13rule1) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz13rule2) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz13rule3) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz13rule4) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz1_1) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz1_2) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz1_3) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz1_4) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz1_5) =>
% 98.40/13.01 ((
% 98.40/13.01 (breln1all2) =>
% 98.40/13.01 ((
% 98.40/13.01 (breln1SetBreln1) =>
% 98.40/13.01 ((
% 98.40/13.01 (choice2fnsingleton) =>
% 98.40/13.01 ((
% 98.40/13.01 (!!) @ (
% 98.40/13.01 (('#B') @ (
% 98.40/13.01 !!) @
% 98.40/13.01 (
% 98.40/13.01 (
% 98.40/13.01 ('#S') @ (
% 98.40/13.01 (
% 98.40/13.01 ('#B') @ (
% 98.40/13.01 '#B') @
% 98.40/13.01 breln1)) @
% 98.40/13.01 (
% 98.40/13.01 (
% 98.40/13.01 ('#S') @ dpsetconstr @
% 98.40/13.01 (
% 98.40/13.01 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.40/13.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1206])).
% 98.40/13.01 thf(zip_derived_cl1223, plain,
% 98.40/13.01 (~ (((binintersectSubset4) =>
% 98.40/13.01 (((binintersectSubset1) =>
% 98.40/13.01 (((bs114d) =>
% 98.40/13.01 (((setminusI) =>
% 98.40/13.01 (((setminusEL) =>
% 98.40/13.01 (((setminusER) =>
% 98.40/13.01 (((setminusSubset2) =>
% 98.40/13.01 (((setminusERneg) =>
% 98.40/13.01 (((setminusELneg) =>
% 98.40/13.01 (((setminusILneg) =>
% 98.40/13.01 (((setminusIRneg) =>
% 98.40/13.01 (((setminusLsub) =>
% 98.40/13.01 (((setminusSubset1) =>
% 98.40/13.01 (((symdiffE) =>
% 98.40/13.01 (((symdiffI1) =>
% 98.40/13.01 (((symdiffI2) =>
% 98.40/13.01 (((symdiffIneg1) =>
% 98.40/13.01 (((symdiffIneg2) =>
% 98.40/13.01 (((secondinupair) =>
% 98.40/13.01 (((setukpairIL) =>
% 98.40/13.01 (((setukpairIR) =>
% 98.40/13.01 (((kpairiskpair) =>
% 98.40/13.01 (((kpairp) =>
% 98.40/13.01 (((singletonsubset) =>
% 98.40/13.01 (((singletoninpowerset) =>
% 98.40/13.01 (((singletoninpowunion) =>
% 98.40/13.01 (((upairset2E) =>
% 98.40/13.01 (((upairsubunion) =>
% 98.40/13.01 (((upairinpowunion) =>
% 98.40/13.01 (((ubforcartprodlem1) =>
% 98.40/13.01 ((
% 98.40/13.01 (ubforcartprodlem2) =>
% 98.40/13.01 ((
% 98.40/13.01 (ubforcartprodlem3) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodpairin) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodmempair1) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodmempair) =>
% 98.40/13.01 ((
% 98.40/13.01 (setunionE2) =>
% 98.40/13.01 ((
% 98.40/13.01 (setunionsingleton1) =>
% 98.40/13.01 ((
% 98.40/13.01 (setunionsingleton2) =>
% 98.40/13.01 ((
% 98.40/13.01 (setunionsingleton) =>
% 98.40/13.01 ((
% 98.40/13.01 (singletonprop) =>
% 98.40/13.01 ((
% 98.40/13.01 (ex1E1) =>
% 98.40/13.01 ((
% 98.40/13.01 (ex1I) =>
% 98.40/13.01 ((
% 98.40/13.01 (ex1I2) =>
% 98.40/13.01 ((
% 98.40/13.01 (singletonsuniq) =>
% 98.40/13.01 ((
% 98.40/13.01 (setukpairinjL1) =>
% 98.40/13.01 ((
% 98.40/13.01 (kfstsingleton) =>
% 98.40/13.01 ((
% 98.40/13.01 (theprop) =>
% 98.40/13.01 ((
% 98.40/13.01 (kfstpairEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodfstin) =>
% 98.40/13.01 ((
% 98.40/13.01 (setukpairinjL2) =>
% 98.40/13.01 ((
% 98.40/13.01 (setukpairinjL) =>
% 98.40/13.01 ((
% 98.40/13.01 (setukpairinjR11) =>
% 98.40/13.01 ((
% 98.40/13.01 (setukpairinjR12) =>
% 98.40/13.01 ((
% 98.40/13.01 (setukpairinjR1) =>
% 98.40/13.01 ((
% 98.40/13.01 (upairequniteq) =>
% 98.40/13.01 ((
% 98.40/13.01 (setukpairinjR2) =>
% 98.40/13.01 ((
% 98.40/13.01 (setukpairinjR) =>
% 98.40/13.01 ((
% 98.40/13.01 (ksndsingleton) =>
% 98.40/13.01 ((
% 98.40/13.01 (ksndpairEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (kpairsurjEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodsndin) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodpairmemEL) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodpairmemER) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodmempaircEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodfstpairEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodsndpairEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodpairsurjEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (dpsetconstrI) =>
% 98.40/13.01 ((
% 98.40/13.01 (dpsetconstrSub) =>
% 98.40/13.01 ((
% 98.40/13.01 (setOfPairsIsBReln) =>
% 98.40/13.01 ((
% 98.40/13.01 (dpsetconstrERa) =>
% 98.40/13.01 ((
% 98.40/13.01 (dpsetconstrEL1) =>
% 98.40/13.01 ((
% 98.40/13.01 (dpsetconstrEL2) =>
% 98.40/13.01 ((
% 98.40/13.01 (dpsetconstrER) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcImageSingleton) =>
% 98.40/13.01 ((
% 98.40/13.01 (apProp) =>
% 98.40/13.01 ((
% 98.40/13.01 (app) =>
% 98.40/13.01 ((
% 98.40/13.01 (infuncsetfunc) =>
% 98.40/13.01 ((
% 98.40/13.01 (ap2p) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcinfuncset) =>
% 98.40/13.01 ((
% 98.40/13.01 (lamProp) =>
% 98.40/13.01 ((
% 98.40/13.01 (lamp) =>
% 98.40/13.01 ((
% 98.40/13.01 (lam2p) =>
% 98.40/13.01 ((
% 98.40/13.01 (brelnall1) =>
% 98.40/13.01 ((
% 98.40/13.01 (brelnall2) =>
% 98.40/13.01 ((
% 98.40/13.01 (ex1E2) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcGraphProp1) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcGraphProp3) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcGraphProp2) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcextLem) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcGraphProp4) =>
% 98.40/13.01 ((
% 98.40/13.01 (subbreln) =>
% 98.40/13.01 ((
% 98.40/13.01 (eqbreln) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcext) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcext2) =>
% 98.40/13.01 ((
% 98.40/13.01 (ap2apEq1) =>
% 98.40/13.01 ((
% 98.40/13.01 (ap2apEq2) =>
% 98.40/13.01 ((
% 98.40/13.01 (beta1) =>
% 98.40/13.01 ((
% 98.40/13.01 (eta1) =>
% 98.40/13.01 ((
% 98.40/13.01 (lam2lamEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (beta2) =>
% 98.40/13.01 ((
% 98.40/13.01 (eta2) =>
% 98.40/13.01 ((
% 98.40/13.01 (iffalseProp1) =>
% 98.40/13.01 ((
% 98.40/13.01 (iffalseProp2) =>
% 98.40/13.01 ((
% 98.40/13.01 (iftrueProp1) =>
% 98.40/13.01 ((
% 98.40/13.01 (iftrueProp2) =>
% 98.40/13.01 ((
% 98.40/13.01 (ifSingleton) =>
% 98.40/13.01 ((
% 98.40/13.01 (ifp) =>
% 98.40/13.01 ((
% 98.40/13.01 (theeq) =>
% 98.40/13.01 ((
% 98.40/13.01 (iftrue) =>
% 98.40/13.01 ((
% 98.40/13.01 (iffalse) =>
% 98.40/13.01 ((
% 98.40/13.01 (iftrueorfalse) =>
% 98.40/13.01 ((
% 98.40/13.01 (binintersectT_lem) =>
% 98.40/13.01 ((
% 98.40/13.01 (binunionT_lem) =>
% 98.40/13.01 ((
% 98.40/13.01 (powersetT_lem) =>
% 98.40/13.01 ((
% 98.40/13.01 (setminusT_lem) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementT_lem) =>
% 98.40/13.01 ((
% 98.40/13.01 (setextT) =>
% 98.40/13.01 ((
% 98.40/13.01 (subsetTI) =>
% 98.40/13.01 ((
% 98.40/13.01 (powersetTI1) =>
% 98.40/13.01 ((
% 98.40/13.01 (powersetTE1) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementTI1) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementTE1) =>
% 98.40/13.01 ((
% 98.40/13.01 (binintersectTELcontra) =>
% 98.40/13.01 ((
% 98.40/13.01 (binintersectTERcontra) =>
% 98.40/13.01 ((
% 98.40/13.01 (contrasubsetT) =>
% 98.40/13.01 ((
% 98.40/13.01 (contrasubsetT1) =>
% 98.40/13.01 ((
% 98.40/13.01 (contrasubsetT2) =>
% 98.40/13.01 ((
% 98.40/13.01 (contrasubsetT3) =>
% 98.40/13.01 ((
% 98.40/13.01 (doubleComplementI1) =>
% 98.40/13.01 ((
% 98.40/13.01 (doubleComplementE1) =>
% 98.40/13.01 ((
% 98.40/13.01 (doubleComplementSub1) =>
% 98.40/13.01 ((
% 98.40/13.01 (doubleComplementSub2) =>
% 98.40/13.01 ((
% 98.40/13.01 (doubleComplementEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementTnotintersectT) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementImpComplementIntersect) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementSubsetComplementIntersect) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementInPowersetComplementIntersect) =>
% 98.40/13.01 ((
% 98.40/13.01 (contraSubsetComplement) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementTcontraSubset) =>
% 98.40/13.01 ((
% 98.40/13.01 (binunionTILcontra) =>
% 98.40/13.01 ((
% 98.40/13.01 (binunionTIRcontra) =>
% 98.40/13.01 ((
% 98.40/13.01 (inIntersectImpInUnion) =>
% 98.40/13.01 ((
% 98.40/13.01 (inIntersectImpInUnion2) =>
% 98.40/13.01 ((
% 98.40/13.01 (inIntersectImpInIntersectUnions) =>
% 98.40/13.01 ((
% 98.40/13.01 (intersectInPowersetIntersectUnions) =>
% 98.40/13.01 ((
% 98.40/13.01 (inComplementUnionImpNotIn1) =>
% 98.40/13.01 ((
% 98.40/13.01 (inComplementUnionImpInComplement1) =>
% 98.40/13.01 ((
% 98.40/13.01 (binunionTE) =>
% 98.40/13.01 ((
% 98.40/13.01 (binunionTEcontra) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan2a1) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementUnionInPowersetComplement) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan2a2) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan1a) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan1b) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan1) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan2a) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan2b2) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan2b) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan2) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz13rule0) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz13rule1) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz13rule2) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz13rule3) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz13rule4) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz1_1) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz1_2) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz1_3) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz1_4) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz1_5) =>
% 98.40/13.01 ((
% 98.40/13.01 (breln1all2) =>
% 98.40/13.01 ((
% 98.40/13.01 (breln1SetBreln1) =>
% 98.40/13.01 ((
% 98.40/13.01 (choice2fnsingleton) =>
% 98.40/13.01 ((
% 98.40/13.01 (!!) @ (
% 98.40/13.01 (('#B') @ (
% 98.40/13.01 !!) @
% 98.40/13.01 (
% 98.40/13.01 (
% 98.40/13.01 ('#S') @ (
% 98.40/13.01 (
% 98.40/13.01 ('#B') @ (
% 98.40/13.01 '#B') @
% 98.40/13.01 breln1)) @
% 98.40/13.01 (
% 98.40/13.01 (
% 98.40/13.01 ('#S') @ dpsetconstr @
% 98.40/13.01 (
% 98.40/13.01 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.40/13.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1216])).
% 98.40/13.01 thf(zip_derived_cl1231, plain,
% 98.40/13.01 (~ (((binintersectSubset1) =>
% 98.40/13.01 (((bs114d) =>
% 98.40/13.01 (((setminusI) =>
% 98.40/13.01 (((setminusEL) =>
% 98.40/13.01 (((setminusER) =>
% 98.40/13.01 (((setminusSubset2) =>
% 98.40/13.01 (((setminusERneg) =>
% 98.40/13.01 (((setminusELneg) =>
% 98.40/13.01 (((setminusILneg) =>
% 98.40/13.01 (((setminusIRneg) =>
% 98.40/13.01 (((setminusLsub) =>
% 98.40/13.01 (((setminusSubset1) =>
% 98.40/13.01 (((symdiffE) =>
% 98.40/13.01 (((symdiffI1) =>
% 98.40/13.01 (((symdiffI2) =>
% 98.40/13.01 (((symdiffIneg1) =>
% 98.40/13.01 (((symdiffIneg2) =>
% 98.40/13.01 (((secondinupair) =>
% 98.40/13.01 (((setukpairIL) =>
% 98.40/13.01 (((setukpairIR) =>
% 98.40/13.01 (((kpairiskpair) =>
% 98.40/13.01 (((kpairp) =>
% 98.40/13.01 (((singletonsubset) =>
% 98.40/13.01 (((singletoninpowerset) =>
% 98.40/13.01 (((singletoninpowunion) =>
% 98.40/13.01 (((upairset2E) =>
% 98.40/13.01 (((upairsubunion) =>
% 98.40/13.01 (((upairinpowunion) =>
% 98.40/13.01 (((ubforcartprodlem1) =>
% 98.40/13.01 (((ubforcartprodlem2) =>
% 98.40/13.01 ((
% 98.40/13.01 (ubforcartprodlem3) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodpairin) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodmempair1) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodmempair) =>
% 98.40/13.01 ((
% 98.40/13.01 (setunionE2) =>
% 98.40/13.01 ((
% 98.40/13.01 (setunionsingleton1) =>
% 98.40/13.01 ((
% 98.40/13.01 (setunionsingleton2) =>
% 98.40/13.01 ((
% 98.40/13.01 (setunionsingleton) =>
% 98.40/13.01 ((
% 98.40/13.01 (singletonprop) =>
% 98.40/13.01 ((
% 98.40/13.01 (ex1E1) =>
% 98.40/13.01 ((
% 98.40/13.01 (ex1I) =>
% 98.40/13.01 ((
% 98.40/13.01 (ex1I2) =>
% 98.40/13.01 ((
% 98.40/13.01 (singletonsuniq) =>
% 98.40/13.01 ((
% 98.40/13.01 (setukpairinjL1) =>
% 98.40/13.01 ((
% 98.40/13.01 (kfstsingleton) =>
% 98.40/13.01 ((
% 98.40/13.01 (theprop) =>
% 98.40/13.01 ((
% 98.40/13.01 (kfstpairEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodfstin) =>
% 98.40/13.01 ((
% 98.40/13.01 (setukpairinjL2) =>
% 98.40/13.01 ((
% 98.40/13.01 (setukpairinjL) =>
% 98.40/13.01 ((
% 98.40/13.01 (setukpairinjR11) =>
% 98.40/13.01 ((
% 98.40/13.01 (setukpairinjR12) =>
% 98.40/13.01 ((
% 98.40/13.01 (setukpairinjR1) =>
% 98.40/13.01 ((
% 98.40/13.01 (upairequniteq) =>
% 98.40/13.01 ((
% 98.40/13.01 (setukpairinjR2) =>
% 98.40/13.01 ((
% 98.40/13.01 (setukpairinjR) =>
% 98.40/13.01 ((
% 98.40/13.01 (ksndsingleton) =>
% 98.40/13.01 ((
% 98.40/13.01 (ksndpairEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (kpairsurjEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodsndin) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodpairmemEL) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodpairmemER) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodmempaircEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodfstpairEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodsndpairEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodpairsurjEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (dpsetconstrI) =>
% 98.40/13.01 ((
% 98.40/13.01 (dpsetconstrSub) =>
% 98.40/13.01 ((
% 98.40/13.01 (setOfPairsIsBReln) =>
% 98.40/13.01 ((
% 98.40/13.01 (dpsetconstrERa) =>
% 98.40/13.01 ((
% 98.40/13.01 (dpsetconstrEL1) =>
% 98.40/13.01 ((
% 98.40/13.01 (dpsetconstrEL2) =>
% 98.40/13.01 ((
% 98.40/13.01 (dpsetconstrER) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcImageSingleton) =>
% 98.40/13.01 ((
% 98.40/13.01 (apProp) =>
% 98.40/13.01 ((
% 98.40/13.01 (app) =>
% 98.40/13.01 ((
% 98.40/13.01 (infuncsetfunc) =>
% 98.40/13.01 ((
% 98.40/13.01 (ap2p) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcinfuncset) =>
% 98.40/13.01 ((
% 98.40/13.01 (lamProp) =>
% 98.40/13.01 ((
% 98.40/13.01 (lamp) =>
% 98.40/13.01 ((
% 98.40/13.01 (lam2p) =>
% 98.40/13.01 ((
% 98.40/13.01 (brelnall1) =>
% 98.40/13.01 ((
% 98.40/13.01 (brelnall2) =>
% 98.40/13.01 ((
% 98.40/13.01 (ex1E2) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcGraphProp1) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcGraphProp3) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcGraphProp2) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcextLem) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcGraphProp4) =>
% 98.40/13.01 ((
% 98.40/13.01 (subbreln) =>
% 98.40/13.01 ((
% 98.40/13.01 (eqbreln) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcext) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcext2) =>
% 98.40/13.01 ((
% 98.40/13.01 (ap2apEq1) =>
% 98.40/13.01 ((
% 98.40/13.01 (ap2apEq2) =>
% 98.40/13.01 ((
% 98.40/13.01 (beta1) =>
% 98.40/13.01 ((
% 98.40/13.01 (eta1) =>
% 98.40/13.01 ((
% 98.40/13.01 (lam2lamEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (beta2) =>
% 98.40/13.01 ((
% 98.40/13.01 (eta2) =>
% 98.40/13.01 ((
% 98.40/13.01 (iffalseProp1) =>
% 98.40/13.01 ((
% 98.40/13.01 (iffalseProp2) =>
% 98.40/13.01 ((
% 98.40/13.01 (iftrueProp1) =>
% 98.40/13.01 ((
% 98.40/13.01 (iftrueProp2) =>
% 98.40/13.01 ((
% 98.40/13.01 (ifSingleton) =>
% 98.40/13.01 ((
% 98.40/13.01 (ifp) =>
% 98.40/13.01 ((
% 98.40/13.01 (theeq) =>
% 98.40/13.01 ((
% 98.40/13.01 (iftrue) =>
% 98.40/13.01 ((
% 98.40/13.01 (iffalse) =>
% 98.40/13.01 ((
% 98.40/13.01 (iftrueorfalse) =>
% 98.40/13.01 ((
% 98.40/13.01 (binintersectT_lem) =>
% 98.40/13.01 ((
% 98.40/13.01 (binunionT_lem) =>
% 98.40/13.01 ((
% 98.40/13.01 (powersetT_lem) =>
% 98.40/13.01 ((
% 98.40/13.01 (setminusT_lem) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementT_lem) =>
% 98.40/13.01 ((
% 98.40/13.01 (setextT) =>
% 98.40/13.01 ((
% 98.40/13.01 (subsetTI) =>
% 98.40/13.01 ((
% 98.40/13.01 (powersetTI1) =>
% 98.40/13.01 ((
% 98.40/13.01 (powersetTE1) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementTI1) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementTE1) =>
% 98.40/13.01 ((
% 98.40/13.01 (binintersectTELcontra) =>
% 98.40/13.01 ((
% 98.40/13.01 (binintersectTERcontra) =>
% 98.40/13.01 ((
% 98.40/13.01 (contrasubsetT) =>
% 98.40/13.01 ((
% 98.40/13.01 (contrasubsetT1) =>
% 98.40/13.01 ((
% 98.40/13.01 (contrasubsetT2) =>
% 98.40/13.01 ((
% 98.40/13.01 (contrasubsetT3) =>
% 98.40/13.01 ((
% 98.40/13.01 (doubleComplementI1) =>
% 98.40/13.01 ((
% 98.40/13.01 (doubleComplementE1) =>
% 98.40/13.01 ((
% 98.40/13.01 (doubleComplementSub1) =>
% 98.40/13.01 ((
% 98.40/13.01 (doubleComplementSub2) =>
% 98.40/13.01 ((
% 98.40/13.01 (doubleComplementEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementTnotintersectT) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementImpComplementIntersect) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementSubsetComplementIntersect) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementInPowersetComplementIntersect) =>
% 98.40/13.01 ((
% 98.40/13.01 (contraSubsetComplement) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementTcontraSubset) =>
% 98.40/13.01 ((
% 98.40/13.01 (binunionTILcontra) =>
% 98.40/13.01 ((
% 98.40/13.01 (binunionTIRcontra) =>
% 98.40/13.01 ((
% 98.40/13.01 (inIntersectImpInUnion) =>
% 98.40/13.01 ((
% 98.40/13.01 (inIntersectImpInUnion2) =>
% 98.40/13.01 ((
% 98.40/13.01 (inIntersectImpInIntersectUnions) =>
% 98.40/13.01 ((
% 98.40/13.01 (intersectInPowersetIntersectUnions) =>
% 98.40/13.01 ((
% 98.40/13.01 (inComplementUnionImpNotIn1) =>
% 98.40/13.01 ((
% 98.40/13.01 (inComplementUnionImpInComplement1) =>
% 98.40/13.01 ((
% 98.40/13.01 (binunionTE) =>
% 98.40/13.01 ((
% 98.40/13.01 (binunionTEcontra) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan2a1) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementUnionInPowersetComplement) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan2a2) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan1a) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan1b) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan1) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan2a) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan2b2) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan2b) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan2) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz13rule0) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz13rule1) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz13rule2) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz13rule3) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz13rule4) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz1_1) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz1_2) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz1_3) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz1_4) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz1_5) =>
% 98.40/13.01 ((
% 98.40/13.01 (breln1all2) =>
% 98.40/13.01 ((
% 98.40/13.01 (breln1SetBreln1) =>
% 98.40/13.01 ((
% 98.40/13.01 (choice2fnsingleton) =>
% 98.40/13.01 ((
% 98.40/13.01 (!!) @ (
% 98.40/13.01 (('#B') @ (
% 98.40/13.01 !!) @
% 98.40/13.01 (
% 98.40/13.01 (
% 98.40/13.01 ('#S') @ (
% 98.40/13.01 (
% 98.40/13.01 ('#B') @ (
% 98.40/13.01 '#B') @
% 98.40/13.01 breln1)) @
% 98.40/13.01 (
% 98.40/13.01 (
% 98.40/13.01 ('#S') @ dpsetconstr @
% 98.40/13.01 (
% 98.40/13.01 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.40/13.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1223])).
% 98.40/13.01 thf(zip_derived_cl1239, plain,
% 98.40/13.01 (~ (((bs114d) =>
% 98.40/13.01 (((setminusI) =>
% 98.40/13.01 (((setminusEL) =>
% 98.40/13.01 (((setminusER) =>
% 98.40/13.01 (((setminusSubset2) =>
% 98.40/13.01 (((setminusERneg) =>
% 98.40/13.01 (((setminusELneg) =>
% 98.40/13.01 (((setminusILneg) =>
% 98.40/13.01 (((setminusIRneg) =>
% 98.40/13.01 (((setminusLsub) =>
% 98.40/13.01 (((setminusSubset1) =>
% 98.40/13.01 (((symdiffE) =>
% 98.40/13.01 (((symdiffI1) =>
% 98.40/13.01 (((symdiffI2) =>
% 98.40/13.01 (((symdiffIneg1) =>
% 98.40/13.01 (((symdiffIneg2) =>
% 98.40/13.01 (((secondinupair) =>
% 98.40/13.01 (((setukpairIL) =>
% 98.40/13.01 (((setukpairIR) =>
% 98.40/13.01 (((kpairiskpair) =>
% 98.40/13.01 (((kpairp) =>
% 98.40/13.01 (((singletonsubset) =>
% 98.40/13.01 (((singletoninpowerset) =>
% 98.40/13.01 (((singletoninpowunion) =>
% 98.40/13.01 (((upairset2E) =>
% 98.40/13.01 (((upairsubunion) =>
% 98.40/13.01 (((upairinpowunion) =>
% 98.40/13.01 (((ubforcartprodlem1) =>
% 98.40/13.01 (((ubforcartprodlem2) =>
% 98.40/13.01 (((ubforcartprodlem3) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodpairin) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodmempair1) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodmempair) =>
% 98.40/13.01 ((
% 98.40/13.01 (setunionE2) =>
% 98.40/13.01 ((
% 98.40/13.01 (setunionsingleton1) =>
% 98.40/13.01 ((
% 98.40/13.01 (setunionsingleton2) =>
% 98.40/13.01 ((
% 98.40/13.01 (setunionsingleton) =>
% 98.40/13.01 ((
% 98.40/13.01 (singletonprop) =>
% 98.40/13.01 ((
% 98.40/13.01 (ex1E1) =>
% 98.40/13.01 ((
% 98.40/13.01 (ex1I) =>
% 98.40/13.01 ((
% 98.40/13.01 (ex1I2) =>
% 98.40/13.01 ((
% 98.40/13.01 (singletonsuniq) =>
% 98.40/13.01 ((
% 98.40/13.01 (setukpairinjL1) =>
% 98.40/13.01 ((
% 98.40/13.01 (kfstsingleton) =>
% 98.40/13.01 ((
% 98.40/13.01 (theprop) =>
% 98.40/13.01 ((
% 98.40/13.01 (kfstpairEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodfstin) =>
% 98.40/13.01 ((
% 98.40/13.01 (setukpairinjL2) =>
% 98.40/13.01 ((
% 98.40/13.01 (setukpairinjL) =>
% 98.40/13.01 ((
% 98.40/13.01 (setukpairinjR11) =>
% 98.40/13.01 ((
% 98.40/13.01 (setukpairinjR12) =>
% 98.40/13.01 ((
% 98.40/13.01 (setukpairinjR1) =>
% 98.40/13.01 ((
% 98.40/13.01 (upairequniteq) =>
% 98.40/13.01 ((
% 98.40/13.01 (setukpairinjR2) =>
% 98.40/13.01 ((
% 98.40/13.01 (setukpairinjR) =>
% 98.40/13.01 ((
% 98.40/13.01 (ksndsingleton) =>
% 98.40/13.01 ((
% 98.40/13.01 (ksndpairEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (kpairsurjEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodsndin) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodpairmemEL) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodpairmemER) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodmempaircEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodfstpairEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodsndpairEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodpairsurjEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (dpsetconstrI) =>
% 98.40/13.01 ((
% 98.40/13.01 (dpsetconstrSub) =>
% 98.40/13.01 ((
% 98.40/13.01 (setOfPairsIsBReln) =>
% 98.40/13.01 ((
% 98.40/13.01 (dpsetconstrERa) =>
% 98.40/13.01 ((
% 98.40/13.01 (dpsetconstrEL1) =>
% 98.40/13.01 ((
% 98.40/13.01 (dpsetconstrEL2) =>
% 98.40/13.01 ((
% 98.40/13.01 (dpsetconstrER) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcImageSingleton) =>
% 98.40/13.01 ((
% 98.40/13.01 (apProp) =>
% 98.40/13.01 ((
% 98.40/13.01 (app) =>
% 98.40/13.01 ((
% 98.40/13.01 (infuncsetfunc) =>
% 98.40/13.01 ((
% 98.40/13.01 (ap2p) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcinfuncset) =>
% 98.40/13.01 ((
% 98.40/13.01 (lamProp) =>
% 98.40/13.01 ((
% 98.40/13.01 (lamp) =>
% 98.40/13.01 ((
% 98.40/13.01 (lam2p) =>
% 98.40/13.01 ((
% 98.40/13.01 (brelnall1) =>
% 98.40/13.01 ((
% 98.40/13.01 (brelnall2) =>
% 98.40/13.01 ((
% 98.40/13.01 (ex1E2) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcGraphProp1) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcGraphProp3) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcGraphProp2) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcextLem) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcGraphProp4) =>
% 98.40/13.01 ((
% 98.40/13.01 (subbreln) =>
% 98.40/13.01 ((
% 98.40/13.01 (eqbreln) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcext) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcext2) =>
% 98.40/13.01 ((
% 98.40/13.01 (ap2apEq1) =>
% 98.40/13.01 ((
% 98.40/13.01 (ap2apEq2) =>
% 98.40/13.01 ((
% 98.40/13.01 (beta1) =>
% 98.40/13.01 ((
% 98.40/13.01 (eta1) =>
% 98.40/13.01 ((
% 98.40/13.01 (lam2lamEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (beta2) =>
% 98.40/13.01 ((
% 98.40/13.01 (eta2) =>
% 98.40/13.01 ((
% 98.40/13.01 (iffalseProp1) =>
% 98.40/13.01 ((
% 98.40/13.01 (iffalseProp2) =>
% 98.40/13.01 ((
% 98.40/13.01 (iftrueProp1) =>
% 98.40/13.01 ((
% 98.40/13.01 (iftrueProp2) =>
% 98.40/13.01 ((
% 98.40/13.01 (ifSingleton) =>
% 98.40/13.01 ((
% 98.40/13.01 (ifp) =>
% 98.40/13.01 ((
% 98.40/13.01 (theeq) =>
% 98.40/13.01 ((
% 98.40/13.01 (iftrue) =>
% 98.40/13.01 ((
% 98.40/13.01 (iffalse) =>
% 98.40/13.01 ((
% 98.40/13.01 (iftrueorfalse) =>
% 98.40/13.01 ((
% 98.40/13.01 (binintersectT_lem) =>
% 98.40/13.01 ((
% 98.40/13.01 (binunionT_lem) =>
% 98.40/13.01 ((
% 98.40/13.01 (powersetT_lem) =>
% 98.40/13.01 ((
% 98.40/13.01 (setminusT_lem) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementT_lem) =>
% 98.40/13.01 ((
% 98.40/13.01 (setextT) =>
% 98.40/13.01 ((
% 98.40/13.01 (subsetTI) =>
% 98.40/13.01 ((
% 98.40/13.01 (powersetTI1) =>
% 98.40/13.01 ((
% 98.40/13.01 (powersetTE1) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementTI1) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementTE1) =>
% 98.40/13.01 ((
% 98.40/13.01 (binintersectTELcontra) =>
% 98.40/13.01 ((
% 98.40/13.01 (binintersectTERcontra) =>
% 98.40/13.01 ((
% 98.40/13.01 (contrasubsetT) =>
% 98.40/13.01 ((
% 98.40/13.01 (contrasubsetT1) =>
% 98.40/13.01 ((
% 98.40/13.01 (contrasubsetT2) =>
% 98.40/13.01 ((
% 98.40/13.01 (contrasubsetT3) =>
% 98.40/13.01 ((
% 98.40/13.01 (doubleComplementI1) =>
% 98.40/13.01 ((
% 98.40/13.01 (doubleComplementE1) =>
% 98.40/13.01 ((
% 98.40/13.01 (doubleComplementSub1) =>
% 98.40/13.01 ((
% 98.40/13.01 (doubleComplementSub2) =>
% 98.40/13.01 ((
% 98.40/13.01 (doubleComplementEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementTnotintersectT) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementImpComplementIntersect) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementSubsetComplementIntersect) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementInPowersetComplementIntersect) =>
% 98.40/13.01 ((
% 98.40/13.01 (contraSubsetComplement) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementTcontraSubset) =>
% 98.40/13.01 ((
% 98.40/13.01 (binunionTILcontra) =>
% 98.40/13.01 ((
% 98.40/13.01 (binunionTIRcontra) =>
% 98.40/13.01 ((
% 98.40/13.01 (inIntersectImpInUnion) =>
% 98.40/13.01 ((
% 98.40/13.01 (inIntersectImpInUnion2) =>
% 98.40/13.01 ((
% 98.40/13.01 (inIntersectImpInIntersectUnions) =>
% 98.40/13.01 ((
% 98.40/13.01 (intersectInPowersetIntersectUnions) =>
% 98.40/13.01 ((
% 98.40/13.01 (inComplementUnionImpNotIn1) =>
% 98.40/13.01 ((
% 98.40/13.01 (inComplementUnionImpInComplement1) =>
% 98.40/13.01 ((
% 98.40/13.01 (binunionTE) =>
% 98.40/13.01 ((
% 98.40/13.01 (binunionTEcontra) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan2a1) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementUnionInPowersetComplement) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan2a2) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan1a) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan1b) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan1) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan2a) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan2b2) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan2b) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan2) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz13rule0) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz13rule1) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz13rule2) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz13rule3) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz13rule4) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz1_1) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz1_2) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz1_3) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz1_4) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz1_5) =>
% 98.40/13.01 ((
% 98.40/13.01 (breln1all2) =>
% 98.40/13.01 ((
% 98.40/13.01 (breln1SetBreln1) =>
% 98.40/13.01 ((
% 98.40/13.01 (choice2fnsingleton) =>
% 98.40/13.01 ((
% 98.40/13.01 (!!) @ (
% 98.40/13.01 (('#B') @ (
% 98.40/13.01 !!) @
% 98.40/13.01 (
% 98.40/13.01 (
% 98.40/13.01 ('#S') @ (
% 98.40/13.01 (
% 98.40/13.01 ('#B') @ (
% 98.40/13.01 '#B') @
% 98.40/13.01 breln1)) @
% 98.40/13.01 (
% 98.40/13.01 (
% 98.40/13.01 ('#S') @ dpsetconstr @
% 98.40/13.01 (
% 98.40/13.01 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.40/13.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1231])).
% 98.40/13.01 thf(zip_derived_cl1247, plain,
% 98.40/13.01 (~ (((setminusI) =>
% 98.40/13.01 (((setminusEL) =>
% 98.40/13.01 (((setminusER) =>
% 98.40/13.01 (((setminusSubset2) =>
% 98.40/13.01 (((setminusERneg) =>
% 98.40/13.01 (((setminusELneg) =>
% 98.40/13.01 (((setminusILneg) =>
% 98.40/13.01 (((setminusIRneg) =>
% 98.40/13.01 (((setminusLsub) =>
% 98.40/13.01 (((setminusSubset1) =>
% 98.40/13.01 (((symdiffE) =>
% 98.40/13.01 (((symdiffI1) =>
% 98.40/13.01 (((symdiffI2) =>
% 98.40/13.01 (((symdiffIneg1) =>
% 98.40/13.01 (((symdiffIneg2) =>
% 98.40/13.01 (((secondinupair) =>
% 98.40/13.01 (((setukpairIL) =>
% 98.40/13.01 (((setukpairIR) =>
% 98.40/13.01 (((kpairiskpair) =>
% 98.40/13.01 (((kpairp) =>
% 98.40/13.01 (((singletonsubset) =>
% 98.40/13.01 (((singletoninpowerset) =>
% 98.40/13.01 (((singletoninpowunion) =>
% 98.40/13.01 (((upairset2E) =>
% 98.40/13.01 (((upairsubunion) =>
% 98.40/13.01 (((upairinpowunion) =>
% 98.40/13.01 (((ubforcartprodlem1) =>
% 98.40/13.01 (((ubforcartprodlem2) =>
% 98.40/13.01 (((ubforcartprodlem3) =>
% 98.40/13.01 (((cartprodpairin) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodmempair1) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodmempair) =>
% 98.40/13.01 ((
% 98.40/13.01 (setunionE2) =>
% 98.40/13.01 ((
% 98.40/13.01 (setunionsingleton1) =>
% 98.40/13.01 ((
% 98.40/13.01 (setunionsingleton2) =>
% 98.40/13.01 ((
% 98.40/13.01 (setunionsingleton) =>
% 98.40/13.01 ((
% 98.40/13.01 (singletonprop) =>
% 98.40/13.01 ((
% 98.40/13.01 (ex1E1) =>
% 98.40/13.01 ((
% 98.40/13.01 (ex1I) =>
% 98.40/13.01 ((
% 98.40/13.01 (ex1I2) =>
% 98.40/13.01 ((
% 98.40/13.01 (singletonsuniq) =>
% 98.40/13.01 ((
% 98.40/13.01 (setukpairinjL1) =>
% 98.40/13.01 ((
% 98.40/13.01 (kfstsingleton) =>
% 98.40/13.01 ((
% 98.40/13.01 (theprop) =>
% 98.40/13.01 ((
% 98.40/13.01 (kfstpairEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodfstin) =>
% 98.40/13.01 ((
% 98.40/13.01 (setukpairinjL2) =>
% 98.40/13.01 ((
% 98.40/13.01 (setukpairinjL) =>
% 98.40/13.01 ((
% 98.40/13.01 (setukpairinjR11) =>
% 98.40/13.01 ((
% 98.40/13.01 (setukpairinjR12) =>
% 98.40/13.01 ((
% 98.40/13.01 (setukpairinjR1) =>
% 98.40/13.01 ((
% 98.40/13.01 (upairequniteq) =>
% 98.40/13.01 ((
% 98.40/13.01 (setukpairinjR2) =>
% 98.40/13.01 ((
% 98.40/13.01 (setukpairinjR) =>
% 98.40/13.01 ((
% 98.40/13.01 (ksndsingleton) =>
% 98.40/13.01 ((
% 98.40/13.01 (ksndpairEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (kpairsurjEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodsndin) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodpairmemEL) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodpairmemER) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodmempaircEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodfstpairEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodsndpairEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodpairsurjEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (dpsetconstrI) =>
% 98.40/13.01 ((
% 98.40/13.01 (dpsetconstrSub) =>
% 98.40/13.01 ((
% 98.40/13.01 (setOfPairsIsBReln) =>
% 98.40/13.01 ((
% 98.40/13.01 (dpsetconstrERa) =>
% 98.40/13.01 ((
% 98.40/13.01 (dpsetconstrEL1) =>
% 98.40/13.01 ((
% 98.40/13.01 (dpsetconstrEL2) =>
% 98.40/13.01 ((
% 98.40/13.01 (dpsetconstrER) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcImageSingleton) =>
% 98.40/13.01 ((
% 98.40/13.01 (apProp) =>
% 98.40/13.01 ((
% 98.40/13.01 (app) =>
% 98.40/13.01 ((
% 98.40/13.01 (infuncsetfunc) =>
% 98.40/13.01 ((
% 98.40/13.01 (ap2p) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcinfuncset) =>
% 98.40/13.01 ((
% 98.40/13.01 (lamProp) =>
% 98.40/13.01 ((
% 98.40/13.01 (lamp) =>
% 98.40/13.01 ((
% 98.40/13.01 (lam2p) =>
% 98.40/13.01 ((
% 98.40/13.01 (brelnall1) =>
% 98.40/13.01 ((
% 98.40/13.01 (brelnall2) =>
% 98.40/13.01 ((
% 98.40/13.01 (ex1E2) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcGraphProp1) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcGraphProp3) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcGraphProp2) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcextLem) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcGraphProp4) =>
% 98.40/13.01 ((
% 98.40/13.01 (subbreln) =>
% 98.40/13.01 ((
% 98.40/13.01 (eqbreln) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcext) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcext2) =>
% 98.40/13.01 ((
% 98.40/13.01 (ap2apEq1) =>
% 98.40/13.01 ((
% 98.40/13.01 (ap2apEq2) =>
% 98.40/13.01 ((
% 98.40/13.01 (beta1) =>
% 98.40/13.01 ((
% 98.40/13.01 (eta1) =>
% 98.40/13.01 ((
% 98.40/13.01 (lam2lamEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (beta2) =>
% 98.40/13.01 ((
% 98.40/13.01 (eta2) =>
% 98.40/13.01 ((
% 98.40/13.01 (iffalseProp1) =>
% 98.40/13.01 ((
% 98.40/13.01 (iffalseProp2) =>
% 98.40/13.01 ((
% 98.40/13.01 (iftrueProp1) =>
% 98.40/13.01 ((
% 98.40/13.01 (iftrueProp2) =>
% 98.40/13.01 ((
% 98.40/13.01 (ifSingleton) =>
% 98.40/13.01 ((
% 98.40/13.01 (ifp) =>
% 98.40/13.01 ((
% 98.40/13.01 (theeq) =>
% 98.40/13.01 ((
% 98.40/13.01 (iftrue) =>
% 98.40/13.01 ((
% 98.40/13.01 (iffalse) =>
% 98.40/13.01 ((
% 98.40/13.01 (iftrueorfalse) =>
% 98.40/13.01 ((
% 98.40/13.01 (binintersectT_lem) =>
% 98.40/13.01 ((
% 98.40/13.01 (binunionT_lem) =>
% 98.40/13.01 ((
% 98.40/13.01 (powersetT_lem) =>
% 98.40/13.01 ((
% 98.40/13.01 (setminusT_lem) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementT_lem) =>
% 98.40/13.01 ((
% 98.40/13.01 (setextT) =>
% 98.40/13.01 ((
% 98.40/13.01 (subsetTI) =>
% 98.40/13.01 ((
% 98.40/13.01 (powersetTI1) =>
% 98.40/13.01 ((
% 98.40/13.01 (powersetTE1) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementTI1) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementTE1) =>
% 98.40/13.01 ((
% 98.40/13.01 (binintersectTELcontra) =>
% 98.40/13.01 ((
% 98.40/13.01 (binintersectTERcontra) =>
% 98.40/13.01 ((
% 98.40/13.01 (contrasubsetT) =>
% 98.40/13.01 ((
% 98.40/13.01 (contrasubsetT1) =>
% 98.40/13.01 ((
% 98.40/13.01 (contrasubsetT2) =>
% 98.40/13.01 ((
% 98.40/13.01 (contrasubsetT3) =>
% 98.40/13.01 ((
% 98.40/13.01 (doubleComplementI1) =>
% 98.40/13.01 ((
% 98.40/13.01 (doubleComplementE1) =>
% 98.40/13.01 ((
% 98.40/13.01 (doubleComplementSub1) =>
% 98.40/13.01 ((
% 98.40/13.01 (doubleComplementSub2) =>
% 98.40/13.01 ((
% 98.40/13.01 (doubleComplementEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementTnotintersectT) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementImpComplementIntersect) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementSubsetComplementIntersect) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementInPowersetComplementIntersect) =>
% 98.40/13.01 ((
% 98.40/13.01 (contraSubsetComplement) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementTcontraSubset) =>
% 98.40/13.01 ((
% 98.40/13.01 (binunionTILcontra) =>
% 98.40/13.01 ((
% 98.40/13.01 (binunionTIRcontra) =>
% 98.40/13.01 ((
% 98.40/13.01 (inIntersectImpInUnion) =>
% 98.40/13.01 ((
% 98.40/13.01 (inIntersectImpInUnion2) =>
% 98.40/13.01 ((
% 98.40/13.01 (inIntersectImpInIntersectUnions) =>
% 98.40/13.01 ((
% 98.40/13.01 (intersectInPowersetIntersectUnions) =>
% 98.40/13.01 ((
% 98.40/13.01 (inComplementUnionImpNotIn1) =>
% 98.40/13.01 ((
% 98.40/13.01 (inComplementUnionImpInComplement1) =>
% 98.40/13.01 ((
% 98.40/13.01 (binunionTE) =>
% 98.40/13.01 ((
% 98.40/13.01 (binunionTEcontra) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan2a1) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementUnionInPowersetComplement) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan2a2) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan1a) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan1b) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan1) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan2a) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan2b2) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan2b) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan2) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz13rule0) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz13rule1) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz13rule2) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz13rule3) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz13rule4) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz1_1) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz1_2) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz1_3) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz1_4) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz1_5) =>
% 98.40/13.01 ((
% 98.40/13.01 (breln1all2) =>
% 98.40/13.01 ((
% 98.40/13.01 (breln1SetBreln1) =>
% 98.40/13.01 ((
% 98.40/13.01 (choice2fnsingleton) =>
% 98.40/13.01 ((
% 98.40/13.01 (!!) @ (
% 98.40/13.01 (('#B') @ (
% 98.40/13.01 !!) @
% 98.40/13.01 (
% 98.40/13.01 (
% 98.40/13.01 ('#S') @ (
% 98.40/13.01 (
% 98.40/13.01 ('#B') @ (
% 98.40/13.01 '#B') @
% 98.40/13.01 breln1)) @
% 98.40/13.01 (
% 98.40/13.01 (
% 98.40/13.01 ('#S') @ dpsetconstr @
% 98.40/13.01 (
% 98.40/13.01 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.40/13.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1239])).
% 98.40/13.01 thf(zip_derived_cl1255, plain,
% 98.40/13.01 (~ (((setminusEL) =>
% 98.40/13.01 (((setminusER) =>
% 98.40/13.01 (((setminusSubset2) =>
% 98.40/13.01 (((setminusERneg) =>
% 98.40/13.01 (((setminusELneg) =>
% 98.40/13.01 (((setminusILneg) =>
% 98.40/13.01 (((setminusIRneg) =>
% 98.40/13.01 (((setminusLsub) =>
% 98.40/13.01 (((setminusSubset1) =>
% 98.40/13.01 (((symdiffE) =>
% 98.40/13.01 (((symdiffI1) =>
% 98.40/13.01 (((symdiffI2) =>
% 98.40/13.01 (((symdiffIneg1) =>
% 98.40/13.01 (((symdiffIneg2) =>
% 98.40/13.01 (((secondinupair) =>
% 98.40/13.01 (((setukpairIL) =>
% 98.40/13.01 (((setukpairIR) =>
% 98.40/13.01 (((kpairiskpair) =>
% 98.40/13.01 (((kpairp) =>
% 98.40/13.01 (((singletonsubset) =>
% 98.40/13.01 (((singletoninpowerset) =>
% 98.40/13.01 (((singletoninpowunion) =>
% 98.40/13.01 (((upairset2E) =>
% 98.40/13.01 (((upairsubunion) =>
% 98.40/13.01 (((upairinpowunion) =>
% 98.40/13.01 (((ubforcartprodlem1) =>
% 98.40/13.01 (((ubforcartprodlem2) =>
% 98.40/13.01 (((ubforcartprodlem3) =>
% 98.40/13.01 (((cartprodpairin) =>
% 98.40/13.01 (((cartprodmempair1) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodmempair) =>
% 98.40/13.01 ((
% 98.40/13.01 (setunionE2) =>
% 98.40/13.01 ((
% 98.40/13.01 (setunionsingleton1) =>
% 98.40/13.01 ((
% 98.40/13.01 (setunionsingleton2) =>
% 98.40/13.01 ((
% 98.40/13.01 (setunionsingleton) =>
% 98.40/13.01 ((
% 98.40/13.01 (singletonprop) =>
% 98.40/13.01 ((
% 98.40/13.01 (ex1E1) =>
% 98.40/13.01 ((
% 98.40/13.01 (ex1I) =>
% 98.40/13.01 ((
% 98.40/13.01 (ex1I2) =>
% 98.40/13.01 ((
% 98.40/13.01 (singletonsuniq) =>
% 98.40/13.01 ((
% 98.40/13.01 (setukpairinjL1) =>
% 98.40/13.01 ((
% 98.40/13.01 (kfstsingleton) =>
% 98.40/13.01 ((
% 98.40/13.01 (theprop) =>
% 98.40/13.01 ((
% 98.40/13.01 (kfstpairEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodfstin) =>
% 98.40/13.01 ((
% 98.40/13.01 (setukpairinjL2) =>
% 98.40/13.01 ((
% 98.40/13.01 (setukpairinjL) =>
% 98.40/13.01 ((
% 98.40/13.01 (setukpairinjR11) =>
% 98.40/13.01 ((
% 98.40/13.01 (setukpairinjR12) =>
% 98.40/13.01 ((
% 98.40/13.01 (setukpairinjR1) =>
% 98.40/13.01 ((
% 98.40/13.01 (upairequniteq) =>
% 98.40/13.01 ((
% 98.40/13.01 (setukpairinjR2) =>
% 98.40/13.01 ((
% 98.40/13.01 (setukpairinjR) =>
% 98.40/13.01 ((
% 98.40/13.01 (ksndsingleton) =>
% 98.40/13.01 ((
% 98.40/13.01 (ksndpairEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (kpairsurjEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodsndin) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodpairmemEL) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodpairmemER) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodmempaircEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodfstpairEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodsndpairEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodpairsurjEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (dpsetconstrI) =>
% 98.40/13.01 ((
% 98.40/13.01 (dpsetconstrSub) =>
% 98.40/13.01 ((
% 98.40/13.01 (setOfPairsIsBReln) =>
% 98.40/13.01 ((
% 98.40/13.01 (dpsetconstrERa) =>
% 98.40/13.01 ((
% 98.40/13.01 (dpsetconstrEL1) =>
% 98.40/13.01 ((
% 98.40/13.01 (dpsetconstrEL2) =>
% 98.40/13.01 ((
% 98.40/13.01 (dpsetconstrER) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcImageSingleton) =>
% 98.40/13.01 ((
% 98.40/13.01 (apProp) =>
% 98.40/13.01 ((
% 98.40/13.01 (app) =>
% 98.40/13.01 ((
% 98.40/13.01 (infuncsetfunc) =>
% 98.40/13.01 ((
% 98.40/13.01 (ap2p) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcinfuncset) =>
% 98.40/13.01 ((
% 98.40/13.01 (lamProp) =>
% 98.40/13.01 ((
% 98.40/13.01 (lamp) =>
% 98.40/13.01 ((
% 98.40/13.01 (lam2p) =>
% 98.40/13.01 ((
% 98.40/13.01 (brelnall1) =>
% 98.40/13.01 ((
% 98.40/13.01 (brelnall2) =>
% 98.40/13.01 ((
% 98.40/13.01 (ex1E2) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcGraphProp1) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcGraphProp3) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcGraphProp2) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcextLem) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcGraphProp4) =>
% 98.40/13.01 ((
% 98.40/13.01 (subbreln) =>
% 98.40/13.01 ((
% 98.40/13.01 (eqbreln) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcext) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcext2) =>
% 98.40/13.01 ((
% 98.40/13.01 (ap2apEq1) =>
% 98.40/13.01 ((
% 98.40/13.01 (ap2apEq2) =>
% 98.40/13.01 ((
% 98.40/13.01 (beta1) =>
% 98.40/13.01 ((
% 98.40/13.01 (eta1) =>
% 98.40/13.01 ((
% 98.40/13.01 (lam2lamEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (beta2) =>
% 98.40/13.01 ((
% 98.40/13.01 (eta2) =>
% 98.40/13.01 ((
% 98.40/13.01 (iffalseProp1) =>
% 98.40/13.01 ((
% 98.40/13.01 (iffalseProp2) =>
% 98.40/13.01 ((
% 98.40/13.01 (iftrueProp1) =>
% 98.40/13.01 ((
% 98.40/13.01 (iftrueProp2) =>
% 98.40/13.01 ((
% 98.40/13.01 (ifSingleton) =>
% 98.40/13.01 ((
% 98.40/13.01 (ifp) =>
% 98.40/13.01 ((
% 98.40/13.01 (theeq) =>
% 98.40/13.01 ((
% 98.40/13.01 (iftrue) =>
% 98.40/13.01 ((
% 98.40/13.01 (iffalse) =>
% 98.40/13.01 ((
% 98.40/13.01 (iftrueorfalse) =>
% 98.40/13.01 ((
% 98.40/13.01 (binintersectT_lem) =>
% 98.40/13.01 ((
% 98.40/13.01 (binunionT_lem) =>
% 98.40/13.01 ((
% 98.40/13.01 (powersetT_lem) =>
% 98.40/13.01 ((
% 98.40/13.01 (setminusT_lem) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementT_lem) =>
% 98.40/13.01 ((
% 98.40/13.01 (setextT) =>
% 98.40/13.01 ((
% 98.40/13.01 (subsetTI) =>
% 98.40/13.01 ((
% 98.40/13.01 (powersetTI1) =>
% 98.40/13.01 ((
% 98.40/13.01 (powersetTE1) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementTI1) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementTE1) =>
% 98.40/13.01 ((
% 98.40/13.01 (binintersectTELcontra) =>
% 98.40/13.01 ((
% 98.40/13.01 (binintersectTERcontra) =>
% 98.40/13.01 ((
% 98.40/13.01 (contrasubsetT) =>
% 98.40/13.01 ((
% 98.40/13.01 (contrasubsetT1) =>
% 98.40/13.01 ((
% 98.40/13.01 (contrasubsetT2) =>
% 98.40/13.01 ((
% 98.40/13.01 (contrasubsetT3) =>
% 98.40/13.01 ((
% 98.40/13.01 (doubleComplementI1) =>
% 98.40/13.01 ((
% 98.40/13.01 (doubleComplementE1) =>
% 98.40/13.01 ((
% 98.40/13.01 (doubleComplementSub1) =>
% 98.40/13.01 ((
% 98.40/13.01 (doubleComplementSub2) =>
% 98.40/13.01 ((
% 98.40/13.01 (doubleComplementEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementTnotintersectT) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementImpComplementIntersect) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementSubsetComplementIntersect) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementInPowersetComplementIntersect) =>
% 98.40/13.01 ((
% 98.40/13.01 (contraSubsetComplement) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementTcontraSubset) =>
% 98.40/13.01 ((
% 98.40/13.01 (binunionTILcontra) =>
% 98.40/13.01 ((
% 98.40/13.01 (binunionTIRcontra) =>
% 98.40/13.01 ((
% 98.40/13.01 (inIntersectImpInUnion) =>
% 98.40/13.01 ((
% 98.40/13.01 (inIntersectImpInUnion2) =>
% 98.40/13.01 ((
% 98.40/13.01 (inIntersectImpInIntersectUnions) =>
% 98.40/13.01 ((
% 98.40/13.01 (intersectInPowersetIntersectUnions) =>
% 98.40/13.01 ((
% 98.40/13.01 (inComplementUnionImpNotIn1) =>
% 98.40/13.01 ((
% 98.40/13.01 (inComplementUnionImpInComplement1) =>
% 98.40/13.01 ((
% 98.40/13.01 (binunionTE) =>
% 98.40/13.01 ((
% 98.40/13.01 (binunionTEcontra) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan2a1) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementUnionInPowersetComplement) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan2a2) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan1a) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan1b) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan1) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan2a) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan2b2) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan2b) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan2) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz13rule0) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz13rule1) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz13rule2) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz13rule3) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz13rule4) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz1_1) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz1_2) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz1_3) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz1_4) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz1_5) =>
% 98.40/13.01 ((
% 98.40/13.01 (breln1all2) =>
% 98.40/13.01 ((
% 98.40/13.01 (breln1SetBreln1) =>
% 98.40/13.01 ((
% 98.40/13.01 (choice2fnsingleton) =>
% 98.40/13.01 ((
% 98.40/13.01 (!!) @ (
% 98.40/13.01 (('#B') @ (
% 98.40/13.01 !!) @
% 98.40/13.01 (
% 98.40/13.01 (
% 98.40/13.01 ('#S') @ (
% 98.40/13.01 (
% 98.40/13.01 ('#B') @ (
% 98.40/13.01 '#B') @
% 98.40/13.01 breln1)) @
% 98.40/13.01 (
% 98.40/13.01 (
% 98.40/13.01 ('#S') @ dpsetconstr @
% 98.40/13.01 (
% 98.40/13.01 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.40/13.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1247])).
% 98.40/13.01 thf(zip_derived_cl1264, plain,
% 98.40/13.01 (~ (((setminusER) =>
% 98.40/13.01 (((setminusSubset2) =>
% 98.40/13.01 (((setminusERneg) =>
% 98.40/13.01 (((setminusELneg) =>
% 98.40/13.01 (((setminusILneg) =>
% 98.40/13.01 (((setminusIRneg) =>
% 98.40/13.01 (((setminusLsub) =>
% 98.40/13.01 (((setminusSubset1) =>
% 98.40/13.01 (((symdiffE) =>
% 98.40/13.01 (((symdiffI1) =>
% 98.40/13.01 (((symdiffI2) =>
% 98.40/13.01 (((symdiffIneg1) =>
% 98.40/13.01 (((symdiffIneg2) =>
% 98.40/13.01 (((secondinupair) =>
% 98.40/13.01 (((setukpairIL) =>
% 98.40/13.01 (((setukpairIR) =>
% 98.40/13.01 (((kpairiskpair) =>
% 98.40/13.01 (((kpairp) =>
% 98.40/13.01 (((singletonsubset) =>
% 98.40/13.01 (((singletoninpowerset) =>
% 98.40/13.01 (((singletoninpowunion) =>
% 98.40/13.01 (((upairset2E) =>
% 98.40/13.01 (((upairsubunion) =>
% 98.40/13.01 (((upairinpowunion) =>
% 98.40/13.01 (((ubforcartprodlem1) =>
% 98.40/13.01 (((ubforcartprodlem2) =>
% 98.40/13.01 (((ubforcartprodlem3) =>
% 98.40/13.01 (((cartprodpairin) =>
% 98.40/13.01 (((cartprodmempair1) =>
% 98.40/13.01 (((cartprodmempair) =>
% 98.40/13.01 ((
% 98.40/13.01 (setunionE2) =>
% 98.40/13.01 ((
% 98.40/13.01 (setunionsingleton1) =>
% 98.40/13.01 ((
% 98.40/13.01 (setunionsingleton2) =>
% 98.40/13.01 ((
% 98.40/13.01 (setunionsingleton) =>
% 98.40/13.01 ((
% 98.40/13.01 (singletonprop) =>
% 98.40/13.01 ((
% 98.40/13.01 (ex1E1) =>
% 98.40/13.01 ((
% 98.40/13.01 (ex1I) =>
% 98.40/13.01 ((
% 98.40/13.01 (ex1I2) =>
% 98.40/13.01 ((
% 98.40/13.01 (singletonsuniq) =>
% 98.40/13.01 ((
% 98.40/13.01 (setukpairinjL1) =>
% 98.40/13.01 ((
% 98.40/13.01 (kfstsingleton) =>
% 98.40/13.01 ((
% 98.40/13.01 (theprop) =>
% 98.40/13.01 ((
% 98.40/13.01 (kfstpairEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodfstin) =>
% 98.40/13.01 ((
% 98.40/13.01 (setukpairinjL2) =>
% 98.40/13.01 ((
% 98.40/13.01 (setukpairinjL) =>
% 98.40/13.01 ((
% 98.40/13.01 (setukpairinjR11) =>
% 98.40/13.01 ((
% 98.40/13.01 (setukpairinjR12) =>
% 98.40/13.01 ((
% 98.40/13.01 (setukpairinjR1) =>
% 98.40/13.01 ((
% 98.40/13.01 (upairequniteq) =>
% 98.40/13.01 ((
% 98.40/13.01 (setukpairinjR2) =>
% 98.40/13.01 ((
% 98.40/13.01 (setukpairinjR) =>
% 98.40/13.01 ((
% 98.40/13.01 (ksndsingleton) =>
% 98.40/13.01 ((
% 98.40/13.01 (ksndpairEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (kpairsurjEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodsndin) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodpairmemEL) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodpairmemER) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodmempaircEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodfstpairEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodsndpairEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodpairsurjEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (dpsetconstrI) =>
% 98.40/13.01 ((
% 98.40/13.01 (dpsetconstrSub) =>
% 98.40/13.01 ((
% 98.40/13.01 (setOfPairsIsBReln) =>
% 98.40/13.01 ((
% 98.40/13.01 (dpsetconstrERa) =>
% 98.40/13.01 ((
% 98.40/13.01 (dpsetconstrEL1) =>
% 98.40/13.01 ((
% 98.40/13.01 (dpsetconstrEL2) =>
% 98.40/13.01 ((
% 98.40/13.01 (dpsetconstrER) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcImageSingleton) =>
% 98.40/13.01 ((
% 98.40/13.01 (apProp) =>
% 98.40/13.01 ((
% 98.40/13.01 (app) =>
% 98.40/13.01 ((
% 98.40/13.01 (infuncsetfunc) =>
% 98.40/13.01 ((
% 98.40/13.01 (ap2p) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcinfuncset) =>
% 98.40/13.01 ((
% 98.40/13.01 (lamProp) =>
% 98.40/13.01 ((
% 98.40/13.01 (lamp) =>
% 98.40/13.01 ((
% 98.40/13.01 (lam2p) =>
% 98.40/13.01 ((
% 98.40/13.01 (brelnall1) =>
% 98.40/13.01 ((
% 98.40/13.01 (brelnall2) =>
% 98.40/13.01 ((
% 98.40/13.01 (ex1E2) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcGraphProp1) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcGraphProp3) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcGraphProp2) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcextLem) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcGraphProp4) =>
% 98.40/13.01 ((
% 98.40/13.01 (subbreln) =>
% 98.40/13.01 ((
% 98.40/13.01 (eqbreln) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcext) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcext2) =>
% 98.40/13.01 ((
% 98.40/13.01 (ap2apEq1) =>
% 98.40/13.01 ((
% 98.40/13.01 (ap2apEq2) =>
% 98.40/13.01 ((
% 98.40/13.01 (beta1) =>
% 98.40/13.01 ((
% 98.40/13.01 (eta1) =>
% 98.40/13.01 ((
% 98.40/13.01 (lam2lamEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (beta2) =>
% 98.40/13.01 ((
% 98.40/13.01 (eta2) =>
% 98.40/13.01 ((
% 98.40/13.01 (iffalseProp1) =>
% 98.40/13.01 ((
% 98.40/13.01 (iffalseProp2) =>
% 98.40/13.01 ((
% 98.40/13.01 (iftrueProp1) =>
% 98.40/13.01 ((
% 98.40/13.01 (iftrueProp2) =>
% 98.40/13.01 ((
% 98.40/13.01 (ifSingleton) =>
% 98.40/13.01 ((
% 98.40/13.01 (ifp) =>
% 98.40/13.01 ((
% 98.40/13.01 (theeq) =>
% 98.40/13.01 ((
% 98.40/13.01 (iftrue) =>
% 98.40/13.01 ((
% 98.40/13.01 (iffalse) =>
% 98.40/13.01 ((
% 98.40/13.01 (iftrueorfalse) =>
% 98.40/13.01 ((
% 98.40/13.01 (binintersectT_lem) =>
% 98.40/13.01 ((
% 98.40/13.01 (binunionT_lem) =>
% 98.40/13.01 ((
% 98.40/13.01 (powersetT_lem) =>
% 98.40/13.01 ((
% 98.40/13.01 (setminusT_lem) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementT_lem) =>
% 98.40/13.01 ((
% 98.40/13.01 (setextT) =>
% 98.40/13.01 ((
% 98.40/13.01 (subsetTI) =>
% 98.40/13.01 ((
% 98.40/13.01 (powersetTI1) =>
% 98.40/13.01 ((
% 98.40/13.01 (powersetTE1) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementTI1) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementTE1) =>
% 98.40/13.01 ((
% 98.40/13.01 (binintersectTELcontra) =>
% 98.40/13.01 ((
% 98.40/13.01 (binintersectTERcontra) =>
% 98.40/13.01 ((
% 98.40/13.01 (contrasubsetT) =>
% 98.40/13.01 ((
% 98.40/13.01 (contrasubsetT1) =>
% 98.40/13.01 ((
% 98.40/13.01 (contrasubsetT2) =>
% 98.40/13.01 ((
% 98.40/13.01 (contrasubsetT3) =>
% 98.40/13.01 ((
% 98.40/13.01 (doubleComplementI1) =>
% 98.40/13.01 ((
% 98.40/13.01 (doubleComplementE1) =>
% 98.40/13.01 ((
% 98.40/13.01 (doubleComplementSub1) =>
% 98.40/13.01 ((
% 98.40/13.01 (doubleComplementSub2) =>
% 98.40/13.01 ((
% 98.40/13.01 (doubleComplementEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementTnotintersectT) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementImpComplementIntersect) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementSubsetComplementIntersect) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementInPowersetComplementIntersect) =>
% 98.40/13.01 ((
% 98.40/13.01 (contraSubsetComplement) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementTcontraSubset) =>
% 98.40/13.01 ((
% 98.40/13.01 (binunionTILcontra) =>
% 98.40/13.01 ((
% 98.40/13.01 (binunionTIRcontra) =>
% 98.40/13.01 ((
% 98.40/13.01 (inIntersectImpInUnion) =>
% 98.40/13.01 ((
% 98.40/13.01 (inIntersectImpInUnion2) =>
% 98.40/13.01 ((
% 98.40/13.01 (inIntersectImpInIntersectUnions) =>
% 98.40/13.01 ((
% 98.40/13.01 (intersectInPowersetIntersectUnions) =>
% 98.40/13.01 ((
% 98.40/13.01 (inComplementUnionImpNotIn1) =>
% 98.40/13.01 ((
% 98.40/13.01 (inComplementUnionImpInComplement1) =>
% 98.40/13.01 ((
% 98.40/13.01 (binunionTE) =>
% 98.40/13.01 ((
% 98.40/13.01 (binunionTEcontra) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan2a1) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementUnionInPowersetComplement) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan2a2) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan1a) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan1b) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan1) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan2a) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan2b2) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan2b) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan2) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz13rule0) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz13rule1) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz13rule2) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz13rule3) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz13rule4) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz1_1) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz1_2) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz1_3) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz1_4) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz1_5) =>
% 98.40/13.01 ((
% 98.40/13.01 (breln1all2) =>
% 98.40/13.01 ((
% 98.40/13.01 (breln1SetBreln1) =>
% 98.40/13.01 ((
% 98.40/13.01 (choice2fnsingleton) =>
% 98.40/13.01 ((
% 98.40/13.01 (!!) @ (
% 98.40/13.01 (('#B') @ (
% 98.40/13.01 !!) @
% 98.40/13.01 (
% 98.40/13.01 (
% 98.40/13.01 ('#S') @ (
% 98.40/13.01 (
% 98.40/13.01 ('#B') @ (
% 98.40/13.01 '#B') @
% 98.40/13.01 breln1)) @
% 98.40/13.01 (
% 98.40/13.01 (
% 98.40/13.01 ('#S') @ dpsetconstr @
% 98.40/13.01 (
% 98.40/13.01 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.40/13.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1255])).
% 98.40/13.01 thf(zip_derived_cl1272, plain,
% 98.40/13.01 (~ (((setminusSubset2) =>
% 98.40/13.01 (((setminusERneg) =>
% 98.40/13.01 (((setminusELneg) =>
% 98.40/13.01 (((setminusILneg) =>
% 98.40/13.01 (((setminusIRneg) =>
% 98.40/13.01 (((setminusLsub) =>
% 98.40/13.01 (((setminusSubset1) =>
% 98.40/13.01 (((symdiffE) =>
% 98.40/13.01 (((symdiffI1) =>
% 98.40/13.01 (((symdiffI2) =>
% 98.40/13.01 (((symdiffIneg1) =>
% 98.40/13.01 (((symdiffIneg2) =>
% 98.40/13.01 (((secondinupair) =>
% 98.40/13.01 (((setukpairIL) =>
% 98.40/13.01 (((setukpairIR) =>
% 98.40/13.01 (((kpairiskpair) =>
% 98.40/13.01 (((kpairp) =>
% 98.40/13.01 (((singletonsubset) =>
% 98.40/13.01 (((singletoninpowerset) =>
% 98.40/13.01 (((singletoninpowunion) =>
% 98.40/13.01 (((upairset2E) =>
% 98.40/13.01 (((upairsubunion) =>
% 98.40/13.01 (((upairinpowunion) =>
% 98.40/13.01 (((ubforcartprodlem1) =>
% 98.40/13.01 (((ubforcartprodlem2) =>
% 98.40/13.01 (((ubforcartprodlem3) =>
% 98.40/13.01 (((cartprodpairin) =>
% 98.40/13.01 (((cartprodmempair1) =>
% 98.40/13.01 (((cartprodmempair) =>
% 98.40/13.01 (((setunionE2) =>
% 98.40/13.01 ((
% 98.40/13.01 (setunionsingleton1) =>
% 98.40/13.01 ((
% 98.40/13.01 (setunionsingleton2) =>
% 98.40/13.01 ((
% 98.40/13.01 (setunionsingleton) =>
% 98.40/13.01 ((
% 98.40/13.01 (singletonprop) =>
% 98.40/13.01 ((
% 98.40/13.01 (ex1E1) =>
% 98.40/13.01 ((
% 98.40/13.01 (ex1I) =>
% 98.40/13.01 ((
% 98.40/13.01 (ex1I2) =>
% 98.40/13.01 ((
% 98.40/13.01 (singletonsuniq) =>
% 98.40/13.01 ((
% 98.40/13.01 (setukpairinjL1) =>
% 98.40/13.01 ((
% 98.40/13.01 (kfstsingleton) =>
% 98.40/13.01 ((
% 98.40/13.01 (theprop) =>
% 98.40/13.01 ((
% 98.40/13.01 (kfstpairEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodfstin) =>
% 98.40/13.01 ((
% 98.40/13.01 (setukpairinjL2) =>
% 98.40/13.01 ((
% 98.40/13.01 (setukpairinjL) =>
% 98.40/13.01 ((
% 98.40/13.01 (setukpairinjR11) =>
% 98.40/13.01 ((
% 98.40/13.01 (setukpairinjR12) =>
% 98.40/13.01 ((
% 98.40/13.01 (setukpairinjR1) =>
% 98.40/13.01 ((
% 98.40/13.01 (upairequniteq) =>
% 98.40/13.01 ((
% 98.40/13.01 (setukpairinjR2) =>
% 98.40/13.01 ((
% 98.40/13.01 (setukpairinjR) =>
% 98.40/13.01 ((
% 98.40/13.01 (ksndsingleton) =>
% 98.40/13.01 ((
% 98.40/13.01 (ksndpairEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (kpairsurjEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodsndin) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodpairmemEL) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodpairmemER) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodmempaircEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodfstpairEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodsndpairEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodpairsurjEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (dpsetconstrI) =>
% 98.40/13.01 ((
% 98.40/13.01 (dpsetconstrSub) =>
% 98.40/13.01 ((
% 98.40/13.01 (setOfPairsIsBReln) =>
% 98.40/13.01 ((
% 98.40/13.01 (dpsetconstrERa) =>
% 98.40/13.01 ((
% 98.40/13.01 (dpsetconstrEL1) =>
% 98.40/13.01 ((
% 98.40/13.01 (dpsetconstrEL2) =>
% 98.40/13.01 ((
% 98.40/13.01 (dpsetconstrER) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcImageSingleton) =>
% 98.40/13.01 ((
% 98.40/13.01 (apProp) =>
% 98.40/13.01 ((
% 98.40/13.01 (app) =>
% 98.40/13.01 ((
% 98.40/13.01 (infuncsetfunc) =>
% 98.40/13.01 ((
% 98.40/13.01 (ap2p) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcinfuncset) =>
% 98.40/13.01 ((
% 98.40/13.01 (lamProp) =>
% 98.40/13.01 ((
% 98.40/13.01 (lamp) =>
% 98.40/13.01 ((
% 98.40/13.01 (lam2p) =>
% 98.40/13.01 ((
% 98.40/13.01 (brelnall1) =>
% 98.40/13.01 ((
% 98.40/13.01 (brelnall2) =>
% 98.40/13.01 ((
% 98.40/13.01 (ex1E2) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcGraphProp1) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcGraphProp3) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcGraphProp2) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcextLem) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcGraphProp4) =>
% 98.40/13.01 ((
% 98.40/13.01 (subbreln) =>
% 98.40/13.01 ((
% 98.40/13.01 (eqbreln) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcext) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcext2) =>
% 98.40/13.01 ((
% 98.40/13.01 (ap2apEq1) =>
% 98.40/13.01 ((
% 98.40/13.01 (ap2apEq2) =>
% 98.40/13.01 ((
% 98.40/13.01 (beta1) =>
% 98.40/13.01 ((
% 98.40/13.01 (eta1) =>
% 98.40/13.01 ((
% 98.40/13.01 (lam2lamEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (beta2) =>
% 98.40/13.01 ((
% 98.40/13.01 (eta2) =>
% 98.40/13.01 ((
% 98.40/13.01 (iffalseProp1) =>
% 98.40/13.01 ((
% 98.40/13.01 (iffalseProp2) =>
% 98.40/13.01 ((
% 98.40/13.01 (iftrueProp1) =>
% 98.40/13.01 ((
% 98.40/13.01 (iftrueProp2) =>
% 98.40/13.01 ((
% 98.40/13.01 (ifSingleton) =>
% 98.40/13.01 ((
% 98.40/13.01 (ifp) =>
% 98.40/13.01 ((
% 98.40/13.01 (theeq) =>
% 98.40/13.01 ((
% 98.40/13.01 (iftrue) =>
% 98.40/13.01 ((
% 98.40/13.01 (iffalse) =>
% 98.40/13.01 ((
% 98.40/13.01 (iftrueorfalse) =>
% 98.40/13.01 ((
% 98.40/13.01 (binintersectT_lem) =>
% 98.40/13.01 ((
% 98.40/13.01 (binunionT_lem) =>
% 98.40/13.01 ((
% 98.40/13.01 (powersetT_lem) =>
% 98.40/13.01 ((
% 98.40/13.01 (setminusT_lem) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementT_lem) =>
% 98.40/13.01 ((
% 98.40/13.01 (setextT) =>
% 98.40/13.01 ((
% 98.40/13.01 (subsetTI) =>
% 98.40/13.01 ((
% 98.40/13.01 (powersetTI1) =>
% 98.40/13.01 ((
% 98.40/13.01 (powersetTE1) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementTI1) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementTE1) =>
% 98.40/13.01 ((
% 98.40/13.01 (binintersectTELcontra) =>
% 98.40/13.01 ((
% 98.40/13.01 (binintersectTERcontra) =>
% 98.40/13.01 ((
% 98.40/13.01 (contrasubsetT) =>
% 98.40/13.01 ((
% 98.40/13.01 (contrasubsetT1) =>
% 98.40/13.01 ((
% 98.40/13.01 (contrasubsetT2) =>
% 98.40/13.01 ((
% 98.40/13.01 (contrasubsetT3) =>
% 98.40/13.01 ((
% 98.40/13.01 (doubleComplementI1) =>
% 98.40/13.01 ((
% 98.40/13.01 (doubleComplementE1) =>
% 98.40/13.01 ((
% 98.40/13.01 (doubleComplementSub1) =>
% 98.40/13.01 ((
% 98.40/13.01 (doubleComplementSub2) =>
% 98.40/13.01 ((
% 98.40/13.01 (doubleComplementEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementTnotintersectT) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementImpComplementIntersect) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementSubsetComplementIntersect) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementInPowersetComplementIntersect) =>
% 98.40/13.01 ((
% 98.40/13.01 (contraSubsetComplement) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementTcontraSubset) =>
% 98.40/13.01 ((
% 98.40/13.01 (binunionTILcontra) =>
% 98.40/13.01 ((
% 98.40/13.01 (binunionTIRcontra) =>
% 98.40/13.01 ((
% 98.40/13.01 (inIntersectImpInUnion) =>
% 98.40/13.01 ((
% 98.40/13.01 (inIntersectImpInUnion2) =>
% 98.40/13.01 ((
% 98.40/13.01 (inIntersectImpInIntersectUnions) =>
% 98.40/13.01 ((
% 98.40/13.01 (intersectInPowersetIntersectUnions) =>
% 98.40/13.01 ((
% 98.40/13.01 (inComplementUnionImpNotIn1) =>
% 98.40/13.01 ((
% 98.40/13.01 (inComplementUnionImpInComplement1) =>
% 98.40/13.01 ((
% 98.40/13.01 (binunionTE) =>
% 98.40/13.01 ((
% 98.40/13.01 (binunionTEcontra) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan2a1) =>
% 98.40/13.01 ((
% 98.40/13.01 (complementUnionInPowersetComplement) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan2a2) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan1a) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan1b) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan1) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan2a) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan2b2) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan2b) =>
% 98.40/13.01 ((
% 98.40/13.01 (demorgan2) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz13rule0) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz13rule1) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz13rule2) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz13rule3) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz13rule4) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz1_1) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz1_2) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz1_3) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz1_4) =>
% 98.40/13.01 ((
% 98.40/13.01 (woz1_5) =>
% 98.40/13.01 ((
% 98.40/13.01 (breln1all2) =>
% 98.40/13.01 ((
% 98.40/13.01 (breln1SetBreln1) =>
% 98.40/13.01 ((
% 98.40/13.01 (choice2fnsingleton) =>
% 98.40/13.01 ((
% 98.40/13.01 (!!) @ (
% 98.40/13.01 (('#B') @ (
% 98.40/13.01 !!) @
% 98.40/13.01 (
% 98.40/13.01 (
% 98.40/13.01 ('#S') @ (
% 98.40/13.01 (
% 98.40/13.01 ('#B') @ (
% 98.40/13.01 '#B') @
% 98.40/13.01 breln1)) @
% 98.40/13.01 (
% 98.40/13.01 (
% 98.40/13.01 ('#S') @ dpsetconstr @
% 98.40/13.01 (
% 98.40/13.01 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.40/13.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1264])).
% 98.40/13.01 thf(zip_derived_cl1280, plain,
% 98.40/13.01 (~ (((setminusERneg) =>
% 98.40/13.01 (((setminusELneg) =>
% 98.40/13.01 (((setminusILneg) =>
% 98.40/13.01 (((setminusIRneg) =>
% 98.40/13.01 (((setminusLsub) =>
% 98.40/13.01 (((setminusSubset1) =>
% 98.40/13.01 (((symdiffE) =>
% 98.40/13.01 (((symdiffI1) =>
% 98.40/13.01 (((symdiffI2) =>
% 98.40/13.01 (((symdiffIneg1) =>
% 98.40/13.01 (((symdiffIneg2) =>
% 98.40/13.01 (((secondinupair) =>
% 98.40/13.01 (((setukpairIL) =>
% 98.40/13.01 (((setukpairIR) =>
% 98.40/13.01 (((kpairiskpair) =>
% 98.40/13.01 (((kpairp) =>
% 98.40/13.01 (((singletonsubset) =>
% 98.40/13.01 (((singletoninpowerset) =>
% 98.40/13.01 (((singletoninpowunion) =>
% 98.40/13.01 (((upairset2E) =>
% 98.40/13.01 (((upairsubunion) =>
% 98.40/13.01 (((upairinpowunion) =>
% 98.40/13.01 (((ubforcartprodlem1) =>
% 98.40/13.01 (((ubforcartprodlem2) =>
% 98.40/13.01 (((ubforcartprodlem3) =>
% 98.40/13.01 (((cartprodpairin) =>
% 98.40/13.01 (((cartprodmempair1) =>
% 98.40/13.01 (((cartprodmempair) =>
% 98.40/13.01 (((setunionE2) =>
% 98.40/13.01 (((setunionsingleton1) =>
% 98.40/13.01 ((
% 98.40/13.01 (setunionsingleton2) =>
% 98.40/13.01 ((
% 98.40/13.01 (setunionsingleton) =>
% 98.40/13.01 ((
% 98.40/13.01 (singletonprop) =>
% 98.40/13.01 ((
% 98.40/13.01 (ex1E1) =>
% 98.40/13.01 ((
% 98.40/13.01 (ex1I) =>
% 98.40/13.01 ((
% 98.40/13.01 (ex1I2) =>
% 98.40/13.01 ((
% 98.40/13.01 (singletonsuniq) =>
% 98.40/13.01 ((
% 98.40/13.01 (setukpairinjL1) =>
% 98.40/13.01 ((
% 98.40/13.01 (kfstsingleton) =>
% 98.40/13.01 ((
% 98.40/13.01 (theprop) =>
% 98.40/13.01 ((
% 98.40/13.01 (kfstpairEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodfstin) =>
% 98.40/13.01 ((
% 98.40/13.01 (setukpairinjL2) =>
% 98.40/13.01 ((
% 98.40/13.01 (setukpairinjL) =>
% 98.40/13.01 ((
% 98.40/13.01 (setukpairinjR11) =>
% 98.40/13.01 ((
% 98.40/13.01 (setukpairinjR12) =>
% 98.40/13.01 ((
% 98.40/13.01 (setukpairinjR1) =>
% 98.40/13.01 ((
% 98.40/13.01 (upairequniteq) =>
% 98.40/13.01 ((
% 98.40/13.01 (setukpairinjR2) =>
% 98.40/13.01 ((
% 98.40/13.01 (setukpairinjR) =>
% 98.40/13.01 ((
% 98.40/13.01 (ksndsingleton) =>
% 98.40/13.01 ((
% 98.40/13.01 (ksndpairEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (kpairsurjEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodsndin) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodpairmemEL) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodpairmemER) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodmempaircEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodfstpairEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodsndpairEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (cartprodpairsurjEq) =>
% 98.40/13.01 ((
% 98.40/13.01 (dpsetconstrI) =>
% 98.40/13.01 ((
% 98.40/13.01 (dpsetconstrSub) =>
% 98.40/13.01 ((
% 98.40/13.01 (setOfPairsIsBReln) =>
% 98.40/13.01 ((
% 98.40/13.01 (dpsetconstrERa) =>
% 98.40/13.01 ((
% 98.40/13.01 (dpsetconstrEL1) =>
% 98.40/13.01 ((
% 98.40/13.01 (dpsetconstrEL2) =>
% 98.40/13.01 ((
% 98.40/13.01 (dpsetconstrER) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcImageSingleton) =>
% 98.40/13.01 ((
% 98.40/13.01 (apProp) =>
% 98.40/13.01 ((
% 98.40/13.01 (app) =>
% 98.40/13.01 ((
% 98.40/13.01 (infuncsetfunc) =>
% 98.40/13.01 ((
% 98.40/13.01 (ap2p) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcinfuncset) =>
% 98.40/13.01 ((
% 98.40/13.01 (lamProp) =>
% 98.40/13.01 ((
% 98.40/13.01 (lamp) =>
% 98.40/13.01 ((
% 98.40/13.01 (lam2p) =>
% 98.40/13.01 ((
% 98.40/13.01 (brelnall1) =>
% 98.40/13.01 ((
% 98.40/13.01 (brelnall2) =>
% 98.40/13.01 ((
% 98.40/13.01 (ex1E2) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcGraphProp1) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcGraphProp3) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcGraphProp2) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcextLem) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcGraphProp4) =>
% 98.40/13.01 ((
% 98.40/13.01 (subbreln) =>
% 98.40/13.01 ((
% 98.40/13.01 (eqbreln) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcext) =>
% 98.40/13.01 ((
% 98.40/13.01 (funcext2) =>
% 98.91/13.01 ((
% 98.91/13.01 (ap2apEq1) =>
% 98.91/13.01 ((
% 98.91/13.01 (ap2apEq2) =>
% 98.91/13.01 ((
% 98.91/13.01 (beta1) =>
% 98.91/13.01 ((
% 98.91/13.01 (eta1) =>
% 98.91/13.01 ((
% 98.91/13.01 (lam2lamEq) =>
% 98.91/13.01 ((
% 98.91/13.01 (beta2) =>
% 98.91/13.01 ((
% 98.91/13.01 (eta2) =>
% 98.91/13.01 ((
% 98.91/13.01 (iffalseProp1) =>
% 98.91/13.01 ((
% 98.91/13.01 (iffalseProp2) =>
% 98.91/13.01 ((
% 98.91/13.01 (iftrueProp1) =>
% 98.91/13.01 ((
% 98.91/13.01 (iftrueProp2) =>
% 98.91/13.01 ((
% 98.91/13.01 (ifSingleton) =>
% 98.91/13.01 ((
% 98.91/13.01 (ifp) =>
% 98.91/13.01 ((
% 98.91/13.01 (theeq) =>
% 98.91/13.01 ((
% 98.91/13.01 (iftrue) =>
% 98.91/13.01 ((
% 98.91/13.01 (iffalse) =>
% 98.91/13.01 ((
% 98.91/13.01 (iftrueorfalse) =>
% 98.91/13.01 ((
% 98.91/13.01 (binintersectT_lem) =>
% 98.91/13.01 ((
% 98.91/13.01 (binunionT_lem) =>
% 98.91/13.01 ((
% 98.91/13.01 (powersetT_lem) =>
% 98.91/13.01 ((
% 98.91/13.01 (setminusT_lem) =>
% 98.91/13.01 ((
% 98.91/13.01 (complementT_lem) =>
% 98.91/13.01 ((
% 98.91/13.01 (setextT) =>
% 98.91/13.01 ((
% 98.91/13.01 (subsetTI) =>
% 98.91/13.01 ((
% 98.91/13.01 (powersetTI1) =>
% 98.91/13.01 ((
% 98.91/13.01 (powersetTE1) =>
% 98.91/13.01 ((
% 98.91/13.01 (complementTI1) =>
% 98.91/13.01 ((
% 98.91/13.01 (complementTE1) =>
% 98.91/13.01 ((
% 98.91/13.01 (binintersectTELcontra) =>
% 98.91/13.01 ((
% 98.91/13.01 (binintersectTERcontra) =>
% 98.91/13.01 ((
% 98.91/13.01 (contrasubsetT) =>
% 98.91/13.01 ((
% 98.91/13.01 (contrasubsetT1) =>
% 98.91/13.01 ((
% 98.91/13.01 (contrasubsetT2) =>
% 98.91/13.01 ((
% 98.91/13.01 (contrasubsetT3) =>
% 98.91/13.01 ((
% 98.91/13.01 (doubleComplementI1) =>
% 98.91/13.01 ((
% 98.91/13.01 (doubleComplementE1) =>
% 98.91/13.01 ((
% 98.91/13.01 (doubleComplementSub1) =>
% 98.91/13.01 ((
% 98.91/13.01 (doubleComplementSub2) =>
% 98.91/13.01 ((
% 98.91/13.01 (doubleComplementEq) =>
% 98.91/13.01 ((
% 98.91/13.01 (complementTnotintersectT) =>
% 98.91/13.01 ((
% 98.91/13.01 (complementImpComplementIntersect) =>
% 98.91/13.01 ((
% 98.91/13.01 (complementSubsetComplementIntersect) =>
% 98.91/13.01 ((
% 98.91/13.01 (complementInPowersetComplementIntersect) =>
% 98.91/13.01 ((
% 98.91/13.01 (contraSubsetComplement) =>
% 98.91/13.01 ((
% 98.91/13.01 (complementTcontraSubset) =>
% 98.91/13.01 ((
% 98.91/13.01 (binunionTILcontra) =>
% 98.91/13.01 ((
% 98.91/13.01 (binunionTIRcontra) =>
% 98.91/13.01 ((
% 98.91/13.01 (inIntersectImpInUnion) =>
% 98.91/13.01 ((
% 98.91/13.01 (inIntersectImpInUnion2) =>
% 98.91/13.01 ((
% 98.91/13.01 (inIntersectImpInIntersectUnions) =>
% 98.91/13.01 ((
% 98.91/13.01 (intersectInPowersetIntersectUnions) =>
% 98.91/13.01 ((
% 98.91/13.01 (inComplementUnionImpNotIn1) =>
% 98.91/13.01 ((
% 98.91/13.01 (inComplementUnionImpInComplement1) =>
% 98.91/13.01 ((
% 98.91/13.01 (binunionTE) =>
% 98.91/13.01 ((
% 98.91/13.01 (binunionTEcontra) =>
% 98.91/13.01 ((
% 98.91/13.01 (demorgan2a1) =>
% 98.91/13.01 ((
% 98.91/13.01 (complementUnionInPowersetComplement) =>
% 98.91/13.01 ((
% 98.91/13.01 (demorgan2a2) =>
% 98.91/13.01 ((
% 98.91/13.01 (demorgan1a) =>
% 98.91/13.01 ((
% 98.91/13.01 (demorgan1b) =>
% 98.91/13.01 ((
% 98.91/13.01 (demorgan1) =>
% 98.91/13.01 ((
% 98.91/13.01 (demorgan2a) =>
% 98.91/13.01 ((
% 98.91/13.01 (demorgan2b2) =>
% 98.91/13.01 ((
% 98.91/13.01 (demorgan2b) =>
% 98.91/13.01 ((
% 98.91/13.01 (demorgan2) =>
% 98.91/13.01 ((
% 98.91/13.01 (woz13rule0) =>
% 98.91/13.01 ((
% 98.91/13.01 (woz13rule1) =>
% 98.91/13.01 ((
% 98.91/13.01 (woz13rule2) =>
% 98.91/13.01 ((
% 98.91/13.01 (woz13rule3) =>
% 98.91/13.01 ((
% 98.91/13.01 (woz13rule4) =>
% 98.91/13.01 ((
% 98.91/13.01 (woz1_1) =>
% 98.91/13.01 ((
% 98.91/13.01 (woz1_2) =>
% 98.91/13.01 ((
% 98.91/13.01 (woz1_3) =>
% 98.91/13.01 ((
% 98.91/13.01 (woz1_4) =>
% 98.91/13.01 ((
% 98.91/13.01 (woz1_5) =>
% 98.91/13.01 ((
% 98.91/13.01 (breln1all2) =>
% 98.91/13.01 ((
% 98.91/13.01 (breln1SetBreln1) =>
% 98.91/13.01 ((
% 98.91/13.01 (choice2fnsingleton) =>
% 98.91/13.01 ((
% 98.91/13.01 (!!) @ (
% 98.91/13.01 (('#B') @ (
% 98.91/13.01 !!) @
% 98.91/13.01 (
% 98.91/13.01 (
% 98.91/13.01 ('#S') @ (
% 98.91/13.01 (
% 98.91/13.01 ('#B') @ (
% 98.91/13.01 '#B') @
% 98.91/13.01 breln1)) @
% 98.91/13.01 (
% 98.91/13.01 (
% 98.91/13.01 ('#S') @ dpsetconstr @
% 98.91/13.01 (
% 98.91/13.01 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.91/13.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1272])).
% 98.91/13.01 thf(zip_derived_cl1288, plain,
% 98.91/13.01 (~ (((setminusELneg) =>
% 98.91/13.01 (((setminusILneg) =>
% 98.91/13.01 (((setminusIRneg) =>
% 98.91/13.01 (((setminusLsub) =>
% 98.91/13.01 (((setminusSubset1) =>
% 98.91/13.01 (((symdiffE) =>
% 98.91/13.01 (((symdiffI1) =>
% 98.91/13.01 (((symdiffI2) =>
% 98.91/13.01 (((symdiffIneg1) =>
% 98.91/13.01 (((symdiffIneg2) =>
% 98.91/13.01 (((secondinupair) =>
% 98.91/13.01 (((setukpairIL) =>
% 98.91/13.01 (((setukpairIR) =>
% 98.91/13.01 (((kpairiskpair) =>
% 98.91/13.01 (((kpairp) =>
% 98.91/13.01 (((singletonsubset) =>
% 98.91/13.01 (((singletoninpowerset) =>
% 98.91/13.01 (((singletoninpowunion) =>
% 98.91/13.01 (((upairset2E) =>
% 98.91/13.01 (((upairsubunion) =>
% 98.91/13.01 (((upairinpowunion) =>
% 98.91/13.01 (((ubforcartprodlem1) =>
% 98.91/13.01 (((ubforcartprodlem2) =>
% 98.91/13.01 (((ubforcartprodlem3) =>
% 98.91/13.01 (((cartprodpairin) =>
% 98.91/13.01 (((cartprodmempair1) =>
% 98.91/13.01 (((cartprodmempair) =>
% 98.91/13.01 (((setunionE2) =>
% 98.91/13.01 (((setunionsingleton1) =>
% 98.91/13.01 (((setunionsingleton2) =>
% 98.91/13.01 ((
% 98.91/13.01 (setunionsingleton) =>
% 98.91/13.01 ((
% 98.91/13.01 (singletonprop) =>
% 98.91/13.01 ((
% 98.91/13.01 (ex1E1) =>
% 98.91/13.01 ((
% 98.91/13.01 (ex1I) =>
% 98.91/13.01 ((
% 98.91/13.01 (ex1I2) =>
% 98.91/13.01 ((
% 98.91/13.01 (singletonsuniq) =>
% 98.91/13.01 ((
% 98.91/13.01 (setukpairinjL1) =>
% 98.91/13.01 ((
% 98.91/13.01 (kfstsingleton) =>
% 98.91/13.01 ((
% 98.91/13.01 (theprop) =>
% 98.91/13.01 ((
% 98.91/13.01 (kfstpairEq) =>
% 98.91/13.01 ((
% 98.91/13.01 (cartprodfstin) =>
% 98.91/13.01 ((
% 98.91/13.01 (setukpairinjL2) =>
% 98.91/13.01 ((
% 98.91/13.01 (setukpairinjL) =>
% 98.91/13.01 ((
% 98.91/13.01 (setukpairinjR11) =>
% 98.91/13.01 ((
% 98.91/13.01 (setukpairinjR12) =>
% 98.91/13.01 ((
% 98.91/13.01 (setukpairinjR1) =>
% 98.91/13.01 ((
% 98.91/13.01 (upairequniteq) =>
% 98.91/13.01 ((
% 98.91/13.01 (setukpairinjR2) =>
% 98.91/13.01 ((
% 98.91/13.01 (setukpairinjR) =>
% 98.91/13.01 ((
% 98.91/13.01 (ksndsingleton) =>
% 98.91/13.01 ((
% 98.91/13.01 (ksndpairEq) =>
% 98.91/13.01 ((
% 98.91/13.01 (kpairsurjEq) =>
% 98.91/13.01 ((
% 98.91/13.01 (cartprodsndin) =>
% 98.91/13.01 ((
% 98.91/13.01 (cartprodpairmemEL) =>
% 98.91/13.01 ((
% 98.91/13.01 (cartprodpairmemER) =>
% 98.91/13.01 ((
% 98.91/13.01 (cartprodmempaircEq) =>
% 98.91/13.01 ((
% 98.91/13.01 (cartprodfstpairEq) =>
% 98.91/13.01 ((
% 98.91/13.01 (cartprodsndpairEq) =>
% 98.91/13.01 ((
% 98.91/13.01 (cartprodpairsurjEq) =>
% 98.91/13.01 ((
% 98.91/13.01 (dpsetconstrI) =>
% 98.91/13.01 ((
% 98.91/13.01 (dpsetconstrSub) =>
% 98.91/13.01 ((
% 98.91/13.01 (setOfPairsIsBReln) =>
% 98.91/13.01 ((
% 98.91/13.01 (dpsetconstrERa) =>
% 98.91/13.01 ((
% 98.91/13.01 (dpsetconstrEL1) =>
% 98.91/13.01 ((
% 98.91/13.01 (dpsetconstrEL2) =>
% 98.91/13.01 ((
% 98.91/13.01 (dpsetconstrER) =>
% 98.91/13.01 ((
% 98.91/13.01 (funcImageSingleton) =>
% 98.91/13.01 ((
% 98.91/13.01 (apProp) =>
% 98.91/13.01 ((
% 98.91/13.01 (app) =>
% 98.91/13.01 ((
% 98.91/13.01 (infuncsetfunc) =>
% 98.91/13.01 ((
% 98.91/13.01 (ap2p) =>
% 98.91/13.01 ((
% 98.91/13.01 (funcinfuncset) =>
% 98.91/13.01 ((
% 98.91/13.01 (lamProp) =>
% 98.91/13.01 ((
% 98.91/13.01 (lamp) =>
% 98.91/13.01 ((
% 98.91/13.01 (lam2p) =>
% 98.91/13.01 ((
% 98.91/13.01 (brelnall1) =>
% 98.91/13.01 ((
% 98.91/13.01 (brelnall2) =>
% 98.91/13.01 ((
% 98.91/13.01 (ex1E2) =>
% 98.91/13.01 ((
% 98.91/13.01 (funcGraphProp1) =>
% 98.91/13.01 ((
% 98.91/13.01 (funcGraphProp3) =>
% 98.91/13.01 ((
% 98.91/13.01 (funcGraphProp2) =>
% 98.91/13.01 ((
% 98.91/13.01 (funcextLem) =>
% 98.91/13.01 ((
% 98.91/13.01 (funcGraphProp4) =>
% 98.91/13.01 ((
% 98.91/13.01 (subbreln) =>
% 98.91/13.01 ((
% 98.91/13.01 (eqbreln) =>
% 98.91/13.01 ((
% 98.91/13.01 (funcext) =>
% 98.91/13.01 ((
% 98.91/13.01 (funcext2) =>
% 98.91/13.01 ((
% 98.91/13.01 (ap2apEq1) =>
% 98.91/13.01 ((
% 98.91/13.01 (ap2apEq2) =>
% 98.91/13.01 ((
% 98.91/13.01 (beta1) =>
% 98.91/13.01 ((
% 98.91/13.01 (eta1) =>
% 98.91/13.01 ((
% 98.91/13.01 (lam2lamEq) =>
% 98.91/13.01 ((
% 98.91/13.01 (beta2) =>
% 98.91/13.01 ((
% 98.91/13.01 (eta2) =>
% 98.91/13.01 ((
% 98.91/13.01 (iffalseProp1) =>
% 98.91/13.01 ((
% 98.91/13.01 (iffalseProp2) =>
% 98.91/13.01 ((
% 98.91/13.01 (iftrueProp1) =>
% 98.91/13.01 ((
% 98.91/13.01 (iftrueProp2) =>
% 98.91/13.01 ((
% 98.91/13.01 (ifSingleton) =>
% 98.91/13.01 ((
% 98.91/13.01 (ifp) =>
% 98.91/13.01 ((
% 98.91/13.01 (theeq) =>
% 98.91/13.01 ((
% 98.91/13.01 (iftrue) =>
% 98.91/13.01 ((
% 98.91/13.01 (iffalse) =>
% 98.91/13.01 ((
% 98.91/13.01 (iftrueorfalse) =>
% 98.91/13.01 ((
% 98.91/13.01 (binintersectT_lem) =>
% 98.91/13.01 ((
% 98.91/13.01 (binunionT_lem) =>
% 98.91/13.01 ((
% 98.91/13.01 (powersetT_lem) =>
% 98.91/13.01 ((
% 98.91/13.01 (setminusT_lem) =>
% 98.91/13.01 ((
% 98.91/13.01 (complementT_lem) =>
% 98.91/13.01 ((
% 98.91/13.01 (setextT) =>
% 98.91/13.01 ((
% 98.91/13.01 (subsetTI) =>
% 98.91/13.01 ((
% 98.91/13.01 (powersetTI1) =>
% 98.91/13.01 ((
% 98.91/13.01 (powersetTE1) =>
% 98.91/13.01 ((
% 98.91/13.01 (complementTI1) =>
% 98.91/13.01 ((
% 98.91/13.01 (complementTE1) =>
% 98.91/13.01 ((
% 98.91/13.01 (binintersectTELcontra) =>
% 98.91/13.01 ((
% 98.91/13.01 (binintersectTERcontra) =>
% 98.91/13.01 ((
% 98.91/13.01 (contrasubsetT) =>
% 98.91/13.01 ((
% 98.91/13.01 (contrasubsetT1) =>
% 98.91/13.01 ((
% 98.91/13.01 (contrasubsetT2) =>
% 98.91/13.01 ((
% 98.91/13.01 (contrasubsetT3) =>
% 98.91/13.01 ((
% 98.91/13.01 (doubleComplementI1) =>
% 98.91/13.01 ((
% 98.91/13.01 (doubleComplementE1) =>
% 98.91/13.01 ((
% 98.91/13.01 (doubleComplementSub1) =>
% 98.91/13.01 ((
% 98.91/13.01 (doubleComplementSub2) =>
% 98.91/13.01 ((
% 98.91/13.01 (doubleComplementEq) =>
% 98.91/13.01 ((
% 98.91/13.01 (complementTnotintersectT) =>
% 98.91/13.01 ((
% 98.91/13.01 (complementImpComplementIntersect) =>
% 98.91/13.01 ((
% 98.91/13.01 (complementSubsetComplementIntersect) =>
% 98.91/13.01 ((
% 98.91/13.01 (complementInPowersetComplementIntersect) =>
% 98.91/13.01 ((
% 98.91/13.01 (contraSubsetComplement) =>
% 98.91/13.01 ((
% 98.91/13.01 (complementTcontraSubset) =>
% 98.91/13.01 ((
% 98.91/13.01 (binunionTILcontra) =>
% 98.91/13.01 ((
% 98.91/13.01 (binunionTIRcontra) =>
% 98.91/13.01 ((
% 98.91/13.01 (inIntersectImpInUnion) =>
% 98.91/13.01 ((
% 98.91/13.01 (inIntersectImpInUnion2) =>
% 98.91/13.01 ((
% 98.91/13.01 (inIntersectImpInIntersectUnions) =>
% 98.91/13.01 ((
% 98.91/13.01 (intersectInPowersetIntersectUnions) =>
% 98.91/13.01 ((
% 98.91/13.01 (inComplementUnionImpNotIn1) =>
% 98.91/13.01 ((
% 98.91/13.01 (inComplementUnionImpInComplement1) =>
% 98.91/13.01 ((
% 98.91/13.01 (binunionTE) =>
% 98.91/13.01 ((
% 98.91/13.01 (binunionTEcontra) =>
% 98.91/13.01 ((
% 98.91/13.01 (demorgan2a1) =>
% 98.91/13.01 ((
% 98.91/13.01 (complementUnionInPowersetComplement) =>
% 98.91/13.01 ((
% 98.91/13.01 (demorgan2a2) =>
% 98.91/13.01 ((
% 98.91/13.01 (demorgan1a) =>
% 98.91/13.01 ((
% 98.91/13.01 (demorgan1b) =>
% 98.91/13.01 ((
% 98.91/13.01 (demorgan1) =>
% 98.91/13.01 ((
% 98.91/13.01 (demorgan2a) =>
% 98.91/13.01 ((
% 98.91/13.01 (demorgan2b2) =>
% 98.91/13.01 ((
% 98.91/13.01 (demorgan2b) =>
% 98.91/13.01 ((
% 98.91/13.01 (demorgan2) =>
% 98.91/13.01 ((
% 98.91/13.01 (woz13rule0) =>
% 98.91/13.01 ((
% 98.91/13.01 (woz13rule1) =>
% 98.91/13.01 ((
% 98.91/13.01 (woz13rule2) =>
% 98.91/13.01 ((
% 98.91/13.01 (woz13rule3) =>
% 98.91/13.01 ((
% 98.91/13.01 (woz13rule4) =>
% 98.91/13.01 ((
% 98.91/13.01 (woz1_1) =>
% 98.91/13.01 ((
% 98.91/13.01 (woz1_2) =>
% 98.91/13.01 ((
% 98.91/13.01 (woz1_3) =>
% 98.91/13.01 ((
% 98.91/13.01 (woz1_4) =>
% 98.91/13.01 ((
% 98.91/13.01 (woz1_5) =>
% 98.91/13.01 ((
% 98.91/13.01 (breln1all2) =>
% 98.91/13.01 ((
% 98.91/13.01 (breln1SetBreln1) =>
% 98.91/13.01 ((
% 98.91/13.01 (choice2fnsingleton) =>
% 98.91/13.01 ((
% 98.91/13.01 (!!) @ (
% 98.91/13.01 (('#B') @ (
% 98.91/13.01 !!) @
% 98.91/13.01 (
% 98.91/13.01 (
% 98.91/13.01 ('#S') @ (
% 98.91/13.01 (
% 98.91/13.01 ('#B') @ (
% 98.91/13.01 '#B') @
% 98.91/13.01 breln1)) @
% 98.91/13.01 (
% 98.91/13.01 (
% 98.91/13.01 ('#S') @ dpsetconstr @
% 98.91/13.01 (
% 98.91/13.02 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.91/13.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1280])).
% 98.91/13.02 thf(zip_derived_cl1296, plain,
% 98.91/13.02 (~ (((setminusILneg) =>
% 98.91/13.02 (((setminusIRneg) =>
% 98.91/13.02 (((setminusLsub) =>
% 98.91/13.02 (((setminusSubset1) =>
% 98.91/13.02 (((symdiffE) =>
% 98.91/13.02 (((symdiffI1) =>
% 98.91/13.02 (((symdiffI2) =>
% 98.91/13.02 (((symdiffIneg1) =>
% 98.91/13.02 (((symdiffIneg2) =>
% 98.91/13.02 (((secondinupair) =>
% 98.91/13.02 (((setukpairIL) =>
% 98.91/13.02 (((setukpairIR) =>
% 98.91/13.02 (((kpairiskpair) =>
% 98.91/13.02 (((kpairp) =>
% 98.91/13.02 (((singletonsubset) =>
% 98.91/13.02 (((singletoninpowerset) =>
% 98.91/13.02 (((singletoninpowunion) =>
% 98.91/13.02 (((upairset2E) =>
% 98.91/13.02 (((upairsubunion) =>
% 98.91/13.02 (((upairinpowunion) =>
% 98.91/13.02 (((ubforcartprodlem1) =>
% 98.91/13.02 (((ubforcartprodlem2) =>
% 98.91/13.02 (((ubforcartprodlem3) =>
% 98.91/13.02 (((cartprodpairin) =>
% 98.91/13.02 (((cartprodmempair1) =>
% 98.91/13.02 (((cartprodmempair) =>
% 98.91/13.02 (((setunionE2) =>
% 98.91/13.02 (((setunionsingleton1) =>
% 98.91/13.02 (((setunionsingleton2) =>
% 98.91/13.02 (((setunionsingleton) =>
% 98.91/13.02 ((
% 98.91/13.02 (singletonprop) =>
% 98.91/13.02 ((
% 98.91/13.02 (ex1E1) =>
% 98.91/13.02 ((
% 98.91/13.02 (ex1I) =>
% 98.91/13.02 ((
% 98.91/13.02 (ex1I2) =>
% 98.91/13.02 ((
% 98.91/13.02 (singletonsuniq) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjL1) =>
% 98.91/13.02 ((
% 98.91/13.02 (kfstsingleton) =>
% 98.91/13.02 ((
% 98.91/13.02 (theprop) =>
% 98.91/13.02 ((
% 98.91/13.02 (kfstpairEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodfstin) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjL2) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjL) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjR11) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjR12) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjR1) =>
% 98.91/13.02 ((
% 98.91/13.02 (upairequniteq) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjR2) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjR) =>
% 98.91/13.02 ((
% 98.91/13.02 (ksndsingleton) =>
% 98.91/13.02 ((
% 98.91/13.02 (ksndpairEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (kpairsurjEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodsndin) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodpairmemEL) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodpairmemER) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodmempaircEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodfstpairEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodsndpairEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodpairsurjEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrI) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrSub) =>
% 98.91/13.02 ((
% 98.91/13.02 (setOfPairsIsBReln) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrERa) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrEL1) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrEL2) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrER) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcImageSingleton) =>
% 98.91/13.02 ((
% 98.91/13.02 (apProp) =>
% 98.91/13.02 ((
% 98.91/13.02 (app) =>
% 98.91/13.02 ((
% 98.91/13.02 (infuncsetfunc) =>
% 98.91/13.02 ((
% 98.91/13.02 (ap2p) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcinfuncset) =>
% 98.91/13.02 ((
% 98.91/13.02 (lamProp) =>
% 98.91/13.02 ((
% 98.91/13.02 (lamp) =>
% 98.91/13.02 ((
% 98.91/13.02 (lam2p) =>
% 98.91/13.02 ((
% 98.91/13.02 (brelnall1) =>
% 98.91/13.02 ((
% 98.91/13.02 (brelnall2) =>
% 98.91/13.02 ((
% 98.91/13.02 (ex1E2) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcGraphProp1) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcGraphProp3) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcGraphProp2) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcextLem) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcGraphProp4) =>
% 98.91/13.02 ((
% 98.91/13.02 (subbreln) =>
% 98.91/13.02 ((
% 98.91/13.02 (eqbreln) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcext) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcext2) =>
% 98.91/13.02 ((
% 98.91/13.02 (ap2apEq1) =>
% 98.91/13.02 ((
% 98.91/13.02 (ap2apEq2) =>
% 98.91/13.02 ((
% 98.91/13.02 (beta1) =>
% 98.91/13.02 ((
% 98.91/13.02 (eta1) =>
% 98.91/13.02 ((
% 98.91/13.02 (lam2lamEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (beta2) =>
% 98.91/13.02 ((
% 98.91/13.02 (eta2) =>
% 98.91/13.02 ((
% 98.91/13.02 (iffalseProp1) =>
% 98.91/13.02 ((
% 98.91/13.02 (iffalseProp2) =>
% 98.91/13.02 ((
% 98.91/13.02 (iftrueProp1) =>
% 98.91/13.02 ((
% 98.91/13.02 (iftrueProp2) =>
% 98.91/13.02 ((
% 98.91/13.02 (ifSingleton) =>
% 98.91/13.02 ((
% 98.91/13.02 (ifp) =>
% 98.91/13.02 ((
% 98.91/13.02 (theeq) =>
% 98.91/13.02 ((
% 98.91/13.02 (iftrue) =>
% 98.91/13.02 ((
% 98.91/13.02 (iffalse) =>
% 98.91/13.02 ((
% 98.91/13.02 (iftrueorfalse) =>
% 98.91/13.02 ((
% 98.91/13.02 (binintersectT_lem) =>
% 98.91/13.02 ((
% 98.91/13.02 (binunionT_lem) =>
% 98.91/13.02 ((
% 98.91/13.02 (powersetT_lem) =>
% 98.91/13.02 ((
% 98.91/13.02 (setminusT_lem) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementT_lem) =>
% 98.91/13.02 ((
% 98.91/13.02 (setextT) =>
% 98.91/13.02 ((
% 98.91/13.02 (subsetTI) =>
% 98.91/13.02 ((
% 98.91/13.02 (powersetTI1) =>
% 98.91/13.02 ((
% 98.91/13.02 (powersetTE1) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementTI1) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementTE1) =>
% 98.91/13.02 ((
% 98.91/13.02 (binintersectTELcontra) =>
% 98.91/13.02 ((
% 98.91/13.02 (binintersectTERcontra) =>
% 98.91/13.02 ((
% 98.91/13.02 (contrasubsetT) =>
% 98.91/13.02 ((
% 98.91/13.02 (contrasubsetT1) =>
% 98.91/13.02 ((
% 98.91/13.02 (contrasubsetT2) =>
% 98.91/13.02 ((
% 98.91/13.02 (contrasubsetT3) =>
% 98.91/13.02 ((
% 98.91/13.02 (doubleComplementI1) =>
% 98.91/13.02 ((
% 98.91/13.02 (doubleComplementE1) =>
% 98.91/13.02 ((
% 98.91/13.02 (doubleComplementSub1) =>
% 98.91/13.02 ((
% 98.91/13.02 (doubleComplementSub2) =>
% 98.91/13.02 ((
% 98.91/13.02 (doubleComplementEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementTnotintersectT) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementImpComplementIntersect) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementSubsetComplementIntersect) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementInPowersetComplementIntersect) =>
% 98.91/13.02 ((
% 98.91/13.02 (contraSubsetComplement) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementTcontraSubset) =>
% 98.91/13.02 ((
% 98.91/13.02 (binunionTILcontra) =>
% 98.91/13.02 ((
% 98.91/13.02 (binunionTIRcontra) =>
% 98.91/13.02 ((
% 98.91/13.02 (inIntersectImpInUnion) =>
% 98.91/13.02 ((
% 98.91/13.02 (inIntersectImpInUnion2) =>
% 98.91/13.02 ((
% 98.91/13.02 (inIntersectImpInIntersectUnions) =>
% 98.91/13.02 ((
% 98.91/13.02 (intersectInPowersetIntersectUnions) =>
% 98.91/13.02 ((
% 98.91/13.02 (inComplementUnionImpNotIn1) =>
% 98.91/13.02 ((
% 98.91/13.02 (inComplementUnionImpInComplement1) =>
% 98.91/13.02 ((
% 98.91/13.02 (binunionTE) =>
% 98.91/13.02 ((
% 98.91/13.02 (binunionTEcontra) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2a1) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementUnionInPowersetComplement) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2a2) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan1a) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan1b) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan1) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2a) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2b2) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2b) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz13rule0) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz13rule1) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz13rule2) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz13rule3) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz13rule4) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz1_1) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz1_2) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz1_3) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz1_4) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz1_5) =>
% 98.91/13.02 ((
% 98.91/13.02 (breln1all2) =>
% 98.91/13.02 ((
% 98.91/13.02 (breln1SetBreln1) =>
% 98.91/13.02 ((
% 98.91/13.02 (choice2fnsingleton) =>
% 98.91/13.02 ((
% 98.91/13.02 (!!) @ (
% 98.91/13.02 (('#B') @ (
% 98.91/13.02 !!) @
% 98.91/13.02 (
% 98.91/13.02 (
% 98.91/13.02 ('#S') @ (
% 98.91/13.02 (
% 98.91/13.02 ('#B') @ (
% 98.91/13.02 '#B') @
% 98.91/13.02 breln1)) @
% 98.91/13.02 (
% 98.91/13.02 (
% 98.91/13.02 ('#S') @ dpsetconstr @
% 98.91/13.02 (
% 98.91/13.02 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.91/13.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1288])).
% 98.91/13.02 thf(zip_derived_cl1305, plain,
% 98.91/13.02 (~ (((setminusIRneg) =>
% 98.91/13.02 (((setminusLsub) =>
% 98.91/13.02 (((setminusSubset1) =>
% 98.91/13.02 (((symdiffE) =>
% 98.91/13.02 (((symdiffI1) =>
% 98.91/13.02 (((symdiffI2) =>
% 98.91/13.02 (((symdiffIneg1) =>
% 98.91/13.02 (((symdiffIneg2) =>
% 98.91/13.02 (((secondinupair) =>
% 98.91/13.02 (((setukpairIL) =>
% 98.91/13.02 (((setukpairIR) =>
% 98.91/13.02 (((kpairiskpair) =>
% 98.91/13.02 (((kpairp) =>
% 98.91/13.02 (((singletonsubset) =>
% 98.91/13.02 (((singletoninpowerset) =>
% 98.91/13.02 (((singletoninpowunion) =>
% 98.91/13.02 (((upairset2E) =>
% 98.91/13.02 (((upairsubunion) =>
% 98.91/13.02 (((upairinpowunion) =>
% 98.91/13.02 (((ubforcartprodlem1) =>
% 98.91/13.02 (((ubforcartprodlem2) =>
% 98.91/13.02 (((ubforcartprodlem3) =>
% 98.91/13.02 (((cartprodpairin) =>
% 98.91/13.02 (((cartprodmempair1) =>
% 98.91/13.02 (((cartprodmempair) =>
% 98.91/13.02 (((setunionE2) =>
% 98.91/13.02 (((setunionsingleton1) =>
% 98.91/13.02 (((setunionsingleton2) =>
% 98.91/13.02 (((setunionsingleton) =>
% 98.91/13.02 (((singletonprop) =>
% 98.91/13.02 ((
% 98.91/13.02 (ex1E1) =>
% 98.91/13.02 ((
% 98.91/13.02 (ex1I) =>
% 98.91/13.02 ((
% 98.91/13.02 (ex1I2) =>
% 98.91/13.02 ((
% 98.91/13.02 (singletonsuniq) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjL1) =>
% 98.91/13.02 ((
% 98.91/13.02 (kfstsingleton) =>
% 98.91/13.02 ((
% 98.91/13.02 (theprop) =>
% 98.91/13.02 ((
% 98.91/13.02 (kfstpairEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodfstin) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjL2) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjL) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjR11) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjR12) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjR1) =>
% 98.91/13.02 ((
% 98.91/13.02 (upairequniteq) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjR2) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjR) =>
% 98.91/13.02 ((
% 98.91/13.02 (ksndsingleton) =>
% 98.91/13.02 ((
% 98.91/13.02 (ksndpairEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (kpairsurjEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodsndin) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodpairmemEL) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodpairmemER) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodmempaircEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodfstpairEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodsndpairEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodpairsurjEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrI) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrSub) =>
% 98.91/13.02 ((
% 98.91/13.02 (setOfPairsIsBReln) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrERa) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrEL1) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrEL2) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrER) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcImageSingleton) =>
% 98.91/13.02 ((
% 98.91/13.02 (apProp) =>
% 98.91/13.02 ((
% 98.91/13.02 (app) =>
% 98.91/13.02 ((
% 98.91/13.02 (infuncsetfunc) =>
% 98.91/13.02 ((
% 98.91/13.02 (ap2p) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcinfuncset) =>
% 98.91/13.02 ((
% 98.91/13.02 (lamProp) =>
% 98.91/13.02 ((
% 98.91/13.02 (lamp) =>
% 98.91/13.02 ((
% 98.91/13.02 (lam2p) =>
% 98.91/13.02 ((
% 98.91/13.02 (brelnall1) =>
% 98.91/13.02 ((
% 98.91/13.02 (brelnall2) =>
% 98.91/13.02 ((
% 98.91/13.02 (ex1E2) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcGraphProp1) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcGraphProp3) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcGraphProp2) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcextLem) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcGraphProp4) =>
% 98.91/13.02 ((
% 98.91/13.02 (subbreln) =>
% 98.91/13.02 ((
% 98.91/13.02 (eqbreln) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcext) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcext2) =>
% 98.91/13.02 ((
% 98.91/13.02 (ap2apEq1) =>
% 98.91/13.02 ((
% 98.91/13.02 (ap2apEq2) =>
% 98.91/13.02 ((
% 98.91/13.02 (beta1) =>
% 98.91/13.02 ((
% 98.91/13.02 (eta1) =>
% 98.91/13.02 ((
% 98.91/13.02 (lam2lamEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (beta2) =>
% 98.91/13.02 ((
% 98.91/13.02 (eta2) =>
% 98.91/13.02 ((
% 98.91/13.02 (iffalseProp1) =>
% 98.91/13.02 ((
% 98.91/13.02 (iffalseProp2) =>
% 98.91/13.02 ((
% 98.91/13.02 (iftrueProp1) =>
% 98.91/13.02 ((
% 98.91/13.02 (iftrueProp2) =>
% 98.91/13.02 ((
% 98.91/13.02 (ifSingleton) =>
% 98.91/13.02 ((
% 98.91/13.02 (ifp) =>
% 98.91/13.02 ((
% 98.91/13.02 (theeq) =>
% 98.91/13.02 ((
% 98.91/13.02 (iftrue) =>
% 98.91/13.02 ((
% 98.91/13.02 (iffalse) =>
% 98.91/13.02 ((
% 98.91/13.02 (iftrueorfalse) =>
% 98.91/13.02 ((
% 98.91/13.02 (binintersectT_lem) =>
% 98.91/13.02 ((
% 98.91/13.02 (binunionT_lem) =>
% 98.91/13.02 ((
% 98.91/13.02 (powersetT_lem) =>
% 98.91/13.02 ((
% 98.91/13.02 (setminusT_lem) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementT_lem) =>
% 98.91/13.02 ((
% 98.91/13.02 (setextT) =>
% 98.91/13.02 ((
% 98.91/13.02 (subsetTI) =>
% 98.91/13.02 ((
% 98.91/13.02 (powersetTI1) =>
% 98.91/13.02 ((
% 98.91/13.02 (powersetTE1) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementTI1) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementTE1) =>
% 98.91/13.02 ((
% 98.91/13.02 (binintersectTELcontra) =>
% 98.91/13.02 ((
% 98.91/13.02 (binintersectTERcontra) =>
% 98.91/13.02 ((
% 98.91/13.02 (contrasubsetT) =>
% 98.91/13.02 ((
% 98.91/13.02 (contrasubsetT1) =>
% 98.91/13.02 ((
% 98.91/13.02 (contrasubsetT2) =>
% 98.91/13.02 ((
% 98.91/13.02 (contrasubsetT3) =>
% 98.91/13.02 ((
% 98.91/13.02 (doubleComplementI1) =>
% 98.91/13.02 ((
% 98.91/13.02 (doubleComplementE1) =>
% 98.91/13.02 ((
% 98.91/13.02 (doubleComplementSub1) =>
% 98.91/13.02 ((
% 98.91/13.02 (doubleComplementSub2) =>
% 98.91/13.02 ((
% 98.91/13.02 (doubleComplementEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementTnotintersectT) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementImpComplementIntersect) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementSubsetComplementIntersect) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementInPowersetComplementIntersect) =>
% 98.91/13.02 ((
% 98.91/13.02 (contraSubsetComplement) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementTcontraSubset) =>
% 98.91/13.02 ((
% 98.91/13.02 (binunionTILcontra) =>
% 98.91/13.02 ((
% 98.91/13.02 (binunionTIRcontra) =>
% 98.91/13.02 ((
% 98.91/13.02 (inIntersectImpInUnion) =>
% 98.91/13.02 ((
% 98.91/13.02 (inIntersectImpInUnion2) =>
% 98.91/13.02 ((
% 98.91/13.02 (inIntersectImpInIntersectUnions) =>
% 98.91/13.02 ((
% 98.91/13.02 (intersectInPowersetIntersectUnions) =>
% 98.91/13.02 ((
% 98.91/13.02 (inComplementUnionImpNotIn1) =>
% 98.91/13.02 ((
% 98.91/13.02 (inComplementUnionImpInComplement1) =>
% 98.91/13.02 ((
% 98.91/13.02 (binunionTE) =>
% 98.91/13.02 ((
% 98.91/13.02 (binunionTEcontra) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2a1) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementUnionInPowersetComplement) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2a2) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan1a) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan1b) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan1) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2a) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2b2) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2b) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz13rule0) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz13rule1) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz13rule2) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz13rule3) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz13rule4) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz1_1) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz1_2) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz1_3) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz1_4) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz1_5) =>
% 98.91/13.02 ((
% 98.91/13.02 (breln1all2) =>
% 98.91/13.02 ((
% 98.91/13.02 (breln1SetBreln1) =>
% 98.91/13.02 ((
% 98.91/13.02 (choice2fnsingleton) =>
% 98.91/13.02 ((
% 98.91/13.02 (!!) @ (
% 98.91/13.02 (('#B') @ (
% 98.91/13.02 !!) @
% 98.91/13.02 (
% 98.91/13.02 (
% 98.91/13.02 ('#S') @ (
% 98.91/13.02 (
% 98.91/13.02 ('#B') @ (
% 98.91/13.02 '#B') @
% 98.91/13.02 breln1)) @
% 98.91/13.02 (
% 98.91/13.02 (
% 98.91/13.02 ('#S') @ dpsetconstr @
% 98.91/13.02 (
% 98.91/13.02 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.91/13.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1296])).
% 98.91/13.02 thf(zip_derived_cl1313, plain,
% 98.91/13.02 (~ (((setminusLsub) =>
% 98.91/13.02 (((setminusSubset1) =>
% 98.91/13.02 (((symdiffE) =>
% 98.91/13.02 (((symdiffI1) =>
% 98.91/13.02 (((symdiffI2) =>
% 98.91/13.02 (((symdiffIneg1) =>
% 98.91/13.02 (((symdiffIneg2) =>
% 98.91/13.02 (((secondinupair) =>
% 98.91/13.02 (((setukpairIL) =>
% 98.91/13.02 (((setukpairIR) =>
% 98.91/13.02 (((kpairiskpair) =>
% 98.91/13.02 (((kpairp) =>
% 98.91/13.02 (((singletonsubset) =>
% 98.91/13.02 (((singletoninpowerset) =>
% 98.91/13.02 (((singletoninpowunion) =>
% 98.91/13.02 (((upairset2E) =>
% 98.91/13.02 (((upairsubunion) =>
% 98.91/13.02 (((upairinpowunion) =>
% 98.91/13.02 (((ubforcartprodlem1) =>
% 98.91/13.02 (((ubforcartprodlem2) =>
% 98.91/13.02 (((ubforcartprodlem3) =>
% 98.91/13.02 (((cartprodpairin) =>
% 98.91/13.02 (((cartprodmempair1) =>
% 98.91/13.02 (((cartprodmempair) =>
% 98.91/13.02 (((setunionE2) =>
% 98.91/13.02 (((setunionsingleton1) =>
% 98.91/13.02 (((setunionsingleton2) =>
% 98.91/13.02 (((setunionsingleton) =>
% 98.91/13.02 (((singletonprop) =>
% 98.91/13.02 (((ex1E1) =>
% 98.91/13.02 ((
% 98.91/13.02 (ex1I) =>
% 98.91/13.02 ((
% 98.91/13.02 (ex1I2) =>
% 98.91/13.02 ((
% 98.91/13.02 (singletonsuniq) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjL1) =>
% 98.91/13.02 ((
% 98.91/13.02 (kfstsingleton) =>
% 98.91/13.02 ((
% 98.91/13.02 (theprop) =>
% 98.91/13.02 ((
% 98.91/13.02 (kfstpairEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodfstin) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjL2) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjL) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjR11) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjR12) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjR1) =>
% 98.91/13.02 ((
% 98.91/13.02 (upairequniteq) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjR2) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjR) =>
% 98.91/13.02 ((
% 98.91/13.02 (ksndsingleton) =>
% 98.91/13.02 ((
% 98.91/13.02 (ksndpairEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (kpairsurjEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodsndin) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodpairmemEL) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodpairmemER) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodmempaircEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodfstpairEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodsndpairEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodpairsurjEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrI) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrSub) =>
% 98.91/13.02 ((
% 98.91/13.02 (setOfPairsIsBReln) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrERa) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrEL1) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrEL2) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrER) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcImageSingleton) =>
% 98.91/13.02 ((
% 98.91/13.02 (apProp) =>
% 98.91/13.02 ((
% 98.91/13.02 (app) =>
% 98.91/13.02 ((
% 98.91/13.02 (infuncsetfunc) =>
% 98.91/13.02 ((
% 98.91/13.02 (ap2p) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcinfuncset) =>
% 98.91/13.02 ((
% 98.91/13.02 (lamProp) =>
% 98.91/13.02 ((
% 98.91/13.02 (lamp) =>
% 98.91/13.02 ((
% 98.91/13.02 (lam2p) =>
% 98.91/13.02 ((
% 98.91/13.02 (brelnall1) =>
% 98.91/13.02 ((
% 98.91/13.02 (brelnall2) =>
% 98.91/13.02 ((
% 98.91/13.02 (ex1E2) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcGraphProp1) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcGraphProp3) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcGraphProp2) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcextLem) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcGraphProp4) =>
% 98.91/13.02 ((
% 98.91/13.02 (subbreln) =>
% 98.91/13.02 ((
% 98.91/13.02 (eqbreln) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcext) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcext2) =>
% 98.91/13.02 ((
% 98.91/13.02 (ap2apEq1) =>
% 98.91/13.02 ((
% 98.91/13.02 (ap2apEq2) =>
% 98.91/13.02 ((
% 98.91/13.02 (beta1) =>
% 98.91/13.02 ((
% 98.91/13.02 (eta1) =>
% 98.91/13.02 ((
% 98.91/13.02 (lam2lamEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (beta2) =>
% 98.91/13.02 ((
% 98.91/13.02 (eta2) =>
% 98.91/13.02 ((
% 98.91/13.02 (iffalseProp1) =>
% 98.91/13.02 ((
% 98.91/13.02 (iffalseProp2) =>
% 98.91/13.02 ((
% 98.91/13.02 (iftrueProp1) =>
% 98.91/13.02 ((
% 98.91/13.02 (iftrueProp2) =>
% 98.91/13.02 ((
% 98.91/13.02 (ifSingleton) =>
% 98.91/13.02 ((
% 98.91/13.02 (ifp) =>
% 98.91/13.02 ((
% 98.91/13.02 (theeq) =>
% 98.91/13.02 ((
% 98.91/13.02 (iftrue) =>
% 98.91/13.02 ((
% 98.91/13.02 (iffalse) =>
% 98.91/13.02 ((
% 98.91/13.02 (iftrueorfalse) =>
% 98.91/13.02 ((
% 98.91/13.02 (binintersectT_lem) =>
% 98.91/13.02 ((
% 98.91/13.02 (binunionT_lem) =>
% 98.91/13.02 ((
% 98.91/13.02 (powersetT_lem) =>
% 98.91/13.02 ((
% 98.91/13.02 (setminusT_lem) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementT_lem) =>
% 98.91/13.02 ((
% 98.91/13.02 (setextT) =>
% 98.91/13.02 ((
% 98.91/13.02 (subsetTI) =>
% 98.91/13.02 ((
% 98.91/13.02 (powersetTI1) =>
% 98.91/13.02 ((
% 98.91/13.02 (powersetTE1) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementTI1) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementTE1) =>
% 98.91/13.02 ((
% 98.91/13.02 (binintersectTELcontra) =>
% 98.91/13.02 ((
% 98.91/13.02 (binintersectTERcontra) =>
% 98.91/13.02 ((
% 98.91/13.02 (contrasubsetT) =>
% 98.91/13.02 ((
% 98.91/13.02 (contrasubsetT1) =>
% 98.91/13.02 ((
% 98.91/13.02 (contrasubsetT2) =>
% 98.91/13.02 ((
% 98.91/13.02 (contrasubsetT3) =>
% 98.91/13.02 ((
% 98.91/13.02 (doubleComplementI1) =>
% 98.91/13.02 ((
% 98.91/13.02 (doubleComplementE1) =>
% 98.91/13.02 ((
% 98.91/13.02 (doubleComplementSub1) =>
% 98.91/13.02 ((
% 98.91/13.02 (doubleComplementSub2) =>
% 98.91/13.02 ((
% 98.91/13.02 (doubleComplementEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementTnotintersectT) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementImpComplementIntersect) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementSubsetComplementIntersect) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementInPowersetComplementIntersect) =>
% 98.91/13.02 ((
% 98.91/13.02 (contraSubsetComplement) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementTcontraSubset) =>
% 98.91/13.02 ((
% 98.91/13.02 (binunionTILcontra) =>
% 98.91/13.02 ((
% 98.91/13.02 (binunionTIRcontra) =>
% 98.91/13.02 ((
% 98.91/13.02 (inIntersectImpInUnion) =>
% 98.91/13.02 ((
% 98.91/13.02 (inIntersectImpInUnion2) =>
% 98.91/13.02 ((
% 98.91/13.02 (inIntersectImpInIntersectUnions) =>
% 98.91/13.02 ((
% 98.91/13.02 (intersectInPowersetIntersectUnions) =>
% 98.91/13.02 ((
% 98.91/13.02 (inComplementUnionImpNotIn1) =>
% 98.91/13.02 ((
% 98.91/13.02 (inComplementUnionImpInComplement1) =>
% 98.91/13.02 ((
% 98.91/13.02 (binunionTE) =>
% 98.91/13.02 ((
% 98.91/13.02 (binunionTEcontra) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2a1) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementUnionInPowersetComplement) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2a2) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan1a) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan1b) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan1) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2a) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2b2) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2b) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz13rule0) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz13rule1) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz13rule2) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz13rule3) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz13rule4) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz1_1) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz1_2) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz1_3) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz1_4) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz1_5) =>
% 98.91/13.02 ((
% 98.91/13.02 (breln1all2) =>
% 98.91/13.02 ((
% 98.91/13.02 (breln1SetBreln1) =>
% 98.91/13.02 ((
% 98.91/13.02 (choice2fnsingleton) =>
% 98.91/13.02 ((
% 98.91/13.02 (!!) @ (
% 98.91/13.02 (('#B') @ (
% 98.91/13.02 !!) @
% 98.91/13.02 (
% 98.91/13.02 (
% 98.91/13.02 ('#S') @ (
% 98.91/13.02 (
% 98.91/13.02 ('#B') @ (
% 98.91/13.02 '#B') @
% 98.91/13.02 breln1)) @
% 98.91/13.02 (
% 98.91/13.02 (
% 98.91/13.02 ('#S') @ dpsetconstr @
% 98.91/13.02 (
% 98.91/13.02 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.91/13.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1305])).
% 98.91/13.02 thf(zip_derived_cl1321, plain,
% 98.91/13.02 (~ (((setminusSubset1) =>
% 98.91/13.02 (((symdiffE) =>
% 98.91/13.02 (((symdiffI1) =>
% 98.91/13.02 (((symdiffI2) =>
% 98.91/13.02 (((symdiffIneg1) =>
% 98.91/13.02 (((symdiffIneg2) =>
% 98.91/13.02 (((secondinupair) =>
% 98.91/13.02 (((setukpairIL) =>
% 98.91/13.02 (((setukpairIR) =>
% 98.91/13.02 (((kpairiskpair) =>
% 98.91/13.02 (((kpairp) =>
% 98.91/13.02 (((singletonsubset) =>
% 98.91/13.02 (((singletoninpowerset) =>
% 98.91/13.02 (((singletoninpowunion) =>
% 98.91/13.02 (((upairset2E) =>
% 98.91/13.02 (((upairsubunion) =>
% 98.91/13.02 (((upairinpowunion) =>
% 98.91/13.02 (((ubforcartprodlem1) =>
% 98.91/13.02 (((ubforcartprodlem2) =>
% 98.91/13.02 (((ubforcartprodlem3) =>
% 98.91/13.02 (((cartprodpairin) =>
% 98.91/13.02 (((cartprodmempair1) =>
% 98.91/13.02 (((cartprodmempair) =>
% 98.91/13.02 (((setunionE2) =>
% 98.91/13.02 (((setunionsingleton1) =>
% 98.91/13.02 (((setunionsingleton2) =>
% 98.91/13.02 (((setunionsingleton) =>
% 98.91/13.02 (((singletonprop) =>
% 98.91/13.02 (((ex1E1) =>
% 98.91/13.02 (((ex1I) =>
% 98.91/13.02 ((
% 98.91/13.02 (ex1I2) =>
% 98.91/13.02 ((
% 98.91/13.02 (singletonsuniq) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjL1) =>
% 98.91/13.02 ((
% 98.91/13.02 (kfstsingleton) =>
% 98.91/13.02 ((
% 98.91/13.02 (theprop) =>
% 98.91/13.02 ((
% 98.91/13.02 (kfstpairEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodfstin) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjL2) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjL) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjR11) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjR12) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjR1) =>
% 98.91/13.02 ((
% 98.91/13.02 (upairequniteq) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjR2) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjR) =>
% 98.91/13.02 ((
% 98.91/13.02 (ksndsingleton) =>
% 98.91/13.02 ((
% 98.91/13.02 (ksndpairEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (kpairsurjEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodsndin) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodpairmemEL) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodpairmemER) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodmempaircEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodfstpairEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodsndpairEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodpairsurjEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrI) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrSub) =>
% 98.91/13.02 ((
% 98.91/13.02 (setOfPairsIsBReln) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrERa) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrEL1) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrEL2) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrER) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcImageSingleton) =>
% 98.91/13.02 ((
% 98.91/13.02 (apProp) =>
% 98.91/13.02 ((
% 98.91/13.02 (app) =>
% 98.91/13.02 ((
% 98.91/13.02 (infuncsetfunc) =>
% 98.91/13.02 ((
% 98.91/13.02 (ap2p) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcinfuncset) =>
% 98.91/13.02 ((
% 98.91/13.02 (lamProp) =>
% 98.91/13.02 ((
% 98.91/13.02 (lamp) =>
% 98.91/13.02 ((
% 98.91/13.02 (lam2p) =>
% 98.91/13.02 ((
% 98.91/13.02 (brelnall1) =>
% 98.91/13.02 ((
% 98.91/13.02 (brelnall2) =>
% 98.91/13.02 ((
% 98.91/13.02 (ex1E2) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcGraphProp1) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcGraphProp3) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcGraphProp2) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcextLem) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcGraphProp4) =>
% 98.91/13.02 ((
% 98.91/13.02 (subbreln) =>
% 98.91/13.02 ((
% 98.91/13.02 (eqbreln) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcext) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcext2) =>
% 98.91/13.02 ((
% 98.91/13.02 (ap2apEq1) =>
% 98.91/13.02 ((
% 98.91/13.02 (ap2apEq2) =>
% 98.91/13.02 ((
% 98.91/13.02 (beta1) =>
% 98.91/13.02 ((
% 98.91/13.02 (eta1) =>
% 98.91/13.02 ((
% 98.91/13.02 (lam2lamEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (beta2) =>
% 98.91/13.02 ((
% 98.91/13.02 (eta2) =>
% 98.91/13.02 ((
% 98.91/13.02 (iffalseProp1) =>
% 98.91/13.02 ((
% 98.91/13.02 (iffalseProp2) =>
% 98.91/13.02 ((
% 98.91/13.02 (iftrueProp1) =>
% 98.91/13.02 ((
% 98.91/13.02 (iftrueProp2) =>
% 98.91/13.02 ((
% 98.91/13.02 (ifSingleton) =>
% 98.91/13.02 ((
% 98.91/13.02 (ifp) =>
% 98.91/13.02 ((
% 98.91/13.02 (theeq) =>
% 98.91/13.02 ((
% 98.91/13.02 (iftrue) =>
% 98.91/13.02 ((
% 98.91/13.02 (iffalse) =>
% 98.91/13.02 ((
% 98.91/13.02 (iftrueorfalse) =>
% 98.91/13.02 ((
% 98.91/13.02 (binintersectT_lem) =>
% 98.91/13.02 ((
% 98.91/13.02 (binunionT_lem) =>
% 98.91/13.02 ((
% 98.91/13.02 (powersetT_lem) =>
% 98.91/13.02 ((
% 98.91/13.02 (setminusT_lem) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementT_lem) =>
% 98.91/13.02 ((
% 98.91/13.02 (setextT) =>
% 98.91/13.02 ((
% 98.91/13.02 (subsetTI) =>
% 98.91/13.02 ((
% 98.91/13.02 (powersetTI1) =>
% 98.91/13.02 ((
% 98.91/13.02 (powersetTE1) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementTI1) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementTE1) =>
% 98.91/13.02 ((
% 98.91/13.02 (binintersectTELcontra) =>
% 98.91/13.02 ((
% 98.91/13.02 (binintersectTERcontra) =>
% 98.91/13.02 ((
% 98.91/13.02 (contrasubsetT) =>
% 98.91/13.02 ((
% 98.91/13.02 (contrasubsetT1) =>
% 98.91/13.02 ((
% 98.91/13.02 (contrasubsetT2) =>
% 98.91/13.02 ((
% 98.91/13.02 (contrasubsetT3) =>
% 98.91/13.02 ((
% 98.91/13.02 (doubleComplementI1) =>
% 98.91/13.02 ((
% 98.91/13.02 (doubleComplementE1) =>
% 98.91/13.02 ((
% 98.91/13.02 (doubleComplementSub1) =>
% 98.91/13.02 ((
% 98.91/13.02 (doubleComplementSub2) =>
% 98.91/13.02 ((
% 98.91/13.02 (doubleComplementEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementTnotintersectT) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementImpComplementIntersect) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementSubsetComplementIntersect) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementInPowersetComplementIntersect) =>
% 98.91/13.02 ((
% 98.91/13.02 (contraSubsetComplement) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementTcontraSubset) =>
% 98.91/13.02 ((
% 98.91/13.02 (binunionTILcontra) =>
% 98.91/13.02 ((
% 98.91/13.02 (binunionTIRcontra) =>
% 98.91/13.02 ((
% 98.91/13.02 (inIntersectImpInUnion) =>
% 98.91/13.02 ((
% 98.91/13.02 (inIntersectImpInUnion2) =>
% 98.91/13.02 ((
% 98.91/13.02 (inIntersectImpInIntersectUnions) =>
% 98.91/13.02 ((
% 98.91/13.02 (intersectInPowersetIntersectUnions) =>
% 98.91/13.02 ((
% 98.91/13.02 (inComplementUnionImpNotIn1) =>
% 98.91/13.02 ((
% 98.91/13.02 (inComplementUnionImpInComplement1) =>
% 98.91/13.02 ((
% 98.91/13.02 (binunionTE) =>
% 98.91/13.02 ((
% 98.91/13.02 (binunionTEcontra) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2a1) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementUnionInPowersetComplement) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2a2) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan1a) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan1b) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan1) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2a) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2b2) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2b) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz13rule0) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz13rule1) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz13rule2) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz13rule3) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz13rule4) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz1_1) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz1_2) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz1_3) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz1_4) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz1_5) =>
% 98.91/13.02 ((
% 98.91/13.02 (breln1all2) =>
% 98.91/13.02 ((
% 98.91/13.02 (breln1SetBreln1) =>
% 98.91/13.02 ((
% 98.91/13.02 (choice2fnsingleton) =>
% 98.91/13.02 ((
% 98.91/13.02 (!!) @ (
% 98.91/13.02 (('#B') @ (
% 98.91/13.02 !!) @
% 98.91/13.02 (
% 98.91/13.02 (
% 98.91/13.02 ('#S') @ (
% 98.91/13.02 (
% 98.91/13.02 ('#B') @ (
% 98.91/13.02 '#B') @
% 98.91/13.02 breln1)) @
% 98.91/13.02 (
% 98.91/13.02 (
% 98.91/13.02 ('#S') @ dpsetconstr @
% 98.91/13.02 (
% 98.91/13.02 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.91/13.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1313])).
% 98.91/13.02 thf(zip_derived_cl1329, plain,
% 98.91/13.02 (~ (((symdiffE) =>
% 98.91/13.02 (((symdiffI1) =>
% 98.91/13.02 (((symdiffI2) =>
% 98.91/13.02 (((symdiffIneg1) =>
% 98.91/13.02 (((symdiffIneg2) =>
% 98.91/13.02 (((secondinupair) =>
% 98.91/13.02 (((setukpairIL) =>
% 98.91/13.02 (((setukpairIR) =>
% 98.91/13.02 (((kpairiskpair) =>
% 98.91/13.02 (((kpairp) =>
% 98.91/13.02 (((singletonsubset) =>
% 98.91/13.02 (((singletoninpowerset) =>
% 98.91/13.02 (((singletoninpowunion) =>
% 98.91/13.02 (((upairset2E) =>
% 98.91/13.02 (((upairsubunion) =>
% 98.91/13.02 (((upairinpowunion) =>
% 98.91/13.02 (((ubforcartprodlem1) =>
% 98.91/13.02 (((ubforcartprodlem2) =>
% 98.91/13.02 (((ubforcartprodlem3) =>
% 98.91/13.02 (((cartprodpairin) =>
% 98.91/13.02 (((cartprodmempair1) =>
% 98.91/13.02 (((cartprodmempair) =>
% 98.91/13.02 (((setunionE2) =>
% 98.91/13.02 (((setunionsingleton1) =>
% 98.91/13.02 (((setunionsingleton2) =>
% 98.91/13.02 (((setunionsingleton) =>
% 98.91/13.02 (((singletonprop) =>
% 98.91/13.02 (((ex1E1) =>
% 98.91/13.02 (((ex1I) =>
% 98.91/13.02 (((ex1I2) =>
% 98.91/13.02 ((
% 98.91/13.02 (singletonsuniq) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjL1) =>
% 98.91/13.02 ((
% 98.91/13.02 (kfstsingleton) =>
% 98.91/13.02 ((
% 98.91/13.02 (theprop) =>
% 98.91/13.02 ((
% 98.91/13.02 (kfstpairEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodfstin) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjL2) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjL) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjR11) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjR12) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjR1) =>
% 98.91/13.02 ((
% 98.91/13.02 (upairequniteq) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjR2) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjR) =>
% 98.91/13.02 ((
% 98.91/13.02 (ksndsingleton) =>
% 98.91/13.02 ((
% 98.91/13.02 (ksndpairEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (kpairsurjEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodsndin) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodpairmemEL) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodpairmemER) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodmempaircEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodfstpairEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodsndpairEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodpairsurjEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrI) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrSub) =>
% 98.91/13.02 ((
% 98.91/13.02 (setOfPairsIsBReln) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrERa) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrEL1) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrEL2) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrER) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcImageSingleton) =>
% 98.91/13.02 ((
% 98.91/13.02 (apProp) =>
% 98.91/13.02 ((
% 98.91/13.02 (app) =>
% 98.91/13.02 ((
% 98.91/13.02 (infuncsetfunc) =>
% 98.91/13.02 ((
% 98.91/13.02 (ap2p) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcinfuncset) =>
% 98.91/13.02 ((
% 98.91/13.02 (lamProp) =>
% 98.91/13.02 ((
% 98.91/13.02 (lamp) =>
% 98.91/13.02 ((
% 98.91/13.02 (lam2p) =>
% 98.91/13.02 ((
% 98.91/13.02 (brelnall1) =>
% 98.91/13.02 ((
% 98.91/13.02 (brelnall2) =>
% 98.91/13.02 ((
% 98.91/13.02 (ex1E2) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcGraphProp1) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcGraphProp3) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcGraphProp2) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcextLem) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcGraphProp4) =>
% 98.91/13.02 ((
% 98.91/13.02 (subbreln) =>
% 98.91/13.02 ((
% 98.91/13.02 (eqbreln) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcext) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcext2) =>
% 98.91/13.02 ((
% 98.91/13.02 (ap2apEq1) =>
% 98.91/13.02 ((
% 98.91/13.02 (ap2apEq2) =>
% 98.91/13.02 ((
% 98.91/13.02 (beta1) =>
% 98.91/13.02 ((
% 98.91/13.02 (eta1) =>
% 98.91/13.02 ((
% 98.91/13.02 (lam2lamEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (beta2) =>
% 98.91/13.02 ((
% 98.91/13.02 (eta2) =>
% 98.91/13.02 ((
% 98.91/13.02 (iffalseProp1) =>
% 98.91/13.02 ((
% 98.91/13.02 (iffalseProp2) =>
% 98.91/13.02 ((
% 98.91/13.02 (iftrueProp1) =>
% 98.91/13.02 ((
% 98.91/13.02 (iftrueProp2) =>
% 98.91/13.02 ((
% 98.91/13.02 (ifSingleton) =>
% 98.91/13.02 ((
% 98.91/13.02 (ifp) =>
% 98.91/13.02 ((
% 98.91/13.02 (theeq) =>
% 98.91/13.02 ((
% 98.91/13.02 (iftrue) =>
% 98.91/13.02 ((
% 98.91/13.02 (iffalse) =>
% 98.91/13.02 ((
% 98.91/13.02 (iftrueorfalse) =>
% 98.91/13.02 ((
% 98.91/13.02 (binintersectT_lem) =>
% 98.91/13.02 ((
% 98.91/13.02 (binunionT_lem) =>
% 98.91/13.02 ((
% 98.91/13.02 (powersetT_lem) =>
% 98.91/13.02 ((
% 98.91/13.02 (setminusT_lem) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementT_lem) =>
% 98.91/13.02 ((
% 98.91/13.02 (setextT) =>
% 98.91/13.02 ((
% 98.91/13.02 (subsetTI) =>
% 98.91/13.02 ((
% 98.91/13.02 (powersetTI1) =>
% 98.91/13.02 ((
% 98.91/13.02 (powersetTE1) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementTI1) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementTE1) =>
% 98.91/13.02 ((
% 98.91/13.02 (binintersectTELcontra) =>
% 98.91/13.02 ((
% 98.91/13.02 (binintersectTERcontra) =>
% 98.91/13.02 ((
% 98.91/13.02 (contrasubsetT) =>
% 98.91/13.02 ((
% 98.91/13.02 (contrasubsetT1) =>
% 98.91/13.02 ((
% 98.91/13.02 (contrasubsetT2) =>
% 98.91/13.02 ((
% 98.91/13.02 (contrasubsetT3) =>
% 98.91/13.02 ((
% 98.91/13.02 (doubleComplementI1) =>
% 98.91/13.02 ((
% 98.91/13.02 (doubleComplementE1) =>
% 98.91/13.02 ((
% 98.91/13.02 (doubleComplementSub1) =>
% 98.91/13.02 ((
% 98.91/13.02 (doubleComplementSub2) =>
% 98.91/13.02 ((
% 98.91/13.02 (doubleComplementEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementTnotintersectT) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementImpComplementIntersect) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementSubsetComplementIntersect) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementInPowersetComplementIntersect) =>
% 98.91/13.02 ((
% 98.91/13.02 (contraSubsetComplement) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementTcontraSubset) =>
% 98.91/13.02 ((
% 98.91/13.02 (binunionTILcontra) =>
% 98.91/13.02 ((
% 98.91/13.02 (binunionTIRcontra) =>
% 98.91/13.02 ((
% 98.91/13.02 (inIntersectImpInUnion) =>
% 98.91/13.02 ((
% 98.91/13.02 (inIntersectImpInUnion2) =>
% 98.91/13.02 ((
% 98.91/13.02 (inIntersectImpInIntersectUnions) =>
% 98.91/13.02 ((
% 98.91/13.02 (intersectInPowersetIntersectUnions) =>
% 98.91/13.02 ((
% 98.91/13.02 (inComplementUnionImpNotIn1) =>
% 98.91/13.02 ((
% 98.91/13.02 (inComplementUnionImpInComplement1) =>
% 98.91/13.02 ((
% 98.91/13.02 (binunionTE) =>
% 98.91/13.02 ((
% 98.91/13.02 (binunionTEcontra) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2a1) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementUnionInPowersetComplement) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2a2) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan1a) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan1b) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan1) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2a) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2b2) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2b) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz13rule0) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz13rule1) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz13rule2) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz13rule3) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz13rule4) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz1_1) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz1_2) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz1_3) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz1_4) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz1_5) =>
% 98.91/13.02 ((
% 98.91/13.02 (breln1all2) =>
% 98.91/13.02 ((
% 98.91/13.02 (breln1SetBreln1) =>
% 98.91/13.02 ((
% 98.91/13.02 (choice2fnsingleton) =>
% 98.91/13.02 ((
% 98.91/13.02 (!!) @ (
% 98.91/13.02 (('#B') @ (
% 98.91/13.02 !!) @
% 98.91/13.02 (
% 98.91/13.02 (
% 98.91/13.02 ('#S') @ (
% 98.91/13.02 (
% 98.91/13.02 ('#B') @ (
% 98.91/13.02 '#B') @
% 98.91/13.02 breln1)) @
% 98.91/13.02 (
% 98.91/13.02 (
% 98.91/13.02 ('#S') @ dpsetconstr @
% 98.91/13.02 (
% 98.91/13.02 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.91/13.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1321])).
% 98.91/13.02 thf(zip_derived_cl1338, plain,
% 98.91/13.02 (~ (((symdiffI1) =>
% 98.91/13.02 (((symdiffI2) =>
% 98.91/13.02 (((symdiffIneg1) =>
% 98.91/13.02 (((symdiffIneg2) =>
% 98.91/13.02 (((secondinupair) =>
% 98.91/13.02 (((setukpairIL) =>
% 98.91/13.02 (((setukpairIR) =>
% 98.91/13.02 (((kpairiskpair) =>
% 98.91/13.02 (((kpairp) =>
% 98.91/13.02 (((singletonsubset) =>
% 98.91/13.02 (((singletoninpowerset) =>
% 98.91/13.02 (((singletoninpowunion) =>
% 98.91/13.02 (((upairset2E) =>
% 98.91/13.02 (((upairsubunion) =>
% 98.91/13.02 (((upairinpowunion) =>
% 98.91/13.02 (((ubforcartprodlem1) =>
% 98.91/13.02 (((ubforcartprodlem2) =>
% 98.91/13.02 (((ubforcartprodlem3) =>
% 98.91/13.02 (((cartprodpairin) =>
% 98.91/13.02 (((cartprodmempair1) =>
% 98.91/13.02 (((cartprodmempair) =>
% 98.91/13.02 (((setunionE2) =>
% 98.91/13.02 (((setunionsingleton1) =>
% 98.91/13.02 (((setunionsingleton2) =>
% 98.91/13.02 (((setunionsingleton) =>
% 98.91/13.02 (((singletonprop) =>
% 98.91/13.02 (((ex1E1) =>
% 98.91/13.02 (((ex1I) =>
% 98.91/13.02 (((ex1I2) =>
% 98.91/13.02 (((singletonsuniq) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjL1) =>
% 98.91/13.02 ((
% 98.91/13.02 (kfstsingleton) =>
% 98.91/13.02 ((
% 98.91/13.02 (theprop) =>
% 98.91/13.02 ((
% 98.91/13.02 (kfstpairEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodfstin) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjL2) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjL) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjR11) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjR12) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjR1) =>
% 98.91/13.02 ((
% 98.91/13.02 (upairequniteq) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjR2) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjR) =>
% 98.91/13.02 ((
% 98.91/13.02 (ksndsingleton) =>
% 98.91/13.02 ((
% 98.91/13.02 (ksndpairEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (kpairsurjEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodsndin) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodpairmemEL) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodpairmemER) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodmempaircEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodfstpairEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodsndpairEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodpairsurjEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrI) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrSub) =>
% 98.91/13.02 ((
% 98.91/13.02 (setOfPairsIsBReln) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrERa) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrEL1) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrEL2) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrER) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcImageSingleton) =>
% 98.91/13.02 ((
% 98.91/13.02 (apProp) =>
% 98.91/13.02 ((
% 98.91/13.02 (app) =>
% 98.91/13.02 ((
% 98.91/13.02 (infuncsetfunc) =>
% 98.91/13.02 ((
% 98.91/13.02 (ap2p) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcinfuncset) =>
% 98.91/13.02 ((
% 98.91/13.02 (lamProp) =>
% 98.91/13.02 ((
% 98.91/13.02 (lamp) =>
% 98.91/13.02 ((
% 98.91/13.02 (lam2p) =>
% 98.91/13.02 ((
% 98.91/13.02 (brelnall1) =>
% 98.91/13.02 ((
% 98.91/13.02 (brelnall2) =>
% 98.91/13.02 ((
% 98.91/13.02 (ex1E2) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcGraphProp1) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcGraphProp3) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcGraphProp2) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcextLem) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcGraphProp4) =>
% 98.91/13.02 ((
% 98.91/13.02 (subbreln) =>
% 98.91/13.02 ((
% 98.91/13.02 (eqbreln) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcext) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcext2) =>
% 98.91/13.02 ((
% 98.91/13.02 (ap2apEq1) =>
% 98.91/13.02 ((
% 98.91/13.02 (ap2apEq2) =>
% 98.91/13.02 ((
% 98.91/13.02 (beta1) =>
% 98.91/13.02 ((
% 98.91/13.02 (eta1) =>
% 98.91/13.02 ((
% 98.91/13.02 (lam2lamEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (beta2) =>
% 98.91/13.02 ((
% 98.91/13.02 (eta2) =>
% 98.91/13.02 ((
% 98.91/13.02 (iffalseProp1) =>
% 98.91/13.02 ((
% 98.91/13.02 (iffalseProp2) =>
% 98.91/13.02 ((
% 98.91/13.02 (iftrueProp1) =>
% 98.91/13.02 ((
% 98.91/13.02 (iftrueProp2) =>
% 98.91/13.02 ((
% 98.91/13.02 (ifSingleton) =>
% 98.91/13.02 ((
% 98.91/13.02 (ifp) =>
% 98.91/13.02 ((
% 98.91/13.02 (theeq) =>
% 98.91/13.02 ((
% 98.91/13.02 (iftrue) =>
% 98.91/13.02 ((
% 98.91/13.02 (iffalse) =>
% 98.91/13.02 ((
% 98.91/13.02 (iftrueorfalse) =>
% 98.91/13.02 ((
% 98.91/13.02 (binintersectT_lem) =>
% 98.91/13.02 ((
% 98.91/13.02 (binunionT_lem) =>
% 98.91/13.02 ((
% 98.91/13.02 (powersetT_lem) =>
% 98.91/13.02 ((
% 98.91/13.02 (setminusT_lem) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementT_lem) =>
% 98.91/13.02 ((
% 98.91/13.02 (setextT) =>
% 98.91/13.02 ((
% 98.91/13.02 (subsetTI) =>
% 98.91/13.02 ((
% 98.91/13.02 (powersetTI1) =>
% 98.91/13.02 ((
% 98.91/13.02 (powersetTE1) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementTI1) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementTE1) =>
% 98.91/13.02 ((
% 98.91/13.02 (binintersectTELcontra) =>
% 98.91/13.02 ((
% 98.91/13.02 (binintersectTERcontra) =>
% 98.91/13.02 ((
% 98.91/13.02 (contrasubsetT) =>
% 98.91/13.02 ((
% 98.91/13.02 (contrasubsetT1) =>
% 98.91/13.02 ((
% 98.91/13.02 (contrasubsetT2) =>
% 98.91/13.02 ((
% 98.91/13.02 (contrasubsetT3) =>
% 98.91/13.02 ((
% 98.91/13.02 (doubleComplementI1) =>
% 98.91/13.02 ((
% 98.91/13.02 (doubleComplementE1) =>
% 98.91/13.02 ((
% 98.91/13.02 (doubleComplementSub1) =>
% 98.91/13.02 ((
% 98.91/13.02 (doubleComplementSub2) =>
% 98.91/13.02 ((
% 98.91/13.02 (doubleComplementEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementTnotintersectT) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementImpComplementIntersect) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementSubsetComplementIntersect) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementInPowersetComplementIntersect) =>
% 98.91/13.02 ((
% 98.91/13.02 (contraSubsetComplement) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementTcontraSubset) =>
% 98.91/13.02 ((
% 98.91/13.02 (binunionTILcontra) =>
% 98.91/13.02 ((
% 98.91/13.02 (binunionTIRcontra) =>
% 98.91/13.02 ((
% 98.91/13.02 (inIntersectImpInUnion) =>
% 98.91/13.02 ((
% 98.91/13.02 (inIntersectImpInUnion2) =>
% 98.91/13.02 ((
% 98.91/13.02 (inIntersectImpInIntersectUnions) =>
% 98.91/13.02 ((
% 98.91/13.02 (intersectInPowersetIntersectUnions) =>
% 98.91/13.02 ((
% 98.91/13.02 (inComplementUnionImpNotIn1) =>
% 98.91/13.02 ((
% 98.91/13.02 (inComplementUnionImpInComplement1) =>
% 98.91/13.02 ((
% 98.91/13.02 (binunionTE) =>
% 98.91/13.02 ((
% 98.91/13.02 (binunionTEcontra) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2a1) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementUnionInPowersetComplement) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2a2) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan1a) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan1b) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan1) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2a) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2b2) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2b) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz13rule0) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz13rule1) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz13rule2) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz13rule3) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz13rule4) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz1_1) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz1_2) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz1_3) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz1_4) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz1_5) =>
% 98.91/13.02 ((
% 98.91/13.02 (breln1all2) =>
% 98.91/13.02 ((
% 98.91/13.02 (breln1SetBreln1) =>
% 98.91/13.02 ((
% 98.91/13.02 (choice2fnsingleton) =>
% 98.91/13.02 ((
% 98.91/13.02 (!!) @ (
% 98.91/13.02 (('#B') @ (
% 98.91/13.02 !!) @
% 98.91/13.02 (
% 98.91/13.02 (
% 98.91/13.02 ('#S') @ (
% 98.91/13.02 (
% 98.91/13.02 ('#B') @ (
% 98.91/13.02 '#B') @
% 98.91/13.02 breln1)) @
% 98.91/13.02 (
% 98.91/13.02 (
% 98.91/13.02 ('#S') @ dpsetconstr @
% 98.91/13.02 (
% 98.91/13.02 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.91/13.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1329])).
% 98.91/13.02 thf(zip_derived_cl1347, plain,
% 98.91/13.02 (~ (((symdiffI2) =>
% 98.91/13.02 (((symdiffIneg1) =>
% 98.91/13.02 (((symdiffIneg2) =>
% 98.91/13.02 (((secondinupair) =>
% 98.91/13.02 (((setukpairIL) =>
% 98.91/13.02 (((setukpairIR) =>
% 98.91/13.02 (((kpairiskpair) =>
% 98.91/13.02 (((kpairp) =>
% 98.91/13.02 (((singletonsubset) =>
% 98.91/13.02 (((singletoninpowerset) =>
% 98.91/13.02 (((singletoninpowunion) =>
% 98.91/13.02 (((upairset2E) =>
% 98.91/13.02 (((upairsubunion) =>
% 98.91/13.02 (((upairinpowunion) =>
% 98.91/13.02 (((ubforcartprodlem1) =>
% 98.91/13.02 (((ubforcartprodlem2) =>
% 98.91/13.02 (((ubforcartprodlem3) =>
% 98.91/13.02 (((cartprodpairin) =>
% 98.91/13.02 (((cartprodmempair1) =>
% 98.91/13.02 (((cartprodmempair) =>
% 98.91/13.02 (((setunionE2) =>
% 98.91/13.02 (((setunionsingleton1) =>
% 98.91/13.02 (((setunionsingleton2) =>
% 98.91/13.02 (((setunionsingleton) =>
% 98.91/13.02 (((singletonprop) =>
% 98.91/13.02 (((ex1E1) =>
% 98.91/13.02 (((ex1I) =>
% 98.91/13.02 (((ex1I2) =>
% 98.91/13.02 (((singletonsuniq) =>
% 98.91/13.02 (((setukpairinjL1) =>
% 98.91/13.02 ((
% 98.91/13.02 (kfstsingleton) =>
% 98.91/13.02 ((
% 98.91/13.02 (theprop) =>
% 98.91/13.02 ((
% 98.91/13.02 (kfstpairEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodfstin) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjL2) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjL) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjR11) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjR12) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjR1) =>
% 98.91/13.02 ((
% 98.91/13.02 (upairequniteq) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjR2) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjR) =>
% 98.91/13.02 ((
% 98.91/13.02 (ksndsingleton) =>
% 98.91/13.02 ((
% 98.91/13.02 (ksndpairEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (kpairsurjEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodsndin) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodpairmemEL) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodpairmemER) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodmempaircEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodfstpairEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodsndpairEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodpairsurjEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrI) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrSub) =>
% 98.91/13.02 ((
% 98.91/13.02 (setOfPairsIsBReln) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrERa) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrEL1) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrEL2) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrER) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcImageSingleton) =>
% 98.91/13.02 ((
% 98.91/13.02 (apProp) =>
% 98.91/13.02 ((
% 98.91/13.02 (app) =>
% 98.91/13.02 ((
% 98.91/13.02 (infuncsetfunc) =>
% 98.91/13.02 ((
% 98.91/13.02 (ap2p) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcinfuncset) =>
% 98.91/13.02 ((
% 98.91/13.02 (lamProp) =>
% 98.91/13.02 ((
% 98.91/13.02 (lamp) =>
% 98.91/13.02 ((
% 98.91/13.02 (lam2p) =>
% 98.91/13.02 ((
% 98.91/13.02 (brelnall1) =>
% 98.91/13.02 ((
% 98.91/13.02 (brelnall2) =>
% 98.91/13.02 ((
% 98.91/13.02 (ex1E2) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcGraphProp1) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcGraphProp3) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcGraphProp2) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcextLem) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcGraphProp4) =>
% 98.91/13.02 ((
% 98.91/13.02 (subbreln) =>
% 98.91/13.02 ((
% 98.91/13.02 (eqbreln) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcext) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcext2) =>
% 98.91/13.02 ((
% 98.91/13.02 (ap2apEq1) =>
% 98.91/13.02 ((
% 98.91/13.02 (ap2apEq2) =>
% 98.91/13.02 ((
% 98.91/13.02 (beta1) =>
% 98.91/13.02 ((
% 98.91/13.02 (eta1) =>
% 98.91/13.02 ((
% 98.91/13.02 (lam2lamEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (beta2) =>
% 98.91/13.02 ((
% 98.91/13.02 (eta2) =>
% 98.91/13.02 ((
% 98.91/13.02 (iffalseProp1) =>
% 98.91/13.02 ((
% 98.91/13.02 (iffalseProp2) =>
% 98.91/13.02 ((
% 98.91/13.02 (iftrueProp1) =>
% 98.91/13.02 ((
% 98.91/13.02 (iftrueProp2) =>
% 98.91/13.02 ((
% 98.91/13.02 (ifSingleton) =>
% 98.91/13.02 ((
% 98.91/13.02 (ifp) =>
% 98.91/13.02 ((
% 98.91/13.02 (theeq) =>
% 98.91/13.02 ((
% 98.91/13.02 (iftrue) =>
% 98.91/13.02 ((
% 98.91/13.02 (iffalse) =>
% 98.91/13.02 ((
% 98.91/13.02 (iftrueorfalse) =>
% 98.91/13.02 ((
% 98.91/13.02 (binintersectT_lem) =>
% 98.91/13.02 ((
% 98.91/13.02 (binunionT_lem) =>
% 98.91/13.02 ((
% 98.91/13.02 (powersetT_lem) =>
% 98.91/13.02 ((
% 98.91/13.02 (setminusT_lem) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementT_lem) =>
% 98.91/13.02 ((
% 98.91/13.02 (setextT) =>
% 98.91/13.02 ((
% 98.91/13.02 (subsetTI) =>
% 98.91/13.02 ((
% 98.91/13.02 (powersetTI1) =>
% 98.91/13.02 ((
% 98.91/13.02 (powersetTE1) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementTI1) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementTE1) =>
% 98.91/13.02 ((
% 98.91/13.02 (binintersectTELcontra) =>
% 98.91/13.02 ((
% 98.91/13.02 (binintersectTERcontra) =>
% 98.91/13.02 ((
% 98.91/13.02 (contrasubsetT) =>
% 98.91/13.02 ((
% 98.91/13.02 (contrasubsetT1) =>
% 98.91/13.02 ((
% 98.91/13.02 (contrasubsetT2) =>
% 98.91/13.02 ((
% 98.91/13.02 (contrasubsetT3) =>
% 98.91/13.02 ((
% 98.91/13.02 (doubleComplementI1) =>
% 98.91/13.02 ((
% 98.91/13.02 (doubleComplementE1) =>
% 98.91/13.02 ((
% 98.91/13.02 (doubleComplementSub1) =>
% 98.91/13.02 ((
% 98.91/13.02 (doubleComplementSub2) =>
% 98.91/13.02 ((
% 98.91/13.02 (doubleComplementEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementTnotintersectT) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementImpComplementIntersect) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementSubsetComplementIntersect) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementInPowersetComplementIntersect) =>
% 98.91/13.02 ((
% 98.91/13.02 (contraSubsetComplement) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementTcontraSubset) =>
% 98.91/13.02 ((
% 98.91/13.02 (binunionTILcontra) =>
% 98.91/13.02 ((
% 98.91/13.02 (binunionTIRcontra) =>
% 98.91/13.02 ((
% 98.91/13.02 (inIntersectImpInUnion) =>
% 98.91/13.02 ((
% 98.91/13.02 (inIntersectImpInUnion2) =>
% 98.91/13.02 ((
% 98.91/13.02 (inIntersectImpInIntersectUnions) =>
% 98.91/13.02 ((
% 98.91/13.02 (intersectInPowersetIntersectUnions) =>
% 98.91/13.02 ((
% 98.91/13.02 (inComplementUnionImpNotIn1) =>
% 98.91/13.02 ((
% 98.91/13.02 (inComplementUnionImpInComplement1) =>
% 98.91/13.02 ((
% 98.91/13.02 (binunionTE) =>
% 98.91/13.02 ((
% 98.91/13.02 (binunionTEcontra) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2a1) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementUnionInPowersetComplement) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2a2) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan1a) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan1b) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan1) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2a) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2b2) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2b) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz13rule0) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz13rule1) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz13rule2) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz13rule3) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz13rule4) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz1_1) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz1_2) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz1_3) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz1_4) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz1_5) =>
% 98.91/13.02 ((
% 98.91/13.02 (breln1all2) =>
% 98.91/13.02 ((
% 98.91/13.02 (breln1SetBreln1) =>
% 98.91/13.02 ((
% 98.91/13.02 (choice2fnsingleton) =>
% 98.91/13.02 ((
% 98.91/13.02 (!!) @ (
% 98.91/13.02 (('#B') @ (
% 98.91/13.02 !!) @
% 98.91/13.02 (
% 98.91/13.02 (
% 98.91/13.02 ('#S') @ (
% 98.91/13.02 (
% 98.91/13.02 ('#B') @ (
% 98.91/13.02 '#B') @
% 98.91/13.02 breln1)) @
% 98.91/13.02 (
% 98.91/13.02 (
% 98.91/13.02 ('#S') @ dpsetconstr @
% 98.91/13.02 (
% 98.91/13.02 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.91/13.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1338])).
% 98.91/13.02 thf(zip_derived_cl1354, plain,
% 98.91/13.02 (~ (((symdiffIneg1) =>
% 98.91/13.02 (((symdiffIneg2) =>
% 98.91/13.02 (((secondinupair) =>
% 98.91/13.02 (((setukpairIL) =>
% 98.91/13.02 (((setukpairIR) =>
% 98.91/13.02 (((kpairiskpair) =>
% 98.91/13.02 (((kpairp) =>
% 98.91/13.02 (((singletonsubset) =>
% 98.91/13.02 (((singletoninpowerset) =>
% 98.91/13.02 (((singletoninpowunion) =>
% 98.91/13.02 (((upairset2E) =>
% 98.91/13.02 (((upairsubunion) =>
% 98.91/13.02 (((upairinpowunion) =>
% 98.91/13.02 (((ubforcartprodlem1) =>
% 98.91/13.02 (((ubforcartprodlem2) =>
% 98.91/13.02 (((ubforcartprodlem3) =>
% 98.91/13.02 (((cartprodpairin) =>
% 98.91/13.02 (((cartprodmempair1) =>
% 98.91/13.02 (((cartprodmempair) =>
% 98.91/13.02 (((setunionE2) =>
% 98.91/13.02 (((setunionsingleton1) =>
% 98.91/13.02 (((setunionsingleton2) =>
% 98.91/13.02 (((setunionsingleton) =>
% 98.91/13.02 (((singletonprop) =>
% 98.91/13.02 (((ex1E1) =>
% 98.91/13.02 (((ex1I) =>
% 98.91/13.02 (((ex1I2) =>
% 98.91/13.02 (((singletonsuniq) =>
% 98.91/13.02 (((setukpairinjL1) =>
% 98.91/13.02 (((kfstsingleton) =>
% 98.91/13.02 ((
% 98.91/13.02 (theprop) =>
% 98.91/13.02 ((
% 98.91/13.02 (kfstpairEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodfstin) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjL2) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjL) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjR11) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjR12) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjR1) =>
% 98.91/13.02 ((
% 98.91/13.02 (upairequniteq) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjR2) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjR) =>
% 98.91/13.02 ((
% 98.91/13.02 (ksndsingleton) =>
% 98.91/13.02 ((
% 98.91/13.02 (ksndpairEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (kpairsurjEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodsndin) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodpairmemEL) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodpairmemER) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodmempaircEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodfstpairEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodsndpairEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodpairsurjEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrI) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrSub) =>
% 98.91/13.02 ((
% 98.91/13.02 (setOfPairsIsBReln) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrERa) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrEL1) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrEL2) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrER) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcImageSingleton) =>
% 98.91/13.02 ((
% 98.91/13.02 (apProp) =>
% 98.91/13.02 ((
% 98.91/13.02 (app) =>
% 98.91/13.02 ((
% 98.91/13.02 (infuncsetfunc) =>
% 98.91/13.02 ((
% 98.91/13.02 (ap2p) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcinfuncset) =>
% 98.91/13.02 ((
% 98.91/13.02 (lamProp) =>
% 98.91/13.02 ((
% 98.91/13.02 (lamp) =>
% 98.91/13.02 ((
% 98.91/13.02 (lam2p) =>
% 98.91/13.02 ((
% 98.91/13.02 (brelnall1) =>
% 98.91/13.02 ((
% 98.91/13.02 (brelnall2) =>
% 98.91/13.02 ((
% 98.91/13.02 (ex1E2) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcGraphProp1) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcGraphProp3) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcGraphProp2) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcextLem) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcGraphProp4) =>
% 98.91/13.02 ((
% 98.91/13.02 (subbreln) =>
% 98.91/13.02 ((
% 98.91/13.02 (eqbreln) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcext) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcext2) =>
% 98.91/13.02 ((
% 98.91/13.02 (ap2apEq1) =>
% 98.91/13.02 ((
% 98.91/13.02 (ap2apEq2) =>
% 98.91/13.02 ((
% 98.91/13.02 (beta1) =>
% 98.91/13.02 ((
% 98.91/13.02 (eta1) =>
% 98.91/13.02 ((
% 98.91/13.02 (lam2lamEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (beta2) =>
% 98.91/13.02 ((
% 98.91/13.02 (eta2) =>
% 98.91/13.02 ((
% 98.91/13.02 (iffalseProp1) =>
% 98.91/13.02 ((
% 98.91/13.02 (iffalseProp2) =>
% 98.91/13.02 ((
% 98.91/13.02 (iftrueProp1) =>
% 98.91/13.02 ((
% 98.91/13.02 (iftrueProp2) =>
% 98.91/13.02 ((
% 98.91/13.02 (ifSingleton) =>
% 98.91/13.02 ((
% 98.91/13.02 (ifp) =>
% 98.91/13.02 ((
% 98.91/13.02 (theeq) =>
% 98.91/13.02 ((
% 98.91/13.02 (iftrue) =>
% 98.91/13.02 ((
% 98.91/13.02 (iffalse) =>
% 98.91/13.02 ((
% 98.91/13.02 (iftrueorfalse) =>
% 98.91/13.02 ((
% 98.91/13.02 (binintersectT_lem) =>
% 98.91/13.02 ((
% 98.91/13.02 (binunionT_lem) =>
% 98.91/13.02 ((
% 98.91/13.02 (powersetT_lem) =>
% 98.91/13.02 ((
% 98.91/13.02 (setminusT_lem) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementT_lem) =>
% 98.91/13.02 ((
% 98.91/13.02 (setextT) =>
% 98.91/13.02 ((
% 98.91/13.02 (subsetTI) =>
% 98.91/13.02 ((
% 98.91/13.02 (powersetTI1) =>
% 98.91/13.02 ((
% 98.91/13.02 (powersetTE1) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementTI1) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementTE1) =>
% 98.91/13.02 ((
% 98.91/13.02 (binintersectTELcontra) =>
% 98.91/13.02 ((
% 98.91/13.02 (binintersectTERcontra) =>
% 98.91/13.02 ((
% 98.91/13.02 (contrasubsetT) =>
% 98.91/13.02 ((
% 98.91/13.02 (contrasubsetT1) =>
% 98.91/13.02 ((
% 98.91/13.02 (contrasubsetT2) =>
% 98.91/13.02 ((
% 98.91/13.02 (contrasubsetT3) =>
% 98.91/13.02 ((
% 98.91/13.02 (doubleComplementI1) =>
% 98.91/13.02 ((
% 98.91/13.02 (doubleComplementE1) =>
% 98.91/13.02 ((
% 98.91/13.02 (doubleComplementSub1) =>
% 98.91/13.02 ((
% 98.91/13.02 (doubleComplementSub2) =>
% 98.91/13.02 ((
% 98.91/13.02 (doubleComplementEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementTnotintersectT) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementImpComplementIntersect) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementSubsetComplementIntersect) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementInPowersetComplementIntersect) =>
% 98.91/13.02 ((
% 98.91/13.02 (contraSubsetComplement) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementTcontraSubset) =>
% 98.91/13.02 ((
% 98.91/13.02 (binunionTILcontra) =>
% 98.91/13.02 ((
% 98.91/13.02 (binunionTIRcontra) =>
% 98.91/13.02 ((
% 98.91/13.02 (inIntersectImpInUnion) =>
% 98.91/13.02 ((
% 98.91/13.02 (inIntersectImpInUnion2) =>
% 98.91/13.02 ((
% 98.91/13.02 (inIntersectImpInIntersectUnions) =>
% 98.91/13.02 ((
% 98.91/13.02 (intersectInPowersetIntersectUnions) =>
% 98.91/13.02 ((
% 98.91/13.02 (inComplementUnionImpNotIn1) =>
% 98.91/13.02 ((
% 98.91/13.02 (inComplementUnionImpInComplement1) =>
% 98.91/13.02 ((
% 98.91/13.02 (binunionTE) =>
% 98.91/13.02 ((
% 98.91/13.02 (binunionTEcontra) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2a1) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementUnionInPowersetComplement) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2a2) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan1a) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan1b) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan1) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2a) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2b2) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2b) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz13rule0) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz13rule1) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz13rule2) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz13rule3) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz13rule4) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz1_1) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz1_2) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz1_3) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz1_4) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz1_5) =>
% 98.91/13.02 ((
% 98.91/13.02 (breln1all2) =>
% 98.91/13.02 ((
% 98.91/13.02 (breln1SetBreln1) =>
% 98.91/13.02 ((
% 98.91/13.02 (choice2fnsingleton) =>
% 98.91/13.02 ((
% 98.91/13.02 (!!) @ (
% 98.91/13.02 (('#B') @ (
% 98.91/13.02 !!) @
% 98.91/13.02 (
% 98.91/13.02 (
% 98.91/13.02 ('#S') @ (
% 98.91/13.02 (
% 98.91/13.02 ('#B') @ (
% 98.91/13.02 '#B') @
% 98.91/13.02 breln1)) @
% 98.91/13.02 (
% 98.91/13.02 (
% 98.91/13.02 ('#S') @ dpsetconstr @
% 98.91/13.02 (
% 98.91/13.02 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.91/13.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1347])).
% 98.91/13.02 thf(zip_derived_cl1361, plain,
% 98.91/13.02 (~ (((symdiffIneg2) =>
% 98.91/13.02 (((secondinupair) =>
% 98.91/13.02 (((setukpairIL) =>
% 98.91/13.02 (((setukpairIR) =>
% 98.91/13.02 (((kpairiskpair) =>
% 98.91/13.02 (((kpairp) =>
% 98.91/13.02 (((singletonsubset) =>
% 98.91/13.02 (((singletoninpowerset) =>
% 98.91/13.02 (((singletoninpowunion) =>
% 98.91/13.02 (((upairset2E) =>
% 98.91/13.02 (((upairsubunion) =>
% 98.91/13.02 (((upairinpowunion) =>
% 98.91/13.02 (((ubforcartprodlem1) =>
% 98.91/13.02 (((ubforcartprodlem2) =>
% 98.91/13.02 (((ubforcartprodlem3) =>
% 98.91/13.02 (((cartprodpairin) =>
% 98.91/13.02 (((cartprodmempair1) =>
% 98.91/13.02 (((cartprodmempair) =>
% 98.91/13.02 (((setunionE2) =>
% 98.91/13.02 (((setunionsingleton1) =>
% 98.91/13.02 (((setunionsingleton2) =>
% 98.91/13.02 (((setunionsingleton) =>
% 98.91/13.02 (((singletonprop) =>
% 98.91/13.02 (((ex1E1) =>
% 98.91/13.02 (((ex1I) =>
% 98.91/13.02 (((ex1I2) =>
% 98.91/13.02 (((singletonsuniq) =>
% 98.91/13.02 (((setukpairinjL1) =>
% 98.91/13.02 (((kfstsingleton) =>
% 98.91/13.02 (((theprop) =>
% 98.91/13.02 ((
% 98.91/13.02 (kfstpairEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodfstin) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjL2) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjL) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjR11) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjR12) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjR1) =>
% 98.91/13.02 ((
% 98.91/13.02 (upairequniteq) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjR2) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjR) =>
% 98.91/13.02 ((
% 98.91/13.02 (ksndsingleton) =>
% 98.91/13.02 ((
% 98.91/13.02 (ksndpairEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (kpairsurjEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodsndin) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodpairmemEL) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodpairmemER) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodmempaircEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodfstpairEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodsndpairEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodpairsurjEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrI) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrSub) =>
% 98.91/13.02 ((
% 98.91/13.02 (setOfPairsIsBReln) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrERa) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrEL1) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrEL2) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrER) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcImageSingleton) =>
% 98.91/13.02 ((
% 98.91/13.02 (apProp) =>
% 98.91/13.02 ((
% 98.91/13.02 (app) =>
% 98.91/13.02 ((
% 98.91/13.02 (infuncsetfunc) =>
% 98.91/13.02 ((
% 98.91/13.02 (ap2p) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcinfuncset) =>
% 98.91/13.02 ((
% 98.91/13.02 (lamProp) =>
% 98.91/13.02 ((
% 98.91/13.02 (lamp) =>
% 98.91/13.02 ((
% 98.91/13.02 (lam2p) =>
% 98.91/13.02 ((
% 98.91/13.02 (brelnall1) =>
% 98.91/13.02 ((
% 98.91/13.02 (brelnall2) =>
% 98.91/13.02 ((
% 98.91/13.02 (ex1E2) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcGraphProp1) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcGraphProp3) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcGraphProp2) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcextLem) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcGraphProp4) =>
% 98.91/13.02 ((
% 98.91/13.02 (subbreln) =>
% 98.91/13.02 ((
% 98.91/13.02 (eqbreln) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcext) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcext2) =>
% 98.91/13.02 ((
% 98.91/13.02 (ap2apEq1) =>
% 98.91/13.02 ((
% 98.91/13.02 (ap2apEq2) =>
% 98.91/13.02 ((
% 98.91/13.02 (beta1) =>
% 98.91/13.02 ((
% 98.91/13.02 (eta1) =>
% 98.91/13.02 ((
% 98.91/13.02 (lam2lamEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (beta2) =>
% 98.91/13.02 ((
% 98.91/13.02 (eta2) =>
% 98.91/13.02 ((
% 98.91/13.02 (iffalseProp1) =>
% 98.91/13.02 ((
% 98.91/13.02 (iffalseProp2) =>
% 98.91/13.02 ((
% 98.91/13.02 (iftrueProp1) =>
% 98.91/13.02 ((
% 98.91/13.02 (iftrueProp2) =>
% 98.91/13.02 ((
% 98.91/13.02 (ifSingleton) =>
% 98.91/13.02 ((
% 98.91/13.02 (ifp) =>
% 98.91/13.02 ((
% 98.91/13.02 (theeq) =>
% 98.91/13.02 ((
% 98.91/13.02 (iftrue) =>
% 98.91/13.02 ((
% 98.91/13.02 (iffalse) =>
% 98.91/13.02 ((
% 98.91/13.02 (iftrueorfalse) =>
% 98.91/13.02 ((
% 98.91/13.02 (binintersectT_lem) =>
% 98.91/13.02 ((
% 98.91/13.02 (binunionT_lem) =>
% 98.91/13.02 ((
% 98.91/13.02 (powersetT_lem) =>
% 98.91/13.02 ((
% 98.91/13.02 (setminusT_lem) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementT_lem) =>
% 98.91/13.02 ((
% 98.91/13.02 (setextT) =>
% 98.91/13.02 ((
% 98.91/13.02 (subsetTI) =>
% 98.91/13.02 ((
% 98.91/13.02 (powersetTI1) =>
% 98.91/13.02 ((
% 98.91/13.02 (powersetTE1) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementTI1) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementTE1) =>
% 98.91/13.02 ((
% 98.91/13.02 (binintersectTELcontra) =>
% 98.91/13.02 ((
% 98.91/13.02 (binintersectTERcontra) =>
% 98.91/13.02 ((
% 98.91/13.02 (contrasubsetT) =>
% 98.91/13.02 ((
% 98.91/13.02 (contrasubsetT1) =>
% 98.91/13.02 ((
% 98.91/13.02 (contrasubsetT2) =>
% 98.91/13.02 ((
% 98.91/13.02 (contrasubsetT3) =>
% 98.91/13.02 ((
% 98.91/13.02 (doubleComplementI1) =>
% 98.91/13.02 ((
% 98.91/13.02 (doubleComplementE1) =>
% 98.91/13.02 ((
% 98.91/13.02 (doubleComplementSub1) =>
% 98.91/13.02 ((
% 98.91/13.02 (doubleComplementSub2) =>
% 98.91/13.02 ((
% 98.91/13.02 (doubleComplementEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementTnotintersectT) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementImpComplementIntersect) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementSubsetComplementIntersect) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementInPowersetComplementIntersect) =>
% 98.91/13.02 ((
% 98.91/13.02 (contraSubsetComplement) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementTcontraSubset) =>
% 98.91/13.02 ((
% 98.91/13.02 (binunionTILcontra) =>
% 98.91/13.02 ((
% 98.91/13.02 (binunionTIRcontra) =>
% 98.91/13.02 ((
% 98.91/13.02 (inIntersectImpInUnion) =>
% 98.91/13.02 ((
% 98.91/13.02 (inIntersectImpInUnion2) =>
% 98.91/13.02 ((
% 98.91/13.02 (inIntersectImpInIntersectUnions) =>
% 98.91/13.02 ((
% 98.91/13.02 (intersectInPowersetIntersectUnions) =>
% 98.91/13.02 ((
% 98.91/13.02 (inComplementUnionImpNotIn1) =>
% 98.91/13.02 ((
% 98.91/13.02 (inComplementUnionImpInComplement1) =>
% 98.91/13.02 ((
% 98.91/13.02 (binunionTE) =>
% 98.91/13.02 ((
% 98.91/13.02 (binunionTEcontra) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2a1) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementUnionInPowersetComplement) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2a2) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan1a) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan1b) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan1) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2a) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2b2) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2b) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz13rule0) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz13rule1) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz13rule2) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz13rule3) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz13rule4) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz1_1) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz1_2) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz1_3) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz1_4) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz1_5) =>
% 98.91/13.02 ((
% 98.91/13.02 (breln1all2) =>
% 98.91/13.02 ((
% 98.91/13.02 (breln1SetBreln1) =>
% 98.91/13.02 ((
% 98.91/13.02 (choice2fnsingleton) =>
% 98.91/13.02 ((
% 98.91/13.02 (!!) @ (
% 98.91/13.02 (('#B') @ (
% 98.91/13.02 !!) @
% 98.91/13.02 (
% 98.91/13.02 (
% 98.91/13.02 ('#S') @ (
% 98.91/13.02 (
% 98.91/13.02 ('#B') @ (
% 98.91/13.02 '#B') @
% 98.91/13.02 breln1)) @
% 98.91/13.02 (
% 98.91/13.02 (
% 98.91/13.02 ('#S') @ dpsetconstr @
% 98.91/13.02 (
% 98.91/13.02 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.91/13.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1354])).
% 98.91/13.02 thf(zip_derived_cl1369, plain,
% 98.91/13.02 (~ (((secondinupair) =>
% 98.91/13.02 (((setukpairIL) =>
% 98.91/13.02 (((setukpairIR) =>
% 98.91/13.02 (((kpairiskpair) =>
% 98.91/13.02 (((kpairp) =>
% 98.91/13.02 (((singletonsubset) =>
% 98.91/13.02 (((singletoninpowerset) =>
% 98.91/13.02 (((singletoninpowunion) =>
% 98.91/13.02 (((upairset2E) =>
% 98.91/13.02 (((upairsubunion) =>
% 98.91/13.02 (((upairinpowunion) =>
% 98.91/13.02 (((ubforcartprodlem1) =>
% 98.91/13.02 (((ubforcartprodlem2) =>
% 98.91/13.02 (((ubforcartprodlem3) =>
% 98.91/13.02 (((cartprodpairin) =>
% 98.91/13.02 (((cartprodmempair1) =>
% 98.91/13.02 (((cartprodmempair) =>
% 98.91/13.02 (((setunionE2) =>
% 98.91/13.02 (((setunionsingleton1) =>
% 98.91/13.02 (((setunionsingleton2) =>
% 98.91/13.02 (((setunionsingleton) =>
% 98.91/13.02 (((singletonprop) =>
% 98.91/13.02 (((ex1E1) =>
% 98.91/13.02 (((ex1I) =>
% 98.91/13.02 (((ex1I2) =>
% 98.91/13.02 (((singletonsuniq) =>
% 98.91/13.02 (((setukpairinjL1) =>
% 98.91/13.02 (((kfstsingleton) =>
% 98.91/13.02 (((theprop) =>
% 98.91/13.02 (((kfstpairEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodfstin) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjL2) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjL) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjR11) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjR12) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjR1) =>
% 98.91/13.02 ((
% 98.91/13.02 (upairequniteq) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjR2) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjR) =>
% 98.91/13.02 ((
% 98.91/13.02 (ksndsingleton) =>
% 98.91/13.02 ((
% 98.91/13.02 (ksndpairEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (kpairsurjEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodsndin) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodpairmemEL) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodpairmemER) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodmempaircEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodfstpairEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodsndpairEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodpairsurjEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrI) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrSub) =>
% 98.91/13.02 ((
% 98.91/13.02 (setOfPairsIsBReln) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrERa) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrEL1) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrEL2) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrER) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcImageSingleton) =>
% 98.91/13.02 ((
% 98.91/13.02 (apProp) =>
% 98.91/13.02 ((
% 98.91/13.02 (app) =>
% 98.91/13.02 ((
% 98.91/13.02 (infuncsetfunc) =>
% 98.91/13.02 ((
% 98.91/13.02 (ap2p) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcinfuncset) =>
% 98.91/13.02 ((
% 98.91/13.02 (lamProp) =>
% 98.91/13.02 ((
% 98.91/13.02 (lamp) =>
% 98.91/13.02 ((
% 98.91/13.02 (lam2p) =>
% 98.91/13.02 ((
% 98.91/13.02 (brelnall1) =>
% 98.91/13.02 ((
% 98.91/13.02 (brelnall2) =>
% 98.91/13.02 ((
% 98.91/13.02 (ex1E2) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcGraphProp1) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcGraphProp3) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcGraphProp2) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcextLem) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcGraphProp4) =>
% 98.91/13.02 ((
% 98.91/13.02 (subbreln) =>
% 98.91/13.02 ((
% 98.91/13.02 (eqbreln) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcext) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcext2) =>
% 98.91/13.02 ((
% 98.91/13.02 (ap2apEq1) =>
% 98.91/13.02 ((
% 98.91/13.02 (ap2apEq2) =>
% 98.91/13.02 ((
% 98.91/13.02 (beta1) =>
% 98.91/13.02 ((
% 98.91/13.02 (eta1) =>
% 98.91/13.02 ((
% 98.91/13.02 (lam2lamEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (beta2) =>
% 98.91/13.02 ((
% 98.91/13.02 (eta2) =>
% 98.91/13.02 ((
% 98.91/13.02 (iffalseProp1) =>
% 98.91/13.02 ((
% 98.91/13.02 (iffalseProp2) =>
% 98.91/13.02 ((
% 98.91/13.02 (iftrueProp1) =>
% 98.91/13.02 ((
% 98.91/13.02 (iftrueProp2) =>
% 98.91/13.02 ((
% 98.91/13.02 (ifSingleton) =>
% 98.91/13.02 ((
% 98.91/13.02 (ifp) =>
% 98.91/13.02 ((
% 98.91/13.02 (theeq) =>
% 98.91/13.02 ((
% 98.91/13.02 (iftrue) =>
% 98.91/13.02 ((
% 98.91/13.02 (iffalse) =>
% 98.91/13.02 ((
% 98.91/13.02 (iftrueorfalse) =>
% 98.91/13.02 ((
% 98.91/13.02 (binintersectT_lem) =>
% 98.91/13.02 ((
% 98.91/13.02 (binunionT_lem) =>
% 98.91/13.02 ((
% 98.91/13.02 (powersetT_lem) =>
% 98.91/13.02 ((
% 98.91/13.02 (setminusT_lem) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementT_lem) =>
% 98.91/13.02 ((
% 98.91/13.02 (setextT) =>
% 98.91/13.02 ((
% 98.91/13.02 (subsetTI) =>
% 98.91/13.02 ((
% 98.91/13.02 (powersetTI1) =>
% 98.91/13.02 ((
% 98.91/13.02 (powersetTE1) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementTI1) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementTE1) =>
% 98.91/13.02 ((
% 98.91/13.02 (binintersectTELcontra) =>
% 98.91/13.02 ((
% 98.91/13.02 (binintersectTERcontra) =>
% 98.91/13.02 ((
% 98.91/13.02 (contrasubsetT) =>
% 98.91/13.02 ((
% 98.91/13.02 (contrasubsetT1) =>
% 98.91/13.02 ((
% 98.91/13.02 (contrasubsetT2) =>
% 98.91/13.02 ((
% 98.91/13.02 (contrasubsetT3) =>
% 98.91/13.02 ((
% 98.91/13.02 (doubleComplementI1) =>
% 98.91/13.02 ((
% 98.91/13.02 (doubleComplementE1) =>
% 98.91/13.02 ((
% 98.91/13.02 (doubleComplementSub1) =>
% 98.91/13.02 ((
% 98.91/13.02 (doubleComplementSub2) =>
% 98.91/13.02 ((
% 98.91/13.02 (doubleComplementEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementTnotintersectT) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementImpComplementIntersect) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementSubsetComplementIntersect) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementInPowersetComplementIntersect) =>
% 98.91/13.02 ((
% 98.91/13.02 (contraSubsetComplement) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementTcontraSubset) =>
% 98.91/13.02 ((
% 98.91/13.02 (binunionTILcontra) =>
% 98.91/13.02 ((
% 98.91/13.02 (binunionTIRcontra) =>
% 98.91/13.02 ((
% 98.91/13.02 (inIntersectImpInUnion) =>
% 98.91/13.02 ((
% 98.91/13.02 (inIntersectImpInUnion2) =>
% 98.91/13.02 ((
% 98.91/13.02 (inIntersectImpInIntersectUnions) =>
% 98.91/13.02 ((
% 98.91/13.02 (intersectInPowersetIntersectUnions) =>
% 98.91/13.02 ((
% 98.91/13.02 (inComplementUnionImpNotIn1) =>
% 98.91/13.02 ((
% 98.91/13.02 (inComplementUnionImpInComplement1) =>
% 98.91/13.02 ((
% 98.91/13.02 (binunionTE) =>
% 98.91/13.02 ((
% 98.91/13.02 (binunionTEcontra) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2a1) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementUnionInPowersetComplement) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2a2) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan1a) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan1b) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan1) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2a) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2b2) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2b) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz13rule0) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz13rule1) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz13rule2) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz13rule3) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz13rule4) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz1_1) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz1_2) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz1_3) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz1_4) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz1_5) =>
% 98.91/13.02 ((
% 98.91/13.02 (breln1all2) =>
% 98.91/13.02 ((
% 98.91/13.02 (breln1SetBreln1) =>
% 98.91/13.02 ((
% 98.91/13.02 (choice2fnsingleton) =>
% 98.91/13.02 ((
% 98.91/13.02 (!!) @ (
% 98.91/13.02 (('#B') @ (
% 98.91/13.02 !!) @
% 98.91/13.02 (
% 98.91/13.02 (
% 98.91/13.02 ('#S') @ (
% 98.91/13.02 (
% 98.91/13.02 ('#B') @ (
% 98.91/13.02 '#B') @
% 98.91/13.02 breln1)) @
% 98.91/13.02 (
% 98.91/13.02 (
% 98.91/13.02 ('#S') @ dpsetconstr @
% 98.91/13.02 (
% 98.91/13.02 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.91/13.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1361])).
% 98.91/13.02 thf(zip_derived_cl1377, plain,
% 98.91/13.02 (~ (((setukpairIL) =>
% 98.91/13.02 (((setukpairIR) =>
% 98.91/13.02 (((kpairiskpair) =>
% 98.91/13.02 (((kpairp) =>
% 98.91/13.02 (((singletonsubset) =>
% 98.91/13.02 (((singletoninpowerset) =>
% 98.91/13.02 (((singletoninpowunion) =>
% 98.91/13.02 (((upairset2E) =>
% 98.91/13.02 (((upairsubunion) =>
% 98.91/13.02 (((upairinpowunion) =>
% 98.91/13.02 (((ubforcartprodlem1) =>
% 98.91/13.02 (((ubforcartprodlem2) =>
% 98.91/13.02 (((ubforcartprodlem3) =>
% 98.91/13.02 (((cartprodpairin) =>
% 98.91/13.02 (((cartprodmempair1) =>
% 98.91/13.02 (((cartprodmempair) =>
% 98.91/13.02 (((setunionE2) =>
% 98.91/13.02 (((setunionsingleton1) =>
% 98.91/13.02 (((setunionsingleton2) =>
% 98.91/13.02 (((setunionsingleton) =>
% 98.91/13.02 (((singletonprop) =>
% 98.91/13.02 (((ex1E1) =>
% 98.91/13.02 (((ex1I) =>
% 98.91/13.02 (((ex1I2) =>
% 98.91/13.02 (((singletonsuniq) =>
% 98.91/13.02 (((setukpairinjL1) =>
% 98.91/13.02 (((kfstsingleton) =>
% 98.91/13.02 (((theprop) =>
% 98.91/13.02 (((kfstpairEq) =>
% 98.91/13.02 (((cartprodfstin) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjL2) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjL) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjR11) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjR12) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjR1) =>
% 98.91/13.02 ((
% 98.91/13.02 (upairequniteq) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjR2) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjR) =>
% 98.91/13.02 ((
% 98.91/13.02 (ksndsingleton) =>
% 98.91/13.02 ((
% 98.91/13.02 (ksndpairEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (kpairsurjEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodsndin) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodpairmemEL) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodpairmemER) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodmempaircEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodfstpairEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodsndpairEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodpairsurjEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrI) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrSub) =>
% 98.91/13.02 ((
% 98.91/13.02 (setOfPairsIsBReln) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrERa) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrEL1) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrEL2) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrER) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcImageSingleton) =>
% 98.91/13.02 ((
% 98.91/13.02 (apProp) =>
% 98.91/13.02 ((
% 98.91/13.02 (app) =>
% 98.91/13.02 ((
% 98.91/13.02 (infuncsetfunc) =>
% 98.91/13.02 ((
% 98.91/13.02 (ap2p) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcinfuncset) =>
% 98.91/13.02 ((
% 98.91/13.02 (lamProp) =>
% 98.91/13.02 ((
% 98.91/13.02 (lamp) =>
% 98.91/13.02 ((
% 98.91/13.02 (lam2p) =>
% 98.91/13.02 ((
% 98.91/13.02 (brelnall1) =>
% 98.91/13.02 ((
% 98.91/13.02 (brelnall2) =>
% 98.91/13.02 ((
% 98.91/13.02 (ex1E2) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcGraphProp1) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcGraphProp3) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcGraphProp2) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcextLem) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcGraphProp4) =>
% 98.91/13.02 ((
% 98.91/13.02 (subbreln) =>
% 98.91/13.02 ((
% 98.91/13.02 (eqbreln) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcext) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcext2) =>
% 98.91/13.02 ((
% 98.91/13.02 (ap2apEq1) =>
% 98.91/13.02 ((
% 98.91/13.02 (ap2apEq2) =>
% 98.91/13.02 ((
% 98.91/13.02 (beta1) =>
% 98.91/13.02 ((
% 98.91/13.02 (eta1) =>
% 98.91/13.02 ((
% 98.91/13.02 (lam2lamEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (beta2) =>
% 98.91/13.02 ((
% 98.91/13.02 (eta2) =>
% 98.91/13.02 ((
% 98.91/13.02 (iffalseProp1) =>
% 98.91/13.02 ((
% 98.91/13.02 (iffalseProp2) =>
% 98.91/13.02 ((
% 98.91/13.02 (iftrueProp1) =>
% 98.91/13.02 ((
% 98.91/13.02 (iftrueProp2) =>
% 98.91/13.02 ((
% 98.91/13.02 (ifSingleton) =>
% 98.91/13.02 ((
% 98.91/13.02 (ifp) =>
% 98.91/13.02 ((
% 98.91/13.02 (theeq) =>
% 98.91/13.02 ((
% 98.91/13.02 (iftrue) =>
% 98.91/13.02 ((
% 98.91/13.02 (iffalse) =>
% 98.91/13.02 ((
% 98.91/13.02 (iftrueorfalse) =>
% 98.91/13.02 ((
% 98.91/13.02 (binintersectT_lem) =>
% 98.91/13.02 ((
% 98.91/13.02 (binunionT_lem) =>
% 98.91/13.02 ((
% 98.91/13.02 (powersetT_lem) =>
% 98.91/13.02 ((
% 98.91/13.02 (setminusT_lem) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementT_lem) =>
% 98.91/13.02 ((
% 98.91/13.02 (setextT) =>
% 98.91/13.02 ((
% 98.91/13.02 (subsetTI) =>
% 98.91/13.02 ((
% 98.91/13.02 (powersetTI1) =>
% 98.91/13.02 ((
% 98.91/13.02 (powersetTE1) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementTI1) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementTE1) =>
% 98.91/13.02 ((
% 98.91/13.02 (binintersectTELcontra) =>
% 98.91/13.02 ((
% 98.91/13.02 (binintersectTERcontra) =>
% 98.91/13.02 ((
% 98.91/13.02 (contrasubsetT) =>
% 98.91/13.02 ((
% 98.91/13.02 (contrasubsetT1) =>
% 98.91/13.02 ((
% 98.91/13.02 (contrasubsetT2) =>
% 98.91/13.02 ((
% 98.91/13.02 (contrasubsetT3) =>
% 98.91/13.02 ((
% 98.91/13.02 (doubleComplementI1) =>
% 98.91/13.02 ((
% 98.91/13.02 (doubleComplementE1) =>
% 98.91/13.02 ((
% 98.91/13.02 (doubleComplementSub1) =>
% 98.91/13.02 ((
% 98.91/13.02 (doubleComplementSub2) =>
% 98.91/13.02 ((
% 98.91/13.02 (doubleComplementEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementTnotintersectT) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementImpComplementIntersect) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementSubsetComplementIntersect) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementInPowersetComplementIntersect) =>
% 98.91/13.02 ((
% 98.91/13.02 (contraSubsetComplement) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementTcontraSubset) =>
% 98.91/13.02 ((
% 98.91/13.02 (binunionTILcontra) =>
% 98.91/13.02 ((
% 98.91/13.02 (binunionTIRcontra) =>
% 98.91/13.02 ((
% 98.91/13.02 (inIntersectImpInUnion) =>
% 98.91/13.02 ((
% 98.91/13.02 (inIntersectImpInUnion2) =>
% 98.91/13.02 ((
% 98.91/13.02 (inIntersectImpInIntersectUnions) =>
% 98.91/13.02 ((
% 98.91/13.02 (intersectInPowersetIntersectUnions) =>
% 98.91/13.02 ((
% 98.91/13.02 (inComplementUnionImpNotIn1) =>
% 98.91/13.02 ((
% 98.91/13.02 (inComplementUnionImpInComplement1) =>
% 98.91/13.02 ((
% 98.91/13.02 (binunionTE) =>
% 98.91/13.02 ((
% 98.91/13.02 (binunionTEcontra) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2a1) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementUnionInPowersetComplement) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2a2) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan1a) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan1b) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan1) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2a) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2b2) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2b) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz13rule0) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz13rule1) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz13rule2) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz13rule3) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz13rule4) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz1_1) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz1_2) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz1_3) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz1_4) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz1_5) =>
% 98.91/13.02 ((
% 98.91/13.02 (breln1all2) =>
% 98.91/13.02 ((
% 98.91/13.02 (breln1SetBreln1) =>
% 98.91/13.02 ((
% 98.91/13.02 (choice2fnsingleton) =>
% 98.91/13.02 ((
% 98.91/13.02 (!!) @ (
% 98.91/13.02 (('#B') @ (
% 98.91/13.02 !!) @
% 98.91/13.02 (
% 98.91/13.02 (
% 98.91/13.02 ('#S') @ (
% 98.91/13.02 (
% 98.91/13.02 ('#B') @ (
% 98.91/13.02 '#B') @
% 98.91/13.02 breln1)) @
% 98.91/13.02 (
% 98.91/13.02 (
% 98.91/13.02 ('#S') @ dpsetconstr @
% 98.91/13.02 (
% 98.91/13.02 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.91/13.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1369])).
% 98.91/13.02 thf(zip_derived_cl1386, plain,
% 98.91/13.02 (~ (((setukpairIR) =>
% 98.91/13.02 (((kpairiskpair) =>
% 98.91/13.02 (((kpairp) =>
% 98.91/13.02 (((singletonsubset) =>
% 98.91/13.02 (((singletoninpowerset) =>
% 98.91/13.02 (((singletoninpowunion) =>
% 98.91/13.02 (((upairset2E) =>
% 98.91/13.02 (((upairsubunion) =>
% 98.91/13.02 (((upairinpowunion) =>
% 98.91/13.02 (((ubforcartprodlem1) =>
% 98.91/13.02 (((ubforcartprodlem2) =>
% 98.91/13.02 (((ubforcartprodlem3) =>
% 98.91/13.02 (((cartprodpairin) =>
% 98.91/13.02 (((cartprodmempair1) =>
% 98.91/13.02 (((cartprodmempair) =>
% 98.91/13.02 (((setunionE2) =>
% 98.91/13.02 (((setunionsingleton1) =>
% 98.91/13.02 (((setunionsingleton2) =>
% 98.91/13.02 (((setunionsingleton) =>
% 98.91/13.02 (((singletonprop) =>
% 98.91/13.02 (((ex1E1) =>
% 98.91/13.02 (((ex1I) =>
% 98.91/13.02 (((ex1I2) =>
% 98.91/13.02 (((singletonsuniq) =>
% 98.91/13.02 (((setukpairinjL1) =>
% 98.91/13.02 (((kfstsingleton) =>
% 98.91/13.02 (((theprop) =>
% 98.91/13.02 (((kfstpairEq) =>
% 98.91/13.02 (((cartprodfstin) =>
% 98.91/13.02 (((setukpairinjL2) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjL) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjR11) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjR12) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjR1) =>
% 98.91/13.02 ((
% 98.91/13.02 (upairequniteq) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjR2) =>
% 98.91/13.02 ((
% 98.91/13.02 (setukpairinjR) =>
% 98.91/13.02 ((
% 98.91/13.02 (ksndsingleton) =>
% 98.91/13.02 ((
% 98.91/13.02 (ksndpairEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (kpairsurjEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodsndin) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodpairmemEL) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodpairmemER) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodmempaircEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodfstpairEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodsndpairEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (cartprodpairsurjEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrI) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrSub) =>
% 98.91/13.02 ((
% 98.91/13.02 (setOfPairsIsBReln) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrERa) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrEL1) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrEL2) =>
% 98.91/13.02 ((
% 98.91/13.02 (dpsetconstrER) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcImageSingleton) =>
% 98.91/13.02 ((
% 98.91/13.02 (apProp) =>
% 98.91/13.02 ((
% 98.91/13.02 (app) =>
% 98.91/13.02 ((
% 98.91/13.02 (infuncsetfunc) =>
% 98.91/13.02 ((
% 98.91/13.02 (ap2p) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcinfuncset) =>
% 98.91/13.02 ((
% 98.91/13.02 (lamProp) =>
% 98.91/13.02 ((
% 98.91/13.02 (lamp) =>
% 98.91/13.02 ((
% 98.91/13.02 (lam2p) =>
% 98.91/13.02 ((
% 98.91/13.02 (brelnall1) =>
% 98.91/13.02 ((
% 98.91/13.02 (brelnall2) =>
% 98.91/13.02 ((
% 98.91/13.02 (ex1E2) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcGraphProp1) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcGraphProp3) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcGraphProp2) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcextLem) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcGraphProp4) =>
% 98.91/13.02 ((
% 98.91/13.02 (subbreln) =>
% 98.91/13.02 ((
% 98.91/13.02 (eqbreln) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcext) =>
% 98.91/13.02 ((
% 98.91/13.02 (funcext2) =>
% 98.91/13.02 ((
% 98.91/13.02 (ap2apEq1) =>
% 98.91/13.02 ((
% 98.91/13.02 (ap2apEq2) =>
% 98.91/13.02 ((
% 98.91/13.02 (beta1) =>
% 98.91/13.02 ((
% 98.91/13.02 (eta1) =>
% 98.91/13.02 ((
% 98.91/13.02 (lam2lamEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (beta2) =>
% 98.91/13.02 ((
% 98.91/13.02 (eta2) =>
% 98.91/13.02 ((
% 98.91/13.02 (iffalseProp1) =>
% 98.91/13.02 ((
% 98.91/13.02 (iffalseProp2) =>
% 98.91/13.02 ((
% 98.91/13.02 (iftrueProp1) =>
% 98.91/13.02 ((
% 98.91/13.02 (iftrueProp2) =>
% 98.91/13.02 ((
% 98.91/13.02 (ifSingleton) =>
% 98.91/13.02 ((
% 98.91/13.02 (ifp) =>
% 98.91/13.02 ((
% 98.91/13.02 (theeq) =>
% 98.91/13.02 ((
% 98.91/13.02 (iftrue) =>
% 98.91/13.02 ((
% 98.91/13.02 (iffalse) =>
% 98.91/13.02 ((
% 98.91/13.02 (iftrueorfalse) =>
% 98.91/13.02 ((
% 98.91/13.02 (binintersectT_lem) =>
% 98.91/13.02 ((
% 98.91/13.02 (binunionT_lem) =>
% 98.91/13.02 ((
% 98.91/13.02 (powersetT_lem) =>
% 98.91/13.02 ((
% 98.91/13.02 (setminusT_lem) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementT_lem) =>
% 98.91/13.02 ((
% 98.91/13.02 (setextT) =>
% 98.91/13.02 ((
% 98.91/13.02 (subsetTI) =>
% 98.91/13.02 ((
% 98.91/13.02 (powersetTI1) =>
% 98.91/13.02 ((
% 98.91/13.02 (powersetTE1) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementTI1) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementTE1) =>
% 98.91/13.02 ((
% 98.91/13.02 (binintersectTELcontra) =>
% 98.91/13.02 ((
% 98.91/13.02 (binintersectTERcontra) =>
% 98.91/13.02 ((
% 98.91/13.02 (contrasubsetT) =>
% 98.91/13.02 ((
% 98.91/13.02 (contrasubsetT1) =>
% 98.91/13.02 ((
% 98.91/13.02 (contrasubsetT2) =>
% 98.91/13.02 ((
% 98.91/13.02 (contrasubsetT3) =>
% 98.91/13.02 ((
% 98.91/13.02 (doubleComplementI1) =>
% 98.91/13.02 ((
% 98.91/13.02 (doubleComplementE1) =>
% 98.91/13.02 ((
% 98.91/13.02 (doubleComplementSub1) =>
% 98.91/13.02 ((
% 98.91/13.02 (doubleComplementSub2) =>
% 98.91/13.02 ((
% 98.91/13.02 (doubleComplementEq) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementTnotintersectT) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementImpComplementIntersect) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementSubsetComplementIntersect) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementInPowersetComplementIntersect) =>
% 98.91/13.02 ((
% 98.91/13.02 (contraSubsetComplement) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementTcontraSubset) =>
% 98.91/13.02 ((
% 98.91/13.02 (binunionTILcontra) =>
% 98.91/13.02 ((
% 98.91/13.02 (binunionTIRcontra) =>
% 98.91/13.02 ((
% 98.91/13.02 (inIntersectImpInUnion) =>
% 98.91/13.02 ((
% 98.91/13.02 (inIntersectImpInUnion2) =>
% 98.91/13.02 ((
% 98.91/13.02 (inIntersectImpInIntersectUnions) =>
% 98.91/13.02 ((
% 98.91/13.02 (intersectInPowersetIntersectUnions) =>
% 98.91/13.02 ((
% 98.91/13.02 (inComplementUnionImpNotIn1) =>
% 98.91/13.02 ((
% 98.91/13.02 (inComplementUnionImpInComplement1) =>
% 98.91/13.02 ((
% 98.91/13.02 (binunionTE) =>
% 98.91/13.02 ((
% 98.91/13.02 (binunionTEcontra) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2a1) =>
% 98.91/13.02 ((
% 98.91/13.02 (complementUnionInPowersetComplement) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2a2) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan1a) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan1b) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan1) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2a) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2b2) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2b) =>
% 98.91/13.02 ((
% 98.91/13.02 (demorgan2) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz13rule0) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz13rule1) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz13rule2) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz13rule3) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz13rule4) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz1_1) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz1_2) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz1_3) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz1_4) =>
% 98.91/13.02 ((
% 98.91/13.02 (woz1_5) =>
% 98.91/13.03 ((
% 98.91/13.03 (breln1all2) =>
% 98.91/13.03 ((
% 98.91/13.03 (breln1SetBreln1) =>
% 98.91/13.03 ((
% 98.91/13.03 (choice2fnsingleton) =>
% 98.91/13.03 ((
% 98.91/13.03 (!!) @ (
% 98.91/13.03 (('#B') @ (
% 98.91/13.03 !!) @
% 98.91/13.03 (
% 98.91/13.03 (
% 98.91/13.03 ('#S') @ (
% 98.91/13.03 (
% 98.91/13.03 ('#B') @ (
% 98.91/13.03 '#B') @
% 98.91/13.03 breln1)) @
% 98.91/13.03 (
% 98.91/13.03 (
% 98.91/13.03 ('#S') @ dpsetconstr @
% 98.91/13.03 (
% 98.91/13.03 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.91/13.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1377])).
% 98.91/13.03 thf(zip_derived_cl1396, plain,
% 98.91/13.03 (~ (((kpairiskpair) =>
% 98.91/13.03 (((kpairp) =>
% 98.91/13.03 (((singletonsubset) =>
% 98.91/13.03 (((singletoninpowerset) =>
% 98.91/13.03 (((singletoninpowunion) =>
% 98.91/13.03 (((upairset2E) =>
% 98.91/13.03 (((upairsubunion) =>
% 98.91/13.03 (((upairinpowunion) =>
% 98.91/13.03 (((ubforcartprodlem1) =>
% 98.91/13.03 (((ubforcartprodlem2) =>
% 98.91/13.03 (((ubforcartprodlem3) =>
% 98.91/13.03 (((cartprodpairin) =>
% 98.91/13.03 (((cartprodmempair1) =>
% 98.91/13.03 (((cartprodmempair) =>
% 98.91/13.03 (((setunionE2) =>
% 98.91/13.03 (((setunionsingleton1) =>
% 98.91/13.03 (((setunionsingleton2) =>
% 98.91/13.03 (((setunionsingleton) =>
% 98.91/13.03 (((singletonprop) =>
% 98.91/13.03 (((ex1E1) =>
% 98.91/13.03 (((ex1I) =>
% 98.91/13.03 (((ex1I2) =>
% 98.91/13.03 (((singletonsuniq) =>
% 98.91/13.03 (((setukpairinjL1) =>
% 98.91/13.03 (((kfstsingleton) =>
% 98.91/13.03 (((theprop) =>
% 98.91/13.03 (((kfstpairEq) =>
% 98.91/13.03 (((cartprodfstin) =>
% 98.91/13.03 (((setukpairinjL2) =>
% 98.91/13.03 (((setukpairinjL) =>
% 98.91/13.03 ((
% 98.91/13.03 (setukpairinjR11) =>
% 98.91/13.03 ((
% 98.91/13.03 (setukpairinjR12) =>
% 98.91/13.03 ((
% 98.91/13.03 (setukpairinjR1) =>
% 98.91/13.03 ((
% 98.91/13.03 (upairequniteq) =>
% 98.91/13.03 ((
% 98.91/13.03 (setukpairinjR2) =>
% 98.91/13.03 ((
% 98.91/13.03 (setukpairinjR) =>
% 98.91/13.03 ((
% 98.91/13.03 (ksndsingleton) =>
% 98.91/13.03 ((
% 98.91/13.03 (ksndpairEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (kpairsurjEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodsndin) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodpairmemEL) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodpairmemER) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodmempaircEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodfstpairEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodsndpairEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodpairsurjEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrI) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrSub) =>
% 98.91/13.03 ((
% 98.91/13.03 (setOfPairsIsBReln) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrERa) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrEL1) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrEL2) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrER) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcImageSingleton) =>
% 98.91/13.03 ((
% 98.91/13.03 (apProp) =>
% 98.91/13.03 ((
% 98.91/13.03 (app) =>
% 98.91/13.03 ((
% 98.91/13.03 (infuncsetfunc) =>
% 98.91/13.03 ((
% 98.91/13.03 (ap2p) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcinfuncset) =>
% 98.91/13.03 ((
% 98.91/13.03 (lamProp) =>
% 98.91/13.03 ((
% 98.91/13.03 (lamp) =>
% 98.91/13.03 ((
% 98.91/13.03 (lam2p) =>
% 98.91/13.03 ((
% 98.91/13.03 (brelnall1) =>
% 98.91/13.03 ((
% 98.91/13.03 (brelnall2) =>
% 98.91/13.03 ((
% 98.91/13.03 (ex1E2) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcGraphProp1) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcGraphProp3) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcGraphProp2) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcextLem) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcGraphProp4) =>
% 98.91/13.03 ((
% 98.91/13.03 (subbreln) =>
% 98.91/13.03 ((
% 98.91/13.03 (eqbreln) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcext) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcext2) =>
% 98.91/13.03 ((
% 98.91/13.03 (ap2apEq1) =>
% 98.91/13.03 ((
% 98.91/13.03 (ap2apEq2) =>
% 98.91/13.03 ((
% 98.91/13.03 (beta1) =>
% 98.91/13.03 ((
% 98.91/13.03 (eta1) =>
% 98.91/13.03 ((
% 98.91/13.03 (lam2lamEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (beta2) =>
% 98.91/13.03 ((
% 98.91/13.03 (eta2) =>
% 98.91/13.03 ((
% 98.91/13.03 (iffalseProp1) =>
% 98.91/13.03 ((
% 98.91/13.03 (iffalseProp2) =>
% 98.91/13.03 ((
% 98.91/13.03 (iftrueProp1) =>
% 98.91/13.03 ((
% 98.91/13.03 (iftrueProp2) =>
% 98.91/13.03 ((
% 98.91/13.03 (ifSingleton) =>
% 98.91/13.03 ((
% 98.91/13.03 (ifp) =>
% 98.91/13.03 ((
% 98.91/13.03 (theeq) =>
% 98.91/13.03 ((
% 98.91/13.03 (iftrue) =>
% 98.91/13.03 ((
% 98.91/13.03 (iffalse) =>
% 98.91/13.03 ((
% 98.91/13.03 (iftrueorfalse) =>
% 98.91/13.03 ((
% 98.91/13.03 (binintersectT_lem) =>
% 98.91/13.03 ((
% 98.91/13.03 (binunionT_lem) =>
% 98.91/13.03 ((
% 98.91/13.03 (powersetT_lem) =>
% 98.91/13.03 ((
% 98.91/13.03 (setminusT_lem) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementT_lem) =>
% 98.91/13.03 ((
% 98.91/13.03 (setextT) =>
% 98.91/13.03 ((
% 98.91/13.03 (subsetTI) =>
% 98.91/13.03 ((
% 98.91/13.03 (powersetTI1) =>
% 98.91/13.03 ((
% 98.91/13.03 (powersetTE1) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementTI1) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementTE1) =>
% 98.91/13.03 ((
% 98.91/13.03 (binintersectTELcontra) =>
% 98.91/13.03 ((
% 98.91/13.03 (binintersectTERcontra) =>
% 98.91/13.03 ((
% 98.91/13.03 (contrasubsetT) =>
% 98.91/13.03 ((
% 98.91/13.03 (contrasubsetT1) =>
% 98.91/13.03 ((
% 98.91/13.03 (contrasubsetT2) =>
% 98.91/13.03 ((
% 98.91/13.03 (contrasubsetT3) =>
% 98.91/13.03 ((
% 98.91/13.03 (doubleComplementI1) =>
% 98.91/13.03 ((
% 98.91/13.03 (doubleComplementE1) =>
% 98.91/13.03 ((
% 98.91/13.03 (doubleComplementSub1) =>
% 98.91/13.03 ((
% 98.91/13.03 (doubleComplementSub2) =>
% 98.91/13.03 ((
% 98.91/13.03 (doubleComplementEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementTnotintersectT) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementImpComplementIntersect) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementSubsetComplementIntersect) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementInPowersetComplementIntersect) =>
% 98.91/13.03 ((
% 98.91/13.03 (contraSubsetComplement) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementTcontraSubset) =>
% 98.91/13.03 ((
% 98.91/13.03 (binunionTILcontra) =>
% 98.91/13.03 ((
% 98.91/13.03 (binunionTIRcontra) =>
% 98.91/13.03 ((
% 98.91/13.03 (inIntersectImpInUnion) =>
% 98.91/13.03 ((
% 98.91/13.03 (inIntersectImpInUnion2) =>
% 98.91/13.03 ((
% 98.91/13.03 (inIntersectImpInIntersectUnions) =>
% 98.91/13.03 ((
% 98.91/13.03 (intersectInPowersetIntersectUnions) =>
% 98.91/13.03 ((
% 98.91/13.03 (inComplementUnionImpNotIn1) =>
% 98.91/13.03 ((
% 98.91/13.03 (inComplementUnionImpInComplement1) =>
% 98.91/13.03 ((
% 98.91/13.03 (binunionTE) =>
% 98.91/13.03 ((
% 98.91/13.03 (binunionTEcontra) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2a1) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementUnionInPowersetComplement) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2a2) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan1a) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan1b) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan1) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2a) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2b2) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2b) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz13rule0) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz13rule1) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz13rule2) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz13rule3) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz13rule4) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz1_1) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz1_2) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz1_3) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz1_4) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz1_5) =>
% 98.91/13.03 ((
% 98.91/13.03 (breln1all2) =>
% 98.91/13.03 ((
% 98.91/13.03 (breln1SetBreln1) =>
% 98.91/13.03 ((
% 98.91/13.03 (choice2fnsingleton) =>
% 98.91/13.03 ((
% 98.91/13.03 (!!) @ (
% 98.91/13.03 (('#B') @ (
% 98.91/13.03 !!) @
% 98.91/13.03 (
% 98.91/13.03 (
% 98.91/13.03 ('#S') @ (
% 98.91/13.03 (
% 98.91/13.03 ('#B') @ (
% 98.91/13.03 '#B') @
% 98.91/13.03 breln1)) @
% 98.91/13.03 (
% 98.91/13.03 (
% 98.91/13.03 ('#S') @ dpsetconstr @
% 98.91/13.03 (
% 98.91/13.03 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.91/13.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1386])).
% 98.91/13.03 thf(zip_derived_cl1407, plain,
% 98.91/13.03 (~ (((kpairp) =>
% 98.91/13.03 (((singletonsubset) =>
% 98.91/13.03 (((singletoninpowerset) =>
% 98.91/13.03 (((singletoninpowunion) =>
% 98.91/13.03 (((upairset2E) =>
% 98.91/13.03 (((upairsubunion) =>
% 98.91/13.03 (((upairinpowunion) =>
% 98.91/13.03 (((ubforcartprodlem1) =>
% 98.91/13.03 (((ubforcartprodlem2) =>
% 98.91/13.03 (((ubforcartprodlem3) =>
% 98.91/13.03 (((cartprodpairin) =>
% 98.91/13.03 (((cartprodmempair1) =>
% 98.91/13.03 (((cartprodmempair) =>
% 98.91/13.03 (((setunionE2) =>
% 98.91/13.03 (((setunionsingleton1) =>
% 98.91/13.03 (((setunionsingleton2) =>
% 98.91/13.03 (((setunionsingleton) =>
% 98.91/13.03 (((singletonprop) =>
% 98.91/13.03 (((ex1E1) =>
% 98.91/13.03 (((ex1I) =>
% 98.91/13.03 (((ex1I2) =>
% 98.91/13.03 (((singletonsuniq) =>
% 98.91/13.03 (((setukpairinjL1) =>
% 98.91/13.03 (((kfstsingleton) =>
% 98.91/13.03 (((theprop) =>
% 98.91/13.03 (((kfstpairEq) =>
% 98.91/13.03 (((cartprodfstin) =>
% 98.91/13.03 (((setukpairinjL2) =>
% 98.91/13.03 (((setukpairinjL) =>
% 98.91/13.03 (((setukpairinjR11) =>
% 98.91/13.03 ((
% 98.91/13.03 (setukpairinjR12) =>
% 98.91/13.03 ((
% 98.91/13.03 (setukpairinjR1) =>
% 98.91/13.03 ((
% 98.91/13.03 (upairequniteq) =>
% 98.91/13.03 ((
% 98.91/13.03 (setukpairinjR2) =>
% 98.91/13.03 ((
% 98.91/13.03 (setukpairinjR) =>
% 98.91/13.03 ((
% 98.91/13.03 (ksndsingleton) =>
% 98.91/13.03 ((
% 98.91/13.03 (ksndpairEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (kpairsurjEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodsndin) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodpairmemEL) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodpairmemER) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodmempaircEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodfstpairEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodsndpairEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodpairsurjEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrI) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrSub) =>
% 98.91/13.03 ((
% 98.91/13.03 (setOfPairsIsBReln) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrERa) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrEL1) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrEL2) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrER) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcImageSingleton) =>
% 98.91/13.03 ((
% 98.91/13.03 (apProp) =>
% 98.91/13.03 ((
% 98.91/13.03 (app) =>
% 98.91/13.03 ((
% 98.91/13.03 (infuncsetfunc) =>
% 98.91/13.03 ((
% 98.91/13.03 (ap2p) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcinfuncset) =>
% 98.91/13.03 ((
% 98.91/13.03 (lamProp) =>
% 98.91/13.03 ((
% 98.91/13.03 (lamp) =>
% 98.91/13.03 ((
% 98.91/13.03 (lam2p) =>
% 98.91/13.03 ((
% 98.91/13.03 (brelnall1) =>
% 98.91/13.03 ((
% 98.91/13.03 (brelnall2) =>
% 98.91/13.03 ((
% 98.91/13.03 (ex1E2) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcGraphProp1) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcGraphProp3) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcGraphProp2) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcextLem) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcGraphProp4) =>
% 98.91/13.03 ((
% 98.91/13.03 (subbreln) =>
% 98.91/13.03 ((
% 98.91/13.03 (eqbreln) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcext) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcext2) =>
% 98.91/13.03 ((
% 98.91/13.03 (ap2apEq1) =>
% 98.91/13.03 ((
% 98.91/13.03 (ap2apEq2) =>
% 98.91/13.03 ((
% 98.91/13.03 (beta1) =>
% 98.91/13.03 ((
% 98.91/13.03 (eta1) =>
% 98.91/13.03 ((
% 98.91/13.03 (lam2lamEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (beta2) =>
% 98.91/13.03 ((
% 98.91/13.03 (eta2) =>
% 98.91/13.03 ((
% 98.91/13.03 (iffalseProp1) =>
% 98.91/13.03 ((
% 98.91/13.03 (iffalseProp2) =>
% 98.91/13.03 ((
% 98.91/13.03 (iftrueProp1) =>
% 98.91/13.03 ((
% 98.91/13.03 (iftrueProp2) =>
% 98.91/13.03 ((
% 98.91/13.03 (ifSingleton) =>
% 98.91/13.03 ((
% 98.91/13.03 (ifp) =>
% 98.91/13.03 ((
% 98.91/13.03 (theeq) =>
% 98.91/13.03 ((
% 98.91/13.03 (iftrue) =>
% 98.91/13.03 ((
% 98.91/13.03 (iffalse) =>
% 98.91/13.03 ((
% 98.91/13.03 (iftrueorfalse) =>
% 98.91/13.03 ((
% 98.91/13.03 (binintersectT_lem) =>
% 98.91/13.03 ((
% 98.91/13.03 (binunionT_lem) =>
% 98.91/13.03 ((
% 98.91/13.03 (powersetT_lem) =>
% 98.91/13.03 ((
% 98.91/13.03 (setminusT_lem) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementT_lem) =>
% 98.91/13.03 ((
% 98.91/13.03 (setextT) =>
% 98.91/13.03 ((
% 98.91/13.03 (subsetTI) =>
% 98.91/13.03 ((
% 98.91/13.03 (powersetTI1) =>
% 98.91/13.03 ((
% 98.91/13.03 (powersetTE1) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementTI1) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementTE1) =>
% 98.91/13.03 ((
% 98.91/13.03 (binintersectTELcontra) =>
% 98.91/13.03 ((
% 98.91/13.03 (binintersectTERcontra) =>
% 98.91/13.03 ((
% 98.91/13.03 (contrasubsetT) =>
% 98.91/13.03 ((
% 98.91/13.03 (contrasubsetT1) =>
% 98.91/13.03 ((
% 98.91/13.03 (contrasubsetT2) =>
% 98.91/13.03 ((
% 98.91/13.03 (contrasubsetT3) =>
% 98.91/13.03 ((
% 98.91/13.03 (doubleComplementI1) =>
% 98.91/13.03 ((
% 98.91/13.03 (doubleComplementE1) =>
% 98.91/13.03 ((
% 98.91/13.03 (doubleComplementSub1) =>
% 98.91/13.03 ((
% 98.91/13.03 (doubleComplementSub2) =>
% 98.91/13.03 ((
% 98.91/13.03 (doubleComplementEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementTnotintersectT) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementImpComplementIntersect) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementSubsetComplementIntersect) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementInPowersetComplementIntersect) =>
% 98.91/13.03 ((
% 98.91/13.03 (contraSubsetComplement) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementTcontraSubset) =>
% 98.91/13.03 ((
% 98.91/13.03 (binunionTILcontra) =>
% 98.91/13.03 ((
% 98.91/13.03 (binunionTIRcontra) =>
% 98.91/13.03 ((
% 98.91/13.03 (inIntersectImpInUnion) =>
% 98.91/13.03 ((
% 98.91/13.03 (inIntersectImpInUnion2) =>
% 98.91/13.03 ((
% 98.91/13.03 (inIntersectImpInIntersectUnions) =>
% 98.91/13.03 ((
% 98.91/13.03 (intersectInPowersetIntersectUnions) =>
% 98.91/13.03 ((
% 98.91/13.03 (inComplementUnionImpNotIn1) =>
% 98.91/13.03 ((
% 98.91/13.03 (inComplementUnionImpInComplement1) =>
% 98.91/13.03 ((
% 98.91/13.03 (binunionTE) =>
% 98.91/13.03 ((
% 98.91/13.03 (binunionTEcontra) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2a1) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementUnionInPowersetComplement) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2a2) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan1a) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan1b) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan1) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2a) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2b2) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2b) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz13rule0) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz13rule1) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz13rule2) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz13rule3) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz13rule4) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz1_1) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz1_2) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz1_3) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz1_4) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz1_5) =>
% 98.91/13.03 ((
% 98.91/13.03 (breln1all2) =>
% 98.91/13.03 ((
% 98.91/13.03 (breln1SetBreln1) =>
% 98.91/13.03 ((
% 98.91/13.03 (choice2fnsingleton) =>
% 98.91/13.03 ((
% 98.91/13.03 (!!) @ (
% 98.91/13.03 (('#B') @ (
% 98.91/13.03 !!) @
% 98.91/13.03 (
% 98.91/13.03 (
% 98.91/13.03 ('#S') @ (
% 98.91/13.03 (
% 98.91/13.03 ('#B') @ (
% 98.91/13.03 '#B') @
% 98.91/13.03 breln1)) @
% 98.91/13.03 (
% 98.91/13.03 (
% 98.91/13.03 ('#S') @ dpsetconstr @
% 98.91/13.03 (
% 98.91/13.03 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.91/13.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1396])).
% 98.91/13.03 thf(zip_derived_cl1420, plain,
% 98.91/13.03 (~ (((singletonsubset) =>
% 98.91/13.03 (((singletoninpowerset) =>
% 98.91/13.03 (((singletoninpowunion) =>
% 98.91/13.03 (((upairset2E) =>
% 98.91/13.03 (((upairsubunion) =>
% 98.91/13.03 (((upairinpowunion) =>
% 98.91/13.03 (((ubforcartprodlem1) =>
% 98.91/13.03 (((ubforcartprodlem2) =>
% 98.91/13.03 (((ubforcartprodlem3) =>
% 98.91/13.03 (((cartprodpairin) =>
% 98.91/13.03 (((cartprodmempair1) =>
% 98.91/13.03 (((cartprodmempair) =>
% 98.91/13.03 (((setunionE2) =>
% 98.91/13.03 (((setunionsingleton1) =>
% 98.91/13.03 (((setunionsingleton2) =>
% 98.91/13.03 (((setunionsingleton) =>
% 98.91/13.03 (((singletonprop) =>
% 98.91/13.03 (((ex1E1) =>
% 98.91/13.03 (((ex1I) =>
% 98.91/13.03 (((ex1I2) =>
% 98.91/13.03 (((singletonsuniq) =>
% 98.91/13.03 (((setukpairinjL1) =>
% 98.91/13.03 (((kfstsingleton) =>
% 98.91/13.03 (((theprop) =>
% 98.91/13.03 (((kfstpairEq) =>
% 98.91/13.03 (((cartprodfstin) =>
% 98.91/13.03 (((setukpairinjL2) =>
% 98.91/13.03 (((setukpairinjL) =>
% 98.91/13.03 (((setukpairinjR11) =>
% 98.91/13.03 (((setukpairinjR12) =>
% 98.91/13.03 ((
% 98.91/13.03 (setukpairinjR1) =>
% 98.91/13.03 ((
% 98.91/13.03 (upairequniteq) =>
% 98.91/13.03 ((
% 98.91/13.03 (setukpairinjR2) =>
% 98.91/13.03 ((
% 98.91/13.03 (setukpairinjR) =>
% 98.91/13.03 ((
% 98.91/13.03 (ksndsingleton) =>
% 98.91/13.03 ((
% 98.91/13.03 (ksndpairEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (kpairsurjEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodsndin) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodpairmemEL) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodpairmemER) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodmempaircEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodfstpairEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodsndpairEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodpairsurjEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrI) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrSub) =>
% 98.91/13.03 ((
% 98.91/13.03 (setOfPairsIsBReln) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrERa) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrEL1) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrEL2) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrER) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcImageSingleton) =>
% 98.91/13.03 ((
% 98.91/13.03 (apProp) =>
% 98.91/13.03 ((
% 98.91/13.03 (app) =>
% 98.91/13.03 ((
% 98.91/13.03 (infuncsetfunc) =>
% 98.91/13.03 ((
% 98.91/13.03 (ap2p) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcinfuncset) =>
% 98.91/13.03 ((
% 98.91/13.03 (lamProp) =>
% 98.91/13.03 ((
% 98.91/13.03 (lamp) =>
% 98.91/13.03 ((
% 98.91/13.03 (lam2p) =>
% 98.91/13.03 ((
% 98.91/13.03 (brelnall1) =>
% 98.91/13.03 ((
% 98.91/13.03 (brelnall2) =>
% 98.91/13.03 ((
% 98.91/13.03 (ex1E2) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcGraphProp1) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcGraphProp3) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcGraphProp2) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcextLem) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcGraphProp4) =>
% 98.91/13.03 ((
% 98.91/13.03 (subbreln) =>
% 98.91/13.03 ((
% 98.91/13.03 (eqbreln) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcext) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcext2) =>
% 98.91/13.03 ((
% 98.91/13.03 (ap2apEq1) =>
% 98.91/13.03 ((
% 98.91/13.03 (ap2apEq2) =>
% 98.91/13.03 ((
% 98.91/13.03 (beta1) =>
% 98.91/13.03 ((
% 98.91/13.03 (eta1) =>
% 98.91/13.03 ((
% 98.91/13.03 (lam2lamEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (beta2) =>
% 98.91/13.03 ((
% 98.91/13.03 (eta2) =>
% 98.91/13.03 ((
% 98.91/13.03 (iffalseProp1) =>
% 98.91/13.03 ((
% 98.91/13.03 (iffalseProp2) =>
% 98.91/13.03 ((
% 98.91/13.03 (iftrueProp1) =>
% 98.91/13.03 ((
% 98.91/13.03 (iftrueProp2) =>
% 98.91/13.03 ((
% 98.91/13.03 (ifSingleton) =>
% 98.91/13.03 ((
% 98.91/13.03 (ifp) =>
% 98.91/13.03 ((
% 98.91/13.03 (theeq) =>
% 98.91/13.03 ((
% 98.91/13.03 (iftrue) =>
% 98.91/13.03 ((
% 98.91/13.03 (iffalse) =>
% 98.91/13.03 ((
% 98.91/13.03 (iftrueorfalse) =>
% 98.91/13.03 ((
% 98.91/13.03 (binintersectT_lem) =>
% 98.91/13.03 ((
% 98.91/13.03 (binunionT_lem) =>
% 98.91/13.03 ((
% 98.91/13.03 (powersetT_lem) =>
% 98.91/13.03 ((
% 98.91/13.03 (setminusT_lem) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementT_lem) =>
% 98.91/13.03 ((
% 98.91/13.03 (setextT) =>
% 98.91/13.03 ((
% 98.91/13.03 (subsetTI) =>
% 98.91/13.03 ((
% 98.91/13.03 (powersetTI1) =>
% 98.91/13.03 ((
% 98.91/13.03 (powersetTE1) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementTI1) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementTE1) =>
% 98.91/13.03 ((
% 98.91/13.03 (binintersectTELcontra) =>
% 98.91/13.03 ((
% 98.91/13.03 (binintersectTERcontra) =>
% 98.91/13.03 ((
% 98.91/13.03 (contrasubsetT) =>
% 98.91/13.03 ((
% 98.91/13.03 (contrasubsetT1) =>
% 98.91/13.03 ((
% 98.91/13.03 (contrasubsetT2) =>
% 98.91/13.03 ((
% 98.91/13.03 (contrasubsetT3) =>
% 98.91/13.03 ((
% 98.91/13.03 (doubleComplementI1) =>
% 98.91/13.03 ((
% 98.91/13.03 (doubleComplementE1) =>
% 98.91/13.03 ((
% 98.91/13.03 (doubleComplementSub1) =>
% 98.91/13.03 ((
% 98.91/13.03 (doubleComplementSub2) =>
% 98.91/13.03 ((
% 98.91/13.03 (doubleComplementEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementTnotintersectT) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementImpComplementIntersect) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementSubsetComplementIntersect) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementInPowersetComplementIntersect) =>
% 98.91/13.03 ((
% 98.91/13.03 (contraSubsetComplement) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementTcontraSubset) =>
% 98.91/13.03 ((
% 98.91/13.03 (binunionTILcontra) =>
% 98.91/13.03 ((
% 98.91/13.03 (binunionTIRcontra) =>
% 98.91/13.03 ((
% 98.91/13.03 (inIntersectImpInUnion) =>
% 98.91/13.03 ((
% 98.91/13.03 (inIntersectImpInUnion2) =>
% 98.91/13.03 ((
% 98.91/13.03 (inIntersectImpInIntersectUnions) =>
% 98.91/13.03 ((
% 98.91/13.03 (intersectInPowersetIntersectUnions) =>
% 98.91/13.03 ((
% 98.91/13.03 (inComplementUnionImpNotIn1) =>
% 98.91/13.03 ((
% 98.91/13.03 (inComplementUnionImpInComplement1) =>
% 98.91/13.03 ((
% 98.91/13.03 (binunionTE) =>
% 98.91/13.03 ((
% 98.91/13.03 (binunionTEcontra) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2a1) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementUnionInPowersetComplement) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2a2) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan1a) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan1b) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan1) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2a) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2b2) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2b) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz13rule0) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz13rule1) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz13rule2) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz13rule3) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz13rule4) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz1_1) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz1_2) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz1_3) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz1_4) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz1_5) =>
% 98.91/13.03 ((
% 98.91/13.03 (breln1all2) =>
% 98.91/13.03 ((
% 98.91/13.03 (breln1SetBreln1) =>
% 98.91/13.03 ((
% 98.91/13.03 (choice2fnsingleton) =>
% 98.91/13.03 ((
% 98.91/13.03 (!!) @ (
% 98.91/13.03 (('#B') @ (
% 98.91/13.03 !!) @
% 98.91/13.03 (
% 98.91/13.03 (
% 98.91/13.03 ('#S') @ (
% 98.91/13.03 (
% 98.91/13.03 ('#B') @ (
% 98.91/13.03 '#B') @
% 98.91/13.03 breln1)) @
% 98.91/13.03 (
% 98.91/13.03 (
% 98.91/13.03 ('#S') @ dpsetconstr @
% 98.91/13.03 (
% 98.91/13.03 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.91/13.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1407])).
% 98.91/13.03 thf(zip_derived_cl1433, plain,
% 98.91/13.03 (~ (((singletoninpowerset) =>
% 98.91/13.03 (((singletoninpowunion) =>
% 98.91/13.03 (((upairset2E) =>
% 98.91/13.03 (((upairsubunion) =>
% 98.91/13.03 (((upairinpowunion) =>
% 98.91/13.03 (((ubforcartprodlem1) =>
% 98.91/13.03 (((ubforcartprodlem2) =>
% 98.91/13.03 (((ubforcartprodlem3) =>
% 98.91/13.03 (((cartprodpairin) =>
% 98.91/13.03 (((cartprodmempair1) =>
% 98.91/13.03 (((cartprodmempair) =>
% 98.91/13.03 (((setunionE2) =>
% 98.91/13.03 (((setunionsingleton1) =>
% 98.91/13.03 (((setunionsingleton2) =>
% 98.91/13.03 (((setunionsingleton) =>
% 98.91/13.03 (((singletonprop) =>
% 98.91/13.03 (((ex1E1) =>
% 98.91/13.03 (((ex1I) =>
% 98.91/13.03 (((ex1I2) =>
% 98.91/13.03 (((singletonsuniq) =>
% 98.91/13.03 (((setukpairinjL1) =>
% 98.91/13.03 (((kfstsingleton) =>
% 98.91/13.03 (((theprop) =>
% 98.91/13.03 (((kfstpairEq) =>
% 98.91/13.03 (((cartprodfstin) =>
% 98.91/13.03 (((setukpairinjL2) =>
% 98.91/13.03 (((setukpairinjL) =>
% 98.91/13.03 (((setukpairinjR11) =>
% 98.91/13.03 (((setukpairinjR12) =>
% 98.91/13.03 (((setukpairinjR1) =>
% 98.91/13.03 ((
% 98.91/13.03 (upairequniteq) =>
% 98.91/13.03 ((
% 98.91/13.03 (setukpairinjR2) =>
% 98.91/13.03 ((
% 98.91/13.03 (setukpairinjR) =>
% 98.91/13.03 ((
% 98.91/13.03 (ksndsingleton) =>
% 98.91/13.03 ((
% 98.91/13.03 (ksndpairEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (kpairsurjEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodsndin) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodpairmemEL) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodpairmemER) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodmempaircEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodfstpairEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodsndpairEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodpairsurjEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrI) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrSub) =>
% 98.91/13.03 ((
% 98.91/13.03 (setOfPairsIsBReln) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrERa) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrEL1) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrEL2) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrER) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcImageSingleton) =>
% 98.91/13.03 ((
% 98.91/13.03 (apProp) =>
% 98.91/13.03 ((
% 98.91/13.03 (app) =>
% 98.91/13.03 ((
% 98.91/13.03 (infuncsetfunc) =>
% 98.91/13.03 ((
% 98.91/13.03 (ap2p) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcinfuncset) =>
% 98.91/13.03 ((
% 98.91/13.03 (lamProp) =>
% 98.91/13.03 ((
% 98.91/13.03 (lamp) =>
% 98.91/13.03 ((
% 98.91/13.03 (lam2p) =>
% 98.91/13.03 ((
% 98.91/13.03 (brelnall1) =>
% 98.91/13.03 ((
% 98.91/13.03 (brelnall2) =>
% 98.91/13.03 ((
% 98.91/13.03 (ex1E2) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcGraphProp1) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcGraphProp3) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcGraphProp2) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcextLem) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcGraphProp4) =>
% 98.91/13.03 ((
% 98.91/13.03 (subbreln) =>
% 98.91/13.03 ((
% 98.91/13.03 (eqbreln) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcext) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcext2) =>
% 98.91/13.03 ((
% 98.91/13.03 (ap2apEq1) =>
% 98.91/13.03 ((
% 98.91/13.03 (ap2apEq2) =>
% 98.91/13.03 ((
% 98.91/13.03 (beta1) =>
% 98.91/13.03 ((
% 98.91/13.03 (eta1) =>
% 98.91/13.03 ((
% 98.91/13.03 (lam2lamEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (beta2) =>
% 98.91/13.03 ((
% 98.91/13.03 (eta2) =>
% 98.91/13.03 ((
% 98.91/13.03 (iffalseProp1) =>
% 98.91/13.03 ((
% 98.91/13.03 (iffalseProp2) =>
% 98.91/13.03 ((
% 98.91/13.03 (iftrueProp1) =>
% 98.91/13.03 ((
% 98.91/13.03 (iftrueProp2) =>
% 98.91/13.03 ((
% 98.91/13.03 (ifSingleton) =>
% 98.91/13.03 ((
% 98.91/13.03 (ifp) =>
% 98.91/13.03 ((
% 98.91/13.03 (theeq) =>
% 98.91/13.03 ((
% 98.91/13.03 (iftrue) =>
% 98.91/13.03 ((
% 98.91/13.03 (iffalse) =>
% 98.91/13.03 ((
% 98.91/13.03 (iftrueorfalse) =>
% 98.91/13.03 ((
% 98.91/13.03 (binintersectT_lem) =>
% 98.91/13.03 ((
% 98.91/13.03 (binunionT_lem) =>
% 98.91/13.03 ((
% 98.91/13.03 (powersetT_lem) =>
% 98.91/13.03 ((
% 98.91/13.03 (setminusT_lem) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementT_lem) =>
% 98.91/13.03 ((
% 98.91/13.03 (setextT) =>
% 98.91/13.03 ((
% 98.91/13.03 (subsetTI) =>
% 98.91/13.03 ((
% 98.91/13.03 (powersetTI1) =>
% 98.91/13.03 ((
% 98.91/13.03 (powersetTE1) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementTI1) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementTE1) =>
% 98.91/13.03 ((
% 98.91/13.03 (binintersectTELcontra) =>
% 98.91/13.03 ((
% 98.91/13.03 (binintersectTERcontra) =>
% 98.91/13.03 ((
% 98.91/13.03 (contrasubsetT) =>
% 98.91/13.03 ((
% 98.91/13.03 (contrasubsetT1) =>
% 98.91/13.03 ((
% 98.91/13.03 (contrasubsetT2) =>
% 98.91/13.03 ((
% 98.91/13.03 (contrasubsetT3) =>
% 98.91/13.03 ((
% 98.91/13.03 (doubleComplementI1) =>
% 98.91/13.03 ((
% 98.91/13.03 (doubleComplementE1) =>
% 98.91/13.03 ((
% 98.91/13.03 (doubleComplementSub1) =>
% 98.91/13.03 ((
% 98.91/13.03 (doubleComplementSub2) =>
% 98.91/13.03 ((
% 98.91/13.03 (doubleComplementEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementTnotintersectT) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementImpComplementIntersect) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementSubsetComplementIntersect) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementInPowersetComplementIntersect) =>
% 98.91/13.03 ((
% 98.91/13.03 (contraSubsetComplement) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementTcontraSubset) =>
% 98.91/13.03 ((
% 98.91/13.03 (binunionTILcontra) =>
% 98.91/13.03 ((
% 98.91/13.03 (binunionTIRcontra) =>
% 98.91/13.03 ((
% 98.91/13.03 (inIntersectImpInUnion) =>
% 98.91/13.03 ((
% 98.91/13.03 (inIntersectImpInUnion2) =>
% 98.91/13.03 ((
% 98.91/13.03 (inIntersectImpInIntersectUnions) =>
% 98.91/13.03 ((
% 98.91/13.03 (intersectInPowersetIntersectUnions) =>
% 98.91/13.03 ((
% 98.91/13.03 (inComplementUnionImpNotIn1) =>
% 98.91/13.03 ((
% 98.91/13.03 (inComplementUnionImpInComplement1) =>
% 98.91/13.03 ((
% 98.91/13.03 (binunionTE) =>
% 98.91/13.03 ((
% 98.91/13.03 (binunionTEcontra) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2a1) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementUnionInPowersetComplement) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2a2) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan1a) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan1b) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan1) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2a) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2b2) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2b) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz13rule0) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz13rule1) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz13rule2) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz13rule3) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz13rule4) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz1_1) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz1_2) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz1_3) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz1_4) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz1_5) =>
% 98.91/13.03 ((
% 98.91/13.03 (breln1all2) =>
% 98.91/13.03 ((
% 98.91/13.03 (breln1SetBreln1) =>
% 98.91/13.03 ((
% 98.91/13.03 (choice2fnsingleton) =>
% 98.91/13.03 ((
% 98.91/13.03 (!!) @ (
% 98.91/13.03 (('#B') @ (
% 98.91/13.03 !!) @
% 98.91/13.03 (
% 98.91/13.03 (
% 98.91/13.03 ('#S') @ (
% 98.91/13.03 (
% 98.91/13.03 ('#B') @ (
% 98.91/13.03 '#B') @
% 98.91/13.03 breln1)) @
% 98.91/13.03 (
% 98.91/13.03 (
% 98.91/13.03 ('#S') @ dpsetconstr @
% 98.91/13.03 (
% 98.91/13.03 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.91/13.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1420])).
% 98.91/13.03 thf(zip_derived_cl1444, plain,
% 98.91/13.03 (~ (((singletoninpowunion) =>
% 98.91/13.03 (((upairset2E) =>
% 98.91/13.03 (((upairsubunion) =>
% 98.91/13.03 (((upairinpowunion) =>
% 98.91/13.03 (((ubforcartprodlem1) =>
% 98.91/13.03 (((ubforcartprodlem2) =>
% 98.91/13.03 (((ubforcartprodlem3) =>
% 98.91/13.03 (((cartprodpairin) =>
% 98.91/13.03 (((cartprodmempair1) =>
% 98.91/13.03 (((cartprodmempair) =>
% 98.91/13.03 (((setunionE2) =>
% 98.91/13.03 (((setunionsingleton1) =>
% 98.91/13.03 (((setunionsingleton2) =>
% 98.91/13.03 (((setunionsingleton) =>
% 98.91/13.03 (((singletonprop) =>
% 98.91/13.03 (((ex1E1) =>
% 98.91/13.03 (((ex1I) =>
% 98.91/13.03 (((ex1I2) =>
% 98.91/13.03 (((singletonsuniq) =>
% 98.91/13.03 (((setukpairinjL1) =>
% 98.91/13.03 (((kfstsingleton) =>
% 98.91/13.03 (((theprop) =>
% 98.91/13.03 (((kfstpairEq) =>
% 98.91/13.03 (((cartprodfstin) =>
% 98.91/13.03 (((setukpairinjL2) =>
% 98.91/13.03 (((setukpairinjL) =>
% 98.91/13.03 (((setukpairinjR11) =>
% 98.91/13.03 (((setukpairinjR12) =>
% 98.91/13.03 (((setukpairinjR1) =>
% 98.91/13.03 (((upairequniteq) =>
% 98.91/13.03 ((
% 98.91/13.03 (setukpairinjR2) =>
% 98.91/13.03 ((
% 98.91/13.03 (setukpairinjR) =>
% 98.91/13.03 ((
% 98.91/13.03 (ksndsingleton) =>
% 98.91/13.03 ((
% 98.91/13.03 (ksndpairEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (kpairsurjEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodsndin) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodpairmemEL) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodpairmemER) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodmempaircEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodfstpairEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodsndpairEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodpairsurjEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrI) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrSub) =>
% 98.91/13.03 ((
% 98.91/13.03 (setOfPairsIsBReln) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrERa) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrEL1) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrEL2) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrER) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcImageSingleton) =>
% 98.91/13.03 ((
% 98.91/13.03 (apProp) =>
% 98.91/13.03 ((
% 98.91/13.03 (app) =>
% 98.91/13.03 ((
% 98.91/13.03 (infuncsetfunc) =>
% 98.91/13.03 ((
% 98.91/13.03 (ap2p) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcinfuncset) =>
% 98.91/13.03 ((
% 98.91/13.03 (lamProp) =>
% 98.91/13.03 ((
% 98.91/13.03 (lamp) =>
% 98.91/13.03 ((
% 98.91/13.03 (lam2p) =>
% 98.91/13.03 ((
% 98.91/13.03 (brelnall1) =>
% 98.91/13.03 ((
% 98.91/13.03 (brelnall2) =>
% 98.91/13.03 ((
% 98.91/13.03 (ex1E2) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcGraphProp1) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcGraphProp3) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcGraphProp2) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcextLem) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcGraphProp4) =>
% 98.91/13.03 ((
% 98.91/13.03 (subbreln) =>
% 98.91/13.03 ((
% 98.91/13.03 (eqbreln) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcext) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcext2) =>
% 98.91/13.03 ((
% 98.91/13.03 (ap2apEq1) =>
% 98.91/13.03 ((
% 98.91/13.03 (ap2apEq2) =>
% 98.91/13.03 ((
% 98.91/13.03 (beta1) =>
% 98.91/13.03 ((
% 98.91/13.03 (eta1) =>
% 98.91/13.03 ((
% 98.91/13.03 (lam2lamEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (beta2) =>
% 98.91/13.03 ((
% 98.91/13.03 (eta2) =>
% 98.91/13.03 ((
% 98.91/13.03 (iffalseProp1) =>
% 98.91/13.03 ((
% 98.91/13.03 (iffalseProp2) =>
% 98.91/13.03 ((
% 98.91/13.03 (iftrueProp1) =>
% 98.91/13.03 ((
% 98.91/13.03 (iftrueProp2) =>
% 98.91/13.03 ((
% 98.91/13.03 (ifSingleton) =>
% 98.91/13.03 ((
% 98.91/13.03 (ifp) =>
% 98.91/13.03 ((
% 98.91/13.03 (theeq) =>
% 98.91/13.03 ((
% 98.91/13.03 (iftrue) =>
% 98.91/13.03 ((
% 98.91/13.03 (iffalse) =>
% 98.91/13.03 ((
% 98.91/13.03 (iftrueorfalse) =>
% 98.91/13.03 ((
% 98.91/13.03 (binintersectT_lem) =>
% 98.91/13.03 ((
% 98.91/13.03 (binunionT_lem) =>
% 98.91/13.03 ((
% 98.91/13.03 (powersetT_lem) =>
% 98.91/13.03 ((
% 98.91/13.03 (setminusT_lem) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementT_lem) =>
% 98.91/13.03 ((
% 98.91/13.03 (setextT) =>
% 98.91/13.03 ((
% 98.91/13.03 (subsetTI) =>
% 98.91/13.03 ((
% 98.91/13.03 (powersetTI1) =>
% 98.91/13.03 ((
% 98.91/13.03 (powersetTE1) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementTI1) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementTE1) =>
% 98.91/13.03 ((
% 98.91/13.03 (binintersectTELcontra) =>
% 98.91/13.03 ((
% 98.91/13.03 (binintersectTERcontra) =>
% 98.91/13.03 ((
% 98.91/13.03 (contrasubsetT) =>
% 98.91/13.03 ((
% 98.91/13.03 (contrasubsetT1) =>
% 98.91/13.03 ((
% 98.91/13.03 (contrasubsetT2) =>
% 98.91/13.03 ((
% 98.91/13.03 (contrasubsetT3) =>
% 98.91/13.03 ((
% 98.91/13.03 (doubleComplementI1) =>
% 98.91/13.03 ((
% 98.91/13.03 (doubleComplementE1) =>
% 98.91/13.03 ((
% 98.91/13.03 (doubleComplementSub1) =>
% 98.91/13.03 ((
% 98.91/13.03 (doubleComplementSub2) =>
% 98.91/13.03 ((
% 98.91/13.03 (doubleComplementEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementTnotintersectT) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementImpComplementIntersect) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementSubsetComplementIntersect) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementInPowersetComplementIntersect) =>
% 98.91/13.03 ((
% 98.91/13.03 (contraSubsetComplement) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementTcontraSubset) =>
% 98.91/13.03 ((
% 98.91/13.03 (binunionTILcontra) =>
% 98.91/13.03 ((
% 98.91/13.03 (binunionTIRcontra) =>
% 98.91/13.03 ((
% 98.91/13.03 (inIntersectImpInUnion) =>
% 98.91/13.03 ((
% 98.91/13.03 (inIntersectImpInUnion2) =>
% 98.91/13.03 ((
% 98.91/13.03 (inIntersectImpInIntersectUnions) =>
% 98.91/13.03 ((
% 98.91/13.03 (intersectInPowersetIntersectUnions) =>
% 98.91/13.03 ((
% 98.91/13.03 (inComplementUnionImpNotIn1) =>
% 98.91/13.03 ((
% 98.91/13.03 (inComplementUnionImpInComplement1) =>
% 98.91/13.03 ((
% 98.91/13.03 (binunionTE) =>
% 98.91/13.03 ((
% 98.91/13.03 (binunionTEcontra) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2a1) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementUnionInPowersetComplement) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2a2) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan1a) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan1b) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan1) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2a) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2b2) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2b) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz13rule0) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz13rule1) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz13rule2) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz13rule3) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz13rule4) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz1_1) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz1_2) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz1_3) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz1_4) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz1_5) =>
% 98.91/13.03 ((
% 98.91/13.03 (breln1all2) =>
% 98.91/13.03 ((
% 98.91/13.03 (breln1SetBreln1) =>
% 98.91/13.03 ((
% 98.91/13.03 (choice2fnsingleton) =>
% 98.91/13.03 ((
% 98.91/13.03 (!!) @ (
% 98.91/13.03 (('#B') @ (
% 98.91/13.03 !!) @
% 98.91/13.03 (
% 98.91/13.03 (
% 98.91/13.03 ('#S') @ (
% 98.91/13.03 (
% 98.91/13.03 ('#B') @ (
% 98.91/13.03 '#B') @
% 98.91/13.03 breln1)) @
% 98.91/13.03 (
% 98.91/13.03 (
% 98.91/13.03 ('#S') @ dpsetconstr @
% 98.91/13.03 (
% 98.91/13.03 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.91/13.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1433])).
% 98.91/13.03 thf(zip_derived_cl1452, plain,
% 98.91/13.03 (~ (((upairset2E) =>
% 98.91/13.03 (((upairsubunion) =>
% 98.91/13.03 (((upairinpowunion) =>
% 98.91/13.03 (((ubforcartprodlem1) =>
% 98.91/13.03 (((ubforcartprodlem2) =>
% 98.91/13.03 (((ubforcartprodlem3) =>
% 98.91/13.03 (((cartprodpairin) =>
% 98.91/13.03 (((cartprodmempair1) =>
% 98.91/13.03 (((cartprodmempair) =>
% 98.91/13.03 (((setunionE2) =>
% 98.91/13.03 (((setunionsingleton1) =>
% 98.91/13.03 (((setunionsingleton2) =>
% 98.91/13.03 (((setunionsingleton) =>
% 98.91/13.03 (((singletonprop) =>
% 98.91/13.03 (((ex1E1) =>
% 98.91/13.03 (((ex1I) =>
% 98.91/13.03 (((ex1I2) =>
% 98.91/13.03 (((singletonsuniq) =>
% 98.91/13.03 (((setukpairinjL1) =>
% 98.91/13.03 (((kfstsingleton) =>
% 98.91/13.03 (((theprop) =>
% 98.91/13.03 (((kfstpairEq) =>
% 98.91/13.03 (((cartprodfstin) =>
% 98.91/13.03 (((setukpairinjL2) =>
% 98.91/13.03 (((setukpairinjL) =>
% 98.91/13.03 (((setukpairinjR11) =>
% 98.91/13.03 (((setukpairinjR12) =>
% 98.91/13.03 (((setukpairinjR1) =>
% 98.91/13.03 (((upairequniteq) =>
% 98.91/13.03 (((setukpairinjR2) =>
% 98.91/13.03 ((
% 98.91/13.03 (setukpairinjR) =>
% 98.91/13.03 ((
% 98.91/13.03 (ksndsingleton) =>
% 98.91/13.03 ((
% 98.91/13.03 (ksndpairEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (kpairsurjEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodsndin) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodpairmemEL) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodpairmemER) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodmempaircEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodfstpairEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodsndpairEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodpairsurjEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrI) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrSub) =>
% 98.91/13.03 ((
% 98.91/13.03 (setOfPairsIsBReln) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrERa) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrEL1) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrEL2) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrER) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcImageSingleton) =>
% 98.91/13.03 ((
% 98.91/13.03 (apProp) =>
% 98.91/13.03 ((
% 98.91/13.03 (app) =>
% 98.91/13.03 ((
% 98.91/13.03 (infuncsetfunc) =>
% 98.91/13.03 ((
% 98.91/13.03 (ap2p) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcinfuncset) =>
% 98.91/13.03 ((
% 98.91/13.03 (lamProp) =>
% 98.91/13.03 ((
% 98.91/13.03 (lamp) =>
% 98.91/13.03 ((
% 98.91/13.03 (lam2p) =>
% 98.91/13.03 ((
% 98.91/13.03 (brelnall1) =>
% 98.91/13.03 ((
% 98.91/13.03 (brelnall2) =>
% 98.91/13.03 ((
% 98.91/13.03 (ex1E2) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcGraphProp1) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcGraphProp3) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcGraphProp2) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcextLem) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcGraphProp4) =>
% 98.91/13.03 ((
% 98.91/13.03 (subbreln) =>
% 98.91/13.03 ((
% 98.91/13.03 (eqbreln) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcext) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcext2) =>
% 98.91/13.03 ((
% 98.91/13.03 (ap2apEq1) =>
% 98.91/13.03 ((
% 98.91/13.03 (ap2apEq2) =>
% 98.91/13.03 ((
% 98.91/13.03 (beta1) =>
% 98.91/13.03 ((
% 98.91/13.03 (eta1) =>
% 98.91/13.03 ((
% 98.91/13.03 (lam2lamEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (beta2) =>
% 98.91/13.03 ((
% 98.91/13.03 (eta2) =>
% 98.91/13.03 ((
% 98.91/13.03 (iffalseProp1) =>
% 98.91/13.03 ((
% 98.91/13.03 (iffalseProp2) =>
% 98.91/13.03 ((
% 98.91/13.03 (iftrueProp1) =>
% 98.91/13.03 ((
% 98.91/13.03 (iftrueProp2) =>
% 98.91/13.03 ((
% 98.91/13.03 (ifSingleton) =>
% 98.91/13.03 ((
% 98.91/13.03 (ifp) =>
% 98.91/13.03 ((
% 98.91/13.03 (theeq) =>
% 98.91/13.03 ((
% 98.91/13.03 (iftrue) =>
% 98.91/13.03 ((
% 98.91/13.03 (iffalse) =>
% 98.91/13.03 ((
% 98.91/13.03 (iftrueorfalse) =>
% 98.91/13.03 ((
% 98.91/13.03 (binintersectT_lem) =>
% 98.91/13.03 ((
% 98.91/13.03 (binunionT_lem) =>
% 98.91/13.03 ((
% 98.91/13.03 (powersetT_lem) =>
% 98.91/13.03 ((
% 98.91/13.03 (setminusT_lem) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementT_lem) =>
% 98.91/13.03 ((
% 98.91/13.03 (setextT) =>
% 98.91/13.03 ((
% 98.91/13.03 (subsetTI) =>
% 98.91/13.03 ((
% 98.91/13.03 (powersetTI1) =>
% 98.91/13.03 ((
% 98.91/13.03 (powersetTE1) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementTI1) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementTE1) =>
% 98.91/13.03 ((
% 98.91/13.03 (binintersectTELcontra) =>
% 98.91/13.03 ((
% 98.91/13.03 (binintersectTERcontra) =>
% 98.91/13.03 ((
% 98.91/13.03 (contrasubsetT) =>
% 98.91/13.03 ((
% 98.91/13.03 (contrasubsetT1) =>
% 98.91/13.03 ((
% 98.91/13.03 (contrasubsetT2) =>
% 98.91/13.03 ((
% 98.91/13.03 (contrasubsetT3) =>
% 98.91/13.03 ((
% 98.91/13.03 (doubleComplementI1) =>
% 98.91/13.03 ((
% 98.91/13.03 (doubleComplementE1) =>
% 98.91/13.03 ((
% 98.91/13.03 (doubleComplementSub1) =>
% 98.91/13.03 ((
% 98.91/13.03 (doubleComplementSub2) =>
% 98.91/13.03 ((
% 98.91/13.03 (doubleComplementEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementTnotintersectT) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementImpComplementIntersect) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementSubsetComplementIntersect) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementInPowersetComplementIntersect) =>
% 98.91/13.03 ((
% 98.91/13.03 (contraSubsetComplement) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementTcontraSubset) =>
% 98.91/13.03 ((
% 98.91/13.03 (binunionTILcontra) =>
% 98.91/13.03 ((
% 98.91/13.03 (binunionTIRcontra) =>
% 98.91/13.03 ((
% 98.91/13.03 (inIntersectImpInUnion) =>
% 98.91/13.03 ((
% 98.91/13.03 (inIntersectImpInUnion2) =>
% 98.91/13.03 ((
% 98.91/13.03 (inIntersectImpInIntersectUnions) =>
% 98.91/13.03 ((
% 98.91/13.03 (intersectInPowersetIntersectUnions) =>
% 98.91/13.03 ((
% 98.91/13.03 (inComplementUnionImpNotIn1) =>
% 98.91/13.03 ((
% 98.91/13.03 (inComplementUnionImpInComplement1) =>
% 98.91/13.03 ((
% 98.91/13.03 (binunionTE) =>
% 98.91/13.03 ((
% 98.91/13.03 (binunionTEcontra) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2a1) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementUnionInPowersetComplement) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2a2) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan1a) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan1b) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan1) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2a) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2b2) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2b) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz13rule0) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz13rule1) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz13rule2) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz13rule3) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz13rule4) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz1_1) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz1_2) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz1_3) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz1_4) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz1_5) =>
% 98.91/13.03 ((
% 98.91/13.03 (breln1all2) =>
% 98.91/13.03 ((
% 98.91/13.03 (breln1SetBreln1) =>
% 98.91/13.03 ((
% 98.91/13.03 (choice2fnsingleton) =>
% 98.91/13.03 ((
% 98.91/13.03 (!!) @ (
% 98.91/13.03 (('#B') @ (
% 98.91/13.03 !!) @
% 98.91/13.03 (
% 98.91/13.03 (
% 98.91/13.03 ('#S') @ (
% 98.91/13.03 (
% 98.91/13.03 ('#B') @ (
% 98.91/13.03 '#B') @
% 98.91/13.03 breln1)) @
% 98.91/13.03 (
% 98.91/13.03 (
% 98.91/13.03 ('#S') @ dpsetconstr @
% 98.91/13.03 (
% 98.91/13.03 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.91/13.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1444])).
% 98.91/13.03 thf(zip_derived_cl1459, plain,
% 98.91/13.03 (~ (((upairsubunion) =>
% 98.91/13.03 (((upairinpowunion) =>
% 98.91/13.03 (((ubforcartprodlem1) =>
% 98.91/13.03 (((ubforcartprodlem2) =>
% 98.91/13.03 (((ubforcartprodlem3) =>
% 98.91/13.03 (((cartprodpairin) =>
% 98.91/13.03 (((cartprodmempair1) =>
% 98.91/13.03 (((cartprodmempair) =>
% 98.91/13.03 (((setunionE2) =>
% 98.91/13.03 (((setunionsingleton1) =>
% 98.91/13.03 (((setunionsingleton2) =>
% 98.91/13.03 (((setunionsingleton) =>
% 98.91/13.03 (((singletonprop) =>
% 98.91/13.03 (((ex1E1) =>
% 98.91/13.03 (((ex1I) =>
% 98.91/13.03 (((ex1I2) =>
% 98.91/13.03 (((singletonsuniq) =>
% 98.91/13.03 (((setukpairinjL1) =>
% 98.91/13.03 (((kfstsingleton) =>
% 98.91/13.03 (((theprop) =>
% 98.91/13.03 (((kfstpairEq) =>
% 98.91/13.03 (((cartprodfstin) =>
% 98.91/13.03 (((setukpairinjL2) =>
% 98.91/13.03 (((setukpairinjL) =>
% 98.91/13.03 (((setukpairinjR11) =>
% 98.91/13.03 (((setukpairinjR12) =>
% 98.91/13.03 (((setukpairinjR1) =>
% 98.91/13.03 (((upairequniteq) =>
% 98.91/13.03 (((setukpairinjR2) =>
% 98.91/13.03 (((setukpairinjR) =>
% 98.91/13.03 ((
% 98.91/13.03 (ksndsingleton) =>
% 98.91/13.03 ((
% 98.91/13.03 (ksndpairEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (kpairsurjEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodsndin) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodpairmemEL) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodpairmemER) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodmempaircEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodfstpairEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodsndpairEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodpairsurjEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrI) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrSub) =>
% 98.91/13.03 ((
% 98.91/13.03 (setOfPairsIsBReln) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrERa) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrEL1) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrEL2) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrER) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcImageSingleton) =>
% 98.91/13.03 ((
% 98.91/13.03 (apProp) =>
% 98.91/13.03 ((
% 98.91/13.03 (app) =>
% 98.91/13.03 ((
% 98.91/13.03 (infuncsetfunc) =>
% 98.91/13.03 ((
% 98.91/13.03 (ap2p) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcinfuncset) =>
% 98.91/13.03 ((
% 98.91/13.03 (lamProp) =>
% 98.91/13.03 ((
% 98.91/13.03 (lamp) =>
% 98.91/13.03 ((
% 98.91/13.03 (lam2p) =>
% 98.91/13.03 ((
% 98.91/13.03 (brelnall1) =>
% 98.91/13.03 ((
% 98.91/13.03 (brelnall2) =>
% 98.91/13.03 ((
% 98.91/13.03 (ex1E2) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcGraphProp1) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcGraphProp3) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcGraphProp2) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcextLem) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcGraphProp4) =>
% 98.91/13.03 ((
% 98.91/13.03 (subbreln) =>
% 98.91/13.03 ((
% 98.91/13.03 (eqbreln) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcext) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcext2) =>
% 98.91/13.03 ((
% 98.91/13.03 (ap2apEq1) =>
% 98.91/13.03 ((
% 98.91/13.03 (ap2apEq2) =>
% 98.91/13.03 ((
% 98.91/13.03 (beta1) =>
% 98.91/13.03 ((
% 98.91/13.03 (eta1) =>
% 98.91/13.03 ((
% 98.91/13.03 (lam2lamEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (beta2) =>
% 98.91/13.03 ((
% 98.91/13.03 (eta2) =>
% 98.91/13.03 ((
% 98.91/13.03 (iffalseProp1) =>
% 98.91/13.03 ((
% 98.91/13.03 (iffalseProp2) =>
% 98.91/13.03 ((
% 98.91/13.03 (iftrueProp1) =>
% 98.91/13.03 ((
% 98.91/13.03 (iftrueProp2) =>
% 98.91/13.03 ((
% 98.91/13.03 (ifSingleton) =>
% 98.91/13.03 ((
% 98.91/13.03 (ifp) =>
% 98.91/13.03 ((
% 98.91/13.03 (theeq) =>
% 98.91/13.03 ((
% 98.91/13.03 (iftrue) =>
% 98.91/13.03 ((
% 98.91/13.03 (iffalse) =>
% 98.91/13.03 ((
% 98.91/13.03 (iftrueorfalse) =>
% 98.91/13.03 ((
% 98.91/13.03 (binintersectT_lem) =>
% 98.91/13.03 ((
% 98.91/13.03 (binunionT_lem) =>
% 98.91/13.03 ((
% 98.91/13.03 (powersetT_lem) =>
% 98.91/13.03 ((
% 98.91/13.03 (setminusT_lem) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementT_lem) =>
% 98.91/13.03 ((
% 98.91/13.03 (setextT) =>
% 98.91/13.03 ((
% 98.91/13.03 (subsetTI) =>
% 98.91/13.03 ((
% 98.91/13.03 (powersetTI1) =>
% 98.91/13.03 ((
% 98.91/13.03 (powersetTE1) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementTI1) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementTE1) =>
% 98.91/13.03 ((
% 98.91/13.03 (binintersectTELcontra) =>
% 98.91/13.03 ((
% 98.91/13.03 (binintersectTERcontra) =>
% 98.91/13.03 ((
% 98.91/13.03 (contrasubsetT) =>
% 98.91/13.03 ((
% 98.91/13.03 (contrasubsetT1) =>
% 98.91/13.03 ((
% 98.91/13.03 (contrasubsetT2) =>
% 98.91/13.03 ((
% 98.91/13.03 (contrasubsetT3) =>
% 98.91/13.03 ((
% 98.91/13.03 (doubleComplementI1) =>
% 98.91/13.03 ((
% 98.91/13.03 (doubleComplementE1) =>
% 98.91/13.03 ((
% 98.91/13.03 (doubleComplementSub1) =>
% 98.91/13.03 ((
% 98.91/13.03 (doubleComplementSub2) =>
% 98.91/13.03 ((
% 98.91/13.03 (doubleComplementEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementTnotintersectT) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementImpComplementIntersect) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementSubsetComplementIntersect) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementInPowersetComplementIntersect) =>
% 98.91/13.03 ((
% 98.91/13.03 (contraSubsetComplement) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementTcontraSubset) =>
% 98.91/13.03 ((
% 98.91/13.03 (binunionTILcontra) =>
% 98.91/13.03 ((
% 98.91/13.03 (binunionTIRcontra) =>
% 98.91/13.03 ((
% 98.91/13.03 (inIntersectImpInUnion) =>
% 98.91/13.03 ((
% 98.91/13.03 (inIntersectImpInUnion2) =>
% 98.91/13.03 ((
% 98.91/13.03 (inIntersectImpInIntersectUnions) =>
% 98.91/13.03 ((
% 98.91/13.03 (intersectInPowersetIntersectUnions) =>
% 98.91/13.03 ((
% 98.91/13.03 (inComplementUnionImpNotIn1) =>
% 98.91/13.03 ((
% 98.91/13.03 (inComplementUnionImpInComplement1) =>
% 98.91/13.03 ((
% 98.91/13.03 (binunionTE) =>
% 98.91/13.03 ((
% 98.91/13.03 (binunionTEcontra) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2a1) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementUnionInPowersetComplement) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2a2) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan1a) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan1b) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan1) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2a) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2b2) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2b) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz13rule0) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz13rule1) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz13rule2) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz13rule3) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz13rule4) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz1_1) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz1_2) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz1_3) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz1_4) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz1_5) =>
% 98.91/13.03 ((
% 98.91/13.03 (breln1all2) =>
% 98.91/13.03 ((
% 98.91/13.03 (breln1SetBreln1) =>
% 98.91/13.03 ((
% 98.91/13.03 (choice2fnsingleton) =>
% 98.91/13.03 ((
% 98.91/13.03 (!!) @ (
% 98.91/13.03 (('#B') @ (
% 98.91/13.03 !!) @
% 98.91/13.03 (
% 98.91/13.03 (
% 98.91/13.03 ('#S') @ (
% 98.91/13.03 (
% 98.91/13.03 ('#B') @ (
% 98.91/13.03 '#B') @
% 98.91/13.03 breln1)) @
% 98.91/13.03 (
% 98.91/13.03 (
% 98.91/13.03 ('#S') @ dpsetconstr @
% 98.91/13.03 (
% 98.91/13.03 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.91/13.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1452])).
% 98.91/13.03 thf(zip_derived_cl1466, plain,
% 98.91/13.03 (~ (((upairinpowunion) =>
% 98.91/13.03 (((ubforcartprodlem1) =>
% 98.91/13.03 (((ubforcartprodlem2) =>
% 98.91/13.03 (((ubforcartprodlem3) =>
% 98.91/13.03 (((cartprodpairin) =>
% 98.91/13.03 (((cartprodmempair1) =>
% 98.91/13.03 (((cartprodmempair) =>
% 98.91/13.03 (((setunionE2) =>
% 98.91/13.03 (((setunionsingleton1) =>
% 98.91/13.03 (((setunionsingleton2) =>
% 98.91/13.03 (((setunionsingleton) =>
% 98.91/13.03 (((singletonprop) =>
% 98.91/13.03 (((ex1E1) =>
% 98.91/13.03 (((ex1I) =>
% 98.91/13.03 (((ex1I2) =>
% 98.91/13.03 (((singletonsuniq) =>
% 98.91/13.03 (((setukpairinjL1) =>
% 98.91/13.03 (((kfstsingleton) =>
% 98.91/13.03 (((theprop) =>
% 98.91/13.03 (((kfstpairEq) =>
% 98.91/13.03 (((cartprodfstin) =>
% 98.91/13.03 (((setukpairinjL2) =>
% 98.91/13.03 (((setukpairinjL) =>
% 98.91/13.03 (((setukpairinjR11) =>
% 98.91/13.03 (((setukpairinjR12) =>
% 98.91/13.03 (((setukpairinjR1) =>
% 98.91/13.03 (((upairequniteq) =>
% 98.91/13.03 (((setukpairinjR2) =>
% 98.91/13.03 (((setukpairinjR) =>
% 98.91/13.03 (((ksndsingleton) =>
% 98.91/13.03 ((
% 98.91/13.03 (ksndpairEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (kpairsurjEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodsndin) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodpairmemEL) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodpairmemER) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodmempaircEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodfstpairEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodsndpairEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodpairsurjEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrI) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrSub) =>
% 98.91/13.03 ((
% 98.91/13.03 (setOfPairsIsBReln) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrERa) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrEL1) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrEL2) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrER) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcImageSingleton) =>
% 98.91/13.03 ((
% 98.91/13.03 (apProp) =>
% 98.91/13.03 ((
% 98.91/13.03 (app) =>
% 98.91/13.03 ((
% 98.91/13.03 (infuncsetfunc) =>
% 98.91/13.03 ((
% 98.91/13.03 (ap2p) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcinfuncset) =>
% 98.91/13.03 ((
% 98.91/13.03 (lamProp) =>
% 98.91/13.03 ((
% 98.91/13.03 (lamp) =>
% 98.91/13.03 ((
% 98.91/13.03 (lam2p) =>
% 98.91/13.03 ((
% 98.91/13.03 (brelnall1) =>
% 98.91/13.03 ((
% 98.91/13.03 (brelnall2) =>
% 98.91/13.03 ((
% 98.91/13.03 (ex1E2) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcGraphProp1) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcGraphProp3) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcGraphProp2) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcextLem) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcGraphProp4) =>
% 98.91/13.03 ((
% 98.91/13.03 (subbreln) =>
% 98.91/13.03 ((
% 98.91/13.03 (eqbreln) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcext) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcext2) =>
% 98.91/13.03 ((
% 98.91/13.03 (ap2apEq1) =>
% 98.91/13.03 ((
% 98.91/13.03 (ap2apEq2) =>
% 98.91/13.03 ((
% 98.91/13.03 (beta1) =>
% 98.91/13.03 ((
% 98.91/13.03 (eta1) =>
% 98.91/13.03 ((
% 98.91/13.03 (lam2lamEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (beta2) =>
% 98.91/13.03 ((
% 98.91/13.03 (eta2) =>
% 98.91/13.03 ((
% 98.91/13.03 (iffalseProp1) =>
% 98.91/13.03 ((
% 98.91/13.03 (iffalseProp2) =>
% 98.91/13.03 ((
% 98.91/13.03 (iftrueProp1) =>
% 98.91/13.03 ((
% 98.91/13.03 (iftrueProp2) =>
% 98.91/13.03 ((
% 98.91/13.03 (ifSingleton) =>
% 98.91/13.03 ((
% 98.91/13.03 (ifp) =>
% 98.91/13.03 ((
% 98.91/13.03 (theeq) =>
% 98.91/13.03 ((
% 98.91/13.03 (iftrue) =>
% 98.91/13.03 ((
% 98.91/13.03 (iffalse) =>
% 98.91/13.03 ((
% 98.91/13.03 (iftrueorfalse) =>
% 98.91/13.03 ((
% 98.91/13.03 (binintersectT_lem) =>
% 98.91/13.03 ((
% 98.91/13.03 (binunionT_lem) =>
% 98.91/13.03 ((
% 98.91/13.03 (powersetT_lem) =>
% 98.91/13.03 ((
% 98.91/13.03 (setminusT_lem) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementT_lem) =>
% 98.91/13.03 ((
% 98.91/13.03 (setextT) =>
% 98.91/13.03 ((
% 98.91/13.03 (subsetTI) =>
% 98.91/13.03 ((
% 98.91/13.03 (powersetTI1) =>
% 98.91/13.03 ((
% 98.91/13.03 (powersetTE1) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementTI1) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementTE1) =>
% 98.91/13.03 ((
% 98.91/13.03 (binintersectTELcontra) =>
% 98.91/13.03 ((
% 98.91/13.03 (binintersectTERcontra) =>
% 98.91/13.03 ((
% 98.91/13.03 (contrasubsetT) =>
% 98.91/13.03 ((
% 98.91/13.03 (contrasubsetT1) =>
% 98.91/13.03 ((
% 98.91/13.03 (contrasubsetT2) =>
% 98.91/13.03 ((
% 98.91/13.03 (contrasubsetT3) =>
% 98.91/13.03 ((
% 98.91/13.03 (doubleComplementI1) =>
% 98.91/13.03 ((
% 98.91/13.03 (doubleComplementE1) =>
% 98.91/13.03 ((
% 98.91/13.03 (doubleComplementSub1) =>
% 98.91/13.03 ((
% 98.91/13.03 (doubleComplementSub2) =>
% 98.91/13.03 ((
% 98.91/13.03 (doubleComplementEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementTnotintersectT) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementImpComplementIntersect) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementSubsetComplementIntersect) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementInPowersetComplementIntersect) =>
% 98.91/13.03 ((
% 98.91/13.03 (contraSubsetComplement) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementTcontraSubset) =>
% 98.91/13.03 ((
% 98.91/13.03 (binunionTILcontra) =>
% 98.91/13.03 ((
% 98.91/13.03 (binunionTIRcontra) =>
% 98.91/13.03 ((
% 98.91/13.03 (inIntersectImpInUnion) =>
% 98.91/13.03 ((
% 98.91/13.03 (inIntersectImpInUnion2) =>
% 98.91/13.03 ((
% 98.91/13.03 (inIntersectImpInIntersectUnions) =>
% 98.91/13.03 ((
% 98.91/13.03 (intersectInPowersetIntersectUnions) =>
% 98.91/13.03 ((
% 98.91/13.03 (inComplementUnionImpNotIn1) =>
% 98.91/13.03 ((
% 98.91/13.03 (inComplementUnionImpInComplement1) =>
% 98.91/13.03 ((
% 98.91/13.03 (binunionTE) =>
% 98.91/13.03 ((
% 98.91/13.03 (binunionTEcontra) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2a1) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementUnionInPowersetComplement) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2a2) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan1a) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan1b) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan1) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2a) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2b2) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2b) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz13rule0) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz13rule1) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz13rule2) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz13rule3) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz13rule4) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz1_1) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz1_2) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz1_3) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz1_4) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz1_5) =>
% 98.91/13.03 ((
% 98.91/13.03 (breln1all2) =>
% 98.91/13.03 ((
% 98.91/13.03 (breln1SetBreln1) =>
% 98.91/13.03 ((
% 98.91/13.03 (choice2fnsingleton) =>
% 98.91/13.03 ((
% 98.91/13.03 (!!) @ (
% 98.91/13.03 (('#B') @ (
% 98.91/13.03 !!) @
% 98.91/13.03 (
% 98.91/13.03 (
% 98.91/13.03 ('#S') @ (
% 98.91/13.03 (
% 98.91/13.03 ('#B') @ (
% 98.91/13.03 '#B') @
% 98.91/13.03 breln1)) @
% 98.91/13.03 (
% 98.91/13.03 (
% 98.91/13.03 ('#S') @ dpsetconstr @
% 98.91/13.03 (
% 98.91/13.03 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.91/13.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1459])).
% 98.91/13.03 thf(zip_derived_cl1473, plain,
% 98.91/13.03 (~ (((ubforcartprodlem1) =>
% 98.91/13.03 (((ubforcartprodlem2) =>
% 98.91/13.03 (((ubforcartprodlem3) =>
% 98.91/13.03 (((cartprodpairin) =>
% 98.91/13.03 (((cartprodmempair1) =>
% 98.91/13.03 (((cartprodmempair) =>
% 98.91/13.03 (((setunionE2) =>
% 98.91/13.03 (((setunionsingleton1) =>
% 98.91/13.03 (((setunionsingleton2) =>
% 98.91/13.03 (((setunionsingleton) =>
% 98.91/13.03 (((singletonprop) =>
% 98.91/13.03 (((ex1E1) =>
% 98.91/13.03 (((ex1I) =>
% 98.91/13.03 (((ex1I2) =>
% 98.91/13.03 (((singletonsuniq) =>
% 98.91/13.03 (((setukpairinjL1) =>
% 98.91/13.03 (((kfstsingleton) =>
% 98.91/13.03 (((theprop) =>
% 98.91/13.03 (((kfstpairEq) =>
% 98.91/13.03 (((cartprodfstin) =>
% 98.91/13.03 (((setukpairinjL2) =>
% 98.91/13.03 (((setukpairinjL) =>
% 98.91/13.03 (((setukpairinjR11) =>
% 98.91/13.03 (((setukpairinjR12) =>
% 98.91/13.03 (((setukpairinjR1) =>
% 98.91/13.03 (((upairequniteq) =>
% 98.91/13.03 (((setukpairinjR2) =>
% 98.91/13.03 (((setukpairinjR) =>
% 98.91/13.03 (((ksndsingleton) =>
% 98.91/13.03 (((ksndpairEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (kpairsurjEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodsndin) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodpairmemEL) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodpairmemER) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodmempaircEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodfstpairEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodsndpairEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodpairsurjEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrI) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrSub) =>
% 98.91/13.03 ((
% 98.91/13.03 (setOfPairsIsBReln) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrERa) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrEL1) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrEL2) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrER) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcImageSingleton) =>
% 98.91/13.03 ((
% 98.91/13.03 (apProp) =>
% 98.91/13.03 ((
% 98.91/13.03 (app) =>
% 98.91/13.03 ((
% 98.91/13.03 (infuncsetfunc) =>
% 98.91/13.03 ((
% 98.91/13.03 (ap2p) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcinfuncset) =>
% 98.91/13.03 ((
% 98.91/13.03 (lamProp) =>
% 98.91/13.03 ((
% 98.91/13.03 (lamp) =>
% 98.91/13.03 ((
% 98.91/13.03 (lam2p) =>
% 98.91/13.03 ((
% 98.91/13.03 (brelnall1) =>
% 98.91/13.03 ((
% 98.91/13.03 (brelnall2) =>
% 98.91/13.03 ((
% 98.91/13.03 (ex1E2) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcGraphProp1) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcGraphProp3) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcGraphProp2) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcextLem) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcGraphProp4) =>
% 98.91/13.03 ((
% 98.91/13.03 (subbreln) =>
% 98.91/13.03 ((
% 98.91/13.03 (eqbreln) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcext) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcext2) =>
% 98.91/13.03 ((
% 98.91/13.03 (ap2apEq1) =>
% 98.91/13.03 ((
% 98.91/13.03 (ap2apEq2) =>
% 98.91/13.03 ((
% 98.91/13.03 (beta1) =>
% 98.91/13.03 ((
% 98.91/13.03 (eta1) =>
% 98.91/13.03 ((
% 98.91/13.03 (lam2lamEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (beta2) =>
% 98.91/13.03 ((
% 98.91/13.03 (eta2) =>
% 98.91/13.03 ((
% 98.91/13.03 (iffalseProp1) =>
% 98.91/13.03 ((
% 98.91/13.03 (iffalseProp2) =>
% 98.91/13.03 ((
% 98.91/13.03 (iftrueProp1) =>
% 98.91/13.03 ((
% 98.91/13.03 (iftrueProp2) =>
% 98.91/13.03 ((
% 98.91/13.03 (ifSingleton) =>
% 98.91/13.03 ((
% 98.91/13.03 (ifp) =>
% 98.91/13.03 ((
% 98.91/13.03 (theeq) =>
% 98.91/13.03 ((
% 98.91/13.03 (iftrue) =>
% 98.91/13.03 ((
% 98.91/13.03 (iffalse) =>
% 98.91/13.03 ((
% 98.91/13.03 (iftrueorfalse) =>
% 98.91/13.03 ((
% 98.91/13.03 (binintersectT_lem) =>
% 98.91/13.03 ((
% 98.91/13.03 (binunionT_lem) =>
% 98.91/13.03 ((
% 98.91/13.03 (powersetT_lem) =>
% 98.91/13.03 ((
% 98.91/13.03 (setminusT_lem) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementT_lem) =>
% 98.91/13.03 ((
% 98.91/13.03 (setextT) =>
% 98.91/13.03 ((
% 98.91/13.03 (subsetTI) =>
% 98.91/13.03 ((
% 98.91/13.03 (powersetTI1) =>
% 98.91/13.03 ((
% 98.91/13.03 (powersetTE1) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementTI1) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementTE1) =>
% 98.91/13.03 ((
% 98.91/13.03 (binintersectTELcontra) =>
% 98.91/13.03 ((
% 98.91/13.03 (binintersectTERcontra) =>
% 98.91/13.03 ((
% 98.91/13.03 (contrasubsetT) =>
% 98.91/13.03 ((
% 98.91/13.03 (contrasubsetT1) =>
% 98.91/13.03 ((
% 98.91/13.03 (contrasubsetT2) =>
% 98.91/13.03 ((
% 98.91/13.03 (contrasubsetT3) =>
% 98.91/13.03 ((
% 98.91/13.03 (doubleComplementI1) =>
% 98.91/13.03 ((
% 98.91/13.03 (doubleComplementE1) =>
% 98.91/13.03 ((
% 98.91/13.03 (doubleComplementSub1) =>
% 98.91/13.03 ((
% 98.91/13.03 (doubleComplementSub2) =>
% 98.91/13.03 ((
% 98.91/13.03 (doubleComplementEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementTnotintersectT) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementImpComplementIntersect) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementSubsetComplementIntersect) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementInPowersetComplementIntersect) =>
% 98.91/13.03 ((
% 98.91/13.03 (contraSubsetComplement) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementTcontraSubset) =>
% 98.91/13.03 ((
% 98.91/13.03 (binunionTILcontra) =>
% 98.91/13.03 ((
% 98.91/13.03 (binunionTIRcontra) =>
% 98.91/13.03 ((
% 98.91/13.03 (inIntersectImpInUnion) =>
% 98.91/13.03 ((
% 98.91/13.03 (inIntersectImpInUnion2) =>
% 98.91/13.03 ((
% 98.91/13.03 (inIntersectImpInIntersectUnions) =>
% 98.91/13.03 ((
% 98.91/13.03 (intersectInPowersetIntersectUnions) =>
% 98.91/13.03 ((
% 98.91/13.03 (inComplementUnionImpNotIn1) =>
% 98.91/13.03 ((
% 98.91/13.03 (inComplementUnionImpInComplement1) =>
% 98.91/13.03 ((
% 98.91/13.03 (binunionTE) =>
% 98.91/13.03 ((
% 98.91/13.03 (binunionTEcontra) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2a1) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementUnionInPowersetComplement) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2a2) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan1a) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan1b) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan1) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2a) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2b2) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2b) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz13rule0) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz13rule1) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz13rule2) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz13rule3) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz13rule4) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz1_1) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz1_2) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz1_3) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz1_4) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz1_5) =>
% 98.91/13.03 ((
% 98.91/13.03 (breln1all2) =>
% 98.91/13.03 ((
% 98.91/13.03 (breln1SetBreln1) =>
% 98.91/13.03 ((
% 98.91/13.03 (choice2fnsingleton) =>
% 98.91/13.03 ((
% 98.91/13.03 (!!) @ (
% 98.91/13.03 (('#B') @ (
% 98.91/13.03 !!) @
% 98.91/13.03 (
% 98.91/13.03 (
% 98.91/13.03 ('#S') @ (
% 98.91/13.03 (
% 98.91/13.03 ('#B') @ (
% 98.91/13.03 '#B') @
% 98.91/13.03 breln1)) @
% 98.91/13.03 (
% 98.91/13.03 (
% 98.91/13.03 ('#S') @ dpsetconstr @
% 98.91/13.03 (
% 98.91/13.03 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.91/13.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1466])).
% 98.91/13.03 thf(zip_derived_cl1480, plain,
% 98.91/13.03 (~ (((ubforcartprodlem2) =>
% 98.91/13.03 (((ubforcartprodlem3) =>
% 98.91/13.03 (((cartprodpairin) =>
% 98.91/13.03 (((cartprodmempair1) =>
% 98.91/13.03 (((cartprodmempair) =>
% 98.91/13.03 (((setunionE2) =>
% 98.91/13.03 (((setunionsingleton1) =>
% 98.91/13.03 (((setunionsingleton2) =>
% 98.91/13.03 (((setunionsingleton) =>
% 98.91/13.03 (((singletonprop) =>
% 98.91/13.03 (((ex1E1) =>
% 98.91/13.03 (((ex1I) =>
% 98.91/13.03 (((ex1I2) =>
% 98.91/13.03 (((singletonsuniq) =>
% 98.91/13.03 (((setukpairinjL1) =>
% 98.91/13.03 (((kfstsingleton) =>
% 98.91/13.03 (((theprop) =>
% 98.91/13.03 (((kfstpairEq) =>
% 98.91/13.03 (((cartprodfstin) =>
% 98.91/13.03 (((setukpairinjL2) =>
% 98.91/13.03 (((setukpairinjL) =>
% 98.91/13.03 (((setukpairinjR11) =>
% 98.91/13.03 (((setukpairinjR12) =>
% 98.91/13.03 (((setukpairinjR1) =>
% 98.91/13.03 (((upairequniteq) =>
% 98.91/13.03 (((setukpairinjR2) =>
% 98.91/13.03 (((setukpairinjR) =>
% 98.91/13.03 (((ksndsingleton) =>
% 98.91/13.03 (((ksndpairEq) =>
% 98.91/13.03 (((kpairsurjEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodsndin) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodpairmemEL) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodpairmemER) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodmempaircEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodfstpairEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodsndpairEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodpairsurjEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrI) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrSub) =>
% 98.91/13.03 ((
% 98.91/13.03 (setOfPairsIsBReln) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrERa) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrEL1) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrEL2) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrER) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcImageSingleton) =>
% 98.91/13.03 ((
% 98.91/13.03 (apProp) =>
% 98.91/13.03 ((
% 98.91/13.03 (app) =>
% 98.91/13.03 ((
% 98.91/13.03 (infuncsetfunc) =>
% 98.91/13.03 ((
% 98.91/13.03 (ap2p) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcinfuncset) =>
% 98.91/13.03 ((
% 98.91/13.03 (lamProp) =>
% 98.91/13.03 ((
% 98.91/13.03 (lamp) =>
% 98.91/13.03 ((
% 98.91/13.03 (lam2p) =>
% 98.91/13.03 ((
% 98.91/13.03 (brelnall1) =>
% 98.91/13.03 ((
% 98.91/13.03 (brelnall2) =>
% 98.91/13.03 ((
% 98.91/13.03 (ex1E2) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcGraphProp1) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcGraphProp3) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcGraphProp2) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcextLem) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcGraphProp4) =>
% 98.91/13.03 ((
% 98.91/13.03 (subbreln) =>
% 98.91/13.03 ((
% 98.91/13.03 (eqbreln) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcext) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcext2) =>
% 98.91/13.03 ((
% 98.91/13.03 (ap2apEq1) =>
% 98.91/13.03 ((
% 98.91/13.03 (ap2apEq2) =>
% 98.91/13.03 ((
% 98.91/13.03 (beta1) =>
% 98.91/13.03 ((
% 98.91/13.03 (eta1) =>
% 98.91/13.03 ((
% 98.91/13.03 (lam2lamEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (beta2) =>
% 98.91/13.03 ((
% 98.91/13.03 (eta2) =>
% 98.91/13.03 ((
% 98.91/13.03 (iffalseProp1) =>
% 98.91/13.03 ((
% 98.91/13.03 (iffalseProp2) =>
% 98.91/13.03 ((
% 98.91/13.03 (iftrueProp1) =>
% 98.91/13.03 ((
% 98.91/13.03 (iftrueProp2) =>
% 98.91/13.03 ((
% 98.91/13.03 (ifSingleton) =>
% 98.91/13.03 ((
% 98.91/13.03 (ifp) =>
% 98.91/13.03 ((
% 98.91/13.03 (theeq) =>
% 98.91/13.03 ((
% 98.91/13.03 (iftrue) =>
% 98.91/13.03 ((
% 98.91/13.03 (iffalse) =>
% 98.91/13.03 ((
% 98.91/13.03 (iftrueorfalse) =>
% 98.91/13.03 ((
% 98.91/13.03 (binintersectT_lem) =>
% 98.91/13.03 ((
% 98.91/13.03 (binunionT_lem) =>
% 98.91/13.03 ((
% 98.91/13.03 (powersetT_lem) =>
% 98.91/13.03 ((
% 98.91/13.03 (setminusT_lem) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementT_lem) =>
% 98.91/13.03 ((
% 98.91/13.03 (setextT) =>
% 98.91/13.03 ((
% 98.91/13.03 (subsetTI) =>
% 98.91/13.03 ((
% 98.91/13.03 (powersetTI1) =>
% 98.91/13.03 ((
% 98.91/13.03 (powersetTE1) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementTI1) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementTE1) =>
% 98.91/13.03 ((
% 98.91/13.03 (binintersectTELcontra) =>
% 98.91/13.03 ((
% 98.91/13.03 (binintersectTERcontra) =>
% 98.91/13.03 ((
% 98.91/13.03 (contrasubsetT) =>
% 98.91/13.03 ((
% 98.91/13.03 (contrasubsetT1) =>
% 98.91/13.03 ((
% 98.91/13.03 (contrasubsetT2) =>
% 98.91/13.03 ((
% 98.91/13.03 (contrasubsetT3) =>
% 98.91/13.03 ((
% 98.91/13.03 (doubleComplementI1) =>
% 98.91/13.03 ((
% 98.91/13.03 (doubleComplementE1) =>
% 98.91/13.03 ((
% 98.91/13.03 (doubleComplementSub1) =>
% 98.91/13.03 ((
% 98.91/13.03 (doubleComplementSub2) =>
% 98.91/13.03 ((
% 98.91/13.03 (doubleComplementEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementTnotintersectT) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementImpComplementIntersect) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementSubsetComplementIntersect) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementInPowersetComplementIntersect) =>
% 98.91/13.03 ((
% 98.91/13.03 (contraSubsetComplement) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementTcontraSubset) =>
% 98.91/13.03 ((
% 98.91/13.03 (binunionTILcontra) =>
% 98.91/13.03 ((
% 98.91/13.03 (binunionTIRcontra) =>
% 98.91/13.03 ((
% 98.91/13.03 (inIntersectImpInUnion) =>
% 98.91/13.03 ((
% 98.91/13.03 (inIntersectImpInUnion2) =>
% 98.91/13.03 ((
% 98.91/13.03 (inIntersectImpInIntersectUnions) =>
% 98.91/13.03 ((
% 98.91/13.03 (intersectInPowersetIntersectUnions) =>
% 98.91/13.03 ((
% 98.91/13.03 (inComplementUnionImpNotIn1) =>
% 98.91/13.03 ((
% 98.91/13.03 (inComplementUnionImpInComplement1) =>
% 98.91/13.03 ((
% 98.91/13.03 (binunionTE) =>
% 98.91/13.03 ((
% 98.91/13.03 (binunionTEcontra) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2a1) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementUnionInPowersetComplement) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2a2) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan1a) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan1b) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan1) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2a) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2b2) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2b) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz13rule0) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz13rule1) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz13rule2) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz13rule3) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz13rule4) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz1_1) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz1_2) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz1_3) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz1_4) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz1_5) =>
% 98.91/13.03 ((
% 98.91/13.03 (breln1all2) =>
% 98.91/13.03 ((
% 98.91/13.03 (breln1SetBreln1) =>
% 98.91/13.03 ((
% 98.91/13.03 (choice2fnsingleton) =>
% 98.91/13.03 ((
% 98.91/13.03 (!!) @ (
% 98.91/13.03 (('#B') @ (
% 98.91/13.03 !!) @
% 98.91/13.03 (
% 98.91/13.03 (
% 98.91/13.03 ('#S') @ (
% 98.91/13.03 (
% 98.91/13.03 ('#B') @ (
% 98.91/13.03 '#B') @
% 98.91/13.03 breln1)) @
% 98.91/13.03 (
% 98.91/13.03 (
% 98.91/13.03 ('#S') @ dpsetconstr @
% 98.91/13.03 (
% 98.91/13.03 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.91/13.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1473])).
% 98.91/13.03 thf(zip_derived_cl1488, plain,
% 98.91/13.03 (~ (((ubforcartprodlem3) =>
% 98.91/13.03 (((cartprodpairin) =>
% 98.91/13.03 (((cartprodmempair1) =>
% 98.91/13.03 (((cartprodmempair) =>
% 98.91/13.03 (((setunionE2) =>
% 98.91/13.03 (((setunionsingleton1) =>
% 98.91/13.03 (((setunionsingleton2) =>
% 98.91/13.03 (((setunionsingleton) =>
% 98.91/13.03 (((singletonprop) =>
% 98.91/13.03 (((ex1E1) =>
% 98.91/13.03 (((ex1I) =>
% 98.91/13.03 (((ex1I2) =>
% 98.91/13.03 (((singletonsuniq) =>
% 98.91/13.03 (((setukpairinjL1) =>
% 98.91/13.03 (((kfstsingleton) =>
% 98.91/13.03 (((theprop) =>
% 98.91/13.03 (((kfstpairEq) =>
% 98.91/13.03 (((cartprodfstin) =>
% 98.91/13.03 (((setukpairinjL2) =>
% 98.91/13.03 (((setukpairinjL) =>
% 98.91/13.03 (((setukpairinjR11) =>
% 98.91/13.03 (((setukpairinjR12) =>
% 98.91/13.03 (((setukpairinjR1) =>
% 98.91/13.03 (((upairequniteq) =>
% 98.91/13.03 (((setukpairinjR2) =>
% 98.91/13.03 (((setukpairinjR) =>
% 98.91/13.03 (((ksndsingleton) =>
% 98.91/13.03 (((ksndpairEq) =>
% 98.91/13.03 (((kpairsurjEq) =>
% 98.91/13.03 (((cartprodsndin) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodpairmemEL) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodpairmemER) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodmempaircEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodfstpairEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodsndpairEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodpairsurjEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrI) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrSub) =>
% 98.91/13.03 ((
% 98.91/13.03 (setOfPairsIsBReln) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrERa) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrEL1) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrEL2) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrER) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcImageSingleton) =>
% 98.91/13.03 ((
% 98.91/13.03 (apProp) =>
% 98.91/13.03 ((
% 98.91/13.03 (app) =>
% 98.91/13.03 ((
% 98.91/13.03 (infuncsetfunc) =>
% 98.91/13.03 ((
% 98.91/13.03 (ap2p) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcinfuncset) =>
% 98.91/13.03 ((
% 98.91/13.03 (lamProp) =>
% 98.91/13.03 ((
% 98.91/13.03 (lamp) =>
% 98.91/13.03 ((
% 98.91/13.03 (lam2p) =>
% 98.91/13.03 ((
% 98.91/13.03 (brelnall1) =>
% 98.91/13.03 ((
% 98.91/13.03 (brelnall2) =>
% 98.91/13.03 ((
% 98.91/13.03 (ex1E2) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcGraphProp1) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcGraphProp3) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcGraphProp2) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcextLem) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcGraphProp4) =>
% 98.91/13.03 ((
% 98.91/13.03 (subbreln) =>
% 98.91/13.03 ((
% 98.91/13.03 (eqbreln) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcext) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcext2) =>
% 98.91/13.03 ((
% 98.91/13.03 (ap2apEq1) =>
% 98.91/13.03 ((
% 98.91/13.03 (ap2apEq2) =>
% 98.91/13.03 ((
% 98.91/13.03 (beta1) =>
% 98.91/13.03 ((
% 98.91/13.03 (eta1) =>
% 98.91/13.03 ((
% 98.91/13.03 (lam2lamEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (beta2) =>
% 98.91/13.03 ((
% 98.91/13.03 (eta2) =>
% 98.91/13.03 ((
% 98.91/13.03 (iffalseProp1) =>
% 98.91/13.03 ((
% 98.91/13.03 (iffalseProp2) =>
% 98.91/13.03 ((
% 98.91/13.03 (iftrueProp1) =>
% 98.91/13.03 ((
% 98.91/13.03 (iftrueProp2) =>
% 98.91/13.03 ((
% 98.91/13.03 (ifSingleton) =>
% 98.91/13.03 ((
% 98.91/13.03 (ifp) =>
% 98.91/13.03 ((
% 98.91/13.03 (theeq) =>
% 98.91/13.03 ((
% 98.91/13.03 (iftrue) =>
% 98.91/13.03 ((
% 98.91/13.03 (iffalse) =>
% 98.91/13.03 ((
% 98.91/13.03 (iftrueorfalse) =>
% 98.91/13.03 ((
% 98.91/13.03 (binintersectT_lem) =>
% 98.91/13.03 ((
% 98.91/13.03 (binunionT_lem) =>
% 98.91/13.03 ((
% 98.91/13.03 (powersetT_lem) =>
% 98.91/13.03 ((
% 98.91/13.03 (setminusT_lem) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementT_lem) =>
% 98.91/13.03 ((
% 98.91/13.03 (setextT) =>
% 98.91/13.03 ((
% 98.91/13.03 (subsetTI) =>
% 98.91/13.03 ((
% 98.91/13.03 (powersetTI1) =>
% 98.91/13.03 ((
% 98.91/13.03 (powersetTE1) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementTI1) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementTE1) =>
% 98.91/13.03 ((
% 98.91/13.03 (binintersectTELcontra) =>
% 98.91/13.03 ((
% 98.91/13.03 (binintersectTERcontra) =>
% 98.91/13.03 ((
% 98.91/13.03 (contrasubsetT) =>
% 98.91/13.03 ((
% 98.91/13.03 (contrasubsetT1) =>
% 98.91/13.03 ((
% 98.91/13.03 (contrasubsetT2) =>
% 98.91/13.03 ((
% 98.91/13.03 (contrasubsetT3) =>
% 98.91/13.03 ((
% 98.91/13.03 (doubleComplementI1) =>
% 98.91/13.03 ((
% 98.91/13.03 (doubleComplementE1) =>
% 98.91/13.03 ((
% 98.91/13.03 (doubleComplementSub1) =>
% 98.91/13.03 ((
% 98.91/13.03 (doubleComplementSub2) =>
% 98.91/13.03 ((
% 98.91/13.03 (doubleComplementEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementTnotintersectT) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementImpComplementIntersect) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementSubsetComplementIntersect) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementInPowersetComplementIntersect) =>
% 98.91/13.03 ((
% 98.91/13.03 (contraSubsetComplement) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementTcontraSubset) =>
% 98.91/13.03 ((
% 98.91/13.03 (binunionTILcontra) =>
% 98.91/13.03 ((
% 98.91/13.03 (binunionTIRcontra) =>
% 98.91/13.03 ((
% 98.91/13.03 (inIntersectImpInUnion) =>
% 98.91/13.03 ((
% 98.91/13.03 (inIntersectImpInUnion2) =>
% 98.91/13.03 ((
% 98.91/13.03 (inIntersectImpInIntersectUnions) =>
% 98.91/13.03 ((
% 98.91/13.03 (intersectInPowersetIntersectUnions) =>
% 98.91/13.03 ((
% 98.91/13.03 (inComplementUnionImpNotIn1) =>
% 98.91/13.03 ((
% 98.91/13.03 (inComplementUnionImpInComplement1) =>
% 98.91/13.03 ((
% 98.91/13.03 (binunionTE) =>
% 98.91/13.03 ((
% 98.91/13.03 (binunionTEcontra) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2a1) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementUnionInPowersetComplement) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2a2) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan1a) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan1b) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan1) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2a) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2b2) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2b) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz13rule0) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz13rule1) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz13rule2) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz13rule3) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz13rule4) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz1_1) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz1_2) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz1_3) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz1_4) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz1_5) =>
% 98.91/13.03 ((
% 98.91/13.03 (breln1all2) =>
% 98.91/13.03 ((
% 98.91/13.03 (breln1SetBreln1) =>
% 98.91/13.03 ((
% 98.91/13.03 (choice2fnsingleton) =>
% 98.91/13.03 ((
% 98.91/13.03 (!!) @ (
% 98.91/13.03 (('#B') @ (
% 98.91/13.03 !!) @
% 98.91/13.03 (
% 98.91/13.03 (
% 98.91/13.03 ('#S') @ (
% 98.91/13.03 (
% 98.91/13.03 ('#B') @ (
% 98.91/13.03 '#B') @
% 98.91/13.03 breln1)) @
% 98.91/13.03 (
% 98.91/13.03 (
% 98.91/13.03 ('#S') @ dpsetconstr @
% 98.91/13.03 (
% 98.91/13.03 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.91/13.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1480])).
% 98.91/13.03 thf(zip_derived_cl1496, plain,
% 98.91/13.03 (~ (((cartprodpairin) =>
% 98.91/13.03 (((cartprodmempair1) =>
% 98.91/13.03 (((cartprodmempair) =>
% 98.91/13.03 (((setunionE2) =>
% 98.91/13.03 (((setunionsingleton1) =>
% 98.91/13.03 (((setunionsingleton2) =>
% 98.91/13.03 (((setunionsingleton) =>
% 98.91/13.03 (((singletonprop) =>
% 98.91/13.03 (((ex1E1) =>
% 98.91/13.03 (((ex1I) =>
% 98.91/13.03 (((ex1I2) =>
% 98.91/13.03 (((singletonsuniq) =>
% 98.91/13.03 (((setukpairinjL1) =>
% 98.91/13.03 (((kfstsingleton) =>
% 98.91/13.03 (((theprop) =>
% 98.91/13.03 (((kfstpairEq) =>
% 98.91/13.03 (((cartprodfstin) =>
% 98.91/13.03 (((setukpairinjL2) =>
% 98.91/13.03 (((setukpairinjL) =>
% 98.91/13.03 (((setukpairinjR11) =>
% 98.91/13.03 (((setukpairinjR12) =>
% 98.91/13.03 (((setukpairinjR1) =>
% 98.91/13.03 (((upairequniteq) =>
% 98.91/13.03 (((setukpairinjR2) =>
% 98.91/13.03 (((setukpairinjR) =>
% 98.91/13.03 (((ksndsingleton) =>
% 98.91/13.03 (((ksndpairEq) =>
% 98.91/13.03 (((kpairsurjEq) =>
% 98.91/13.03 (((cartprodsndin) =>
% 98.91/13.03 (((cartprodpairmemEL) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodpairmemER) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodmempaircEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodfstpairEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodsndpairEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodpairsurjEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrI) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrSub) =>
% 98.91/13.03 ((
% 98.91/13.03 (setOfPairsIsBReln) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrERa) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrEL1) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrEL2) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrER) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcImageSingleton) =>
% 98.91/13.03 ((
% 98.91/13.03 (apProp) =>
% 98.91/13.03 ((
% 98.91/13.03 (app) =>
% 98.91/13.03 ((
% 98.91/13.03 (infuncsetfunc) =>
% 98.91/13.03 ((
% 98.91/13.03 (ap2p) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcinfuncset) =>
% 98.91/13.03 ((
% 98.91/13.03 (lamProp) =>
% 98.91/13.03 ((
% 98.91/13.03 (lamp) =>
% 98.91/13.03 ((
% 98.91/13.03 (lam2p) =>
% 98.91/13.03 ((
% 98.91/13.03 (brelnall1) =>
% 98.91/13.03 ((
% 98.91/13.03 (brelnall2) =>
% 98.91/13.03 ((
% 98.91/13.03 (ex1E2) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcGraphProp1) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcGraphProp3) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcGraphProp2) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcextLem) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcGraphProp4) =>
% 98.91/13.03 ((
% 98.91/13.03 (subbreln) =>
% 98.91/13.03 ((
% 98.91/13.03 (eqbreln) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcext) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcext2) =>
% 98.91/13.03 ((
% 98.91/13.03 (ap2apEq1) =>
% 98.91/13.03 ((
% 98.91/13.03 (ap2apEq2) =>
% 98.91/13.03 ((
% 98.91/13.03 (beta1) =>
% 98.91/13.03 ((
% 98.91/13.03 (eta1) =>
% 98.91/13.03 ((
% 98.91/13.03 (lam2lamEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (beta2) =>
% 98.91/13.03 ((
% 98.91/13.03 (eta2) =>
% 98.91/13.03 ((
% 98.91/13.03 (iffalseProp1) =>
% 98.91/13.03 ((
% 98.91/13.03 (iffalseProp2) =>
% 98.91/13.03 ((
% 98.91/13.03 (iftrueProp1) =>
% 98.91/13.03 ((
% 98.91/13.03 (iftrueProp2) =>
% 98.91/13.03 ((
% 98.91/13.03 (ifSingleton) =>
% 98.91/13.03 ((
% 98.91/13.03 (ifp) =>
% 98.91/13.03 ((
% 98.91/13.03 (theeq) =>
% 98.91/13.03 ((
% 98.91/13.03 (iftrue) =>
% 98.91/13.03 ((
% 98.91/13.03 (iffalse) =>
% 98.91/13.03 ((
% 98.91/13.03 (iftrueorfalse) =>
% 98.91/13.03 ((
% 98.91/13.03 (binintersectT_lem) =>
% 98.91/13.03 ((
% 98.91/13.03 (binunionT_lem) =>
% 98.91/13.03 ((
% 98.91/13.03 (powersetT_lem) =>
% 98.91/13.03 ((
% 98.91/13.03 (setminusT_lem) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementT_lem) =>
% 98.91/13.03 ((
% 98.91/13.03 (setextT) =>
% 98.91/13.03 ((
% 98.91/13.03 (subsetTI) =>
% 98.91/13.03 ((
% 98.91/13.03 (powersetTI1) =>
% 98.91/13.03 ((
% 98.91/13.03 (powersetTE1) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementTI1) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementTE1) =>
% 98.91/13.03 ((
% 98.91/13.03 (binintersectTELcontra) =>
% 98.91/13.03 ((
% 98.91/13.03 (binintersectTERcontra) =>
% 98.91/13.03 ((
% 98.91/13.03 (contrasubsetT) =>
% 98.91/13.03 ((
% 98.91/13.03 (contrasubsetT1) =>
% 98.91/13.03 ((
% 98.91/13.03 (contrasubsetT2) =>
% 98.91/13.03 ((
% 98.91/13.03 (contrasubsetT3) =>
% 98.91/13.03 ((
% 98.91/13.03 (doubleComplementI1) =>
% 98.91/13.03 ((
% 98.91/13.03 (doubleComplementE1) =>
% 98.91/13.03 ((
% 98.91/13.03 (doubleComplementSub1) =>
% 98.91/13.03 ((
% 98.91/13.03 (doubleComplementSub2) =>
% 98.91/13.03 ((
% 98.91/13.03 (doubleComplementEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementTnotintersectT) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementImpComplementIntersect) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementSubsetComplementIntersect) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementInPowersetComplementIntersect) =>
% 98.91/13.03 ((
% 98.91/13.03 (contraSubsetComplement) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementTcontraSubset) =>
% 98.91/13.03 ((
% 98.91/13.03 (binunionTILcontra) =>
% 98.91/13.03 ((
% 98.91/13.03 (binunionTIRcontra) =>
% 98.91/13.03 ((
% 98.91/13.03 (inIntersectImpInUnion) =>
% 98.91/13.03 ((
% 98.91/13.03 (inIntersectImpInUnion2) =>
% 98.91/13.03 ((
% 98.91/13.03 (inIntersectImpInIntersectUnions) =>
% 98.91/13.03 ((
% 98.91/13.03 (intersectInPowersetIntersectUnions) =>
% 98.91/13.03 ((
% 98.91/13.03 (inComplementUnionImpNotIn1) =>
% 98.91/13.03 ((
% 98.91/13.03 (inComplementUnionImpInComplement1) =>
% 98.91/13.03 ((
% 98.91/13.03 (binunionTE) =>
% 98.91/13.03 ((
% 98.91/13.03 (binunionTEcontra) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2a1) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementUnionInPowersetComplement) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2a2) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan1a) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan1b) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan1) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2a) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2b2) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2b) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz13rule0) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz13rule1) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz13rule2) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz13rule3) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz13rule4) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz1_1) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz1_2) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz1_3) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz1_4) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz1_5) =>
% 98.91/13.03 ((
% 98.91/13.03 (breln1all2) =>
% 98.91/13.03 ((
% 98.91/13.03 (breln1SetBreln1) =>
% 98.91/13.03 ((
% 98.91/13.03 (choice2fnsingleton) =>
% 98.91/13.03 ((
% 98.91/13.03 (!!) @ (
% 98.91/13.03 (('#B') @ (
% 98.91/13.03 !!) @
% 98.91/13.03 (
% 98.91/13.03 (
% 98.91/13.03 ('#S') @ (
% 98.91/13.03 (
% 98.91/13.03 ('#B') @ (
% 98.91/13.03 '#B') @
% 98.91/13.03 breln1)) @
% 98.91/13.03 (
% 98.91/13.03 (
% 98.91/13.03 ('#S') @ dpsetconstr @
% 98.91/13.03 (
% 98.91/13.03 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.91/13.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1488])).
% 98.91/13.03 thf(zip_derived_cl1505, plain,
% 98.91/13.03 (~ (((cartprodmempair1) =>
% 98.91/13.03 (((cartprodmempair) =>
% 98.91/13.03 (((setunionE2) =>
% 98.91/13.03 (((setunionsingleton1) =>
% 98.91/13.03 (((setunionsingleton2) =>
% 98.91/13.03 (((setunionsingleton) =>
% 98.91/13.03 (((singletonprop) =>
% 98.91/13.03 (((ex1E1) =>
% 98.91/13.03 (((ex1I) =>
% 98.91/13.03 (((ex1I2) =>
% 98.91/13.03 (((singletonsuniq) =>
% 98.91/13.03 (((setukpairinjL1) =>
% 98.91/13.03 (((kfstsingleton) =>
% 98.91/13.03 (((theprop) =>
% 98.91/13.03 (((kfstpairEq) =>
% 98.91/13.03 (((cartprodfstin) =>
% 98.91/13.03 (((setukpairinjL2) =>
% 98.91/13.03 (((setukpairinjL) =>
% 98.91/13.03 (((setukpairinjR11) =>
% 98.91/13.03 (((setukpairinjR12) =>
% 98.91/13.03 (((setukpairinjR1) =>
% 98.91/13.03 (((upairequniteq) =>
% 98.91/13.03 (((setukpairinjR2) =>
% 98.91/13.03 (((setukpairinjR) =>
% 98.91/13.03 (((ksndsingleton) =>
% 98.91/13.03 (((ksndpairEq) =>
% 98.91/13.03 (((kpairsurjEq) =>
% 98.91/13.03 (((cartprodsndin) =>
% 98.91/13.03 (((cartprodpairmemEL) =>
% 98.91/13.03 (((cartprodpairmemER) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodmempaircEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodfstpairEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodsndpairEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodpairsurjEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrI) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrSub) =>
% 98.91/13.03 ((
% 98.91/13.03 (setOfPairsIsBReln) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrERa) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrEL1) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrEL2) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrER) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcImageSingleton) =>
% 98.91/13.03 ((
% 98.91/13.03 (apProp) =>
% 98.91/13.03 ((
% 98.91/13.03 (app) =>
% 98.91/13.03 ((
% 98.91/13.03 (infuncsetfunc) =>
% 98.91/13.03 ((
% 98.91/13.03 (ap2p) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcinfuncset) =>
% 98.91/13.03 ((
% 98.91/13.03 (lamProp) =>
% 98.91/13.03 ((
% 98.91/13.03 (lamp) =>
% 98.91/13.03 ((
% 98.91/13.03 (lam2p) =>
% 98.91/13.03 ((
% 98.91/13.03 (brelnall1) =>
% 98.91/13.03 ((
% 98.91/13.03 (brelnall2) =>
% 98.91/13.03 ((
% 98.91/13.03 (ex1E2) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcGraphProp1) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcGraphProp3) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcGraphProp2) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcextLem) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcGraphProp4) =>
% 98.91/13.03 ((
% 98.91/13.03 (subbreln) =>
% 98.91/13.03 ((
% 98.91/13.03 (eqbreln) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcext) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcext2) =>
% 98.91/13.03 ((
% 98.91/13.03 (ap2apEq1) =>
% 98.91/13.03 ((
% 98.91/13.03 (ap2apEq2) =>
% 98.91/13.03 ((
% 98.91/13.03 (beta1) =>
% 98.91/13.03 ((
% 98.91/13.03 (eta1) =>
% 98.91/13.03 ((
% 98.91/13.03 (lam2lamEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (beta2) =>
% 98.91/13.03 ((
% 98.91/13.03 (eta2) =>
% 98.91/13.03 ((
% 98.91/13.03 (iffalseProp1) =>
% 98.91/13.03 ((
% 98.91/13.03 (iffalseProp2) =>
% 98.91/13.03 ((
% 98.91/13.03 (iftrueProp1) =>
% 98.91/13.03 ((
% 98.91/13.03 (iftrueProp2) =>
% 98.91/13.03 ((
% 98.91/13.03 (ifSingleton) =>
% 98.91/13.03 ((
% 98.91/13.03 (ifp) =>
% 98.91/13.03 ((
% 98.91/13.03 (theeq) =>
% 98.91/13.03 ((
% 98.91/13.03 (iftrue) =>
% 98.91/13.03 ((
% 98.91/13.03 (iffalse) =>
% 98.91/13.03 ((
% 98.91/13.03 (iftrueorfalse) =>
% 98.91/13.03 ((
% 98.91/13.03 (binintersectT_lem) =>
% 98.91/13.03 ((
% 98.91/13.03 (binunionT_lem) =>
% 98.91/13.03 ((
% 98.91/13.03 (powersetT_lem) =>
% 98.91/13.03 ((
% 98.91/13.03 (setminusT_lem) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementT_lem) =>
% 98.91/13.03 ((
% 98.91/13.03 (setextT) =>
% 98.91/13.03 ((
% 98.91/13.03 (subsetTI) =>
% 98.91/13.03 ((
% 98.91/13.03 (powersetTI1) =>
% 98.91/13.03 ((
% 98.91/13.03 (powersetTE1) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementTI1) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementTE1) =>
% 98.91/13.03 ((
% 98.91/13.03 (binintersectTELcontra) =>
% 98.91/13.03 ((
% 98.91/13.03 (binintersectTERcontra) =>
% 98.91/13.03 ((
% 98.91/13.03 (contrasubsetT) =>
% 98.91/13.03 ((
% 98.91/13.03 (contrasubsetT1) =>
% 98.91/13.03 ((
% 98.91/13.03 (contrasubsetT2) =>
% 98.91/13.03 ((
% 98.91/13.03 (contrasubsetT3) =>
% 98.91/13.03 ((
% 98.91/13.03 (doubleComplementI1) =>
% 98.91/13.03 ((
% 98.91/13.03 (doubleComplementE1) =>
% 98.91/13.03 ((
% 98.91/13.03 (doubleComplementSub1) =>
% 98.91/13.03 ((
% 98.91/13.03 (doubleComplementSub2) =>
% 98.91/13.03 ((
% 98.91/13.03 (doubleComplementEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementTnotintersectT) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementImpComplementIntersect) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementSubsetComplementIntersect) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementInPowersetComplementIntersect) =>
% 98.91/13.03 ((
% 98.91/13.03 (contraSubsetComplement) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementTcontraSubset) =>
% 98.91/13.03 ((
% 98.91/13.03 (binunionTILcontra) =>
% 98.91/13.03 ((
% 98.91/13.03 (binunionTIRcontra) =>
% 98.91/13.03 ((
% 98.91/13.03 (inIntersectImpInUnion) =>
% 98.91/13.03 ((
% 98.91/13.03 (inIntersectImpInUnion2) =>
% 98.91/13.03 ((
% 98.91/13.03 (inIntersectImpInIntersectUnions) =>
% 98.91/13.03 ((
% 98.91/13.03 (intersectInPowersetIntersectUnions) =>
% 98.91/13.03 ((
% 98.91/13.03 (inComplementUnionImpNotIn1) =>
% 98.91/13.03 ((
% 98.91/13.03 (inComplementUnionImpInComplement1) =>
% 98.91/13.03 ((
% 98.91/13.03 (binunionTE) =>
% 98.91/13.03 ((
% 98.91/13.03 (binunionTEcontra) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2a1) =>
% 98.91/13.03 ((
% 98.91/13.03 (complementUnionInPowersetComplement) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2a2) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan1a) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan1b) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan1) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2a) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2b2) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2b) =>
% 98.91/13.03 ((
% 98.91/13.03 (demorgan2) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz13rule0) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz13rule1) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz13rule2) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz13rule3) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz13rule4) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz1_1) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz1_2) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz1_3) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz1_4) =>
% 98.91/13.03 ((
% 98.91/13.03 (woz1_5) =>
% 98.91/13.03 ((
% 98.91/13.03 (breln1all2) =>
% 98.91/13.03 ((
% 98.91/13.03 (breln1SetBreln1) =>
% 98.91/13.03 ((
% 98.91/13.03 (choice2fnsingleton) =>
% 98.91/13.03 ((
% 98.91/13.03 (!!) @ (
% 98.91/13.03 (('#B') @ (
% 98.91/13.03 !!) @
% 98.91/13.03 (
% 98.91/13.03 (
% 98.91/13.03 ('#S') @ (
% 98.91/13.03 (
% 98.91/13.03 ('#B') @ (
% 98.91/13.03 '#B') @
% 98.91/13.03 breln1)) @
% 98.91/13.03 (
% 98.91/13.03 (
% 98.91/13.03 ('#S') @ dpsetconstr @
% 98.91/13.03 (
% 98.91/13.03 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.91/13.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1496])).
% 98.91/13.03 thf(zip_derived_cl1515, plain,
% 98.91/13.03 (~ (((cartprodmempair) =>
% 98.91/13.03 (((setunionE2) =>
% 98.91/13.03 (((setunionsingleton1) =>
% 98.91/13.03 (((setunionsingleton2) =>
% 98.91/13.03 (((setunionsingleton) =>
% 98.91/13.03 (((singletonprop) =>
% 98.91/13.03 (((ex1E1) =>
% 98.91/13.03 (((ex1I) =>
% 98.91/13.03 (((ex1I2) =>
% 98.91/13.03 (((singletonsuniq) =>
% 98.91/13.03 (((setukpairinjL1) =>
% 98.91/13.03 (((kfstsingleton) =>
% 98.91/13.03 (((theprop) =>
% 98.91/13.03 (((kfstpairEq) =>
% 98.91/13.03 (((cartprodfstin) =>
% 98.91/13.03 (((setukpairinjL2) =>
% 98.91/13.03 (((setukpairinjL) =>
% 98.91/13.03 (((setukpairinjR11) =>
% 98.91/13.03 (((setukpairinjR12) =>
% 98.91/13.03 (((setukpairinjR1) =>
% 98.91/13.03 (((upairequniteq) =>
% 98.91/13.03 (((setukpairinjR2) =>
% 98.91/13.03 (((setukpairinjR) =>
% 98.91/13.03 (((ksndsingleton) =>
% 98.91/13.03 (((ksndpairEq) =>
% 98.91/13.03 (((kpairsurjEq) =>
% 98.91/13.03 (((cartprodsndin) =>
% 98.91/13.03 (((cartprodpairmemEL) =>
% 98.91/13.03 (((cartprodpairmemER) =>
% 98.91/13.03 (((cartprodmempaircEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodfstpairEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodsndpairEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (cartprodpairsurjEq) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrI) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrSub) =>
% 98.91/13.03 ((
% 98.91/13.03 (setOfPairsIsBReln) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrERa) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrEL1) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrEL2) =>
% 98.91/13.03 ((
% 98.91/13.03 (dpsetconstrER) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcImageSingleton) =>
% 98.91/13.03 ((
% 98.91/13.03 (apProp) =>
% 98.91/13.03 ((
% 98.91/13.03 (app) =>
% 98.91/13.03 ((
% 98.91/13.03 (infuncsetfunc) =>
% 98.91/13.03 ((
% 98.91/13.03 (ap2p) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcinfuncset) =>
% 98.91/13.03 ((
% 98.91/13.03 (lamProp) =>
% 98.91/13.03 ((
% 98.91/13.03 (lamp) =>
% 98.91/13.03 ((
% 98.91/13.03 (lam2p) =>
% 98.91/13.03 ((
% 98.91/13.03 (brelnall1) =>
% 98.91/13.03 ((
% 98.91/13.03 (brelnall2) =>
% 98.91/13.03 ((
% 98.91/13.03 (ex1E2) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcGraphProp1) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcGraphProp3) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcGraphProp2) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcextLem) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcGraphProp4) =>
% 98.91/13.03 ((
% 98.91/13.03 (subbreln) =>
% 98.91/13.03 ((
% 98.91/13.03 (eqbreln) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcext) =>
% 98.91/13.03 ((
% 98.91/13.03 (funcext2) =>
% 98.91/13.03 ((
% 98.91/13.03 (ap2apEq1) =>
% 98.91/13.03 ((
% 98.91/13.04 (ap2apEq2) =>
% 98.91/13.04 ((
% 98.91/13.04 (beta1) =>
% 98.91/13.04 ((
% 98.91/13.04 (eta1) =>
% 98.91/13.04 ((
% 98.91/13.04 (lam2lamEq) =>
% 98.91/13.04 ((
% 98.91/13.04 (beta2) =>
% 98.91/13.04 ((
% 98.91/13.04 (eta2) =>
% 98.91/13.04 ((
% 98.91/13.04 (iffalseProp1) =>
% 98.91/13.04 ((
% 98.91/13.04 (iffalseProp2) =>
% 98.91/13.04 ((
% 98.91/13.04 (iftrueProp1) =>
% 98.91/13.04 ((
% 98.91/13.04 (iftrueProp2) =>
% 98.91/13.04 ((
% 98.91/13.04 (ifSingleton) =>
% 98.91/13.04 ((
% 98.91/13.04 (ifp) =>
% 98.91/13.04 ((
% 98.91/13.04 (theeq) =>
% 98.91/13.04 ((
% 98.91/13.04 (iftrue) =>
% 98.91/13.04 ((
% 98.91/13.04 (iffalse) =>
% 98.91/13.04 ((
% 98.91/13.04 (iftrueorfalse) =>
% 98.91/13.04 ((
% 98.91/13.04 (binintersectT_lem) =>
% 98.91/13.04 ((
% 98.91/13.04 (binunionT_lem) =>
% 98.91/13.04 ((
% 98.91/13.04 (powersetT_lem) =>
% 98.91/13.04 ((
% 98.91/13.04 (setminusT_lem) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementT_lem) =>
% 98.91/13.04 ((
% 98.91/13.04 (setextT) =>
% 98.91/13.04 ((
% 98.91/13.04 (subsetTI) =>
% 98.91/13.04 ((
% 98.91/13.04 (powersetTI1) =>
% 98.91/13.04 ((
% 98.91/13.04 (powersetTE1) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementTI1) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementTE1) =>
% 98.91/13.04 ((
% 98.91/13.04 (binintersectTELcontra) =>
% 98.91/13.04 ((
% 98.91/13.04 (binintersectTERcontra) =>
% 98.91/13.04 ((
% 98.91/13.04 (contrasubsetT) =>
% 98.91/13.04 ((
% 98.91/13.04 (contrasubsetT1) =>
% 98.91/13.04 ((
% 98.91/13.04 (contrasubsetT2) =>
% 98.91/13.04 ((
% 98.91/13.04 (contrasubsetT3) =>
% 98.91/13.04 ((
% 98.91/13.04 (doubleComplementI1) =>
% 98.91/13.04 ((
% 98.91/13.04 (doubleComplementE1) =>
% 98.91/13.04 ((
% 98.91/13.04 (doubleComplementSub1) =>
% 98.91/13.04 ((
% 98.91/13.04 (doubleComplementSub2) =>
% 98.91/13.04 ((
% 98.91/13.04 (doubleComplementEq) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementTnotintersectT) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementImpComplementIntersect) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementSubsetComplementIntersect) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementInPowersetComplementIntersect) =>
% 98.91/13.04 ((
% 98.91/13.04 (contraSubsetComplement) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementTcontraSubset) =>
% 98.91/13.04 ((
% 98.91/13.04 (binunionTILcontra) =>
% 98.91/13.04 ((
% 98.91/13.04 (binunionTIRcontra) =>
% 98.91/13.04 ((
% 98.91/13.04 (inIntersectImpInUnion) =>
% 98.91/13.04 ((
% 98.91/13.04 (inIntersectImpInUnion2) =>
% 98.91/13.04 ((
% 98.91/13.04 (inIntersectImpInIntersectUnions) =>
% 98.91/13.04 ((
% 98.91/13.04 (intersectInPowersetIntersectUnions) =>
% 98.91/13.04 ((
% 98.91/13.04 (inComplementUnionImpNotIn1) =>
% 98.91/13.04 ((
% 98.91/13.04 (inComplementUnionImpInComplement1) =>
% 98.91/13.04 ((
% 98.91/13.04 (binunionTE) =>
% 98.91/13.04 ((
% 98.91/13.04 (binunionTEcontra) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan2a1) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementUnionInPowersetComplement) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan2a2) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan1a) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan1b) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan1) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan2a) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan2b2) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan2b) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan2) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz13rule0) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz13rule1) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz13rule2) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz13rule3) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz13rule4) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz1_1) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz1_2) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz1_3) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz1_4) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz1_5) =>
% 98.91/13.04 ((
% 98.91/13.04 (breln1all2) =>
% 98.91/13.04 ((
% 98.91/13.04 (breln1SetBreln1) =>
% 98.91/13.04 ((
% 98.91/13.04 (choice2fnsingleton) =>
% 98.91/13.04 ((
% 98.91/13.04 (!!) @ (
% 98.91/13.04 (('#B') @ (
% 98.91/13.04 !!) @
% 98.91/13.04 (
% 98.91/13.04 (
% 98.91/13.04 ('#S') @ (
% 98.91/13.04 (
% 98.91/13.04 ('#B') @ (
% 98.91/13.04 '#B') @
% 98.91/13.04 breln1)) @
% 98.91/13.04 (
% 98.91/13.04 (
% 98.91/13.04 ('#S') @ dpsetconstr @
% 98.91/13.04 (
% 98.91/13.04 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.91/13.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1505])).
% 98.91/13.04 thf(zip_derived_cl1525, plain,
% 98.91/13.04 (~ (((setunionE2) =>
% 98.91/13.04 (((setunionsingleton1) =>
% 98.91/13.04 (((setunionsingleton2) =>
% 98.91/13.04 (((setunionsingleton) =>
% 98.91/13.04 (((singletonprop) =>
% 98.91/13.04 (((ex1E1) =>
% 98.91/13.04 (((ex1I) =>
% 98.91/13.04 (((ex1I2) =>
% 98.91/13.04 (((singletonsuniq) =>
% 98.91/13.04 (((setukpairinjL1) =>
% 98.91/13.04 (((kfstsingleton) =>
% 98.91/13.04 (((theprop) =>
% 98.91/13.04 (((kfstpairEq) =>
% 98.91/13.04 (((cartprodfstin) =>
% 98.91/13.04 (((setukpairinjL2) =>
% 98.91/13.04 (((setukpairinjL) =>
% 98.91/13.04 (((setukpairinjR11) =>
% 98.91/13.04 (((setukpairinjR12) =>
% 98.91/13.04 (((setukpairinjR1) =>
% 98.91/13.04 (((upairequniteq) =>
% 98.91/13.04 (((setukpairinjR2) =>
% 98.91/13.04 (((setukpairinjR) =>
% 98.91/13.04 (((ksndsingleton) =>
% 98.91/13.04 (((ksndpairEq) =>
% 98.91/13.04 (((kpairsurjEq) =>
% 98.91/13.04 (((cartprodsndin) =>
% 98.91/13.04 (((cartprodpairmemEL) =>
% 98.91/13.04 (((cartprodpairmemER) =>
% 98.91/13.04 (((cartprodmempaircEq) =>
% 98.91/13.04 (((cartprodfstpairEq) =>
% 98.91/13.04 ((
% 98.91/13.04 (cartprodsndpairEq) =>
% 98.91/13.04 ((
% 98.91/13.04 (cartprodpairsurjEq) =>
% 98.91/13.04 ((
% 98.91/13.04 (dpsetconstrI) =>
% 98.91/13.04 ((
% 98.91/13.04 (dpsetconstrSub) =>
% 98.91/13.04 ((
% 98.91/13.04 (setOfPairsIsBReln) =>
% 98.91/13.04 ((
% 98.91/13.04 (dpsetconstrERa) =>
% 98.91/13.04 ((
% 98.91/13.04 (dpsetconstrEL1) =>
% 98.91/13.04 ((
% 98.91/13.04 (dpsetconstrEL2) =>
% 98.91/13.04 ((
% 98.91/13.04 (dpsetconstrER) =>
% 98.91/13.04 ((
% 98.91/13.04 (funcImageSingleton) =>
% 98.91/13.04 ((
% 98.91/13.04 (apProp) =>
% 98.91/13.04 ((
% 98.91/13.04 (app) =>
% 98.91/13.04 ((
% 98.91/13.04 (infuncsetfunc) =>
% 98.91/13.04 ((
% 98.91/13.04 (ap2p) =>
% 98.91/13.04 ((
% 98.91/13.04 (funcinfuncset) =>
% 98.91/13.04 ((
% 98.91/13.04 (lamProp) =>
% 98.91/13.04 ((
% 98.91/13.04 (lamp) =>
% 98.91/13.04 ((
% 98.91/13.04 (lam2p) =>
% 98.91/13.04 ((
% 98.91/13.04 (brelnall1) =>
% 98.91/13.04 ((
% 98.91/13.04 (brelnall2) =>
% 98.91/13.04 ((
% 98.91/13.04 (ex1E2) =>
% 98.91/13.04 ((
% 98.91/13.04 (funcGraphProp1) =>
% 98.91/13.04 ((
% 98.91/13.04 (funcGraphProp3) =>
% 98.91/13.04 ((
% 98.91/13.04 (funcGraphProp2) =>
% 98.91/13.04 ((
% 98.91/13.04 (funcextLem) =>
% 98.91/13.04 ((
% 98.91/13.04 (funcGraphProp4) =>
% 98.91/13.04 ((
% 98.91/13.04 (subbreln) =>
% 98.91/13.04 ((
% 98.91/13.04 (eqbreln) =>
% 98.91/13.04 ((
% 98.91/13.04 (funcext) =>
% 98.91/13.04 ((
% 98.91/13.04 (funcext2) =>
% 98.91/13.04 ((
% 98.91/13.04 (ap2apEq1) =>
% 98.91/13.04 ((
% 98.91/13.04 (ap2apEq2) =>
% 98.91/13.04 ((
% 98.91/13.04 (beta1) =>
% 98.91/13.04 ((
% 98.91/13.04 (eta1) =>
% 98.91/13.04 ((
% 98.91/13.04 (lam2lamEq) =>
% 98.91/13.04 ((
% 98.91/13.04 (beta2) =>
% 98.91/13.04 ((
% 98.91/13.04 (eta2) =>
% 98.91/13.04 ((
% 98.91/13.04 (iffalseProp1) =>
% 98.91/13.04 ((
% 98.91/13.04 (iffalseProp2) =>
% 98.91/13.04 ((
% 98.91/13.04 (iftrueProp1) =>
% 98.91/13.04 ((
% 98.91/13.04 (iftrueProp2) =>
% 98.91/13.04 ((
% 98.91/13.04 (ifSingleton) =>
% 98.91/13.04 ((
% 98.91/13.04 (ifp) =>
% 98.91/13.04 ((
% 98.91/13.04 (theeq) =>
% 98.91/13.04 ((
% 98.91/13.04 (iftrue) =>
% 98.91/13.04 ((
% 98.91/13.04 (iffalse) =>
% 98.91/13.04 ((
% 98.91/13.04 (iftrueorfalse) =>
% 98.91/13.04 ((
% 98.91/13.04 (binintersectT_lem) =>
% 98.91/13.04 ((
% 98.91/13.04 (binunionT_lem) =>
% 98.91/13.04 ((
% 98.91/13.04 (powersetT_lem) =>
% 98.91/13.04 ((
% 98.91/13.04 (setminusT_lem) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementT_lem) =>
% 98.91/13.04 ((
% 98.91/13.04 (setextT) =>
% 98.91/13.04 ((
% 98.91/13.04 (subsetTI) =>
% 98.91/13.04 ((
% 98.91/13.04 (powersetTI1) =>
% 98.91/13.04 ((
% 98.91/13.04 (powersetTE1) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementTI1) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementTE1) =>
% 98.91/13.04 ((
% 98.91/13.04 (binintersectTELcontra) =>
% 98.91/13.04 ((
% 98.91/13.04 (binintersectTERcontra) =>
% 98.91/13.04 ((
% 98.91/13.04 (contrasubsetT) =>
% 98.91/13.04 ((
% 98.91/13.04 (contrasubsetT1) =>
% 98.91/13.04 ((
% 98.91/13.04 (contrasubsetT2) =>
% 98.91/13.04 ((
% 98.91/13.04 (contrasubsetT3) =>
% 98.91/13.04 ((
% 98.91/13.04 (doubleComplementI1) =>
% 98.91/13.04 ((
% 98.91/13.04 (doubleComplementE1) =>
% 98.91/13.04 ((
% 98.91/13.04 (doubleComplementSub1) =>
% 98.91/13.04 ((
% 98.91/13.04 (doubleComplementSub2) =>
% 98.91/13.04 ((
% 98.91/13.04 (doubleComplementEq) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementTnotintersectT) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementImpComplementIntersect) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementSubsetComplementIntersect) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementInPowersetComplementIntersect) =>
% 98.91/13.04 ((
% 98.91/13.04 (contraSubsetComplement) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementTcontraSubset) =>
% 98.91/13.04 ((
% 98.91/13.04 (binunionTILcontra) =>
% 98.91/13.04 ((
% 98.91/13.04 (binunionTIRcontra) =>
% 98.91/13.04 ((
% 98.91/13.04 (inIntersectImpInUnion) =>
% 98.91/13.04 ((
% 98.91/13.04 (inIntersectImpInUnion2) =>
% 98.91/13.04 ((
% 98.91/13.04 (inIntersectImpInIntersectUnions) =>
% 98.91/13.04 ((
% 98.91/13.04 (intersectInPowersetIntersectUnions) =>
% 98.91/13.04 ((
% 98.91/13.04 (inComplementUnionImpNotIn1) =>
% 98.91/13.04 ((
% 98.91/13.04 (inComplementUnionImpInComplement1) =>
% 98.91/13.04 ((
% 98.91/13.04 (binunionTE) =>
% 98.91/13.04 ((
% 98.91/13.04 (binunionTEcontra) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan2a1) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementUnionInPowersetComplement) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan2a2) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan1a) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan1b) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan1) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan2a) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan2b2) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan2b) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan2) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz13rule0) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz13rule1) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz13rule2) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz13rule3) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz13rule4) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz1_1) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz1_2) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz1_3) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz1_4) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz1_5) =>
% 98.91/13.04 ((
% 98.91/13.04 (breln1all2) =>
% 98.91/13.04 ((
% 98.91/13.04 (breln1SetBreln1) =>
% 98.91/13.04 ((
% 98.91/13.04 (choice2fnsingleton) =>
% 98.91/13.04 ((
% 98.91/13.04 (!!) @ (
% 98.91/13.04 (('#B') @ (
% 98.91/13.04 !!) @
% 98.91/13.04 (
% 98.91/13.04 (
% 98.91/13.04 ('#S') @ (
% 98.91/13.04 (
% 98.91/13.04 ('#B') @ (
% 98.91/13.04 '#B') @
% 98.91/13.04 breln1)) @
% 98.91/13.04 (
% 98.91/13.04 (
% 98.91/13.04 ('#S') @ dpsetconstr @
% 98.91/13.04 (
% 98.91/13.04 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.91/13.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1515])).
% 98.91/13.04 thf(zip_derived_cl1535, plain,
% 98.91/13.04 (~ (((setunionsingleton1) =>
% 98.91/13.04 (((setunionsingleton2) =>
% 98.91/13.04 (((setunionsingleton) =>
% 98.91/13.04 (((singletonprop) =>
% 98.91/13.04 (((ex1E1) =>
% 98.91/13.04 (((ex1I) =>
% 98.91/13.04 (((ex1I2) =>
% 98.91/13.04 (((singletonsuniq) =>
% 98.91/13.04 (((setukpairinjL1) =>
% 98.91/13.04 (((kfstsingleton) =>
% 98.91/13.04 (((theprop) =>
% 98.91/13.04 (((kfstpairEq) =>
% 98.91/13.04 (((cartprodfstin) =>
% 98.91/13.04 (((setukpairinjL2) =>
% 98.91/13.04 (((setukpairinjL) =>
% 98.91/13.04 (((setukpairinjR11) =>
% 98.91/13.04 (((setukpairinjR12) =>
% 98.91/13.04 (((setukpairinjR1) =>
% 98.91/13.04 (((upairequniteq) =>
% 98.91/13.04 (((setukpairinjR2) =>
% 98.91/13.04 (((setukpairinjR) =>
% 98.91/13.04 (((ksndsingleton) =>
% 98.91/13.04 (((ksndpairEq) =>
% 98.91/13.04 (((kpairsurjEq) =>
% 98.91/13.04 (((cartprodsndin) =>
% 98.91/13.04 (((cartprodpairmemEL) =>
% 98.91/13.04 (((cartprodpairmemER) =>
% 98.91/13.04 (((cartprodmempaircEq) =>
% 98.91/13.04 (((cartprodfstpairEq) =>
% 98.91/13.04 (((cartprodsndpairEq) =>
% 98.91/13.04 ((
% 98.91/13.04 (cartprodpairsurjEq) =>
% 98.91/13.04 ((
% 98.91/13.04 (dpsetconstrI) =>
% 98.91/13.04 ((
% 98.91/13.04 (dpsetconstrSub) =>
% 98.91/13.04 ((
% 98.91/13.04 (setOfPairsIsBReln) =>
% 98.91/13.04 ((
% 98.91/13.04 (dpsetconstrERa) =>
% 98.91/13.04 ((
% 98.91/13.04 (dpsetconstrEL1) =>
% 98.91/13.04 ((
% 98.91/13.04 (dpsetconstrEL2) =>
% 98.91/13.04 ((
% 98.91/13.04 (dpsetconstrER) =>
% 98.91/13.04 ((
% 98.91/13.04 (funcImageSingleton) =>
% 98.91/13.04 ((
% 98.91/13.04 (apProp) =>
% 98.91/13.04 ((
% 98.91/13.04 (app) =>
% 98.91/13.04 ((
% 98.91/13.04 (infuncsetfunc) =>
% 98.91/13.04 ((
% 98.91/13.04 (ap2p) =>
% 98.91/13.04 ((
% 98.91/13.04 (funcinfuncset) =>
% 98.91/13.04 ((
% 98.91/13.04 (lamProp) =>
% 98.91/13.04 ((
% 98.91/13.04 (lamp) =>
% 98.91/13.04 ((
% 98.91/13.04 (lam2p) =>
% 98.91/13.04 ((
% 98.91/13.04 (brelnall1) =>
% 98.91/13.04 ((
% 98.91/13.04 (brelnall2) =>
% 98.91/13.04 ((
% 98.91/13.04 (ex1E2) =>
% 98.91/13.04 ((
% 98.91/13.04 (funcGraphProp1) =>
% 98.91/13.04 ((
% 98.91/13.04 (funcGraphProp3) =>
% 98.91/13.04 ((
% 98.91/13.04 (funcGraphProp2) =>
% 98.91/13.04 ((
% 98.91/13.04 (funcextLem) =>
% 98.91/13.04 ((
% 98.91/13.04 (funcGraphProp4) =>
% 98.91/13.04 ((
% 98.91/13.04 (subbreln) =>
% 98.91/13.04 ((
% 98.91/13.04 (eqbreln) =>
% 98.91/13.04 ((
% 98.91/13.04 (funcext) =>
% 98.91/13.04 ((
% 98.91/13.04 (funcext2) =>
% 98.91/13.04 ((
% 98.91/13.04 (ap2apEq1) =>
% 98.91/13.04 ((
% 98.91/13.04 (ap2apEq2) =>
% 98.91/13.04 ((
% 98.91/13.04 (beta1) =>
% 98.91/13.04 ((
% 98.91/13.04 (eta1) =>
% 98.91/13.04 ((
% 98.91/13.04 (lam2lamEq) =>
% 98.91/13.04 ((
% 98.91/13.04 (beta2) =>
% 98.91/13.04 ((
% 98.91/13.04 (eta2) =>
% 98.91/13.04 ((
% 98.91/13.04 (iffalseProp1) =>
% 98.91/13.04 ((
% 98.91/13.04 (iffalseProp2) =>
% 98.91/13.04 ((
% 98.91/13.04 (iftrueProp1) =>
% 98.91/13.04 ((
% 98.91/13.04 (iftrueProp2) =>
% 98.91/13.04 ((
% 98.91/13.04 (ifSingleton) =>
% 98.91/13.04 ((
% 98.91/13.04 (ifp) =>
% 98.91/13.04 ((
% 98.91/13.04 (theeq) =>
% 98.91/13.04 ((
% 98.91/13.04 (iftrue) =>
% 98.91/13.04 ((
% 98.91/13.04 (iffalse) =>
% 98.91/13.04 ((
% 98.91/13.04 (iftrueorfalse) =>
% 98.91/13.04 ((
% 98.91/13.04 (binintersectT_lem) =>
% 98.91/13.04 ((
% 98.91/13.04 (binunionT_lem) =>
% 98.91/13.04 ((
% 98.91/13.04 (powersetT_lem) =>
% 98.91/13.04 ((
% 98.91/13.04 (setminusT_lem) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementT_lem) =>
% 98.91/13.04 ((
% 98.91/13.04 (setextT) =>
% 98.91/13.04 ((
% 98.91/13.04 (subsetTI) =>
% 98.91/13.04 ((
% 98.91/13.04 (powersetTI1) =>
% 98.91/13.04 ((
% 98.91/13.04 (powersetTE1) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementTI1) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementTE1) =>
% 98.91/13.04 ((
% 98.91/13.04 (binintersectTELcontra) =>
% 98.91/13.04 ((
% 98.91/13.04 (binintersectTERcontra) =>
% 98.91/13.04 ((
% 98.91/13.04 (contrasubsetT) =>
% 98.91/13.04 ((
% 98.91/13.04 (contrasubsetT1) =>
% 98.91/13.04 ((
% 98.91/13.04 (contrasubsetT2) =>
% 98.91/13.04 ((
% 98.91/13.04 (contrasubsetT3) =>
% 98.91/13.04 ((
% 98.91/13.04 (doubleComplementI1) =>
% 98.91/13.04 ((
% 98.91/13.04 (doubleComplementE1) =>
% 98.91/13.04 ((
% 98.91/13.04 (doubleComplementSub1) =>
% 98.91/13.04 ((
% 98.91/13.04 (doubleComplementSub2) =>
% 98.91/13.04 ((
% 98.91/13.04 (doubleComplementEq) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementTnotintersectT) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementImpComplementIntersect) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementSubsetComplementIntersect) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementInPowersetComplementIntersect) =>
% 98.91/13.04 ((
% 98.91/13.04 (contraSubsetComplement) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementTcontraSubset) =>
% 98.91/13.04 ((
% 98.91/13.04 (binunionTILcontra) =>
% 98.91/13.04 ((
% 98.91/13.04 (binunionTIRcontra) =>
% 98.91/13.04 ((
% 98.91/13.04 (inIntersectImpInUnion) =>
% 98.91/13.04 ((
% 98.91/13.04 (inIntersectImpInUnion2) =>
% 98.91/13.04 ((
% 98.91/13.04 (inIntersectImpInIntersectUnions) =>
% 98.91/13.04 ((
% 98.91/13.04 (intersectInPowersetIntersectUnions) =>
% 98.91/13.04 ((
% 98.91/13.04 (inComplementUnionImpNotIn1) =>
% 98.91/13.04 ((
% 98.91/13.04 (inComplementUnionImpInComplement1) =>
% 98.91/13.04 ((
% 98.91/13.04 (binunionTE) =>
% 98.91/13.04 ((
% 98.91/13.04 (binunionTEcontra) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan2a1) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementUnionInPowersetComplement) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan2a2) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan1a) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan1b) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan1) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan2a) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan2b2) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan2b) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan2) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz13rule0) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz13rule1) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz13rule2) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz13rule3) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz13rule4) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz1_1) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz1_2) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz1_3) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz1_4) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz1_5) =>
% 98.91/13.04 ((
% 98.91/13.04 (breln1all2) =>
% 98.91/13.04 ((
% 98.91/13.04 (breln1SetBreln1) =>
% 98.91/13.04 ((
% 98.91/13.04 (choice2fnsingleton) =>
% 98.91/13.04 ((
% 98.91/13.04 (!!) @ (
% 98.91/13.04 (('#B') @ (
% 98.91/13.04 !!) @
% 98.91/13.04 (
% 98.91/13.04 (
% 98.91/13.04 ('#S') @ (
% 98.91/13.04 (
% 98.91/13.04 ('#B') @ (
% 98.91/13.04 '#B') @
% 98.91/13.04 breln1)) @
% 98.91/13.04 (
% 98.91/13.04 (
% 98.91/13.04 ('#S') @ dpsetconstr @
% 98.91/13.04 (
% 98.91/13.04 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.91/13.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1525])).
% 98.91/13.04 thf(zip_derived_cl1545, plain,
% 98.91/13.04 (~ (((setunionsingleton2) =>
% 98.91/13.04 (((setunionsingleton) =>
% 98.91/13.04 (((singletonprop) =>
% 98.91/13.04 (((ex1E1) =>
% 98.91/13.04 (((ex1I) =>
% 98.91/13.04 (((ex1I2) =>
% 98.91/13.04 (((singletonsuniq) =>
% 98.91/13.04 (((setukpairinjL1) =>
% 98.91/13.04 (((kfstsingleton) =>
% 98.91/13.04 (((theprop) =>
% 98.91/13.04 (((kfstpairEq) =>
% 98.91/13.04 (((cartprodfstin) =>
% 98.91/13.04 (((setukpairinjL2) =>
% 98.91/13.04 (((setukpairinjL) =>
% 98.91/13.04 (((setukpairinjR11) =>
% 98.91/13.04 (((setukpairinjR12) =>
% 98.91/13.04 (((setukpairinjR1) =>
% 98.91/13.04 (((upairequniteq) =>
% 98.91/13.04 (((setukpairinjR2) =>
% 98.91/13.04 (((setukpairinjR) =>
% 98.91/13.04 (((ksndsingleton) =>
% 98.91/13.04 (((ksndpairEq) =>
% 98.91/13.04 (((kpairsurjEq) =>
% 98.91/13.04 (((cartprodsndin) =>
% 98.91/13.04 (((cartprodpairmemEL) =>
% 98.91/13.04 (((cartprodpairmemER) =>
% 98.91/13.04 (((cartprodmempaircEq) =>
% 98.91/13.04 (((cartprodfstpairEq) =>
% 98.91/13.04 (((cartprodsndpairEq) =>
% 98.91/13.04 (((cartprodpairsurjEq) =>
% 98.91/13.04 ((
% 98.91/13.04 (dpsetconstrI) =>
% 98.91/13.04 ((
% 98.91/13.04 (dpsetconstrSub) =>
% 98.91/13.04 ((
% 98.91/13.04 (setOfPairsIsBReln) =>
% 98.91/13.04 ((
% 98.91/13.04 (dpsetconstrERa) =>
% 98.91/13.04 ((
% 98.91/13.04 (dpsetconstrEL1) =>
% 98.91/13.04 ((
% 98.91/13.04 (dpsetconstrEL2) =>
% 98.91/13.04 ((
% 98.91/13.04 (dpsetconstrER) =>
% 98.91/13.04 ((
% 98.91/13.04 (funcImageSingleton) =>
% 98.91/13.04 ((
% 98.91/13.04 (apProp) =>
% 98.91/13.04 ((
% 98.91/13.04 (app) =>
% 98.91/13.04 ((
% 98.91/13.04 (infuncsetfunc) =>
% 98.91/13.04 ((
% 98.91/13.04 (ap2p) =>
% 98.91/13.04 ((
% 98.91/13.04 (funcinfuncset) =>
% 98.91/13.04 ((
% 98.91/13.04 (lamProp) =>
% 98.91/13.04 ((
% 98.91/13.04 (lamp) =>
% 98.91/13.04 ((
% 98.91/13.04 (lam2p) =>
% 98.91/13.04 ((
% 98.91/13.04 (brelnall1) =>
% 98.91/13.04 ((
% 98.91/13.04 (brelnall2) =>
% 98.91/13.04 ((
% 98.91/13.04 (ex1E2) =>
% 98.91/13.04 ((
% 98.91/13.04 (funcGraphProp1) =>
% 98.91/13.04 ((
% 98.91/13.04 (funcGraphProp3) =>
% 98.91/13.04 ((
% 98.91/13.04 (funcGraphProp2) =>
% 98.91/13.04 ((
% 98.91/13.04 (funcextLem) =>
% 98.91/13.04 ((
% 98.91/13.04 (funcGraphProp4) =>
% 98.91/13.04 ((
% 98.91/13.04 (subbreln) =>
% 98.91/13.04 ((
% 98.91/13.04 (eqbreln) =>
% 98.91/13.04 ((
% 98.91/13.04 (funcext) =>
% 98.91/13.04 ((
% 98.91/13.04 (funcext2) =>
% 98.91/13.04 ((
% 98.91/13.04 (ap2apEq1) =>
% 98.91/13.04 ((
% 98.91/13.04 (ap2apEq2) =>
% 98.91/13.04 ((
% 98.91/13.04 (beta1) =>
% 98.91/13.04 ((
% 98.91/13.04 (eta1) =>
% 98.91/13.04 ((
% 98.91/13.04 (lam2lamEq) =>
% 98.91/13.04 ((
% 98.91/13.04 (beta2) =>
% 98.91/13.04 ((
% 98.91/13.04 (eta2) =>
% 98.91/13.04 ((
% 98.91/13.04 (iffalseProp1) =>
% 98.91/13.04 ((
% 98.91/13.04 (iffalseProp2) =>
% 98.91/13.04 ((
% 98.91/13.04 (iftrueProp1) =>
% 98.91/13.04 ((
% 98.91/13.04 (iftrueProp2) =>
% 98.91/13.04 ((
% 98.91/13.04 (ifSingleton) =>
% 98.91/13.04 ((
% 98.91/13.04 (ifp) =>
% 98.91/13.04 ((
% 98.91/13.04 (theeq) =>
% 98.91/13.04 ((
% 98.91/13.04 (iftrue) =>
% 98.91/13.04 ((
% 98.91/13.04 (iffalse) =>
% 98.91/13.04 ((
% 98.91/13.04 (iftrueorfalse) =>
% 98.91/13.04 ((
% 98.91/13.04 (binintersectT_lem) =>
% 98.91/13.04 ((
% 98.91/13.04 (binunionT_lem) =>
% 98.91/13.04 ((
% 98.91/13.04 (powersetT_lem) =>
% 98.91/13.04 ((
% 98.91/13.04 (setminusT_lem) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementT_lem) =>
% 98.91/13.04 ((
% 98.91/13.04 (setextT) =>
% 98.91/13.04 ((
% 98.91/13.04 (subsetTI) =>
% 98.91/13.04 ((
% 98.91/13.04 (powersetTI1) =>
% 98.91/13.04 ((
% 98.91/13.04 (powersetTE1) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementTI1) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementTE1) =>
% 98.91/13.04 ((
% 98.91/13.04 (binintersectTELcontra) =>
% 98.91/13.04 ((
% 98.91/13.04 (binintersectTERcontra) =>
% 98.91/13.04 ((
% 98.91/13.04 (contrasubsetT) =>
% 98.91/13.04 ((
% 98.91/13.04 (contrasubsetT1) =>
% 98.91/13.04 ((
% 98.91/13.04 (contrasubsetT2) =>
% 98.91/13.04 ((
% 98.91/13.04 (contrasubsetT3) =>
% 98.91/13.04 ((
% 98.91/13.04 (doubleComplementI1) =>
% 98.91/13.04 ((
% 98.91/13.04 (doubleComplementE1) =>
% 98.91/13.04 ((
% 98.91/13.04 (doubleComplementSub1) =>
% 98.91/13.04 ((
% 98.91/13.04 (doubleComplementSub2) =>
% 98.91/13.04 ((
% 98.91/13.04 (doubleComplementEq) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementTnotintersectT) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementImpComplementIntersect) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementSubsetComplementIntersect) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementInPowersetComplementIntersect) =>
% 98.91/13.04 ((
% 98.91/13.04 (contraSubsetComplement) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementTcontraSubset) =>
% 98.91/13.04 ((
% 98.91/13.04 (binunionTILcontra) =>
% 98.91/13.04 ((
% 98.91/13.04 (binunionTIRcontra) =>
% 98.91/13.04 ((
% 98.91/13.04 (inIntersectImpInUnion) =>
% 98.91/13.04 ((
% 98.91/13.04 (inIntersectImpInUnion2) =>
% 98.91/13.04 ((
% 98.91/13.04 (inIntersectImpInIntersectUnions) =>
% 98.91/13.04 ((
% 98.91/13.04 (intersectInPowersetIntersectUnions) =>
% 98.91/13.04 ((
% 98.91/13.04 (inComplementUnionImpNotIn1) =>
% 98.91/13.04 ((
% 98.91/13.04 (inComplementUnionImpInComplement1) =>
% 98.91/13.04 ((
% 98.91/13.04 (binunionTE) =>
% 98.91/13.04 ((
% 98.91/13.04 (binunionTEcontra) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan2a1) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementUnionInPowersetComplement) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan2a2) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan1a) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan1b) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan1) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan2a) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan2b2) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan2b) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan2) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz13rule0) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz13rule1) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz13rule2) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz13rule3) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz13rule4) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz1_1) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz1_2) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz1_3) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz1_4) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz1_5) =>
% 98.91/13.04 ((
% 98.91/13.04 (breln1all2) =>
% 98.91/13.04 ((
% 98.91/13.04 (breln1SetBreln1) =>
% 98.91/13.04 ((
% 98.91/13.04 (choice2fnsingleton) =>
% 98.91/13.04 ((
% 98.91/13.04 (!!) @ (
% 98.91/13.04 (('#B') @ (
% 98.91/13.04 !!) @
% 98.91/13.04 (
% 98.91/13.04 (
% 98.91/13.04 ('#S') @ (
% 98.91/13.04 (
% 98.91/13.04 ('#B') @ (
% 98.91/13.04 '#B') @
% 98.91/13.04 breln1)) @
% 98.91/13.04 (
% 98.91/13.04 (
% 98.91/13.04 ('#S') @ dpsetconstr @
% 98.91/13.04 (
% 98.91/13.04 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.91/13.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1535])).
% 98.91/13.04 thf(zip_derived_cl1555, plain,
% 98.91/13.04 (~ (((setunionsingleton) =>
% 98.91/13.04 (((singletonprop) =>
% 98.91/13.04 (((ex1E1) =>
% 98.91/13.04 (((ex1I) =>
% 98.91/13.04 (((ex1I2) =>
% 98.91/13.04 (((singletonsuniq) =>
% 98.91/13.04 (((setukpairinjL1) =>
% 98.91/13.04 (((kfstsingleton) =>
% 98.91/13.04 (((theprop) =>
% 98.91/13.04 (((kfstpairEq) =>
% 98.91/13.04 (((cartprodfstin) =>
% 98.91/13.04 (((setukpairinjL2) =>
% 98.91/13.04 (((setukpairinjL) =>
% 98.91/13.04 (((setukpairinjR11) =>
% 98.91/13.04 (((setukpairinjR12) =>
% 98.91/13.04 (((setukpairinjR1) =>
% 98.91/13.04 (((upairequniteq) =>
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% 98.91/13.04 (((setukpairinjR) =>
% 98.91/13.04 (((ksndsingleton) =>
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% 98.91/13.04 (((cartprodmempaircEq) =>
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% 98.91/13.04 ((
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% 98.91/13.04 ((
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% 98.91/13.04 ((
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% 98.91/13.04 (ap2apEq2) =>
% 98.91/13.04 ((
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% 98.91/13.04 ((
% 98.91/13.04 (eta1) =>
% 98.91/13.04 ((
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% 98.91/13.04 ((
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% 98.91/13.04 ((
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% 98.91/13.04 ((
% 98.91/13.04 (powersetT_lem) =>
% 98.91/13.04 ((
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% 98.91/13.04 ((
% 98.91/13.04 (complementT_lem) =>
% 98.91/13.04 ((
% 98.91/13.04 (setextT) =>
% 98.91/13.04 ((
% 98.91/13.04 (subsetTI) =>
% 98.91/13.04 ((
% 98.91/13.04 (powersetTI1) =>
% 98.91/13.04 ((
% 98.91/13.04 (powersetTE1) =>
% 98.91/13.04 ((
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% 98.91/13.04 ((
% 98.91/13.04 (complementTE1) =>
% 98.91/13.04 ((
% 98.91/13.04 (binintersectTELcontra) =>
% 98.91/13.04 ((
% 98.91/13.04 (binintersectTERcontra) =>
% 98.91/13.04 ((
% 98.91/13.04 (contrasubsetT) =>
% 98.91/13.04 ((
% 98.91/13.04 (contrasubsetT1) =>
% 98.91/13.04 ((
% 98.91/13.04 (contrasubsetT2) =>
% 98.91/13.04 ((
% 98.91/13.04 (contrasubsetT3) =>
% 98.91/13.04 ((
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% 98.91/13.04 ((
% 98.91/13.04 (doubleComplementE1) =>
% 98.91/13.04 ((
% 98.91/13.04 (doubleComplementSub1) =>
% 98.91/13.04 ((
% 98.91/13.04 (doubleComplementSub2) =>
% 98.91/13.04 ((
% 98.91/13.04 (doubleComplementEq) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementTnotintersectT) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementImpComplementIntersect) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementSubsetComplementIntersect) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementInPowersetComplementIntersect) =>
% 98.91/13.04 ((
% 98.91/13.04 (contraSubsetComplement) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementTcontraSubset) =>
% 98.91/13.04 ((
% 98.91/13.04 (binunionTILcontra) =>
% 98.91/13.04 ((
% 98.91/13.04 (binunionTIRcontra) =>
% 98.91/13.04 ((
% 98.91/13.04 (inIntersectImpInUnion) =>
% 98.91/13.04 ((
% 98.91/13.04 (inIntersectImpInUnion2) =>
% 98.91/13.04 ((
% 98.91/13.04 (inIntersectImpInIntersectUnions) =>
% 98.91/13.04 ((
% 98.91/13.04 (intersectInPowersetIntersectUnions) =>
% 98.91/13.04 ((
% 98.91/13.04 (inComplementUnionImpNotIn1) =>
% 98.91/13.04 ((
% 98.91/13.04 (inComplementUnionImpInComplement1) =>
% 98.91/13.04 ((
% 98.91/13.04 (binunionTE) =>
% 98.91/13.04 ((
% 98.91/13.04 (binunionTEcontra) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan2a1) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementUnionInPowersetComplement) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan2a2) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan1a) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan1b) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan1) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan2a) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan2b2) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan2b) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan2) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz13rule0) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz13rule1) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz13rule2) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz13rule3) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz13rule4) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz1_1) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz1_2) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz1_3) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz1_4) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz1_5) =>
% 98.91/13.04 ((
% 98.91/13.04 (breln1all2) =>
% 98.91/13.04 ((
% 98.91/13.04 (breln1SetBreln1) =>
% 98.91/13.04 ((
% 98.91/13.04 (choice2fnsingleton) =>
% 98.91/13.04 ((
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% 98.91/13.04 (('#B') @ (
% 98.91/13.04 !!) @
% 98.91/13.04 (
% 98.91/13.04 (
% 98.91/13.04 ('#S') @ (
% 98.91/13.04 (
% 98.91/13.04 ('#B') @ (
% 98.91/13.04 '#B') @
% 98.91/13.04 breln1)) @
% 98.91/13.04 (
% 98.91/13.04 (
% 98.91/13.04 ('#S') @ dpsetconstr @
% 98.91/13.04 (
% 98.91/13.04 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.91/13.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1545])).
% 98.91/13.04 thf(zip_derived_cl1565, plain,
% 98.91/13.04 (~ (((singletonprop) =>
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% 98.91/13.04 (((ex1I2) =>
% 98.91/13.04 (((singletonsuniq) =>
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% 98.91/13.04 (((theprop) =>
% 98.91/13.04 (((kfstpairEq) =>
% 98.91/13.04 (((cartprodfstin) =>
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% 98.91/13.04 (((setukpairinjR11) =>
% 98.91/13.04 (((setukpairinjR12) =>
% 98.91/13.04 (((setukpairinjR1) =>
% 98.91/13.04 (((upairequniteq) =>
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% 98.91/13.04 (((setukpairinjR) =>
% 98.91/13.04 (((ksndsingleton) =>
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% 98.91/13.04 (((kpairsurjEq) =>
% 98.91/13.04 (((cartprodsndin) =>
% 98.91/13.04 (((cartprodpairmemEL) =>
% 98.91/13.04 (((cartprodpairmemER) =>
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% 98.91/13.04 (((dpsetconstrSub) =>
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% 98.91/13.04 ((
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% 98.91/13.04 ((
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% 98.91/13.04 ((
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% 98.91/13.04 ((
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% 98.91/13.04 ((
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% 98.91/13.04 ((
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% 98.91/13.04 ((
% 98.91/13.04 (brelnall2) =>
% 98.91/13.04 ((
% 98.91/13.04 (ex1E2) =>
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% 98.91/13.04 ((
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% 98.91/13.04 ((
% 98.91/13.04 (ap2apEq2) =>
% 98.91/13.04 ((
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% 98.91/13.04 ((
% 98.91/13.04 (eta1) =>
% 98.91/13.04 ((
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% 98.91/13.04 ((
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% 98.91/13.04 ((
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% 98.91/13.04 ((
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% 98.91/13.04 (complementSubsetComplementIntersect) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementInPowersetComplementIntersect) =>
% 98.91/13.04 ((
% 98.91/13.04 (contraSubsetComplement) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementTcontraSubset) =>
% 98.91/13.04 ((
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% 98.91/13.04 ((
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% 98.91/13.04 ((
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% 98.91/13.04 ((
% 98.91/13.04 (inIntersectImpInUnion2) =>
% 98.91/13.04 ((
% 98.91/13.04 (inIntersectImpInIntersectUnions) =>
% 98.91/13.04 ((
% 98.91/13.04 (intersectInPowersetIntersectUnions) =>
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% 98.91/13.04 (inComplementUnionImpNotIn1) =>
% 98.91/13.04 ((
% 98.91/13.04 (inComplementUnionImpInComplement1) =>
% 98.91/13.04 ((
% 98.91/13.04 (binunionTE) =>
% 98.91/13.04 ((
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% 98.91/13.04 ((
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% 98.91/13.04 ((
% 98.91/13.04 (complementUnionInPowersetComplement) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan2a2) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan1a) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan1b) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan1) =>
% 98.91/13.04 ((
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% 98.91/13.04 ((
% 98.91/13.04 (demorgan2b2) =>
% 98.91/13.04 ((
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% 98.91/13.04 ((
% 98.91/13.04 (demorgan2) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz13rule0) =>
% 98.91/13.04 ((
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% 98.91/13.04 ((
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% 98.91/13.04 ((
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% 98.91/13.04 ((
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% 98.91/13.04 ((
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% 98.91/13.04 ((
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% 98.91/13.04 ((
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% 98.91/13.04 (
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% 98.91/13.04 (
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% 98.91/13.04 (
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% 98.91/13.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1555])).
% 98.91/13.04 thf(zip_derived_cl1574, plain,
% 98.91/13.04 (~ (((ex1E1) =>
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% 98.91/13.04 (((cartprodfstin) =>
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% 98.91/13.04 (((setukpairinjL) =>
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% 98.91/13.04 (((setukpairinjR1) =>
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% 98.91/13.04 (((ksndpairEq) =>
% 98.91/13.04 (((kpairsurjEq) =>
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% 98.91/13.04 (((cartprodpairmemER) =>
% 98.91/13.04 (((cartprodmempaircEq) =>
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% 98.91/13.04 (((cartprodpairsurjEq) =>
% 98.91/13.04 (((dpsetconstrI) =>
% 98.91/13.04 (((dpsetconstrSub) =>
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% 98.91/13.04 ((
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% 98.91/13.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1565])).
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% 98.91/13.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1574])).
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% 98.91/13.04 ((
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% 98.91/13.04 ((
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% 98.91/13.04 ((
% 98.91/13.04 (ap2apEq2) =>
% 98.91/13.04 ((
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% 98.91/13.04 ((
% 98.91/13.04 (eta1) =>
% 98.91/13.04 ((
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% 98.91/13.04 ((
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% 98.91/13.04 ((
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% 98.91/13.04 ((
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% 98.91/13.04 ((
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% 98.91/13.04 ((
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% 98.91/13.04 ((
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% 98.91/13.04 ((
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% 98.91/13.04 ((
% 98.91/13.04 (powersetT_lem) =>
% 98.91/13.04 ((
% 98.91/13.04 (setminusT_lem) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementT_lem) =>
% 98.91/13.04 ((
% 98.91/13.04 (setextT) =>
% 98.91/13.04 ((
% 98.91/13.04 (subsetTI) =>
% 98.91/13.04 ((
% 98.91/13.04 (powersetTI1) =>
% 98.91/13.04 ((
% 98.91/13.04 (powersetTE1) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementTI1) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementTE1) =>
% 98.91/13.04 ((
% 98.91/13.04 (binintersectTELcontra) =>
% 98.91/13.04 ((
% 98.91/13.04 (binintersectTERcontra) =>
% 98.91/13.04 ((
% 98.91/13.04 (contrasubsetT) =>
% 98.91/13.04 ((
% 98.91/13.04 (contrasubsetT1) =>
% 98.91/13.04 ((
% 98.91/13.04 (contrasubsetT2) =>
% 98.91/13.04 ((
% 98.91/13.04 (contrasubsetT3) =>
% 98.91/13.04 ((
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% 98.91/13.04 ((
% 98.91/13.04 (doubleComplementE1) =>
% 98.91/13.04 ((
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% 98.91/13.04 ((
% 98.91/13.04 (doubleComplementSub2) =>
% 98.91/13.04 ((
% 98.91/13.04 (doubleComplementEq) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementTnotintersectT) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementImpComplementIntersect) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementSubsetComplementIntersect) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementInPowersetComplementIntersect) =>
% 98.91/13.04 ((
% 98.91/13.04 (contraSubsetComplement) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementTcontraSubset) =>
% 98.91/13.04 ((
% 98.91/13.04 (binunionTILcontra) =>
% 98.91/13.04 ((
% 98.91/13.04 (binunionTIRcontra) =>
% 98.91/13.04 ((
% 98.91/13.04 (inIntersectImpInUnion) =>
% 98.91/13.04 ((
% 98.91/13.04 (inIntersectImpInUnion2) =>
% 98.91/13.04 ((
% 98.91/13.04 (inIntersectImpInIntersectUnions) =>
% 98.91/13.04 ((
% 98.91/13.04 (intersectInPowersetIntersectUnions) =>
% 98.91/13.04 ((
% 98.91/13.04 (inComplementUnionImpNotIn1) =>
% 98.91/13.04 ((
% 98.91/13.04 (inComplementUnionImpInComplement1) =>
% 98.91/13.04 ((
% 98.91/13.04 (binunionTE) =>
% 98.91/13.04 ((
% 98.91/13.04 (binunionTEcontra) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan2a1) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementUnionInPowersetComplement) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan2a2) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan1a) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan1b) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan1) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan2a) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan2b2) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan2b) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan2) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz13rule0) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz13rule1) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz13rule2) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz13rule3) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz13rule4) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz1_1) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz1_2) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz1_3) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz1_4) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz1_5) =>
% 98.91/13.04 ((
% 98.91/13.04 (breln1all2) =>
% 98.91/13.04 ((
% 98.91/13.04 (breln1SetBreln1) =>
% 98.91/13.04 ((
% 98.91/13.04 (choice2fnsingleton) =>
% 98.91/13.04 ((
% 98.91/13.04 (!!) @ (
% 98.91/13.04 (('#B') @ (
% 98.91/13.04 !!) @
% 98.91/13.04 (
% 98.91/13.04 (
% 98.91/13.04 ('#S') @ (
% 98.91/13.04 (
% 98.91/13.04 ('#B') @ (
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% 98.91/13.04 (
% 98.91/13.04 (
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% 98.91/13.04 (
% 98.91/13.04 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.91/13.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1582])).
% 98.91/13.04 thf(zip_derived_cl1599, plain,
% 98.91/13.04 (~ (((singletonsuniq) =>
% 98.91/13.04 (((setukpairinjL1) =>
% 98.91/13.04 (((kfstsingleton) =>
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% 98.91/13.04 (((kfstpairEq) =>
% 98.91/13.04 (((cartprodfstin) =>
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% 98.91/13.04 (((setukpairinjL) =>
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% 98.91/13.04 (((setukpairinjR12) =>
% 98.91/13.04 (((setukpairinjR1) =>
% 98.91/13.04 (((upairequniteq) =>
% 98.91/13.04 (((setukpairinjR2) =>
% 98.91/13.04 (((setukpairinjR) =>
% 98.91/13.04 (((ksndsingleton) =>
% 98.91/13.04 (((ksndpairEq) =>
% 98.91/13.04 (((kpairsurjEq) =>
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% 98.91/13.04 (((cartprodpairmemEL) =>
% 98.91/13.04 (((cartprodpairmemER) =>
% 98.91/13.04 (((cartprodmempaircEq) =>
% 98.91/13.04 (((cartprodfstpairEq) =>
% 98.91/13.04 (((cartprodsndpairEq) =>
% 98.91/13.04 (((cartprodpairsurjEq) =>
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% 98.91/13.04 (((dpsetconstrSub) =>
% 98.91/13.04 (((setOfPairsIsBReln) =>
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% 98.91/13.04 (((dpsetconstrEL2) =>
% 98.91/13.04 ((
% 98.91/13.04 (dpsetconstrER) =>
% 98.91/13.04 ((
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% 98.91/13.04 ((
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% 98.91/13.04 ((
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% 98.91/13.04 ((
% 98.91/13.04 (infuncsetfunc) =>
% 98.91/13.04 ((
% 98.91/13.04 (ap2p) =>
% 98.91/13.04 ((
% 98.91/13.04 (funcinfuncset) =>
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% 98.91/13.04 ((
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% 98.91/13.04 ((
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% 98.91/13.04 (brelnall1) =>
% 98.91/13.04 ((
% 98.91/13.04 (brelnall2) =>
% 98.91/13.04 ((
% 98.91/13.04 (ex1E2) =>
% 98.91/13.04 ((
% 98.91/13.04 (funcGraphProp1) =>
% 98.91/13.04 ((
% 98.91/13.04 (funcGraphProp3) =>
% 98.91/13.04 ((
% 98.91/13.04 (funcGraphProp2) =>
% 98.91/13.04 ((
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% 98.91/13.04 ((
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% 98.91/13.04 ((
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% 98.91/13.04 ((
% 98.91/13.04 (ap2apEq2) =>
% 98.91/13.04 ((
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% 98.91/13.04 ((
% 98.91/13.04 (eta1) =>
% 98.91/13.04 ((
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% 98.91/13.04 ((
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% 98.91/13.04 ((
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% 98.91/13.04 ((
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% 98.91/13.04 ((
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% 98.91/13.04 ((
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% 98.91/13.04 ((
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% 98.91/13.04 ((
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% 98.91/13.04 ((
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% 98.91/13.04 ((
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% 98.91/13.04 ((
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% 98.91/13.04 ((
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% 98.91/13.04 ((
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% 98.91/13.04 ((
% 98.91/13.04 (contrasubsetT3) =>
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% 98.91/13.04 ((
% 98.91/13.04 (doubleComplementE1) =>
% 98.91/13.04 ((
% 98.91/13.04 (doubleComplementSub1) =>
% 98.91/13.04 ((
% 98.91/13.04 (doubleComplementSub2) =>
% 98.91/13.04 ((
% 98.91/13.04 (doubleComplementEq) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementTnotintersectT) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementImpComplementIntersect) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementSubsetComplementIntersect) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementInPowersetComplementIntersect) =>
% 98.91/13.04 ((
% 98.91/13.04 (contraSubsetComplement) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementTcontraSubset) =>
% 98.91/13.04 ((
% 98.91/13.04 (binunionTILcontra) =>
% 98.91/13.04 ((
% 98.91/13.04 (binunionTIRcontra) =>
% 98.91/13.04 ((
% 98.91/13.04 (inIntersectImpInUnion) =>
% 98.91/13.04 ((
% 98.91/13.04 (inIntersectImpInUnion2) =>
% 98.91/13.04 ((
% 98.91/13.04 (inIntersectImpInIntersectUnions) =>
% 98.91/13.04 ((
% 98.91/13.04 (intersectInPowersetIntersectUnions) =>
% 98.91/13.04 ((
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% 98.91/13.04 ((
% 98.91/13.04 (inComplementUnionImpInComplement1) =>
% 98.91/13.04 ((
% 98.91/13.04 (binunionTE) =>
% 98.91/13.04 ((
% 98.91/13.04 (binunionTEcontra) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan2a1) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementUnionInPowersetComplement) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan2a2) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan1a) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan1b) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan1) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan2a) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan2b2) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan2b) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan2) =>
% 98.91/13.04 ((
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% 98.91/13.04 ((
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% 98.91/13.04 ((
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% 98.91/13.04 ((
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% 98.91/13.04 ((
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% 98.91/13.04 ((
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% 98.91/13.04 ((
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% 98.91/13.04 ((
% 98.91/13.04 (woz1_4) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz1_5) =>
% 98.91/13.04 ((
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% 98.91/13.04 ((
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% 98.91/13.04 ((
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% 98.91/13.04 ((
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% 98.91/13.04 (
% 98.91/13.04 (
% 98.91/13.04 ('#S') @ dpsetconstr @
% 98.91/13.04 (
% 98.91/13.04 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.91/13.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1591])).
% 98.91/13.04 thf(zip_derived_cl1607, plain,
% 98.91/13.04 (~ (((setukpairinjL1) =>
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% 98.91/13.04 (((theprop) =>
% 98.91/13.04 (((kfstpairEq) =>
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% 98.91/13.04 (((setukpairinjR11) =>
% 98.91/13.04 (((setukpairinjR12) =>
% 98.91/13.04 (((setukpairinjR1) =>
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% 98.91/13.04 (((setukpairinjR2) =>
% 98.91/13.04 (((setukpairinjR) =>
% 98.91/13.04 (((ksndsingleton) =>
% 98.91/13.04 (((ksndpairEq) =>
% 98.91/13.04 (((kpairsurjEq) =>
% 98.91/13.04 (((cartprodsndin) =>
% 98.91/13.04 (((cartprodpairmemEL) =>
% 98.91/13.04 (((cartprodpairmemER) =>
% 98.91/13.04 (((cartprodmempaircEq) =>
% 98.91/13.04 (((cartprodfstpairEq) =>
% 98.91/13.04 (((cartprodsndpairEq) =>
% 98.91/13.04 (((cartprodpairsurjEq) =>
% 98.91/13.04 (((dpsetconstrI) =>
% 98.91/13.04 (((dpsetconstrSub) =>
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% 98.91/13.04 (((dpsetconstrERa) =>
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% 98.91/13.04 (((dpsetconstrEL2) =>
% 98.91/13.04 (((dpsetconstrER) =>
% 98.91/13.04 ((
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% 98.91/13.04 ((
% 98.91/13.04 (apProp) =>
% 98.91/13.04 ((
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% 98.91/13.04 ((
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% 98.91/13.04 ((
% 98.91/13.04 (ap2p) =>
% 98.91/13.04 ((
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% 98.91/13.04 ((
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% 98.91/13.04 ((
% 98.91/13.04 (lam2p) =>
% 98.91/13.04 ((
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% 98.91/13.04 ((
% 98.91/13.04 (brelnall2) =>
% 98.91/13.04 ((
% 98.91/13.04 (ex1E2) =>
% 98.91/13.04 ((
% 98.91/13.04 (funcGraphProp1) =>
% 98.91/13.04 ((
% 98.91/13.04 (funcGraphProp3) =>
% 98.91/13.04 ((
% 98.91/13.04 (funcGraphProp2) =>
% 98.91/13.04 ((
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% 98.91/13.04 ((
% 98.91/13.04 (funcGraphProp4) =>
% 98.91/13.04 ((
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% 98.91/13.04 ((
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% 98.91/13.04 ((
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% 98.91/13.04 ((
% 98.91/13.04 (funcext2) =>
% 98.91/13.04 ((
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% 98.91/13.04 ((
% 98.91/13.04 (ap2apEq2) =>
% 98.91/13.04 ((
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% 98.91/13.04 ((
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% 98.91/13.04 ((
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% 98.91/13.04 ((
% 98.91/13.04 (beta2) =>
% 98.91/13.04 ((
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% 98.91/13.04 ((
% 98.91/13.04 (iffalseProp1) =>
% 98.91/13.04 ((
% 98.91/13.04 (iffalseProp2) =>
% 98.91/13.04 ((
% 98.91/13.04 (iftrueProp1) =>
% 98.91/13.04 ((
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% 98.91/13.04 ((
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% 98.91/13.04 ((
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% 98.91/13.04 ((
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% 98.91/13.04 ((
% 98.91/13.04 (iftrue) =>
% 98.91/13.04 ((
% 98.91/13.04 (iffalse) =>
% 98.91/13.04 ((
% 98.91/13.04 (iftrueorfalse) =>
% 98.91/13.04 ((
% 98.91/13.04 (binintersectT_lem) =>
% 98.91/13.04 ((
% 98.91/13.04 (binunionT_lem) =>
% 98.91/13.04 ((
% 98.91/13.04 (powersetT_lem) =>
% 98.91/13.04 ((
% 98.91/13.04 (setminusT_lem) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementT_lem) =>
% 98.91/13.04 ((
% 98.91/13.04 (setextT) =>
% 98.91/13.04 ((
% 98.91/13.04 (subsetTI) =>
% 98.91/13.04 ((
% 98.91/13.04 (powersetTI1) =>
% 98.91/13.04 ((
% 98.91/13.04 (powersetTE1) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementTI1) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementTE1) =>
% 98.91/13.04 ((
% 98.91/13.04 (binintersectTELcontra) =>
% 98.91/13.04 ((
% 98.91/13.04 (binintersectTERcontra) =>
% 98.91/13.04 ((
% 98.91/13.04 (contrasubsetT) =>
% 98.91/13.04 ((
% 98.91/13.04 (contrasubsetT1) =>
% 98.91/13.04 ((
% 98.91/13.04 (contrasubsetT2) =>
% 98.91/13.04 ((
% 98.91/13.04 (contrasubsetT3) =>
% 98.91/13.04 ((
% 98.91/13.04 (doubleComplementI1) =>
% 98.91/13.04 ((
% 98.91/13.04 (doubleComplementE1) =>
% 98.91/13.04 ((
% 98.91/13.04 (doubleComplementSub1) =>
% 98.91/13.04 ((
% 98.91/13.04 (doubleComplementSub2) =>
% 98.91/13.04 ((
% 98.91/13.04 (doubleComplementEq) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementTnotintersectT) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementImpComplementIntersect) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementSubsetComplementIntersect) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementInPowersetComplementIntersect) =>
% 98.91/13.04 ((
% 98.91/13.04 (contraSubsetComplement) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementTcontraSubset) =>
% 98.91/13.04 ((
% 98.91/13.04 (binunionTILcontra) =>
% 98.91/13.04 ((
% 98.91/13.04 (binunionTIRcontra) =>
% 98.91/13.04 ((
% 98.91/13.04 (inIntersectImpInUnion) =>
% 98.91/13.04 ((
% 98.91/13.04 (inIntersectImpInUnion2) =>
% 98.91/13.04 ((
% 98.91/13.04 (inIntersectImpInIntersectUnions) =>
% 98.91/13.04 ((
% 98.91/13.04 (intersectInPowersetIntersectUnions) =>
% 98.91/13.04 ((
% 98.91/13.04 (inComplementUnionImpNotIn1) =>
% 98.91/13.04 ((
% 98.91/13.04 (inComplementUnionImpInComplement1) =>
% 98.91/13.04 ((
% 98.91/13.04 (binunionTE) =>
% 98.91/13.04 ((
% 98.91/13.04 (binunionTEcontra) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan2a1) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementUnionInPowersetComplement) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan2a2) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan1a) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan1b) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan1) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan2a) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan2b2) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan2b) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan2) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz13rule0) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz13rule1) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz13rule2) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz13rule3) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz13rule4) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz1_1) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz1_2) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz1_3) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz1_4) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz1_5) =>
% 98.91/13.04 ((
% 98.91/13.04 (breln1all2) =>
% 98.91/13.04 ((
% 98.91/13.04 (breln1SetBreln1) =>
% 98.91/13.04 ((
% 98.91/13.04 (choice2fnsingleton) =>
% 98.91/13.04 ((
% 98.91/13.04 (!!) @ (
% 98.91/13.04 (('#B') @ (
% 98.91/13.04 !!) @
% 98.91/13.04 (
% 98.91/13.04 (
% 98.91/13.04 ('#S') @ (
% 98.91/13.04 (
% 98.91/13.04 ('#B') @ (
% 98.91/13.04 '#B') @
% 98.91/13.04 breln1)) @
% 98.91/13.04 (
% 98.91/13.04 (
% 98.91/13.04 ('#S') @ dpsetconstr @
% 98.91/13.04 (
% 98.91/13.04 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.91/13.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1599])).
% 98.91/13.04 thf(zip_derived_cl1615, plain,
% 98.91/13.04 (~ (((kfstsingleton) =>
% 98.91/13.04 (((theprop) =>
% 98.91/13.04 (((kfstpairEq) =>
% 98.91/13.04 (((cartprodfstin) =>
% 98.91/13.04 (((setukpairinjL2) =>
% 98.91/13.04 (((setukpairinjL) =>
% 98.91/13.04 (((setukpairinjR11) =>
% 98.91/13.04 (((setukpairinjR12) =>
% 98.91/13.04 (((setukpairinjR1) =>
% 98.91/13.04 (((upairequniteq) =>
% 98.91/13.04 (((setukpairinjR2) =>
% 98.91/13.04 (((setukpairinjR) =>
% 98.91/13.04 (((ksndsingleton) =>
% 98.91/13.04 (((ksndpairEq) =>
% 98.91/13.04 (((kpairsurjEq) =>
% 98.91/13.04 (((cartprodsndin) =>
% 98.91/13.04 (((cartprodpairmemEL) =>
% 98.91/13.04 (((cartprodpairmemER) =>
% 98.91/13.04 (((cartprodmempaircEq) =>
% 98.91/13.04 (((cartprodfstpairEq) =>
% 98.91/13.04 (((cartprodsndpairEq) =>
% 98.91/13.04 (((cartprodpairsurjEq) =>
% 98.91/13.04 (((dpsetconstrI) =>
% 98.91/13.04 (((dpsetconstrSub) =>
% 98.91/13.04 (((setOfPairsIsBReln) =>
% 98.91/13.04 (((dpsetconstrERa) =>
% 98.91/13.04 (((dpsetconstrEL1) =>
% 98.91/13.04 (((dpsetconstrEL2) =>
% 98.91/13.04 (((dpsetconstrER) =>
% 98.91/13.04 (((funcImageSingleton) =>
% 98.91/13.04 ((
% 98.91/13.04 (apProp) =>
% 98.91/13.04 ((
% 98.91/13.04 (app) =>
% 98.91/13.04 ((
% 98.91/13.04 (infuncsetfunc) =>
% 98.91/13.04 ((
% 98.91/13.04 (ap2p) =>
% 98.91/13.04 ((
% 98.91/13.04 (funcinfuncset) =>
% 98.91/13.04 ((
% 98.91/13.04 (lamProp) =>
% 98.91/13.04 ((
% 98.91/13.04 (lamp) =>
% 98.91/13.04 ((
% 98.91/13.04 (lam2p) =>
% 98.91/13.04 ((
% 98.91/13.04 (brelnall1) =>
% 98.91/13.04 ((
% 98.91/13.04 (brelnall2) =>
% 98.91/13.04 ((
% 98.91/13.04 (ex1E2) =>
% 98.91/13.04 ((
% 98.91/13.04 (funcGraphProp1) =>
% 98.91/13.04 ((
% 98.91/13.04 (funcGraphProp3) =>
% 98.91/13.04 ((
% 98.91/13.04 (funcGraphProp2) =>
% 98.91/13.04 ((
% 98.91/13.04 (funcextLem) =>
% 98.91/13.04 ((
% 98.91/13.04 (funcGraphProp4) =>
% 98.91/13.04 ((
% 98.91/13.04 (subbreln) =>
% 98.91/13.04 ((
% 98.91/13.04 (eqbreln) =>
% 98.91/13.04 ((
% 98.91/13.04 (funcext) =>
% 98.91/13.04 ((
% 98.91/13.04 (funcext2) =>
% 98.91/13.04 ((
% 98.91/13.04 (ap2apEq1) =>
% 98.91/13.04 ((
% 98.91/13.04 (ap2apEq2) =>
% 98.91/13.04 ((
% 98.91/13.04 (beta1) =>
% 98.91/13.04 ((
% 98.91/13.04 (eta1) =>
% 98.91/13.04 ((
% 98.91/13.04 (lam2lamEq) =>
% 98.91/13.04 ((
% 98.91/13.04 (beta2) =>
% 98.91/13.04 ((
% 98.91/13.04 (eta2) =>
% 98.91/13.04 ((
% 98.91/13.04 (iffalseProp1) =>
% 98.91/13.04 ((
% 98.91/13.04 (iffalseProp2) =>
% 98.91/13.04 ((
% 98.91/13.04 (iftrueProp1) =>
% 98.91/13.04 ((
% 98.91/13.04 (iftrueProp2) =>
% 98.91/13.04 ((
% 98.91/13.04 (ifSingleton) =>
% 98.91/13.04 ((
% 98.91/13.04 (ifp) =>
% 98.91/13.04 ((
% 98.91/13.04 (theeq) =>
% 98.91/13.04 ((
% 98.91/13.04 (iftrue) =>
% 98.91/13.04 ((
% 98.91/13.04 (iffalse) =>
% 98.91/13.04 ((
% 98.91/13.04 (iftrueorfalse) =>
% 98.91/13.04 ((
% 98.91/13.04 (binintersectT_lem) =>
% 98.91/13.04 ((
% 98.91/13.04 (binunionT_lem) =>
% 98.91/13.04 ((
% 98.91/13.04 (powersetT_lem) =>
% 98.91/13.04 ((
% 98.91/13.04 (setminusT_lem) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementT_lem) =>
% 98.91/13.04 ((
% 98.91/13.04 (setextT) =>
% 98.91/13.04 ((
% 98.91/13.04 (subsetTI) =>
% 98.91/13.04 ((
% 98.91/13.04 (powersetTI1) =>
% 98.91/13.04 ((
% 98.91/13.04 (powersetTE1) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementTI1) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementTE1) =>
% 98.91/13.04 ((
% 98.91/13.04 (binintersectTELcontra) =>
% 98.91/13.04 ((
% 98.91/13.04 (binintersectTERcontra) =>
% 98.91/13.04 ((
% 98.91/13.04 (contrasubsetT) =>
% 98.91/13.04 ((
% 98.91/13.04 (contrasubsetT1) =>
% 98.91/13.04 ((
% 98.91/13.04 (contrasubsetT2) =>
% 98.91/13.04 ((
% 98.91/13.04 (contrasubsetT3) =>
% 98.91/13.04 ((
% 98.91/13.04 (doubleComplementI1) =>
% 98.91/13.04 ((
% 98.91/13.04 (doubleComplementE1) =>
% 98.91/13.04 ((
% 98.91/13.04 (doubleComplementSub1) =>
% 98.91/13.04 ((
% 98.91/13.04 (doubleComplementSub2) =>
% 98.91/13.04 ((
% 98.91/13.04 (doubleComplementEq) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementTnotintersectT) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementImpComplementIntersect) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementSubsetComplementIntersect) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementInPowersetComplementIntersect) =>
% 98.91/13.04 ((
% 98.91/13.04 (contraSubsetComplement) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementTcontraSubset) =>
% 98.91/13.04 ((
% 98.91/13.04 (binunionTILcontra) =>
% 98.91/13.04 ((
% 98.91/13.04 (binunionTIRcontra) =>
% 98.91/13.04 ((
% 98.91/13.04 (inIntersectImpInUnion) =>
% 98.91/13.04 ((
% 98.91/13.04 (inIntersectImpInUnion2) =>
% 98.91/13.04 ((
% 98.91/13.04 (inIntersectImpInIntersectUnions) =>
% 98.91/13.04 ((
% 98.91/13.04 (intersectInPowersetIntersectUnions) =>
% 98.91/13.04 ((
% 98.91/13.04 (inComplementUnionImpNotIn1) =>
% 98.91/13.04 ((
% 98.91/13.04 (inComplementUnionImpInComplement1) =>
% 98.91/13.04 ((
% 98.91/13.04 (binunionTE) =>
% 98.91/13.04 ((
% 98.91/13.04 (binunionTEcontra) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan2a1) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementUnionInPowersetComplement) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan2a2) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan1a) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan1b) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan1) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan2a) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan2b2) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan2b) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan2) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz13rule0) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz13rule1) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz13rule2) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz13rule3) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz13rule4) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz1_1) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz1_2) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz1_3) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz1_4) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz1_5) =>
% 98.91/13.04 ((
% 98.91/13.04 (breln1all2) =>
% 98.91/13.04 ((
% 98.91/13.04 (breln1SetBreln1) =>
% 98.91/13.04 ((
% 98.91/13.04 (choice2fnsingleton) =>
% 98.91/13.04 ((
% 98.91/13.04 (!!) @ (
% 98.91/13.04 (('#B') @ (
% 98.91/13.04 !!) @
% 98.91/13.04 (
% 98.91/13.04 (
% 98.91/13.04 ('#S') @ (
% 98.91/13.04 (
% 98.91/13.04 ('#B') @ (
% 98.91/13.04 '#B') @
% 98.91/13.04 breln1)) @
% 98.91/13.04 (
% 98.91/13.04 (
% 98.91/13.04 ('#S') @ dpsetconstr @
% 98.91/13.04 (
% 98.91/13.04 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.91/13.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1607])).
% 98.91/13.04 thf(zip_derived_cl1625, plain,
% 98.91/13.04 (~ (((theprop) =>
% 98.91/13.04 (((kfstpairEq) =>
% 98.91/13.04 (((cartprodfstin) =>
% 98.91/13.04 (((setukpairinjL2) =>
% 98.91/13.04 (((setukpairinjL) =>
% 98.91/13.04 (((setukpairinjR11) =>
% 98.91/13.04 (((setukpairinjR12) =>
% 98.91/13.04 (((setukpairinjR1) =>
% 98.91/13.04 (((upairequniteq) =>
% 98.91/13.04 (((setukpairinjR2) =>
% 98.91/13.04 (((setukpairinjR) =>
% 98.91/13.04 (((ksndsingleton) =>
% 98.91/13.04 (((ksndpairEq) =>
% 98.91/13.04 (((kpairsurjEq) =>
% 98.91/13.04 (((cartprodsndin) =>
% 98.91/13.04 (((cartprodpairmemEL) =>
% 98.91/13.04 (((cartprodpairmemER) =>
% 98.91/13.04 (((cartprodmempaircEq) =>
% 98.91/13.04 (((cartprodfstpairEq) =>
% 98.91/13.04 (((cartprodsndpairEq) =>
% 98.91/13.04 (((cartprodpairsurjEq) =>
% 98.91/13.04 (((dpsetconstrI) =>
% 98.91/13.04 (((dpsetconstrSub) =>
% 98.91/13.04 (((setOfPairsIsBReln) =>
% 98.91/13.04 (((dpsetconstrERa) =>
% 98.91/13.04 (((dpsetconstrEL1) =>
% 98.91/13.04 (((dpsetconstrEL2) =>
% 98.91/13.04 (((dpsetconstrER) =>
% 98.91/13.04 (((funcImageSingleton) =>
% 98.91/13.04 (((apProp) =>
% 98.91/13.04 ((
% 98.91/13.04 (app) =>
% 98.91/13.04 ((
% 98.91/13.04 (infuncsetfunc) =>
% 98.91/13.04 ((
% 98.91/13.04 (ap2p) =>
% 98.91/13.04 ((
% 98.91/13.04 (funcinfuncset) =>
% 98.91/13.04 ((
% 98.91/13.04 (lamProp) =>
% 98.91/13.04 ((
% 98.91/13.04 (lamp) =>
% 98.91/13.04 ((
% 98.91/13.04 (lam2p) =>
% 98.91/13.04 ((
% 98.91/13.04 (brelnall1) =>
% 98.91/13.04 ((
% 98.91/13.04 (brelnall2) =>
% 98.91/13.04 ((
% 98.91/13.04 (ex1E2) =>
% 98.91/13.04 ((
% 98.91/13.04 (funcGraphProp1) =>
% 98.91/13.04 ((
% 98.91/13.04 (funcGraphProp3) =>
% 98.91/13.04 ((
% 98.91/13.04 (funcGraphProp2) =>
% 98.91/13.04 ((
% 98.91/13.04 (funcextLem) =>
% 98.91/13.04 ((
% 98.91/13.04 (funcGraphProp4) =>
% 98.91/13.04 ((
% 98.91/13.04 (subbreln) =>
% 98.91/13.04 ((
% 98.91/13.04 (eqbreln) =>
% 98.91/13.04 ((
% 98.91/13.04 (funcext) =>
% 98.91/13.04 ((
% 98.91/13.04 (funcext2) =>
% 98.91/13.04 ((
% 98.91/13.04 (ap2apEq1) =>
% 98.91/13.04 ((
% 98.91/13.04 (ap2apEq2) =>
% 98.91/13.04 ((
% 98.91/13.04 (beta1) =>
% 98.91/13.04 ((
% 98.91/13.04 (eta1) =>
% 98.91/13.04 ((
% 98.91/13.04 (lam2lamEq) =>
% 98.91/13.04 ((
% 98.91/13.04 (beta2) =>
% 98.91/13.04 ((
% 98.91/13.04 (eta2) =>
% 98.91/13.04 ((
% 98.91/13.04 (iffalseProp1) =>
% 98.91/13.04 ((
% 98.91/13.04 (iffalseProp2) =>
% 98.91/13.04 ((
% 98.91/13.04 (iftrueProp1) =>
% 98.91/13.04 ((
% 98.91/13.04 (iftrueProp2) =>
% 98.91/13.04 ((
% 98.91/13.04 (ifSingleton) =>
% 98.91/13.04 ((
% 98.91/13.04 (ifp) =>
% 98.91/13.04 ((
% 98.91/13.04 (theeq) =>
% 98.91/13.04 ((
% 98.91/13.04 (iftrue) =>
% 98.91/13.04 ((
% 98.91/13.04 (iffalse) =>
% 98.91/13.04 ((
% 98.91/13.04 (iftrueorfalse) =>
% 98.91/13.04 ((
% 98.91/13.04 (binintersectT_lem) =>
% 98.91/13.04 ((
% 98.91/13.04 (binunionT_lem) =>
% 98.91/13.04 ((
% 98.91/13.04 (powersetT_lem) =>
% 98.91/13.04 ((
% 98.91/13.04 (setminusT_lem) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementT_lem) =>
% 98.91/13.04 ((
% 98.91/13.04 (setextT) =>
% 98.91/13.04 ((
% 98.91/13.04 (subsetTI) =>
% 98.91/13.04 ((
% 98.91/13.04 (powersetTI1) =>
% 98.91/13.04 ((
% 98.91/13.04 (powersetTE1) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementTI1) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementTE1) =>
% 98.91/13.04 ((
% 98.91/13.04 (binintersectTELcontra) =>
% 98.91/13.04 ((
% 98.91/13.04 (binintersectTERcontra) =>
% 98.91/13.04 ((
% 98.91/13.04 (contrasubsetT) =>
% 98.91/13.04 ((
% 98.91/13.04 (contrasubsetT1) =>
% 98.91/13.04 ((
% 98.91/13.04 (contrasubsetT2) =>
% 98.91/13.04 ((
% 98.91/13.04 (contrasubsetT3) =>
% 98.91/13.04 ((
% 98.91/13.04 (doubleComplementI1) =>
% 98.91/13.04 ((
% 98.91/13.04 (doubleComplementE1) =>
% 98.91/13.04 ((
% 98.91/13.04 (doubleComplementSub1) =>
% 98.91/13.04 ((
% 98.91/13.04 (doubleComplementSub2) =>
% 98.91/13.04 ((
% 98.91/13.04 (doubleComplementEq) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementTnotintersectT) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementImpComplementIntersect) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementSubsetComplementIntersect) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementInPowersetComplementIntersect) =>
% 98.91/13.04 ((
% 98.91/13.04 (contraSubsetComplement) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementTcontraSubset) =>
% 98.91/13.04 ((
% 98.91/13.04 (binunionTILcontra) =>
% 98.91/13.04 ((
% 98.91/13.04 (binunionTIRcontra) =>
% 98.91/13.04 ((
% 98.91/13.04 (inIntersectImpInUnion) =>
% 98.91/13.04 ((
% 98.91/13.04 (inIntersectImpInUnion2) =>
% 98.91/13.04 ((
% 98.91/13.04 (inIntersectImpInIntersectUnions) =>
% 98.91/13.04 ((
% 98.91/13.04 (intersectInPowersetIntersectUnions) =>
% 98.91/13.04 ((
% 98.91/13.04 (inComplementUnionImpNotIn1) =>
% 98.91/13.04 ((
% 98.91/13.04 (inComplementUnionImpInComplement1) =>
% 98.91/13.04 ((
% 98.91/13.04 (binunionTE) =>
% 98.91/13.04 ((
% 98.91/13.04 (binunionTEcontra) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan2a1) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementUnionInPowersetComplement) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan2a2) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan1a) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan1b) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan1) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan2a) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan2b2) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan2b) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan2) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz13rule0) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz13rule1) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz13rule2) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz13rule3) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz13rule4) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz1_1) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz1_2) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz1_3) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz1_4) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz1_5) =>
% 98.91/13.04 ((
% 98.91/13.04 (breln1all2) =>
% 98.91/13.04 ((
% 98.91/13.04 (breln1SetBreln1) =>
% 98.91/13.04 ((
% 98.91/13.04 (choice2fnsingleton) =>
% 98.91/13.04 ((
% 98.91/13.04 (!!) @ (
% 98.91/13.04 (('#B') @ (
% 98.91/13.04 !!) @
% 98.91/13.04 (
% 98.91/13.04 (
% 98.91/13.04 ('#S') @ (
% 98.91/13.04 (
% 98.91/13.04 ('#B') @ (
% 98.91/13.04 '#B') @
% 98.91/13.04 breln1)) @
% 98.91/13.04 (
% 98.91/13.04 (
% 98.91/13.04 ('#S') @ dpsetconstr @
% 98.91/13.04 (
% 98.91/13.04 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.91/13.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1615])).
% 98.91/13.04 thf(zip_derived_cl1637, plain,
% 98.91/13.04 (~ (((kfstpairEq) =>
% 98.91/13.04 (((cartprodfstin) =>
% 98.91/13.04 (((setukpairinjL2) =>
% 98.91/13.04 (((setukpairinjL) =>
% 98.91/13.04 (((setukpairinjR11) =>
% 98.91/13.04 (((setukpairinjR12) =>
% 98.91/13.04 (((setukpairinjR1) =>
% 98.91/13.04 (((upairequniteq) =>
% 98.91/13.04 (((setukpairinjR2) =>
% 98.91/13.04 (((setukpairinjR) =>
% 98.91/13.04 (((ksndsingleton) =>
% 98.91/13.04 (((ksndpairEq) =>
% 98.91/13.04 (((kpairsurjEq) =>
% 98.91/13.04 (((cartprodsndin) =>
% 98.91/13.04 (((cartprodpairmemEL) =>
% 98.91/13.04 (((cartprodpairmemER) =>
% 98.91/13.04 (((cartprodmempaircEq) =>
% 98.91/13.04 (((cartprodfstpairEq) =>
% 98.91/13.04 (((cartprodsndpairEq) =>
% 98.91/13.04 (((cartprodpairsurjEq) =>
% 98.91/13.04 (((dpsetconstrI) =>
% 98.91/13.04 (((dpsetconstrSub) =>
% 98.91/13.04 (((setOfPairsIsBReln) =>
% 98.91/13.04 (((dpsetconstrERa) =>
% 98.91/13.04 (((dpsetconstrEL1) =>
% 98.91/13.04 (((dpsetconstrEL2) =>
% 98.91/13.04 (((dpsetconstrER) =>
% 98.91/13.04 (((funcImageSingleton) =>
% 98.91/13.04 (((apProp) =>
% 98.91/13.04 (((app) =>
% 98.91/13.04 ((
% 98.91/13.04 (infuncsetfunc) =>
% 98.91/13.04 ((
% 98.91/13.04 (ap2p) =>
% 98.91/13.04 ((
% 98.91/13.04 (funcinfuncset) =>
% 98.91/13.04 ((
% 98.91/13.04 (lamProp) =>
% 98.91/13.04 ((
% 98.91/13.04 (lamp) =>
% 98.91/13.04 ((
% 98.91/13.04 (lam2p) =>
% 98.91/13.04 ((
% 98.91/13.04 (brelnall1) =>
% 98.91/13.04 ((
% 98.91/13.04 (brelnall2) =>
% 98.91/13.04 ((
% 98.91/13.04 (ex1E2) =>
% 98.91/13.04 ((
% 98.91/13.04 (funcGraphProp1) =>
% 98.91/13.04 ((
% 98.91/13.04 (funcGraphProp3) =>
% 98.91/13.04 ((
% 98.91/13.04 (funcGraphProp2) =>
% 98.91/13.04 ((
% 98.91/13.04 (funcextLem) =>
% 98.91/13.04 ((
% 98.91/13.04 (funcGraphProp4) =>
% 98.91/13.04 ((
% 98.91/13.04 (subbreln) =>
% 98.91/13.04 ((
% 98.91/13.04 (eqbreln) =>
% 98.91/13.04 ((
% 98.91/13.04 (funcext) =>
% 98.91/13.04 ((
% 98.91/13.04 (funcext2) =>
% 98.91/13.04 ((
% 98.91/13.04 (ap2apEq1) =>
% 98.91/13.04 ((
% 98.91/13.04 (ap2apEq2) =>
% 98.91/13.04 ((
% 98.91/13.04 (beta1) =>
% 98.91/13.04 ((
% 98.91/13.04 (eta1) =>
% 98.91/13.04 ((
% 98.91/13.04 (lam2lamEq) =>
% 98.91/13.04 ((
% 98.91/13.04 (beta2) =>
% 98.91/13.04 ((
% 98.91/13.04 (eta2) =>
% 98.91/13.04 ((
% 98.91/13.04 (iffalseProp1) =>
% 98.91/13.04 ((
% 98.91/13.04 (iffalseProp2) =>
% 98.91/13.04 ((
% 98.91/13.04 (iftrueProp1) =>
% 98.91/13.04 ((
% 98.91/13.04 (iftrueProp2) =>
% 98.91/13.04 ((
% 98.91/13.04 (ifSingleton) =>
% 98.91/13.04 ((
% 98.91/13.04 (ifp) =>
% 98.91/13.04 ((
% 98.91/13.04 (theeq) =>
% 98.91/13.04 ((
% 98.91/13.04 (iftrue) =>
% 98.91/13.04 ((
% 98.91/13.04 (iffalse) =>
% 98.91/13.04 ((
% 98.91/13.04 (iftrueorfalse) =>
% 98.91/13.04 ((
% 98.91/13.04 (binintersectT_lem) =>
% 98.91/13.04 ((
% 98.91/13.04 (binunionT_lem) =>
% 98.91/13.04 ((
% 98.91/13.04 (powersetT_lem) =>
% 98.91/13.04 ((
% 98.91/13.04 (setminusT_lem) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementT_lem) =>
% 98.91/13.04 ((
% 98.91/13.04 (setextT) =>
% 98.91/13.04 ((
% 98.91/13.04 (subsetTI) =>
% 98.91/13.04 ((
% 98.91/13.04 (powersetTI1) =>
% 98.91/13.04 ((
% 98.91/13.04 (powersetTE1) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementTI1) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementTE1) =>
% 98.91/13.04 ((
% 98.91/13.04 (binintersectTELcontra) =>
% 98.91/13.04 ((
% 98.91/13.04 (binintersectTERcontra) =>
% 98.91/13.04 ((
% 98.91/13.04 (contrasubsetT) =>
% 98.91/13.04 ((
% 98.91/13.04 (contrasubsetT1) =>
% 98.91/13.04 ((
% 98.91/13.04 (contrasubsetT2) =>
% 98.91/13.04 ((
% 98.91/13.04 (contrasubsetT3) =>
% 98.91/13.04 ((
% 98.91/13.04 (doubleComplementI1) =>
% 98.91/13.04 ((
% 98.91/13.04 (doubleComplementE1) =>
% 98.91/13.04 ((
% 98.91/13.04 (doubleComplementSub1) =>
% 98.91/13.04 ((
% 98.91/13.04 (doubleComplementSub2) =>
% 98.91/13.04 ((
% 98.91/13.04 (doubleComplementEq) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementTnotintersectT) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementImpComplementIntersect) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementSubsetComplementIntersect) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementInPowersetComplementIntersect) =>
% 98.91/13.04 ((
% 98.91/13.04 (contraSubsetComplement) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementTcontraSubset) =>
% 98.91/13.04 ((
% 98.91/13.04 (binunionTILcontra) =>
% 98.91/13.04 ((
% 98.91/13.04 (binunionTIRcontra) =>
% 98.91/13.04 ((
% 98.91/13.04 (inIntersectImpInUnion) =>
% 98.91/13.04 ((
% 98.91/13.04 (inIntersectImpInUnion2) =>
% 98.91/13.04 ((
% 98.91/13.04 (inIntersectImpInIntersectUnions) =>
% 98.91/13.04 ((
% 98.91/13.04 (intersectInPowersetIntersectUnions) =>
% 98.91/13.04 ((
% 98.91/13.04 (inComplementUnionImpNotIn1) =>
% 98.91/13.04 ((
% 98.91/13.04 (inComplementUnionImpInComplement1) =>
% 98.91/13.04 ((
% 98.91/13.04 (binunionTE) =>
% 98.91/13.04 ((
% 98.91/13.04 (binunionTEcontra) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan2a1) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementUnionInPowersetComplement) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan2a2) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan1a) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan1b) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan1) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan2a) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan2b2) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan2b) =>
% 98.91/13.04 ((
% 98.91/13.04 (demorgan2) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz13rule0) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz13rule1) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz13rule2) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz13rule3) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz13rule4) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz1_1) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz1_2) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz1_3) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz1_4) =>
% 98.91/13.04 ((
% 98.91/13.04 (woz1_5) =>
% 98.91/13.04 ((
% 98.91/13.04 (breln1all2) =>
% 98.91/13.04 ((
% 98.91/13.04 (breln1SetBreln1) =>
% 98.91/13.04 ((
% 98.91/13.04 (choice2fnsingleton) =>
% 98.91/13.04 ((
% 98.91/13.04 (!!) @ (
% 98.91/13.04 (('#B') @ (
% 98.91/13.04 !!) @
% 98.91/13.04 (
% 98.91/13.04 (
% 98.91/13.04 ('#S') @ (
% 98.91/13.04 (
% 98.91/13.04 ('#B') @ (
% 98.91/13.04 '#B') @
% 98.91/13.04 breln1)) @
% 98.91/13.04 (
% 98.91/13.04 (
% 98.91/13.04 ('#S') @ dpsetconstr @
% 98.91/13.04 (
% 98.91/13.04 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.91/13.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1625])).
% 98.91/13.04 thf(zip_derived_cl1649, plain,
% 98.91/13.04 (~ (((cartprodfstin) =>
% 98.91/13.04 (((setukpairinjL2) =>
% 98.91/13.04 (((setukpairinjL) =>
% 98.91/13.04 (((setukpairinjR11) =>
% 98.91/13.04 (((setukpairinjR12) =>
% 98.91/13.04 (((setukpairinjR1) =>
% 98.91/13.04 (((upairequniteq) =>
% 98.91/13.04 (((setukpairinjR2) =>
% 98.91/13.04 (((setukpairinjR) =>
% 98.91/13.04 (((ksndsingleton) =>
% 98.91/13.04 (((ksndpairEq) =>
% 98.91/13.04 (((kpairsurjEq) =>
% 98.91/13.04 (((cartprodsndin) =>
% 98.91/13.04 (((cartprodpairmemEL) =>
% 98.91/13.04 (((cartprodpairmemER) =>
% 98.91/13.04 (((cartprodmempaircEq) =>
% 98.91/13.04 (((cartprodfstpairEq) =>
% 98.91/13.04 (((cartprodsndpairEq) =>
% 98.91/13.04 (((cartprodpairsurjEq) =>
% 98.91/13.04 (((dpsetconstrI) =>
% 98.91/13.04 (((dpsetconstrSub) =>
% 98.91/13.04 (((setOfPairsIsBReln) =>
% 98.91/13.04 (((dpsetconstrERa) =>
% 98.91/13.04 (((dpsetconstrEL1) =>
% 98.91/13.04 (((dpsetconstrEL2) =>
% 98.91/13.04 (((dpsetconstrER) =>
% 98.91/13.04 (((funcImageSingleton) =>
% 98.91/13.04 (((apProp) =>
% 98.91/13.04 (((app) =>
% 98.91/13.04 (((infuncsetfunc) =>
% 98.91/13.04 ((
% 98.91/13.04 (ap2p) =>
% 98.91/13.04 ((
% 98.91/13.04 (funcinfuncset) =>
% 98.91/13.04 ((
% 98.91/13.04 (lamProp) =>
% 98.91/13.04 ((
% 98.91/13.04 (lamp) =>
% 98.91/13.04 ((
% 98.91/13.04 (lam2p) =>
% 98.91/13.04 ((
% 98.91/13.04 (brelnall1) =>
% 98.91/13.04 ((
% 98.91/13.04 (brelnall2) =>
% 98.91/13.04 ((
% 98.91/13.04 (ex1E2) =>
% 98.91/13.04 ((
% 98.91/13.04 (funcGraphProp1) =>
% 98.91/13.04 ((
% 98.91/13.04 (funcGraphProp3) =>
% 98.91/13.04 ((
% 98.91/13.04 (funcGraphProp2) =>
% 98.91/13.04 ((
% 98.91/13.04 (funcextLem) =>
% 98.91/13.04 ((
% 98.91/13.04 (funcGraphProp4) =>
% 98.91/13.04 ((
% 98.91/13.04 (subbreln) =>
% 98.91/13.04 ((
% 98.91/13.04 (eqbreln) =>
% 98.91/13.04 ((
% 98.91/13.04 (funcext) =>
% 98.91/13.04 ((
% 98.91/13.04 (funcext2) =>
% 98.91/13.04 ((
% 98.91/13.04 (ap2apEq1) =>
% 98.91/13.04 ((
% 98.91/13.04 (ap2apEq2) =>
% 98.91/13.04 ((
% 98.91/13.04 (beta1) =>
% 98.91/13.04 ((
% 98.91/13.04 (eta1) =>
% 98.91/13.04 ((
% 98.91/13.04 (lam2lamEq) =>
% 98.91/13.04 ((
% 98.91/13.04 (beta2) =>
% 98.91/13.04 ((
% 98.91/13.04 (eta2) =>
% 98.91/13.04 ((
% 98.91/13.04 (iffalseProp1) =>
% 98.91/13.04 ((
% 98.91/13.04 (iffalseProp2) =>
% 98.91/13.04 ((
% 98.91/13.04 (iftrueProp1) =>
% 98.91/13.04 ((
% 98.91/13.04 (iftrueProp2) =>
% 98.91/13.04 ((
% 98.91/13.04 (ifSingleton) =>
% 98.91/13.04 ((
% 98.91/13.04 (ifp) =>
% 98.91/13.04 ((
% 98.91/13.04 (theeq) =>
% 98.91/13.04 ((
% 98.91/13.04 (iftrue) =>
% 98.91/13.04 ((
% 98.91/13.04 (iffalse) =>
% 98.91/13.04 ((
% 98.91/13.04 (iftrueorfalse) =>
% 98.91/13.04 ((
% 98.91/13.04 (binintersectT_lem) =>
% 98.91/13.04 ((
% 98.91/13.04 (binunionT_lem) =>
% 98.91/13.04 ((
% 98.91/13.04 (powersetT_lem) =>
% 98.91/13.04 ((
% 98.91/13.04 (setminusT_lem) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementT_lem) =>
% 98.91/13.04 ((
% 98.91/13.04 (setextT) =>
% 98.91/13.04 ((
% 98.91/13.04 (subsetTI) =>
% 98.91/13.04 ((
% 98.91/13.04 (powersetTI1) =>
% 98.91/13.04 ((
% 98.91/13.04 (powersetTE1) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementTI1) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementTE1) =>
% 98.91/13.04 ((
% 98.91/13.04 (binintersectTELcontra) =>
% 98.91/13.04 ((
% 98.91/13.04 (binintersectTERcontra) =>
% 98.91/13.04 ((
% 98.91/13.04 (contrasubsetT) =>
% 98.91/13.04 ((
% 98.91/13.04 (contrasubsetT1) =>
% 98.91/13.04 ((
% 98.91/13.04 (contrasubsetT2) =>
% 98.91/13.04 ((
% 98.91/13.04 (contrasubsetT3) =>
% 98.91/13.04 ((
% 98.91/13.04 (doubleComplementI1) =>
% 98.91/13.04 ((
% 98.91/13.04 (doubleComplementE1) =>
% 98.91/13.04 ((
% 98.91/13.04 (doubleComplementSub1) =>
% 98.91/13.04 ((
% 98.91/13.04 (doubleComplementSub2) =>
% 98.91/13.04 ((
% 98.91/13.04 (doubleComplementEq) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementTnotintersectT) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementImpComplementIntersect) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementSubsetComplementIntersect) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementInPowersetComplementIntersect) =>
% 98.91/13.04 ((
% 98.91/13.04 (contraSubsetComplement) =>
% 98.91/13.04 ((
% 98.91/13.04 (complementTcontraSubset) =>
% 98.91/13.04 ((
% 98.91/13.04 (binunionTILcontra) =>
% 98.91/13.04 ((
% 98.91/13.04 (binunionTIRcontra) =>
% 98.91/13.04 ((
% 98.91/13.04 (inIntersectImpInUnion) =>
% 98.91/13.05 ((
% 98.91/13.05 (inIntersectImpInUnion2) =>
% 98.91/13.05 ((
% 98.91/13.05 (inIntersectImpInIntersectUnions) =>
% 98.91/13.05 ((
% 98.91/13.05 (intersectInPowersetIntersectUnions) =>
% 98.91/13.05 ((
% 98.91/13.05 (inComplementUnionImpNotIn1) =>
% 98.91/13.05 ((
% 98.91/13.05 (inComplementUnionImpInComplement1) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionTE) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionTEcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2a1) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementUnionInPowersetComplement) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2a2) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan1a) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan1b) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan1) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2a) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2b2) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2b) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule0) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule1) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule2) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule3) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule4) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_1) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_2) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_3) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_4) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_5) =>
% 98.91/13.05 ((
% 98.91/13.05 (breln1all2) =>
% 98.91/13.05 ((
% 98.91/13.05 (breln1SetBreln1) =>
% 98.91/13.05 ((
% 98.91/13.05 (choice2fnsingleton) =>
% 98.91/13.05 ((
% 98.91/13.05 (!!) @ (
% 98.91/13.05 (('#B') @ (
% 98.91/13.05 !!) @
% 98.91/13.05 (
% 98.91/13.05 (
% 98.91/13.05 ('#S') @ (
% 98.91/13.05 (
% 98.91/13.05 ('#B') @ (
% 98.91/13.05 '#B') @
% 98.91/13.05 breln1)) @
% 98.91/13.05 (
% 98.91/13.05 (
% 98.91/13.05 ('#S') @ dpsetconstr @
% 98.91/13.05 (
% 98.91/13.05 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.91/13.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1637])).
% 98.91/13.05 thf(zip_derived_cl1664, plain,
% 98.91/13.05 (~ (((setukpairinjL2) =>
% 98.91/13.05 (((setukpairinjL) =>
% 98.91/13.05 (((setukpairinjR11) =>
% 98.91/13.05 (((setukpairinjR12) =>
% 98.91/13.05 (((setukpairinjR1) =>
% 98.91/13.05 (((upairequniteq) =>
% 98.91/13.05 (((setukpairinjR2) =>
% 98.91/13.05 (((setukpairinjR) =>
% 98.91/13.05 (((ksndsingleton) =>
% 98.91/13.05 (((ksndpairEq) =>
% 98.91/13.05 (((kpairsurjEq) =>
% 98.91/13.05 (((cartprodsndin) =>
% 98.91/13.05 (((cartprodpairmemEL) =>
% 98.91/13.05 (((cartprodpairmemER) =>
% 98.91/13.05 (((cartprodmempaircEq) =>
% 98.91/13.05 (((cartprodfstpairEq) =>
% 98.91/13.05 (((cartprodsndpairEq) =>
% 98.91/13.05 (((cartprodpairsurjEq) =>
% 98.91/13.05 (((dpsetconstrI) =>
% 98.91/13.05 (((dpsetconstrSub) =>
% 98.91/13.05 (((setOfPairsIsBReln) =>
% 98.91/13.05 (((dpsetconstrERa) =>
% 98.91/13.05 (((dpsetconstrEL1) =>
% 98.91/13.05 (((dpsetconstrEL2) =>
% 98.91/13.05 (((dpsetconstrER) =>
% 98.91/13.05 (((funcImageSingleton) =>
% 98.91/13.05 (((apProp) =>
% 98.91/13.05 (((app) =>
% 98.91/13.05 (((infuncsetfunc) =>
% 98.91/13.05 (((ap2p) =>
% 98.91/13.05 ((
% 98.91/13.05 (funcinfuncset) =>
% 98.91/13.05 ((
% 98.91/13.05 (lamProp) =>
% 98.91/13.05 ((
% 98.91/13.05 (lamp) =>
% 98.91/13.05 ((
% 98.91/13.05 (lam2p) =>
% 98.91/13.05 ((
% 98.91/13.05 (brelnall1) =>
% 98.91/13.05 ((
% 98.91/13.05 (brelnall2) =>
% 98.91/13.05 ((
% 98.91/13.05 (ex1E2) =>
% 98.91/13.05 ((
% 98.91/13.05 (funcGraphProp1) =>
% 98.91/13.05 ((
% 98.91/13.05 (funcGraphProp3) =>
% 98.91/13.05 ((
% 98.91/13.05 (funcGraphProp2) =>
% 98.91/13.05 ((
% 98.91/13.05 (funcextLem) =>
% 98.91/13.05 ((
% 98.91/13.05 (funcGraphProp4) =>
% 98.91/13.05 ((
% 98.91/13.05 (subbreln) =>
% 98.91/13.05 ((
% 98.91/13.05 (eqbreln) =>
% 98.91/13.05 ((
% 98.91/13.05 (funcext) =>
% 98.91/13.05 ((
% 98.91/13.05 (funcext2) =>
% 98.91/13.05 ((
% 98.91/13.05 (ap2apEq1) =>
% 98.91/13.05 ((
% 98.91/13.05 (ap2apEq2) =>
% 98.91/13.05 ((
% 98.91/13.05 (beta1) =>
% 98.91/13.05 ((
% 98.91/13.05 (eta1) =>
% 98.91/13.05 ((
% 98.91/13.05 (lam2lamEq) =>
% 98.91/13.05 ((
% 98.91/13.05 (beta2) =>
% 98.91/13.05 ((
% 98.91/13.05 (eta2) =>
% 98.91/13.05 ((
% 98.91/13.05 (iffalseProp1) =>
% 98.91/13.05 ((
% 98.91/13.05 (iffalseProp2) =>
% 98.91/13.05 ((
% 98.91/13.05 (iftrueProp1) =>
% 98.91/13.05 ((
% 98.91/13.05 (iftrueProp2) =>
% 98.91/13.05 ((
% 98.91/13.05 (ifSingleton) =>
% 98.91/13.05 ((
% 98.91/13.05 (ifp) =>
% 98.91/13.05 ((
% 98.91/13.05 (theeq) =>
% 98.91/13.05 ((
% 98.91/13.05 (iftrue) =>
% 98.91/13.05 ((
% 98.91/13.05 (iffalse) =>
% 98.91/13.05 ((
% 98.91/13.05 (iftrueorfalse) =>
% 98.91/13.05 ((
% 98.91/13.05 (binintersectT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (powersetT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (setminusT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (setextT) =>
% 98.91/13.05 ((
% 98.91/13.05 (subsetTI) =>
% 98.91/13.05 ((
% 98.91/13.05 (powersetTI1) =>
% 98.91/13.05 ((
% 98.91/13.05 (powersetTE1) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementTI1) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementTE1) =>
% 98.91/13.05 ((
% 98.91/13.05 (binintersectTELcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (binintersectTERcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (contrasubsetT) =>
% 98.91/13.05 ((
% 98.91/13.05 (contrasubsetT1) =>
% 98.91/13.05 ((
% 98.91/13.05 (contrasubsetT2) =>
% 98.91/13.05 ((
% 98.91/13.05 (contrasubsetT3) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementI1) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementE1) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementSub1) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementSub2) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementEq) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementTnotintersectT) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementImpComplementIntersect) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementSubsetComplementIntersect) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementInPowersetComplementIntersect) =>
% 98.91/13.05 ((
% 98.91/13.05 (contraSubsetComplement) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementTcontraSubset) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionTILcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionTIRcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (inIntersectImpInUnion) =>
% 98.91/13.05 ((
% 98.91/13.05 (inIntersectImpInUnion2) =>
% 98.91/13.05 ((
% 98.91/13.05 (inIntersectImpInIntersectUnions) =>
% 98.91/13.05 ((
% 98.91/13.05 (intersectInPowersetIntersectUnions) =>
% 98.91/13.05 ((
% 98.91/13.05 (inComplementUnionImpNotIn1) =>
% 98.91/13.05 ((
% 98.91/13.05 (inComplementUnionImpInComplement1) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionTE) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionTEcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2a1) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementUnionInPowersetComplement) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2a2) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan1a) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan1b) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan1) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2a) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2b2) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2b) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule0) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule1) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule2) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule3) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule4) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_1) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_2) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_3) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_4) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_5) =>
% 98.91/13.05 ((
% 98.91/13.05 (breln1all2) =>
% 98.91/13.05 ((
% 98.91/13.05 (breln1SetBreln1) =>
% 98.91/13.05 ((
% 98.91/13.05 (choice2fnsingleton) =>
% 98.91/13.05 ((
% 98.91/13.05 (!!) @ (
% 98.91/13.05 (('#B') @ (
% 98.91/13.05 !!) @
% 98.91/13.05 (
% 98.91/13.05 (
% 98.91/13.05 ('#S') @ (
% 98.91/13.05 (
% 98.91/13.05 ('#B') @ (
% 98.91/13.05 '#B') @
% 98.91/13.05 breln1)) @
% 98.91/13.05 (
% 98.91/13.05 (
% 98.91/13.05 ('#S') @ dpsetconstr @
% 98.91/13.05 (
% 98.91/13.05 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.91/13.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1649])).
% 98.91/13.05 thf(zip_derived_cl1678, plain,
% 98.91/13.05 (~ (((setukpairinjL) =>
% 98.91/13.05 (((setukpairinjR11) =>
% 98.91/13.05 (((setukpairinjR12) =>
% 98.91/13.05 (((setukpairinjR1) =>
% 98.91/13.05 (((upairequniteq) =>
% 98.91/13.05 (((setukpairinjR2) =>
% 98.91/13.05 (((setukpairinjR) =>
% 98.91/13.05 (((ksndsingleton) =>
% 98.91/13.05 (((ksndpairEq) =>
% 98.91/13.05 (((kpairsurjEq) =>
% 98.91/13.05 (((cartprodsndin) =>
% 98.91/13.05 (((cartprodpairmemEL) =>
% 98.91/13.05 (((cartprodpairmemER) =>
% 98.91/13.05 (((cartprodmempaircEq) =>
% 98.91/13.05 (((cartprodfstpairEq) =>
% 98.91/13.05 (((cartprodsndpairEq) =>
% 98.91/13.05 (((cartprodpairsurjEq) =>
% 98.91/13.05 (((dpsetconstrI) =>
% 98.91/13.05 (((dpsetconstrSub) =>
% 98.91/13.05 (((setOfPairsIsBReln) =>
% 98.91/13.05 (((dpsetconstrERa) =>
% 98.91/13.05 (((dpsetconstrEL1) =>
% 98.91/13.05 (((dpsetconstrEL2) =>
% 98.91/13.05 (((dpsetconstrER) =>
% 98.91/13.05 (((funcImageSingleton) =>
% 98.91/13.05 (((apProp) =>
% 98.91/13.05 (((app) =>
% 98.91/13.05 (((infuncsetfunc) =>
% 98.91/13.05 (((ap2p) =>
% 98.91/13.05 (((funcinfuncset) =>
% 98.91/13.05 ((
% 98.91/13.05 (lamProp) =>
% 98.91/13.05 ((
% 98.91/13.05 (lamp) =>
% 98.91/13.05 ((
% 98.91/13.05 (lam2p) =>
% 98.91/13.05 ((
% 98.91/13.05 (brelnall1) =>
% 98.91/13.05 ((
% 98.91/13.05 (brelnall2) =>
% 98.91/13.05 ((
% 98.91/13.05 (ex1E2) =>
% 98.91/13.05 ((
% 98.91/13.05 (funcGraphProp1) =>
% 98.91/13.05 ((
% 98.91/13.05 (funcGraphProp3) =>
% 98.91/13.05 ((
% 98.91/13.05 (funcGraphProp2) =>
% 98.91/13.05 ((
% 98.91/13.05 (funcextLem) =>
% 98.91/13.05 ((
% 98.91/13.05 (funcGraphProp4) =>
% 98.91/13.05 ((
% 98.91/13.05 (subbreln) =>
% 98.91/13.05 ((
% 98.91/13.05 (eqbreln) =>
% 98.91/13.05 ((
% 98.91/13.05 (funcext) =>
% 98.91/13.05 ((
% 98.91/13.05 (funcext2) =>
% 98.91/13.05 ((
% 98.91/13.05 (ap2apEq1) =>
% 98.91/13.05 ((
% 98.91/13.05 (ap2apEq2) =>
% 98.91/13.05 ((
% 98.91/13.05 (beta1) =>
% 98.91/13.05 ((
% 98.91/13.05 (eta1) =>
% 98.91/13.05 ((
% 98.91/13.05 (lam2lamEq) =>
% 98.91/13.05 ((
% 98.91/13.05 (beta2) =>
% 98.91/13.05 ((
% 98.91/13.05 (eta2) =>
% 98.91/13.05 ((
% 98.91/13.05 (iffalseProp1) =>
% 98.91/13.05 ((
% 98.91/13.05 (iffalseProp2) =>
% 98.91/13.05 ((
% 98.91/13.05 (iftrueProp1) =>
% 98.91/13.05 ((
% 98.91/13.05 (iftrueProp2) =>
% 98.91/13.05 ((
% 98.91/13.05 (ifSingleton) =>
% 98.91/13.05 ((
% 98.91/13.05 (ifp) =>
% 98.91/13.05 ((
% 98.91/13.05 (theeq) =>
% 98.91/13.05 ((
% 98.91/13.05 (iftrue) =>
% 98.91/13.05 ((
% 98.91/13.05 (iffalse) =>
% 98.91/13.05 ((
% 98.91/13.05 (iftrueorfalse) =>
% 98.91/13.05 ((
% 98.91/13.05 (binintersectT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (powersetT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (setminusT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (setextT) =>
% 98.91/13.05 ((
% 98.91/13.05 (subsetTI) =>
% 98.91/13.05 ((
% 98.91/13.05 (powersetTI1) =>
% 98.91/13.05 ((
% 98.91/13.05 (powersetTE1) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementTI1) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementTE1) =>
% 98.91/13.05 ((
% 98.91/13.05 (binintersectTELcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (binintersectTERcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (contrasubsetT) =>
% 98.91/13.05 ((
% 98.91/13.05 (contrasubsetT1) =>
% 98.91/13.05 ((
% 98.91/13.05 (contrasubsetT2) =>
% 98.91/13.05 ((
% 98.91/13.05 (contrasubsetT3) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementI1) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementE1) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementSub1) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementSub2) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementEq) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementTnotintersectT) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementImpComplementIntersect) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementSubsetComplementIntersect) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementInPowersetComplementIntersect) =>
% 98.91/13.05 ((
% 98.91/13.05 (contraSubsetComplement) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementTcontraSubset) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionTILcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionTIRcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (inIntersectImpInUnion) =>
% 98.91/13.05 ((
% 98.91/13.05 (inIntersectImpInUnion2) =>
% 98.91/13.05 ((
% 98.91/13.05 (inIntersectImpInIntersectUnions) =>
% 98.91/13.05 ((
% 98.91/13.05 (intersectInPowersetIntersectUnions) =>
% 98.91/13.05 ((
% 98.91/13.05 (inComplementUnionImpNotIn1) =>
% 98.91/13.05 ((
% 98.91/13.05 (inComplementUnionImpInComplement1) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionTE) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionTEcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2a1) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementUnionInPowersetComplement) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2a2) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan1a) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan1b) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan1) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2a) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2b2) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2b) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule0) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule1) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule2) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule3) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule4) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_1) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_2) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_3) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_4) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_5) =>
% 98.91/13.05 ((
% 98.91/13.05 (breln1all2) =>
% 98.91/13.05 ((
% 98.91/13.05 (breln1SetBreln1) =>
% 98.91/13.05 ((
% 98.91/13.05 (choice2fnsingleton) =>
% 98.91/13.05 ((
% 98.91/13.05 (!!) @ (
% 98.91/13.05 (('#B') @ (
% 98.91/13.05 !!) @
% 98.91/13.05 (
% 98.91/13.05 (
% 98.91/13.05 ('#S') @ (
% 98.91/13.05 (
% 98.91/13.05 ('#B') @ (
% 98.91/13.05 '#B') @
% 98.91/13.05 breln1)) @
% 98.91/13.05 (
% 98.91/13.05 (
% 98.91/13.05 ('#S') @ dpsetconstr @
% 98.91/13.05 (
% 98.91/13.05 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.91/13.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1664])).
% 98.91/13.05 thf(zip_derived_cl1695, plain,
% 98.91/13.05 (~ (((setukpairinjR11) =>
% 98.91/13.05 (((setukpairinjR12) =>
% 98.91/13.05 (((setukpairinjR1) =>
% 98.91/13.05 (((upairequniteq) =>
% 98.91/13.05 (((setukpairinjR2) =>
% 98.91/13.05 (((setukpairinjR) =>
% 98.91/13.05 (((ksndsingleton) =>
% 98.91/13.05 (((ksndpairEq) =>
% 98.91/13.05 (((kpairsurjEq) =>
% 98.91/13.05 (((cartprodsndin) =>
% 98.91/13.05 (((cartprodpairmemEL) =>
% 98.91/13.05 (((cartprodpairmemER) =>
% 98.91/13.05 (((cartprodmempaircEq) =>
% 98.91/13.05 (((cartprodfstpairEq) =>
% 98.91/13.05 (((cartprodsndpairEq) =>
% 98.91/13.05 (((cartprodpairsurjEq) =>
% 98.91/13.05 (((dpsetconstrI) =>
% 98.91/13.05 (((dpsetconstrSub) =>
% 98.91/13.05 (((setOfPairsIsBReln) =>
% 98.91/13.05 (((dpsetconstrERa) =>
% 98.91/13.05 (((dpsetconstrEL1) =>
% 98.91/13.05 (((dpsetconstrEL2) =>
% 98.91/13.05 (((dpsetconstrER) =>
% 98.91/13.05 (((funcImageSingleton) =>
% 98.91/13.05 (((apProp) =>
% 98.91/13.05 (((app) =>
% 98.91/13.05 (((infuncsetfunc) =>
% 98.91/13.05 (((ap2p) =>
% 98.91/13.05 (((funcinfuncset) =>
% 98.91/13.05 (((lamProp) =>
% 98.91/13.05 ((
% 98.91/13.05 (lamp) =>
% 98.91/13.05 ((
% 98.91/13.05 (lam2p) =>
% 98.91/13.05 ((
% 98.91/13.05 (brelnall1) =>
% 98.91/13.05 ((
% 98.91/13.05 (brelnall2) =>
% 98.91/13.05 ((
% 98.91/13.05 (ex1E2) =>
% 98.91/13.05 ((
% 98.91/13.05 (funcGraphProp1) =>
% 98.91/13.05 ((
% 98.91/13.05 (funcGraphProp3) =>
% 98.91/13.05 ((
% 98.91/13.05 (funcGraphProp2) =>
% 98.91/13.05 ((
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% 98.91/13.05 ((
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% 98.91/13.05 ((
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% 98.91/13.05 ((
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% 98.91/13.05 ((
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% 98.91/13.05 ((
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% 98.91/13.05 ((
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% 98.91/13.05 ((
% 98.91/13.05 (ap2apEq2) =>
% 98.91/13.05 ((
% 98.91/13.05 (beta1) =>
% 98.91/13.05 ((
% 98.91/13.05 (eta1) =>
% 98.91/13.05 ((
% 98.91/13.05 (lam2lamEq) =>
% 98.91/13.05 ((
% 98.91/13.05 (beta2) =>
% 98.91/13.05 ((
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% 98.91/13.05 ((
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% 98.91/13.05 ((
% 98.91/13.05 (iffalseProp2) =>
% 98.91/13.05 ((
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% 98.91/13.05 ((
% 98.91/13.05 (iftrueProp2) =>
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% 98.91/13.05 ((
% 98.91/13.05 (ifp) =>
% 98.91/13.05 ((
% 98.91/13.05 (theeq) =>
% 98.91/13.05 ((
% 98.91/13.05 (iftrue) =>
% 98.91/13.05 ((
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% 98.91/13.05 ((
% 98.91/13.05 (iftrueorfalse) =>
% 98.91/13.05 ((
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% 98.91/13.05 ((
% 98.91/13.05 (binunionT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (powersetT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (setminusT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (setextT) =>
% 98.91/13.05 ((
% 98.91/13.05 (subsetTI) =>
% 98.91/13.05 ((
% 98.91/13.05 (powersetTI1) =>
% 98.91/13.05 ((
% 98.91/13.05 (powersetTE1) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementTI1) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementTE1) =>
% 98.91/13.05 ((
% 98.91/13.05 (binintersectTELcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (binintersectTERcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (contrasubsetT) =>
% 98.91/13.05 ((
% 98.91/13.05 (contrasubsetT1) =>
% 98.91/13.05 ((
% 98.91/13.05 (contrasubsetT2) =>
% 98.91/13.05 ((
% 98.91/13.05 (contrasubsetT3) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementI1) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementE1) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementSub1) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementSub2) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementEq) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementTnotintersectT) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementImpComplementIntersect) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementSubsetComplementIntersect) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementInPowersetComplementIntersect) =>
% 98.91/13.05 ((
% 98.91/13.05 (contraSubsetComplement) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementTcontraSubset) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionTILcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionTIRcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (inIntersectImpInUnion) =>
% 98.91/13.05 ((
% 98.91/13.05 (inIntersectImpInUnion2) =>
% 98.91/13.05 ((
% 98.91/13.05 (inIntersectImpInIntersectUnions) =>
% 98.91/13.05 ((
% 98.91/13.05 (intersectInPowersetIntersectUnions) =>
% 98.91/13.05 ((
% 98.91/13.05 (inComplementUnionImpNotIn1) =>
% 98.91/13.05 ((
% 98.91/13.05 (inComplementUnionImpInComplement1) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionTE) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionTEcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2a1) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementUnionInPowersetComplement) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2a2) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan1a) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan1b) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan1) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2a) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2b2) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2b) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule0) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule1) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule2) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule3) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule4) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_1) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_2) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_3) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_4) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_5) =>
% 98.91/13.05 ((
% 98.91/13.05 (breln1all2) =>
% 98.91/13.05 ((
% 98.91/13.05 (breln1SetBreln1) =>
% 98.91/13.05 ((
% 98.91/13.05 (choice2fnsingleton) =>
% 98.91/13.05 ((
% 98.91/13.05 (!!) @ (
% 98.91/13.05 (('#B') @ (
% 98.91/13.05 !!) @
% 98.91/13.05 (
% 98.91/13.05 (
% 98.91/13.05 ('#S') @ (
% 98.91/13.05 (
% 98.91/13.05 ('#B') @ (
% 98.91/13.05 '#B') @
% 98.91/13.05 breln1)) @
% 98.91/13.05 (
% 98.91/13.05 (
% 98.91/13.05 ('#S') @ dpsetconstr @
% 98.91/13.05 (
% 98.91/13.05 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.91/13.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1678])).
% 98.91/13.05 thf(zip_derived_cl1711, plain,
% 98.91/13.05 (~ (((setukpairinjR12) =>
% 98.91/13.05 (((setukpairinjR1) =>
% 98.91/13.05 (((upairequniteq) =>
% 98.91/13.05 (((setukpairinjR2) =>
% 98.91/13.05 (((setukpairinjR) =>
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% 98.91/13.05 (((ksndpairEq) =>
% 98.91/13.05 (((kpairsurjEq) =>
% 98.91/13.05 (((cartprodsndin) =>
% 98.91/13.05 (((cartprodpairmemEL) =>
% 98.91/13.05 (((cartprodpairmemER) =>
% 98.91/13.05 (((cartprodmempaircEq) =>
% 98.91/13.05 (((cartprodfstpairEq) =>
% 98.91/13.05 (((cartprodsndpairEq) =>
% 98.91/13.05 (((cartprodpairsurjEq) =>
% 98.91/13.05 (((dpsetconstrI) =>
% 98.91/13.05 (((dpsetconstrSub) =>
% 98.91/13.05 (((setOfPairsIsBReln) =>
% 98.91/13.05 (((dpsetconstrERa) =>
% 98.91/13.05 (((dpsetconstrEL1) =>
% 98.91/13.05 (((dpsetconstrEL2) =>
% 98.91/13.05 (((dpsetconstrER) =>
% 98.91/13.05 (((funcImageSingleton) =>
% 98.91/13.05 (((apProp) =>
% 98.91/13.05 (((app) =>
% 98.91/13.05 (((infuncsetfunc) =>
% 98.91/13.05 (((ap2p) =>
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% 98.91/13.05 ((
% 98.91/13.05 (lam2p) =>
% 98.91/13.05 ((
% 98.91/13.05 (brelnall1) =>
% 98.91/13.05 ((
% 98.91/13.05 (brelnall2) =>
% 98.91/13.05 ((
% 98.91/13.05 (ex1E2) =>
% 98.91/13.05 ((
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% 98.91/13.05 ((
% 98.91/13.05 (funcGraphProp3) =>
% 98.91/13.05 ((
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% 98.91/13.05 ((
% 98.91/13.05 (funcextLem) =>
% 98.91/13.05 ((
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% 98.91/13.05 ((
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% 98.91/13.05 ((
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% 98.91/13.05 ((
% 98.91/13.05 (funcext2) =>
% 98.91/13.05 ((
% 98.91/13.05 (ap2apEq1) =>
% 98.91/13.05 ((
% 98.91/13.05 (ap2apEq2) =>
% 98.91/13.05 ((
% 98.91/13.05 (beta1) =>
% 98.91/13.05 ((
% 98.91/13.05 (eta1) =>
% 98.91/13.05 ((
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% 98.91/13.05 ((
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% 98.91/13.05 ((
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% 98.91/13.05 ((
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% 98.91/13.05 ((
% 98.91/13.05 (iftrueorfalse) =>
% 98.91/13.05 ((
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% 98.91/13.05 ((
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% 98.91/13.05 ((
% 98.91/13.05 (powersetT_lem) =>
% 98.91/13.05 ((
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% 98.91/13.05 ((
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% 98.91/13.05 ((
% 98.91/13.05 (setextT) =>
% 98.91/13.05 ((
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% 98.91/13.05 ((
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% 98.91/13.05 ((
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% 98.91/13.05 ((
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% 98.91/13.05 ((
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% 98.91/13.05 ((
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% 98.91/13.05 ((
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% 98.91/13.05 ((
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% 98.91/13.05 ((
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% 98.91/13.05 ((
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% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementSub2) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementEq) =>
% 98.91/13.05 ((
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% 98.91/13.05 ((
% 98.91/13.05 (complementImpComplementIntersect) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementSubsetComplementIntersect) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementInPowersetComplementIntersect) =>
% 98.91/13.05 ((
% 98.91/13.05 (contraSubsetComplement) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementTcontraSubset) =>
% 98.91/13.05 ((
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% 98.91/13.05 ((
% 98.91/13.05 (binunionTIRcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (inIntersectImpInUnion) =>
% 98.91/13.05 ((
% 98.91/13.05 (inIntersectImpInUnion2) =>
% 98.91/13.05 ((
% 98.91/13.05 (inIntersectImpInIntersectUnions) =>
% 98.91/13.05 ((
% 98.91/13.05 (intersectInPowersetIntersectUnions) =>
% 98.91/13.05 ((
% 98.91/13.05 (inComplementUnionImpNotIn1) =>
% 98.91/13.05 ((
% 98.91/13.05 (inComplementUnionImpInComplement1) =>
% 98.91/13.05 ((
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% 98.91/13.05 ((
% 98.91/13.05 (binunionTEcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2a1) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementUnionInPowersetComplement) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2a2) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan1a) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan1b) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan1) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2a) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2b2) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2b) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule0) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule1) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule2) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule3) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule4) =>
% 98.91/13.05 ((
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% 98.91/13.05 ((
% 98.91/13.05 (woz1_2) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_3) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_4) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_5) =>
% 98.91/13.05 ((
% 98.91/13.05 (breln1all2) =>
% 98.91/13.05 ((
% 98.91/13.05 (breln1SetBreln1) =>
% 98.91/13.05 ((
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% 98.91/13.05 ((
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% 98.91/13.05 (
% 98.91/13.05 ('#S') @ (
% 98.91/13.05 (
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% 98.91/13.05 (
% 98.91/13.05 (
% 98.91/13.05 ('#S') @ dpsetconstr @
% 98.91/13.05 (
% 98.91/13.05 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.91/13.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1695])).
% 98.91/13.05 thf(zip_derived_cl1725, plain,
% 98.91/13.05 (~ (((setukpairinjR1) =>
% 98.91/13.05 (((upairequniteq) =>
% 98.91/13.05 (((setukpairinjR2) =>
% 98.91/13.05 (((setukpairinjR) =>
% 98.91/13.05 (((ksndsingleton) =>
% 98.91/13.05 (((ksndpairEq) =>
% 98.91/13.05 (((kpairsurjEq) =>
% 98.91/13.05 (((cartprodsndin) =>
% 98.91/13.05 (((cartprodpairmemEL) =>
% 98.91/13.05 (((cartprodpairmemER) =>
% 98.91/13.05 (((cartprodmempaircEq) =>
% 98.91/13.05 (((cartprodfstpairEq) =>
% 98.91/13.05 (((cartprodsndpairEq) =>
% 98.91/13.05 (((cartprodpairsurjEq) =>
% 98.91/13.05 (((dpsetconstrI) =>
% 98.91/13.05 (((dpsetconstrSub) =>
% 98.91/13.05 (((setOfPairsIsBReln) =>
% 98.91/13.05 (((dpsetconstrERa) =>
% 98.91/13.05 (((dpsetconstrEL1) =>
% 98.91/13.05 (((dpsetconstrEL2) =>
% 98.91/13.05 (((dpsetconstrER) =>
% 98.91/13.05 (((funcImageSingleton) =>
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% 98.91/13.05 (((app) =>
% 98.91/13.05 (((infuncsetfunc) =>
% 98.91/13.05 (((ap2p) =>
% 98.91/13.05 (((funcinfuncset) =>
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% 98.91/13.05 (((lam2p) =>
% 98.91/13.05 ((
% 98.91/13.05 (brelnall1) =>
% 98.91/13.05 ((
% 98.91/13.05 (brelnall2) =>
% 98.91/13.05 ((
% 98.91/13.05 (ex1E2) =>
% 98.91/13.05 ((
% 98.91/13.05 (funcGraphProp1) =>
% 98.91/13.05 ((
% 98.91/13.05 (funcGraphProp3) =>
% 98.91/13.05 ((
% 98.91/13.05 (funcGraphProp2) =>
% 98.91/13.05 ((
% 98.91/13.05 (funcextLem) =>
% 98.91/13.05 ((
% 98.91/13.05 (funcGraphProp4) =>
% 98.91/13.05 ((
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% 98.91/13.05 ((
% 98.91/13.05 (eqbreln) =>
% 98.91/13.05 ((
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% 98.91/13.05 ((
% 98.91/13.05 (funcext2) =>
% 98.91/13.05 ((
% 98.91/13.05 (ap2apEq1) =>
% 98.91/13.05 ((
% 98.91/13.05 (ap2apEq2) =>
% 98.91/13.05 ((
% 98.91/13.05 (beta1) =>
% 98.91/13.05 ((
% 98.91/13.05 (eta1) =>
% 98.91/13.05 ((
% 98.91/13.05 (lam2lamEq) =>
% 98.91/13.05 ((
% 98.91/13.05 (beta2) =>
% 98.91/13.05 ((
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% 98.91/13.05 ((
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% 98.91/13.05 ((
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% 98.91/13.05 ((
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% 98.91/13.05 ((
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% 98.91/13.05 ((
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% 98.91/13.05 ((
% 98.91/13.05 (ifp) =>
% 98.91/13.05 ((
% 98.91/13.05 (theeq) =>
% 98.91/13.05 ((
% 98.91/13.05 (iftrue) =>
% 98.91/13.05 ((
% 98.91/13.05 (iffalse) =>
% 98.91/13.05 ((
% 98.91/13.05 (iftrueorfalse) =>
% 98.91/13.05 ((
% 98.91/13.05 (binintersectT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (powersetT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (setminusT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (setextT) =>
% 98.91/13.05 ((
% 98.91/13.05 (subsetTI) =>
% 98.91/13.05 ((
% 98.91/13.05 (powersetTI1) =>
% 98.91/13.05 ((
% 98.91/13.05 (powersetTE1) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementTI1) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementTE1) =>
% 98.91/13.05 ((
% 98.91/13.05 (binintersectTELcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (binintersectTERcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (contrasubsetT) =>
% 98.91/13.05 ((
% 98.91/13.05 (contrasubsetT1) =>
% 98.91/13.05 ((
% 98.91/13.05 (contrasubsetT2) =>
% 98.91/13.05 ((
% 98.91/13.05 (contrasubsetT3) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementI1) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementE1) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementSub1) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementSub2) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementEq) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementTnotintersectT) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementImpComplementIntersect) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementSubsetComplementIntersect) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementInPowersetComplementIntersect) =>
% 98.91/13.05 ((
% 98.91/13.05 (contraSubsetComplement) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementTcontraSubset) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionTILcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionTIRcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (inIntersectImpInUnion) =>
% 98.91/13.05 ((
% 98.91/13.05 (inIntersectImpInUnion2) =>
% 98.91/13.05 ((
% 98.91/13.05 (inIntersectImpInIntersectUnions) =>
% 98.91/13.05 ((
% 98.91/13.05 (intersectInPowersetIntersectUnions) =>
% 98.91/13.05 ((
% 98.91/13.05 (inComplementUnionImpNotIn1) =>
% 98.91/13.05 ((
% 98.91/13.05 (inComplementUnionImpInComplement1) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionTE) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionTEcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2a1) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementUnionInPowersetComplement) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2a2) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan1a) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan1b) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan1) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2a) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2b2) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2b) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule0) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule1) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule2) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule3) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule4) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_1) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_2) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_3) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_4) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_5) =>
% 98.91/13.05 ((
% 98.91/13.05 (breln1all2) =>
% 98.91/13.05 ((
% 98.91/13.05 (breln1SetBreln1) =>
% 98.91/13.05 ((
% 98.91/13.05 (choice2fnsingleton) =>
% 98.91/13.05 ((
% 98.91/13.05 (!!) @ (
% 98.91/13.05 (('#B') @ (
% 98.91/13.05 !!) @
% 98.91/13.05 (
% 98.91/13.05 (
% 98.91/13.05 ('#S') @ (
% 98.91/13.05 (
% 98.91/13.05 ('#B') @ (
% 98.91/13.05 '#B') @
% 98.91/13.05 breln1)) @
% 98.91/13.05 (
% 98.91/13.05 (
% 98.91/13.05 ('#S') @ dpsetconstr @
% 98.91/13.05 (
% 98.91/13.05 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.91/13.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1711])).
% 98.91/13.05 thf(zip_derived_cl1738, plain,
% 98.91/13.05 (~ (((upairequniteq) =>
% 98.91/13.05 (((setukpairinjR2) =>
% 98.91/13.05 (((setukpairinjR) =>
% 98.91/13.05 (((ksndsingleton) =>
% 98.91/13.05 (((ksndpairEq) =>
% 98.91/13.05 (((kpairsurjEq) =>
% 98.91/13.05 (((cartprodsndin) =>
% 98.91/13.05 (((cartprodpairmemEL) =>
% 98.91/13.05 (((cartprodpairmemER) =>
% 98.91/13.05 (((cartprodmempaircEq) =>
% 98.91/13.05 (((cartprodfstpairEq) =>
% 98.91/13.05 (((cartprodsndpairEq) =>
% 98.91/13.05 (((cartprodpairsurjEq) =>
% 98.91/13.05 (((dpsetconstrI) =>
% 98.91/13.05 (((dpsetconstrSub) =>
% 98.91/13.05 (((setOfPairsIsBReln) =>
% 98.91/13.05 (((dpsetconstrERa) =>
% 98.91/13.05 (((dpsetconstrEL1) =>
% 98.91/13.05 (((dpsetconstrEL2) =>
% 98.91/13.05 (((dpsetconstrER) =>
% 98.91/13.05 (((funcImageSingleton) =>
% 98.91/13.05 (((apProp) =>
% 98.91/13.05 (((app) =>
% 98.91/13.05 (((infuncsetfunc) =>
% 98.91/13.05 (((ap2p) =>
% 98.91/13.05 (((funcinfuncset) =>
% 98.91/13.05 (((lamProp) =>
% 98.91/13.05 (((lamp) =>
% 98.91/13.05 (((lam2p) =>
% 98.91/13.05 (((brelnall1) =>
% 98.91/13.05 ((
% 98.91/13.05 (brelnall2) =>
% 98.91/13.05 ((
% 98.91/13.05 (ex1E2) =>
% 98.91/13.05 ((
% 98.91/13.05 (funcGraphProp1) =>
% 98.91/13.05 ((
% 98.91/13.05 (funcGraphProp3) =>
% 98.91/13.05 ((
% 98.91/13.05 (funcGraphProp2) =>
% 98.91/13.05 ((
% 98.91/13.05 (funcextLem) =>
% 98.91/13.05 ((
% 98.91/13.05 (funcGraphProp4) =>
% 98.91/13.05 ((
% 98.91/13.05 (subbreln) =>
% 98.91/13.05 ((
% 98.91/13.05 (eqbreln) =>
% 98.91/13.05 ((
% 98.91/13.05 (funcext) =>
% 98.91/13.05 ((
% 98.91/13.05 (funcext2) =>
% 98.91/13.05 ((
% 98.91/13.05 (ap2apEq1) =>
% 98.91/13.05 ((
% 98.91/13.05 (ap2apEq2) =>
% 98.91/13.05 ((
% 98.91/13.05 (beta1) =>
% 98.91/13.05 ((
% 98.91/13.05 (eta1) =>
% 98.91/13.05 ((
% 98.91/13.05 (lam2lamEq) =>
% 98.91/13.05 ((
% 98.91/13.05 (beta2) =>
% 98.91/13.05 ((
% 98.91/13.05 (eta2) =>
% 98.91/13.05 ((
% 98.91/13.05 (iffalseProp1) =>
% 98.91/13.05 ((
% 98.91/13.05 (iffalseProp2) =>
% 98.91/13.05 ((
% 98.91/13.05 (iftrueProp1) =>
% 98.91/13.05 ((
% 98.91/13.05 (iftrueProp2) =>
% 98.91/13.05 ((
% 98.91/13.05 (ifSingleton) =>
% 98.91/13.05 ((
% 98.91/13.05 (ifp) =>
% 98.91/13.05 ((
% 98.91/13.05 (theeq) =>
% 98.91/13.05 ((
% 98.91/13.05 (iftrue) =>
% 98.91/13.05 ((
% 98.91/13.05 (iffalse) =>
% 98.91/13.05 ((
% 98.91/13.05 (iftrueorfalse) =>
% 98.91/13.05 ((
% 98.91/13.05 (binintersectT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (powersetT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (setminusT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (setextT) =>
% 98.91/13.05 ((
% 98.91/13.05 (subsetTI) =>
% 98.91/13.05 ((
% 98.91/13.05 (powersetTI1) =>
% 98.91/13.05 ((
% 98.91/13.05 (powersetTE1) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementTI1) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementTE1) =>
% 98.91/13.05 ((
% 98.91/13.05 (binintersectTELcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (binintersectTERcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (contrasubsetT) =>
% 98.91/13.05 ((
% 98.91/13.05 (contrasubsetT1) =>
% 98.91/13.05 ((
% 98.91/13.05 (contrasubsetT2) =>
% 98.91/13.05 ((
% 98.91/13.05 (contrasubsetT3) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementI1) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementE1) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementSub1) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementSub2) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementEq) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementTnotintersectT) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementImpComplementIntersect) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementSubsetComplementIntersect) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementInPowersetComplementIntersect) =>
% 98.91/13.05 ((
% 98.91/13.05 (contraSubsetComplement) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementTcontraSubset) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionTILcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionTIRcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (inIntersectImpInUnion) =>
% 98.91/13.05 ((
% 98.91/13.05 (inIntersectImpInUnion2) =>
% 98.91/13.05 ((
% 98.91/13.05 (inIntersectImpInIntersectUnions) =>
% 98.91/13.05 ((
% 98.91/13.05 (intersectInPowersetIntersectUnions) =>
% 98.91/13.05 ((
% 98.91/13.05 (inComplementUnionImpNotIn1) =>
% 98.91/13.05 ((
% 98.91/13.05 (inComplementUnionImpInComplement1) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionTE) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionTEcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2a1) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementUnionInPowersetComplement) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2a2) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan1a) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan1b) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan1) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2a) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2b2) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2b) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule0) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule1) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule2) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule3) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule4) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_1) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_2) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_3) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_4) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_5) =>
% 98.91/13.05 ((
% 98.91/13.05 (breln1all2) =>
% 98.91/13.05 ((
% 98.91/13.05 (breln1SetBreln1) =>
% 98.91/13.05 ((
% 98.91/13.05 (choice2fnsingleton) =>
% 98.91/13.05 ((
% 98.91/13.05 (!!) @ (
% 98.91/13.05 (('#B') @ (
% 98.91/13.05 !!) @
% 98.91/13.05 (
% 98.91/13.05 (
% 98.91/13.05 ('#S') @ (
% 98.91/13.05 (
% 98.91/13.05 ('#B') @ (
% 98.91/13.05 '#B') @
% 98.91/13.05 breln1)) @
% 98.91/13.05 (
% 98.91/13.05 (
% 98.91/13.05 ('#S') @ dpsetconstr @
% 98.91/13.05 (
% 98.91/13.05 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.91/13.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1725])).
% 98.91/13.05 thf(zip_derived_cl1749, plain,
% 98.91/13.05 (~ (((setukpairinjR2) =>
% 98.91/13.05 (((setukpairinjR) =>
% 98.91/13.05 (((ksndsingleton) =>
% 98.91/13.05 (((ksndpairEq) =>
% 98.91/13.05 (((kpairsurjEq) =>
% 98.91/13.05 (((cartprodsndin) =>
% 98.91/13.05 (((cartprodpairmemEL) =>
% 98.91/13.05 (((cartprodpairmemER) =>
% 98.91/13.05 (((cartprodmempaircEq) =>
% 98.91/13.05 (((cartprodfstpairEq) =>
% 98.91/13.05 (((cartprodsndpairEq) =>
% 98.91/13.05 (((cartprodpairsurjEq) =>
% 98.91/13.05 (((dpsetconstrI) =>
% 98.91/13.05 (((dpsetconstrSub) =>
% 98.91/13.05 (((setOfPairsIsBReln) =>
% 98.91/13.05 (((dpsetconstrERa) =>
% 98.91/13.05 (((dpsetconstrEL1) =>
% 98.91/13.05 (((dpsetconstrEL2) =>
% 98.91/13.05 (((dpsetconstrER) =>
% 98.91/13.05 (((funcImageSingleton) =>
% 98.91/13.05 (((apProp) =>
% 98.91/13.05 (((app) =>
% 98.91/13.05 (((infuncsetfunc) =>
% 98.91/13.05 (((ap2p) =>
% 98.91/13.05 (((funcinfuncset) =>
% 98.91/13.05 (((lamProp) =>
% 98.91/13.05 (((lamp) =>
% 98.91/13.05 (((lam2p) =>
% 98.91/13.05 (((brelnall1) =>
% 98.91/13.05 (((brelnall2) =>
% 98.91/13.05 ((
% 98.91/13.05 (ex1E2) =>
% 98.91/13.05 ((
% 98.91/13.05 (funcGraphProp1) =>
% 98.91/13.05 ((
% 98.91/13.05 (funcGraphProp3) =>
% 98.91/13.05 ((
% 98.91/13.05 (funcGraphProp2) =>
% 98.91/13.05 ((
% 98.91/13.05 (funcextLem) =>
% 98.91/13.05 ((
% 98.91/13.05 (funcGraphProp4) =>
% 98.91/13.05 ((
% 98.91/13.05 (subbreln) =>
% 98.91/13.05 ((
% 98.91/13.05 (eqbreln) =>
% 98.91/13.05 ((
% 98.91/13.05 (funcext) =>
% 98.91/13.05 ((
% 98.91/13.05 (funcext2) =>
% 98.91/13.05 ((
% 98.91/13.05 (ap2apEq1) =>
% 98.91/13.05 ((
% 98.91/13.05 (ap2apEq2) =>
% 98.91/13.05 ((
% 98.91/13.05 (beta1) =>
% 98.91/13.05 ((
% 98.91/13.05 (eta1) =>
% 98.91/13.05 ((
% 98.91/13.05 (lam2lamEq) =>
% 98.91/13.05 ((
% 98.91/13.05 (beta2) =>
% 98.91/13.05 ((
% 98.91/13.05 (eta2) =>
% 98.91/13.05 ((
% 98.91/13.05 (iffalseProp1) =>
% 98.91/13.05 ((
% 98.91/13.05 (iffalseProp2) =>
% 98.91/13.05 ((
% 98.91/13.05 (iftrueProp1) =>
% 98.91/13.05 ((
% 98.91/13.05 (iftrueProp2) =>
% 98.91/13.05 ((
% 98.91/13.05 (ifSingleton) =>
% 98.91/13.05 ((
% 98.91/13.05 (ifp) =>
% 98.91/13.05 ((
% 98.91/13.05 (theeq) =>
% 98.91/13.05 ((
% 98.91/13.05 (iftrue) =>
% 98.91/13.05 ((
% 98.91/13.05 (iffalse) =>
% 98.91/13.05 ((
% 98.91/13.05 (iftrueorfalse) =>
% 98.91/13.05 ((
% 98.91/13.05 (binintersectT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (powersetT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (setminusT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (setextT) =>
% 98.91/13.05 ((
% 98.91/13.05 (subsetTI) =>
% 98.91/13.05 ((
% 98.91/13.05 (powersetTI1) =>
% 98.91/13.05 ((
% 98.91/13.05 (powersetTE1) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementTI1) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementTE1) =>
% 98.91/13.05 ((
% 98.91/13.05 (binintersectTELcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (binintersectTERcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (contrasubsetT) =>
% 98.91/13.05 ((
% 98.91/13.05 (contrasubsetT1) =>
% 98.91/13.05 ((
% 98.91/13.05 (contrasubsetT2) =>
% 98.91/13.05 ((
% 98.91/13.05 (contrasubsetT3) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementI1) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementE1) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementSub1) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementSub2) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementEq) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementTnotintersectT) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementImpComplementIntersect) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementSubsetComplementIntersect) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementInPowersetComplementIntersect) =>
% 98.91/13.05 ((
% 98.91/13.05 (contraSubsetComplement) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementTcontraSubset) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionTILcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionTIRcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (inIntersectImpInUnion) =>
% 98.91/13.05 ((
% 98.91/13.05 (inIntersectImpInUnion2) =>
% 98.91/13.05 ((
% 98.91/13.05 (inIntersectImpInIntersectUnions) =>
% 98.91/13.05 ((
% 98.91/13.05 (intersectInPowersetIntersectUnions) =>
% 98.91/13.05 ((
% 98.91/13.05 (inComplementUnionImpNotIn1) =>
% 98.91/13.05 ((
% 98.91/13.05 (inComplementUnionImpInComplement1) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionTE) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionTEcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2a1) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementUnionInPowersetComplement) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2a2) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan1a) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan1b) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan1) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2a) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2b2) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2b) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule0) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule1) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule2) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule3) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule4) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_1) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_2) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_3) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_4) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_5) =>
% 98.91/13.05 ((
% 98.91/13.05 (breln1all2) =>
% 98.91/13.05 ((
% 98.91/13.05 (breln1SetBreln1) =>
% 98.91/13.05 ((
% 98.91/13.05 (choice2fnsingleton) =>
% 98.91/13.05 ((
% 98.91/13.05 (!!) @ (
% 98.91/13.05 (('#B') @ (
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% 98.91/13.05 (
% 98.91/13.05 (
% 98.91/13.05 ('#S') @ (
% 98.91/13.05 (
% 98.91/13.05 ('#B') @ (
% 98.91/13.05 '#B') @
% 98.91/13.05 breln1)) @
% 98.91/13.05 (
% 98.91/13.05 (
% 98.91/13.05 ('#S') @ dpsetconstr @
% 98.91/13.05 (
% 98.91/13.05 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.91/13.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1738])).
% 98.91/13.05 thf(zip_derived_cl1760, plain,
% 98.91/13.05 (~ (((setukpairinjR) =>
% 98.91/13.05 (((ksndsingleton) =>
% 98.91/13.05 (((ksndpairEq) =>
% 98.91/13.05 (((kpairsurjEq) =>
% 98.91/13.05 (((cartprodsndin) =>
% 98.91/13.05 (((cartprodpairmemEL) =>
% 98.91/13.05 (((cartprodpairmemER) =>
% 98.91/13.05 (((cartprodmempaircEq) =>
% 98.91/13.05 (((cartprodfstpairEq) =>
% 98.91/13.05 (((cartprodsndpairEq) =>
% 98.91/13.05 (((cartprodpairsurjEq) =>
% 98.91/13.05 (((dpsetconstrI) =>
% 98.91/13.05 (((dpsetconstrSub) =>
% 98.91/13.05 (((setOfPairsIsBReln) =>
% 98.91/13.05 (((dpsetconstrERa) =>
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% 98.91/13.05 (((dpsetconstrEL2) =>
% 98.91/13.05 (((dpsetconstrER) =>
% 98.91/13.05 (((funcImageSingleton) =>
% 98.91/13.05 (((apProp) =>
% 98.91/13.05 (((app) =>
% 98.91/13.05 (((infuncsetfunc) =>
% 98.91/13.05 (((ap2p) =>
% 98.91/13.05 (((funcinfuncset) =>
% 98.91/13.05 (((lamProp) =>
% 98.91/13.05 (((lamp) =>
% 98.91/13.05 (((lam2p) =>
% 98.91/13.05 (((brelnall1) =>
% 98.91/13.05 (((brelnall2) =>
% 98.91/13.05 (((ex1E2) =>
% 98.91/13.05 ((
% 98.91/13.05 (funcGraphProp1) =>
% 98.91/13.05 ((
% 98.91/13.05 (funcGraphProp3) =>
% 98.91/13.05 ((
% 98.91/13.05 (funcGraphProp2) =>
% 98.91/13.05 ((
% 98.91/13.05 (funcextLem) =>
% 98.91/13.05 ((
% 98.91/13.05 (funcGraphProp4) =>
% 98.91/13.05 ((
% 98.91/13.05 (subbreln) =>
% 98.91/13.05 ((
% 98.91/13.05 (eqbreln) =>
% 98.91/13.05 ((
% 98.91/13.05 (funcext) =>
% 98.91/13.05 ((
% 98.91/13.05 (funcext2) =>
% 98.91/13.05 ((
% 98.91/13.05 (ap2apEq1) =>
% 98.91/13.05 ((
% 98.91/13.05 (ap2apEq2) =>
% 98.91/13.05 ((
% 98.91/13.05 (beta1) =>
% 98.91/13.05 ((
% 98.91/13.05 (eta1) =>
% 98.91/13.05 ((
% 98.91/13.05 (lam2lamEq) =>
% 98.91/13.05 ((
% 98.91/13.05 (beta2) =>
% 98.91/13.05 ((
% 98.91/13.05 (eta2) =>
% 98.91/13.05 ((
% 98.91/13.05 (iffalseProp1) =>
% 98.91/13.05 ((
% 98.91/13.05 (iffalseProp2) =>
% 98.91/13.05 ((
% 98.91/13.05 (iftrueProp1) =>
% 98.91/13.05 ((
% 98.91/13.05 (iftrueProp2) =>
% 98.91/13.05 ((
% 98.91/13.05 (ifSingleton) =>
% 98.91/13.05 ((
% 98.91/13.05 (ifp) =>
% 98.91/13.05 ((
% 98.91/13.05 (theeq) =>
% 98.91/13.05 ((
% 98.91/13.05 (iftrue) =>
% 98.91/13.05 ((
% 98.91/13.05 (iffalse) =>
% 98.91/13.05 ((
% 98.91/13.05 (iftrueorfalse) =>
% 98.91/13.05 ((
% 98.91/13.05 (binintersectT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (powersetT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (setminusT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (setextT) =>
% 98.91/13.05 ((
% 98.91/13.05 (subsetTI) =>
% 98.91/13.05 ((
% 98.91/13.05 (powersetTI1) =>
% 98.91/13.05 ((
% 98.91/13.05 (powersetTE1) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementTI1) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementTE1) =>
% 98.91/13.05 ((
% 98.91/13.05 (binintersectTELcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (binintersectTERcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (contrasubsetT) =>
% 98.91/13.05 ((
% 98.91/13.05 (contrasubsetT1) =>
% 98.91/13.05 ((
% 98.91/13.05 (contrasubsetT2) =>
% 98.91/13.05 ((
% 98.91/13.05 (contrasubsetT3) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementI1) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementE1) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementSub1) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementSub2) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementEq) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementTnotintersectT) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementImpComplementIntersect) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementSubsetComplementIntersect) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementInPowersetComplementIntersect) =>
% 98.91/13.05 ((
% 98.91/13.05 (contraSubsetComplement) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementTcontraSubset) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionTILcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionTIRcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (inIntersectImpInUnion) =>
% 98.91/13.05 ((
% 98.91/13.05 (inIntersectImpInUnion2) =>
% 98.91/13.05 ((
% 98.91/13.05 (inIntersectImpInIntersectUnions) =>
% 98.91/13.05 ((
% 98.91/13.05 (intersectInPowersetIntersectUnions) =>
% 98.91/13.05 ((
% 98.91/13.05 (inComplementUnionImpNotIn1) =>
% 98.91/13.05 ((
% 98.91/13.05 (inComplementUnionImpInComplement1) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionTE) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionTEcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2a1) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementUnionInPowersetComplement) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2a2) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan1a) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan1b) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan1) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2a) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2b2) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2b) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule0) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule1) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule2) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule3) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule4) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_1) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_2) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_3) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_4) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_5) =>
% 98.91/13.05 ((
% 98.91/13.05 (breln1all2) =>
% 98.91/13.05 ((
% 98.91/13.05 (breln1SetBreln1) =>
% 98.91/13.05 ((
% 98.91/13.05 (choice2fnsingleton) =>
% 98.91/13.05 ((
% 98.91/13.05 (!!) @ (
% 98.91/13.05 (('#B') @ (
% 98.91/13.05 !!) @
% 98.91/13.05 (
% 98.91/13.05 (
% 98.91/13.05 ('#S') @ (
% 98.91/13.05 (
% 98.91/13.05 ('#B') @ (
% 98.91/13.05 '#B') @
% 98.91/13.05 breln1)) @
% 98.91/13.05 (
% 98.91/13.05 (
% 98.91/13.05 ('#S') @ dpsetconstr @
% 98.91/13.05 (
% 98.91/13.05 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.91/13.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1749])).
% 98.91/13.05 thf(zip_derived_cl1770, plain,
% 98.91/13.05 (~ (((ksndsingleton) =>
% 98.91/13.05 (((ksndpairEq) =>
% 98.91/13.05 (((kpairsurjEq) =>
% 98.91/13.05 (((cartprodsndin) =>
% 98.91/13.05 (((cartprodpairmemEL) =>
% 98.91/13.05 (((cartprodpairmemER) =>
% 98.91/13.05 (((cartprodmempaircEq) =>
% 98.91/13.05 (((cartprodfstpairEq) =>
% 98.91/13.05 (((cartprodsndpairEq) =>
% 98.91/13.05 (((cartprodpairsurjEq) =>
% 98.91/13.05 (((dpsetconstrI) =>
% 98.91/13.05 (((dpsetconstrSub) =>
% 98.91/13.05 (((setOfPairsIsBReln) =>
% 98.91/13.05 (((dpsetconstrERa) =>
% 98.91/13.05 (((dpsetconstrEL1) =>
% 98.91/13.05 (((dpsetconstrEL2) =>
% 98.91/13.05 (((dpsetconstrER) =>
% 98.91/13.05 (((funcImageSingleton) =>
% 98.91/13.05 (((apProp) =>
% 98.91/13.05 (((app) =>
% 98.91/13.05 (((infuncsetfunc) =>
% 98.91/13.05 (((ap2p) =>
% 98.91/13.05 (((funcinfuncset) =>
% 98.91/13.05 (((lamProp) =>
% 98.91/13.05 (((lamp) =>
% 98.91/13.05 (((lam2p) =>
% 98.91/13.05 (((brelnall1) =>
% 98.91/13.05 (((brelnall2) =>
% 98.91/13.05 (((ex1E2) =>
% 98.91/13.05 (((funcGraphProp1) =>
% 98.91/13.05 ((
% 98.91/13.05 (funcGraphProp3) =>
% 98.91/13.05 ((
% 98.91/13.05 (funcGraphProp2) =>
% 98.91/13.05 ((
% 98.91/13.05 (funcextLem) =>
% 98.91/13.05 ((
% 98.91/13.05 (funcGraphProp4) =>
% 98.91/13.05 ((
% 98.91/13.05 (subbreln) =>
% 98.91/13.05 ((
% 98.91/13.05 (eqbreln) =>
% 98.91/13.05 ((
% 98.91/13.05 (funcext) =>
% 98.91/13.05 ((
% 98.91/13.05 (funcext2) =>
% 98.91/13.05 ((
% 98.91/13.05 (ap2apEq1) =>
% 98.91/13.05 ((
% 98.91/13.05 (ap2apEq2) =>
% 98.91/13.05 ((
% 98.91/13.05 (beta1) =>
% 98.91/13.05 ((
% 98.91/13.05 (eta1) =>
% 98.91/13.05 ((
% 98.91/13.05 (lam2lamEq) =>
% 98.91/13.05 ((
% 98.91/13.05 (beta2) =>
% 98.91/13.05 ((
% 98.91/13.05 (eta2) =>
% 98.91/13.05 ((
% 98.91/13.05 (iffalseProp1) =>
% 98.91/13.05 ((
% 98.91/13.05 (iffalseProp2) =>
% 98.91/13.05 ((
% 98.91/13.05 (iftrueProp1) =>
% 98.91/13.05 ((
% 98.91/13.05 (iftrueProp2) =>
% 98.91/13.05 ((
% 98.91/13.05 (ifSingleton) =>
% 98.91/13.05 ((
% 98.91/13.05 (ifp) =>
% 98.91/13.05 ((
% 98.91/13.05 (theeq) =>
% 98.91/13.05 ((
% 98.91/13.05 (iftrue) =>
% 98.91/13.05 ((
% 98.91/13.05 (iffalse) =>
% 98.91/13.05 ((
% 98.91/13.05 (iftrueorfalse) =>
% 98.91/13.05 ((
% 98.91/13.05 (binintersectT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (powersetT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (setminusT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (setextT) =>
% 98.91/13.05 ((
% 98.91/13.05 (subsetTI) =>
% 98.91/13.05 ((
% 98.91/13.05 (powersetTI1) =>
% 98.91/13.05 ((
% 98.91/13.05 (powersetTE1) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementTI1) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementTE1) =>
% 98.91/13.05 ((
% 98.91/13.05 (binintersectTELcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (binintersectTERcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (contrasubsetT) =>
% 98.91/13.05 ((
% 98.91/13.05 (contrasubsetT1) =>
% 98.91/13.05 ((
% 98.91/13.05 (contrasubsetT2) =>
% 98.91/13.05 ((
% 98.91/13.05 (contrasubsetT3) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementI1) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementE1) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementSub1) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementSub2) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementEq) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementTnotintersectT) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementImpComplementIntersect) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementSubsetComplementIntersect) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementInPowersetComplementIntersect) =>
% 98.91/13.05 ((
% 98.91/13.05 (contraSubsetComplement) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementTcontraSubset) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionTILcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionTIRcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (inIntersectImpInUnion) =>
% 98.91/13.05 ((
% 98.91/13.05 (inIntersectImpInUnion2) =>
% 98.91/13.05 ((
% 98.91/13.05 (inIntersectImpInIntersectUnions) =>
% 98.91/13.05 ((
% 98.91/13.05 (intersectInPowersetIntersectUnions) =>
% 98.91/13.05 ((
% 98.91/13.05 (inComplementUnionImpNotIn1) =>
% 98.91/13.05 ((
% 98.91/13.05 (inComplementUnionImpInComplement1) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionTE) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionTEcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2a1) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementUnionInPowersetComplement) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2a2) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan1a) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan1b) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan1) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2a) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2b2) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2b) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule0) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule1) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule2) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule3) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule4) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_1) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_2) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_3) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_4) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_5) =>
% 98.91/13.05 ((
% 98.91/13.05 (breln1all2) =>
% 98.91/13.05 ((
% 98.91/13.05 (breln1SetBreln1) =>
% 98.91/13.05 ((
% 98.91/13.05 (choice2fnsingleton) =>
% 98.91/13.05 ((
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% 98.91/13.05 (('#B') @ (
% 98.91/13.05 !!) @
% 98.91/13.05 (
% 98.91/13.05 (
% 98.91/13.05 ('#S') @ (
% 98.91/13.05 (
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% 98.91/13.05 (
% 98.91/13.05 (
% 98.91/13.05 ('#S') @ dpsetconstr @
% 98.91/13.05 (
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% 98.91/13.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1760])).
% 98.91/13.05 thf(zip_derived_cl1779, plain,
% 98.91/13.05 (~ (((ksndpairEq) =>
% 98.91/13.05 (((kpairsurjEq) =>
% 98.91/13.05 (((cartprodsndin) =>
% 98.91/13.05 (((cartprodpairmemEL) =>
% 98.91/13.05 (((cartprodpairmemER) =>
% 98.91/13.05 (((cartprodmempaircEq) =>
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% 98.91/13.05 (((cartprodsndpairEq) =>
% 98.91/13.05 (((cartprodpairsurjEq) =>
% 98.91/13.05 (((dpsetconstrI) =>
% 98.91/13.05 (((dpsetconstrSub) =>
% 98.91/13.05 (((setOfPairsIsBReln) =>
% 98.91/13.05 (((dpsetconstrERa) =>
% 98.91/13.05 (((dpsetconstrEL1) =>
% 98.91/13.05 (((dpsetconstrEL2) =>
% 98.91/13.05 (((dpsetconstrER) =>
% 98.91/13.05 (((funcImageSingleton) =>
% 98.91/13.05 (((apProp) =>
% 98.91/13.05 (((app) =>
% 98.91/13.05 (((infuncsetfunc) =>
% 98.91/13.05 (((ap2p) =>
% 98.91/13.05 (((funcinfuncset) =>
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% 98.91/13.05 (((lam2p) =>
% 98.91/13.05 (((brelnall1) =>
% 98.91/13.05 (((brelnall2) =>
% 98.91/13.05 (((ex1E2) =>
% 98.91/13.05 (((funcGraphProp1) =>
% 98.91/13.05 (((funcGraphProp3) =>
% 98.91/13.05 ((
% 98.91/13.05 (funcGraphProp2) =>
% 98.91/13.05 ((
% 98.91/13.05 (funcextLem) =>
% 98.91/13.05 ((
% 98.91/13.05 (funcGraphProp4) =>
% 98.91/13.05 ((
% 98.91/13.05 (subbreln) =>
% 98.91/13.05 ((
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% 98.91/13.05 ((
% 98.91/13.05 (funcext) =>
% 98.91/13.05 ((
% 98.91/13.05 (funcext2) =>
% 98.91/13.05 ((
% 98.91/13.05 (ap2apEq1) =>
% 98.91/13.05 ((
% 98.91/13.05 (ap2apEq2) =>
% 98.91/13.05 ((
% 98.91/13.05 (beta1) =>
% 98.91/13.05 ((
% 98.91/13.05 (eta1) =>
% 98.91/13.05 ((
% 98.91/13.05 (lam2lamEq) =>
% 98.91/13.05 ((
% 98.91/13.05 (beta2) =>
% 98.91/13.05 ((
% 98.91/13.05 (eta2) =>
% 98.91/13.05 ((
% 98.91/13.05 (iffalseProp1) =>
% 98.91/13.05 ((
% 98.91/13.05 (iffalseProp2) =>
% 98.91/13.05 ((
% 98.91/13.05 (iftrueProp1) =>
% 98.91/13.05 ((
% 98.91/13.05 (iftrueProp2) =>
% 98.91/13.05 ((
% 98.91/13.05 (ifSingleton) =>
% 98.91/13.05 ((
% 98.91/13.05 (ifp) =>
% 98.91/13.05 ((
% 98.91/13.05 (theeq) =>
% 98.91/13.05 ((
% 98.91/13.05 (iftrue) =>
% 98.91/13.05 ((
% 98.91/13.05 (iffalse) =>
% 98.91/13.05 ((
% 98.91/13.05 (iftrueorfalse) =>
% 98.91/13.05 ((
% 98.91/13.05 (binintersectT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (powersetT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (setminusT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (setextT) =>
% 98.91/13.05 ((
% 98.91/13.05 (subsetTI) =>
% 98.91/13.05 ((
% 98.91/13.05 (powersetTI1) =>
% 98.91/13.05 ((
% 98.91/13.05 (powersetTE1) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementTI1) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementTE1) =>
% 98.91/13.05 ((
% 98.91/13.05 (binintersectTELcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (binintersectTERcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (contrasubsetT) =>
% 98.91/13.05 ((
% 98.91/13.05 (contrasubsetT1) =>
% 98.91/13.05 ((
% 98.91/13.05 (contrasubsetT2) =>
% 98.91/13.05 ((
% 98.91/13.05 (contrasubsetT3) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementI1) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementE1) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementSub1) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementSub2) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementEq) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementTnotintersectT) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementImpComplementIntersect) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementSubsetComplementIntersect) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementInPowersetComplementIntersect) =>
% 98.91/13.05 ((
% 98.91/13.05 (contraSubsetComplement) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementTcontraSubset) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionTILcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionTIRcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (inIntersectImpInUnion) =>
% 98.91/13.05 ((
% 98.91/13.05 (inIntersectImpInUnion2) =>
% 98.91/13.05 ((
% 98.91/13.05 (inIntersectImpInIntersectUnions) =>
% 98.91/13.05 ((
% 98.91/13.05 (intersectInPowersetIntersectUnions) =>
% 98.91/13.05 ((
% 98.91/13.05 (inComplementUnionImpNotIn1) =>
% 98.91/13.05 ((
% 98.91/13.05 (inComplementUnionImpInComplement1) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionTE) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionTEcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2a1) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementUnionInPowersetComplement) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2a2) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan1a) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan1b) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan1) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2a) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2b2) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2b) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule0) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule1) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule2) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule3) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule4) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_1) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_2) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_3) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_4) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_5) =>
% 98.91/13.05 ((
% 98.91/13.05 (breln1all2) =>
% 98.91/13.05 ((
% 98.91/13.05 (breln1SetBreln1) =>
% 98.91/13.05 ((
% 98.91/13.05 (choice2fnsingleton) =>
% 98.91/13.05 ((
% 98.91/13.05 (!!) @ (
% 98.91/13.05 (('#B') @ (
% 98.91/13.05 !!) @
% 98.91/13.05 (
% 98.91/13.05 (
% 98.91/13.05 ('#S') @ (
% 98.91/13.05 (
% 98.91/13.05 ('#B') @ (
% 98.91/13.05 '#B') @
% 98.91/13.05 breln1)) @
% 98.91/13.05 (
% 98.91/13.05 (
% 98.91/13.05 ('#S') @ dpsetconstr @
% 98.91/13.05 (
% 98.91/13.05 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.91/13.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1770])).
% 98.91/13.05 thf(zip_derived_cl1787, plain,
% 98.91/13.05 (~ (((kpairsurjEq) =>
% 98.91/13.05 (((cartprodsndin) =>
% 98.91/13.05 (((cartprodpairmemEL) =>
% 98.91/13.05 (((cartprodpairmemER) =>
% 98.91/13.05 (((cartprodmempaircEq) =>
% 98.91/13.05 (((cartprodfstpairEq) =>
% 98.91/13.05 (((cartprodsndpairEq) =>
% 98.91/13.05 (((cartprodpairsurjEq) =>
% 98.91/13.05 (((dpsetconstrI) =>
% 98.91/13.05 (((dpsetconstrSub) =>
% 98.91/13.05 (((setOfPairsIsBReln) =>
% 98.91/13.05 (((dpsetconstrERa) =>
% 98.91/13.05 (((dpsetconstrEL1) =>
% 98.91/13.05 (((dpsetconstrEL2) =>
% 98.91/13.05 (((dpsetconstrER) =>
% 98.91/13.05 (((funcImageSingleton) =>
% 98.91/13.05 (((apProp) =>
% 98.91/13.05 (((app) =>
% 98.91/13.05 (((infuncsetfunc) =>
% 98.91/13.05 (((ap2p) =>
% 98.91/13.05 (((funcinfuncset) =>
% 98.91/13.05 (((lamProp) =>
% 98.91/13.05 (((lamp) =>
% 98.91/13.05 (((lam2p) =>
% 98.91/13.05 (((brelnall1) =>
% 98.91/13.05 (((brelnall2) =>
% 98.91/13.05 (((ex1E2) =>
% 98.91/13.05 (((funcGraphProp1) =>
% 98.91/13.05 (((funcGraphProp3) =>
% 98.91/13.05 (((funcGraphProp2) =>
% 98.91/13.05 ((
% 98.91/13.05 (funcextLem) =>
% 98.91/13.05 ((
% 98.91/13.05 (funcGraphProp4) =>
% 98.91/13.05 ((
% 98.91/13.05 (subbreln) =>
% 98.91/13.05 ((
% 98.91/13.05 (eqbreln) =>
% 98.91/13.05 ((
% 98.91/13.05 (funcext) =>
% 98.91/13.05 ((
% 98.91/13.05 (funcext2) =>
% 98.91/13.05 ((
% 98.91/13.05 (ap2apEq1) =>
% 98.91/13.05 ((
% 98.91/13.05 (ap2apEq2) =>
% 98.91/13.05 ((
% 98.91/13.05 (beta1) =>
% 98.91/13.05 ((
% 98.91/13.05 (eta1) =>
% 98.91/13.05 ((
% 98.91/13.05 (lam2lamEq) =>
% 98.91/13.05 ((
% 98.91/13.05 (beta2) =>
% 98.91/13.05 ((
% 98.91/13.05 (eta2) =>
% 98.91/13.05 ((
% 98.91/13.05 (iffalseProp1) =>
% 98.91/13.05 ((
% 98.91/13.05 (iffalseProp2) =>
% 98.91/13.05 ((
% 98.91/13.05 (iftrueProp1) =>
% 98.91/13.05 ((
% 98.91/13.05 (iftrueProp2) =>
% 98.91/13.05 ((
% 98.91/13.05 (ifSingleton) =>
% 98.91/13.05 ((
% 98.91/13.05 (ifp) =>
% 98.91/13.05 ((
% 98.91/13.05 (theeq) =>
% 98.91/13.05 ((
% 98.91/13.05 (iftrue) =>
% 98.91/13.05 ((
% 98.91/13.05 (iffalse) =>
% 98.91/13.05 ((
% 98.91/13.05 (iftrueorfalse) =>
% 98.91/13.05 ((
% 98.91/13.05 (binintersectT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (powersetT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (setminusT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (setextT) =>
% 98.91/13.05 ((
% 98.91/13.05 (subsetTI) =>
% 98.91/13.05 ((
% 98.91/13.05 (powersetTI1) =>
% 98.91/13.05 ((
% 98.91/13.05 (powersetTE1) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementTI1) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementTE1) =>
% 98.91/13.05 ((
% 98.91/13.05 (binintersectTELcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (binintersectTERcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (contrasubsetT) =>
% 98.91/13.05 ((
% 98.91/13.05 (contrasubsetT1) =>
% 98.91/13.05 ((
% 98.91/13.05 (contrasubsetT2) =>
% 98.91/13.05 ((
% 98.91/13.05 (contrasubsetT3) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementI1) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementE1) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementSub1) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementSub2) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementEq) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementTnotintersectT) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementImpComplementIntersect) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementSubsetComplementIntersect) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementInPowersetComplementIntersect) =>
% 98.91/13.05 ((
% 98.91/13.05 (contraSubsetComplement) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementTcontraSubset) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionTILcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionTIRcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (inIntersectImpInUnion) =>
% 98.91/13.05 ((
% 98.91/13.05 (inIntersectImpInUnion2) =>
% 98.91/13.05 ((
% 98.91/13.05 (inIntersectImpInIntersectUnions) =>
% 98.91/13.05 ((
% 98.91/13.05 (intersectInPowersetIntersectUnions) =>
% 98.91/13.05 ((
% 98.91/13.05 (inComplementUnionImpNotIn1) =>
% 98.91/13.05 ((
% 98.91/13.05 (inComplementUnionImpInComplement1) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionTE) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionTEcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2a1) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementUnionInPowersetComplement) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2a2) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan1a) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan1b) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan1) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2a) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2b2) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2b) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule0) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule1) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule2) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule3) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule4) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_1) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_2) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_3) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_4) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_5) =>
% 98.91/13.05 ((
% 98.91/13.05 (breln1all2) =>
% 98.91/13.05 ((
% 98.91/13.05 (breln1SetBreln1) =>
% 98.91/13.05 ((
% 98.91/13.05 (choice2fnsingleton) =>
% 98.91/13.05 ((
% 98.91/13.05 (!!) @ (
% 98.91/13.05 (('#B') @ (
% 98.91/13.05 !!) @
% 98.91/13.05 (
% 98.91/13.05 (
% 98.91/13.05 ('#S') @ (
% 98.91/13.05 (
% 98.91/13.05 ('#B') @ (
% 98.91/13.05 '#B') @
% 98.91/13.05 breln1)) @
% 98.91/13.05 (
% 98.91/13.05 (
% 98.91/13.05 ('#S') @ dpsetconstr @
% 98.91/13.05 (
% 98.91/13.05 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.91/13.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1779])).
% 98.91/13.05 thf(zip_derived_cl1796, plain,
% 98.91/13.05 (~ (((cartprodsndin) =>
% 98.91/13.05 (((cartprodpairmemEL) =>
% 98.91/13.05 (((cartprodpairmemER) =>
% 98.91/13.05 (((cartprodmempaircEq) =>
% 98.91/13.05 (((cartprodfstpairEq) =>
% 98.91/13.05 (((cartprodsndpairEq) =>
% 98.91/13.05 (((cartprodpairsurjEq) =>
% 98.91/13.05 (((dpsetconstrI) =>
% 98.91/13.05 (((dpsetconstrSub) =>
% 98.91/13.05 (((setOfPairsIsBReln) =>
% 98.91/13.05 (((dpsetconstrERa) =>
% 98.91/13.05 (((dpsetconstrEL1) =>
% 98.91/13.05 (((dpsetconstrEL2) =>
% 98.91/13.05 (((dpsetconstrER) =>
% 98.91/13.05 (((funcImageSingleton) =>
% 98.91/13.05 (((apProp) =>
% 98.91/13.05 (((app) =>
% 98.91/13.05 (((infuncsetfunc) =>
% 98.91/13.05 (((ap2p) =>
% 98.91/13.05 (((funcinfuncset) =>
% 98.91/13.05 (((lamProp) =>
% 98.91/13.05 (((lamp) =>
% 98.91/13.05 (((lam2p) =>
% 98.91/13.05 (((brelnall1) =>
% 98.91/13.05 (((brelnall2) =>
% 98.91/13.05 (((ex1E2) =>
% 98.91/13.05 (((funcGraphProp1) =>
% 98.91/13.05 (((funcGraphProp3) =>
% 98.91/13.05 (((funcGraphProp2) =>
% 98.91/13.05 (((funcextLem) =>
% 98.91/13.05 ((
% 98.91/13.05 (funcGraphProp4) =>
% 98.91/13.05 ((
% 98.91/13.05 (subbreln) =>
% 98.91/13.05 ((
% 98.91/13.05 (eqbreln) =>
% 98.91/13.05 ((
% 98.91/13.05 (funcext) =>
% 98.91/13.05 ((
% 98.91/13.05 (funcext2) =>
% 98.91/13.05 ((
% 98.91/13.05 (ap2apEq1) =>
% 98.91/13.05 ((
% 98.91/13.05 (ap2apEq2) =>
% 98.91/13.05 ((
% 98.91/13.05 (beta1) =>
% 98.91/13.05 ((
% 98.91/13.05 (eta1) =>
% 98.91/13.05 ((
% 98.91/13.05 (lam2lamEq) =>
% 98.91/13.05 ((
% 98.91/13.05 (beta2) =>
% 98.91/13.05 ((
% 98.91/13.05 (eta2) =>
% 98.91/13.05 ((
% 98.91/13.05 (iffalseProp1) =>
% 98.91/13.05 ((
% 98.91/13.05 (iffalseProp2) =>
% 98.91/13.05 ((
% 98.91/13.05 (iftrueProp1) =>
% 98.91/13.05 ((
% 98.91/13.05 (iftrueProp2) =>
% 98.91/13.05 ((
% 98.91/13.05 (ifSingleton) =>
% 98.91/13.05 ((
% 98.91/13.05 (ifp) =>
% 98.91/13.05 ((
% 98.91/13.05 (theeq) =>
% 98.91/13.05 ((
% 98.91/13.05 (iftrue) =>
% 98.91/13.05 ((
% 98.91/13.05 (iffalse) =>
% 98.91/13.05 ((
% 98.91/13.05 (iftrueorfalse) =>
% 98.91/13.05 ((
% 98.91/13.05 (binintersectT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (powersetT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (setminusT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (setextT) =>
% 98.91/13.05 ((
% 98.91/13.05 (subsetTI) =>
% 98.91/13.05 ((
% 98.91/13.05 (powersetTI1) =>
% 98.91/13.05 ((
% 98.91/13.05 (powersetTE1) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementTI1) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementTE1) =>
% 98.91/13.05 ((
% 98.91/13.05 (binintersectTELcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (binintersectTERcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (contrasubsetT) =>
% 98.91/13.05 ((
% 98.91/13.05 (contrasubsetT1) =>
% 98.91/13.05 ((
% 98.91/13.05 (contrasubsetT2) =>
% 98.91/13.05 ((
% 98.91/13.05 (contrasubsetT3) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementI1) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementE1) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementSub1) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementSub2) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementEq) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementTnotintersectT) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementImpComplementIntersect) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementSubsetComplementIntersect) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementInPowersetComplementIntersect) =>
% 98.91/13.05 ((
% 98.91/13.05 (contraSubsetComplement) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementTcontraSubset) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionTILcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionTIRcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (inIntersectImpInUnion) =>
% 98.91/13.05 ((
% 98.91/13.05 (inIntersectImpInUnion2) =>
% 98.91/13.05 ((
% 98.91/13.05 (inIntersectImpInIntersectUnions) =>
% 98.91/13.05 ((
% 98.91/13.05 (intersectInPowersetIntersectUnions) =>
% 98.91/13.05 ((
% 98.91/13.05 (inComplementUnionImpNotIn1) =>
% 98.91/13.05 ((
% 98.91/13.05 (inComplementUnionImpInComplement1) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionTE) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionTEcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2a1) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementUnionInPowersetComplement) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2a2) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan1a) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan1b) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan1) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2a) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2b2) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2b) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule0) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule1) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule2) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule3) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule4) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_1) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_2) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_3) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_4) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_5) =>
% 98.91/13.05 ((
% 98.91/13.05 (breln1all2) =>
% 98.91/13.05 ((
% 98.91/13.05 (breln1SetBreln1) =>
% 98.91/13.05 ((
% 98.91/13.05 (choice2fnsingleton) =>
% 98.91/13.05 ((
% 98.91/13.05 (!!) @ (
% 98.91/13.05 (('#B') @ (
% 98.91/13.05 !!) @
% 98.91/13.05 (
% 98.91/13.05 (
% 98.91/13.05 ('#S') @ (
% 98.91/13.05 (
% 98.91/13.05 ('#B') @ (
% 98.91/13.05 '#B') @
% 98.91/13.05 breln1)) @
% 98.91/13.05 (
% 98.91/13.05 (
% 98.91/13.05 ('#S') @ dpsetconstr @
% 98.91/13.05 (
% 98.91/13.05 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.91/13.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1787])).
% 98.91/13.05 thf(zip_derived_cl1807, plain,
% 98.91/13.05 (~ (((cartprodpairmemEL) =>
% 98.91/13.05 (((cartprodpairmemER) =>
% 98.91/13.05 (((cartprodmempaircEq) =>
% 98.91/13.05 (((cartprodfstpairEq) =>
% 98.91/13.05 (((cartprodsndpairEq) =>
% 98.91/13.05 (((cartprodpairsurjEq) =>
% 98.91/13.05 (((dpsetconstrI) =>
% 98.91/13.05 (((dpsetconstrSub) =>
% 98.91/13.05 (((setOfPairsIsBReln) =>
% 98.91/13.05 (((dpsetconstrERa) =>
% 98.91/13.05 (((dpsetconstrEL1) =>
% 98.91/13.05 (((dpsetconstrEL2) =>
% 98.91/13.05 (((dpsetconstrER) =>
% 98.91/13.05 (((funcImageSingleton) =>
% 98.91/13.05 (((apProp) =>
% 98.91/13.05 (((app) =>
% 98.91/13.05 (((infuncsetfunc) =>
% 98.91/13.05 (((ap2p) =>
% 98.91/13.05 (((funcinfuncset) =>
% 98.91/13.05 (((lamProp) =>
% 98.91/13.05 (((lamp) =>
% 98.91/13.05 (((lam2p) =>
% 98.91/13.05 (((brelnall1) =>
% 98.91/13.05 (((brelnall2) =>
% 98.91/13.05 (((ex1E2) =>
% 98.91/13.05 (((funcGraphProp1) =>
% 98.91/13.05 (((funcGraphProp3) =>
% 98.91/13.05 (((funcGraphProp2) =>
% 98.91/13.05 (((funcextLem) =>
% 98.91/13.05 (((funcGraphProp4) =>
% 98.91/13.05 ((
% 98.91/13.05 (subbreln) =>
% 98.91/13.05 ((
% 98.91/13.05 (eqbreln) =>
% 98.91/13.05 ((
% 98.91/13.05 (funcext) =>
% 98.91/13.05 ((
% 98.91/13.05 (funcext2) =>
% 98.91/13.05 ((
% 98.91/13.05 (ap2apEq1) =>
% 98.91/13.05 ((
% 98.91/13.05 (ap2apEq2) =>
% 98.91/13.05 ((
% 98.91/13.05 (beta1) =>
% 98.91/13.05 ((
% 98.91/13.05 (eta1) =>
% 98.91/13.05 ((
% 98.91/13.05 (lam2lamEq) =>
% 98.91/13.05 ((
% 98.91/13.05 (beta2) =>
% 98.91/13.05 ((
% 98.91/13.05 (eta2) =>
% 98.91/13.05 ((
% 98.91/13.05 (iffalseProp1) =>
% 98.91/13.05 ((
% 98.91/13.05 (iffalseProp2) =>
% 98.91/13.05 ((
% 98.91/13.05 (iftrueProp1) =>
% 98.91/13.05 ((
% 98.91/13.05 (iftrueProp2) =>
% 98.91/13.05 ((
% 98.91/13.05 (ifSingleton) =>
% 98.91/13.05 ((
% 98.91/13.05 (ifp) =>
% 98.91/13.05 ((
% 98.91/13.05 (theeq) =>
% 98.91/13.05 ((
% 98.91/13.05 (iftrue) =>
% 98.91/13.05 ((
% 98.91/13.05 (iffalse) =>
% 98.91/13.05 ((
% 98.91/13.05 (iftrueorfalse) =>
% 98.91/13.05 ((
% 98.91/13.05 (binintersectT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (powersetT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (setminusT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (setextT) =>
% 98.91/13.05 ((
% 98.91/13.05 (subsetTI) =>
% 98.91/13.05 ((
% 98.91/13.05 (powersetTI1) =>
% 98.91/13.05 ((
% 98.91/13.05 (powersetTE1) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementTI1) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementTE1) =>
% 98.91/13.05 ((
% 98.91/13.05 (binintersectTELcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (binintersectTERcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (contrasubsetT) =>
% 98.91/13.05 ((
% 98.91/13.05 (contrasubsetT1) =>
% 98.91/13.05 ((
% 98.91/13.05 (contrasubsetT2) =>
% 98.91/13.05 ((
% 98.91/13.05 (contrasubsetT3) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementI1) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementE1) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementSub1) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementSub2) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementEq) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementTnotintersectT) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementImpComplementIntersect) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementSubsetComplementIntersect) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementInPowersetComplementIntersect) =>
% 98.91/13.05 ((
% 98.91/13.05 (contraSubsetComplement) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementTcontraSubset) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionTILcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionTIRcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (inIntersectImpInUnion) =>
% 98.91/13.05 ((
% 98.91/13.05 (inIntersectImpInUnion2) =>
% 98.91/13.05 ((
% 98.91/13.05 (inIntersectImpInIntersectUnions) =>
% 98.91/13.05 ((
% 98.91/13.05 (intersectInPowersetIntersectUnions) =>
% 98.91/13.05 ((
% 98.91/13.05 (inComplementUnionImpNotIn1) =>
% 98.91/13.05 ((
% 98.91/13.05 (inComplementUnionImpInComplement1) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionTE) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionTEcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2a1) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementUnionInPowersetComplement) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2a2) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan1a) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan1b) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan1) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2a) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2b2) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2b) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule0) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule1) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule2) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule3) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule4) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_1) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_2) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_3) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_4) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_5) =>
% 98.91/13.05 ((
% 98.91/13.05 (breln1all2) =>
% 98.91/13.05 ((
% 98.91/13.05 (breln1SetBreln1) =>
% 98.91/13.05 ((
% 98.91/13.05 (choice2fnsingleton) =>
% 98.91/13.05 ((
% 98.91/13.05 (!!) @ (
% 98.91/13.05 (('#B') @ (
% 98.91/13.05 !!) @
% 98.91/13.05 (
% 98.91/13.05 (
% 98.91/13.05 ('#S') @ (
% 98.91/13.05 (
% 98.91/13.05 ('#B') @ (
% 98.91/13.05 '#B') @
% 98.91/13.05 breln1)) @
% 98.91/13.05 (
% 98.91/13.05 (
% 98.91/13.05 ('#S') @ dpsetconstr @
% 98.91/13.05 (
% 98.91/13.05 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.91/13.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1796])).
% 98.91/13.05 thf(zip_derived_cl1816, plain,
% 98.91/13.05 (~ (((cartprodpairmemER) =>
% 98.91/13.05 (((cartprodmempaircEq) =>
% 98.91/13.05 (((cartprodfstpairEq) =>
% 98.91/13.05 (((cartprodsndpairEq) =>
% 98.91/13.05 (((cartprodpairsurjEq) =>
% 98.91/13.05 (((dpsetconstrI) =>
% 98.91/13.05 (((dpsetconstrSub) =>
% 98.91/13.05 (((setOfPairsIsBReln) =>
% 98.91/13.05 (((dpsetconstrERa) =>
% 98.91/13.05 (((dpsetconstrEL1) =>
% 98.91/13.05 (((dpsetconstrEL2) =>
% 98.91/13.05 (((dpsetconstrER) =>
% 98.91/13.05 (((funcImageSingleton) =>
% 98.91/13.05 (((apProp) =>
% 98.91/13.05 (((app) =>
% 98.91/13.05 (((infuncsetfunc) =>
% 98.91/13.05 (((ap2p) =>
% 98.91/13.05 (((funcinfuncset) =>
% 98.91/13.05 (((lamProp) =>
% 98.91/13.05 (((lamp) =>
% 98.91/13.05 (((lam2p) =>
% 98.91/13.05 (((brelnall1) =>
% 98.91/13.05 (((brelnall2) =>
% 98.91/13.05 (((ex1E2) =>
% 98.91/13.05 (((funcGraphProp1) =>
% 98.91/13.05 (((funcGraphProp3) =>
% 98.91/13.05 (((funcGraphProp2) =>
% 98.91/13.05 (((funcextLem) =>
% 98.91/13.05 (((funcGraphProp4) =>
% 98.91/13.05 (((subbreln) =>
% 98.91/13.05 ((
% 98.91/13.05 (eqbreln) =>
% 98.91/13.05 ((
% 98.91/13.05 (funcext) =>
% 98.91/13.05 ((
% 98.91/13.05 (funcext2) =>
% 98.91/13.05 ((
% 98.91/13.05 (ap2apEq1) =>
% 98.91/13.05 ((
% 98.91/13.05 (ap2apEq2) =>
% 98.91/13.05 ((
% 98.91/13.05 (beta1) =>
% 98.91/13.05 ((
% 98.91/13.05 (eta1) =>
% 98.91/13.05 ((
% 98.91/13.05 (lam2lamEq) =>
% 98.91/13.05 ((
% 98.91/13.05 (beta2) =>
% 98.91/13.05 ((
% 98.91/13.05 (eta2) =>
% 98.91/13.05 ((
% 98.91/13.05 (iffalseProp1) =>
% 98.91/13.05 ((
% 98.91/13.05 (iffalseProp2) =>
% 98.91/13.05 ((
% 98.91/13.05 (iftrueProp1) =>
% 98.91/13.05 ((
% 98.91/13.05 (iftrueProp2) =>
% 98.91/13.05 ((
% 98.91/13.05 (ifSingleton) =>
% 98.91/13.05 ((
% 98.91/13.05 (ifp) =>
% 98.91/13.05 ((
% 98.91/13.05 (theeq) =>
% 98.91/13.05 ((
% 98.91/13.05 (iftrue) =>
% 98.91/13.05 ((
% 98.91/13.05 (iffalse) =>
% 98.91/13.05 ((
% 98.91/13.05 (iftrueorfalse) =>
% 98.91/13.05 ((
% 98.91/13.05 (binintersectT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (powersetT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (setminusT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (setextT) =>
% 98.91/13.05 ((
% 98.91/13.05 (subsetTI) =>
% 98.91/13.05 ((
% 98.91/13.05 (powersetTI1) =>
% 98.91/13.05 ((
% 98.91/13.05 (powersetTE1) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementTI1) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementTE1) =>
% 98.91/13.05 ((
% 98.91/13.05 (binintersectTELcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (binintersectTERcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (contrasubsetT) =>
% 98.91/13.05 ((
% 98.91/13.05 (contrasubsetT1) =>
% 98.91/13.05 ((
% 98.91/13.05 (contrasubsetT2) =>
% 98.91/13.05 ((
% 98.91/13.05 (contrasubsetT3) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementI1) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementE1) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementSub1) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementSub2) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementEq) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementTnotintersectT) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementImpComplementIntersect) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementSubsetComplementIntersect) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementInPowersetComplementIntersect) =>
% 98.91/13.05 ((
% 98.91/13.05 (contraSubsetComplement) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementTcontraSubset) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionTILcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionTIRcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (inIntersectImpInUnion) =>
% 98.91/13.05 ((
% 98.91/13.05 (inIntersectImpInUnion2) =>
% 98.91/13.05 ((
% 98.91/13.05 (inIntersectImpInIntersectUnions) =>
% 98.91/13.05 ((
% 98.91/13.05 (intersectInPowersetIntersectUnions) =>
% 98.91/13.05 ((
% 98.91/13.05 (inComplementUnionImpNotIn1) =>
% 98.91/13.05 ((
% 98.91/13.05 (inComplementUnionImpInComplement1) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionTE) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionTEcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2a1) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementUnionInPowersetComplement) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2a2) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan1a) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan1b) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan1) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2a) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2b2) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2b) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule0) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule1) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule2) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule3) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule4) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_1) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_2) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_3) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_4) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_5) =>
% 98.91/13.05 ((
% 98.91/13.05 (breln1all2) =>
% 98.91/13.05 ((
% 98.91/13.05 (breln1SetBreln1) =>
% 98.91/13.05 ((
% 98.91/13.05 (choice2fnsingleton) =>
% 98.91/13.05 ((
% 98.91/13.05 (!!) @ (
% 98.91/13.05 (('#B') @ (
% 98.91/13.05 !!) @
% 98.91/13.05 (
% 98.91/13.05 (
% 98.91/13.05 ('#S') @ (
% 98.91/13.05 (
% 98.91/13.05 ('#B') @ (
% 98.91/13.05 '#B') @
% 98.91/13.05 breln1)) @
% 98.91/13.05 (
% 98.91/13.05 (
% 98.91/13.05 ('#S') @ dpsetconstr @
% 98.91/13.05 (
% 98.91/13.05 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.91/13.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1807])).
% 98.91/13.05 thf(zip_derived_cl1825, plain,
% 98.91/13.05 (~ (((cartprodmempaircEq) =>
% 98.91/13.05 (((cartprodfstpairEq) =>
% 98.91/13.05 (((cartprodsndpairEq) =>
% 98.91/13.05 (((cartprodpairsurjEq) =>
% 98.91/13.05 (((dpsetconstrI) =>
% 98.91/13.05 (((dpsetconstrSub) =>
% 98.91/13.05 (((setOfPairsIsBReln) =>
% 98.91/13.05 (((dpsetconstrERa) =>
% 98.91/13.05 (((dpsetconstrEL1) =>
% 98.91/13.05 (((dpsetconstrEL2) =>
% 98.91/13.05 (((dpsetconstrER) =>
% 98.91/13.05 (((funcImageSingleton) =>
% 98.91/13.05 (((apProp) =>
% 98.91/13.05 (((app) =>
% 98.91/13.05 (((infuncsetfunc) =>
% 98.91/13.05 (((ap2p) =>
% 98.91/13.05 (((funcinfuncset) =>
% 98.91/13.05 (((lamProp) =>
% 98.91/13.05 (((lamp) =>
% 98.91/13.05 (((lam2p) =>
% 98.91/13.05 (((brelnall1) =>
% 98.91/13.05 (((brelnall2) =>
% 98.91/13.05 (((ex1E2) =>
% 98.91/13.05 (((funcGraphProp1) =>
% 98.91/13.05 (((funcGraphProp3) =>
% 98.91/13.05 (((funcGraphProp2) =>
% 98.91/13.05 (((funcextLem) =>
% 98.91/13.05 (((funcGraphProp4) =>
% 98.91/13.05 (((subbreln) =>
% 98.91/13.05 (((eqbreln) =>
% 98.91/13.05 ((
% 98.91/13.05 (funcext) =>
% 98.91/13.05 ((
% 98.91/13.05 (funcext2) =>
% 98.91/13.05 ((
% 98.91/13.05 (ap2apEq1) =>
% 98.91/13.05 ((
% 98.91/13.05 (ap2apEq2) =>
% 98.91/13.05 ((
% 98.91/13.05 (beta1) =>
% 98.91/13.05 ((
% 98.91/13.05 (eta1) =>
% 98.91/13.05 ((
% 98.91/13.05 (lam2lamEq) =>
% 98.91/13.05 ((
% 98.91/13.05 (beta2) =>
% 98.91/13.05 ((
% 98.91/13.05 (eta2) =>
% 98.91/13.05 ((
% 98.91/13.05 (iffalseProp1) =>
% 98.91/13.05 ((
% 98.91/13.05 (iffalseProp2) =>
% 98.91/13.05 ((
% 98.91/13.05 (iftrueProp1) =>
% 98.91/13.05 ((
% 98.91/13.05 (iftrueProp2) =>
% 98.91/13.05 ((
% 98.91/13.05 (ifSingleton) =>
% 98.91/13.05 ((
% 98.91/13.05 (ifp) =>
% 98.91/13.05 ((
% 98.91/13.05 (theeq) =>
% 98.91/13.05 ((
% 98.91/13.05 (iftrue) =>
% 98.91/13.05 ((
% 98.91/13.05 (iffalse) =>
% 98.91/13.05 ((
% 98.91/13.05 (iftrueorfalse) =>
% 98.91/13.05 ((
% 98.91/13.05 (binintersectT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (powersetT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (setminusT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (setextT) =>
% 98.91/13.05 ((
% 98.91/13.05 (subsetTI) =>
% 98.91/13.05 ((
% 98.91/13.05 (powersetTI1) =>
% 98.91/13.05 ((
% 98.91/13.05 (powersetTE1) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementTI1) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementTE1) =>
% 98.91/13.05 ((
% 98.91/13.05 (binintersectTELcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (binintersectTERcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (contrasubsetT) =>
% 98.91/13.05 ((
% 98.91/13.05 (contrasubsetT1) =>
% 98.91/13.05 ((
% 98.91/13.05 (contrasubsetT2) =>
% 98.91/13.05 ((
% 98.91/13.05 (contrasubsetT3) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementI1) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementE1) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementSub1) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementSub2) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementEq) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementTnotintersectT) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementImpComplementIntersect) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementSubsetComplementIntersect) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementInPowersetComplementIntersect) =>
% 98.91/13.05 ((
% 98.91/13.05 (contraSubsetComplement) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementTcontraSubset) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionTILcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionTIRcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (inIntersectImpInUnion) =>
% 98.91/13.05 ((
% 98.91/13.05 (inIntersectImpInUnion2) =>
% 98.91/13.05 ((
% 98.91/13.05 (inIntersectImpInIntersectUnions) =>
% 98.91/13.05 ((
% 98.91/13.05 (intersectInPowersetIntersectUnions) =>
% 98.91/13.05 ((
% 98.91/13.05 (inComplementUnionImpNotIn1) =>
% 98.91/13.05 ((
% 98.91/13.05 (inComplementUnionImpInComplement1) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionTE) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionTEcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2a1) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementUnionInPowersetComplement) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2a2) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan1a) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan1b) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan1) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2a) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2b2) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2b) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule0) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule1) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule2) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule3) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule4) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_1) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_2) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_3) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_4) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_5) =>
% 98.91/13.05 ((
% 98.91/13.05 (breln1all2) =>
% 98.91/13.05 ((
% 98.91/13.05 (breln1SetBreln1) =>
% 98.91/13.05 ((
% 98.91/13.05 (choice2fnsingleton) =>
% 98.91/13.05 ((
% 98.91/13.05 (!!) @ (
% 98.91/13.05 (('#B') @ (
% 98.91/13.05 !!) @
% 98.91/13.05 (
% 98.91/13.05 (
% 98.91/13.05 ('#S') @ (
% 98.91/13.05 (
% 98.91/13.05 ('#B') @ (
% 98.91/13.05 '#B') @
% 98.91/13.05 breln1)) @
% 98.91/13.05 (
% 98.91/13.05 (
% 98.91/13.05 ('#S') @ dpsetconstr @
% 98.91/13.05 (
% 98.91/13.05 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.91/13.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1816])).
% 98.91/13.05 thf(zip_derived_cl1833, plain,
% 98.91/13.05 (~ (((cartprodfstpairEq) =>
% 98.91/13.05 (((cartprodsndpairEq) =>
% 98.91/13.05 (((cartprodpairsurjEq) =>
% 98.91/13.05 (((dpsetconstrI) =>
% 98.91/13.05 (((dpsetconstrSub) =>
% 98.91/13.05 (((setOfPairsIsBReln) =>
% 98.91/13.05 (((dpsetconstrERa) =>
% 98.91/13.05 (((dpsetconstrEL1) =>
% 98.91/13.05 (((dpsetconstrEL2) =>
% 98.91/13.05 (((dpsetconstrER) =>
% 98.91/13.05 (((funcImageSingleton) =>
% 98.91/13.05 (((apProp) =>
% 98.91/13.05 (((app) =>
% 98.91/13.05 (((infuncsetfunc) =>
% 98.91/13.05 (((ap2p) =>
% 98.91/13.05 (((funcinfuncset) =>
% 98.91/13.05 (((lamProp) =>
% 98.91/13.05 (((lamp) =>
% 98.91/13.05 (((lam2p) =>
% 98.91/13.05 (((brelnall1) =>
% 98.91/13.05 (((brelnall2) =>
% 98.91/13.05 (((ex1E2) =>
% 98.91/13.05 (((funcGraphProp1) =>
% 98.91/13.05 (((funcGraphProp3) =>
% 98.91/13.05 (((funcGraphProp2) =>
% 98.91/13.05 (((funcextLem) =>
% 98.91/13.05 (((funcGraphProp4) =>
% 98.91/13.05 (((subbreln) =>
% 98.91/13.05 (((eqbreln) =>
% 98.91/13.05 (((funcext) =>
% 98.91/13.05 ((
% 98.91/13.05 (funcext2) =>
% 98.91/13.05 ((
% 98.91/13.05 (ap2apEq1) =>
% 98.91/13.05 ((
% 98.91/13.05 (ap2apEq2) =>
% 98.91/13.05 ((
% 98.91/13.05 (beta1) =>
% 98.91/13.05 ((
% 98.91/13.05 (eta1) =>
% 98.91/13.05 ((
% 98.91/13.05 (lam2lamEq) =>
% 98.91/13.05 ((
% 98.91/13.05 (beta2) =>
% 98.91/13.05 ((
% 98.91/13.05 (eta2) =>
% 98.91/13.05 ((
% 98.91/13.05 (iffalseProp1) =>
% 98.91/13.05 ((
% 98.91/13.05 (iffalseProp2) =>
% 98.91/13.05 ((
% 98.91/13.05 (iftrueProp1) =>
% 98.91/13.05 ((
% 98.91/13.05 (iftrueProp2) =>
% 98.91/13.05 ((
% 98.91/13.05 (ifSingleton) =>
% 98.91/13.05 ((
% 98.91/13.05 (ifp) =>
% 98.91/13.05 ((
% 98.91/13.05 (theeq) =>
% 98.91/13.05 ((
% 98.91/13.05 (iftrue) =>
% 98.91/13.05 ((
% 98.91/13.05 (iffalse) =>
% 98.91/13.05 ((
% 98.91/13.05 (iftrueorfalse) =>
% 98.91/13.05 ((
% 98.91/13.05 (binintersectT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (powersetT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (setminusT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementT_lem) =>
% 98.91/13.05 ((
% 98.91/13.05 (setextT) =>
% 98.91/13.05 ((
% 98.91/13.05 (subsetTI) =>
% 98.91/13.05 ((
% 98.91/13.05 (powersetTI1) =>
% 98.91/13.05 ((
% 98.91/13.05 (powersetTE1) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementTI1) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementTE1) =>
% 98.91/13.05 ((
% 98.91/13.05 (binintersectTELcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (binintersectTERcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (contrasubsetT) =>
% 98.91/13.05 ((
% 98.91/13.05 (contrasubsetT1) =>
% 98.91/13.05 ((
% 98.91/13.05 (contrasubsetT2) =>
% 98.91/13.05 ((
% 98.91/13.05 (contrasubsetT3) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementI1) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementE1) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementSub1) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementSub2) =>
% 98.91/13.05 ((
% 98.91/13.05 (doubleComplementEq) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementTnotintersectT) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementImpComplementIntersect) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementSubsetComplementIntersect) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementInPowersetComplementIntersect) =>
% 98.91/13.05 ((
% 98.91/13.05 (contraSubsetComplement) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementTcontraSubset) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionTILcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionTIRcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (inIntersectImpInUnion) =>
% 98.91/13.05 ((
% 98.91/13.05 (inIntersectImpInUnion2) =>
% 98.91/13.05 ((
% 98.91/13.05 (inIntersectImpInIntersectUnions) =>
% 98.91/13.05 ((
% 98.91/13.05 (intersectInPowersetIntersectUnions) =>
% 98.91/13.05 ((
% 98.91/13.05 (inComplementUnionImpNotIn1) =>
% 98.91/13.05 ((
% 98.91/13.05 (inComplementUnionImpInComplement1) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionTE) =>
% 98.91/13.05 ((
% 98.91/13.05 (binunionTEcontra) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2a1) =>
% 98.91/13.05 ((
% 98.91/13.05 (complementUnionInPowersetComplement) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2a2) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan1a) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan1b) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan1) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2a) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2b2) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2b) =>
% 98.91/13.05 ((
% 98.91/13.05 (demorgan2) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule0) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule1) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule2) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule3) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz13rule4) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_1) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_2) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_3) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_4) =>
% 98.91/13.05 ((
% 98.91/13.05 (woz1_5) =>
% 98.91/13.05 ((
% 98.91/13.05 (breln1all2) =>
% 98.91/13.05 ((
% 98.91/13.05 (breln1SetBreln1) =>
% 98.91/13.05 ((
% 98.91/13.05 (choice2fnsingleton) =>
% 98.91/13.05 ((
% 98.91/13.05 (!!) @ (
% 98.91/13.05 (('#B') @ (
% 98.91/13.05 !!) @
% 98.91/13.05 (
% 98.91/13.05 (
% 98.91/13.05 ('#S') @ (
% 98.91/13.05 (
% 98.91/13.05 ('#B') @ (
% 98.91/13.05 '#B') @
% 98.91/13.05 breln1)) @
% 98.91/13.05 (
% 98.91/13.06 (
% 98.91/13.06 ('#S') @ dpsetconstr @
% 98.91/13.06 (
% 98.91/13.06 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.91/13.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1825])).
% 98.91/13.06 thf(zip_derived_cl1840, plain,
% 98.91/13.06 (~ (((cartprodsndpairEq) =>
% 98.91/13.06 (((cartprodpairsurjEq) =>
% 98.91/13.06 (((dpsetconstrI) =>
% 98.91/13.06 (((dpsetconstrSub) =>
% 98.91/13.06 (((setOfPairsIsBReln) =>
% 98.91/13.06 (((dpsetconstrERa) =>
% 98.91/13.06 (((dpsetconstrEL1) =>
% 98.91/13.06 (((dpsetconstrEL2) =>
% 98.91/13.06 (((dpsetconstrER) =>
% 98.91/13.06 (((funcImageSingleton) =>
% 98.91/13.06 (((apProp) =>
% 98.91/13.06 (((app) =>
% 98.91/13.06 (((infuncsetfunc) =>
% 98.91/13.06 (((ap2p) =>
% 98.91/13.06 (((funcinfuncset) =>
% 98.91/13.06 (((lamProp) =>
% 98.91/13.06 (((lamp) =>
% 98.91/13.06 (((lam2p) =>
% 98.91/13.06 (((brelnall1) =>
% 98.91/13.06 (((brelnall2) =>
% 98.91/13.06 (((ex1E2) =>
% 98.91/13.06 (((funcGraphProp1) =>
% 98.91/13.06 (((funcGraphProp3) =>
% 98.91/13.06 (((funcGraphProp2) =>
% 98.91/13.06 (((funcextLem) =>
% 98.91/13.06 (((funcGraphProp4) =>
% 98.91/13.06 (((subbreln) =>
% 98.91/13.06 (((eqbreln) =>
% 98.91/13.06 (((funcext) =>
% 98.91/13.06 (((funcext2) =>
% 98.91/13.06 ((
% 98.91/13.06 (ap2apEq1) =>
% 98.91/13.06 ((
% 98.91/13.06 (ap2apEq2) =>
% 98.91/13.06 ((
% 98.91/13.06 (beta1) =>
% 98.91/13.06 ((
% 98.91/13.06 (eta1) =>
% 98.91/13.06 ((
% 98.91/13.06 (lam2lamEq) =>
% 98.91/13.06 ((
% 98.91/13.06 (beta2) =>
% 98.91/13.06 ((
% 98.91/13.06 (eta2) =>
% 98.91/13.06 ((
% 98.91/13.06 (iffalseProp1) =>
% 98.91/13.06 ((
% 98.91/13.06 (iffalseProp2) =>
% 98.91/13.06 ((
% 98.91/13.06 (iftrueProp1) =>
% 98.91/13.06 ((
% 98.91/13.06 (iftrueProp2) =>
% 98.91/13.06 ((
% 98.91/13.06 (ifSingleton) =>
% 98.91/13.06 ((
% 98.91/13.06 (ifp) =>
% 98.91/13.06 ((
% 98.91/13.06 (theeq) =>
% 98.91/13.06 ((
% 98.91/13.06 (iftrue) =>
% 98.91/13.06 ((
% 98.91/13.06 (iffalse) =>
% 98.91/13.06 ((
% 98.91/13.06 (iftrueorfalse) =>
% 98.91/13.06 ((
% 98.91/13.06 (binintersectT_lem) =>
% 98.91/13.06 ((
% 98.91/13.06 (binunionT_lem) =>
% 98.91/13.06 ((
% 98.91/13.06 (powersetT_lem) =>
% 98.91/13.06 ((
% 98.91/13.06 (setminusT_lem) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementT_lem) =>
% 98.91/13.06 ((
% 98.91/13.06 (setextT) =>
% 98.91/13.06 ((
% 98.91/13.06 (subsetTI) =>
% 98.91/13.06 ((
% 98.91/13.06 (powersetTI1) =>
% 98.91/13.06 ((
% 98.91/13.06 (powersetTE1) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementTI1) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementTE1) =>
% 98.91/13.06 ((
% 98.91/13.06 (binintersectTELcontra) =>
% 98.91/13.06 ((
% 98.91/13.06 (binintersectTERcontra) =>
% 98.91/13.06 ((
% 98.91/13.06 (contrasubsetT) =>
% 98.91/13.06 ((
% 98.91/13.06 (contrasubsetT1) =>
% 98.91/13.06 ((
% 98.91/13.06 (contrasubsetT2) =>
% 98.91/13.06 ((
% 98.91/13.06 (contrasubsetT3) =>
% 98.91/13.06 ((
% 98.91/13.06 (doubleComplementI1) =>
% 98.91/13.06 ((
% 98.91/13.06 (doubleComplementE1) =>
% 98.91/13.06 ((
% 98.91/13.06 (doubleComplementSub1) =>
% 98.91/13.06 ((
% 98.91/13.06 (doubleComplementSub2) =>
% 98.91/13.06 ((
% 98.91/13.06 (doubleComplementEq) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementTnotintersectT) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementImpComplementIntersect) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementSubsetComplementIntersect) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementInPowersetComplementIntersect) =>
% 98.91/13.06 ((
% 98.91/13.06 (contraSubsetComplement) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementTcontraSubset) =>
% 98.91/13.06 ((
% 98.91/13.06 (binunionTILcontra) =>
% 98.91/13.06 ((
% 98.91/13.06 (binunionTIRcontra) =>
% 98.91/13.06 ((
% 98.91/13.06 (inIntersectImpInUnion) =>
% 98.91/13.06 ((
% 98.91/13.06 (inIntersectImpInUnion2) =>
% 98.91/13.06 ((
% 98.91/13.06 (inIntersectImpInIntersectUnions) =>
% 98.91/13.06 ((
% 98.91/13.06 (intersectInPowersetIntersectUnions) =>
% 98.91/13.06 ((
% 98.91/13.06 (inComplementUnionImpNotIn1) =>
% 98.91/13.06 ((
% 98.91/13.06 (inComplementUnionImpInComplement1) =>
% 98.91/13.06 ((
% 98.91/13.06 (binunionTE) =>
% 98.91/13.06 ((
% 98.91/13.06 (binunionTEcontra) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2a1) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementUnionInPowersetComplement) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2a2) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan1a) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan1b) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan1) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2a) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2b2) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2b) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz13rule0) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz13rule1) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz13rule2) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz13rule3) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz13rule4) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz1_1) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz1_2) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz1_3) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz1_4) =>
% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1833])).
% 98.91/13.06 thf(zip_derived_cl1848, plain,
% 98.91/13.06 (~ (((cartprodpairsurjEq) =>
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% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 ((
% 98.91/13.06 (setextT) =>
% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 ((
% 98.91/13.06 (contrasubsetT1) =>
% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 ((
% 98.91/13.06 (doubleComplementSub2) =>
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% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 ((
% 98.91/13.06 (complementSubsetComplementIntersect) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementInPowersetComplementIntersect) =>
% 98.91/13.06 ((
% 98.91/13.06 (contraSubsetComplement) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementTcontraSubset) =>
% 98.91/13.06 ((
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% 98.91/13.06 ((
% 98.91/13.06 (binunionTIRcontra) =>
% 98.91/13.06 ((
% 98.91/13.06 (inIntersectImpInUnion) =>
% 98.91/13.06 ((
% 98.91/13.06 (inIntersectImpInUnion2) =>
% 98.91/13.06 ((
% 98.91/13.06 (inIntersectImpInIntersectUnions) =>
% 98.91/13.06 ((
% 98.91/13.06 (intersectInPowersetIntersectUnions) =>
% 98.91/13.06 ((
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% 98.91/13.06 ((
% 98.91/13.06 (inComplementUnionImpInComplement1) =>
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% 98.91/13.06 ((
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% 98.91/13.06 ((
% 98.91/13.06 (demorgan2a1) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementUnionInPowersetComplement) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2a2) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan1a) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan1b) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan1) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2a) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2b2) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2b) =>
% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1840])).
% 98.91/13.06 thf(zip_derived_cl1856, plain,
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% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 ((
% 98.91/13.06 (demorgan2a) =>
% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1848])).
% 98.91/13.06 thf(zip_derived_cl1865, plain,
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% 98.91/13.06 ((
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% 98.91/13.06 ((
% 98.91/13.06 (complementSubsetComplementIntersect) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementInPowersetComplementIntersect) =>
% 98.91/13.06 ((
% 98.91/13.06 (contraSubsetComplement) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementTcontraSubset) =>
% 98.91/13.06 ((
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% 98.91/13.06 ((
% 98.91/13.06 (binunionTIRcontra) =>
% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 ((
% 98.91/13.06 (complementUnionInPowersetComplement) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2a2) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan1a) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan1b) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan1) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2a) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2b2) =>
% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1856])).
% 98.91/13.06 thf(zip_derived_cl1874, plain,
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% 98.91/13.06 ((
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% 98.91/13.06 ((
% 98.91/13.06 (setextT) =>
% 98.91/13.06 ((
% 98.91/13.06 (subsetTI) =>
% 98.91/13.06 ((
% 98.91/13.06 (powersetTI1) =>
% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 (contrasubsetT) =>
% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 ((
% 98.91/13.06 (contrasubsetT3) =>
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% 98.91/13.06 ((
% 98.91/13.06 (doubleComplementE1) =>
% 98.91/13.06 ((
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% 98.91/13.06 ((
% 98.91/13.06 (doubleComplementSub2) =>
% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 ((
% 98.91/13.06 (complementSubsetComplementIntersect) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementInPowersetComplementIntersect) =>
% 98.91/13.06 ((
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% 98.91/13.06 ((
% 98.91/13.06 (binunionTIRcontra) =>
% 98.91/13.06 ((
% 98.91/13.06 (inIntersectImpInUnion) =>
% 98.91/13.06 ((
% 98.91/13.06 (inIntersectImpInUnion2) =>
% 98.91/13.06 ((
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% 98.91/13.06 (intersectInPowersetIntersectUnions) =>
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% 98.91/13.06 ((
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% 98.91/13.06 ((
% 98.91/13.06 (complementUnionInPowersetComplement) =>
% 98.91/13.06 ((
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% 98.91/13.06 ((
% 98.91/13.06 (demorgan1a) =>
% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 ((
% 98.91/13.06 (demorgan2a) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2b2) =>
% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1865])).
% 98.91/13.06 thf(zip_derived_cl1883, plain,
% 98.91/13.06 (~ (((dpsetconstrERa) =>
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% 98.91/13.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1874])).
% 98.91/13.06 thf(zip_derived_cl1893, plain,
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% 98.91/13.06 (theeq) =>
% 98.91/13.06 ((
% 98.91/13.06 (iftrue) =>
% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 ((
% 98.91/13.06 (powersetT_lem) =>
% 98.91/13.06 ((
% 98.91/13.06 (setminusT_lem) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementT_lem) =>
% 98.91/13.06 ((
% 98.91/13.06 (setextT) =>
% 98.91/13.06 ((
% 98.91/13.06 (subsetTI) =>
% 98.91/13.06 ((
% 98.91/13.06 (powersetTI1) =>
% 98.91/13.06 ((
% 98.91/13.06 (powersetTE1) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementTI1) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementTE1) =>
% 98.91/13.06 ((
% 98.91/13.06 (binintersectTELcontra) =>
% 98.91/13.06 ((
% 98.91/13.06 (binintersectTERcontra) =>
% 98.91/13.06 ((
% 98.91/13.06 (contrasubsetT) =>
% 98.91/13.06 ((
% 98.91/13.06 (contrasubsetT1) =>
% 98.91/13.06 ((
% 98.91/13.06 (contrasubsetT2) =>
% 98.91/13.06 ((
% 98.91/13.06 (contrasubsetT3) =>
% 98.91/13.06 ((
% 98.91/13.06 (doubleComplementI1) =>
% 98.91/13.06 ((
% 98.91/13.06 (doubleComplementE1) =>
% 98.91/13.06 ((
% 98.91/13.06 (doubleComplementSub1) =>
% 98.91/13.06 ((
% 98.91/13.06 (doubleComplementSub2) =>
% 98.91/13.06 ((
% 98.91/13.06 (doubleComplementEq) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementTnotintersectT) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementImpComplementIntersect) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementSubsetComplementIntersect) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementInPowersetComplementIntersect) =>
% 98.91/13.06 ((
% 98.91/13.06 (contraSubsetComplement) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementTcontraSubset) =>
% 98.91/13.06 ((
% 98.91/13.06 (binunionTILcontra) =>
% 98.91/13.06 ((
% 98.91/13.06 (binunionTIRcontra) =>
% 98.91/13.06 ((
% 98.91/13.06 (inIntersectImpInUnion) =>
% 98.91/13.06 ((
% 98.91/13.06 (inIntersectImpInUnion2) =>
% 98.91/13.06 ((
% 98.91/13.06 (inIntersectImpInIntersectUnions) =>
% 98.91/13.06 ((
% 98.91/13.06 (intersectInPowersetIntersectUnions) =>
% 98.91/13.06 ((
% 98.91/13.06 (inComplementUnionImpNotIn1) =>
% 98.91/13.06 ((
% 98.91/13.06 (inComplementUnionImpInComplement1) =>
% 98.91/13.06 ((
% 98.91/13.06 (binunionTE) =>
% 98.91/13.06 ((
% 98.91/13.06 (binunionTEcontra) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2a1) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementUnionInPowersetComplement) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2a2) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan1a) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan1b) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan1) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2a) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2b2) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2b) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz13rule0) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz13rule1) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz13rule2) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz13rule3) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz13rule4) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz1_1) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz1_2) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz1_3) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz1_4) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz1_5) =>
% 98.91/13.06 ((
% 98.91/13.06 (breln1all2) =>
% 98.91/13.06 ((
% 98.91/13.06 (breln1SetBreln1) =>
% 98.91/13.06 ((
% 98.91/13.06 (choice2fnsingleton) =>
% 98.91/13.06 ((
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% 98.91/13.06 (
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% 98.91/13.06 (
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% 98.91/13.06 (
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% 98.91/13.06 (
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% 98.91/13.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1883])).
% 98.91/13.06 thf(zip_derived_cl1903, plain,
% 98.91/13.06 (~ (((dpsetconstrEL2) =>
% 98.91/13.06 (((dpsetconstrER) =>
% 98.91/13.06 (((funcImageSingleton) =>
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% 98.91/13.06 (((funcext2) =>
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% 98.91/13.06 (((ap2apEq2) =>
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% 98.91/13.06 (((eta1) =>
% 98.91/13.06 (((lam2lamEq) =>
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% 98.91/13.06 (((eta2) =>
% 98.91/13.06 ((
% 98.91/13.06 (iffalseProp1) =>
% 98.91/13.06 ((
% 98.91/13.06 (iffalseProp2) =>
% 98.91/13.06 ((
% 98.91/13.06 (iftrueProp1) =>
% 98.91/13.06 ((
% 98.91/13.06 (iftrueProp2) =>
% 98.91/13.06 ((
% 98.91/13.06 (ifSingleton) =>
% 98.91/13.06 ((
% 98.91/13.06 (ifp) =>
% 98.91/13.06 ((
% 98.91/13.06 (theeq) =>
% 98.91/13.06 ((
% 98.91/13.06 (iftrue) =>
% 98.91/13.06 ((
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% 98.91/13.06 ((
% 98.91/13.06 (iftrueorfalse) =>
% 98.91/13.06 ((
% 98.91/13.06 (binintersectT_lem) =>
% 98.91/13.06 ((
% 98.91/13.06 (binunionT_lem) =>
% 98.91/13.06 ((
% 98.91/13.06 (powersetT_lem) =>
% 98.91/13.06 ((
% 98.91/13.06 (setminusT_lem) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementT_lem) =>
% 98.91/13.06 ((
% 98.91/13.06 (setextT) =>
% 98.91/13.06 ((
% 98.91/13.06 (subsetTI) =>
% 98.91/13.06 ((
% 98.91/13.06 (powersetTI1) =>
% 98.91/13.06 ((
% 98.91/13.06 (powersetTE1) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementTI1) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementTE1) =>
% 98.91/13.06 ((
% 98.91/13.06 (binintersectTELcontra) =>
% 98.91/13.06 ((
% 98.91/13.06 (binintersectTERcontra) =>
% 98.91/13.06 ((
% 98.91/13.06 (contrasubsetT) =>
% 98.91/13.06 ((
% 98.91/13.06 (contrasubsetT1) =>
% 98.91/13.06 ((
% 98.91/13.06 (contrasubsetT2) =>
% 98.91/13.06 ((
% 98.91/13.06 (contrasubsetT3) =>
% 98.91/13.06 ((
% 98.91/13.06 (doubleComplementI1) =>
% 98.91/13.06 ((
% 98.91/13.06 (doubleComplementE1) =>
% 98.91/13.06 ((
% 98.91/13.06 (doubleComplementSub1) =>
% 98.91/13.06 ((
% 98.91/13.06 (doubleComplementSub2) =>
% 98.91/13.06 ((
% 98.91/13.06 (doubleComplementEq) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementTnotintersectT) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementImpComplementIntersect) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementSubsetComplementIntersect) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementInPowersetComplementIntersect) =>
% 98.91/13.06 ((
% 98.91/13.06 (contraSubsetComplement) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementTcontraSubset) =>
% 98.91/13.06 ((
% 98.91/13.06 (binunionTILcontra) =>
% 98.91/13.06 ((
% 98.91/13.06 (binunionTIRcontra) =>
% 98.91/13.06 ((
% 98.91/13.06 (inIntersectImpInUnion) =>
% 98.91/13.06 ((
% 98.91/13.06 (inIntersectImpInUnion2) =>
% 98.91/13.06 ((
% 98.91/13.06 (inIntersectImpInIntersectUnions) =>
% 98.91/13.06 ((
% 98.91/13.06 (intersectInPowersetIntersectUnions) =>
% 98.91/13.06 ((
% 98.91/13.06 (inComplementUnionImpNotIn1) =>
% 98.91/13.06 ((
% 98.91/13.06 (inComplementUnionImpInComplement1) =>
% 98.91/13.06 ((
% 98.91/13.06 (binunionTE) =>
% 98.91/13.06 ((
% 98.91/13.06 (binunionTEcontra) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2a1) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementUnionInPowersetComplement) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2a2) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan1a) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan1b) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan1) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2a) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2b2) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2b) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz13rule0) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz13rule1) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz13rule2) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz13rule3) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz13rule4) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz1_1) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz1_2) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz1_3) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz1_4) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz1_5) =>
% 98.91/13.06 ((
% 98.91/13.06 (breln1all2) =>
% 98.91/13.06 ((
% 98.91/13.06 (breln1SetBreln1) =>
% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 ('#S') @ (
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% 98.91/13.06 (
% 98.91/13.06 (
% 98.91/13.06 ('#S') @ dpsetconstr @
% 98.91/13.06 (
% 98.91/13.06 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.91/13.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1893])).
% 98.91/13.06 thf(zip_derived_cl1914, plain,
% 98.91/13.06 (~ (((dpsetconstrER) =>
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% 98.91/13.06 ((
% 98.91/13.06 (binunionT_lem) =>
% 98.91/13.06 ((
% 98.91/13.06 (powersetT_lem) =>
% 98.91/13.06 ((
% 98.91/13.06 (setminusT_lem) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementT_lem) =>
% 98.91/13.06 ((
% 98.91/13.06 (setextT) =>
% 98.91/13.06 ((
% 98.91/13.06 (subsetTI) =>
% 98.91/13.06 ((
% 98.91/13.06 (powersetTI1) =>
% 98.91/13.06 ((
% 98.91/13.06 (powersetTE1) =>
% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 ((
% 98.91/13.06 (binintersectTERcontra) =>
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% 98.91/13.06 ((
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% 98.91/13.06 ((
% 98.91/13.06 (contrasubsetT2) =>
% 98.91/13.06 ((
% 98.91/13.06 (contrasubsetT3) =>
% 98.91/13.06 ((
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% 98.91/13.06 ((
% 98.91/13.06 (doubleComplementE1) =>
% 98.91/13.06 ((
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% 98.91/13.06 ((
% 98.91/13.06 (doubleComplementSub2) =>
% 98.91/13.06 ((
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% 98.91/13.06 ((
% 98.91/13.06 (complementTnotintersectT) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementImpComplementIntersect) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementSubsetComplementIntersect) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementInPowersetComplementIntersect) =>
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% 98.91/13.06 (contraSubsetComplement) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementTcontraSubset) =>
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% 98.91/13.06 ((
% 98.91/13.06 (binunionTIRcontra) =>
% 98.91/13.06 ((
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% 98.91/13.06 ((
% 98.91/13.06 (inIntersectImpInUnion2) =>
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% 98.91/13.06 (inIntersectImpInIntersectUnions) =>
% 98.91/13.06 ((
% 98.91/13.06 (intersectInPowersetIntersectUnions) =>
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% 98.91/13.06 (inComplementUnionImpNotIn1) =>
% 98.91/13.06 ((
% 98.91/13.06 (inComplementUnionImpInComplement1) =>
% 98.91/13.06 ((
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% 98.91/13.06 ((
% 98.91/13.06 (binunionTEcontra) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2a1) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementUnionInPowersetComplement) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2a2) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan1a) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan1b) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan1) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2a) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2b2) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2b) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz13rule0) =>
% 98.91/13.06 ((
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% 98.91/13.06 ((
% 98.91/13.06 (woz13rule2) =>
% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 ((
% 98.91/13.06 (woz1_2) =>
% 98.91/13.06 ((
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% 98.91/13.06 ((
% 98.91/13.06 (woz1_4) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz1_5) =>
% 98.91/13.06 ((
% 98.91/13.06 (breln1all2) =>
% 98.91/13.06 ((
% 98.91/13.06 (breln1SetBreln1) =>
% 98.91/13.06 ((
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% 98.91/13.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1903])).
% 98.91/13.06 thf(zip_derived_cl1923, plain,
% 98.91/13.06 (~ (((funcImageSingleton) =>
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% 98.91/13.06 (((lam2p) =>
% 98.91/13.06 (((brelnall1) =>
% 98.91/13.06 (((brelnall2) =>
% 98.91/13.06 (((ex1E2) =>
% 98.91/13.06 (((funcGraphProp1) =>
% 98.91/13.06 (((funcGraphProp3) =>
% 98.91/13.06 (((funcGraphProp2) =>
% 98.91/13.06 (((funcextLem) =>
% 98.91/13.06 (((funcGraphProp4) =>
% 98.91/13.06 (((subbreln) =>
% 98.91/13.06 (((eqbreln) =>
% 98.91/13.06 (((funcext) =>
% 98.91/13.06 (((funcext2) =>
% 98.91/13.06 (((ap2apEq1) =>
% 98.91/13.06 (((ap2apEq2) =>
% 98.91/13.06 (((beta1) =>
% 98.91/13.06 (((eta1) =>
% 98.91/13.06 (((lam2lamEq) =>
% 98.91/13.06 (((beta2) =>
% 98.91/13.06 (((eta2) =>
% 98.91/13.06 (((iffalseProp1) =>
% 98.91/13.06 (((iffalseProp2) =>
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% 98.91/13.06 (iftrueProp1) =>
% 98.91/13.06 ((
% 98.91/13.06 (iftrueProp2) =>
% 98.91/13.06 ((
% 98.91/13.06 (ifSingleton) =>
% 98.91/13.06 ((
% 98.91/13.06 (ifp) =>
% 98.91/13.06 ((
% 98.91/13.06 (theeq) =>
% 98.91/13.06 ((
% 98.91/13.06 (iftrue) =>
% 98.91/13.06 ((
% 98.91/13.06 (iffalse) =>
% 98.91/13.06 ((
% 98.91/13.06 (iftrueorfalse) =>
% 98.91/13.06 ((
% 98.91/13.06 (binintersectT_lem) =>
% 98.91/13.06 ((
% 98.91/13.06 (binunionT_lem) =>
% 98.91/13.06 ((
% 98.91/13.06 (powersetT_lem) =>
% 98.91/13.06 ((
% 98.91/13.06 (setminusT_lem) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementT_lem) =>
% 98.91/13.06 ((
% 98.91/13.06 (setextT) =>
% 98.91/13.06 ((
% 98.91/13.06 (subsetTI) =>
% 98.91/13.06 ((
% 98.91/13.06 (powersetTI1) =>
% 98.91/13.06 ((
% 98.91/13.06 (powersetTE1) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementTI1) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementTE1) =>
% 98.91/13.06 ((
% 98.91/13.06 (binintersectTELcontra) =>
% 98.91/13.06 ((
% 98.91/13.06 (binintersectTERcontra) =>
% 98.91/13.06 ((
% 98.91/13.06 (contrasubsetT) =>
% 98.91/13.06 ((
% 98.91/13.06 (contrasubsetT1) =>
% 98.91/13.06 ((
% 98.91/13.06 (contrasubsetT2) =>
% 98.91/13.06 ((
% 98.91/13.06 (contrasubsetT3) =>
% 98.91/13.06 ((
% 98.91/13.06 (doubleComplementI1) =>
% 98.91/13.06 ((
% 98.91/13.06 (doubleComplementE1) =>
% 98.91/13.06 ((
% 98.91/13.06 (doubleComplementSub1) =>
% 98.91/13.06 ((
% 98.91/13.06 (doubleComplementSub2) =>
% 98.91/13.06 ((
% 98.91/13.06 (doubleComplementEq) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementTnotintersectT) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementImpComplementIntersect) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementSubsetComplementIntersect) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementInPowersetComplementIntersect) =>
% 98.91/13.06 ((
% 98.91/13.06 (contraSubsetComplement) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementTcontraSubset) =>
% 98.91/13.06 ((
% 98.91/13.06 (binunionTILcontra) =>
% 98.91/13.06 ((
% 98.91/13.06 (binunionTIRcontra) =>
% 98.91/13.06 ((
% 98.91/13.06 (inIntersectImpInUnion) =>
% 98.91/13.06 ((
% 98.91/13.06 (inIntersectImpInUnion2) =>
% 98.91/13.06 ((
% 98.91/13.06 (inIntersectImpInIntersectUnions) =>
% 98.91/13.06 ((
% 98.91/13.06 (intersectInPowersetIntersectUnions) =>
% 98.91/13.06 ((
% 98.91/13.06 (inComplementUnionImpNotIn1) =>
% 98.91/13.06 ((
% 98.91/13.06 (inComplementUnionImpInComplement1) =>
% 98.91/13.06 ((
% 98.91/13.06 (binunionTE) =>
% 98.91/13.06 ((
% 98.91/13.06 (binunionTEcontra) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2a1) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementUnionInPowersetComplement) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2a2) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan1a) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan1b) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan1) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2a) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2b2) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2b) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz13rule0) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz13rule1) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz13rule2) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz13rule3) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz13rule4) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz1_1) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz1_2) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz1_3) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz1_4) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz1_5) =>
% 98.91/13.06 ((
% 98.91/13.06 (breln1all2) =>
% 98.91/13.06 ((
% 98.91/13.06 (breln1SetBreln1) =>
% 98.91/13.06 ((
% 98.91/13.06 (choice2fnsingleton) =>
% 98.91/13.06 ((
% 98.91/13.06 (!!) @ (
% 98.91/13.06 (('#B') @ (
% 98.91/13.06 !!) @
% 98.91/13.06 (
% 98.91/13.06 (
% 98.91/13.06 ('#S') @ (
% 98.91/13.06 (
% 98.91/13.06 ('#B') @ (
% 98.91/13.06 '#B') @
% 98.91/13.06 breln1)) @
% 98.91/13.06 (
% 98.91/13.06 (
% 98.91/13.06 ('#S') @ dpsetconstr @
% 98.91/13.06 (
% 98.91/13.06 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.91/13.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1914])).
% 98.91/13.06 thf(zip_derived_cl1932, plain,
% 98.91/13.06 (~ (((apProp) =>
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% 98.91/13.06 (((infuncsetfunc) =>
% 98.91/13.06 (((ap2p) =>
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% 98.91/13.06 (((lam2p) =>
% 98.91/13.06 (((brelnall1) =>
% 98.91/13.06 (((brelnall2) =>
% 98.91/13.06 (((ex1E2) =>
% 98.91/13.06 (((funcGraphProp1) =>
% 98.91/13.06 (((funcGraphProp3) =>
% 98.91/13.06 (((funcGraphProp2) =>
% 98.91/13.06 (((funcextLem) =>
% 98.91/13.06 (((funcGraphProp4) =>
% 98.91/13.06 (((subbreln) =>
% 98.91/13.06 (((eqbreln) =>
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% 98.91/13.06 (((funcext2) =>
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% 98.91/13.06 (((ap2apEq2) =>
% 98.91/13.06 (((beta1) =>
% 98.91/13.06 (((eta1) =>
% 98.91/13.06 (((lam2lamEq) =>
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% 98.91/13.06 ((
% 98.91/13.06 (ifSingleton) =>
% 98.91/13.06 ((
% 98.91/13.06 (ifp) =>
% 98.91/13.06 ((
% 98.91/13.06 (theeq) =>
% 98.91/13.06 ((
% 98.91/13.06 (iftrue) =>
% 98.91/13.06 ((
% 98.91/13.06 (iffalse) =>
% 98.91/13.06 ((
% 98.91/13.06 (iftrueorfalse) =>
% 98.91/13.06 ((
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% 98.91/13.06 ((
% 98.91/13.06 (binunionT_lem) =>
% 98.91/13.06 ((
% 98.91/13.06 (powersetT_lem) =>
% 98.91/13.06 ((
% 98.91/13.06 (setminusT_lem) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementT_lem) =>
% 98.91/13.06 ((
% 98.91/13.06 (setextT) =>
% 98.91/13.06 ((
% 98.91/13.06 (subsetTI) =>
% 98.91/13.06 ((
% 98.91/13.06 (powersetTI1) =>
% 98.91/13.06 ((
% 98.91/13.06 (powersetTE1) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementTI1) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementTE1) =>
% 98.91/13.06 ((
% 98.91/13.06 (binintersectTELcontra) =>
% 98.91/13.06 ((
% 98.91/13.06 (binintersectTERcontra) =>
% 98.91/13.06 ((
% 98.91/13.06 (contrasubsetT) =>
% 98.91/13.06 ((
% 98.91/13.06 (contrasubsetT1) =>
% 98.91/13.06 ((
% 98.91/13.06 (contrasubsetT2) =>
% 98.91/13.06 ((
% 98.91/13.06 (contrasubsetT3) =>
% 98.91/13.06 ((
% 98.91/13.06 (doubleComplementI1) =>
% 98.91/13.06 ((
% 98.91/13.06 (doubleComplementE1) =>
% 98.91/13.06 ((
% 98.91/13.06 (doubleComplementSub1) =>
% 98.91/13.06 ((
% 98.91/13.06 (doubleComplementSub2) =>
% 98.91/13.06 ((
% 98.91/13.06 (doubleComplementEq) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementTnotintersectT) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementImpComplementIntersect) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementSubsetComplementIntersect) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementInPowersetComplementIntersect) =>
% 98.91/13.06 ((
% 98.91/13.06 (contraSubsetComplement) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementTcontraSubset) =>
% 98.91/13.06 ((
% 98.91/13.06 (binunionTILcontra) =>
% 98.91/13.06 ((
% 98.91/13.06 (binunionTIRcontra) =>
% 98.91/13.06 ((
% 98.91/13.06 (inIntersectImpInUnion) =>
% 98.91/13.06 ((
% 98.91/13.06 (inIntersectImpInUnion2) =>
% 98.91/13.06 ((
% 98.91/13.06 (inIntersectImpInIntersectUnions) =>
% 98.91/13.06 ((
% 98.91/13.06 (intersectInPowersetIntersectUnions) =>
% 98.91/13.06 ((
% 98.91/13.06 (inComplementUnionImpNotIn1) =>
% 98.91/13.06 ((
% 98.91/13.06 (inComplementUnionImpInComplement1) =>
% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 ((
% 98.91/13.06 (complementUnionInPowersetComplement) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2a2) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan1a) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan1b) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan1) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2a) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2b2) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2b) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz13rule0) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz13rule1) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz13rule2) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz13rule3) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz13rule4) =>
% 98.91/13.06 ((
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% 98.91/13.06 ((
% 98.91/13.06 (woz1_2) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz1_3) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz1_4) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz1_5) =>
% 98.91/13.06 ((
% 98.91/13.06 (breln1all2) =>
% 98.91/13.06 ((
% 98.91/13.06 (breln1SetBreln1) =>
% 98.91/13.06 ((
% 98.91/13.06 (choice2fnsingleton) =>
% 98.91/13.06 ((
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% 98.91/13.06 (('#B') @ (
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% 98.91/13.06 (
% 98.91/13.06 (
% 98.91/13.06 ('#S') @ (
% 98.91/13.06 (
% 98.91/13.06 ('#B') @ (
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% 98.91/13.06 (
% 98.91/13.06 (
% 98.91/13.06 ('#S') @ dpsetconstr @
% 98.91/13.06 (
% 98.91/13.06 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.91/13.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1923])).
% 98.91/13.06 thf(zip_derived_cl1941, plain,
% 98.91/13.06 (~ (((app) =>
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% 98.91/13.06 (((lam2p) =>
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% 98.91/13.06 (((brelnall2) =>
% 98.91/13.06 (((ex1E2) =>
% 98.91/13.06 (((funcGraphProp1) =>
% 98.91/13.06 (((funcGraphProp3) =>
% 98.91/13.06 (((funcGraphProp2) =>
% 98.91/13.06 (((funcextLem) =>
% 98.91/13.06 (((funcGraphProp4) =>
% 98.91/13.06 (((subbreln) =>
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% 98.91/13.06 (((funcext) =>
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% 98.91/13.06 (((eta1) =>
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% 98.91/13.06 (iftrue) =>
% 98.91/13.06 ((
% 98.91/13.06 (iffalse) =>
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% 98.91/13.06 ((
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% 98.91/13.06 ((
% 98.91/13.06 (powersetT_lem) =>
% 98.91/13.06 ((
% 98.91/13.06 (setminusT_lem) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementT_lem) =>
% 98.91/13.06 ((
% 98.91/13.06 (setextT) =>
% 98.91/13.06 ((
% 98.91/13.06 (subsetTI) =>
% 98.91/13.06 ((
% 98.91/13.06 (powersetTI1) =>
% 98.91/13.06 ((
% 98.91/13.06 (powersetTE1) =>
% 98.91/13.06 ((
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% 98.91/13.06 ((
% 98.91/13.06 (complementTE1) =>
% 98.91/13.06 ((
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% 98.91/13.06 ((
% 98.91/13.06 (binintersectTERcontra) =>
% 98.91/13.06 ((
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% 98.91/13.06 ((
% 98.91/13.06 (contrasubsetT1) =>
% 98.91/13.06 ((
% 98.91/13.06 (contrasubsetT2) =>
% 98.91/13.06 ((
% 98.91/13.06 (contrasubsetT3) =>
% 98.91/13.06 ((
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% 98.91/13.06 ((
% 98.91/13.06 (doubleComplementE1) =>
% 98.91/13.06 ((
% 98.91/13.06 (doubleComplementSub1) =>
% 98.91/13.06 ((
% 98.91/13.06 (doubleComplementSub2) =>
% 98.91/13.06 ((
% 98.91/13.06 (doubleComplementEq) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementTnotintersectT) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementImpComplementIntersect) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementSubsetComplementIntersect) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementInPowersetComplementIntersect) =>
% 98.91/13.06 ((
% 98.91/13.06 (contraSubsetComplement) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementTcontraSubset) =>
% 98.91/13.06 ((
% 98.91/13.06 (binunionTILcontra) =>
% 98.91/13.06 ((
% 98.91/13.06 (binunionTIRcontra) =>
% 98.91/13.06 ((
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% 98.91/13.06 ((
% 98.91/13.06 (inIntersectImpInUnion2) =>
% 98.91/13.06 ((
% 98.91/13.06 (inIntersectImpInIntersectUnions) =>
% 98.91/13.06 ((
% 98.91/13.06 (intersectInPowersetIntersectUnions) =>
% 98.91/13.06 ((
% 98.91/13.06 (inComplementUnionImpNotIn1) =>
% 98.91/13.06 ((
% 98.91/13.06 (inComplementUnionImpInComplement1) =>
% 98.91/13.06 ((
% 98.91/13.06 (binunionTE) =>
% 98.91/13.06 ((
% 98.91/13.06 (binunionTEcontra) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2a1) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementUnionInPowersetComplement) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2a2) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan1a) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan1b) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan1) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2a) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2b2) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2b) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz13rule0) =>
% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 ((
% 98.91/13.06 (woz1_4) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz1_5) =>
% 98.91/13.06 ((
% 98.91/13.06 (breln1all2) =>
% 98.91/13.06 ((
% 98.91/13.06 (breln1SetBreln1) =>
% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 (('#B') @ (
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% 98.91/13.06 (
% 98.91/13.06 (
% 98.91/13.06 ('#S') @ (
% 98.91/13.06 (
% 98.91/13.06 ('#B') @ (
% 98.91/13.06 '#B') @
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% 98.91/13.06 (
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% 98.91/13.06 ('#S') @ dpsetconstr @
% 98.91/13.06 (
% 98.91/13.06 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.91/13.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1932])).
% 98.91/13.06 thf(zip_derived_cl1951, plain,
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% 98.91/13.06 (((lam2p) =>
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% 98.91/13.06 (((funcGraphProp1) =>
% 98.91/13.06 (((funcGraphProp3) =>
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% 98.91/13.06 (((funcextLem) =>
% 98.91/13.06 (((funcGraphProp4) =>
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% 98.91/13.06 (((funcext2) =>
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% 98.91/13.06 (((ap2apEq2) =>
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% 98.91/13.06 ((
% 98.91/13.06 (theeq) =>
% 98.91/13.06 ((
% 98.91/13.06 (iftrue) =>
% 98.91/13.06 ((
% 98.91/13.06 (iffalse) =>
% 98.91/13.06 ((
% 98.91/13.06 (iftrueorfalse) =>
% 98.91/13.06 ((
% 98.91/13.06 (binintersectT_lem) =>
% 98.91/13.06 ((
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% 98.91/13.06 ((
% 98.91/13.06 (powersetT_lem) =>
% 98.91/13.06 ((
% 98.91/13.06 (setminusT_lem) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementT_lem) =>
% 98.91/13.06 ((
% 98.91/13.06 (setextT) =>
% 98.91/13.06 ((
% 98.91/13.06 (subsetTI) =>
% 98.91/13.06 ((
% 98.91/13.06 (powersetTI1) =>
% 98.91/13.06 ((
% 98.91/13.06 (powersetTE1) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementTI1) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementTE1) =>
% 98.91/13.06 ((
% 98.91/13.06 (binintersectTELcontra) =>
% 98.91/13.06 ((
% 98.91/13.06 (binintersectTERcontra) =>
% 98.91/13.06 ((
% 98.91/13.06 (contrasubsetT) =>
% 98.91/13.06 ((
% 98.91/13.06 (contrasubsetT1) =>
% 98.91/13.06 ((
% 98.91/13.06 (contrasubsetT2) =>
% 98.91/13.06 ((
% 98.91/13.06 (contrasubsetT3) =>
% 98.91/13.06 ((
% 98.91/13.06 (doubleComplementI1) =>
% 98.91/13.06 ((
% 98.91/13.06 (doubleComplementE1) =>
% 98.91/13.06 ((
% 98.91/13.06 (doubleComplementSub1) =>
% 98.91/13.06 ((
% 98.91/13.06 (doubleComplementSub2) =>
% 98.91/13.06 ((
% 98.91/13.06 (doubleComplementEq) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementTnotintersectT) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementImpComplementIntersect) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementSubsetComplementIntersect) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementInPowersetComplementIntersect) =>
% 98.91/13.06 ((
% 98.91/13.06 (contraSubsetComplement) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementTcontraSubset) =>
% 98.91/13.06 ((
% 98.91/13.06 (binunionTILcontra) =>
% 98.91/13.06 ((
% 98.91/13.06 (binunionTIRcontra) =>
% 98.91/13.06 ((
% 98.91/13.06 (inIntersectImpInUnion) =>
% 98.91/13.06 ((
% 98.91/13.06 (inIntersectImpInUnion2) =>
% 98.91/13.06 ((
% 98.91/13.06 (inIntersectImpInIntersectUnions) =>
% 98.91/13.06 ((
% 98.91/13.06 (intersectInPowersetIntersectUnions) =>
% 98.91/13.06 ((
% 98.91/13.06 (inComplementUnionImpNotIn1) =>
% 98.91/13.06 ((
% 98.91/13.06 (inComplementUnionImpInComplement1) =>
% 98.91/13.06 ((
% 98.91/13.06 (binunionTE) =>
% 98.91/13.06 ((
% 98.91/13.06 (binunionTEcontra) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2a1) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementUnionInPowersetComplement) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2a2) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan1a) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan1b) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan1) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2a) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2b2) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2b) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz13rule0) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz13rule1) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz13rule2) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz13rule3) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz13rule4) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz1_1) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz1_2) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz1_3) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz1_4) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz1_5) =>
% 98.91/13.06 ((
% 98.91/13.06 (breln1all2) =>
% 98.91/13.06 ((
% 98.91/13.06 (breln1SetBreln1) =>
% 98.91/13.06 ((
% 98.91/13.06 (choice2fnsingleton) =>
% 98.91/13.06 ((
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% 98.91/13.06 (('#B') @ (
% 98.91/13.06 !!) @
% 98.91/13.06 (
% 98.91/13.06 (
% 98.91/13.06 ('#S') @ (
% 98.91/13.06 (
% 98.91/13.06 ('#B') @ (
% 98.91/13.06 '#B') @
% 98.91/13.06 breln1)) @
% 98.91/13.06 (
% 98.91/13.06 (
% 98.91/13.06 ('#S') @ dpsetconstr @
% 98.91/13.06 (
% 98.91/13.06 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.91/13.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1941])).
% 98.91/13.06 thf(zip_derived_cl1961, plain,
% 98.91/13.06 (~ (((ap2p) =>
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% 98.91/13.06 (((lamProp) =>
% 98.91/13.06 (((lamp) =>
% 98.91/13.06 (((lam2p) =>
% 98.91/13.06 (((brelnall1) =>
% 98.91/13.06 (((brelnall2) =>
% 98.91/13.06 (((ex1E2) =>
% 98.91/13.06 (((funcGraphProp1) =>
% 98.91/13.06 (((funcGraphProp3) =>
% 98.91/13.06 (((funcGraphProp2) =>
% 98.91/13.06 (((funcextLem) =>
% 98.91/13.06 (((funcGraphProp4) =>
% 98.91/13.06 (((subbreln) =>
% 98.91/13.06 (((eqbreln) =>
% 98.91/13.06 (((funcext) =>
% 98.91/13.06 (((funcext2) =>
% 98.91/13.06 (((ap2apEq1) =>
% 98.91/13.06 (((ap2apEq2) =>
% 98.91/13.06 (((beta1) =>
% 98.91/13.06 (((eta1) =>
% 98.91/13.06 (((lam2lamEq) =>
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% 98.91/13.06 (theeq) =>
% 98.91/13.06 ((
% 98.91/13.06 (iftrue) =>
% 98.91/13.06 ((
% 98.91/13.06 (iffalse) =>
% 98.91/13.06 ((
% 98.91/13.06 (iftrueorfalse) =>
% 98.91/13.06 ((
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% 98.91/13.06 ((
% 98.91/13.06 (binunionT_lem) =>
% 98.91/13.06 ((
% 98.91/13.06 (powersetT_lem) =>
% 98.91/13.06 ((
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% 98.91/13.06 ((
% 98.91/13.06 (complementT_lem) =>
% 98.91/13.06 ((
% 98.91/13.06 (setextT) =>
% 98.91/13.06 ((
% 98.91/13.06 (subsetTI) =>
% 98.91/13.06 ((
% 98.91/13.06 (powersetTI1) =>
% 98.91/13.06 ((
% 98.91/13.06 (powersetTE1) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementTI1) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementTE1) =>
% 98.91/13.06 ((
% 98.91/13.06 (binintersectTELcontra) =>
% 98.91/13.06 ((
% 98.91/13.06 (binintersectTERcontra) =>
% 98.91/13.06 ((
% 98.91/13.06 (contrasubsetT) =>
% 98.91/13.06 ((
% 98.91/13.06 (contrasubsetT1) =>
% 98.91/13.06 ((
% 98.91/13.06 (contrasubsetT2) =>
% 98.91/13.06 ((
% 98.91/13.06 (contrasubsetT3) =>
% 98.91/13.06 ((
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% 98.91/13.06 ((
% 98.91/13.06 (doubleComplementE1) =>
% 98.91/13.06 ((
% 98.91/13.06 (doubleComplementSub1) =>
% 98.91/13.06 ((
% 98.91/13.06 (doubleComplementSub2) =>
% 98.91/13.06 ((
% 98.91/13.06 (doubleComplementEq) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementTnotintersectT) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementImpComplementIntersect) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementSubsetComplementIntersect) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementInPowersetComplementIntersect) =>
% 98.91/13.06 ((
% 98.91/13.06 (contraSubsetComplement) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementTcontraSubset) =>
% 98.91/13.06 ((
% 98.91/13.06 (binunionTILcontra) =>
% 98.91/13.06 ((
% 98.91/13.06 (binunionTIRcontra) =>
% 98.91/13.06 ((
% 98.91/13.06 (inIntersectImpInUnion) =>
% 98.91/13.06 ((
% 98.91/13.06 (inIntersectImpInUnion2) =>
% 98.91/13.06 ((
% 98.91/13.06 (inIntersectImpInIntersectUnions) =>
% 98.91/13.06 ((
% 98.91/13.06 (intersectInPowersetIntersectUnions) =>
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% 98.91/13.06 (inComplementUnionImpNotIn1) =>
% 98.91/13.06 ((
% 98.91/13.06 (inComplementUnionImpInComplement1) =>
% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 ((
% 98.91/13.06 (demorgan2a1) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementUnionInPowersetComplement) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2a2) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan1a) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan1b) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan1) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2a) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2b2) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2b) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz13rule0) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz13rule1) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz13rule2) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz13rule3) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz13rule4) =>
% 98.91/13.06 ((
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% 98.91/13.06 ((
% 98.91/13.06 (woz1_2) =>
% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 (
% 98.91/13.06 ('#S') @ (
% 98.91/13.06 (
% 98.91/13.06 ('#B') @ (
% 98.91/13.06 '#B') @
% 98.91/13.06 breln1)) @
% 98.91/13.06 (
% 98.91/13.06 (
% 98.91/13.06 ('#S') @ dpsetconstr @
% 98.91/13.06 (
% 98.91/13.06 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.91/13.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1951])).
% 98.91/13.06 thf(zip_derived_cl1972, plain,
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% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 (
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% 98.91/13.06 ('#S') @ dpsetconstr @
% 98.91/13.06 (
% 98.91/13.06 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.91/13.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1961])).
% 98.91/13.06 thf(zip_derived_cl1983, plain,
% 98.91/13.06 (~ (((lamProp) =>
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% 98.91/13.06 (((lam2p) =>
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% 98.91/13.06 ((
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% 98.91/13.06 ((
% 98.91/13.06 (powersetT_lem) =>
% 98.91/13.06 ((
% 98.91/13.06 (setminusT_lem) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementT_lem) =>
% 98.91/13.06 ((
% 98.91/13.06 (setextT) =>
% 98.91/13.06 ((
% 98.91/13.06 (subsetTI) =>
% 98.91/13.06 ((
% 98.91/13.06 (powersetTI1) =>
% 98.91/13.06 ((
% 98.91/13.06 (powersetTE1) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementTI1) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementTE1) =>
% 98.91/13.06 ((
% 98.91/13.06 (binintersectTELcontra) =>
% 98.91/13.06 ((
% 98.91/13.06 (binintersectTERcontra) =>
% 98.91/13.06 ((
% 98.91/13.06 (contrasubsetT) =>
% 98.91/13.06 ((
% 98.91/13.06 (contrasubsetT1) =>
% 98.91/13.06 ((
% 98.91/13.06 (contrasubsetT2) =>
% 98.91/13.06 ((
% 98.91/13.06 (contrasubsetT3) =>
% 98.91/13.06 ((
% 98.91/13.06 (doubleComplementI1) =>
% 98.91/13.06 ((
% 98.91/13.06 (doubleComplementE1) =>
% 98.91/13.06 ((
% 98.91/13.06 (doubleComplementSub1) =>
% 98.91/13.06 ((
% 98.91/13.06 (doubleComplementSub2) =>
% 98.91/13.06 ((
% 98.91/13.06 (doubleComplementEq) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementTnotintersectT) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementImpComplementIntersect) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementSubsetComplementIntersect) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementInPowersetComplementIntersect) =>
% 98.91/13.06 ((
% 98.91/13.06 (contraSubsetComplement) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementTcontraSubset) =>
% 98.91/13.06 ((
% 98.91/13.06 (binunionTILcontra) =>
% 98.91/13.06 ((
% 98.91/13.06 (binunionTIRcontra) =>
% 98.91/13.06 ((
% 98.91/13.06 (inIntersectImpInUnion) =>
% 98.91/13.06 ((
% 98.91/13.06 (inIntersectImpInUnion2) =>
% 98.91/13.06 ((
% 98.91/13.06 (inIntersectImpInIntersectUnions) =>
% 98.91/13.06 ((
% 98.91/13.06 (intersectInPowersetIntersectUnions) =>
% 98.91/13.06 ((
% 98.91/13.06 (inComplementUnionImpNotIn1) =>
% 98.91/13.06 ((
% 98.91/13.06 (inComplementUnionImpInComplement1) =>
% 98.91/13.06 ((
% 98.91/13.06 (binunionTE) =>
% 98.91/13.06 ((
% 98.91/13.06 (binunionTEcontra) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2a1) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementUnionInPowersetComplement) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2a2) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan1a) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan1b) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan1) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2a) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2b2) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2b) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz13rule0) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz13rule1) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz13rule2) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz13rule3) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz13rule4) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz1_1) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz1_2) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz1_3) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz1_4) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz1_5) =>
% 98.91/13.06 ((
% 98.91/13.06 (breln1all2) =>
% 98.91/13.06 ((
% 98.91/13.06 (breln1SetBreln1) =>
% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 !!) @
% 98.91/13.06 (
% 98.91/13.06 (
% 98.91/13.06 ('#S') @ (
% 98.91/13.06 (
% 98.91/13.06 ('#B') @ (
% 98.91/13.06 '#B') @
% 98.91/13.06 breln1)) @
% 98.91/13.06 (
% 98.91/13.06 (
% 98.91/13.06 ('#S') @ dpsetconstr @
% 98.91/13.06 (
% 98.91/13.06 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.91/13.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1972])).
% 98.91/13.06 thf(zip_derived_cl1993, plain,
% 98.91/13.06 (~ (((lamp) =>
% 98.91/13.06 (((lam2p) =>
% 98.91/13.06 (((brelnall1) =>
% 98.91/13.06 (((brelnall2) =>
% 98.91/13.06 (((ex1E2) =>
% 98.91/13.06 (((funcGraphProp1) =>
% 98.91/13.06 (((funcGraphProp3) =>
% 98.91/13.06 (((funcGraphProp2) =>
% 98.91/13.06 (((funcextLem) =>
% 98.91/13.06 (((funcGraphProp4) =>
% 98.91/13.06 (((subbreln) =>
% 98.91/13.06 (((eqbreln) =>
% 98.91/13.06 (((funcext) =>
% 98.91/13.06 (((funcext2) =>
% 98.91/13.06 (((ap2apEq1) =>
% 98.91/13.06 (((ap2apEq2) =>
% 98.91/13.06 (((beta1) =>
% 98.91/13.06 (((eta1) =>
% 98.91/13.06 (((lam2lamEq) =>
% 98.91/13.06 (((beta2) =>
% 98.91/13.06 (((eta2) =>
% 98.91/13.06 (((iffalseProp1) =>
% 98.91/13.06 (((iffalseProp2) =>
% 98.91/13.06 (((iftrueProp1) =>
% 98.91/13.06 (((iftrueProp2) =>
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% 98.91/13.06 (((theeq) =>
% 98.91/13.06 (((iftrue) =>
% 98.91/13.06 (((iffalse) =>
% 98.91/13.06 ((
% 98.91/13.06 (iftrueorfalse) =>
% 98.91/13.06 ((
% 98.91/13.06 (binintersectT_lem) =>
% 98.91/13.06 ((
% 98.91/13.06 (binunionT_lem) =>
% 98.91/13.06 ((
% 98.91/13.06 (powersetT_lem) =>
% 98.91/13.06 ((
% 98.91/13.06 (setminusT_lem) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementT_lem) =>
% 98.91/13.06 ((
% 98.91/13.06 (setextT) =>
% 98.91/13.06 ((
% 98.91/13.06 (subsetTI) =>
% 98.91/13.06 ((
% 98.91/13.06 (powersetTI1) =>
% 98.91/13.06 ((
% 98.91/13.06 (powersetTE1) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementTI1) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementTE1) =>
% 98.91/13.06 ((
% 98.91/13.06 (binintersectTELcontra) =>
% 98.91/13.06 ((
% 98.91/13.06 (binintersectTERcontra) =>
% 98.91/13.06 ((
% 98.91/13.06 (contrasubsetT) =>
% 98.91/13.06 ((
% 98.91/13.06 (contrasubsetT1) =>
% 98.91/13.06 ((
% 98.91/13.06 (contrasubsetT2) =>
% 98.91/13.06 ((
% 98.91/13.06 (contrasubsetT3) =>
% 98.91/13.06 ((
% 98.91/13.06 (doubleComplementI1) =>
% 98.91/13.06 ((
% 98.91/13.06 (doubleComplementE1) =>
% 98.91/13.06 ((
% 98.91/13.06 (doubleComplementSub1) =>
% 98.91/13.06 ((
% 98.91/13.06 (doubleComplementSub2) =>
% 98.91/13.06 ((
% 98.91/13.06 (doubleComplementEq) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementTnotintersectT) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementImpComplementIntersect) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementSubsetComplementIntersect) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementInPowersetComplementIntersect) =>
% 98.91/13.06 ((
% 98.91/13.06 (contraSubsetComplement) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementTcontraSubset) =>
% 98.91/13.06 ((
% 98.91/13.06 (binunionTILcontra) =>
% 98.91/13.06 ((
% 98.91/13.06 (binunionTIRcontra) =>
% 98.91/13.06 ((
% 98.91/13.06 (inIntersectImpInUnion) =>
% 98.91/13.06 ((
% 98.91/13.06 (inIntersectImpInUnion2) =>
% 98.91/13.06 ((
% 98.91/13.06 (inIntersectImpInIntersectUnions) =>
% 98.91/13.06 ((
% 98.91/13.06 (intersectInPowersetIntersectUnions) =>
% 98.91/13.06 ((
% 98.91/13.06 (inComplementUnionImpNotIn1) =>
% 98.91/13.06 ((
% 98.91/13.06 (inComplementUnionImpInComplement1) =>
% 98.91/13.06 ((
% 98.91/13.06 (binunionTE) =>
% 98.91/13.06 ((
% 98.91/13.06 (binunionTEcontra) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2a1) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementUnionInPowersetComplement) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2a2) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan1a) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan1b) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan1) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2a) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2b2) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2b) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan2) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz13rule0) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz13rule1) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz13rule2) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz13rule3) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz13rule4) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz1_1) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz1_2) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz1_3) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz1_4) =>
% 98.91/13.06 ((
% 98.91/13.06 (woz1_5) =>
% 98.91/13.06 ((
% 98.91/13.06 (breln1all2) =>
% 98.91/13.06 ((
% 98.91/13.06 (breln1SetBreln1) =>
% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 (
% 98.91/13.06 (
% 98.91/13.06 ('#S') @ (
% 98.91/13.06 (
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% 98.91/13.06 breln1)) @
% 98.91/13.06 (
% 98.91/13.06 (
% 98.91/13.06 ('#S') @ dpsetconstr @
% 98.91/13.06 (
% 98.91/13.06 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.91/13.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1983])).
% 98.91/13.06 thf(zip_derived_cl2003, plain,
% 98.91/13.06 (~ (((lam2p) =>
% 98.91/13.06 (((brelnall1) =>
% 98.91/13.06 (((brelnall2) =>
% 98.91/13.06 (((ex1E2) =>
% 98.91/13.06 (((funcGraphProp1) =>
% 98.91/13.06 (((funcGraphProp3) =>
% 98.91/13.06 (((funcGraphProp2) =>
% 98.91/13.06 (((funcextLem) =>
% 98.91/13.06 (((funcGraphProp4) =>
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% 98.91/13.06 (((eqbreln) =>
% 98.91/13.06 (((funcext) =>
% 98.91/13.06 (((funcext2) =>
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% 98.91/13.06 (((beta1) =>
% 98.91/13.06 (((eta1) =>
% 98.91/13.06 (((lam2lamEq) =>
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% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 ((
% 98.91/13.06 (complementT_lem) =>
% 98.91/13.06 ((
% 98.91/13.06 (setextT) =>
% 98.91/13.06 ((
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% 98.91/13.06 ((
% 98.91/13.06 (powersetTI1) =>
% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 ((
% 98.91/13.06 (contrasubsetT) =>
% 98.91/13.06 ((
% 98.91/13.06 (contrasubsetT1) =>
% 98.91/13.06 ((
% 98.91/13.06 (contrasubsetT2) =>
% 98.91/13.06 ((
% 98.91/13.06 (contrasubsetT3) =>
% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 ((
% 98.91/13.06 (doubleComplementSub1) =>
% 98.91/13.06 ((
% 98.91/13.06 (doubleComplementSub2) =>
% 98.91/13.06 ((
% 98.91/13.06 (doubleComplementEq) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementTnotintersectT) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementImpComplementIntersect) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementSubsetComplementIntersect) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementInPowersetComplementIntersect) =>
% 98.91/13.06 ((
% 98.91/13.06 (contraSubsetComplement) =>
% 98.91/13.06 ((
% 98.91/13.06 (complementTcontraSubset) =>
% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 ((
% 98.91/13.06 (inIntersectImpInUnion2) =>
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% 98.91/13.06 (inIntersectImpInIntersectUnions) =>
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% 98.91/13.06 (intersectInPowersetIntersectUnions) =>
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% 98.91/13.06 ((
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% 98.91/13.06 ((
% 98.91/13.06 (complementUnionInPowersetComplement) =>
% 98.91/13.06 ((
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% 98.91/13.06 ((
% 98.91/13.06 (demorgan1a) =>
% 98.91/13.06 ((
% 98.91/13.06 (demorgan1b) =>
% 98.91/13.06 ((
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% 98.91/13.06 ((
% 98.91/13.06 (demorgan2a) =>
% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 ((
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% 98.91/13.06 (
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% 98.91/13.06 (
% 98.91/13.06 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.91/13.06 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1993])).
% 98.91/13.06 thf(zip_derived_cl2013, plain,
% 98.91/13.06 (~ (((brelnall1) =>
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% 98.91/13.07 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2013])).
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% 98.91/13.07 (inIntersectImpInIntersectUnions) =>
% 98.91/13.07 ((
% 98.91/13.07 (intersectInPowersetIntersectUnions) =>
% 98.91/13.07 ((
% 98.91/13.07 (inComplementUnionImpNotIn1) =>
% 98.91/13.07 ((
% 98.91/13.07 (inComplementUnionImpInComplement1) =>
% 98.91/13.07 ((
% 98.91/13.07 (binunionTE) =>
% 98.91/13.07 ((
% 98.91/13.07 (binunionTEcontra) =>
% 98.91/13.07 ((
% 98.91/13.07 (demorgan2a1) =>
% 98.91/13.07 ((
% 98.91/13.07 (complementUnionInPowersetComplement) =>
% 98.91/13.07 ((
% 98.91/13.07 (demorgan2a2) =>
% 98.91/13.07 ((
% 98.91/13.07 (demorgan1a) =>
% 98.91/13.07 ((
% 98.91/13.07 (demorgan1b) =>
% 98.91/13.07 ((
% 98.91/13.07 (demorgan1) =>
% 98.91/13.07 ((
% 98.91/13.07 (demorgan2a) =>
% 98.91/13.07 ((
% 98.91/13.07 (demorgan2b2) =>
% 98.91/13.07 ((
% 98.91/13.07 (demorgan2b) =>
% 98.91/13.07 ((
% 98.91/13.07 (demorgan2) =>
% 98.91/13.07 ((
% 98.91/13.07 (woz13rule0) =>
% 98.91/13.07 ((
% 98.91/13.07 (woz13rule1) =>
% 98.91/13.07 ((
% 98.91/13.07 (woz13rule2) =>
% 98.91/13.07 ((
% 98.91/13.07 (woz13rule3) =>
% 98.91/13.07 ((
% 98.91/13.07 (woz13rule4) =>
% 98.91/13.07 ((
% 98.91/13.07 (woz1_1) =>
% 98.91/13.07 ((
% 98.91/13.07 (woz1_2) =>
% 98.91/13.07 ((
% 98.91/13.07 (woz1_3) =>
% 98.91/13.07 ((
% 98.91/13.07 (woz1_4) =>
% 98.91/13.07 ((
% 98.91/13.07 (woz1_5) =>
% 98.91/13.07 ((
% 98.91/13.07 (breln1all2) =>
% 98.91/13.07 ((
% 98.91/13.07 (breln1SetBreln1) =>
% 98.91/13.07 ((
% 98.91/13.07 (choice2fnsingleton) =>
% 98.91/13.07 ((
% 98.91/13.07 (!!) @ (
% 98.91/13.07 (('#B') @ (
% 98.91/13.07 !!) @
% 98.91/13.07 (
% 98.91/13.07 (
% 98.91/13.07 ('#S') @ (
% 98.91/13.07 (
% 98.91/13.07 ('#B') @ (
% 98.91/13.07 '#B') @
% 98.91/13.07 breln1)) @
% 98.91/13.07 (
% 98.91/13.07 (
% 98.91/13.07 ('#S') @ dpsetconstr @
% 98.91/13.07 (
% 98.91/13.07 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.91/13.07 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2060])).
% 98.91/13.07 thf(zip_derived_cl2084, plain,
% 98.91/13.07 (~ (((funcGraphProp4) =>
% 98.91/13.07 (((subbreln) =>
% 98.91/13.07 (((eqbreln) =>
% 98.91/13.07 (((funcext) =>
% 98.91/13.07 (((funcext2) =>
% 98.91/13.07 (((ap2apEq1) =>
% 98.91/13.07 (((ap2apEq2) =>
% 98.91/13.07 (((beta1) =>
% 98.91/13.07 (((eta1) =>
% 98.91/13.07 (((lam2lamEq) =>
% 98.91/13.07 (((beta2) =>
% 98.91/13.07 (((eta2) =>
% 98.91/13.07 (((iffalseProp1) =>
% 98.91/13.07 (((iffalseProp2) =>
% 98.91/13.07 (((iftrueProp1) =>
% 98.91/13.07 (((iftrueProp2) =>
% 98.91/13.07 (((ifSingleton) =>
% 98.91/13.07 (((ifp) =>
% 98.91/13.07 (((theeq) =>
% 98.91/13.07 (((iftrue) =>
% 98.91/13.07 (((iffalse) =>
% 98.91/13.07 (((iftrueorfalse) =>
% 98.91/13.07 (((binintersectT_lem) =>
% 98.91/13.07 (((binunionT_lem) =>
% 98.91/13.07 (((powersetT_lem) =>
% 98.91/13.07 (((setminusT_lem) =>
% 98.91/13.07 (((complementT_lem) =>
% 98.91/13.07 (((setextT) =>
% 98.91/13.07 (((subsetTI) =>
% 98.91/13.07 (((powersetTI1) =>
% 98.91/13.07 ((
% 98.91/13.07 (powersetTE1) =>
% 98.91/13.07 ((
% 98.91/13.07 (complementTI1) =>
% 98.91/13.07 ((
% 98.91/13.07 (complementTE1) =>
% 98.91/13.07 ((
% 98.91/13.07 (binintersectTELcontra) =>
% 98.91/13.07 ((
% 98.91/13.07 (binintersectTERcontra) =>
% 98.91/13.07 ((
% 98.91/13.07 (contrasubsetT) =>
% 98.91/13.07 ((
% 98.91/13.07 (contrasubsetT1) =>
% 98.91/13.07 ((
% 98.91/13.07 (contrasubsetT2) =>
% 98.91/13.07 ((
% 98.91/13.07 (contrasubsetT3) =>
% 98.91/13.07 ((
% 98.91/13.07 (doubleComplementI1) =>
% 98.91/13.07 ((
% 98.91/13.07 (doubleComplementE1) =>
% 98.91/13.07 ((
% 98.91/13.07 (doubleComplementSub1) =>
% 98.91/13.07 ((
% 98.91/13.07 (doubleComplementSub2) =>
% 98.91/13.07 ((
% 98.91/13.07 (doubleComplementEq) =>
% 98.91/13.07 ((
% 98.91/13.07 (complementTnotintersectT) =>
% 98.91/13.07 ((
% 98.91/13.07 (complementImpComplementIntersect) =>
% 98.91/13.07 ((
% 98.91/13.07 (complementSubsetComplementIntersect) =>
% 98.91/13.07 ((
% 98.91/13.07 (complementInPowersetComplementIntersect) =>
% 98.91/13.07 ((
% 98.91/13.07 (contraSubsetComplement) =>
% 98.91/13.07 ((
% 98.91/13.07 (complementTcontraSubset) =>
% 98.91/13.07 ((
% 98.91/13.07 (binunionTILcontra) =>
% 98.91/13.07 ((
% 98.91/13.07 (binunionTIRcontra) =>
% 98.91/13.07 ((
% 98.91/13.07 (inIntersectImpInUnion) =>
% 98.91/13.07 ((
% 98.91/13.07 (inIntersectImpInUnion2) =>
% 98.91/13.07 ((
% 98.91/13.07 (inIntersectImpInIntersectUnions) =>
% 98.91/13.07 ((
% 98.91/13.07 (intersectInPowersetIntersectUnions) =>
% 98.91/13.07 ((
% 98.91/13.07 (inComplementUnionImpNotIn1) =>
% 98.91/13.07 ((
% 98.91/13.07 (inComplementUnionImpInComplement1) =>
% 98.91/13.07 ((
% 98.91/13.07 (binunionTE) =>
% 98.91/13.07 ((
% 98.91/13.07 (binunionTEcontra) =>
% 98.91/13.07 ((
% 98.91/13.07 (demorgan2a1) =>
% 98.91/13.07 ((
% 98.91/13.07 (complementUnionInPowersetComplement) =>
% 98.91/13.07 ((
% 98.91/13.07 (demorgan2a2) =>
% 98.91/13.07 ((
% 98.91/13.07 (demorgan1a) =>
% 98.91/13.07 ((
% 98.91/13.07 (demorgan1b) =>
% 98.91/13.07 ((
% 98.91/13.07 (demorgan1) =>
% 98.91/13.07 ((
% 98.91/13.07 (demorgan2a) =>
% 98.91/13.07 ((
% 98.91/13.07 (demorgan2b2) =>
% 98.91/13.07 ((
% 98.91/13.07 (demorgan2b) =>
% 98.91/13.07 ((
% 98.91/13.07 (demorgan2) =>
% 98.91/13.07 ((
% 98.91/13.07 (woz13rule0) =>
% 98.91/13.07 ((
% 98.91/13.07 (woz13rule1) =>
% 98.91/13.07 ((
% 98.91/13.07 (woz13rule2) =>
% 98.91/13.07 ((
% 98.91/13.07 (woz13rule3) =>
% 98.91/13.07 ((
% 98.91/13.07 (woz13rule4) =>
% 98.91/13.07 ((
% 98.91/13.07 (woz1_1) =>
% 98.91/13.07 ((
% 98.91/13.07 (woz1_2) =>
% 98.91/13.07 ((
% 98.91/13.07 (woz1_3) =>
% 98.91/13.07 ((
% 98.91/13.07 (woz1_4) =>
% 98.91/13.07 ((
% 98.91/13.07 (woz1_5) =>
% 98.91/13.07 ((
% 98.91/13.07 (breln1all2) =>
% 98.91/13.07 ((
% 98.91/13.07 (breln1SetBreln1) =>
% 98.91/13.07 ((
% 98.91/13.07 (choice2fnsingleton) =>
% 98.91/13.07 ((
% 98.91/13.07 (!!) @ (
% 98.91/13.07 (('#B') @ (
% 98.91/13.07 !!) @
% 98.91/13.07 (
% 98.91/13.07 (
% 98.91/13.07 ('#S') @ (
% 98.91/13.07 (
% 98.91/13.07 ('#B') @ (
% 98.91/13.07 '#B') @
% 98.91/13.07 breln1)) @
% 98.91/13.07 (
% 98.91/13.07 (
% 98.91/13.07 ('#S') @ dpsetconstr @
% 98.91/13.07 (
% 98.91/13.07 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.91/13.07 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2072])).
% 98.91/13.07 thf(zip_derived_cl2094, plain,
% 98.91/13.07 (~ (((subbreln) =>
% 98.91/13.07 (((eqbreln) =>
% 98.91/13.07 (((funcext) =>
% 98.91/13.07 (((funcext2) =>
% 98.91/13.07 (((ap2apEq1) =>
% 98.91/13.07 (((ap2apEq2) =>
% 98.91/13.07 (((beta1) =>
% 98.91/13.07 (((eta1) =>
% 98.91/13.07 (((lam2lamEq) =>
% 98.91/13.07 (((beta2) =>
% 98.91/13.07 (((eta2) =>
% 98.91/13.07 (((iffalseProp1) =>
% 98.91/13.07 (((iffalseProp2) =>
% 98.91/13.07 (((iftrueProp1) =>
% 98.91/13.07 (((iftrueProp2) =>
% 98.91/13.07 (((ifSingleton) =>
% 98.91/13.07 (((ifp) =>
% 98.91/13.07 (((theeq) =>
% 98.91/13.07 (((iftrue) =>
% 98.91/13.07 (((iffalse) =>
% 98.91/13.07 (((iftrueorfalse) =>
% 98.91/13.07 (((binintersectT_lem) =>
% 98.91/13.07 (((binunionT_lem) =>
% 98.91/13.07 (((powersetT_lem) =>
% 98.91/13.07 (((setminusT_lem) =>
% 98.91/13.07 (((complementT_lem) =>
% 98.91/13.07 (((setextT) =>
% 98.91/13.07 (((subsetTI) =>
% 98.91/13.07 (((powersetTI1) =>
% 98.91/13.07 (((powersetTE1) =>
% 98.91/13.07 ((
% 98.91/13.07 (complementTI1) =>
% 98.91/13.07 ((
% 98.91/13.07 (complementTE1) =>
% 98.91/13.07 ((
% 98.91/13.07 (binintersectTELcontra) =>
% 98.91/13.07 ((
% 98.91/13.07 (binintersectTERcontra) =>
% 98.91/13.07 ((
% 98.91/13.07 (contrasubsetT) =>
% 98.91/13.07 ((
% 98.91/13.07 (contrasubsetT1) =>
% 98.91/13.07 ((
% 98.91/13.07 (contrasubsetT2) =>
% 98.91/13.07 ((
% 98.91/13.07 (contrasubsetT3) =>
% 98.91/13.07 ((
% 98.91/13.07 (doubleComplementI1) =>
% 98.91/13.07 ((
% 98.91/13.07 (doubleComplementE1) =>
% 98.91/13.07 ((
% 98.91/13.07 (doubleComplementSub1) =>
% 98.91/13.07 ((
% 98.91/13.07 (doubleComplementSub2) =>
% 98.91/13.07 ((
% 98.91/13.07 (doubleComplementEq) =>
% 98.91/13.07 ((
% 98.91/13.07 (complementTnotintersectT) =>
% 98.91/13.07 ((
% 98.91/13.07 (complementImpComplementIntersect) =>
% 98.91/13.07 ((
% 98.91/13.07 (complementSubsetComplementIntersect) =>
% 98.91/13.07 ((
% 98.91/13.07 (complementInPowersetComplementIntersect) =>
% 98.91/13.07 ((
% 98.91/13.07 (contraSubsetComplement) =>
% 98.91/13.07 ((
% 98.91/13.07 (complementTcontraSubset) =>
% 98.91/13.07 ((
% 98.91/13.07 (binunionTILcontra) =>
% 98.91/13.07 ((
% 98.91/13.07 (binunionTIRcontra) =>
% 98.91/13.07 ((
% 98.91/13.07 (inIntersectImpInUnion) =>
% 98.91/13.07 ((
% 98.91/13.07 (inIntersectImpInUnion2) =>
% 98.91/13.07 ((
% 98.91/13.07 (inIntersectImpInIntersectUnions) =>
% 98.91/13.07 ((
% 98.91/13.07 (intersectInPowersetIntersectUnions) =>
% 98.91/13.07 ((
% 98.91/13.07 (inComplementUnionImpNotIn1) =>
% 98.91/13.07 ((
% 98.91/13.07 (inComplementUnionImpInComplement1) =>
% 98.91/13.07 ((
% 98.91/13.07 (binunionTE) =>
% 98.91/13.07 ((
% 98.91/13.07 (binunionTEcontra) =>
% 98.91/13.07 ((
% 98.91/13.07 (demorgan2a1) =>
% 98.91/13.07 ((
% 98.91/13.07 (complementUnionInPowersetComplement) =>
% 98.91/13.07 ((
% 98.91/13.07 (demorgan2a2) =>
% 98.91/13.07 ((
% 98.91/13.07 (demorgan1a) =>
% 98.91/13.07 ((
% 98.91/13.07 (demorgan1b) =>
% 98.91/13.07 ((
% 98.91/13.07 (demorgan1) =>
% 98.91/13.07 ((
% 98.91/13.07 (demorgan2a) =>
% 98.91/13.07 ((
% 98.91/13.07 (demorgan2b2) =>
% 98.91/13.07 ((
% 98.91/13.07 (demorgan2b) =>
% 98.91/13.07 ((
% 98.91/13.07 (demorgan2) =>
% 98.91/13.07 ((
% 98.91/13.07 (woz13rule0) =>
% 98.91/13.07 ((
% 98.91/13.07 (woz13rule1) =>
% 98.91/13.07 ((
% 98.91/13.07 (woz13rule2) =>
% 98.91/13.07 ((
% 98.91/13.07 (woz13rule3) =>
% 98.91/13.07 ((
% 98.91/13.07 (woz13rule4) =>
% 98.91/13.07 ((
% 98.91/13.07 (woz1_1) =>
% 98.91/13.07 ((
% 98.91/13.07 (woz1_2) =>
% 98.91/13.07 ((
% 98.91/13.07 (woz1_3) =>
% 98.91/13.07 ((
% 98.91/13.07 (woz1_4) =>
% 98.91/13.07 ((
% 98.91/13.07 (woz1_5) =>
% 98.91/13.07 ((
% 98.91/13.07 (breln1all2) =>
% 98.91/13.07 ((
% 98.91/13.07 (breln1SetBreln1) =>
% 98.91/13.07 ((
% 98.91/13.07 (choice2fnsingleton) =>
% 98.91/13.07 ((
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% 98.91/13.07 (('#B') @ (
% 98.91/13.07 !!) @
% 98.91/13.07 (
% 98.91/13.07 (
% 98.91/13.07 ('#S') @ (
% 98.91/13.07 (
% 98.91/13.07 ('#B') @ (
% 98.91/13.07 '#B') @
% 98.91/13.07 breln1)) @
% 98.91/13.07 (
% 98.91/13.07 (
% 98.91/13.07 ('#S') @ dpsetconstr @
% 98.91/13.07 (
% 98.91/13.07 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.91/13.07 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2084])).
% 98.91/13.07 thf(zip_derived_cl2105, plain,
% 98.91/13.07 (~ (((eqbreln) =>
% 98.91/13.07 (((funcext) =>
% 98.91/13.07 (((funcext2) =>
% 98.91/13.07 (((ap2apEq1) =>
% 98.91/13.07 (((ap2apEq2) =>
% 98.91/13.07 (((beta1) =>
% 98.91/13.07 (((eta1) =>
% 98.91/13.07 (((lam2lamEq) =>
% 98.91/13.07 (((beta2) =>
% 98.91/13.07 (((eta2) =>
% 98.91/13.07 (((iffalseProp1) =>
% 98.91/13.07 (((iffalseProp2) =>
% 98.91/13.07 (((iftrueProp1) =>
% 98.91/13.07 (((iftrueProp2) =>
% 98.91/13.07 (((ifSingleton) =>
% 98.91/13.07 (((ifp) =>
% 98.91/13.07 (((theeq) =>
% 98.91/13.07 (((iftrue) =>
% 98.91/13.07 (((iffalse) =>
% 98.91/13.07 (((iftrueorfalse) =>
% 98.91/13.07 (((binintersectT_lem) =>
% 98.91/13.07 (((binunionT_lem) =>
% 98.91/13.07 (((powersetT_lem) =>
% 98.91/13.07 (((setminusT_lem) =>
% 98.91/13.07 (((complementT_lem) =>
% 98.91/13.07 (((setextT) =>
% 98.91/13.07 (((subsetTI) =>
% 98.91/13.07 (((powersetTI1) =>
% 98.91/13.07 (((powersetTE1) =>
% 98.91/13.07 (((complementTI1) =>
% 98.91/13.07 ((
% 98.91/13.07 (complementTE1) =>
% 98.91/13.07 ((
% 98.91/13.07 (binintersectTELcontra) =>
% 98.91/13.07 ((
% 98.91/13.07 (binintersectTERcontra) =>
% 98.91/13.07 ((
% 98.91/13.07 (contrasubsetT) =>
% 98.91/13.07 ((
% 99.29/13.07 (contrasubsetT1) =>
% 99.29/13.07 ((
% 99.29/13.07 (contrasubsetT2) =>
% 99.29/13.07 ((
% 99.29/13.07 (contrasubsetT3) =>
% 99.29/13.07 ((
% 99.29/13.07 (doubleComplementI1) =>
% 99.29/13.07 ((
% 99.29/13.07 (doubleComplementE1) =>
% 99.29/13.07 ((
% 99.29/13.07 (doubleComplementSub1) =>
% 99.29/13.07 ((
% 99.29/13.07 (doubleComplementSub2) =>
% 99.29/13.07 ((
% 99.29/13.07 (doubleComplementEq) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementTnotintersectT) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementImpComplementIntersect) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementSubsetComplementIntersect) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementInPowersetComplementIntersect) =>
% 99.29/13.07 ((
% 99.29/13.07 (contraSubsetComplement) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementTcontraSubset) =>
% 99.29/13.07 ((
% 99.29/13.07 (binunionTILcontra) =>
% 99.29/13.07 ((
% 99.29/13.07 (binunionTIRcontra) =>
% 99.29/13.07 ((
% 99.29/13.07 (inIntersectImpInUnion) =>
% 99.29/13.07 ((
% 99.29/13.07 (inIntersectImpInUnion2) =>
% 99.29/13.07 ((
% 99.29/13.07 (inIntersectImpInIntersectUnions) =>
% 99.29/13.07 ((
% 99.29/13.07 (intersectInPowersetIntersectUnions) =>
% 99.29/13.07 ((
% 99.29/13.07 (inComplementUnionImpNotIn1) =>
% 99.29/13.07 ((
% 99.29/13.07 (inComplementUnionImpInComplement1) =>
% 99.29/13.07 ((
% 99.29/13.07 (binunionTE) =>
% 99.29/13.07 ((
% 99.29/13.07 (binunionTEcontra) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2a1) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementUnionInPowersetComplement) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2a2) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan1a) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan1b) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan1) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2a) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2b2) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2b) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz13rule0) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz13rule1) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz13rule2) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz13rule3) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz13rule4) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz1_1) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz1_2) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz1_3) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz1_4) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz1_5) =>
% 99.29/13.07 ((
% 99.29/13.07 (breln1all2) =>
% 99.29/13.07 ((
% 99.29/13.07 (breln1SetBreln1) =>
% 99.29/13.07 ((
% 99.29/13.07 (choice2fnsingleton) =>
% 99.29/13.07 ((
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% 99.29/13.07 (('#B') @ (
% 99.29/13.07 !!) @
% 99.29/13.07 (
% 99.29/13.07 (
% 99.29/13.07 ('#S') @ (
% 99.29/13.07 (
% 99.29/13.07 ('#B') @ (
% 99.29/13.07 '#B') @
% 99.29/13.07 breln1)) @
% 99.29/13.07 (
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% 99.29/13.07 ('#S') @ dpsetconstr @
% 99.29/13.07 (
% 99.29/13.07 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.29/13.07 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2094])).
% 99.29/13.07 thf(zip_derived_cl2118, plain,
% 99.29/13.07 (~ (((funcext) =>
% 99.29/13.07 (((funcext2) =>
% 99.29/13.07 (((ap2apEq1) =>
% 99.29/13.07 (((ap2apEq2) =>
% 99.29/13.07 (((beta1) =>
% 99.29/13.07 (((eta1) =>
% 99.29/13.07 (((lam2lamEq) =>
% 99.29/13.07 (((beta2) =>
% 99.29/13.07 (((eta2) =>
% 99.29/13.07 (((iffalseProp1) =>
% 99.29/13.07 (((iffalseProp2) =>
% 99.29/13.07 (((iftrueProp1) =>
% 99.29/13.07 (((iftrueProp2) =>
% 99.29/13.07 (((ifSingleton) =>
% 99.29/13.07 (((ifp) =>
% 99.29/13.07 (((theeq) =>
% 99.29/13.07 (((iftrue) =>
% 99.29/13.07 (((iffalse) =>
% 99.29/13.07 (((iftrueorfalse) =>
% 99.29/13.07 (((binintersectT_lem) =>
% 99.29/13.07 (((binunionT_lem) =>
% 99.29/13.07 (((powersetT_lem) =>
% 99.29/13.07 (((setminusT_lem) =>
% 99.29/13.07 (((complementT_lem) =>
% 99.29/13.07 (((setextT) =>
% 99.29/13.07 (((subsetTI) =>
% 99.29/13.07 (((powersetTI1) =>
% 99.29/13.07 (((powersetTE1) =>
% 99.29/13.07 (((complementTI1) =>
% 99.29/13.07 (((complementTE1) =>
% 99.29/13.07 ((
% 99.29/13.07 (binintersectTELcontra) =>
% 99.29/13.07 ((
% 99.29/13.07 (binintersectTERcontra) =>
% 99.29/13.07 ((
% 99.29/13.07 (contrasubsetT) =>
% 99.29/13.07 ((
% 99.29/13.07 (contrasubsetT1) =>
% 99.29/13.07 ((
% 99.29/13.07 (contrasubsetT2) =>
% 99.29/13.07 ((
% 99.29/13.07 (contrasubsetT3) =>
% 99.29/13.07 ((
% 99.29/13.07 (doubleComplementI1) =>
% 99.29/13.07 ((
% 99.29/13.07 (doubleComplementE1) =>
% 99.29/13.07 ((
% 99.29/13.07 (doubleComplementSub1) =>
% 99.29/13.07 ((
% 99.29/13.07 (doubleComplementSub2) =>
% 99.29/13.07 ((
% 99.29/13.07 (doubleComplementEq) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementTnotintersectT) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementImpComplementIntersect) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementSubsetComplementIntersect) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementInPowersetComplementIntersect) =>
% 99.29/13.07 ((
% 99.29/13.07 (contraSubsetComplement) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementTcontraSubset) =>
% 99.29/13.07 ((
% 99.29/13.07 (binunionTILcontra) =>
% 99.29/13.07 ((
% 99.29/13.07 (binunionTIRcontra) =>
% 99.29/13.07 ((
% 99.29/13.07 (inIntersectImpInUnion) =>
% 99.29/13.07 ((
% 99.29/13.07 (inIntersectImpInUnion2) =>
% 99.29/13.07 ((
% 99.29/13.07 (inIntersectImpInIntersectUnions) =>
% 99.29/13.07 ((
% 99.29/13.07 (intersectInPowersetIntersectUnions) =>
% 99.29/13.07 ((
% 99.29/13.07 (inComplementUnionImpNotIn1) =>
% 99.29/13.07 ((
% 99.29/13.07 (inComplementUnionImpInComplement1) =>
% 99.29/13.07 ((
% 99.29/13.07 (binunionTE) =>
% 99.29/13.07 ((
% 99.29/13.07 (binunionTEcontra) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2a1) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementUnionInPowersetComplement) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2a2) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan1a) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan1b) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan1) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2a) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2b2) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2b) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz13rule0) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz13rule1) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz13rule2) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz13rule3) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz13rule4) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz1_1) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz1_2) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz1_3) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz1_4) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz1_5) =>
% 99.29/13.07 ((
% 99.29/13.07 (breln1all2) =>
% 99.29/13.07 ((
% 99.29/13.07 (breln1SetBreln1) =>
% 99.29/13.07 ((
% 99.29/13.07 (choice2fnsingleton) =>
% 99.29/13.07 ((
% 99.29/13.07 (!!) @ (
% 99.29/13.07 (('#B') @ (
% 99.29/13.07 !!) @
% 99.29/13.07 (
% 99.29/13.07 (
% 99.29/13.07 ('#S') @ (
% 99.29/13.07 (
% 99.29/13.07 ('#B') @ (
% 99.29/13.07 '#B') @
% 99.29/13.07 breln1)) @
% 99.29/13.07 (
% 99.29/13.07 (
% 99.29/13.07 ('#S') @ dpsetconstr @
% 99.29/13.07 (
% 99.29/13.07 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.29/13.07 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2105])).
% 99.29/13.07 thf(zip_derived_cl2133, plain,
% 99.29/13.07 (~ (((funcext2) =>
% 99.29/13.07 (((ap2apEq1) =>
% 99.29/13.07 (((ap2apEq2) =>
% 99.29/13.07 (((beta1) =>
% 99.29/13.07 (((eta1) =>
% 99.29/13.07 (((lam2lamEq) =>
% 99.29/13.07 (((beta2) =>
% 99.29/13.07 (((eta2) =>
% 99.29/13.07 (((iffalseProp1) =>
% 99.29/13.07 (((iffalseProp2) =>
% 99.29/13.07 (((iftrueProp1) =>
% 99.29/13.07 (((iftrueProp2) =>
% 99.29/13.07 (((ifSingleton) =>
% 99.29/13.07 (((ifp) =>
% 99.29/13.07 (((theeq) =>
% 99.29/13.07 (((iftrue) =>
% 99.29/13.07 (((iffalse) =>
% 99.29/13.07 (((iftrueorfalse) =>
% 99.29/13.07 (((binintersectT_lem) =>
% 99.29/13.07 (((binunionT_lem) =>
% 99.29/13.07 (((powersetT_lem) =>
% 99.29/13.07 (((setminusT_lem) =>
% 99.29/13.07 (((complementT_lem) =>
% 99.29/13.07 (((setextT) =>
% 99.29/13.07 (((subsetTI) =>
% 99.29/13.07 (((powersetTI1) =>
% 99.29/13.07 (((powersetTE1) =>
% 99.29/13.07 (((complementTI1) =>
% 99.29/13.07 (((complementTE1) =>
% 99.29/13.07 (((binintersectTELcontra) =>
% 99.29/13.07 ((
% 99.29/13.07 (binintersectTERcontra) =>
% 99.29/13.07 ((
% 99.29/13.07 (contrasubsetT) =>
% 99.29/13.07 ((
% 99.29/13.07 (contrasubsetT1) =>
% 99.29/13.07 ((
% 99.29/13.07 (contrasubsetT2) =>
% 99.29/13.07 ((
% 99.29/13.07 (contrasubsetT3) =>
% 99.29/13.07 ((
% 99.29/13.07 (doubleComplementI1) =>
% 99.29/13.07 ((
% 99.29/13.07 (doubleComplementE1) =>
% 99.29/13.07 ((
% 99.29/13.07 (doubleComplementSub1) =>
% 99.29/13.07 ((
% 99.29/13.07 (doubleComplementSub2) =>
% 99.29/13.07 ((
% 99.29/13.07 (doubleComplementEq) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementTnotintersectT) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementImpComplementIntersect) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementSubsetComplementIntersect) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementInPowersetComplementIntersect) =>
% 99.29/13.07 ((
% 99.29/13.07 (contraSubsetComplement) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementTcontraSubset) =>
% 99.29/13.07 ((
% 99.29/13.07 (binunionTILcontra) =>
% 99.29/13.07 ((
% 99.29/13.07 (binunionTIRcontra) =>
% 99.29/13.07 ((
% 99.29/13.07 (inIntersectImpInUnion) =>
% 99.29/13.07 ((
% 99.29/13.07 (inIntersectImpInUnion2) =>
% 99.29/13.07 ((
% 99.29/13.07 (inIntersectImpInIntersectUnions) =>
% 99.29/13.07 ((
% 99.29/13.07 (intersectInPowersetIntersectUnions) =>
% 99.29/13.07 ((
% 99.29/13.07 (inComplementUnionImpNotIn1) =>
% 99.29/13.07 ((
% 99.29/13.07 (inComplementUnionImpInComplement1) =>
% 99.29/13.07 ((
% 99.29/13.07 (binunionTE) =>
% 99.29/13.07 ((
% 99.29/13.07 (binunionTEcontra) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2a1) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementUnionInPowersetComplement) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2a2) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan1a) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan1b) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan1) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2a) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2b2) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2b) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz13rule0) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz13rule1) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz13rule2) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz13rule3) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz13rule4) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz1_1) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz1_2) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz1_3) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz1_4) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz1_5) =>
% 99.29/13.07 ((
% 99.29/13.07 (breln1all2) =>
% 99.29/13.07 ((
% 99.29/13.07 (breln1SetBreln1) =>
% 99.29/13.07 ((
% 99.29/13.07 (choice2fnsingleton) =>
% 99.29/13.07 ((
% 99.29/13.07 (!!) @ (
% 99.29/13.07 (('#B') @ (
% 99.29/13.07 !!) @
% 99.29/13.07 (
% 99.29/13.07 (
% 99.29/13.07 ('#S') @ (
% 99.29/13.07 (
% 99.29/13.07 ('#B') @ (
% 99.29/13.07 '#B') @
% 99.29/13.07 breln1)) @
% 99.29/13.07 (
% 99.29/13.07 (
% 99.29/13.07 ('#S') @ dpsetconstr @
% 99.29/13.07 (
% 99.29/13.07 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.29/13.07 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2118])).
% 99.29/13.07 thf(zip_derived_cl2149, plain,
% 99.29/13.07 (~ (((ap2apEq1) =>
% 99.29/13.07 (((ap2apEq2) =>
% 99.29/13.07 (((beta1) =>
% 99.29/13.07 (((eta1) =>
% 99.29/13.07 (((lam2lamEq) =>
% 99.29/13.07 (((beta2) =>
% 99.29/13.07 (((eta2) =>
% 99.29/13.07 (((iffalseProp1) =>
% 99.29/13.07 (((iffalseProp2) =>
% 99.29/13.07 (((iftrueProp1) =>
% 99.29/13.07 (((iftrueProp2) =>
% 99.29/13.07 (((ifSingleton) =>
% 99.29/13.07 (((ifp) =>
% 99.29/13.07 (((theeq) =>
% 99.29/13.07 (((iftrue) =>
% 99.29/13.07 (((iffalse) =>
% 99.29/13.07 (((iftrueorfalse) =>
% 99.29/13.07 (((binintersectT_lem) =>
% 99.29/13.07 (((binunionT_lem) =>
% 99.29/13.07 (((powersetT_lem) =>
% 99.29/13.07 (((setminusT_lem) =>
% 99.29/13.07 (((complementT_lem) =>
% 99.29/13.07 (((setextT) =>
% 99.29/13.07 (((subsetTI) =>
% 99.29/13.07 (((powersetTI1) =>
% 99.29/13.07 (((powersetTE1) =>
% 99.29/13.07 (((complementTI1) =>
% 99.29/13.07 (((complementTE1) =>
% 99.29/13.07 (((binintersectTELcontra) =>
% 99.29/13.07 (((binintersectTERcontra) =>
% 99.29/13.07 ((
% 99.29/13.07 (contrasubsetT) =>
% 99.29/13.07 ((
% 99.29/13.07 (contrasubsetT1) =>
% 99.29/13.07 ((
% 99.29/13.07 (contrasubsetT2) =>
% 99.29/13.07 ((
% 99.29/13.07 (contrasubsetT3) =>
% 99.29/13.07 ((
% 99.29/13.07 (doubleComplementI1) =>
% 99.29/13.07 ((
% 99.29/13.07 (doubleComplementE1) =>
% 99.29/13.07 ((
% 99.29/13.07 (doubleComplementSub1) =>
% 99.29/13.07 ((
% 99.29/13.07 (doubleComplementSub2) =>
% 99.29/13.07 ((
% 99.29/13.07 (doubleComplementEq) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementTnotintersectT) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementImpComplementIntersect) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementSubsetComplementIntersect) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementInPowersetComplementIntersect) =>
% 99.29/13.07 ((
% 99.29/13.07 (contraSubsetComplement) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementTcontraSubset) =>
% 99.29/13.07 ((
% 99.29/13.07 (binunionTILcontra) =>
% 99.29/13.07 ((
% 99.29/13.07 (binunionTIRcontra) =>
% 99.29/13.07 ((
% 99.29/13.07 (inIntersectImpInUnion) =>
% 99.29/13.07 ((
% 99.29/13.07 (inIntersectImpInUnion2) =>
% 99.29/13.07 ((
% 99.29/13.07 (inIntersectImpInIntersectUnions) =>
% 99.29/13.07 ((
% 99.29/13.07 (intersectInPowersetIntersectUnions) =>
% 99.29/13.07 ((
% 99.29/13.07 (inComplementUnionImpNotIn1) =>
% 99.29/13.07 ((
% 99.29/13.07 (inComplementUnionImpInComplement1) =>
% 99.29/13.07 ((
% 99.29/13.07 (binunionTE) =>
% 99.29/13.07 ((
% 99.29/13.07 (binunionTEcontra) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2a1) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementUnionInPowersetComplement) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2a2) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan1a) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan1b) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan1) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2a) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2b2) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2b) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz13rule0) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz13rule1) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz13rule2) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz13rule3) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz13rule4) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz1_1) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz1_2) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz1_3) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz1_4) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz1_5) =>
% 99.29/13.07 ((
% 99.29/13.07 (breln1all2) =>
% 99.29/13.07 ((
% 99.29/13.07 (breln1SetBreln1) =>
% 99.29/13.07 ((
% 99.29/13.07 (choice2fnsingleton) =>
% 99.29/13.07 ((
% 99.29/13.07 (!!) @ (
% 99.29/13.07 (('#B') @ (
% 99.29/13.07 !!) @
% 99.29/13.07 (
% 99.29/13.07 (
% 99.29/13.07 ('#S') @ (
% 99.29/13.07 (
% 99.29/13.07 ('#B') @ (
% 99.29/13.07 '#B') @
% 99.29/13.07 breln1)) @
% 99.29/13.07 (
% 99.29/13.07 (
% 99.29/13.07 ('#S') @ dpsetconstr @
% 99.29/13.07 (
% 99.29/13.07 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.29/13.07 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2133])).
% 99.29/13.07 thf(zip_derived_cl2166, plain,
% 99.29/13.07 (~ (((ap2apEq2) =>
% 99.29/13.07 (((beta1) =>
% 99.29/13.07 (((eta1) =>
% 99.29/13.07 (((lam2lamEq) =>
% 99.29/13.07 (((beta2) =>
% 99.29/13.07 (((eta2) =>
% 99.29/13.07 (((iffalseProp1) =>
% 99.29/13.07 (((iffalseProp2) =>
% 99.29/13.07 (((iftrueProp1) =>
% 99.29/13.07 (((iftrueProp2) =>
% 99.29/13.07 (((ifSingleton) =>
% 99.29/13.07 (((ifp) =>
% 99.29/13.07 (((theeq) =>
% 99.29/13.07 (((iftrue) =>
% 99.29/13.07 (((iffalse) =>
% 99.29/13.07 (((iftrueorfalse) =>
% 99.29/13.07 (((binintersectT_lem) =>
% 99.29/13.07 (((binunionT_lem) =>
% 99.29/13.07 (((powersetT_lem) =>
% 99.29/13.07 (((setminusT_lem) =>
% 99.29/13.07 (((complementT_lem) =>
% 99.29/13.07 (((setextT) =>
% 99.29/13.07 (((subsetTI) =>
% 99.29/13.07 (((powersetTI1) =>
% 99.29/13.07 (((powersetTE1) =>
% 99.29/13.07 (((complementTI1) =>
% 99.29/13.07 (((complementTE1) =>
% 99.29/13.07 (((binintersectTELcontra) =>
% 99.29/13.07 (((binintersectTERcontra) =>
% 99.29/13.07 (((contrasubsetT) =>
% 99.29/13.07 ((
% 99.29/13.07 (contrasubsetT1) =>
% 99.29/13.07 ((
% 99.29/13.07 (contrasubsetT2) =>
% 99.29/13.07 ((
% 99.29/13.07 (contrasubsetT3) =>
% 99.29/13.07 ((
% 99.29/13.07 (doubleComplementI1) =>
% 99.29/13.07 ((
% 99.29/13.07 (doubleComplementE1) =>
% 99.29/13.07 ((
% 99.29/13.07 (doubleComplementSub1) =>
% 99.29/13.07 ((
% 99.29/13.07 (doubleComplementSub2) =>
% 99.29/13.07 ((
% 99.29/13.07 (doubleComplementEq) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementTnotintersectT) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementImpComplementIntersect) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementSubsetComplementIntersect) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementInPowersetComplementIntersect) =>
% 99.29/13.07 ((
% 99.29/13.07 (contraSubsetComplement) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementTcontraSubset) =>
% 99.29/13.07 ((
% 99.29/13.07 (binunionTILcontra) =>
% 99.29/13.07 ((
% 99.29/13.07 (binunionTIRcontra) =>
% 99.29/13.07 ((
% 99.29/13.07 (inIntersectImpInUnion) =>
% 99.29/13.07 ((
% 99.29/13.07 (inIntersectImpInUnion2) =>
% 99.29/13.07 ((
% 99.29/13.07 (inIntersectImpInIntersectUnions) =>
% 99.29/13.07 ((
% 99.29/13.07 (intersectInPowersetIntersectUnions) =>
% 99.29/13.07 ((
% 99.29/13.07 (inComplementUnionImpNotIn1) =>
% 99.29/13.07 ((
% 99.29/13.07 (inComplementUnionImpInComplement1) =>
% 99.29/13.07 ((
% 99.29/13.07 (binunionTE) =>
% 99.29/13.07 ((
% 99.29/13.07 (binunionTEcontra) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2a1) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementUnionInPowersetComplement) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2a2) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan1a) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan1b) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan1) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2a) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2b2) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2b) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz13rule0) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz13rule1) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz13rule2) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz13rule3) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz13rule4) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz1_1) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz1_2) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz1_3) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz1_4) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz1_5) =>
% 99.29/13.07 ((
% 99.29/13.07 (breln1all2) =>
% 99.29/13.07 ((
% 99.29/13.07 (breln1SetBreln1) =>
% 99.29/13.07 ((
% 99.29/13.07 (choice2fnsingleton) =>
% 99.29/13.07 ((
% 99.29/13.07 (!!) @ (
% 99.29/13.07 (('#B') @ (
% 99.29/13.07 !!) @
% 99.29/13.07 (
% 99.29/13.07 (
% 99.29/13.07 ('#S') @ (
% 99.29/13.07 (
% 99.29/13.07 ('#B') @ (
% 99.29/13.07 '#B') @
% 99.29/13.07 breln1)) @
% 99.29/13.07 (
% 99.29/13.07 (
% 99.29/13.07 ('#S') @ dpsetconstr @
% 99.29/13.07 (
% 99.29/13.07 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.29/13.07 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2149])).
% 99.29/13.07 thf(zip_derived_cl2185, plain,
% 99.29/13.07 (~ (((beta1) =>
% 99.29/13.07 (((eta1) =>
% 99.29/13.07 (((lam2lamEq) =>
% 99.29/13.07 (((beta2) =>
% 99.29/13.07 (((eta2) =>
% 99.29/13.07 (((iffalseProp1) =>
% 99.29/13.07 (((iffalseProp2) =>
% 99.29/13.07 (((iftrueProp1) =>
% 99.29/13.07 (((iftrueProp2) =>
% 99.29/13.07 (((ifSingleton) =>
% 99.29/13.07 (((ifp) =>
% 99.29/13.07 (((theeq) =>
% 99.29/13.07 (((iftrue) =>
% 99.29/13.07 (((iffalse) =>
% 99.29/13.07 (((iftrueorfalse) =>
% 99.29/13.07 (((binintersectT_lem) =>
% 99.29/13.07 (((binunionT_lem) =>
% 99.29/13.07 (((powersetT_lem) =>
% 99.29/13.07 (((setminusT_lem) =>
% 99.29/13.07 (((complementT_lem) =>
% 99.29/13.07 (((setextT) =>
% 99.29/13.07 (((subsetTI) =>
% 99.29/13.07 (((powersetTI1) =>
% 99.29/13.07 (((powersetTE1) =>
% 99.29/13.07 (((complementTI1) =>
% 99.29/13.07 (((complementTE1) =>
% 99.29/13.07 (((binintersectTELcontra) =>
% 99.29/13.07 (((binintersectTERcontra) =>
% 99.29/13.07 (((contrasubsetT) =>
% 99.29/13.07 (((contrasubsetT1) =>
% 99.29/13.07 ((
% 99.29/13.07 (contrasubsetT2) =>
% 99.29/13.07 ((
% 99.29/13.07 (contrasubsetT3) =>
% 99.29/13.07 ((
% 99.29/13.07 (doubleComplementI1) =>
% 99.29/13.07 ((
% 99.29/13.07 (doubleComplementE1) =>
% 99.29/13.07 ((
% 99.29/13.07 (doubleComplementSub1) =>
% 99.29/13.07 ((
% 99.29/13.07 (doubleComplementSub2) =>
% 99.29/13.07 ((
% 99.29/13.07 (doubleComplementEq) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementTnotintersectT) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementImpComplementIntersect) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementSubsetComplementIntersect) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementInPowersetComplementIntersect) =>
% 99.29/13.07 ((
% 99.29/13.07 (contraSubsetComplement) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementTcontraSubset) =>
% 99.29/13.07 ((
% 99.29/13.07 (binunionTILcontra) =>
% 99.29/13.07 ((
% 99.29/13.07 (binunionTIRcontra) =>
% 99.29/13.07 ((
% 99.29/13.07 (inIntersectImpInUnion) =>
% 99.29/13.07 ((
% 99.29/13.07 (inIntersectImpInUnion2) =>
% 99.29/13.07 ((
% 99.29/13.07 (inIntersectImpInIntersectUnions) =>
% 99.29/13.07 ((
% 99.29/13.07 (intersectInPowersetIntersectUnions) =>
% 99.29/13.07 ((
% 99.29/13.07 (inComplementUnionImpNotIn1) =>
% 99.29/13.07 ((
% 99.29/13.07 (inComplementUnionImpInComplement1) =>
% 99.29/13.07 ((
% 99.29/13.07 (binunionTE) =>
% 99.29/13.07 ((
% 99.29/13.07 (binunionTEcontra) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2a1) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementUnionInPowersetComplement) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2a2) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan1a) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan1b) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan1) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2a) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2b2) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2b) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz13rule0) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz13rule1) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz13rule2) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz13rule3) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz13rule4) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz1_1) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz1_2) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz1_3) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz1_4) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz1_5) =>
% 99.29/13.07 ((
% 99.29/13.07 (breln1all2) =>
% 99.29/13.07 ((
% 99.29/13.07 (breln1SetBreln1) =>
% 99.29/13.07 ((
% 99.29/13.07 (choice2fnsingleton) =>
% 99.29/13.07 ((
% 99.29/13.07 (!!) @ (
% 99.29/13.07 (('#B') @ (
% 99.29/13.07 !!) @
% 99.29/13.07 (
% 99.29/13.07 (
% 99.29/13.07 ('#S') @ (
% 99.29/13.07 (
% 99.29/13.07 ('#B') @ (
% 99.29/13.07 '#B') @
% 99.29/13.07 breln1)) @
% 99.29/13.07 (
% 99.29/13.07 (
% 99.29/13.07 ('#S') @ dpsetconstr @
% 99.29/13.07 (
% 99.29/13.07 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.29/13.07 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2166])).
% 99.29/13.07 thf(zip_derived_cl2203, plain,
% 99.29/13.07 (~ (((eta1) =>
% 99.29/13.07 (((lam2lamEq) =>
% 99.29/13.07 (((beta2) =>
% 99.29/13.07 (((eta2) =>
% 99.29/13.07 (((iffalseProp1) =>
% 99.29/13.07 (((iffalseProp2) =>
% 99.29/13.07 (((iftrueProp1) =>
% 99.29/13.07 (((iftrueProp2) =>
% 99.29/13.07 (((ifSingleton) =>
% 99.29/13.07 (((ifp) =>
% 99.29/13.07 (((theeq) =>
% 99.29/13.07 (((iftrue) =>
% 99.29/13.07 (((iffalse) =>
% 99.29/13.07 (((iftrueorfalse) =>
% 99.29/13.07 (((binintersectT_lem) =>
% 99.29/13.07 (((binunionT_lem) =>
% 99.29/13.07 (((powersetT_lem) =>
% 99.29/13.07 (((setminusT_lem) =>
% 99.29/13.07 (((complementT_lem) =>
% 99.29/13.07 (((setextT) =>
% 99.29/13.07 (((subsetTI) =>
% 99.29/13.07 (((powersetTI1) =>
% 99.29/13.07 (((powersetTE1) =>
% 99.29/13.07 (((complementTI1) =>
% 99.29/13.07 (((complementTE1) =>
% 99.29/13.07 (((binintersectTELcontra) =>
% 99.29/13.07 (((binintersectTERcontra) =>
% 99.29/13.07 (((contrasubsetT) =>
% 99.29/13.07 (((contrasubsetT1) =>
% 99.29/13.07 (((contrasubsetT2) =>
% 99.29/13.07 ((
% 99.29/13.07 (contrasubsetT3) =>
% 99.29/13.07 ((
% 99.29/13.07 (doubleComplementI1) =>
% 99.29/13.07 ((
% 99.29/13.07 (doubleComplementE1) =>
% 99.29/13.07 ((
% 99.29/13.07 (doubleComplementSub1) =>
% 99.29/13.07 ((
% 99.29/13.07 (doubleComplementSub2) =>
% 99.29/13.07 ((
% 99.29/13.07 (doubleComplementEq) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementTnotintersectT) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementImpComplementIntersect) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementSubsetComplementIntersect) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementInPowersetComplementIntersect) =>
% 99.29/13.07 ((
% 99.29/13.07 (contraSubsetComplement) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementTcontraSubset) =>
% 99.29/13.07 ((
% 99.29/13.07 (binunionTILcontra) =>
% 99.29/13.07 ((
% 99.29/13.07 (binunionTIRcontra) =>
% 99.29/13.07 ((
% 99.29/13.07 (inIntersectImpInUnion) =>
% 99.29/13.07 ((
% 99.29/13.07 (inIntersectImpInUnion2) =>
% 99.29/13.07 ((
% 99.29/13.07 (inIntersectImpInIntersectUnions) =>
% 99.29/13.07 ((
% 99.29/13.07 (intersectInPowersetIntersectUnions) =>
% 99.29/13.07 ((
% 99.29/13.07 (inComplementUnionImpNotIn1) =>
% 99.29/13.07 ((
% 99.29/13.07 (inComplementUnionImpInComplement1) =>
% 99.29/13.07 ((
% 99.29/13.07 (binunionTE) =>
% 99.29/13.07 ((
% 99.29/13.07 (binunionTEcontra) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2a1) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementUnionInPowersetComplement) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2a2) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan1a) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan1b) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan1) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2a) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2b2) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2b) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz13rule0) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz13rule1) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz13rule2) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz13rule3) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz13rule4) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz1_1) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz1_2) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz1_3) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz1_4) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz1_5) =>
% 99.29/13.07 ((
% 99.29/13.07 (breln1all2) =>
% 99.29/13.07 ((
% 99.29/13.07 (breln1SetBreln1) =>
% 99.29/13.07 ((
% 99.29/13.07 (choice2fnsingleton) =>
% 99.29/13.07 ((
% 99.29/13.07 (!!) @ (
% 99.29/13.07 (('#B') @ (
% 99.29/13.07 !!) @
% 99.29/13.07 (
% 99.29/13.07 (
% 99.29/13.07 ('#S') @ (
% 99.29/13.07 (
% 99.29/13.07 ('#B') @ (
% 99.29/13.07 '#B') @
% 99.29/13.07 breln1)) @
% 99.29/13.07 (
% 99.29/13.07 (
% 99.29/13.07 ('#S') @ dpsetconstr @
% 99.29/13.07 (
% 99.29/13.07 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.29/13.07 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2185])).
% 99.29/13.07 thf(zip_derived_cl2219, plain,
% 99.29/13.07 (~ (((lam2lamEq) =>
% 99.29/13.07 (((beta2) =>
% 99.29/13.07 (((eta2) =>
% 99.29/13.07 (((iffalseProp1) =>
% 99.29/13.07 (((iffalseProp2) =>
% 99.29/13.07 (((iftrueProp1) =>
% 99.29/13.07 (((iftrueProp2) =>
% 99.29/13.07 (((ifSingleton) =>
% 99.29/13.07 (((ifp) =>
% 99.29/13.07 (((theeq) =>
% 99.29/13.07 (((iftrue) =>
% 99.29/13.07 (((iffalse) =>
% 99.29/13.07 (((iftrueorfalse) =>
% 99.29/13.07 (((binintersectT_lem) =>
% 99.29/13.07 (((binunionT_lem) =>
% 99.29/13.07 (((powersetT_lem) =>
% 99.29/13.07 (((setminusT_lem) =>
% 99.29/13.07 (((complementT_lem) =>
% 99.29/13.07 (((setextT) =>
% 99.29/13.07 (((subsetTI) =>
% 99.29/13.07 (((powersetTI1) =>
% 99.29/13.07 (((powersetTE1) =>
% 99.29/13.07 (((complementTI1) =>
% 99.29/13.07 (((complementTE1) =>
% 99.29/13.07 (((binintersectTELcontra) =>
% 99.29/13.07 (((binintersectTERcontra) =>
% 99.29/13.07 (((contrasubsetT) =>
% 99.29/13.07 (((contrasubsetT1) =>
% 99.29/13.07 (((contrasubsetT2) =>
% 99.29/13.07 (((contrasubsetT3) =>
% 99.29/13.07 ((
% 99.29/13.07 (doubleComplementI1) =>
% 99.29/13.07 ((
% 99.29/13.07 (doubleComplementE1) =>
% 99.29/13.07 ((
% 99.29/13.07 (doubleComplementSub1) =>
% 99.29/13.07 ((
% 99.29/13.07 (doubleComplementSub2) =>
% 99.29/13.07 ((
% 99.29/13.07 (doubleComplementEq) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementTnotintersectT) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementImpComplementIntersect) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementSubsetComplementIntersect) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementInPowersetComplementIntersect) =>
% 99.29/13.07 ((
% 99.29/13.07 (contraSubsetComplement) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementTcontraSubset) =>
% 99.29/13.07 ((
% 99.29/13.07 (binunionTILcontra) =>
% 99.29/13.07 ((
% 99.29/13.07 (binunionTIRcontra) =>
% 99.29/13.07 ((
% 99.29/13.07 (inIntersectImpInUnion) =>
% 99.29/13.07 ((
% 99.29/13.07 (inIntersectImpInUnion2) =>
% 99.29/13.07 ((
% 99.29/13.07 (inIntersectImpInIntersectUnions) =>
% 99.29/13.07 ((
% 99.29/13.07 (intersectInPowersetIntersectUnions) =>
% 99.29/13.07 ((
% 99.29/13.07 (inComplementUnionImpNotIn1) =>
% 99.29/13.07 ((
% 99.29/13.07 (inComplementUnionImpInComplement1) =>
% 99.29/13.07 ((
% 99.29/13.07 (binunionTE) =>
% 99.29/13.07 ((
% 99.29/13.07 (binunionTEcontra) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2a1) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementUnionInPowersetComplement) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2a2) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan1a) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan1b) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan1) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2a) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2b2) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2b) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz13rule0) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz13rule1) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz13rule2) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz13rule3) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz13rule4) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz1_1) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz1_2) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz1_3) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz1_4) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz1_5) =>
% 99.29/13.07 ((
% 99.29/13.07 (breln1all2) =>
% 99.29/13.07 ((
% 99.29/13.07 (breln1SetBreln1) =>
% 99.29/13.07 ((
% 99.29/13.07 (choice2fnsingleton) =>
% 99.29/13.07 ((
% 99.29/13.07 (!!) @ (
% 99.29/13.07 (('#B') @ (
% 99.29/13.07 !!) @
% 99.29/13.07 (
% 99.29/13.07 (
% 99.29/13.07 ('#S') @ (
% 99.29/13.07 (
% 99.29/13.07 ('#B') @ (
% 99.29/13.07 '#B') @
% 99.29/13.07 breln1)) @
% 99.29/13.07 (
% 99.29/13.07 (
% 99.29/13.07 ('#S') @ dpsetconstr @
% 99.29/13.07 (
% 99.29/13.07 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.29/13.07 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2203])).
% 99.29/13.07 thf(zip_derived_cl2235, plain,
% 99.29/13.07 (~ (((beta2) =>
% 99.29/13.07 (((eta2) =>
% 99.29/13.07 (((iffalseProp1) =>
% 99.29/13.07 (((iffalseProp2) =>
% 99.29/13.07 (((iftrueProp1) =>
% 99.29/13.07 (((iftrueProp2) =>
% 99.29/13.07 (((ifSingleton) =>
% 99.29/13.07 (((ifp) =>
% 99.29/13.07 (((theeq) =>
% 99.29/13.07 (((iftrue) =>
% 99.29/13.07 (((iffalse) =>
% 99.29/13.07 (((iftrueorfalse) =>
% 99.29/13.07 (((binintersectT_lem) =>
% 99.29/13.07 (((binunionT_lem) =>
% 99.29/13.07 (((powersetT_lem) =>
% 99.29/13.07 (((setminusT_lem) =>
% 99.29/13.07 (((complementT_lem) =>
% 99.29/13.07 (((setextT) =>
% 99.29/13.07 (((subsetTI) =>
% 99.29/13.07 (((powersetTI1) =>
% 99.29/13.07 (((powersetTE1) =>
% 99.29/13.07 (((complementTI1) =>
% 99.29/13.07 (((complementTE1) =>
% 99.29/13.07 (((binintersectTELcontra) =>
% 99.29/13.07 (((binintersectTERcontra) =>
% 99.29/13.07 (((contrasubsetT) =>
% 99.29/13.07 (((contrasubsetT1) =>
% 99.29/13.07 (((contrasubsetT2) =>
% 99.29/13.07 (((contrasubsetT3) =>
% 99.29/13.07 (((doubleComplementI1) =>
% 99.29/13.07 ((
% 99.29/13.07 (doubleComplementE1) =>
% 99.29/13.07 ((
% 99.29/13.07 (doubleComplementSub1) =>
% 99.29/13.07 ((
% 99.29/13.07 (doubleComplementSub2) =>
% 99.29/13.07 ((
% 99.29/13.07 (doubleComplementEq) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementTnotintersectT) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementImpComplementIntersect) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementSubsetComplementIntersect) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementInPowersetComplementIntersect) =>
% 99.29/13.07 ((
% 99.29/13.07 (contraSubsetComplement) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementTcontraSubset) =>
% 99.29/13.07 ((
% 99.29/13.07 (binunionTILcontra) =>
% 99.29/13.07 ((
% 99.29/13.07 (binunionTIRcontra) =>
% 99.29/13.07 ((
% 99.29/13.07 (inIntersectImpInUnion) =>
% 99.29/13.07 ((
% 99.29/13.07 (inIntersectImpInUnion2) =>
% 99.29/13.07 ((
% 99.29/13.07 (inIntersectImpInIntersectUnions) =>
% 99.29/13.07 ((
% 99.29/13.07 (intersectInPowersetIntersectUnions) =>
% 99.29/13.07 ((
% 99.29/13.07 (inComplementUnionImpNotIn1) =>
% 99.29/13.07 ((
% 99.29/13.07 (inComplementUnionImpInComplement1) =>
% 99.29/13.07 ((
% 99.29/13.07 (binunionTE) =>
% 99.29/13.07 ((
% 99.29/13.07 (binunionTEcontra) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2a1) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementUnionInPowersetComplement) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2a2) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan1a) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan1b) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan1) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2a) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2b2) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2b) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz13rule0) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz13rule1) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz13rule2) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz13rule3) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz13rule4) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz1_1) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz1_2) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz1_3) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz1_4) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz1_5) =>
% 99.29/13.07 ((
% 99.29/13.07 (breln1all2) =>
% 99.29/13.07 ((
% 99.29/13.07 (breln1SetBreln1) =>
% 99.29/13.07 ((
% 99.29/13.07 (choice2fnsingleton) =>
% 99.29/13.07 ((
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% 99.29/13.07 (('#B') @ (
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% 99.29/13.07 (
% 99.29/13.07 (
% 99.29/13.07 ('#S') @ (
% 99.29/13.07 (
% 99.29/13.07 ('#B') @ (
% 99.29/13.07 '#B') @
% 99.29/13.07 breln1)) @
% 99.29/13.07 (
% 99.29/13.07 (
% 99.29/13.07 ('#S') @ dpsetconstr @
% 99.29/13.07 (
% 99.29/13.07 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.29/13.07 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2219])).
% 99.29/13.07 thf(zip_derived_cl2251, plain,
% 99.29/13.07 (~ (((eta2) =>
% 99.29/13.07 (((iffalseProp1) =>
% 99.29/13.07 (((iffalseProp2) =>
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% 99.29/13.07 (((iftrueProp2) =>
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% 99.29/13.07 (((theeq) =>
% 99.29/13.07 (((iftrue) =>
% 99.29/13.07 (((iffalse) =>
% 99.29/13.07 (((iftrueorfalse) =>
% 99.29/13.07 (((binintersectT_lem) =>
% 99.29/13.07 (((binunionT_lem) =>
% 99.29/13.07 (((powersetT_lem) =>
% 99.29/13.07 (((setminusT_lem) =>
% 99.29/13.07 (((complementT_lem) =>
% 99.29/13.07 (((setextT) =>
% 99.29/13.07 (((subsetTI) =>
% 99.29/13.07 (((powersetTI1) =>
% 99.29/13.07 (((powersetTE1) =>
% 99.29/13.07 (((complementTI1) =>
% 99.29/13.07 (((complementTE1) =>
% 99.29/13.07 (((binintersectTELcontra) =>
% 99.29/13.07 (((binintersectTERcontra) =>
% 99.29/13.07 (((contrasubsetT) =>
% 99.29/13.07 (((contrasubsetT1) =>
% 99.29/13.07 (((contrasubsetT2) =>
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% 99.29/13.07 (((doubleComplementI1) =>
% 99.29/13.07 (((doubleComplementE1) =>
% 99.29/13.07 ((
% 99.29/13.07 (doubleComplementSub1) =>
% 99.29/13.07 ((
% 99.29/13.07 (doubleComplementSub2) =>
% 99.29/13.07 ((
% 99.29/13.07 (doubleComplementEq) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementTnotintersectT) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementImpComplementIntersect) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementSubsetComplementIntersect) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementInPowersetComplementIntersect) =>
% 99.29/13.07 ((
% 99.29/13.07 (contraSubsetComplement) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementTcontraSubset) =>
% 99.29/13.07 ((
% 99.29/13.07 (binunionTILcontra) =>
% 99.29/13.07 ((
% 99.29/13.07 (binunionTIRcontra) =>
% 99.29/13.07 ((
% 99.29/13.07 (inIntersectImpInUnion) =>
% 99.29/13.07 ((
% 99.29/13.07 (inIntersectImpInUnion2) =>
% 99.29/13.07 ((
% 99.29/13.07 (inIntersectImpInIntersectUnions) =>
% 99.29/13.07 ((
% 99.29/13.07 (intersectInPowersetIntersectUnions) =>
% 99.29/13.07 ((
% 99.29/13.07 (inComplementUnionImpNotIn1) =>
% 99.29/13.07 ((
% 99.29/13.07 (inComplementUnionImpInComplement1) =>
% 99.29/13.07 ((
% 99.29/13.07 (binunionTE) =>
% 99.29/13.07 ((
% 99.29/13.07 (binunionTEcontra) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2a1) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementUnionInPowersetComplement) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2a2) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan1a) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan1b) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan1) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2a) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2b2) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2b) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz13rule0) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz13rule1) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz13rule2) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz13rule3) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz13rule4) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz1_1) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz1_2) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz1_3) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz1_4) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz1_5) =>
% 99.29/13.07 ((
% 99.29/13.07 (breln1all2) =>
% 99.29/13.07 ((
% 99.29/13.07 (breln1SetBreln1) =>
% 99.29/13.07 ((
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% 99.29/13.07 ((
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% 99.29/13.07 (
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% 99.29/13.07 ('#S') @ (
% 99.29/13.07 (
% 99.29/13.07 ('#B') @ (
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% 99.29/13.07 (
% 99.29/13.07 (
% 99.29/13.07 ('#S') @ dpsetconstr @
% 99.29/13.07 (
% 99.29/13.07 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.29/13.07 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2235])).
% 99.29/13.07 thf(zip_derived_cl2268, plain,
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% 99.29/13.07 (((iftrueProp2) =>
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% 99.29/13.07 (((theeq) =>
% 99.29/13.07 (((iftrue) =>
% 99.29/13.07 (((iffalse) =>
% 99.29/13.07 (((iftrueorfalse) =>
% 99.29/13.07 (((binintersectT_lem) =>
% 99.29/13.07 (((binunionT_lem) =>
% 99.29/13.07 (((powersetT_lem) =>
% 99.29/13.07 (((setminusT_lem) =>
% 99.29/13.07 (((complementT_lem) =>
% 99.29/13.07 (((setextT) =>
% 99.29/13.07 (((subsetTI) =>
% 99.29/13.07 (((powersetTI1) =>
% 99.29/13.07 (((powersetTE1) =>
% 99.29/13.07 (((complementTI1) =>
% 99.29/13.07 (((complementTE1) =>
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% 99.29/13.07 (((binintersectTERcontra) =>
% 99.29/13.07 (((contrasubsetT) =>
% 99.29/13.07 (((contrasubsetT1) =>
% 99.29/13.07 (((contrasubsetT2) =>
% 99.29/13.07 (((contrasubsetT3) =>
% 99.29/13.07 (((doubleComplementI1) =>
% 99.29/13.07 (((doubleComplementE1) =>
% 99.29/13.07 (((doubleComplementSub1) =>
% 99.29/13.07 ((
% 99.29/13.07 (doubleComplementSub2) =>
% 99.29/13.07 ((
% 99.29/13.07 (doubleComplementEq) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementTnotintersectT) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementImpComplementIntersect) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementSubsetComplementIntersect) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementInPowersetComplementIntersect) =>
% 99.29/13.07 ((
% 99.29/13.07 (contraSubsetComplement) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementTcontraSubset) =>
% 99.29/13.07 ((
% 99.29/13.07 (binunionTILcontra) =>
% 99.29/13.07 ((
% 99.29/13.07 (binunionTIRcontra) =>
% 99.29/13.07 ((
% 99.29/13.07 (inIntersectImpInUnion) =>
% 99.29/13.07 ((
% 99.29/13.07 (inIntersectImpInUnion2) =>
% 99.29/13.07 ((
% 99.29/13.07 (inIntersectImpInIntersectUnions) =>
% 99.29/13.07 ((
% 99.29/13.07 (intersectInPowersetIntersectUnions) =>
% 99.29/13.07 ((
% 99.29/13.07 (inComplementUnionImpNotIn1) =>
% 99.29/13.07 ((
% 99.29/13.07 (inComplementUnionImpInComplement1) =>
% 99.29/13.07 ((
% 99.29/13.07 (binunionTE) =>
% 99.29/13.07 ((
% 99.29/13.07 (binunionTEcontra) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2a1) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementUnionInPowersetComplement) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2a2) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan1a) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan1b) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan1) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2a) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2b2) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2b) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz13rule0) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz13rule1) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz13rule2) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz13rule3) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz13rule4) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz1_1) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz1_2) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz1_3) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz1_4) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz1_5) =>
% 99.29/13.07 ((
% 99.29/13.07 (breln1all2) =>
% 99.29/13.07 ((
% 99.29/13.07 (breln1SetBreln1) =>
% 99.29/13.07 ((
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% 99.29/13.07 ((
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% 99.29/13.07 (
% 99.29/13.07 (
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% 99.29/13.07 (
% 99.29/13.07 (
% 99.29/13.07 ('#S') @ dpsetconstr @
% 99.29/13.07 (
% 99.29/13.07 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.29/13.07 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2251])).
% 99.29/13.07 thf(zip_derived_cl2286, plain,
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% 99.29/13.07 (((iftrue) =>
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% 99.29/13.07 (((iftrueorfalse) =>
% 99.29/13.07 (((binintersectT_lem) =>
% 99.29/13.07 (((binunionT_lem) =>
% 99.29/13.07 (((powersetT_lem) =>
% 99.29/13.07 (((setminusT_lem) =>
% 99.29/13.07 (((complementT_lem) =>
% 99.29/13.07 (((setextT) =>
% 99.29/13.07 (((subsetTI) =>
% 99.29/13.07 (((powersetTI1) =>
% 99.29/13.07 (((powersetTE1) =>
% 99.29/13.07 (((complementTI1) =>
% 99.29/13.07 (((complementTE1) =>
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% 99.29/13.07 (((binintersectTERcontra) =>
% 99.29/13.07 (((contrasubsetT) =>
% 99.29/13.07 (((contrasubsetT1) =>
% 99.29/13.07 (((contrasubsetT2) =>
% 99.29/13.07 (((contrasubsetT3) =>
% 99.29/13.07 (((doubleComplementI1) =>
% 99.29/13.07 (((doubleComplementE1) =>
% 99.29/13.07 (((doubleComplementSub1) =>
% 99.29/13.07 (((doubleComplementSub2) =>
% 99.29/13.07 ((
% 99.29/13.07 (doubleComplementEq) =>
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% 99.29/13.07 (complementTnotintersectT) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementImpComplementIntersect) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementSubsetComplementIntersect) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementInPowersetComplementIntersect) =>
% 99.29/13.07 ((
% 99.29/13.07 (contraSubsetComplement) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementTcontraSubset) =>
% 99.29/13.07 ((
% 99.29/13.07 (binunionTILcontra) =>
% 99.29/13.07 ((
% 99.29/13.07 (binunionTIRcontra) =>
% 99.29/13.07 ((
% 99.29/13.07 (inIntersectImpInUnion) =>
% 99.29/13.07 ((
% 99.29/13.07 (inIntersectImpInUnion2) =>
% 99.29/13.07 ((
% 99.29/13.07 (inIntersectImpInIntersectUnions) =>
% 99.29/13.07 ((
% 99.29/13.07 (intersectInPowersetIntersectUnions) =>
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% 99.29/13.07 (inComplementUnionImpNotIn1) =>
% 99.29/13.07 ((
% 99.29/13.07 (inComplementUnionImpInComplement1) =>
% 99.29/13.07 ((
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% 99.29/13.07 ((
% 99.29/13.07 (binunionTEcontra) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2a1) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementUnionInPowersetComplement) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2a2) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan1a) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan1b) =>
% 99.29/13.07 ((
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% 99.29/13.07 ((
% 99.29/13.07 (demorgan2a) =>
% 99.29/13.07 ((
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% 99.29/13.07 ((
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% 99.29/13.07 ((
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% 99.29/13.07 ((
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% 99.29/13.07 ((
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% 99.29/13.07 ((
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% 99.29/13.07 ((
% 99.29/13.07 (woz1_2) =>
% 99.29/13.07 ((
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% 99.29/13.07 ((
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% 99.29/13.07 ((
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% 99.29/13.07 (
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% 99.29/13.07 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2268])).
% 99.29/13.07 thf(zip_derived_cl2306, plain,
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% 99.29/13.07 (((doubleComplementSub2) =>
% 99.29/13.07 (((doubleComplementEq) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementTnotintersectT) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementImpComplementIntersect) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementSubsetComplementIntersect) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementInPowersetComplementIntersect) =>
% 99.29/13.07 ((
% 99.29/13.07 (contraSubsetComplement) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementTcontraSubset) =>
% 99.29/13.07 ((
% 99.29/13.07 (binunionTILcontra) =>
% 99.29/13.07 ((
% 99.29/13.07 (binunionTIRcontra) =>
% 99.29/13.07 ((
% 99.29/13.07 (inIntersectImpInUnion) =>
% 99.29/13.07 ((
% 99.29/13.07 (inIntersectImpInUnion2) =>
% 99.29/13.07 ((
% 99.29/13.07 (inIntersectImpInIntersectUnions) =>
% 99.29/13.07 ((
% 99.29/13.07 (intersectInPowersetIntersectUnions) =>
% 99.29/13.07 ((
% 99.29/13.07 (inComplementUnionImpNotIn1) =>
% 99.29/13.07 ((
% 99.29/13.07 (inComplementUnionImpInComplement1) =>
% 99.29/13.07 ((
% 99.29/13.07 (binunionTE) =>
% 99.29/13.07 ((
% 99.29/13.07 (binunionTEcontra) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2a1) =>
% 99.29/13.07 ((
% 99.29/13.07 (complementUnionInPowersetComplement) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2a2) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan1a) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan1b) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan1) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2a) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2b2) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2b) =>
% 99.29/13.07 ((
% 99.29/13.07 (demorgan2) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz13rule0) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz13rule1) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz13rule2) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz13rule3) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz13rule4) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz1_1) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz1_2) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz1_3) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz1_4) =>
% 99.29/13.07 ((
% 99.29/13.07 (woz1_5) =>
% 99.29/13.07 ((
% 99.29/13.07 (breln1all2) =>
% 99.29/13.07 ((
% 99.29/13.07 (breln1SetBreln1) =>
% 99.29/13.07 ((
% 99.29/13.07 (choice2fnsingleton) =>
% 99.29/13.07 ((
% 99.29/13.07 (!!) @ (
% 99.29/13.07 (('#B') @ (
% 99.29/13.07 !!) @
% 99.29/13.07 (
% 99.29/13.07 (
% 99.29/13.07 ('#S') @ (
% 99.29/13.07 (
% 99.29/13.07 ('#B') @ (
% 99.29/13.07 '#B') @
% 99.29/13.07 breln1)) @
% 99.29/13.07 (
% 99.29/13.07 (
% 99.29/13.07 ('#S') @ dpsetconstr @
% 99.29/13.07 (
% 99.29/13.07 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.29/13.07 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2286])).
% 99.29/13.07 thf(zip_derived_cl2328, plain,
% 99.29/13.07 (~ (((iftrueProp2) =>
% 99.29/13.07 (((ifSingleton) =>
% 99.29/13.07 (((ifp) =>
% 99.29/13.07 (((theeq) =>
% 99.29/13.07 (((iftrue) =>
% 99.29/13.07 (((iffalse) =>
% 99.29/13.07 (((iftrueorfalse) =>
% 99.29/13.07 (((binintersectT_lem) =>
% 99.29/13.07 (((binunionT_lem) =>
% 99.29/13.07 (((powersetT_lem) =>
% 99.29/13.07 (((setminusT_lem) =>
% 99.29/13.07 (((complementT_lem) =>
% 99.29/13.07 (((setextT) =>
% 99.29/13.07 (((subsetTI) =>
% 99.29/13.07 (((powersetTI1) =>
% 99.29/13.07 (((powersetTE1) =>
% 99.29/13.07 (((complementTI1) =>
% 99.29/13.07 (((complementTE1) =>
% 99.29/13.07 (((binintersectTELcontra) =>
% 99.29/13.07 (((binintersectTERcontra) =>
% 99.29/13.07 (((contrasubsetT) =>
% 99.29/13.07 (((contrasubsetT1) =>
% 99.29/13.07 (((contrasubsetT2) =>
% 99.29/13.07 (((contrasubsetT3) =>
% 99.29/13.07 (((doubleComplementI1) =>
% 99.29/13.07 (((doubleComplementE1) =>
% 99.29/13.07 (((doubleComplementSub1) =>
% 99.29/13.08 (((doubleComplementSub2) =>
% 99.29/13.08 (((doubleComplementEq) =>
% 99.29/13.08 (((complementTnotintersectT) =>
% 99.29/13.08 ((
% 99.29/13.08 (complementImpComplementIntersect) =>
% 99.29/13.08 ((
% 99.29/13.08 (complementSubsetComplementIntersect) =>
% 99.29/13.08 ((
% 99.29/13.08 (complementInPowersetComplementIntersect) =>
% 99.29/13.08 ((
% 99.29/13.08 (contraSubsetComplement) =>
% 99.29/13.08 ((
% 99.29/13.08 (complementTcontraSubset) =>
% 99.29/13.08 ((
% 99.29/13.08 (binunionTILcontra) =>
% 99.29/13.08 ((
% 99.29/13.08 (binunionTIRcontra) =>
% 99.29/13.08 ((
% 99.29/13.08 (inIntersectImpInUnion) =>
% 99.29/13.08 ((
% 99.29/13.08 (inIntersectImpInUnion2) =>
% 99.29/13.08 ((
% 99.29/13.08 (inIntersectImpInIntersectUnions) =>
% 99.29/13.08 ((
% 99.29/13.08 (intersectInPowersetIntersectUnions) =>
% 99.29/13.08 ((
% 99.29/13.08 (inComplementUnionImpNotIn1) =>
% 99.29/13.08 ((
% 99.29/13.08 (inComplementUnionImpInComplement1) =>
% 99.29/13.08 ((
% 99.29/13.08 (binunionTE) =>
% 99.29/13.08 ((
% 99.29/13.08 (binunionTEcontra) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2a1) =>
% 99.29/13.08 ((
% 99.29/13.08 (complementUnionInPowersetComplement) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2a2) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan1a) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan1b) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan1) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2a) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2b2) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2b) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule0) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule1) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule3) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule4) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_1) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_3) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_4) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_5) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1all2) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1SetBreln1) =>
% 99.29/13.08 ((
% 99.29/13.08 (choice2fnsingleton) =>
% 99.29/13.08 ((
% 99.29/13.08 (!!) @ (
% 99.29/13.08 (('#B') @ (
% 99.29/13.08 !!) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ (
% 99.29/13.08 (
% 99.29/13.08 ('#B') @ (
% 99.29/13.08 '#B') @
% 99.29/13.08 breln1)) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ dpsetconstr @
% 99.29/13.08 (
% 99.29/13.08 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.29/13.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2306])).
% 99.29/13.08 thf(zip_derived_cl2344, plain,
% 99.29/13.08 (~ (((ifSingleton) =>
% 99.29/13.08 (((ifp) =>
% 99.29/13.08 (((theeq) =>
% 99.29/13.08 (((iftrue) =>
% 99.29/13.08 (((iffalse) =>
% 99.29/13.08 (((iftrueorfalse) =>
% 99.29/13.08 (((binintersectT_lem) =>
% 99.29/13.08 (((binunionT_lem) =>
% 99.29/13.08 (((powersetT_lem) =>
% 99.29/13.08 (((setminusT_lem) =>
% 99.29/13.08 (((complementT_lem) =>
% 99.29/13.08 (((setextT) =>
% 99.29/13.08 (((subsetTI) =>
% 99.29/13.08 (((powersetTI1) =>
% 99.29/13.08 (((powersetTE1) =>
% 99.29/13.08 (((complementTI1) =>
% 99.29/13.08 (((complementTE1) =>
% 99.29/13.08 (((binintersectTELcontra) =>
% 99.29/13.08 (((binintersectTERcontra) =>
% 99.29/13.08 (((contrasubsetT) =>
% 99.29/13.08 (((contrasubsetT1) =>
% 99.29/13.08 (((contrasubsetT2) =>
% 99.29/13.08 (((contrasubsetT3) =>
% 99.29/13.08 (((doubleComplementI1) =>
% 99.29/13.08 (((doubleComplementE1) =>
% 99.29/13.08 (((doubleComplementSub1) =>
% 99.29/13.08 (((doubleComplementSub2) =>
% 99.29/13.08 (((doubleComplementEq) =>
% 99.29/13.08 (((complementTnotintersectT) =>
% 99.29/13.08 (((complementImpComplementIntersect) =>
% 99.29/13.08 ((
% 99.29/13.08 (complementSubsetComplementIntersect) =>
% 99.29/13.08 ((
% 99.29/13.08 (complementInPowersetComplementIntersect) =>
% 99.29/13.08 ((
% 99.29/13.08 (contraSubsetComplement) =>
% 99.29/13.08 ((
% 99.29/13.08 (complementTcontraSubset) =>
% 99.29/13.08 ((
% 99.29/13.08 (binunionTILcontra) =>
% 99.29/13.08 ((
% 99.29/13.08 (binunionTIRcontra) =>
% 99.29/13.08 ((
% 99.29/13.08 (inIntersectImpInUnion) =>
% 99.29/13.08 ((
% 99.29/13.08 (inIntersectImpInUnion2) =>
% 99.29/13.08 ((
% 99.29/13.08 (inIntersectImpInIntersectUnions) =>
% 99.29/13.08 ((
% 99.29/13.08 (intersectInPowersetIntersectUnions) =>
% 99.29/13.08 ((
% 99.29/13.08 (inComplementUnionImpNotIn1) =>
% 99.29/13.08 ((
% 99.29/13.08 (inComplementUnionImpInComplement1) =>
% 99.29/13.08 ((
% 99.29/13.08 (binunionTE) =>
% 99.29/13.08 ((
% 99.29/13.08 (binunionTEcontra) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2a1) =>
% 99.29/13.08 ((
% 99.29/13.08 (complementUnionInPowersetComplement) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2a2) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan1a) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan1b) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan1) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2a) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2b2) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2b) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule0) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule1) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule3) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule4) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_1) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_3) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_4) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_5) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1all2) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1SetBreln1) =>
% 99.29/13.08 ((
% 99.29/13.08 (choice2fnsingleton) =>
% 99.29/13.08 ((
% 99.29/13.08 (!!) @ (
% 99.29/13.08 (('#B') @ (
% 99.29/13.08 !!) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ (
% 99.29/13.08 (
% 99.29/13.08 ('#B') @ (
% 99.29/13.08 '#B') @
% 99.29/13.08 breln1)) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ dpsetconstr @
% 99.29/13.08 (
% 99.29/13.08 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.29/13.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2328])).
% 99.29/13.08 thf(zip_derived_cl2360, plain,
% 99.29/13.08 (~ (((ifp) =>
% 99.29/13.08 (((theeq) =>
% 99.29/13.08 (((iftrue) =>
% 99.29/13.08 (((iffalse) =>
% 99.29/13.08 (((iftrueorfalse) =>
% 99.29/13.08 (((binintersectT_lem) =>
% 99.29/13.08 (((binunionT_lem) =>
% 99.29/13.08 (((powersetT_lem) =>
% 99.29/13.08 (((setminusT_lem) =>
% 99.29/13.08 (((complementT_lem) =>
% 99.29/13.08 (((setextT) =>
% 99.29/13.08 (((subsetTI) =>
% 99.29/13.08 (((powersetTI1) =>
% 99.29/13.08 (((powersetTE1) =>
% 99.29/13.08 (((complementTI1) =>
% 99.29/13.08 (((complementTE1) =>
% 99.29/13.08 (((binintersectTELcontra) =>
% 99.29/13.08 (((binintersectTERcontra) =>
% 99.29/13.08 (((contrasubsetT) =>
% 99.29/13.08 (((contrasubsetT1) =>
% 99.29/13.08 (((contrasubsetT2) =>
% 99.29/13.08 (((contrasubsetT3) =>
% 99.29/13.08 (((doubleComplementI1) =>
% 99.29/13.08 (((doubleComplementE1) =>
% 99.29/13.08 (((doubleComplementSub1) =>
% 99.29/13.08 (((doubleComplementSub2) =>
% 99.29/13.08 (((doubleComplementEq) =>
% 99.29/13.08 (((complementTnotintersectT) =>
% 99.29/13.08 (((complementImpComplementIntersect) =>
% 99.29/13.08 (((complementSubsetComplementIntersect) =>
% 99.29/13.08 ((
% 99.29/13.08 (complementInPowersetComplementIntersect) =>
% 99.29/13.08 ((
% 99.29/13.08 (contraSubsetComplement) =>
% 99.29/13.08 ((
% 99.29/13.08 (complementTcontraSubset) =>
% 99.29/13.08 ((
% 99.29/13.08 (binunionTILcontra) =>
% 99.29/13.08 ((
% 99.29/13.08 (binunionTIRcontra) =>
% 99.29/13.08 ((
% 99.29/13.08 (inIntersectImpInUnion) =>
% 99.29/13.08 ((
% 99.29/13.08 (inIntersectImpInUnion2) =>
% 99.29/13.08 ((
% 99.29/13.08 (inIntersectImpInIntersectUnions) =>
% 99.29/13.08 ((
% 99.29/13.08 (intersectInPowersetIntersectUnions) =>
% 99.29/13.08 ((
% 99.29/13.08 (inComplementUnionImpNotIn1) =>
% 99.29/13.08 ((
% 99.29/13.08 (inComplementUnionImpInComplement1) =>
% 99.29/13.08 ((
% 99.29/13.08 (binunionTE) =>
% 99.29/13.08 ((
% 99.29/13.08 (binunionTEcontra) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2a1) =>
% 99.29/13.08 ((
% 99.29/13.08 (complementUnionInPowersetComplement) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2a2) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan1a) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan1b) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan1) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2a) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2b2) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2b) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule0) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule1) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule3) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule4) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_1) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_3) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_4) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_5) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1all2) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1SetBreln1) =>
% 99.29/13.08 ((
% 99.29/13.08 (choice2fnsingleton) =>
% 99.29/13.08 ((
% 99.29/13.08 (!!) @ (
% 99.29/13.08 (('#B') @ (
% 99.29/13.08 !!) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ (
% 99.29/13.08 (
% 99.29/13.08 ('#B') @ (
% 99.29/13.08 '#B') @
% 99.29/13.08 breln1)) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ dpsetconstr @
% 99.29/13.08 (
% 99.29/13.08 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.29/13.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2344])).
% 99.29/13.08 thf(zip_derived_cl2381, plain,
% 99.29/13.08 (~ (((theeq) =>
% 99.29/13.08 (((iftrue) =>
% 99.29/13.08 (((iffalse) =>
% 99.29/13.08 (((iftrueorfalse) =>
% 99.29/13.08 (((binintersectT_lem) =>
% 99.29/13.08 (((binunionT_lem) =>
% 99.29/13.08 (((powersetT_lem) =>
% 99.29/13.08 (((setminusT_lem) =>
% 99.29/13.08 (((complementT_lem) =>
% 99.29/13.08 (((setextT) =>
% 99.29/13.08 (((subsetTI) =>
% 99.29/13.08 (((powersetTI1) =>
% 99.29/13.08 (((powersetTE1) =>
% 99.29/13.08 (((complementTI1) =>
% 99.29/13.08 (((complementTE1) =>
% 99.29/13.08 (((binintersectTELcontra) =>
% 99.29/13.08 (((binintersectTERcontra) =>
% 99.29/13.08 (((contrasubsetT) =>
% 99.29/13.08 (((contrasubsetT1) =>
% 99.29/13.08 (((contrasubsetT2) =>
% 99.29/13.08 (((contrasubsetT3) =>
% 99.29/13.08 (((doubleComplementI1) =>
% 99.29/13.08 (((doubleComplementE1) =>
% 99.29/13.08 (((doubleComplementSub1) =>
% 99.29/13.08 (((doubleComplementSub2) =>
% 99.29/13.08 (((doubleComplementEq) =>
% 99.29/13.08 (((complementTnotintersectT) =>
% 99.29/13.08 (((complementImpComplementIntersect) =>
% 99.29/13.08 (((complementSubsetComplementIntersect) =>
% 99.29/13.08 (((complementInPowersetComplementIntersect) =>
% 99.29/13.08 ((
% 99.29/13.08 (contraSubsetComplement) =>
% 99.29/13.08 ((
% 99.29/13.08 (complementTcontraSubset) =>
% 99.29/13.08 ((
% 99.29/13.08 (binunionTILcontra) =>
% 99.29/13.08 ((
% 99.29/13.08 (binunionTIRcontra) =>
% 99.29/13.08 ((
% 99.29/13.08 (inIntersectImpInUnion) =>
% 99.29/13.08 ((
% 99.29/13.08 (inIntersectImpInUnion2) =>
% 99.29/13.08 ((
% 99.29/13.08 (inIntersectImpInIntersectUnions) =>
% 99.29/13.08 ((
% 99.29/13.08 (intersectInPowersetIntersectUnions) =>
% 99.29/13.08 ((
% 99.29/13.08 (inComplementUnionImpNotIn1) =>
% 99.29/13.08 ((
% 99.29/13.08 (inComplementUnionImpInComplement1) =>
% 99.29/13.08 ((
% 99.29/13.08 (binunionTE) =>
% 99.29/13.08 ((
% 99.29/13.08 (binunionTEcontra) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2a1) =>
% 99.29/13.08 ((
% 99.29/13.08 (complementUnionInPowersetComplement) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2a2) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan1a) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan1b) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan1) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2a) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2b2) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2b) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule0) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule1) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule3) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule4) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_1) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_3) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_4) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_5) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1all2) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1SetBreln1) =>
% 99.29/13.08 ((
% 99.29/13.08 (choice2fnsingleton) =>
% 99.29/13.08 ((
% 99.29/13.08 (!!) @ (
% 99.29/13.08 (('#B') @ (
% 99.29/13.08 !!) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ (
% 99.29/13.08 (
% 99.29/13.08 ('#B') @ (
% 99.29/13.08 '#B') @
% 99.29/13.08 breln1)) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ dpsetconstr @
% 99.29/13.08 (
% 99.29/13.08 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.29/13.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2360])).
% 99.29/13.08 thf(zip_derived_cl2399, plain,
% 99.29/13.08 (~ (((iftrue) =>
% 99.29/13.08 (((iffalse) =>
% 99.29/13.08 (((iftrueorfalse) =>
% 99.29/13.08 (((binintersectT_lem) =>
% 99.29/13.08 (((binunionT_lem) =>
% 99.29/13.08 (((powersetT_lem) =>
% 99.29/13.08 (((setminusT_lem) =>
% 99.29/13.08 (((complementT_lem) =>
% 99.29/13.08 (((setextT) =>
% 99.29/13.08 (((subsetTI) =>
% 99.29/13.08 (((powersetTI1) =>
% 99.29/13.08 (((powersetTE1) =>
% 99.29/13.08 (((complementTI1) =>
% 99.29/13.08 (((complementTE1) =>
% 99.29/13.08 (((binintersectTELcontra) =>
% 99.29/13.08 (((binintersectTERcontra) =>
% 99.29/13.08 (((contrasubsetT) =>
% 99.29/13.08 (((contrasubsetT1) =>
% 99.29/13.08 (((contrasubsetT2) =>
% 99.29/13.08 (((contrasubsetT3) =>
% 99.29/13.08 (((doubleComplementI1) =>
% 99.29/13.08 (((doubleComplementE1) =>
% 99.29/13.08 (((doubleComplementSub1) =>
% 99.29/13.08 (((doubleComplementSub2) =>
% 99.29/13.08 (((doubleComplementEq) =>
% 99.29/13.08 (((complementTnotintersectT) =>
% 99.29/13.08 (((complementImpComplementIntersect) =>
% 99.29/13.08 (((complementSubsetComplementIntersect) =>
% 99.29/13.08 (((complementInPowersetComplementIntersect) =>
% 99.29/13.08 (((contraSubsetComplement) =>
% 99.29/13.08 ((
% 99.29/13.08 (complementTcontraSubset) =>
% 99.29/13.08 ((
% 99.29/13.08 (binunionTILcontra) =>
% 99.29/13.08 ((
% 99.29/13.08 (binunionTIRcontra) =>
% 99.29/13.08 ((
% 99.29/13.08 (inIntersectImpInUnion) =>
% 99.29/13.08 ((
% 99.29/13.08 (inIntersectImpInUnion2) =>
% 99.29/13.08 ((
% 99.29/13.08 (inIntersectImpInIntersectUnions) =>
% 99.29/13.08 ((
% 99.29/13.08 (intersectInPowersetIntersectUnions) =>
% 99.29/13.08 ((
% 99.29/13.08 (inComplementUnionImpNotIn1) =>
% 99.29/13.08 ((
% 99.29/13.08 (inComplementUnionImpInComplement1) =>
% 99.29/13.08 ((
% 99.29/13.08 (binunionTE) =>
% 99.29/13.08 ((
% 99.29/13.08 (binunionTEcontra) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2a1) =>
% 99.29/13.08 ((
% 99.29/13.08 (complementUnionInPowersetComplement) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2a2) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan1a) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan1b) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan1) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2a) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2b2) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2b) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule0) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule1) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule3) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule4) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_1) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_3) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_4) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_5) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1all2) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1SetBreln1) =>
% 99.29/13.08 ((
% 99.29/13.08 (choice2fnsingleton) =>
% 99.29/13.08 ((
% 99.29/13.08 (!!) @ (
% 99.29/13.08 (('#B') @ (
% 99.29/13.08 !!) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ (
% 99.29/13.08 (
% 99.29/13.08 ('#B') @ (
% 99.29/13.08 '#B') @
% 99.29/13.08 breln1)) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ dpsetconstr @
% 99.29/13.08 (
% 99.29/13.08 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.29/13.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2381])).
% 99.29/13.08 thf(zip_derived_cl2415, plain,
% 99.29/13.08 (~ (((iffalse) =>
% 99.29/13.08 (((iftrueorfalse) =>
% 99.29/13.08 (((binintersectT_lem) =>
% 99.29/13.08 (((binunionT_lem) =>
% 99.29/13.08 (((powersetT_lem) =>
% 99.29/13.08 (((setminusT_lem) =>
% 99.29/13.08 (((complementT_lem) =>
% 99.29/13.08 (((setextT) =>
% 99.29/13.08 (((subsetTI) =>
% 99.29/13.08 (((powersetTI1) =>
% 99.29/13.08 (((powersetTE1) =>
% 99.29/13.08 (((complementTI1) =>
% 99.29/13.08 (((complementTE1) =>
% 99.29/13.08 (((binintersectTELcontra) =>
% 99.29/13.08 (((binintersectTERcontra) =>
% 99.29/13.08 (((contrasubsetT) =>
% 99.29/13.08 (((contrasubsetT1) =>
% 99.29/13.08 (((contrasubsetT2) =>
% 99.29/13.08 (((contrasubsetT3) =>
% 99.29/13.08 (((doubleComplementI1) =>
% 99.29/13.08 (((doubleComplementE1) =>
% 99.29/13.08 (((doubleComplementSub1) =>
% 99.29/13.08 (((doubleComplementSub2) =>
% 99.29/13.08 (((doubleComplementEq) =>
% 99.29/13.08 (((complementTnotintersectT) =>
% 99.29/13.08 (((complementImpComplementIntersect) =>
% 99.29/13.08 (((complementSubsetComplementIntersect) =>
% 99.29/13.08 (((complementInPowersetComplementIntersect) =>
% 99.29/13.08 (((contraSubsetComplement) =>
% 99.29/13.08 (((complementTcontraSubset) =>
% 99.29/13.08 ((
% 99.29/13.08 (binunionTILcontra) =>
% 99.29/13.08 ((
% 99.29/13.08 (binunionTIRcontra) =>
% 99.29/13.08 ((
% 99.29/13.08 (inIntersectImpInUnion) =>
% 99.29/13.08 ((
% 99.29/13.08 (inIntersectImpInUnion2) =>
% 99.29/13.08 ((
% 99.29/13.08 (inIntersectImpInIntersectUnions) =>
% 99.29/13.08 ((
% 99.29/13.08 (intersectInPowersetIntersectUnions) =>
% 99.29/13.08 ((
% 99.29/13.08 (inComplementUnionImpNotIn1) =>
% 99.29/13.08 ((
% 99.29/13.08 (inComplementUnionImpInComplement1) =>
% 99.29/13.08 ((
% 99.29/13.08 (binunionTE) =>
% 99.29/13.08 ((
% 99.29/13.08 (binunionTEcontra) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2a1) =>
% 99.29/13.08 ((
% 99.29/13.08 (complementUnionInPowersetComplement) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2a2) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan1a) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan1b) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan1) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2a) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2b2) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2b) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule0) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule1) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule3) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule4) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_1) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_3) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_4) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_5) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1all2) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1SetBreln1) =>
% 99.29/13.08 ((
% 99.29/13.08 (choice2fnsingleton) =>
% 99.29/13.08 ((
% 99.29/13.08 (!!) @ (
% 99.29/13.08 (('#B') @ (
% 99.29/13.08 !!) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ (
% 99.29/13.08 (
% 99.29/13.08 ('#B') @ (
% 99.29/13.08 '#B') @
% 99.29/13.08 breln1)) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ dpsetconstr @
% 99.29/13.08 (
% 99.29/13.08 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.29/13.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2399])).
% 99.29/13.08 thf(zip_derived_cl2434, plain,
% 99.29/13.08 (~ (((iftrueorfalse) =>
% 99.29/13.08 (((binintersectT_lem) =>
% 99.29/13.08 (((binunionT_lem) =>
% 99.29/13.08 (((powersetT_lem) =>
% 99.29/13.08 (((setminusT_lem) =>
% 99.29/13.08 (((complementT_lem) =>
% 99.29/13.08 (((setextT) =>
% 99.29/13.08 (((subsetTI) =>
% 99.29/13.08 (((powersetTI1) =>
% 99.29/13.08 (((powersetTE1) =>
% 99.29/13.08 (((complementTI1) =>
% 99.29/13.08 (((complementTE1) =>
% 99.29/13.08 (((binintersectTELcontra) =>
% 99.29/13.08 (((binintersectTERcontra) =>
% 99.29/13.08 (((contrasubsetT) =>
% 99.29/13.08 (((contrasubsetT1) =>
% 99.29/13.08 (((contrasubsetT2) =>
% 99.29/13.08 (((contrasubsetT3) =>
% 99.29/13.08 (((doubleComplementI1) =>
% 99.29/13.08 (((doubleComplementE1) =>
% 99.29/13.08 (((doubleComplementSub1) =>
% 99.29/13.08 (((doubleComplementSub2) =>
% 99.29/13.08 (((doubleComplementEq) =>
% 99.29/13.08 (((complementTnotintersectT) =>
% 99.29/13.08 (((complementImpComplementIntersect) =>
% 99.29/13.08 (((complementSubsetComplementIntersect) =>
% 99.29/13.08 (((complementInPowersetComplementIntersect) =>
% 99.29/13.08 (((contraSubsetComplement) =>
% 99.29/13.08 (((complementTcontraSubset) =>
% 99.29/13.08 (((binunionTILcontra) =>
% 99.29/13.08 ((
% 99.29/13.08 (binunionTIRcontra) =>
% 99.29/13.08 ((
% 99.29/13.08 (inIntersectImpInUnion) =>
% 99.29/13.08 ((
% 99.29/13.08 (inIntersectImpInUnion2) =>
% 99.29/13.08 ((
% 99.29/13.08 (inIntersectImpInIntersectUnions) =>
% 99.29/13.08 ((
% 99.29/13.08 (intersectInPowersetIntersectUnions) =>
% 99.29/13.08 ((
% 99.29/13.08 (inComplementUnionImpNotIn1) =>
% 99.29/13.08 ((
% 99.29/13.08 (inComplementUnionImpInComplement1) =>
% 99.29/13.08 ((
% 99.29/13.08 (binunionTE) =>
% 99.29/13.08 ((
% 99.29/13.08 (binunionTEcontra) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2a1) =>
% 99.29/13.08 ((
% 99.29/13.08 (complementUnionInPowersetComplement) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2a2) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan1a) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan1b) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan1) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2a) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2b2) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2b) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule0) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule1) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule3) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule4) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_1) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_3) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_4) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_5) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1all2) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1SetBreln1) =>
% 99.29/13.08 ((
% 99.29/13.08 (choice2fnsingleton) =>
% 99.29/13.08 ((
% 99.29/13.08 (!!) @ (
% 99.29/13.08 (('#B') @ (
% 99.29/13.08 !!) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ (
% 99.29/13.08 (
% 99.29/13.08 ('#B') @ (
% 99.29/13.08 '#B') @
% 99.29/13.08 breln1)) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ dpsetconstr @
% 99.29/13.08 (
% 99.29/13.08 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.29/13.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2415])).
% 99.29/13.08 thf(zip_derived_cl2449, plain,
% 99.29/13.08 (~ (((binintersectT_lem) =>
% 99.29/13.08 (((binunionT_lem) =>
% 99.29/13.08 (((powersetT_lem) =>
% 99.29/13.08 (((setminusT_lem) =>
% 99.29/13.08 (((complementT_lem) =>
% 99.29/13.08 (((setextT) =>
% 99.29/13.08 (((subsetTI) =>
% 99.29/13.08 (((powersetTI1) =>
% 99.29/13.08 (((powersetTE1) =>
% 99.29/13.08 (((complementTI1) =>
% 99.29/13.08 (((complementTE1) =>
% 99.29/13.08 (((binintersectTELcontra) =>
% 99.29/13.08 (((binintersectTERcontra) =>
% 99.29/13.08 (((contrasubsetT) =>
% 99.29/13.08 (((contrasubsetT1) =>
% 99.29/13.08 (((contrasubsetT2) =>
% 99.29/13.08 (((contrasubsetT3) =>
% 99.29/13.08 (((doubleComplementI1) =>
% 99.29/13.08 (((doubleComplementE1) =>
% 99.29/13.08 (((doubleComplementSub1) =>
% 99.29/13.08 (((doubleComplementSub2) =>
% 99.29/13.08 (((doubleComplementEq) =>
% 99.29/13.08 (((complementTnotintersectT) =>
% 99.29/13.08 (((complementImpComplementIntersect) =>
% 99.29/13.08 (((complementSubsetComplementIntersect) =>
% 99.29/13.08 (((complementInPowersetComplementIntersect) =>
% 99.29/13.08 (((contraSubsetComplement) =>
% 99.29/13.08 (((complementTcontraSubset) =>
% 99.29/13.08 (((binunionTILcontra) =>
% 99.29/13.08 (((binunionTIRcontra) =>
% 99.29/13.08 ((
% 99.29/13.08 (inIntersectImpInUnion) =>
% 99.29/13.08 ((
% 99.29/13.08 (inIntersectImpInUnion2) =>
% 99.29/13.08 ((
% 99.29/13.08 (inIntersectImpInIntersectUnions) =>
% 99.29/13.08 ((
% 99.29/13.08 (intersectInPowersetIntersectUnions) =>
% 99.29/13.08 ((
% 99.29/13.08 (inComplementUnionImpNotIn1) =>
% 99.29/13.08 ((
% 99.29/13.08 (inComplementUnionImpInComplement1) =>
% 99.29/13.08 ((
% 99.29/13.08 (binunionTE) =>
% 99.29/13.08 ((
% 99.29/13.08 (binunionTEcontra) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2a1) =>
% 99.29/13.08 ((
% 99.29/13.08 (complementUnionInPowersetComplement) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2a2) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan1a) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan1b) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan1) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2a) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2b2) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2b) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule0) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule1) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule3) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule4) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_1) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_3) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_4) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_5) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1all2) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1SetBreln1) =>
% 99.29/13.08 ((
% 99.29/13.08 (choice2fnsingleton) =>
% 99.29/13.08 ((
% 99.29/13.08 (!!) @ (
% 99.29/13.08 (('#B') @ (
% 99.29/13.08 !!) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ (
% 99.29/13.08 (
% 99.29/13.08 ('#B') @ (
% 99.29/13.08 '#B') @
% 99.29/13.08 breln1)) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ dpsetconstr @
% 99.29/13.08 (
% 99.29/13.08 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.29/13.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2434])).
% 99.29/13.08 thf(zip_derived_cl2461, plain,
% 99.29/13.08 (~ (((binunionT_lem) =>
% 99.29/13.08 (((powersetT_lem) =>
% 99.29/13.08 (((setminusT_lem) =>
% 99.29/13.08 (((complementT_lem) =>
% 99.29/13.08 (((setextT) =>
% 99.29/13.08 (((subsetTI) =>
% 99.29/13.08 (((powersetTI1) =>
% 99.29/13.08 (((powersetTE1) =>
% 99.29/13.08 (((complementTI1) =>
% 99.29/13.08 (((complementTE1) =>
% 99.29/13.08 (((binintersectTELcontra) =>
% 99.29/13.08 (((binintersectTERcontra) =>
% 99.29/13.08 (((contrasubsetT) =>
% 99.29/13.08 (((contrasubsetT1) =>
% 99.29/13.08 (((contrasubsetT2) =>
% 99.29/13.08 (((contrasubsetT3) =>
% 99.29/13.08 (((doubleComplementI1) =>
% 99.29/13.08 (((doubleComplementE1) =>
% 99.29/13.08 (((doubleComplementSub1) =>
% 99.29/13.08 (((doubleComplementSub2) =>
% 99.29/13.08 (((doubleComplementEq) =>
% 99.29/13.08 (((complementTnotintersectT) =>
% 99.29/13.08 (((complementImpComplementIntersect) =>
% 99.29/13.08 (((complementSubsetComplementIntersect) =>
% 99.29/13.08 (((complementInPowersetComplementIntersect) =>
% 99.29/13.08 (((contraSubsetComplement) =>
% 99.29/13.08 (((complementTcontraSubset) =>
% 99.29/13.08 (((binunionTILcontra) =>
% 99.29/13.08 (((binunionTIRcontra) =>
% 99.29/13.08 (((inIntersectImpInUnion) =>
% 99.29/13.08 ((
% 99.29/13.08 (inIntersectImpInUnion2) =>
% 99.29/13.08 ((
% 99.29/13.08 (inIntersectImpInIntersectUnions) =>
% 99.29/13.08 ((
% 99.29/13.08 (intersectInPowersetIntersectUnions) =>
% 99.29/13.08 ((
% 99.29/13.08 (inComplementUnionImpNotIn1) =>
% 99.29/13.08 ((
% 99.29/13.08 (inComplementUnionImpInComplement1) =>
% 99.29/13.08 ((
% 99.29/13.08 (binunionTE) =>
% 99.29/13.08 ((
% 99.29/13.08 (binunionTEcontra) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2a1) =>
% 99.29/13.08 ((
% 99.29/13.08 (complementUnionInPowersetComplement) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2a2) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan1a) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan1b) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan1) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2a) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2b2) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2b) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule0) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule1) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule3) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule4) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_1) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_3) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_4) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_5) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1all2) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1SetBreln1) =>
% 99.29/13.08 ((
% 99.29/13.08 (choice2fnsingleton) =>
% 99.29/13.08 ((
% 99.29/13.08 (!!) @ (
% 99.29/13.08 (('#B') @ (
% 99.29/13.08 !!) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ (
% 99.29/13.08 (
% 99.29/13.08 ('#B') @ (
% 99.29/13.08 '#B') @
% 99.29/13.08 breln1)) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ dpsetconstr @
% 99.29/13.08 (
% 99.29/13.08 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.29/13.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2449])).
% 99.29/13.08 thf(zip_derived_cl2472, plain,
% 99.29/13.08 (~ (((powersetT_lem) =>
% 99.29/13.08 (((setminusT_lem) =>
% 99.29/13.08 (((complementT_lem) =>
% 99.29/13.08 (((setextT) =>
% 99.29/13.08 (((subsetTI) =>
% 99.29/13.08 (((powersetTI1) =>
% 99.29/13.08 (((powersetTE1) =>
% 99.29/13.08 (((complementTI1) =>
% 99.29/13.08 (((complementTE1) =>
% 99.29/13.08 (((binintersectTELcontra) =>
% 99.29/13.08 (((binintersectTERcontra) =>
% 99.29/13.08 (((contrasubsetT) =>
% 99.29/13.08 (((contrasubsetT1) =>
% 99.29/13.08 (((contrasubsetT2) =>
% 99.29/13.08 (((contrasubsetT3) =>
% 99.29/13.08 (((doubleComplementI1) =>
% 99.29/13.08 (((doubleComplementE1) =>
% 99.29/13.08 (((doubleComplementSub1) =>
% 99.29/13.08 (((doubleComplementSub2) =>
% 99.29/13.08 (((doubleComplementEq) =>
% 99.29/13.08 (((complementTnotintersectT) =>
% 99.29/13.08 (((complementImpComplementIntersect) =>
% 99.29/13.08 (((complementSubsetComplementIntersect) =>
% 99.29/13.08 (((complementInPowersetComplementIntersect) =>
% 99.29/13.08 (((contraSubsetComplement) =>
% 99.29/13.08 (((complementTcontraSubset) =>
% 99.29/13.08 (((binunionTILcontra) =>
% 99.29/13.08 (((binunionTIRcontra) =>
% 99.29/13.08 (((inIntersectImpInUnion) =>
% 99.29/13.08 (((inIntersectImpInUnion2) =>
% 99.29/13.08 ((
% 99.29/13.08 (inIntersectImpInIntersectUnions) =>
% 99.29/13.08 ((
% 99.29/13.08 (intersectInPowersetIntersectUnions) =>
% 99.29/13.08 ((
% 99.29/13.08 (inComplementUnionImpNotIn1) =>
% 99.29/13.08 ((
% 99.29/13.08 (inComplementUnionImpInComplement1) =>
% 99.29/13.08 ((
% 99.29/13.08 (binunionTE) =>
% 99.29/13.08 ((
% 99.29/13.08 (binunionTEcontra) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2a1) =>
% 99.29/13.08 ((
% 99.29/13.08 (complementUnionInPowersetComplement) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2a2) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan1a) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan1b) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan1) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2a) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2b2) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2b) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule0) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule1) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule3) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule4) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_1) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_3) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_4) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_5) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1all2) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1SetBreln1) =>
% 99.29/13.08 ((
% 99.29/13.08 (choice2fnsingleton) =>
% 99.29/13.08 ((
% 99.29/13.08 (!!) @ (
% 99.29/13.08 (('#B') @ (
% 99.29/13.08 !!) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ (
% 99.29/13.08 (
% 99.29/13.08 ('#B') @ (
% 99.29/13.08 '#B') @
% 99.29/13.08 breln1)) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ dpsetconstr @
% 99.29/13.08 (
% 99.29/13.08 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.29/13.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2461])).
% 99.29/13.08 thf(zip_derived_cl2483, plain,
% 99.29/13.08 (~ (((setminusT_lem) =>
% 99.29/13.08 (((complementT_lem) =>
% 99.29/13.08 (((setextT) =>
% 99.29/13.08 (((subsetTI) =>
% 99.29/13.08 (((powersetTI1) =>
% 99.29/13.08 (((powersetTE1) =>
% 99.29/13.08 (((complementTI1) =>
% 99.29/13.08 (((complementTE1) =>
% 99.29/13.08 (((binintersectTELcontra) =>
% 99.29/13.08 (((binintersectTERcontra) =>
% 99.29/13.08 (((contrasubsetT) =>
% 99.29/13.08 (((contrasubsetT1) =>
% 99.29/13.08 (((contrasubsetT2) =>
% 99.29/13.08 (((contrasubsetT3) =>
% 99.29/13.08 (((doubleComplementI1) =>
% 99.29/13.08 (((doubleComplementE1) =>
% 99.29/13.08 (((doubleComplementSub1) =>
% 99.29/13.08 (((doubleComplementSub2) =>
% 99.29/13.08 (((doubleComplementEq) =>
% 99.29/13.08 (((complementTnotintersectT) =>
% 99.29/13.08 (((complementImpComplementIntersect) =>
% 99.29/13.08 (((complementSubsetComplementIntersect) =>
% 99.29/13.08 (((complementInPowersetComplementIntersect) =>
% 99.29/13.08 (((contraSubsetComplement) =>
% 99.29/13.08 (((complementTcontraSubset) =>
% 99.29/13.08 (((binunionTILcontra) =>
% 99.29/13.08 (((binunionTIRcontra) =>
% 99.29/13.08 (((inIntersectImpInUnion) =>
% 99.29/13.08 (((inIntersectImpInUnion2) =>
% 99.29/13.08 (((inIntersectImpInIntersectUnions) =>
% 99.29/13.08 ((
% 99.29/13.08 (intersectInPowersetIntersectUnions) =>
% 99.29/13.08 ((
% 99.29/13.08 (inComplementUnionImpNotIn1) =>
% 99.29/13.08 ((
% 99.29/13.08 (inComplementUnionImpInComplement1) =>
% 99.29/13.08 ((
% 99.29/13.08 (binunionTE) =>
% 99.29/13.08 ((
% 99.29/13.08 (binunionTEcontra) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2a1) =>
% 99.29/13.08 ((
% 99.29/13.08 (complementUnionInPowersetComplement) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2a2) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan1a) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan1b) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan1) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2a) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2b2) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2b) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule0) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule1) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule3) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule4) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_1) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_3) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_4) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_5) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1all2) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1SetBreln1) =>
% 99.29/13.08 ((
% 99.29/13.08 (choice2fnsingleton) =>
% 99.29/13.08 ((
% 99.29/13.08 (!!) @ (
% 99.29/13.08 (('#B') @ (
% 99.29/13.08 !!) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ (
% 99.29/13.08 (
% 99.29/13.08 ('#B') @ (
% 99.29/13.08 '#B') @
% 99.29/13.08 breln1)) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ dpsetconstr @
% 99.29/13.08 (
% 99.29/13.08 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.29/13.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2472])).
% 99.29/13.08 thf(zip_derived_cl2492, plain,
% 99.29/13.08 (~ (((complementT_lem) =>
% 99.29/13.08 (((setextT) =>
% 99.29/13.08 (((subsetTI) =>
% 99.29/13.08 (((powersetTI1) =>
% 99.29/13.08 (((powersetTE1) =>
% 99.29/13.08 (((complementTI1) =>
% 99.29/13.08 (((complementTE1) =>
% 99.29/13.08 (((binintersectTELcontra) =>
% 99.29/13.08 (((binintersectTERcontra) =>
% 99.29/13.08 (((contrasubsetT) =>
% 99.29/13.08 (((contrasubsetT1) =>
% 99.29/13.08 (((contrasubsetT2) =>
% 99.29/13.08 (((contrasubsetT3) =>
% 99.29/13.08 (((doubleComplementI1) =>
% 99.29/13.08 (((doubleComplementE1) =>
% 99.29/13.08 (((doubleComplementSub1) =>
% 99.29/13.08 (((doubleComplementSub2) =>
% 99.29/13.08 (((doubleComplementEq) =>
% 99.29/13.08 (((complementTnotintersectT) =>
% 99.29/13.08 (((complementImpComplementIntersect) =>
% 99.29/13.08 (((complementSubsetComplementIntersect) =>
% 99.29/13.08 (((complementInPowersetComplementIntersect) =>
% 99.29/13.08 (((contraSubsetComplement) =>
% 99.29/13.08 (((complementTcontraSubset) =>
% 99.29/13.08 (((binunionTILcontra) =>
% 99.29/13.08 (((binunionTIRcontra) =>
% 99.29/13.08 (((inIntersectImpInUnion) =>
% 99.29/13.08 (((inIntersectImpInUnion2) =>
% 99.29/13.08 (((inIntersectImpInIntersectUnions) =>
% 99.29/13.08 (((intersectInPowersetIntersectUnions) =>
% 99.29/13.08 ((
% 99.29/13.08 (inComplementUnionImpNotIn1) =>
% 99.29/13.08 ((
% 99.29/13.08 (inComplementUnionImpInComplement1) =>
% 99.29/13.08 ((
% 99.29/13.08 (binunionTE) =>
% 99.29/13.08 ((
% 99.29/13.08 (binunionTEcontra) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2a1) =>
% 99.29/13.08 ((
% 99.29/13.08 (complementUnionInPowersetComplement) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2a2) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan1a) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan1b) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan1) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2a) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2b2) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2b) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule0) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule1) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule3) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule4) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_1) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_3) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_4) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_5) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1all2) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1SetBreln1) =>
% 99.29/13.08 ((
% 99.29/13.08 (choice2fnsingleton) =>
% 99.29/13.08 ((
% 99.29/13.08 (!!) @ (
% 99.29/13.08 (('#B') @ (
% 99.29/13.08 !!) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ (
% 99.29/13.08 (
% 99.29/13.08 ('#B') @ (
% 99.29/13.08 '#B') @
% 99.29/13.08 breln1)) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ dpsetconstr @
% 99.29/13.08 (
% 99.29/13.08 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.29/13.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2483])).
% 99.29/13.08 thf(zip_derived_cl2502, plain,
% 99.29/13.08 (~ (((setextT) =>
% 99.29/13.08 (((subsetTI) =>
% 99.29/13.08 (((powersetTI1) =>
% 99.29/13.08 (((powersetTE1) =>
% 99.29/13.08 (((complementTI1) =>
% 99.29/13.08 (((complementTE1) =>
% 99.29/13.08 (((binintersectTELcontra) =>
% 99.29/13.08 (((binintersectTERcontra) =>
% 99.29/13.08 (((contrasubsetT) =>
% 99.29/13.08 (((contrasubsetT1) =>
% 99.29/13.08 (((contrasubsetT2) =>
% 99.29/13.08 (((contrasubsetT3) =>
% 99.29/13.08 (((doubleComplementI1) =>
% 99.29/13.08 (((doubleComplementE1) =>
% 99.29/13.08 (((doubleComplementSub1) =>
% 99.29/13.08 (((doubleComplementSub2) =>
% 99.29/13.08 (((doubleComplementEq) =>
% 99.29/13.08 (((complementTnotintersectT) =>
% 99.29/13.08 (((complementImpComplementIntersect) =>
% 99.29/13.08 (((complementSubsetComplementIntersect) =>
% 99.29/13.08 (((complementInPowersetComplementIntersect) =>
% 99.29/13.08 (((contraSubsetComplement) =>
% 99.29/13.08 (((complementTcontraSubset) =>
% 99.29/13.08 (((binunionTILcontra) =>
% 99.29/13.08 (((binunionTIRcontra) =>
% 99.29/13.08 (((inIntersectImpInUnion) =>
% 99.29/13.08 (((inIntersectImpInUnion2) =>
% 99.29/13.08 (((inIntersectImpInIntersectUnions) =>
% 99.29/13.08 (((intersectInPowersetIntersectUnions) =>
% 99.29/13.08 (((inComplementUnionImpNotIn1) =>
% 99.29/13.08 ((
% 99.29/13.08 (inComplementUnionImpInComplement1) =>
% 99.29/13.08 ((
% 99.29/13.08 (binunionTE) =>
% 99.29/13.08 ((
% 99.29/13.08 (binunionTEcontra) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2a1) =>
% 99.29/13.08 ((
% 99.29/13.08 (complementUnionInPowersetComplement) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2a2) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan1a) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan1b) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan1) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2a) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2b2) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2b) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule0) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule1) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule3) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule4) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_1) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_3) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_4) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_5) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1all2) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1SetBreln1) =>
% 99.29/13.08 ((
% 99.29/13.08 (choice2fnsingleton) =>
% 99.29/13.08 ((
% 99.29/13.08 (!!) @ (
% 99.29/13.08 (('#B') @ (
% 99.29/13.08 !!) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ (
% 99.29/13.08 (
% 99.29/13.08 ('#B') @ (
% 99.29/13.08 '#B') @
% 99.29/13.08 breln1)) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ dpsetconstr @
% 99.29/13.08 (
% 99.29/13.08 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.29/13.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2492])).
% 99.29/13.08 thf(zip_derived_cl2513, plain,
% 99.29/13.08 (~ (((subsetTI) =>
% 99.29/13.08 (((powersetTI1) =>
% 99.29/13.08 (((powersetTE1) =>
% 99.29/13.08 (((complementTI1) =>
% 99.29/13.08 (((complementTE1) =>
% 99.29/13.08 (((binintersectTELcontra) =>
% 99.29/13.08 (((binintersectTERcontra) =>
% 99.29/13.08 (((contrasubsetT) =>
% 99.29/13.08 (((contrasubsetT1) =>
% 99.29/13.08 (((contrasubsetT2) =>
% 99.29/13.08 (((contrasubsetT3) =>
% 99.29/13.08 (((doubleComplementI1) =>
% 99.29/13.08 (((doubleComplementE1) =>
% 99.29/13.08 (((doubleComplementSub1) =>
% 99.29/13.08 (((doubleComplementSub2) =>
% 99.29/13.08 (((doubleComplementEq) =>
% 99.29/13.08 (((complementTnotintersectT) =>
% 99.29/13.08 (((complementImpComplementIntersect) =>
% 99.29/13.08 (((complementSubsetComplementIntersect) =>
% 99.29/13.08 (((complementInPowersetComplementIntersect) =>
% 99.29/13.08 (((contraSubsetComplement) =>
% 99.29/13.08 (((complementTcontraSubset) =>
% 99.29/13.08 (((binunionTILcontra) =>
% 99.29/13.08 (((binunionTIRcontra) =>
% 99.29/13.08 (((inIntersectImpInUnion) =>
% 99.29/13.08 (((inIntersectImpInUnion2) =>
% 99.29/13.08 (((inIntersectImpInIntersectUnions) =>
% 99.29/13.08 (((intersectInPowersetIntersectUnions) =>
% 99.29/13.08 (((inComplementUnionImpNotIn1) =>
% 99.29/13.08 (((inComplementUnionImpInComplement1) =>
% 99.29/13.08 ((
% 99.29/13.08 (binunionTE) =>
% 99.29/13.08 ((
% 99.29/13.08 (binunionTEcontra) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2a1) =>
% 99.29/13.08 ((
% 99.29/13.08 (complementUnionInPowersetComplement) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2a2) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan1a) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan1b) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan1) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2a) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2b2) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2b) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule0) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule1) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule3) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule4) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_1) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_3) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_4) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_5) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1all2) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1SetBreln1) =>
% 99.29/13.08 ((
% 99.29/13.08 (choice2fnsingleton) =>
% 99.29/13.08 ((
% 99.29/13.08 (!!) @ (
% 99.29/13.08 (('#B') @ (
% 99.29/13.08 !!) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ (
% 99.29/13.08 (
% 99.29/13.08 ('#B') @ (
% 99.29/13.08 '#B') @
% 99.29/13.08 breln1)) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ dpsetconstr @
% 99.29/13.08 (
% 99.29/13.08 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.29/13.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2502])).
% 99.29/13.08 thf(zip_derived_cl2525, plain,
% 99.29/13.08 (~ (((powersetTI1) =>
% 99.29/13.08 (((powersetTE1) =>
% 99.29/13.08 (((complementTI1) =>
% 99.29/13.08 (((complementTE1) =>
% 99.29/13.08 (((binintersectTELcontra) =>
% 99.29/13.08 (((binintersectTERcontra) =>
% 99.29/13.08 (((contrasubsetT) =>
% 99.29/13.08 (((contrasubsetT1) =>
% 99.29/13.08 (((contrasubsetT2) =>
% 99.29/13.08 (((contrasubsetT3) =>
% 99.29/13.08 (((doubleComplementI1) =>
% 99.29/13.08 (((doubleComplementE1) =>
% 99.29/13.08 (((doubleComplementSub1) =>
% 99.29/13.08 (((doubleComplementSub2) =>
% 99.29/13.08 (((doubleComplementEq) =>
% 99.29/13.08 (((complementTnotintersectT) =>
% 99.29/13.08 (((complementImpComplementIntersect) =>
% 99.29/13.08 (((complementSubsetComplementIntersect) =>
% 99.29/13.08 (((complementInPowersetComplementIntersect) =>
% 99.29/13.08 (((contraSubsetComplement) =>
% 99.29/13.08 (((complementTcontraSubset) =>
% 99.29/13.08 (((binunionTILcontra) =>
% 99.29/13.08 (((binunionTIRcontra) =>
% 99.29/13.08 (((inIntersectImpInUnion) =>
% 99.29/13.08 (((inIntersectImpInUnion2) =>
% 99.29/13.08 (((inIntersectImpInIntersectUnions) =>
% 99.29/13.08 (((intersectInPowersetIntersectUnions) =>
% 99.29/13.08 (((inComplementUnionImpNotIn1) =>
% 99.29/13.08 (((inComplementUnionImpInComplement1) =>
% 99.29/13.08 (((binunionTE) =>
% 99.29/13.08 ((
% 99.29/13.08 (binunionTEcontra) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2a1) =>
% 99.29/13.08 ((
% 99.29/13.08 (complementUnionInPowersetComplement) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2a2) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan1a) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan1b) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan1) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2a) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2b2) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2b) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule0) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule1) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule3) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule4) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_1) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_3) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_4) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_5) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1all2) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1SetBreln1) =>
% 99.29/13.08 ((
% 99.29/13.08 (choice2fnsingleton) =>
% 99.29/13.08 ((
% 99.29/13.08 (!!) @ (
% 99.29/13.08 (('#B') @ (
% 99.29/13.08 !!) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ (
% 99.29/13.08 (
% 99.29/13.08 ('#B') @ (
% 99.29/13.08 '#B') @
% 99.29/13.08 breln1)) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ dpsetconstr @
% 99.29/13.08 (
% 99.29/13.08 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.29/13.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2513])).
% 99.29/13.08 thf(zip_derived_cl2534, plain,
% 99.29/13.08 (~ (((powersetTE1) =>
% 99.29/13.08 (((complementTI1) =>
% 99.29/13.08 (((complementTE1) =>
% 99.29/13.08 (((binintersectTELcontra) =>
% 99.29/13.08 (((binintersectTERcontra) =>
% 99.29/13.08 (((contrasubsetT) =>
% 99.29/13.08 (((contrasubsetT1) =>
% 99.29/13.08 (((contrasubsetT2) =>
% 99.29/13.08 (((contrasubsetT3) =>
% 99.29/13.08 (((doubleComplementI1) =>
% 99.29/13.08 (((doubleComplementE1) =>
% 99.29/13.08 (((doubleComplementSub1) =>
% 99.29/13.08 (((doubleComplementSub2) =>
% 99.29/13.08 (((doubleComplementEq) =>
% 99.29/13.08 (((complementTnotintersectT) =>
% 99.29/13.08 (((complementImpComplementIntersect) =>
% 99.29/13.08 (((complementSubsetComplementIntersect) =>
% 99.29/13.08 (((complementInPowersetComplementIntersect) =>
% 99.29/13.08 (((contraSubsetComplement) =>
% 99.29/13.08 (((complementTcontraSubset) =>
% 99.29/13.08 (((binunionTILcontra) =>
% 99.29/13.08 (((binunionTIRcontra) =>
% 99.29/13.08 (((inIntersectImpInUnion) =>
% 99.29/13.08 (((inIntersectImpInUnion2) =>
% 99.29/13.08 (((inIntersectImpInIntersectUnions) =>
% 99.29/13.08 (((intersectInPowersetIntersectUnions) =>
% 99.29/13.08 (((inComplementUnionImpNotIn1) =>
% 99.29/13.08 (((inComplementUnionImpInComplement1) =>
% 99.29/13.08 (((binunionTE) =>
% 99.29/13.08 (((binunionTEcontra) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2a1) =>
% 99.29/13.08 ((
% 99.29/13.08 (complementUnionInPowersetComplement) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2a2) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan1a) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan1b) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan1) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2a) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2b2) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2b) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule0) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule1) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule3) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule4) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_1) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_3) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_4) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_5) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1all2) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1SetBreln1) =>
% 99.29/13.08 ((
% 99.29/13.08 (choice2fnsingleton) =>
% 99.29/13.08 ((
% 99.29/13.08 (!!) @ (
% 99.29/13.08 (('#B') @ (
% 99.29/13.08 !!) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ (
% 99.29/13.08 (
% 99.29/13.08 ('#B') @ (
% 99.29/13.08 '#B') @
% 99.29/13.08 breln1)) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ dpsetconstr @
% 99.29/13.08 (
% 99.29/13.08 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.29/13.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2525])).
% 99.29/13.08 thf(zip_derived_cl2542, plain,
% 99.29/13.08 (~ (((complementTI1) =>
% 99.29/13.08 (((complementTE1) =>
% 99.29/13.08 (((binintersectTELcontra) =>
% 99.29/13.08 (((binintersectTERcontra) =>
% 99.29/13.08 (((contrasubsetT) =>
% 99.29/13.08 (((contrasubsetT1) =>
% 99.29/13.08 (((contrasubsetT2) =>
% 99.29/13.08 (((contrasubsetT3) =>
% 99.29/13.08 (((doubleComplementI1) =>
% 99.29/13.08 (((doubleComplementE1) =>
% 99.29/13.08 (((doubleComplementSub1) =>
% 99.29/13.08 (((doubleComplementSub2) =>
% 99.29/13.08 (((doubleComplementEq) =>
% 99.29/13.08 (((complementTnotintersectT) =>
% 99.29/13.08 (((complementImpComplementIntersect) =>
% 99.29/13.08 (((complementSubsetComplementIntersect) =>
% 99.29/13.08 (((complementInPowersetComplementIntersect) =>
% 99.29/13.08 (((contraSubsetComplement) =>
% 99.29/13.08 (((complementTcontraSubset) =>
% 99.29/13.08 (((binunionTILcontra) =>
% 99.29/13.08 (((binunionTIRcontra) =>
% 99.29/13.08 (((inIntersectImpInUnion) =>
% 99.29/13.08 (((inIntersectImpInUnion2) =>
% 99.29/13.08 (((inIntersectImpInIntersectUnions) =>
% 99.29/13.08 (((intersectInPowersetIntersectUnions) =>
% 99.29/13.08 (((inComplementUnionImpNotIn1) =>
% 99.29/13.08 (((inComplementUnionImpInComplement1) =>
% 99.29/13.08 (((binunionTE) =>
% 99.29/13.08 (((binunionTEcontra) =>
% 99.29/13.08 (((demorgan2a1) =>
% 99.29/13.08 ((
% 99.29/13.08 (complementUnionInPowersetComplement) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2a2) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan1a) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan1b) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan1) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2a) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2b2) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2b) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule0) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule1) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule3) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule4) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_1) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_3) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_4) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_5) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1all2) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1SetBreln1) =>
% 99.29/13.08 ((
% 99.29/13.08 (choice2fnsingleton) =>
% 99.29/13.08 ((
% 99.29/13.08 (!!) @ (
% 99.29/13.08 (('#B') @ (
% 99.29/13.08 !!) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ (
% 99.29/13.08 (
% 99.29/13.08 ('#B') @ (
% 99.29/13.08 '#B') @
% 99.29/13.08 breln1)) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ dpsetconstr @
% 99.29/13.08 (
% 99.29/13.08 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.29/13.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2534])).
% 99.29/13.08 thf(zip_derived_cl2550, plain,
% 99.29/13.08 (~ (((complementTE1) =>
% 99.29/13.08 (((binintersectTELcontra) =>
% 99.29/13.08 (((binintersectTERcontra) =>
% 99.29/13.08 (((contrasubsetT) =>
% 99.29/13.08 (((contrasubsetT1) =>
% 99.29/13.08 (((contrasubsetT2) =>
% 99.29/13.08 (((contrasubsetT3) =>
% 99.29/13.08 (((doubleComplementI1) =>
% 99.29/13.08 (((doubleComplementE1) =>
% 99.29/13.08 (((doubleComplementSub1) =>
% 99.29/13.08 (((doubleComplementSub2) =>
% 99.29/13.08 (((doubleComplementEq) =>
% 99.29/13.08 (((complementTnotintersectT) =>
% 99.29/13.08 (((complementImpComplementIntersect) =>
% 99.29/13.08 (((complementSubsetComplementIntersect) =>
% 99.29/13.08 (((complementInPowersetComplementIntersect) =>
% 99.29/13.08 (((contraSubsetComplement) =>
% 99.29/13.08 (((complementTcontraSubset) =>
% 99.29/13.08 (((binunionTILcontra) =>
% 99.29/13.08 (((binunionTIRcontra) =>
% 99.29/13.08 (((inIntersectImpInUnion) =>
% 99.29/13.08 (((inIntersectImpInUnion2) =>
% 99.29/13.08 (((inIntersectImpInIntersectUnions) =>
% 99.29/13.08 (((intersectInPowersetIntersectUnions) =>
% 99.29/13.08 (((inComplementUnionImpNotIn1) =>
% 99.29/13.08 (((inComplementUnionImpInComplement1) =>
% 99.29/13.08 (((binunionTE) =>
% 99.29/13.08 (((binunionTEcontra) =>
% 99.29/13.08 (((demorgan2a1) =>
% 99.29/13.08 (((complementUnionInPowersetComplement) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2a2) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan1a) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan1b) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan1) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2a) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2b2) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2b) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule0) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule1) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule3) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule4) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_1) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_3) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_4) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_5) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1all2) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1SetBreln1) =>
% 99.29/13.08 ((
% 99.29/13.08 (choice2fnsingleton) =>
% 99.29/13.08 ((
% 99.29/13.08 (!!) @ (
% 99.29/13.08 (('#B') @ (
% 99.29/13.08 !!) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ (
% 99.29/13.08 (
% 99.29/13.08 ('#B') @ (
% 99.29/13.08 '#B') @
% 99.29/13.08 breln1)) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ dpsetconstr @
% 99.29/13.08 (
% 99.29/13.08 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.29/13.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2542])).
% 99.29/13.08 thf(zip_derived_cl2558, plain,
% 99.29/13.08 (~ (((binintersectTELcontra) =>
% 99.29/13.08 (((binintersectTERcontra) =>
% 99.29/13.08 (((contrasubsetT) =>
% 99.29/13.08 (((contrasubsetT1) =>
% 99.29/13.08 (((contrasubsetT2) =>
% 99.29/13.08 (((contrasubsetT3) =>
% 99.29/13.08 (((doubleComplementI1) =>
% 99.29/13.08 (((doubleComplementE1) =>
% 99.29/13.08 (((doubleComplementSub1) =>
% 99.29/13.08 (((doubleComplementSub2) =>
% 99.29/13.08 (((doubleComplementEq) =>
% 99.29/13.08 (((complementTnotintersectT) =>
% 99.29/13.08 (((complementImpComplementIntersect) =>
% 99.29/13.08 (((complementSubsetComplementIntersect) =>
% 99.29/13.08 (((complementInPowersetComplementIntersect) =>
% 99.29/13.08 (((contraSubsetComplement) =>
% 99.29/13.08 (((complementTcontraSubset) =>
% 99.29/13.08 (((binunionTILcontra) =>
% 99.29/13.08 (((binunionTIRcontra) =>
% 99.29/13.08 (((inIntersectImpInUnion) =>
% 99.29/13.08 (((inIntersectImpInUnion2) =>
% 99.29/13.08 (((inIntersectImpInIntersectUnions) =>
% 99.29/13.08 (((intersectInPowersetIntersectUnions) =>
% 99.29/13.08 (((inComplementUnionImpNotIn1) =>
% 99.29/13.08 (((inComplementUnionImpInComplement1) =>
% 99.29/13.08 (((binunionTE) =>
% 99.29/13.08 (((binunionTEcontra) =>
% 99.29/13.08 (((demorgan2a1) =>
% 99.29/13.08 (((complementUnionInPowersetComplement) =>
% 99.29/13.08 (((demorgan2a2) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan1a) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan1b) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan1) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2a) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2b2) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2b) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule0) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule1) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule3) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule4) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_1) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_3) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_4) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_5) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1all2) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1SetBreln1) =>
% 99.29/13.08 ((
% 99.29/13.08 (choice2fnsingleton) =>
% 99.29/13.08 ((
% 99.29/13.08 (!!) @ (
% 99.29/13.08 (('#B') @ (
% 99.29/13.08 !!) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ (
% 99.29/13.08 (
% 99.29/13.08 ('#B') @ (
% 99.29/13.08 '#B') @
% 99.29/13.08 breln1)) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ dpsetconstr @
% 99.29/13.08 (
% 99.29/13.08 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.29/13.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2550])).
% 99.29/13.08 thf(zip_derived_cl2567, plain,
% 99.29/13.08 (~ (((binintersectTERcontra) =>
% 99.29/13.08 (((contrasubsetT) =>
% 99.29/13.08 (((contrasubsetT1) =>
% 99.29/13.08 (((contrasubsetT2) =>
% 99.29/13.08 (((contrasubsetT3) =>
% 99.29/13.08 (((doubleComplementI1) =>
% 99.29/13.08 (((doubleComplementE1) =>
% 99.29/13.08 (((doubleComplementSub1) =>
% 99.29/13.08 (((doubleComplementSub2) =>
% 99.29/13.08 (((doubleComplementEq) =>
% 99.29/13.08 (((complementTnotintersectT) =>
% 99.29/13.08 (((complementImpComplementIntersect) =>
% 99.29/13.08 (((complementSubsetComplementIntersect) =>
% 99.29/13.08 (((complementInPowersetComplementIntersect) =>
% 99.29/13.08 (((contraSubsetComplement) =>
% 99.29/13.08 (((complementTcontraSubset) =>
% 99.29/13.08 (((binunionTILcontra) =>
% 99.29/13.08 (((binunionTIRcontra) =>
% 99.29/13.08 (((inIntersectImpInUnion) =>
% 99.29/13.08 (((inIntersectImpInUnion2) =>
% 99.29/13.08 (((inIntersectImpInIntersectUnions) =>
% 99.29/13.08 (((intersectInPowersetIntersectUnions) =>
% 99.29/13.08 (((inComplementUnionImpNotIn1) =>
% 99.29/13.08 (((inComplementUnionImpInComplement1) =>
% 99.29/13.08 (((binunionTE) =>
% 99.29/13.08 (((binunionTEcontra) =>
% 99.29/13.08 (((demorgan2a1) =>
% 99.29/13.08 (((complementUnionInPowersetComplement) =>
% 99.29/13.08 (((demorgan2a2) =>
% 99.29/13.08 (((demorgan1a) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan1b) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan1) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2a) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2b2) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2b) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule0) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule1) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule3) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule4) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_1) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_3) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_4) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_5) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1all2) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1SetBreln1) =>
% 99.29/13.08 ((
% 99.29/13.08 (choice2fnsingleton) =>
% 99.29/13.08 ((
% 99.29/13.08 (!!) @ (
% 99.29/13.08 (('#B') @ (
% 99.29/13.08 !!) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ (
% 99.29/13.08 (
% 99.29/13.08 ('#B') @ (
% 99.29/13.08 '#B') @
% 99.29/13.08 breln1)) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ dpsetconstr @
% 99.29/13.08 (
% 99.29/13.08 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.29/13.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2558])).
% 99.29/13.08 thf(zip_derived_cl2577, plain,
% 99.29/13.08 (~ (((contrasubsetT) =>
% 99.29/13.08 (((contrasubsetT1) =>
% 99.29/13.08 (((contrasubsetT2) =>
% 99.29/13.08 (((contrasubsetT3) =>
% 99.29/13.08 (((doubleComplementI1) =>
% 99.29/13.08 (((doubleComplementE1) =>
% 99.29/13.08 (((doubleComplementSub1) =>
% 99.29/13.08 (((doubleComplementSub2) =>
% 99.29/13.08 (((doubleComplementEq) =>
% 99.29/13.08 (((complementTnotintersectT) =>
% 99.29/13.08 (((complementImpComplementIntersect) =>
% 99.29/13.08 (((complementSubsetComplementIntersect) =>
% 99.29/13.08 (((complementInPowersetComplementIntersect) =>
% 99.29/13.08 (((contraSubsetComplement) =>
% 99.29/13.08 (((complementTcontraSubset) =>
% 99.29/13.08 (((binunionTILcontra) =>
% 99.29/13.08 (((binunionTIRcontra) =>
% 99.29/13.08 (((inIntersectImpInUnion) =>
% 99.29/13.08 (((inIntersectImpInUnion2) =>
% 99.29/13.08 (((inIntersectImpInIntersectUnions) =>
% 99.29/13.08 (((intersectInPowersetIntersectUnions) =>
% 99.29/13.08 (((inComplementUnionImpNotIn1) =>
% 99.29/13.08 (((inComplementUnionImpInComplement1) =>
% 99.29/13.08 (((binunionTE) =>
% 99.29/13.08 (((binunionTEcontra) =>
% 99.29/13.08 (((demorgan2a1) =>
% 99.29/13.08 (((complementUnionInPowersetComplement) =>
% 99.29/13.08 (((demorgan2a2) =>
% 99.29/13.08 (((demorgan1a) =>
% 99.29/13.08 (((demorgan1b) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan1) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2a) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2b2) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2b) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule0) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule1) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule3) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule4) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_1) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_3) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_4) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_5) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1all2) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1SetBreln1) =>
% 99.29/13.08 ((
% 99.29/13.08 (choice2fnsingleton) =>
% 99.29/13.08 ((
% 99.29/13.08 (!!) @ (
% 99.29/13.08 (('#B') @ (
% 99.29/13.08 !!) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ (
% 99.29/13.08 (
% 99.29/13.08 ('#B') @ (
% 99.29/13.08 '#B') @
% 99.29/13.08 breln1)) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ dpsetconstr @
% 99.29/13.08 (
% 99.29/13.08 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.29/13.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2567])).
% 99.29/13.08 thf(zip_derived_cl2588, plain,
% 99.29/13.08 (~ (((contrasubsetT1) =>
% 99.29/13.08 (((contrasubsetT2) =>
% 99.29/13.08 (((contrasubsetT3) =>
% 99.29/13.08 (((doubleComplementI1) =>
% 99.29/13.08 (((doubleComplementE1) =>
% 99.29/13.08 (((doubleComplementSub1) =>
% 99.29/13.08 (((doubleComplementSub2) =>
% 99.29/13.08 (((doubleComplementEq) =>
% 99.29/13.08 (((complementTnotintersectT) =>
% 99.29/13.08 (((complementImpComplementIntersect) =>
% 99.29/13.08 (((complementSubsetComplementIntersect) =>
% 99.29/13.08 (((complementInPowersetComplementIntersect) =>
% 99.29/13.08 (((contraSubsetComplement) =>
% 99.29/13.08 (((complementTcontraSubset) =>
% 99.29/13.08 (((binunionTILcontra) =>
% 99.29/13.08 (((binunionTIRcontra) =>
% 99.29/13.08 (((inIntersectImpInUnion) =>
% 99.29/13.08 (((inIntersectImpInUnion2) =>
% 99.29/13.08 (((inIntersectImpInIntersectUnions) =>
% 99.29/13.08 (((intersectInPowersetIntersectUnions) =>
% 99.29/13.08 (((inComplementUnionImpNotIn1) =>
% 99.29/13.08 (((inComplementUnionImpInComplement1) =>
% 99.29/13.08 (((binunionTE) =>
% 99.29/13.08 (((binunionTEcontra) =>
% 99.29/13.08 (((demorgan2a1) =>
% 99.29/13.08 (((complementUnionInPowersetComplement) =>
% 99.29/13.08 (((demorgan2a2) =>
% 99.29/13.08 (((demorgan1a) =>
% 99.29/13.08 (((demorgan1b) =>
% 99.29/13.08 (((demorgan1) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2a) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2b2) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2b) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule0) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule1) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule3) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule4) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_1) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_3) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_4) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_5) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1all2) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1SetBreln1) =>
% 99.29/13.08 ((
% 99.29/13.08 (choice2fnsingleton) =>
% 99.29/13.08 ((
% 99.29/13.08 (!!) @ (
% 99.29/13.08 (('#B') @ (
% 99.29/13.08 !!) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ (
% 99.29/13.08 (
% 99.29/13.08 ('#B') @ (
% 99.29/13.08 '#B') @
% 99.29/13.08 breln1)) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ dpsetconstr @
% 99.29/13.08 (
% 99.29/13.08 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.29/13.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2577])).
% 99.29/13.08 thf(zip_derived_cl2601, plain,
% 99.29/13.08 (~ (((contrasubsetT2) =>
% 99.29/13.08 (((contrasubsetT3) =>
% 99.29/13.08 (((doubleComplementI1) =>
% 99.29/13.08 (((doubleComplementE1) =>
% 99.29/13.08 (((doubleComplementSub1) =>
% 99.29/13.08 (((doubleComplementSub2) =>
% 99.29/13.08 (((doubleComplementEq) =>
% 99.29/13.08 (((complementTnotintersectT) =>
% 99.29/13.08 (((complementImpComplementIntersect) =>
% 99.29/13.08 (((complementSubsetComplementIntersect) =>
% 99.29/13.08 (((complementInPowersetComplementIntersect) =>
% 99.29/13.08 (((contraSubsetComplement) =>
% 99.29/13.08 (((complementTcontraSubset) =>
% 99.29/13.08 (((binunionTILcontra) =>
% 99.29/13.08 (((binunionTIRcontra) =>
% 99.29/13.08 (((inIntersectImpInUnion) =>
% 99.29/13.08 (((inIntersectImpInUnion2) =>
% 99.29/13.08 (((inIntersectImpInIntersectUnions) =>
% 99.29/13.08 (((intersectInPowersetIntersectUnions) =>
% 99.29/13.08 (((inComplementUnionImpNotIn1) =>
% 99.29/13.08 (((inComplementUnionImpInComplement1) =>
% 99.29/13.08 (((binunionTE) =>
% 99.29/13.08 (((binunionTEcontra) =>
% 99.29/13.08 (((demorgan2a1) =>
% 99.29/13.08 (((complementUnionInPowersetComplement) =>
% 99.29/13.08 (((demorgan2a2) =>
% 99.29/13.08 (((demorgan1a) =>
% 99.29/13.08 (((demorgan1b) =>
% 99.29/13.08 (((demorgan1) =>
% 99.29/13.08 (((demorgan2a) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2b2) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2b) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule0) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule1) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule3) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule4) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_1) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_3) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_4) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_5) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1all2) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1SetBreln1) =>
% 99.29/13.08 ((
% 99.29/13.08 (choice2fnsingleton) =>
% 99.29/13.08 ((
% 99.29/13.08 (!!) @ (
% 99.29/13.08 (('#B') @ (
% 99.29/13.08 !!) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ (
% 99.29/13.08 (
% 99.29/13.08 ('#B') @ (
% 99.29/13.08 '#B') @
% 99.29/13.08 breln1)) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ dpsetconstr @
% 99.29/13.08 (
% 99.29/13.08 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.29/13.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2588])).
% 99.29/13.08 thf(zip_derived_cl2617, plain,
% 99.29/13.08 (~ (((contrasubsetT3) =>
% 99.29/13.08 (((doubleComplementI1) =>
% 99.29/13.08 (((doubleComplementE1) =>
% 99.29/13.08 (((doubleComplementSub1) =>
% 99.29/13.08 (((doubleComplementSub2) =>
% 99.29/13.08 (((doubleComplementEq) =>
% 99.29/13.08 (((complementTnotintersectT) =>
% 99.29/13.08 (((complementImpComplementIntersect) =>
% 99.29/13.08 (((complementSubsetComplementIntersect) =>
% 99.29/13.08 (((complementInPowersetComplementIntersect) =>
% 99.29/13.08 (((contraSubsetComplement) =>
% 99.29/13.08 (((complementTcontraSubset) =>
% 99.29/13.08 (((binunionTILcontra) =>
% 99.29/13.08 (((binunionTIRcontra) =>
% 99.29/13.08 (((inIntersectImpInUnion) =>
% 99.29/13.08 (((inIntersectImpInUnion2) =>
% 99.29/13.08 (((inIntersectImpInIntersectUnions) =>
% 99.29/13.08 (((intersectInPowersetIntersectUnions) =>
% 99.29/13.08 (((inComplementUnionImpNotIn1) =>
% 99.29/13.08 (((inComplementUnionImpInComplement1) =>
% 99.29/13.08 (((binunionTE) =>
% 99.29/13.08 (((binunionTEcontra) =>
% 99.29/13.08 (((demorgan2a1) =>
% 99.29/13.08 (((complementUnionInPowersetComplement) =>
% 99.29/13.08 (((demorgan2a2) =>
% 99.29/13.08 (((demorgan1a) =>
% 99.29/13.08 (((demorgan1b) =>
% 99.29/13.08 (((demorgan1) =>
% 99.29/13.08 (((demorgan2a) =>
% 99.29/13.08 (((demorgan2b2) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2b) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule0) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule1) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule3) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule4) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_1) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_3) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_4) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_5) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1all2) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1SetBreln1) =>
% 99.29/13.08 ((
% 99.29/13.08 (choice2fnsingleton) =>
% 99.29/13.08 ((
% 99.29/13.08 (!!) @ (
% 99.29/13.08 (('#B') @ (
% 99.29/13.08 !!) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ (
% 99.29/13.08 (
% 99.29/13.08 ('#B') @ (
% 99.29/13.08 '#B') @
% 99.29/13.08 breln1)) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ dpsetconstr @
% 99.29/13.08 (
% 99.29/13.08 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.29/13.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2601])).
% 99.29/13.08 thf(zip_derived_cl2636, plain,
% 99.29/13.08 (~ (((doubleComplementI1) =>
% 99.29/13.08 (((doubleComplementE1) =>
% 99.29/13.08 (((doubleComplementSub1) =>
% 99.29/13.08 (((doubleComplementSub2) =>
% 99.29/13.08 (((doubleComplementEq) =>
% 99.29/13.08 (((complementTnotintersectT) =>
% 99.29/13.08 (((complementImpComplementIntersect) =>
% 99.29/13.08 (((complementSubsetComplementIntersect) =>
% 99.29/13.08 (((complementInPowersetComplementIntersect) =>
% 99.29/13.08 (((contraSubsetComplement) =>
% 99.29/13.08 (((complementTcontraSubset) =>
% 99.29/13.08 (((binunionTILcontra) =>
% 99.29/13.08 (((binunionTIRcontra) =>
% 99.29/13.08 (((inIntersectImpInUnion) =>
% 99.29/13.08 (((inIntersectImpInUnion2) =>
% 99.29/13.08 (((inIntersectImpInIntersectUnions) =>
% 99.29/13.08 (((intersectInPowersetIntersectUnions) =>
% 99.29/13.08 (((inComplementUnionImpNotIn1) =>
% 99.29/13.08 (((inComplementUnionImpInComplement1) =>
% 99.29/13.08 (((binunionTE) =>
% 99.29/13.08 (((binunionTEcontra) =>
% 99.29/13.08 (((demorgan2a1) =>
% 99.29/13.08 (((complementUnionInPowersetComplement) =>
% 99.29/13.08 (((demorgan2a2) =>
% 99.29/13.08 (((demorgan1a) =>
% 99.29/13.08 (((demorgan1b) =>
% 99.29/13.08 (((demorgan1) =>
% 99.29/13.08 (((demorgan2a) =>
% 99.29/13.08 (((demorgan2b2) =>
% 99.29/13.08 (((demorgan2b) =>
% 99.29/13.08 ((
% 99.29/13.08 (demorgan2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule0) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule1) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule3) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule4) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_1) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_3) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_4) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_5) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1all2) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1SetBreln1) =>
% 99.29/13.08 ((
% 99.29/13.08 (choice2fnsingleton) =>
% 99.29/13.08 ((
% 99.29/13.08 (!!) @ (
% 99.29/13.08 (('#B') @ (
% 99.29/13.08 !!) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ (
% 99.29/13.08 (
% 99.29/13.08 ('#B') @ (
% 99.29/13.08 '#B') @
% 99.29/13.08 breln1)) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ dpsetconstr @
% 99.29/13.08 (
% 99.29/13.08 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.29/13.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2617])).
% 99.29/13.08 thf(zip_derived_cl2655, plain,
% 99.29/13.08 (~ (((doubleComplementE1) =>
% 99.29/13.08 (((doubleComplementSub1) =>
% 99.29/13.08 (((doubleComplementSub2) =>
% 99.29/13.08 (((doubleComplementEq) =>
% 99.29/13.08 (((complementTnotintersectT) =>
% 99.29/13.08 (((complementImpComplementIntersect) =>
% 99.29/13.08 (((complementSubsetComplementIntersect) =>
% 99.29/13.08 (((complementInPowersetComplementIntersect) =>
% 99.29/13.08 (((contraSubsetComplement) =>
% 99.29/13.08 (((complementTcontraSubset) =>
% 99.29/13.08 (((binunionTILcontra) =>
% 99.29/13.08 (((binunionTIRcontra) =>
% 99.29/13.08 (((inIntersectImpInUnion) =>
% 99.29/13.08 (((inIntersectImpInUnion2) =>
% 99.29/13.08 (((inIntersectImpInIntersectUnions) =>
% 99.29/13.08 (((intersectInPowersetIntersectUnions) =>
% 99.29/13.08 (((inComplementUnionImpNotIn1) =>
% 99.29/13.08 (((inComplementUnionImpInComplement1) =>
% 99.29/13.08 (((binunionTE) =>
% 99.29/13.08 (((binunionTEcontra) =>
% 99.29/13.08 (((demorgan2a1) =>
% 99.29/13.08 (((complementUnionInPowersetComplement) =>
% 99.29/13.08 (((demorgan2a2) =>
% 99.29/13.08 (((demorgan1a) =>
% 99.29/13.08 (((demorgan1b) =>
% 99.29/13.08 (((demorgan1) =>
% 99.29/13.08 (((demorgan2a) =>
% 99.29/13.08 (((demorgan2b2) =>
% 99.29/13.08 (((demorgan2b) =>
% 99.29/13.08 (((demorgan2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule0) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule1) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule3) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule4) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_1) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_3) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_4) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_5) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1all2) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1SetBreln1) =>
% 99.29/13.08 ((
% 99.29/13.08 (choice2fnsingleton) =>
% 99.29/13.08 ((
% 99.29/13.08 (!!) @ (
% 99.29/13.08 (('#B') @ (
% 99.29/13.08 !!) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ (
% 99.29/13.08 (
% 99.29/13.08 ('#B') @ (
% 99.29/13.08 '#B') @
% 99.29/13.08 breln1)) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ dpsetconstr @
% 99.29/13.08 (
% 99.29/13.08 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.29/13.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2636])).
% 99.29/13.08 thf(zip_derived_cl2672, plain,
% 99.29/13.08 (~ (((doubleComplementSub1) =>
% 99.29/13.08 (((doubleComplementSub2) =>
% 99.29/13.08 (((doubleComplementEq) =>
% 99.29/13.08 (((complementTnotintersectT) =>
% 99.29/13.08 (((complementImpComplementIntersect) =>
% 99.29/13.08 (((complementSubsetComplementIntersect) =>
% 99.29/13.08 (((complementInPowersetComplementIntersect) =>
% 99.29/13.08 (((contraSubsetComplement) =>
% 99.29/13.08 (((complementTcontraSubset) =>
% 99.29/13.08 (((binunionTILcontra) =>
% 99.29/13.08 (((binunionTIRcontra) =>
% 99.29/13.08 (((inIntersectImpInUnion) =>
% 99.29/13.08 (((inIntersectImpInUnion2) =>
% 99.29/13.08 (((inIntersectImpInIntersectUnions) =>
% 99.29/13.08 (((intersectInPowersetIntersectUnions) =>
% 99.29/13.08 (((inComplementUnionImpNotIn1) =>
% 99.29/13.08 (((inComplementUnionImpInComplement1) =>
% 99.29/13.08 (((binunionTE) =>
% 99.29/13.08 (((binunionTEcontra) =>
% 99.29/13.08 (((demorgan2a1) =>
% 99.29/13.08 (((complementUnionInPowersetComplement) =>
% 99.29/13.08 (((demorgan2a2) =>
% 99.29/13.08 (((demorgan1a) =>
% 99.29/13.08 (((demorgan1b) =>
% 99.29/13.08 (((demorgan1) =>
% 99.29/13.08 (((demorgan2a) =>
% 99.29/13.08 (((demorgan2b2) =>
% 99.29/13.08 (((demorgan2b) =>
% 99.29/13.08 (((demorgan2) =>
% 99.29/13.08 (((woz13rule0) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule1) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule3) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule4) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_1) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_3) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_4) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_5) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1all2) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1SetBreln1) =>
% 99.29/13.08 ((
% 99.29/13.08 (choice2fnsingleton) =>
% 99.29/13.08 ((
% 99.29/13.08 (!!) @ (
% 99.29/13.08 (('#B') @ (
% 99.29/13.08 !!) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ (
% 99.29/13.08 (
% 99.29/13.08 ('#B') @ (
% 99.29/13.08 '#B') @
% 99.29/13.08 breln1)) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ dpsetconstr @
% 99.29/13.08 (
% 99.29/13.08 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.29/13.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2655])).
% 99.29/13.08 thf(zip_derived_cl2687, plain,
% 99.29/13.08 (~ (((doubleComplementSub2) =>
% 99.29/13.08 (((doubleComplementEq) =>
% 99.29/13.08 (((complementTnotintersectT) =>
% 99.29/13.08 (((complementImpComplementIntersect) =>
% 99.29/13.08 (((complementSubsetComplementIntersect) =>
% 99.29/13.08 (((complementInPowersetComplementIntersect) =>
% 99.29/13.08 (((contraSubsetComplement) =>
% 99.29/13.08 (((complementTcontraSubset) =>
% 99.29/13.08 (((binunionTILcontra) =>
% 99.29/13.08 (((binunionTIRcontra) =>
% 99.29/13.08 (((inIntersectImpInUnion) =>
% 99.29/13.08 (((inIntersectImpInUnion2) =>
% 99.29/13.08 (((inIntersectImpInIntersectUnions) =>
% 99.29/13.08 (((intersectInPowersetIntersectUnions) =>
% 99.29/13.08 (((inComplementUnionImpNotIn1) =>
% 99.29/13.08 (((inComplementUnionImpInComplement1) =>
% 99.29/13.08 (((binunionTE) =>
% 99.29/13.08 (((binunionTEcontra) =>
% 99.29/13.08 (((demorgan2a1) =>
% 99.29/13.08 (((complementUnionInPowersetComplement) =>
% 99.29/13.08 (((demorgan2a2) =>
% 99.29/13.08 (((demorgan1a) =>
% 99.29/13.08 (((demorgan1b) =>
% 99.29/13.08 (((demorgan1) =>
% 99.29/13.08 (((demorgan2a) =>
% 99.29/13.08 (((demorgan2b2) =>
% 99.29/13.08 (((demorgan2b) =>
% 99.29/13.08 (((demorgan2) =>
% 99.29/13.08 (((woz13rule0) =>
% 99.29/13.08 (((woz13rule1) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule3) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule4) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_1) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_3) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_4) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_5) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1all2) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1SetBreln1) =>
% 99.29/13.08 ((
% 99.29/13.08 (choice2fnsingleton) =>
% 99.29/13.08 ((
% 99.29/13.08 (!!) @ (
% 99.29/13.08 (('#B') @ (
% 99.29/13.08 !!) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ (
% 99.29/13.08 (
% 99.29/13.08 ('#B') @ (
% 99.29/13.08 '#B') @
% 99.29/13.08 breln1)) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ dpsetconstr @
% 99.29/13.08 (
% 99.29/13.08 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.29/13.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2672])).
% 99.29/13.08 thf(zip_derived_cl2699, plain,
% 99.29/13.08 (~ (((doubleComplementEq) =>
% 99.29/13.08 (((complementTnotintersectT) =>
% 99.29/13.08 (((complementImpComplementIntersect) =>
% 99.29/13.08 (((complementSubsetComplementIntersect) =>
% 99.29/13.08 (((complementInPowersetComplementIntersect) =>
% 99.29/13.08 (((contraSubsetComplement) =>
% 99.29/13.08 (((complementTcontraSubset) =>
% 99.29/13.08 (((binunionTILcontra) =>
% 99.29/13.08 (((binunionTIRcontra) =>
% 99.29/13.08 (((inIntersectImpInUnion) =>
% 99.29/13.08 (((inIntersectImpInUnion2) =>
% 99.29/13.08 (((inIntersectImpInIntersectUnions) =>
% 99.29/13.08 (((intersectInPowersetIntersectUnions) =>
% 99.29/13.08 (((inComplementUnionImpNotIn1) =>
% 99.29/13.08 (((inComplementUnionImpInComplement1) =>
% 99.29/13.08 (((binunionTE) =>
% 99.29/13.08 (((binunionTEcontra) =>
% 99.29/13.08 (((demorgan2a1) =>
% 99.29/13.08 (((complementUnionInPowersetComplement) =>
% 99.29/13.08 (((demorgan2a2) =>
% 99.29/13.08 (((demorgan1a) =>
% 99.29/13.08 (((demorgan1b) =>
% 99.29/13.08 (((demorgan1) =>
% 99.29/13.08 (((demorgan2a) =>
% 99.29/13.08 (((demorgan2b2) =>
% 99.29/13.08 (((demorgan2b) =>
% 99.29/13.08 (((demorgan2) =>
% 99.29/13.08 (((woz13rule0) =>
% 99.29/13.08 (((woz13rule1) =>
% 99.29/13.08 (((woz13rule2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule3) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule4) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_1) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_3) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_4) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_5) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1all2) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1SetBreln1) =>
% 99.29/13.08 ((
% 99.29/13.08 (choice2fnsingleton) =>
% 99.29/13.08 ((
% 99.29/13.08 (!!) @ (
% 99.29/13.08 (('#B') @ (
% 99.29/13.08 !!) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ (
% 99.29/13.08 (
% 99.29/13.08 ('#B') @ (
% 99.29/13.08 '#B') @
% 99.29/13.08 breln1)) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ dpsetconstr @
% 99.29/13.08 (
% 99.29/13.08 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.29/13.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2687])).
% 99.29/13.08 thf(zip_derived_cl2711, plain,
% 99.29/13.08 (~ (((complementTnotintersectT) =>
% 99.29/13.08 (((complementImpComplementIntersect) =>
% 99.29/13.08 (((complementSubsetComplementIntersect) =>
% 99.29/13.08 (((complementInPowersetComplementIntersect) =>
% 99.29/13.08 (((contraSubsetComplement) =>
% 99.29/13.08 (((complementTcontraSubset) =>
% 99.29/13.08 (((binunionTILcontra) =>
% 99.29/13.08 (((binunionTIRcontra) =>
% 99.29/13.08 (((inIntersectImpInUnion) =>
% 99.29/13.08 (((inIntersectImpInUnion2) =>
% 99.29/13.08 (((inIntersectImpInIntersectUnions) =>
% 99.29/13.08 (((intersectInPowersetIntersectUnions) =>
% 99.29/13.08 (((inComplementUnionImpNotIn1) =>
% 99.29/13.08 (((inComplementUnionImpInComplement1) =>
% 99.29/13.08 (((binunionTE) =>
% 99.29/13.08 (((binunionTEcontra) =>
% 99.29/13.08 (((demorgan2a1) =>
% 99.29/13.08 (((complementUnionInPowersetComplement) =>
% 99.29/13.08 (((demorgan2a2) =>
% 99.29/13.08 (((demorgan1a) =>
% 99.29/13.08 (((demorgan1b) =>
% 99.29/13.08 (((demorgan1) =>
% 99.29/13.08 (((demorgan2a) =>
% 99.29/13.08 (((demorgan2b2) =>
% 99.29/13.08 (((demorgan2b) =>
% 99.29/13.08 (((demorgan2) =>
% 99.29/13.08 (((woz13rule0) =>
% 99.29/13.08 (((woz13rule1) =>
% 99.29/13.08 (((woz13rule2) =>
% 99.29/13.08 (((woz13rule3) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz13rule4) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_1) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_3) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_4) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_5) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1all2) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1SetBreln1) =>
% 99.29/13.08 ((
% 99.29/13.08 (choice2fnsingleton) =>
% 99.29/13.08 ((
% 99.29/13.08 (!!) @ (
% 99.29/13.08 (('#B') @ (
% 99.29/13.08 !!) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ (
% 99.29/13.08 (
% 99.29/13.08 ('#B') @ (
% 99.29/13.08 '#B') @
% 99.29/13.08 breln1)) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ dpsetconstr @
% 99.29/13.08 (
% 99.29/13.08 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.29/13.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2699])).
% 99.29/13.08 thf(zip_derived_cl2723, plain,
% 99.29/13.08 (~ (((complementImpComplementIntersect) =>
% 99.29/13.08 (((complementSubsetComplementIntersect) =>
% 99.29/13.08 (((complementInPowersetComplementIntersect) =>
% 99.29/13.08 (((contraSubsetComplement) =>
% 99.29/13.08 (((complementTcontraSubset) =>
% 99.29/13.08 (((binunionTILcontra) =>
% 99.29/13.08 (((binunionTIRcontra) =>
% 99.29/13.08 (((inIntersectImpInUnion) =>
% 99.29/13.08 (((inIntersectImpInUnion2) =>
% 99.29/13.08 (((inIntersectImpInIntersectUnions) =>
% 99.29/13.08 (((intersectInPowersetIntersectUnions) =>
% 99.29/13.08 (((inComplementUnionImpNotIn1) =>
% 99.29/13.08 (((inComplementUnionImpInComplement1) =>
% 99.29/13.08 (((binunionTE) =>
% 99.29/13.08 (((binunionTEcontra) =>
% 99.29/13.08 (((demorgan2a1) =>
% 99.29/13.08 (((complementUnionInPowersetComplement) =>
% 99.29/13.08 (((demorgan2a2) =>
% 99.29/13.08 (((demorgan1a) =>
% 99.29/13.08 (((demorgan1b) =>
% 99.29/13.08 (((demorgan1) =>
% 99.29/13.08 (((demorgan2a) =>
% 99.29/13.08 (((demorgan2b2) =>
% 99.29/13.08 (((demorgan2b) =>
% 99.29/13.08 (((demorgan2) =>
% 99.29/13.08 (((woz13rule0) =>
% 99.29/13.08 (((woz13rule1) =>
% 99.29/13.08 (((woz13rule2) =>
% 99.29/13.08 (((woz13rule3) =>
% 99.29/13.08 (((woz13rule4) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_1) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_3) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_4) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_5) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1all2) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1SetBreln1) =>
% 99.29/13.08 ((
% 99.29/13.08 (choice2fnsingleton) =>
% 99.29/13.08 ((
% 99.29/13.08 (!!) @ (
% 99.29/13.08 (('#B') @ (
% 99.29/13.08 !!) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ (
% 99.29/13.08 (
% 99.29/13.08 ('#B') @ (
% 99.29/13.08 '#B') @
% 99.29/13.08 breln1)) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ dpsetconstr @
% 99.29/13.08 (
% 99.29/13.08 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.29/13.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2711])).
% 99.29/13.08 thf(zip_derived_cl2735, plain,
% 99.29/13.08 (~ (((complementSubsetComplementIntersect) =>
% 99.29/13.08 (((complementInPowersetComplementIntersect) =>
% 99.29/13.08 (((contraSubsetComplement) =>
% 99.29/13.08 (((complementTcontraSubset) =>
% 99.29/13.08 (((binunionTILcontra) =>
% 99.29/13.08 (((binunionTIRcontra) =>
% 99.29/13.08 (((inIntersectImpInUnion) =>
% 99.29/13.08 (((inIntersectImpInUnion2) =>
% 99.29/13.08 (((inIntersectImpInIntersectUnions) =>
% 99.29/13.08 (((intersectInPowersetIntersectUnions) =>
% 99.29/13.08 (((inComplementUnionImpNotIn1) =>
% 99.29/13.08 (((inComplementUnionImpInComplement1) =>
% 99.29/13.08 (((binunionTE) =>
% 99.29/13.08 (((binunionTEcontra) =>
% 99.29/13.08 (((demorgan2a1) =>
% 99.29/13.08 (((complementUnionInPowersetComplement) =>
% 99.29/13.08 (((demorgan2a2) =>
% 99.29/13.08 (((demorgan1a) =>
% 99.29/13.08 (((demorgan1b) =>
% 99.29/13.08 (((demorgan1) =>
% 99.29/13.08 (((demorgan2a) =>
% 99.29/13.08 (((demorgan2b2) =>
% 99.29/13.08 (((demorgan2b) =>
% 99.29/13.08 (((demorgan2) =>
% 99.29/13.08 (((woz13rule0) =>
% 99.29/13.08 (((woz13rule1) =>
% 99.29/13.08 (((woz13rule2) =>
% 99.29/13.08 (((woz13rule3) =>
% 99.29/13.08 (((woz13rule4) =>
% 99.29/13.08 (((woz1_1) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_3) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_4) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_5) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1all2) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1SetBreln1) =>
% 99.29/13.08 ((
% 99.29/13.08 (choice2fnsingleton) =>
% 99.29/13.08 ((
% 99.29/13.08 (!!) @ (
% 99.29/13.08 (('#B') @ (
% 99.29/13.08 !!) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ (
% 99.29/13.08 (
% 99.29/13.08 ('#B') @ (
% 99.29/13.08 '#B') @
% 99.29/13.08 breln1)) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ dpsetconstr @
% 99.29/13.08 (
% 99.29/13.08 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.29/13.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2723])).
% 99.29/13.08 thf(zip_derived_cl2745, plain,
% 99.29/13.08 (~ (((complementInPowersetComplementIntersect) =>
% 99.29/13.08 (((contraSubsetComplement) =>
% 99.29/13.08 (((complementTcontraSubset) =>
% 99.29/13.08 (((binunionTILcontra) =>
% 99.29/13.08 (((binunionTIRcontra) =>
% 99.29/13.08 (((inIntersectImpInUnion) =>
% 99.29/13.08 (((inIntersectImpInUnion2) =>
% 99.29/13.08 (((inIntersectImpInIntersectUnions) =>
% 99.29/13.08 (((intersectInPowersetIntersectUnions) =>
% 99.29/13.08 (((inComplementUnionImpNotIn1) =>
% 99.29/13.08 (((inComplementUnionImpInComplement1) =>
% 99.29/13.08 (((binunionTE) =>
% 99.29/13.08 (((binunionTEcontra) =>
% 99.29/13.08 (((demorgan2a1) =>
% 99.29/13.08 (((complementUnionInPowersetComplement) =>
% 99.29/13.08 (((demorgan2a2) =>
% 99.29/13.08 (((demorgan1a) =>
% 99.29/13.08 (((demorgan1b) =>
% 99.29/13.08 (((demorgan1) =>
% 99.29/13.08 (((demorgan2a) =>
% 99.29/13.08 (((demorgan2b2) =>
% 99.29/13.08 (((demorgan2b) =>
% 99.29/13.08 (((demorgan2) =>
% 99.29/13.08 (((woz13rule0) =>
% 99.29/13.08 (((woz13rule1) =>
% 99.29/13.08 (((woz13rule2) =>
% 99.29/13.08 (((woz13rule3) =>
% 99.29/13.08 (((woz13rule4) =>
% 99.29/13.08 (((woz1_1) =>
% 99.29/13.08 (((woz1_2) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_3) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_4) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_5) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1all2) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1SetBreln1) =>
% 99.29/13.08 ((
% 99.29/13.08 (choice2fnsingleton) =>
% 99.29/13.08 ((
% 99.29/13.08 (!!) @ (
% 99.29/13.08 (('#B') @ (
% 99.29/13.08 !!) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ (
% 99.29/13.08 (
% 99.29/13.08 ('#B') @ (
% 99.29/13.08 '#B') @
% 99.29/13.08 breln1)) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ dpsetconstr @
% 99.29/13.08 (
% 99.29/13.08 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.29/13.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2735])).
% 99.29/13.08 thf(zip_derived_cl2753, plain,
% 99.29/13.08 (~ (((contraSubsetComplement) =>
% 99.29/13.08 (((complementTcontraSubset) =>
% 99.29/13.08 (((binunionTILcontra) =>
% 99.29/13.08 (((binunionTIRcontra) =>
% 99.29/13.08 (((inIntersectImpInUnion) =>
% 99.29/13.08 (((inIntersectImpInUnion2) =>
% 99.29/13.08 (((inIntersectImpInIntersectUnions) =>
% 99.29/13.08 (((intersectInPowersetIntersectUnions) =>
% 99.29/13.08 (((inComplementUnionImpNotIn1) =>
% 99.29/13.08 (((inComplementUnionImpInComplement1) =>
% 99.29/13.08 (((binunionTE) =>
% 99.29/13.08 (((binunionTEcontra) =>
% 99.29/13.08 (((demorgan2a1) =>
% 99.29/13.08 (((complementUnionInPowersetComplement) =>
% 99.29/13.08 (((demorgan2a2) =>
% 99.29/13.08 (((demorgan1a) =>
% 99.29/13.08 (((demorgan1b) =>
% 99.29/13.08 (((demorgan1) =>
% 99.29/13.08 (((demorgan2a) =>
% 99.29/13.08 (((demorgan2b2) =>
% 99.29/13.08 (((demorgan2b) =>
% 99.29/13.08 (((demorgan2) =>
% 99.29/13.08 (((woz13rule0) =>
% 99.29/13.08 (((woz13rule1) =>
% 99.29/13.08 (((woz13rule2) =>
% 99.29/13.08 (((woz13rule3) =>
% 99.29/13.08 (((woz13rule4) =>
% 99.29/13.08 (((woz1_1) =>
% 99.29/13.08 (((woz1_2) =>
% 99.29/13.08 (((woz1_3) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_4) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_5) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1all2) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1SetBreln1) =>
% 99.29/13.08 ((
% 99.29/13.08 (choice2fnsingleton) =>
% 99.29/13.08 ((
% 99.29/13.08 (!!) @ (
% 99.29/13.08 (('#B') @ (
% 99.29/13.08 !!) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ (
% 99.29/13.08 (
% 99.29/13.08 ('#B') @ (
% 99.29/13.08 '#B') @
% 99.29/13.08 breln1)) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ dpsetconstr @
% 99.29/13.08 (
% 99.29/13.08 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.29/13.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2745])).
% 99.29/13.08 thf(zip_derived_cl2761, plain,
% 99.29/13.08 (~ (((complementTcontraSubset) =>
% 99.29/13.08 (((binunionTILcontra) =>
% 99.29/13.08 (((binunionTIRcontra) =>
% 99.29/13.08 (((inIntersectImpInUnion) =>
% 99.29/13.08 (((inIntersectImpInUnion2) =>
% 99.29/13.08 (((inIntersectImpInIntersectUnions) =>
% 99.29/13.08 (((intersectInPowersetIntersectUnions) =>
% 99.29/13.08 (((inComplementUnionImpNotIn1) =>
% 99.29/13.08 (((inComplementUnionImpInComplement1) =>
% 99.29/13.08 (((binunionTE) =>
% 99.29/13.08 (((binunionTEcontra) =>
% 99.29/13.08 (((demorgan2a1) =>
% 99.29/13.08 (((complementUnionInPowersetComplement) =>
% 99.29/13.08 (((demorgan2a2) =>
% 99.29/13.08 (((demorgan1a) =>
% 99.29/13.08 (((demorgan1b) =>
% 99.29/13.08 (((demorgan1) =>
% 99.29/13.08 (((demorgan2a) =>
% 99.29/13.08 (((demorgan2b2) =>
% 99.29/13.08 (((demorgan2b) =>
% 99.29/13.08 (((demorgan2) =>
% 99.29/13.08 (((woz13rule0) =>
% 99.29/13.08 (((woz13rule1) =>
% 99.29/13.08 (((woz13rule2) =>
% 99.29/13.08 (((woz13rule3) =>
% 99.29/13.08 (((woz13rule4) =>
% 99.29/13.08 (((woz1_1) =>
% 99.29/13.08 (((woz1_2) =>
% 99.29/13.08 (((woz1_3) =>
% 99.29/13.08 (((woz1_4) =>
% 99.29/13.08 ((
% 99.29/13.08 (woz1_5) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1all2) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1SetBreln1) =>
% 99.29/13.08 ((
% 99.29/13.08 (choice2fnsingleton) =>
% 99.29/13.08 ((
% 99.29/13.08 (!!) @ (
% 99.29/13.08 (('#B') @ (
% 99.29/13.08 !!) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ (
% 99.29/13.08 (
% 99.29/13.08 ('#B') @ (
% 99.29/13.08 '#B') @
% 99.29/13.08 breln1)) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ dpsetconstr @
% 99.29/13.08 (
% 99.29/13.08 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.29/13.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2753])).
% 99.29/13.08 thf(zip_derived_cl2769, plain,
% 99.29/13.08 (~ (((binunionTILcontra) =>
% 99.29/13.08 (((binunionTIRcontra) =>
% 99.29/13.08 (((inIntersectImpInUnion) =>
% 99.29/13.08 (((inIntersectImpInUnion2) =>
% 99.29/13.08 (((inIntersectImpInIntersectUnions) =>
% 99.29/13.08 (((intersectInPowersetIntersectUnions) =>
% 99.29/13.08 (((inComplementUnionImpNotIn1) =>
% 99.29/13.08 (((inComplementUnionImpInComplement1) =>
% 99.29/13.08 (((binunionTE) =>
% 99.29/13.08 (((binunionTEcontra) =>
% 99.29/13.08 (((demorgan2a1) =>
% 99.29/13.08 (((complementUnionInPowersetComplement) =>
% 99.29/13.08 (((demorgan2a2) =>
% 99.29/13.08 (((demorgan1a) =>
% 99.29/13.08 (((demorgan1b) =>
% 99.29/13.08 (((demorgan1) =>
% 99.29/13.08 (((demorgan2a) =>
% 99.29/13.08 (((demorgan2b2) =>
% 99.29/13.08 (((demorgan2b) =>
% 99.29/13.08 (((demorgan2) =>
% 99.29/13.08 (((woz13rule0) =>
% 99.29/13.08 (((woz13rule1) =>
% 99.29/13.08 (((woz13rule2) =>
% 99.29/13.08 (((woz13rule3) =>
% 99.29/13.08 (((woz13rule4) =>
% 99.29/13.08 (((woz1_1) =>
% 99.29/13.08 (((woz1_2) =>
% 99.29/13.08 (((woz1_3) =>
% 99.29/13.08 (((woz1_4) =>
% 99.29/13.08 (((woz1_5) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1all2) =>
% 99.29/13.08 ((
% 99.29/13.08 (breln1SetBreln1) =>
% 99.29/13.08 ((
% 99.29/13.08 (choice2fnsingleton) =>
% 99.29/13.08 ((
% 99.29/13.08 (!!) @ (
% 99.29/13.08 (('#B') @ (
% 99.29/13.08 !!) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ (
% 99.29/13.08 (
% 99.29/13.08 ('#B') @ (
% 99.29/13.08 '#B') @
% 99.29/13.08 breln1)) @
% 99.29/13.08 (
% 99.29/13.08 (
% 99.29/13.08 ('#S') @ dpsetconstr @
% 99.29/13.08 (
% 99.29/13.08 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.29/13.08 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2761])).
% 99.29/13.08 thf(zip_derived_cl2778, plain,
% 99.29/13.08 (~ (((binunionTIRcontra) =>
% 99.29/13.08 (((inIntersectImpInUnion) =>
% 99.29/13.08 (((inIntersectImpInUnion2) =>
% 99.29/13.08 (((inIntersectImpInIntersectUnions) =>
% 99.29/13.08 (((intersectInPowersetIntersectUnions) =>
% 99.29/13.08 (((inComplementUnionImpNotIn1) =>
% 99.29/13.08 (((inComplementUnionImpInComplement1) =>
% 99.29/13.08 (((binunionTE) =>
% 99.29/13.08 (((binunionTEcontra) =>
% 99.29/13.08 (((demorgan2a1) =>
% 99.29/13.08 (((complementUnionInPowersetComplement) =>
% 99.29/13.08 (((demorgan2a2) =>
% 99.29/13.09 (((demorgan1a) =>
% 99.29/13.09 (((demorgan1b) =>
% 99.29/13.09 (((demorgan1) =>
% 99.29/13.09 (((demorgan2a) =>
% 99.29/13.09 (((demorgan2b2) =>
% 99.29/13.09 (((demorgan2b) =>
% 99.29/13.09 (((demorgan2) =>
% 99.29/13.09 (((woz13rule0) =>
% 99.29/13.09 (((woz13rule1) =>
% 99.29/13.09 (((woz13rule2) =>
% 99.29/13.09 (((woz13rule3) =>
% 99.29/13.09 (((woz13rule4) =>
% 99.29/13.09 (((woz1_1) =>
% 99.29/13.09 (((woz1_2) =>
% 99.29/13.09 (((woz1_3) =>
% 99.29/13.09 (((woz1_4) =>
% 99.29/13.09 (((woz1_5) =>
% 99.29/13.09 (((breln1all2) =>
% 99.29/13.09 ((
% 99.29/13.09 (breln1SetBreln1) =>
% 99.29/13.09 ((
% 99.29/13.09 (choice2fnsingleton) =>
% 99.29/13.09 ((
% 99.29/13.09 (!!) @ (
% 99.29/13.09 (('#B') @ (
% 99.29/13.09 !!) @
% 99.29/13.09 (
% 99.29/13.09 (
% 99.29/13.09 ('#S') @ (
% 99.29/13.09 (
% 99.29/13.09 ('#B') @ (
% 99.29/13.09 '#B') @
% 99.29/13.09 breln1)) @
% 99.29/13.09 (
% 99.29/13.09 (
% 99.29/13.09 ('#S') @ dpsetconstr @
% 99.29/13.09 (
% 99.29/13.09 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.29/13.09 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2769])).
% 99.29/13.09 thf(zip_derived_cl2788, plain,
% 99.29/13.09 (~ (((inIntersectImpInUnion) =>
% 99.29/13.09 (((inIntersectImpInUnion2) =>
% 99.29/13.09 (((inIntersectImpInIntersectUnions) =>
% 99.29/13.09 (((intersectInPowersetIntersectUnions) =>
% 99.29/13.09 (((inComplementUnionImpNotIn1) =>
% 99.29/13.09 (((inComplementUnionImpInComplement1) =>
% 99.29/13.09 (((binunionTE) =>
% 99.29/13.09 (((binunionTEcontra) =>
% 99.29/13.09 (((demorgan2a1) =>
% 99.29/13.09 (((complementUnionInPowersetComplement) =>
% 99.29/13.09 (((demorgan2a2) =>
% 99.29/13.09 (((demorgan1a) =>
% 99.29/13.09 (((demorgan1b) =>
% 99.29/13.09 (((demorgan1) =>
% 99.29/13.09 (((demorgan2a) =>
% 99.29/13.09 (((demorgan2b2) =>
% 99.29/13.09 (((demorgan2b) =>
% 99.29/13.09 (((demorgan2) =>
% 99.29/13.09 (((woz13rule0) =>
% 99.29/13.09 (((woz13rule1) =>
% 99.29/13.09 (((woz13rule2) =>
% 99.29/13.09 (((woz13rule3) =>
% 99.29/13.09 (((woz13rule4) =>
% 99.29/13.09 (((woz1_1) =>
% 99.29/13.09 (((woz1_2) =>
% 99.29/13.09 (((woz1_3) =>
% 99.29/13.09 (((woz1_4) =>
% 99.29/13.09 (((woz1_5) =>
% 99.29/13.09 (((breln1all2) =>
% 99.29/13.09 (((breln1SetBreln1) =>
% 99.29/13.09 ((
% 99.29/13.09 (choice2fnsingleton) =>
% 99.29/13.09 ((
% 99.29/13.09 (!!) @ (
% 99.29/13.09 (('#B') @ (
% 99.29/13.09 !!) @
% 99.29/13.09 (
% 99.29/13.09 (
% 99.29/13.09 ('#S') @ (
% 99.29/13.09 (
% 99.29/13.09 ('#B') @ (
% 99.29/13.09 '#B') @
% 99.29/13.09 breln1)) @
% 99.29/13.09 (
% 99.29/13.09 (
% 99.29/13.09 ('#S') @ dpsetconstr @
% 99.29/13.09 (
% 99.29/13.09 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.29/13.09 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2778])).
% 99.29/13.09 thf(zip_derived_cl2799, plain,
% 99.29/13.09 (~ (((inIntersectImpInUnion2) =>
% 99.29/13.09 (((inIntersectImpInIntersectUnions) =>
% 99.29/13.09 (((intersectInPowersetIntersectUnions) =>
% 99.29/13.09 (((inComplementUnionImpNotIn1) =>
% 99.29/13.09 (((inComplementUnionImpInComplement1) =>
% 99.29/13.09 (((binunionTE) =>
% 99.29/13.09 (((binunionTEcontra) =>
% 99.29/13.09 (((demorgan2a1) =>
% 99.29/13.09 (((complementUnionInPowersetComplement) =>
% 99.29/13.09 (((demorgan2a2) =>
% 99.29/13.09 (((demorgan1a) =>
% 99.29/13.09 (((demorgan1b) =>
% 99.29/13.09 (((demorgan1) =>
% 99.29/13.09 (((demorgan2a) =>
% 99.29/13.09 (((demorgan2b2) =>
% 99.29/13.09 (((demorgan2b) =>
% 99.29/13.09 (((demorgan2) =>
% 99.29/13.09 (((woz13rule0) =>
% 99.29/13.09 (((woz13rule1) =>
% 99.29/13.09 (((woz13rule2) =>
% 99.29/13.09 (((woz13rule3) =>
% 99.29/13.09 (((woz13rule4) =>
% 99.29/13.09 (((woz1_1) =>
% 99.29/13.09 (((woz1_2) =>
% 99.29/13.09 (((woz1_3) =>
% 99.29/13.09 (((woz1_4) =>
% 99.29/13.09 (((woz1_5) =>
% 99.29/13.09 (((breln1all2) =>
% 99.29/13.09 (((breln1SetBreln1) =>
% 99.29/13.09 (((choice2fnsingleton) =>
% 99.29/13.09 ((
% 99.29/13.09 (!!) @ (
% 99.29/13.09 (('#B') @ (
% 99.29/13.09 !!) @
% 99.29/13.09 (
% 99.29/13.09 (
% 99.29/13.09 ('#S') @ (
% 99.29/13.09 (
% 99.29/13.09 ('#B') @ (
% 99.29/13.09 '#B') @
% 99.29/13.09 breln1)) @
% 99.29/13.09 (
% 99.29/13.09 (
% 99.29/13.09 ('#S') @ dpsetconstr @
% 99.29/13.09 (
% 99.29/13.09 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.29/13.09 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2788])).
% 99.29/13.09 thf(zip_derived_cl2810, plain,
% 99.29/13.09 (~ (((inIntersectImpInIntersectUnions) =>
% 99.29/13.09 (((intersectInPowersetIntersectUnions) =>
% 99.29/13.09 (((inComplementUnionImpNotIn1) =>
% 99.29/13.09 (((inComplementUnionImpInComplement1) =>
% 99.29/13.09 (((binunionTE) =>
% 99.29/13.09 (((binunionTEcontra) =>
% 99.29/13.09 (((demorgan2a1) =>
% 99.29/13.09 (((complementUnionInPowersetComplement) =>
% 99.29/13.09 (((demorgan2a2) =>
% 99.29/13.09 (((demorgan1a) =>
% 99.29/13.09 (((demorgan1b) =>
% 99.29/13.09 (((demorgan1) =>
% 99.29/13.09 (((demorgan2a) =>
% 99.29/13.09 (((demorgan2b2) =>
% 99.29/13.09 (((demorgan2b) =>
% 99.29/13.09 (((demorgan2) =>
% 99.29/13.09 (((woz13rule0) =>
% 99.29/13.09 (((woz13rule1) =>
% 99.29/13.09 (((woz13rule2) =>
% 99.29/13.09 (((woz13rule3) =>
% 99.29/13.09 (((woz13rule4) =>
% 99.29/13.09 (((woz1_1) =>
% 99.29/13.09 (((woz1_2) =>
% 99.29/13.09 (((woz1_3) =>
% 99.29/13.09 (((woz1_4) =>
% 99.29/13.09 (((woz1_5) =>
% 99.29/13.09 (((breln1all2) =>
% 99.29/13.09 (((breln1SetBreln1) =>
% 99.29/13.09 (((choice2fnsingleton) =>
% 99.29/13.09 (((!!) @ (
% 99.29/13.09 (('#B') @ (
% 99.29/13.09 !!) @
% 99.29/13.09 (
% 99.29/13.09 (
% 99.29/13.09 ('#S') @ (
% 99.29/13.09 (
% 99.29/13.09 ('#B') @ (
% 99.29/13.09 '#B') @
% 99.29/13.09 breln1)) @
% 99.29/13.09 (
% 99.29/13.09 (
% 99.29/13.09 ('#S') @ dpsetconstr @
% 99.29/13.09 (
% 99.29/13.09 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.29/13.09 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2799])).
% 99.29/13.09 thf(zip_derived_cl2820, plain,
% 99.29/13.09 (~ (((intersectInPowersetIntersectUnions) =>
% 99.29/13.09 (((inComplementUnionImpNotIn1) =>
% 99.29/13.09 (((inComplementUnionImpInComplement1) =>
% 99.29/13.09 (((binunionTE) =>
% 99.29/13.09 (((binunionTEcontra) =>
% 99.29/13.09 (((demorgan2a1) =>
% 99.29/13.09 (((complementUnionInPowersetComplement) =>
% 99.29/13.09 (((demorgan2a2) =>
% 99.29/13.09 (((demorgan1a) =>
% 99.29/13.09 (((demorgan1b) =>
% 99.29/13.09 (((demorgan1) =>
% 99.29/13.09 (((demorgan2a) =>
% 99.29/13.09 (((demorgan2b2) =>
% 99.29/13.09 (((demorgan2b) =>
% 99.29/13.09 (((demorgan2) =>
% 99.29/13.09 (((woz13rule0) =>
% 99.29/13.09 (((woz13rule1) =>
% 99.29/13.09 (((woz13rule2) =>
% 99.29/13.09 (((woz13rule3) =>
% 99.29/13.09 (((woz13rule4) =>
% 99.29/13.09 (((woz1_1) =>
% 99.29/13.09 (((woz1_2) =>
% 99.29/13.09 (((woz1_3) =>
% 99.29/13.09 (((woz1_4) =>
% 99.29/13.09 (((woz1_5) =>
% 99.29/13.09 (((breln1all2) =>
% 99.29/13.09 (((breln1SetBreln1) =>
% 99.29/13.09 (((choice2fnsingleton) =>
% 99.29/13.09 (((!!) @ (
% 99.29/13.09 (('#B') @ (
% 99.29/13.09 !!) @
% 99.29/13.09 ((('#S') @ (
% 99.29/13.09 (
% 99.29/13.09 ('#B') @ (
% 99.29/13.09 '#B') @
% 99.29/13.09 breln1)) @
% 99.29/13.09 (
% 99.29/13.09 (
% 99.29/13.09 ('#S') @ dpsetconstr @
% 99.29/13.09 (
% 99.29/13.09 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.29/13.09 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2810])).
% 99.29/13.09 thf(zip_derived_cl2830, plain,
% 99.29/13.09 (~ (((inComplementUnionImpNotIn1) =>
% 99.29/13.09 (((inComplementUnionImpInComplement1) =>
% 99.29/13.09 (((binunionTE) =>
% 99.29/13.09 (((binunionTEcontra) =>
% 99.29/13.09 (((demorgan2a1) =>
% 99.29/13.09 (((complementUnionInPowersetComplement) =>
% 99.29/13.09 (((demorgan2a2) =>
% 99.29/13.09 (((demorgan1a) =>
% 99.29/13.09 (((demorgan1b) =>
% 99.29/13.09 (((demorgan1) =>
% 99.29/13.09 (((demorgan2a) =>
% 99.29/13.09 (((demorgan2b2) =>
% 99.29/13.09 (((demorgan2b) =>
% 99.29/13.09 (((demorgan2) =>
% 99.29/13.09 (((woz13rule0) =>
% 99.29/13.09 (((woz13rule1) =>
% 99.29/13.09 (((woz13rule2) =>
% 99.29/13.09 (((woz13rule3) =>
% 99.29/13.09 (((woz13rule4) =>
% 99.29/13.09 (((woz1_1) =>
% 99.29/13.09 (((woz1_2) =>
% 99.29/13.09 (((woz1_3) =>
% 99.29/13.09 (((woz1_4) =>
% 99.29/13.09 (((woz1_5) =>
% 99.29/13.09 (((breln1all2) =>
% 99.29/13.09 (((breln1SetBreln1) =>
% 99.29/13.09 (((choice2fnsingleton) =>
% 99.29/13.09 (((!!) @ (
% 99.29/13.09 (('#B') @ (
% 99.29/13.09 !!) @
% 99.29/13.09 ((('#S') @ (
% 99.29/13.09 (('#B') @ (
% 99.29/13.09 '#B') @
% 99.29/13.09 breln1)) @
% 99.29/13.09 ((('#S') @ dpsetconstr @
% 99.29/13.09 (
% 99.29/13.09 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.29/13.09 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2820])).
% 99.29/13.09 thf(zip_derived_cl2841, plain,
% 99.29/13.09 (~ (((inComplementUnionImpInComplement1) =>
% 99.29/13.09 (((binunionTE) =>
% 99.29/13.09 (((binunionTEcontra) =>
% 99.29/13.09 (((demorgan2a1) =>
% 99.29/13.09 (((complementUnionInPowersetComplement) =>
% 99.29/13.09 (((demorgan2a2) =>
% 99.29/13.09 (((demorgan1a) =>
% 99.29/13.09 (((demorgan1b) =>
% 99.29/13.09 (((demorgan1) =>
% 99.29/13.09 (((demorgan2a) =>
% 99.29/13.09 (((demorgan2b2) =>
% 99.29/13.09 (((demorgan2b) =>
% 99.29/13.09 (((demorgan2) =>
% 99.29/13.09 (((woz13rule0) =>
% 99.29/13.09 (((woz13rule1) =>
% 99.29/13.09 (((woz13rule2) =>
% 99.29/13.09 (((woz13rule3) =>
% 99.29/13.09 (((woz13rule4) =>
% 99.29/13.09 (((woz1_1) =>
% 99.29/13.09 (((woz1_2) =>
% 99.29/13.09 (((woz1_3) =>
% 99.29/13.09 (((woz1_4) =>
% 99.29/13.09 (((woz1_5) =>
% 99.29/13.09 (((breln1all2) =>
% 99.29/13.09 (((breln1SetBreln1) =>
% 99.29/13.09 (((choice2fnsingleton) =>
% 99.29/13.09 (((!!) @ (
% 99.29/13.09 (('#B') @ (
% 99.29/13.09 !!) @
% 99.29/13.09 ((('#S') @ (
% 99.29/13.09 (('#B') @ (
% 99.29/13.09 '#B') @
% 99.29/13.09 breln1)) @
% 99.29/13.09 ((('#S') @ dpsetconstr @
% 99.29/13.09 ('#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.29/13.09 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2830])).
% 99.29/13.09 thf(zip_derived_cl2852, plain,
% 99.29/13.09 (~ (((binunionTE) =>
% 99.29/13.09 (((binunionTEcontra) =>
% 99.29/13.09 (((demorgan2a1) =>
% 99.29/13.09 (((complementUnionInPowersetComplement) =>
% 99.29/13.09 (((demorgan2a2) =>
% 99.29/13.09 (((demorgan1a) =>
% 99.29/13.09 (((demorgan1b) =>
% 99.29/13.09 (((demorgan1) =>
% 99.29/13.09 (((demorgan2a) =>
% 99.29/13.09 (((demorgan2b2) =>
% 99.29/13.09 (((demorgan2b) =>
% 99.29/13.09 (((demorgan2) =>
% 99.29/13.09 (((woz13rule0) =>
% 99.29/13.09 (((woz13rule1) =>
% 99.29/13.09 (((woz13rule2) =>
% 99.29/13.09 (((woz13rule3) =>
% 99.29/13.09 (((woz13rule4) =>
% 99.29/13.09 (((woz1_1) =>
% 99.29/13.09 (((woz1_2) =>
% 99.29/13.09 (((woz1_3) =>
% 99.29/13.09 (((woz1_4) =>
% 99.29/13.09 (((woz1_5) =>
% 99.29/13.09 (((breln1all2) =>
% 99.29/13.09 (((breln1SetBreln1) =>
% 99.29/13.09 (((choice2fnsingleton) =>
% 99.29/13.09 (((!!) @ ((('#B') @ (
% 99.29/13.09 !!) @
% 99.29/13.09 (
% 99.29/13.09 (
% 99.29/13.09 ('#S') @ (
% 99.29/13.09 (
% 99.29/13.09 ('#B') @ (
% 99.29/13.09 '#B') @
% 99.29/13.09 breln1)) @
% 99.29/13.09 (
% 99.29/13.09 (
% 99.29/13.09 ('#S') @ dpsetconstr @
% 99.29/13.09 (
% 99.29/13.09 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.29/13.09 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2841])).
% 99.29/13.09 thf(zip_derived_cl2864, plain,
% 99.29/13.09 (~ (((binunionTEcontra) =>
% 99.29/13.09 (((demorgan2a1) =>
% 99.29/13.09 (((complementUnionInPowersetComplement) =>
% 99.29/13.09 (((demorgan2a2) =>
% 99.29/13.09 (((demorgan1a) =>
% 99.29/13.09 (((demorgan1b) =>
% 99.29/13.09 (((demorgan1) =>
% 99.29/13.09 (((demorgan2a) =>
% 99.29/13.09 (((demorgan2b2) =>
% 99.29/13.09 (((demorgan2b) =>
% 99.29/13.09 (((demorgan2) =>
% 99.29/13.09 (((woz13rule0) =>
% 99.29/13.09 (((woz13rule1) =>
% 99.29/13.09 (((woz13rule2) =>
% 99.29/13.09 (((woz13rule3) =>
% 99.29/13.09 (((woz13rule4) =>
% 99.29/13.09 (((woz1_1) =>
% 99.29/13.09 (((woz1_2) =>
% 99.29/13.09 (((woz1_3) =>
% 99.29/13.09 (((woz1_4) =>
% 99.29/13.09 (((woz1_5) =>
% 99.29/13.09 (((breln1all2) =>
% 99.29/13.09 (((breln1SetBreln1) =>
% 99.29/13.09 (((choice2fnsingleton) =>
% 99.29/13.09 (((!!) @ ((('#B') @ (
% 99.29/13.09 !!) @
% 99.29/13.09 ((('#S') @ (
% 99.29/13.09 (
% 99.29/13.09 ('#B') @ (
% 99.29/13.09 '#B') @
% 99.29/13.09 breln1)) @
% 99.29/13.09 (
% 99.29/13.09 (
% 99.29/13.09 ('#S') @ dpsetconstr @
% 99.29/13.09 (
% 99.29/13.09 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.29/13.09 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2852])).
% 99.29/13.09 thf(zip_derived_cl2876, plain,
% 99.29/13.09 (~ (((demorgan2a1) =>
% 99.29/13.09 (((complementUnionInPowersetComplement) =>
% 99.29/13.09 (((demorgan2a2) =>
% 99.29/13.09 (((demorgan1a) =>
% 99.29/13.09 (((demorgan1b) =>
% 99.29/13.09 (((demorgan1) =>
% 99.29/13.09 (((demorgan2a) =>
% 99.29/13.09 (((demorgan2b2) =>
% 99.29/13.09 (((demorgan2b) =>
% 99.29/13.09 (((demorgan2) =>
% 99.29/13.09 (((woz13rule0) =>
% 99.29/13.09 (((woz13rule1) =>
% 99.29/13.09 (((woz13rule2) =>
% 99.29/13.09 (((woz13rule3) =>
% 99.29/13.09 (((woz13rule4) =>
% 99.29/13.09 (((woz1_1) =>
% 99.29/13.09 (((woz1_2) =>
% 99.29/13.09 (((woz1_3) =>
% 99.29/13.09 (((woz1_4) =>
% 99.29/13.09 (((woz1_5) =>
% 99.29/13.09 (((breln1all2) =>
% 99.29/13.09 (((breln1SetBreln1) =>
% 99.29/13.09 (((choice2fnsingleton) =>
% 99.29/13.09 (((!!) @ ((('#B') @ (
% 99.29/13.09 !!) @
% 99.29/13.09 ((('#S') @ (
% 99.29/13.09 (('#B') @ (
% 99.29/13.09 '#B') @
% 99.29/13.09 breln1)) @
% 99.29/13.09 ((('#S') @ dpsetconstr @
% 99.29/13.09 (
% 99.29/13.09 '#I')))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.29/13.09 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2864])).
% 99.29/13.09 thf(zip_derived_cl2888, plain,
% 99.29/13.09 (~ (((complementUnionInPowersetComplement) =>
% 99.29/13.09 (((demorgan2a2) =>
% 99.29/13.09 (((demorgan1a) =>
% 99.29/13.09 (((demorgan1b) =>
% 99.29/13.09 (((demorgan1) =>
% 99.29/13.09 (((demorgan2a) =>
% 99.29/13.09 (((demorgan2b2) =>
% 99.29/13.09 (((demorgan2b) =>
% 99.29/13.09 (((demorgan2) =>
% 99.29/13.09 (((woz13rule0) =>
% 99.29/13.09 (((woz13rule1) =>
% 99.29/13.09 (((woz13rule2) =>
% 99.29/13.09 (((woz13rule3) =>
% 99.29/13.09 (((woz13rule4) =>
% 99.29/13.09 (((woz1_1) =>
% 99.29/13.09 (((woz1_2) =>
% 99.29/13.09 (((woz1_3) =>
% 99.29/13.09 (((woz1_4) =>
% 99.29/13.09 (((woz1_5) =>
% 99.29/13.09 (((breln1all2) =>
% 99.29/13.09 (((breln1SetBreln1) =>
% 99.29/13.09 (((choice2fnsingleton) =>
% 99.29/13.09 (((!!) @ ((('#B') @ (
% 99.29/13.09 !!) @
% 99.29/13.09 ((('#S') @ (
% 99.29/13.09 (('#B') @ (
% 99.29/13.09 '#B') @
% 99.29/13.09 breln1)) @
% 99.29/13.09 ((('#S') @ dpsetconstr @
% 99.29/13.09 ('#I')))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.29/13.09 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2876])).
% 99.29/13.09 thf(zip_derived_cl2900, plain,
% 99.29/13.09 (~ (((demorgan2a2) =>
% 99.29/13.09 (((demorgan1a) =>
% 99.29/13.09 (((demorgan1b) =>
% 99.29/13.09 (((demorgan1) =>
% 99.29/13.09 (((demorgan2a) =>
% 99.29/13.09 (((demorgan2b2) =>
% 99.29/13.09 (((demorgan2b) =>
% 99.29/13.09 (((demorgan2) =>
% 99.29/13.09 (((woz13rule0) =>
% 99.29/13.09 (((woz13rule1) =>
% 99.29/13.09 (((woz13rule2) =>
% 99.29/13.09 (((woz13rule3) =>
% 99.29/13.09 (((woz13rule4) =>
% 99.29/13.09 (((woz1_1) =>
% 99.29/13.09 (((woz1_2) =>
% 99.29/13.09 (((woz1_3) =>
% 99.29/13.09 (((woz1_4) =>
% 99.29/13.09 (((woz1_5) =>
% 99.29/13.09 (((breln1all2) =>
% 99.29/13.09 (((breln1SetBreln1) =>
% 99.29/13.09 (((choice2fnsingleton) =>
% 99.29/13.09 (((!!) @ ((('#B') @ (
% 99.29/13.09 !!) @
% 99.29/13.09 ((('#S') @ (
% 99.29/13.09 (('#B') @ (
% 99.29/13.09 '#B') @ breln1)) @
% 99.29/13.09 ((('#S') @ dpsetconstr @
% 99.29/13.09 ('#I')))))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.29/13.09 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2888])).
% 99.29/13.09 thf(zip_derived_cl2913, plain,
% 99.29/13.09 (~ (((demorgan1a) =>
% 99.29/13.09 (((demorgan1b) =>
% 99.29/13.09 (((demorgan1) =>
% 99.29/13.09 (((demorgan2a) =>
% 99.29/13.09 (((demorgan2b2) =>
% 99.29/13.09 (((demorgan2b) =>
% 99.29/13.09 (((demorgan2) =>
% 99.29/13.09 (((woz13rule0) =>
% 99.29/13.09 (((woz13rule1) =>
% 99.29/13.09 (((woz13rule2) =>
% 99.29/13.09 (((woz13rule3) =>
% 99.29/13.09 (((woz13rule4) =>
% 99.29/13.09 (((woz1_1) =>
% 99.29/13.09 (((woz1_2) =>
% 99.29/13.09 (((woz1_3) =>
% 99.29/13.09 (((woz1_4) =>
% 99.29/13.09 (((woz1_5) =>
% 99.29/13.09 (((breln1all2) =>
% 99.29/13.09 (((breln1SetBreln1) =>
% 99.29/13.09 (((choice2fnsingleton) =>
% 99.29/13.09 (((!!) @ ((('#B') @ (!!) @
% 99.29/13.09 ((('#S') @ (
% 99.29/13.09 (('#B') @ (
% 99.29/13.09 '#B') @ breln1)) @
% 99.29/13.09 ((('#S') @ dpsetconstr @
% 99.29/13.09 ('#I')))))))))))))))))))))))))))))))))))))))))))))))))),
% 99.29/13.09 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2900])).
% 99.29/13.09 thf(zip_derived_cl2927, plain,
% 99.29/13.09 (~ (((demorgan1b) =>
% 99.29/13.09 (((demorgan1) =>
% 99.29/13.09 (((demorgan2a) =>
% 99.29/13.09 (((demorgan2b2) =>
% 99.29/13.09 (((demorgan2b) =>
% 99.29/13.09 (((demorgan2) =>
% 99.29/13.09 (((woz13rule0) =>
% 99.29/13.09 (((woz13rule1) =>
% 99.29/13.09 (((woz13rule2) =>
% 99.29/13.09 (((woz13rule3) =>
% 99.29/13.09 (((woz13rule4) =>
% 99.29/13.09 (((woz1_1) =>
% 99.29/13.09 (((woz1_2) =>
% 99.29/13.09 (((woz1_3) =>
% 99.29/13.09 (((woz1_4) =>
% 99.29/13.09 (((woz1_5) =>
% 99.29/13.09 (((breln1all2) =>
% 99.29/13.09 (((breln1SetBreln1) =>
% 99.29/13.09 (((choice2fnsingleton) =>
% 99.29/13.09 (((!!) @ ((('#B') @ (!!) @
% 99.29/13.09 ((('#S') @ ((
% 99.29/13.09 ('#B') @ (
% 99.29/13.09 '#B') @
% 99.29/13.09 breln1)) @
% 99.29/13.09 ((('#S') @ dpsetconstr @
% 99.29/13.09 ('#I')))))))))))))))))))))))))))))))))))))))))))))))),
% 99.29/13.09 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2913])).
% 99.29/13.09 thf(zip_derived_cl2940, plain,
% 99.29/13.09 (~ (((demorgan1) =>
% 99.29/13.09 (((demorgan2a) =>
% 99.29/13.09 (((demorgan2b2) =>
% 99.29/13.09 (((demorgan2b) =>
% 99.29/13.09 (((demorgan2) =>
% 99.29/13.09 (((woz13rule0) =>
% 99.29/13.09 (((woz13rule1) =>
% 99.29/13.09 (((woz13rule2) =>
% 99.29/13.09 (((woz13rule3) =>
% 99.29/13.09 (((woz13rule4) =>
% 99.29/13.09 (((woz1_1) =>
% 99.29/13.09 (((woz1_2) =>
% 99.29/13.09 (((woz1_3) =>
% 99.29/13.09 (((woz1_4) =>
% 99.29/13.09 (((woz1_5) =>
% 99.29/13.09 (((breln1all2) =>
% 99.29/13.09 (((breln1SetBreln1) =>
% 99.29/13.09 (((choice2fnsingleton) =>
% 99.29/13.09 (((!!) @ ((('#B') @ (!!) @
% 99.29/13.09 ((('#S') @ ((('#B') @ (
% 99.29/13.09 '#B') @
% 99.29/13.09 breln1)) @
% 99.29/13.09 ((('#S') @ dpsetconstr @
% 99.29/13.09 ('#I')))))))))))))))))))))))))))))))))))))))))))))),
% 99.29/13.09 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2927])).
% 99.29/13.09 thf(zip_derived_cl2953, plain,
% 99.29/13.09 (~ (((demorgan2a) =>
% 99.29/13.09 (((demorgan2b2) =>
% 99.29/13.09 (((demorgan2b) =>
% 99.29/13.09 (((demorgan2) =>
% 99.29/13.09 (((woz13rule0) =>
% 99.29/13.09 (((woz13rule1) =>
% 99.29/13.09 (((woz13rule2) =>
% 99.29/13.09 (((woz13rule3) =>
% 99.29/13.09 (((woz13rule4) =>
% 99.29/13.09 (((woz1_1) =>
% 99.29/13.09 (((woz1_2) =>
% 99.29/13.09 (((woz1_3) =>
% 99.29/13.09 (((woz1_4) =>
% 99.29/13.09 (((woz1_5) =>
% 99.29/13.09 (((breln1all2) =>
% 99.29/13.09 (((breln1SetBreln1) =>
% 99.29/13.09 (((choice2fnsingleton) =>
% 99.29/13.09 (((!!) @ ((('#B') @ (!!) @
% 99.29/13.09 ((('#S') @ ((('#B') @ (
% 99.29/13.09 '#B') @
% 99.29/13.09 breln1)) @
% 99.29/13.09 ((('#S') @ dpsetconstr @
% 99.29/13.09 ('#I')))))))))))))))))))))))))))))))))))))))))))),
% 99.29/13.09 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2940])).
% 99.29/13.09 thf(zip_derived_cl2965, plain,
% 99.29/13.09 (~ (((demorgan2b2) =>
% 99.29/13.09 (((demorgan2b) =>
% 99.29/13.09 (((demorgan2) =>
% 99.29/13.09 (((woz13rule0) =>
% 99.29/13.09 (((woz13rule1) =>
% 99.29/13.09 (((woz13rule2) =>
% 99.29/13.09 (((woz13rule3) =>
% 99.29/13.09 (((woz13rule4) =>
% 99.29/13.09 (((woz1_1) =>
% 99.29/13.09 (((woz1_2) =>
% 99.29/13.09 (((woz1_3) =>
% 99.29/13.09 (((woz1_4) =>
% 99.29/13.09 (((woz1_5) =>
% 99.29/13.09 (((breln1all2) =>
% 99.29/13.09 (((breln1SetBreln1) =>
% 99.29/13.09 (((choice2fnsingleton) =>
% 99.29/13.09 (((!!) @ ((('#B') @ (!!) @
% 99.29/13.09 ((('#S') @ ((('#B') @ (
% 99.29/13.09 '#B') @ breln1)) @
% 99.29/13.09 ((('#S') @ dpsetconstr @
% 99.29/13.09 ('#I')))))))))))))))))))))))))))))))))))))))))),
% 99.29/13.09 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2953])).
% 99.29/13.09 thf(zip_derived_cl2977, plain,
% 99.29/13.09 (~ (((demorgan2b) =>
% 99.29/13.09 (((demorgan2) =>
% 99.29/13.09 (((woz13rule0) =>
% 99.29/13.09 (((woz13rule1) =>
% 99.29/13.09 (((woz13rule2) =>
% 99.29/13.09 (((woz13rule3) =>
% 99.29/13.09 (((woz13rule4) =>
% 99.29/13.09 (((woz1_1) =>
% 99.29/13.09 (((woz1_2) =>
% 99.29/13.09 (((woz1_3) =>
% 99.29/13.09 (((woz1_4) =>
% 99.29/13.09 (((woz1_5) =>
% 99.29/13.09 (((breln1all2) =>
% 99.29/13.09 (((breln1SetBreln1) =>
% 99.29/13.09 (((choice2fnsingleton) =>
% 99.29/13.09 (((!!) @ ((('#B') @ (!!) @
% 99.29/13.09 ((('#S') @ ((('#B') @ (
% 99.29/13.09 '#B') @ breln1)) @
% 99.29/13.09 ((('#S') @ dpsetconstr @
% 99.29/13.09 ('#I')))))))))))))))))))))))))))))))))))))))),
% 99.29/13.09 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2965])).
% 99.29/13.09 thf(zip_derived_cl2989, plain,
% 99.29/13.09 (~ (((demorgan2) =>
% 99.29/13.09 (((woz13rule0) =>
% 99.29/13.09 (((woz13rule1) =>
% 99.29/13.09 (((woz13rule2) =>
% 99.29/13.09 (((woz13rule3) =>
% 99.29/13.09 (((woz13rule4) =>
% 99.29/13.09 (((woz1_1) =>
% 99.29/13.09 (((woz1_2) =>
% 99.29/13.09 (((woz1_3) =>
% 99.29/13.09 (((woz1_4) =>
% 99.29/13.09 (((woz1_5) =>
% 99.29/13.09 (((breln1all2) =>
% 99.29/13.09 (((breln1SetBreln1) =>
% 99.29/13.09 (((choice2fnsingleton) =>
% 99.29/13.09 (((!!) @ ((('#B') @ (!!) @
% 99.29/13.09 ((('#S') @ ((('#B') @ (
% 99.29/13.09 '#B') @ breln1)) @
% 99.29/13.09 ((('#S') @ dpsetconstr @
% 99.29/13.09 ('#I')))))))))))))))))))))))))))))))))))))),
% 99.29/13.09 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2977])).
% 99.29/13.09 thf(zip_derived_cl3002, plain,
% 99.29/13.09 (~ (((woz13rule0) =>
% 99.29/13.09 (((woz13rule1) =>
% 99.29/13.09 (((woz13rule2) =>
% 99.29/13.09 (((woz13rule3) =>
% 99.29/13.09 (((woz13rule4) =>
% 99.29/13.09 (((woz1_1) =>
% 99.29/13.09 (((woz1_2) =>
% 99.29/13.09 (((woz1_3) =>
% 99.29/13.09 (((woz1_4) =>
% 99.29/13.09 (((woz1_5) =>
% 99.29/13.09 (((breln1all2) =>
% 99.29/13.09 (((breln1SetBreln1) =>
% 99.29/13.09 (((choice2fnsingleton) =>
% 99.29/13.09 (((!!) @ ((('#B') @ (!!) @
% 99.29/13.09 ((('#S') @ ((('#B') @ ('#B') @
% 99.29/13.09 breln1)) @
% 99.29/13.09 ((('#S') @ dpsetconstr @ ('#I')))))))))))))))))))))))))))))))))))),
% 99.29/13.09 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2989])).
% 99.29/13.09 thf(zip_derived_cl3015, plain,
% 99.29/13.09 (~ (((woz13rule1) =>
% 99.29/13.09 (((woz13rule2) =>
% 99.29/13.09 (((woz13rule3) =>
% 99.29/13.09 (((woz13rule4) =>
% 99.29/13.09 (((woz1_1) =>
% 99.29/13.09 (((woz1_2) =>
% 99.29/13.09 (((woz1_3) =>
% 99.29/13.09 (((woz1_4) =>
% 99.29/13.09 (((woz1_5) =>
% 99.29/13.09 (((breln1all2) =>
% 99.29/13.09 (((breln1SetBreln1) =>
% 99.29/13.09 (((choice2fnsingleton) =>
% 99.29/13.09 (((!!) @ ((('#B') @ (!!) @
% 99.29/13.09 ((('#S') @ ((('#B') @ ('#B') @
% 99.29/13.09 breln1)) @
% 99.29/13.09 ((('#S') @ dpsetconstr @ ('#I')))))))))))))))))))))))))))))))))),
% 99.29/13.09 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3002])).
% 99.29/13.09 thf(zip_derived_cl3029, plain,
% 99.29/13.09 (~ (((woz13rule2) =>
% 99.29/13.09 (((woz13rule3) =>
% 99.29/13.09 (((woz13rule4) =>
% 99.29/13.09 (((woz1_1) =>
% 99.29/13.09 (((woz1_2) =>
% 99.29/13.09 (((woz1_3) =>
% 99.29/13.09 (((woz1_4) =>
% 99.29/13.09 (((woz1_5) =>
% 99.29/13.09 (((breln1all2) =>
% 99.29/13.09 (((breln1SetBreln1) =>
% 99.29/13.09 (((choice2fnsingleton) =>
% 99.29/13.09 (((!!) @ ((('#B') @ (!!) @
% 99.29/13.09 ((('#S') @ ((('#B') @ ('#B') @ breln1)) @
% 99.29/13.09 ((('#S') @ dpsetconstr @ ('#I')))))))))))))))))))))))))))))))),
% 99.29/13.09 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3015])).
% 99.29/13.09 thf(zip_derived_cl3045, plain,
% 99.29/13.09 (~ (((woz13rule3) =>
% 99.29/13.09 (((woz13rule4) =>
% 99.29/13.09 (((woz1_1) =>
% 99.29/13.09 (((woz1_2) =>
% 99.29/13.09 (((woz1_3) =>
% 99.29/13.09 (((woz1_4) =>
% 99.29/13.09 (((woz1_5) =>
% 99.29/13.09 (((breln1all2) =>
% 99.29/13.09 (((breln1SetBreln1) =>
% 99.29/13.09 (((choice2fnsingleton) =>
% 99.29/13.09 (((!!) @ ((('#B') @ (!!) @
% 99.29/13.09 ((('#S') @ ((('#B') @ ('#B') @ breln1)) @
% 99.29/13.09 ((('#S') @ dpsetconstr @ ('#I')))))))))))))))))))))))))))))),
% 99.29/13.09 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3029])).
% 99.29/13.09 thf(zip_derived_cl3058, plain,
% 99.29/13.09 (~ (((woz13rule4) =>
% 99.29/13.09 (((woz1_1) =>
% 99.29/13.09 (((woz1_2) =>
% 99.29/13.09 (((woz1_3) =>
% 99.29/13.09 (((woz1_4) =>
% 99.29/13.09 (((woz1_5) =>
% 99.29/13.09 (((breln1all2) =>
% 99.29/13.09 (((breln1SetBreln1) =>
% 99.29/13.09 (((choice2fnsingleton) =>
% 99.29/13.09 (((!!) @ ((('#B') @ (!!) @
% 99.29/13.09 ((('#S') @ ((('#B') @ ('#B') @ breln1)) @
% 99.29/13.09 ((('#S') @ dpsetconstr @ ('#I')))))))))))))))))))))))))))),
% 99.29/13.09 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3045])).
% 99.29/13.09 thf(zip_derived_cl3069, plain,
% 99.29/13.09 (~ (((woz1_1) =>
% 99.29/13.09 (((woz1_2) =>
% 99.29/13.09 (((woz1_3) =>
% 99.29/13.09 (((woz1_4) =>
% 99.29/13.09 (((woz1_5) =>
% 99.29/13.09 (((breln1all2) =>
% 99.29/13.09 (((breln1SetBreln1) =>
% 99.29/13.09 (((choice2fnsingleton) =>
% 99.29/13.09 (((!!) @ ((('#B') @ (!!) @
% 99.29/13.09 ((('#S') @ ((('#B') @ ('#B') @ breln1)) @
% 99.29/13.09 ((('#S') @ dpsetconstr @ ('#I')))))))))))))))))))))))))),
% 99.29/13.09 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3058])).
% 99.29/13.09 thf(zip_derived_cl3081, plain,
% 99.29/13.09 (~ (((woz1_2) =>
% 99.29/13.09 (((woz1_3) =>
% 99.29/13.09 (((woz1_4) =>
% 99.29/13.09 (((woz1_5) =>
% 99.29/13.09 (((breln1all2) =>
% 99.29/13.09 (((breln1SetBreln1) =>
% 99.29/13.09 (((choice2fnsingleton) =>
% 99.29/13.09 (((!!) @ ((('#B') @ (!!) @
% 99.29/13.09 ((('#S') @ ((('#B') @ ('#B') @ breln1)) @
% 99.29/13.09 ((('#S') @ dpsetconstr @ ('#I')))))))))))))))))))))))),
% 99.29/13.09 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3069])).
% 99.29/13.09 thf(zip_derived_cl3093, plain,
% 99.29/13.09 (~ (((woz1_3) =>
% 99.29/13.09 (((woz1_4) =>
% 99.29/13.09 (((woz1_5) =>
% 99.29/13.09 (((breln1all2) =>
% 99.29/13.09 (((breln1SetBreln1) =>
% 99.29/13.09 (((choice2fnsingleton) =>
% 99.29/13.09 (((!!) @ ((('#B') @ (!!) @
% 99.29/13.09 ((('#S') @ ((('#B') @ ('#B') @ breln1)) @
% 99.29/13.09 ((('#S') @ dpsetconstr @ ('#I')))))))))))))))))))))),
% 99.29/13.09 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3081])).
% 99.29/13.09 thf(zip_derived_cl3105, plain,
% 99.29/13.09 (~ (((woz1_4) =>
% 99.29/13.09 (((woz1_5) =>
% 99.29/13.09 (((breln1all2) =>
% 99.29/13.09 (((breln1SetBreln1) =>
% 99.29/13.09 (((choice2fnsingleton) =>
% 99.29/13.09 (((!!) @ ((('#B') @ (!!) @
% 99.29/13.09 ((('#S') @ ((('#B') @ ('#B') @ breln1)) @
% 99.29/13.09 ((('#S') @ dpsetconstr @ ('#I')))))))))))))))))))),
% 99.29/13.09 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3093])).
% 99.29/13.09 thf(zip_derived_cl3116, plain,
% 99.29/13.09 (~ (((woz1_5) =>
% 99.29/13.09 (((breln1all2) =>
% 99.29/13.09 (((breln1SetBreln1) =>
% 99.29/13.09 (((choice2fnsingleton) =>
% 99.29/13.09 (((!!) @ ((('#B') @ (!!) @
% 99.29/13.09 ((('#S') @ ((('#B') @ ('#B') @ breln1)) @
% 99.29/13.09 ((('#S') @ dpsetconstr @ ('#I')))))))))))))))))),
% 99.29/13.09 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3105])).
% 99.29/13.09 thf(zip_derived_cl3127, plain,
% 99.29/13.09 (~ (((breln1all2) =>
% 99.29/13.09 (((breln1SetBreln1) =>
% 99.29/13.09 (((choice2fnsingleton) =>
% 99.29/13.09 (((!!) @ ((('#B') @ (!!) @
% 99.29/13.09 ((('#S') @ ((('#B') @ ('#B') @ breln1)) @
% 99.29/13.09 ((('#S') @ dpsetconstr @ ('#I')))))))))))))))),
% 99.29/13.09 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3116])).
% 99.29/13.09 thf(zip_derived_cl3139, plain,
% 99.29/13.09 (~ (((breln1SetBreln1) =>
% 99.29/13.09 (((choice2fnsingleton) =>
% 99.29/13.09 (((!!) @ ((('#B') @ (!!) @
% 99.29/13.09 ((('#S') @ ((('#B') @ ('#B') @ breln1)) @
% 99.29/13.09 ((('#S') @ dpsetconstr @ ('#I')))))))))))))),
% 99.29/13.09 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3127])).
% 99.29/13.09 thf(zip_derived_cl3151, plain,
% 99.29/13.09 (~ (((choice2fnsingleton) =>
% 99.29/13.09 (((!!) @ ((('#B') @ (!!) @
% 99.29/13.09 ((('#S') @ ((('#B') @ ('#B') @ breln1)) @
% 99.29/13.09 ((('#S') @ dpsetconstr @ ('#I')))))))))))),
% 99.29/13.09 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3139])).
% 99.29/13.09 thf(zip_derived_cl3162, plain,
% 99.29/13.09 (~ (((!!) @ ((('#B') @ (!!) @
% 99.29/13.09 ((('#S') @ ((('#B') @ ('#B') @ breln1)) @
% 99.29/13.09 ((('#S') @ dpsetconstr @ ('#I')))))))))),
% 99.29/13.09 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3151])).
% 99.29/13.09 thf(zip_derived_cl3173, plain,
% 99.29/13.09 (~ (((!!) @ ((('#B') @ (breln1 @ '#sk42') @
% 99.29/13.09 (dpsetconstr @ '#sk42' @ '#sk42')))))),
% 99.29/13.09 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl3162])).
% 99.29/13.09 thf(zip_derived_cl3184, plain,
% 99.29/13.09 (~ (breln1 @ '#sk42' @ (dpsetconstr @ '#sk42' @ '#sk42' @ '#sk43'))),
% 99.29/13.09 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl3173])).
% 99.29/13.09 thf(breln, axiom,(( breln @ (X1)@ (X2)@ (X0)) =
% 99.29/13.09 ((subset @ X0 @ (cartprod @ X1 @ X2))))).
% 99.29/13.09 thf('4', plain,
% 99.29/13.09 (![X2:$i,X1:$i,X0:$i]:
% 99.29/13.09 ( ( breln @ X1 @ X2 @ X0 ) = ( subset @ X0 @ ( cartprod @ X1 @ X2 ) ) )),
% 99.29/13.09 define([status(thm)])).
% 99.29/13.09 thf(breln1, axiom,(( breln1 @ (X0)@ (X1)) = ((breln @ X0 @ X0 @ X1)))).
% 99.29/13.09 thf('5', plain,
% 99.29/13.09 (![X1:$i,X0:$i]: ( ( breln1 @ X0 @ X1 ) = ( breln @ X0 @ X0 @ X1 ) )),
% 99.29/13.09 define([status(thm)])).
% 99.29/13.09 thf(zip_derived_cl3194, plain,
% 99.29/13.09 (~ (subset @ (dpsetconstr @ '#sk42' @ '#sk42' @ '#sk43') @
% 99.29/13.09 (cartprod @ '#sk42' @ '#sk42'))),
% 99.29/13.09 inference('rw', [status(thm)], [zip_derived_cl3184, '4', '5'])).
% 99.29/13.09 thf(zip_derived_cl1873, plain, ( (dpsetconstrSub)),
% 99.29/13.09 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1865])).
% 99.29/13.09 thf(dpsetconstrSub, axiom, (dpsetconstrSub) =>
% 99.29/13.09 ((((!!) @ (^[Y0 : $i]:
% 99.29/13.09 (((!!) @ (^[Y1 : $i]:
% 99.29/13.09 (((!!) @ (^[Y2 : $i > $i > $o]:
% 99.29/13.09 (subset @
% 99.29/13.09 (dpsetconstr @ Y0 @ Y1 @
% 99.29/13.09 (^[Y3 : $i,Y4 : $i]: (Y2 @ Y3 @ Y4))) @
% 99.29/13.09 (cartprod @ Y0 @ Y1)))))))))))
% 99.29/13.09 = ($true))).
% 99.29/13.09 thf('6', plain,
% 99.29/13.09 (( dpsetconstrSub ) <=>
% 99.29/13.09 ( ![X5:$i,X7:$i,X9:( $i > $i > $o )]:
% 99.29/13.09 ( subset @
% 99.29/13.09 ( dpsetconstr @ X5 @ X7 @ ( ^[V_1:$i,V_2:$i]: ( X9 @ V_1 @ V_2 ) ) ) @
% 99.29/13.09 ( cartprod @ X5 @ X7 ) ) )),
% 99.29/13.09 inference('rw.lit', [status(esa)], [dpsetconstrSub])).
% 99.29/13.09 thf(zip_derived_cl1881, plain,
% 99.29/13.09 ( (((!!) @ (^[Y0 : $i]:
% 99.29/13.09 (((!!) @ (^[Y1 : $i]:
% 99.29/13.09 (((!!) @ (^[Y2 : $i > $i > $o]:
% 99.29/13.09 (subset @
% 99.29/13.09 (dpsetconstr @ Y0 @ Y1 @
% 99.29/13.09 (^[Y3 : $i,Y4 : $i]:
% 99.29/13.09 (Y2 @ Y3 @ Y4))) @
% 99.29/13.09 (cartprod @ Y0 @ Y1)))))))))))),
% 99.29/13.09 inference('rw_clause', [status(thm)], [zip_derived_cl1873, '6'])).
% 99.29/13.09 thf(zip_derived_cl1889, plain,
% 99.29/13.09 ( (((!!) @ ((('#B') @ (!!) @
% 99.29/13.09 ((('#B') @ ((('#B') @ (!!))) @
% 99.29/13.09 ((('#S') @ ((('#B') @ ('#S') @
% 99.29/13.09 ((('#B') @ ((('#B') @ ('#C'))) @
% 99.29/13.09 ((('#B') @ ((('#B') @ ((('#B') @ subset)))) @
% 99.29/13.09 dpsetconstr)))))) @
% 99.29/13.09 cartprod))))))))),
% 99.29/13.09 inference('comb-normalize', [status(thm)], [zip_derived_cl1881])).
% 99.29/13.09 thf(zip_derived_cl1890, plain,
% 99.29/13.09 (![X2 : $i]:
% 99.29/13.09 (((!!) @ ((('#B') @ (!!) @
% 99.29/13.09 ((('#S') @ ((('#B') @ ('#C') @
% 99.29/13.09 ((('#B') @ ((('#B') @ subset)) @
% 99.29/13.09 (dpsetconstr @ X2))))) @
% 99.29/13.09 (cartprod @ X2)))))))),
% 99.29/13.09 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1889])).
% 99.29/13.09 thf(zip_derived_cl1898, plain,
% 99.29/13.09 (![X2 : $i, X4 : $i]:
% 99.29/13.09 (((!!) @ ((('#C') @ ((('#B') @ subset @ (dpsetconstr @ X2 @ X4))) @
% 99.29/13.09 (cartprod @ X2 @ X4)))))),
% 99.29/13.09 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1890])).
% 99.29/13.09 thf(zip_derived_cl1908, plain,
% 99.29/13.09 (![X2 : $i, X4 : $i, X6 : $i > $i > $o]:
% 99.29/13.09 (subset @ (dpsetconstr @ X2 @ X4 @ X6) @ (cartprod @ X2 @ X4))),
% 99.29/13.09 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1898])).
% 99.29/13.09 thf(zip_derived_cl3236, plain, ($false),
% 99.29/13.09 inference('demod', [status(thm)],
% 99.29/13.09 [zip_derived_cl3194, zip_derived_cl1908])).
% 99.29/13.09
% 99.29/13.09 % SZS output end Refutation
% 99.29/13.09
% 99.29/13.09
% 99.29/13.09 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s
% 99.29/13.09 % Terminating...
% 99.30/13.23 % Runner terminated.
% 99.34/13.25 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------