%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU683^1 : 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.5g0itM79Vl true
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 2 04:55:45 PM UTC 2025
% Result : Theorem 88.47s 26.73s
% Output : Refutation 89.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/1.08 % Problem : SEU683^1 : TPTP v9.2.0. Released v3.7.0.
% 0.10/1.17 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.5g0itM79Vl true
% 0.10/1.58 % Computer : n012.cluster.edu
% 0.10/1.58 % Model : x86_64 x86_64
% 0.10/1.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/1.58 % Memory : 8042.1875MB
% 0.10/1.58 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/1.58 % CPULimit : 300
% 0.10/1.58 % WCLimit : 300
% 0.10/1.58 % DateTime : Wed Oct 1 16:00:54 EDT 2025
% 0.10/1.59 % CPUTime :
% 0.10/1.59 % Running portfolio for 300 s
% 0.10/1.59 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/1.61 % Number of cores: 8
% 0.10/1.62 % Python version: Python 3.6.8
% 0.10/1.64 % Running in HO mode
% 0.48/2.28 % Total configuration time : 828
% 0.48/2.28 % Estimated wc time : 1656
% 0.48/2.28 % Estimated cpu time (8 cpus) : 207.0
% 0.51/2.66 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.51/2.68 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.51/2.69 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.51/2.71 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.51/2.72 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.52/2.77 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.52/2.78 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.51/2.81 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 88.47/26.73 % Solved by lams/40_b.comb.sh.
% 88.47/26.73 % done 0 iterations in 23.180s
% 88.47/26.73 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 88.47/26.73 % SZS output start Refutation
% 88.47/26.73 thf(setadjoinAx_type, type, setadjoinAx: $o).
% 88.47/26.73 thf(cartprodmempaircEq_type, type, cartprodmempaircEq: $o).
% 88.47/26.73 thf(notdexE_type, type, notdexE: $o).
% 88.47/26.73 thf(setunionAx_type, type, setunionAx: $o).
% 88.47/26.73 thf(setminusELneg_type, type, setminusELneg: $o).
% 88.47/26.73 thf(kpairsurjEq_type, type, kpairsurjEq: $o).
% 88.47/26.73 thf(powersetE_type, type, powersetE: $o).
% 88.47/26.73 thf(omegaSAx_type, type, omegaSAx: $o).
% 88.47/26.73 thf(exuI1_type, type, exuI1: $o).
% 88.47/26.73 thf(exuI2_type, type, exuI2: $o).
% 88.47/26.73 thf(notequalI2_type, type, notequalI2: $o).
% 88.47/26.73 thf(kpairiskpair_type, type, kpairiskpair: $o).
% 88.47/26.73 thf(upairsubunion_type, type, upairsubunion: $o).
% 88.47/26.73 thf(powerset__Cong_type, type, powerset__Cong: $o).
% 88.47/26.73 thf(setminusILneg_type, type, setminusILneg: $o).
% 88.47/26.73 thf(wellorderingAx_type, type, wellorderingAx: $o).
% 88.47/26.73 thf(setadjoinSub2_type, type, setadjoinSub2: $o).
% 88.47/26.73 thf(binintersectSubset5_type, type, binintersectSubset5: $o).
% 88.47/26.73 thf(upairinpowunion_type, type, upairinpowunion: $o).
% 88.47/26.73 thf(setoftrueEq_type, type, setoftrueEq: $o).
% 88.47/26.73 thf(emptyset__Cong_type, type, emptyset__Cong: $o).
% 88.47/26.73 thf(cartprodpairmemER_type, type, cartprodpairmemER: $o).
% 88.47/26.73 thf(lamProp_type, type, lamProp: $o).
% 88.47/26.73 thf(app_type, type, app: $o).
% 88.47/26.73 thf(dpsetconstrI_type, type, dpsetconstrI: $o).
% 88.47/26.73 thf(dpsetconstrER_type, type, dpsetconstrER: $o).
% 88.47/26.73 thf(sepInPowerset_type, type, sepInPowerset: $o).
% 88.47/26.73 thf(setukpairIR_type, type, setukpairIR: $o).
% 88.47/26.73 thf(binunionE_type, type, binunionE: $o).
% 88.47/26.73 thf(setext_type, type, setext: $o).
% 88.47/26.73 thf(emptyinPowerset_type, type, emptyinPowerset: $o).
% 88.47/26.73 thf(ubforcartprodlem1_type, type, ubforcartprodlem1: $o).
% 88.47/26.73 thf(setukpairinjR12_type, type, setukpairinjR12: $o).
% 88.47/26.73 thf(descr__Cong_type, type, descr__Cong: $o).
% 88.47/26.73 thf(binintersectSubset1_type, type, binintersectSubset1: $o).
% 88.47/26.73 thf(in_type, type, in: $i > $i > $o).
% 88.47/26.73 thf(dpsetconstrSub_type, type, dpsetconstrSub: $o).
% 88.47/26.73 thf(cartprodfstpairEq_type, type, cartprodfstpairEq: $o).
% 88.47/26.73 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o).
% 88.47/26.73 thf(setadjoinIR_type, type, setadjoinIR: $o).
% 88.47/26.73 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o).
% 88.47/26.73 thf(symdiffI2_type, type, symdiffI2: $o).
% 88.47/26.73 thf(upairset2IR_type, type, upairset2IR: $o).
% 88.47/26.73 thf(subsetE_type, type, subsetE: $o).
% 88.47/26.73 thf(prop2set2propI_type, type, prop2set2propI: $o).
% 88.47/26.73 thf(dsetconstrEL_type, type, dsetconstrEL: $o).
% 88.47/26.73 thf(setbeta_type, type, setbeta: $o).
% 88.47/26.73 thf(eqinunit_type, type, eqinunit: $o).
% 88.47/26.73 thf(upairsetIL_type, type, upairsetIL: $o).
% 88.47/26.73 thf(powersetI1_type, type, powersetI1: $o).
% 88.47/26.73 thf(binintersectSubset3_type, type, binintersectSubset3: $o).
% 88.47/26.73 thf(setukpairinjR_type, type, setukpairinjR: $o).
% 88.47/26.73 thf(cartprodfstin_type, type, cartprodfstin: $o).
% 88.47/26.73 thf(setminusIRneg_type, type, setminusIRneg: $o).
% 88.47/26.73 thf(powersetAx_type, type, powersetAx: $o).
% 88.47/26.73 thf(singletonprop_type, type, singletonprop: $o).
% 88.47/26.73 thf(binintersectSubset4_type, type, binintersectSubset4: $o).
% 88.47/26.73 thf(singletoninpowunion_type, type, singletoninpowunion: $o).
% 88.47/26.73 thf(powersetI_type, type, powersetI: $o).
% 88.47/26.73 thf(cartprodmempair_type, type, cartprodmempair: $o).
% 88.47/26.73 thf(upairsetIR_type, type, upairsetIR: $o).
% 88.47/26.73 thf(cartprodsndpairEq_type, type, cartprodsndpairEq: $o).
% 88.47/26.73 thf(funcinfuncset_type, type, funcinfuncset: $o).
% 88.47/26.73 thf(inCongP_type, type, inCongP: $o).
% 88.47/26.73 thf(setukpairinjL_type, type, setukpairinjL: $o).
% 88.47/26.73 thf(setadjoinSub_type, type, setadjoinSub: $o).
% 88.47/26.73 thf(exuE3e_type, type, exuE3e: $o).
% 88.47/26.73 thf(emptysetE_type, type, emptysetE: $o).
% 88.47/26.73 thf(upairequniteq_type, type, upairequniteq: $o).
% 88.47/26.73 thf(binintersectSubset2_type, type, binintersectSubset2: $o).
% 88.47/26.73 thf(setunionI_type, type, setunionI: $o).
% 88.47/26.73 thf(setunion__Cong_type, type, setunion__Cong: $o).
% 88.47/26.73 thf(prop2setI_type, type, prop2setI: $o).
% 88.47/26.73 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o).
% 88.47/26.73 thf(setminusER_type, type, setminusER: $o).
% 88.47/26.73 thf(exuE2_type, type, exuE2: $o).
% 88.47/26.73 thf(emptyset_type, type, emptyset: $i).
% 88.47/26.73 thf(powersetsubset_type, type, powersetsubset: $o).
% 88.47/26.73 thf(setukpairinjR1_type, type, setukpairinjR1: $o).
% 88.47/26.73 thf(dpsetconstrERa_type, type, dpsetconstrERa: $o).
% 88.47/26.73 thf(subPowSU_type, type, subPowSU: $o).
% 88.47/26.73 thf(ex1_type, type, ex1: $i > ($i > $o) > $o).
% 88.47/26.73 thf(notequalI1_type, type, notequalI1: $o).
% 88.47/26.73 thf(notinemptyset_type, type, notinemptyset: $o).
% 88.47/26.73 thf('#sk37_type', type, '#sk37': $i).
% 88.47/26.73 thf(nonemptyI1_type, type, nonemptyI1: $o).
% 88.47/26.73 thf(subsetTrans_type, type, subsetTrans: $o).
% 88.47/26.73 thf(setukpairinjR2_type, type, setukpairinjR2: $o).
% 88.47/26.73 thf(kpairp_type, type, kpairp: $o).
% 88.47/26.73 thf(setminusI_type, type, setminusI: $o).
% 88.47/26.73 thf(binunionIL_type, type, binunionIL: $o).
% 88.47/26.73 thf(setunionsingleton_type, type, setunionsingleton: $o).
% 88.47/26.73 thf(subsetE2_type, type, subsetE2: $o).
% 88.47/26.73 thf(singletonsswitch_type, type, singletonsswitch: $o).
% 88.47/26.73 thf(kfstpairEq_type, type, kfstpairEq: $o).
% 88.47/26.73 thf(ubforcartprodlem3_type, type, ubforcartprodlem3: $o).
% 88.47/26.73 thf(setextsub_type, type, setextsub: $o).
% 88.47/26.73 thf(binunionLsub_type, type, binunionLsub: $o).
% 88.47/26.73 thf(setunionsingleton1_type, type, setunionsingleton1: $o).
% 88.47/26.73 thf(emptysetsubset_type, type, emptysetsubset: $o).
% 88.47/26.73 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o).
% 88.47/26.73 thf(setunionE_type, type, setunionE: $o).
% 88.47/26.73 thf(setminusSubset1_type, type, setminusSubset1: $o).
% 88.47/26.73 thf(emptyinunitempty_type, type, emptyinunitempty: $o).
% 88.47/26.73 thf(binunionIR_type, type, binunionIR: $o).
% 88.47/26.73 thf(setadjoinE_type, type, setadjoinE: $o).
% 88.47/26.73 thf(cartprodpairmemEL_type, type, cartprodpairmemEL: $o).
% 88.47/26.73 thf(singletonsuniq_type, type, singletonsuniq: $o).
% 88.47/26.73 thf(dpsetconstrEL2_type, type, dpsetconstrEL2: $o).
% 88.47/26.73 thf(lamp_type, type, lamp: $o).
% 88.47/26.73 thf(setadjoinIL_type, type, setadjoinIL: $o).
% 88.47/26.73 thf(exuE1_type, type, exuE1: $o).
% 88.47/26.73 thf(ubforcartprodlem2_type, type, ubforcartprodlem2: $o).
% 88.47/26.73 thf(binintersectRsub_type, type, binintersectRsub: $o).
% 88.47/26.73 thf(setminusLsub_type, type, setminusLsub: $o).
% 88.47/26.73 thf(brelnall2_type, type, brelnall2: $o).
% 88.47/26.73 thf(notinsingleton_type, type, notinsingleton: $o).
% 88.47/26.73 thf(dpsetconstrEL1_type, type, dpsetconstrEL1: $o).
% 88.47/26.73 thf(eqimpsubset2_type, type, eqimpsubset2: $o).
% 88.47/26.73 thf(exuEu_type, type, exuEu: $o).
% 88.47/26.73 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o).
% 88.47/26.73 thf(ex1I2_type, type, ex1I2: $o).
% 88.47/26.73 thf(upairsetE_type, type, upairsetE: $o).
% 88.47/26.73 thf(omega0Ax_type, type, omega0Ax: $o).
% 88.47/26.73 thf(funcImageSingleton_type, type, funcImageSingleton: $o).
% 88.47/26.73 thf(notsubsetI_type, type, notsubsetI: $o).
% 88.47/26.73 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o).
% 88.47/26.73 thf(setextAx_type, type, setextAx: $o).
% 88.47/26.73 thf(powersetE1_type, type, powersetE1: $o).
% 88.47/26.73 thf(bs114d_type, type, bs114d: $o).
% 88.47/26.73 thf(noeltsimpempty_type, type, noeltsimpempty: $o).
% 88.47/26.73 thf(binintersectLsub_type, type, binintersectLsub: $o).
% 88.47/26.73 thf(subsetI1_type, type, subsetI1: $o).
% 88.47/26.73 thf(symdiffE_type, type, symdiffE: $o).
% 88.47/26.73 thf(descrp_type, type, descrp: $o).
% 88.47/26.73 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o).
% 88.47/26.73 thf(foundationAx_type, type, foundationAx: $o).
% 88.47/26.73 thf(emptysetAx_type, type, emptysetAx: $o).
% 88.47/26.73 thf(emptyI_type, type, emptyI: $o).
% 88.47/26.73 thf(setadjoinOr_type, type, setadjoinOr: $o).
% 88.47/26.73 thf(binintersectEL_type, type, binintersectEL: $o).
% 88.47/26.73 thf(emptyE1_type, type, emptyE1: $o).
% 88.47/26.73 thf(emptyInPowerset_type, type, emptyInPowerset: $o).
% 88.47/26.73 thf(vacuousDall_type, type, vacuousDall: $o).
% 88.47/26.73 thf(dsetconstr_type, type, dsetconstr: $i > ($i > $o) > $i).
% 88.47/26.73 thf(dsetconstrER_type, type, dsetconstrER: $o).
% 88.47/26.73 thf(binintersectI_type, type, binintersectI: $o).
% 88.47/26.73 thf(cartprodpairin_type, type, cartprodpairin: $o).
% 88.47/26.73 thf('#sk34_type', type, '#sk34': $i > ($i > $o) > $i).
% 88.47/26.73 thf(ex1I_type, type, ex1I: $o).
% 88.47/26.73 thf(cartprodmempair1_type, type, cartprodmempair1: $o).
% 88.47/26.73 thf(cartprodsndin_type, type, cartprodsndin: $o).
% 88.47/26.73 thf(lam2p_type, type, lam2p: $o).
% 88.47/26.73 thf(setukpairinjR11_type, type, setukpairinjR11: $o).
% 88.47/26.73 thf(singleton_type, type, singleton: $i > $o).
% 88.47/26.73 thf(symdiffI1_type, type, symdiffI1: $o).
% 88.47/26.73 thf(subsetI2_type, type, subsetI2: $o).
% 88.47/26.73 thf(setOfPairsIsBReln_type, type, setOfPairsIsBReln: $o).
% 88.47/26.73 thf(symdiffIneg1_type, type, symdiffIneg1: $o).
% 88.47/26.73 thf(theprop_type, type, theprop: $o).
% 88.47/26.73 thf(setminusERneg_type, type, setminusERneg: $o).
% 88.47/26.73 thf(symdiffIneg2_type, type, symdiffIneg2: $o).
% 88.47/26.73 thf(omega__Cong_type, type, omega__Cong: $o).
% 88.47/26.73 thf(subsetRefl_type, type, subsetRefl: $o).
% 88.47/26.73 thf(uniqinunit_type, type, uniqinunit: $o).
% 88.47/26.73 thf(infuncsetfunc_type, type, infuncsetfunc: $o).
% 88.47/26.73 thf(setminusSubset2_type, type, setminusSubset2: $o).
% 88.47/26.73 thf(prop2setE_type, type, prop2setE: $o).
% 88.47/26.73 thf(binunionEcases_type, type, binunionEcases: $o).
% 88.47/26.73 thf(omega_type, type, omega: $i).
% 88.47/26.73 thf(nonemptyI_type, type, nonemptyI: $o).
% 88.47/26.73 thf('#sk33_type', type, '#sk33': $i > ($i > $o) > $i).
% 88.47/26.73 thf(apProp_type, type, apProp: $o).
% 88.47/26.73 thf(disjointsetsI1_type, type, disjointsetsI1: $o).
% 88.47/26.73 thf(exuE3u_type, type, exuE3u: $o).
% 88.47/26.73 thf('#sk32_type', type, '#sk32': $i > ($i > $o) > $i).
% 88.47/26.73 thf(setminusEL_type, type, setminusEL: $o).
% 88.47/26.73 thf(setunionsingleton2_type, type, setunionsingleton2: $o).
% 88.47/26.73 thf(sepSubset_type, type, sepSubset: $o).
% 88.47/26.73 thf(upairset2E_type, type, upairset2E: $o).
% 88.47/26.73 thf(eqimpsubset1_type, type, eqimpsubset1: $o).
% 88.47/26.73 thf(exuI3_type, type, exuI3: $o).
% 88.47/26.73 thf(notdallE_type, type, notdallE: $o).
% 88.47/26.73 thf(binintersectER_type, type, binintersectER: $o).
% 88.47/26.73 thf(ksndsingleton_type, type, ksndsingleton: $o).
% 88.47/26.73 thf(kfstsingleton_type, type, kfstsingleton: $o).
% 88.47/26.73 thf(dsetconstrI_type, type, dsetconstrI: $o).
% 88.47/26.73 thf(cartprodpairsurjEq_type, type, cartprodpairsurjEq: $o).
% 88.47/26.73 thf('#sk38_type', type, '#sk38': $i > $o).
% 88.47/26.73 thf(setadjoin_type, type, setadjoin: $i > $i > $i).
% 88.47/26.73 thf(brelnall1_type, type, brelnall1: $o).
% 88.47/26.73 thf(exu__Cong_type, type, exu__Cong: $o).
% 88.47/26.73 thf(ksndpairEq_type, type, ksndpairEq: $o).
% 88.47/26.73 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o).
% 88.47/26.73 thf(ex1E1_type, type, ex1E1: $o).
% 88.47/26.73 thf(secondinupair_type, type, secondinupair: $o).
% 88.47/26.73 thf(singletonsubset_type, type, singletonsubset: $o).
% 88.47/26.73 thf(singletoninpowerset_type, type, singletoninpowerset: $o).
% 88.47/26.73 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o).
% 88.47/26.73 thf(replAx_type, type, replAx: $o).
% 88.47/26.73 thf(nonemptyE1_type, type, nonemptyE1: $o).
% 88.47/26.73 thf(omegaIndAx_type, type, omegaIndAx: $o).
% 88.47/26.73 thf(setukpairIL_type, type, setukpairIL: $o).
% 88.47/26.73 thf(setunionE2_type, type, setunionE2: $o).
% 88.47/26.73 thf(inPowerset_type, type, inPowerset: $o).
% 88.47/26.73 thf(ap2p_type, type, ap2p: $o).
% 88.47/26.73 thf(in__Cong_type, type, in__Cong: $o).
% 88.47/26.73 thf(setukpairinjL2_type, type, setukpairinjL2: $o).
% 88.47/26.73 thf(binunionRsub_type, type, binunionRsub: $o).
% 88.47/26.73 thf(subset2powerset_type, type, subset2powerset: $o).
% 88.47/26.73 thf(setukpairinjL1_type, type, setukpairinjL1: $o).
% 88.47/26.73 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)).
% 88.47/26.73 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)).
% 88.47/26.73 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)).
% 88.47/26.73 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)).
% 88.47/26.73 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)).
% 88.47/26.73 thf(ex1E2, conjecture,
% 88.47/26.73 (( setextAx ) =>
% 88.47/26.73 ( ( emptysetAx ) =>
% 88.47/26.73 ( ( setadjoinAx ) =>
% 88.47/26.73 ( ( powersetAx ) =>
% 88.47/26.73 ( ( setunionAx ) =>
% 88.47/26.73 ( ( omega0Ax ) =>
% 88.47/26.73 ( ( omegaSAx ) =>
% 88.47/26.73 ( ( omegaIndAx ) =>
% 88.47/26.73 ( ( replAx ) =>
% 88.47/26.73 ( ( foundationAx ) =>
% 88.47/26.73 ( ( wellorderingAx ) =>
% 88.47/26.73 ( ( descrp ) =>
% 88.47/26.73 ( ( dsetconstrI ) =>
% 88.47/26.73 ( ( dsetconstrEL ) =>
% 88.47/26.73 ( ( dsetconstrER ) =>
% 88.47/26.73 ( ( exuE1 ) =>
% 88.47/26.73 ( ( prop2setE ) =>
% 88.47/26.73 ( ( emptysetE ) =>
% 88.47/26.73 ( ( emptysetimpfalse ) =>
% 88.47/26.73 ( ( notinemptyset ) =>
% 88.47/26.73 ( ( exuE3e ) =>
% 88.47/26.73 ( ( setext ) =>
% 88.47/26.73 ( ( emptyI ) =>
% 88.47/26.73 ( ( noeltsimpempty ) =>
% 88.47/26.73 ( ( setbeta ) =>
% 88.47/26.73 ( ( nonemptyE1 ) =>
% 88.47/26.73 ( ( nonemptyI ) =>
% 88.47/26.73 ( ( nonemptyI1 ) =>
% 88.47/26.73 ( ( setadjoinIL ) =>
% 88.47/26.73 ( ( emptyinunitempty ) =>
% 88.47/26.73 ( ( setadjoinIR ) =>
% 88.47/26.73 ( ( setadjoinE ) =>
% 88.47/26.73 ( (
% 88.47/26.73 setadjoinOr ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 setoftrueEq ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 powersetI ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 emptyinPowerset ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 emptyInPowerset ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 powersetE ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 setunionI ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 setunionE ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 subPowSU ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 exuE2 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 nonemptyImpWitness ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 uniqinunit ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 notinsingleton ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 eqinunit ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 singletonsswitch ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 upairsetE ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 upairsetIL ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 upairsetIR ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 emptyE1 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 vacuousDall ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 quantDeMorgan1 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 quantDeMorgan2 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 quantDeMorgan3 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 quantDeMorgan4 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 prop2setI ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 prop2set2propI ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 notdexE ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 notdallE ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 exuI1 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 exuI3 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 exuI2 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 inCongP ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 in__Cong ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 exuE3u ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 exu__Cong ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 emptyset__Cong ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 setadjoin__Cong ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 powerset__Cong ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 setunion__Cong ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 omega__Cong ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 exuEu ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 descr__Cong ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 dsetconstr__Cong ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 subsetI1 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 eqimpsubset2 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 eqimpsubset1 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 subsetI2 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 emptysetsubset ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 subsetE ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 subsetE2 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 notsubsetI ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 notequalI1 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 notequalI2 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 subsetRefl ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 subsetTrans ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 setadjoinSub ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 setadjoinSub2 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 subset2powerset ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 setextsub ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 subsetemptysetimpeq ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 powersetI1 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 powersetE1 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 inPowerset ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 powersetsubset ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 sepInPowerset ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 sepSubset ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 binunionIL ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 upairset2IR ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 binunionIR ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 binunionEcases ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 binunionE ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 binunionLsub ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 binunionRsub ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 binintersectI ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 binintersectSubset5 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 binintersectEL ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 binintersectLsub ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 binintersectSubset2 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 binintersectSubset3 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 binintersectER ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 disjointsetsI1 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 binintersectRsub ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 binintersectSubset4 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 binintersectSubset1 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 bs114d ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 setminusI ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 setminusEL ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 setminusER ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 setminusSubset2 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 setminusERneg ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 setminusELneg ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 setminusILneg ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 setminusIRneg ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 setminusLsub ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 setminusSubset1 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 symdiffE ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 symdiffI1 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 symdiffI2 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 symdiffIneg1 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 symdiffIneg2 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 secondinupair ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 setukpairIL ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 setukpairIR ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 kpairiskpair ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 kpairp ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 singletonsubset ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 singletoninpowerset ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 singletoninpowunion ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 upairset2E ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 upairsubunion ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 upairinpowunion ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ubforcartprodlem1 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ubforcartprodlem2 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ubforcartprodlem3 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 cartprodpairin ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 cartprodmempair1 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 cartprodmempair ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 setunionE2 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 setunionsingleton1 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 setunionsingleton2 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 setunionsingleton ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 singletonprop ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ex1E1 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ex1I ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ex1I2 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 singletonsuniq ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 setukpairinjL1 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 kfstsingleton ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 theprop ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 kfstpairEq ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 cartprodfstin ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 setukpairinjL2 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 setukpairinjL ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 setukpairinjR11 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 setukpairinjR12 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 setukpairinjR1 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 upairequniteq ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 setukpairinjR2 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 setukpairinjR ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ksndsingleton ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ksndpairEq ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 kpairsurjEq ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 cartprodsndin ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 cartprodpairmemEL ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 cartprodpairmemER ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 cartprodmempaircEq ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 cartprodfstpairEq ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 cartprodsndpairEq ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 cartprodpairsurjEq ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 dpsetconstrI ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 dpsetconstrSub ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 setOfPairsIsBReln ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 dpsetconstrERa ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 dpsetconstrEL1 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 dpsetconstrEL2 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 dpsetconstrER ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 funcImageSingleton ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 apProp ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 app ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 infuncsetfunc ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ap2p ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 funcinfuncset ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 lamProp ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 lamp ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 lam2p ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 brelnall1 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 brelnall2 ) =>
% 88.47/26.73 (
% 88.47/26.73 ![
% 88.47/26.73 A:$i,
% 88.47/26.73 Xphi:(
% 88.47/26.73 $i > $o )]:
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ex1 @
% 88.47/26.73 A @
% 88.47/26.73 (
% 88.47/26.73 ^[
% 88.47/26.73 Xx:$i]:
% 88.47/26.73 (
% 88.47/26.73 Xphi @ Xx ) ) ) =>
% 88.47/26.73 (
% 88.47/26.73 ![
% 88.47/26.73 Xx:$i]:
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 in @
% 88.47/26.73 Xx @ A ) =>
% 88.47/26.73 (
% 88.47/26.73 ![
% 88.47/26.73 Xy:$i]:
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 in @
% 88.47/26.73 Xy @ A ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 Xphi @ Xx ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 Xphi @ Xy ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 Xx ) =
% 88.47/26.73 (
% 88.47/26.73 Xy ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 88.47/26.73 thf(zf_stmt_0, negated_conjecture,
% 88.47/26.73 (~( ( setextAx ) =>
% 88.47/26.73 ( ( emptysetAx ) =>
% 88.47/26.73 ( ( setadjoinAx ) =>
% 88.47/26.73 ( ( powersetAx ) =>
% 88.47/26.73 ( ( setunionAx ) =>
% 88.47/26.73 ( ( omega0Ax ) =>
% 88.47/26.73 ( ( omegaSAx ) =>
% 88.47/26.73 ( ( omegaIndAx ) =>
% 88.47/26.73 ( ( replAx ) =>
% 88.47/26.73 ( ( foundationAx ) =>
% 88.47/26.73 ( ( wellorderingAx ) =>
% 88.47/26.73 ( ( descrp ) =>
% 88.47/26.73 ( ( dsetconstrI ) =>
% 88.47/26.73 ( ( dsetconstrEL ) =>
% 88.47/26.73 ( ( dsetconstrER ) =>
% 88.47/26.73 ( ( exuE1 ) =>
% 88.47/26.73 ( ( prop2setE ) =>
% 88.47/26.73 ( ( emptysetE ) =>
% 88.47/26.73 ( ( emptysetimpfalse ) =>
% 88.47/26.73 ( ( notinemptyset ) =>
% 88.47/26.73 ( ( exuE3e ) =>
% 88.47/26.73 ( ( setext ) =>
% 88.47/26.73 ( ( emptyI ) =>
% 88.47/26.73 ( ( noeltsimpempty ) =>
% 88.47/26.73 ( ( setbeta ) =>
% 88.47/26.73 ( ( nonemptyE1 ) =>
% 88.47/26.73 ( ( nonemptyI ) =>
% 88.47/26.73 ( ( nonemptyI1 ) =>
% 88.47/26.73 ( ( setadjoinIL ) =>
% 88.47/26.73 ( ( emptyinunitempty ) =>
% 88.47/26.73 ( ( setadjoinIR ) =>
% 88.47/26.73 ( (
% 88.47/26.73 setadjoinE ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 setadjoinOr ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 setoftrueEq ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 powersetI ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 emptyinPowerset ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 emptyInPowerset ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 powersetE ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 setunionI ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 setunionE ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 subPowSU ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 exuE2 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 nonemptyImpWitness ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 uniqinunit ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 notinsingleton ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 eqinunit ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 singletonsswitch ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 upairsetE ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 upairsetIL ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 upairsetIR ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 emptyE1 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 vacuousDall ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 quantDeMorgan1 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 quantDeMorgan2 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 quantDeMorgan3 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 quantDeMorgan4 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 prop2setI ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 prop2set2propI ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 notdexE ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 notdallE ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 exuI1 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 exuI3 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 exuI2 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 inCongP ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 in__Cong ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 exuE3u ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 exu__Cong ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 emptyset__Cong ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 setadjoin__Cong ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 powerset__Cong ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 setunion__Cong ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 omega__Cong ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 exuEu ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 descr__Cong ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 dsetconstr__Cong ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 subsetI1 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 eqimpsubset2 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 eqimpsubset1 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 subsetI2 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 emptysetsubset ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 subsetE ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 subsetE2 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 notsubsetI ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 notequalI1 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 notequalI2 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 subsetRefl ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 subsetTrans ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 setadjoinSub ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 setadjoinSub2 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 subset2powerset ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 setextsub ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 subsetemptysetimpeq ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 powersetI1 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 powersetE1 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 inPowerset ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 powersetsubset ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 sepInPowerset ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 sepSubset ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 binunionIL ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 upairset2IR ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 binunionIR ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 binunionEcases ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 binunionE ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 binunionLsub ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 binunionRsub ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 binintersectI ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 binintersectSubset5 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 binintersectEL ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 binintersectLsub ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 binintersectSubset2 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 binintersectSubset3 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 binintersectER ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 disjointsetsI1 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 binintersectRsub ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 binintersectSubset4 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 binintersectSubset1 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 bs114d ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 setminusI ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 setminusEL ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 setminusER ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 setminusSubset2 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 setminusERneg ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 setminusELneg ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 setminusILneg ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 setminusIRneg ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 setminusLsub ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 setminusSubset1 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 symdiffE ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 symdiffI1 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 symdiffI2 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 symdiffIneg1 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 symdiffIneg2 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 secondinupair ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 setukpairIL ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 setukpairIR ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 kpairiskpair ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 kpairp ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 singletonsubset ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 singletoninpowerset ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 singletoninpowunion ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 upairset2E ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 upairsubunion ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 upairinpowunion ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ubforcartprodlem1 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ubforcartprodlem2 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ubforcartprodlem3 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 cartprodpairin ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 cartprodmempair1 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 cartprodmempair ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 setunionE2 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 setunionsingleton1 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 setunionsingleton2 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 setunionsingleton ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 singletonprop ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ex1E1 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ex1I ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ex1I2 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 singletonsuniq ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 setukpairinjL1 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 kfstsingleton ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 theprop ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 kfstpairEq ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 cartprodfstin ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 setukpairinjL2 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 setukpairinjL ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 setukpairinjR11 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 setukpairinjR12 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 setukpairinjR1 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 upairequniteq ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 setukpairinjR2 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 setukpairinjR ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ksndsingleton ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ksndpairEq ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 kpairsurjEq ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 cartprodsndin ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 cartprodpairmemEL ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 cartprodpairmemER ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 cartprodmempaircEq ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 cartprodfstpairEq ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 cartprodsndpairEq ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 cartprodpairsurjEq ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 dpsetconstrI ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 dpsetconstrSub ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 setOfPairsIsBReln ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 dpsetconstrERa ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 dpsetconstrEL1 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 dpsetconstrEL2 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 dpsetconstrER ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 funcImageSingleton ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 apProp ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 app ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 infuncsetfunc ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ap2p ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 funcinfuncset ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 lamProp ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 lamp ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 lam2p ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 brelnall1 ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 brelnall2 ) =>
% 88.47/26.73 (
% 88.47/26.73 ![
% 88.47/26.73 A:$i,
% 88.47/26.73 Xphi:(
% 88.47/26.73 $i > $o )]:
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ex1 @
% 88.47/26.73 A @
% 88.47/26.73 (
% 88.47/26.73 ^[
% 88.47/26.73 Xx:$i]:
% 88.47/26.73 (
% 88.47/26.73 Xphi @ Xx ) ) ) =>
% 88.47/26.73 (
% 88.47/26.73 ![
% 88.47/26.73 Xx:$i]:
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 in @
% 88.47/26.73 Xx @ A ) =>
% 88.47/26.73 (
% 88.47/26.73 ![
% 88.47/26.73 Xy:$i]:
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 in @
% 88.47/26.73 Xy @ A ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 Xphi @ Xx ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 Xphi @ Xy ) =>
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 Xx ) =
% 88.47/26.73 (
% 88.47/26.73 Xy ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 88.47/26.73 inference('cnf.neg', [status(esa)], [ex1E2])).
% 88.47/26.73 thf(zip_derived_cl0, plain,
% 88.47/26.73 (~ (((setextAx) =>
% 88.47/26.73 (((emptysetAx) =>
% 88.47/26.73 (((setadjoinAx) =>
% 88.47/26.73 (((powersetAx) =>
% 88.47/26.73 (((setunionAx) =>
% 88.47/26.73 (((omega0Ax) =>
% 88.47/26.73 (((omegaSAx) =>
% 88.47/26.73 (((omegaIndAx) =>
% 88.47/26.73 (((replAx) =>
% 88.47/26.73 (((foundationAx) =>
% 88.47/26.73 (((wellorderingAx) =>
% 88.47/26.73 (((descrp) =>
% 88.47/26.73 (((dsetconstrI) =>
% 88.47/26.73 (((dsetconstrEL) =>
% 88.47/26.73 (((dsetconstrER) =>
% 88.47/26.73 (((exuE1) =>
% 88.47/26.73 (((prop2setE) =>
% 88.47/26.73 (((emptysetE) =>
% 88.47/26.73 (((emptysetimpfalse) =>
% 88.47/26.73 (((notinemptyset) =>
% 88.47/26.73 (((exuE3e) =>
% 88.47/26.73 (((setext) =>
% 88.47/26.73 (((emptyI) =>
% 88.47/26.73 (((noeltsimpempty) =>
% 88.47/26.73 (((setbeta) =>
% 88.47/26.73 (((nonemptyE1) =>
% 88.47/26.73 (((nonemptyI) =>
% 88.47/26.73 (((nonemptyI1) =>
% 88.47/26.73 (((setadjoinIL) =>
% 88.47/26.73 (((emptyinunitempty) =>
% 88.47/26.73 ((
% 88.47/26.73 (setadjoinIR) =>
% 88.47/26.73 ((
% 88.47/26.73 (setadjoinE) =>
% 88.47/26.73 ((
% 88.47/26.73 (setadjoinOr) =>
% 88.47/26.73 ((
% 88.47/26.73 (setoftrueEq) =>
% 88.47/26.73 ((
% 88.47/26.73 (powersetI) =>
% 88.47/26.73 ((
% 88.47/26.73 (emptyinPowerset) =>
% 88.47/26.73 ((
% 88.47/26.73 (emptyInPowerset) =>
% 88.47/26.73 ((
% 88.47/26.73 (powersetE) =>
% 88.47/26.73 ((
% 88.47/26.73 (setunionI) =>
% 88.47/26.73 ((
% 88.47/26.73 (setunionE) =>
% 88.47/26.73 ((
% 88.47/26.73 (subPowSU) =>
% 88.47/26.73 ((
% 88.47/26.73 (exuE2) =>
% 88.47/26.73 ((
% 88.47/26.73 (nonemptyImpWitness) =>
% 88.47/26.73 ((
% 88.47/26.73 (uniqinunit) =>
% 88.47/26.73 ((
% 88.47/26.73 (notinsingleton) =>
% 88.47/26.73 ((
% 88.47/26.73 (eqinunit) =>
% 88.47/26.73 ((
% 88.47/26.73 (singletonsswitch) =>
% 88.47/26.73 ((
% 88.47/26.73 (upairsetE) =>
% 88.47/26.73 ((
% 88.47/26.73 (upairsetIL) =>
% 88.47/26.73 ((
% 88.47/26.73 (upairsetIR) =>
% 88.47/26.73 ((
% 88.47/26.73 (emptyE1) =>
% 88.47/26.73 ((
% 88.47/26.73 (vacuousDall) =>
% 88.47/26.73 ((
% 88.47/26.73 (quantDeMorgan1) =>
% 88.47/26.73 ((
% 88.47/26.73 (quantDeMorgan2) =>
% 88.47/26.73 ((
% 88.47/26.73 (quantDeMorgan3) =>
% 88.47/26.73 ((
% 88.47/26.73 (quantDeMorgan4) =>
% 88.47/26.73 ((
% 88.47/26.73 (prop2setI) =>
% 88.47/26.73 ((
% 88.47/26.73 (prop2set2propI) =>
% 88.47/26.73 ((
% 88.47/26.73 (notdexE) =>
% 88.47/26.73 ((
% 88.47/26.73 (notdallE) =>
% 88.47/26.73 ((
% 88.47/26.73 (exuI1) =>
% 88.47/26.73 ((
% 88.47/26.73 (exuI3) =>
% 88.47/26.73 ((
% 88.47/26.73 (exuI2) =>
% 88.47/26.73 ((
% 88.47/26.73 (inCongP) =>
% 88.47/26.73 ((
% 88.47/26.73 (in__Cong) =>
% 88.47/26.73 ((
% 88.47/26.73 (exuE3u) =>
% 88.47/26.73 ((
% 88.47/26.73 (exu__Cong) =>
% 88.47/26.73 ((
% 88.47/26.73 (emptyset__Cong) =>
% 88.47/26.73 ((
% 88.47/26.73 (setadjoin__Cong) =>
% 88.47/26.73 ((
% 88.47/26.73 (powerset__Cong) =>
% 88.47/26.73 ((
% 88.47/26.73 (setunion__Cong) =>
% 88.47/26.73 ((
% 88.47/26.73 (omega__Cong) =>
% 88.47/26.73 ((
% 88.47/26.73 (exuEu) =>
% 88.47/26.73 ((
% 88.47/26.73 (descr__Cong) =>
% 88.47/26.73 ((
% 88.47/26.73 (dsetconstr__Cong) =>
% 88.47/26.73 ((
% 88.47/26.73 (subsetI1) =>
% 88.47/26.73 ((
% 88.47/26.73 (eqimpsubset2) =>
% 88.47/26.73 ((
% 88.47/26.73 (eqimpsubset1) =>
% 88.47/26.73 ((
% 88.47/26.73 (subsetI2) =>
% 88.47/26.73 ((
% 88.47/26.73 (emptysetsubset) =>
% 88.47/26.73 ((
% 88.47/26.73 (subsetE) =>
% 88.47/26.73 ((
% 88.47/26.73 (subsetE2) =>
% 88.47/26.73 ((
% 88.47/26.73 (notsubsetI) =>
% 88.47/26.73 ((
% 88.47/26.73 (notequalI1) =>
% 88.47/26.73 ((
% 88.47/26.73 (notequalI2) =>
% 88.47/26.73 ((
% 88.47/26.73 (subsetRefl) =>
% 88.47/26.73 ((
% 88.47/26.73 (subsetTrans) =>
% 88.47/26.73 ((
% 88.47/26.73 (setadjoinSub) =>
% 88.47/26.73 ((
% 88.47/26.73 (setadjoinSub2) =>
% 88.47/26.73 ((
% 88.47/26.73 (subset2powerset) =>
% 88.47/26.73 ((
% 88.47/26.73 (setextsub) =>
% 88.47/26.73 ((
% 88.47/26.73 (subsetemptysetimpeq) =>
% 88.47/26.73 ((
% 88.47/26.73 (powersetI1) =>
% 88.47/26.73 ((
% 88.47/26.73 (powersetE1) =>
% 88.47/26.73 ((
% 88.47/26.73 (inPowerset) =>
% 88.47/26.73 ((
% 88.47/26.73 (powersetsubset) =>
% 88.47/26.73 ((
% 88.47/26.73 (sepInPowerset) =>
% 88.47/26.73 ((
% 88.47/26.73 (sepSubset) =>
% 88.47/26.73 ((
% 88.47/26.73 (binunionIL) =>
% 88.47/26.73 ((
% 88.47/26.73 (upairset2IR) =>
% 88.47/26.73 ((
% 88.47/26.73 (binunionIR) =>
% 88.47/26.73 ((
% 88.47/26.73 (binunionEcases) =>
% 88.47/26.73 ((
% 88.47/26.73 (binunionE) =>
% 88.47/26.73 ((
% 88.47/26.73 (binunionLsub) =>
% 88.47/26.73 ((
% 88.47/26.73 (binunionRsub) =>
% 88.47/26.73 ((
% 88.47/26.73 (binintersectI) =>
% 88.47/26.73 ((
% 88.47/26.73 (binintersectSubset5) =>
% 88.47/26.73 ((
% 88.47/26.73 (binintersectEL) =>
% 88.47/26.73 ((
% 88.47/26.73 (binintersectLsub) =>
% 88.47/26.73 ((
% 88.47/26.73 (binintersectSubset2) =>
% 88.47/26.73 ((
% 88.47/26.73 (binintersectSubset3) =>
% 88.47/26.73 ((
% 88.47/26.73 (binintersectER) =>
% 88.47/26.73 ((
% 88.47/26.73 (disjointsetsI1) =>
% 88.47/26.73 ((
% 88.47/26.73 (binintersectRsub) =>
% 88.47/26.73 ((
% 88.47/26.73 (binintersectSubset4) =>
% 88.47/26.73 ((
% 88.47/26.73 (binintersectSubset1) =>
% 88.47/26.73 ((
% 88.47/26.73 (bs114d) =>
% 88.47/26.73 ((
% 88.47/26.73 (setminusI) =>
% 88.47/26.73 ((
% 88.47/26.73 (setminusEL) =>
% 88.47/26.73 ((
% 88.47/26.73 (setminusER) =>
% 88.47/26.73 ((
% 88.47/26.73 (setminusSubset2) =>
% 88.47/26.73 ((
% 88.47/26.73 (setminusERneg) =>
% 88.47/26.73 ((
% 88.47/26.73 (setminusELneg) =>
% 88.47/26.73 ((
% 88.47/26.73 (setminusILneg) =>
% 88.47/26.73 ((
% 88.47/26.73 (setminusIRneg) =>
% 88.47/26.73 ((
% 88.47/26.73 (setminusLsub) =>
% 88.47/26.73 ((
% 88.47/26.73 (setminusSubset1) =>
% 88.47/26.73 ((
% 88.47/26.73 (symdiffE) =>
% 88.47/26.73 ((
% 88.47/26.73 (symdiffI1) =>
% 88.47/26.73 ((
% 88.47/26.73 (symdiffI2) =>
% 88.47/26.73 ((
% 88.47/26.73 (symdiffIneg1) =>
% 88.47/26.73 ((
% 88.47/26.73 (symdiffIneg2) =>
% 88.47/26.73 ((
% 88.47/26.73 (secondinupair) =>
% 88.47/26.73 ((
% 88.47/26.73 (setukpairIL) =>
% 88.47/26.73 ((
% 88.47/26.73 (setukpairIR) =>
% 88.47/26.73 ((
% 88.47/26.73 (kpairiskpair) =>
% 88.47/26.73 ((
% 88.47/26.73 (kpairp) =>
% 88.47/26.73 ((
% 88.47/26.73 (singletonsubset) =>
% 88.47/26.73 ((
% 88.47/26.73 (singletoninpowerset) =>
% 88.47/26.73 ((
% 88.47/26.73 (singletoninpowunion) =>
% 88.47/26.73 ((
% 88.47/26.73 (upairset2E) =>
% 88.47/26.73 ((
% 88.47/26.73 (upairsubunion) =>
% 88.47/26.73 ((
% 88.47/26.73 (upairinpowunion) =>
% 88.47/26.73 ((
% 88.47/26.73 (ubforcartprodlem1) =>
% 88.47/26.73 ((
% 88.47/26.73 (ubforcartprodlem2) =>
% 88.47/26.73 ((
% 88.47/26.73 (ubforcartprodlem3) =>
% 88.47/26.73 ((
% 88.47/26.73 (cartprodpairin) =>
% 88.47/26.73 ((
% 88.47/26.73 (cartprodmempair1) =>
% 88.47/26.73 ((
% 88.47/26.73 (cartprodmempair) =>
% 88.47/26.73 ((
% 88.47/26.73 (setunionE2) =>
% 88.47/26.73 ((
% 88.47/26.73 (setunionsingleton1) =>
% 88.47/26.73 ((
% 88.47/26.73 (setunionsingleton2) =>
% 88.47/26.73 ((
% 88.47/26.73 (setunionsingleton) =>
% 88.47/26.73 ((
% 88.47/26.73 (singletonprop) =>
% 88.47/26.73 ((
% 88.47/26.73 (ex1E1) =>
% 88.47/26.73 ((
% 88.47/26.73 (ex1I) =>
% 88.47/26.73 ((
% 88.47/26.73 (ex1I2) =>
% 88.47/26.73 ((
% 88.47/26.73 (singletonsuniq) =>
% 88.47/26.73 ((
% 88.47/26.73 (setukpairinjL1) =>
% 88.47/26.73 ((
% 88.47/26.73 (kfstsingleton) =>
% 88.47/26.73 ((
% 88.47/26.73 (theprop) =>
% 88.47/26.73 ((
% 88.47/26.73 (kfstpairEq) =>
% 88.47/26.73 ((
% 88.47/26.73 (cartprodfstin) =>
% 88.47/26.73 ((
% 88.47/26.73 (setukpairinjL2) =>
% 88.47/26.73 ((
% 88.47/26.73 (setukpairinjL) =>
% 88.47/26.73 ((
% 88.47/26.73 (setukpairinjR11) =>
% 88.47/26.73 ((
% 88.47/26.73 (setukpairinjR12) =>
% 88.47/26.73 ((
% 88.47/26.73 (setukpairinjR1) =>
% 88.47/26.73 ((
% 88.47/26.73 (upairequniteq) =>
% 88.47/26.73 ((
% 88.47/26.73 (setukpairinjR2) =>
% 88.47/26.73 ((
% 88.47/26.73 (setukpairinjR) =>
% 88.47/26.73 ((
% 88.47/26.73 (ksndsingleton) =>
% 88.47/26.73 ((
% 88.47/26.73 (ksndpairEq) =>
% 88.47/26.73 ((
% 88.47/26.73 (kpairsurjEq) =>
% 88.47/26.73 ((
% 88.47/26.73 (cartprodsndin) =>
% 88.47/26.73 ((
% 88.47/26.73 (cartprodpairmemEL) =>
% 88.47/26.73 ((
% 88.47/26.73 (cartprodpairmemER) =>
% 88.47/26.73 ((
% 88.47/26.73 (cartprodmempaircEq) =>
% 88.47/26.73 ((
% 88.47/26.73 (cartprodfstpairEq) =>
% 88.47/26.73 ((
% 88.47/26.73 (cartprodsndpairEq) =>
% 88.47/26.73 ((
% 88.47/26.73 (cartprodpairsurjEq) =>
% 88.47/26.73 ((
% 88.47/26.73 (dpsetconstrI) =>
% 88.47/26.73 ((
% 88.47/26.73 (dpsetconstrSub) =>
% 88.47/26.73 ((
% 88.47/26.73 (setOfPairsIsBReln) =>
% 88.47/26.73 ((
% 88.47/26.73 (dpsetconstrERa) =>
% 88.47/26.73 ((
% 88.47/26.73 (dpsetconstrEL1) =>
% 88.47/26.73 ((
% 88.47/26.73 (dpsetconstrEL2) =>
% 88.47/26.73 ((
% 88.47/26.73 (dpsetconstrER) =>
% 88.47/26.73 ((
% 88.47/26.73 (funcImageSingleton) =>
% 88.47/26.73 ((
% 88.47/26.73 (apProp) =>
% 88.47/26.73 ((
% 88.47/26.73 (app) =>
% 88.47/26.73 ((
% 88.47/26.73 (infuncsetfunc) =>
% 88.47/26.73 ((
% 88.47/26.73 (ap2p) =>
% 88.47/26.73 ((
% 88.47/26.73 (funcinfuncset) =>
% 88.47/26.73 ((
% 88.47/26.73 (lamProp) =>
% 88.47/26.73 ((
% 88.47/26.73 (lamp) =>
% 88.47/26.73 ((
% 88.47/26.73 (lam2p) =>
% 88.47/26.73 ((
% 88.47/26.73 (brelnall1) =>
% 88.47/26.73 ((
% 88.47/26.73 (brelnall2) =>
% 88.47/26.73 ((
% 88.47/26.73 (!!) @ (
% 88.47/26.73 ^[Y0 : $i]:
% 88.47/26.73 ((
% 88.47/26.73 (!!) @ (
% 88.47/26.73 ^[Y1 : $i > $o]:
% 88.47/26.73 ((
% 88.47/26.73 (ex1 @
% 88.47/26.73 Y0 @
% 88.47/26.73 (
% 88.47/26.73 ^[Y2 : $i]:
% 88.47/26.73 (Y1 @ Y2))) =>
% 88.47/26.73 ((
% 88.47/26.73 (!!) @ (
% 88.47/26.73 ^[Y2 : $i]:
% 88.47/26.73 ((
% 88.47/26.73 (in @
% 88.47/26.73 Y2 @
% 88.47/26.73 Y0) =>
% 88.47/26.73 ((
% 88.47/26.73 (!!) @ (
% 88.47/26.73 ^[Y3 : $i]:
% 88.47/26.73 ((
% 88.47/26.73 (in @
% 88.47/26.73 Y3 @
% 88.47/26.73 Y0) =>
% 88.47/26.73 ((
% 88.47/26.73 (Y1 @
% 88.47/26.73 Y2) =>
% 88.47/26.73 ((
% 88.47/26.73 (Y1 @
% 88.47/26.73 Y3) =>
% 88.47/26.73 ((
% 88.47/26.73 (Y2) =
% 88.47/26.73 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 88.47/26.73 inference('cnf', [status(esa)], [zf_stmt_0])).
% 88.47/26.73 thf(zip_derived_cl1, plain,
% 88.47/26.73 (~ (((setextAx) =>
% 88.47/26.73 (((emptysetAx) =>
% 88.47/26.73 (((setadjoinAx) =>
% 88.47/26.73 (((powersetAx) =>
% 88.47/26.73 (((setunionAx) =>
% 88.47/26.73 (((omega0Ax) =>
% 88.47/26.73 (((omegaSAx) =>
% 88.47/26.73 (((omegaIndAx) =>
% 88.47/26.73 (((replAx) =>
% 88.47/26.73 (((foundationAx) =>
% 88.47/26.73 (((wellorderingAx) =>
% 88.47/26.73 (((descrp) =>
% 88.47/26.73 (((dsetconstrI) =>
% 88.47/26.73 (((dsetconstrEL) =>
% 88.47/26.73 (((dsetconstrER) =>
% 88.47/26.73 (((exuE1) =>
% 88.47/26.73 (((prop2setE) =>
% 88.47/26.73 (((emptysetE) =>
% 88.47/26.73 (((emptysetimpfalse) =>
% 88.47/26.73 (((notinemptyset) =>
% 88.47/26.73 (((exuE3e) =>
% 88.47/26.73 (((setext) =>
% 88.47/26.73 (((emptyI) =>
% 88.47/26.73 (((noeltsimpempty) =>
% 88.47/26.73 (((setbeta) =>
% 88.47/26.73 (((nonemptyE1) =>
% 88.47/26.73 (((nonemptyI) =>
% 88.47/26.73 (((nonemptyI1) =>
% 88.47/26.73 (((setadjoinIL) =>
% 88.47/26.73 (((emptyinunitempty) =>
% 88.47/26.73 ((
% 88.47/26.73 (setadjoinIR) =>
% 88.47/26.73 ((
% 88.47/26.73 (setadjoinE) =>
% 88.47/26.73 ((
% 88.47/26.73 (setadjoinOr) =>
% 88.47/26.73 ((
% 88.47/26.73 (setoftrueEq) =>
% 88.47/26.73 ((
% 88.47/26.73 (powersetI) =>
% 88.47/26.73 ((
% 88.47/26.73 (emptyinPowerset) =>
% 88.47/26.73 ((
% 88.47/26.73 (emptyInPowerset) =>
% 88.47/26.73 ((
% 88.47/26.73 (powersetE) =>
% 88.47/26.73 ((
% 88.47/26.73 (setunionI) =>
% 88.47/26.73 ((
% 88.47/26.73 (setunionE) =>
% 88.47/26.73 ((
% 88.47/26.73 (subPowSU) =>
% 88.47/26.73 ((
% 88.47/26.73 (exuE2) =>
% 88.47/26.73 ((
% 88.47/26.73 (nonemptyImpWitness) =>
% 88.47/26.73 ((
% 88.47/26.73 (uniqinunit) =>
% 88.47/26.73 ((
% 88.47/26.73 (notinsingleton) =>
% 88.47/26.73 ((
% 88.47/26.73 (eqinunit) =>
% 88.47/26.73 ((
% 88.47/26.73 (singletonsswitch) =>
% 88.47/26.73 ((
% 88.47/26.73 (upairsetE) =>
% 88.47/26.73 ((
% 88.47/26.73 (upairsetIL) =>
% 88.47/26.73 ((
% 88.47/26.73 (upairsetIR) =>
% 88.47/26.73 ((
% 88.47/26.73 (emptyE1) =>
% 88.47/26.73 ((
% 88.47/26.73 (vacuousDall) =>
% 88.47/26.73 ((
% 88.47/26.73 (quantDeMorgan1) =>
% 88.47/26.73 ((
% 88.47/26.73 (quantDeMorgan2) =>
% 88.47/26.73 ((
% 88.47/26.73 (quantDeMorgan3) =>
% 88.47/26.73 ((
% 88.47/26.73 (quantDeMorgan4) =>
% 88.47/26.73 ((
% 88.47/26.73 (prop2setI) =>
% 88.47/26.73 ((
% 88.47/26.73 (prop2set2propI) =>
% 88.47/26.73 ((
% 88.47/26.73 (notdexE) =>
% 88.47/26.73 ((
% 88.47/26.73 (notdallE) =>
% 88.47/26.73 ((
% 88.47/26.73 (exuI1) =>
% 88.47/26.73 ((
% 88.47/26.73 (exuI3) =>
% 88.47/26.73 ((
% 88.47/26.73 (exuI2) =>
% 88.47/26.73 ((
% 88.47/26.73 (inCongP) =>
% 88.47/26.73 ((
% 88.47/26.73 (in__Cong) =>
% 88.47/26.73 ((
% 88.47/26.73 (exuE3u) =>
% 88.47/26.73 ((
% 88.47/26.73 (exu__Cong) =>
% 88.47/26.73 ((
% 88.47/26.73 (emptyset__Cong) =>
% 88.47/26.73 ((
% 88.47/26.73 (setadjoin__Cong) =>
% 88.47/26.73 ((
% 88.47/26.73 (powerset__Cong) =>
% 88.47/26.73 ((
% 88.47/26.73 (setunion__Cong) =>
% 88.47/26.73 ((
% 88.47/26.73 (omega__Cong) =>
% 88.47/26.73 ((
% 88.47/26.73 (exuEu) =>
% 88.47/26.73 ((
% 88.47/26.73 (descr__Cong) =>
% 88.47/26.73 ((
% 88.47/26.73 (dsetconstr__Cong) =>
% 88.47/26.73 ((
% 88.47/26.73 (subsetI1) =>
% 88.47/26.73 ((
% 88.47/26.73 (eqimpsubset2) =>
% 88.47/26.73 ((
% 88.47/26.73 (eqimpsubset1) =>
% 88.47/26.73 ((
% 88.47/26.73 (subsetI2) =>
% 88.47/26.73 ((
% 88.47/26.73 (emptysetsubset) =>
% 88.47/26.73 ((
% 88.47/26.73 (subsetE) =>
% 88.47/26.73 ((
% 88.47/26.73 (subsetE2) =>
% 88.47/26.73 ((
% 88.47/26.73 (notsubsetI) =>
% 88.47/26.73 ((
% 88.47/26.73 (notequalI1) =>
% 88.47/26.73 ((
% 88.47/26.73 (notequalI2) =>
% 88.47/26.73 ((
% 88.47/26.73 (subsetRefl) =>
% 88.47/26.73 ((
% 88.47/26.73 (subsetTrans) =>
% 88.47/26.73 ((
% 88.47/26.73 (setadjoinSub) =>
% 88.47/26.73 ((
% 88.47/26.73 (setadjoinSub2) =>
% 88.47/26.73 ((
% 88.47/26.73 (subset2powerset) =>
% 88.47/26.73 ((
% 88.47/26.73 (setextsub) =>
% 88.47/26.73 ((
% 88.47/26.73 (subsetemptysetimpeq) =>
% 88.47/26.73 ((
% 88.47/26.73 (powersetI1) =>
% 88.47/26.73 ((
% 88.47/26.73 (powersetE1) =>
% 88.47/26.73 ((
% 88.47/26.73 (inPowerset) =>
% 88.47/26.73 ((
% 88.47/26.73 (powersetsubset) =>
% 88.47/26.73 ((
% 88.47/26.73 (sepInPowerset) =>
% 88.47/26.73 ((
% 88.47/26.73 (sepSubset) =>
% 88.47/26.73 ((
% 88.47/26.73 (binunionIL) =>
% 88.47/26.73 ((
% 88.47/26.73 (upairset2IR) =>
% 88.47/26.73 ((
% 88.47/26.73 (binunionIR) =>
% 88.47/26.73 ((
% 88.47/26.73 (binunionEcases) =>
% 88.47/26.73 ((
% 88.47/26.73 (binunionE) =>
% 88.47/26.73 ((
% 88.47/26.73 (binunionLsub) =>
% 88.47/26.73 ((
% 88.47/26.73 (binunionRsub) =>
% 88.47/26.73 ((
% 88.47/26.73 (binintersectI) =>
% 88.47/26.73 ((
% 88.47/26.73 (binintersectSubset5) =>
% 88.47/26.73 ((
% 88.47/26.73 (binintersectEL) =>
% 88.47/26.73 ((
% 88.47/26.73 (binintersectLsub) =>
% 88.47/26.73 ((
% 88.47/26.73 (binintersectSubset2) =>
% 88.47/26.73 ((
% 88.47/26.73 (binintersectSubset3) =>
% 88.47/26.73 ((
% 88.47/26.73 (binintersectER) =>
% 88.47/26.73 ((
% 88.47/26.73 (disjointsetsI1) =>
% 88.47/26.73 ((
% 88.47/26.73 (binintersectRsub) =>
% 88.47/26.73 ((
% 88.47/26.73 (binintersectSubset4) =>
% 88.47/26.73 ((
% 88.47/26.73 (binintersectSubset1) =>
% 88.47/26.73 ((
% 88.47/26.73 (bs114d) =>
% 88.47/26.73 ((
% 88.47/26.73 (setminusI) =>
% 88.47/26.73 ((
% 88.47/26.73 (setminusEL) =>
% 88.47/26.73 ((
% 88.47/26.73 (setminusER) =>
% 88.47/26.73 ((
% 88.47/26.73 (setminusSubset2) =>
% 88.47/26.73 ((
% 88.47/26.73 (setminusERneg) =>
% 88.47/26.73 ((
% 88.47/26.73 (setminusELneg) =>
% 88.47/26.73 ((
% 88.47/26.73 (setminusILneg) =>
% 88.47/26.73 ((
% 88.47/26.73 (setminusIRneg) =>
% 88.47/26.73 ((
% 88.47/26.73 (setminusLsub) =>
% 88.47/26.73 ((
% 88.47/26.73 (setminusSubset1) =>
% 88.47/26.73 ((
% 88.47/26.73 (symdiffE) =>
% 88.47/26.73 ((
% 88.47/26.73 (symdiffI1) =>
% 88.47/26.73 ((
% 88.47/26.73 (symdiffI2) =>
% 88.47/26.73 ((
% 88.47/26.73 (symdiffIneg1) =>
% 88.47/26.73 ((
% 88.47/26.73 (symdiffIneg2) =>
% 88.47/26.73 ((
% 88.47/26.73 (secondinupair) =>
% 88.47/26.73 ((
% 88.47/26.73 (setukpairIL) =>
% 88.47/26.73 ((
% 88.47/26.73 (setukpairIR) =>
% 88.47/26.73 ((
% 88.47/26.73 (kpairiskpair) =>
% 88.47/26.73 ((
% 88.47/26.73 (kpairp) =>
% 88.47/26.73 ((
% 88.47/26.73 (singletonsubset) =>
% 88.47/26.73 ((
% 88.47/26.73 (singletoninpowerset) =>
% 88.47/26.73 ((
% 88.47/26.73 (singletoninpowunion) =>
% 88.47/26.73 ((
% 88.47/26.73 (upairset2E) =>
% 88.47/26.73 ((
% 88.47/26.73 (upairsubunion) =>
% 88.47/26.73 ((
% 88.47/26.73 (upairinpowunion) =>
% 88.47/26.73 ((
% 88.47/26.73 (ubforcartprodlem1) =>
% 88.47/26.73 ((
% 88.47/26.73 (ubforcartprodlem2) =>
% 88.47/26.73 ((
% 88.47/26.73 (ubforcartprodlem3) =>
% 88.47/26.73 ((
% 88.47/26.73 (cartprodpairin) =>
% 88.47/26.73 ((
% 88.47/26.73 (cartprodmempair1) =>
% 88.47/26.73 ((
% 88.47/26.73 (cartprodmempair) =>
% 88.47/26.73 ((
% 88.47/26.73 (setunionE2) =>
% 88.47/26.73 ((
% 88.47/26.73 (setunionsingleton1) =>
% 88.47/26.73 ((
% 88.47/26.73 (setunionsingleton2) =>
% 88.47/26.73 ((
% 88.47/26.73 (setunionsingleton) =>
% 88.47/26.73 ((
% 88.47/26.73 (singletonprop) =>
% 88.47/26.73 ((
% 88.47/26.73 (ex1E1) =>
% 88.47/26.73 ((
% 88.47/26.73 (ex1I) =>
% 88.47/26.73 ((
% 88.47/26.73 (ex1I2) =>
% 88.47/26.73 ((
% 88.47/26.73 (singletonsuniq) =>
% 88.47/26.73 ((
% 88.47/26.73 (setukpairinjL1) =>
% 88.47/26.73 ((
% 88.47/26.73 (kfstsingleton) =>
% 88.47/26.73 ((
% 88.47/26.73 (theprop) =>
% 88.47/26.73 ((
% 88.47/26.73 (kfstpairEq) =>
% 88.47/26.73 ((
% 88.47/26.73 (cartprodfstin) =>
% 88.47/26.73 ((
% 88.47/26.73 (setukpairinjL2) =>
% 88.47/26.73 ((
% 88.47/26.73 (setukpairinjL) =>
% 88.47/26.73 ((
% 88.47/26.73 (setukpairinjR11) =>
% 88.47/26.73 ((
% 88.47/26.73 (setukpairinjR12) =>
% 88.47/26.73 ((
% 88.47/26.73 (setukpairinjR1) =>
% 88.47/26.73 ((
% 88.47/26.73 (upairequniteq) =>
% 88.47/26.73 ((
% 88.47/26.73 (setukpairinjR2) =>
% 88.47/26.73 ((
% 88.47/26.73 (setukpairinjR) =>
% 88.47/26.73 ((
% 88.47/26.73 (ksndsingleton) =>
% 88.47/26.73 ((
% 88.47/26.73 (ksndpairEq) =>
% 88.47/26.73 ((
% 88.47/26.73 (kpairsurjEq) =>
% 88.47/26.73 ((
% 88.47/26.73 (cartprodsndin) =>
% 88.47/26.73 ((
% 88.47/26.73 (cartprodpairmemEL) =>
% 88.47/26.73 ((
% 88.47/26.73 (cartprodpairmemER) =>
% 88.47/26.73 ((
% 88.47/26.73 (cartprodmempaircEq) =>
% 88.47/26.73 ((
% 88.47/26.73 (cartprodfstpairEq) =>
% 88.47/26.73 ((
% 88.47/26.73 (cartprodsndpairEq) =>
% 88.47/26.73 ((
% 88.47/26.73 (cartprodpairsurjEq) =>
% 88.47/26.73 ((
% 88.47/26.73 (dpsetconstrI) =>
% 88.47/26.73 ((
% 88.47/26.73 (dpsetconstrSub) =>
% 88.47/26.73 ((
% 88.47/26.73 (setOfPairsIsBReln) =>
% 88.47/26.73 ((
% 88.47/26.73 (dpsetconstrERa) =>
% 88.47/26.73 ((
% 88.47/26.73 (dpsetconstrEL1) =>
% 88.47/26.73 ((
% 88.47/26.73 (dpsetconstrEL2) =>
% 88.47/26.73 ((
% 88.47/26.73 (dpsetconstrER) =>
% 88.47/26.73 ((
% 88.47/26.73 (funcImageSingleton) =>
% 88.47/26.73 ((
% 88.47/26.73 (apProp) =>
% 88.47/26.73 ((
% 88.47/26.73 (app) =>
% 88.47/26.73 ((
% 88.47/26.73 (infuncsetfunc) =>
% 88.47/26.73 ((
% 88.47/26.73 (ap2p) =>
% 88.47/26.73 ((
% 88.47/26.73 (funcinfuncset) =>
% 88.47/26.73 ((
% 88.47/26.73 (lamProp) =>
% 88.47/26.73 ((
% 88.47/26.73 (lamp) =>
% 88.47/26.73 ((
% 88.47/26.73 (lam2p) =>
% 88.47/26.73 ((
% 88.47/26.73 (brelnall1) =>
% 88.47/26.73 ((
% 88.47/26.73 (brelnall2) =>
% 88.47/26.73 ((
% 88.47/26.73 (!!) @ (
% 88.47/26.73 (('#B') @ (
% 88.47/26.73 !!) @
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ('#S') @ (
% 88.47/26.73 (
% 88.47/26.73 ('#B') @ (
% 88.47/26.73 '#S') @
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ('#B') @ (
% 88.47/26.73 (
% 88.47/26.73 ('#B') @ (
% 88.47/26.73 =>))) @
% 88.47/26.73 ex1)))) @
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ('#B') @ (
% 88.47/26.73 (
% 88.47/26.73 ('#B') @ (
% 88.47/26.73 !!))) @
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ('#S') @ (
% 88.47/26.73 (
% 88.47/26.73 ('#B') @ (
% 88.47/26.73 '#B') @
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ('#B') @ (
% 88.47/26.73 '#S') @
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ('#B') @ (
% 88.47/26.73 (
% 88.47/26.73 ('#B') @ (
% 88.47/26.73 =>))) @
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ('#C') @ in)))))))) @
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ('#B') @ (
% 88.47/26.73 (
% 88.47/26.73 ('#B') @ (
% 88.47/26.73 (
% 88.47/26.73 ('#B') @ (
% 88.47/26.73 !!))))) @
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ('#C') @ (
% 88.47/26.73 (
% 88.47/26.73 ('#B') @ (
% 88.47/26.73 '#B') @
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ('#B') @ (
% 88.47/26.73 '#B') @
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ('#B') @ (
% 88.47/26.73 '#S') @
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ('#B') @ (
% 88.47/26.73 (
% 88.47/26.73 ('#B') @ (
% 88.47/26.73 =>))) @
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ('#C') @ in)))))))))) @
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ('#S') @ (
% 88.47/26.73 (
% 88.47/26.73 ('#B') @ (
% 88.47/26.73 '#S') @
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ('#B') @ (
% 88.47/26.73 (
% 88.47/26.73 ('#B') @ (
% 88.47/26.73 '#B'))) @
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ('#B') @ (
% 88.47/26.73 =>))))))) @
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ('#C') @ (
% 88.47/26.73 (
% 88.47/26.73 ('#B') @ (
% 88.47/26.73 '#B') @
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ('#B') @ (
% 88.47/26.73 '#S') @
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ('#B') @ (
% 88.47/26.73 =>))))))) @
% 88.47/26.73 (
% 88.47/26.73 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 88.47/26.73 inference('lams2combs', [status(thm)], [zip_derived_cl0])).
% 88.47/26.73 thf(omega0Ax, axiom,(( omega0Ax ) = ((in @ emptyset @ omega)))).
% 88.47/26.73 thf('0', plain, (( omega0Ax ) = ( in @ emptyset @ omega )),
% 88.47/26.73 define([status(thm)])).
% 88.47/26.73 thf(emptyinunitempty, axiom,(( emptyinunitempty ) =
% 88.47/26.73 ((in @ emptyset @ (setadjoin @ emptyset @ emptyset))))).
% 88.47/26.73 thf('1', plain,
% 88.47/26.73 (( emptyinunitempty ) =
% 88.47/26.73 ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )),
% 88.47/26.73 define([status(thm)])).
% 88.47/26.73 thf(emptyset__Cong, axiom,(( emptyset__Cong ) =
% 88.47/26.73 ((((emptyset) = (emptyset)))))).
% 88.47/26.73 thf('2', plain, (( emptyset__Cong ) = ( ( emptyset ) = ( emptyset ) )),
% 88.47/26.73 define([status(thm)])).
% 88.47/26.73 thf(omega__Cong, axiom,(( omega__Cong ) = ((((omega) = (omega)))))).
% 88.47/26.73 thf('3', plain, (( omega__Cong ) = ( ( omega ) = ( omega ) )),
% 88.47/26.73 define([status(thm)])).
% 88.47/26.73 thf(zip_derived_cl2, plain,
% 88.47/26.73 (~ (((setextAx) =>
% 88.47/26.73 (((emptysetAx) =>
% 88.47/26.73 (((setadjoinAx) =>
% 88.47/26.73 (((powersetAx) =>
% 88.47/26.73 (((setunionAx) =>
% 88.47/26.73 (((in @ emptyset @ omega) =>
% 88.47/26.73 (((omegaSAx) =>
% 88.47/26.73 (((omegaIndAx) =>
% 88.47/26.73 (((replAx) =>
% 88.47/26.73 (((foundationAx) =>
% 88.47/26.73 (((wellorderingAx) =>
% 88.47/26.73 (((descrp) =>
% 88.47/26.73 (((dsetconstrI) =>
% 88.47/26.73 (((dsetconstrEL) =>
% 88.47/26.73 (((dsetconstrER) =>
% 88.47/26.73 (((exuE1) =>
% 88.47/26.73 (((prop2setE) =>
% 88.47/26.73 (((emptysetE) =>
% 88.47/26.73 (((emptysetimpfalse) =>
% 88.47/26.73 (((notinemptyset) =>
% 88.47/26.73 (((exuE3e) =>
% 88.47/26.73 (((setext) =>
% 88.47/26.73 (((emptyI) =>
% 88.47/26.73 (((noeltsimpempty) =>
% 88.47/26.73 (((setbeta) =>
% 88.47/26.73 (((nonemptyE1) =>
% 88.47/26.73 (((nonemptyI) =>
% 88.47/26.73 (((nonemptyI1) =>
% 88.47/26.73 (((setadjoinIL) =>
% 88.47/26.73 (((in @
% 88.47/26.73 emptyset @
% 88.47/26.73 (setadjoin @
% 88.47/26.73 emptyset @
% 88.47/26.73 emptyset)) =>
% 88.47/26.73 ((
% 88.47/26.73 (setadjoinIR) =>
% 88.47/26.73 ((
% 88.47/26.73 (setadjoinE) =>
% 88.47/26.73 ((
% 88.47/26.73 (setadjoinOr) =>
% 88.47/26.73 ((
% 88.47/26.73 (setoftrueEq) =>
% 88.47/26.73 ((
% 88.47/26.73 (powersetI) =>
% 88.47/26.73 ((
% 88.47/26.73 (emptyinPowerset) =>
% 88.47/26.73 ((
% 88.47/26.73 (emptyInPowerset) =>
% 88.47/26.73 ((
% 88.47/26.73 (powersetE) =>
% 88.47/26.73 ((
% 88.47/26.73 (setunionI) =>
% 88.47/26.73 ((
% 88.47/26.73 (setunionE) =>
% 88.47/26.73 ((
% 88.47/26.73 (subPowSU) =>
% 88.47/26.73 ((
% 88.47/26.73 (exuE2) =>
% 88.47/26.73 ((
% 88.47/26.73 (nonemptyImpWitness) =>
% 88.47/26.73 ((
% 88.47/26.73 (uniqinunit) =>
% 88.47/26.73 ((
% 88.47/26.73 (notinsingleton) =>
% 88.47/26.73 ((
% 88.47/26.73 (eqinunit) =>
% 88.47/26.73 ((
% 88.47/26.73 (singletonsswitch) =>
% 88.47/26.73 ((
% 88.47/26.73 (upairsetE) =>
% 88.47/26.73 ((
% 88.47/26.73 (upairsetIL) =>
% 88.47/26.73 ((
% 88.47/26.73 (upairsetIR) =>
% 88.47/26.73 ((
% 88.47/26.73 (emptyE1) =>
% 88.47/26.73 ((
% 88.47/26.73 (vacuousDall) =>
% 88.47/26.73 ((
% 88.47/26.73 (quantDeMorgan1) =>
% 88.47/26.73 ((
% 88.47/26.73 (quantDeMorgan2) =>
% 88.47/26.73 ((
% 88.47/26.73 (quantDeMorgan3) =>
% 88.47/26.73 ((
% 88.47/26.73 (quantDeMorgan4) =>
% 88.47/26.73 ((
% 88.47/26.73 (prop2setI) =>
% 88.47/26.73 ((
% 88.47/26.73 (prop2set2propI) =>
% 88.47/26.73 ((
% 88.47/26.73 (notdexE) =>
% 88.47/26.73 ((
% 88.47/26.73 (notdallE) =>
% 88.47/26.73 ((
% 88.47/26.73 (exuI1) =>
% 88.47/26.73 ((
% 88.47/26.73 (exuI3) =>
% 88.47/26.73 ((
% 88.47/26.73 (exuI2) =>
% 88.47/26.73 ((
% 88.47/26.73 (inCongP) =>
% 88.47/26.73 ((
% 88.47/26.73 (in__Cong) =>
% 88.47/26.73 ((
% 88.47/26.73 (exuE3u) =>
% 88.47/26.73 ((
% 88.47/26.73 (exu__Cong) =>
% 88.47/26.73 ((
% 88.47/26.73 ((
% 88.47/26.73 (emptyset) =
% 88.47/26.73 (emptyset))) =>
% 88.47/26.73 ((
% 88.47/26.73 (setadjoin__Cong) =>
% 88.47/26.73 ((
% 88.47/26.73 (powerset__Cong) =>
% 88.47/26.73 ((
% 88.47/26.73 (setunion__Cong) =>
% 88.47/26.73 ((
% 88.47/26.73 ((
% 88.47/26.73 (omega) =
% 88.47/26.73 (omega))) =>
% 88.47/26.73 ((
% 88.47/26.73 (exuEu) =>
% 88.47/26.73 ((
% 88.47/26.73 (descr__Cong) =>
% 88.47/26.73 ((
% 88.47/26.73 (dsetconstr__Cong) =>
% 88.47/26.73 ((
% 88.47/26.73 (subsetI1) =>
% 88.47/26.73 ((
% 88.47/26.73 (eqimpsubset2) =>
% 88.47/26.73 ((
% 88.47/26.73 (eqimpsubset1) =>
% 88.47/26.73 ((
% 88.47/26.73 (subsetI2) =>
% 88.47/26.73 ((
% 88.47/26.73 (emptysetsubset) =>
% 88.47/26.73 ((
% 88.47/26.73 (subsetE) =>
% 88.47/26.73 ((
% 88.47/26.73 (subsetE2) =>
% 88.47/26.73 ((
% 88.47/26.73 (notsubsetI) =>
% 88.47/26.73 ((
% 88.47/26.73 (notequalI1) =>
% 88.47/26.73 ((
% 88.47/26.73 (notequalI2) =>
% 88.47/26.73 ((
% 88.47/26.73 (subsetRefl) =>
% 88.47/26.73 ((
% 88.47/26.73 (subsetTrans) =>
% 88.47/26.73 ((
% 88.47/26.73 (setadjoinSub) =>
% 88.47/26.73 ((
% 88.47/26.73 (setadjoinSub2) =>
% 88.47/26.73 ((
% 88.47/26.73 (subset2powerset) =>
% 88.47/26.73 ((
% 88.47/26.73 (setextsub) =>
% 88.47/26.73 ((
% 88.47/26.73 (subsetemptysetimpeq) =>
% 88.47/26.73 ((
% 88.47/26.73 (powersetI1) =>
% 88.47/26.73 ((
% 88.47/26.73 (powersetE1) =>
% 88.47/26.73 ((
% 88.47/26.73 (inPowerset) =>
% 88.47/26.73 ((
% 88.47/26.73 (powersetsubset) =>
% 88.47/26.73 ((
% 88.47/26.73 (sepInPowerset) =>
% 88.47/26.73 ((
% 88.47/26.73 (sepSubset) =>
% 88.47/26.73 ((
% 88.47/26.73 (binunionIL) =>
% 88.47/26.73 ((
% 88.47/26.73 (upairset2IR) =>
% 88.47/26.73 ((
% 88.47/26.73 (binunionIR) =>
% 88.47/26.73 ((
% 88.47/26.73 (binunionEcases) =>
% 88.47/26.73 ((
% 88.47/26.73 (binunionE) =>
% 88.47/26.73 ((
% 88.47/26.73 (binunionLsub) =>
% 88.47/26.73 ((
% 88.47/26.73 (binunionRsub) =>
% 88.47/26.73 ((
% 88.47/26.73 (binintersectI) =>
% 88.47/26.73 ((
% 88.47/26.73 (binintersectSubset5) =>
% 88.47/26.73 ((
% 88.47/26.73 (binintersectEL) =>
% 88.47/26.73 ((
% 88.47/26.73 (binintersectLsub) =>
% 88.47/26.73 ((
% 88.47/26.73 (binintersectSubset2) =>
% 88.47/26.73 ((
% 88.47/26.73 (binintersectSubset3) =>
% 88.47/26.73 ((
% 88.47/26.73 (binintersectER) =>
% 88.47/26.73 ((
% 88.47/26.73 (disjointsetsI1) =>
% 88.47/26.73 ((
% 88.47/26.73 (binintersectRsub) =>
% 88.47/26.73 ((
% 88.47/26.73 (binintersectSubset4) =>
% 88.47/26.73 ((
% 88.47/26.73 (binintersectSubset1) =>
% 88.47/26.73 ((
% 88.47/26.73 (bs114d) =>
% 88.47/26.73 ((
% 88.47/26.73 (setminusI) =>
% 88.47/26.73 ((
% 88.47/26.73 (setminusEL) =>
% 88.47/26.73 ((
% 88.47/26.73 (setminusER) =>
% 88.47/26.73 ((
% 88.47/26.73 (setminusSubset2) =>
% 88.47/26.73 ((
% 88.47/26.73 (setminusERneg) =>
% 88.47/26.73 ((
% 88.47/26.73 (setminusELneg) =>
% 88.47/26.73 ((
% 88.47/26.73 (setminusILneg) =>
% 88.47/26.73 ((
% 88.47/26.73 (setminusIRneg) =>
% 88.47/26.73 ((
% 88.47/26.73 (setminusLsub) =>
% 88.47/26.73 ((
% 88.47/26.73 (setminusSubset1) =>
% 88.47/26.73 ((
% 88.47/26.73 (symdiffE) =>
% 88.47/26.73 ((
% 88.47/26.73 (symdiffI1) =>
% 88.47/26.73 ((
% 88.47/26.73 (symdiffI2) =>
% 88.47/26.73 ((
% 88.47/26.73 (symdiffIneg1) =>
% 88.47/26.73 ((
% 88.47/26.73 (symdiffIneg2) =>
% 88.47/26.73 ((
% 88.47/26.73 (secondinupair) =>
% 88.47/26.73 ((
% 88.47/26.73 (setukpairIL) =>
% 88.47/26.73 ((
% 88.47/26.73 (setukpairIR) =>
% 88.47/26.73 ((
% 88.47/26.73 (kpairiskpair) =>
% 88.47/26.73 ((
% 88.47/26.73 (kpairp) =>
% 88.47/26.73 ((
% 88.47/26.73 (singletonsubset) =>
% 88.47/26.73 ((
% 88.47/26.73 (singletoninpowerset) =>
% 88.47/26.73 ((
% 88.47/26.73 (singletoninpowunion) =>
% 88.47/26.73 ((
% 88.47/26.73 (upairset2E) =>
% 88.47/26.73 ((
% 88.47/26.73 (upairsubunion) =>
% 88.47/26.73 ((
% 88.47/26.73 (upairinpowunion) =>
% 88.47/26.73 ((
% 88.47/26.73 (ubforcartprodlem1) =>
% 88.47/26.73 ((
% 88.47/26.73 (ubforcartprodlem2) =>
% 88.47/26.73 ((
% 88.47/26.73 (ubforcartprodlem3) =>
% 88.47/26.73 ((
% 88.47/26.73 (cartprodpairin) =>
% 88.47/26.73 ((
% 88.47/26.73 (cartprodmempair1) =>
% 88.47/26.73 ((
% 88.47/26.73 (cartprodmempair) =>
% 88.47/26.73 ((
% 88.47/26.73 (setunionE2) =>
% 88.47/26.73 ((
% 88.47/26.73 (setunionsingleton1) =>
% 88.47/26.73 ((
% 88.47/26.73 (setunionsingleton2) =>
% 88.47/26.73 ((
% 88.47/26.73 (setunionsingleton) =>
% 88.47/26.73 ((
% 88.47/26.73 (singletonprop) =>
% 88.47/26.73 ((
% 88.47/26.73 (ex1E1) =>
% 88.47/26.73 ((
% 88.47/26.73 (ex1I) =>
% 88.47/26.73 ((
% 88.47/26.73 (ex1I2) =>
% 88.47/26.73 ((
% 88.47/26.73 (singletonsuniq) =>
% 88.47/26.73 ((
% 88.47/26.73 (setukpairinjL1) =>
% 88.47/26.73 ((
% 88.47/26.73 (kfstsingleton) =>
% 88.47/26.73 ((
% 88.47/26.73 (theprop) =>
% 88.47/26.73 ((
% 88.47/26.73 (kfstpairEq) =>
% 88.47/26.73 ((
% 88.47/26.73 (cartprodfstin) =>
% 88.47/26.73 ((
% 88.47/26.73 (setukpairinjL2) =>
% 88.47/26.73 ((
% 88.47/26.73 (setukpairinjL) =>
% 88.47/26.73 ((
% 88.47/26.73 (setukpairinjR11) =>
% 88.47/26.73 ((
% 88.47/26.73 (setukpairinjR12) =>
% 88.47/26.73 ((
% 88.47/26.73 (setukpairinjR1) =>
% 88.47/26.73 ((
% 88.47/26.73 (upairequniteq) =>
% 88.47/26.73 ((
% 88.47/26.73 (setukpairinjR2) =>
% 88.47/26.73 ((
% 88.47/26.73 (setukpairinjR) =>
% 88.47/26.73 ((
% 88.47/26.73 (ksndsingleton) =>
% 88.47/26.73 ((
% 88.47/26.73 (ksndpairEq) =>
% 88.47/26.73 ((
% 88.47/26.73 (kpairsurjEq) =>
% 88.47/26.73 ((
% 88.47/26.73 (cartprodsndin) =>
% 88.47/26.73 ((
% 88.47/26.73 (cartprodpairmemEL) =>
% 88.47/26.73 ((
% 88.47/26.73 (cartprodpairmemER) =>
% 88.47/26.73 ((
% 88.47/26.73 (cartprodmempaircEq) =>
% 88.47/26.73 ((
% 88.47/26.73 (cartprodfstpairEq) =>
% 88.47/26.73 ((
% 88.47/26.73 (cartprodsndpairEq) =>
% 88.47/26.73 ((
% 88.47/26.73 (cartprodpairsurjEq) =>
% 88.47/26.73 ((
% 88.47/26.73 (dpsetconstrI) =>
% 88.47/26.73 ((
% 88.47/26.73 (dpsetconstrSub) =>
% 88.47/26.73 ((
% 88.47/26.73 (setOfPairsIsBReln) =>
% 88.47/26.73 ((
% 88.47/26.73 (dpsetconstrERa) =>
% 88.47/26.73 ((
% 88.47/26.73 (dpsetconstrEL1) =>
% 88.47/26.73 ((
% 88.47/26.73 (dpsetconstrEL2) =>
% 88.47/26.73 ((
% 88.47/26.73 (dpsetconstrER) =>
% 88.47/26.73 ((
% 88.47/26.73 (funcImageSingleton) =>
% 88.47/26.73 ((
% 88.47/26.73 (apProp) =>
% 88.47/26.73 ((
% 88.47/26.73 (app) =>
% 88.47/26.73 ((
% 88.47/26.73 (infuncsetfunc) =>
% 88.47/26.73 ((
% 88.47/26.73 (ap2p) =>
% 88.47/26.73 ((
% 88.47/26.73 (funcinfuncset) =>
% 88.47/26.73 ((
% 88.47/26.73 (lamProp) =>
% 88.47/26.73 ((
% 88.47/26.73 (lamp) =>
% 88.47/26.73 ((
% 88.47/26.73 (lam2p) =>
% 88.47/26.73 ((
% 88.47/26.73 (brelnall1) =>
% 88.47/26.73 ((
% 88.47/26.73 (brelnall2) =>
% 88.47/26.73 ((
% 88.47/26.73 (!!) @ (
% 88.47/26.73 (('#B') @ (
% 88.47/26.73 !!) @
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ('#S') @ (
% 88.47/26.73 (
% 88.47/26.73 ('#B') @ (
% 88.47/26.73 '#S') @
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ('#B') @ (
% 88.47/26.73 (
% 88.47/26.73 ('#B') @ (
% 88.47/26.73 =>))) @
% 88.47/26.73 ex1)))) @
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ('#B') @ (
% 88.47/26.73 (
% 88.47/26.73 ('#B') @ (
% 88.47/26.73 !!))) @
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ('#S') @ (
% 88.47/26.73 (
% 88.47/26.73 ('#B') @ (
% 88.47/26.73 '#B') @
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ('#B') @ (
% 88.47/26.73 '#S') @
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ('#B') @ (
% 88.47/26.73 (
% 88.47/26.73 ('#B') @ (
% 88.47/26.73 =>))) @
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ('#C') @ in)))))))) @
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ('#B') @ (
% 88.47/26.73 (
% 88.47/26.73 ('#B') @ (
% 88.47/26.73 (
% 88.47/26.73 ('#B') @ (
% 88.47/26.73 !!))))) @
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ('#C') @ (
% 88.47/26.73 (
% 88.47/26.73 ('#B') @ (
% 88.47/26.73 '#B') @
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ('#B') @ (
% 88.47/26.73 '#B') @
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ('#B') @ (
% 88.47/26.73 '#S') @
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ('#B') @ (
% 88.47/26.73 (
% 88.47/26.73 ('#B') @ (
% 88.47/26.73 =>))) @
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ('#C') @ in)))))))))) @
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ('#S') @ (
% 88.47/26.73 (
% 88.47/26.73 ('#B') @ (
% 88.47/26.73 '#S') @
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ('#B') @ (
% 88.47/26.73 (
% 88.47/26.73 ('#B') @ (
% 88.47/26.73 '#B'))) @
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ('#B') @ (
% 88.47/26.73 =>))))))) @
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ('#C') @ (
% 88.47/26.73 (
% 88.47/26.73 ('#B') @ (
% 88.47/26.73 '#B') @
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ('#B') @ (
% 88.47/26.73 '#S') @
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ('#B') @ (
% 88.47/26.73 =>))))))) @
% 88.47/26.73 (
% 88.47/26.73 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 88.47/26.73 inference('rw', [status(thm)], [zip_derived_cl1, '0', '1', '2', '3'])).
% 88.47/26.73 thf(zip_derived_cl3, plain,
% 88.47/26.73 (~ (((setextAx) =>
% 88.47/26.73 (((emptysetAx) =>
% 88.47/26.73 (((setadjoinAx) =>
% 88.47/26.73 (((powersetAx) =>
% 88.47/26.73 (((setunionAx) =>
% 88.47/26.73 (((in @ emptyset @ omega) =>
% 88.47/26.73 (((omegaSAx) =>
% 88.47/26.73 (((omegaIndAx) =>
% 88.47/26.73 (((replAx) =>
% 88.47/26.73 (((foundationAx) =>
% 88.47/26.73 (((wellorderingAx) =>
% 88.47/26.73 (((descrp) =>
% 88.47/26.73 (((dsetconstrI) =>
% 88.47/26.73 (((dsetconstrEL) =>
% 88.47/26.73 (((dsetconstrER) =>
% 88.47/26.73 (((exuE1) =>
% 88.47/26.73 (((prop2setE) =>
% 88.47/26.73 (((emptysetE) =>
% 88.47/26.73 (((emptysetimpfalse) =>
% 88.47/26.73 (((notinemptyset) =>
% 88.47/26.73 (((exuE3e) =>
% 88.47/26.73 (((setext) =>
% 88.47/26.73 (((emptyI) =>
% 88.47/26.73 (((noeltsimpempty) =>
% 88.47/26.73 (((setbeta) =>
% 88.47/26.73 (((nonemptyE1) =>
% 88.47/26.73 (((nonemptyI) =>
% 88.47/26.73 (((nonemptyI1) =>
% 88.47/26.73 (((setadjoinIL) =>
% 88.47/26.73 (((in @
% 88.47/26.73 emptyset @
% 88.47/26.73 (setadjoin @
% 88.47/26.73 emptyset @
% 88.47/26.73 emptyset)) =>
% 88.47/26.73 ((
% 88.47/26.73 (setadjoinIR) =>
% 88.47/26.73 ((
% 88.47/26.73 (setadjoinE) =>
% 88.47/26.73 ((
% 88.47/26.73 (setadjoinOr) =>
% 88.47/26.73 ((
% 88.47/26.73 (setoftrueEq) =>
% 88.47/26.73 ((
% 88.47/26.73 (powersetI) =>
% 88.47/26.73 ((
% 88.47/26.73 (emptyinPowerset) =>
% 88.47/26.73 ((
% 88.47/26.73 (emptyInPowerset) =>
% 88.47/26.73 ((
% 88.47/26.73 (powersetE) =>
% 88.47/26.73 ((
% 88.47/26.73 (setunionI) =>
% 88.47/26.73 ((
% 88.47/26.73 (setunionE) =>
% 88.47/26.73 ((
% 88.47/26.73 (subPowSU) =>
% 88.47/26.73 ((
% 88.47/26.73 (exuE2) =>
% 88.47/26.73 ((
% 88.47/26.73 (nonemptyImpWitness) =>
% 88.47/26.73 ((
% 88.47/26.73 (uniqinunit) =>
% 88.47/26.73 ((
% 88.47/26.73 (notinsingleton) =>
% 88.47/26.73 ((
% 88.47/26.73 (eqinunit) =>
% 88.47/26.73 ((
% 88.47/26.73 (singletonsswitch) =>
% 88.47/26.73 ((
% 88.47/26.73 (upairsetE) =>
% 88.47/26.73 ((
% 88.47/26.73 (upairsetIL) =>
% 88.47/26.73 ((
% 88.47/26.73 (upairsetIR) =>
% 88.47/26.73 ((
% 88.47/26.73 (emptyE1) =>
% 88.47/26.73 ((
% 88.47/26.73 (vacuousDall) =>
% 88.47/26.73 ((
% 88.47/26.73 (quantDeMorgan1) =>
% 88.47/26.73 ((
% 88.47/26.73 (quantDeMorgan2) =>
% 88.47/26.73 ((
% 88.47/26.73 (quantDeMorgan3) =>
% 88.47/26.73 ((
% 88.47/26.73 (quantDeMorgan4) =>
% 88.47/26.73 ((
% 88.47/26.73 (prop2setI) =>
% 88.47/26.73 ((
% 88.47/26.73 (prop2set2propI) =>
% 88.47/26.73 ((
% 88.47/26.73 (notdexE) =>
% 88.47/26.73 ((
% 88.47/26.73 (notdallE) =>
% 88.47/26.73 ((
% 88.47/26.73 (exuI1) =>
% 88.47/26.73 ((
% 88.47/26.73 (exuI3) =>
% 88.47/26.73 ((
% 88.47/26.73 (exuI2) =>
% 88.47/26.73 ((
% 88.47/26.73 (inCongP) =>
% 88.47/26.73 ((
% 88.47/26.73 (in__Cong) =>
% 88.47/26.73 ((
% 88.47/26.73 (exuE3u) =>
% 88.47/26.73 ((
% 88.47/26.73 (exu__Cong) =>
% 88.47/26.73 ((
% 88.47/26.73 (setadjoin__Cong) =>
% 88.47/26.73 ((
% 88.47/26.73 (powerset__Cong) =>
% 88.47/26.73 ((
% 88.47/26.73 (setunion__Cong) =>
% 88.47/26.73 ((
% 88.47/26.73 (exuEu) =>
% 88.47/26.73 ((
% 88.47/26.73 (descr__Cong) =>
% 88.47/26.73 ((
% 88.47/26.73 (dsetconstr__Cong) =>
% 88.47/26.73 ((
% 88.47/26.73 (subsetI1) =>
% 88.47/26.73 ((
% 88.47/26.73 (eqimpsubset2) =>
% 88.47/26.73 ((
% 88.47/26.73 (eqimpsubset1) =>
% 88.47/26.73 ((
% 88.47/26.73 (subsetI2) =>
% 88.47/26.73 ((
% 88.47/26.73 (emptysetsubset) =>
% 88.47/26.73 ((
% 88.47/26.73 (subsetE) =>
% 88.47/26.73 ((
% 88.47/26.73 (subsetE2) =>
% 88.47/26.73 ((
% 88.47/26.73 (notsubsetI) =>
% 88.47/26.73 ((
% 88.47/26.73 (notequalI1) =>
% 88.47/26.73 ((
% 88.47/26.73 (notequalI2) =>
% 88.47/26.73 ((
% 88.47/26.73 (subsetRefl) =>
% 88.47/26.73 ((
% 88.47/26.73 (subsetTrans) =>
% 88.47/26.73 ((
% 88.47/26.73 (setadjoinSub) =>
% 88.47/26.73 ((
% 88.47/26.73 (setadjoinSub2) =>
% 88.47/26.73 ((
% 88.47/26.73 (subset2powerset) =>
% 88.47/26.73 ((
% 88.47/26.73 (setextsub) =>
% 88.47/26.73 ((
% 88.47/26.73 (subsetemptysetimpeq) =>
% 88.47/26.73 ((
% 88.47/26.73 (powersetI1) =>
% 88.47/26.73 ((
% 88.47/26.73 (powersetE1) =>
% 88.47/26.73 ((
% 88.47/26.73 (inPowerset) =>
% 88.47/26.73 ((
% 88.47/26.73 (powersetsubset) =>
% 88.47/26.73 ((
% 88.47/26.73 (sepInPowerset) =>
% 88.47/26.73 ((
% 88.47/26.73 (sepSubset) =>
% 88.47/26.73 ((
% 88.47/26.73 (binunionIL) =>
% 88.47/26.73 ((
% 88.47/26.73 (upairset2IR) =>
% 88.47/26.73 ((
% 88.47/26.73 (binunionIR) =>
% 88.47/26.73 ((
% 88.47/26.73 (binunionEcases) =>
% 88.47/26.73 ((
% 88.47/26.73 (binunionE) =>
% 88.47/26.73 ((
% 88.47/26.73 (binunionLsub) =>
% 88.47/26.73 ((
% 88.47/26.73 (binunionRsub) =>
% 88.47/26.73 ((
% 88.47/26.73 (binintersectI) =>
% 88.47/26.73 ((
% 88.47/26.73 (binintersectSubset5) =>
% 88.47/26.73 ((
% 88.47/26.73 (binintersectEL) =>
% 88.47/26.73 ((
% 88.47/26.73 (binintersectLsub) =>
% 88.47/26.73 ((
% 88.47/26.73 (binintersectSubset2) =>
% 88.47/26.73 ((
% 88.47/26.73 (binintersectSubset3) =>
% 88.47/26.73 ((
% 88.47/26.73 (binintersectER) =>
% 88.47/26.73 ((
% 88.47/26.73 (disjointsetsI1) =>
% 88.47/26.73 ((
% 88.47/26.73 (binintersectRsub) =>
% 88.47/26.73 ((
% 88.47/26.73 (binintersectSubset4) =>
% 88.47/26.73 ((
% 88.47/26.73 (binintersectSubset1) =>
% 88.47/26.73 ((
% 88.47/26.73 (bs114d) =>
% 88.47/26.73 ((
% 88.47/26.73 (setminusI) =>
% 88.47/26.73 ((
% 88.47/26.73 (setminusEL) =>
% 88.47/26.73 ((
% 88.47/26.73 (setminusER) =>
% 88.47/26.73 ((
% 88.47/26.73 (setminusSubset2) =>
% 88.47/26.73 ((
% 88.47/26.73 (setminusERneg) =>
% 88.47/26.73 ((
% 88.47/26.73 (setminusELneg) =>
% 88.47/26.73 ((
% 88.47/26.73 (setminusILneg) =>
% 88.47/26.73 ((
% 88.47/26.73 (setminusIRneg) =>
% 88.47/26.73 ((
% 88.47/26.73 (setminusLsub) =>
% 88.47/26.73 ((
% 88.47/26.73 (setminusSubset1) =>
% 88.47/26.73 ((
% 88.47/26.73 (symdiffE) =>
% 88.47/26.73 ((
% 88.47/26.73 (symdiffI1) =>
% 88.47/26.73 ((
% 88.47/26.73 (symdiffI2) =>
% 88.47/26.73 ((
% 88.47/26.73 (symdiffIneg1) =>
% 88.47/26.73 ((
% 88.47/26.73 (symdiffIneg2) =>
% 88.47/26.73 ((
% 88.47/26.73 (secondinupair) =>
% 88.47/26.73 ((
% 88.47/26.73 (setukpairIL) =>
% 88.47/26.73 ((
% 88.47/26.73 (setukpairIR) =>
% 88.47/26.73 ((
% 88.47/26.73 (kpairiskpair) =>
% 88.47/26.73 ((
% 88.47/26.73 (kpairp) =>
% 88.47/26.73 ((
% 88.47/26.73 (singletonsubset) =>
% 88.47/26.73 ((
% 88.47/26.73 (singletoninpowerset) =>
% 88.47/26.73 ((
% 88.47/26.73 (singletoninpowunion) =>
% 88.47/26.73 ((
% 88.47/26.73 (upairset2E) =>
% 88.47/26.73 ((
% 88.47/26.73 (upairsubunion) =>
% 88.47/26.73 ((
% 88.47/26.73 (upairinpowunion) =>
% 88.47/26.73 ((
% 88.47/26.73 (ubforcartprodlem1) =>
% 88.47/26.73 ((
% 88.47/26.73 (ubforcartprodlem2) =>
% 88.47/26.73 ((
% 88.47/26.73 (ubforcartprodlem3) =>
% 88.47/26.73 ((
% 88.47/26.73 (cartprodpairin) =>
% 88.47/26.73 ((
% 88.47/26.73 (cartprodmempair1) =>
% 88.47/26.73 ((
% 88.47/26.73 (cartprodmempair) =>
% 88.47/26.73 ((
% 88.47/26.73 (setunionE2) =>
% 88.47/26.73 ((
% 88.47/26.73 (setunionsingleton1) =>
% 88.47/26.73 ((
% 88.47/26.73 (setunionsingleton2) =>
% 88.47/26.73 ((
% 88.47/26.73 (setunionsingleton) =>
% 88.47/26.73 ((
% 88.47/26.73 (singletonprop) =>
% 88.47/26.73 ((
% 88.47/26.73 (ex1E1) =>
% 88.47/26.73 ((
% 88.47/26.73 (ex1I) =>
% 88.47/26.73 ((
% 88.47/26.73 (ex1I2) =>
% 88.47/26.73 ((
% 88.47/26.73 (singletonsuniq) =>
% 88.47/26.73 ((
% 88.47/26.73 (setukpairinjL1) =>
% 88.47/26.73 ((
% 88.47/26.73 (kfstsingleton) =>
% 88.47/26.73 ((
% 88.47/26.73 (theprop) =>
% 88.47/26.73 ((
% 88.47/26.73 (kfstpairEq) =>
% 88.47/26.73 ((
% 88.47/26.73 (cartprodfstin) =>
% 88.47/26.73 ((
% 88.47/26.73 (setukpairinjL2) =>
% 88.47/26.73 ((
% 88.47/26.73 (setukpairinjL) =>
% 88.47/26.73 ((
% 88.47/26.73 (setukpairinjR11) =>
% 88.47/26.73 ((
% 88.47/26.73 (setukpairinjR12) =>
% 88.47/26.73 ((
% 88.47/26.73 (setukpairinjR1) =>
% 88.47/26.73 ((
% 88.47/26.73 (upairequniteq) =>
% 88.47/26.73 ((
% 88.47/26.73 (setukpairinjR2) =>
% 88.47/26.73 ((
% 88.47/26.73 (setukpairinjR) =>
% 88.47/26.73 ((
% 88.47/26.73 (ksndsingleton) =>
% 88.47/26.73 ((
% 88.47/26.73 (ksndpairEq) =>
% 88.47/26.73 ((
% 88.47/26.73 (kpairsurjEq) =>
% 88.47/26.73 ((
% 88.47/26.73 (cartprodsndin) =>
% 88.47/26.73 ((
% 88.47/26.73 (cartprodpairmemEL) =>
% 88.47/26.73 ((
% 88.47/26.73 (cartprodpairmemER) =>
% 88.47/26.73 ((
% 88.47/26.73 (cartprodmempaircEq) =>
% 88.47/26.73 ((
% 88.47/26.73 (cartprodfstpairEq) =>
% 88.47/26.73 ((
% 88.47/26.73 (cartprodsndpairEq) =>
% 88.47/26.73 ((
% 88.47/26.73 (cartprodpairsurjEq) =>
% 88.47/26.73 ((
% 88.47/26.73 (dpsetconstrI) =>
% 88.47/26.73 ((
% 88.47/26.73 (dpsetconstrSub) =>
% 88.47/26.73 ((
% 88.47/26.73 (setOfPairsIsBReln) =>
% 88.47/26.73 ((
% 88.47/26.73 (dpsetconstrERa) =>
% 88.47/26.73 ((
% 88.47/26.73 (dpsetconstrEL1) =>
% 88.47/26.73 ((
% 88.47/26.73 (dpsetconstrEL2) =>
% 88.47/26.73 ((
% 88.47/26.73 (dpsetconstrER) =>
% 88.47/26.73 ((
% 88.47/26.73 (funcImageSingleton) =>
% 88.47/26.73 ((
% 88.47/26.73 (apProp) =>
% 88.47/26.73 ((
% 88.47/26.73 (app) =>
% 88.47/26.73 ((
% 88.47/26.73 (infuncsetfunc) =>
% 88.47/26.73 ((
% 88.47/26.73 (ap2p) =>
% 88.47/26.73 ((
% 88.47/26.73 (funcinfuncset) =>
% 88.47/26.73 ((
% 88.47/26.73 (lamProp) =>
% 88.47/26.73 ((
% 88.47/26.73 (lamp) =>
% 88.47/26.73 ((
% 88.47/26.73 (lam2p) =>
% 88.47/26.73 ((
% 88.47/26.73 (brelnall1) =>
% 88.47/26.73 ((
% 88.47/26.73 (brelnall2) =>
% 88.47/26.73 ((
% 88.47/26.73 (!!) @ (
% 88.47/26.73 (('#B') @ (
% 88.47/26.73 !!) @
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ('#S') @ (
% 88.47/26.73 (
% 88.47/26.73 ('#B') @ (
% 88.47/26.73 '#S') @
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ('#B') @ (
% 88.47/26.73 (
% 88.47/26.73 ('#B') @ (
% 88.47/26.73 =>))) @
% 88.47/26.73 ex1)))) @
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ('#B') @ (
% 88.47/26.73 (
% 88.47/26.73 ('#B') @ (
% 88.47/26.73 !!))) @
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ('#S') @ (
% 88.47/26.73 (
% 88.47/26.73 ('#B') @ (
% 88.47/26.73 '#B') @
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ('#B') @ (
% 88.47/26.73 '#S') @
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ('#B') @ (
% 88.47/26.73 (
% 88.47/26.73 ('#B') @ (
% 88.47/26.73 =>))) @
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ('#C') @ in)))))))) @
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ('#B') @ (
% 88.47/26.73 (
% 88.47/26.73 ('#B') @ (
% 88.47/26.73 (
% 88.47/26.73 ('#B') @ (
% 88.47/26.73 !!))))) @
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ('#C') @ (
% 88.47/26.73 (
% 88.47/26.73 ('#B') @ (
% 88.47/26.73 '#B') @
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ('#B') @ (
% 88.47/26.73 '#B') @
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ('#B') @ (
% 88.47/26.73 '#S') @
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ('#B') @ (
% 88.47/26.73 (
% 88.47/26.73 ('#B') @ (
% 88.47/26.73 =>))) @
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ('#C') @ in)))))))))) @
% 88.47/26.73 (
% 88.47/26.73 (
% 88.47/26.73 ('#S') @ (
% 88.47/26.73 (
% 88.47/26.73 ('#B') @ (
% 88.47/26.73 '#S') @
% 88.47/26.74 (
% 88.47/26.74 (
% 88.47/26.74 ('#B') @ (
% 88.47/26.74 (
% 88.47/26.74 ('#B') @ (
% 88.47/26.74 '#B'))) @
% 88.47/26.74 (
% 88.47/26.74 (
% 88.47/26.74 ('#B') @ (
% 88.47/26.74 =>))))))) @
% 88.47/26.74 (
% 88.47/26.74 (
% 88.47/26.74 ('#C') @ (
% 88.47/26.74 (
% 88.47/26.74 ('#B') @ (
% 88.47/26.74 '#B') @
% 88.47/26.74 (
% 88.47/26.74 (
% 88.47/26.74 ('#B') @ (
% 88.47/26.74 '#S') @
% 88.47/26.74 (
% 88.47/26.74 (
% 88.47/26.74 ('#B') @ (
% 88.47/26.74 =>))))))) @
% 88.47/26.74 (
% 88.47/26.74 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 88.47/26.74 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl2])).
% 88.47/26.74 thf(zip_derived_cl5, plain,
% 88.47/26.74 (~ (((emptysetAx) =>
% 88.47/26.74 (((setadjoinAx) =>
% 88.47/26.74 (((powersetAx) =>
% 88.47/26.74 (((setunionAx) =>
% 88.47/26.74 (((in @ emptyset @ omega) =>
% 88.47/26.74 (((omegaSAx) =>
% 88.47/26.74 (((omegaIndAx) =>
% 88.47/26.74 (((replAx) =>
% 88.47/26.74 (((foundationAx) =>
% 88.47/26.74 (((wellorderingAx) =>
% 88.47/26.74 (((descrp) =>
% 88.47/26.74 (((dsetconstrI) =>
% 88.47/26.74 (((dsetconstrEL) =>
% 88.47/26.74 (((dsetconstrER) =>
% 88.47/26.74 (((exuE1) =>
% 88.47/26.74 (((prop2setE) =>
% 88.47/26.74 (((emptysetE) =>
% 88.47/26.74 (((emptysetimpfalse) =>
% 88.47/26.74 (((notinemptyset) =>
% 88.47/26.74 (((exuE3e) =>
% 88.47/26.74 (((setext) =>
% 88.47/26.74 (((emptyI) =>
% 88.47/26.74 (((noeltsimpempty) =>
% 88.47/26.74 (((setbeta) =>
% 88.47/26.74 (((nonemptyE1) =>
% 88.47/26.74 (((nonemptyI) =>
% 88.47/26.74 (((nonemptyI1) =>
% 88.47/26.74 (((setadjoinIL) =>
% 88.47/26.74 (((in @
% 88.47/26.74 emptyset @
% 88.47/26.74 (setadjoin @
% 88.47/26.74 emptyset @
% 88.47/26.74 emptyset)) =>
% 88.47/26.74 (((setadjoinIR) =>
% 88.47/26.74 ((
% 88.47/26.74 (setadjoinE) =>
% 88.47/26.74 ((
% 88.47/26.74 (setadjoinOr) =>
% 88.47/26.74 ((
% 88.47/26.74 (setoftrueEq) =>
% 88.47/26.74 ((
% 88.47/26.74 (powersetI) =>
% 88.47/26.74 ((
% 88.47/26.74 (emptyinPowerset) =>
% 88.47/26.74 ((
% 88.47/26.74 (emptyInPowerset) =>
% 88.47/26.74 ((
% 88.47/26.74 (powersetE) =>
% 88.47/26.74 ((
% 88.47/26.74 (setunionI) =>
% 88.47/26.74 ((
% 88.47/26.74 (setunionE) =>
% 88.47/26.74 ((
% 88.47/26.74 (subPowSU) =>
% 88.47/26.74 ((
% 88.47/26.74 (exuE2) =>
% 88.47/26.74 ((
% 88.47/26.74 (nonemptyImpWitness) =>
% 88.47/26.74 ((
% 88.47/26.74 (uniqinunit) =>
% 88.47/26.74 ((
% 88.47/26.74 (notinsingleton) =>
% 88.47/26.74 ((
% 88.47/26.74 (eqinunit) =>
% 88.47/26.74 ((
% 88.47/26.74 (singletonsswitch) =>
% 88.47/26.74 ((
% 88.47/26.74 (upairsetE) =>
% 88.47/26.74 ((
% 88.47/26.74 (upairsetIL) =>
% 88.47/26.74 ((
% 88.47/26.74 (upairsetIR) =>
% 88.47/26.74 ((
% 88.47/26.74 (emptyE1) =>
% 88.47/26.74 ((
% 88.47/26.74 (vacuousDall) =>
% 88.47/26.74 ((
% 88.47/26.74 (quantDeMorgan1) =>
% 88.47/26.74 ((
% 88.47/26.74 (quantDeMorgan2) =>
% 88.47/26.74 ((
% 88.47/26.74 (quantDeMorgan3) =>
% 88.47/26.74 ((
% 88.47/26.74 (quantDeMorgan4) =>
% 88.47/26.74 ((
% 88.47/26.74 (prop2setI) =>
% 88.47/26.74 ((
% 88.47/26.74 (prop2set2propI) =>
% 88.47/26.74 ((
% 88.47/26.74 (notdexE) =>
% 88.47/26.74 ((
% 88.47/26.74 (notdallE) =>
% 88.47/26.74 ((
% 88.47/26.74 (exuI1) =>
% 88.47/26.74 ((
% 88.47/26.74 (exuI3) =>
% 88.47/26.74 ((
% 88.47/26.74 (exuI2) =>
% 88.47/26.74 ((
% 88.47/26.74 (inCongP) =>
% 88.47/26.74 ((
% 88.47/26.74 (in__Cong) =>
% 88.47/26.74 ((
% 88.47/26.74 (exuE3u) =>
% 88.47/26.74 ((
% 88.47/26.74 (exu__Cong) =>
% 88.47/26.74 ((
% 88.47/26.74 (setadjoin__Cong) =>
% 88.47/26.74 ((
% 88.47/26.74 (powerset__Cong) =>
% 88.47/26.74 ((
% 88.47/26.74 (setunion__Cong) =>
% 88.47/26.74 ((
% 88.47/26.74 (exuEu) =>
% 88.47/26.74 ((
% 88.47/26.74 (descr__Cong) =>
% 88.47/26.74 ((
% 88.47/26.74 (dsetconstr__Cong) =>
% 88.47/26.74 ((
% 88.47/26.74 (subsetI1) =>
% 88.47/26.74 ((
% 88.47/26.74 (eqimpsubset2) =>
% 88.47/26.74 ((
% 88.47/26.74 (eqimpsubset1) =>
% 88.47/26.74 ((
% 88.47/26.74 (subsetI2) =>
% 88.47/26.74 ((
% 88.47/26.74 (emptysetsubset) =>
% 88.47/26.74 ((
% 88.47/26.74 (subsetE) =>
% 88.47/26.74 ((
% 88.47/26.74 (subsetE2) =>
% 88.47/26.74 ((
% 88.47/26.74 (notsubsetI) =>
% 88.47/26.74 ((
% 88.47/26.74 (notequalI1) =>
% 88.47/26.74 ((
% 88.47/26.74 (notequalI2) =>
% 88.47/26.74 ((
% 88.47/26.74 (subsetRefl) =>
% 88.47/26.74 ((
% 88.47/26.74 (subsetTrans) =>
% 88.47/26.74 ((
% 88.47/26.74 (setadjoinSub) =>
% 88.47/26.74 ((
% 88.47/26.74 (setadjoinSub2) =>
% 88.47/26.74 ((
% 88.47/26.74 (subset2powerset) =>
% 88.47/26.74 ((
% 88.47/26.74 (setextsub) =>
% 88.47/26.74 ((
% 88.47/26.74 (subsetemptysetimpeq) =>
% 88.47/26.74 ((
% 88.47/26.74 (powersetI1) =>
% 88.47/26.74 ((
% 88.47/26.74 (powersetE1) =>
% 88.47/26.74 ((
% 88.47/26.74 (inPowerset) =>
% 88.47/26.74 ((
% 88.47/26.74 (powersetsubset) =>
% 88.47/26.74 ((
% 88.47/26.74 (sepInPowerset) =>
% 88.47/26.74 ((
% 88.47/26.74 (sepSubset) =>
% 88.47/26.74 ((
% 88.47/26.74 (binunionIL) =>
% 88.47/26.74 ((
% 88.47/26.74 (upairset2IR) =>
% 88.47/26.74 ((
% 88.47/26.74 (binunionIR) =>
% 88.47/26.74 ((
% 88.47/26.74 (binunionEcases) =>
% 88.47/26.74 ((
% 88.47/26.74 (binunionE) =>
% 88.47/26.74 ((
% 88.47/26.74 (binunionLsub) =>
% 88.47/26.74 ((
% 88.47/26.74 (binunionRsub) =>
% 88.47/26.74 ((
% 88.47/26.74 (binintersectI) =>
% 88.47/26.74 ((
% 88.47/26.74 (binintersectSubset5) =>
% 88.47/26.74 ((
% 88.47/26.74 (binintersectEL) =>
% 88.47/26.74 ((
% 88.47/26.74 (binintersectLsub) =>
% 88.47/26.74 ((
% 88.47/26.74 (binintersectSubset2) =>
% 88.47/26.74 ((
% 88.47/26.74 (binintersectSubset3) =>
% 88.47/26.74 ((
% 88.47/26.74 (binintersectER) =>
% 88.47/26.74 ((
% 88.47/26.74 (disjointsetsI1) =>
% 88.47/26.74 ((
% 88.47/26.74 (binintersectRsub) =>
% 88.47/26.74 ((
% 88.47/26.74 (binintersectSubset4) =>
% 88.47/26.74 ((
% 88.47/26.74 (binintersectSubset1) =>
% 88.47/26.74 ((
% 88.47/26.74 (bs114d) =>
% 88.47/26.74 ((
% 88.47/26.74 (setminusI) =>
% 88.47/26.74 ((
% 88.47/26.74 (setminusEL) =>
% 88.47/26.74 ((
% 88.47/26.74 (setminusER) =>
% 88.47/26.74 ((
% 88.47/26.74 (setminusSubset2) =>
% 88.47/26.74 ((
% 88.47/26.74 (setminusERneg) =>
% 88.47/26.74 ((
% 88.47/26.74 (setminusELneg) =>
% 88.47/26.74 ((
% 88.47/26.74 (setminusILneg) =>
% 88.47/26.74 ((
% 88.47/26.74 (setminusIRneg) =>
% 88.47/26.74 ((
% 88.47/26.74 (setminusLsub) =>
% 88.47/26.74 ((
% 88.47/26.74 (setminusSubset1) =>
% 88.47/26.74 ((
% 88.47/26.74 (symdiffE) =>
% 88.47/26.74 ((
% 88.47/26.74 (symdiffI1) =>
% 88.47/26.74 ((
% 88.47/26.74 (symdiffI2) =>
% 88.47/26.74 ((
% 88.47/26.74 (symdiffIneg1) =>
% 88.47/26.74 ((
% 88.47/26.74 (symdiffIneg2) =>
% 88.47/26.74 ((
% 88.47/26.74 (secondinupair) =>
% 88.47/26.74 ((
% 88.47/26.74 (setukpairIL) =>
% 88.47/26.74 ((
% 88.47/26.74 (setukpairIR) =>
% 88.47/26.74 ((
% 88.47/26.74 (kpairiskpair) =>
% 88.47/26.74 ((
% 88.47/26.74 (kpairp) =>
% 88.47/26.74 ((
% 88.47/26.74 (singletonsubset) =>
% 88.47/26.74 ((
% 88.47/26.74 (singletoninpowerset) =>
% 88.47/26.74 ((
% 88.47/26.74 (singletoninpowunion) =>
% 88.47/26.74 ((
% 88.47/26.74 (upairset2E) =>
% 88.47/26.74 ((
% 88.47/26.74 (upairsubunion) =>
% 88.47/26.74 ((
% 88.47/26.74 (upairinpowunion) =>
% 88.47/26.74 ((
% 88.47/26.74 (ubforcartprodlem1) =>
% 88.47/26.74 ((
% 88.47/26.74 (ubforcartprodlem2) =>
% 88.47/26.74 ((
% 88.47/26.74 (ubforcartprodlem3) =>
% 88.47/26.74 ((
% 88.47/26.74 (cartprodpairin) =>
% 88.47/26.74 ((
% 88.47/26.74 (cartprodmempair1) =>
% 88.47/26.74 ((
% 88.47/26.74 (cartprodmempair) =>
% 88.47/26.74 ((
% 88.47/26.74 (setunionE2) =>
% 88.47/26.74 ((
% 88.47/26.74 (setunionsingleton1) =>
% 88.47/26.74 ((
% 88.47/26.74 (setunionsingleton2) =>
% 88.47/26.74 ((
% 88.47/26.74 (setunionsingleton) =>
% 88.47/26.74 ((
% 88.47/26.74 (singletonprop) =>
% 88.47/26.74 ((
% 88.47/26.74 (ex1E1) =>
% 88.47/26.74 ((
% 88.47/26.74 (ex1I) =>
% 88.47/26.74 ((
% 88.47/26.74 (ex1I2) =>
% 88.47/26.74 ((
% 88.47/26.74 (singletonsuniq) =>
% 88.47/26.74 ((
% 88.47/26.74 (setukpairinjL1) =>
% 88.47/26.74 ((
% 88.47/26.74 (kfstsingleton) =>
% 88.47/26.74 ((
% 88.47/26.74 (theprop) =>
% 88.47/26.74 ((
% 88.47/26.74 (kfstpairEq) =>
% 88.47/26.74 ((
% 88.47/26.74 (cartprodfstin) =>
% 88.47/26.74 ((
% 88.47/26.74 (setukpairinjL2) =>
% 88.47/26.74 ((
% 88.47/26.74 (setukpairinjL) =>
% 88.47/26.74 ((
% 88.47/26.74 (setukpairinjR11) =>
% 88.47/26.74 ((
% 88.47/26.74 (setukpairinjR12) =>
% 88.47/26.74 ((
% 88.47/26.74 (setukpairinjR1) =>
% 88.47/26.74 ((
% 88.47/26.74 (upairequniteq) =>
% 88.47/26.74 ((
% 88.47/26.74 (setukpairinjR2) =>
% 88.47/26.74 ((
% 88.47/26.74 (setukpairinjR) =>
% 88.47/26.74 ((
% 88.47/26.74 (ksndsingleton) =>
% 88.47/26.74 ((
% 88.47/26.74 (ksndpairEq) =>
% 88.47/26.74 ((
% 88.47/26.74 (kpairsurjEq) =>
% 88.47/26.74 ((
% 88.47/26.74 (cartprodsndin) =>
% 88.47/26.74 ((
% 88.47/26.74 (cartprodpairmemEL) =>
% 88.47/26.74 ((
% 88.47/26.74 (cartprodpairmemER) =>
% 88.47/26.74 ((
% 88.47/26.74 (cartprodmempaircEq) =>
% 88.47/26.74 ((
% 88.47/26.74 (cartprodfstpairEq) =>
% 88.47/26.74 ((
% 88.47/26.74 (cartprodsndpairEq) =>
% 88.47/26.74 ((
% 88.47/26.74 (cartprodpairsurjEq) =>
% 88.47/26.74 ((
% 88.47/26.74 (dpsetconstrI) =>
% 88.47/26.74 ((
% 88.47/26.74 (dpsetconstrSub) =>
% 88.47/26.74 ((
% 88.47/26.74 (setOfPairsIsBReln) =>
% 88.47/26.74 ((
% 88.47/26.74 (dpsetconstrERa) =>
% 88.47/26.74 ((
% 88.47/26.74 (dpsetconstrEL1) =>
% 88.47/26.74 ((
% 88.47/26.74 (dpsetconstrEL2) =>
% 88.47/26.74 ((
% 88.47/26.74 (dpsetconstrER) =>
% 88.47/26.74 ((
% 88.47/26.74 (funcImageSingleton) =>
% 88.47/26.74 ((
% 88.47/26.74 (apProp) =>
% 88.47/26.74 ((
% 88.47/26.74 (app) =>
% 88.47/26.74 ((
% 88.47/26.74 (infuncsetfunc) =>
% 88.47/26.74 ((
% 88.47/26.74 (ap2p) =>
% 88.47/26.74 ((
% 88.47/26.74 (funcinfuncset) =>
% 88.47/26.74 ((
% 88.47/26.74 (lamProp) =>
% 88.47/26.74 ((
% 88.47/26.74 (lamp) =>
% 88.47/26.74 ((
% 88.47/26.74 (lam2p) =>
% 88.47/26.74 ((
% 88.47/26.74 (brelnall1) =>
% 88.47/26.74 ((
% 88.47/26.74 (brelnall2) =>
% 88.47/26.74 ((
% 88.47/26.74 (!!) @ (
% 88.47/26.74 (('#B') @ (
% 88.47/26.74 !!) @
% 88.47/26.74 (
% 88.47/26.74 (
% 88.47/26.74 ('#S') @ (
% 88.47/26.74 (
% 88.47/26.74 ('#B') @ (
% 88.47/26.74 '#S') @
% 88.47/26.74 (
% 88.47/26.74 (
% 88.47/26.74 ('#B') @ (
% 88.47/26.74 (
% 88.47/26.74 ('#B') @ (
% 88.47/26.74 =>))) @
% 88.47/26.74 ex1)))) @
% 88.47/26.74 (
% 88.47/26.74 (
% 88.47/26.74 ('#B') @ (
% 88.47/26.74 (
% 88.47/26.74 ('#B') @ (
% 88.47/26.74 !!))) @
% 88.47/26.74 (
% 88.47/26.74 (
% 88.47/26.74 ('#S') @ (
% 88.47/26.74 (
% 88.47/26.74 ('#B') @ (
% 88.47/26.74 '#B') @
% 88.47/26.74 (
% 88.47/26.74 (
% 88.47/26.74 ('#B') @ (
% 88.47/26.74 '#S') @
% 88.47/26.74 (
% 88.47/26.74 (
% 88.47/26.74 ('#B') @ (
% 88.47/26.74 (
% 88.47/26.74 ('#B') @ (
% 88.47/26.74 =>))) @
% 88.47/26.74 (
% 88.47/26.74 (
% 88.47/26.74 ('#C') @ in)))))))) @
% 88.47/26.74 (
% 88.47/26.74 (
% 88.47/26.74 ('#B') @ (
% 88.47/26.74 (
% 88.47/26.74 ('#B') @ (
% 88.47/26.74 (
% 88.47/26.74 ('#B') @ (
% 88.47/26.74 !!))))) @
% 88.47/26.74 (
% 88.47/26.74 (
% 88.47/26.74 ('#C') @ (
% 88.47/26.74 (
% 88.47/26.74 ('#B') @ (
% 88.47/26.74 '#B') @
% 88.47/26.74 (
% 88.47/26.74 (
% 88.47/26.74 ('#B') @ (
% 88.47/26.74 '#B') @
% 88.47/26.74 (
% 88.47/26.74 (
% 88.47/26.74 ('#B') @ (
% 88.47/26.74 '#S') @
% 88.47/26.74 (
% 88.47/26.74 (
% 88.47/26.74 ('#B') @ (
% 88.47/26.74 (
% 88.47/26.74 ('#B') @ (
% 88.47/26.74 =>))) @
% 88.47/26.74 (
% 88.47/26.74 (
% 88.47/26.74 ('#C') @ in)))))))))) @
% 88.47/26.74 (
% 88.47/26.74 (
% 88.47/26.74 ('#S') @ (
% 88.47/26.74 (
% 88.47/26.74 ('#B') @ (
% 88.47/26.74 '#S') @
% 88.47/26.74 (
% 88.47/26.74 (
% 88.47/26.74 ('#B') @ (
% 88.47/26.74 (
% 88.47/26.74 ('#B') @ (
% 88.47/26.74 '#B'))) @
% 88.47/26.74 (
% 88.47/26.74 (
% 88.47/26.74 ('#B') @ (
% 88.47/26.74 =>))))))) @
% 88.47/26.74 (
% 88.47/26.74 (
% 88.47/26.74 ('#C') @ (
% 88.47/26.74 (
% 88.47/26.74 ('#B') @ (
% 88.47/26.74 '#B') @
% 88.47/26.74 (
% 88.47/26.74 (
% 88.47/26.74 ('#B') @ (
% 88.47/26.74 '#S') @
% 88.47/26.74 (
% 88.47/26.74 (
% 88.47/26.74 ('#B') @ (
% 88.47/26.74 =>))))))) @
% 88.47/26.74 (
% 88.47/26.74 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 88.47/26.74 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3])).
% 88.47/26.74 thf(zip_derived_cl8, plain,
% 88.47/26.74 (~ (((setadjoinAx) =>
% 88.47/26.74 (((powersetAx) =>
% 88.47/26.74 (((setunionAx) =>
% 88.47/26.74 (((in @ emptyset @ omega) =>
% 88.47/26.74 (((omegaSAx) =>
% 88.47/26.74 (((omegaIndAx) =>
% 88.47/26.74 (((replAx) =>
% 88.47/26.74 (((foundationAx) =>
% 88.47/26.74 (((wellorderingAx) =>
% 88.47/26.74 (((descrp) =>
% 88.47/26.74 (((dsetconstrI) =>
% 88.47/26.74 (((dsetconstrEL) =>
% 88.47/26.74 (((dsetconstrER) =>
% 88.47/26.74 (((exuE1) =>
% 88.47/26.74 (((prop2setE) =>
% 88.47/26.74 (((emptysetE) =>
% 88.47/26.74 (((emptysetimpfalse) =>
% 88.47/26.74 (((notinemptyset) =>
% 88.47/26.74 (((exuE3e) =>
% 88.47/26.74 (((setext) =>
% 88.47/26.74 (((emptyI) =>
% 88.47/26.74 (((noeltsimpempty) =>
% 88.47/26.74 (((setbeta) =>
% 88.47/26.74 (((nonemptyE1) =>
% 88.47/26.74 (((nonemptyI) =>
% 88.47/26.74 (((nonemptyI1) =>
% 88.47/26.74 (((setadjoinIL) =>
% 88.47/26.74 (((in @
% 88.47/26.74 emptyset @
% 88.47/26.74 (setadjoin @
% 88.47/26.74 emptyset @
% 88.47/26.74 emptyset)) =>
% 88.47/26.74 (((setadjoinIR) =>
% 88.47/26.74 (((setadjoinE) =>
% 88.47/26.74 ((
% 88.47/26.74 (setadjoinOr) =>
% 88.47/26.74 ((
% 88.47/26.74 (setoftrueEq) =>
% 88.47/26.74 ((
% 88.47/26.74 (powersetI) =>
% 88.47/26.74 ((
% 88.47/26.74 (emptyinPowerset) =>
% 88.47/26.74 ((
% 88.47/26.74 (emptyInPowerset) =>
% 88.47/26.74 ((
% 88.47/26.74 (powersetE) =>
% 88.47/26.74 ((
% 88.47/26.74 (setunionI) =>
% 88.47/26.74 ((
% 88.47/26.74 (setunionE) =>
% 88.47/26.74 ((
% 88.47/26.74 (subPowSU) =>
% 88.47/26.74 ((
% 88.47/26.74 (exuE2) =>
% 88.47/26.74 ((
% 88.47/26.74 (nonemptyImpWitness) =>
% 88.47/26.74 ((
% 88.47/26.74 (uniqinunit) =>
% 88.47/26.74 ((
% 88.47/26.74 (notinsingleton) =>
% 88.47/26.74 ((
% 88.47/26.74 (eqinunit) =>
% 88.47/26.74 ((
% 88.47/26.74 (singletonsswitch) =>
% 88.47/26.74 ((
% 88.47/26.74 (upairsetE) =>
% 88.47/26.74 ((
% 88.47/26.74 (upairsetIL) =>
% 88.47/26.74 ((
% 88.47/26.74 (upairsetIR) =>
% 88.47/26.74 ((
% 88.47/26.74 (emptyE1) =>
% 88.47/26.74 ((
% 88.47/26.74 (vacuousDall) =>
% 88.47/26.74 ((
% 88.47/26.74 (quantDeMorgan1) =>
% 88.47/26.74 ((
% 88.47/26.74 (quantDeMorgan2) =>
% 88.47/26.74 ((
% 88.47/26.74 (quantDeMorgan3) =>
% 88.47/26.74 ((
% 88.47/26.74 (quantDeMorgan4) =>
% 88.47/26.74 ((
% 88.47/26.74 (prop2setI) =>
% 88.47/26.74 ((
% 88.47/26.74 (prop2set2propI) =>
% 88.47/26.74 ((
% 88.47/26.74 (notdexE) =>
% 88.47/26.74 ((
% 88.47/26.74 (notdallE) =>
% 88.47/26.74 ((
% 88.47/26.74 (exuI1) =>
% 88.47/26.74 ((
% 88.47/26.74 (exuI3) =>
% 88.47/26.74 ((
% 88.47/26.74 (exuI2) =>
% 88.47/26.74 ((
% 88.47/26.74 (inCongP) =>
% 88.47/26.74 ((
% 88.47/26.74 (in__Cong) =>
% 88.47/26.74 ((
% 88.47/26.74 (exuE3u) =>
% 88.47/26.74 ((
% 88.47/26.74 (exu__Cong) =>
% 88.47/26.74 ((
% 88.47/26.74 (setadjoin__Cong) =>
% 88.47/26.74 ((
% 88.47/26.74 (powerset__Cong) =>
% 88.47/26.74 ((
% 88.47/26.74 (setunion__Cong) =>
% 88.47/26.74 ((
% 88.47/26.74 (exuEu) =>
% 88.47/26.74 ((
% 88.47/26.74 (descr__Cong) =>
% 88.47/26.74 ((
% 88.47/26.74 (dsetconstr__Cong) =>
% 88.47/26.74 ((
% 88.47/26.74 (subsetI1) =>
% 88.47/26.74 ((
% 88.47/26.74 (eqimpsubset2) =>
% 88.47/26.74 ((
% 88.47/26.74 (eqimpsubset1) =>
% 88.47/26.74 ((
% 88.47/26.74 (subsetI2) =>
% 88.47/26.74 ((
% 88.47/26.74 (emptysetsubset) =>
% 88.47/26.74 ((
% 88.47/26.74 (subsetE) =>
% 88.47/26.74 ((
% 88.47/26.74 (subsetE2) =>
% 88.47/26.74 ((
% 88.47/26.74 (notsubsetI) =>
% 88.47/26.74 ((
% 88.47/26.74 (notequalI1) =>
% 88.47/26.74 ((
% 88.47/26.74 (notequalI2) =>
% 88.47/26.74 ((
% 88.47/26.74 (subsetRefl) =>
% 88.47/26.74 ((
% 88.47/26.74 (subsetTrans) =>
% 88.47/26.74 ((
% 88.47/26.74 (setadjoinSub) =>
% 88.47/26.74 ((
% 88.47/26.74 (setadjoinSub2) =>
% 88.47/26.74 ((
% 88.47/26.74 (subset2powerset) =>
% 88.47/26.74 ((
% 88.47/26.74 (setextsub) =>
% 88.47/26.74 ((
% 88.47/26.74 (subsetemptysetimpeq) =>
% 88.47/26.74 ((
% 88.47/26.74 (powersetI1) =>
% 88.47/26.74 ((
% 88.47/26.74 (powersetE1) =>
% 88.47/26.74 ((
% 88.47/26.74 (inPowerset) =>
% 88.47/26.74 ((
% 88.47/26.74 (powersetsubset) =>
% 88.47/26.74 ((
% 88.47/26.74 (sepInPowerset) =>
% 88.47/26.74 ((
% 88.47/26.74 (sepSubset) =>
% 88.47/26.74 ((
% 88.47/26.74 (binunionIL) =>
% 88.47/26.74 ((
% 88.47/26.74 (upairset2IR) =>
% 88.47/26.74 ((
% 88.47/26.74 (binunionIR) =>
% 88.47/26.74 ((
% 88.47/26.74 (binunionEcases) =>
% 88.47/26.74 ((
% 88.47/26.74 (binunionE) =>
% 88.47/26.74 ((
% 88.47/26.74 (binunionLsub) =>
% 88.47/26.74 ((
% 88.47/26.74 (binunionRsub) =>
% 88.47/26.74 ((
% 88.47/26.74 (binintersectI) =>
% 88.47/26.74 ((
% 88.47/26.74 (binintersectSubset5) =>
% 88.47/26.74 ((
% 88.47/26.74 (binintersectEL) =>
% 88.47/26.74 ((
% 88.47/26.74 (binintersectLsub) =>
% 88.47/26.74 ((
% 88.47/26.74 (binintersectSubset2) =>
% 88.47/26.74 ((
% 88.47/26.74 (binintersectSubset3) =>
% 88.47/26.74 ((
% 88.47/26.74 (binintersectER) =>
% 88.47/26.74 ((
% 88.47/26.74 (disjointsetsI1) =>
% 88.47/26.74 ((
% 88.47/26.74 (binintersectRsub) =>
% 88.47/26.74 ((
% 88.47/26.74 (binintersectSubset4) =>
% 88.47/26.74 ((
% 88.47/26.74 (binintersectSubset1) =>
% 88.47/26.74 ((
% 88.47/26.74 (bs114d) =>
% 88.47/26.74 ((
% 88.47/26.74 (setminusI) =>
% 88.47/26.74 ((
% 88.47/26.74 (setminusEL) =>
% 88.47/26.74 ((
% 88.47/26.74 (setminusER) =>
% 88.47/26.74 ((
% 88.47/26.74 (setminusSubset2) =>
% 88.47/26.74 ((
% 88.47/26.74 (setminusERneg) =>
% 88.47/26.74 ((
% 88.47/26.74 (setminusELneg) =>
% 88.47/26.74 ((
% 88.47/26.74 (setminusILneg) =>
% 88.47/26.74 ((
% 88.47/26.74 (setminusIRneg) =>
% 88.47/26.74 ((
% 88.47/26.74 (setminusLsub) =>
% 88.47/26.74 ((
% 88.47/26.74 (setminusSubset1) =>
% 88.47/26.74 ((
% 88.47/26.74 (symdiffE) =>
% 88.47/26.74 ((
% 88.47/26.74 (symdiffI1) =>
% 88.47/26.74 ((
% 88.47/26.74 (symdiffI2) =>
% 88.47/26.74 ((
% 88.47/26.74 (symdiffIneg1) =>
% 88.47/26.74 ((
% 88.47/26.74 (symdiffIneg2) =>
% 88.47/26.74 ((
% 88.47/26.74 (secondinupair) =>
% 88.47/26.74 ((
% 88.47/26.74 (setukpairIL) =>
% 88.47/26.74 ((
% 88.47/26.74 (setukpairIR) =>
% 88.47/26.74 ((
% 88.47/26.74 (kpairiskpair) =>
% 88.47/26.74 ((
% 88.47/26.74 (kpairp) =>
% 88.47/26.74 ((
% 88.47/26.74 (singletonsubset) =>
% 88.47/26.74 ((
% 88.47/26.74 (singletoninpowerset) =>
% 88.47/26.74 ((
% 88.47/26.74 (singletoninpowunion) =>
% 88.47/26.74 ((
% 88.47/26.74 (upairset2E) =>
% 88.47/26.74 ((
% 88.47/26.74 (upairsubunion) =>
% 88.47/26.74 ((
% 88.47/26.74 (upairinpowunion) =>
% 88.47/26.74 ((
% 88.47/26.74 (ubforcartprodlem1) =>
% 88.47/26.74 ((
% 88.47/26.74 (ubforcartprodlem2) =>
% 88.47/26.74 ((
% 88.47/26.74 (ubforcartprodlem3) =>
% 88.47/26.74 ((
% 88.47/26.74 (cartprodpairin) =>
% 88.47/26.74 ((
% 88.47/26.74 (cartprodmempair1) =>
% 88.47/26.74 ((
% 88.47/26.74 (cartprodmempair) =>
% 88.47/26.74 ((
% 88.47/26.74 (setunionE2) =>
% 88.47/26.74 ((
% 88.47/26.74 (setunionsingleton1) =>
% 88.47/26.74 ((
% 88.47/26.74 (setunionsingleton2) =>
% 88.47/26.74 ((
% 88.47/26.74 (setunionsingleton) =>
% 88.47/26.74 ((
% 88.47/26.74 (singletonprop) =>
% 88.47/26.74 ((
% 88.47/26.74 (ex1E1) =>
% 88.47/26.74 ((
% 88.47/26.74 (ex1I) =>
% 88.47/26.74 ((
% 88.47/26.74 (ex1I2) =>
% 88.47/26.74 ((
% 88.47/26.74 (singletonsuniq) =>
% 88.47/26.74 ((
% 88.47/26.74 (setukpairinjL1) =>
% 88.47/26.74 ((
% 88.47/26.74 (kfstsingleton) =>
% 88.47/26.74 ((
% 88.47/26.74 (theprop) =>
% 88.47/26.74 ((
% 88.47/26.74 (kfstpairEq) =>
% 88.47/26.74 ((
% 88.47/26.74 (cartprodfstin) =>
% 88.47/26.74 ((
% 88.47/26.74 (setukpairinjL2) =>
% 88.47/26.74 ((
% 88.47/26.74 (setukpairinjL) =>
% 88.47/26.74 ((
% 88.47/26.74 (setukpairinjR11) =>
% 88.47/26.74 ((
% 88.47/26.74 (setukpairinjR12) =>
% 88.47/26.74 ((
% 88.47/26.74 (setukpairinjR1) =>
% 88.47/26.74 ((
% 88.47/26.74 (upairequniteq) =>
% 88.47/26.74 ((
% 88.47/26.74 (setukpairinjR2) =>
% 88.47/26.74 ((
% 88.47/26.74 (setukpairinjR) =>
% 88.47/26.74 ((
% 88.47/26.74 (ksndsingleton) =>
% 88.47/26.74 ((
% 88.47/26.74 (ksndpairEq) =>
% 88.47/26.74 ((
% 88.47/26.74 (kpairsurjEq) =>
% 88.47/26.74 ((
% 88.47/26.74 (cartprodsndin) =>
% 88.47/26.74 ((
% 88.47/26.74 (cartprodpairmemEL) =>
% 88.47/26.74 ((
% 88.47/26.74 (cartprodpairmemER) =>
% 88.47/26.74 ((
% 88.47/26.74 (cartprodmempaircEq) =>
% 88.47/26.74 ((
% 88.47/26.74 (cartprodfstpairEq) =>
% 88.47/26.74 ((
% 88.47/26.74 (cartprodsndpairEq) =>
% 88.47/26.74 ((
% 88.47/26.74 (cartprodpairsurjEq) =>
% 88.47/26.74 ((
% 88.47/26.74 (dpsetconstrI) =>
% 88.47/26.74 ((
% 88.47/26.74 (dpsetconstrSub) =>
% 88.47/26.74 ((
% 88.47/26.74 (setOfPairsIsBReln) =>
% 88.47/26.74 ((
% 88.47/26.74 (dpsetconstrERa) =>
% 88.47/26.74 ((
% 88.47/26.74 (dpsetconstrEL1) =>
% 88.47/26.74 ((
% 88.47/26.74 (dpsetconstrEL2) =>
% 88.47/26.74 ((
% 88.47/26.74 (dpsetconstrER) =>
% 88.47/26.74 ((
% 88.47/26.74 (funcImageSingleton) =>
% 88.47/26.74 ((
% 88.47/26.74 (apProp) =>
% 88.47/26.74 ((
% 88.47/26.74 (app) =>
% 88.47/26.74 ((
% 88.47/26.74 (infuncsetfunc) =>
% 88.47/26.74 ((
% 88.47/26.74 (ap2p) =>
% 88.47/26.74 ((
% 88.47/26.74 (funcinfuncset) =>
% 88.47/26.74 ((
% 88.47/26.74 (lamProp) =>
% 88.47/26.74 ((
% 88.47/26.74 (lamp) =>
% 88.47/26.74 ((
% 88.47/26.74 (lam2p) =>
% 88.47/26.74 ((
% 88.47/26.74 (brelnall1) =>
% 88.47/26.74 ((
% 88.47/26.74 (brelnall2) =>
% 88.47/26.74 ((
% 88.47/26.74 (!!) @ (
% 88.47/26.74 (('#B') @ (
% 88.47/26.74 !!) @
% 88.47/26.74 (
% 88.47/26.74 (
% 88.47/26.74 ('#S') @ (
% 88.47/26.74 (
% 88.47/26.74 ('#B') @ (
% 88.47/26.74 '#S') @
% 88.47/26.74 (
% 88.47/26.74 (
% 88.47/26.74 ('#B') @ (
% 88.47/26.74 (
% 88.47/26.74 ('#B') @ (
% 88.47/26.74 =>))) @
% 88.47/26.74 ex1)))) @
% 88.47/26.74 (
% 88.47/26.74 (
% 88.47/26.74 ('#B') @ (
% 88.47/26.74 (
% 88.47/26.74 ('#B') @ (
% 88.47/26.74 !!))) @
% 88.47/26.74 (
% 88.47/26.74 (
% 88.47/26.74 ('#S') @ (
% 88.47/26.74 (
% 88.47/26.74 ('#B') @ (
% 88.47/26.74 '#B') @
% 88.47/26.74 (
% 88.47/26.74 (
% 88.47/26.74 ('#B') @ (
% 88.47/26.74 '#S') @
% 88.47/26.74 (
% 88.47/26.74 (
% 88.47/26.74 ('#B') @ (
% 88.47/26.74 (
% 88.47/26.74 ('#B') @ (
% 88.47/26.74 =>))) @
% 88.47/26.74 (
% 88.47/26.74 (
% 88.47/26.74 ('#C') @ in)))))))) @
% 88.47/26.74 (
% 88.47/26.74 (
% 88.47/26.74 ('#B') @ (
% 88.47/26.74 (
% 88.47/26.74 ('#B') @ (
% 88.47/26.74 (
% 88.47/26.74 ('#B') @ (
% 88.47/26.74 !!))))) @
% 88.47/26.74 (
% 88.47/26.74 (
% 88.47/26.74 ('#C') @ (
% 88.47/26.74 (
% 88.47/26.74 ('#B') @ (
% 88.47/26.74 '#B') @
% 88.47/26.74 (
% 88.47/26.74 (
% 88.47/26.74 ('#B') @ (
% 88.47/26.74 '#B') @
% 88.47/26.74 (
% 88.47/26.74 (
% 88.47/26.74 ('#B') @ (
% 88.47/26.74 '#S') @
% 88.47/26.74 (
% 88.47/26.74 (
% 88.47/26.74 ('#B') @ (
% 88.47/26.74 (
% 88.47/26.74 ('#B') @ (
% 88.47/26.74 =>))) @
% 88.47/26.74 (
% 88.47/26.74 (
% 88.47/26.74 ('#C') @ in)))))))))) @
% 88.47/26.74 (
% 88.47/26.74 (
% 88.47/26.74 ('#S') @ (
% 88.47/26.74 (
% 88.47/26.74 ('#B') @ (
% 88.47/26.74 '#S') @
% 88.47/26.74 (
% 88.47/26.74 (
% 88.47/26.74 ('#B') @ (
% 88.47/26.74 (
% 88.47/26.74 ('#B') @ (
% 88.47/26.74 '#B'))) @
% 88.47/26.74 (
% 88.47/26.74 (
% 88.47/26.74 ('#B') @ (
% 88.47/26.74 =>))))))) @
% 88.47/26.74 (
% 88.47/26.74 (
% 88.47/26.74 ('#C') @ (
% 88.47/26.74 (
% 88.47/26.74 ('#B') @ (
% 88.47/26.74 '#B') @
% 88.47/26.74 (
% 88.47/26.74 (
% 88.47/26.74 ('#B') @ (
% 88.47/26.74 '#S') @
% 88.47/26.74 (
% 88.47/26.74 (
% 88.47/26.74 ('#B') @ (
% 88.47/26.74 =>))))))) @
% 88.47/26.74 (
% 88.47/26.74 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 88.47/26.74 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5])).
% 88.47/26.74 thf(zip_derived_cl13, plain,
% 88.47/26.74 (~ (((powersetAx) =>
% 88.47/26.74 (((setunionAx) =>
% 88.47/26.74 (((in @ emptyset @ omega) =>
% 88.47/26.74 (((omegaSAx) =>
% 88.47/26.74 (((omegaIndAx) =>
% 88.47/26.74 (((replAx) =>
% 88.47/26.74 (((foundationAx) =>
% 88.47/26.74 (((wellorderingAx) =>
% 88.47/26.74 (((descrp) =>
% 88.47/26.74 (((dsetconstrI) =>
% 88.47/26.74 (((dsetconstrEL) =>
% 88.47/26.74 (((dsetconstrER) =>
% 88.47/26.74 (((exuE1) =>
% 88.47/26.74 (((prop2setE) =>
% 88.47/26.74 (((emptysetE) =>
% 88.47/26.74 (((emptysetimpfalse) =>
% 88.47/26.74 (((notinemptyset) =>
% 88.47/26.74 (((exuE3e) =>
% 88.47/26.74 (((setext) =>
% 88.47/26.74 (((emptyI) =>
% 88.47/26.74 (((noeltsimpempty) =>
% 88.47/26.74 (((setbeta) =>
% 88.47/26.74 (((nonemptyE1) =>
% 88.47/26.74 (((nonemptyI) =>
% 88.47/26.74 (((nonemptyI1) =>
% 88.47/26.74 (((setadjoinIL) =>
% 88.47/26.74 (((in @
% 88.47/26.74 emptyset @
% 88.47/26.74 (setadjoin @
% 88.47/26.74 emptyset @
% 88.47/26.74 emptyset)) =>
% 88.47/26.74 (((setadjoinIR) =>
% 88.47/26.74 (((setadjoinE) =>
% 88.47/26.74 (((setadjoinOr) =>
% 88.47/26.74 ((
% 88.47/26.74 (setoftrueEq) =>
% 88.47/26.74 ((
% 88.47/26.74 (powersetI) =>
% 88.47/26.74 ((
% 88.47/26.74 (emptyinPowerset) =>
% 88.47/26.74 ((
% 88.47/26.74 (emptyInPowerset) =>
% 88.47/26.74 ((
% 88.47/26.74 (powersetE) =>
% 88.47/26.74 ((
% 88.47/26.74 (setunionI) =>
% 88.47/26.74 ((
% 88.47/26.74 (setunionE) =>
% 88.47/26.74 ((
% 88.47/26.74 (subPowSU) =>
% 88.47/26.74 ((
% 88.47/26.74 (exuE2) =>
% 88.47/26.74 ((
% 88.47/26.74 (nonemptyImpWitness) =>
% 88.47/26.74 ((
% 88.47/26.74 (uniqinunit) =>
% 88.47/26.74 ((
% 88.47/26.74 (notinsingleton) =>
% 88.47/26.74 ((
% 88.47/26.74 (eqinunit) =>
% 88.47/26.74 ((
% 88.47/26.74 (singletonsswitch) =>
% 88.47/26.74 ((
% 88.47/26.74 (upairsetE) =>
% 88.47/26.74 ((
% 88.47/26.74 (upairsetIL) =>
% 88.47/26.74 ((
% 88.47/26.74 (upairsetIR) =>
% 88.47/26.74 ((
% 88.47/26.74 (emptyE1) =>
% 88.47/26.74 ((
% 88.47/26.74 (vacuousDall) =>
% 88.47/26.74 ((
% 88.47/26.74 (quantDeMorgan1) =>
% 88.47/26.74 ((
% 88.47/26.74 (quantDeMorgan2) =>
% 88.47/26.74 ((
% 88.47/26.74 (quantDeMorgan3) =>
% 88.47/26.74 ((
% 88.47/26.74 (quantDeMorgan4) =>
% 88.47/26.74 ((
% 88.47/26.74 (prop2setI) =>
% 88.47/26.74 ((
% 88.47/26.74 (prop2set2propI) =>
% 88.47/26.74 ((
% 88.47/26.74 (notdexE) =>
% 88.47/26.74 ((
% 88.47/26.74 (notdallE) =>
% 88.47/26.74 ((
% 88.47/26.74 (exuI1) =>
% 88.47/26.74 ((
% 88.47/26.74 (exuI3) =>
% 88.47/26.74 ((
% 88.47/26.74 (exuI2) =>
% 88.47/26.74 ((
% 88.47/26.74 (inCongP) =>
% 88.47/26.74 ((
% 88.47/26.74 (in__Cong) =>
% 88.47/26.74 ((
% 88.47/26.74 (exuE3u) =>
% 88.47/26.74 ((
% 88.47/26.74 (exu__Cong) =>
% 88.47/26.74 ((
% 88.47/26.74 (setadjoin__Cong) =>
% 88.47/26.74 ((
% 88.47/26.74 (powerset__Cong) =>
% 88.47/26.74 ((
% 88.47/26.74 (setunion__Cong) =>
% 88.47/26.74 ((
% 88.47/26.74 (exuEu) =>
% 88.47/26.74 ((
% 88.47/26.74 (descr__Cong) =>
% 88.47/26.74 ((
% 88.47/26.74 (dsetconstr__Cong) =>
% 88.47/26.74 ((
% 88.47/26.74 (subsetI1) =>
% 88.47/26.74 ((
% 88.47/26.74 (eqimpsubset2) =>
% 88.47/26.74 ((
% 88.47/26.74 (eqimpsubset1) =>
% 88.47/26.74 ((
% 88.47/26.74 (subsetI2) =>
% 88.47/26.74 ((
% 88.47/26.74 (emptysetsubset) =>
% 88.47/26.74 ((
% 88.47/26.74 (subsetE) =>
% 88.47/26.74 ((
% 88.47/26.74 (subsetE2) =>
% 88.47/26.74 ((
% 88.47/26.74 (notsubsetI) =>
% 88.47/26.74 ((
% 88.47/26.74 (notequalI1) =>
% 88.47/26.74 ((
% 88.47/26.74 (notequalI2) =>
% 88.47/26.74 ((
% 88.47/26.74 (subsetRefl) =>
% 88.47/26.74 ((
% 88.47/26.74 (subsetTrans) =>
% 88.47/26.74 ((
% 88.47/26.74 (setadjoinSub) =>
% 88.47/26.74 ((
% 88.47/26.74 (setadjoinSub2) =>
% 88.47/26.74 ((
% 88.47/26.74 (subset2powerset) =>
% 88.47/26.74 ((
% 88.47/26.74 (setextsub) =>
% 88.47/26.74 ((
% 88.47/26.74 (subsetemptysetimpeq) =>
% 88.47/26.74 ((
% 88.47/26.74 (powersetI1) =>
% 88.47/26.74 ((
% 88.47/26.74 (powersetE1) =>
% 88.47/26.74 ((
% 88.47/26.74 (inPowerset) =>
% 88.47/26.74 ((
% 88.47/26.74 (powersetsubset) =>
% 88.47/26.74 ((
% 88.47/26.74 (sepInPowerset) =>
% 88.47/26.74 ((
% 88.47/26.74 (sepSubset) =>
% 88.47/26.74 ((
% 88.47/26.74 (binunionIL) =>
% 88.47/26.74 ((
% 88.47/26.74 (upairset2IR) =>
% 88.47/26.74 ((
% 88.47/26.74 (binunionIR) =>
% 88.47/26.74 ((
% 88.47/26.74 (binunionEcases) =>
% 88.47/26.74 ((
% 88.47/26.74 (binunionE) =>
% 88.47/26.74 ((
% 88.47/26.74 (binunionLsub) =>
% 88.47/26.74 ((
% 88.47/26.74 (binunionRsub) =>
% 88.47/26.74 ((
% 88.47/26.74 (binintersectI) =>
% 88.47/26.74 ((
% 88.47/26.74 (binintersectSubset5) =>
% 88.47/26.74 ((
% 88.47/26.74 (binintersectEL) =>
% 88.47/26.74 ((
% 88.47/26.74 (binintersectLsub) =>
% 88.47/26.74 ((
% 88.47/26.74 (binintersectSubset2) =>
% 88.47/26.74 ((
% 88.47/26.74 (binintersectSubset3) =>
% 88.47/26.74 ((
% 88.47/26.74 (binintersectER) =>
% 88.47/26.74 ((
% 88.47/26.74 (disjointsetsI1) =>
% 88.47/26.74 ((
% 88.47/26.74 (binintersectRsub) =>
% 88.47/26.74 ((
% 88.47/26.74 (binintersectSubset4) =>
% 88.47/26.74 ((
% 88.47/26.74 (binintersectSubset1) =>
% 88.47/26.74 ((
% 88.47/26.74 (bs114d) =>
% 88.47/26.74 ((
% 88.47/26.74 (setminusI) =>
% 88.47/26.74 ((
% 88.47/26.74 (setminusEL) =>
% 88.47/26.74 ((
% 88.47/26.74 (setminusER) =>
% 88.47/26.74 ((
% 88.47/26.74 (setminusSubset2) =>
% 88.47/26.74 ((
% 88.47/26.74 (setminusERneg) =>
% 88.47/26.74 ((
% 88.47/26.74 (setminusELneg) =>
% 88.47/26.74 ((
% 88.47/26.74 (setminusILneg) =>
% 88.47/26.74 ((
% 88.47/26.74 (setminusIRneg) =>
% 88.47/26.74 ((
% 88.47/26.74 (setminusLsub) =>
% 88.47/26.74 ((
% 88.47/26.74 (setminusSubset1) =>
% 88.47/26.74 ((
% 88.47/26.74 (symdiffE) =>
% 88.47/26.74 ((
% 88.47/26.74 (symdiffI1) =>
% 88.47/26.74 ((
% 88.47/26.74 (symdiffI2) =>
% 88.47/26.74 ((
% 88.47/26.74 (symdiffIneg1) =>
% 88.47/26.74 ((
% 88.47/26.74 (symdiffIneg2) =>
% 88.47/26.74 ((
% 88.47/26.74 (secondinupair) =>
% 88.47/26.74 ((
% 88.47/26.74 (setukpairIL) =>
% 88.47/26.74 ((
% 88.47/26.74 (setukpairIR) =>
% 88.47/26.74 ((
% 88.47/26.74 (kpairiskpair) =>
% 88.47/26.74 ((
% 88.47/26.74 (kpairp) =>
% 88.47/26.74 ((
% 88.47/26.74 (singletonsubset) =>
% 88.47/26.74 ((
% 88.47/26.74 (singletoninpowerset) =>
% 88.47/26.74 ((
% 88.47/26.74 (singletoninpowunion) =>
% 88.47/26.74 ((
% 88.47/26.74 (upairset2E) =>
% 88.47/26.74 ((
% 88.47/26.74 (upairsubunion) =>
% 88.47/26.74 ((
% 88.47/26.74 (upairinpowunion) =>
% 88.47/26.74 ((
% 88.47/26.74 (ubforcartprodlem1) =>
% 88.47/26.74 ((
% 88.47/26.74 (ubforcartprodlem2) =>
% 88.47/26.74 ((
% 88.47/26.74 (ubforcartprodlem3) =>
% 88.47/26.74 ((
% 88.47/26.74 (cartprodpairin) =>
% 88.47/26.74 ((
% 88.47/26.74 (cartprodmempair1) =>
% 88.47/26.74 ((
% 88.47/26.74 (cartprodmempair) =>
% 88.47/26.74 ((
% 88.47/26.74 (setunionE2) =>
% 88.47/26.74 ((
% 88.47/26.74 (setunionsingleton1) =>
% 88.47/26.74 ((
% 88.47/26.74 (setunionsingleton2) =>
% 88.47/26.74 ((
% 88.47/26.74 (setunionsingleton) =>
% 88.47/26.74 ((
% 88.47/26.74 (singletonprop) =>
% 88.47/26.74 ((
% 88.47/26.74 (ex1E1) =>
% 88.47/26.74 ((
% 88.47/26.74 (ex1I) =>
% 88.47/26.74 ((
% 88.47/26.74 (ex1I2) =>
% 88.47/26.74 ((
% 88.47/26.74 (singletonsuniq) =>
% 88.47/26.74 ((
% 88.47/26.74 (setukpairinjL1) =>
% 88.47/26.74 ((
% 88.47/26.74 (kfstsingleton) =>
% 88.47/26.74 ((
% 88.47/26.74 (theprop) =>
% 88.47/26.74 ((
% 88.47/26.74 (kfstpairEq) =>
% 88.47/26.74 ((
% 88.47/26.74 (cartprodfstin) =>
% 88.47/26.74 ((
% 88.47/26.74 (setukpairinjL2) =>
% 88.47/26.74 ((
% 88.47/26.74 (setukpairinjL) =>
% 88.47/26.74 ((
% 88.47/26.74 (setukpairinjR11) =>
% 88.47/26.74 ((
% 88.47/26.74 (setukpairinjR12) =>
% 88.47/26.74 ((
% 88.47/26.74 (setukpairinjR1) =>
% 88.47/26.74 ((
% 88.47/26.74 (upairequniteq) =>
% 88.47/26.74 ((
% 88.47/26.74 (setukpairinjR2) =>
% 88.47/26.74 ((
% 88.47/26.74 (setukpairinjR) =>
% 88.47/26.74 ((
% 88.47/26.74 (ksndsingleton) =>
% 88.47/26.74 ((
% 88.47/26.74 (ksndpairEq) =>
% 88.47/26.74 ((
% 88.47/26.74 (kpairsurjEq) =>
% 88.47/26.74 ((
% 88.47/26.74 (cartprodsndin) =>
% 88.47/26.74 ((
% 88.47/26.74 (cartprodpairmemEL) =>
% 88.47/26.74 ((
% 88.47/26.74 (cartprodpairmemER) =>
% 88.47/26.74 ((
% 88.47/26.74 (cartprodmempaircEq) =>
% 88.47/26.74 ((
% 88.47/26.74 (cartprodfstpairEq) =>
% 88.47/26.74 ((
% 88.47/26.74 (cartprodsndpairEq) =>
% 88.47/26.74 ((
% 88.47/26.74 (cartprodpairsurjEq) =>
% 88.47/26.74 ((
% 88.47/26.74 (dpsetconstrI) =>
% 88.47/26.74 ((
% 88.47/26.74 (dpsetconstrSub) =>
% 88.47/26.74 ((
% 88.47/26.74 (setOfPairsIsBReln) =>
% 88.47/26.74 ((
% 88.47/26.74 (dpsetconstrERa) =>
% 88.47/26.74 ((
% 88.47/26.74 (dpsetconstrEL1) =>
% 88.47/26.74 ((
% 88.47/26.74 (dpsetconstrEL2) =>
% 88.47/26.74 ((
% 88.47/26.74 (dpsetconstrER) =>
% 88.47/26.74 ((
% 88.47/26.74 (funcImageSingleton) =>
% 88.47/26.74 ((
% 88.47/26.74 (apProp) =>
% 88.47/26.74 ((
% 88.47/26.74 (app) =>
% 88.47/26.74 ((
% 88.47/26.74 (infuncsetfunc) =>
% 88.47/26.74 ((
% 88.47/26.74 (ap2p) =>
% 88.47/26.74 ((
% 88.47/26.74 (funcinfuncset) =>
% 88.47/26.74 ((
% 88.47/26.74 (lamProp) =>
% 88.47/26.74 ((
% 88.47/26.74 (lamp) =>
% 88.47/26.74 ((
% 88.47/26.74 (lam2p) =>
% 88.47/26.74 ((
% 88.47/26.74 (brelnall1) =>
% 88.47/26.74 ((
% 88.47/26.74 (brelnall2) =>
% 88.47/26.74 ((
% 88.47/26.74 (!!) @ (
% 88.47/26.74 (('#B') @ (
% 88.47/26.74 !!) @
% 88.47/26.74 (
% 88.47/26.74 (
% 88.47/26.74 ('#S') @ (
% 88.47/26.74 (
% 88.47/26.74 ('#B') @ (
% 88.47/26.74 '#S') @
% 88.47/26.74 (
% 88.47/26.74 (
% 88.47/26.74 ('#B') @ (
% 88.47/26.74 (
% 88.47/26.74 ('#B') @ (
% 88.47/26.74 =>))) @
% 88.47/26.74 ex1)))) @
% 88.47/26.74 (
% 88.47/26.74 (
% 88.47/26.74 ('#B') @ (
% 88.47/26.74 (
% 88.47/26.74 ('#B') @ (
% 88.47/26.74 !!))) @
% 88.47/26.74 (
% 88.47/26.74 (
% 88.47/26.74 ('#S') @ (
% 88.47/26.74 (
% 88.47/26.74 ('#B') @ (
% 88.47/26.74 '#B') @
% 88.47/26.74 (
% 88.47/26.74 (
% 88.47/26.74 ('#B') @ (
% 88.47/26.74 '#S') @
% 88.47/26.74 (
% 88.47/26.74 (
% 88.47/26.74 ('#B') @ (
% 88.47/26.74 (
% 88.47/26.74 ('#B') @ (
% 88.47/26.74 =>))) @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#C') @ in)))))))) @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 !!))))) @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#C') @ (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 '#B') @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 '#B') @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 '#S') @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 =>))) @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#C') @ in)))))))))) @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#S') @ (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 '#S') @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 '#B'))) @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 =>))))))) @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#C') @ (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 '#B') @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 '#S') @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 =>))))))) @
% 88.47/26.75 (
% 88.47/26.75 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 88.47/26.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl8])).
% 88.47/26.75 thf(zip_derived_cl19, plain,
% 88.47/26.75 (~ (((setunionAx) =>
% 88.47/26.75 (((in @ emptyset @ omega) =>
% 88.47/26.75 (((omegaSAx) =>
% 88.47/26.75 (((omegaIndAx) =>
% 88.47/26.75 (((replAx) =>
% 88.47/26.75 (((foundationAx) =>
% 88.47/26.75 (((wellorderingAx) =>
% 88.47/26.75 (((descrp) =>
% 88.47/26.75 (((dsetconstrI) =>
% 88.47/26.75 (((dsetconstrEL) =>
% 88.47/26.75 (((dsetconstrER) =>
% 88.47/26.75 (((exuE1) =>
% 88.47/26.75 (((prop2setE) =>
% 88.47/26.75 (((emptysetE) =>
% 88.47/26.75 (((emptysetimpfalse) =>
% 88.47/26.75 (((notinemptyset) =>
% 88.47/26.75 (((exuE3e) =>
% 88.47/26.75 (((setext) =>
% 88.47/26.75 (((emptyI) =>
% 88.47/26.75 (((noeltsimpempty) =>
% 88.47/26.75 (((setbeta) =>
% 88.47/26.75 (((nonemptyE1) =>
% 88.47/26.75 (((nonemptyI) =>
% 88.47/26.75 (((nonemptyI1) =>
% 88.47/26.75 (((setadjoinIL) =>
% 88.47/26.75 (((in @ emptyset @
% 88.47/26.75 (setadjoin @
% 88.47/26.75 emptyset @
% 88.47/26.75 emptyset)) =>
% 88.47/26.75 (((setadjoinIR) =>
% 88.47/26.75 (((setadjoinE) =>
% 88.47/26.75 (((setadjoinOr) =>
% 88.47/26.75 (((setoftrueEq) =>
% 88.47/26.75 ((
% 88.47/26.75 (powersetI) =>
% 88.47/26.75 ((
% 88.47/26.75 (emptyinPowerset) =>
% 88.47/26.75 ((
% 88.47/26.75 (emptyInPowerset) =>
% 88.47/26.75 ((
% 88.47/26.75 (powersetE) =>
% 88.47/26.75 ((
% 88.47/26.75 (setunionI) =>
% 88.47/26.75 ((
% 88.47/26.75 (setunionE) =>
% 88.47/26.75 ((
% 88.47/26.75 (subPowSU) =>
% 88.47/26.75 ((
% 88.47/26.75 (exuE2) =>
% 88.47/26.75 ((
% 88.47/26.75 (nonemptyImpWitness) =>
% 88.47/26.75 ((
% 88.47/26.75 (uniqinunit) =>
% 88.47/26.75 ((
% 88.47/26.75 (notinsingleton) =>
% 88.47/26.75 ((
% 88.47/26.75 (eqinunit) =>
% 88.47/26.75 ((
% 88.47/26.75 (singletonsswitch) =>
% 88.47/26.75 ((
% 88.47/26.75 (upairsetE) =>
% 88.47/26.75 ((
% 88.47/26.75 (upairsetIL) =>
% 88.47/26.75 ((
% 88.47/26.75 (upairsetIR) =>
% 88.47/26.75 ((
% 88.47/26.75 (emptyE1) =>
% 88.47/26.75 ((
% 88.47/26.75 (vacuousDall) =>
% 88.47/26.75 ((
% 88.47/26.75 (quantDeMorgan1) =>
% 88.47/26.75 ((
% 88.47/26.75 (quantDeMorgan2) =>
% 88.47/26.75 ((
% 88.47/26.75 (quantDeMorgan3) =>
% 88.47/26.75 ((
% 88.47/26.75 (quantDeMorgan4) =>
% 88.47/26.75 ((
% 88.47/26.75 (prop2setI) =>
% 88.47/26.75 ((
% 88.47/26.75 (prop2set2propI) =>
% 88.47/26.75 ((
% 88.47/26.75 (notdexE) =>
% 88.47/26.75 ((
% 88.47/26.75 (notdallE) =>
% 88.47/26.75 ((
% 88.47/26.75 (exuI1) =>
% 88.47/26.75 ((
% 88.47/26.75 (exuI3) =>
% 88.47/26.75 ((
% 88.47/26.75 (exuI2) =>
% 88.47/26.75 ((
% 88.47/26.75 (inCongP) =>
% 88.47/26.75 ((
% 88.47/26.75 (in__Cong) =>
% 88.47/26.75 ((
% 88.47/26.75 (exuE3u) =>
% 88.47/26.75 ((
% 88.47/26.75 (exu__Cong) =>
% 88.47/26.75 ((
% 88.47/26.75 (setadjoin__Cong) =>
% 88.47/26.75 ((
% 88.47/26.75 (powerset__Cong) =>
% 88.47/26.75 ((
% 88.47/26.75 (setunion__Cong) =>
% 88.47/26.75 ((
% 88.47/26.75 (exuEu) =>
% 88.47/26.75 ((
% 88.47/26.75 (descr__Cong) =>
% 88.47/26.75 ((
% 88.47/26.75 (dsetconstr__Cong) =>
% 88.47/26.75 ((
% 88.47/26.75 (subsetI1) =>
% 88.47/26.75 ((
% 88.47/26.75 (eqimpsubset2) =>
% 88.47/26.75 ((
% 88.47/26.75 (eqimpsubset1) =>
% 88.47/26.75 ((
% 88.47/26.75 (subsetI2) =>
% 88.47/26.75 ((
% 88.47/26.75 (emptysetsubset) =>
% 88.47/26.75 ((
% 88.47/26.75 (subsetE) =>
% 88.47/26.75 ((
% 88.47/26.75 (subsetE2) =>
% 88.47/26.75 ((
% 88.47/26.75 (notsubsetI) =>
% 88.47/26.75 ((
% 88.47/26.75 (notequalI1) =>
% 88.47/26.75 ((
% 88.47/26.75 (notequalI2) =>
% 88.47/26.75 ((
% 88.47/26.75 (subsetRefl) =>
% 88.47/26.75 ((
% 88.47/26.75 (subsetTrans) =>
% 88.47/26.75 ((
% 88.47/26.75 (setadjoinSub) =>
% 88.47/26.75 ((
% 88.47/26.75 (setadjoinSub2) =>
% 88.47/26.75 ((
% 88.47/26.75 (subset2powerset) =>
% 88.47/26.75 ((
% 88.47/26.75 (setextsub) =>
% 88.47/26.75 ((
% 88.47/26.75 (subsetemptysetimpeq) =>
% 88.47/26.75 ((
% 88.47/26.75 (powersetI1) =>
% 88.47/26.75 ((
% 88.47/26.75 (powersetE1) =>
% 88.47/26.75 ((
% 88.47/26.75 (inPowerset) =>
% 88.47/26.75 ((
% 88.47/26.75 (powersetsubset) =>
% 88.47/26.75 ((
% 88.47/26.75 (sepInPowerset) =>
% 88.47/26.75 ((
% 88.47/26.75 (sepSubset) =>
% 88.47/26.75 ((
% 88.47/26.75 (binunionIL) =>
% 88.47/26.75 ((
% 88.47/26.75 (upairset2IR) =>
% 88.47/26.75 ((
% 88.47/26.75 (binunionIR) =>
% 88.47/26.75 ((
% 88.47/26.75 (binunionEcases) =>
% 88.47/26.75 ((
% 88.47/26.75 (binunionE) =>
% 88.47/26.75 ((
% 88.47/26.75 (binunionLsub) =>
% 88.47/26.75 ((
% 88.47/26.75 (binunionRsub) =>
% 88.47/26.75 ((
% 88.47/26.75 (binintersectI) =>
% 88.47/26.75 ((
% 88.47/26.75 (binintersectSubset5) =>
% 88.47/26.75 ((
% 88.47/26.75 (binintersectEL) =>
% 88.47/26.75 ((
% 88.47/26.75 (binintersectLsub) =>
% 88.47/26.75 ((
% 88.47/26.75 (binintersectSubset2) =>
% 88.47/26.75 ((
% 88.47/26.75 (binintersectSubset3) =>
% 88.47/26.75 ((
% 88.47/26.75 (binintersectER) =>
% 88.47/26.75 ((
% 88.47/26.75 (disjointsetsI1) =>
% 88.47/26.75 ((
% 88.47/26.75 (binintersectRsub) =>
% 88.47/26.75 ((
% 88.47/26.75 (binintersectSubset4) =>
% 88.47/26.75 ((
% 88.47/26.75 (binintersectSubset1) =>
% 88.47/26.75 ((
% 88.47/26.75 (bs114d) =>
% 88.47/26.75 ((
% 88.47/26.75 (setminusI) =>
% 88.47/26.75 ((
% 88.47/26.75 (setminusEL) =>
% 88.47/26.75 ((
% 88.47/26.75 (setminusER) =>
% 88.47/26.75 ((
% 88.47/26.75 (setminusSubset2) =>
% 88.47/26.75 ((
% 88.47/26.75 (setminusERneg) =>
% 88.47/26.75 ((
% 88.47/26.75 (setminusELneg) =>
% 88.47/26.75 ((
% 88.47/26.75 (setminusILneg) =>
% 88.47/26.75 ((
% 88.47/26.75 (setminusIRneg) =>
% 88.47/26.75 ((
% 88.47/26.75 (setminusLsub) =>
% 88.47/26.75 ((
% 88.47/26.75 (setminusSubset1) =>
% 88.47/26.75 ((
% 88.47/26.75 (symdiffE) =>
% 88.47/26.75 ((
% 88.47/26.75 (symdiffI1) =>
% 88.47/26.75 ((
% 88.47/26.75 (symdiffI2) =>
% 88.47/26.75 ((
% 88.47/26.75 (symdiffIneg1) =>
% 88.47/26.75 ((
% 88.47/26.75 (symdiffIneg2) =>
% 88.47/26.75 ((
% 88.47/26.75 (secondinupair) =>
% 88.47/26.75 ((
% 88.47/26.75 (setukpairIL) =>
% 88.47/26.75 ((
% 88.47/26.75 (setukpairIR) =>
% 88.47/26.75 ((
% 88.47/26.75 (kpairiskpair) =>
% 88.47/26.75 ((
% 88.47/26.75 (kpairp) =>
% 88.47/26.75 ((
% 88.47/26.75 (singletonsubset) =>
% 88.47/26.75 ((
% 88.47/26.75 (singletoninpowerset) =>
% 88.47/26.75 ((
% 88.47/26.75 (singletoninpowunion) =>
% 88.47/26.75 ((
% 88.47/26.75 (upairset2E) =>
% 88.47/26.75 ((
% 88.47/26.75 (upairsubunion) =>
% 88.47/26.75 ((
% 88.47/26.75 (upairinpowunion) =>
% 88.47/26.75 ((
% 88.47/26.75 (ubforcartprodlem1) =>
% 88.47/26.75 ((
% 88.47/26.75 (ubforcartprodlem2) =>
% 88.47/26.75 ((
% 88.47/26.75 (ubforcartprodlem3) =>
% 88.47/26.75 ((
% 88.47/26.75 (cartprodpairin) =>
% 88.47/26.75 ((
% 88.47/26.75 (cartprodmempair1) =>
% 88.47/26.75 ((
% 88.47/26.75 (cartprodmempair) =>
% 88.47/26.75 ((
% 88.47/26.75 (setunionE2) =>
% 88.47/26.75 ((
% 88.47/26.75 (setunionsingleton1) =>
% 88.47/26.75 ((
% 88.47/26.75 (setunionsingleton2) =>
% 88.47/26.75 ((
% 88.47/26.75 (setunionsingleton) =>
% 88.47/26.75 ((
% 88.47/26.75 (singletonprop) =>
% 88.47/26.75 ((
% 88.47/26.75 (ex1E1) =>
% 88.47/26.75 ((
% 88.47/26.75 (ex1I) =>
% 88.47/26.75 ((
% 88.47/26.75 (ex1I2) =>
% 88.47/26.75 ((
% 88.47/26.75 (singletonsuniq) =>
% 88.47/26.75 ((
% 88.47/26.75 (setukpairinjL1) =>
% 88.47/26.75 ((
% 88.47/26.75 (kfstsingleton) =>
% 88.47/26.75 ((
% 88.47/26.75 (theprop) =>
% 88.47/26.75 ((
% 88.47/26.75 (kfstpairEq) =>
% 88.47/26.75 ((
% 88.47/26.75 (cartprodfstin) =>
% 88.47/26.75 ((
% 88.47/26.75 (setukpairinjL2) =>
% 88.47/26.75 ((
% 88.47/26.75 (setukpairinjL) =>
% 88.47/26.75 ((
% 88.47/26.75 (setukpairinjR11) =>
% 88.47/26.75 ((
% 88.47/26.75 (setukpairinjR12) =>
% 88.47/26.75 ((
% 88.47/26.75 (setukpairinjR1) =>
% 88.47/26.75 ((
% 88.47/26.75 (upairequniteq) =>
% 88.47/26.75 ((
% 88.47/26.75 (setukpairinjR2) =>
% 88.47/26.75 ((
% 88.47/26.75 (setukpairinjR) =>
% 88.47/26.75 ((
% 88.47/26.75 (ksndsingleton) =>
% 88.47/26.75 ((
% 88.47/26.75 (ksndpairEq) =>
% 88.47/26.75 ((
% 88.47/26.75 (kpairsurjEq) =>
% 88.47/26.75 ((
% 88.47/26.75 (cartprodsndin) =>
% 88.47/26.75 ((
% 88.47/26.75 (cartprodpairmemEL) =>
% 88.47/26.75 ((
% 88.47/26.75 (cartprodpairmemER) =>
% 88.47/26.75 ((
% 88.47/26.75 (cartprodmempaircEq) =>
% 88.47/26.75 ((
% 88.47/26.75 (cartprodfstpairEq) =>
% 88.47/26.75 ((
% 88.47/26.75 (cartprodsndpairEq) =>
% 88.47/26.75 ((
% 88.47/26.75 (cartprodpairsurjEq) =>
% 88.47/26.75 ((
% 88.47/26.75 (dpsetconstrI) =>
% 88.47/26.75 ((
% 88.47/26.75 (dpsetconstrSub) =>
% 88.47/26.75 ((
% 88.47/26.75 (setOfPairsIsBReln) =>
% 88.47/26.75 ((
% 88.47/26.75 (dpsetconstrERa) =>
% 88.47/26.75 ((
% 88.47/26.75 (dpsetconstrEL1) =>
% 88.47/26.75 ((
% 88.47/26.75 (dpsetconstrEL2) =>
% 88.47/26.75 ((
% 88.47/26.75 (dpsetconstrER) =>
% 88.47/26.75 ((
% 88.47/26.75 (funcImageSingleton) =>
% 88.47/26.75 ((
% 88.47/26.75 (apProp) =>
% 88.47/26.75 ((
% 88.47/26.75 (app) =>
% 88.47/26.75 ((
% 88.47/26.75 (infuncsetfunc) =>
% 88.47/26.75 ((
% 88.47/26.75 (ap2p) =>
% 88.47/26.75 ((
% 88.47/26.75 (funcinfuncset) =>
% 88.47/26.75 ((
% 88.47/26.75 (lamProp) =>
% 88.47/26.75 ((
% 88.47/26.75 (lamp) =>
% 88.47/26.75 ((
% 88.47/26.75 (lam2p) =>
% 88.47/26.75 ((
% 88.47/26.75 (brelnall1) =>
% 88.47/26.75 ((
% 88.47/26.75 (brelnall2) =>
% 88.47/26.75 ((
% 88.47/26.75 (!!) @ (
% 88.47/26.75 (('#B') @ (
% 88.47/26.75 !!) @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#S') @ (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 '#S') @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 =>))) @
% 88.47/26.75 ex1)))) @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 !!))) @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#S') @ (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 '#B') @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 '#S') @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 =>))) @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#C') @ in)))))))) @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 !!))))) @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#C') @ (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 '#B') @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 '#B') @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 '#S') @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 =>))) @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#C') @ in)))))))))) @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#S') @ (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 '#S') @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 '#B'))) @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 =>))))))) @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#C') @ (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 '#B') @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 '#S') @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 =>))))))) @
% 88.47/26.75 (
% 88.47/26.75 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 88.47/26.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl13])).
% 88.47/26.75 thf(zip_derived_cl25, plain,
% 88.47/26.75 (~ (((in @ emptyset @ omega) =>
% 88.47/26.75 (((omegaSAx) =>
% 88.47/26.75 (((omegaIndAx) =>
% 88.47/26.75 (((replAx) =>
% 88.47/26.75 (((foundationAx) =>
% 88.47/26.75 (((wellorderingAx) =>
% 88.47/26.75 (((descrp) =>
% 88.47/26.75 (((dsetconstrI) =>
% 88.47/26.75 (((dsetconstrEL) =>
% 88.47/26.75 (((dsetconstrER) =>
% 88.47/26.75 (((exuE1) =>
% 88.47/26.75 (((prop2setE) =>
% 88.47/26.75 (((emptysetE) =>
% 88.47/26.75 (((emptysetimpfalse) =>
% 88.47/26.75 (((notinemptyset) =>
% 88.47/26.75 (((exuE3e) =>
% 88.47/26.75 (((setext) =>
% 88.47/26.75 (((emptyI) =>
% 88.47/26.75 (((noeltsimpempty) =>
% 88.47/26.75 (((setbeta) =>
% 88.47/26.75 (((nonemptyE1) =>
% 88.47/26.75 (((nonemptyI) =>
% 88.47/26.75 (((nonemptyI1) =>
% 88.47/26.75 (((setadjoinIL) =>
% 88.47/26.75 (((in @ emptyset @
% 88.47/26.75 (setadjoin @
% 88.47/26.75 emptyset @ emptyset)) =>
% 88.47/26.75 (((setadjoinIR) =>
% 88.47/26.75 (((setadjoinE) =>
% 88.47/26.75 (((setadjoinOr) =>
% 88.47/26.75 (((setoftrueEq) =>
% 88.47/26.75 (((powersetI) =>
% 88.47/26.75 ((
% 88.47/26.75 (emptyinPowerset) =>
% 88.47/26.75 ((
% 88.47/26.75 (emptyInPowerset) =>
% 88.47/26.75 ((
% 88.47/26.75 (powersetE) =>
% 88.47/26.75 ((
% 88.47/26.75 (setunionI) =>
% 88.47/26.75 ((
% 88.47/26.75 (setunionE) =>
% 88.47/26.75 ((
% 88.47/26.75 (subPowSU) =>
% 88.47/26.75 ((
% 88.47/26.75 (exuE2) =>
% 88.47/26.75 ((
% 88.47/26.75 (nonemptyImpWitness) =>
% 88.47/26.75 ((
% 88.47/26.75 (uniqinunit) =>
% 88.47/26.75 ((
% 88.47/26.75 (notinsingleton) =>
% 88.47/26.75 ((
% 88.47/26.75 (eqinunit) =>
% 88.47/26.75 ((
% 88.47/26.75 (singletonsswitch) =>
% 88.47/26.75 ((
% 88.47/26.75 (upairsetE) =>
% 88.47/26.75 ((
% 88.47/26.75 (upairsetIL) =>
% 88.47/26.75 ((
% 88.47/26.75 (upairsetIR) =>
% 88.47/26.75 ((
% 88.47/26.75 (emptyE1) =>
% 88.47/26.75 ((
% 88.47/26.75 (vacuousDall) =>
% 88.47/26.75 ((
% 88.47/26.75 (quantDeMorgan1) =>
% 88.47/26.75 ((
% 88.47/26.75 (quantDeMorgan2) =>
% 88.47/26.75 ((
% 88.47/26.75 (quantDeMorgan3) =>
% 88.47/26.75 ((
% 88.47/26.75 (quantDeMorgan4) =>
% 88.47/26.75 ((
% 88.47/26.75 (prop2setI) =>
% 88.47/26.75 ((
% 88.47/26.75 (prop2set2propI) =>
% 88.47/26.75 ((
% 88.47/26.75 (notdexE) =>
% 88.47/26.75 ((
% 88.47/26.75 (notdallE) =>
% 88.47/26.75 ((
% 88.47/26.75 (exuI1) =>
% 88.47/26.75 ((
% 88.47/26.75 (exuI3) =>
% 88.47/26.75 ((
% 88.47/26.75 (exuI2) =>
% 88.47/26.75 ((
% 88.47/26.75 (inCongP) =>
% 88.47/26.75 ((
% 88.47/26.75 (in__Cong) =>
% 88.47/26.75 ((
% 88.47/26.75 (exuE3u) =>
% 88.47/26.75 ((
% 88.47/26.75 (exu__Cong) =>
% 88.47/26.75 ((
% 88.47/26.75 (setadjoin__Cong) =>
% 88.47/26.75 ((
% 88.47/26.75 (powerset__Cong) =>
% 88.47/26.75 ((
% 88.47/26.75 (setunion__Cong) =>
% 88.47/26.75 ((
% 88.47/26.75 (exuEu) =>
% 88.47/26.75 ((
% 88.47/26.75 (descr__Cong) =>
% 88.47/26.75 ((
% 88.47/26.75 (dsetconstr__Cong) =>
% 88.47/26.75 ((
% 88.47/26.75 (subsetI1) =>
% 88.47/26.75 ((
% 88.47/26.75 (eqimpsubset2) =>
% 88.47/26.75 ((
% 88.47/26.75 (eqimpsubset1) =>
% 88.47/26.75 ((
% 88.47/26.75 (subsetI2) =>
% 88.47/26.75 ((
% 88.47/26.75 (emptysetsubset) =>
% 88.47/26.75 ((
% 88.47/26.75 (subsetE) =>
% 88.47/26.75 ((
% 88.47/26.75 (subsetE2) =>
% 88.47/26.75 ((
% 88.47/26.75 (notsubsetI) =>
% 88.47/26.75 ((
% 88.47/26.75 (notequalI1) =>
% 88.47/26.75 ((
% 88.47/26.75 (notequalI2) =>
% 88.47/26.75 ((
% 88.47/26.75 (subsetRefl) =>
% 88.47/26.75 ((
% 88.47/26.75 (subsetTrans) =>
% 88.47/26.75 ((
% 88.47/26.75 (setadjoinSub) =>
% 88.47/26.75 ((
% 88.47/26.75 (setadjoinSub2) =>
% 88.47/26.75 ((
% 88.47/26.75 (subset2powerset) =>
% 88.47/26.75 ((
% 88.47/26.75 (setextsub) =>
% 88.47/26.75 ((
% 88.47/26.75 (subsetemptysetimpeq) =>
% 88.47/26.75 ((
% 88.47/26.75 (powersetI1) =>
% 88.47/26.75 ((
% 88.47/26.75 (powersetE1) =>
% 88.47/26.75 ((
% 88.47/26.75 (inPowerset) =>
% 88.47/26.75 ((
% 88.47/26.75 (powersetsubset) =>
% 88.47/26.75 ((
% 88.47/26.75 (sepInPowerset) =>
% 88.47/26.75 ((
% 88.47/26.75 (sepSubset) =>
% 88.47/26.75 ((
% 88.47/26.75 (binunionIL) =>
% 88.47/26.75 ((
% 88.47/26.75 (upairset2IR) =>
% 88.47/26.75 ((
% 88.47/26.75 (binunionIR) =>
% 88.47/26.75 ((
% 88.47/26.75 (binunionEcases) =>
% 88.47/26.75 ((
% 88.47/26.75 (binunionE) =>
% 88.47/26.75 ((
% 88.47/26.75 (binunionLsub) =>
% 88.47/26.75 ((
% 88.47/26.75 (binunionRsub) =>
% 88.47/26.75 ((
% 88.47/26.75 (binintersectI) =>
% 88.47/26.75 ((
% 88.47/26.75 (binintersectSubset5) =>
% 88.47/26.75 ((
% 88.47/26.75 (binintersectEL) =>
% 88.47/26.75 ((
% 88.47/26.75 (binintersectLsub) =>
% 88.47/26.75 ((
% 88.47/26.75 (binintersectSubset2) =>
% 88.47/26.75 ((
% 88.47/26.75 (binintersectSubset3) =>
% 88.47/26.75 ((
% 88.47/26.75 (binintersectER) =>
% 88.47/26.75 ((
% 88.47/26.75 (disjointsetsI1) =>
% 88.47/26.75 ((
% 88.47/26.75 (binintersectRsub) =>
% 88.47/26.75 ((
% 88.47/26.75 (binintersectSubset4) =>
% 88.47/26.75 ((
% 88.47/26.75 (binintersectSubset1) =>
% 88.47/26.75 ((
% 88.47/26.75 (bs114d) =>
% 88.47/26.75 ((
% 88.47/26.75 (setminusI) =>
% 88.47/26.75 ((
% 88.47/26.75 (setminusEL) =>
% 88.47/26.75 ((
% 88.47/26.75 (setminusER) =>
% 88.47/26.75 ((
% 88.47/26.75 (setminusSubset2) =>
% 88.47/26.75 ((
% 88.47/26.75 (setminusERneg) =>
% 88.47/26.75 ((
% 88.47/26.75 (setminusELneg) =>
% 88.47/26.75 ((
% 88.47/26.75 (setminusILneg) =>
% 88.47/26.75 ((
% 88.47/26.75 (setminusIRneg) =>
% 88.47/26.75 ((
% 88.47/26.75 (setminusLsub) =>
% 88.47/26.75 ((
% 88.47/26.75 (setminusSubset1) =>
% 88.47/26.75 ((
% 88.47/26.75 (symdiffE) =>
% 88.47/26.75 ((
% 88.47/26.75 (symdiffI1) =>
% 88.47/26.75 ((
% 88.47/26.75 (symdiffI2) =>
% 88.47/26.75 ((
% 88.47/26.75 (symdiffIneg1) =>
% 88.47/26.75 ((
% 88.47/26.75 (symdiffIneg2) =>
% 88.47/26.75 ((
% 88.47/26.75 (secondinupair) =>
% 88.47/26.75 ((
% 88.47/26.75 (setukpairIL) =>
% 88.47/26.75 ((
% 88.47/26.75 (setukpairIR) =>
% 88.47/26.75 ((
% 88.47/26.75 (kpairiskpair) =>
% 88.47/26.75 ((
% 88.47/26.75 (kpairp) =>
% 88.47/26.75 ((
% 88.47/26.75 (singletonsubset) =>
% 88.47/26.75 ((
% 88.47/26.75 (singletoninpowerset) =>
% 88.47/26.75 ((
% 88.47/26.75 (singletoninpowunion) =>
% 88.47/26.75 ((
% 88.47/26.75 (upairset2E) =>
% 88.47/26.75 ((
% 88.47/26.75 (upairsubunion) =>
% 88.47/26.75 ((
% 88.47/26.75 (upairinpowunion) =>
% 88.47/26.75 ((
% 88.47/26.75 (ubforcartprodlem1) =>
% 88.47/26.75 ((
% 88.47/26.75 (ubforcartprodlem2) =>
% 88.47/26.75 ((
% 88.47/26.75 (ubforcartprodlem3) =>
% 88.47/26.75 ((
% 88.47/26.75 (cartprodpairin) =>
% 88.47/26.75 ((
% 88.47/26.75 (cartprodmempair1) =>
% 88.47/26.75 ((
% 88.47/26.75 (cartprodmempair) =>
% 88.47/26.75 ((
% 88.47/26.75 (setunionE2) =>
% 88.47/26.75 ((
% 88.47/26.75 (setunionsingleton1) =>
% 88.47/26.75 ((
% 88.47/26.75 (setunionsingleton2) =>
% 88.47/26.75 ((
% 88.47/26.75 (setunionsingleton) =>
% 88.47/26.75 ((
% 88.47/26.75 (singletonprop) =>
% 88.47/26.75 ((
% 88.47/26.75 (ex1E1) =>
% 88.47/26.75 ((
% 88.47/26.75 (ex1I) =>
% 88.47/26.75 ((
% 88.47/26.75 (ex1I2) =>
% 88.47/26.75 ((
% 88.47/26.75 (singletonsuniq) =>
% 88.47/26.75 ((
% 88.47/26.75 (setukpairinjL1) =>
% 88.47/26.75 ((
% 88.47/26.75 (kfstsingleton) =>
% 88.47/26.75 ((
% 88.47/26.75 (theprop) =>
% 88.47/26.75 ((
% 88.47/26.75 (kfstpairEq) =>
% 88.47/26.75 ((
% 88.47/26.75 (cartprodfstin) =>
% 88.47/26.75 ((
% 88.47/26.75 (setukpairinjL2) =>
% 88.47/26.75 ((
% 88.47/26.75 (setukpairinjL) =>
% 88.47/26.75 ((
% 88.47/26.75 (setukpairinjR11) =>
% 88.47/26.75 ((
% 88.47/26.75 (setukpairinjR12) =>
% 88.47/26.75 ((
% 88.47/26.75 (setukpairinjR1) =>
% 88.47/26.75 ((
% 88.47/26.75 (upairequniteq) =>
% 88.47/26.75 ((
% 88.47/26.75 (setukpairinjR2) =>
% 88.47/26.75 ((
% 88.47/26.75 (setukpairinjR) =>
% 88.47/26.75 ((
% 88.47/26.75 (ksndsingleton) =>
% 88.47/26.75 ((
% 88.47/26.75 (ksndpairEq) =>
% 88.47/26.75 ((
% 88.47/26.75 (kpairsurjEq) =>
% 88.47/26.75 ((
% 88.47/26.75 (cartprodsndin) =>
% 88.47/26.75 ((
% 88.47/26.75 (cartprodpairmemEL) =>
% 88.47/26.75 ((
% 88.47/26.75 (cartprodpairmemER) =>
% 88.47/26.75 ((
% 88.47/26.75 (cartprodmempaircEq) =>
% 88.47/26.75 ((
% 88.47/26.75 (cartprodfstpairEq) =>
% 88.47/26.75 ((
% 88.47/26.75 (cartprodsndpairEq) =>
% 88.47/26.75 ((
% 88.47/26.75 (cartprodpairsurjEq) =>
% 88.47/26.75 ((
% 88.47/26.75 (dpsetconstrI) =>
% 88.47/26.75 ((
% 88.47/26.75 (dpsetconstrSub) =>
% 88.47/26.75 ((
% 88.47/26.75 (setOfPairsIsBReln) =>
% 88.47/26.75 ((
% 88.47/26.75 (dpsetconstrERa) =>
% 88.47/26.75 ((
% 88.47/26.75 (dpsetconstrEL1) =>
% 88.47/26.75 ((
% 88.47/26.75 (dpsetconstrEL2) =>
% 88.47/26.75 ((
% 88.47/26.75 (dpsetconstrER) =>
% 88.47/26.75 ((
% 88.47/26.75 (funcImageSingleton) =>
% 88.47/26.75 ((
% 88.47/26.75 (apProp) =>
% 88.47/26.75 ((
% 88.47/26.75 (app) =>
% 88.47/26.75 ((
% 88.47/26.75 (infuncsetfunc) =>
% 88.47/26.75 ((
% 88.47/26.75 (ap2p) =>
% 88.47/26.75 ((
% 88.47/26.75 (funcinfuncset) =>
% 88.47/26.75 ((
% 88.47/26.75 (lamProp) =>
% 88.47/26.75 ((
% 88.47/26.75 (lamp) =>
% 88.47/26.75 ((
% 88.47/26.75 (lam2p) =>
% 88.47/26.75 ((
% 88.47/26.75 (brelnall1) =>
% 88.47/26.75 ((
% 88.47/26.75 (brelnall2) =>
% 88.47/26.75 ((
% 88.47/26.75 (!!) @ (
% 88.47/26.75 (('#B') @ (
% 88.47/26.75 !!) @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#S') @ (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 '#S') @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 =>))) @
% 88.47/26.75 ex1)))) @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 !!))) @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#S') @ (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 '#B') @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 '#S') @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 =>))) @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#C') @ in)))))))) @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 !!))))) @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#C') @ (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 '#B') @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 '#B') @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 '#S') @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 =>))) @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#C') @ in)))))))))) @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#S') @ (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 '#S') @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 '#B'))) @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 =>))))))) @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#C') @ (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 '#B') @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 '#S') @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 =>))))))) @
% 88.47/26.75 (
% 88.47/26.75 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 88.47/26.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl19])).
% 88.47/26.75 thf(zip_derived_cl33, plain,
% 88.47/26.75 (~ (((omegaSAx) =>
% 88.47/26.75 (((omegaIndAx) =>
% 88.47/26.75 (((replAx) =>
% 88.47/26.75 (((foundationAx) =>
% 88.47/26.75 (((wellorderingAx) =>
% 88.47/26.75 (((descrp) =>
% 88.47/26.75 (((dsetconstrI) =>
% 88.47/26.75 (((dsetconstrEL) =>
% 88.47/26.75 (((dsetconstrER) =>
% 88.47/26.75 (((exuE1) =>
% 88.47/26.75 (((prop2setE) =>
% 88.47/26.75 (((emptysetE) =>
% 88.47/26.75 (((emptysetimpfalse) =>
% 88.47/26.75 (((notinemptyset) =>
% 88.47/26.75 (((exuE3e) =>
% 88.47/26.75 (((setext) =>
% 88.47/26.75 (((emptyI) =>
% 88.47/26.75 (((noeltsimpempty) =>
% 88.47/26.75 (((setbeta) =>
% 88.47/26.75 (((nonemptyE1) =>
% 88.47/26.75 (((nonemptyI) =>
% 88.47/26.75 (((nonemptyI1) =>
% 88.47/26.75 (((setadjoinIL) =>
% 88.47/26.75 (((in @ emptyset @
% 88.47/26.75 (setadjoin @
% 88.47/26.75 emptyset @ emptyset)) =>
% 88.47/26.75 (((setadjoinIR) =>
% 88.47/26.75 (((setadjoinE) =>
% 88.47/26.75 (((setadjoinOr) =>
% 88.47/26.75 (((setoftrueEq) =>
% 88.47/26.75 (((powersetI) =>
% 88.47/26.75 (((emptyinPowerset) =>
% 88.47/26.75 ((
% 88.47/26.75 (emptyInPowerset) =>
% 88.47/26.75 ((
% 88.47/26.75 (powersetE) =>
% 88.47/26.75 ((
% 88.47/26.75 (setunionI) =>
% 88.47/26.75 ((
% 88.47/26.75 (setunionE) =>
% 88.47/26.75 ((
% 88.47/26.75 (subPowSU) =>
% 88.47/26.75 ((
% 88.47/26.75 (exuE2) =>
% 88.47/26.75 ((
% 88.47/26.75 (nonemptyImpWitness) =>
% 88.47/26.75 ((
% 88.47/26.75 (uniqinunit) =>
% 88.47/26.75 ((
% 88.47/26.75 (notinsingleton) =>
% 88.47/26.75 ((
% 88.47/26.75 (eqinunit) =>
% 88.47/26.75 ((
% 88.47/26.75 (singletonsswitch) =>
% 88.47/26.75 ((
% 88.47/26.75 (upairsetE) =>
% 88.47/26.75 ((
% 88.47/26.75 (upairsetIL) =>
% 88.47/26.75 ((
% 88.47/26.75 (upairsetIR) =>
% 88.47/26.75 ((
% 88.47/26.75 (emptyE1) =>
% 88.47/26.75 ((
% 88.47/26.75 (vacuousDall) =>
% 88.47/26.75 ((
% 88.47/26.75 (quantDeMorgan1) =>
% 88.47/26.75 ((
% 88.47/26.75 (quantDeMorgan2) =>
% 88.47/26.75 ((
% 88.47/26.75 (quantDeMorgan3) =>
% 88.47/26.75 ((
% 88.47/26.75 (quantDeMorgan4) =>
% 88.47/26.75 ((
% 88.47/26.75 (prop2setI) =>
% 88.47/26.75 ((
% 88.47/26.75 (prop2set2propI) =>
% 88.47/26.75 ((
% 88.47/26.75 (notdexE) =>
% 88.47/26.75 ((
% 88.47/26.75 (notdallE) =>
% 88.47/26.75 ((
% 88.47/26.75 (exuI1) =>
% 88.47/26.75 ((
% 88.47/26.75 (exuI3) =>
% 88.47/26.75 ((
% 88.47/26.75 (exuI2) =>
% 88.47/26.75 ((
% 88.47/26.75 (inCongP) =>
% 88.47/26.75 ((
% 88.47/26.75 (in__Cong) =>
% 88.47/26.75 ((
% 88.47/26.75 (exuE3u) =>
% 88.47/26.75 ((
% 88.47/26.75 (exu__Cong) =>
% 88.47/26.75 ((
% 88.47/26.75 (setadjoin__Cong) =>
% 88.47/26.75 ((
% 88.47/26.75 (powerset__Cong) =>
% 88.47/26.75 ((
% 88.47/26.75 (setunion__Cong) =>
% 88.47/26.75 ((
% 88.47/26.75 (exuEu) =>
% 88.47/26.75 ((
% 88.47/26.75 (descr__Cong) =>
% 88.47/26.75 ((
% 88.47/26.75 (dsetconstr__Cong) =>
% 88.47/26.75 ((
% 88.47/26.75 (subsetI1) =>
% 88.47/26.75 ((
% 88.47/26.75 (eqimpsubset2) =>
% 88.47/26.75 ((
% 88.47/26.75 (eqimpsubset1) =>
% 88.47/26.75 ((
% 88.47/26.75 (subsetI2) =>
% 88.47/26.75 ((
% 88.47/26.75 (emptysetsubset) =>
% 88.47/26.75 ((
% 88.47/26.75 (subsetE) =>
% 88.47/26.75 ((
% 88.47/26.75 (subsetE2) =>
% 88.47/26.75 ((
% 88.47/26.75 (notsubsetI) =>
% 88.47/26.75 ((
% 88.47/26.75 (notequalI1) =>
% 88.47/26.75 ((
% 88.47/26.75 (notequalI2) =>
% 88.47/26.75 ((
% 88.47/26.75 (subsetRefl) =>
% 88.47/26.75 ((
% 88.47/26.75 (subsetTrans) =>
% 88.47/26.75 ((
% 88.47/26.75 (setadjoinSub) =>
% 88.47/26.75 ((
% 88.47/26.75 (setadjoinSub2) =>
% 88.47/26.75 ((
% 88.47/26.75 (subset2powerset) =>
% 88.47/26.75 ((
% 88.47/26.75 (setextsub) =>
% 88.47/26.75 ((
% 88.47/26.75 (subsetemptysetimpeq) =>
% 88.47/26.75 ((
% 88.47/26.75 (powersetI1) =>
% 88.47/26.75 ((
% 88.47/26.75 (powersetE1) =>
% 88.47/26.75 ((
% 88.47/26.75 (inPowerset) =>
% 88.47/26.75 ((
% 88.47/26.75 (powersetsubset) =>
% 88.47/26.75 ((
% 88.47/26.75 (sepInPowerset) =>
% 88.47/26.75 ((
% 88.47/26.75 (sepSubset) =>
% 88.47/26.75 ((
% 88.47/26.75 (binunionIL) =>
% 88.47/26.75 ((
% 88.47/26.75 (upairset2IR) =>
% 88.47/26.75 ((
% 88.47/26.75 (binunionIR) =>
% 88.47/26.75 ((
% 88.47/26.75 (binunionEcases) =>
% 88.47/26.75 ((
% 88.47/26.75 (binunionE) =>
% 88.47/26.75 ((
% 88.47/26.75 (binunionLsub) =>
% 88.47/26.75 ((
% 88.47/26.75 (binunionRsub) =>
% 88.47/26.75 ((
% 88.47/26.75 (binintersectI) =>
% 88.47/26.75 ((
% 88.47/26.75 (binintersectSubset5) =>
% 88.47/26.75 ((
% 88.47/26.75 (binintersectEL) =>
% 88.47/26.75 ((
% 88.47/26.75 (binintersectLsub) =>
% 88.47/26.75 ((
% 88.47/26.75 (binintersectSubset2) =>
% 88.47/26.75 ((
% 88.47/26.75 (binintersectSubset3) =>
% 88.47/26.75 ((
% 88.47/26.75 (binintersectER) =>
% 88.47/26.75 ((
% 88.47/26.75 (disjointsetsI1) =>
% 88.47/26.75 ((
% 88.47/26.75 (binintersectRsub) =>
% 88.47/26.75 ((
% 88.47/26.75 (binintersectSubset4) =>
% 88.47/26.75 ((
% 88.47/26.75 (binintersectSubset1) =>
% 88.47/26.75 ((
% 88.47/26.75 (bs114d) =>
% 88.47/26.75 ((
% 88.47/26.75 (setminusI) =>
% 88.47/26.75 ((
% 88.47/26.75 (setminusEL) =>
% 88.47/26.75 ((
% 88.47/26.75 (setminusER) =>
% 88.47/26.75 ((
% 88.47/26.75 (setminusSubset2) =>
% 88.47/26.75 ((
% 88.47/26.75 (setminusERneg) =>
% 88.47/26.75 ((
% 88.47/26.75 (setminusELneg) =>
% 88.47/26.75 ((
% 88.47/26.75 (setminusILneg) =>
% 88.47/26.75 ((
% 88.47/26.75 (setminusIRneg) =>
% 88.47/26.75 ((
% 88.47/26.75 (setminusLsub) =>
% 88.47/26.75 ((
% 88.47/26.75 (setminusSubset1) =>
% 88.47/26.75 ((
% 88.47/26.75 (symdiffE) =>
% 88.47/26.75 ((
% 88.47/26.75 (symdiffI1) =>
% 88.47/26.75 ((
% 88.47/26.75 (symdiffI2) =>
% 88.47/26.75 ((
% 88.47/26.75 (symdiffIneg1) =>
% 88.47/26.75 ((
% 88.47/26.75 (symdiffIneg2) =>
% 88.47/26.75 ((
% 88.47/26.75 (secondinupair) =>
% 88.47/26.75 ((
% 88.47/26.75 (setukpairIL) =>
% 88.47/26.75 ((
% 88.47/26.75 (setukpairIR) =>
% 88.47/26.75 ((
% 88.47/26.75 (kpairiskpair) =>
% 88.47/26.75 ((
% 88.47/26.75 (kpairp) =>
% 88.47/26.75 ((
% 88.47/26.75 (singletonsubset) =>
% 88.47/26.75 ((
% 88.47/26.75 (singletoninpowerset) =>
% 88.47/26.75 ((
% 88.47/26.75 (singletoninpowunion) =>
% 88.47/26.75 ((
% 88.47/26.75 (upairset2E) =>
% 88.47/26.75 ((
% 88.47/26.75 (upairsubunion) =>
% 88.47/26.75 ((
% 88.47/26.75 (upairinpowunion) =>
% 88.47/26.75 ((
% 88.47/26.75 (ubforcartprodlem1) =>
% 88.47/26.75 ((
% 88.47/26.75 (ubforcartprodlem2) =>
% 88.47/26.75 ((
% 88.47/26.75 (ubforcartprodlem3) =>
% 88.47/26.75 ((
% 88.47/26.75 (cartprodpairin) =>
% 88.47/26.75 ((
% 88.47/26.75 (cartprodmempair1) =>
% 88.47/26.75 ((
% 88.47/26.75 (cartprodmempair) =>
% 88.47/26.75 ((
% 88.47/26.75 (setunionE2) =>
% 88.47/26.75 ((
% 88.47/26.75 (setunionsingleton1) =>
% 88.47/26.75 ((
% 88.47/26.75 (setunionsingleton2) =>
% 88.47/26.75 ((
% 88.47/26.75 (setunionsingleton) =>
% 88.47/26.75 ((
% 88.47/26.75 (singletonprop) =>
% 88.47/26.75 ((
% 88.47/26.75 (ex1E1) =>
% 88.47/26.75 ((
% 88.47/26.75 (ex1I) =>
% 88.47/26.75 ((
% 88.47/26.75 (ex1I2) =>
% 88.47/26.75 ((
% 88.47/26.75 (singletonsuniq) =>
% 88.47/26.75 ((
% 88.47/26.75 (setukpairinjL1) =>
% 88.47/26.75 ((
% 88.47/26.75 (kfstsingleton) =>
% 88.47/26.75 ((
% 88.47/26.75 (theprop) =>
% 88.47/26.75 ((
% 88.47/26.75 (kfstpairEq) =>
% 88.47/26.75 ((
% 88.47/26.75 (cartprodfstin) =>
% 88.47/26.75 ((
% 88.47/26.75 (setukpairinjL2) =>
% 88.47/26.75 ((
% 88.47/26.75 (setukpairinjL) =>
% 88.47/26.75 ((
% 88.47/26.75 (setukpairinjR11) =>
% 88.47/26.75 ((
% 88.47/26.75 (setukpairinjR12) =>
% 88.47/26.75 ((
% 88.47/26.75 (setukpairinjR1) =>
% 88.47/26.75 ((
% 88.47/26.75 (upairequniteq) =>
% 88.47/26.75 ((
% 88.47/26.75 (setukpairinjR2) =>
% 88.47/26.75 ((
% 88.47/26.75 (setukpairinjR) =>
% 88.47/26.75 ((
% 88.47/26.75 (ksndsingleton) =>
% 88.47/26.75 ((
% 88.47/26.75 (ksndpairEq) =>
% 88.47/26.75 ((
% 88.47/26.75 (kpairsurjEq) =>
% 88.47/26.75 ((
% 88.47/26.75 (cartprodsndin) =>
% 88.47/26.75 ((
% 88.47/26.75 (cartprodpairmemEL) =>
% 88.47/26.75 ((
% 88.47/26.75 (cartprodpairmemER) =>
% 88.47/26.75 ((
% 88.47/26.75 (cartprodmempaircEq) =>
% 88.47/26.75 ((
% 88.47/26.75 (cartprodfstpairEq) =>
% 88.47/26.75 ((
% 88.47/26.75 (cartprodsndpairEq) =>
% 88.47/26.75 ((
% 88.47/26.75 (cartprodpairsurjEq) =>
% 88.47/26.75 ((
% 88.47/26.75 (dpsetconstrI) =>
% 88.47/26.75 ((
% 88.47/26.75 (dpsetconstrSub) =>
% 88.47/26.75 ((
% 88.47/26.75 (setOfPairsIsBReln) =>
% 88.47/26.75 ((
% 88.47/26.75 (dpsetconstrERa) =>
% 88.47/26.75 ((
% 88.47/26.75 (dpsetconstrEL1) =>
% 88.47/26.75 ((
% 88.47/26.75 (dpsetconstrEL2) =>
% 88.47/26.75 ((
% 88.47/26.75 (dpsetconstrER) =>
% 88.47/26.75 ((
% 88.47/26.75 (funcImageSingleton) =>
% 88.47/26.75 ((
% 88.47/26.75 (apProp) =>
% 88.47/26.75 ((
% 88.47/26.75 (app) =>
% 88.47/26.75 ((
% 88.47/26.75 (infuncsetfunc) =>
% 88.47/26.75 ((
% 88.47/26.75 (ap2p) =>
% 88.47/26.75 ((
% 88.47/26.75 (funcinfuncset) =>
% 88.47/26.75 ((
% 88.47/26.75 (lamProp) =>
% 88.47/26.75 ((
% 88.47/26.75 (lamp) =>
% 88.47/26.75 ((
% 88.47/26.75 (lam2p) =>
% 88.47/26.75 ((
% 88.47/26.75 (brelnall1) =>
% 88.47/26.75 ((
% 88.47/26.75 (brelnall2) =>
% 88.47/26.75 ((
% 88.47/26.75 (!!) @ (
% 88.47/26.75 (('#B') @ (
% 88.47/26.75 !!) @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#S') @ (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 '#S') @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 =>))) @
% 88.47/26.75 ex1)))) @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 !!))) @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#S') @ (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 '#B') @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 '#S') @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 =>))) @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#C') @ in)))))))) @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 !!))))) @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#C') @ (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 '#B') @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 '#B') @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 '#S') @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 =>))) @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#C') @ in)))))))))) @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#S') @ (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 '#S') @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 '#B'))) @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 =>))))))) @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#C') @ (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 '#B') @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 '#S') @
% 88.47/26.75 (
% 88.47/26.75 (
% 88.47/26.75 ('#B') @ (
% 88.47/26.75 =>))))))) @
% 88.47/26.75 (
% 88.47/26.75 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 88.47/26.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl25])).
% 88.47/26.75 thf(zip_derived_cl40, plain,
% 88.47/26.75 (~ (((omegaIndAx) =>
% 88.47/26.75 (((replAx) =>
% 88.47/26.75 (((foundationAx) =>
% 88.47/26.75 (((wellorderingAx) =>
% 88.47/26.75 (((descrp) =>
% 88.47/26.75 (((dsetconstrI) =>
% 88.47/26.75 (((dsetconstrEL) =>
% 88.47/26.75 (((dsetconstrER) =>
% 88.47/26.75 (((exuE1) =>
% 88.47/26.75 (((prop2setE) =>
% 88.47/26.75 (((emptysetE) =>
% 88.47/26.75 (((emptysetimpfalse) =>
% 88.47/26.75 (((notinemptyset) =>
% 88.47/26.75 (((exuE3e) =>
% 88.47/26.75 (((setext) =>
% 88.47/26.75 (((emptyI) =>
% 88.47/26.75 (((noeltsimpempty) =>
% 88.47/26.75 (((setbeta) =>
% 88.47/26.75 (((nonemptyE1) =>
% 88.47/26.75 (((nonemptyI) =>
% 88.47/26.75 (((nonemptyI1) =>
% 88.47/26.75 (((setadjoinIL) =>
% 88.47/26.75 (((in @ emptyset @
% 88.47/26.75 (setadjoin @ emptyset @
% 88.47/26.75 emptyset)) =>
% 88.47/26.75 (((setadjoinIR) =>
% 88.47/26.75 (((setadjoinE) =>
% 88.47/26.75 (((setadjoinOr) =>
% 88.47/26.75 (((setoftrueEq) =>
% 88.47/26.75 (((powersetI) =>
% 88.47/26.75 (((emptyinPowerset) =>
% 88.47/26.75 (((emptyInPowerset) =>
% 88.47/26.75 ((
% 88.47/26.75 (powersetE) =>
% 88.47/26.75 ((
% 88.47/26.75 (setunionI) =>
% 88.47/26.75 ((
% 88.47/26.75 (setunionE) =>
% 88.47/26.75 ((
% 88.47/26.75 (subPowSU) =>
% 88.47/26.75 ((
% 88.47/26.75 (exuE2) =>
% 88.47/26.75 ((
% 88.47/26.75 (nonemptyImpWitness) =>
% 88.47/26.75 ((
% 88.47/26.75 (uniqinunit) =>
% 88.47/26.75 ((
% 88.47/26.75 (notinsingleton) =>
% 88.47/26.75 ((
% 88.47/26.75 (eqinunit) =>
% 88.47/26.75 ((
% 88.47/26.75 (singletonsswitch) =>
% 88.47/26.75 ((
% 88.47/26.75 (upairsetE) =>
% 88.47/26.75 ((
% 88.47/26.75 (upairsetIL) =>
% 88.47/26.75 ((
% 88.47/26.75 (upairsetIR) =>
% 88.47/26.75 ((
% 88.47/26.75 (emptyE1) =>
% 88.47/26.75 ((
% 88.47/26.75 (vacuousDall) =>
% 88.47/26.75 ((
% 88.47/26.75 (quantDeMorgan1) =>
% 88.47/26.75 ((
% 88.47/26.75 (quantDeMorgan2) =>
% 88.47/26.75 ((
% 88.47/26.75 (quantDeMorgan3) =>
% 88.47/26.75 ((
% 88.47/26.75 (quantDeMorgan4) =>
% 88.47/26.75 ((
% 88.47/26.75 (prop2setI) =>
% 88.47/26.75 ((
% 88.47/26.75 (prop2set2propI) =>
% 88.47/26.75 ((
% 88.47/26.75 (notdexE) =>
% 88.47/26.75 ((
% 88.47/26.75 (notdallE) =>
% 88.47/26.75 ((
% 88.47/26.75 (exuI1) =>
% 88.47/26.75 ((
% 88.47/26.75 (exuI3) =>
% 88.47/26.75 ((
% 88.47/26.75 (exuI2) =>
% 88.47/26.75 ((
% 88.47/26.75 (inCongP) =>
% 88.47/26.75 ((
% 88.47/26.75 (in__Cong) =>
% 88.47/26.75 ((
% 88.47/26.75 (exuE3u) =>
% 88.47/26.75 ((
% 88.47/26.75 (exu__Cong) =>
% 88.47/26.75 ((
% 88.47/26.75 (setadjoin__Cong) =>
% 88.47/26.75 ((
% 88.47/26.75 (powerset__Cong) =>
% 88.47/26.75 ((
% 88.47/26.75 (setunion__Cong) =>
% 88.47/26.75 ((
% 88.47/26.75 (exuEu) =>
% 88.47/26.75 ((
% 88.47/26.75 (descr__Cong) =>
% 88.47/26.75 ((
% 88.47/26.75 (dsetconstr__Cong) =>
% 88.47/26.75 ((
% 88.47/26.75 (subsetI1) =>
% 88.47/26.75 ((
% 88.47/26.75 (eqimpsubset2) =>
% 88.47/26.75 ((
% 88.47/26.75 (eqimpsubset1) =>
% 88.47/26.75 ((
% 88.47/26.75 (subsetI2) =>
% 88.47/26.75 ((
% 88.47/26.75 (emptysetsubset) =>
% 88.47/26.75 ((
% 88.47/26.75 (subsetE) =>
% 88.47/26.75 ((
% 88.47/26.75 (subsetE2) =>
% 88.47/26.75 ((
% 88.47/26.75 (notsubsetI) =>
% 88.47/26.75 ((
% 88.47/26.75 (notequalI1) =>
% 88.47/26.75 ((
% 88.47/26.76 (notequalI2) =>
% 88.47/26.76 ((
% 88.47/26.76 (subsetRefl) =>
% 88.47/26.76 ((
% 88.47/26.76 (subsetTrans) =>
% 88.47/26.76 ((
% 88.47/26.76 (setadjoinSub) =>
% 88.47/26.76 ((
% 88.47/26.76 (setadjoinSub2) =>
% 88.47/26.76 ((
% 88.47/26.76 (subset2powerset) =>
% 88.47/26.76 ((
% 88.47/26.76 (setextsub) =>
% 88.47/26.76 ((
% 88.47/26.76 (subsetemptysetimpeq) =>
% 88.47/26.76 ((
% 88.47/26.76 (powersetI1) =>
% 88.47/26.76 ((
% 88.47/26.76 (powersetE1) =>
% 88.47/26.76 ((
% 88.47/26.76 (inPowerset) =>
% 88.47/26.76 ((
% 88.47/26.76 (powersetsubset) =>
% 88.47/26.76 ((
% 88.47/26.76 (sepInPowerset) =>
% 88.47/26.76 ((
% 88.47/26.76 (sepSubset) =>
% 88.47/26.76 ((
% 88.47/26.76 (binunionIL) =>
% 88.47/26.76 ((
% 88.47/26.76 (upairset2IR) =>
% 88.47/26.76 ((
% 88.47/26.76 (binunionIR) =>
% 88.47/26.76 ((
% 88.47/26.76 (binunionEcases) =>
% 88.47/26.76 ((
% 88.47/26.76 (binunionE) =>
% 88.47/26.76 ((
% 88.47/26.76 (binunionLsub) =>
% 88.47/26.76 ((
% 88.47/26.76 (binunionRsub) =>
% 88.47/26.76 ((
% 88.47/26.76 (binintersectI) =>
% 88.47/26.76 ((
% 88.47/26.76 (binintersectSubset5) =>
% 88.47/26.76 ((
% 88.47/26.76 (binintersectEL) =>
% 88.47/26.76 ((
% 88.47/26.76 (binintersectLsub) =>
% 88.47/26.76 ((
% 88.47/26.76 (binintersectSubset2) =>
% 88.47/26.76 ((
% 88.47/26.76 (binintersectSubset3) =>
% 88.47/26.76 ((
% 88.47/26.76 (binintersectER) =>
% 88.47/26.76 ((
% 88.47/26.76 (disjointsetsI1) =>
% 88.47/26.76 ((
% 88.47/26.76 (binintersectRsub) =>
% 88.47/26.76 ((
% 88.47/26.76 (binintersectSubset4) =>
% 88.47/26.76 ((
% 88.47/26.76 (binintersectSubset1) =>
% 88.47/26.76 ((
% 88.47/26.76 (bs114d) =>
% 88.47/26.76 ((
% 88.47/26.76 (setminusI) =>
% 88.47/26.76 ((
% 88.47/26.76 (setminusEL) =>
% 88.47/26.76 ((
% 88.47/26.76 (setminusER) =>
% 88.47/26.76 ((
% 88.47/26.76 (setminusSubset2) =>
% 88.47/26.76 ((
% 88.47/26.76 (setminusERneg) =>
% 88.47/26.76 ((
% 88.47/26.76 (setminusELneg) =>
% 88.47/26.76 ((
% 88.47/26.76 (setminusILneg) =>
% 88.47/26.76 ((
% 88.47/26.76 (setminusIRneg) =>
% 88.47/26.76 ((
% 88.47/26.76 (setminusLsub) =>
% 88.47/26.76 ((
% 88.47/26.76 (setminusSubset1) =>
% 88.47/26.76 ((
% 88.47/26.76 (symdiffE) =>
% 88.47/26.76 ((
% 88.47/26.76 (symdiffI1) =>
% 88.47/26.76 ((
% 88.47/26.76 (symdiffI2) =>
% 88.47/26.76 ((
% 88.47/26.76 (symdiffIneg1) =>
% 88.47/26.76 ((
% 88.47/26.76 (symdiffIneg2) =>
% 88.47/26.76 ((
% 88.47/26.76 (secondinupair) =>
% 88.47/26.76 ((
% 88.47/26.76 (setukpairIL) =>
% 88.47/26.76 ((
% 88.47/26.76 (setukpairIR) =>
% 88.47/26.76 ((
% 88.47/26.76 (kpairiskpair) =>
% 88.47/26.76 ((
% 88.47/26.76 (kpairp) =>
% 88.47/26.76 ((
% 88.47/26.76 (singletonsubset) =>
% 88.47/26.76 ((
% 88.47/26.76 (singletoninpowerset) =>
% 88.47/26.76 ((
% 88.47/26.76 (singletoninpowunion) =>
% 88.47/26.76 ((
% 88.47/26.76 (upairset2E) =>
% 88.47/26.76 ((
% 88.47/26.76 (upairsubunion) =>
% 88.47/26.76 ((
% 88.47/26.76 (upairinpowunion) =>
% 88.47/26.76 ((
% 88.47/26.76 (ubforcartprodlem1) =>
% 88.47/26.76 ((
% 88.47/26.76 (ubforcartprodlem2) =>
% 88.47/26.76 ((
% 88.47/26.76 (ubforcartprodlem3) =>
% 88.47/26.76 ((
% 88.47/26.76 (cartprodpairin) =>
% 88.47/26.76 ((
% 88.47/26.76 (cartprodmempair1) =>
% 88.47/26.76 ((
% 88.47/26.76 (cartprodmempair) =>
% 88.47/26.76 ((
% 88.47/26.76 (setunionE2) =>
% 88.47/26.76 ((
% 88.47/26.76 (setunionsingleton1) =>
% 88.47/26.76 ((
% 88.47/26.76 (setunionsingleton2) =>
% 88.47/26.76 ((
% 88.47/26.76 (setunionsingleton) =>
% 88.47/26.76 ((
% 88.47/26.76 (singletonprop) =>
% 88.47/26.76 ((
% 88.47/26.76 (ex1E1) =>
% 88.47/26.76 ((
% 88.47/26.76 (ex1I) =>
% 88.47/26.76 ((
% 88.47/26.76 (ex1I2) =>
% 88.47/26.76 ((
% 88.47/26.76 (singletonsuniq) =>
% 88.47/26.76 ((
% 88.47/26.76 (setukpairinjL1) =>
% 88.47/26.76 ((
% 88.47/26.76 (kfstsingleton) =>
% 88.47/26.76 ((
% 88.47/26.76 (theprop) =>
% 88.47/26.76 ((
% 88.47/26.76 (kfstpairEq) =>
% 88.47/26.76 ((
% 88.47/26.76 (cartprodfstin) =>
% 88.47/26.76 ((
% 88.47/26.76 (setukpairinjL2) =>
% 88.47/26.76 ((
% 88.47/26.76 (setukpairinjL) =>
% 88.47/26.76 ((
% 88.47/26.76 (setukpairinjR11) =>
% 88.47/26.76 ((
% 88.47/26.76 (setukpairinjR12) =>
% 88.47/26.76 ((
% 88.47/26.76 (setukpairinjR1) =>
% 88.47/26.76 ((
% 88.47/26.76 (upairequniteq) =>
% 88.47/26.76 ((
% 88.47/26.76 (setukpairinjR2) =>
% 88.47/26.76 ((
% 88.47/26.76 (setukpairinjR) =>
% 88.47/26.76 ((
% 88.47/26.76 (ksndsingleton) =>
% 88.47/26.76 ((
% 88.47/26.76 (ksndpairEq) =>
% 88.47/26.76 ((
% 88.47/26.76 (kpairsurjEq) =>
% 88.47/26.76 ((
% 88.47/26.76 (cartprodsndin) =>
% 88.47/26.76 ((
% 88.47/26.76 (cartprodpairmemEL) =>
% 88.47/26.76 ((
% 88.47/26.76 (cartprodpairmemER) =>
% 88.47/26.76 ((
% 88.47/26.76 (cartprodmempaircEq) =>
% 88.47/26.76 ((
% 88.47/26.76 (cartprodfstpairEq) =>
% 88.47/26.76 ((
% 88.47/26.76 (cartprodsndpairEq) =>
% 88.47/26.76 ((
% 88.47/26.76 (cartprodpairsurjEq) =>
% 88.47/26.76 ((
% 88.47/26.76 (dpsetconstrI) =>
% 88.47/26.76 ((
% 88.47/26.76 (dpsetconstrSub) =>
% 88.47/26.76 ((
% 88.47/26.76 (setOfPairsIsBReln) =>
% 88.47/26.76 ((
% 88.47/26.76 (dpsetconstrERa) =>
% 88.47/26.76 ((
% 88.47/26.76 (dpsetconstrEL1) =>
% 88.47/26.76 ((
% 88.47/26.76 (dpsetconstrEL2) =>
% 88.47/26.76 ((
% 88.47/26.76 (dpsetconstrER) =>
% 88.47/26.76 ((
% 88.47/26.76 (funcImageSingleton) =>
% 88.47/26.76 ((
% 88.47/26.76 (apProp) =>
% 88.47/26.76 ((
% 88.47/26.76 (app) =>
% 88.47/26.76 ((
% 88.47/26.76 (infuncsetfunc) =>
% 88.47/26.76 ((
% 88.47/26.76 (ap2p) =>
% 88.47/26.76 ((
% 88.47/26.76 (funcinfuncset) =>
% 88.47/26.76 ((
% 88.47/26.76 (lamProp) =>
% 88.47/26.76 ((
% 88.47/26.76 (lamp) =>
% 88.47/26.76 ((
% 88.47/26.76 (lam2p) =>
% 88.47/26.76 ((
% 88.47/26.76 (brelnall1) =>
% 88.47/26.76 ((
% 88.47/26.76 (brelnall2) =>
% 88.47/26.76 ((
% 88.47/26.76 (!!) @ (
% 88.47/26.76 (('#B') @ (
% 88.47/26.76 !!) @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#S') @ (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 '#S') @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 =>))) @
% 88.47/26.76 ex1)))) @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 !!))) @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#S') @ (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 '#B') @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 '#S') @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 =>))) @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#C') @ in)))))))) @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 !!))))) @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#C') @ (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 '#B') @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 '#B') @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 '#S') @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 =>))) @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#C') @ in)))))))))) @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#S') @ (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 '#S') @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 '#B'))) @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 =>))))))) @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#C') @ (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 '#B') @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 '#S') @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 =>))))))) @
% 88.47/26.76 (
% 88.47/26.76 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 88.47/26.76 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl33])).
% 88.47/26.76 thf(zip_derived_cl46, plain,
% 88.47/26.76 (~ (((replAx) =>
% 88.47/26.76 (((foundationAx) =>
% 88.47/26.76 (((wellorderingAx) =>
% 88.47/26.76 (((descrp) =>
% 88.47/26.76 (((dsetconstrI) =>
% 88.47/26.76 (((dsetconstrEL) =>
% 88.47/26.76 (((dsetconstrER) =>
% 88.47/26.76 (((exuE1) =>
% 88.47/26.76 (((prop2setE) =>
% 88.47/26.76 (((emptysetE) =>
% 88.47/26.76 (((emptysetimpfalse) =>
% 88.47/26.76 (((notinemptyset) =>
% 88.47/26.76 (((exuE3e) =>
% 88.47/26.76 (((setext) =>
% 88.47/26.76 (((emptyI) =>
% 88.47/26.76 (((noeltsimpempty) =>
% 88.47/26.76 (((setbeta) =>
% 88.47/26.76 (((nonemptyE1) =>
% 88.47/26.76 (((nonemptyI) =>
% 88.47/26.76 (((nonemptyI1) =>
% 88.47/26.76 (((setadjoinIL) =>
% 88.47/26.76 (((in @ emptyset @
% 88.47/26.76 (setadjoin @ emptyset @
% 88.47/26.76 emptyset)) =>
% 88.47/26.76 (((setadjoinIR) =>
% 88.47/26.76 (((setadjoinE) =>
% 88.47/26.76 (((setadjoinOr) =>
% 88.47/26.76 (((setoftrueEq) =>
% 88.47/26.76 (((powersetI) =>
% 88.47/26.76 (((emptyinPowerset) =>
% 88.47/26.76 (((emptyInPowerset) =>
% 88.47/26.76 (((powersetE) =>
% 88.47/26.76 ((
% 88.47/26.76 (setunionI) =>
% 88.47/26.76 ((
% 88.47/26.76 (setunionE) =>
% 88.47/26.76 ((
% 88.47/26.76 (subPowSU) =>
% 88.47/26.76 ((
% 88.47/26.76 (exuE2) =>
% 88.47/26.76 ((
% 88.47/26.76 (nonemptyImpWitness) =>
% 88.47/26.76 ((
% 88.47/26.76 (uniqinunit) =>
% 88.47/26.76 ((
% 88.47/26.76 (notinsingleton) =>
% 88.47/26.76 ((
% 88.47/26.76 (eqinunit) =>
% 88.47/26.76 ((
% 88.47/26.76 (singletonsswitch) =>
% 88.47/26.76 ((
% 88.47/26.76 (upairsetE) =>
% 88.47/26.76 ((
% 88.47/26.76 (upairsetIL) =>
% 88.47/26.76 ((
% 88.47/26.76 (upairsetIR) =>
% 88.47/26.76 ((
% 88.47/26.76 (emptyE1) =>
% 88.47/26.76 ((
% 88.47/26.76 (vacuousDall) =>
% 88.47/26.76 ((
% 88.47/26.76 (quantDeMorgan1) =>
% 88.47/26.76 ((
% 88.47/26.76 (quantDeMorgan2) =>
% 88.47/26.76 ((
% 88.47/26.76 (quantDeMorgan3) =>
% 88.47/26.76 ((
% 88.47/26.76 (quantDeMorgan4) =>
% 88.47/26.76 ((
% 88.47/26.76 (prop2setI) =>
% 88.47/26.76 ((
% 88.47/26.76 (prop2set2propI) =>
% 88.47/26.76 ((
% 88.47/26.76 (notdexE) =>
% 88.47/26.76 ((
% 88.47/26.76 (notdallE) =>
% 88.47/26.76 ((
% 88.47/26.76 (exuI1) =>
% 88.47/26.76 ((
% 88.47/26.76 (exuI3) =>
% 88.47/26.76 ((
% 88.47/26.76 (exuI2) =>
% 88.47/26.76 ((
% 88.47/26.76 (inCongP) =>
% 88.47/26.76 ((
% 88.47/26.76 (in__Cong) =>
% 88.47/26.76 ((
% 88.47/26.76 (exuE3u) =>
% 88.47/26.76 ((
% 88.47/26.76 (exu__Cong) =>
% 88.47/26.76 ((
% 88.47/26.76 (setadjoin__Cong) =>
% 88.47/26.76 ((
% 88.47/26.76 (powerset__Cong) =>
% 88.47/26.76 ((
% 88.47/26.76 (setunion__Cong) =>
% 88.47/26.76 ((
% 88.47/26.76 (exuEu) =>
% 88.47/26.76 ((
% 88.47/26.76 (descr__Cong) =>
% 88.47/26.76 ((
% 88.47/26.76 (dsetconstr__Cong) =>
% 88.47/26.76 ((
% 88.47/26.76 (subsetI1) =>
% 88.47/26.76 ((
% 88.47/26.76 (eqimpsubset2) =>
% 88.47/26.76 ((
% 88.47/26.76 (eqimpsubset1) =>
% 88.47/26.76 ((
% 88.47/26.76 (subsetI2) =>
% 88.47/26.76 ((
% 88.47/26.76 (emptysetsubset) =>
% 88.47/26.76 ((
% 88.47/26.76 (subsetE) =>
% 88.47/26.76 ((
% 88.47/26.76 (subsetE2) =>
% 88.47/26.76 ((
% 88.47/26.76 (notsubsetI) =>
% 88.47/26.76 ((
% 88.47/26.76 (notequalI1) =>
% 88.47/26.76 ((
% 88.47/26.76 (notequalI2) =>
% 88.47/26.76 ((
% 88.47/26.76 (subsetRefl) =>
% 88.47/26.76 ((
% 88.47/26.76 (subsetTrans) =>
% 88.47/26.76 ((
% 88.47/26.76 (setadjoinSub) =>
% 88.47/26.76 ((
% 88.47/26.76 (setadjoinSub2) =>
% 88.47/26.76 ((
% 88.47/26.76 (subset2powerset) =>
% 88.47/26.76 ((
% 88.47/26.76 (setextsub) =>
% 88.47/26.76 ((
% 88.47/26.76 (subsetemptysetimpeq) =>
% 88.47/26.76 ((
% 88.47/26.76 (powersetI1) =>
% 88.47/26.76 ((
% 88.47/26.76 (powersetE1) =>
% 88.47/26.76 ((
% 88.47/26.76 (inPowerset) =>
% 88.47/26.76 ((
% 88.47/26.76 (powersetsubset) =>
% 88.47/26.76 ((
% 88.47/26.76 (sepInPowerset) =>
% 88.47/26.76 ((
% 88.47/26.76 (sepSubset) =>
% 88.47/26.76 ((
% 88.47/26.76 (binunionIL) =>
% 88.47/26.76 ((
% 88.47/26.76 (upairset2IR) =>
% 88.47/26.76 ((
% 88.47/26.76 (binunionIR) =>
% 88.47/26.76 ((
% 88.47/26.76 (binunionEcases) =>
% 88.47/26.76 ((
% 88.47/26.76 (binunionE) =>
% 88.47/26.76 ((
% 88.47/26.76 (binunionLsub) =>
% 88.47/26.76 ((
% 88.47/26.76 (binunionRsub) =>
% 88.47/26.76 ((
% 88.47/26.76 (binintersectI) =>
% 88.47/26.76 ((
% 88.47/26.76 (binintersectSubset5) =>
% 88.47/26.76 ((
% 88.47/26.76 (binintersectEL) =>
% 88.47/26.76 ((
% 88.47/26.76 (binintersectLsub) =>
% 88.47/26.76 ((
% 88.47/26.76 (binintersectSubset2) =>
% 88.47/26.76 ((
% 88.47/26.76 (binintersectSubset3) =>
% 88.47/26.76 ((
% 88.47/26.76 (binintersectER) =>
% 88.47/26.76 ((
% 88.47/26.76 (disjointsetsI1) =>
% 88.47/26.76 ((
% 88.47/26.76 (binintersectRsub) =>
% 88.47/26.76 ((
% 88.47/26.76 (binintersectSubset4) =>
% 88.47/26.76 ((
% 88.47/26.76 (binintersectSubset1) =>
% 88.47/26.76 ((
% 88.47/26.76 (bs114d) =>
% 88.47/26.76 ((
% 88.47/26.76 (setminusI) =>
% 88.47/26.76 ((
% 88.47/26.76 (setminusEL) =>
% 88.47/26.76 ((
% 88.47/26.76 (setminusER) =>
% 88.47/26.76 ((
% 88.47/26.76 (setminusSubset2) =>
% 88.47/26.76 ((
% 88.47/26.76 (setminusERneg) =>
% 88.47/26.76 ((
% 88.47/26.76 (setminusELneg) =>
% 88.47/26.76 ((
% 88.47/26.76 (setminusILneg) =>
% 88.47/26.76 ((
% 88.47/26.76 (setminusIRneg) =>
% 88.47/26.76 ((
% 88.47/26.76 (setminusLsub) =>
% 88.47/26.76 ((
% 88.47/26.76 (setminusSubset1) =>
% 88.47/26.76 ((
% 88.47/26.76 (symdiffE) =>
% 88.47/26.76 ((
% 88.47/26.76 (symdiffI1) =>
% 88.47/26.76 ((
% 88.47/26.76 (symdiffI2) =>
% 88.47/26.76 ((
% 88.47/26.76 (symdiffIneg1) =>
% 88.47/26.76 ((
% 88.47/26.76 (symdiffIneg2) =>
% 88.47/26.76 ((
% 88.47/26.76 (secondinupair) =>
% 88.47/26.76 ((
% 88.47/26.76 (setukpairIL) =>
% 88.47/26.76 ((
% 88.47/26.76 (setukpairIR) =>
% 88.47/26.76 ((
% 88.47/26.76 (kpairiskpair) =>
% 88.47/26.76 ((
% 88.47/26.76 (kpairp) =>
% 88.47/26.76 ((
% 88.47/26.76 (singletonsubset) =>
% 88.47/26.76 ((
% 88.47/26.76 (singletoninpowerset) =>
% 88.47/26.76 ((
% 88.47/26.76 (singletoninpowunion) =>
% 88.47/26.76 ((
% 88.47/26.76 (upairset2E) =>
% 88.47/26.76 ((
% 88.47/26.76 (upairsubunion) =>
% 88.47/26.76 ((
% 88.47/26.76 (upairinpowunion) =>
% 88.47/26.76 ((
% 88.47/26.76 (ubforcartprodlem1) =>
% 88.47/26.76 ((
% 88.47/26.76 (ubforcartprodlem2) =>
% 88.47/26.76 ((
% 88.47/26.76 (ubforcartprodlem3) =>
% 88.47/26.76 ((
% 88.47/26.76 (cartprodpairin) =>
% 88.47/26.76 ((
% 88.47/26.76 (cartprodmempair1) =>
% 88.47/26.76 ((
% 88.47/26.76 (cartprodmempair) =>
% 88.47/26.76 ((
% 88.47/26.76 (setunionE2) =>
% 88.47/26.76 ((
% 88.47/26.76 (setunionsingleton1) =>
% 88.47/26.76 ((
% 88.47/26.76 (setunionsingleton2) =>
% 88.47/26.76 ((
% 88.47/26.76 (setunionsingleton) =>
% 88.47/26.76 ((
% 88.47/26.76 (singletonprop) =>
% 88.47/26.76 ((
% 88.47/26.76 (ex1E1) =>
% 88.47/26.76 ((
% 88.47/26.76 (ex1I) =>
% 88.47/26.76 ((
% 88.47/26.76 (ex1I2) =>
% 88.47/26.76 ((
% 88.47/26.76 (singletonsuniq) =>
% 88.47/26.76 ((
% 88.47/26.76 (setukpairinjL1) =>
% 88.47/26.76 ((
% 88.47/26.76 (kfstsingleton) =>
% 88.47/26.76 ((
% 88.47/26.76 (theprop) =>
% 88.47/26.76 ((
% 88.47/26.76 (kfstpairEq) =>
% 88.47/26.76 ((
% 88.47/26.76 (cartprodfstin) =>
% 88.47/26.76 ((
% 88.47/26.76 (setukpairinjL2) =>
% 88.47/26.76 ((
% 88.47/26.76 (setukpairinjL) =>
% 88.47/26.76 ((
% 88.47/26.76 (setukpairinjR11) =>
% 88.47/26.76 ((
% 88.47/26.76 (setukpairinjR12) =>
% 88.47/26.76 ((
% 88.47/26.76 (setukpairinjR1) =>
% 88.47/26.76 ((
% 88.47/26.76 (upairequniteq) =>
% 88.47/26.76 ((
% 88.47/26.76 (setukpairinjR2) =>
% 88.47/26.76 ((
% 88.47/26.76 (setukpairinjR) =>
% 88.47/26.76 ((
% 88.47/26.76 (ksndsingleton) =>
% 88.47/26.76 ((
% 88.47/26.76 (ksndpairEq) =>
% 88.47/26.76 ((
% 88.47/26.76 (kpairsurjEq) =>
% 88.47/26.76 ((
% 88.47/26.76 (cartprodsndin) =>
% 88.47/26.76 ((
% 88.47/26.76 (cartprodpairmemEL) =>
% 88.47/26.76 ((
% 88.47/26.76 (cartprodpairmemER) =>
% 88.47/26.76 ((
% 88.47/26.76 (cartprodmempaircEq) =>
% 88.47/26.76 ((
% 88.47/26.76 (cartprodfstpairEq) =>
% 88.47/26.76 ((
% 88.47/26.76 (cartprodsndpairEq) =>
% 88.47/26.76 ((
% 88.47/26.76 (cartprodpairsurjEq) =>
% 88.47/26.76 ((
% 88.47/26.76 (dpsetconstrI) =>
% 88.47/26.76 ((
% 88.47/26.76 (dpsetconstrSub) =>
% 88.47/26.76 ((
% 88.47/26.76 (setOfPairsIsBReln) =>
% 88.47/26.76 ((
% 88.47/26.76 (dpsetconstrERa) =>
% 88.47/26.76 ((
% 88.47/26.76 (dpsetconstrEL1) =>
% 88.47/26.76 ((
% 88.47/26.76 (dpsetconstrEL2) =>
% 88.47/26.76 ((
% 88.47/26.76 (dpsetconstrER) =>
% 88.47/26.76 ((
% 88.47/26.76 (funcImageSingleton) =>
% 88.47/26.76 ((
% 88.47/26.76 (apProp) =>
% 88.47/26.76 ((
% 88.47/26.76 (app) =>
% 88.47/26.76 ((
% 88.47/26.76 (infuncsetfunc) =>
% 88.47/26.76 ((
% 88.47/26.76 (ap2p) =>
% 88.47/26.76 ((
% 88.47/26.76 (funcinfuncset) =>
% 88.47/26.76 ((
% 88.47/26.76 (lamProp) =>
% 88.47/26.76 ((
% 88.47/26.76 (lamp) =>
% 88.47/26.76 ((
% 88.47/26.76 (lam2p) =>
% 88.47/26.76 ((
% 88.47/26.76 (brelnall1) =>
% 88.47/26.76 ((
% 88.47/26.76 (brelnall2) =>
% 88.47/26.76 ((
% 88.47/26.76 (!!) @ (
% 88.47/26.76 (('#B') @ (
% 88.47/26.76 !!) @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#S') @ (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 '#S') @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 =>))) @
% 88.47/26.76 ex1)))) @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 !!))) @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#S') @ (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 '#B') @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 '#S') @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 =>))) @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#C') @ in)))))))) @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 !!))))) @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#C') @ (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 '#B') @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 '#B') @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 '#S') @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 =>))) @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#C') @ in)))))))))) @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#S') @ (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 '#S') @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 '#B'))) @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 =>))))))) @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#C') @ (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 '#B') @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 '#S') @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 =>))))))) @
% 88.47/26.76 (
% 88.47/26.76 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 88.47/26.76 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl40])).
% 88.47/26.76 thf(zip_derived_cl52, plain,
% 88.47/26.76 (~ (((foundationAx) =>
% 88.47/26.76 (((wellorderingAx) =>
% 88.47/26.76 (((descrp) =>
% 88.47/26.76 (((dsetconstrI) =>
% 88.47/26.76 (((dsetconstrEL) =>
% 88.47/26.76 (((dsetconstrER) =>
% 88.47/26.76 (((exuE1) =>
% 88.47/26.76 (((prop2setE) =>
% 88.47/26.76 (((emptysetE) =>
% 88.47/26.76 (((emptysetimpfalse) =>
% 88.47/26.76 (((notinemptyset) =>
% 88.47/26.76 (((exuE3e) =>
% 88.47/26.76 (((setext) =>
% 88.47/26.76 (((emptyI) =>
% 88.47/26.76 (((noeltsimpempty) =>
% 88.47/26.76 (((setbeta) =>
% 88.47/26.76 (((nonemptyE1) =>
% 88.47/26.76 (((nonemptyI) =>
% 88.47/26.76 (((nonemptyI1) =>
% 88.47/26.76 (((setadjoinIL) =>
% 88.47/26.76 (((in @ emptyset @
% 88.47/26.76 (setadjoin @ emptyset @
% 88.47/26.76 emptyset)) =>
% 88.47/26.76 (((setadjoinIR) =>
% 88.47/26.76 (((setadjoinE) =>
% 88.47/26.76 (((setadjoinOr) =>
% 88.47/26.76 (((setoftrueEq) =>
% 88.47/26.76 (((powersetI) =>
% 88.47/26.76 (((emptyinPowerset) =>
% 88.47/26.76 (((emptyInPowerset) =>
% 88.47/26.76 (((powersetE) =>
% 88.47/26.76 (((setunionI) =>
% 88.47/26.76 ((
% 88.47/26.76 (setunionE) =>
% 88.47/26.76 ((
% 88.47/26.76 (subPowSU) =>
% 88.47/26.76 ((
% 88.47/26.76 (exuE2) =>
% 88.47/26.76 ((
% 88.47/26.76 (nonemptyImpWitness) =>
% 88.47/26.76 ((
% 88.47/26.76 (uniqinunit) =>
% 88.47/26.76 ((
% 88.47/26.76 (notinsingleton) =>
% 88.47/26.76 ((
% 88.47/26.76 (eqinunit) =>
% 88.47/26.76 ((
% 88.47/26.76 (singletonsswitch) =>
% 88.47/26.76 ((
% 88.47/26.76 (upairsetE) =>
% 88.47/26.76 ((
% 88.47/26.76 (upairsetIL) =>
% 88.47/26.76 ((
% 88.47/26.76 (upairsetIR) =>
% 88.47/26.76 ((
% 88.47/26.76 (emptyE1) =>
% 88.47/26.76 ((
% 88.47/26.76 (vacuousDall) =>
% 88.47/26.76 ((
% 88.47/26.76 (quantDeMorgan1) =>
% 88.47/26.76 ((
% 88.47/26.76 (quantDeMorgan2) =>
% 88.47/26.76 ((
% 88.47/26.76 (quantDeMorgan3) =>
% 88.47/26.76 ((
% 88.47/26.76 (quantDeMorgan4) =>
% 88.47/26.76 ((
% 88.47/26.76 (prop2setI) =>
% 88.47/26.76 ((
% 88.47/26.76 (prop2set2propI) =>
% 88.47/26.76 ((
% 88.47/26.76 (notdexE) =>
% 88.47/26.76 ((
% 88.47/26.76 (notdallE) =>
% 88.47/26.76 ((
% 88.47/26.76 (exuI1) =>
% 88.47/26.76 ((
% 88.47/26.76 (exuI3) =>
% 88.47/26.76 ((
% 88.47/26.76 (exuI2) =>
% 88.47/26.76 ((
% 88.47/26.76 (inCongP) =>
% 88.47/26.76 ((
% 88.47/26.76 (in__Cong) =>
% 88.47/26.76 ((
% 88.47/26.76 (exuE3u) =>
% 88.47/26.76 ((
% 88.47/26.76 (exu__Cong) =>
% 88.47/26.76 ((
% 88.47/26.76 (setadjoin__Cong) =>
% 88.47/26.76 ((
% 88.47/26.76 (powerset__Cong) =>
% 88.47/26.76 ((
% 88.47/26.76 (setunion__Cong) =>
% 88.47/26.76 ((
% 88.47/26.76 (exuEu) =>
% 88.47/26.76 ((
% 88.47/26.76 (descr__Cong) =>
% 88.47/26.76 ((
% 88.47/26.76 (dsetconstr__Cong) =>
% 88.47/26.76 ((
% 88.47/26.76 (subsetI1) =>
% 88.47/26.76 ((
% 88.47/26.76 (eqimpsubset2) =>
% 88.47/26.76 ((
% 88.47/26.76 (eqimpsubset1) =>
% 88.47/26.76 ((
% 88.47/26.76 (subsetI2) =>
% 88.47/26.76 ((
% 88.47/26.76 (emptysetsubset) =>
% 88.47/26.76 ((
% 88.47/26.76 (subsetE) =>
% 88.47/26.76 ((
% 88.47/26.76 (subsetE2) =>
% 88.47/26.76 ((
% 88.47/26.76 (notsubsetI) =>
% 88.47/26.76 ((
% 88.47/26.76 (notequalI1) =>
% 88.47/26.76 ((
% 88.47/26.76 (notequalI2) =>
% 88.47/26.76 ((
% 88.47/26.76 (subsetRefl) =>
% 88.47/26.76 ((
% 88.47/26.76 (subsetTrans) =>
% 88.47/26.76 ((
% 88.47/26.76 (setadjoinSub) =>
% 88.47/26.76 ((
% 88.47/26.76 (setadjoinSub2) =>
% 88.47/26.76 ((
% 88.47/26.76 (subset2powerset) =>
% 88.47/26.76 ((
% 88.47/26.76 (setextsub) =>
% 88.47/26.76 ((
% 88.47/26.76 (subsetemptysetimpeq) =>
% 88.47/26.76 ((
% 88.47/26.76 (powersetI1) =>
% 88.47/26.76 ((
% 88.47/26.76 (powersetE1) =>
% 88.47/26.76 ((
% 88.47/26.76 (inPowerset) =>
% 88.47/26.76 ((
% 88.47/26.76 (powersetsubset) =>
% 88.47/26.76 ((
% 88.47/26.76 (sepInPowerset) =>
% 88.47/26.76 ((
% 88.47/26.76 (sepSubset) =>
% 88.47/26.76 ((
% 88.47/26.76 (binunionIL) =>
% 88.47/26.76 ((
% 88.47/26.76 (upairset2IR) =>
% 88.47/26.76 ((
% 88.47/26.76 (binunionIR) =>
% 88.47/26.76 ((
% 88.47/26.76 (binunionEcases) =>
% 88.47/26.76 ((
% 88.47/26.76 (binunionE) =>
% 88.47/26.76 ((
% 88.47/26.76 (binunionLsub) =>
% 88.47/26.76 ((
% 88.47/26.76 (binunionRsub) =>
% 88.47/26.76 ((
% 88.47/26.76 (binintersectI) =>
% 88.47/26.76 ((
% 88.47/26.76 (binintersectSubset5) =>
% 88.47/26.76 ((
% 88.47/26.76 (binintersectEL) =>
% 88.47/26.76 ((
% 88.47/26.76 (binintersectLsub) =>
% 88.47/26.76 ((
% 88.47/26.76 (binintersectSubset2) =>
% 88.47/26.76 ((
% 88.47/26.76 (binintersectSubset3) =>
% 88.47/26.76 ((
% 88.47/26.76 (binintersectER) =>
% 88.47/26.76 ((
% 88.47/26.76 (disjointsetsI1) =>
% 88.47/26.76 ((
% 88.47/26.76 (binintersectRsub) =>
% 88.47/26.76 ((
% 88.47/26.76 (binintersectSubset4) =>
% 88.47/26.76 ((
% 88.47/26.76 (binintersectSubset1) =>
% 88.47/26.76 ((
% 88.47/26.76 (bs114d) =>
% 88.47/26.76 ((
% 88.47/26.76 (setminusI) =>
% 88.47/26.76 ((
% 88.47/26.76 (setminusEL) =>
% 88.47/26.76 ((
% 88.47/26.76 (setminusER) =>
% 88.47/26.76 ((
% 88.47/26.76 (setminusSubset2) =>
% 88.47/26.76 ((
% 88.47/26.76 (setminusERneg) =>
% 88.47/26.76 ((
% 88.47/26.76 (setminusELneg) =>
% 88.47/26.76 ((
% 88.47/26.76 (setminusILneg) =>
% 88.47/26.76 ((
% 88.47/26.76 (setminusIRneg) =>
% 88.47/26.76 ((
% 88.47/26.76 (setminusLsub) =>
% 88.47/26.76 ((
% 88.47/26.76 (setminusSubset1) =>
% 88.47/26.76 ((
% 88.47/26.76 (symdiffE) =>
% 88.47/26.76 ((
% 88.47/26.76 (symdiffI1) =>
% 88.47/26.76 ((
% 88.47/26.76 (symdiffI2) =>
% 88.47/26.76 ((
% 88.47/26.76 (symdiffIneg1) =>
% 88.47/26.76 ((
% 88.47/26.76 (symdiffIneg2) =>
% 88.47/26.76 ((
% 88.47/26.76 (secondinupair) =>
% 88.47/26.76 ((
% 88.47/26.76 (setukpairIL) =>
% 88.47/26.76 ((
% 88.47/26.76 (setukpairIR) =>
% 88.47/26.76 ((
% 88.47/26.76 (kpairiskpair) =>
% 88.47/26.76 ((
% 88.47/26.76 (kpairp) =>
% 88.47/26.76 ((
% 88.47/26.76 (singletonsubset) =>
% 88.47/26.76 ((
% 88.47/26.76 (singletoninpowerset) =>
% 88.47/26.76 ((
% 88.47/26.76 (singletoninpowunion) =>
% 88.47/26.76 ((
% 88.47/26.76 (upairset2E) =>
% 88.47/26.76 ((
% 88.47/26.76 (upairsubunion) =>
% 88.47/26.76 ((
% 88.47/26.76 (upairinpowunion) =>
% 88.47/26.76 ((
% 88.47/26.76 (ubforcartprodlem1) =>
% 88.47/26.76 ((
% 88.47/26.76 (ubforcartprodlem2) =>
% 88.47/26.76 ((
% 88.47/26.76 (ubforcartprodlem3) =>
% 88.47/26.76 ((
% 88.47/26.76 (cartprodpairin) =>
% 88.47/26.76 ((
% 88.47/26.76 (cartprodmempair1) =>
% 88.47/26.76 ((
% 88.47/26.76 (cartprodmempair) =>
% 88.47/26.76 ((
% 88.47/26.76 (setunionE2) =>
% 88.47/26.76 ((
% 88.47/26.76 (setunionsingleton1) =>
% 88.47/26.76 ((
% 88.47/26.76 (setunionsingleton2) =>
% 88.47/26.76 ((
% 88.47/26.76 (setunionsingleton) =>
% 88.47/26.76 ((
% 88.47/26.76 (singletonprop) =>
% 88.47/26.76 ((
% 88.47/26.76 (ex1E1) =>
% 88.47/26.76 ((
% 88.47/26.76 (ex1I) =>
% 88.47/26.76 ((
% 88.47/26.76 (ex1I2) =>
% 88.47/26.76 ((
% 88.47/26.76 (singletonsuniq) =>
% 88.47/26.76 ((
% 88.47/26.76 (setukpairinjL1) =>
% 88.47/26.76 ((
% 88.47/26.76 (kfstsingleton) =>
% 88.47/26.76 ((
% 88.47/26.76 (theprop) =>
% 88.47/26.76 ((
% 88.47/26.76 (kfstpairEq) =>
% 88.47/26.76 ((
% 88.47/26.76 (cartprodfstin) =>
% 88.47/26.76 ((
% 88.47/26.76 (setukpairinjL2) =>
% 88.47/26.76 ((
% 88.47/26.76 (setukpairinjL) =>
% 88.47/26.76 ((
% 88.47/26.76 (setukpairinjR11) =>
% 88.47/26.76 ((
% 88.47/26.76 (setukpairinjR12) =>
% 88.47/26.76 ((
% 88.47/26.76 (setukpairinjR1) =>
% 88.47/26.76 ((
% 88.47/26.76 (upairequniteq) =>
% 88.47/26.76 ((
% 88.47/26.76 (setukpairinjR2) =>
% 88.47/26.76 ((
% 88.47/26.76 (setukpairinjR) =>
% 88.47/26.76 ((
% 88.47/26.76 (ksndsingleton) =>
% 88.47/26.76 ((
% 88.47/26.76 (ksndpairEq) =>
% 88.47/26.76 ((
% 88.47/26.76 (kpairsurjEq) =>
% 88.47/26.76 ((
% 88.47/26.76 (cartprodsndin) =>
% 88.47/26.76 ((
% 88.47/26.76 (cartprodpairmemEL) =>
% 88.47/26.76 ((
% 88.47/26.76 (cartprodpairmemER) =>
% 88.47/26.76 ((
% 88.47/26.76 (cartprodmempaircEq) =>
% 88.47/26.76 ((
% 88.47/26.76 (cartprodfstpairEq) =>
% 88.47/26.76 ((
% 88.47/26.76 (cartprodsndpairEq) =>
% 88.47/26.76 ((
% 88.47/26.76 (cartprodpairsurjEq) =>
% 88.47/26.76 ((
% 88.47/26.76 (dpsetconstrI) =>
% 88.47/26.76 ((
% 88.47/26.76 (dpsetconstrSub) =>
% 88.47/26.76 ((
% 88.47/26.76 (setOfPairsIsBReln) =>
% 88.47/26.76 ((
% 88.47/26.76 (dpsetconstrERa) =>
% 88.47/26.76 ((
% 88.47/26.76 (dpsetconstrEL1) =>
% 88.47/26.76 ((
% 88.47/26.76 (dpsetconstrEL2) =>
% 88.47/26.76 ((
% 88.47/26.76 (dpsetconstrER) =>
% 88.47/26.76 ((
% 88.47/26.76 (funcImageSingleton) =>
% 88.47/26.76 ((
% 88.47/26.76 (apProp) =>
% 88.47/26.76 ((
% 88.47/26.76 (app) =>
% 88.47/26.76 ((
% 88.47/26.76 (infuncsetfunc) =>
% 88.47/26.76 ((
% 88.47/26.76 (ap2p) =>
% 88.47/26.76 ((
% 88.47/26.76 (funcinfuncset) =>
% 88.47/26.76 ((
% 88.47/26.76 (lamProp) =>
% 88.47/26.76 ((
% 88.47/26.76 (lamp) =>
% 88.47/26.76 ((
% 88.47/26.76 (lam2p) =>
% 88.47/26.76 ((
% 88.47/26.76 (brelnall1) =>
% 88.47/26.76 ((
% 88.47/26.76 (brelnall2) =>
% 88.47/26.76 ((
% 88.47/26.76 (!!) @ (
% 88.47/26.76 (('#B') @ (
% 88.47/26.76 !!) @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#S') @ (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 '#S') @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 =>))) @
% 88.47/26.76 ex1)))) @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 !!))) @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#S') @ (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 '#B') @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 '#S') @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 =>))) @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#C') @ in)))))))) @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 !!))))) @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#C') @ (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 '#B') @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 '#B') @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 '#S') @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 =>))) @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#C') @ in)))))))))) @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#S') @ (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 '#S') @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 '#B'))) @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 =>))))))) @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#C') @ (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 '#B') @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 '#S') @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 =>))))))) @
% 88.47/26.76 (
% 88.47/26.76 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 88.47/26.76 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl46])).
% 88.47/26.76 thf(zip_derived_cl58, plain,
% 88.47/26.76 (~ (((wellorderingAx) =>
% 88.47/26.76 (((descrp) =>
% 88.47/26.76 (((dsetconstrI) =>
% 88.47/26.76 (((dsetconstrEL) =>
% 88.47/26.76 (((dsetconstrER) =>
% 88.47/26.76 (((exuE1) =>
% 88.47/26.76 (((prop2setE) =>
% 88.47/26.76 (((emptysetE) =>
% 88.47/26.76 (((emptysetimpfalse) =>
% 88.47/26.76 (((notinemptyset) =>
% 88.47/26.76 (((exuE3e) =>
% 88.47/26.76 (((setext) =>
% 88.47/26.76 (((emptyI) =>
% 88.47/26.76 (((noeltsimpempty) =>
% 88.47/26.76 (((setbeta) =>
% 88.47/26.76 (((nonemptyE1) =>
% 88.47/26.76 (((nonemptyI) =>
% 88.47/26.76 (((nonemptyI1) =>
% 88.47/26.76 (((setadjoinIL) =>
% 88.47/26.76 (((in @ emptyset @
% 88.47/26.76 (setadjoin @ emptyset @
% 88.47/26.76 emptyset)) =>
% 88.47/26.76 (((setadjoinIR) =>
% 88.47/26.76 (((setadjoinE) =>
% 88.47/26.76 (((setadjoinOr) =>
% 88.47/26.76 (((setoftrueEq) =>
% 88.47/26.76 (((powersetI) =>
% 88.47/26.76 (((emptyinPowerset) =>
% 88.47/26.76 (((emptyInPowerset) =>
% 88.47/26.76 (((powersetE) =>
% 88.47/26.76 (((setunionI) =>
% 88.47/26.76 (((setunionE) =>
% 88.47/26.76 ((
% 88.47/26.76 (subPowSU) =>
% 88.47/26.76 ((
% 88.47/26.76 (exuE2) =>
% 88.47/26.76 ((
% 88.47/26.76 (nonemptyImpWitness) =>
% 88.47/26.76 ((
% 88.47/26.76 (uniqinunit) =>
% 88.47/26.76 ((
% 88.47/26.76 (notinsingleton) =>
% 88.47/26.76 ((
% 88.47/26.76 (eqinunit) =>
% 88.47/26.76 ((
% 88.47/26.76 (singletonsswitch) =>
% 88.47/26.76 ((
% 88.47/26.76 (upairsetE) =>
% 88.47/26.76 ((
% 88.47/26.76 (upairsetIL) =>
% 88.47/26.76 ((
% 88.47/26.76 (upairsetIR) =>
% 88.47/26.76 ((
% 88.47/26.76 (emptyE1) =>
% 88.47/26.76 ((
% 88.47/26.76 (vacuousDall) =>
% 88.47/26.76 ((
% 88.47/26.76 (quantDeMorgan1) =>
% 88.47/26.76 ((
% 88.47/26.76 (quantDeMorgan2) =>
% 88.47/26.76 ((
% 88.47/26.76 (quantDeMorgan3) =>
% 88.47/26.76 ((
% 88.47/26.76 (quantDeMorgan4) =>
% 88.47/26.76 ((
% 88.47/26.76 (prop2setI) =>
% 88.47/26.76 ((
% 88.47/26.76 (prop2set2propI) =>
% 88.47/26.76 ((
% 88.47/26.76 (notdexE) =>
% 88.47/26.76 ((
% 88.47/26.76 (notdallE) =>
% 88.47/26.76 ((
% 88.47/26.76 (exuI1) =>
% 88.47/26.76 ((
% 88.47/26.76 (exuI3) =>
% 88.47/26.76 ((
% 88.47/26.76 (exuI2) =>
% 88.47/26.76 ((
% 88.47/26.76 (inCongP) =>
% 88.47/26.76 ((
% 88.47/26.76 (in__Cong) =>
% 88.47/26.76 ((
% 88.47/26.76 (exuE3u) =>
% 88.47/26.76 ((
% 88.47/26.76 (exu__Cong) =>
% 88.47/26.76 ((
% 88.47/26.76 (setadjoin__Cong) =>
% 88.47/26.76 ((
% 88.47/26.76 (powerset__Cong) =>
% 88.47/26.76 ((
% 88.47/26.76 (setunion__Cong) =>
% 88.47/26.76 ((
% 88.47/26.76 (exuEu) =>
% 88.47/26.76 ((
% 88.47/26.76 (descr__Cong) =>
% 88.47/26.76 ((
% 88.47/26.76 (dsetconstr__Cong) =>
% 88.47/26.76 ((
% 88.47/26.76 (subsetI1) =>
% 88.47/26.76 ((
% 88.47/26.76 (eqimpsubset2) =>
% 88.47/26.76 ((
% 88.47/26.76 (eqimpsubset1) =>
% 88.47/26.76 ((
% 88.47/26.76 (subsetI2) =>
% 88.47/26.76 ((
% 88.47/26.76 (emptysetsubset) =>
% 88.47/26.76 ((
% 88.47/26.76 (subsetE) =>
% 88.47/26.76 ((
% 88.47/26.76 (subsetE2) =>
% 88.47/26.76 ((
% 88.47/26.76 (notsubsetI) =>
% 88.47/26.76 ((
% 88.47/26.76 (notequalI1) =>
% 88.47/26.76 ((
% 88.47/26.76 (notequalI2) =>
% 88.47/26.76 ((
% 88.47/26.76 (subsetRefl) =>
% 88.47/26.76 ((
% 88.47/26.76 (subsetTrans) =>
% 88.47/26.76 ((
% 88.47/26.76 (setadjoinSub) =>
% 88.47/26.76 ((
% 88.47/26.76 (setadjoinSub2) =>
% 88.47/26.76 ((
% 88.47/26.76 (subset2powerset) =>
% 88.47/26.76 ((
% 88.47/26.76 (setextsub) =>
% 88.47/26.76 ((
% 88.47/26.76 (subsetemptysetimpeq) =>
% 88.47/26.76 ((
% 88.47/26.76 (powersetI1) =>
% 88.47/26.76 ((
% 88.47/26.76 (powersetE1) =>
% 88.47/26.76 ((
% 88.47/26.76 (inPowerset) =>
% 88.47/26.76 ((
% 88.47/26.76 (powersetsubset) =>
% 88.47/26.76 ((
% 88.47/26.76 (sepInPowerset) =>
% 88.47/26.76 ((
% 88.47/26.76 (sepSubset) =>
% 88.47/26.76 ((
% 88.47/26.76 (binunionIL) =>
% 88.47/26.76 ((
% 88.47/26.76 (upairset2IR) =>
% 88.47/26.76 ((
% 88.47/26.76 (binunionIR) =>
% 88.47/26.76 ((
% 88.47/26.76 (binunionEcases) =>
% 88.47/26.76 ((
% 88.47/26.76 (binunionE) =>
% 88.47/26.76 ((
% 88.47/26.76 (binunionLsub) =>
% 88.47/26.76 ((
% 88.47/26.76 (binunionRsub) =>
% 88.47/26.76 ((
% 88.47/26.76 (binintersectI) =>
% 88.47/26.76 ((
% 88.47/26.76 (binintersectSubset5) =>
% 88.47/26.76 ((
% 88.47/26.76 (binintersectEL) =>
% 88.47/26.76 ((
% 88.47/26.76 (binintersectLsub) =>
% 88.47/26.76 ((
% 88.47/26.76 (binintersectSubset2) =>
% 88.47/26.76 ((
% 88.47/26.76 (binintersectSubset3) =>
% 88.47/26.76 ((
% 88.47/26.76 (binintersectER) =>
% 88.47/26.76 ((
% 88.47/26.76 (disjointsetsI1) =>
% 88.47/26.76 ((
% 88.47/26.76 (binintersectRsub) =>
% 88.47/26.76 ((
% 88.47/26.76 (binintersectSubset4) =>
% 88.47/26.76 ((
% 88.47/26.76 (binintersectSubset1) =>
% 88.47/26.76 ((
% 88.47/26.76 (bs114d) =>
% 88.47/26.76 ((
% 88.47/26.76 (setminusI) =>
% 88.47/26.76 ((
% 88.47/26.76 (setminusEL) =>
% 88.47/26.76 ((
% 88.47/26.76 (setminusER) =>
% 88.47/26.76 ((
% 88.47/26.76 (setminusSubset2) =>
% 88.47/26.76 ((
% 88.47/26.76 (setminusERneg) =>
% 88.47/26.76 ((
% 88.47/26.76 (setminusELneg) =>
% 88.47/26.76 ((
% 88.47/26.76 (setminusILneg) =>
% 88.47/26.76 ((
% 88.47/26.76 (setminusIRneg) =>
% 88.47/26.76 ((
% 88.47/26.76 (setminusLsub) =>
% 88.47/26.76 ((
% 88.47/26.76 (setminusSubset1) =>
% 88.47/26.76 ((
% 88.47/26.76 (symdiffE) =>
% 88.47/26.76 ((
% 88.47/26.76 (symdiffI1) =>
% 88.47/26.76 ((
% 88.47/26.76 (symdiffI2) =>
% 88.47/26.76 ((
% 88.47/26.76 (symdiffIneg1) =>
% 88.47/26.76 ((
% 88.47/26.76 (symdiffIneg2) =>
% 88.47/26.76 ((
% 88.47/26.76 (secondinupair) =>
% 88.47/26.76 ((
% 88.47/26.76 (setukpairIL) =>
% 88.47/26.76 ((
% 88.47/26.76 (setukpairIR) =>
% 88.47/26.76 ((
% 88.47/26.76 (kpairiskpair) =>
% 88.47/26.76 ((
% 88.47/26.76 (kpairp) =>
% 88.47/26.76 ((
% 88.47/26.76 (singletonsubset) =>
% 88.47/26.76 ((
% 88.47/26.76 (singletoninpowerset) =>
% 88.47/26.76 ((
% 88.47/26.76 (singletoninpowunion) =>
% 88.47/26.76 ((
% 88.47/26.76 (upairset2E) =>
% 88.47/26.76 ((
% 88.47/26.76 (upairsubunion) =>
% 88.47/26.76 ((
% 88.47/26.76 (upairinpowunion) =>
% 88.47/26.76 ((
% 88.47/26.76 (ubforcartprodlem1) =>
% 88.47/26.76 ((
% 88.47/26.76 (ubforcartprodlem2) =>
% 88.47/26.76 ((
% 88.47/26.76 (ubforcartprodlem3) =>
% 88.47/26.76 ((
% 88.47/26.76 (cartprodpairin) =>
% 88.47/26.76 ((
% 88.47/26.76 (cartprodmempair1) =>
% 88.47/26.76 ((
% 88.47/26.76 (cartprodmempair) =>
% 88.47/26.76 ((
% 88.47/26.76 (setunionE2) =>
% 88.47/26.76 ((
% 88.47/26.76 (setunionsingleton1) =>
% 88.47/26.76 ((
% 88.47/26.76 (setunionsingleton2) =>
% 88.47/26.76 ((
% 88.47/26.76 (setunionsingleton) =>
% 88.47/26.76 ((
% 88.47/26.76 (singletonprop) =>
% 88.47/26.76 ((
% 88.47/26.76 (ex1E1) =>
% 88.47/26.76 ((
% 88.47/26.76 (ex1I) =>
% 88.47/26.76 ((
% 88.47/26.76 (ex1I2) =>
% 88.47/26.76 ((
% 88.47/26.76 (singletonsuniq) =>
% 88.47/26.76 ((
% 88.47/26.76 (setukpairinjL1) =>
% 88.47/26.76 ((
% 88.47/26.76 (kfstsingleton) =>
% 88.47/26.76 ((
% 88.47/26.76 (theprop) =>
% 88.47/26.76 ((
% 88.47/26.76 (kfstpairEq) =>
% 88.47/26.76 ((
% 88.47/26.76 (cartprodfstin) =>
% 88.47/26.76 ((
% 88.47/26.76 (setukpairinjL2) =>
% 88.47/26.76 ((
% 88.47/26.76 (setukpairinjL) =>
% 88.47/26.76 ((
% 88.47/26.76 (setukpairinjR11) =>
% 88.47/26.76 ((
% 88.47/26.76 (setukpairinjR12) =>
% 88.47/26.76 ((
% 88.47/26.76 (setukpairinjR1) =>
% 88.47/26.76 ((
% 88.47/26.76 (upairequniteq) =>
% 88.47/26.76 ((
% 88.47/26.76 (setukpairinjR2) =>
% 88.47/26.76 ((
% 88.47/26.76 (setukpairinjR) =>
% 88.47/26.76 ((
% 88.47/26.76 (ksndsingleton) =>
% 88.47/26.76 ((
% 88.47/26.76 (ksndpairEq) =>
% 88.47/26.76 ((
% 88.47/26.76 (kpairsurjEq) =>
% 88.47/26.76 ((
% 88.47/26.76 (cartprodsndin) =>
% 88.47/26.76 ((
% 88.47/26.76 (cartprodpairmemEL) =>
% 88.47/26.76 ((
% 88.47/26.76 (cartprodpairmemER) =>
% 88.47/26.76 ((
% 88.47/26.76 (cartprodmempaircEq) =>
% 88.47/26.76 ((
% 88.47/26.76 (cartprodfstpairEq) =>
% 88.47/26.76 ((
% 88.47/26.76 (cartprodsndpairEq) =>
% 88.47/26.76 ((
% 88.47/26.76 (cartprodpairsurjEq) =>
% 88.47/26.76 ((
% 88.47/26.76 (dpsetconstrI) =>
% 88.47/26.76 ((
% 88.47/26.76 (dpsetconstrSub) =>
% 88.47/26.76 ((
% 88.47/26.76 (setOfPairsIsBReln) =>
% 88.47/26.76 ((
% 88.47/26.76 (dpsetconstrERa) =>
% 88.47/26.76 ((
% 88.47/26.76 (dpsetconstrEL1) =>
% 88.47/26.76 ((
% 88.47/26.76 (dpsetconstrEL2) =>
% 88.47/26.76 ((
% 88.47/26.76 (dpsetconstrER) =>
% 88.47/26.76 ((
% 88.47/26.76 (funcImageSingleton) =>
% 88.47/26.76 ((
% 88.47/26.76 (apProp) =>
% 88.47/26.76 ((
% 88.47/26.76 (app) =>
% 88.47/26.76 ((
% 88.47/26.76 (infuncsetfunc) =>
% 88.47/26.76 ((
% 88.47/26.76 (ap2p) =>
% 88.47/26.76 ((
% 88.47/26.76 (funcinfuncset) =>
% 88.47/26.76 ((
% 88.47/26.76 (lamProp) =>
% 88.47/26.76 ((
% 88.47/26.76 (lamp) =>
% 88.47/26.76 ((
% 88.47/26.76 (lam2p) =>
% 88.47/26.76 ((
% 88.47/26.76 (brelnall1) =>
% 88.47/26.76 ((
% 88.47/26.76 (brelnall2) =>
% 88.47/26.76 ((
% 88.47/26.76 (!!) @ (
% 88.47/26.76 (('#B') @ (
% 88.47/26.76 !!) @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#S') @ (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 '#S') @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 =>))) @
% 88.47/26.76 ex1)))) @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 !!))) @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#S') @ (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 '#B') @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 '#S') @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 =>))) @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#C') @ in)))))))) @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 !!))))) @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#C') @ (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 '#B') @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 '#B') @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 '#S') @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 =>))) @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#C') @ in)))))))))) @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#S') @ (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 '#S') @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 '#B'))) @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 =>))))))) @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#C') @ (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 '#B') @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 '#S') @
% 88.47/26.76 (
% 88.47/26.76 (
% 88.47/26.76 ('#B') @ (
% 88.47/26.76 =>))))))) @
% 88.47/26.76 (
% 88.47/26.76 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 88.47/26.76 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl52])).
% 88.47/26.76 thf(zip_derived_cl64, plain,
% 88.47/26.76 (~ (((descrp) =>
% 88.47/26.76 (((dsetconstrI) =>
% 88.47/26.76 (((dsetconstrEL) =>
% 88.47/26.76 (((dsetconstrER) =>
% 88.47/26.76 (((exuE1) =>
% 88.47/26.76 (((prop2setE) =>
% 88.47/26.76 (((emptysetE) =>
% 88.47/26.76 (((emptysetimpfalse) =>
% 88.47/26.76 (((notinemptyset) =>
% 88.47/26.76 (((exuE3e) =>
% 88.47/26.76 (((setext) =>
% 88.47/26.76 (((emptyI) =>
% 88.47/26.76 (((noeltsimpempty) =>
% 88.47/26.76 (((setbeta) =>
% 88.47/26.76 (((nonemptyE1) =>
% 88.47/26.76 (((nonemptyI) =>
% 88.47/26.76 (((nonemptyI1) =>
% 88.47/26.76 (((setadjoinIL) =>
% 88.47/26.76 (((in @ emptyset @
% 88.47/26.76 (setadjoin @ emptyset @ emptyset)) =>
% 88.47/26.76 (((setadjoinIR) =>
% 88.47/26.76 (((setadjoinE) =>
% 88.47/26.76 (((setadjoinOr) =>
% 88.47/26.76 (((setoftrueEq) =>
% 88.47/26.76 (((powersetI) =>
% 88.47/26.76 (((emptyinPowerset) =>
% 88.47/26.76 (((emptyInPowerset) =>
% 88.47/26.76 (((powersetE) =>
% 88.47/26.76 (((setunionI) =>
% 88.47/26.76 (((setunionE) =>
% 88.47/26.76 (((subPowSU) =>
% 88.47/26.76 ((
% 88.47/26.76 (exuE2) =>
% 88.47/26.76 ((
% 88.47/26.76 (nonemptyImpWitness) =>
% 88.47/26.76 ((
% 88.47/26.76 (uniqinunit) =>
% 88.47/26.76 ((
% 88.47/26.76 (notinsingleton) =>
% 88.47/26.76 ((
% 88.47/26.76 (eqinunit) =>
% 88.47/26.76 ((
% 88.47/26.76 (singletonsswitch) =>
% 88.47/26.76 ((
% 88.47/26.76 (upairsetE) =>
% 88.47/26.76 ((
% 88.47/26.76 (upairsetIL) =>
% 88.47/26.76 ((
% 88.47/26.76 (upairsetIR) =>
% 88.47/26.76 ((
% 88.47/26.76 (emptyE1) =>
% 88.47/26.76 ((
% 88.47/26.76 (vacuousDall) =>
% 88.47/26.76 ((
% 88.47/26.76 (quantDeMorgan1) =>
% 88.47/26.76 ((
% 88.47/26.76 (quantDeMorgan2) =>
% 88.47/26.76 ((
% 88.47/26.76 (quantDeMorgan3) =>
% 88.47/26.76 ((
% 88.47/26.76 (quantDeMorgan4) =>
% 88.47/26.76 ((
% 88.47/26.76 (prop2setI) =>
% 88.47/26.76 ((
% 88.47/26.76 (prop2set2propI) =>
% 88.47/26.76 ((
% 88.47/26.76 (notdexE) =>
% 88.47/26.76 ((
% 88.47/26.76 (notdallE) =>
% 88.47/26.76 ((
% 88.47/26.76 (exuI1) =>
% 88.47/26.76 ((
% 88.47/26.76 (exuI3) =>
% 88.47/26.76 ((
% 88.47/26.76 (exuI2) =>
% 88.47/26.76 ((
% 88.47/26.76 (inCongP) =>
% 88.47/26.76 ((
% 88.47/26.76 (in__Cong) =>
% 88.47/26.76 ((
% 88.47/26.76 (exuE3u) =>
% 88.47/26.76 ((
% 88.47/26.76 (exu__Cong) =>
% 88.47/26.76 ((
% 88.47/26.76 (setadjoin__Cong) =>
% 88.47/26.76 ((
% 88.47/26.76 (powerset__Cong) =>
% 88.47/26.76 ((
% 88.47/26.76 (setunion__Cong) =>
% 88.47/26.76 ((
% 88.47/26.76 (exuEu) =>
% 88.47/26.76 ((
% 88.47/26.76 (descr__Cong) =>
% 88.47/26.76 ((
% 88.47/26.76 (dsetconstr__Cong) =>
% 88.47/26.76 ((
% 88.47/26.76 (subsetI1) =>
% 88.47/26.76 ((
% 88.47/26.76 (eqimpsubset2) =>
% 88.47/26.76 ((
% 88.47/26.76 (eqimpsubset1) =>
% 88.47/26.76 ((
% 88.47/26.76 (subsetI2) =>
% 88.47/26.76 ((
% 88.47/26.76 (emptysetsubset) =>
% 88.47/26.76 ((
% 88.47/26.76 (subsetE) =>
% 88.47/26.76 ((
% 88.47/26.76 (subsetE2) =>
% 88.47/26.76 ((
% 88.47/26.76 (notsubsetI) =>
% 88.47/26.76 ((
% 88.47/26.76 (notequalI1) =>
% 88.47/26.76 ((
% 88.47/26.76 (notequalI2) =>
% 88.47/26.76 ((
% 88.47/26.76 (subsetRefl) =>
% 88.47/26.76 ((
% 88.47/26.76 (subsetTrans) =>
% 88.47/26.76 ((
% 88.47/26.76 (setadjoinSub) =>
% 88.47/26.76 ((
% 88.47/26.76 (setadjoinSub2) =>
% 88.47/26.76 ((
% 88.47/26.76 (subset2powerset) =>
% 88.47/26.76 ((
% 88.47/26.76 (setextsub) =>
% 88.47/26.76 ((
% 88.47/26.76 (subsetemptysetimpeq) =>
% 88.47/26.76 ((
% 88.47/26.76 (powersetI1) =>
% 88.47/26.76 ((
% 88.47/26.76 (powersetE1) =>
% 88.47/26.76 ((
% 88.47/26.76 (inPowerset) =>
% 88.47/26.76 ((
% 88.47/26.76 (powersetsubset) =>
% 88.47/26.76 ((
% 88.47/26.76 (sepInPowerset) =>
% 88.47/26.76 ((
% 88.47/26.76 (sepSubset) =>
% 88.47/26.76 ((
% 88.47/26.76 (binunionIL) =>
% 88.47/26.76 ((
% 88.47/26.76 (upairset2IR) =>
% 88.47/26.76 ((
% 88.47/26.76 (binunionIR) =>
% 88.47/26.76 ((
% 88.47/26.76 (binunionEcases) =>
% 88.47/26.76 ((
% 88.47/26.76 (binunionE) =>
% 88.47/26.76 ((
% 88.47/26.76 (binunionLsub) =>
% 88.47/26.76 ((
% 88.47/26.76 (binunionRsub) =>
% 88.47/26.76 ((
% 88.47/26.76 (binintersectI) =>
% 88.47/26.76 ((
% 88.47/26.76 (binintersectSubset5) =>
% 88.47/26.76 ((
% 88.47/26.76 (binintersectEL) =>
% 88.47/26.76 ((
% 88.47/26.76 (binintersectLsub) =>
% 88.47/26.76 ((
% 88.47/26.76 (binintersectSubset2) =>
% 88.47/26.76 ((
% 88.47/26.76 (binintersectSubset3) =>
% 88.47/26.76 ((
% 88.47/26.76 (binintersectER) =>
% 88.47/26.76 ((
% 88.47/26.76 (disjointsetsI1) =>
% 88.47/26.76 ((
% 88.47/26.76 (binintersectRsub) =>
% 88.47/26.76 ((
% 88.47/26.76 (binintersectSubset4) =>
% 88.47/26.76 ((
% 88.47/26.76 (binintersectSubset1) =>
% 88.47/26.76 ((
% 88.47/26.76 (bs114d) =>
% 88.47/26.76 ((
% 88.47/26.76 (setminusI) =>
% 88.47/26.76 ((
% 88.47/26.76 (setminusEL) =>
% 88.47/26.76 ((
% 88.47/26.76 (setminusER) =>
% 88.47/26.76 ((
% 88.47/26.76 (setminusSubset2) =>
% 88.47/26.76 ((
% 88.47/26.76 (setminusERneg) =>
% 88.47/26.76 ((
% 88.47/26.76 (setminusELneg) =>
% 88.47/26.76 ((
% 88.47/26.76 (setminusILneg) =>
% 88.47/26.76 ((
% 88.47/26.76 (setminusIRneg) =>
% 88.47/26.76 ((
% 88.47/26.76 (setminusLsub) =>
% 88.47/26.76 ((
% 88.47/26.76 (setminusSubset1) =>
% 88.47/26.76 ((
% 88.47/26.76 (symdiffE) =>
% 88.47/26.76 ((
% 88.47/26.76 (symdiffI1) =>
% 88.47/26.76 ((
% 88.47/26.76 (symdiffI2) =>
% 88.47/26.76 ((
% 88.47/26.76 (symdiffIneg1) =>
% 88.47/26.76 ((
% 88.47/26.76 (symdiffIneg2) =>
% 88.47/26.76 ((
% 88.47/26.76 (secondinupair) =>
% 88.47/26.76 ((
% 88.47/26.76 (setukpairIL) =>
% 88.47/26.76 ((
% 88.47/26.76 (setukpairIR) =>
% 88.47/26.76 ((
% 88.47/26.76 (kpairiskpair) =>
% 88.47/26.76 ((
% 88.47/26.76 (kpairp) =>
% 88.47/26.76 ((
% 88.47/26.76 (singletonsubset) =>
% 88.47/26.76 ((
% 88.47/26.76 (singletoninpowerset) =>
% 88.47/26.76 ((
% 88.47/26.76 (singletoninpowunion) =>
% 88.47/26.76 ((
% 88.47/26.76 (upairset2E) =>
% 88.47/26.76 ((
% 88.47/26.76 (upairsubunion) =>
% 88.47/26.76 ((
% 88.47/26.76 (upairinpowunion) =>
% 88.47/26.76 ((
% 88.47/26.76 (ubforcartprodlem1) =>
% 88.47/26.76 ((
% 88.47/26.76 (ubforcartprodlem2) =>
% 88.47/26.76 ((
% 88.47/26.76 (ubforcartprodlem3) =>
% 88.47/26.76 ((
% 88.47/26.76 (cartprodpairin) =>
% 88.47/26.76 ((
% 88.47/26.76 (cartprodmempair1) =>
% 88.47/26.76 ((
% 88.47/26.76 (cartprodmempair) =>
% 88.47/26.76 ((
% 88.47/26.76 (setunionE2) =>
% 88.47/26.76 ((
% 88.47/26.76 (setunionsingleton1) =>
% 88.47/26.76 ((
% 88.47/26.76 (setunionsingleton2) =>
% 88.47/26.76 ((
% 88.47/26.76 (setunionsingleton) =>
% 88.47/26.76 ((
% 88.47/26.76 (singletonprop) =>
% 88.47/26.76 ((
% 88.47/26.76 (ex1E1) =>
% 88.47/26.76 ((
% 88.47/26.76 (ex1I) =>
% 88.47/26.76 ((
% 88.47/26.76 (ex1I2) =>
% 88.47/26.76 ((
% 88.47/26.76 (singletonsuniq) =>
% 88.47/26.76 ((
% 88.47/26.76 (setukpairinjL1) =>
% 88.68/26.76 ((
% 88.68/26.76 (kfstsingleton) =>
% 88.68/26.76 ((
% 88.68/26.76 (theprop) =>
% 88.68/26.76 ((
% 88.68/26.76 (kfstpairEq) =>
% 88.68/26.76 ((
% 88.68/26.76 (cartprodfstin) =>
% 88.68/26.76 ((
% 88.68/26.76 (setukpairinjL2) =>
% 88.68/26.76 ((
% 88.68/26.76 (setukpairinjL) =>
% 88.68/26.76 ((
% 88.68/26.76 (setukpairinjR11) =>
% 88.68/26.76 ((
% 88.68/26.76 (setukpairinjR12) =>
% 88.68/26.76 ((
% 88.68/26.76 (setukpairinjR1) =>
% 88.68/26.76 ((
% 88.68/26.76 (upairequniteq) =>
% 88.68/26.76 ((
% 88.68/26.76 (setukpairinjR2) =>
% 88.68/26.76 ((
% 88.68/26.76 (setukpairinjR) =>
% 88.68/26.76 ((
% 88.68/26.76 (ksndsingleton) =>
% 88.68/26.76 ((
% 88.68/26.76 (ksndpairEq) =>
% 88.68/26.76 ((
% 88.68/26.76 (kpairsurjEq) =>
% 88.68/26.76 ((
% 88.68/26.76 (cartprodsndin) =>
% 88.68/26.76 ((
% 88.68/26.76 (cartprodpairmemEL) =>
% 88.68/26.76 ((
% 88.68/26.76 (cartprodpairmemER) =>
% 88.68/26.76 ((
% 88.68/26.76 (cartprodmempaircEq) =>
% 88.68/26.76 ((
% 88.68/26.76 (cartprodfstpairEq) =>
% 88.68/26.76 ((
% 88.68/26.76 (cartprodsndpairEq) =>
% 88.68/26.76 ((
% 88.68/26.76 (cartprodpairsurjEq) =>
% 88.68/26.76 ((
% 88.68/26.76 (dpsetconstrI) =>
% 88.68/26.76 ((
% 88.68/26.76 (dpsetconstrSub) =>
% 88.68/26.76 ((
% 88.68/26.76 (setOfPairsIsBReln) =>
% 88.68/26.76 ((
% 88.68/26.76 (dpsetconstrERa) =>
% 88.68/26.76 ((
% 88.68/26.76 (dpsetconstrEL1) =>
% 88.68/26.76 ((
% 88.68/26.76 (dpsetconstrEL2) =>
% 88.68/26.76 ((
% 88.68/26.76 (dpsetconstrER) =>
% 88.68/26.76 ((
% 88.68/26.76 (funcImageSingleton) =>
% 88.68/26.76 ((
% 88.68/26.76 (apProp) =>
% 88.68/26.76 ((
% 88.68/26.76 (app) =>
% 88.68/26.76 ((
% 88.68/26.76 (infuncsetfunc) =>
% 88.68/26.76 ((
% 88.68/26.76 (ap2p) =>
% 88.68/26.76 ((
% 88.68/26.76 (funcinfuncset) =>
% 88.68/26.76 ((
% 88.68/26.76 (lamProp) =>
% 88.68/26.76 ((
% 88.68/26.76 (lamp) =>
% 88.68/26.76 ((
% 88.68/26.76 (lam2p) =>
% 88.68/26.76 ((
% 88.68/26.76 (brelnall1) =>
% 88.68/26.76 ((
% 88.68/26.76 (brelnall2) =>
% 88.68/26.76 ((
% 88.68/26.76 (!!) @ (
% 88.68/26.76 (('#B') @ (
% 88.68/26.76 !!) @
% 88.68/26.76 (
% 88.68/26.76 (
% 88.68/26.76 ('#S') @ (
% 88.68/26.76 (
% 88.68/26.76 ('#B') @ (
% 88.68/26.76 '#S') @
% 88.68/26.76 (
% 88.68/26.76 (
% 88.68/26.76 ('#B') @ (
% 88.68/26.76 (
% 88.68/26.76 ('#B') @ (
% 88.68/26.76 =>))) @
% 88.68/26.76 ex1)))) @
% 88.68/26.76 (
% 88.68/26.76 (
% 88.68/26.76 ('#B') @ (
% 88.68/26.76 (
% 88.68/26.76 ('#B') @ (
% 88.68/26.76 !!))) @
% 88.68/26.76 (
% 88.68/26.76 (
% 88.68/26.76 ('#S') @ (
% 88.68/26.76 (
% 88.68/26.76 ('#B') @ (
% 88.68/26.76 '#B') @
% 88.68/26.76 (
% 88.68/26.76 (
% 88.68/26.76 ('#B') @ (
% 88.68/26.76 '#S') @
% 88.68/26.76 (
% 88.68/26.76 (
% 88.68/26.76 ('#B') @ (
% 88.68/26.76 (
% 88.68/26.76 ('#B') @ (
% 88.68/26.76 =>))) @
% 88.68/26.76 (
% 88.68/26.76 (
% 88.68/26.76 ('#C') @ in)))))))) @
% 88.68/26.76 (
% 88.68/26.76 (
% 88.68/26.76 ('#B') @ (
% 88.68/26.76 (
% 88.68/26.76 ('#B') @ (
% 88.68/26.76 (
% 88.68/26.76 ('#B') @ (
% 88.68/26.76 !!))))) @
% 88.68/26.76 (
% 88.68/26.76 (
% 88.68/26.76 ('#C') @ (
% 88.68/26.76 (
% 88.68/26.76 ('#B') @ (
% 88.68/26.76 '#B') @
% 88.68/26.76 (
% 88.68/26.76 (
% 88.68/26.76 ('#B') @ (
% 88.68/26.76 '#B') @
% 88.68/26.76 (
% 88.68/26.76 (
% 88.68/26.76 ('#B') @ (
% 88.68/26.76 '#S') @
% 88.68/26.76 (
% 88.68/26.76 (
% 88.68/26.76 ('#B') @ (
% 88.68/26.76 (
% 88.68/26.76 ('#B') @ (
% 88.68/26.76 =>))) @
% 88.68/26.76 (
% 88.68/26.76 (
% 88.68/26.76 ('#C') @ in)))))))))) @
% 88.68/26.76 (
% 88.68/26.76 (
% 88.68/26.76 ('#S') @ (
% 88.68/26.76 (
% 88.68/26.76 ('#B') @ (
% 88.68/26.76 '#S') @
% 88.68/26.76 (
% 88.68/26.76 (
% 88.68/26.76 ('#B') @ (
% 88.68/26.76 (
% 88.68/26.76 ('#B') @ (
% 88.68/26.76 '#B'))) @
% 88.68/26.76 (
% 88.68/26.76 (
% 88.68/26.76 ('#B') @ (
% 88.68/26.76 =>))))))) @
% 88.68/26.76 (
% 88.68/26.76 (
% 88.68/26.76 ('#C') @ (
% 88.68/26.76 (
% 88.68/26.76 ('#B') @ (
% 88.68/26.76 '#B') @
% 88.68/26.76 (
% 88.68/26.76 (
% 88.68/26.76 ('#B') @ (
% 88.68/26.76 '#S') @
% 88.68/26.76 (
% 88.68/26.76 (
% 88.68/26.76 ('#B') @ (
% 88.68/26.76 =>))))))) @
% 88.68/26.76 (
% 88.68/26.76 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 88.68/26.76 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl58])).
% 88.68/26.76 thf(zip_derived_cl71, plain,
% 88.68/26.76 (~ (((dsetconstrI) =>
% 88.68/26.76 (((dsetconstrEL) =>
% 88.68/26.76 (((dsetconstrER) =>
% 88.68/26.76 (((exuE1) =>
% 88.68/26.76 (((prop2setE) =>
% 88.68/26.76 (((emptysetE) =>
% 88.68/26.76 (((emptysetimpfalse) =>
% 88.68/26.76 (((notinemptyset) =>
% 88.68/26.76 (((exuE3e) =>
% 88.68/26.76 (((setext) =>
% 88.68/26.76 (((emptyI) =>
% 88.68/26.76 (((noeltsimpempty) =>
% 88.68/26.76 (((setbeta) =>
% 88.68/26.76 (((nonemptyE1) =>
% 88.68/26.76 (((nonemptyI) =>
% 88.68/26.76 (((nonemptyI1) =>
% 88.68/26.76 (((setadjoinIL) =>
% 88.68/26.76 (((in @ emptyset @
% 88.68/26.76 (setadjoin @ emptyset @ emptyset)) =>
% 88.68/26.76 (((setadjoinIR) =>
% 88.68/26.76 (((setadjoinE) =>
% 88.68/26.76 (((setadjoinOr) =>
% 88.68/26.76 (((setoftrueEq) =>
% 88.68/26.76 (((powersetI) =>
% 88.68/26.76 (((emptyinPowerset) =>
% 88.68/26.76 (((emptyInPowerset) =>
% 88.68/26.76 (((powersetE) =>
% 88.68/26.76 (((setunionI) =>
% 88.68/26.76 (((setunionE) =>
% 88.68/26.76 (((subPowSU) =>
% 88.68/26.76 (((exuE2) =>
% 88.68/26.76 ((
% 88.68/26.76 (nonemptyImpWitness) =>
% 88.68/26.76 ((
% 88.68/26.76 (uniqinunit) =>
% 88.68/26.76 ((
% 88.68/26.76 (notinsingleton) =>
% 88.68/26.76 ((
% 88.68/26.76 (eqinunit) =>
% 88.68/26.76 ((
% 88.68/26.76 (singletonsswitch) =>
% 88.68/26.76 ((
% 88.68/26.76 (upairsetE) =>
% 88.68/26.76 ((
% 88.68/26.76 (upairsetIL) =>
% 88.68/26.76 ((
% 88.68/26.76 (upairsetIR) =>
% 88.68/26.76 ((
% 88.68/26.76 (emptyE1) =>
% 88.68/26.76 ((
% 88.68/26.76 (vacuousDall) =>
% 88.68/26.76 ((
% 88.68/26.76 (quantDeMorgan1) =>
% 88.68/26.76 ((
% 88.68/26.76 (quantDeMorgan2) =>
% 88.68/26.76 ((
% 88.68/26.76 (quantDeMorgan3) =>
% 88.68/26.76 ((
% 88.68/26.76 (quantDeMorgan4) =>
% 88.68/26.76 ((
% 88.68/26.76 (prop2setI) =>
% 88.68/26.76 ((
% 88.68/26.76 (prop2set2propI) =>
% 88.68/26.76 ((
% 88.68/26.76 (notdexE) =>
% 88.68/26.76 ((
% 88.68/26.76 (notdallE) =>
% 88.68/26.76 ((
% 88.68/26.76 (exuI1) =>
% 88.68/26.76 ((
% 88.68/26.76 (exuI3) =>
% 88.68/26.76 ((
% 88.68/26.76 (exuI2) =>
% 88.68/26.76 ((
% 88.68/26.76 (inCongP) =>
% 88.68/26.76 ((
% 88.68/26.76 (in__Cong) =>
% 88.68/26.76 ((
% 88.68/26.76 (exuE3u) =>
% 88.68/26.76 ((
% 88.68/26.76 (exu__Cong) =>
% 88.68/26.76 ((
% 88.68/26.76 (setadjoin__Cong) =>
% 88.68/26.76 ((
% 88.68/26.76 (powerset__Cong) =>
% 88.68/26.76 ((
% 88.68/26.76 (setunion__Cong) =>
% 88.68/26.76 ((
% 88.68/26.76 (exuEu) =>
% 88.68/26.76 ((
% 88.68/26.76 (descr__Cong) =>
% 88.68/26.76 ((
% 88.68/26.76 (dsetconstr__Cong) =>
% 88.68/26.76 ((
% 88.68/26.76 (subsetI1) =>
% 88.68/26.76 ((
% 88.68/26.76 (eqimpsubset2) =>
% 88.68/26.76 ((
% 88.68/26.76 (eqimpsubset1) =>
% 88.68/26.76 ((
% 88.68/26.76 (subsetI2) =>
% 88.68/26.76 ((
% 88.68/26.76 (emptysetsubset) =>
% 88.68/26.76 ((
% 88.68/26.76 (subsetE) =>
% 88.68/26.76 ((
% 88.68/26.76 (subsetE2) =>
% 88.68/26.76 ((
% 88.68/26.76 (notsubsetI) =>
% 88.68/26.76 ((
% 88.68/26.76 (notequalI1) =>
% 88.68/26.76 ((
% 88.68/26.76 (notequalI2) =>
% 88.68/26.76 ((
% 88.68/26.76 (subsetRefl) =>
% 88.68/26.76 ((
% 88.68/26.76 (subsetTrans) =>
% 88.68/26.76 ((
% 88.68/26.76 (setadjoinSub) =>
% 88.68/26.76 ((
% 88.68/26.76 (setadjoinSub2) =>
% 88.68/26.76 ((
% 88.68/26.76 (subset2powerset) =>
% 88.68/26.76 ((
% 88.68/26.76 (setextsub) =>
% 88.68/26.76 ((
% 88.68/26.76 (subsetemptysetimpeq) =>
% 88.68/26.76 ((
% 88.68/26.76 (powersetI1) =>
% 88.68/26.76 ((
% 88.68/26.76 (powersetE1) =>
% 88.68/26.76 ((
% 88.68/26.76 (inPowerset) =>
% 88.68/26.76 ((
% 88.68/26.76 (powersetsubset) =>
% 88.68/26.76 ((
% 88.68/26.76 (sepInPowerset) =>
% 88.68/26.76 ((
% 88.68/26.76 (sepSubset) =>
% 88.68/26.76 ((
% 88.68/26.76 (binunionIL) =>
% 88.68/26.76 ((
% 88.68/26.76 (upairset2IR) =>
% 88.68/26.76 ((
% 88.68/26.76 (binunionIR) =>
% 88.68/26.76 ((
% 88.68/26.76 (binunionEcases) =>
% 88.68/26.76 ((
% 88.68/26.76 (binunionE) =>
% 88.68/26.76 ((
% 88.68/26.76 (binunionLsub) =>
% 88.68/26.76 ((
% 88.68/26.76 (binunionRsub) =>
% 88.68/26.76 ((
% 88.68/26.76 (binintersectI) =>
% 88.68/26.76 ((
% 88.68/26.76 (binintersectSubset5) =>
% 88.68/26.76 ((
% 88.68/26.76 (binintersectEL) =>
% 88.68/26.76 ((
% 88.68/26.76 (binintersectLsub) =>
% 88.68/26.76 ((
% 88.68/26.76 (binintersectSubset2) =>
% 88.68/26.76 ((
% 88.68/26.76 (binintersectSubset3) =>
% 88.68/26.76 ((
% 88.68/26.76 (binintersectER) =>
% 88.68/26.76 ((
% 88.68/26.76 (disjointsetsI1) =>
% 88.68/26.76 ((
% 88.68/26.76 (binintersectRsub) =>
% 88.68/26.76 ((
% 88.68/26.76 (binintersectSubset4) =>
% 88.68/26.76 ((
% 88.68/26.76 (binintersectSubset1) =>
% 88.68/26.76 ((
% 88.68/26.76 (bs114d) =>
% 88.68/26.76 ((
% 88.68/26.76 (setminusI) =>
% 88.68/26.76 ((
% 88.68/26.76 (setminusEL) =>
% 88.68/26.76 ((
% 88.68/26.76 (setminusER) =>
% 88.68/26.76 ((
% 88.68/26.76 (setminusSubset2) =>
% 88.68/26.76 ((
% 88.68/26.76 (setminusERneg) =>
% 88.68/26.76 ((
% 88.68/26.76 (setminusELneg) =>
% 88.68/26.76 ((
% 88.68/26.76 (setminusILneg) =>
% 88.68/26.76 ((
% 88.68/26.76 (setminusIRneg) =>
% 88.68/26.76 ((
% 88.68/26.76 (setminusLsub) =>
% 88.68/26.76 ((
% 88.68/26.76 (setminusSubset1) =>
% 88.68/26.76 ((
% 88.68/26.76 (symdiffE) =>
% 88.68/26.76 ((
% 88.68/26.76 (symdiffI1) =>
% 88.68/26.76 ((
% 88.68/26.76 (symdiffI2) =>
% 88.68/26.76 ((
% 88.68/26.76 (symdiffIneg1) =>
% 88.68/26.76 ((
% 88.68/26.76 (symdiffIneg2) =>
% 88.68/26.76 ((
% 88.68/26.76 (secondinupair) =>
% 88.68/26.76 ((
% 88.68/26.76 (setukpairIL) =>
% 88.68/26.76 ((
% 88.68/26.76 (setukpairIR) =>
% 88.68/26.76 ((
% 88.68/26.76 (kpairiskpair) =>
% 88.68/26.76 ((
% 88.68/26.76 (kpairp) =>
% 88.68/26.76 ((
% 88.68/26.76 (singletonsubset) =>
% 88.68/26.76 ((
% 88.68/26.76 (singletoninpowerset) =>
% 88.68/26.76 ((
% 88.68/26.76 (singletoninpowunion) =>
% 88.68/26.76 ((
% 88.68/26.76 (upairset2E) =>
% 88.68/26.76 ((
% 88.68/26.76 (upairsubunion) =>
% 88.68/26.76 ((
% 88.68/26.76 (upairinpowunion) =>
% 88.68/26.76 ((
% 88.68/26.76 (ubforcartprodlem1) =>
% 88.68/26.76 ((
% 88.68/26.76 (ubforcartprodlem2) =>
% 88.68/26.76 ((
% 88.68/26.76 (ubforcartprodlem3) =>
% 88.68/26.76 ((
% 88.68/26.76 (cartprodpairin) =>
% 88.68/26.76 ((
% 88.68/26.76 (cartprodmempair1) =>
% 88.68/26.76 ((
% 88.68/26.76 (cartprodmempair) =>
% 88.68/26.76 ((
% 88.68/26.76 (setunionE2) =>
% 88.68/26.76 ((
% 88.68/26.76 (setunionsingleton1) =>
% 88.68/26.76 ((
% 88.68/26.76 (setunionsingleton2) =>
% 88.68/26.76 ((
% 88.68/26.76 (setunionsingleton) =>
% 88.68/26.76 ((
% 88.68/26.76 (singletonprop) =>
% 88.68/26.76 ((
% 88.68/26.76 (ex1E1) =>
% 88.68/26.76 ((
% 88.68/26.76 (ex1I) =>
% 88.68/26.76 ((
% 88.68/26.76 (ex1I2) =>
% 88.68/26.76 ((
% 88.68/26.76 (singletonsuniq) =>
% 88.68/26.76 ((
% 88.68/26.76 (setukpairinjL1) =>
% 88.68/26.76 ((
% 88.68/26.76 (kfstsingleton) =>
% 88.68/26.76 ((
% 88.68/26.76 (theprop) =>
% 88.68/26.76 ((
% 88.68/26.76 (kfstpairEq) =>
% 88.68/26.76 ((
% 88.68/26.76 (cartprodfstin) =>
% 88.68/26.76 ((
% 88.68/26.76 (setukpairinjL2) =>
% 88.68/26.76 ((
% 88.68/26.76 (setukpairinjL) =>
% 88.68/26.76 ((
% 88.68/26.76 (setukpairinjR11) =>
% 88.68/26.76 ((
% 88.68/26.76 (setukpairinjR12) =>
% 88.68/26.76 ((
% 88.68/26.76 (setukpairinjR1) =>
% 88.68/26.76 ((
% 88.68/26.76 (upairequniteq) =>
% 88.68/26.76 ((
% 88.68/26.76 (setukpairinjR2) =>
% 88.68/26.76 ((
% 88.68/26.76 (setukpairinjR) =>
% 88.68/26.76 ((
% 88.68/26.76 (ksndsingleton) =>
% 88.68/26.76 ((
% 88.68/26.76 (ksndpairEq) =>
% 88.68/26.76 ((
% 88.68/26.76 (kpairsurjEq) =>
% 88.68/26.76 ((
% 88.68/26.76 (cartprodsndin) =>
% 88.68/26.76 ((
% 88.68/26.76 (cartprodpairmemEL) =>
% 88.68/26.76 ((
% 88.68/26.76 (cartprodpairmemER) =>
% 88.68/26.76 ((
% 88.68/26.76 (cartprodmempaircEq) =>
% 88.68/26.76 ((
% 88.68/26.76 (cartprodfstpairEq) =>
% 88.68/26.76 ((
% 88.68/26.76 (cartprodsndpairEq) =>
% 88.68/26.76 ((
% 88.68/26.76 (cartprodpairsurjEq) =>
% 88.68/26.76 ((
% 88.68/26.76 (dpsetconstrI) =>
% 88.68/26.76 ((
% 88.68/26.76 (dpsetconstrSub) =>
% 88.68/26.76 ((
% 88.68/26.76 (setOfPairsIsBReln) =>
% 88.68/26.76 ((
% 88.68/26.76 (dpsetconstrERa) =>
% 88.68/26.76 ((
% 88.68/26.76 (dpsetconstrEL1) =>
% 88.68/26.76 ((
% 88.68/26.76 (dpsetconstrEL2) =>
% 88.68/26.76 ((
% 88.68/26.76 (dpsetconstrER) =>
% 88.68/26.76 ((
% 88.68/26.76 (funcImageSingleton) =>
% 88.68/26.76 ((
% 88.68/26.76 (apProp) =>
% 88.68/26.76 ((
% 88.68/26.76 (app) =>
% 88.68/26.76 ((
% 88.68/26.76 (infuncsetfunc) =>
% 88.68/26.76 ((
% 88.68/26.76 (ap2p) =>
% 88.68/26.76 ((
% 88.68/26.76 (funcinfuncset) =>
% 88.68/26.76 ((
% 88.68/26.76 (lamProp) =>
% 88.68/26.76 ((
% 88.68/26.76 (lamp) =>
% 88.68/26.76 ((
% 88.68/26.76 (lam2p) =>
% 88.68/26.76 ((
% 88.68/26.76 (brelnall1) =>
% 88.68/26.76 ((
% 88.68/26.76 (brelnall2) =>
% 88.68/26.76 ((
% 88.68/26.76 (!!) @ (
% 88.68/26.76 (('#B') @ (
% 88.68/26.76 !!) @
% 88.68/26.76 (
% 88.68/26.76 (
% 88.68/26.76 ('#S') @ (
% 88.68/26.76 (
% 88.68/26.76 ('#B') @ (
% 88.68/26.76 '#S') @
% 88.68/26.76 (
% 88.68/26.76 (
% 88.68/26.76 ('#B') @ (
% 88.68/26.76 (
% 88.68/26.76 ('#B') @ (
% 88.68/26.76 =>))) @
% 88.68/26.76 ex1)))) @
% 88.68/26.76 (
% 88.68/26.76 (
% 88.68/26.76 ('#B') @ (
% 88.68/26.76 (
% 88.68/26.76 ('#B') @ (
% 88.68/26.76 !!))) @
% 88.68/26.76 (
% 88.68/26.76 (
% 88.68/26.76 ('#S') @ (
% 88.68/26.76 (
% 88.68/26.76 ('#B') @ (
% 88.68/26.76 '#B') @
% 88.68/26.76 (
% 88.68/26.76 (
% 88.68/26.76 ('#B') @ (
% 88.68/26.76 '#S') @
% 88.68/26.76 (
% 88.68/26.76 (
% 88.68/26.76 ('#B') @ (
% 88.68/26.76 (
% 88.68/26.76 ('#B') @ (
% 88.68/26.76 =>))) @
% 88.68/26.76 (
% 88.68/26.76 (
% 88.68/26.76 ('#C') @ in)))))))) @
% 88.68/26.76 (
% 88.68/26.76 (
% 88.68/26.76 ('#B') @ (
% 88.68/26.76 (
% 88.68/26.76 ('#B') @ (
% 88.68/26.76 (
% 88.68/26.76 ('#B') @ (
% 88.68/26.76 !!))))) @
% 88.68/26.76 (
% 88.68/26.76 (
% 88.68/26.76 ('#C') @ (
% 88.68/26.76 (
% 88.68/26.76 ('#B') @ (
% 88.68/26.76 '#B') @
% 88.68/26.76 (
% 88.68/26.76 (
% 88.68/26.76 ('#B') @ (
% 88.68/26.76 '#B') @
% 88.68/26.76 (
% 88.68/26.76 (
% 88.68/26.76 ('#B') @ (
% 88.68/26.76 '#S') @
% 88.68/26.76 (
% 88.68/26.76 (
% 88.68/26.76 ('#B') @ (
% 88.68/26.76 (
% 88.68/26.76 ('#B') @ (
% 88.68/26.76 =>))) @
% 88.68/26.76 (
% 88.68/26.76 (
% 88.68/26.76 ('#C') @ in)))))))))) @
% 88.68/26.76 (
% 88.68/26.76 (
% 88.68/26.76 ('#S') @ (
% 88.68/26.76 (
% 88.68/26.76 ('#B') @ (
% 88.68/26.76 '#S') @
% 88.68/26.76 (
% 88.68/26.76 (
% 88.68/26.76 ('#B') @ (
% 88.68/26.76 (
% 88.68/26.76 ('#B') @ (
% 88.68/26.76 '#B'))) @
% 88.68/26.76 (
% 88.68/26.76 (
% 88.68/26.76 ('#B') @ (
% 88.68/26.76 =>))))))) @
% 88.68/26.76 (
% 88.68/26.76 (
% 88.68/26.76 ('#C') @ (
% 88.68/26.76 (
% 88.68/26.76 ('#B') @ (
% 88.68/26.76 '#B') @
% 88.68/26.76 (
% 88.68/26.76 (
% 88.68/26.76 ('#B') @ (
% 88.68/26.76 '#S') @
% 88.68/26.76 (
% 88.68/26.76 (
% 88.68/26.76 ('#B') @ (
% 88.68/26.76 =>))))))) @
% 88.68/26.76 (
% 88.68/26.76 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 88.68/26.76 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl64])).
% 88.68/26.76 thf(zip_derived_cl79, plain,
% 88.68/26.76 (~ (((dsetconstrEL) =>
% 88.68/26.76 (((dsetconstrER) =>
% 88.68/26.76 (((exuE1) =>
% 88.68/26.76 (((prop2setE) =>
% 88.68/26.76 (((emptysetE) =>
% 88.68/26.76 (((emptysetimpfalse) =>
% 88.68/26.76 (((notinemptyset) =>
% 88.68/26.76 (((exuE3e) =>
% 88.68/26.76 (((setext) =>
% 88.68/26.76 (((emptyI) =>
% 88.68/26.76 (((noeltsimpempty) =>
% 88.68/26.76 (((setbeta) =>
% 88.68/26.76 (((nonemptyE1) =>
% 88.68/26.76 (((nonemptyI) =>
% 88.68/26.76 (((nonemptyI1) =>
% 88.68/26.76 (((setadjoinIL) =>
% 88.68/26.76 (((in @ emptyset @
% 88.68/26.76 (setadjoin @ emptyset @ emptyset)) =>
% 88.68/26.76 (((setadjoinIR) =>
% 88.68/26.76 (((setadjoinE) =>
% 88.68/26.76 (((setadjoinOr) =>
% 88.68/26.76 (((setoftrueEq) =>
% 88.68/26.76 (((powersetI) =>
% 88.68/26.76 (((emptyinPowerset) =>
% 88.68/26.76 (((emptyInPowerset) =>
% 88.68/26.76 (((powersetE) =>
% 88.68/26.76 (((setunionI) =>
% 88.68/26.76 (((setunionE) =>
% 88.68/26.76 (((subPowSU) =>
% 88.68/26.76 (((exuE2) =>
% 88.68/26.76 (((nonemptyImpWitness) =>
% 88.68/26.76 ((
% 88.68/26.76 (uniqinunit) =>
% 88.68/26.76 ((
% 88.68/26.76 (notinsingleton) =>
% 88.68/26.76 ((
% 88.68/26.76 (eqinunit) =>
% 88.68/26.76 ((
% 88.68/26.76 (singletonsswitch) =>
% 88.68/26.76 ((
% 88.68/26.76 (upairsetE) =>
% 88.68/26.76 ((
% 88.68/26.76 (upairsetIL) =>
% 88.68/26.76 ((
% 88.68/26.76 (upairsetIR) =>
% 88.68/26.76 ((
% 88.68/26.76 (emptyE1) =>
% 88.68/26.76 ((
% 88.68/26.76 (vacuousDall) =>
% 88.68/26.76 ((
% 88.68/26.76 (quantDeMorgan1) =>
% 88.68/26.76 ((
% 88.68/26.76 (quantDeMorgan2) =>
% 88.68/26.76 ((
% 88.68/26.76 (quantDeMorgan3) =>
% 88.68/26.76 ((
% 88.68/26.76 (quantDeMorgan4) =>
% 88.68/26.76 ((
% 88.68/26.76 (prop2setI) =>
% 88.68/26.76 ((
% 88.68/26.76 (prop2set2propI) =>
% 88.68/26.76 ((
% 88.68/26.76 (notdexE) =>
% 88.68/26.76 ((
% 88.68/26.76 (notdallE) =>
% 88.68/26.76 ((
% 88.68/26.76 (exuI1) =>
% 88.68/26.76 ((
% 88.68/26.76 (exuI3) =>
% 88.68/26.76 ((
% 88.68/26.76 (exuI2) =>
% 88.68/26.76 ((
% 88.68/26.76 (inCongP) =>
% 88.68/26.76 ((
% 88.68/26.76 (in__Cong) =>
% 88.68/26.76 ((
% 88.68/26.76 (exuE3u) =>
% 88.68/26.76 ((
% 88.68/26.76 (exu__Cong) =>
% 88.68/26.76 ((
% 88.68/26.76 (setadjoin__Cong) =>
% 88.68/26.76 ((
% 88.68/26.76 (powerset__Cong) =>
% 88.68/26.76 ((
% 88.68/26.76 (setunion__Cong) =>
% 88.68/26.76 ((
% 88.68/26.76 (exuEu) =>
% 88.68/26.76 ((
% 88.68/26.76 (descr__Cong) =>
% 88.68/26.76 ((
% 88.68/26.76 (dsetconstr__Cong) =>
% 88.68/26.76 ((
% 88.68/26.76 (subsetI1) =>
% 88.68/26.76 ((
% 88.68/26.76 (eqimpsubset2) =>
% 88.68/26.76 ((
% 88.68/26.76 (eqimpsubset1) =>
% 88.68/26.76 ((
% 88.68/26.76 (subsetI2) =>
% 88.68/26.76 ((
% 88.68/26.76 (emptysetsubset) =>
% 88.68/26.76 ((
% 88.68/26.76 (subsetE) =>
% 88.68/26.76 ((
% 88.68/26.76 (subsetE2) =>
% 88.68/26.76 ((
% 88.68/26.76 (notsubsetI) =>
% 88.68/26.76 ((
% 88.68/26.76 (notequalI1) =>
% 88.68/26.76 ((
% 88.68/26.76 (notequalI2) =>
% 88.68/26.76 ((
% 88.68/26.76 (subsetRefl) =>
% 88.68/26.76 ((
% 88.68/26.76 (subsetTrans) =>
% 88.68/26.76 ((
% 88.68/26.76 (setadjoinSub) =>
% 88.68/26.76 ((
% 88.68/26.76 (setadjoinSub2) =>
% 88.68/26.76 ((
% 88.68/26.76 (subset2powerset) =>
% 88.68/26.76 ((
% 88.68/26.76 (setextsub) =>
% 88.68/26.76 ((
% 88.68/26.76 (subsetemptysetimpeq) =>
% 88.68/26.76 ((
% 88.68/26.76 (powersetI1) =>
% 88.68/26.76 ((
% 88.68/26.76 (powersetE1) =>
% 88.68/26.76 ((
% 88.68/26.76 (inPowerset) =>
% 88.68/26.76 ((
% 88.68/26.76 (powersetsubset) =>
% 88.68/26.76 ((
% 88.68/26.76 (sepInPowerset) =>
% 88.68/26.76 ((
% 88.68/26.76 (sepSubset) =>
% 88.68/26.76 ((
% 88.68/26.76 (binunionIL) =>
% 88.68/26.76 ((
% 88.68/26.76 (upairset2IR) =>
% 88.68/26.76 ((
% 88.68/26.76 (binunionIR) =>
% 88.68/26.76 ((
% 88.68/26.76 (binunionEcases) =>
% 88.68/26.76 ((
% 88.68/26.76 (binunionE) =>
% 88.68/26.76 ((
% 88.68/26.76 (binunionLsub) =>
% 88.68/26.76 ((
% 88.68/26.76 (binunionRsub) =>
% 88.68/26.76 ((
% 88.68/26.76 (binintersectI) =>
% 88.68/26.76 ((
% 88.68/26.76 (binintersectSubset5) =>
% 88.68/26.76 ((
% 88.68/26.76 (binintersectEL) =>
% 88.68/26.76 ((
% 88.68/26.76 (binintersectLsub) =>
% 88.68/26.76 ((
% 88.68/26.76 (binintersectSubset2) =>
% 88.68/26.76 ((
% 88.68/26.76 (binintersectSubset3) =>
% 88.68/26.76 ((
% 88.68/26.76 (binintersectER) =>
% 88.68/26.76 ((
% 88.68/26.76 (disjointsetsI1) =>
% 88.68/26.76 ((
% 88.68/26.76 (binintersectRsub) =>
% 88.68/26.76 ((
% 88.68/26.76 (binintersectSubset4) =>
% 88.68/26.76 ((
% 88.68/26.76 (binintersectSubset1) =>
% 88.68/26.76 ((
% 88.68/26.76 (bs114d) =>
% 88.68/26.76 ((
% 88.68/26.76 (setminusI) =>
% 88.68/26.76 ((
% 88.68/26.76 (setminusEL) =>
% 88.68/26.76 ((
% 88.68/26.76 (setminusER) =>
% 88.68/26.76 ((
% 88.68/26.76 (setminusSubset2) =>
% 88.68/26.76 ((
% 88.68/26.76 (setminusERneg) =>
% 88.68/26.76 ((
% 88.68/26.76 (setminusELneg) =>
% 88.68/26.76 ((
% 88.68/26.76 (setminusILneg) =>
% 88.68/26.76 ((
% 88.68/26.76 (setminusIRneg) =>
% 88.68/26.76 ((
% 88.68/26.76 (setminusLsub) =>
% 88.68/26.76 ((
% 88.68/26.76 (setminusSubset1) =>
% 88.68/26.76 ((
% 88.68/26.76 (symdiffE) =>
% 88.68/26.76 ((
% 88.68/26.76 (symdiffI1) =>
% 88.68/26.76 ((
% 88.68/26.76 (symdiffI2) =>
% 88.68/26.76 ((
% 88.68/26.76 (symdiffIneg1) =>
% 88.68/26.76 ((
% 88.68/26.76 (symdiffIneg2) =>
% 88.68/26.76 ((
% 88.68/26.76 (secondinupair) =>
% 88.68/26.76 ((
% 88.68/26.76 (setukpairIL) =>
% 88.68/26.76 ((
% 88.68/26.76 (setukpairIR) =>
% 88.68/26.76 ((
% 88.68/26.76 (kpairiskpair) =>
% 88.68/26.76 ((
% 88.68/26.76 (kpairp) =>
% 88.68/26.76 ((
% 88.68/26.76 (singletonsubset) =>
% 88.68/26.76 ((
% 88.68/26.76 (singletoninpowerset) =>
% 88.68/26.76 ((
% 88.68/26.76 (singletoninpowunion) =>
% 88.68/26.76 ((
% 88.68/26.76 (upairset2E) =>
% 88.68/26.76 ((
% 88.68/26.76 (upairsubunion) =>
% 88.68/26.76 ((
% 88.68/26.76 (upairinpowunion) =>
% 88.68/26.76 ((
% 88.68/26.76 (ubforcartprodlem1) =>
% 88.68/26.76 ((
% 88.68/26.76 (ubforcartprodlem2) =>
% 88.68/26.76 ((
% 88.68/26.76 (ubforcartprodlem3) =>
% 88.68/26.76 ((
% 88.68/26.76 (cartprodpairin) =>
% 88.68/26.76 ((
% 88.68/26.76 (cartprodmempair1) =>
% 88.68/26.76 ((
% 88.68/26.76 (cartprodmempair) =>
% 88.68/26.76 ((
% 88.68/26.76 (setunionE2) =>
% 88.68/26.76 ((
% 88.68/26.76 (setunionsingleton1) =>
% 88.68/26.76 ((
% 88.68/26.76 (setunionsingleton2) =>
% 88.68/26.76 ((
% 88.68/26.76 (setunionsingleton) =>
% 88.68/26.76 ((
% 88.68/26.76 (singletonprop) =>
% 88.68/26.76 ((
% 88.68/26.76 (ex1E1) =>
% 88.68/26.76 ((
% 88.68/26.76 (ex1I) =>
% 88.68/26.76 ((
% 88.68/26.76 (ex1I2) =>
% 88.68/26.76 ((
% 88.68/26.76 (singletonsuniq) =>
% 88.68/26.76 ((
% 88.68/26.76 (setukpairinjL1) =>
% 88.68/26.76 ((
% 88.68/26.76 (kfstsingleton) =>
% 88.68/26.76 ((
% 88.68/26.76 (theprop) =>
% 88.68/26.76 ((
% 88.68/26.76 (kfstpairEq) =>
% 88.68/26.76 ((
% 88.68/26.76 (cartprodfstin) =>
% 88.68/26.76 ((
% 88.68/26.76 (setukpairinjL2) =>
% 88.68/26.76 ((
% 88.68/26.76 (setukpairinjL) =>
% 88.68/26.76 ((
% 88.68/26.76 (setukpairinjR11) =>
% 88.68/26.76 ((
% 88.68/26.76 (setukpairinjR12) =>
% 88.68/26.76 ((
% 88.68/26.76 (setukpairinjR1) =>
% 88.68/26.76 ((
% 88.68/26.76 (upairequniteq) =>
% 88.68/26.76 ((
% 88.68/26.76 (setukpairinjR2) =>
% 88.68/26.76 ((
% 88.68/26.76 (setukpairinjR) =>
% 88.68/26.76 ((
% 88.68/26.76 (ksndsingleton) =>
% 88.68/26.76 ((
% 88.68/26.76 (ksndpairEq) =>
% 88.68/26.76 ((
% 88.68/26.76 (kpairsurjEq) =>
% 88.68/26.76 ((
% 88.68/26.76 (cartprodsndin) =>
% 88.68/26.76 ((
% 88.68/26.76 (cartprodpairmemEL) =>
% 88.68/26.76 ((
% 88.68/26.76 (cartprodpairmemER) =>
% 88.68/26.76 ((
% 88.68/26.76 (cartprodmempaircEq) =>
% 88.68/26.76 ((
% 88.68/26.76 (cartprodfstpairEq) =>
% 88.68/26.76 ((
% 88.68/26.76 (cartprodsndpairEq) =>
% 88.68/26.76 ((
% 88.68/26.76 (cartprodpairsurjEq) =>
% 88.68/26.76 ((
% 88.68/26.76 (dpsetconstrI) =>
% 88.68/26.76 ((
% 88.68/26.76 (dpsetconstrSub) =>
% 88.68/26.76 ((
% 88.68/26.76 (setOfPairsIsBReln) =>
% 88.68/26.76 ((
% 88.68/26.76 (dpsetconstrERa) =>
% 88.68/26.76 ((
% 88.68/26.76 (dpsetconstrEL1) =>
% 88.68/26.76 ((
% 88.68/26.76 (dpsetconstrEL2) =>
% 88.68/26.76 ((
% 88.68/26.76 (dpsetconstrER) =>
% 88.68/26.76 ((
% 88.68/26.76 (funcImageSingleton) =>
% 88.68/26.76 ((
% 88.68/26.76 (apProp) =>
% 88.68/26.76 ((
% 88.68/26.76 (app) =>
% 88.68/26.76 ((
% 88.68/26.76 (infuncsetfunc) =>
% 88.68/26.76 ((
% 88.68/26.76 (ap2p) =>
% 88.68/26.76 ((
% 88.68/26.76 (funcinfuncset) =>
% 88.68/26.76 ((
% 88.68/26.76 (lamProp) =>
% 88.68/26.76 ((
% 88.68/26.76 (lamp) =>
% 88.68/26.76 ((
% 88.68/26.76 (lam2p) =>
% 88.68/26.76 ((
% 88.68/26.76 (brelnall1) =>
% 88.68/26.76 ((
% 88.68/26.76 (brelnall2) =>
% 88.68/26.76 ((
% 88.68/26.76 (!!) @ (
% 88.68/26.76 (('#B') @ (
% 88.68/26.76 !!) @
% 88.68/26.76 (
% 88.68/26.76 (
% 88.68/26.76 ('#S') @ (
% 88.68/26.76 (
% 88.68/26.76 ('#B') @ (
% 88.68/26.76 '#S') @
% 88.68/26.76 (
% 88.68/26.76 (
% 88.68/26.76 ('#B') @ (
% 88.68/26.76 (
% 88.68/26.76 ('#B') @ (
% 88.68/26.76 =>))) @
% 88.68/26.76 ex1)))) @
% 88.68/26.76 (
% 88.68/26.76 (
% 88.68/26.76 ('#B') @ (
% 88.68/26.76 (
% 88.68/26.76 ('#B') @ (
% 88.68/26.76 !!))) @
% 88.68/26.76 (
% 88.68/26.76 (
% 88.68/26.76 ('#S') @ (
% 88.68/26.76 (
% 88.68/26.76 ('#B') @ (
% 88.68/26.76 '#B') @
% 88.68/26.76 (
% 88.68/26.76 (
% 88.68/26.76 ('#B') @ (
% 88.68/26.76 '#S') @
% 88.68/26.76 (
% 88.68/26.76 (
% 88.68/26.76 ('#B') @ (
% 88.68/26.76 (
% 88.68/26.76 ('#B') @ (
% 88.68/26.76 =>))) @
% 88.68/26.76 (
% 88.68/26.76 (
% 88.68/26.76 ('#C') @ in)))))))) @
% 88.68/26.76 (
% 88.68/26.76 (
% 88.68/26.76 ('#B') @ (
% 88.68/26.76 (
% 88.68/26.76 ('#B') @ (
% 88.68/26.76 (
% 88.68/26.76 ('#B') @ (
% 88.68/26.76 !!))))) @
% 88.68/26.76 (
% 88.68/26.76 (
% 88.68/26.76 ('#C') @ (
% 88.68/26.76 (
% 88.68/26.76 ('#B') @ (
% 88.68/26.76 '#B') @
% 88.68/26.76 (
% 88.68/26.76 (
% 88.68/26.76 ('#B') @ (
% 88.68/26.76 '#B') @
% 88.68/26.76 (
% 88.68/26.76 (
% 88.68/26.76 ('#B') @ (
% 88.68/26.78 '#S') @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 =>))) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#C') @ in)))))))))) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#S') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#S') @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#B'))) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 =>))))))) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#C') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#B') @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#S') @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 =>))))))) @
% 88.68/26.78 (
% 88.68/26.78 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 88.68/26.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl71])).
% 88.68/26.78 thf(zip_derived_cl89, plain,
% 88.68/26.78 (~ (((dsetconstrER) =>
% 88.68/26.78 (((exuE1) =>
% 88.68/26.78 (((prop2setE) =>
% 88.68/26.78 (((emptysetE) =>
% 88.68/26.78 (((emptysetimpfalse) =>
% 88.68/26.78 (((notinemptyset) =>
% 88.68/26.78 (((exuE3e) =>
% 88.68/26.78 (((setext) =>
% 88.68/26.78 (((emptyI) =>
% 88.68/26.78 (((noeltsimpempty) =>
% 88.68/26.78 (((setbeta) =>
% 88.68/26.78 (((nonemptyE1) =>
% 88.68/26.78 (((nonemptyI) =>
% 88.68/26.78 (((nonemptyI1) =>
% 88.68/26.78 (((setadjoinIL) =>
% 88.68/26.78 (((in @ emptyset @
% 88.68/26.78 (setadjoin @ emptyset @ emptyset)) =>
% 88.68/26.78 (((setadjoinIR) =>
% 88.68/26.78 (((setadjoinE) =>
% 88.68/26.78 (((setadjoinOr) =>
% 88.68/26.78 (((setoftrueEq) =>
% 88.68/26.78 (((powersetI) =>
% 88.68/26.78 (((emptyinPowerset) =>
% 88.68/26.78 (((emptyInPowerset) =>
% 88.68/26.78 (((powersetE) =>
% 88.68/26.78 (((setunionI) =>
% 88.68/26.78 (((setunionE) =>
% 88.68/26.78 (((subPowSU) =>
% 88.68/26.78 (((exuE2) =>
% 88.68/26.78 (((nonemptyImpWitness) =>
% 88.68/26.78 (((uniqinunit) =>
% 88.68/26.78 ((
% 88.68/26.78 (notinsingleton) =>
% 88.68/26.78 ((
% 88.68/26.78 (eqinunit) =>
% 88.68/26.78 ((
% 88.68/26.78 (singletonsswitch) =>
% 88.68/26.78 ((
% 88.68/26.78 (upairsetE) =>
% 88.68/26.78 ((
% 88.68/26.78 (upairsetIL) =>
% 88.68/26.78 ((
% 88.68/26.78 (upairsetIR) =>
% 88.68/26.78 ((
% 88.68/26.78 (emptyE1) =>
% 88.68/26.78 ((
% 88.68/26.78 (vacuousDall) =>
% 88.68/26.78 ((
% 88.68/26.78 (quantDeMorgan1) =>
% 88.68/26.78 ((
% 88.68/26.78 (quantDeMorgan2) =>
% 88.68/26.78 ((
% 88.68/26.78 (quantDeMorgan3) =>
% 88.68/26.78 ((
% 88.68/26.78 (quantDeMorgan4) =>
% 88.68/26.78 ((
% 88.68/26.78 (prop2setI) =>
% 88.68/26.78 ((
% 88.68/26.78 (prop2set2propI) =>
% 88.68/26.78 ((
% 88.68/26.78 (notdexE) =>
% 88.68/26.78 ((
% 88.68/26.78 (notdallE) =>
% 88.68/26.78 ((
% 88.68/26.78 (exuI1) =>
% 88.68/26.78 ((
% 88.68/26.78 (exuI3) =>
% 88.68/26.78 ((
% 88.68/26.78 (exuI2) =>
% 88.68/26.78 ((
% 88.68/26.78 (inCongP) =>
% 88.68/26.78 ((
% 88.68/26.78 (in__Cong) =>
% 88.68/26.78 ((
% 88.68/26.78 (exuE3u) =>
% 88.68/26.78 ((
% 88.68/26.78 (exu__Cong) =>
% 88.68/26.78 ((
% 88.68/26.78 (setadjoin__Cong) =>
% 88.68/26.78 ((
% 88.68/26.78 (powerset__Cong) =>
% 88.68/26.78 ((
% 88.68/26.78 (setunion__Cong) =>
% 88.68/26.78 ((
% 88.68/26.78 (exuEu) =>
% 88.68/26.78 ((
% 88.68/26.78 (descr__Cong) =>
% 88.68/26.78 ((
% 88.68/26.78 (dsetconstr__Cong) =>
% 88.68/26.78 ((
% 88.68/26.78 (subsetI1) =>
% 88.68/26.78 ((
% 88.68/26.78 (eqimpsubset2) =>
% 88.68/26.78 ((
% 88.68/26.78 (eqimpsubset1) =>
% 88.68/26.78 ((
% 88.68/26.78 (subsetI2) =>
% 88.68/26.78 ((
% 88.68/26.78 (emptysetsubset) =>
% 88.68/26.78 ((
% 88.68/26.78 (subsetE) =>
% 88.68/26.78 ((
% 88.68/26.78 (subsetE2) =>
% 88.68/26.78 ((
% 88.68/26.78 (notsubsetI) =>
% 88.68/26.78 ((
% 88.68/26.78 (notequalI1) =>
% 88.68/26.78 ((
% 88.68/26.78 (notequalI2) =>
% 88.68/26.78 ((
% 88.68/26.78 (subsetRefl) =>
% 88.68/26.78 ((
% 88.68/26.78 (subsetTrans) =>
% 88.68/26.78 ((
% 88.68/26.78 (setadjoinSub) =>
% 88.68/26.78 ((
% 88.68/26.78 (setadjoinSub2) =>
% 88.68/26.78 ((
% 88.68/26.78 (subset2powerset) =>
% 88.68/26.78 ((
% 88.68/26.78 (setextsub) =>
% 88.68/26.78 ((
% 88.68/26.78 (subsetemptysetimpeq) =>
% 88.68/26.78 ((
% 88.68/26.78 (powersetI1) =>
% 88.68/26.78 ((
% 88.68/26.78 (powersetE1) =>
% 88.68/26.78 ((
% 88.68/26.78 (inPowerset) =>
% 88.68/26.78 ((
% 88.68/26.78 (powersetsubset) =>
% 88.68/26.78 ((
% 88.68/26.78 (sepInPowerset) =>
% 88.68/26.78 ((
% 88.68/26.78 (sepSubset) =>
% 88.68/26.78 ((
% 88.68/26.78 (binunionIL) =>
% 88.68/26.78 ((
% 88.68/26.78 (upairset2IR) =>
% 88.68/26.78 ((
% 88.68/26.78 (binunionIR) =>
% 88.68/26.78 ((
% 88.68/26.78 (binunionEcases) =>
% 88.68/26.78 ((
% 88.68/26.78 (binunionE) =>
% 88.68/26.78 ((
% 88.68/26.78 (binunionLsub) =>
% 88.68/26.78 ((
% 88.68/26.78 (binunionRsub) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectI) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectSubset5) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectEL) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectLsub) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectSubset2) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectSubset3) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectER) =>
% 88.68/26.78 ((
% 88.68/26.78 (disjointsetsI1) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectRsub) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectSubset4) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectSubset1) =>
% 88.68/26.78 ((
% 88.68/26.78 (bs114d) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusI) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusEL) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusER) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusSubset2) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusERneg) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusELneg) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusILneg) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusIRneg) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusLsub) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusSubset1) =>
% 88.68/26.78 ((
% 88.68/26.78 (symdiffE) =>
% 88.68/26.78 ((
% 88.68/26.78 (symdiffI1) =>
% 88.68/26.78 ((
% 88.68/26.78 (symdiffI2) =>
% 88.68/26.78 ((
% 88.68/26.78 (symdiffIneg1) =>
% 88.68/26.78 ((
% 88.68/26.78 (symdiffIneg2) =>
% 88.68/26.78 ((
% 88.68/26.78 (secondinupair) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairIL) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairIR) =>
% 88.68/26.78 ((
% 88.68/26.78 (kpairiskpair) =>
% 88.68/26.78 ((
% 88.68/26.78 (kpairp) =>
% 88.68/26.78 ((
% 88.68/26.78 (singletonsubset) =>
% 88.68/26.78 ((
% 88.68/26.78 (singletoninpowerset) =>
% 88.68/26.78 ((
% 88.68/26.78 (singletoninpowunion) =>
% 88.68/26.78 ((
% 88.68/26.78 (upairset2E) =>
% 88.68/26.78 ((
% 88.68/26.78 (upairsubunion) =>
% 88.68/26.78 ((
% 88.68/26.78 (upairinpowunion) =>
% 88.68/26.78 ((
% 88.68/26.78 (ubforcartprodlem1) =>
% 88.68/26.78 ((
% 88.68/26.78 (ubforcartprodlem2) =>
% 88.68/26.78 ((
% 88.68/26.78 (ubforcartprodlem3) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodpairin) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodmempair1) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodmempair) =>
% 88.68/26.78 ((
% 88.68/26.78 (setunionE2) =>
% 88.68/26.78 ((
% 88.68/26.78 (setunionsingleton1) =>
% 88.68/26.78 ((
% 88.68/26.78 (setunionsingleton2) =>
% 88.68/26.78 ((
% 88.68/26.78 (setunionsingleton) =>
% 88.68/26.78 ((
% 88.68/26.78 (singletonprop) =>
% 88.68/26.78 ((
% 88.68/26.78 (ex1E1) =>
% 88.68/26.78 ((
% 88.68/26.78 (ex1I) =>
% 88.68/26.78 ((
% 88.68/26.78 (ex1I2) =>
% 88.68/26.78 ((
% 88.68/26.78 (singletonsuniq) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairinjL1) =>
% 88.68/26.78 ((
% 88.68/26.78 (kfstsingleton) =>
% 88.68/26.78 ((
% 88.68/26.78 (theprop) =>
% 88.68/26.78 ((
% 88.68/26.78 (kfstpairEq) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodfstin) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairinjL2) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairinjL) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairinjR11) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairinjR12) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairinjR1) =>
% 88.68/26.78 ((
% 88.68/26.78 (upairequniteq) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairinjR2) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairinjR) =>
% 88.68/26.78 ((
% 88.68/26.78 (ksndsingleton) =>
% 88.68/26.78 ((
% 88.68/26.78 (ksndpairEq) =>
% 88.68/26.78 ((
% 88.68/26.78 (kpairsurjEq) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodsndin) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodpairmemEL) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodpairmemER) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodmempaircEq) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodfstpairEq) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodsndpairEq) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodpairsurjEq) =>
% 88.68/26.78 ((
% 88.68/26.78 (dpsetconstrI) =>
% 88.68/26.78 ((
% 88.68/26.78 (dpsetconstrSub) =>
% 88.68/26.78 ((
% 88.68/26.78 (setOfPairsIsBReln) =>
% 88.68/26.78 ((
% 88.68/26.78 (dpsetconstrERa) =>
% 88.68/26.78 ((
% 88.68/26.78 (dpsetconstrEL1) =>
% 88.68/26.78 ((
% 88.68/26.78 (dpsetconstrEL2) =>
% 88.68/26.78 ((
% 88.68/26.78 (dpsetconstrER) =>
% 88.68/26.78 ((
% 88.68/26.78 (funcImageSingleton) =>
% 88.68/26.78 ((
% 88.68/26.78 (apProp) =>
% 88.68/26.78 ((
% 88.68/26.78 (app) =>
% 88.68/26.78 ((
% 88.68/26.78 (infuncsetfunc) =>
% 88.68/26.78 ((
% 88.68/26.78 (ap2p) =>
% 88.68/26.78 ((
% 88.68/26.78 (funcinfuncset) =>
% 88.68/26.78 ((
% 88.68/26.78 (lamProp) =>
% 88.68/26.78 ((
% 88.68/26.78 (lamp) =>
% 88.68/26.78 ((
% 88.68/26.78 (lam2p) =>
% 88.68/26.78 ((
% 88.68/26.78 (brelnall1) =>
% 88.68/26.78 ((
% 88.68/26.78 (brelnall2) =>
% 88.68/26.78 ((
% 88.68/26.78 (!!) @ (
% 88.68/26.78 (('#B') @ (
% 88.68/26.78 !!) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#S') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#S') @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 =>))) @
% 88.68/26.78 ex1)))) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 !!))) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#S') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#B') @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#S') @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 =>))) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#C') @ in)))))))) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 !!))))) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#C') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#B') @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#B') @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#S') @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 =>))) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#C') @ in)))))))))) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#S') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#S') @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#B'))) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 =>))))))) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#C') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#B') @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#S') @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 =>))))))) @
% 88.68/26.78 (
% 88.68/26.78 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 88.68/26.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl79])).
% 88.68/26.78 thf(zip_derived_cl105, plain,
% 88.68/26.78 (~ (((exuE1) =>
% 88.68/26.78 (((prop2setE) =>
% 88.68/26.78 (((emptysetE) =>
% 88.68/26.78 (((emptysetimpfalse) =>
% 88.68/26.78 (((notinemptyset) =>
% 88.68/26.78 (((exuE3e) =>
% 88.68/26.78 (((setext) =>
% 88.68/26.78 (((emptyI) =>
% 88.68/26.78 (((noeltsimpempty) =>
% 88.68/26.78 (((setbeta) =>
% 88.68/26.78 (((nonemptyE1) =>
% 88.68/26.78 (((nonemptyI) =>
% 88.68/26.78 (((nonemptyI1) =>
% 88.68/26.78 (((setadjoinIL) =>
% 88.68/26.78 (((in @ emptyset @
% 88.68/26.78 (setadjoin @ emptyset @ emptyset)) =>
% 88.68/26.78 (((setadjoinIR) =>
% 88.68/26.78 (((setadjoinE) =>
% 88.68/26.78 (((setadjoinOr) =>
% 88.68/26.78 (((setoftrueEq) =>
% 88.68/26.78 (((powersetI) =>
% 88.68/26.78 (((emptyinPowerset) =>
% 88.68/26.78 (((emptyInPowerset) =>
% 88.68/26.78 (((powersetE) =>
% 88.68/26.78 (((setunionI) =>
% 88.68/26.78 (((setunionE) =>
% 88.68/26.78 (((subPowSU) =>
% 88.68/26.78 (((exuE2) =>
% 88.68/26.78 (((nonemptyImpWitness) =>
% 88.68/26.78 (((uniqinunit) =>
% 88.68/26.78 (((notinsingleton) =>
% 88.68/26.78 ((
% 88.68/26.78 (eqinunit) =>
% 88.68/26.78 ((
% 88.68/26.78 (singletonsswitch) =>
% 88.68/26.78 ((
% 88.68/26.78 (upairsetE) =>
% 88.68/26.78 ((
% 88.68/26.78 (upairsetIL) =>
% 88.68/26.78 ((
% 88.68/26.78 (upairsetIR) =>
% 88.68/26.78 ((
% 88.68/26.78 (emptyE1) =>
% 88.68/26.78 ((
% 88.68/26.78 (vacuousDall) =>
% 88.68/26.78 ((
% 88.68/26.78 (quantDeMorgan1) =>
% 88.68/26.78 ((
% 88.68/26.78 (quantDeMorgan2) =>
% 88.68/26.78 ((
% 88.68/26.78 (quantDeMorgan3) =>
% 88.68/26.78 ((
% 88.68/26.78 (quantDeMorgan4) =>
% 88.68/26.78 ((
% 88.68/26.78 (prop2setI) =>
% 88.68/26.78 ((
% 88.68/26.78 (prop2set2propI) =>
% 88.68/26.78 ((
% 88.68/26.78 (notdexE) =>
% 88.68/26.78 ((
% 88.68/26.78 (notdallE) =>
% 88.68/26.78 ((
% 88.68/26.78 (exuI1) =>
% 88.68/26.78 ((
% 88.68/26.78 (exuI3) =>
% 88.68/26.78 ((
% 88.68/26.78 (exuI2) =>
% 88.68/26.78 ((
% 88.68/26.78 (inCongP) =>
% 88.68/26.78 ((
% 88.68/26.78 (in__Cong) =>
% 88.68/26.78 ((
% 88.68/26.78 (exuE3u) =>
% 88.68/26.78 ((
% 88.68/26.78 (exu__Cong) =>
% 88.68/26.78 ((
% 88.68/26.78 (setadjoin__Cong) =>
% 88.68/26.78 ((
% 88.68/26.78 (powerset__Cong) =>
% 88.68/26.78 ((
% 88.68/26.78 (setunion__Cong) =>
% 88.68/26.78 ((
% 88.68/26.78 (exuEu) =>
% 88.68/26.78 ((
% 88.68/26.78 (descr__Cong) =>
% 88.68/26.78 ((
% 88.68/26.78 (dsetconstr__Cong) =>
% 88.68/26.78 ((
% 88.68/26.78 (subsetI1) =>
% 88.68/26.78 ((
% 88.68/26.78 (eqimpsubset2) =>
% 88.68/26.78 ((
% 88.68/26.78 (eqimpsubset1) =>
% 88.68/26.78 ((
% 88.68/26.78 (subsetI2) =>
% 88.68/26.78 ((
% 88.68/26.78 (emptysetsubset) =>
% 88.68/26.78 ((
% 88.68/26.78 (subsetE) =>
% 88.68/26.78 ((
% 88.68/26.78 (subsetE2) =>
% 88.68/26.78 ((
% 88.68/26.78 (notsubsetI) =>
% 88.68/26.78 ((
% 88.68/26.78 (notequalI1) =>
% 88.68/26.78 ((
% 88.68/26.78 (notequalI2) =>
% 88.68/26.78 ((
% 88.68/26.78 (subsetRefl) =>
% 88.68/26.78 ((
% 88.68/26.78 (subsetTrans) =>
% 88.68/26.78 ((
% 88.68/26.78 (setadjoinSub) =>
% 88.68/26.78 ((
% 88.68/26.78 (setadjoinSub2) =>
% 88.68/26.78 ((
% 88.68/26.78 (subset2powerset) =>
% 88.68/26.78 ((
% 88.68/26.78 (setextsub) =>
% 88.68/26.78 ((
% 88.68/26.78 (subsetemptysetimpeq) =>
% 88.68/26.78 ((
% 88.68/26.78 (powersetI1) =>
% 88.68/26.78 ((
% 88.68/26.78 (powersetE1) =>
% 88.68/26.78 ((
% 88.68/26.78 (inPowerset) =>
% 88.68/26.78 ((
% 88.68/26.78 (powersetsubset) =>
% 88.68/26.78 ((
% 88.68/26.78 (sepInPowerset) =>
% 88.68/26.78 ((
% 88.68/26.78 (sepSubset) =>
% 88.68/26.78 ((
% 88.68/26.78 (binunionIL) =>
% 88.68/26.78 ((
% 88.68/26.78 (upairset2IR) =>
% 88.68/26.78 ((
% 88.68/26.78 (binunionIR) =>
% 88.68/26.78 ((
% 88.68/26.78 (binunionEcases) =>
% 88.68/26.78 ((
% 88.68/26.78 (binunionE) =>
% 88.68/26.78 ((
% 88.68/26.78 (binunionLsub) =>
% 88.68/26.78 ((
% 88.68/26.78 (binunionRsub) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectI) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectSubset5) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectEL) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectLsub) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectSubset2) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectSubset3) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectER) =>
% 88.68/26.78 ((
% 88.68/26.78 (disjointsetsI1) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectRsub) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectSubset4) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectSubset1) =>
% 88.68/26.78 ((
% 88.68/26.78 (bs114d) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusI) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusEL) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusER) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusSubset2) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusERneg) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusELneg) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusILneg) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusIRneg) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusLsub) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusSubset1) =>
% 88.68/26.78 ((
% 88.68/26.78 (symdiffE) =>
% 88.68/26.78 ((
% 88.68/26.78 (symdiffI1) =>
% 88.68/26.78 ((
% 88.68/26.78 (symdiffI2) =>
% 88.68/26.78 ((
% 88.68/26.78 (symdiffIneg1) =>
% 88.68/26.78 ((
% 88.68/26.78 (symdiffIneg2) =>
% 88.68/26.78 ((
% 88.68/26.78 (secondinupair) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairIL) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairIR) =>
% 88.68/26.78 ((
% 88.68/26.78 (kpairiskpair) =>
% 88.68/26.78 ((
% 88.68/26.78 (kpairp) =>
% 88.68/26.78 ((
% 88.68/26.78 (singletonsubset) =>
% 88.68/26.78 ((
% 88.68/26.78 (singletoninpowerset) =>
% 88.68/26.78 ((
% 88.68/26.78 (singletoninpowunion) =>
% 88.68/26.78 ((
% 88.68/26.78 (upairset2E) =>
% 88.68/26.78 ((
% 88.68/26.78 (upairsubunion) =>
% 88.68/26.78 ((
% 88.68/26.78 (upairinpowunion) =>
% 88.68/26.78 ((
% 88.68/26.78 (ubforcartprodlem1) =>
% 88.68/26.78 ((
% 88.68/26.78 (ubforcartprodlem2) =>
% 88.68/26.78 ((
% 88.68/26.78 (ubforcartprodlem3) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodpairin) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodmempair1) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodmempair) =>
% 88.68/26.78 ((
% 88.68/26.78 (setunionE2) =>
% 88.68/26.78 ((
% 88.68/26.78 (setunionsingleton1) =>
% 88.68/26.78 ((
% 88.68/26.78 (setunionsingleton2) =>
% 88.68/26.78 ((
% 88.68/26.78 (setunionsingleton) =>
% 88.68/26.78 ((
% 88.68/26.78 (singletonprop) =>
% 88.68/26.78 ((
% 88.68/26.78 (ex1E1) =>
% 88.68/26.78 ((
% 88.68/26.78 (ex1I) =>
% 88.68/26.78 ((
% 88.68/26.78 (ex1I2) =>
% 88.68/26.78 ((
% 88.68/26.78 (singletonsuniq) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairinjL1) =>
% 88.68/26.78 ((
% 88.68/26.78 (kfstsingleton) =>
% 88.68/26.78 ((
% 88.68/26.78 (theprop) =>
% 88.68/26.78 ((
% 88.68/26.78 (kfstpairEq) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodfstin) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairinjL2) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairinjL) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairinjR11) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairinjR12) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairinjR1) =>
% 88.68/26.78 ((
% 88.68/26.78 (upairequniteq) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairinjR2) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairinjR) =>
% 88.68/26.78 ((
% 88.68/26.78 (ksndsingleton) =>
% 88.68/26.78 ((
% 88.68/26.78 (ksndpairEq) =>
% 88.68/26.78 ((
% 88.68/26.78 (kpairsurjEq) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodsndin) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodpairmemEL) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodpairmemER) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodmempaircEq) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodfstpairEq) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodsndpairEq) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodpairsurjEq) =>
% 88.68/26.78 ((
% 88.68/26.78 (dpsetconstrI) =>
% 88.68/26.78 ((
% 88.68/26.78 (dpsetconstrSub) =>
% 88.68/26.78 ((
% 88.68/26.78 (setOfPairsIsBReln) =>
% 88.68/26.78 ((
% 88.68/26.78 (dpsetconstrERa) =>
% 88.68/26.78 ((
% 88.68/26.78 (dpsetconstrEL1) =>
% 88.68/26.78 ((
% 88.68/26.78 (dpsetconstrEL2) =>
% 88.68/26.78 ((
% 88.68/26.78 (dpsetconstrER) =>
% 88.68/26.78 ((
% 88.68/26.78 (funcImageSingleton) =>
% 88.68/26.78 ((
% 88.68/26.78 (apProp) =>
% 88.68/26.78 ((
% 88.68/26.78 (app) =>
% 88.68/26.78 ((
% 88.68/26.78 (infuncsetfunc) =>
% 88.68/26.78 ((
% 88.68/26.78 (ap2p) =>
% 88.68/26.78 ((
% 88.68/26.78 (funcinfuncset) =>
% 88.68/26.78 ((
% 88.68/26.78 (lamProp) =>
% 88.68/26.78 ((
% 88.68/26.78 (lamp) =>
% 88.68/26.78 ((
% 88.68/26.78 (lam2p) =>
% 88.68/26.78 ((
% 88.68/26.78 (brelnall1) =>
% 88.68/26.78 ((
% 88.68/26.78 (brelnall2) =>
% 88.68/26.78 ((
% 88.68/26.78 (!!) @ (
% 88.68/26.78 (('#B') @ (
% 88.68/26.78 !!) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#S') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#S') @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 =>))) @
% 88.68/26.78 ex1)))) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 !!))) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#S') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#B') @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#S') @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 =>))) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#C') @ in)))))))) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 !!))))) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#C') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#B') @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#B') @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#S') @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 =>))) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#C') @ in)))))))))) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#S') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#S') @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#B'))) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 =>))))))) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#C') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#B') @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#S') @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 =>))))))) @
% 88.68/26.78 (
% 88.68/26.78 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 88.68/26.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl89])).
% 88.68/26.78 thf(zip_derived_cl123, plain,
% 88.68/26.78 (~ (((prop2setE) =>
% 88.68/26.78 (((emptysetE) =>
% 88.68/26.78 (((emptysetimpfalse) =>
% 88.68/26.78 (((notinemptyset) =>
% 88.68/26.78 (((exuE3e) =>
% 88.68/26.78 (((setext) =>
% 88.68/26.78 (((emptyI) =>
% 88.68/26.78 (((noeltsimpempty) =>
% 88.68/26.78 (((setbeta) =>
% 88.68/26.78 (((nonemptyE1) =>
% 88.68/26.78 (((nonemptyI) =>
% 88.68/26.78 (((nonemptyI1) =>
% 88.68/26.78 (((setadjoinIL) =>
% 88.68/26.78 (((in @ emptyset @
% 88.68/26.78 (setadjoin @ emptyset @ emptyset)) =>
% 88.68/26.78 (((setadjoinIR) =>
% 88.68/26.78 (((setadjoinE) =>
% 88.68/26.78 (((setadjoinOr) =>
% 88.68/26.78 (((setoftrueEq) =>
% 88.68/26.78 (((powersetI) =>
% 88.68/26.78 (((emptyinPowerset) =>
% 88.68/26.78 (((emptyInPowerset) =>
% 88.68/26.78 (((powersetE) =>
% 88.68/26.78 (((setunionI) =>
% 88.68/26.78 (((setunionE) =>
% 88.68/26.78 (((subPowSU) =>
% 88.68/26.78 (((exuE2) =>
% 88.68/26.78 (((nonemptyImpWitness) =>
% 88.68/26.78 (((uniqinunit) =>
% 88.68/26.78 (((notinsingleton) =>
% 88.68/26.78 (((eqinunit) =>
% 88.68/26.78 ((
% 88.68/26.78 (singletonsswitch) =>
% 88.68/26.78 ((
% 88.68/26.78 (upairsetE) =>
% 88.68/26.78 ((
% 88.68/26.78 (upairsetIL) =>
% 88.68/26.78 ((
% 88.68/26.78 (upairsetIR) =>
% 88.68/26.78 ((
% 88.68/26.78 (emptyE1) =>
% 88.68/26.78 ((
% 88.68/26.78 (vacuousDall) =>
% 88.68/26.78 ((
% 88.68/26.78 (quantDeMorgan1) =>
% 88.68/26.78 ((
% 88.68/26.78 (quantDeMorgan2) =>
% 88.68/26.78 ((
% 88.68/26.78 (quantDeMorgan3) =>
% 88.68/26.78 ((
% 88.68/26.78 (quantDeMorgan4) =>
% 88.68/26.78 ((
% 88.68/26.78 (prop2setI) =>
% 88.68/26.78 ((
% 88.68/26.78 (prop2set2propI) =>
% 88.68/26.78 ((
% 88.68/26.78 (notdexE) =>
% 88.68/26.78 ((
% 88.68/26.78 (notdallE) =>
% 88.68/26.78 ((
% 88.68/26.78 (exuI1) =>
% 88.68/26.78 ((
% 88.68/26.78 (exuI3) =>
% 88.68/26.78 ((
% 88.68/26.78 (exuI2) =>
% 88.68/26.78 ((
% 88.68/26.78 (inCongP) =>
% 88.68/26.78 ((
% 88.68/26.78 (in__Cong) =>
% 88.68/26.78 ((
% 88.68/26.78 (exuE3u) =>
% 88.68/26.78 ((
% 88.68/26.78 (exu__Cong) =>
% 88.68/26.78 ((
% 88.68/26.78 (setadjoin__Cong) =>
% 88.68/26.78 ((
% 88.68/26.78 (powerset__Cong) =>
% 88.68/26.78 ((
% 88.68/26.78 (setunion__Cong) =>
% 88.68/26.78 ((
% 88.68/26.78 (exuEu) =>
% 88.68/26.78 ((
% 88.68/26.78 (descr__Cong) =>
% 88.68/26.78 ((
% 88.68/26.78 (dsetconstr__Cong) =>
% 88.68/26.78 ((
% 88.68/26.78 (subsetI1) =>
% 88.68/26.78 ((
% 88.68/26.78 (eqimpsubset2) =>
% 88.68/26.78 ((
% 88.68/26.78 (eqimpsubset1) =>
% 88.68/26.78 ((
% 88.68/26.78 (subsetI2) =>
% 88.68/26.78 ((
% 88.68/26.78 (emptysetsubset) =>
% 88.68/26.78 ((
% 88.68/26.78 (subsetE) =>
% 88.68/26.78 ((
% 88.68/26.78 (subsetE2) =>
% 88.68/26.78 ((
% 88.68/26.78 (notsubsetI) =>
% 88.68/26.78 ((
% 88.68/26.78 (notequalI1) =>
% 88.68/26.78 ((
% 88.68/26.78 (notequalI2) =>
% 88.68/26.78 ((
% 88.68/26.78 (subsetRefl) =>
% 88.68/26.78 ((
% 88.68/26.78 (subsetTrans) =>
% 88.68/26.78 ((
% 88.68/26.78 (setadjoinSub) =>
% 88.68/26.78 ((
% 88.68/26.78 (setadjoinSub2) =>
% 88.68/26.78 ((
% 88.68/26.78 (subset2powerset) =>
% 88.68/26.78 ((
% 88.68/26.78 (setextsub) =>
% 88.68/26.78 ((
% 88.68/26.78 (subsetemptysetimpeq) =>
% 88.68/26.78 ((
% 88.68/26.78 (powersetI1) =>
% 88.68/26.78 ((
% 88.68/26.78 (powersetE1) =>
% 88.68/26.78 ((
% 88.68/26.78 (inPowerset) =>
% 88.68/26.78 ((
% 88.68/26.78 (powersetsubset) =>
% 88.68/26.78 ((
% 88.68/26.78 (sepInPowerset) =>
% 88.68/26.78 ((
% 88.68/26.78 (sepSubset) =>
% 88.68/26.78 ((
% 88.68/26.78 (binunionIL) =>
% 88.68/26.78 ((
% 88.68/26.78 (upairset2IR) =>
% 88.68/26.78 ((
% 88.68/26.78 (binunionIR) =>
% 88.68/26.78 ((
% 88.68/26.78 (binunionEcases) =>
% 88.68/26.78 ((
% 88.68/26.78 (binunionE) =>
% 88.68/26.78 ((
% 88.68/26.78 (binunionLsub) =>
% 88.68/26.78 ((
% 88.68/26.78 (binunionRsub) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectI) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectSubset5) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectEL) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectLsub) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectSubset2) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectSubset3) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectER) =>
% 88.68/26.78 ((
% 88.68/26.78 (disjointsetsI1) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectRsub) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectSubset4) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectSubset1) =>
% 88.68/26.78 ((
% 88.68/26.78 (bs114d) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusI) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusEL) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusER) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusSubset2) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusERneg) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusELneg) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusILneg) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusIRneg) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusLsub) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusSubset1) =>
% 88.68/26.78 ((
% 88.68/26.78 (symdiffE) =>
% 88.68/26.78 ((
% 88.68/26.78 (symdiffI1) =>
% 88.68/26.78 ((
% 88.68/26.78 (symdiffI2) =>
% 88.68/26.78 ((
% 88.68/26.78 (symdiffIneg1) =>
% 88.68/26.78 ((
% 88.68/26.78 (symdiffIneg2) =>
% 88.68/26.78 ((
% 88.68/26.78 (secondinupair) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairIL) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairIR) =>
% 88.68/26.78 ((
% 88.68/26.78 (kpairiskpair) =>
% 88.68/26.78 ((
% 88.68/26.78 (kpairp) =>
% 88.68/26.78 ((
% 88.68/26.78 (singletonsubset) =>
% 88.68/26.78 ((
% 88.68/26.78 (singletoninpowerset) =>
% 88.68/26.78 ((
% 88.68/26.78 (singletoninpowunion) =>
% 88.68/26.78 ((
% 88.68/26.78 (upairset2E) =>
% 88.68/26.78 ((
% 88.68/26.78 (upairsubunion) =>
% 88.68/26.78 ((
% 88.68/26.78 (upairinpowunion) =>
% 88.68/26.78 ((
% 88.68/26.78 (ubforcartprodlem1) =>
% 88.68/26.78 ((
% 88.68/26.78 (ubforcartprodlem2) =>
% 88.68/26.78 ((
% 88.68/26.78 (ubforcartprodlem3) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodpairin) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodmempair1) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodmempair) =>
% 88.68/26.78 ((
% 88.68/26.78 (setunionE2) =>
% 88.68/26.78 ((
% 88.68/26.78 (setunionsingleton1) =>
% 88.68/26.78 ((
% 88.68/26.78 (setunionsingleton2) =>
% 88.68/26.78 ((
% 88.68/26.78 (setunionsingleton) =>
% 88.68/26.78 ((
% 88.68/26.78 (singletonprop) =>
% 88.68/26.78 ((
% 88.68/26.78 (ex1E1) =>
% 88.68/26.78 ((
% 88.68/26.78 (ex1I) =>
% 88.68/26.78 ((
% 88.68/26.78 (ex1I2) =>
% 88.68/26.78 ((
% 88.68/26.78 (singletonsuniq) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairinjL1) =>
% 88.68/26.78 ((
% 88.68/26.78 (kfstsingleton) =>
% 88.68/26.78 ((
% 88.68/26.78 (theprop) =>
% 88.68/26.78 ((
% 88.68/26.78 (kfstpairEq) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodfstin) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairinjL2) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairinjL) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairinjR11) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairinjR12) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairinjR1) =>
% 88.68/26.78 ((
% 88.68/26.78 (upairequniteq) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairinjR2) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairinjR) =>
% 88.68/26.78 ((
% 88.68/26.78 (ksndsingleton) =>
% 88.68/26.78 ((
% 88.68/26.78 (ksndpairEq) =>
% 88.68/26.78 ((
% 88.68/26.78 (kpairsurjEq) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodsndin) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodpairmemEL) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodpairmemER) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodmempaircEq) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodfstpairEq) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodsndpairEq) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodpairsurjEq) =>
% 88.68/26.78 ((
% 88.68/26.78 (dpsetconstrI) =>
% 88.68/26.78 ((
% 88.68/26.78 (dpsetconstrSub) =>
% 88.68/26.78 ((
% 88.68/26.78 (setOfPairsIsBReln) =>
% 88.68/26.78 ((
% 88.68/26.78 (dpsetconstrERa) =>
% 88.68/26.78 ((
% 88.68/26.78 (dpsetconstrEL1) =>
% 88.68/26.78 ((
% 88.68/26.78 (dpsetconstrEL2) =>
% 88.68/26.78 ((
% 88.68/26.78 (dpsetconstrER) =>
% 88.68/26.78 ((
% 88.68/26.78 (funcImageSingleton) =>
% 88.68/26.78 ((
% 88.68/26.78 (apProp) =>
% 88.68/26.78 ((
% 88.68/26.78 (app) =>
% 88.68/26.78 ((
% 88.68/26.78 (infuncsetfunc) =>
% 88.68/26.78 ((
% 88.68/26.78 (ap2p) =>
% 88.68/26.78 ((
% 88.68/26.78 (funcinfuncset) =>
% 88.68/26.78 ((
% 88.68/26.78 (lamProp) =>
% 88.68/26.78 ((
% 88.68/26.78 (lamp) =>
% 88.68/26.78 ((
% 88.68/26.78 (lam2p) =>
% 88.68/26.78 ((
% 88.68/26.78 (brelnall1) =>
% 88.68/26.78 ((
% 88.68/26.78 (brelnall2) =>
% 88.68/26.78 ((
% 88.68/26.78 (!!) @ (
% 88.68/26.78 (('#B') @ (
% 88.68/26.78 !!) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#S') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#S') @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 =>))) @
% 88.68/26.78 ex1)))) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 !!))) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#S') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#B') @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#S') @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 =>))) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#C') @ in)))))))) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 !!))))) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#C') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#B') @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#B') @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#S') @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 =>))) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#C') @ in)))))))))) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#S') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#S') @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#B'))) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 =>))))))) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#C') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#B') @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#S') @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 =>))))))) @
% 88.68/26.78 (
% 88.68/26.78 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 88.68/26.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl105])).
% 88.68/26.78 thf(zip_derived_cl142, plain,
% 88.68/26.78 (~ (((emptysetE) =>
% 88.68/26.78 (((emptysetimpfalse) =>
% 88.68/26.78 (((notinemptyset) =>
% 88.68/26.78 (((exuE3e) =>
% 88.68/26.78 (((setext) =>
% 88.68/26.78 (((emptyI) =>
% 88.68/26.78 (((noeltsimpempty) =>
% 88.68/26.78 (((setbeta) =>
% 88.68/26.78 (((nonemptyE1) =>
% 88.68/26.78 (((nonemptyI) =>
% 88.68/26.78 (((nonemptyI1) =>
% 88.68/26.78 (((setadjoinIL) =>
% 88.68/26.78 (((in @ emptyset @
% 88.68/26.78 (setadjoin @ emptyset @ emptyset)) =>
% 88.68/26.78 (((setadjoinIR) =>
% 88.68/26.78 (((setadjoinE) =>
% 88.68/26.78 (((setadjoinOr) =>
% 88.68/26.78 (((setoftrueEq) =>
% 88.68/26.78 (((powersetI) =>
% 88.68/26.78 (((emptyinPowerset) =>
% 88.68/26.78 (((emptyInPowerset) =>
% 88.68/26.78 (((powersetE) =>
% 88.68/26.78 (((setunionI) =>
% 88.68/26.78 (((setunionE) =>
% 88.68/26.78 (((subPowSU) =>
% 88.68/26.78 (((exuE2) =>
% 88.68/26.78 (((nonemptyImpWitness) =>
% 88.68/26.78 (((uniqinunit) =>
% 88.68/26.78 (((notinsingleton) =>
% 88.68/26.78 (((eqinunit) =>
% 88.68/26.78 (((singletonsswitch) =>
% 88.68/26.78 ((
% 88.68/26.78 (upairsetE) =>
% 88.68/26.78 ((
% 88.68/26.78 (upairsetIL) =>
% 88.68/26.78 ((
% 88.68/26.78 (upairsetIR) =>
% 88.68/26.78 ((
% 88.68/26.78 (emptyE1) =>
% 88.68/26.78 ((
% 88.68/26.78 (vacuousDall) =>
% 88.68/26.78 ((
% 88.68/26.78 (quantDeMorgan1) =>
% 88.68/26.78 ((
% 88.68/26.78 (quantDeMorgan2) =>
% 88.68/26.78 ((
% 88.68/26.78 (quantDeMorgan3) =>
% 88.68/26.78 ((
% 88.68/26.78 (quantDeMorgan4) =>
% 88.68/26.78 ((
% 88.68/26.78 (prop2setI) =>
% 88.68/26.78 ((
% 88.68/26.78 (prop2set2propI) =>
% 88.68/26.78 ((
% 88.68/26.78 (notdexE) =>
% 88.68/26.78 ((
% 88.68/26.78 (notdallE) =>
% 88.68/26.78 ((
% 88.68/26.78 (exuI1) =>
% 88.68/26.78 ((
% 88.68/26.78 (exuI3) =>
% 88.68/26.78 ((
% 88.68/26.78 (exuI2) =>
% 88.68/26.78 ((
% 88.68/26.78 (inCongP) =>
% 88.68/26.78 ((
% 88.68/26.78 (in__Cong) =>
% 88.68/26.78 ((
% 88.68/26.78 (exuE3u) =>
% 88.68/26.78 ((
% 88.68/26.78 (exu__Cong) =>
% 88.68/26.78 ((
% 88.68/26.78 (setadjoin__Cong) =>
% 88.68/26.78 ((
% 88.68/26.78 (powerset__Cong) =>
% 88.68/26.78 ((
% 88.68/26.78 (setunion__Cong) =>
% 88.68/26.78 ((
% 88.68/26.78 (exuEu) =>
% 88.68/26.78 ((
% 88.68/26.78 (descr__Cong) =>
% 88.68/26.78 ((
% 88.68/26.78 (dsetconstr__Cong) =>
% 88.68/26.78 ((
% 88.68/26.78 (subsetI1) =>
% 88.68/26.78 ((
% 88.68/26.78 (eqimpsubset2) =>
% 88.68/26.78 ((
% 88.68/26.78 (eqimpsubset1) =>
% 88.68/26.78 ((
% 88.68/26.78 (subsetI2) =>
% 88.68/26.78 ((
% 88.68/26.78 (emptysetsubset) =>
% 88.68/26.78 ((
% 88.68/26.78 (subsetE) =>
% 88.68/26.78 ((
% 88.68/26.78 (subsetE2) =>
% 88.68/26.78 ((
% 88.68/26.78 (notsubsetI) =>
% 88.68/26.78 ((
% 88.68/26.78 (notequalI1) =>
% 88.68/26.78 ((
% 88.68/26.78 (notequalI2) =>
% 88.68/26.78 ((
% 88.68/26.78 (subsetRefl) =>
% 88.68/26.78 ((
% 88.68/26.78 (subsetTrans) =>
% 88.68/26.78 ((
% 88.68/26.78 (setadjoinSub) =>
% 88.68/26.78 ((
% 88.68/26.78 (setadjoinSub2) =>
% 88.68/26.78 ((
% 88.68/26.78 (subset2powerset) =>
% 88.68/26.78 ((
% 88.68/26.78 (setextsub) =>
% 88.68/26.78 ((
% 88.68/26.78 (subsetemptysetimpeq) =>
% 88.68/26.78 ((
% 88.68/26.78 (powersetI1) =>
% 88.68/26.78 ((
% 88.68/26.78 (powersetE1) =>
% 88.68/26.78 ((
% 88.68/26.78 (inPowerset) =>
% 88.68/26.78 ((
% 88.68/26.78 (powersetsubset) =>
% 88.68/26.78 ((
% 88.68/26.78 (sepInPowerset) =>
% 88.68/26.78 ((
% 88.68/26.78 (sepSubset) =>
% 88.68/26.78 ((
% 88.68/26.78 (binunionIL) =>
% 88.68/26.78 ((
% 88.68/26.78 (upairset2IR) =>
% 88.68/26.78 ((
% 88.68/26.78 (binunionIR) =>
% 88.68/26.78 ((
% 88.68/26.78 (binunionEcases) =>
% 88.68/26.78 ((
% 88.68/26.78 (binunionE) =>
% 88.68/26.78 ((
% 88.68/26.78 (binunionLsub) =>
% 88.68/26.78 ((
% 88.68/26.78 (binunionRsub) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectI) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectSubset5) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectEL) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectLsub) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectSubset2) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectSubset3) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectER) =>
% 88.68/26.78 ((
% 88.68/26.78 (disjointsetsI1) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectRsub) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectSubset4) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectSubset1) =>
% 88.68/26.78 ((
% 88.68/26.78 (bs114d) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusI) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusEL) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusER) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusSubset2) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusERneg) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusELneg) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusILneg) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusIRneg) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusLsub) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusSubset1) =>
% 88.68/26.78 ((
% 88.68/26.78 (symdiffE) =>
% 88.68/26.78 ((
% 88.68/26.78 (symdiffI1) =>
% 88.68/26.78 ((
% 88.68/26.78 (symdiffI2) =>
% 88.68/26.78 ((
% 88.68/26.78 (symdiffIneg1) =>
% 88.68/26.78 ((
% 88.68/26.78 (symdiffIneg2) =>
% 88.68/26.78 ((
% 88.68/26.78 (secondinupair) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairIL) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairIR) =>
% 88.68/26.78 ((
% 88.68/26.78 (kpairiskpair) =>
% 88.68/26.78 ((
% 88.68/26.78 (kpairp) =>
% 88.68/26.78 ((
% 88.68/26.78 (singletonsubset) =>
% 88.68/26.78 ((
% 88.68/26.78 (singletoninpowerset) =>
% 88.68/26.78 ((
% 88.68/26.78 (singletoninpowunion) =>
% 88.68/26.78 ((
% 88.68/26.78 (upairset2E) =>
% 88.68/26.78 ((
% 88.68/26.78 (upairsubunion) =>
% 88.68/26.78 ((
% 88.68/26.78 (upairinpowunion) =>
% 88.68/26.78 ((
% 88.68/26.78 (ubforcartprodlem1) =>
% 88.68/26.78 ((
% 88.68/26.78 (ubforcartprodlem2) =>
% 88.68/26.78 ((
% 88.68/26.78 (ubforcartprodlem3) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodpairin) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodmempair1) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodmempair) =>
% 88.68/26.78 ((
% 88.68/26.78 (setunionE2) =>
% 88.68/26.78 ((
% 88.68/26.78 (setunionsingleton1) =>
% 88.68/26.78 ((
% 88.68/26.78 (setunionsingleton2) =>
% 88.68/26.78 ((
% 88.68/26.78 (setunionsingleton) =>
% 88.68/26.78 ((
% 88.68/26.78 (singletonprop) =>
% 88.68/26.78 ((
% 88.68/26.78 (ex1E1) =>
% 88.68/26.78 ((
% 88.68/26.78 (ex1I) =>
% 88.68/26.78 ((
% 88.68/26.78 (ex1I2) =>
% 88.68/26.78 ((
% 88.68/26.78 (singletonsuniq) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairinjL1) =>
% 88.68/26.78 ((
% 88.68/26.78 (kfstsingleton) =>
% 88.68/26.78 ((
% 88.68/26.78 (theprop) =>
% 88.68/26.78 ((
% 88.68/26.78 (kfstpairEq) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodfstin) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairinjL2) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairinjL) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairinjR11) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairinjR12) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairinjR1) =>
% 88.68/26.78 ((
% 88.68/26.78 (upairequniteq) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairinjR2) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairinjR) =>
% 88.68/26.78 ((
% 88.68/26.78 (ksndsingleton) =>
% 88.68/26.78 ((
% 88.68/26.78 (ksndpairEq) =>
% 88.68/26.78 ((
% 88.68/26.78 (kpairsurjEq) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodsndin) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodpairmemEL) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodpairmemER) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodmempaircEq) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodfstpairEq) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodsndpairEq) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodpairsurjEq) =>
% 88.68/26.78 ((
% 88.68/26.78 (dpsetconstrI) =>
% 88.68/26.78 ((
% 88.68/26.78 (dpsetconstrSub) =>
% 88.68/26.78 ((
% 88.68/26.78 (setOfPairsIsBReln) =>
% 88.68/26.78 ((
% 88.68/26.78 (dpsetconstrERa) =>
% 88.68/26.78 ((
% 88.68/26.78 (dpsetconstrEL1) =>
% 88.68/26.78 ((
% 88.68/26.78 (dpsetconstrEL2) =>
% 88.68/26.78 ((
% 88.68/26.78 (dpsetconstrER) =>
% 88.68/26.78 ((
% 88.68/26.78 (funcImageSingleton) =>
% 88.68/26.78 ((
% 88.68/26.78 (apProp) =>
% 88.68/26.78 ((
% 88.68/26.78 (app) =>
% 88.68/26.78 ((
% 88.68/26.78 (infuncsetfunc) =>
% 88.68/26.78 ((
% 88.68/26.78 (ap2p) =>
% 88.68/26.78 ((
% 88.68/26.78 (funcinfuncset) =>
% 88.68/26.78 ((
% 88.68/26.78 (lamProp) =>
% 88.68/26.78 ((
% 88.68/26.78 (lamp) =>
% 88.68/26.78 ((
% 88.68/26.78 (lam2p) =>
% 88.68/26.78 ((
% 88.68/26.78 (brelnall1) =>
% 88.68/26.78 ((
% 88.68/26.78 (brelnall2) =>
% 88.68/26.78 ((
% 88.68/26.78 (!!) @ (
% 88.68/26.78 (('#B') @ (
% 88.68/26.78 !!) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#S') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#S') @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 =>))) @
% 88.68/26.78 ex1)))) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 !!))) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#S') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#B') @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#S') @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 =>))) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#C') @ in)))))))) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 !!))))) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#C') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#B') @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#B') @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#S') @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 =>))) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#C') @ in)))))))))) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#S') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#S') @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#B'))) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 =>))))))) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#C') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#B') @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#S') @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 =>))))))) @
% 88.68/26.78 (
% 88.68/26.78 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 88.68/26.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl123])).
% 88.68/26.78 thf(zip_derived_cl158, plain,
% 88.68/26.78 (~ (((emptysetimpfalse) =>
% 88.68/26.78 (((notinemptyset) =>
% 88.68/26.78 (((exuE3e) =>
% 88.68/26.78 (((setext) =>
% 88.68/26.78 (((emptyI) =>
% 88.68/26.78 (((noeltsimpempty) =>
% 88.68/26.78 (((setbeta) =>
% 88.68/26.78 (((nonemptyE1) =>
% 88.68/26.78 (((nonemptyI) =>
% 88.68/26.78 (((nonemptyI1) =>
% 88.68/26.78 (((setadjoinIL) =>
% 88.68/26.78 (((in @ emptyset @
% 88.68/26.78 (setadjoin @ emptyset @ emptyset)) =>
% 88.68/26.78 (((setadjoinIR) =>
% 88.68/26.78 (((setadjoinE) =>
% 88.68/26.78 (((setadjoinOr) =>
% 88.68/26.78 (((setoftrueEq) =>
% 88.68/26.78 (((powersetI) =>
% 88.68/26.78 (((emptyinPowerset) =>
% 88.68/26.78 (((emptyInPowerset) =>
% 88.68/26.78 (((powersetE) =>
% 88.68/26.78 (((setunionI) =>
% 88.68/26.78 (((setunionE) =>
% 88.68/26.78 (((subPowSU) =>
% 88.68/26.78 (((exuE2) =>
% 88.68/26.78 (((nonemptyImpWitness) =>
% 88.68/26.78 (((uniqinunit) =>
% 88.68/26.78 (((notinsingleton) =>
% 88.68/26.78 (((eqinunit) =>
% 88.68/26.78 (((singletonsswitch) =>
% 88.68/26.78 (((upairsetE) =>
% 88.68/26.78 ((
% 88.68/26.78 (upairsetIL) =>
% 88.68/26.78 ((
% 88.68/26.78 (upairsetIR) =>
% 88.68/26.78 ((
% 88.68/26.78 (emptyE1) =>
% 88.68/26.78 ((
% 88.68/26.78 (vacuousDall) =>
% 88.68/26.78 ((
% 88.68/26.78 (quantDeMorgan1) =>
% 88.68/26.78 ((
% 88.68/26.78 (quantDeMorgan2) =>
% 88.68/26.78 ((
% 88.68/26.78 (quantDeMorgan3) =>
% 88.68/26.78 ((
% 88.68/26.78 (quantDeMorgan4) =>
% 88.68/26.78 ((
% 88.68/26.78 (prop2setI) =>
% 88.68/26.78 ((
% 88.68/26.78 (prop2set2propI) =>
% 88.68/26.78 ((
% 88.68/26.78 (notdexE) =>
% 88.68/26.78 ((
% 88.68/26.78 (notdallE) =>
% 88.68/26.78 ((
% 88.68/26.78 (exuI1) =>
% 88.68/26.78 ((
% 88.68/26.78 (exuI3) =>
% 88.68/26.78 ((
% 88.68/26.78 (exuI2) =>
% 88.68/26.78 ((
% 88.68/26.78 (inCongP) =>
% 88.68/26.78 ((
% 88.68/26.78 (in__Cong) =>
% 88.68/26.78 ((
% 88.68/26.78 (exuE3u) =>
% 88.68/26.78 ((
% 88.68/26.78 (exu__Cong) =>
% 88.68/26.78 ((
% 88.68/26.78 (setadjoin__Cong) =>
% 88.68/26.78 ((
% 88.68/26.78 (powerset__Cong) =>
% 88.68/26.78 ((
% 88.68/26.78 (setunion__Cong) =>
% 88.68/26.78 ((
% 88.68/26.78 (exuEu) =>
% 88.68/26.78 ((
% 88.68/26.78 (descr__Cong) =>
% 88.68/26.78 ((
% 88.68/26.78 (dsetconstr__Cong) =>
% 88.68/26.78 ((
% 88.68/26.78 (subsetI1) =>
% 88.68/26.78 ((
% 88.68/26.78 (eqimpsubset2) =>
% 88.68/26.78 ((
% 88.68/26.78 (eqimpsubset1) =>
% 88.68/26.78 ((
% 88.68/26.78 (subsetI2) =>
% 88.68/26.78 ((
% 88.68/26.78 (emptysetsubset) =>
% 88.68/26.78 ((
% 88.68/26.78 (subsetE) =>
% 88.68/26.78 ((
% 88.68/26.78 (subsetE2) =>
% 88.68/26.78 ((
% 88.68/26.78 (notsubsetI) =>
% 88.68/26.78 ((
% 88.68/26.78 (notequalI1) =>
% 88.68/26.78 ((
% 88.68/26.78 (notequalI2) =>
% 88.68/26.78 ((
% 88.68/26.78 (subsetRefl) =>
% 88.68/26.78 ((
% 88.68/26.78 (subsetTrans) =>
% 88.68/26.78 ((
% 88.68/26.78 (setadjoinSub) =>
% 88.68/26.78 ((
% 88.68/26.78 (setadjoinSub2) =>
% 88.68/26.78 ((
% 88.68/26.78 (subset2powerset) =>
% 88.68/26.78 ((
% 88.68/26.78 (setextsub) =>
% 88.68/26.78 ((
% 88.68/26.78 (subsetemptysetimpeq) =>
% 88.68/26.78 ((
% 88.68/26.78 (powersetI1) =>
% 88.68/26.78 ((
% 88.68/26.78 (powersetE1) =>
% 88.68/26.78 ((
% 88.68/26.78 (inPowerset) =>
% 88.68/26.78 ((
% 88.68/26.78 (powersetsubset) =>
% 88.68/26.78 ((
% 88.68/26.78 (sepInPowerset) =>
% 88.68/26.78 ((
% 88.68/26.78 (sepSubset) =>
% 88.68/26.78 ((
% 88.68/26.78 (binunionIL) =>
% 88.68/26.78 ((
% 88.68/26.78 (upairset2IR) =>
% 88.68/26.78 ((
% 88.68/26.78 (binunionIR) =>
% 88.68/26.78 ((
% 88.68/26.78 (binunionEcases) =>
% 88.68/26.78 ((
% 88.68/26.78 (binunionE) =>
% 88.68/26.78 ((
% 88.68/26.78 (binunionLsub) =>
% 88.68/26.78 ((
% 88.68/26.78 (binunionRsub) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectI) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectSubset5) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectEL) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectLsub) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectSubset2) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectSubset3) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectER) =>
% 88.68/26.78 ((
% 88.68/26.78 (disjointsetsI1) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectRsub) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectSubset4) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectSubset1) =>
% 88.68/26.78 ((
% 88.68/26.78 (bs114d) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusI) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusEL) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusER) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusSubset2) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusERneg) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusELneg) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusILneg) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusIRneg) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusLsub) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusSubset1) =>
% 88.68/26.78 ((
% 88.68/26.78 (symdiffE) =>
% 88.68/26.78 ((
% 88.68/26.78 (symdiffI1) =>
% 88.68/26.78 ((
% 88.68/26.78 (symdiffI2) =>
% 88.68/26.78 ((
% 88.68/26.78 (symdiffIneg1) =>
% 88.68/26.78 ((
% 88.68/26.78 (symdiffIneg2) =>
% 88.68/26.78 ((
% 88.68/26.78 (secondinupair) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairIL) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairIR) =>
% 88.68/26.78 ((
% 88.68/26.78 (kpairiskpair) =>
% 88.68/26.78 ((
% 88.68/26.78 (kpairp) =>
% 88.68/26.78 ((
% 88.68/26.78 (singletonsubset) =>
% 88.68/26.78 ((
% 88.68/26.78 (singletoninpowerset) =>
% 88.68/26.78 ((
% 88.68/26.78 (singletoninpowunion) =>
% 88.68/26.78 ((
% 88.68/26.78 (upairset2E) =>
% 88.68/26.78 ((
% 88.68/26.78 (upairsubunion) =>
% 88.68/26.78 ((
% 88.68/26.78 (upairinpowunion) =>
% 88.68/26.78 ((
% 88.68/26.78 (ubforcartprodlem1) =>
% 88.68/26.78 ((
% 88.68/26.78 (ubforcartprodlem2) =>
% 88.68/26.78 ((
% 88.68/26.78 (ubforcartprodlem3) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodpairin) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodmempair1) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodmempair) =>
% 88.68/26.78 ((
% 88.68/26.78 (setunionE2) =>
% 88.68/26.78 ((
% 88.68/26.78 (setunionsingleton1) =>
% 88.68/26.78 ((
% 88.68/26.78 (setunionsingleton2) =>
% 88.68/26.78 ((
% 88.68/26.78 (setunionsingleton) =>
% 88.68/26.78 ((
% 88.68/26.78 (singletonprop) =>
% 88.68/26.78 ((
% 88.68/26.78 (ex1E1) =>
% 88.68/26.78 ((
% 88.68/26.78 (ex1I) =>
% 88.68/26.78 ((
% 88.68/26.78 (ex1I2) =>
% 88.68/26.78 ((
% 88.68/26.78 (singletonsuniq) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairinjL1) =>
% 88.68/26.78 ((
% 88.68/26.78 (kfstsingleton) =>
% 88.68/26.78 ((
% 88.68/26.78 (theprop) =>
% 88.68/26.78 ((
% 88.68/26.78 (kfstpairEq) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodfstin) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairinjL2) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairinjL) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairinjR11) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairinjR12) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairinjR1) =>
% 88.68/26.78 ((
% 88.68/26.78 (upairequniteq) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairinjR2) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairinjR) =>
% 88.68/26.78 ((
% 88.68/26.78 (ksndsingleton) =>
% 88.68/26.78 ((
% 88.68/26.78 (ksndpairEq) =>
% 88.68/26.78 ((
% 88.68/26.78 (kpairsurjEq) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodsndin) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodpairmemEL) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodpairmemER) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodmempaircEq) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodfstpairEq) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodsndpairEq) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodpairsurjEq) =>
% 88.68/26.78 ((
% 88.68/26.78 (dpsetconstrI) =>
% 88.68/26.78 ((
% 88.68/26.78 (dpsetconstrSub) =>
% 88.68/26.78 ((
% 88.68/26.78 (setOfPairsIsBReln) =>
% 88.68/26.78 ((
% 88.68/26.78 (dpsetconstrERa) =>
% 88.68/26.78 ((
% 88.68/26.78 (dpsetconstrEL1) =>
% 88.68/26.78 ((
% 88.68/26.78 (dpsetconstrEL2) =>
% 88.68/26.78 ((
% 88.68/26.78 (dpsetconstrER) =>
% 88.68/26.78 ((
% 88.68/26.78 (funcImageSingleton) =>
% 88.68/26.78 ((
% 88.68/26.78 (apProp) =>
% 88.68/26.78 ((
% 88.68/26.78 (app) =>
% 88.68/26.78 ((
% 88.68/26.78 (infuncsetfunc) =>
% 88.68/26.78 ((
% 88.68/26.78 (ap2p) =>
% 88.68/26.78 ((
% 88.68/26.78 (funcinfuncset) =>
% 88.68/26.78 ((
% 88.68/26.78 (lamProp) =>
% 88.68/26.78 ((
% 88.68/26.78 (lamp) =>
% 88.68/26.78 ((
% 88.68/26.78 (lam2p) =>
% 88.68/26.78 ((
% 88.68/26.78 (brelnall1) =>
% 88.68/26.78 ((
% 88.68/26.78 (brelnall2) =>
% 88.68/26.78 ((
% 88.68/26.78 (!!) @ (
% 88.68/26.78 (('#B') @ (
% 88.68/26.78 !!) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#S') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#S') @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 =>))) @
% 88.68/26.78 ex1)))) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 !!))) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#S') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#B') @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#S') @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 =>))) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#C') @ in)))))))) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 !!))))) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#C') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#B') @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#B') @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#S') @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 =>))) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#C') @ in)))))))))) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#S') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#S') @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#B'))) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 =>))))))) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#C') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#B') @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#S') @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 =>))))))) @
% 88.68/26.78 (
% 88.68/26.78 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 88.68/26.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl142])).
% 88.68/26.78 thf(zip_derived_cl174, plain,
% 88.68/26.78 (~ (((notinemptyset) =>
% 88.68/26.78 (((exuE3e) =>
% 88.68/26.78 (((setext) =>
% 88.68/26.78 (((emptyI) =>
% 88.68/26.78 (((noeltsimpempty) =>
% 88.68/26.78 (((setbeta) =>
% 88.68/26.78 (((nonemptyE1) =>
% 88.68/26.78 (((nonemptyI) =>
% 88.68/26.78 (((nonemptyI1) =>
% 88.68/26.78 (((setadjoinIL) =>
% 88.68/26.78 (((in @ emptyset @
% 88.68/26.78 (setadjoin @ emptyset @ emptyset)) =>
% 88.68/26.78 (((setadjoinIR) =>
% 88.68/26.78 (((setadjoinE) =>
% 88.68/26.78 (((setadjoinOr) =>
% 88.68/26.78 (((setoftrueEq) =>
% 88.68/26.78 (((powersetI) =>
% 88.68/26.78 (((emptyinPowerset) =>
% 88.68/26.78 (((emptyInPowerset) =>
% 88.68/26.78 (((powersetE) =>
% 88.68/26.78 (((setunionI) =>
% 88.68/26.78 (((setunionE) =>
% 88.68/26.78 (((subPowSU) =>
% 88.68/26.78 (((exuE2) =>
% 88.68/26.78 (((nonemptyImpWitness) =>
% 88.68/26.78 (((uniqinunit) =>
% 88.68/26.78 (((notinsingleton) =>
% 88.68/26.78 (((eqinunit) =>
% 88.68/26.78 (((singletonsswitch) =>
% 88.68/26.78 (((upairsetE) =>
% 88.68/26.78 (((upairsetIL) =>
% 88.68/26.78 ((
% 88.68/26.78 (upairsetIR) =>
% 88.68/26.78 ((
% 88.68/26.78 (emptyE1) =>
% 88.68/26.78 ((
% 88.68/26.78 (vacuousDall) =>
% 88.68/26.78 ((
% 88.68/26.78 (quantDeMorgan1) =>
% 88.68/26.78 ((
% 88.68/26.78 (quantDeMorgan2) =>
% 88.68/26.78 ((
% 88.68/26.78 (quantDeMorgan3) =>
% 88.68/26.78 ((
% 88.68/26.78 (quantDeMorgan4) =>
% 88.68/26.78 ((
% 88.68/26.78 (prop2setI) =>
% 88.68/26.78 ((
% 88.68/26.78 (prop2set2propI) =>
% 88.68/26.78 ((
% 88.68/26.78 (notdexE) =>
% 88.68/26.78 ((
% 88.68/26.78 (notdallE) =>
% 88.68/26.78 ((
% 88.68/26.78 (exuI1) =>
% 88.68/26.78 ((
% 88.68/26.78 (exuI3) =>
% 88.68/26.78 ((
% 88.68/26.78 (exuI2) =>
% 88.68/26.78 ((
% 88.68/26.78 (inCongP) =>
% 88.68/26.78 ((
% 88.68/26.78 (in__Cong) =>
% 88.68/26.78 ((
% 88.68/26.78 (exuE3u) =>
% 88.68/26.78 ((
% 88.68/26.78 (exu__Cong) =>
% 88.68/26.78 ((
% 88.68/26.78 (setadjoin__Cong) =>
% 88.68/26.78 ((
% 88.68/26.78 (powerset__Cong) =>
% 88.68/26.78 ((
% 88.68/26.78 (setunion__Cong) =>
% 88.68/26.78 ((
% 88.68/26.78 (exuEu) =>
% 88.68/26.78 ((
% 88.68/26.78 (descr__Cong) =>
% 88.68/26.78 ((
% 88.68/26.78 (dsetconstr__Cong) =>
% 88.68/26.78 ((
% 88.68/26.78 (subsetI1) =>
% 88.68/26.78 ((
% 88.68/26.78 (eqimpsubset2) =>
% 88.68/26.78 ((
% 88.68/26.78 (eqimpsubset1) =>
% 88.68/26.78 ((
% 88.68/26.78 (subsetI2) =>
% 88.68/26.78 ((
% 88.68/26.78 (emptysetsubset) =>
% 88.68/26.78 ((
% 88.68/26.78 (subsetE) =>
% 88.68/26.78 ((
% 88.68/26.78 (subsetE2) =>
% 88.68/26.78 ((
% 88.68/26.78 (notsubsetI) =>
% 88.68/26.78 ((
% 88.68/26.78 (notequalI1) =>
% 88.68/26.78 ((
% 88.68/26.78 (notequalI2) =>
% 88.68/26.78 ((
% 88.68/26.78 (subsetRefl) =>
% 88.68/26.78 ((
% 88.68/26.78 (subsetTrans) =>
% 88.68/26.78 ((
% 88.68/26.78 (setadjoinSub) =>
% 88.68/26.78 ((
% 88.68/26.78 (setadjoinSub2) =>
% 88.68/26.78 ((
% 88.68/26.78 (subset2powerset) =>
% 88.68/26.78 ((
% 88.68/26.78 (setextsub) =>
% 88.68/26.78 ((
% 88.68/26.78 (subsetemptysetimpeq) =>
% 88.68/26.78 ((
% 88.68/26.78 (powersetI1) =>
% 88.68/26.78 ((
% 88.68/26.78 (powersetE1) =>
% 88.68/26.78 ((
% 88.68/26.78 (inPowerset) =>
% 88.68/26.78 ((
% 88.68/26.78 (powersetsubset) =>
% 88.68/26.78 ((
% 88.68/26.78 (sepInPowerset) =>
% 88.68/26.78 ((
% 88.68/26.78 (sepSubset) =>
% 88.68/26.78 ((
% 88.68/26.78 (binunionIL) =>
% 88.68/26.78 ((
% 88.68/26.78 (upairset2IR) =>
% 88.68/26.78 ((
% 88.68/26.78 (binunionIR) =>
% 88.68/26.78 ((
% 88.68/26.78 (binunionEcases) =>
% 88.68/26.78 ((
% 88.68/26.78 (binunionE) =>
% 88.68/26.78 ((
% 88.68/26.78 (binunionLsub) =>
% 88.68/26.78 ((
% 88.68/26.78 (binunionRsub) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectI) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectSubset5) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectEL) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectLsub) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectSubset2) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectSubset3) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectER) =>
% 88.68/26.78 ((
% 88.68/26.78 (disjointsetsI1) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectRsub) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectSubset4) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectSubset1) =>
% 88.68/26.78 ((
% 88.68/26.78 (bs114d) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusI) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusEL) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusER) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusSubset2) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusERneg) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusELneg) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusILneg) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusIRneg) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusLsub) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusSubset1) =>
% 88.68/26.78 ((
% 88.68/26.78 (symdiffE) =>
% 88.68/26.78 ((
% 88.68/26.78 (symdiffI1) =>
% 88.68/26.78 ((
% 88.68/26.78 (symdiffI2) =>
% 88.68/26.78 ((
% 88.68/26.78 (symdiffIneg1) =>
% 88.68/26.78 ((
% 88.68/26.78 (symdiffIneg2) =>
% 88.68/26.78 ((
% 88.68/26.78 (secondinupair) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairIL) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairIR) =>
% 88.68/26.78 ((
% 88.68/26.78 (kpairiskpair) =>
% 88.68/26.78 ((
% 88.68/26.78 (kpairp) =>
% 88.68/26.78 ((
% 88.68/26.78 (singletonsubset) =>
% 88.68/26.78 ((
% 88.68/26.78 (singletoninpowerset) =>
% 88.68/26.78 ((
% 88.68/26.78 (singletoninpowunion) =>
% 88.68/26.78 ((
% 88.68/26.78 (upairset2E) =>
% 88.68/26.78 ((
% 88.68/26.78 (upairsubunion) =>
% 88.68/26.78 ((
% 88.68/26.78 (upairinpowunion) =>
% 88.68/26.78 ((
% 88.68/26.78 (ubforcartprodlem1) =>
% 88.68/26.78 ((
% 88.68/26.78 (ubforcartprodlem2) =>
% 88.68/26.78 ((
% 88.68/26.78 (ubforcartprodlem3) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodpairin) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodmempair1) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodmempair) =>
% 88.68/26.78 ((
% 88.68/26.78 (setunionE2) =>
% 88.68/26.78 ((
% 88.68/26.78 (setunionsingleton1) =>
% 88.68/26.78 ((
% 88.68/26.78 (setunionsingleton2) =>
% 88.68/26.78 ((
% 88.68/26.78 (setunionsingleton) =>
% 88.68/26.78 ((
% 88.68/26.78 (singletonprop) =>
% 88.68/26.78 ((
% 88.68/26.78 (ex1E1) =>
% 88.68/26.78 ((
% 88.68/26.78 (ex1I) =>
% 88.68/26.78 ((
% 88.68/26.78 (ex1I2) =>
% 88.68/26.78 ((
% 88.68/26.78 (singletonsuniq) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairinjL1) =>
% 88.68/26.78 ((
% 88.68/26.78 (kfstsingleton) =>
% 88.68/26.78 ((
% 88.68/26.78 (theprop) =>
% 88.68/26.78 ((
% 88.68/26.78 (kfstpairEq) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodfstin) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairinjL2) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairinjL) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairinjR11) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairinjR12) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairinjR1) =>
% 88.68/26.78 ((
% 88.68/26.78 (upairequniteq) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairinjR2) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairinjR) =>
% 88.68/26.78 ((
% 88.68/26.78 (ksndsingleton) =>
% 88.68/26.78 ((
% 88.68/26.78 (ksndpairEq) =>
% 88.68/26.78 ((
% 88.68/26.78 (kpairsurjEq) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodsndin) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodpairmemEL) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodpairmemER) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodmempaircEq) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodfstpairEq) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodsndpairEq) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodpairsurjEq) =>
% 88.68/26.78 ((
% 88.68/26.78 (dpsetconstrI) =>
% 88.68/26.78 ((
% 88.68/26.78 (dpsetconstrSub) =>
% 88.68/26.78 ((
% 88.68/26.78 (setOfPairsIsBReln) =>
% 88.68/26.78 ((
% 88.68/26.78 (dpsetconstrERa) =>
% 88.68/26.78 ((
% 88.68/26.78 (dpsetconstrEL1) =>
% 88.68/26.78 ((
% 88.68/26.78 (dpsetconstrEL2) =>
% 88.68/26.78 ((
% 88.68/26.78 (dpsetconstrER) =>
% 88.68/26.78 ((
% 88.68/26.78 (funcImageSingleton) =>
% 88.68/26.78 ((
% 88.68/26.78 (apProp) =>
% 88.68/26.78 ((
% 88.68/26.78 (app) =>
% 88.68/26.78 ((
% 88.68/26.78 (infuncsetfunc) =>
% 88.68/26.78 ((
% 88.68/26.78 (ap2p) =>
% 88.68/26.78 ((
% 88.68/26.78 (funcinfuncset) =>
% 88.68/26.78 ((
% 88.68/26.78 (lamProp) =>
% 88.68/26.78 ((
% 88.68/26.78 (lamp) =>
% 88.68/26.78 ((
% 88.68/26.78 (lam2p) =>
% 88.68/26.78 ((
% 88.68/26.78 (brelnall1) =>
% 88.68/26.78 ((
% 88.68/26.78 (brelnall2) =>
% 88.68/26.78 ((
% 88.68/26.78 (!!) @ (
% 88.68/26.78 (('#B') @ (
% 88.68/26.78 !!) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#S') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#S') @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 =>))) @
% 88.68/26.78 ex1)))) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 !!))) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#S') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#B') @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#S') @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 =>))) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#C') @ in)))))))) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 !!))))) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#C') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#B') @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#B') @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#S') @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 =>))) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#C') @ in)))))))))) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#S') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#S') @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#B'))) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 =>))))))) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#C') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#B') @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#S') @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 =>))))))) @
% 88.68/26.78 (
% 88.68/26.78 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 88.68/26.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl158])).
% 88.68/26.78 thf(zip_derived_cl189, plain,
% 88.68/26.78 (~ (((exuE3e) =>
% 88.68/26.78 (((setext) =>
% 88.68/26.78 (((emptyI) =>
% 88.68/26.78 (((noeltsimpempty) =>
% 88.68/26.78 (((setbeta) =>
% 88.68/26.78 (((nonemptyE1) =>
% 88.68/26.78 (((nonemptyI) =>
% 88.68/26.78 (((nonemptyI1) =>
% 88.68/26.78 (((setadjoinIL) =>
% 88.68/26.78 (((in @ emptyset @
% 88.68/26.78 (setadjoin @ emptyset @ emptyset)) =>
% 88.68/26.78 (((setadjoinIR) =>
% 88.68/26.78 (((setadjoinE) =>
% 88.68/26.78 (((setadjoinOr) =>
% 88.68/26.78 (((setoftrueEq) =>
% 88.68/26.78 (((powersetI) =>
% 88.68/26.78 (((emptyinPowerset) =>
% 88.68/26.78 (((emptyInPowerset) =>
% 88.68/26.78 (((powersetE) =>
% 88.68/26.78 (((setunionI) =>
% 88.68/26.78 (((setunionE) =>
% 88.68/26.78 (((subPowSU) =>
% 88.68/26.78 (((exuE2) =>
% 88.68/26.78 (((nonemptyImpWitness) =>
% 88.68/26.78 (((uniqinunit) =>
% 88.68/26.78 (((notinsingleton) =>
% 88.68/26.78 (((eqinunit) =>
% 88.68/26.78 (((singletonsswitch) =>
% 88.68/26.78 (((upairsetE) =>
% 88.68/26.78 (((upairsetIL) =>
% 88.68/26.78 (((upairsetIR) =>
% 88.68/26.78 ((
% 88.68/26.78 (emptyE1) =>
% 88.68/26.78 ((
% 88.68/26.78 (vacuousDall) =>
% 88.68/26.78 ((
% 88.68/26.78 (quantDeMorgan1) =>
% 88.68/26.78 ((
% 88.68/26.78 (quantDeMorgan2) =>
% 88.68/26.78 ((
% 88.68/26.78 (quantDeMorgan3) =>
% 88.68/26.78 ((
% 88.68/26.78 (quantDeMorgan4) =>
% 88.68/26.78 ((
% 88.68/26.78 (prop2setI) =>
% 88.68/26.78 ((
% 88.68/26.78 (prop2set2propI) =>
% 88.68/26.78 ((
% 88.68/26.78 (notdexE) =>
% 88.68/26.78 ((
% 88.68/26.78 (notdallE) =>
% 88.68/26.78 ((
% 88.68/26.78 (exuI1) =>
% 88.68/26.78 ((
% 88.68/26.78 (exuI3) =>
% 88.68/26.78 ((
% 88.68/26.78 (exuI2) =>
% 88.68/26.78 ((
% 88.68/26.78 (inCongP) =>
% 88.68/26.78 ((
% 88.68/26.78 (in__Cong) =>
% 88.68/26.78 ((
% 88.68/26.78 (exuE3u) =>
% 88.68/26.78 ((
% 88.68/26.78 (exu__Cong) =>
% 88.68/26.78 ((
% 88.68/26.78 (setadjoin__Cong) =>
% 88.68/26.78 ((
% 88.68/26.78 (powerset__Cong) =>
% 88.68/26.78 ((
% 88.68/26.78 (setunion__Cong) =>
% 88.68/26.78 ((
% 88.68/26.78 (exuEu) =>
% 88.68/26.78 ((
% 88.68/26.78 (descr__Cong) =>
% 88.68/26.78 ((
% 88.68/26.78 (dsetconstr__Cong) =>
% 88.68/26.78 ((
% 88.68/26.78 (subsetI1) =>
% 88.68/26.78 ((
% 88.68/26.78 (eqimpsubset2) =>
% 88.68/26.78 ((
% 88.68/26.78 (eqimpsubset1) =>
% 88.68/26.78 ((
% 88.68/26.78 (subsetI2) =>
% 88.68/26.78 ((
% 88.68/26.78 (emptysetsubset) =>
% 88.68/26.78 ((
% 88.68/26.78 (subsetE) =>
% 88.68/26.78 ((
% 88.68/26.78 (subsetE2) =>
% 88.68/26.78 ((
% 88.68/26.78 (notsubsetI) =>
% 88.68/26.78 ((
% 88.68/26.78 (notequalI1) =>
% 88.68/26.78 ((
% 88.68/26.78 (notequalI2) =>
% 88.68/26.78 ((
% 88.68/26.78 (subsetRefl) =>
% 88.68/26.78 ((
% 88.68/26.78 (subsetTrans) =>
% 88.68/26.78 ((
% 88.68/26.78 (setadjoinSub) =>
% 88.68/26.78 ((
% 88.68/26.78 (setadjoinSub2) =>
% 88.68/26.78 ((
% 88.68/26.78 (subset2powerset) =>
% 88.68/26.78 ((
% 88.68/26.78 (setextsub) =>
% 88.68/26.78 ((
% 88.68/26.78 (subsetemptysetimpeq) =>
% 88.68/26.78 ((
% 88.68/26.78 (powersetI1) =>
% 88.68/26.78 ((
% 88.68/26.78 (powersetE1) =>
% 88.68/26.78 ((
% 88.68/26.78 (inPowerset) =>
% 88.68/26.78 ((
% 88.68/26.78 (powersetsubset) =>
% 88.68/26.78 ((
% 88.68/26.78 (sepInPowerset) =>
% 88.68/26.78 ((
% 88.68/26.78 (sepSubset) =>
% 88.68/26.78 ((
% 88.68/26.78 (binunionIL) =>
% 88.68/26.78 ((
% 88.68/26.78 (upairset2IR) =>
% 88.68/26.78 ((
% 88.68/26.78 (binunionIR) =>
% 88.68/26.78 ((
% 88.68/26.78 (binunionEcases) =>
% 88.68/26.78 ((
% 88.68/26.78 (binunionE) =>
% 88.68/26.78 ((
% 88.68/26.78 (binunionLsub) =>
% 88.68/26.78 ((
% 88.68/26.78 (binunionRsub) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectI) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectSubset5) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectEL) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectLsub) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectSubset2) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectSubset3) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectER) =>
% 88.68/26.78 ((
% 88.68/26.78 (disjointsetsI1) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectRsub) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectSubset4) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectSubset1) =>
% 88.68/26.78 ((
% 88.68/26.78 (bs114d) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusI) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusEL) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusER) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusSubset2) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusERneg) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusELneg) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusILneg) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusIRneg) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusLsub) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusSubset1) =>
% 88.68/26.78 ((
% 88.68/26.78 (symdiffE) =>
% 88.68/26.78 ((
% 88.68/26.78 (symdiffI1) =>
% 88.68/26.78 ((
% 88.68/26.78 (symdiffI2) =>
% 88.68/26.78 ((
% 88.68/26.78 (symdiffIneg1) =>
% 88.68/26.78 ((
% 88.68/26.78 (symdiffIneg2) =>
% 88.68/26.78 ((
% 88.68/26.78 (secondinupair) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairIL) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairIR) =>
% 88.68/26.78 ((
% 88.68/26.78 (kpairiskpair) =>
% 88.68/26.78 ((
% 88.68/26.78 (kpairp) =>
% 88.68/26.78 ((
% 88.68/26.78 (singletonsubset) =>
% 88.68/26.78 ((
% 88.68/26.78 (singletoninpowerset) =>
% 88.68/26.78 ((
% 88.68/26.78 (singletoninpowunion) =>
% 88.68/26.78 ((
% 88.68/26.78 (upairset2E) =>
% 88.68/26.78 ((
% 88.68/26.78 (upairsubunion) =>
% 88.68/26.78 ((
% 88.68/26.78 (upairinpowunion) =>
% 88.68/26.78 ((
% 88.68/26.78 (ubforcartprodlem1) =>
% 88.68/26.78 ((
% 88.68/26.78 (ubforcartprodlem2) =>
% 88.68/26.78 ((
% 88.68/26.78 (ubforcartprodlem3) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodpairin) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodmempair1) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodmempair) =>
% 88.68/26.78 ((
% 88.68/26.78 (setunionE2) =>
% 88.68/26.78 ((
% 88.68/26.78 (setunionsingleton1) =>
% 88.68/26.78 ((
% 88.68/26.78 (setunionsingleton2) =>
% 88.68/26.78 ((
% 88.68/26.78 (setunionsingleton) =>
% 88.68/26.78 ((
% 88.68/26.78 (singletonprop) =>
% 88.68/26.78 ((
% 88.68/26.78 (ex1E1) =>
% 88.68/26.78 ((
% 88.68/26.78 (ex1I) =>
% 88.68/26.78 ((
% 88.68/26.78 (ex1I2) =>
% 88.68/26.78 ((
% 88.68/26.78 (singletonsuniq) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairinjL1) =>
% 88.68/26.78 ((
% 88.68/26.78 (kfstsingleton) =>
% 88.68/26.78 ((
% 88.68/26.78 (theprop) =>
% 88.68/26.78 ((
% 88.68/26.78 (kfstpairEq) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodfstin) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairinjL2) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairinjL) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairinjR11) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairinjR12) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairinjR1) =>
% 88.68/26.78 ((
% 88.68/26.78 (upairequniteq) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairinjR2) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairinjR) =>
% 88.68/26.78 ((
% 88.68/26.78 (ksndsingleton) =>
% 88.68/26.78 ((
% 88.68/26.78 (ksndpairEq) =>
% 88.68/26.78 ((
% 88.68/26.78 (kpairsurjEq) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodsndin) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodpairmemEL) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodpairmemER) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodmempaircEq) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodfstpairEq) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodsndpairEq) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodpairsurjEq) =>
% 88.68/26.78 ((
% 88.68/26.78 (dpsetconstrI) =>
% 88.68/26.78 ((
% 88.68/26.78 (dpsetconstrSub) =>
% 88.68/26.78 ((
% 88.68/26.78 (setOfPairsIsBReln) =>
% 88.68/26.78 ((
% 88.68/26.78 (dpsetconstrERa) =>
% 88.68/26.78 ((
% 88.68/26.78 (dpsetconstrEL1) =>
% 88.68/26.78 ((
% 88.68/26.78 (dpsetconstrEL2) =>
% 88.68/26.78 ((
% 88.68/26.78 (dpsetconstrER) =>
% 88.68/26.78 ((
% 88.68/26.78 (funcImageSingleton) =>
% 88.68/26.78 ((
% 88.68/26.78 (apProp) =>
% 88.68/26.78 ((
% 88.68/26.78 (app) =>
% 88.68/26.78 ((
% 88.68/26.78 (infuncsetfunc) =>
% 88.68/26.78 ((
% 88.68/26.78 (ap2p) =>
% 88.68/26.78 ((
% 88.68/26.78 (funcinfuncset) =>
% 88.68/26.78 ((
% 88.68/26.78 (lamProp) =>
% 88.68/26.78 ((
% 88.68/26.78 (lamp) =>
% 88.68/26.78 ((
% 88.68/26.78 (lam2p) =>
% 88.68/26.78 ((
% 88.68/26.78 (brelnall1) =>
% 88.68/26.78 ((
% 88.68/26.78 (brelnall2) =>
% 88.68/26.78 ((
% 88.68/26.78 (!!) @ (
% 88.68/26.78 (('#B') @ (
% 88.68/26.78 !!) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#S') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#S') @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 =>))) @
% 88.68/26.78 ex1)))) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 !!))) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#S') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#B') @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#S') @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 =>))) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#C') @ in)))))))) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 !!))))) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#C') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#B') @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#B') @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#S') @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 =>))) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#C') @ in)))))))))) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#S') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#S') @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#B'))) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 =>))))))) @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#C') @ (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#B') @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 '#S') @
% 88.68/26.78 (
% 88.68/26.78 (
% 88.68/26.78 ('#B') @ (
% 88.68/26.78 =>))))))) @
% 88.68/26.78 (
% 88.68/26.78 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 88.68/26.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl174])).
% 88.68/26.78 thf(zip_derived_cl206, plain,
% 88.68/26.78 (~ (((setext) =>
% 88.68/26.78 (((emptyI) =>
% 88.68/26.78 (((noeltsimpempty) =>
% 88.68/26.78 (((setbeta) =>
% 88.68/26.78 (((nonemptyE1) =>
% 88.68/26.78 (((nonemptyI) =>
% 88.68/26.78 (((nonemptyI1) =>
% 88.68/26.78 (((setadjoinIL) =>
% 88.68/26.78 (((in @ emptyset @
% 88.68/26.78 (setadjoin @ emptyset @ emptyset)) =>
% 88.68/26.78 (((setadjoinIR) =>
% 88.68/26.78 (((setadjoinE) =>
% 88.68/26.78 (((setadjoinOr) =>
% 88.68/26.78 (((setoftrueEq) =>
% 88.68/26.78 (((powersetI) =>
% 88.68/26.78 (((emptyinPowerset) =>
% 88.68/26.78 (((emptyInPowerset) =>
% 88.68/26.78 (((powersetE) =>
% 88.68/26.78 (((setunionI) =>
% 88.68/26.78 (((setunionE) =>
% 88.68/26.78 (((subPowSU) =>
% 88.68/26.78 (((exuE2) =>
% 88.68/26.78 (((nonemptyImpWitness) =>
% 88.68/26.78 (((uniqinunit) =>
% 88.68/26.78 (((notinsingleton) =>
% 88.68/26.78 (((eqinunit) =>
% 88.68/26.78 (((singletonsswitch) =>
% 88.68/26.78 (((upairsetE) =>
% 88.68/26.78 (((upairsetIL) =>
% 88.68/26.78 (((upairsetIR) =>
% 88.68/26.78 (((emptyE1) =>
% 88.68/26.78 ((
% 88.68/26.78 (vacuousDall) =>
% 88.68/26.78 ((
% 88.68/26.78 (quantDeMorgan1) =>
% 88.68/26.78 ((
% 88.68/26.78 (quantDeMorgan2) =>
% 88.68/26.78 ((
% 88.68/26.78 (quantDeMorgan3) =>
% 88.68/26.78 ((
% 88.68/26.78 (quantDeMorgan4) =>
% 88.68/26.78 ((
% 88.68/26.78 (prop2setI) =>
% 88.68/26.78 ((
% 88.68/26.78 (prop2set2propI) =>
% 88.68/26.78 ((
% 88.68/26.78 (notdexE) =>
% 88.68/26.78 ((
% 88.68/26.78 (notdallE) =>
% 88.68/26.78 ((
% 88.68/26.78 (exuI1) =>
% 88.68/26.78 ((
% 88.68/26.78 (exuI3) =>
% 88.68/26.78 ((
% 88.68/26.78 (exuI2) =>
% 88.68/26.78 ((
% 88.68/26.78 (inCongP) =>
% 88.68/26.78 ((
% 88.68/26.78 (in__Cong) =>
% 88.68/26.78 ((
% 88.68/26.78 (exuE3u) =>
% 88.68/26.78 ((
% 88.68/26.78 (exu__Cong) =>
% 88.68/26.78 ((
% 88.68/26.78 (setadjoin__Cong) =>
% 88.68/26.78 ((
% 88.68/26.78 (powerset__Cong) =>
% 88.68/26.78 ((
% 88.68/26.78 (setunion__Cong) =>
% 88.68/26.78 ((
% 88.68/26.78 (exuEu) =>
% 88.68/26.78 ((
% 88.68/26.78 (descr__Cong) =>
% 88.68/26.78 ((
% 88.68/26.78 (dsetconstr__Cong) =>
% 88.68/26.78 ((
% 88.68/26.78 (subsetI1) =>
% 88.68/26.78 ((
% 88.68/26.78 (eqimpsubset2) =>
% 88.68/26.78 ((
% 88.68/26.78 (eqimpsubset1) =>
% 88.68/26.78 ((
% 88.68/26.78 (subsetI2) =>
% 88.68/26.78 ((
% 88.68/26.78 (emptysetsubset) =>
% 88.68/26.78 ((
% 88.68/26.78 (subsetE) =>
% 88.68/26.78 ((
% 88.68/26.78 (subsetE2) =>
% 88.68/26.78 ((
% 88.68/26.78 (notsubsetI) =>
% 88.68/26.78 ((
% 88.68/26.78 (notequalI1) =>
% 88.68/26.78 ((
% 88.68/26.78 (notequalI2) =>
% 88.68/26.78 ((
% 88.68/26.78 (subsetRefl) =>
% 88.68/26.78 ((
% 88.68/26.78 (subsetTrans) =>
% 88.68/26.78 ((
% 88.68/26.78 (setadjoinSub) =>
% 88.68/26.78 ((
% 88.68/26.78 (setadjoinSub2) =>
% 88.68/26.78 ((
% 88.68/26.78 (subset2powerset) =>
% 88.68/26.78 ((
% 88.68/26.78 (setextsub) =>
% 88.68/26.78 ((
% 88.68/26.78 (subsetemptysetimpeq) =>
% 88.68/26.78 ((
% 88.68/26.78 (powersetI1) =>
% 88.68/26.78 ((
% 88.68/26.78 (powersetE1) =>
% 88.68/26.78 ((
% 88.68/26.78 (inPowerset) =>
% 88.68/26.78 ((
% 88.68/26.78 (powersetsubset) =>
% 88.68/26.78 ((
% 88.68/26.78 (sepInPowerset) =>
% 88.68/26.78 ((
% 88.68/26.78 (sepSubset) =>
% 88.68/26.78 ((
% 88.68/26.78 (binunionIL) =>
% 88.68/26.78 ((
% 88.68/26.78 (upairset2IR) =>
% 88.68/26.78 ((
% 88.68/26.78 (binunionIR) =>
% 88.68/26.78 ((
% 88.68/26.78 (binunionEcases) =>
% 88.68/26.78 ((
% 88.68/26.78 (binunionE) =>
% 88.68/26.78 ((
% 88.68/26.78 (binunionLsub) =>
% 88.68/26.78 ((
% 88.68/26.78 (binunionRsub) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectI) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectSubset5) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectEL) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectLsub) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectSubset2) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectSubset3) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectER) =>
% 88.68/26.78 ((
% 88.68/26.78 (disjointsetsI1) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectRsub) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectSubset4) =>
% 88.68/26.78 ((
% 88.68/26.78 (binintersectSubset1) =>
% 88.68/26.78 ((
% 88.68/26.78 (bs114d) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusI) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusEL) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusER) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusSubset2) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusERneg) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusELneg) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusILneg) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusIRneg) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusLsub) =>
% 88.68/26.78 ((
% 88.68/26.78 (setminusSubset1) =>
% 88.68/26.78 ((
% 88.68/26.78 (symdiffE) =>
% 88.68/26.78 ((
% 88.68/26.78 (symdiffI1) =>
% 88.68/26.78 ((
% 88.68/26.78 (symdiffI2) =>
% 88.68/26.78 ((
% 88.68/26.78 (symdiffIneg1) =>
% 88.68/26.78 ((
% 88.68/26.78 (symdiffIneg2) =>
% 88.68/26.78 ((
% 88.68/26.78 (secondinupair) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairIL) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairIR) =>
% 88.68/26.78 ((
% 88.68/26.78 (kpairiskpair) =>
% 88.68/26.78 ((
% 88.68/26.78 (kpairp) =>
% 88.68/26.78 ((
% 88.68/26.78 (singletonsubset) =>
% 88.68/26.78 ((
% 88.68/26.78 (singletoninpowerset) =>
% 88.68/26.78 ((
% 88.68/26.78 (singletoninpowunion) =>
% 88.68/26.78 ((
% 88.68/26.78 (upairset2E) =>
% 88.68/26.78 ((
% 88.68/26.78 (upairsubunion) =>
% 88.68/26.78 ((
% 88.68/26.78 (upairinpowunion) =>
% 88.68/26.78 ((
% 88.68/26.78 (ubforcartprodlem1) =>
% 88.68/26.78 ((
% 88.68/26.78 (ubforcartprodlem2) =>
% 88.68/26.78 ((
% 88.68/26.78 (ubforcartprodlem3) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodpairin) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodmempair1) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodmempair) =>
% 88.68/26.78 ((
% 88.68/26.78 (setunionE2) =>
% 88.68/26.78 ((
% 88.68/26.78 (setunionsingleton1) =>
% 88.68/26.78 ((
% 88.68/26.78 (setunionsingleton2) =>
% 88.68/26.78 ((
% 88.68/26.78 (setunionsingleton) =>
% 88.68/26.78 ((
% 88.68/26.78 (singletonprop) =>
% 88.68/26.78 ((
% 88.68/26.78 (ex1E1) =>
% 88.68/26.78 ((
% 88.68/26.78 (ex1I) =>
% 88.68/26.78 ((
% 88.68/26.78 (ex1I2) =>
% 88.68/26.78 ((
% 88.68/26.78 (singletonsuniq) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairinjL1) =>
% 88.68/26.78 ((
% 88.68/26.78 (kfstsingleton) =>
% 88.68/26.78 ((
% 88.68/26.78 (theprop) =>
% 88.68/26.78 ((
% 88.68/26.78 (kfstpairEq) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodfstin) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairinjL2) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairinjL) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairinjR11) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairinjR12) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairinjR1) =>
% 88.68/26.78 ((
% 88.68/26.78 (upairequniteq) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairinjR2) =>
% 88.68/26.78 ((
% 88.68/26.78 (setukpairinjR) =>
% 88.68/26.78 ((
% 88.68/26.78 (ksndsingleton) =>
% 88.68/26.78 ((
% 88.68/26.78 (ksndpairEq) =>
% 88.68/26.78 ((
% 88.68/26.78 (kpairsurjEq) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodsndin) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodpairmemEL) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodpairmemER) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodmempaircEq) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodfstpairEq) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodsndpairEq) =>
% 88.68/26.78 ((
% 88.68/26.78 (cartprodpairsurjEq) =>
% 88.68/26.78 ((
% 88.68/26.78 (dpsetconstrI) =>
% 88.68/26.78 ((
% 88.68/26.78 (dpsetconstrSub) =>
% 88.68/26.78 ((
% 88.68/26.78 (setOfPairsIsBReln) =>
% 88.68/26.78 ((
% 88.68/26.78 (dpsetconstrERa) =>
% 88.68/26.78 ((
% 88.68/26.78 (dpsetconstrEL1) =>
% 88.68/26.78 ((
% 88.68/26.78 (dpsetconstrEL2) =>
% 88.68/26.78 ((
% 88.68/26.78 (dpsetconstrER) =>
% 88.68/26.78 ((
% 88.68/26.78 (funcImageSingleton) =>
% 88.68/26.78 ((
% 88.68/26.78 (apProp) =>
% 88.68/26.78 ((
% 88.68/26.78 (app) =>
% 88.68/26.78 ((
% 88.68/26.78 (infuncsetfunc) =>
% 88.68/26.78 ((
% 88.68/26.78 (ap2p) =>
% 88.68/26.78 ((
% 88.68/26.78 (funcinfuncset) =>
% 88.68/26.78 ((
% 88.68/26.79 (lamProp) =>
% 88.68/26.79 ((
% 88.68/26.79 (lamp) =>
% 88.68/26.79 ((
% 88.68/26.79 (lam2p) =>
% 88.68/26.79 ((
% 88.68/26.79 (brelnall1) =>
% 88.68/26.79 ((
% 88.68/26.79 (brelnall2) =>
% 88.68/26.79 ((
% 88.68/26.79 (!!) @ (
% 88.68/26.79 (('#B') @ (
% 88.68/26.79 !!) @
% 88.68/26.79 (
% 88.68/26.79 (
% 88.68/26.79 ('#S') @ (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 '#S') @
% 88.68/26.79 (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 =>))) @
% 88.68/26.79 ex1)))) @
% 88.68/26.79 (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 !!))) @
% 88.68/26.79 (
% 88.68/26.79 (
% 88.68/26.79 ('#S') @ (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 '#B') @
% 88.68/26.79 (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 '#S') @
% 88.68/26.79 (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 =>))) @
% 88.68/26.79 (
% 88.68/26.79 (
% 88.68/26.79 ('#C') @ in)))))))) @
% 88.68/26.79 (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 !!))))) @
% 88.68/26.79 (
% 88.68/26.79 (
% 88.68/26.79 ('#C') @ (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 '#B') @
% 88.68/26.79 (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 '#B') @
% 88.68/26.79 (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 '#S') @
% 88.68/26.79 (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 =>))) @
% 88.68/26.79 (
% 88.68/26.79 (
% 88.68/26.79 ('#C') @ in)))))))))) @
% 88.68/26.79 (
% 88.68/26.79 (
% 88.68/26.79 ('#S') @ (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 '#S') @
% 88.68/26.79 (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 '#B'))) @
% 88.68/26.79 (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 =>))))))) @
% 88.68/26.79 (
% 88.68/26.79 (
% 88.68/26.79 ('#C') @ (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 '#B') @
% 88.68/26.79 (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 '#S') @
% 88.68/26.79 (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 =>))))))) @
% 88.68/26.79 (
% 88.68/26.79 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 88.68/26.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl189])).
% 88.68/26.79 thf(zip_derived_cl222, plain,
% 88.68/26.79 (~ (((emptyI) =>
% 88.68/26.79 (((noeltsimpempty) =>
% 88.68/26.79 (((setbeta) =>
% 88.68/26.79 (((nonemptyE1) =>
% 88.68/26.79 (((nonemptyI) =>
% 88.68/26.79 (((nonemptyI1) =>
% 88.68/26.79 (((setadjoinIL) =>
% 88.68/26.79 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 88.68/26.79 (((setadjoinIR) =>
% 88.68/26.79 (((setadjoinE) =>
% 88.68/26.79 (((setadjoinOr) =>
% 88.68/26.79 (((setoftrueEq) =>
% 88.68/26.79 (((powersetI) =>
% 88.68/26.79 (((emptyinPowerset) =>
% 88.68/26.79 (((emptyInPowerset) =>
% 88.68/26.79 (((powersetE) =>
% 88.68/26.79 (((setunionI) =>
% 88.68/26.79 (((setunionE) =>
% 88.68/26.79 (((subPowSU) =>
% 88.68/26.79 (((exuE2) =>
% 88.68/26.79 (((nonemptyImpWitness) =>
% 88.68/26.79 (((uniqinunit) =>
% 88.68/26.79 (((notinsingleton) =>
% 88.68/26.79 (((eqinunit) =>
% 88.68/26.79 (((singletonsswitch) =>
% 88.68/26.79 (((upairsetE) =>
% 88.68/26.79 (((upairsetIL) =>
% 88.68/26.79 (((upairsetIR) =>
% 88.68/26.79 (((emptyE1) =>
% 88.68/26.79 (((vacuousDall) =>
% 88.68/26.79 ((
% 88.68/26.79 (quantDeMorgan1) =>
% 88.68/26.79 ((
% 88.68/26.79 (quantDeMorgan2) =>
% 88.68/26.79 ((
% 88.68/26.79 (quantDeMorgan3) =>
% 88.68/26.79 ((
% 88.68/26.79 (quantDeMorgan4) =>
% 88.68/26.79 ((
% 88.68/26.79 (prop2setI) =>
% 88.68/26.79 ((
% 88.68/26.79 (prop2set2propI) =>
% 88.68/26.79 ((
% 88.68/26.79 (notdexE) =>
% 88.68/26.79 ((
% 88.68/26.79 (notdallE) =>
% 88.68/26.79 ((
% 88.68/26.79 (exuI1) =>
% 88.68/26.79 ((
% 88.68/26.79 (exuI3) =>
% 88.68/26.79 ((
% 88.68/26.79 (exuI2) =>
% 88.68/26.79 ((
% 88.68/26.79 (inCongP) =>
% 88.68/26.79 ((
% 88.68/26.79 (in__Cong) =>
% 88.68/26.79 ((
% 88.68/26.79 (exuE3u) =>
% 88.68/26.79 ((
% 88.68/26.79 (exu__Cong) =>
% 88.68/26.79 ((
% 88.68/26.79 (setadjoin__Cong) =>
% 88.68/26.79 ((
% 88.68/26.79 (powerset__Cong) =>
% 88.68/26.79 ((
% 88.68/26.79 (setunion__Cong) =>
% 88.68/26.79 ((
% 88.68/26.79 (exuEu) =>
% 88.68/26.79 ((
% 88.68/26.79 (descr__Cong) =>
% 88.68/26.79 ((
% 88.68/26.79 (dsetconstr__Cong) =>
% 88.68/26.79 ((
% 88.68/26.79 (subsetI1) =>
% 88.68/26.79 ((
% 88.68/26.79 (eqimpsubset2) =>
% 88.68/26.79 ((
% 88.68/26.79 (eqimpsubset1) =>
% 88.68/26.79 ((
% 88.68/26.79 (subsetI2) =>
% 88.68/26.79 ((
% 88.68/26.79 (emptysetsubset) =>
% 88.68/26.79 ((
% 88.68/26.79 (subsetE) =>
% 88.68/26.79 ((
% 88.68/26.79 (subsetE2) =>
% 88.68/26.79 ((
% 88.68/26.79 (notsubsetI) =>
% 88.68/26.79 ((
% 88.68/26.79 (notequalI1) =>
% 88.68/26.79 ((
% 88.68/26.79 (notequalI2) =>
% 88.68/26.79 ((
% 88.68/26.79 (subsetRefl) =>
% 88.68/26.79 ((
% 88.68/26.79 (subsetTrans) =>
% 88.68/26.79 ((
% 88.68/26.79 (setadjoinSub) =>
% 88.68/26.79 ((
% 88.68/26.79 (setadjoinSub2) =>
% 88.68/26.79 ((
% 88.68/26.79 (subset2powerset) =>
% 88.68/26.79 ((
% 88.68/26.79 (setextsub) =>
% 88.68/26.79 ((
% 88.68/26.79 (subsetemptysetimpeq) =>
% 88.68/26.79 ((
% 88.68/26.79 (powersetI1) =>
% 88.68/26.79 ((
% 88.68/26.79 (powersetE1) =>
% 88.68/26.79 ((
% 88.68/26.79 (inPowerset) =>
% 88.68/26.79 ((
% 88.68/26.79 (powersetsubset) =>
% 88.68/26.79 ((
% 88.68/26.79 (sepInPowerset) =>
% 88.68/26.79 ((
% 88.68/26.79 (sepSubset) =>
% 88.68/26.79 ((
% 88.68/26.79 (binunionIL) =>
% 88.68/26.79 ((
% 88.68/26.79 (upairset2IR) =>
% 88.68/26.79 ((
% 88.68/26.79 (binunionIR) =>
% 88.68/26.79 ((
% 88.68/26.79 (binunionEcases) =>
% 88.68/26.79 ((
% 88.68/26.79 (binunionE) =>
% 88.68/26.79 ((
% 88.68/26.79 (binunionLsub) =>
% 88.68/26.79 ((
% 88.68/26.79 (binunionRsub) =>
% 88.68/26.79 ((
% 88.68/26.79 (binintersectI) =>
% 88.68/26.79 ((
% 88.68/26.79 (binintersectSubset5) =>
% 88.68/26.79 ((
% 88.68/26.79 (binintersectEL) =>
% 88.68/26.79 ((
% 88.68/26.79 (binintersectLsub) =>
% 88.68/26.79 ((
% 88.68/26.79 (binintersectSubset2) =>
% 88.68/26.79 ((
% 88.68/26.79 (binintersectSubset3) =>
% 88.68/26.79 ((
% 88.68/26.79 (binintersectER) =>
% 88.68/26.79 ((
% 88.68/26.79 (disjointsetsI1) =>
% 88.68/26.79 ((
% 88.68/26.79 (binintersectRsub) =>
% 88.68/26.79 ((
% 88.68/26.79 (binintersectSubset4) =>
% 88.68/26.79 ((
% 88.68/26.79 (binintersectSubset1) =>
% 88.68/26.79 ((
% 88.68/26.79 (bs114d) =>
% 88.68/26.79 ((
% 88.68/26.79 (setminusI) =>
% 88.68/26.79 ((
% 88.68/26.79 (setminusEL) =>
% 88.68/26.79 ((
% 88.68/26.79 (setminusER) =>
% 88.68/26.79 ((
% 88.68/26.79 (setminusSubset2) =>
% 88.68/26.79 ((
% 88.68/26.79 (setminusERneg) =>
% 88.68/26.79 ((
% 88.68/26.79 (setminusELneg) =>
% 88.68/26.79 ((
% 88.68/26.79 (setminusILneg) =>
% 88.68/26.79 ((
% 88.68/26.79 (setminusIRneg) =>
% 88.68/26.79 ((
% 88.68/26.79 (setminusLsub) =>
% 88.68/26.79 ((
% 88.68/26.79 (setminusSubset1) =>
% 88.68/26.79 ((
% 88.68/26.79 (symdiffE) =>
% 88.68/26.79 ((
% 88.68/26.79 (symdiffI1) =>
% 88.68/26.79 ((
% 88.68/26.79 (symdiffI2) =>
% 88.68/26.79 ((
% 88.68/26.79 (symdiffIneg1) =>
% 88.68/26.79 ((
% 88.68/26.79 (symdiffIneg2) =>
% 88.68/26.79 ((
% 88.68/26.79 (secondinupair) =>
% 88.68/26.79 ((
% 88.68/26.79 (setukpairIL) =>
% 88.68/26.79 ((
% 88.68/26.79 (setukpairIR) =>
% 88.68/26.79 ((
% 88.68/26.79 (kpairiskpair) =>
% 88.68/26.79 ((
% 88.68/26.79 (kpairp) =>
% 88.68/26.79 ((
% 88.68/26.79 (singletonsubset) =>
% 88.68/26.79 ((
% 88.68/26.79 (singletoninpowerset) =>
% 88.68/26.79 ((
% 88.68/26.79 (singletoninpowunion) =>
% 88.68/26.79 ((
% 88.68/26.79 (upairset2E) =>
% 88.68/26.79 ((
% 88.68/26.79 (upairsubunion) =>
% 88.68/26.79 ((
% 88.68/26.79 (upairinpowunion) =>
% 88.68/26.79 ((
% 88.68/26.79 (ubforcartprodlem1) =>
% 88.68/26.79 ((
% 88.68/26.79 (ubforcartprodlem2) =>
% 88.68/26.79 ((
% 88.68/26.79 (ubforcartprodlem3) =>
% 88.68/26.79 ((
% 88.68/26.79 (cartprodpairin) =>
% 88.68/26.79 ((
% 88.68/26.79 (cartprodmempair1) =>
% 88.68/26.79 ((
% 88.68/26.79 (cartprodmempair) =>
% 88.68/26.79 ((
% 88.68/26.79 (setunionE2) =>
% 88.68/26.79 ((
% 88.68/26.79 (setunionsingleton1) =>
% 88.68/26.79 ((
% 88.68/26.79 (setunionsingleton2) =>
% 88.68/26.79 ((
% 88.68/26.79 (setunionsingleton) =>
% 88.68/26.79 ((
% 88.68/26.79 (singletonprop) =>
% 88.68/26.79 ((
% 88.68/26.79 (ex1E1) =>
% 88.68/26.79 ((
% 88.68/26.79 (ex1I) =>
% 88.68/26.79 ((
% 88.68/26.79 (ex1I2) =>
% 88.68/26.79 ((
% 88.68/26.79 (singletonsuniq) =>
% 88.68/26.79 ((
% 88.68/26.79 (setukpairinjL1) =>
% 88.68/26.79 ((
% 88.68/26.79 (kfstsingleton) =>
% 88.68/26.79 ((
% 88.68/26.79 (theprop) =>
% 88.68/26.79 ((
% 88.68/26.79 (kfstpairEq) =>
% 88.68/26.79 ((
% 88.68/26.79 (cartprodfstin) =>
% 88.68/26.79 ((
% 88.68/26.79 (setukpairinjL2) =>
% 88.68/26.79 ((
% 88.68/26.79 (setukpairinjL) =>
% 88.68/26.79 ((
% 88.68/26.79 (setukpairinjR11) =>
% 88.68/26.79 ((
% 88.68/26.79 (setukpairinjR12) =>
% 88.68/26.79 ((
% 88.68/26.79 (setukpairinjR1) =>
% 88.68/26.79 ((
% 88.68/26.79 (upairequniteq) =>
% 88.68/26.79 ((
% 88.68/26.79 (setukpairinjR2) =>
% 88.68/26.79 ((
% 88.68/26.79 (setukpairinjR) =>
% 88.68/26.79 ((
% 88.68/26.79 (ksndsingleton) =>
% 88.68/26.79 ((
% 88.68/26.79 (ksndpairEq) =>
% 88.68/26.79 ((
% 88.68/26.79 (kpairsurjEq) =>
% 88.68/26.79 ((
% 88.68/26.79 (cartprodsndin) =>
% 88.68/26.79 ((
% 88.68/26.79 (cartprodpairmemEL) =>
% 88.68/26.79 ((
% 88.68/26.79 (cartprodpairmemER) =>
% 88.68/26.79 ((
% 88.68/26.79 (cartprodmempaircEq) =>
% 88.68/26.79 ((
% 88.68/26.79 (cartprodfstpairEq) =>
% 88.68/26.79 ((
% 88.68/26.79 (cartprodsndpairEq) =>
% 88.68/26.79 ((
% 88.68/26.79 (cartprodpairsurjEq) =>
% 88.68/26.79 ((
% 88.68/26.79 (dpsetconstrI) =>
% 88.68/26.79 ((
% 88.68/26.79 (dpsetconstrSub) =>
% 88.68/26.79 ((
% 88.68/26.79 (setOfPairsIsBReln) =>
% 88.68/26.79 ((
% 88.68/26.79 (dpsetconstrERa) =>
% 88.68/26.79 ((
% 88.68/26.79 (dpsetconstrEL1) =>
% 88.68/26.79 ((
% 88.68/26.79 (dpsetconstrEL2) =>
% 88.68/26.79 ((
% 88.68/26.79 (dpsetconstrER) =>
% 88.68/26.79 ((
% 88.68/26.79 (funcImageSingleton) =>
% 88.68/26.79 ((
% 88.68/26.79 (apProp) =>
% 88.68/26.79 ((
% 88.68/26.79 (app) =>
% 88.68/26.79 ((
% 88.68/26.79 (infuncsetfunc) =>
% 88.68/26.79 ((
% 88.68/26.79 (ap2p) =>
% 88.68/26.79 ((
% 88.68/26.79 (funcinfuncset) =>
% 88.68/26.79 ((
% 88.68/26.79 (lamProp) =>
% 88.68/26.79 ((
% 88.68/26.79 (lamp) =>
% 88.68/26.79 ((
% 88.68/26.79 (lam2p) =>
% 88.68/26.79 ((
% 88.68/26.79 (brelnall1) =>
% 88.68/26.79 ((
% 88.68/26.79 (brelnall2) =>
% 88.68/26.79 ((
% 88.68/26.79 (!!) @ (
% 88.68/26.79 (('#B') @ (
% 88.68/26.79 !!) @
% 88.68/26.79 (
% 88.68/26.79 (
% 88.68/26.79 ('#S') @ (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 '#S') @
% 88.68/26.79 (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 =>))) @
% 88.68/26.79 ex1)))) @
% 88.68/26.79 (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 !!))) @
% 88.68/26.79 (
% 88.68/26.79 (
% 88.68/26.79 ('#S') @ (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 '#B') @
% 88.68/26.79 (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 '#S') @
% 88.68/26.79 (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 =>))) @
% 88.68/26.79 (
% 88.68/26.79 (
% 88.68/26.79 ('#C') @ in)))))))) @
% 88.68/26.79 (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 !!))))) @
% 88.68/26.79 (
% 88.68/26.79 (
% 88.68/26.79 ('#C') @ (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 '#B') @
% 88.68/26.79 (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 '#B') @
% 88.68/26.79 (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 '#S') @
% 88.68/26.79 (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 =>))) @
% 88.68/26.79 (
% 88.68/26.79 (
% 88.68/26.79 ('#C') @ in)))))))))) @
% 88.68/26.79 (
% 88.68/26.79 (
% 88.68/26.79 ('#S') @ (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 '#S') @
% 88.68/26.79 (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 '#B'))) @
% 88.68/26.79 (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 =>))))))) @
% 88.68/26.79 (
% 88.68/26.79 (
% 88.68/26.79 ('#C') @ (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 '#B') @
% 88.68/26.79 (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 '#S') @
% 88.68/26.79 (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 =>))))))) @
% 88.68/26.79 (
% 88.68/26.79 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 88.68/26.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl206])).
% 88.68/26.79 thf(zip_derived_cl236, plain,
% 88.68/26.79 (~ (((noeltsimpempty) =>
% 88.68/26.79 (((setbeta) =>
% 88.68/26.79 (((nonemptyE1) =>
% 88.68/26.79 (((nonemptyI) =>
% 88.68/26.79 (((nonemptyI1) =>
% 88.68/26.79 (((setadjoinIL) =>
% 88.68/26.79 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 88.68/26.79 (((setadjoinIR) =>
% 88.68/26.79 (((setadjoinE) =>
% 88.68/26.79 (((setadjoinOr) =>
% 88.68/26.79 (((setoftrueEq) =>
% 88.68/26.79 (((powersetI) =>
% 88.68/26.79 (((emptyinPowerset) =>
% 88.68/26.79 (((emptyInPowerset) =>
% 88.68/26.79 (((powersetE) =>
% 88.68/26.79 (((setunionI) =>
% 88.68/26.79 (((setunionE) =>
% 88.68/26.79 (((subPowSU) =>
% 88.68/26.79 (((exuE2) =>
% 88.68/26.79 (((nonemptyImpWitness) =>
% 88.68/26.79 (((uniqinunit) =>
% 88.68/26.79 (((notinsingleton) =>
% 88.68/26.79 (((eqinunit) =>
% 88.68/26.79 (((singletonsswitch) =>
% 88.68/26.79 (((upairsetE) =>
% 88.68/26.79 (((upairsetIL) =>
% 88.68/26.79 (((upairsetIR) =>
% 88.68/26.79 (((emptyE1) =>
% 88.68/26.79 (((vacuousDall) =>
% 88.68/26.79 (((quantDeMorgan1) =>
% 88.68/26.79 ((
% 88.68/26.79 (quantDeMorgan2) =>
% 88.68/26.79 ((
% 88.68/26.79 (quantDeMorgan3) =>
% 88.68/26.79 ((
% 88.68/26.79 (quantDeMorgan4) =>
% 88.68/26.79 ((
% 88.68/26.79 (prop2setI) =>
% 88.68/26.79 ((
% 88.68/26.79 (prop2set2propI) =>
% 88.68/26.79 ((
% 88.68/26.79 (notdexE) =>
% 88.68/26.79 ((
% 88.68/26.79 (notdallE) =>
% 88.68/26.79 ((
% 88.68/26.79 (exuI1) =>
% 88.68/26.79 ((
% 88.68/26.79 (exuI3) =>
% 88.68/26.79 ((
% 88.68/26.79 (exuI2) =>
% 88.68/26.79 ((
% 88.68/26.79 (inCongP) =>
% 88.68/26.79 ((
% 88.68/26.79 (in__Cong) =>
% 88.68/26.79 ((
% 88.68/26.79 (exuE3u) =>
% 88.68/26.79 ((
% 88.68/26.79 (exu__Cong) =>
% 88.68/26.79 ((
% 88.68/26.79 (setadjoin__Cong) =>
% 88.68/26.79 ((
% 88.68/26.79 (powerset__Cong) =>
% 88.68/26.79 ((
% 88.68/26.79 (setunion__Cong) =>
% 88.68/26.79 ((
% 88.68/26.79 (exuEu) =>
% 88.68/26.79 ((
% 88.68/26.79 (descr__Cong) =>
% 88.68/26.79 ((
% 88.68/26.79 (dsetconstr__Cong) =>
% 88.68/26.79 ((
% 88.68/26.79 (subsetI1) =>
% 88.68/26.79 ((
% 88.68/26.79 (eqimpsubset2) =>
% 88.68/26.79 ((
% 88.68/26.79 (eqimpsubset1) =>
% 88.68/26.79 ((
% 88.68/26.79 (subsetI2) =>
% 88.68/26.79 ((
% 88.68/26.79 (emptysetsubset) =>
% 88.68/26.79 ((
% 88.68/26.79 (subsetE) =>
% 88.68/26.79 ((
% 88.68/26.79 (subsetE2) =>
% 88.68/26.79 ((
% 88.68/26.79 (notsubsetI) =>
% 88.68/26.79 ((
% 88.68/26.79 (notequalI1) =>
% 88.68/26.79 ((
% 88.68/26.79 (notequalI2) =>
% 88.68/26.79 ((
% 88.68/26.79 (subsetRefl) =>
% 88.68/26.79 ((
% 88.68/26.79 (subsetTrans) =>
% 88.68/26.79 ((
% 88.68/26.79 (setadjoinSub) =>
% 88.68/26.79 ((
% 88.68/26.79 (setadjoinSub2) =>
% 88.68/26.79 ((
% 88.68/26.79 (subset2powerset) =>
% 88.68/26.79 ((
% 88.68/26.79 (setextsub) =>
% 88.68/26.79 ((
% 88.68/26.79 (subsetemptysetimpeq) =>
% 88.68/26.79 ((
% 88.68/26.79 (powersetI1) =>
% 88.68/26.79 ((
% 88.68/26.79 (powersetE1) =>
% 88.68/26.79 ((
% 88.68/26.79 (inPowerset) =>
% 88.68/26.79 ((
% 88.68/26.79 (powersetsubset) =>
% 88.68/26.79 ((
% 88.68/26.79 (sepInPowerset) =>
% 88.68/26.79 ((
% 88.68/26.79 (sepSubset) =>
% 88.68/26.79 ((
% 88.68/26.79 (binunionIL) =>
% 88.68/26.79 ((
% 88.68/26.79 (upairset2IR) =>
% 88.68/26.79 ((
% 88.68/26.79 (binunionIR) =>
% 88.68/26.79 ((
% 88.68/26.79 (binunionEcases) =>
% 88.68/26.79 ((
% 88.68/26.79 (binunionE) =>
% 88.68/26.79 ((
% 88.68/26.79 (binunionLsub) =>
% 88.68/26.79 ((
% 88.68/26.79 (binunionRsub) =>
% 88.68/26.79 ((
% 88.68/26.79 (binintersectI) =>
% 88.68/26.79 ((
% 88.68/26.79 (binintersectSubset5) =>
% 88.68/26.79 ((
% 88.68/26.79 (binintersectEL) =>
% 88.68/26.79 ((
% 88.68/26.79 (binintersectLsub) =>
% 88.68/26.79 ((
% 88.68/26.79 (binintersectSubset2) =>
% 88.68/26.79 ((
% 88.68/26.79 (binintersectSubset3) =>
% 88.68/26.79 ((
% 88.68/26.79 (binintersectER) =>
% 88.68/26.79 ((
% 88.68/26.79 (disjointsetsI1) =>
% 88.68/26.79 ((
% 88.68/26.79 (binintersectRsub) =>
% 88.68/26.79 ((
% 88.68/26.79 (binintersectSubset4) =>
% 88.68/26.79 ((
% 88.68/26.79 (binintersectSubset1) =>
% 88.68/26.79 ((
% 88.68/26.79 (bs114d) =>
% 88.68/26.79 ((
% 88.68/26.79 (setminusI) =>
% 88.68/26.79 ((
% 88.68/26.79 (setminusEL) =>
% 88.68/26.79 ((
% 88.68/26.79 (setminusER) =>
% 88.68/26.79 ((
% 88.68/26.79 (setminusSubset2) =>
% 88.68/26.79 ((
% 88.68/26.79 (setminusERneg) =>
% 88.68/26.79 ((
% 88.68/26.79 (setminusELneg) =>
% 88.68/26.79 ((
% 88.68/26.79 (setminusILneg) =>
% 88.68/26.79 ((
% 88.68/26.79 (setminusIRneg) =>
% 88.68/26.79 ((
% 88.68/26.79 (setminusLsub) =>
% 88.68/26.79 ((
% 88.68/26.79 (setminusSubset1) =>
% 88.68/26.79 ((
% 88.68/26.79 (symdiffE) =>
% 88.68/26.79 ((
% 88.68/26.79 (symdiffI1) =>
% 88.68/26.79 ((
% 88.68/26.79 (symdiffI2) =>
% 88.68/26.79 ((
% 88.68/26.79 (symdiffIneg1) =>
% 88.68/26.79 ((
% 88.68/26.79 (symdiffIneg2) =>
% 88.68/26.79 ((
% 88.68/26.79 (secondinupair) =>
% 88.68/26.79 ((
% 88.68/26.79 (setukpairIL) =>
% 88.68/26.79 ((
% 88.68/26.79 (setukpairIR) =>
% 88.68/26.79 ((
% 88.68/26.79 (kpairiskpair) =>
% 88.68/26.79 ((
% 88.68/26.79 (kpairp) =>
% 88.68/26.79 ((
% 88.68/26.79 (singletonsubset) =>
% 88.68/26.79 ((
% 88.68/26.79 (singletoninpowerset) =>
% 88.68/26.79 ((
% 88.68/26.79 (singletoninpowunion) =>
% 88.68/26.79 ((
% 88.68/26.79 (upairset2E) =>
% 88.68/26.79 ((
% 88.68/26.79 (upairsubunion) =>
% 88.68/26.79 ((
% 88.68/26.79 (upairinpowunion) =>
% 88.68/26.79 ((
% 88.68/26.79 (ubforcartprodlem1) =>
% 88.68/26.79 ((
% 88.68/26.79 (ubforcartprodlem2) =>
% 88.68/26.79 ((
% 88.68/26.79 (ubforcartprodlem3) =>
% 88.68/26.79 ((
% 88.68/26.79 (cartprodpairin) =>
% 88.68/26.79 ((
% 88.68/26.79 (cartprodmempair1) =>
% 88.68/26.79 ((
% 88.68/26.79 (cartprodmempair) =>
% 88.68/26.79 ((
% 88.68/26.79 (setunionE2) =>
% 88.68/26.79 ((
% 88.68/26.79 (setunionsingleton1) =>
% 88.68/26.79 ((
% 88.68/26.79 (setunionsingleton2) =>
% 88.68/26.79 ((
% 88.68/26.79 (setunionsingleton) =>
% 88.68/26.79 ((
% 88.68/26.79 (singletonprop) =>
% 88.68/26.79 ((
% 88.68/26.79 (ex1E1) =>
% 88.68/26.79 ((
% 88.68/26.79 (ex1I) =>
% 88.68/26.79 ((
% 88.68/26.79 (ex1I2) =>
% 88.68/26.79 ((
% 88.68/26.79 (singletonsuniq) =>
% 88.68/26.79 ((
% 88.68/26.79 (setukpairinjL1) =>
% 88.68/26.79 ((
% 88.68/26.79 (kfstsingleton) =>
% 88.68/26.79 ((
% 88.68/26.79 (theprop) =>
% 88.68/26.79 ((
% 88.68/26.79 (kfstpairEq) =>
% 88.68/26.79 ((
% 88.68/26.79 (cartprodfstin) =>
% 88.68/26.79 ((
% 88.68/26.79 (setukpairinjL2) =>
% 88.68/26.79 ((
% 88.68/26.79 (setukpairinjL) =>
% 88.68/26.79 ((
% 88.68/26.79 (setukpairinjR11) =>
% 88.68/26.79 ((
% 88.68/26.79 (setukpairinjR12) =>
% 88.68/26.79 ((
% 88.68/26.79 (setukpairinjR1) =>
% 88.68/26.79 ((
% 88.68/26.79 (upairequniteq) =>
% 88.68/26.79 ((
% 88.68/26.79 (setukpairinjR2) =>
% 88.68/26.79 ((
% 88.68/26.79 (setukpairinjR) =>
% 88.68/26.79 ((
% 88.68/26.79 (ksndsingleton) =>
% 88.68/26.79 ((
% 88.68/26.79 (ksndpairEq) =>
% 88.68/26.79 ((
% 88.68/26.79 (kpairsurjEq) =>
% 88.68/26.79 ((
% 88.68/26.79 (cartprodsndin) =>
% 88.68/26.79 ((
% 88.68/26.79 (cartprodpairmemEL) =>
% 88.68/26.79 ((
% 88.68/26.79 (cartprodpairmemER) =>
% 88.68/26.79 ((
% 88.68/26.79 (cartprodmempaircEq) =>
% 88.68/26.79 ((
% 88.68/26.79 (cartprodfstpairEq) =>
% 88.68/26.79 ((
% 88.68/26.79 (cartprodsndpairEq) =>
% 88.68/26.79 ((
% 88.68/26.79 (cartprodpairsurjEq) =>
% 88.68/26.79 ((
% 88.68/26.79 (dpsetconstrI) =>
% 88.68/26.79 ((
% 88.68/26.79 (dpsetconstrSub) =>
% 88.68/26.79 ((
% 88.68/26.79 (setOfPairsIsBReln) =>
% 88.68/26.79 ((
% 88.68/26.79 (dpsetconstrERa) =>
% 88.68/26.79 ((
% 88.68/26.79 (dpsetconstrEL1) =>
% 88.68/26.79 ((
% 88.68/26.79 (dpsetconstrEL2) =>
% 88.68/26.79 ((
% 88.68/26.79 (dpsetconstrER) =>
% 88.68/26.79 ((
% 88.68/26.79 (funcImageSingleton) =>
% 88.68/26.79 ((
% 88.68/26.79 (apProp) =>
% 88.68/26.79 ((
% 88.68/26.79 (app) =>
% 88.68/26.79 ((
% 88.68/26.79 (infuncsetfunc) =>
% 88.68/26.79 ((
% 88.68/26.79 (ap2p) =>
% 88.68/26.79 ((
% 88.68/26.79 (funcinfuncset) =>
% 88.68/26.79 ((
% 88.68/26.79 (lamProp) =>
% 88.68/26.79 ((
% 88.68/26.79 (lamp) =>
% 88.68/26.79 ((
% 88.68/26.79 (lam2p) =>
% 88.68/26.79 ((
% 88.68/26.79 (brelnall1) =>
% 88.68/26.79 ((
% 88.68/26.79 (brelnall2) =>
% 88.68/26.79 ((
% 88.68/26.79 (!!) @ (
% 88.68/26.79 (('#B') @ (
% 88.68/26.79 !!) @
% 88.68/26.79 (
% 88.68/26.79 (
% 88.68/26.79 ('#S') @ (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 '#S') @
% 88.68/26.79 (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 =>))) @
% 88.68/26.79 ex1)))) @
% 88.68/26.79 (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 !!))) @
% 88.68/26.79 (
% 88.68/26.79 (
% 88.68/26.79 ('#S') @ (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 '#B') @
% 88.68/26.79 (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 '#S') @
% 88.68/26.79 (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 =>))) @
% 88.68/26.79 (
% 88.68/26.79 (
% 88.68/26.79 ('#C') @ in)))))))) @
% 88.68/26.79 (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 !!))))) @
% 88.68/26.79 (
% 88.68/26.79 (
% 88.68/26.79 ('#C') @ (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 '#B') @
% 88.68/26.79 (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 '#B') @
% 88.68/26.79 (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 '#S') @
% 88.68/26.79 (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 =>))) @
% 88.68/26.79 (
% 88.68/26.79 (
% 88.68/26.79 ('#C') @ in)))))))))) @
% 88.68/26.79 (
% 88.68/26.79 (
% 88.68/26.79 ('#S') @ (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 '#S') @
% 88.68/26.79 (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 '#B'))) @
% 88.68/26.79 (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 =>))))))) @
% 88.68/26.79 (
% 88.68/26.79 (
% 88.68/26.79 ('#C') @ (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 '#B') @
% 88.68/26.79 (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 '#S') @
% 88.68/26.79 (
% 88.68/26.79 (
% 88.68/26.79 ('#B') @ (
% 88.68/26.79 =>))))))) @
% 88.68/26.79 (
% 88.68/26.79 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 88.68/26.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl222])).
% 88.68/26.79 thf(zip_derived_cl251, plain,
% 88.68/26.79 (~ (((setbeta) =>
% 88.68/26.79 (((nonemptyE1) =>
% 88.68/26.79 (((nonemptyI) =>
% 88.68/26.79 (((nonemptyI1) =>
% 88.68/26.79 (((setadjoinIL) =>
% 88.68/26.79 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 88.68/26.79 (((setadjoinIR) =>
% 88.68/26.79 (((setadjoinE) =>
% 88.68/26.79 (((setadjoinOr) =>
% 88.68/26.79 (((setoftrueEq) =>
% 88.68/26.79 (((powersetI) =>
% 88.68/26.79 (((emptyinPowerset) =>
% 88.68/26.79 (((emptyInPowerset) =>
% 88.68/26.79 (((powersetE) =>
% 88.68/26.79 (((setunionI) =>
% 88.68/26.79 (((setunionE) =>
% 88.68/26.79 (((subPowSU) =>
% 88.68/26.79 (((exuE2) =>
% 88.68/26.79 (((nonemptyImpWitness) =>
% 88.68/26.79 (((uniqinunit) =>
% 88.68/26.79 (((notinsingleton) =>
% 88.68/26.79 (((eqinunit) =>
% 88.68/26.79 (((singletonsswitch) =>
% 88.68/26.79 (((upairsetE) =>
% 88.68/26.79 (((upairsetIL) =>
% 88.68/26.79 (((upairsetIR) =>
% 88.68/26.79 (((emptyE1) =>
% 88.68/26.79 (((vacuousDall) =>
% 88.68/26.79 (((quantDeMorgan1) =>
% 88.68/26.79 (((quantDeMorgan2) =>
% 88.68/26.79 ((
% 88.68/26.79 (quantDeMorgan3) =>
% 88.68/26.79 ((
% 88.68/26.79 (quantDeMorgan4) =>
% 88.68/26.79 ((
% 88.68/26.79 (prop2setI) =>
% 88.68/26.79 ((
% 88.68/26.79 (prop2set2propI) =>
% 88.68/26.79 ((
% 88.68/26.79 (notdexE) =>
% 88.68/26.79 ((
% 88.68/26.79 (notdallE) =>
% 88.68/26.79 ((
% 88.68/26.79 (exuI1) =>
% 88.68/26.79 ((
% 88.68/26.79 (exuI3) =>
% 88.68/26.79 ((
% 88.68/26.79 (exuI2) =>
% 88.68/26.79 ((
% 88.68/26.79 (inCongP) =>
% 88.68/26.79 ((
% 88.68/26.79 (in__Cong) =>
% 88.68/26.79 ((
% 88.68/26.79 (exuE3u) =>
% 88.68/26.79 ((
% 88.68/26.79 (exu__Cong) =>
% 88.68/26.79 ((
% 88.68/26.79 (setadjoin__Cong) =>
% 88.68/26.79 ((
% 88.68/26.79 (powerset__Cong) =>
% 88.68/26.79 ((
% 88.68/26.79 (setunion__Cong) =>
% 88.68/26.79 ((
% 88.68/26.79 (exuEu) =>
% 88.68/26.79 ((
% 88.68/26.79 (descr__Cong) =>
% 88.68/26.79 ((
% 88.68/26.79 (dsetconstr__Cong) =>
% 88.68/26.79 ((
% 88.68/26.79 (subsetI1) =>
% 88.68/26.79 ((
% 88.68/26.79 (eqimpsubset2) =>
% 88.68/26.79 ((
% 88.68/26.79 (eqimpsubset1) =>
% 88.68/26.79 ((
% 88.68/26.79 (subsetI2) =>
% 88.68/26.79 ((
% 88.68/26.79 (emptysetsubset) =>
% 88.68/26.79 ((
% 88.68/26.79 (subsetE) =>
% 88.68/26.79 ((
% 88.68/26.79 (subsetE2) =>
% 88.68/26.79 ((
% 88.68/26.79 (notsubsetI) =>
% 88.68/26.79 ((
% 88.68/26.79 (notequalI1) =>
% 88.68/26.79 ((
% 88.68/26.79 (notequalI2) =>
% 88.68/26.79 ((
% 88.68/26.79 (subsetRefl) =>
% 88.68/26.79 ((
% 88.68/26.79 (subsetTrans) =>
% 88.68/26.79 ((
% 88.68/26.79 (setadjoinSub) =>
% 88.68/26.79 ((
% 88.68/26.79 (setadjoinSub2) =>
% 88.68/26.79 ((
% 88.68/26.79 (subset2powerset) =>
% 88.68/26.79 ((
% 88.68/26.79 (setextsub) =>
% 88.68/26.79 ((
% 88.68/26.79 (subsetemptysetimpeq) =>
% 88.68/26.79 ((
% 88.68/26.79 (powersetI1) =>
% 88.68/26.79 ((
% 88.68/26.79 (powersetE1) =>
% 88.68/26.79 ((
% 88.68/26.79 (inPowerset) =>
% 88.68/26.79 ((
% 88.68/26.79 (powersetsubset) =>
% 88.68/26.79 ((
% 88.68/26.79 (sepInPowerset) =>
% 88.68/26.79 ((
% 88.68/26.79 (sepSubset) =>
% 88.68/26.79 ((
% 88.68/26.79 (binunionIL) =>
% 88.68/26.79 ((
% 88.68/26.79 (upairset2IR) =>
% 88.68/26.79 ((
% 88.68/26.79 (binunionIR) =>
% 88.68/26.79 ((
% 88.68/26.79 (binunionEcases) =>
% 88.68/26.79 ((
% 88.68/26.79 (binunionE) =>
% 88.68/26.79 ((
% 88.68/26.79 (binunionLsub) =>
% 88.68/26.79 ((
% 88.68/26.79 (binunionRsub) =>
% 88.68/26.79 ((
% 88.68/26.79 (binintersectI) =>
% 88.68/26.79 ((
% 88.68/26.79 (binintersectSubset5) =>
% 88.68/26.79 ((
% 88.68/26.79 (binintersectEL) =>
% 88.68/26.79 ((
% 88.68/26.79 (binintersectLsub) =>
% 88.68/26.79 ((
% 88.68/26.79 (binintersectSubset2) =>
% 88.68/26.79 ((
% 88.68/26.79 (binintersectSubset3) =>
% 88.68/26.79 ((
% 88.68/26.79 (binintersectER) =>
% 88.68/26.79 ((
% 88.68/26.79 (disjointsetsI1) =>
% 88.68/26.79 ((
% 88.68/26.79 (binintersectRsub) =>
% 88.68/26.79 ((
% 88.68/26.79 (binintersectSubset4) =>
% 88.68/26.79 ((
% 88.68/26.79 (binintersectSubset1) =>
% 88.68/26.79 ((
% 88.68/26.79 (bs114d) =>
% 88.68/26.79 ((
% 88.68/26.79 (setminusI) =>
% 88.68/26.79 ((
% 88.68/26.79 (setminusEL) =>
% 88.68/26.79 ((
% 88.68/26.79 (setminusER) =>
% 88.68/26.79 ((
% 88.68/26.79 (setminusSubset2) =>
% 88.68/26.79 ((
% 88.68/26.79 (setminusERneg) =>
% 88.68/26.79 ((
% 88.68/26.79 (setminusELneg) =>
% 88.68/26.79 ((
% 88.68/26.79 (setminusILneg) =>
% 88.68/26.79 ((
% 88.68/26.79 (setminusIRneg) =>
% 88.68/26.79 ((
% 88.68/26.79 (setminusLsub) =>
% 88.68/26.79 ((
% 88.68/26.79 (setminusSubset1) =>
% 88.68/26.79 ((
% 88.68/26.79 (symdiffE) =>
% 88.68/26.79 ((
% 88.68/26.79 (symdiffI1) =>
% 88.68/26.79 ((
% 88.68/26.79 (symdiffI2) =>
% 88.68/26.79 ((
% 88.68/26.79 (symdiffIneg1) =>
% 88.68/26.79 ((
% 88.68/26.79 (symdiffIneg2) =>
% 88.68/26.79 ((
% 88.68/26.79 (secondinupair) =>
% 88.68/26.79 ((
% 88.68/26.79 (setukpairIL) =>
% 88.68/26.79 ((
% 88.68/26.79 (setukpairIR) =>
% 88.68/26.79 ((
% 88.68/26.79 (kpairiskpair) =>
% 88.68/26.79 ((
% 88.68/26.79 (kpairp) =>
% 88.68/26.79 ((
% 88.68/26.79 (singletonsubset) =>
% 88.68/26.79 ((
% 88.68/26.79 (singletoninpowerset) =>
% 88.68/26.79 ((
% 88.68/26.79 (singletoninpowunion) =>
% 88.68/26.79 ((
% 88.68/26.79 (upairset2E) =>
% 88.68/26.79 ((
% 88.68/26.79 (upairsubunion) =>
% 88.68/26.79 ((
% 88.68/26.79 (upairinpowunion) =>
% 88.68/26.79 ((
% 88.68/26.79 (ubforcartprodlem1) =>
% 88.68/26.79 ((
% 88.68/26.79 (ubforcartprodlem2) =>
% 88.68/26.79 ((
% 88.68/26.79 (ubforcartprodlem3) =>
% 88.68/26.79 ((
% 88.68/26.79 (cartprodpairin) =>
% 88.68/26.79 ((
% 88.68/26.79 (cartprodmempair1) =>
% 88.68/26.79 ((
% 88.68/26.79 (cartprodmempair) =>
% 88.68/26.79 ((
% 88.68/26.79 (setunionE2) =>
% 88.68/26.79 ((
% 88.68/26.79 (setunionsingleton1) =>
% 88.68/26.79 ((
% 88.68/26.79 (setunionsingleton2) =>
% 88.68/26.79 ((
% 88.68/26.79 (setunionsingleton) =>
% 88.68/26.79 ((
% 88.68/26.79 (singletonprop) =>
% 88.68/26.79 ((
% 88.68/26.79 (ex1E1) =>
% 88.68/26.79 ((
% 88.68/26.79 (ex1I) =>
% 88.68/26.79 ((
% 88.68/26.79 (ex1I2) =>
% 88.68/26.79 ((
% 88.68/26.79 (singletonsuniq) =>
% 88.68/26.79 ((
% 88.68/26.79 (setukpairinjL1) =>
% 88.68/26.79 ((
% 88.68/26.79 (kfstsingleton) =>
% 88.68/26.79 ((
% 88.68/26.79 (theprop) =>
% 88.68/26.79 ((
% 88.68/26.79 (kfstpairEq) =>
% 88.68/26.79 ((
% 88.68/26.79 (cartprodfstin) =>
% 88.68/26.79 ((
% 88.68/26.79 (setukpairinjL2) =>
% 88.68/26.79 ((
% 88.68/26.79 (setukpairinjL) =>
% 88.68/26.79 ((
% 88.68/26.79 (setukpairinjR11) =>
% 88.68/26.79 ((
% 88.68/26.79 (setukpairinjR12) =>
% 88.68/26.79 ((
% 88.68/26.79 (setukpairinjR1) =>
% 88.68/26.79 ((
% 88.68/26.79 (upairequniteq) =>
% 88.68/26.79 ((
% 88.68/26.79 (setukpairinjR2) =>
% 88.68/26.79 ((
% 88.68/26.79 (setukpairinjR) =>
% 88.68/26.79 ((
% 88.68/26.79 (ksndsingleton) =>
% 88.68/26.79 ((
% 88.68/26.79 (ksndpairEq) =>
% 88.68/26.79 ((
% 88.68/26.79 (kpairsurjEq) =>
% 88.68/26.79 ((
% 88.68/26.79 (cartprodsndin) =>
% 88.68/26.79 ((
% 88.68/26.79 (cartprodpairmemEL) =>
% 88.68/26.79 ((
% 88.68/26.79 (cartprodpairmemER) =>
% 88.68/26.79 ((
% 88.68/26.79 (cartprodmempaircEq) =>
% 88.68/26.79 ((
% 88.68/26.79 (cartprodfstpairEq) =>
% 88.68/26.79 ((
% 88.68/26.79 (cartprodsndpairEq) =>
% 88.68/26.79 ((
% 88.68/26.79 (cartprodpairsurjEq) =>
% 88.68/26.79 ((
% 88.68/26.79 (dpsetconstrI) =>
% 88.68/26.79 ((
% 88.68/26.79 (dpsetconstrSub) =>
% 88.68/26.79 ((
% 88.68/26.79 (setOfPairsIsBReln) =>
% 88.68/26.79 ((
% 88.68/26.79 (dpsetconstrERa) =>
% 88.68/26.79 ((
% 88.68/26.79 (dpsetconstrEL1) =>
% 88.68/26.79 ((
% 88.68/26.79 (dpsetconstrEL2) =>
% 88.68/26.79 ((
% 88.68/26.79 (dpsetconstrER) =>
% 88.68/26.79 ((
% 88.68/26.79 (funcImageSingleton) =>
% 88.68/26.79 ((
% 88.68/26.79 (apProp) =>
% 88.68/26.79 ((
% 88.68/26.80 (app) =>
% 88.68/26.80 ((
% 88.68/26.80 (infuncsetfunc) =>
% 88.68/26.80 ((
% 88.68/26.80 (ap2p) =>
% 88.68/26.80 ((
% 88.68/26.80 (funcinfuncset) =>
% 88.68/26.80 ((
% 88.68/26.80 (lamProp) =>
% 88.68/26.80 ((
% 88.68/26.80 (lamp) =>
% 88.68/26.80 ((
% 88.68/26.80 (lam2p) =>
% 88.68/26.80 ((
% 88.68/26.80 (brelnall1) =>
% 88.68/26.80 ((
% 88.68/26.80 (brelnall2) =>
% 88.68/26.80 ((
% 88.68/26.80 (!!) @ (
% 88.68/26.80 (('#B') @ (
% 88.68/26.80 !!) @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#S') @ (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 '#S') @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 =>))) @
% 88.68/26.80 ex1)))) @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 !!))) @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#S') @ (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 '#B') @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 '#S') @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 =>))) @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#C') @ in)))))))) @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 !!))))) @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#C') @ (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 '#B') @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 '#B') @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 '#S') @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 =>))) @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#C') @ in)))))))))) @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#S') @ (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 '#S') @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 '#B'))) @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 =>))))))) @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#C') @ (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 '#B') @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 '#S') @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 =>))))))) @
% 88.68/26.80 (
% 88.68/26.80 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 88.68/26.80 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl236])).
% 88.68/26.80 thf(zip_derived_cl264, plain,
% 88.68/26.80 (~ (((nonemptyE1) =>
% 88.68/26.80 (((nonemptyI) =>
% 88.68/26.80 (((nonemptyI1) =>
% 88.68/26.80 (((setadjoinIL) =>
% 88.68/26.80 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 88.68/26.80 (((setadjoinIR) =>
% 88.68/26.80 (((setadjoinE) =>
% 88.68/26.80 (((setadjoinOr) =>
% 88.68/26.80 (((setoftrueEq) =>
% 88.68/26.80 (((powersetI) =>
% 88.68/26.80 (((emptyinPowerset) =>
% 88.68/26.80 (((emptyInPowerset) =>
% 88.68/26.80 (((powersetE) =>
% 88.68/26.80 (((setunionI) =>
% 88.68/26.80 (((setunionE) =>
% 88.68/26.80 (((subPowSU) =>
% 88.68/26.80 (((exuE2) =>
% 88.68/26.80 (((nonemptyImpWitness) =>
% 88.68/26.80 (((uniqinunit) =>
% 88.68/26.80 (((notinsingleton) =>
% 88.68/26.80 (((eqinunit) =>
% 88.68/26.80 (((singletonsswitch) =>
% 88.68/26.80 (((upairsetE) =>
% 88.68/26.80 (((upairsetIL) =>
% 88.68/26.80 (((upairsetIR) =>
% 88.68/26.80 (((emptyE1) =>
% 88.68/26.80 (((vacuousDall) =>
% 88.68/26.80 (((quantDeMorgan1) =>
% 88.68/26.80 (((quantDeMorgan2) =>
% 88.68/26.80 (((quantDeMorgan3) =>
% 88.68/26.80 ((
% 88.68/26.80 (quantDeMorgan4) =>
% 88.68/26.80 ((
% 88.68/26.80 (prop2setI) =>
% 88.68/26.80 ((
% 88.68/26.80 (prop2set2propI) =>
% 88.68/26.80 ((
% 88.68/26.80 (notdexE) =>
% 88.68/26.80 ((
% 88.68/26.80 (notdallE) =>
% 88.68/26.80 ((
% 88.68/26.80 (exuI1) =>
% 88.68/26.80 ((
% 88.68/26.80 (exuI3) =>
% 88.68/26.80 ((
% 88.68/26.80 (exuI2) =>
% 88.68/26.80 ((
% 88.68/26.80 (inCongP) =>
% 88.68/26.80 ((
% 88.68/26.80 (in__Cong) =>
% 88.68/26.80 ((
% 88.68/26.80 (exuE3u) =>
% 88.68/26.80 ((
% 88.68/26.80 (exu__Cong) =>
% 88.68/26.80 ((
% 88.68/26.80 (setadjoin__Cong) =>
% 88.68/26.80 ((
% 88.68/26.80 (powerset__Cong) =>
% 88.68/26.80 ((
% 88.68/26.80 (setunion__Cong) =>
% 88.68/26.80 ((
% 88.68/26.80 (exuEu) =>
% 88.68/26.80 ((
% 88.68/26.80 (descr__Cong) =>
% 88.68/26.80 ((
% 88.68/26.80 (dsetconstr__Cong) =>
% 88.68/26.80 ((
% 88.68/26.80 (subsetI1) =>
% 88.68/26.80 ((
% 88.68/26.80 (eqimpsubset2) =>
% 88.68/26.80 ((
% 88.68/26.80 (eqimpsubset1) =>
% 88.68/26.80 ((
% 88.68/26.80 (subsetI2) =>
% 88.68/26.80 ((
% 88.68/26.80 (emptysetsubset) =>
% 88.68/26.80 ((
% 88.68/26.80 (subsetE) =>
% 88.68/26.80 ((
% 88.68/26.80 (subsetE2) =>
% 88.68/26.80 ((
% 88.68/26.80 (notsubsetI) =>
% 88.68/26.80 ((
% 88.68/26.80 (notequalI1) =>
% 88.68/26.80 ((
% 88.68/26.80 (notequalI2) =>
% 88.68/26.80 ((
% 88.68/26.80 (subsetRefl) =>
% 88.68/26.80 ((
% 88.68/26.80 (subsetTrans) =>
% 88.68/26.80 ((
% 88.68/26.80 (setadjoinSub) =>
% 88.68/26.80 ((
% 88.68/26.80 (setadjoinSub2) =>
% 88.68/26.80 ((
% 88.68/26.80 (subset2powerset) =>
% 88.68/26.80 ((
% 88.68/26.80 (setextsub) =>
% 88.68/26.80 ((
% 88.68/26.80 (subsetemptysetimpeq) =>
% 88.68/26.80 ((
% 88.68/26.80 (powersetI1) =>
% 88.68/26.80 ((
% 88.68/26.80 (powersetE1) =>
% 88.68/26.80 ((
% 88.68/26.80 (inPowerset) =>
% 88.68/26.80 ((
% 88.68/26.80 (powersetsubset) =>
% 88.68/26.80 ((
% 88.68/26.80 (sepInPowerset) =>
% 88.68/26.80 ((
% 88.68/26.80 (sepSubset) =>
% 88.68/26.80 ((
% 88.68/26.80 (binunionIL) =>
% 88.68/26.80 ((
% 88.68/26.80 (upairset2IR) =>
% 88.68/26.80 ((
% 88.68/26.80 (binunionIR) =>
% 88.68/26.80 ((
% 88.68/26.80 (binunionEcases) =>
% 88.68/26.80 ((
% 88.68/26.80 (binunionE) =>
% 88.68/26.80 ((
% 88.68/26.80 (binunionLsub) =>
% 88.68/26.80 ((
% 88.68/26.80 (binunionRsub) =>
% 88.68/26.80 ((
% 88.68/26.80 (binintersectI) =>
% 88.68/26.80 ((
% 88.68/26.80 (binintersectSubset5) =>
% 88.68/26.80 ((
% 88.68/26.80 (binintersectEL) =>
% 88.68/26.80 ((
% 88.68/26.80 (binintersectLsub) =>
% 88.68/26.80 ((
% 88.68/26.80 (binintersectSubset2) =>
% 88.68/26.80 ((
% 88.68/26.80 (binintersectSubset3) =>
% 88.68/26.80 ((
% 88.68/26.80 (binintersectER) =>
% 88.68/26.80 ((
% 88.68/26.80 (disjointsetsI1) =>
% 88.68/26.80 ((
% 88.68/26.80 (binintersectRsub) =>
% 88.68/26.80 ((
% 88.68/26.80 (binintersectSubset4) =>
% 88.68/26.80 ((
% 88.68/26.80 (binintersectSubset1) =>
% 88.68/26.80 ((
% 88.68/26.80 (bs114d) =>
% 88.68/26.80 ((
% 88.68/26.80 (setminusI) =>
% 88.68/26.80 ((
% 88.68/26.80 (setminusEL) =>
% 88.68/26.80 ((
% 88.68/26.80 (setminusER) =>
% 88.68/26.80 ((
% 88.68/26.80 (setminusSubset2) =>
% 88.68/26.80 ((
% 88.68/26.80 (setminusERneg) =>
% 88.68/26.80 ((
% 88.68/26.80 (setminusELneg) =>
% 88.68/26.80 ((
% 88.68/26.80 (setminusILneg) =>
% 88.68/26.80 ((
% 88.68/26.80 (setminusIRneg) =>
% 88.68/26.80 ((
% 88.68/26.80 (setminusLsub) =>
% 88.68/26.80 ((
% 88.68/26.80 (setminusSubset1) =>
% 88.68/26.80 ((
% 88.68/26.80 (symdiffE) =>
% 88.68/26.80 ((
% 88.68/26.80 (symdiffI1) =>
% 88.68/26.80 ((
% 88.68/26.80 (symdiffI2) =>
% 88.68/26.80 ((
% 88.68/26.80 (symdiffIneg1) =>
% 88.68/26.80 ((
% 88.68/26.80 (symdiffIneg2) =>
% 88.68/26.80 ((
% 88.68/26.80 (secondinupair) =>
% 88.68/26.80 ((
% 88.68/26.80 (setukpairIL) =>
% 88.68/26.80 ((
% 88.68/26.80 (setukpairIR) =>
% 88.68/26.80 ((
% 88.68/26.80 (kpairiskpair) =>
% 88.68/26.80 ((
% 88.68/26.80 (kpairp) =>
% 88.68/26.80 ((
% 88.68/26.80 (singletonsubset) =>
% 88.68/26.80 ((
% 88.68/26.80 (singletoninpowerset) =>
% 88.68/26.80 ((
% 88.68/26.80 (singletoninpowunion) =>
% 88.68/26.80 ((
% 88.68/26.80 (upairset2E) =>
% 88.68/26.80 ((
% 88.68/26.80 (upairsubunion) =>
% 88.68/26.80 ((
% 88.68/26.80 (upairinpowunion) =>
% 88.68/26.80 ((
% 88.68/26.80 (ubforcartprodlem1) =>
% 88.68/26.80 ((
% 88.68/26.80 (ubforcartprodlem2) =>
% 88.68/26.80 ((
% 88.68/26.80 (ubforcartprodlem3) =>
% 88.68/26.80 ((
% 88.68/26.80 (cartprodpairin) =>
% 88.68/26.80 ((
% 88.68/26.80 (cartprodmempair1) =>
% 88.68/26.80 ((
% 88.68/26.80 (cartprodmempair) =>
% 88.68/26.80 ((
% 88.68/26.80 (setunionE2) =>
% 88.68/26.80 ((
% 88.68/26.80 (setunionsingleton1) =>
% 88.68/26.80 ((
% 88.68/26.80 (setunionsingleton2) =>
% 88.68/26.80 ((
% 88.68/26.80 (setunionsingleton) =>
% 88.68/26.80 ((
% 88.68/26.80 (singletonprop) =>
% 88.68/26.80 ((
% 88.68/26.80 (ex1E1) =>
% 88.68/26.80 ((
% 88.68/26.80 (ex1I) =>
% 88.68/26.80 ((
% 88.68/26.80 (ex1I2) =>
% 88.68/26.80 ((
% 88.68/26.80 (singletonsuniq) =>
% 88.68/26.80 ((
% 88.68/26.80 (setukpairinjL1) =>
% 88.68/26.80 ((
% 88.68/26.80 (kfstsingleton) =>
% 88.68/26.80 ((
% 88.68/26.80 (theprop) =>
% 88.68/26.80 ((
% 88.68/26.80 (kfstpairEq) =>
% 88.68/26.80 ((
% 88.68/26.80 (cartprodfstin) =>
% 88.68/26.80 ((
% 88.68/26.80 (setukpairinjL2) =>
% 88.68/26.80 ((
% 88.68/26.80 (setukpairinjL) =>
% 88.68/26.80 ((
% 88.68/26.80 (setukpairinjR11) =>
% 88.68/26.80 ((
% 88.68/26.80 (setukpairinjR12) =>
% 88.68/26.80 ((
% 88.68/26.80 (setukpairinjR1) =>
% 88.68/26.80 ((
% 88.68/26.80 (upairequniteq) =>
% 88.68/26.80 ((
% 88.68/26.80 (setukpairinjR2) =>
% 88.68/26.80 ((
% 88.68/26.80 (setukpairinjR) =>
% 88.68/26.80 ((
% 88.68/26.80 (ksndsingleton) =>
% 88.68/26.80 ((
% 88.68/26.80 (ksndpairEq) =>
% 88.68/26.80 ((
% 88.68/26.80 (kpairsurjEq) =>
% 88.68/26.80 ((
% 88.68/26.80 (cartprodsndin) =>
% 88.68/26.80 ((
% 88.68/26.80 (cartprodpairmemEL) =>
% 88.68/26.80 ((
% 88.68/26.80 (cartprodpairmemER) =>
% 88.68/26.80 ((
% 88.68/26.80 (cartprodmempaircEq) =>
% 88.68/26.80 ((
% 88.68/26.80 (cartprodfstpairEq) =>
% 88.68/26.80 ((
% 88.68/26.80 (cartprodsndpairEq) =>
% 88.68/26.80 ((
% 88.68/26.80 (cartprodpairsurjEq) =>
% 88.68/26.80 ((
% 88.68/26.80 (dpsetconstrI) =>
% 88.68/26.80 ((
% 88.68/26.80 (dpsetconstrSub) =>
% 88.68/26.80 ((
% 88.68/26.80 (setOfPairsIsBReln) =>
% 88.68/26.80 ((
% 88.68/26.80 (dpsetconstrERa) =>
% 88.68/26.80 ((
% 88.68/26.80 (dpsetconstrEL1) =>
% 88.68/26.80 ((
% 88.68/26.80 (dpsetconstrEL2) =>
% 88.68/26.80 ((
% 88.68/26.80 (dpsetconstrER) =>
% 88.68/26.80 ((
% 88.68/26.80 (funcImageSingleton) =>
% 88.68/26.80 ((
% 88.68/26.80 (apProp) =>
% 88.68/26.80 ((
% 88.68/26.80 (app) =>
% 88.68/26.80 ((
% 88.68/26.80 (infuncsetfunc) =>
% 88.68/26.80 ((
% 88.68/26.80 (ap2p) =>
% 88.68/26.80 ((
% 88.68/26.80 (funcinfuncset) =>
% 88.68/26.80 ((
% 88.68/26.80 (lamProp) =>
% 88.68/26.80 ((
% 88.68/26.80 (lamp) =>
% 88.68/26.80 ((
% 88.68/26.80 (lam2p) =>
% 88.68/26.80 ((
% 88.68/26.80 (brelnall1) =>
% 88.68/26.80 ((
% 88.68/26.80 (brelnall2) =>
% 88.68/26.80 ((
% 88.68/26.80 (!!) @ (
% 88.68/26.80 (('#B') @ (
% 88.68/26.80 !!) @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#S') @ (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 '#S') @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 =>))) @
% 88.68/26.80 ex1)))) @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 !!))) @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#S') @ (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 '#B') @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 '#S') @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 =>))) @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#C') @ in)))))))) @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 !!))))) @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#C') @ (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 '#B') @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 '#B') @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 '#S') @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 =>))) @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#C') @ in)))))))))) @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#S') @ (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 '#S') @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 '#B'))) @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 =>))))))) @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#C') @ (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 '#B') @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 '#S') @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 =>))))))) @
% 88.68/26.80 (
% 88.68/26.80 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 88.68/26.80 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl251])).
% 88.68/26.80 thf(zip_derived_cl280, plain,
% 88.68/26.80 (~ (((nonemptyI) =>
% 88.68/26.80 (((nonemptyI1) =>
% 88.68/26.80 (((setadjoinIL) =>
% 88.68/26.80 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 88.68/26.80 (((setadjoinIR) =>
% 88.68/26.80 (((setadjoinE) =>
% 88.68/26.80 (((setadjoinOr) =>
% 88.68/26.80 (((setoftrueEq) =>
% 88.68/26.80 (((powersetI) =>
% 88.68/26.80 (((emptyinPowerset) =>
% 88.68/26.80 (((emptyInPowerset) =>
% 88.68/26.80 (((powersetE) =>
% 88.68/26.80 (((setunionI) =>
% 88.68/26.80 (((setunionE) =>
% 88.68/26.80 (((subPowSU) =>
% 88.68/26.80 (((exuE2) =>
% 88.68/26.80 (((nonemptyImpWitness) =>
% 88.68/26.80 (((uniqinunit) =>
% 88.68/26.80 (((notinsingleton) =>
% 88.68/26.80 (((eqinunit) =>
% 88.68/26.80 (((singletonsswitch) =>
% 88.68/26.80 (((upairsetE) =>
% 88.68/26.80 (((upairsetIL) =>
% 88.68/26.80 (((upairsetIR) =>
% 88.68/26.80 (((emptyE1) =>
% 88.68/26.80 (((vacuousDall) =>
% 88.68/26.80 (((quantDeMorgan1) =>
% 88.68/26.80 (((quantDeMorgan2) =>
% 88.68/26.80 (((quantDeMorgan3) =>
% 88.68/26.80 (((quantDeMorgan4) =>
% 88.68/26.80 ((
% 88.68/26.80 (prop2setI) =>
% 88.68/26.80 ((
% 88.68/26.80 (prop2set2propI) =>
% 88.68/26.80 ((
% 88.68/26.80 (notdexE) =>
% 88.68/26.80 ((
% 88.68/26.80 (notdallE) =>
% 88.68/26.80 ((
% 88.68/26.80 (exuI1) =>
% 88.68/26.80 ((
% 88.68/26.80 (exuI3) =>
% 88.68/26.80 ((
% 88.68/26.80 (exuI2) =>
% 88.68/26.80 ((
% 88.68/26.80 (inCongP) =>
% 88.68/26.80 ((
% 88.68/26.80 (in__Cong) =>
% 88.68/26.80 ((
% 88.68/26.80 (exuE3u) =>
% 88.68/26.80 ((
% 88.68/26.80 (exu__Cong) =>
% 88.68/26.80 ((
% 88.68/26.80 (setadjoin__Cong) =>
% 88.68/26.80 ((
% 88.68/26.80 (powerset__Cong) =>
% 88.68/26.80 ((
% 88.68/26.80 (setunion__Cong) =>
% 88.68/26.80 ((
% 88.68/26.80 (exuEu) =>
% 88.68/26.80 ((
% 88.68/26.80 (descr__Cong) =>
% 88.68/26.80 ((
% 88.68/26.80 (dsetconstr__Cong) =>
% 88.68/26.80 ((
% 88.68/26.80 (subsetI1) =>
% 88.68/26.80 ((
% 88.68/26.80 (eqimpsubset2) =>
% 88.68/26.80 ((
% 88.68/26.80 (eqimpsubset1) =>
% 88.68/26.80 ((
% 88.68/26.80 (subsetI2) =>
% 88.68/26.80 ((
% 88.68/26.80 (emptysetsubset) =>
% 88.68/26.80 ((
% 88.68/26.80 (subsetE) =>
% 88.68/26.80 ((
% 88.68/26.80 (subsetE2) =>
% 88.68/26.80 ((
% 88.68/26.80 (notsubsetI) =>
% 88.68/26.80 ((
% 88.68/26.80 (notequalI1) =>
% 88.68/26.80 ((
% 88.68/26.80 (notequalI2) =>
% 88.68/26.80 ((
% 88.68/26.80 (subsetRefl) =>
% 88.68/26.80 ((
% 88.68/26.80 (subsetTrans) =>
% 88.68/26.80 ((
% 88.68/26.80 (setadjoinSub) =>
% 88.68/26.80 ((
% 88.68/26.80 (setadjoinSub2) =>
% 88.68/26.80 ((
% 88.68/26.80 (subset2powerset) =>
% 88.68/26.80 ((
% 88.68/26.80 (setextsub) =>
% 88.68/26.80 ((
% 88.68/26.80 (subsetemptysetimpeq) =>
% 88.68/26.80 ((
% 88.68/26.80 (powersetI1) =>
% 88.68/26.80 ((
% 88.68/26.80 (powersetE1) =>
% 88.68/26.80 ((
% 88.68/26.80 (inPowerset) =>
% 88.68/26.80 ((
% 88.68/26.80 (powersetsubset) =>
% 88.68/26.80 ((
% 88.68/26.80 (sepInPowerset) =>
% 88.68/26.80 ((
% 88.68/26.80 (sepSubset) =>
% 88.68/26.80 ((
% 88.68/26.80 (binunionIL) =>
% 88.68/26.80 ((
% 88.68/26.80 (upairset2IR) =>
% 88.68/26.80 ((
% 88.68/26.80 (binunionIR) =>
% 88.68/26.80 ((
% 88.68/26.80 (binunionEcases) =>
% 88.68/26.80 ((
% 88.68/26.80 (binunionE) =>
% 88.68/26.80 ((
% 88.68/26.80 (binunionLsub) =>
% 88.68/26.80 ((
% 88.68/26.80 (binunionRsub) =>
% 88.68/26.80 ((
% 88.68/26.80 (binintersectI) =>
% 88.68/26.80 ((
% 88.68/26.80 (binintersectSubset5) =>
% 88.68/26.80 ((
% 88.68/26.80 (binintersectEL) =>
% 88.68/26.80 ((
% 88.68/26.80 (binintersectLsub) =>
% 88.68/26.80 ((
% 88.68/26.80 (binintersectSubset2) =>
% 88.68/26.80 ((
% 88.68/26.80 (binintersectSubset3) =>
% 88.68/26.80 ((
% 88.68/26.80 (binintersectER) =>
% 88.68/26.80 ((
% 88.68/26.80 (disjointsetsI1) =>
% 88.68/26.80 ((
% 88.68/26.80 (binintersectRsub) =>
% 88.68/26.80 ((
% 88.68/26.80 (binintersectSubset4) =>
% 88.68/26.80 ((
% 88.68/26.80 (binintersectSubset1) =>
% 88.68/26.80 ((
% 88.68/26.80 (bs114d) =>
% 88.68/26.80 ((
% 88.68/26.80 (setminusI) =>
% 88.68/26.80 ((
% 88.68/26.80 (setminusEL) =>
% 88.68/26.80 ((
% 88.68/26.80 (setminusER) =>
% 88.68/26.80 ((
% 88.68/26.80 (setminusSubset2) =>
% 88.68/26.80 ((
% 88.68/26.80 (setminusERneg) =>
% 88.68/26.80 ((
% 88.68/26.80 (setminusELneg) =>
% 88.68/26.80 ((
% 88.68/26.80 (setminusILneg) =>
% 88.68/26.80 ((
% 88.68/26.80 (setminusIRneg) =>
% 88.68/26.80 ((
% 88.68/26.80 (setminusLsub) =>
% 88.68/26.80 ((
% 88.68/26.80 (setminusSubset1) =>
% 88.68/26.80 ((
% 88.68/26.80 (symdiffE) =>
% 88.68/26.80 ((
% 88.68/26.80 (symdiffI1) =>
% 88.68/26.80 ((
% 88.68/26.80 (symdiffI2) =>
% 88.68/26.80 ((
% 88.68/26.80 (symdiffIneg1) =>
% 88.68/26.80 ((
% 88.68/26.80 (symdiffIneg2) =>
% 88.68/26.80 ((
% 88.68/26.80 (secondinupair) =>
% 88.68/26.80 ((
% 88.68/26.80 (setukpairIL) =>
% 88.68/26.80 ((
% 88.68/26.80 (setukpairIR) =>
% 88.68/26.80 ((
% 88.68/26.80 (kpairiskpair) =>
% 88.68/26.80 ((
% 88.68/26.80 (kpairp) =>
% 88.68/26.80 ((
% 88.68/26.80 (singletonsubset) =>
% 88.68/26.80 ((
% 88.68/26.80 (singletoninpowerset) =>
% 88.68/26.80 ((
% 88.68/26.80 (singletoninpowunion) =>
% 88.68/26.80 ((
% 88.68/26.80 (upairset2E) =>
% 88.68/26.80 ((
% 88.68/26.80 (upairsubunion) =>
% 88.68/26.80 ((
% 88.68/26.80 (upairinpowunion) =>
% 88.68/26.80 ((
% 88.68/26.80 (ubforcartprodlem1) =>
% 88.68/26.80 ((
% 88.68/26.80 (ubforcartprodlem2) =>
% 88.68/26.80 ((
% 88.68/26.80 (ubforcartprodlem3) =>
% 88.68/26.80 ((
% 88.68/26.80 (cartprodpairin) =>
% 88.68/26.80 ((
% 88.68/26.80 (cartprodmempair1) =>
% 88.68/26.80 ((
% 88.68/26.80 (cartprodmempair) =>
% 88.68/26.80 ((
% 88.68/26.80 (setunionE2) =>
% 88.68/26.80 ((
% 88.68/26.80 (setunionsingleton1) =>
% 88.68/26.80 ((
% 88.68/26.80 (setunionsingleton2) =>
% 88.68/26.80 ((
% 88.68/26.80 (setunionsingleton) =>
% 88.68/26.80 ((
% 88.68/26.80 (singletonprop) =>
% 88.68/26.80 ((
% 88.68/26.80 (ex1E1) =>
% 88.68/26.80 ((
% 88.68/26.80 (ex1I) =>
% 88.68/26.80 ((
% 88.68/26.80 (ex1I2) =>
% 88.68/26.80 ((
% 88.68/26.80 (singletonsuniq) =>
% 88.68/26.80 ((
% 88.68/26.80 (setukpairinjL1) =>
% 88.68/26.80 ((
% 88.68/26.80 (kfstsingleton) =>
% 88.68/26.80 ((
% 88.68/26.80 (theprop) =>
% 88.68/26.80 ((
% 88.68/26.80 (kfstpairEq) =>
% 88.68/26.80 ((
% 88.68/26.80 (cartprodfstin) =>
% 88.68/26.80 ((
% 88.68/26.80 (setukpairinjL2) =>
% 88.68/26.80 ((
% 88.68/26.80 (setukpairinjL) =>
% 88.68/26.80 ((
% 88.68/26.80 (setukpairinjR11) =>
% 88.68/26.80 ((
% 88.68/26.80 (setukpairinjR12) =>
% 88.68/26.80 ((
% 88.68/26.80 (setukpairinjR1) =>
% 88.68/26.80 ((
% 88.68/26.80 (upairequniteq) =>
% 88.68/26.80 ((
% 88.68/26.80 (setukpairinjR2) =>
% 88.68/26.80 ((
% 88.68/26.80 (setukpairinjR) =>
% 88.68/26.80 ((
% 88.68/26.80 (ksndsingleton) =>
% 88.68/26.80 ((
% 88.68/26.80 (ksndpairEq) =>
% 88.68/26.80 ((
% 88.68/26.80 (kpairsurjEq) =>
% 88.68/26.80 ((
% 88.68/26.80 (cartprodsndin) =>
% 88.68/26.80 ((
% 88.68/26.80 (cartprodpairmemEL) =>
% 88.68/26.80 ((
% 88.68/26.80 (cartprodpairmemER) =>
% 88.68/26.80 ((
% 88.68/26.80 (cartprodmempaircEq) =>
% 88.68/26.80 ((
% 88.68/26.80 (cartprodfstpairEq) =>
% 88.68/26.80 ((
% 88.68/26.80 (cartprodsndpairEq) =>
% 88.68/26.80 ((
% 88.68/26.80 (cartprodpairsurjEq) =>
% 88.68/26.80 ((
% 88.68/26.80 (dpsetconstrI) =>
% 88.68/26.80 ((
% 88.68/26.80 (dpsetconstrSub) =>
% 88.68/26.80 ((
% 88.68/26.80 (setOfPairsIsBReln) =>
% 88.68/26.80 ((
% 88.68/26.80 (dpsetconstrERa) =>
% 88.68/26.80 ((
% 88.68/26.80 (dpsetconstrEL1) =>
% 88.68/26.80 ((
% 88.68/26.80 (dpsetconstrEL2) =>
% 88.68/26.80 ((
% 88.68/26.80 (dpsetconstrER) =>
% 88.68/26.80 ((
% 88.68/26.80 (funcImageSingleton) =>
% 88.68/26.80 ((
% 88.68/26.80 (apProp) =>
% 88.68/26.80 ((
% 88.68/26.80 (app) =>
% 88.68/26.80 ((
% 88.68/26.80 (infuncsetfunc) =>
% 88.68/26.80 ((
% 88.68/26.80 (ap2p) =>
% 88.68/26.80 ((
% 88.68/26.80 (funcinfuncset) =>
% 88.68/26.80 ((
% 88.68/26.80 (lamProp) =>
% 88.68/26.80 ((
% 88.68/26.80 (lamp) =>
% 88.68/26.80 ((
% 88.68/26.80 (lam2p) =>
% 88.68/26.80 ((
% 88.68/26.80 (brelnall1) =>
% 88.68/26.80 ((
% 88.68/26.80 (brelnall2) =>
% 88.68/26.80 ((
% 88.68/26.80 (!!) @ (
% 88.68/26.80 (('#B') @ (
% 88.68/26.80 !!) @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#S') @ (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 '#S') @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 =>))) @
% 88.68/26.80 ex1)))) @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 !!))) @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#S') @ (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 '#B') @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 '#S') @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 =>))) @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#C') @ in)))))))) @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 !!))))) @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#C') @ (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 '#B') @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 '#B') @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 '#S') @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 =>))) @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#C') @ in)))))))))) @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#S') @ (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 '#S') @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 '#B'))) @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 =>))))))) @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#C') @ (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 '#B') @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 '#S') @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 =>))))))) @
% 88.68/26.80 (
% 88.68/26.80 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 88.68/26.80 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl264])).
% 88.68/26.80 thf(zip_derived_cl293, plain,
% 88.68/26.80 (~ (((nonemptyI1) =>
% 88.68/26.80 (((setadjoinIL) =>
% 88.68/26.80 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 88.68/26.80 (((setadjoinIR) =>
% 88.68/26.80 (((setadjoinE) =>
% 88.68/26.80 (((setadjoinOr) =>
% 88.68/26.80 (((setoftrueEq) =>
% 88.68/26.80 (((powersetI) =>
% 88.68/26.80 (((emptyinPowerset) =>
% 88.68/26.80 (((emptyInPowerset) =>
% 88.68/26.80 (((powersetE) =>
% 88.68/26.80 (((setunionI) =>
% 88.68/26.80 (((setunionE) =>
% 88.68/26.80 (((subPowSU) =>
% 88.68/26.80 (((exuE2) =>
% 88.68/26.80 (((nonemptyImpWitness) =>
% 88.68/26.80 (((uniqinunit) =>
% 88.68/26.80 (((notinsingleton) =>
% 88.68/26.80 (((eqinunit) =>
% 88.68/26.80 (((singletonsswitch) =>
% 88.68/26.80 (((upairsetE) =>
% 88.68/26.80 (((upairsetIL) =>
% 88.68/26.80 (((upairsetIR) =>
% 88.68/26.80 (((emptyE1) =>
% 88.68/26.80 (((vacuousDall) =>
% 88.68/26.80 (((quantDeMorgan1) =>
% 88.68/26.80 (((quantDeMorgan2) =>
% 88.68/26.80 (((quantDeMorgan3) =>
% 88.68/26.80 (((quantDeMorgan4) =>
% 88.68/26.80 (((prop2setI) =>
% 88.68/26.80 ((
% 88.68/26.80 (prop2set2propI) =>
% 88.68/26.80 ((
% 88.68/26.80 (notdexE) =>
% 88.68/26.80 ((
% 88.68/26.80 (notdallE) =>
% 88.68/26.80 ((
% 88.68/26.80 (exuI1) =>
% 88.68/26.80 ((
% 88.68/26.80 (exuI3) =>
% 88.68/26.80 ((
% 88.68/26.80 (exuI2) =>
% 88.68/26.80 ((
% 88.68/26.80 (inCongP) =>
% 88.68/26.80 ((
% 88.68/26.80 (in__Cong) =>
% 88.68/26.80 ((
% 88.68/26.80 (exuE3u) =>
% 88.68/26.80 ((
% 88.68/26.80 (exu__Cong) =>
% 88.68/26.80 ((
% 88.68/26.80 (setadjoin__Cong) =>
% 88.68/26.80 ((
% 88.68/26.80 (powerset__Cong) =>
% 88.68/26.80 ((
% 88.68/26.80 (setunion__Cong) =>
% 88.68/26.80 ((
% 88.68/26.80 (exuEu) =>
% 88.68/26.80 ((
% 88.68/26.80 (descr__Cong) =>
% 88.68/26.80 ((
% 88.68/26.80 (dsetconstr__Cong) =>
% 88.68/26.80 ((
% 88.68/26.80 (subsetI1) =>
% 88.68/26.80 ((
% 88.68/26.80 (eqimpsubset2) =>
% 88.68/26.80 ((
% 88.68/26.80 (eqimpsubset1) =>
% 88.68/26.80 ((
% 88.68/26.80 (subsetI2) =>
% 88.68/26.80 ((
% 88.68/26.80 (emptysetsubset) =>
% 88.68/26.80 ((
% 88.68/26.80 (subsetE) =>
% 88.68/26.80 ((
% 88.68/26.80 (subsetE2) =>
% 88.68/26.80 ((
% 88.68/26.80 (notsubsetI) =>
% 88.68/26.80 ((
% 88.68/26.80 (notequalI1) =>
% 88.68/26.80 ((
% 88.68/26.80 (notequalI2) =>
% 88.68/26.80 ((
% 88.68/26.80 (subsetRefl) =>
% 88.68/26.80 ((
% 88.68/26.80 (subsetTrans) =>
% 88.68/26.80 ((
% 88.68/26.80 (setadjoinSub) =>
% 88.68/26.80 ((
% 88.68/26.80 (setadjoinSub2) =>
% 88.68/26.80 ((
% 88.68/26.80 (subset2powerset) =>
% 88.68/26.80 ((
% 88.68/26.80 (setextsub) =>
% 88.68/26.80 ((
% 88.68/26.80 (subsetemptysetimpeq) =>
% 88.68/26.80 ((
% 88.68/26.80 (powersetI1) =>
% 88.68/26.80 ((
% 88.68/26.80 (powersetE1) =>
% 88.68/26.80 ((
% 88.68/26.80 (inPowerset) =>
% 88.68/26.80 ((
% 88.68/26.80 (powersetsubset) =>
% 88.68/26.80 ((
% 88.68/26.80 (sepInPowerset) =>
% 88.68/26.80 ((
% 88.68/26.80 (sepSubset) =>
% 88.68/26.80 ((
% 88.68/26.80 (binunionIL) =>
% 88.68/26.80 ((
% 88.68/26.80 (upairset2IR) =>
% 88.68/26.80 ((
% 88.68/26.80 (binunionIR) =>
% 88.68/26.80 ((
% 88.68/26.80 (binunionEcases) =>
% 88.68/26.80 ((
% 88.68/26.80 (binunionE) =>
% 88.68/26.80 ((
% 88.68/26.80 (binunionLsub) =>
% 88.68/26.80 ((
% 88.68/26.80 (binunionRsub) =>
% 88.68/26.80 ((
% 88.68/26.80 (binintersectI) =>
% 88.68/26.80 ((
% 88.68/26.80 (binintersectSubset5) =>
% 88.68/26.80 ((
% 88.68/26.80 (binintersectEL) =>
% 88.68/26.80 ((
% 88.68/26.80 (binintersectLsub) =>
% 88.68/26.80 ((
% 88.68/26.80 (binintersectSubset2) =>
% 88.68/26.80 ((
% 88.68/26.80 (binintersectSubset3) =>
% 88.68/26.80 ((
% 88.68/26.80 (binintersectER) =>
% 88.68/26.80 ((
% 88.68/26.80 (disjointsetsI1) =>
% 88.68/26.80 ((
% 88.68/26.80 (binintersectRsub) =>
% 88.68/26.80 ((
% 88.68/26.80 (binintersectSubset4) =>
% 88.68/26.80 ((
% 88.68/26.80 (binintersectSubset1) =>
% 88.68/26.80 ((
% 88.68/26.80 (bs114d) =>
% 88.68/26.80 ((
% 88.68/26.80 (setminusI) =>
% 88.68/26.80 ((
% 88.68/26.80 (setminusEL) =>
% 88.68/26.80 ((
% 88.68/26.80 (setminusER) =>
% 88.68/26.80 ((
% 88.68/26.80 (setminusSubset2) =>
% 88.68/26.80 ((
% 88.68/26.80 (setminusERneg) =>
% 88.68/26.80 ((
% 88.68/26.80 (setminusELneg) =>
% 88.68/26.80 ((
% 88.68/26.80 (setminusILneg) =>
% 88.68/26.80 ((
% 88.68/26.80 (setminusIRneg) =>
% 88.68/26.80 ((
% 88.68/26.80 (setminusLsub) =>
% 88.68/26.80 ((
% 88.68/26.80 (setminusSubset1) =>
% 88.68/26.80 ((
% 88.68/26.80 (symdiffE) =>
% 88.68/26.80 ((
% 88.68/26.80 (symdiffI1) =>
% 88.68/26.80 ((
% 88.68/26.80 (symdiffI2) =>
% 88.68/26.80 ((
% 88.68/26.80 (symdiffIneg1) =>
% 88.68/26.80 ((
% 88.68/26.80 (symdiffIneg2) =>
% 88.68/26.80 ((
% 88.68/26.80 (secondinupair) =>
% 88.68/26.80 ((
% 88.68/26.80 (setukpairIL) =>
% 88.68/26.80 ((
% 88.68/26.80 (setukpairIR) =>
% 88.68/26.80 ((
% 88.68/26.80 (kpairiskpair) =>
% 88.68/26.80 ((
% 88.68/26.80 (kpairp) =>
% 88.68/26.80 ((
% 88.68/26.80 (singletonsubset) =>
% 88.68/26.80 ((
% 88.68/26.80 (singletoninpowerset) =>
% 88.68/26.80 ((
% 88.68/26.80 (singletoninpowunion) =>
% 88.68/26.80 ((
% 88.68/26.80 (upairset2E) =>
% 88.68/26.80 ((
% 88.68/26.80 (upairsubunion) =>
% 88.68/26.80 ((
% 88.68/26.80 (upairinpowunion) =>
% 88.68/26.80 ((
% 88.68/26.80 (ubforcartprodlem1) =>
% 88.68/26.80 ((
% 88.68/26.80 (ubforcartprodlem2) =>
% 88.68/26.80 ((
% 88.68/26.80 (ubforcartprodlem3) =>
% 88.68/26.80 ((
% 88.68/26.80 (cartprodpairin) =>
% 88.68/26.80 ((
% 88.68/26.80 (cartprodmempair1) =>
% 88.68/26.80 ((
% 88.68/26.80 (cartprodmempair) =>
% 88.68/26.80 ((
% 88.68/26.80 (setunionE2) =>
% 88.68/26.80 ((
% 88.68/26.80 (setunionsingleton1) =>
% 88.68/26.80 ((
% 88.68/26.80 (setunionsingleton2) =>
% 88.68/26.80 ((
% 88.68/26.80 (setunionsingleton) =>
% 88.68/26.80 ((
% 88.68/26.80 (singletonprop) =>
% 88.68/26.80 ((
% 88.68/26.80 (ex1E1) =>
% 88.68/26.80 ((
% 88.68/26.80 (ex1I) =>
% 88.68/26.80 ((
% 88.68/26.80 (ex1I2) =>
% 88.68/26.80 ((
% 88.68/26.80 (singletonsuniq) =>
% 88.68/26.80 ((
% 88.68/26.80 (setukpairinjL1) =>
% 88.68/26.80 ((
% 88.68/26.80 (kfstsingleton) =>
% 88.68/26.80 ((
% 88.68/26.80 (theprop) =>
% 88.68/26.80 ((
% 88.68/26.80 (kfstpairEq) =>
% 88.68/26.80 ((
% 88.68/26.80 (cartprodfstin) =>
% 88.68/26.80 ((
% 88.68/26.80 (setukpairinjL2) =>
% 88.68/26.80 ((
% 88.68/26.80 (setukpairinjL) =>
% 88.68/26.80 ((
% 88.68/26.80 (setukpairinjR11) =>
% 88.68/26.80 ((
% 88.68/26.80 (setukpairinjR12) =>
% 88.68/26.80 ((
% 88.68/26.80 (setukpairinjR1) =>
% 88.68/26.80 ((
% 88.68/26.80 (upairequniteq) =>
% 88.68/26.80 ((
% 88.68/26.80 (setukpairinjR2) =>
% 88.68/26.80 ((
% 88.68/26.80 (setukpairinjR) =>
% 88.68/26.80 ((
% 88.68/26.80 (ksndsingleton) =>
% 88.68/26.80 ((
% 88.68/26.80 (ksndpairEq) =>
% 88.68/26.80 ((
% 88.68/26.80 (kpairsurjEq) =>
% 88.68/26.80 ((
% 88.68/26.80 (cartprodsndin) =>
% 88.68/26.80 ((
% 88.68/26.80 (cartprodpairmemEL) =>
% 88.68/26.80 ((
% 88.68/26.80 (cartprodpairmemER) =>
% 88.68/26.80 ((
% 88.68/26.80 (cartprodmempaircEq) =>
% 88.68/26.80 ((
% 88.68/26.80 (cartprodfstpairEq) =>
% 88.68/26.80 ((
% 88.68/26.80 (cartprodsndpairEq) =>
% 88.68/26.80 ((
% 88.68/26.80 (cartprodpairsurjEq) =>
% 88.68/26.80 ((
% 88.68/26.80 (dpsetconstrI) =>
% 88.68/26.80 ((
% 88.68/26.80 (dpsetconstrSub) =>
% 88.68/26.80 ((
% 88.68/26.80 (setOfPairsIsBReln) =>
% 88.68/26.80 ((
% 88.68/26.80 (dpsetconstrERa) =>
% 88.68/26.80 ((
% 88.68/26.80 (dpsetconstrEL1) =>
% 88.68/26.80 ((
% 88.68/26.80 (dpsetconstrEL2) =>
% 88.68/26.80 ((
% 88.68/26.80 (dpsetconstrER) =>
% 88.68/26.80 ((
% 88.68/26.80 (funcImageSingleton) =>
% 88.68/26.80 ((
% 88.68/26.80 (apProp) =>
% 88.68/26.80 ((
% 88.68/26.80 (app) =>
% 88.68/26.80 ((
% 88.68/26.80 (infuncsetfunc) =>
% 88.68/26.80 ((
% 88.68/26.80 (ap2p) =>
% 88.68/26.80 ((
% 88.68/26.80 (funcinfuncset) =>
% 88.68/26.80 ((
% 88.68/26.80 (lamProp) =>
% 88.68/26.80 ((
% 88.68/26.80 (lamp) =>
% 88.68/26.80 ((
% 88.68/26.80 (lam2p) =>
% 88.68/26.80 ((
% 88.68/26.80 (brelnall1) =>
% 88.68/26.80 ((
% 88.68/26.80 (brelnall2) =>
% 88.68/26.80 ((
% 88.68/26.80 (!!) @ (
% 88.68/26.80 (('#B') @ (
% 88.68/26.80 !!) @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#S') @ (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 '#S') @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 =>))) @
% 88.68/26.80 ex1)))) @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 !!))) @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#S') @ (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 '#B') @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 '#S') @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 =>))) @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#C') @ in)))))))) @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 !!))))) @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#C') @ (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 '#B') @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 '#B') @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 '#S') @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 =>))) @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#C') @ in)))))))))) @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#S') @ (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 '#S') @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 '#B'))) @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 =>))))))) @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#C') @ (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 '#B') @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 '#S') @
% 88.68/26.80 (
% 88.68/26.80 (
% 88.68/26.80 ('#B') @ (
% 88.68/26.80 =>))))))) @
% 88.68/26.80 (
% 88.68/26.80 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 88.68/26.80 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl280])).
% 88.68/26.80 thf(zip_derived_cl307, plain,
% 88.68/26.80 (~ (((setadjoinIL) =>
% 88.68/26.80 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 88.68/26.80 (((setadjoinIR) =>
% 88.68/26.80 (((setadjoinE) =>
% 88.68/26.80 (((setadjoinOr) =>
% 88.68/26.80 (((setoftrueEq) =>
% 88.68/26.80 (((powersetI) =>
% 88.68/26.80 (((emptyinPowerset) =>
% 88.68/26.80 (((emptyInPowerset) =>
% 88.68/26.80 (((powersetE) =>
% 88.68/26.80 (((setunionI) =>
% 88.68/26.80 (((setunionE) =>
% 88.68/26.80 (((subPowSU) =>
% 88.68/26.80 (((exuE2) =>
% 88.68/26.80 (((nonemptyImpWitness) =>
% 88.68/26.80 (((uniqinunit) =>
% 88.68/26.80 (((notinsingleton) =>
% 88.68/26.80 (((eqinunit) =>
% 88.68/26.80 (((singletonsswitch) =>
% 88.68/26.80 (((upairsetE) =>
% 88.68/26.80 (((upairsetIL) =>
% 88.68/26.80 (((upairsetIR) =>
% 88.68/26.80 (((emptyE1) =>
% 88.68/26.80 (((vacuousDall) =>
% 88.68/26.80 (((quantDeMorgan1) =>
% 88.68/26.80 (((quantDeMorgan2) =>
% 88.68/26.80 (((quantDeMorgan3) =>
% 88.68/26.80 (((quantDeMorgan4) =>
% 88.68/26.80 (((prop2setI) =>
% 88.68/26.80 (((prop2set2propI) =>
% 88.68/26.80 ((
% 88.68/26.80 (notdexE) =>
% 88.68/26.80 ((
% 88.68/26.80 (notdallE) =>
% 88.68/26.80 ((
% 88.68/26.80 (exuI1) =>
% 88.68/26.80 ((
% 88.68/26.80 (exuI3) =>
% 88.68/26.80 ((
% 88.68/26.80 (exuI2) =>
% 88.68/26.80 ((
% 88.68/26.80 (inCongP) =>
% 88.68/26.80 ((
% 88.68/26.80 (in__Cong) =>
% 88.68/26.80 ((
% 88.68/26.80 (exuE3u) =>
% 88.68/26.80 ((
% 88.68/26.80 (exu__Cong) =>
% 88.68/26.80 ((
% 88.68/26.80 (setadjoin__Cong) =>
% 88.68/26.80 ((
% 88.68/26.80 (powerset__Cong) =>
% 88.68/26.80 ((
% 88.68/26.80 (setunion__Cong) =>
% 88.68/26.80 ((
% 88.68/26.80 (exuEu) =>
% 88.68/26.80 ((
% 88.68/26.80 (descr__Cong) =>
% 88.68/26.80 ((
% 88.68/26.80 (dsetconstr__Cong) =>
% 88.68/26.80 ((
% 88.68/26.80 (subsetI1) =>
% 88.68/26.80 ((
% 88.68/26.80 (eqimpsubset2) =>
% 88.68/26.80 ((
% 88.68/26.80 (eqimpsubset1) =>
% 88.68/26.80 ((
% 88.68/26.80 (subsetI2) =>
% 88.68/26.80 ((
% 88.68/26.80 (emptysetsubset) =>
% 88.68/26.80 ((
% 88.68/26.80 (subsetE) =>
% 88.68/26.80 ((
% 88.68/26.80 (subsetE2) =>
% 88.68/26.80 ((
% 88.68/26.80 (notsubsetI) =>
% 88.68/26.80 ((
% 88.68/26.80 (notequalI1) =>
% 88.68/26.80 ((
% 88.68/26.80 (notequalI2) =>
% 88.68/26.80 ((
% 88.68/26.80 (subsetRefl) =>
% 88.68/26.80 ((
% 88.68/26.80 (subsetTrans) =>
% 88.68/26.80 ((
% 88.68/26.80 (setadjoinSub) =>
% 88.68/26.80 ((
% 88.68/26.80 (setadjoinSub2) =>
% 88.68/26.80 ((
% 88.68/26.80 (subset2powerset) =>
% 88.68/26.80 ((
% 88.68/26.80 (setextsub) =>
% 88.68/26.80 ((
% 88.68/26.80 (subsetemptysetimpeq) =>
% 88.68/26.80 ((
% 88.68/26.80 (powersetI1) =>
% 88.68/26.80 ((
% 88.68/26.80 (powersetE1) =>
% 88.68/26.80 ((
% 88.68/26.80 (inPowerset) =>
% 88.68/26.80 ((
% 88.68/26.80 (powersetsubset) =>
% 88.68/26.80 ((
% 88.68/26.80 (sepInPowerset) =>
% 88.68/26.80 ((
% 88.68/26.80 (sepSubset) =>
% 88.68/26.80 ((
% 88.68/26.80 (binunionIL) =>
% 88.68/26.80 ((
% 88.68/26.80 (upairset2IR) =>
% 88.68/26.80 ((
% 88.68/26.80 (binunionIR) =>
% 88.68/26.80 ((
% 88.68/26.80 (binunionEcases) =>
% 88.68/26.80 ((
% 88.68/26.80 (binunionE) =>
% 88.68/26.80 ((
% 88.68/26.80 (binunionLsub) =>
% 88.68/26.80 ((
% 88.68/26.80 (binunionRsub) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectI) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectSubset5) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectEL) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectLsub) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectSubset2) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectSubset3) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectER) =>
% 88.68/26.81 ((
% 88.68/26.81 (disjointsetsI1) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectRsub) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectSubset4) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectSubset1) =>
% 88.68/26.81 ((
% 88.68/26.81 (bs114d) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusI) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusEL) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusER) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusSubset2) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusERneg) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusELneg) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusILneg) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusIRneg) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusLsub) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusSubset1) =>
% 88.68/26.81 ((
% 88.68/26.81 (symdiffE) =>
% 88.68/26.81 ((
% 88.68/26.81 (symdiffI1) =>
% 88.68/26.81 ((
% 88.68/26.81 (symdiffI2) =>
% 88.68/26.81 ((
% 88.68/26.81 (symdiffIneg1) =>
% 88.68/26.81 ((
% 88.68/26.81 (symdiffIneg2) =>
% 88.68/26.81 ((
% 88.68/26.81 (secondinupair) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairIL) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairIR) =>
% 88.68/26.81 ((
% 88.68/26.81 (kpairiskpair) =>
% 88.68/26.81 ((
% 88.68/26.81 (kpairp) =>
% 88.68/26.81 ((
% 88.68/26.81 (singletonsubset) =>
% 88.68/26.81 ((
% 88.68/26.81 (singletoninpowerset) =>
% 88.68/26.81 ((
% 88.68/26.81 (singletoninpowunion) =>
% 88.68/26.81 ((
% 88.68/26.81 (upairset2E) =>
% 88.68/26.81 ((
% 88.68/26.81 (upairsubunion) =>
% 88.68/26.81 ((
% 88.68/26.81 (upairinpowunion) =>
% 88.68/26.81 ((
% 88.68/26.81 (ubforcartprodlem1) =>
% 88.68/26.81 ((
% 88.68/26.81 (ubforcartprodlem2) =>
% 88.68/26.81 ((
% 88.68/26.81 (ubforcartprodlem3) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodpairin) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodmempair1) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodmempair) =>
% 88.68/26.81 ((
% 88.68/26.81 (setunionE2) =>
% 88.68/26.81 ((
% 88.68/26.81 (setunionsingleton1) =>
% 88.68/26.81 ((
% 88.68/26.81 (setunionsingleton2) =>
% 88.68/26.81 ((
% 88.68/26.81 (setunionsingleton) =>
% 88.68/26.81 ((
% 88.68/26.81 (singletonprop) =>
% 88.68/26.81 ((
% 88.68/26.81 (ex1E1) =>
% 88.68/26.81 ((
% 88.68/26.81 (ex1I) =>
% 88.68/26.81 ((
% 88.68/26.81 (ex1I2) =>
% 88.68/26.81 ((
% 88.68/26.81 (singletonsuniq) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairinjL1) =>
% 88.68/26.81 ((
% 88.68/26.81 (kfstsingleton) =>
% 88.68/26.81 ((
% 88.68/26.81 (theprop) =>
% 88.68/26.81 ((
% 88.68/26.81 (kfstpairEq) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodfstin) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairinjL2) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairinjL) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairinjR11) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairinjR12) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairinjR1) =>
% 88.68/26.81 ((
% 88.68/26.81 (upairequniteq) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairinjR2) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairinjR) =>
% 88.68/26.81 ((
% 88.68/26.81 (ksndsingleton) =>
% 88.68/26.81 ((
% 88.68/26.81 (ksndpairEq) =>
% 88.68/26.81 ((
% 88.68/26.81 (kpairsurjEq) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodsndin) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodpairmemEL) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodpairmemER) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodmempaircEq) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodfstpairEq) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodsndpairEq) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodpairsurjEq) =>
% 88.68/26.81 ((
% 88.68/26.81 (dpsetconstrI) =>
% 88.68/26.81 ((
% 88.68/26.81 (dpsetconstrSub) =>
% 88.68/26.81 ((
% 88.68/26.81 (setOfPairsIsBReln) =>
% 88.68/26.81 ((
% 88.68/26.81 (dpsetconstrERa) =>
% 88.68/26.81 ((
% 88.68/26.81 (dpsetconstrEL1) =>
% 88.68/26.81 ((
% 88.68/26.81 (dpsetconstrEL2) =>
% 88.68/26.81 ((
% 88.68/26.81 (dpsetconstrER) =>
% 88.68/26.81 ((
% 88.68/26.81 (funcImageSingleton) =>
% 88.68/26.81 ((
% 88.68/26.81 (apProp) =>
% 88.68/26.81 ((
% 88.68/26.81 (app) =>
% 88.68/26.81 ((
% 88.68/26.81 (infuncsetfunc) =>
% 88.68/26.81 ((
% 88.68/26.81 (ap2p) =>
% 88.68/26.81 ((
% 88.68/26.81 (funcinfuncset) =>
% 88.68/26.81 ((
% 88.68/26.81 (lamProp) =>
% 88.68/26.81 ((
% 88.68/26.81 (lamp) =>
% 88.68/26.81 ((
% 88.68/26.81 (lam2p) =>
% 88.68/26.81 ((
% 88.68/26.81 (brelnall1) =>
% 88.68/26.81 ((
% 88.68/26.81 (brelnall2) =>
% 88.68/26.81 ((
% 88.68/26.81 (!!) @ (
% 88.68/26.81 (('#B') @ (
% 88.68/26.81 !!) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#S') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#S') @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 =>))) @
% 88.68/26.81 ex1)))) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 !!))) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#S') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#B') @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#S') @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 =>))) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#C') @ in)))))))) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 !!))))) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#C') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#B') @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#B') @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#S') @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 =>))) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#C') @ in)))))))))) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#S') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#S') @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#B'))) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 =>))))))) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#C') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#B') @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#S') @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 =>))))))) @
% 88.68/26.81 (
% 88.68/26.81 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 88.68/26.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl293])).
% 88.68/26.81 thf(zip_derived_cl322, plain,
% 88.68/26.81 (~ (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 88.68/26.81 (((setadjoinIR) =>
% 88.68/26.81 (((setadjoinE) =>
% 88.68/26.81 (((setadjoinOr) =>
% 88.68/26.81 (((setoftrueEq) =>
% 88.68/26.81 (((powersetI) =>
% 88.68/26.81 (((emptyinPowerset) =>
% 88.68/26.81 (((emptyInPowerset) =>
% 88.68/26.81 (((powersetE) =>
% 88.68/26.81 (((setunionI) =>
% 88.68/26.81 (((setunionE) =>
% 88.68/26.81 (((subPowSU) =>
% 88.68/26.81 (((exuE2) =>
% 88.68/26.81 (((nonemptyImpWitness) =>
% 88.68/26.81 (((uniqinunit) =>
% 88.68/26.81 (((notinsingleton) =>
% 88.68/26.81 (((eqinunit) =>
% 88.68/26.81 (((singletonsswitch) =>
% 88.68/26.81 (((upairsetE) =>
% 88.68/26.81 (((upairsetIL) =>
% 88.68/26.81 (((upairsetIR) =>
% 88.68/26.81 (((emptyE1) =>
% 88.68/26.81 (((vacuousDall) =>
% 88.68/26.81 (((quantDeMorgan1) =>
% 88.68/26.81 (((quantDeMorgan2) =>
% 88.68/26.81 (((quantDeMorgan3) =>
% 88.68/26.81 (((quantDeMorgan4) =>
% 88.68/26.81 (((prop2setI) =>
% 88.68/26.81 (((prop2set2propI) =>
% 88.68/26.81 (((notdexE) =>
% 88.68/26.81 ((
% 88.68/26.81 (notdallE) =>
% 88.68/26.81 ((
% 88.68/26.81 (exuI1) =>
% 88.68/26.81 ((
% 88.68/26.81 (exuI3) =>
% 88.68/26.81 ((
% 88.68/26.81 (exuI2) =>
% 88.68/26.81 ((
% 88.68/26.81 (inCongP) =>
% 88.68/26.81 ((
% 88.68/26.81 (in__Cong) =>
% 88.68/26.81 ((
% 88.68/26.81 (exuE3u) =>
% 88.68/26.81 ((
% 88.68/26.81 (exu__Cong) =>
% 88.68/26.81 ((
% 88.68/26.81 (setadjoin__Cong) =>
% 88.68/26.81 ((
% 88.68/26.81 (powerset__Cong) =>
% 88.68/26.81 ((
% 88.68/26.81 (setunion__Cong) =>
% 88.68/26.81 ((
% 88.68/26.81 (exuEu) =>
% 88.68/26.81 ((
% 88.68/26.81 (descr__Cong) =>
% 88.68/26.81 ((
% 88.68/26.81 (dsetconstr__Cong) =>
% 88.68/26.81 ((
% 88.68/26.81 (subsetI1) =>
% 88.68/26.81 ((
% 88.68/26.81 (eqimpsubset2) =>
% 88.68/26.81 ((
% 88.68/26.81 (eqimpsubset1) =>
% 88.68/26.81 ((
% 88.68/26.81 (subsetI2) =>
% 88.68/26.81 ((
% 88.68/26.81 (emptysetsubset) =>
% 88.68/26.81 ((
% 88.68/26.81 (subsetE) =>
% 88.68/26.81 ((
% 88.68/26.81 (subsetE2) =>
% 88.68/26.81 ((
% 88.68/26.81 (notsubsetI) =>
% 88.68/26.81 ((
% 88.68/26.81 (notequalI1) =>
% 88.68/26.81 ((
% 88.68/26.81 (notequalI2) =>
% 88.68/26.81 ((
% 88.68/26.81 (subsetRefl) =>
% 88.68/26.81 ((
% 88.68/26.81 (subsetTrans) =>
% 88.68/26.81 ((
% 88.68/26.81 (setadjoinSub) =>
% 88.68/26.81 ((
% 88.68/26.81 (setadjoinSub2) =>
% 88.68/26.81 ((
% 88.68/26.81 (subset2powerset) =>
% 88.68/26.81 ((
% 88.68/26.81 (setextsub) =>
% 88.68/26.81 ((
% 88.68/26.81 (subsetemptysetimpeq) =>
% 88.68/26.81 ((
% 88.68/26.81 (powersetI1) =>
% 88.68/26.81 ((
% 88.68/26.81 (powersetE1) =>
% 88.68/26.81 ((
% 88.68/26.81 (inPowerset) =>
% 88.68/26.81 ((
% 88.68/26.81 (powersetsubset) =>
% 88.68/26.81 ((
% 88.68/26.81 (sepInPowerset) =>
% 88.68/26.81 ((
% 88.68/26.81 (sepSubset) =>
% 88.68/26.81 ((
% 88.68/26.81 (binunionIL) =>
% 88.68/26.81 ((
% 88.68/26.81 (upairset2IR) =>
% 88.68/26.81 ((
% 88.68/26.81 (binunionIR) =>
% 88.68/26.81 ((
% 88.68/26.81 (binunionEcases) =>
% 88.68/26.81 ((
% 88.68/26.81 (binunionE) =>
% 88.68/26.81 ((
% 88.68/26.81 (binunionLsub) =>
% 88.68/26.81 ((
% 88.68/26.81 (binunionRsub) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectI) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectSubset5) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectEL) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectLsub) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectSubset2) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectSubset3) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectER) =>
% 88.68/26.81 ((
% 88.68/26.81 (disjointsetsI1) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectRsub) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectSubset4) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectSubset1) =>
% 88.68/26.81 ((
% 88.68/26.81 (bs114d) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusI) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusEL) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusER) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusSubset2) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusERneg) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusELneg) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusILneg) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusIRneg) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusLsub) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusSubset1) =>
% 88.68/26.81 ((
% 88.68/26.81 (symdiffE) =>
% 88.68/26.81 ((
% 88.68/26.81 (symdiffI1) =>
% 88.68/26.81 ((
% 88.68/26.81 (symdiffI2) =>
% 88.68/26.81 ((
% 88.68/26.81 (symdiffIneg1) =>
% 88.68/26.81 ((
% 88.68/26.81 (symdiffIneg2) =>
% 88.68/26.81 ((
% 88.68/26.81 (secondinupair) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairIL) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairIR) =>
% 88.68/26.81 ((
% 88.68/26.81 (kpairiskpair) =>
% 88.68/26.81 ((
% 88.68/26.81 (kpairp) =>
% 88.68/26.81 ((
% 88.68/26.81 (singletonsubset) =>
% 88.68/26.81 ((
% 88.68/26.81 (singletoninpowerset) =>
% 88.68/26.81 ((
% 88.68/26.81 (singletoninpowunion) =>
% 88.68/26.81 ((
% 88.68/26.81 (upairset2E) =>
% 88.68/26.81 ((
% 88.68/26.81 (upairsubunion) =>
% 88.68/26.81 ((
% 88.68/26.81 (upairinpowunion) =>
% 88.68/26.81 ((
% 88.68/26.81 (ubforcartprodlem1) =>
% 88.68/26.81 ((
% 88.68/26.81 (ubforcartprodlem2) =>
% 88.68/26.81 ((
% 88.68/26.81 (ubforcartprodlem3) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodpairin) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodmempair1) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodmempair) =>
% 88.68/26.81 ((
% 88.68/26.81 (setunionE2) =>
% 88.68/26.81 ((
% 88.68/26.81 (setunionsingleton1) =>
% 88.68/26.81 ((
% 88.68/26.81 (setunionsingleton2) =>
% 88.68/26.81 ((
% 88.68/26.81 (setunionsingleton) =>
% 88.68/26.81 ((
% 88.68/26.81 (singletonprop) =>
% 88.68/26.81 ((
% 88.68/26.81 (ex1E1) =>
% 88.68/26.81 ((
% 88.68/26.81 (ex1I) =>
% 88.68/26.81 ((
% 88.68/26.81 (ex1I2) =>
% 88.68/26.81 ((
% 88.68/26.81 (singletonsuniq) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairinjL1) =>
% 88.68/26.81 ((
% 88.68/26.81 (kfstsingleton) =>
% 88.68/26.81 ((
% 88.68/26.81 (theprop) =>
% 88.68/26.81 ((
% 88.68/26.81 (kfstpairEq) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodfstin) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairinjL2) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairinjL) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairinjR11) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairinjR12) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairinjR1) =>
% 88.68/26.81 ((
% 88.68/26.81 (upairequniteq) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairinjR2) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairinjR) =>
% 88.68/26.81 ((
% 88.68/26.81 (ksndsingleton) =>
% 88.68/26.81 ((
% 88.68/26.81 (ksndpairEq) =>
% 88.68/26.81 ((
% 88.68/26.81 (kpairsurjEq) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodsndin) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodpairmemEL) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodpairmemER) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodmempaircEq) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodfstpairEq) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodsndpairEq) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodpairsurjEq) =>
% 88.68/26.81 ((
% 88.68/26.81 (dpsetconstrI) =>
% 88.68/26.81 ((
% 88.68/26.81 (dpsetconstrSub) =>
% 88.68/26.81 ((
% 88.68/26.81 (setOfPairsIsBReln) =>
% 88.68/26.81 ((
% 88.68/26.81 (dpsetconstrERa) =>
% 88.68/26.81 ((
% 88.68/26.81 (dpsetconstrEL1) =>
% 88.68/26.81 ((
% 88.68/26.81 (dpsetconstrEL2) =>
% 88.68/26.81 ((
% 88.68/26.81 (dpsetconstrER) =>
% 88.68/26.81 ((
% 88.68/26.81 (funcImageSingleton) =>
% 88.68/26.81 ((
% 88.68/26.81 (apProp) =>
% 88.68/26.81 ((
% 88.68/26.81 (app) =>
% 88.68/26.81 ((
% 88.68/26.81 (infuncsetfunc) =>
% 88.68/26.81 ((
% 88.68/26.81 (ap2p) =>
% 88.68/26.81 ((
% 88.68/26.81 (funcinfuncset) =>
% 88.68/26.81 ((
% 88.68/26.81 (lamProp) =>
% 88.68/26.81 ((
% 88.68/26.81 (lamp) =>
% 88.68/26.81 ((
% 88.68/26.81 (lam2p) =>
% 88.68/26.81 ((
% 88.68/26.81 (brelnall1) =>
% 88.68/26.81 ((
% 88.68/26.81 (brelnall2) =>
% 88.68/26.81 ((
% 88.68/26.81 (!!) @ (
% 88.68/26.81 (('#B') @ (
% 88.68/26.81 !!) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#S') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#S') @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 =>))) @
% 88.68/26.81 ex1)))) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 !!))) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#S') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#B') @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#S') @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 =>))) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#C') @ in)))))))) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 !!))))) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#C') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#B') @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#B') @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#S') @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 =>))) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#C') @ in)))))))))) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#S') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#S') @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#B'))) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 =>))))))) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#C') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#B') @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#S') @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 =>))))))) @
% 88.68/26.81 (
% 88.68/26.81 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 88.68/26.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl307])).
% 88.68/26.81 thf(zip_derived_cl337, plain,
% 88.68/26.81 (~ (((setadjoinIR) =>
% 88.68/26.81 (((setadjoinE) =>
% 88.68/26.81 (((setadjoinOr) =>
% 88.68/26.81 (((setoftrueEq) =>
% 88.68/26.81 (((powersetI) =>
% 88.68/26.81 (((emptyinPowerset) =>
% 88.68/26.81 (((emptyInPowerset) =>
% 88.68/26.81 (((powersetE) =>
% 88.68/26.81 (((setunionI) =>
% 88.68/26.81 (((setunionE) =>
% 88.68/26.81 (((subPowSU) =>
% 88.68/26.81 (((exuE2) =>
% 88.68/26.81 (((nonemptyImpWitness) =>
% 88.68/26.81 (((uniqinunit) =>
% 88.68/26.81 (((notinsingleton) =>
% 88.68/26.81 (((eqinunit) =>
% 88.68/26.81 (((singletonsswitch) =>
% 88.68/26.81 (((upairsetE) =>
% 88.68/26.81 (((upairsetIL) =>
% 88.68/26.81 (((upairsetIR) =>
% 88.68/26.81 (((emptyE1) =>
% 88.68/26.81 (((vacuousDall) =>
% 88.68/26.81 (((quantDeMorgan1) =>
% 88.68/26.81 (((quantDeMorgan2) =>
% 88.68/26.81 (((quantDeMorgan3) =>
% 88.68/26.81 (((quantDeMorgan4) =>
% 88.68/26.81 (((prop2setI) =>
% 88.68/26.81 (((prop2set2propI) =>
% 88.68/26.81 (((notdexE) =>
% 88.68/26.81 (((notdallE) =>
% 88.68/26.81 ((
% 88.68/26.81 (exuI1) =>
% 88.68/26.81 ((
% 88.68/26.81 (exuI3) =>
% 88.68/26.81 ((
% 88.68/26.81 (exuI2) =>
% 88.68/26.81 ((
% 88.68/26.81 (inCongP) =>
% 88.68/26.81 ((
% 88.68/26.81 (in__Cong) =>
% 88.68/26.81 ((
% 88.68/26.81 (exuE3u) =>
% 88.68/26.81 ((
% 88.68/26.81 (exu__Cong) =>
% 88.68/26.81 ((
% 88.68/26.81 (setadjoin__Cong) =>
% 88.68/26.81 ((
% 88.68/26.81 (powerset__Cong) =>
% 88.68/26.81 ((
% 88.68/26.81 (setunion__Cong) =>
% 88.68/26.81 ((
% 88.68/26.81 (exuEu) =>
% 88.68/26.81 ((
% 88.68/26.81 (descr__Cong) =>
% 88.68/26.81 ((
% 88.68/26.81 (dsetconstr__Cong) =>
% 88.68/26.81 ((
% 88.68/26.81 (subsetI1) =>
% 88.68/26.81 ((
% 88.68/26.81 (eqimpsubset2) =>
% 88.68/26.81 ((
% 88.68/26.81 (eqimpsubset1) =>
% 88.68/26.81 ((
% 88.68/26.81 (subsetI2) =>
% 88.68/26.81 ((
% 88.68/26.81 (emptysetsubset) =>
% 88.68/26.81 ((
% 88.68/26.81 (subsetE) =>
% 88.68/26.81 ((
% 88.68/26.81 (subsetE2) =>
% 88.68/26.81 ((
% 88.68/26.81 (notsubsetI) =>
% 88.68/26.81 ((
% 88.68/26.81 (notequalI1) =>
% 88.68/26.81 ((
% 88.68/26.81 (notequalI2) =>
% 88.68/26.81 ((
% 88.68/26.81 (subsetRefl) =>
% 88.68/26.81 ((
% 88.68/26.81 (subsetTrans) =>
% 88.68/26.81 ((
% 88.68/26.81 (setadjoinSub) =>
% 88.68/26.81 ((
% 88.68/26.81 (setadjoinSub2) =>
% 88.68/26.81 ((
% 88.68/26.81 (subset2powerset) =>
% 88.68/26.81 ((
% 88.68/26.81 (setextsub) =>
% 88.68/26.81 ((
% 88.68/26.81 (subsetemptysetimpeq) =>
% 88.68/26.81 ((
% 88.68/26.81 (powersetI1) =>
% 88.68/26.81 ((
% 88.68/26.81 (powersetE1) =>
% 88.68/26.81 ((
% 88.68/26.81 (inPowerset) =>
% 88.68/26.81 ((
% 88.68/26.81 (powersetsubset) =>
% 88.68/26.81 ((
% 88.68/26.81 (sepInPowerset) =>
% 88.68/26.81 ((
% 88.68/26.81 (sepSubset) =>
% 88.68/26.81 ((
% 88.68/26.81 (binunionIL) =>
% 88.68/26.81 ((
% 88.68/26.81 (upairset2IR) =>
% 88.68/26.81 ((
% 88.68/26.81 (binunionIR) =>
% 88.68/26.81 ((
% 88.68/26.81 (binunionEcases) =>
% 88.68/26.81 ((
% 88.68/26.81 (binunionE) =>
% 88.68/26.81 ((
% 88.68/26.81 (binunionLsub) =>
% 88.68/26.81 ((
% 88.68/26.81 (binunionRsub) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectI) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectSubset5) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectEL) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectLsub) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectSubset2) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectSubset3) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectER) =>
% 88.68/26.81 ((
% 88.68/26.81 (disjointsetsI1) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectRsub) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectSubset4) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectSubset1) =>
% 88.68/26.81 ((
% 88.68/26.81 (bs114d) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusI) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusEL) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusER) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusSubset2) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusERneg) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusELneg) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusILneg) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusIRneg) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusLsub) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusSubset1) =>
% 88.68/26.81 ((
% 88.68/26.81 (symdiffE) =>
% 88.68/26.81 ((
% 88.68/26.81 (symdiffI1) =>
% 88.68/26.81 ((
% 88.68/26.81 (symdiffI2) =>
% 88.68/26.81 ((
% 88.68/26.81 (symdiffIneg1) =>
% 88.68/26.81 ((
% 88.68/26.81 (symdiffIneg2) =>
% 88.68/26.81 ((
% 88.68/26.81 (secondinupair) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairIL) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairIR) =>
% 88.68/26.81 ((
% 88.68/26.81 (kpairiskpair) =>
% 88.68/26.81 ((
% 88.68/26.81 (kpairp) =>
% 88.68/26.81 ((
% 88.68/26.81 (singletonsubset) =>
% 88.68/26.81 ((
% 88.68/26.81 (singletoninpowerset) =>
% 88.68/26.81 ((
% 88.68/26.81 (singletoninpowunion) =>
% 88.68/26.81 ((
% 88.68/26.81 (upairset2E) =>
% 88.68/26.81 ((
% 88.68/26.81 (upairsubunion) =>
% 88.68/26.81 ((
% 88.68/26.81 (upairinpowunion) =>
% 88.68/26.81 ((
% 88.68/26.81 (ubforcartprodlem1) =>
% 88.68/26.81 ((
% 88.68/26.81 (ubforcartprodlem2) =>
% 88.68/26.81 ((
% 88.68/26.81 (ubforcartprodlem3) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodpairin) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodmempair1) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodmempair) =>
% 88.68/26.81 ((
% 88.68/26.81 (setunionE2) =>
% 88.68/26.81 ((
% 88.68/26.81 (setunionsingleton1) =>
% 88.68/26.81 ((
% 88.68/26.81 (setunionsingleton2) =>
% 88.68/26.81 ((
% 88.68/26.81 (setunionsingleton) =>
% 88.68/26.81 ((
% 88.68/26.81 (singletonprop) =>
% 88.68/26.81 ((
% 88.68/26.81 (ex1E1) =>
% 88.68/26.81 ((
% 88.68/26.81 (ex1I) =>
% 88.68/26.81 ((
% 88.68/26.81 (ex1I2) =>
% 88.68/26.81 ((
% 88.68/26.81 (singletonsuniq) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairinjL1) =>
% 88.68/26.81 ((
% 88.68/26.81 (kfstsingleton) =>
% 88.68/26.81 ((
% 88.68/26.81 (theprop) =>
% 88.68/26.81 ((
% 88.68/26.81 (kfstpairEq) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodfstin) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairinjL2) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairinjL) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairinjR11) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairinjR12) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairinjR1) =>
% 88.68/26.81 ((
% 88.68/26.81 (upairequniteq) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairinjR2) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairinjR) =>
% 88.68/26.81 ((
% 88.68/26.81 (ksndsingleton) =>
% 88.68/26.81 ((
% 88.68/26.81 (ksndpairEq) =>
% 88.68/26.81 ((
% 88.68/26.81 (kpairsurjEq) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodsndin) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodpairmemEL) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodpairmemER) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodmempaircEq) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodfstpairEq) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodsndpairEq) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodpairsurjEq) =>
% 88.68/26.81 ((
% 88.68/26.81 (dpsetconstrI) =>
% 88.68/26.81 ((
% 88.68/26.81 (dpsetconstrSub) =>
% 88.68/26.81 ((
% 88.68/26.81 (setOfPairsIsBReln) =>
% 88.68/26.81 ((
% 88.68/26.81 (dpsetconstrERa) =>
% 88.68/26.81 ((
% 88.68/26.81 (dpsetconstrEL1) =>
% 88.68/26.81 ((
% 88.68/26.81 (dpsetconstrEL2) =>
% 88.68/26.81 ((
% 88.68/26.81 (dpsetconstrER) =>
% 88.68/26.81 ((
% 88.68/26.81 (funcImageSingleton) =>
% 88.68/26.81 ((
% 88.68/26.81 (apProp) =>
% 88.68/26.81 ((
% 88.68/26.81 (app) =>
% 88.68/26.81 ((
% 88.68/26.81 (infuncsetfunc) =>
% 88.68/26.81 ((
% 88.68/26.81 (ap2p) =>
% 88.68/26.81 ((
% 88.68/26.81 (funcinfuncset) =>
% 88.68/26.81 ((
% 88.68/26.81 (lamProp) =>
% 88.68/26.81 ((
% 88.68/26.81 (lamp) =>
% 88.68/26.81 ((
% 88.68/26.81 (lam2p) =>
% 88.68/26.81 ((
% 88.68/26.81 (brelnall1) =>
% 88.68/26.81 ((
% 88.68/26.81 (brelnall2) =>
% 88.68/26.81 ((
% 88.68/26.81 (!!) @ (
% 88.68/26.81 (('#B') @ (
% 88.68/26.81 !!) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#S') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#S') @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 =>))) @
% 88.68/26.81 ex1)))) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 !!))) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#S') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#B') @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#S') @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 =>))) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#C') @ in)))))))) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 !!))))) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#C') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#B') @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#B') @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#S') @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 =>))) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#C') @ in)))))))))) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#S') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#S') @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#B'))) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 =>))))))) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#C') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#B') @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#S') @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 =>))))))) @
% 88.68/26.81 (
% 88.68/26.81 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 88.68/26.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl322])).
% 88.68/26.81 thf(zip_derived_cl349, plain,
% 88.68/26.81 (~ (((setadjoinE) =>
% 88.68/26.81 (((setadjoinOr) =>
% 88.68/26.81 (((setoftrueEq) =>
% 88.68/26.81 (((powersetI) =>
% 88.68/26.81 (((emptyinPowerset) =>
% 88.68/26.81 (((emptyInPowerset) =>
% 88.68/26.81 (((powersetE) =>
% 88.68/26.81 (((setunionI) =>
% 88.68/26.81 (((setunionE) =>
% 88.68/26.81 (((subPowSU) =>
% 88.68/26.81 (((exuE2) =>
% 88.68/26.81 (((nonemptyImpWitness) =>
% 88.68/26.81 (((uniqinunit) =>
% 88.68/26.81 (((notinsingleton) =>
% 88.68/26.81 (((eqinunit) =>
% 88.68/26.81 (((singletonsswitch) =>
% 88.68/26.81 (((upairsetE) =>
% 88.68/26.81 (((upairsetIL) =>
% 88.68/26.81 (((upairsetIR) =>
% 88.68/26.81 (((emptyE1) =>
% 88.68/26.81 (((vacuousDall) =>
% 88.68/26.81 (((quantDeMorgan1) =>
% 88.68/26.81 (((quantDeMorgan2) =>
% 88.68/26.81 (((quantDeMorgan3) =>
% 88.68/26.81 (((quantDeMorgan4) =>
% 88.68/26.81 (((prop2setI) =>
% 88.68/26.81 (((prop2set2propI) =>
% 88.68/26.81 (((notdexE) =>
% 88.68/26.81 (((notdallE) =>
% 88.68/26.81 (((exuI1) =>
% 88.68/26.81 ((
% 88.68/26.81 (exuI3) =>
% 88.68/26.81 ((
% 88.68/26.81 (exuI2) =>
% 88.68/26.81 ((
% 88.68/26.81 (inCongP) =>
% 88.68/26.81 ((
% 88.68/26.81 (in__Cong) =>
% 88.68/26.81 ((
% 88.68/26.81 (exuE3u) =>
% 88.68/26.81 ((
% 88.68/26.81 (exu__Cong) =>
% 88.68/26.81 ((
% 88.68/26.81 (setadjoin__Cong) =>
% 88.68/26.81 ((
% 88.68/26.81 (powerset__Cong) =>
% 88.68/26.81 ((
% 88.68/26.81 (setunion__Cong) =>
% 88.68/26.81 ((
% 88.68/26.81 (exuEu) =>
% 88.68/26.81 ((
% 88.68/26.81 (descr__Cong) =>
% 88.68/26.81 ((
% 88.68/26.81 (dsetconstr__Cong) =>
% 88.68/26.81 ((
% 88.68/26.81 (subsetI1) =>
% 88.68/26.81 ((
% 88.68/26.81 (eqimpsubset2) =>
% 88.68/26.81 ((
% 88.68/26.81 (eqimpsubset1) =>
% 88.68/26.81 ((
% 88.68/26.81 (subsetI2) =>
% 88.68/26.81 ((
% 88.68/26.81 (emptysetsubset) =>
% 88.68/26.81 ((
% 88.68/26.81 (subsetE) =>
% 88.68/26.81 ((
% 88.68/26.81 (subsetE2) =>
% 88.68/26.81 ((
% 88.68/26.81 (notsubsetI) =>
% 88.68/26.81 ((
% 88.68/26.81 (notequalI1) =>
% 88.68/26.81 ((
% 88.68/26.81 (notequalI2) =>
% 88.68/26.81 ((
% 88.68/26.81 (subsetRefl) =>
% 88.68/26.81 ((
% 88.68/26.81 (subsetTrans) =>
% 88.68/26.81 ((
% 88.68/26.81 (setadjoinSub) =>
% 88.68/26.81 ((
% 88.68/26.81 (setadjoinSub2) =>
% 88.68/26.81 ((
% 88.68/26.81 (subset2powerset) =>
% 88.68/26.81 ((
% 88.68/26.81 (setextsub) =>
% 88.68/26.81 ((
% 88.68/26.81 (subsetemptysetimpeq) =>
% 88.68/26.81 ((
% 88.68/26.81 (powersetI1) =>
% 88.68/26.81 ((
% 88.68/26.81 (powersetE1) =>
% 88.68/26.81 ((
% 88.68/26.81 (inPowerset) =>
% 88.68/26.81 ((
% 88.68/26.81 (powersetsubset) =>
% 88.68/26.81 ((
% 88.68/26.81 (sepInPowerset) =>
% 88.68/26.81 ((
% 88.68/26.81 (sepSubset) =>
% 88.68/26.81 ((
% 88.68/26.81 (binunionIL) =>
% 88.68/26.81 ((
% 88.68/26.81 (upairset2IR) =>
% 88.68/26.81 ((
% 88.68/26.81 (binunionIR) =>
% 88.68/26.81 ((
% 88.68/26.81 (binunionEcases) =>
% 88.68/26.81 ((
% 88.68/26.81 (binunionE) =>
% 88.68/26.81 ((
% 88.68/26.81 (binunionLsub) =>
% 88.68/26.81 ((
% 88.68/26.81 (binunionRsub) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectI) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectSubset5) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectEL) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectLsub) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectSubset2) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectSubset3) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectER) =>
% 88.68/26.81 ((
% 88.68/26.81 (disjointsetsI1) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectRsub) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectSubset4) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectSubset1) =>
% 88.68/26.81 ((
% 88.68/26.81 (bs114d) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusI) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusEL) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusER) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusSubset2) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusERneg) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusELneg) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusILneg) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusIRneg) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusLsub) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusSubset1) =>
% 88.68/26.81 ((
% 88.68/26.81 (symdiffE) =>
% 88.68/26.81 ((
% 88.68/26.81 (symdiffI1) =>
% 88.68/26.81 ((
% 88.68/26.81 (symdiffI2) =>
% 88.68/26.81 ((
% 88.68/26.81 (symdiffIneg1) =>
% 88.68/26.81 ((
% 88.68/26.81 (symdiffIneg2) =>
% 88.68/26.81 ((
% 88.68/26.81 (secondinupair) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairIL) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairIR) =>
% 88.68/26.81 ((
% 88.68/26.81 (kpairiskpair) =>
% 88.68/26.81 ((
% 88.68/26.81 (kpairp) =>
% 88.68/26.81 ((
% 88.68/26.81 (singletonsubset) =>
% 88.68/26.81 ((
% 88.68/26.81 (singletoninpowerset) =>
% 88.68/26.81 ((
% 88.68/26.81 (singletoninpowunion) =>
% 88.68/26.81 ((
% 88.68/26.81 (upairset2E) =>
% 88.68/26.81 ((
% 88.68/26.81 (upairsubunion) =>
% 88.68/26.81 ((
% 88.68/26.81 (upairinpowunion) =>
% 88.68/26.81 ((
% 88.68/26.81 (ubforcartprodlem1) =>
% 88.68/26.81 ((
% 88.68/26.81 (ubforcartprodlem2) =>
% 88.68/26.81 ((
% 88.68/26.81 (ubforcartprodlem3) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodpairin) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodmempair1) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodmempair) =>
% 88.68/26.81 ((
% 88.68/26.81 (setunionE2) =>
% 88.68/26.81 ((
% 88.68/26.81 (setunionsingleton1) =>
% 88.68/26.81 ((
% 88.68/26.81 (setunionsingleton2) =>
% 88.68/26.81 ((
% 88.68/26.81 (setunionsingleton) =>
% 88.68/26.81 ((
% 88.68/26.81 (singletonprop) =>
% 88.68/26.81 ((
% 88.68/26.81 (ex1E1) =>
% 88.68/26.81 ((
% 88.68/26.81 (ex1I) =>
% 88.68/26.81 ((
% 88.68/26.81 (ex1I2) =>
% 88.68/26.81 ((
% 88.68/26.81 (singletonsuniq) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairinjL1) =>
% 88.68/26.81 ((
% 88.68/26.81 (kfstsingleton) =>
% 88.68/26.81 ((
% 88.68/26.81 (theprop) =>
% 88.68/26.81 ((
% 88.68/26.81 (kfstpairEq) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodfstin) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairinjL2) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairinjL) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairinjR11) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairinjR12) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairinjR1) =>
% 88.68/26.81 ((
% 88.68/26.81 (upairequniteq) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairinjR2) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairinjR) =>
% 88.68/26.81 ((
% 88.68/26.81 (ksndsingleton) =>
% 88.68/26.81 ((
% 88.68/26.81 (ksndpairEq) =>
% 88.68/26.81 ((
% 88.68/26.81 (kpairsurjEq) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodsndin) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodpairmemEL) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodpairmemER) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodmempaircEq) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodfstpairEq) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodsndpairEq) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodpairsurjEq) =>
% 88.68/26.81 ((
% 88.68/26.81 (dpsetconstrI) =>
% 88.68/26.81 ((
% 88.68/26.81 (dpsetconstrSub) =>
% 88.68/26.81 ((
% 88.68/26.81 (setOfPairsIsBReln) =>
% 88.68/26.81 ((
% 88.68/26.81 (dpsetconstrERa) =>
% 88.68/26.81 ((
% 88.68/26.81 (dpsetconstrEL1) =>
% 88.68/26.81 ((
% 88.68/26.81 (dpsetconstrEL2) =>
% 88.68/26.81 ((
% 88.68/26.81 (dpsetconstrER) =>
% 88.68/26.81 ((
% 88.68/26.81 (funcImageSingleton) =>
% 88.68/26.81 ((
% 88.68/26.81 (apProp) =>
% 88.68/26.81 ((
% 88.68/26.81 (app) =>
% 88.68/26.81 ((
% 88.68/26.81 (infuncsetfunc) =>
% 88.68/26.81 ((
% 88.68/26.81 (ap2p) =>
% 88.68/26.81 ((
% 88.68/26.81 (funcinfuncset) =>
% 88.68/26.81 ((
% 88.68/26.81 (lamProp) =>
% 88.68/26.81 ((
% 88.68/26.81 (lamp) =>
% 88.68/26.81 ((
% 88.68/26.81 (lam2p) =>
% 88.68/26.81 ((
% 88.68/26.81 (brelnall1) =>
% 88.68/26.81 ((
% 88.68/26.81 (brelnall2) =>
% 88.68/26.81 ((
% 88.68/26.81 (!!) @ (
% 88.68/26.81 (('#B') @ (
% 88.68/26.81 !!) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#S') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#S') @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 =>))) @
% 88.68/26.81 ex1)))) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 !!))) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#S') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#B') @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#S') @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 =>))) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#C') @ in)))))))) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 !!))))) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#C') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#B') @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#B') @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#S') @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 =>))) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#C') @ in)))))))))) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#S') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#S') @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#B'))) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 =>))))))) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#C') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#B') @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#S') @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 =>))))))) @
% 88.68/26.81 (
% 88.68/26.81 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 88.68/26.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl337])).
% 88.68/26.81 thf(zip_derived_cl355, plain,
% 88.68/26.81 (~ (((setadjoinOr) =>
% 88.68/26.81 (((setoftrueEq) =>
% 88.68/26.81 (((powersetI) =>
% 88.68/26.81 (((emptyinPowerset) =>
% 88.68/26.81 (((emptyInPowerset) =>
% 88.68/26.81 (((powersetE) =>
% 88.68/26.81 (((setunionI) =>
% 88.68/26.81 (((setunionE) =>
% 88.68/26.81 (((subPowSU) =>
% 88.68/26.81 (((exuE2) =>
% 88.68/26.81 (((nonemptyImpWitness) =>
% 88.68/26.81 (((uniqinunit) =>
% 88.68/26.81 (((notinsingleton) =>
% 88.68/26.81 (((eqinunit) =>
% 88.68/26.81 (((singletonsswitch) =>
% 88.68/26.81 (((upairsetE) =>
% 88.68/26.81 (((upairsetIL) =>
% 88.68/26.81 (((upairsetIR) =>
% 88.68/26.81 (((emptyE1) =>
% 88.68/26.81 (((vacuousDall) =>
% 88.68/26.81 (((quantDeMorgan1) =>
% 88.68/26.81 (((quantDeMorgan2) =>
% 88.68/26.81 (((quantDeMorgan3) =>
% 88.68/26.81 (((quantDeMorgan4) =>
% 88.68/26.81 (((prop2setI) =>
% 88.68/26.81 (((prop2set2propI) =>
% 88.68/26.81 (((notdexE) =>
% 88.68/26.81 (((notdallE) =>
% 88.68/26.81 (((exuI1) =>
% 88.68/26.81 (((exuI3) =>
% 88.68/26.81 ((
% 88.68/26.81 (exuI2) =>
% 88.68/26.81 ((
% 88.68/26.81 (inCongP) =>
% 88.68/26.81 ((
% 88.68/26.81 (in__Cong) =>
% 88.68/26.81 ((
% 88.68/26.81 (exuE3u) =>
% 88.68/26.81 ((
% 88.68/26.81 (exu__Cong) =>
% 88.68/26.81 ((
% 88.68/26.81 (setadjoin__Cong) =>
% 88.68/26.81 ((
% 88.68/26.81 (powerset__Cong) =>
% 88.68/26.81 ((
% 88.68/26.81 (setunion__Cong) =>
% 88.68/26.81 ((
% 88.68/26.81 (exuEu) =>
% 88.68/26.81 ((
% 88.68/26.81 (descr__Cong) =>
% 88.68/26.81 ((
% 88.68/26.81 (dsetconstr__Cong) =>
% 88.68/26.81 ((
% 88.68/26.81 (subsetI1) =>
% 88.68/26.81 ((
% 88.68/26.81 (eqimpsubset2) =>
% 88.68/26.81 ((
% 88.68/26.81 (eqimpsubset1) =>
% 88.68/26.81 ((
% 88.68/26.81 (subsetI2) =>
% 88.68/26.81 ((
% 88.68/26.81 (emptysetsubset) =>
% 88.68/26.81 ((
% 88.68/26.81 (subsetE) =>
% 88.68/26.81 ((
% 88.68/26.81 (subsetE2) =>
% 88.68/26.81 ((
% 88.68/26.81 (notsubsetI) =>
% 88.68/26.81 ((
% 88.68/26.81 (notequalI1) =>
% 88.68/26.81 ((
% 88.68/26.81 (notequalI2) =>
% 88.68/26.81 ((
% 88.68/26.81 (subsetRefl) =>
% 88.68/26.81 ((
% 88.68/26.81 (subsetTrans) =>
% 88.68/26.81 ((
% 88.68/26.81 (setadjoinSub) =>
% 88.68/26.81 ((
% 88.68/26.81 (setadjoinSub2) =>
% 88.68/26.81 ((
% 88.68/26.81 (subset2powerset) =>
% 88.68/26.81 ((
% 88.68/26.81 (setextsub) =>
% 88.68/26.81 ((
% 88.68/26.81 (subsetemptysetimpeq) =>
% 88.68/26.81 ((
% 88.68/26.81 (powersetI1) =>
% 88.68/26.81 ((
% 88.68/26.81 (powersetE1) =>
% 88.68/26.81 ((
% 88.68/26.81 (inPowerset) =>
% 88.68/26.81 ((
% 88.68/26.81 (powersetsubset) =>
% 88.68/26.81 ((
% 88.68/26.81 (sepInPowerset) =>
% 88.68/26.81 ((
% 88.68/26.81 (sepSubset) =>
% 88.68/26.81 ((
% 88.68/26.81 (binunionIL) =>
% 88.68/26.81 ((
% 88.68/26.81 (upairset2IR) =>
% 88.68/26.81 ((
% 88.68/26.81 (binunionIR) =>
% 88.68/26.81 ((
% 88.68/26.81 (binunionEcases) =>
% 88.68/26.81 ((
% 88.68/26.81 (binunionE) =>
% 88.68/26.81 ((
% 88.68/26.81 (binunionLsub) =>
% 88.68/26.81 ((
% 88.68/26.81 (binunionRsub) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectI) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectSubset5) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectEL) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectLsub) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectSubset2) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectSubset3) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectER) =>
% 88.68/26.81 ((
% 88.68/26.81 (disjointsetsI1) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectRsub) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectSubset4) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectSubset1) =>
% 88.68/26.81 ((
% 88.68/26.81 (bs114d) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusI) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusEL) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusER) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusSubset2) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusERneg) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusELneg) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusILneg) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusIRneg) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusLsub) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusSubset1) =>
% 88.68/26.81 ((
% 88.68/26.81 (symdiffE) =>
% 88.68/26.81 ((
% 88.68/26.81 (symdiffI1) =>
% 88.68/26.81 ((
% 88.68/26.81 (symdiffI2) =>
% 88.68/26.81 ((
% 88.68/26.81 (symdiffIneg1) =>
% 88.68/26.81 ((
% 88.68/26.81 (symdiffIneg2) =>
% 88.68/26.81 ((
% 88.68/26.81 (secondinupair) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairIL) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairIR) =>
% 88.68/26.81 ((
% 88.68/26.81 (kpairiskpair) =>
% 88.68/26.81 ((
% 88.68/26.81 (kpairp) =>
% 88.68/26.81 ((
% 88.68/26.81 (singletonsubset) =>
% 88.68/26.81 ((
% 88.68/26.81 (singletoninpowerset) =>
% 88.68/26.81 ((
% 88.68/26.81 (singletoninpowunion) =>
% 88.68/26.81 ((
% 88.68/26.81 (upairset2E) =>
% 88.68/26.81 ((
% 88.68/26.81 (upairsubunion) =>
% 88.68/26.81 ((
% 88.68/26.81 (upairinpowunion) =>
% 88.68/26.81 ((
% 88.68/26.81 (ubforcartprodlem1) =>
% 88.68/26.81 ((
% 88.68/26.81 (ubforcartprodlem2) =>
% 88.68/26.81 ((
% 88.68/26.81 (ubforcartprodlem3) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodpairin) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodmempair1) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodmempair) =>
% 88.68/26.81 ((
% 88.68/26.81 (setunionE2) =>
% 88.68/26.81 ((
% 88.68/26.81 (setunionsingleton1) =>
% 88.68/26.81 ((
% 88.68/26.81 (setunionsingleton2) =>
% 88.68/26.81 ((
% 88.68/26.81 (setunionsingleton) =>
% 88.68/26.81 ((
% 88.68/26.81 (singletonprop) =>
% 88.68/26.81 ((
% 88.68/26.81 (ex1E1) =>
% 88.68/26.81 ((
% 88.68/26.81 (ex1I) =>
% 88.68/26.81 ((
% 88.68/26.81 (ex1I2) =>
% 88.68/26.81 ((
% 88.68/26.81 (singletonsuniq) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairinjL1) =>
% 88.68/26.81 ((
% 88.68/26.81 (kfstsingleton) =>
% 88.68/26.81 ((
% 88.68/26.81 (theprop) =>
% 88.68/26.81 ((
% 88.68/26.81 (kfstpairEq) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodfstin) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairinjL2) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairinjL) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairinjR11) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairinjR12) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairinjR1) =>
% 88.68/26.81 ((
% 88.68/26.81 (upairequniteq) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairinjR2) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairinjR) =>
% 88.68/26.81 ((
% 88.68/26.81 (ksndsingleton) =>
% 88.68/26.81 ((
% 88.68/26.81 (ksndpairEq) =>
% 88.68/26.81 ((
% 88.68/26.81 (kpairsurjEq) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodsndin) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodpairmemEL) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodpairmemER) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodmempaircEq) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodfstpairEq) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodsndpairEq) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodpairsurjEq) =>
% 88.68/26.81 ((
% 88.68/26.81 (dpsetconstrI) =>
% 88.68/26.81 ((
% 88.68/26.81 (dpsetconstrSub) =>
% 88.68/26.81 ((
% 88.68/26.81 (setOfPairsIsBReln) =>
% 88.68/26.81 ((
% 88.68/26.81 (dpsetconstrERa) =>
% 88.68/26.81 ((
% 88.68/26.81 (dpsetconstrEL1) =>
% 88.68/26.81 ((
% 88.68/26.81 (dpsetconstrEL2) =>
% 88.68/26.81 ((
% 88.68/26.81 (dpsetconstrER) =>
% 88.68/26.81 ((
% 88.68/26.81 (funcImageSingleton) =>
% 88.68/26.81 ((
% 88.68/26.81 (apProp) =>
% 88.68/26.81 ((
% 88.68/26.81 (app) =>
% 88.68/26.81 ((
% 88.68/26.81 (infuncsetfunc) =>
% 88.68/26.81 ((
% 88.68/26.81 (ap2p) =>
% 88.68/26.81 ((
% 88.68/26.81 (funcinfuncset) =>
% 88.68/26.81 ((
% 88.68/26.81 (lamProp) =>
% 88.68/26.81 ((
% 88.68/26.81 (lamp) =>
% 88.68/26.81 ((
% 88.68/26.81 (lam2p) =>
% 88.68/26.81 ((
% 88.68/26.81 (brelnall1) =>
% 88.68/26.81 ((
% 88.68/26.81 (brelnall2) =>
% 88.68/26.81 ((
% 88.68/26.81 (!!) @ (
% 88.68/26.81 (('#B') @ (
% 88.68/26.81 !!) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#S') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#S') @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 =>))) @
% 88.68/26.81 ex1)))) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 !!))) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#S') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#B') @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#S') @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 =>))) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#C') @ in)))))))) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 !!))))) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#C') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#B') @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#B') @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#S') @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 =>))) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#C') @ in)))))))))) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#S') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#S') @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#B'))) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 =>))))))) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#C') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#B') @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#S') @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 =>))))))) @
% 88.68/26.81 (
% 88.68/26.81 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 88.68/26.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl349])).
% 88.68/26.81 thf(zip_derived_cl362, plain,
% 88.68/26.81 (~ (((setoftrueEq) =>
% 88.68/26.81 (((powersetI) =>
% 88.68/26.81 (((emptyinPowerset) =>
% 88.68/26.81 (((emptyInPowerset) =>
% 88.68/26.81 (((powersetE) =>
% 88.68/26.81 (((setunionI) =>
% 88.68/26.81 (((setunionE) =>
% 88.68/26.81 (((subPowSU) =>
% 88.68/26.81 (((exuE2) =>
% 88.68/26.81 (((nonemptyImpWitness) =>
% 88.68/26.81 (((uniqinunit) =>
% 88.68/26.81 (((notinsingleton) =>
% 88.68/26.81 (((eqinunit) =>
% 88.68/26.81 (((singletonsswitch) =>
% 88.68/26.81 (((upairsetE) =>
% 88.68/26.81 (((upairsetIL) =>
% 88.68/26.81 (((upairsetIR) =>
% 88.68/26.81 (((emptyE1) =>
% 88.68/26.81 (((vacuousDall) =>
% 88.68/26.81 (((quantDeMorgan1) =>
% 88.68/26.81 (((quantDeMorgan2) =>
% 88.68/26.81 (((quantDeMorgan3) =>
% 88.68/26.81 (((quantDeMorgan4) =>
% 88.68/26.81 (((prop2setI) =>
% 88.68/26.81 (((prop2set2propI) =>
% 88.68/26.81 (((notdexE) =>
% 88.68/26.81 (((notdallE) =>
% 88.68/26.81 (((exuI1) =>
% 88.68/26.81 (((exuI3) =>
% 88.68/26.81 (((exuI2) =>
% 88.68/26.81 ((
% 88.68/26.81 (inCongP) =>
% 88.68/26.81 ((
% 88.68/26.81 (in__Cong) =>
% 88.68/26.81 ((
% 88.68/26.81 (exuE3u) =>
% 88.68/26.81 ((
% 88.68/26.81 (exu__Cong) =>
% 88.68/26.81 ((
% 88.68/26.81 (setadjoin__Cong) =>
% 88.68/26.81 ((
% 88.68/26.81 (powerset__Cong) =>
% 88.68/26.81 ((
% 88.68/26.81 (setunion__Cong) =>
% 88.68/26.81 ((
% 88.68/26.81 (exuEu) =>
% 88.68/26.81 ((
% 88.68/26.81 (descr__Cong) =>
% 88.68/26.81 ((
% 88.68/26.81 (dsetconstr__Cong) =>
% 88.68/26.81 ((
% 88.68/26.81 (subsetI1) =>
% 88.68/26.81 ((
% 88.68/26.81 (eqimpsubset2) =>
% 88.68/26.81 ((
% 88.68/26.81 (eqimpsubset1) =>
% 88.68/26.81 ((
% 88.68/26.81 (subsetI2) =>
% 88.68/26.81 ((
% 88.68/26.81 (emptysetsubset) =>
% 88.68/26.81 ((
% 88.68/26.81 (subsetE) =>
% 88.68/26.81 ((
% 88.68/26.81 (subsetE2) =>
% 88.68/26.81 ((
% 88.68/26.81 (notsubsetI) =>
% 88.68/26.81 ((
% 88.68/26.81 (notequalI1) =>
% 88.68/26.81 ((
% 88.68/26.81 (notequalI2) =>
% 88.68/26.81 ((
% 88.68/26.81 (subsetRefl) =>
% 88.68/26.81 ((
% 88.68/26.81 (subsetTrans) =>
% 88.68/26.81 ((
% 88.68/26.81 (setadjoinSub) =>
% 88.68/26.81 ((
% 88.68/26.81 (setadjoinSub2) =>
% 88.68/26.81 ((
% 88.68/26.81 (subset2powerset) =>
% 88.68/26.81 ((
% 88.68/26.81 (setextsub) =>
% 88.68/26.81 ((
% 88.68/26.81 (subsetemptysetimpeq) =>
% 88.68/26.81 ((
% 88.68/26.81 (powersetI1) =>
% 88.68/26.81 ((
% 88.68/26.81 (powersetE1) =>
% 88.68/26.81 ((
% 88.68/26.81 (inPowerset) =>
% 88.68/26.81 ((
% 88.68/26.81 (powersetsubset) =>
% 88.68/26.81 ((
% 88.68/26.81 (sepInPowerset) =>
% 88.68/26.81 ((
% 88.68/26.81 (sepSubset) =>
% 88.68/26.81 ((
% 88.68/26.81 (binunionIL) =>
% 88.68/26.81 ((
% 88.68/26.81 (upairset2IR) =>
% 88.68/26.81 ((
% 88.68/26.81 (binunionIR) =>
% 88.68/26.81 ((
% 88.68/26.81 (binunionEcases) =>
% 88.68/26.81 ((
% 88.68/26.81 (binunionE) =>
% 88.68/26.81 ((
% 88.68/26.81 (binunionLsub) =>
% 88.68/26.81 ((
% 88.68/26.81 (binunionRsub) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectI) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectSubset5) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectEL) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectLsub) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectSubset2) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectSubset3) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectER) =>
% 88.68/26.81 ((
% 88.68/26.81 (disjointsetsI1) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectRsub) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectSubset4) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectSubset1) =>
% 88.68/26.81 ((
% 88.68/26.81 (bs114d) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusI) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusEL) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusER) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusSubset2) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusERneg) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusELneg) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusILneg) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusIRneg) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusLsub) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusSubset1) =>
% 88.68/26.81 ((
% 88.68/26.81 (symdiffE) =>
% 88.68/26.81 ((
% 88.68/26.81 (symdiffI1) =>
% 88.68/26.81 ((
% 88.68/26.81 (symdiffI2) =>
% 88.68/26.81 ((
% 88.68/26.81 (symdiffIneg1) =>
% 88.68/26.81 ((
% 88.68/26.81 (symdiffIneg2) =>
% 88.68/26.81 ((
% 88.68/26.81 (secondinupair) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairIL) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairIR) =>
% 88.68/26.81 ((
% 88.68/26.81 (kpairiskpair) =>
% 88.68/26.81 ((
% 88.68/26.81 (kpairp) =>
% 88.68/26.81 ((
% 88.68/26.81 (singletonsubset) =>
% 88.68/26.81 ((
% 88.68/26.81 (singletoninpowerset) =>
% 88.68/26.81 ((
% 88.68/26.81 (singletoninpowunion) =>
% 88.68/26.81 ((
% 88.68/26.81 (upairset2E) =>
% 88.68/26.81 ((
% 88.68/26.81 (upairsubunion) =>
% 88.68/26.81 ((
% 88.68/26.81 (upairinpowunion) =>
% 88.68/26.81 ((
% 88.68/26.81 (ubforcartprodlem1) =>
% 88.68/26.81 ((
% 88.68/26.81 (ubforcartprodlem2) =>
% 88.68/26.81 ((
% 88.68/26.81 (ubforcartprodlem3) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodpairin) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodmempair1) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodmempair) =>
% 88.68/26.81 ((
% 88.68/26.81 (setunionE2) =>
% 88.68/26.81 ((
% 88.68/26.81 (setunionsingleton1) =>
% 88.68/26.81 ((
% 88.68/26.81 (setunionsingleton2) =>
% 88.68/26.81 ((
% 88.68/26.81 (setunionsingleton) =>
% 88.68/26.81 ((
% 88.68/26.81 (singletonprop) =>
% 88.68/26.81 ((
% 88.68/26.81 (ex1E1) =>
% 88.68/26.81 ((
% 88.68/26.81 (ex1I) =>
% 88.68/26.81 ((
% 88.68/26.81 (ex1I2) =>
% 88.68/26.81 ((
% 88.68/26.81 (singletonsuniq) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairinjL1) =>
% 88.68/26.81 ((
% 88.68/26.81 (kfstsingleton) =>
% 88.68/26.81 ((
% 88.68/26.81 (theprop) =>
% 88.68/26.81 ((
% 88.68/26.81 (kfstpairEq) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodfstin) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairinjL2) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairinjL) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairinjR11) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairinjR12) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairinjR1) =>
% 88.68/26.81 ((
% 88.68/26.81 (upairequniteq) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairinjR2) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairinjR) =>
% 88.68/26.81 ((
% 88.68/26.81 (ksndsingleton) =>
% 88.68/26.81 ((
% 88.68/26.81 (ksndpairEq) =>
% 88.68/26.81 ((
% 88.68/26.81 (kpairsurjEq) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodsndin) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodpairmemEL) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodpairmemER) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodmempaircEq) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodfstpairEq) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodsndpairEq) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodpairsurjEq) =>
% 88.68/26.81 ((
% 88.68/26.81 (dpsetconstrI) =>
% 88.68/26.81 ((
% 88.68/26.81 (dpsetconstrSub) =>
% 88.68/26.81 ((
% 88.68/26.81 (setOfPairsIsBReln) =>
% 88.68/26.81 ((
% 88.68/26.81 (dpsetconstrERa) =>
% 88.68/26.81 ((
% 88.68/26.81 (dpsetconstrEL1) =>
% 88.68/26.81 ((
% 88.68/26.81 (dpsetconstrEL2) =>
% 88.68/26.81 ((
% 88.68/26.81 (dpsetconstrER) =>
% 88.68/26.81 ((
% 88.68/26.81 (funcImageSingleton) =>
% 88.68/26.81 ((
% 88.68/26.81 (apProp) =>
% 88.68/26.81 ((
% 88.68/26.81 (app) =>
% 88.68/26.81 ((
% 88.68/26.81 (infuncsetfunc) =>
% 88.68/26.81 ((
% 88.68/26.81 (ap2p) =>
% 88.68/26.81 ((
% 88.68/26.81 (funcinfuncset) =>
% 88.68/26.81 ((
% 88.68/26.81 (lamProp) =>
% 88.68/26.81 ((
% 88.68/26.81 (lamp) =>
% 88.68/26.81 ((
% 88.68/26.81 (lam2p) =>
% 88.68/26.81 ((
% 88.68/26.81 (brelnall1) =>
% 88.68/26.81 ((
% 88.68/26.81 (brelnall2) =>
% 88.68/26.81 ((
% 88.68/26.81 (!!) @ (
% 88.68/26.81 (('#B') @ (
% 88.68/26.81 !!) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#S') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#S') @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 =>))) @
% 88.68/26.81 ex1)))) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 !!))) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#S') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#B') @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#S') @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 =>))) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#C') @ in)))))))) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 !!))))) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#C') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#B') @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#B') @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#S') @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 =>))) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#C') @ in)))))))))) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#S') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#S') @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#B'))) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 =>))))))) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#C') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#B') @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#S') @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 =>))))))) @
% 88.68/26.81 (
% 88.68/26.81 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 88.68/26.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl355])).
% 88.68/26.81 thf(zip_derived_cl369, plain,
% 88.68/26.81 (~ (((powersetI) =>
% 88.68/26.81 (((emptyinPowerset) =>
% 88.68/26.81 (((emptyInPowerset) =>
% 88.68/26.81 (((powersetE) =>
% 88.68/26.81 (((setunionI) =>
% 88.68/26.81 (((setunionE) =>
% 88.68/26.81 (((subPowSU) =>
% 88.68/26.81 (((exuE2) =>
% 88.68/26.81 (((nonemptyImpWitness) =>
% 88.68/26.81 (((uniqinunit) =>
% 88.68/26.81 (((notinsingleton) =>
% 88.68/26.81 (((eqinunit) =>
% 88.68/26.81 (((singletonsswitch) =>
% 88.68/26.81 (((upairsetE) =>
% 88.68/26.81 (((upairsetIL) =>
% 88.68/26.81 (((upairsetIR) =>
% 88.68/26.81 (((emptyE1) =>
% 88.68/26.81 (((vacuousDall) =>
% 88.68/26.81 (((quantDeMorgan1) =>
% 88.68/26.81 (((quantDeMorgan2) =>
% 88.68/26.81 (((quantDeMorgan3) =>
% 88.68/26.81 (((quantDeMorgan4) =>
% 88.68/26.81 (((prop2setI) =>
% 88.68/26.81 (((prop2set2propI) =>
% 88.68/26.81 (((notdexE) =>
% 88.68/26.81 (((notdallE) =>
% 88.68/26.81 (((exuI1) =>
% 88.68/26.81 (((exuI3) =>
% 88.68/26.81 (((exuI2) =>
% 88.68/26.81 (((inCongP) =>
% 88.68/26.81 ((
% 88.68/26.81 (in__Cong) =>
% 88.68/26.81 ((
% 88.68/26.81 (exuE3u) =>
% 88.68/26.81 ((
% 88.68/26.81 (exu__Cong) =>
% 88.68/26.81 ((
% 88.68/26.81 (setadjoin__Cong) =>
% 88.68/26.81 ((
% 88.68/26.81 (powerset__Cong) =>
% 88.68/26.81 ((
% 88.68/26.81 (setunion__Cong) =>
% 88.68/26.81 ((
% 88.68/26.81 (exuEu) =>
% 88.68/26.81 ((
% 88.68/26.81 (descr__Cong) =>
% 88.68/26.81 ((
% 88.68/26.81 (dsetconstr__Cong) =>
% 88.68/26.81 ((
% 88.68/26.81 (subsetI1) =>
% 88.68/26.81 ((
% 88.68/26.81 (eqimpsubset2) =>
% 88.68/26.81 ((
% 88.68/26.81 (eqimpsubset1) =>
% 88.68/26.81 ((
% 88.68/26.81 (subsetI2) =>
% 88.68/26.81 ((
% 88.68/26.81 (emptysetsubset) =>
% 88.68/26.81 ((
% 88.68/26.81 (subsetE) =>
% 88.68/26.81 ((
% 88.68/26.81 (subsetE2) =>
% 88.68/26.81 ((
% 88.68/26.81 (notsubsetI) =>
% 88.68/26.81 ((
% 88.68/26.81 (notequalI1) =>
% 88.68/26.81 ((
% 88.68/26.81 (notequalI2) =>
% 88.68/26.81 ((
% 88.68/26.81 (subsetRefl) =>
% 88.68/26.81 ((
% 88.68/26.81 (subsetTrans) =>
% 88.68/26.81 ((
% 88.68/26.81 (setadjoinSub) =>
% 88.68/26.81 ((
% 88.68/26.81 (setadjoinSub2) =>
% 88.68/26.81 ((
% 88.68/26.81 (subset2powerset) =>
% 88.68/26.81 ((
% 88.68/26.81 (setextsub) =>
% 88.68/26.81 ((
% 88.68/26.81 (subsetemptysetimpeq) =>
% 88.68/26.81 ((
% 88.68/26.81 (powersetI1) =>
% 88.68/26.81 ((
% 88.68/26.81 (powersetE1) =>
% 88.68/26.81 ((
% 88.68/26.81 (inPowerset) =>
% 88.68/26.81 ((
% 88.68/26.81 (powersetsubset) =>
% 88.68/26.81 ((
% 88.68/26.81 (sepInPowerset) =>
% 88.68/26.81 ((
% 88.68/26.81 (sepSubset) =>
% 88.68/26.81 ((
% 88.68/26.81 (binunionIL) =>
% 88.68/26.81 ((
% 88.68/26.81 (upairset2IR) =>
% 88.68/26.81 ((
% 88.68/26.81 (binunionIR) =>
% 88.68/26.81 ((
% 88.68/26.81 (binunionEcases) =>
% 88.68/26.81 ((
% 88.68/26.81 (binunionE) =>
% 88.68/26.81 ((
% 88.68/26.81 (binunionLsub) =>
% 88.68/26.81 ((
% 88.68/26.81 (binunionRsub) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectI) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectSubset5) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectEL) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectLsub) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectSubset2) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectSubset3) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectER) =>
% 88.68/26.81 ((
% 88.68/26.81 (disjointsetsI1) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectRsub) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectSubset4) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectSubset1) =>
% 88.68/26.81 ((
% 88.68/26.81 (bs114d) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusI) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusEL) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusER) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusSubset2) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusERneg) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusELneg) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusILneg) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusIRneg) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusLsub) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusSubset1) =>
% 88.68/26.81 ((
% 88.68/26.81 (symdiffE) =>
% 88.68/26.81 ((
% 88.68/26.81 (symdiffI1) =>
% 88.68/26.81 ((
% 88.68/26.81 (symdiffI2) =>
% 88.68/26.81 ((
% 88.68/26.81 (symdiffIneg1) =>
% 88.68/26.81 ((
% 88.68/26.81 (symdiffIneg2) =>
% 88.68/26.81 ((
% 88.68/26.81 (secondinupair) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairIL) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairIR) =>
% 88.68/26.81 ((
% 88.68/26.81 (kpairiskpair) =>
% 88.68/26.81 ((
% 88.68/26.81 (kpairp) =>
% 88.68/26.81 ((
% 88.68/26.81 (singletonsubset) =>
% 88.68/26.81 ((
% 88.68/26.81 (singletoninpowerset) =>
% 88.68/26.81 ((
% 88.68/26.81 (singletoninpowunion) =>
% 88.68/26.81 ((
% 88.68/26.81 (upairset2E) =>
% 88.68/26.81 ((
% 88.68/26.81 (upairsubunion) =>
% 88.68/26.81 ((
% 88.68/26.81 (upairinpowunion) =>
% 88.68/26.81 ((
% 88.68/26.81 (ubforcartprodlem1) =>
% 88.68/26.81 ((
% 88.68/26.81 (ubforcartprodlem2) =>
% 88.68/26.81 ((
% 88.68/26.81 (ubforcartprodlem3) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodpairin) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodmempair1) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodmempair) =>
% 88.68/26.81 ((
% 88.68/26.81 (setunionE2) =>
% 88.68/26.81 ((
% 88.68/26.81 (setunionsingleton1) =>
% 88.68/26.81 ((
% 88.68/26.81 (setunionsingleton2) =>
% 88.68/26.81 ((
% 88.68/26.81 (setunionsingleton) =>
% 88.68/26.81 ((
% 88.68/26.81 (singletonprop) =>
% 88.68/26.81 ((
% 88.68/26.81 (ex1E1) =>
% 88.68/26.81 ((
% 88.68/26.81 (ex1I) =>
% 88.68/26.81 ((
% 88.68/26.81 (ex1I2) =>
% 88.68/26.81 ((
% 88.68/26.81 (singletonsuniq) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairinjL1) =>
% 88.68/26.81 ((
% 88.68/26.81 (kfstsingleton) =>
% 88.68/26.81 ((
% 88.68/26.81 (theprop) =>
% 88.68/26.81 ((
% 88.68/26.81 (kfstpairEq) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodfstin) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairinjL2) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairinjL) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairinjR11) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairinjR12) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairinjR1) =>
% 88.68/26.81 ((
% 88.68/26.81 (upairequniteq) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairinjR2) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairinjR) =>
% 88.68/26.81 ((
% 88.68/26.81 (ksndsingleton) =>
% 88.68/26.81 ((
% 88.68/26.81 (ksndpairEq) =>
% 88.68/26.81 ((
% 88.68/26.81 (kpairsurjEq) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodsndin) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodpairmemEL) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodpairmemER) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodmempaircEq) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodfstpairEq) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodsndpairEq) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodpairsurjEq) =>
% 88.68/26.81 ((
% 88.68/26.81 (dpsetconstrI) =>
% 88.68/26.81 ((
% 88.68/26.81 (dpsetconstrSub) =>
% 88.68/26.81 ((
% 88.68/26.81 (setOfPairsIsBReln) =>
% 88.68/26.81 ((
% 88.68/26.81 (dpsetconstrERa) =>
% 88.68/26.81 ((
% 88.68/26.81 (dpsetconstrEL1) =>
% 88.68/26.81 ((
% 88.68/26.81 (dpsetconstrEL2) =>
% 88.68/26.81 ((
% 88.68/26.81 (dpsetconstrER) =>
% 88.68/26.81 ((
% 88.68/26.81 (funcImageSingleton) =>
% 88.68/26.81 ((
% 88.68/26.81 (apProp) =>
% 88.68/26.81 ((
% 88.68/26.81 (app) =>
% 88.68/26.81 ((
% 88.68/26.81 (infuncsetfunc) =>
% 88.68/26.81 ((
% 88.68/26.81 (ap2p) =>
% 88.68/26.81 ((
% 88.68/26.81 (funcinfuncset) =>
% 88.68/26.81 ((
% 88.68/26.81 (lamProp) =>
% 88.68/26.81 ((
% 88.68/26.81 (lamp) =>
% 88.68/26.81 ((
% 88.68/26.81 (lam2p) =>
% 88.68/26.81 ((
% 88.68/26.81 (brelnall1) =>
% 88.68/26.81 ((
% 88.68/26.81 (brelnall2) =>
% 88.68/26.81 ((
% 88.68/26.81 (!!) @ (
% 88.68/26.81 (('#B') @ (
% 88.68/26.81 !!) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#S') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#S') @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 =>))) @
% 88.68/26.81 ex1)))) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 !!))) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#S') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#B') @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#S') @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 =>))) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#C') @ in)))))))) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 !!))))) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#C') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#B') @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#B') @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#S') @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 =>))) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#C') @ in)))))))))) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#S') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#S') @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#B'))) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 =>))))))) @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#C') @ (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#B') @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 '#S') @
% 88.68/26.81 (
% 88.68/26.81 (
% 88.68/26.81 ('#B') @ (
% 88.68/26.81 =>))))))) @
% 88.68/26.81 (
% 88.68/26.81 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 88.68/26.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl362])).
% 88.68/26.81 thf(zip_derived_cl376, plain,
% 88.68/26.81 (~ (((emptyinPowerset) =>
% 88.68/26.81 (((emptyInPowerset) =>
% 88.68/26.81 (((powersetE) =>
% 88.68/26.81 (((setunionI) =>
% 88.68/26.81 (((setunionE) =>
% 88.68/26.81 (((subPowSU) =>
% 88.68/26.81 (((exuE2) =>
% 88.68/26.81 (((nonemptyImpWitness) =>
% 88.68/26.81 (((uniqinunit) =>
% 88.68/26.81 (((notinsingleton) =>
% 88.68/26.81 (((eqinunit) =>
% 88.68/26.81 (((singletonsswitch) =>
% 88.68/26.81 (((upairsetE) =>
% 88.68/26.81 (((upairsetIL) =>
% 88.68/26.81 (((upairsetIR) =>
% 88.68/26.81 (((emptyE1) =>
% 88.68/26.81 (((vacuousDall) =>
% 88.68/26.81 (((quantDeMorgan1) =>
% 88.68/26.81 (((quantDeMorgan2) =>
% 88.68/26.81 (((quantDeMorgan3) =>
% 88.68/26.81 (((quantDeMorgan4) =>
% 88.68/26.81 (((prop2setI) =>
% 88.68/26.81 (((prop2set2propI) =>
% 88.68/26.81 (((notdexE) =>
% 88.68/26.81 (((notdallE) =>
% 88.68/26.81 (((exuI1) =>
% 88.68/26.81 (((exuI3) =>
% 88.68/26.81 (((exuI2) =>
% 88.68/26.81 (((inCongP) =>
% 88.68/26.81 (((in__Cong) =>
% 88.68/26.81 ((
% 88.68/26.81 (exuE3u) =>
% 88.68/26.81 ((
% 88.68/26.81 (exu__Cong) =>
% 88.68/26.81 ((
% 88.68/26.81 (setadjoin__Cong) =>
% 88.68/26.81 ((
% 88.68/26.81 (powerset__Cong) =>
% 88.68/26.81 ((
% 88.68/26.81 (setunion__Cong) =>
% 88.68/26.81 ((
% 88.68/26.81 (exuEu) =>
% 88.68/26.81 ((
% 88.68/26.81 (descr__Cong) =>
% 88.68/26.81 ((
% 88.68/26.81 (dsetconstr__Cong) =>
% 88.68/26.81 ((
% 88.68/26.81 (subsetI1) =>
% 88.68/26.81 ((
% 88.68/26.81 (eqimpsubset2) =>
% 88.68/26.81 ((
% 88.68/26.81 (eqimpsubset1) =>
% 88.68/26.81 ((
% 88.68/26.81 (subsetI2) =>
% 88.68/26.81 ((
% 88.68/26.81 (emptysetsubset) =>
% 88.68/26.81 ((
% 88.68/26.81 (subsetE) =>
% 88.68/26.81 ((
% 88.68/26.81 (subsetE2) =>
% 88.68/26.81 ((
% 88.68/26.81 (notsubsetI) =>
% 88.68/26.81 ((
% 88.68/26.81 (notequalI1) =>
% 88.68/26.81 ((
% 88.68/26.81 (notequalI2) =>
% 88.68/26.81 ((
% 88.68/26.81 (subsetRefl) =>
% 88.68/26.81 ((
% 88.68/26.81 (subsetTrans) =>
% 88.68/26.81 ((
% 88.68/26.81 (setadjoinSub) =>
% 88.68/26.81 ((
% 88.68/26.81 (setadjoinSub2) =>
% 88.68/26.81 ((
% 88.68/26.81 (subset2powerset) =>
% 88.68/26.81 ((
% 88.68/26.81 (setextsub) =>
% 88.68/26.81 ((
% 88.68/26.81 (subsetemptysetimpeq) =>
% 88.68/26.81 ((
% 88.68/26.81 (powersetI1) =>
% 88.68/26.81 ((
% 88.68/26.81 (powersetE1) =>
% 88.68/26.81 ((
% 88.68/26.81 (inPowerset) =>
% 88.68/26.81 ((
% 88.68/26.81 (powersetsubset) =>
% 88.68/26.81 ((
% 88.68/26.81 (sepInPowerset) =>
% 88.68/26.81 ((
% 88.68/26.81 (sepSubset) =>
% 88.68/26.81 ((
% 88.68/26.81 (binunionIL) =>
% 88.68/26.81 ((
% 88.68/26.81 (upairset2IR) =>
% 88.68/26.81 ((
% 88.68/26.81 (binunionIR) =>
% 88.68/26.81 ((
% 88.68/26.81 (binunionEcases) =>
% 88.68/26.81 ((
% 88.68/26.81 (binunionE) =>
% 88.68/26.81 ((
% 88.68/26.81 (binunionLsub) =>
% 88.68/26.81 ((
% 88.68/26.81 (binunionRsub) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectI) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectSubset5) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectEL) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectLsub) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectSubset2) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectSubset3) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectER) =>
% 88.68/26.81 ((
% 88.68/26.81 (disjointsetsI1) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectRsub) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectSubset4) =>
% 88.68/26.81 ((
% 88.68/26.81 (binintersectSubset1) =>
% 88.68/26.81 ((
% 88.68/26.81 (bs114d) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusI) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusEL) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusER) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusSubset2) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusERneg) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusELneg) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusILneg) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusIRneg) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusLsub) =>
% 88.68/26.81 ((
% 88.68/26.81 (setminusSubset1) =>
% 88.68/26.81 ((
% 88.68/26.81 (symdiffE) =>
% 88.68/26.81 ((
% 88.68/26.81 (symdiffI1) =>
% 88.68/26.81 ((
% 88.68/26.81 (symdiffI2) =>
% 88.68/26.81 ((
% 88.68/26.81 (symdiffIneg1) =>
% 88.68/26.81 ((
% 88.68/26.81 (symdiffIneg2) =>
% 88.68/26.81 ((
% 88.68/26.81 (secondinupair) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairIL) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairIR) =>
% 88.68/26.81 ((
% 88.68/26.81 (kpairiskpair) =>
% 88.68/26.81 ((
% 88.68/26.81 (kpairp) =>
% 88.68/26.81 ((
% 88.68/26.81 (singletonsubset) =>
% 88.68/26.81 ((
% 88.68/26.81 (singletoninpowerset) =>
% 88.68/26.81 ((
% 88.68/26.81 (singletoninpowunion) =>
% 88.68/26.81 ((
% 88.68/26.81 (upairset2E) =>
% 88.68/26.81 ((
% 88.68/26.81 (upairsubunion) =>
% 88.68/26.81 ((
% 88.68/26.81 (upairinpowunion) =>
% 88.68/26.81 ((
% 88.68/26.81 (ubforcartprodlem1) =>
% 88.68/26.81 ((
% 88.68/26.81 (ubforcartprodlem2) =>
% 88.68/26.81 ((
% 88.68/26.81 (ubforcartprodlem3) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodpairin) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodmempair1) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodmempair) =>
% 88.68/26.81 ((
% 88.68/26.81 (setunionE2) =>
% 88.68/26.81 ((
% 88.68/26.81 (setunionsingleton1) =>
% 88.68/26.81 ((
% 88.68/26.81 (setunionsingleton2) =>
% 88.68/26.81 ((
% 88.68/26.81 (setunionsingleton) =>
% 88.68/26.81 ((
% 88.68/26.81 (singletonprop) =>
% 88.68/26.81 ((
% 88.68/26.81 (ex1E1) =>
% 88.68/26.81 ((
% 88.68/26.81 (ex1I) =>
% 88.68/26.81 ((
% 88.68/26.81 (ex1I2) =>
% 88.68/26.81 ((
% 88.68/26.81 (singletonsuniq) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairinjL1) =>
% 88.68/26.81 ((
% 88.68/26.81 (kfstsingleton) =>
% 88.68/26.81 ((
% 88.68/26.81 (theprop) =>
% 88.68/26.81 ((
% 88.68/26.81 (kfstpairEq) =>
% 88.68/26.81 ((
% 88.68/26.81 (cartprodfstin) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairinjL2) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairinjL) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairinjR11) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairinjR12) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairinjR1) =>
% 88.68/26.81 ((
% 88.68/26.81 (upairequniteq) =>
% 88.68/26.81 ((
% 88.68/26.81 (setukpairinjR2) =>
% 88.68/26.82 ((
% 88.68/26.82 (setukpairinjR) =>
% 88.68/26.82 ((
% 88.68/26.82 (ksndsingleton) =>
% 88.68/26.82 ((
% 88.68/26.82 (ksndpairEq) =>
% 88.68/26.82 ((
% 88.68/26.82 (kpairsurjEq) =>
% 88.68/26.82 ((
% 88.68/26.82 (cartprodsndin) =>
% 88.68/26.82 ((
% 88.68/26.82 (cartprodpairmemEL) =>
% 88.68/26.82 ((
% 88.68/26.82 (cartprodpairmemER) =>
% 88.68/26.82 ((
% 88.68/26.82 (cartprodmempaircEq) =>
% 88.68/26.82 ((
% 88.68/26.82 (cartprodfstpairEq) =>
% 88.68/26.82 ((
% 88.68/26.82 (cartprodsndpairEq) =>
% 88.68/26.82 ((
% 88.68/26.82 (cartprodpairsurjEq) =>
% 88.68/26.82 ((
% 88.68/26.82 (dpsetconstrI) =>
% 88.68/26.82 ((
% 88.68/26.82 (dpsetconstrSub) =>
% 88.68/26.82 ((
% 88.68/26.82 (setOfPairsIsBReln) =>
% 88.68/26.82 ((
% 88.68/26.82 (dpsetconstrERa) =>
% 88.68/26.82 ((
% 88.68/26.82 (dpsetconstrEL1) =>
% 88.68/26.82 ((
% 88.68/26.82 (dpsetconstrEL2) =>
% 88.68/26.82 ((
% 88.68/26.82 (dpsetconstrER) =>
% 88.68/26.82 ((
% 88.68/26.82 (funcImageSingleton) =>
% 88.68/26.82 ((
% 88.68/26.82 (apProp) =>
% 88.68/26.82 ((
% 88.68/26.82 (app) =>
% 88.68/26.82 ((
% 88.68/26.82 (infuncsetfunc) =>
% 88.68/26.82 ((
% 88.68/26.82 (ap2p) =>
% 88.68/26.82 ((
% 88.68/26.82 (funcinfuncset) =>
% 88.68/26.82 ((
% 88.68/26.82 (lamProp) =>
% 88.68/26.82 ((
% 88.68/26.82 (lamp) =>
% 88.68/26.82 ((
% 88.68/26.82 (lam2p) =>
% 88.68/26.82 ((
% 88.68/26.82 (brelnall1) =>
% 88.68/26.82 ((
% 88.68/26.82 (brelnall2) =>
% 88.68/26.82 ((
% 88.68/26.82 (!!) @ (
% 88.68/26.82 (('#B') @ (
% 88.68/26.82 !!) @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#S') @ (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 '#S') @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 =>))) @
% 88.68/26.82 ex1)))) @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 !!))) @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#S') @ (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 '#B') @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 '#S') @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 =>))) @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#C') @ in)))))))) @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 !!))))) @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#C') @ (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 '#B') @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 '#B') @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 '#S') @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 =>))) @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#C') @ in)))))))))) @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#S') @ (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 '#S') @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 '#B'))) @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 =>))))))) @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#C') @ (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 '#B') @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 '#S') @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 =>))))))) @
% 88.68/26.82 (
% 88.68/26.82 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 88.68/26.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl369])).
% 88.68/26.82 thf(zip_derived_cl384, plain,
% 88.68/26.82 (~ (((emptyInPowerset) =>
% 88.68/26.82 (((powersetE) =>
% 88.68/26.82 (((setunionI) =>
% 88.68/26.82 (((setunionE) =>
% 88.68/26.82 (((subPowSU) =>
% 88.68/26.82 (((exuE2) =>
% 88.68/26.82 (((nonemptyImpWitness) =>
% 88.68/26.82 (((uniqinunit) =>
% 88.68/26.82 (((notinsingleton) =>
% 88.68/26.82 (((eqinunit) =>
% 88.68/26.82 (((singletonsswitch) =>
% 88.68/26.82 (((upairsetE) =>
% 88.68/26.82 (((upairsetIL) =>
% 88.68/26.82 (((upairsetIR) =>
% 88.68/26.82 (((emptyE1) =>
% 88.68/26.82 (((vacuousDall) =>
% 88.68/26.82 (((quantDeMorgan1) =>
% 88.68/26.82 (((quantDeMorgan2) =>
% 88.68/26.82 (((quantDeMorgan3) =>
% 88.68/26.82 (((quantDeMorgan4) =>
% 88.68/26.82 (((prop2setI) =>
% 88.68/26.82 (((prop2set2propI) =>
% 88.68/26.82 (((notdexE) =>
% 88.68/26.82 (((notdallE) =>
% 88.68/26.82 (((exuI1) =>
% 88.68/26.82 (((exuI3) =>
% 88.68/26.82 (((exuI2) =>
% 88.68/26.82 (((inCongP) =>
% 88.68/26.82 (((in__Cong) =>
% 88.68/26.82 (((exuE3u) =>
% 88.68/26.82 ((
% 88.68/26.82 (exu__Cong) =>
% 88.68/26.82 ((
% 88.68/26.82 (setadjoin__Cong) =>
% 88.68/26.82 ((
% 88.68/26.82 (powerset__Cong) =>
% 88.68/26.82 ((
% 88.68/26.82 (setunion__Cong) =>
% 88.68/26.82 ((
% 88.68/26.82 (exuEu) =>
% 88.68/26.82 ((
% 88.68/26.82 (descr__Cong) =>
% 88.68/26.82 ((
% 88.68/26.82 (dsetconstr__Cong) =>
% 88.68/26.82 ((
% 88.68/26.82 (subsetI1) =>
% 88.68/26.82 ((
% 88.68/26.82 (eqimpsubset2) =>
% 88.68/26.82 ((
% 88.68/26.82 (eqimpsubset1) =>
% 88.68/26.82 ((
% 88.68/26.82 (subsetI2) =>
% 88.68/26.82 ((
% 88.68/26.82 (emptysetsubset) =>
% 88.68/26.82 ((
% 88.68/26.82 (subsetE) =>
% 88.68/26.82 ((
% 88.68/26.82 (subsetE2) =>
% 88.68/26.82 ((
% 88.68/26.82 (notsubsetI) =>
% 88.68/26.82 ((
% 88.68/26.82 (notequalI1) =>
% 88.68/26.82 ((
% 88.68/26.82 (notequalI2) =>
% 88.68/26.82 ((
% 88.68/26.82 (subsetRefl) =>
% 88.68/26.82 ((
% 88.68/26.82 (subsetTrans) =>
% 88.68/26.82 ((
% 88.68/26.82 (setadjoinSub) =>
% 88.68/26.82 ((
% 88.68/26.82 (setadjoinSub2) =>
% 88.68/26.82 ((
% 88.68/26.82 (subset2powerset) =>
% 88.68/26.82 ((
% 88.68/26.82 (setextsub) =>
% 88.68/26.82 ((
% 88.68/26.82 (subsetemptysetimpeq) =>
% 88.68/26.82 ((
% 88.68/26.82 (powersetI1) =>
% 88.68/26.82 ((
% 88.68/26.82 (powersetE1) =>
% 88.68/26.82 ((
% 88.68/26.82 (inPowerset) =>
% 88.68/26.82 ((
% 88.68/26.82 (powersetsubset) =>
% 88.68/26.82 ((
% 88.68/26.82 (sepInPowerset) =>
% 88.68/26.82 ((
% 88.68/26.82 (sepSubset) =>
% 88.68/26.82 ((
% 88.68/26.82 (binunionIL) =>
% 88.68/26.82 ((
% 88.68/26.82 (upairset2IR) =>
% 88.68/26.82 ((
% 88.68/26.82 (binunionIR) =>
% 88.68/26.82 ((
% 88.68/26.82 (binunionEcases) =>
% 88.68/26.82 ((
% 88.68/26.82 (binunionE) =>
% 88.68/26.82 ((
% 88.68/26.82 (binunionLsub) =>
% 88.68/26.82 ((
% 88.68/26.82 (binunionRsub) =>
% 88.68/26.82 ((
% 88.68/26.82 (binintersectI) =>
% 88.68/26.82 ((
% 88.68/26.82 (binintersectSubset5) =>
% 88.68/26.82 ((
% 88.68/26.82 (binintersectEL) =>
% 88.68/26.82 ((
% 88.68/26.82 (binintersectLsub) =>
% 88.68/26.82 ((
% 88.68/26.82 (binintersectSubset2) =>
% 88.68/26.82 ((
% 88.68/26.82 (binintersectSubset3) =>
% 88.68/26.82 ((
% 88.68/26.82 (binintersectER) =>
% 88.68/26.82 ((
% 88.68/26.82 (disjointsetsI1) =>
% 88.68/26.82 ((
% 88.68/26.82 (binintersectRsub) =>
% 88.68/26.82 ((
% 88.68/26.82 (binintersectSubset4) =>
% 88.68/26.82 ((
% 88.68/26.82 (binintersectSubset1) =>
% 88.68/26.82 ((
% 88.68/26.82 (bs114d) =>
% 88.68/26.82 ((
% 88.68/26.82 (setminusI) =>
% 88.68/26.82 ((
% 88.68/26.82 (setminusEL) =>
% 88.68/26.82 ((
% 88.68/26.82 (setminusER) =>
% 88.68/26.82 ((
% 88.68/26.82 (setminusSubset2) =>
% 88.68/26.82 ((
% 88.68/26.82 (setminusERneg) =>
% 88.68/26.82 ((
% 88.68/26.82 (setminusELneg) =>
% 88.68/26.82 ((
% 88.68/26.82 (setminusILneg) =>
% 88.68/26.82 ((
% 88.68/26.82 (setminusIRneg) =>
% 88.68/26.82 ((
% 88.68/26.82 (setminusLsub) =>
% 88.68/26.82 ((
% 88.68/26.82 (setminusSubset1) =>
% 88.68/26.82 ((
% 88.68/26.82 (symdiffE) =>
% 88.68/26.82 ((
% 88.68/26.82 (symdiffI1) =>
% 88.68/26.82 ((
% 88.68/26.82 (symdiffI2) =>
% 88.68/26.82 ((
% 88.68/26.82 (symdiffIneg1) =>
% 88.68/26.82 ((
% 88.68/26.82 (symdiffIneg2) =>
% 88.68/26.82 ((
% 88.68/26.82 (secondinupair) =>
% 88.68/26.82 ((
% 88.68/26.82 (setukpairIL) =>
% 88.68/26.82 ((
% 88.68/26.82 (setukpairIR) =>
% 88.68/26.82 ((
% 88.68/26.82 (kpairiskpair) =>
% 88.68/26.82 ((
% 88.68/26.82 (kpairp) =>
% 88.68/26.82 ((
% 88.68/26.82 (singletonsubset) =>
% 88.68/26.82 ((
% 88.68/26.82 (singletoninpowerset) =>
% 88.68/26.82 ((
% 88.68/26.82 (singletoninpowunion) =>
% 88.68/26.82 ((
% 88.68/26.82 (upairset2E) =>
% 88.68/26.82 ((
% 88.68/26.82 (upairsubunion) =>
% 88.68/26.82 ((
% 88.68/26.82 (upairinpowunion) =>
% 88.68/26.82 ((
% 88.68/26.82 (ubforcartprodlem1) =>
% 88.68/26.82 ((
% 88.68/26.82 (ubforcartprodlem2) =>
% 88.68/26.82 ((
% 88.68/26.82 (ubforcartprodlem3) =>
% 88.68/26.82 ((
% 88.68/26.82 (cartprodpairin) =>
% 88.68/26.82 ((
% 88.68/26.82 (cartprodmempair1) =>
% 88.68/26.82 ((
% 88.68/26.82 (cartprodmempair) =>
% 88.68/26.82 ((
% 88.68/26.82 (setunionE2) =>
% 88.68/26.82 ((
% 88.68/26.82 (setunionsingleton1) =>
% 88.68/26.82 ((
% 88.68/26.82 (setunionsingleton2) =>
% 88.68/26.82 ((
% 88.68/26.82 (setunionsingleton) =>
% 88.68/26.82 ((
% 88.68/26.82 (singletonprop) =>
% 88.68/26.82 ((
% 88.68/26.82 (ex1E1) =>
% 88.68/26.82 ((
% 88.68/26.82 (ex1I) =>
% 88.68/26.82 ((
% 88.68/26.82 (ex1I2) =>
% 88.68/26.82 ((
% 88.68/26.82 (singletonsuniq) =>
% 88.68/26.82 ((
% 88.68/26.82 (setukpairinjL1) =>
% 88.68/26.82 ((
% 88.68/26.82 (kfstsingleton) =>
% 88.68/26.82 ((
% 88.68/26.82 (theprop) =>
% 88.68/26.82 ((
% 88.68/26.82 (kfstpairEq) =>
% 88.68/26.82 ((
% 88.68/26.82 (cartprodfstin) =>
% 88.68/26.82 ((
% 88.68/26.82 (setukpairinjL2) =>
% 88.68/26.82 ((
% 88.68/26.82 (setukpairinjL) =>
% 88.68/26.82 ((
% 88.68/26.82 (setukpairinjR11) =>
% 88.68/26.82 ((
% 88.68/26.82 (setukpairinjR12) =>
% 88.68/26.82 ((
% 88.68/26.82 (setukpairinjR1) =>
% 88.68/26.82 ((
% 88.68/26.82 (upairequniteq) =>
% 88.68/26.82 ((
% 88.68/26.82 (setukpairinjR2) =>
% 88.68/26.82 ((
% 88.68/26.82 (setukpairinjR) =>
% 88.68/26.82 ((
% 88.68/26.82 (ksndsingleton) =>
% 88.68/26.82 ((
% 88.68/26.82 (ksndpairEq) =>
% 88.68/26.82 ((
% 88.68/26.82 (kpairsurjEq) =>
% 88.68/26.82 ((
% 88.68/26.82 (cartprodsndin) =>
% 88.68/26.82 ((
% 88.68/26.82 (cartprodpairmemEL) =>
% 88.68/26.82 ((
% 88.68/26.82 (cartprodpairmemER) =>
% 88.68/26.82 ((
% 88.68/26.82 (cartprodmempaircEq) =>
% 88.68/26.82 ((
% 88.68/26.82 (cartprodfstpairEq) =>
% 88.68/26.82 ((
% 88.68/26.82 (cartprodsndpairEq) =>
% 88.68/26.82 ((
% 88.68/26.82 (cartprodpairsurjEq) =>
% 88.68/26.82 ((
% 88.68/26.82 (dpsetconstrI) =>
% 88.68/26.82 ((
% 88.68/26.82 (dpsetconstrSub) =>
% 88.68/26.82 ((
% 88.68/26.82 (setOfPairsIsBReln) =>
% 88.68/26.82 ((
% 88.68/26.82 (dpsetconstrERa) =>
% 88.68/26.82 ((
% 88.68/26.82 (dpsetconstrEL1) =>
% 88.68/26.82 ((
% 88.68/26.82 (dpsetconstrEL2) =>
% 88.68/26.82 ((
% 88.68/26.82 (dpsetconstrER) =>
% 88.68/26.82 ((
% 88.68/26.82 (funcImageSingleton) =>
% 88.68/26.82 ((
% 88.68/26.82 (apProp) =>
% 88.68/26.82 ((
% 88.68/26.82 (app) =>
% 88.68/26.82 ((
% 88.68/26.82 (infuncsetfunc) =>
% 88.68/26.82 ((
% 88.68/26.82 (ap2p) =>
% 88.68/26.82 ((
% 88.68/26.82 (funcinfuncset) =>
% 88.68/26.82 ((
% 88.68/26.82 (lamProp) =>
% 88.68/26.82 ((
% 88.68/26.82 (lamp) =>
% 88.68/26.82 ((
% 88.68/26.82 (lam2p) =>
% 88.68/26.82 ((
% 88.68/26.82 (brelnall1) =>
% 88.68/26.82 ((
% 88.68/26.82 (brelnall2) =>
% 88.68/26.82 ((
% 88.68/26.82 (!!) @ (
% 88.68/26.82 (('#B') @ (
% 88.68/26.82 !!) @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#S') @ (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 '#S') @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 =>))) @
% 88.68/26.82 ex1)))) @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 !!))) @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#S') @ (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 '#B') @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 '#S') @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 =>))) @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#C') @ in)))))))) @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 !!))))) @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#C') @ (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 '#B') @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 '#B') @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 '#S') @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 =>))) @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#C') @ in)))))))))) @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#S') @ (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 '#S') @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 '#B'))) @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 =>))))))) @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#C') @ (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 '#B') @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 '#S') @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 =>))))))) @
% 88.68/26.82 (
% 88.68/26.82 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 88.68/26.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl376])).
% 88.68/26.82 thf(zip_derived_cl392, plain,
% 88.68/26.82 (~ (((powersetE) =>
% 88.68/26.82 (((setunionI) =>
% 88.68/26.82 (((setunionE) =>
% 88.68/26.82 (((subPowSU) =>
% 88.68/26.82 (((exuE2) =>
% 88.68/26.82 (((nonemptyImpWitness) =>
% 88.68/26.82 (((uniqinunit) =>
% 88.68/26.82 (((notinsingleton) =>
% 88.68/26.82 (((eqinunit) =>
% 88.68/26.82 (((singletonsswitch) =>
% 88.68/26.82 (((upairsetE) =>
% 88.68/26.82 (((upairsetIL) =>
% 88.68/26.82 (((upairsetIR) =>
% 88.68/26.82 (((emptyE1) =>
% 88.68/26.82 (((vacuousDall) =>
% 88.68/26.82 (((quantDeMorgan1) =>
% 88.68/26.82 (((quantDeMorgan2) =>
% 88.68/26.82 (((quantDeMorgan3) =>
% 88.68/26.82 (((quantDeMorgan4) =>
% 88.68/26.82 (((prop2setI) =>
% 88.68/26.82 (((prop2set2propI) =>
% 88.68/26.82 (((notdexE) =>
% 88.68/26.82 (((notdallE) =>
% 88.68/26.82 (((exuI1) =>
% 88.68/26.82 (((exuI3) =>
% 88.68/26.82 (((exuI2) =>
% 88.68/26.82 (((inCongP) =>
% 88.68/26.82 (((in__Cong) =>
% 88.68/26.82 (((exuE3u) =>
% 88.68/26.82 (((exu__Cong) =>
% 88.68/26.82 ((
% 88.68/26.82 (setadjoin__Cong) =>
% 88.68/26.82 ((
% 88.68/26.82 (powerset__Cong) =>
% 88.68/26.82 ((
% 88.68/26.82 (setunion__Cong) =>
% 88.68/26.82 ((
% 88.68/26.82 (exuEu) =>
% 88.68/26.82 ((
% 88.68/26.82 (descr__Cong) =>
% 88.68/26.82 ((
% 88.68/26.82 (dsetconstr__Cong) =>
% 88.68/26.82 ((
% 88.68/26.82 (subsetI1) =>
% 88.68/26.82 ((
% 88.68/26.82 (eqimpsubset2) =>
% 88.68/26.82 ((
% 88.68/26.82 (eqimpsubset1) =>
% 88.68/26.82 ((
% 88.68/26.82 (subsetI2) =>
% 88.68/26.82 ((
% 88.68/26.82 (emptysetsubset) =>
% 88.68/26.82 ((
% 88.68/26.82 (subsetE) =>
% 88.68/26.82 ((
% 88.68/26.82 (subsetE2) =>
% 88.68/26.82 ((
% 88.68/26.82 (notsubsetI) =>
% 88.68/26.82 ((
% 88.68/26.82 (notequalI1) =>
% 88.68/26.82 ((
% 88.68/26.82 (notequalI2) =>
% 88.68/26.82 ((
% 88.68/26.82 (subsetRefl) =>
% 88.68/26.82 ((
% 88.68/26.82 (subsetTrans) =>
% 88.68/26.82 ((
% 88.68/26.82 (setadjoinSub) =>
% 88.68/26.82 ((
% 88.68/26.82 (setadjoinSub2) =>
% 88.68/26.82 ((
% 88.68/26.82 (subset2powerset) =>
% 88.68/26.82 ((
% 88.68/26.82 (setextsub) =>
% 88.68/26.82 ((
% 88.68/26.82 (subsetemptysetimpeq) =>
% 88.68/26.82 ((
% 88.68/26.82 (powersetI1) =>
% 88.68/26.82 ((
% 88.68/26.82 (powersetE1) =>
% 88.68/26.82 ((
% 88.68/26.82 (inPowerset) =>
% 88.68/26.82 ((
% 88.68/26.82 (powersetsubset) =>
% 88.68/26.82 ((
% 88.68/26.82 (sepInPowerset) =>
% 88.68/26.82 ((
% 88.68/26.82 (sepSubset) =>
% 88.68/26.82 ((
% 88.68/26.82 (binunionIL) =>
% 88.68/26.82 ((
% 88.68/26.82 (upairset2IR) =>
% 88.68/26.82 ((
% 88.68/26.82 (binunionIR) =>
% 88.68/26.82 ((
% 88.68/26.82 (binunionEcases) =>
% 88.68/26.82 ((
% 88.68/26.82 (binunionE) =>
% 88.68/26.82 ((
% 88.68/26.82 (binunionLsub) =>
% 88.68/26.82 ((
% 88.68/26.82 (binunionRsub) =>
% 88.68/26.82 ((
% 88.68/26.82 (binintersectI) =>
% 88.68/26.82 ((
% 88.68/26.82 (binintersectSubset5) =>
% 88.68/26.82 ((
% 88.68/26.82 (binintersectEL) =>
% 88.68/26.82 ((
% 88.68/26.82 (binintersectLsub) =>
% 88.68/26.82 ((
% 88.68/26.82 (binintersectSubset2) =>
% 88.68/26.82 ((
% 88.68/26.82 (binintersectSubset3) =>
% 88.68/26.82 ((
% 88.68/26.82 (binintersectER) =>
% 88.68/26.82 ((
% 88.68/26.82 (disjointsetsI1) =>
% 88.68/26.82 ((
% 88.68/26.82 (binintersectRsub) =>
% 88.68/26.82 ((
% 88.68/26.82 (binintersectSubset4) =>
% 88.68/26.82 ((
% 88.68/26.82 (binintersectSubset1) =>
% 88.68/26.82 ((
% 88.68/26.82 (bs114d) =>
% 88.68/26.82 ((
% 88.68/26.82 (setminusI) =>
% 88.68/26.82 ((
% 88.68/26.82 (setminusEL) =>
% 88.68/26.82 ((
% 88.68/26.82 (setminusER) =>
% 88.68/26.82 ((
% 88.68/26.82 (setminusSubset2) =>
% 88.68/26.82 ((
% 88.68/26.82 (setminusERneg) =>
% 88.68/26.82 ((
% 88.68/26.82 (setminusELneg) =>
% 88.68/26.82 ((
% 88.68/26.82 (setminusILneg) =>
% 88.68/26.82 ((
% 88.68/26.82 (setminusIRneg) =>
% 88.68/26.82 ((
% 88.68/26.82 (setminusLsub) =>
% 88.68/26.82 ((
% 88.68/26.82 (setminusSubset1) =>
% 88.68/26.82 ((
% 88.68/26.82 (symdiffE) =>
% 88.68/26.82 ((
% 88.68/26.82 (symdiffI1) =>
% 88.68/26.82 ((
% 88.68/26.82 (symdiffI2) =>
% 88.68/26.82 ((
% 88.68/26.82 (symdiffIneg1) =>
% 88.68/26.82 ((
% 88.68/26.82 (symdiffIneg2) =>
% 88.68/26.82 ((
% 88.68/26.82 (secondinupair) =>
% 88.68/26.82 ((
% 88.68/26.82 (setukpairIL) =>
% 88.68/26.82 ((
% 88.68/26.82 (setukpairIR) =>
% 88.68/26.82 ((
% 88.68/26.82 (kpairiskpair) =>
% 88.68/26.82 ((
% 88.68/26.82 (kpairp) =>
% 88.68/26.82 ((
% 88.68/26.82 (singletonsubset) =>
% 88.68/26.82 ((
% 88.68/26.82 (singletoninpowerset) =>
% 88.68/26.82 ((
% 88.68/26.82 (singletoninpowunion) =>
% 88.68/26.82 ((
% 88.68/26.82 (upairset2E) =>
% 88.68/26.82 ((
% 88.68/26.82 (upairsubunion) =>
% 88.68/26.82 ((
% 88.68/26.82 (upairinpowunion) =>
% 88.68/26.82 ((
% 88.68/26.82 (ubforcartprodlem1) =>
% 88.68/26.82 ((
% 88.68/26.82 (ubforcartprodlem2) =>
% 88.68/26.82 ((
% 88.68/26.82 (ubforcartprodlem3) =>
% 88.68/26.82 ((
% 88.68/26.82 (cartprodpairin) =>
% 88.68/26.82 ((
% 88.68/26.82 (cartprodmempair1) =>
% 88.68/26.82 ((
% 88.68/26.82 (cartprodmempair) =>
% 88.68/26.82 ((
% 88.68/26.82 (setunionE2) =>
% 88.68/26.82 ((
% 88.68/26.82 (setunionsingleton1) =>
% 88.68/26.82 ((
% 88.68/26.82 (setunionsingleton2) =>
% 88.68/26.82 ((
% 88.68/26.82 (setunionsingleton) =>
% 88.68/26.82 ((
% 88.68/26.82 (singletonprop) =>
% 88.68/26.82 ((
% 88.68/26.82 (ex1E1) =>
% 88.68/26.82 ((
% 88.68/26.82 (ex1I) =>
% 88.68/26.82 ((
% 88.68/26.82 (ex1I2) =>
% 88.68/26.82 ((
% 88.68/26.82 (singletonsuniq) =>
% 88.68/26.82 ((
% 88.68/26.82 (setukpairinjL1) =>
% 88.68/26.82 ((
% 88.68/26.82 (kfstsingleton) =>
% 88.68/26.82 ((
% 88.68/26.82 (theprop) =>
% 88.68/26.82 ((
% 88.68/26.82 (kfstpairEq) =>
% 88.68/26.82 ((
% 88.68/26.82 (cartprodfstin) =>
% 88.68/26.82 ((
% 88.68/26.82 (setukpairinjL2) =>
% 88.68/26.82 ((
% 88.68/26.82 (setukpairinjL) =>
% 88.68/26.82 ((
% 88.68/26.82 (setukpairinjR11) =>
% 88.68/26.82 ((
% 88.68/26.82 (setukpairinjR12) =>
% 88.68/26.82 ((
% 88.68/26.82 (setukpairinjR1) =>
% 88.68/26.82 ((
% 88.68/26.82 (upairequniteq) =>
% 88.68/26.82 ((
% 88.68/26.82 (setukpairinjR2) =>
% 88.68/26.82 ((
% 88.68/26.82 (setukpairinjR) =>
% 88.68/26.82 ((
% 88.68/26.82 (ksndsingleton) =>
% 88.68/26.82 ((
% 88.68/26.82 (ksndpairEq) =>
% 88.68/26.82 ((
% 88.68/26.82 (kpairsurjEq) =>
% 88.68/26.82 ((
% 88.68/26.82 (cartprodsndin) =>
% 88.68/26.82 ((
% 88.68/26.82 (cartprodpairmemEL) =>
% 88.68/26.82 ((
% 88.68/26.82 (cartprodpairmemER) =>
% 88.68/26.82 ((
% 88.68/26.82 (cartprodmempaircEq) =>
% 88.68/26.82 ((
% 88.68/26.82 (cartprodfstpairEq) =>
% 88.68/26.82 ((
% 88.68/26.82 (cartprodsndpairEq) =>
% 88.68/26.82 ((
% 88.68/26.82 (cartprodpairsurjEq) =>
% 88.68/26.82 ((
% 88.68/26.82 (dpsetconstrI) =>
% 88.68/26.82 ((
% 88.68/26.82 (dpsetconstrSub) =>
% 88.68/26.82 ((
% 88.68/26.82 (setOfPairsIsBReln) =>
% 88.68/26.82 ((
% 88.68/26.82 (dpsetconstrERa) =>
% 88.68/26.82 ((
% 88.68/26.82 (dpsetconstrEL1) =>
% 88.68/26.82 ((
% 88.68/26.82 (dpsetconstrEL2) =>
% 88.68/26.82 ((
% 88.68/26.82 (dpsetconstrER) =>
% 88.68/26.82 ((
% 88.68/26.82 (funcImageSingleton) =>
% 88.68/26.82 ((
% 88.68/26.82 (apProp) =>
% 88.68/26.82 ((
% 88.68/26.82 (app) =>
% 88.68/26.82 ((
% 88.68/26.82 (infuncsetfunc) =>
% 88.68/26.82 ((
% 88.68/26.82 (ap2p) =>
% 88.68/26.82 ((
% 88.68/26.82 (funcinfuncset) =>
% 88.68/26.82 ((
% 88.68/26.82 (lamProp) =>
% 88.68/26.82 ((
% 88.68/26.82 (lamp) =>
% 88.68/26.82 ((
% 88.68/26.82 (lam2p) =>
% 88.68/26.82 ((
% 88.68/26.82 (brelnall1) =>
% 88.68/26.82 ((
% 88.68/26.82 (brelnall2) =>
% 88.68/26.82 ((
% 88.68/26.82 (!!) @ (
% 88.68/26.82 (('#B') @ (
% 88.68/26.82 !!) @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#S') @ (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 '#S') @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 =>))) @
% 88.68/26.82 ex1)))) @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 !!))) @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#S') @ (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 '#B') @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 '#S') @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 =>))) @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#C') @ in)))))))) @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 !!))))) @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#C') @ (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 '#B') @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 '#B') @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 '#S') @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 =>))) @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#C') @ in)))))))))) @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#S') @ (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 '#S') @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 '#B'))) @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 =>))))))) @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#C') @ (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 '#B') @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 '#S') @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 =>))))))) @
% 88.68/26.82 (
% 88.68/26.82 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 88.68/26.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl384])).
% 88.68/26.82 thf(zip_derived_cl400, plain,
% 88.68/26.82 (~ (((setunionI) =>
% 88.68/26.82 (((setunionE) =>
% 88.68/26.82 (((subPowSU) =>
% 88.68/26.82 (((exuE2) =>
% 88.68/26.82 (((nonemptyImpWitness) =>
% 88.68/26.82 (((uniqinunit) =>
% 88.68/26.82 (((notinsingleton) =>
% 88.68/26.82 (((eqinunit) =>
% 88.68/26.82 (((singletonsswitch) =>
% 88.68/26.82 (((upairsetE) =>
% 88.68/26.82 (((upairsetIL) =>
% 88.68/26.82 (((upairsetIR) =>
% 88.68/26.82 (((emptyE1) =>
% 88.68/26.82 (((vacuousDall) =>
% 88.68/26.82 (((quantDeMorgan1) =>
% 88.68/26.82 (((quantDeMorgan2) =>
% 88.68/26.82 (((quantDeMorgan3) =>
% 88.68/26.82 (((quantDeMorgan4) =>
% 88.68/26.82 (((prop2setI) =>
% 88.68/26.82 (((prop2set2propI) =>
% 88.68/26.82 (((notdexE) =>
% 88.68/26.82 (((notdallE) =>
% 88.68/26.82 (((exuI1) =>
% 88.68/26.82 (((exuI3) =>
% 88.68/26.82 (((exuI2) =>
% 88.68/26.82 (((inCongP) =>
% 88.68/26.82 (((in__Cong) =>
% 88.68/26.82 (((exuE3u) =>
% 88.68/26.82 (((exu__Cong) =>
% 88.68/26.82 (((setadjoin__Cong) =>
% 88.68/26.82 ((
% 88.68/26.82 (powerset__Cong) =>
% 88.68/26.82 ((
% 88.68/26.82 (setunion__Cong) =>
% 88.68/26.82 ((
% 88.68/26.82 (exuEu) =>
% 88.68/26.82 ((
% 88.68/26.82 (descr__Cong) =>
% 88.68/26.82 ((
% 88.68/26.82 (dsetconstr__Cong) =>
% 88.68/26.82 ((
% 88.68/26.82 (subsetI1) =>
% 88.68/26.82 ((
% 88.68/26.82 (eqimpsubset2) =>
% 88.68/26.82 ((
% 88.68/26.82 (eqimpsubset1) =>
% 88.68/26.82 ((
% 88.68/26.82 (subsetI2) =>
% 88.68/26.82 ((
% 88.68/26.82 (emptysetsubset) =>
% 88.68/26.82 ((
% 88.68/26.82 (subsetE) =>
% 88.68/26.82 ((
% 88.68/26.82 (subsetE2) =>
% 88.68/26.82 ((
% 88.68/26.82 (notsubsetI) =>
% 88.68/26.82 ((
% 88.68/26.82 (notequalI1) =>
% 88.68/26.82 ((
% 88.68/26.82 (notequalI2) =>
% 88.68/26.82 ((
% 88.68/26.82 (subsetRefl) =>
% 88.68/26.82 ((
% 88.68/26.82 (subsetTrans) =>
% 88.68/26.82 ((
% 88.68/26.82 (setadjoinSub) =>
% 88.68/26.82 ((
% 88.68/26.82 (setadjoinSub2) =>
% 88.68/26.82 ((
% 88.68/26.82 (subset2powerset) =>
% 88.68/26.82 ((
% 88.68/26.82 (setextsub) =>
% 88.68/26.82 ((
% 88.68/26.82 (subsetemptysetimpeq) =>
% 88.68/26.82 ((
% 88.68/26.82 (powersetI1) =>
% 88.68/26.82 ((
% 88.68/26.82 (powersetE1) =>
% 88.68/26.82 ((
% 88.68/26.82 (inPowerset) =>
% 88.68/26.82 ((
% 88.68/26.82 (powersetsubset) =>
% 88.68/26.82 ((
% 88.68/26.82 (sepInPowerset) =>
% 88.68/26.82 ((
% 88.68/26.82 (sepSubset) =>
% 88.68/26.82 ((
% 88.68/26.82 (binunionIL) =>
% 88.68/26.82 ((
% 88.68/26.82 (upairset2IR) =>
% 88.68/26.82 ((
% 88.68/26.82 (binunionIR) =>
% 88.68/26.82 ((
% 88.68/26.82 (binunionEcases) =>
% 88.68/26.82 ((
% 88.68/26.82 (binunionE) =>
% 88.68/26.82 ((
% 88.68/26.82 (binunionLsub) =>
% 88.68/26.82 ((
% 88.68/26.82 (binunionRsub) =>
% 88.68/26.82 ((
% 88.68/26.82 (binintersectI) =>
% 88.68/26.82 ((
% 88.68/26.82 (binintersectSubset5) =>
% 88.68/26.82 ((
% 88.68/26.82 (binintersectEL) =>
% 88.68/26.82 ((
% 88.68/26.82 (binintersectLsub) =>
% 88.68/26.82 ((
% 88.68/26.82 (binintersectSubset2) =>
% 88.68/26.82 ((
% 88.68/26.82 (binintersectSubset3) =>
% 88.68/26.82 ((
% 88.68/26.82 (binintersectER) =>
% 88.68/26.82 ((
% 88.68/26.82 (disjointsetsI1) =>
% 88.68/26.82 ((
% 88.68/26.82 (binintersectRsub) =>
% 88.68/26.82 ((
% 88.68/26.82 (binintersectSubset4) =>
% 88.68/26.82 ((
% 88.68/26.82 (binintersectSubset1) =>
% 88.68/26.82 ((
% 88.68/26.82 (bs114d) =>
% 88.68/26.82 ((
% 88.68/26.82 (setminusI) =>
% 88.68/26.82 ((
% 88.68/26.82 (setminusEL) =>
% 88.68/26.82 ((
% 88.68/26.82 (setminusER) =>
% 88.68/26.82 ((
% 88.68/26.82 (setminusSubset2) =>
% 88.68/26.82 ((
% 88.68/26.82 (setminusERneg) =>
% 88.68/26.82 ((
% 88.68/26.82 (setminusELneg) =>
% 88.68/26.82 ((
% 88.68/26.82 (setminusILneg) =>
% 88.68/26.82 ((
% 88.68/26.82 (setminusIRneg) =>
% 88.68/26.82 ((
% 88.68/26.82 (setminusLsub) =>
% 88.68/26.82 ((
% 88.68/26.82 (setminusSubset1) =>
% 88.68/26.82 ((
% 88.68/26.82 (symdiffE) =>
% 88.68/26.82 ((
% 88.68/26.82 (symdiffI1) =>
% 88.68/26.82 ((
% 88.68/26.82 (symdiffI2) =>
% 88.68/26.82 ((
% 88.68/26.82 (symdiffIneg1) =>
% 88.68/26.82 ((
% 88.68/26.82 (symdiffIneg2) =>
% 88.68/26.82 ((
% 88.68/26.82 (secondinupair) =>
% 88.68/26.82 ((
% 88.68/26.82 (setukpairIL) =>
% 88.68/26.82 ((
% 88.68/26.82 (setukpairIR) =>
% 88.68/26.82 ((
% 88.68/26.82 (kpairiskpair) =>
% 88.68/26.82 ((
% 88.68/26.82 (kpairp) =>
% 88.68/26.82 ((
% 88.68/26.82 (singletonsubset) =>
% 88.68/26.82 ((
% 88.68/26.82 (singletoninpowerset) =>
% 88.68/26.82 ((
% 88.68/26.82 (singletoninpowunion) =>
% 88.68/26.82 ((
% 88.68/26.82 (upairset2E) =>
% 88.68/26.82 ((
% 88.68/26.82 (upairsubunion) =>
% 88.68/26.82 ((
% 88.68/26.82 (upairinpowunion) =>
% 88.68/26.82 ((
% 88.68/26.82 (ubforcartprodlem1) =>
% 88.68/26.82 ((
% 88.68/26.82 (ubforcartprodlem2) =>
% 88.68/26.82 ((
% 88.68/26.82 (ubforcartprodlem3) =>
% 88.68/26.82 ((
% 88.68/26.82 (cartprodpairin) =>
% 88.68/26.82 ((
% 88.68/26.82 (cartprodmempair1) =>
% 88.68/26.82 ((
% 88.68/26.82 (cartprodmempair) =>
% 88.68/26.82 ((
% 88.68/26.82 (setunionE2) =>
% 88.68/26.82 ((
% 88.68/26.82 (setunionsingleton1) =>
% 88.68/26.82 ((
% 88.68/26.82 (setunionsingleton2) =>
% 88.68/26.82 ((
% 88.68/26.82 (setunionsingleton) =>
% 88.68/26.82 ((
% 88.68/26.82 (singletonprop) =>
% 88.68/26.82 ((
% 88.68/26.82 (ex1E1) =>
% 88.68/26.82 ((
% 88.68/26.82 (ex1I) =>
% 88.68/26.82 ((
% 88.68/26.82 (ex1I2) =>
% 88.68/26.82 ((
% 88.68/26.82 (singletonsuniq) =>
% 88.68/26.82 ((
% 88.68/26.82 (setukpairinjL1) =>
% 88.68/26.82 ((
% 88.68/26.82 (kfstsingleton) =>
% 88.68/26.82 ((
% 88.68/26.82 (theprop) =>
% 88.68/26.82 ((
% 88.68/26.82 (kfstpairEq) =>
% 88.68/26.82 ((
% 88.68/26.82 (cartprodfstin) =>
% 88.68/26.82 ((
% 88.68/26.82 (setukpairinjL2) =>
% 88.68/26.82 ((
% 88.68/26.82 (setukpairinjL) =>
% 88.68/26.82 ((
% 88.68/26.82 (setukpairinjR11) =>
% 88.68/26.82 ((
% 88.68/26.82 (setukpairinjR12) =>
% 88.68/26.82 ((
% 88.68/26.82 (setukpairinjR1) =>
% 88.68/26.82 ((
% 88.68/26.82 (upairequniteq) =>
% 88.68/26.82 ((
% 88.68/26.82 (setukpairinjR2) =>
% 88.68/26.82 ((
% 88.68/26.82 (setukpairinjR) =>
% 88.68/26.82 ((
% 88.68/26.82 (ksndsingleton) =>
% 88.68/26.82 ((
% 88.68/26.82 (ksndpairEq) =>
% 88.68/26.82 ((
% 88.68/26.82 (kpairsurjEq) =>
% 88.68/26.82 ((
% 88.68/26.82 (cartprodsndin) =>
% 88.68/26.82 ((
% 88.68/26.82 (cartprodpairmemEL) =>
% 88.68/26.82 ((
% 88.68/26.82 (cartprodpairmemER) =>
% 88.68/26.82 ((
% 88.68/26.82 (cartprodmempaircEq) =>
% 88.68/26.82 ((
% 88.68/26.82 (cartprodfstpairEq) =>
% 88.68/26.82 ((
% 88.68/26.82 (cartprodsndpairEq) =>
% 88.68/26.82 ((
% 88.68/26.82 (cartprodpairsurjEq) =>
% 88.68/26.82 ((
% 88.68/26.82 (dpsetconstrI) =>
% 88.68/26.82 ((
% 88.68/26.82 (dpsetconstrSub) =>
% 88.68/26.82 ((
% 88.68/26.82 (setOfPairsIsBReln) =>
% 88.68/26.82 ((
% 88.68/26.82 (dpsetconstrERa) =>
% 88.68/26.82 ((
% 88.68/26.82 (dpsetconstrEL1) =>
% 88.68/26.82 ((
% 88.68/26.82 (dpsetconstrEL2) =>
% 88.68/26.82 ((
% 88.68/26.82 (dpsetconstrER) =>
% 88.68/26.82 ((
% 88.68/26.82 (funcImageSingleton) =>
% 88.68/26.82 ((
% 88.68/26.82 (apProp) =>
% 88.68/26.82 ((
% 88.68/26.82 (app) =>
% 88.68/26.82 ((
% 88.68/26.82 (infuncsetfunc) =>
% 88.68/26.82 ((
% 88.68/26.82 (ap2p) =>
% 88.68/26.82 ((
% 88.68/26.82 (funcinfuncset) =>
% 88.68/26.82 ((
% 88.68/26.82 (lamProp) =>
% 88.68/26.82 ((
% 88.68/26.82 (lamp) =>
% 88.68/26.82 ((
% 88.68/26.82 (lam2p) =>
% 88.68/26.82 ((
% 88.68/26.82 (brelnall1) =>
% 88.68/26.82 ((
% 88.68/26.82 (brelnall2) =>
% 88.68/26.82 ((
% 88.68/26.82 (!!) @ (
% 88.68/26.82 (('#B') @ (
% 88.68/26.82 !!) @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#S') @ (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 '#S') @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 =>))) @
% 88.68/26.82 ex1)))) @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 !!))) @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#S') @ (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 '#B') @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 '#S') @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 =>))) @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#C') @ in)))))))) @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 !!))))) @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#C') @ (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 '#B') @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 '#B') @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 '#S') @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 =>))) @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#C') @ in)))))))))) @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#S') @ (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 '#S') @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 '#B'))) @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 =>))))))) @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#C') @ (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 '#B') @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 '#S') @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 =>))))))) @
% 88.68/26.82 (
% 88.68/26.82 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 88.68/26.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl392])).
% 88.68/26.82 thf(zip_derived_cl408, plain,
% 88.68/26.82 (~ (((setunionE) =>
% 88.68/26.82 (((subPowSU) =>
% 88.68/26.82 (((exuE2) =>
% 88.68/26.82 (((nonemptyImpWitness) =>
% 88.68/26.82 (((uniqinunit) =>
% 88.68/26.82 (((notinsingleton) =>
% 88.68/26.82 (((eqinunit) =>
% 88.68/26.82 (((singletonsswitch) =>
% 88.68/26.82 (((upairsetE) =>
% 88.68/26.82 (((upairsetIL) =>
% 88.68/26.82 (((upairsetIR) =>
% 88.68/26.82 (((emptyE1) =>
% 88.68/26.82 (((vacuousDall) =>
% 88.68/26.82 (((quantDeMorgan1) =>
% 88.68/26.82 (((quantDeMorgan2) =>
% 88.68/26.82 (((quantDeMorgan3) =>
% 88.68/26.82 (((quantDeMorgan4) =>
% 88.68/26.82 (((prop2setI) =>
% 88.68/26.82 (((prop2set2propI) =>
% 88.68/26.82 (((notdexE) =>
% 88.68/26.82 (((notdallE) =>
% 88.68/26.82 (((exuI1) =>
% 88.68/26.82 (((exuI3) =>
% 88.68/26.82 (((exuI2) =>
% 88.68/26.82 (((inCongP) =>
% 88.68/26.82 (((in__Cong) =>
% 88.68/26.82 (((exuE3u) =>
% 88.68/26.82 (((exu__Cong) =>
% 88.68/26.82 (((setadjoin__Cong) =>
% 88.68/26.82 (((powerset__Cong) =>
% 88.68/26.82 ((
% 88.68/26.82 (setunion__Cong) =>
% 88.68/26.82 ((
% 88.68/26.82 (exuEu) =>
% 88.68/26.82 ((
% 88.68/26.82 (descr__Cong) =>
% 88.68/26.82 ((
% 88.68/26.82 (dsetconstr__Cong) =>
% 88.68/26.82 ((
% 88.68/26.82 (subsetI1) =>
% 88.68/26.82 ((
% 88.68/26.82 (eqimpsubset2) =>
% 88.68/26.82 ((
% 88.68/26.82 (eqimpsubset1) =>
% 88.68/26.82 ((
% 88.68/26.82 (subsetI2) =>
% 88.68/26.82 ((
% 88.68/26.82 (emptysetsubset) =>
% 88.68/26.82 ((
% 88.68/26.82 (subsetE) =>
% 88.68/26.82 ((
% 88.68/26.82 (subsetE2) =>
% 88.68/26.82 ((
% 88.68/26.82 (notsubsetI) =>
% 88.68/26.82 ((
% 88.68/26.82 (notequalI1) =>
% 88.68/26.82 ((
% 88.68/26.82 (notequalI2) =>
% 88.68/26.82 ((
% 88.68/26.82 (subsetRefl) =>
% 88.68/26.82 ((
% 88.68/26.82 (subsetTrans) =>
% 88.68/26.82 ((
% 88.68/26.82 (setadjoinSub) =>
% 88.68/26.82 ((
% 88.68/26.82 (setadjoinSub2) =>
% 88.68/26.82 ((
% 88.68/26.82 (subset2powerset) =>
% 88.68/26.82 ((
% 88.68/26.82 (setextsub) =>
% 88.68/26.82 ((
% 88.68/26.82 (subsetemptysetimpeq) =>
% 88.68/26.82 ((
% 88.68/26.82 (powersetI1) =>
% 88.68/26.82 ((
% 88.68/26.82 (powersetE1) =>
% 88.68/26.82 ((
% 88.68/26.82 (inPowerset) =>
% 88.68/26.82 ((
% 88.68/26.82 (powersetsubset) =>
% 88.68/26.82 ((
% 88.68/26.82 (sepInPowerset) =>
% 88.68/26.82 ((
% 88.68/26.82 (sepSubset) =>
% 88.68/26.82 ((
% 88.68/26.82 (binunionIL) =>
% 88.68/26.82 ((
% 88.68/26.82 (upairset2IR) =>
% 88.68/26.82 ((
% 88.68/26.82 (binunionIR) =>
% 88.68/26.82 ((
% 88.68/26.82 (binunionEcases) =>
% 88.68/26.82 ((
% 88.68/26.82 (binunionE) =>
% 88.68/26.82 ((
% 88.68/26.82 (binunionLsub) =>
% 88.68/26.82 ((
% 88.68/26.82 (binunionRsub) =>
% 88.68/26.82 ((
% 88.68/26.82 (binintersectI) =>
% 88.68/26.82 ((
% 88.68/26.82 (binintersectSubset5) =>
% 88.68/26.82 ((
% 88.68/26.82 (binintersectEL) =>
% 88.68/26.82 ((
% 88.68/26.82 (binintersectLsub) =>
% 88.68/26.82 ((
% 88.68/26.82 (binintersectSubset2) =>
% 88.68/26.82 ((
% 88.68/26.82 (binintersectSubset3) =>
% 88.68/26.82 ((
% 88.68/26.82 (binintersectER) =>
% 88.68/26.82 ((
% 88.68/26.82 (disjointsetsI1) =>
% 88.68/26.82 ((
% 88.68/26.82 (binintersectRsub) =>
% 88.68/26.82 ((
% 88.68/26.82 (binintersectSubset4) =>
% 88.68/26.82 ((
% 88.68/26.82 (binintersectSubset1) =>
% 88.68/26.82 ((
% 88.68/26.82 (bs114d) =>
% 88.68/26.82 ((
% 88.68/26.82 (setminusI) =>
% 88.68/26.82 ((
% 88.68/26.82 (setminusEL) =>
% 88.68/26.82 ((
% 88.68/26.82 (setminusER) =>
% 88.68/26.82 ((
% 88.68/26.82 (setminusSubset2) =>
% 88.68/26.82 ((
% 88.68/26.82 (setminusERneg) =>
% 88.68/26.82 ((
% 88.68/26.82 (setminusELneg) =>
% 88.68/26.82 ((
% 88.68/26.82 (setminusILneg) =>
% 88.68/26.82 ((
% 88.68/26.82 (setminusIRneg) =>
% 88.68/26.82 ((
% 88.68/26.82 (setminusLsub) =>
% 88.68/26.82 ((
% 88.68/26.82 (setminusSubset1) =>
% 88.68/26.82 ((
% 88.68/26.82 (symdiffE) =>
% 88.68/26.82 ((
% 88.68/26.82 (symdiffI1) =>
% 88.68/26.82 ((
% 88.68/26.82 (symdiffI2) =>
% 88.68/26.82 ((
% 88.68/26.82 (symdiffIneg1) =>
% 88.68/26.82 ((
% 88.68/26.82 (symdiffIneg2) =>
% 88.68/26.82 ((
% 88.68/26.82 (secondinupair) =>
% 88.68/26.82 ((
% 88.68/26.82 (setukpairIL) =>
% 88.68/26.82 ((
% 88.68/26.82 (setukpairIR) =>
% 88.68/26.82 ((
% 88.68/26.82 (kpairiskpair) =>
% 88.68/26.82 ((
% 88.68/26.82 (kpairp) =>
% 88.68/26.82 ((
% 88.68/26.82 (singletonsubset) =>
% 88.68/26.82 ((
% 88.68/26.82 (singletoninpowerset) =>
% 88.68/26.82 ((
% 88.68/26.82 (singletoninpowunion) =>
% 88.68/26.82 ((
% 88.68/26.82 (upairset2E) =>
% 88.68/26.82 ((
% 88.68/26.82 (upairsubunion) =>
% 88.68/26.82 ((
% 88.68/26.82 (upairinpowunion) =>
% 88.68/26.82 ((
% 88.68/26.82 (ubforcartprodlem1) =>
% 88.68/26.82 ((
% 88.68/26.82 (ubforcartprodlem2) =>
% 88.68/26.82 ((
% 88.68/26.82 (ubforcartprodlem3) =>
% 88.68/26.82 ((
% 88.68/26.82 (cartprodpairin) =>
% 88.68/26.82 ((
% 88.68/26.82 (cartprodmempair1) =>
% 88.68/26.82 ((
% 88.68/26.82 (cartprodmempair) =>
% 88.68/26.82 ((
% 88.68/26.82 (setunionE2) =>
% 88.68/26.82 ((
% 88.68/26.82 (setunionsingleton1) =>
% 88.68/26.82 ((
% 88.68/26.82 (setunionsingleton2) =>
% 88.68/26.82 ((
% 88.68/26.82 (setunionsingleton) =>
% 88.68/26.82 ((
% 88.68/26.82 (singletonprop) =>
% 88.68/26.82 ((
% 88.68/26.82 (ex1E1) =>
% 88.68/26.82 ((
% 88.68/26.82 (ex1I) =>
% 88.68/26.82 ((
% 88.68/26.82 (ex1I2) =>
% 88.68/26.82 ((
% 88.68/26.82 (singletonsuniq) =>
% 88.68/26.82 ((
% 88.68/26.82 (setukpairinjL1) =>
% 88.68/26.82 ((
% 88.68/26.82 (kfstsingleton) =>
% 88.68/26.82 ((
% 88.68/26.82 (theprop) =>
% 88.68/26.82 ((
% 88.68/26.82 (kfstpairEq) =>
% 88.68/26.82 ((
% 88.68/26.82 (cartprodfstin) =>
% 88.68/26.82 ((
% 88.68/26.82 (setukpairinjL2) =>
% 88.68/26.82 ((
% 88.68/26.82 (setukpairinjL) =>
% 88.68/26.82 ((
% 88.68/26.82 (setukpairinjR11) =>
% 88.68/26.82 ((
% 88.68/26.82 (setukpairinjR12) =>
% 88.68/26.82 ((
% 88.68/26.82 (setukpairinjR1) =>
% 88.68/26.82 ((
% 88.68/26.82 (upairequniteq) =>
% 88.68/26.82 ((
% 88.68/26.82 (setukpairinjR2) =>
% 88.68/26.82 ((
% 88.68/26.82 (setukpairinjR) =>
% 88.68/26.82 ((
% 88.68/26.82 (ksndsingleton) =>
% 88.68/26.82 ((
% 88.68/26.82 (ksndpairEq) =>
% 88.68/26.82 ((
% 88.68/26.82 (kpairsurjEq) =>
% 88.68/26.82 ((
% 88.68/26.82 (cartprodsndin) =>
% 88.68/26.82 ((
% 88.68/26.82 (cartprodpairmemEL) =>
% 88.68/26.82 ((
% 88.68/26.82 (cartprodpairmemER) =>
% 88.68/26.82 ((
% 88.68/26.82 (cartprodmempaircEq) =>
% 88.68/26.82 ((
% 88.68/26.82 (cartprodfstpairEq) =>
% 88.68/26.82 ((
% 88.68/26.82 (cartprodsndpairEq) =>
% 88.68/26.82 ((
% 88.68/26.82 (cartprodpairsurjEq) =>
% 88.68/26.82 ((
% 88.68/26.82 (dpsetconstrI) =>
% 88.68/26.82 ((
% 88.68/26.82 (dpsetconstrSub) =>
% 88.68/26.82 ((
% 88.68/26.82 (setOfPairsIsBReln) =>
% 88.68/26.82 ((
% 88.68/26.82 (dpsetconstrERa) =>
% 88.68/26.82 ((
% 88.68/26.82 (dpsetconstrEL1) =>
% 88.68/26.82 ((
% 88.68/26.82 (dpsetconstrEL2) =>
% 88.68/26.82 ((
% 88.68/26.82 (dpsetconstrER) =>
% 88.68/26.82 ((
% 88.68/26.82 (funcImageSingleton) =>
% 88.68/26.82 ((
% 88.68/26.82 (apProp) =>
% 88.68/26.82 ((
% 88.68/26.82 (app) =>
% 88.68/26.82 ((
% 88.68/26.82 (infuncsetfunc) =>
% 88.68/26.82 ((
% 88.68/26.82 (ap2p) =>
% 88.68/26.82 ((
% 88.68/26.82 (funcinfuncset) =>
% 88.68/26.82 ((
% 88.68/26.82 (lamProp) =>
% 88.68/26.82 ((
% 88.68/26.82 (lamp) =>
% 88.68/26.82 ((
% 88.68/26.82 (lam2p) =>
% 88.68/26.82 ((
% 88.68/26.82 (brelnall1) =>
% 88.68/26.82 ((
% 88.68/26.82 (brelnall2) =>
% 88.68/26.82 ((
% 88.68/26.82 (!!) @ (
% 88.68/26.82 (('#B') @ (
% 88.68/26.82 !!) @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#S') @ (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 '#S') @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 =>))) @
% 88.68/26.82 ex1)))) @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 !!))) @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#S') @ (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 '#B') @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 '#S') @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 =>))) @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#C') @ in)))))))) @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 !!))))) @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#C') @ (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 '#B') @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 '#B') @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 '#S') @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 =>))) @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#C') @ in)))))))))) @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#S') @ (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 '#S') @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 '#B'))) @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 =>))))))) @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#C') @ (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 '#B') @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 '#S') @
% 88.68/26.82 (
% 88.68/26.82 (
% 88.68/26.82 ('#B') @ (
% 88.68/26.82 =>))))))) @
% 88.68/26.82 (
% 88.68/26.82 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 88.68/26.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl400])).
% 88.68/26.82 thf(zip_derived_cl417, plain,
% 88.68/26.82 (~ (((subPowSU) =>
% 88.68/26.82 (((exuE2) =>
% 88.68/26.82 (((nonemptyImpWitness) =>
% 88.68/26.82 (((uniqinunit) =>
% 88.68/26.82 (((notinsingleton) =>
% 88.68/26.82 (((eqinunit) =>
% 88.68/26.82 (((singletonsswitch) =>
% 88.68/26.82 (((upairsetE) =>
% 88.68/26.82 (((upairsetIL) =>
% 88.68/26.82 (((upairsetIR) =>
% 88.68/26.82 (((emptyE1) =>
% 88.68/26.82 (((vacuousDall) =>
% 88.68/26.82 (((quantDeMorgan1) =>
% 88.68/26.82 (((quantDeMorgan2) =>
% 88.68/26.82 (((quantDeMorgan3) =>
% 88.68/26.82 (((quantDeMorgan4) =>
% 88.68/26.82 (((prop2setI) =>
% 88.68/26.82 (((prop2set2propI) =>
% 88.68/26.82 (((notdexE) =>
% 88.68/26.82 (((notdallE) =>
% 88.68/26.82 (((exuI1) =>
% 88.68/26.82 (((exuI3) =>
% 88.68/26.82 (((exuI2) =>
% 88.68/26.82 (((inCongP) =>
% 88.68/26.82 (((in__Cong) =>
% 88.68/26.82 (((exuE3u) =>
% 88.68/26.82 (((exu__Cong) =>
% 88.68/26.82 (((setadjoin__Cong) =>
% 88.68/26.82 (((powerset__Cong) =>
% 88.68/26.82 (((setunion__Cong) =>
% 88.68/26.82 ((
% 88.68/26.82 (exuEu) =>
% 88.68/26.82 ((
% 88.68/26.82 (descr__Cong) =>
% 88.68/26.82 ((
% 88.68/26.82 (dsetconstr__Cong) =>
% 88.68/26.82 ((
% 88.68/26.82 (subsetI1) =>
% 88.68/26.82 ((
% 88.68/26.82 (eqimpsubset2) =>
% 88.68/26.82 ((
% 88.68/26.82 (eqimpsubset1) =>
% 88.68/26.82 ((
% 88.68/26.82 (subsetI2) =>
% 88.68/26.82 ((
% 88.68/26.82 (emptysetsubset) =>
% 88.68/26.82 ((
% 88.68/26.82 (subsetE) =>
% 88.68/26.82 ((
% 88.68/26.82 (subsetE2) =>
% 88.68/26.82 ((
% 88.68/26.82 (notsubsetI) =>
% 88.68/26.82 ((
% 88.68/26.82 (notequalI1) =>
% 88.68/26.82 ((
% 88.68/26.82 (notequalI2) =>
% 88.68/26.82 ((
% 88.68/26.82 (subsetRefl) =>
% 88.68/26.82 ((
% 88.68/26.82 (subsetTrans) =>
% 88.68/26.82 ((
% 88.68/26.82 (setadjoinSub) =>
% 88.68/26.82 ((
% 88.68/26.82 (setadjoinSub2) =>
% 88.68/26.82 ((
% 88.68/26.82 (subset2powerset) =>
% 88.68/26.82 ((
% 88.68/26.82 (setextsub) =>
% 88.68/26.82 ((
% 88.68/26.82 (subsetemptysetimpeq) =>
% 88.68/26.82 ((
% 88.68/26.82 (powersetI1) =>
% 88.68/26.82 ((
% 88.68/26.82 (powersetE1) =>
% 88.68/26.82 ((
% 88.68/26.82 (inPowerset) =>
% 88.68/26.82 ((
% 88.68/26.82 (powersetsubset) =>
% 88.68/26.82 ((
% 88.68/26.82 (sepInPowerset) =>
% 88.68/26.82 ((
% 88.68/26.82 (sepSubset) =>
% 88.68/26.82 ((
% 88.68/26.82 (binunionIL) =>
% 88.68/26.82 ((
% 88.68/26.82 (upairset2IR) =>
% 88.68/26.82 ((
% 88.68/26.82 (binunionIR) =>
% 88.68/26.82 ((
% 88.68/26.82 (binunionEcases) =>
% 88.68/26.82 ((
% 88.68/26.82 (binunionE) =>
% 88.68/26.82 ((
% 88.68/26.82 (binunionLsub) =>
% 88.68/26.82 ((
% 88.68/26.82 (binunionRsub) =>
% 88.68/26.82 ((
% 88.68/26.82 (binintersectI) =>
% 88.68/26.82 ((
% 88.68/26.82 (binintersectSubset5) =>
% 88.68/26.82 ((
% 88.68/26.82 (binintersectEL) =>
% 88.68/26.82 ((
% 88.68/26.82 (binintersectLsub) =>
% 88.68/26.82 ((
% 88.68/26.82 (binintersectSubset2) =>
% 88.68/26.82 ((
% 88.68/26.82 (binintersectSubset3) =>
% 88.68/26.82 ((
% 88.68/26.82 (binintersectER) =>
% 88.68/26.82 ((
% 88.68/26.82 (disjointsetsI1) =>
% 88.68/26.82 ((
% 88.68/26.82 (binintersectRsub) =>
% 88.68/26.82 ((
% 88.68/26.82 (binintersectSubset4) =>
% 88.68/26.82 ((
% 88.68/26.82 (binintersectSubset1) =>
% 88.68/26.82 ((
% 88.68/26.82 (bs114d) =>
% 88.68/26.82 ((
% 88.68/26.82 (setminusI) =>
% 88.68/26.82 ((
% 88.68/26.82 (setminusEL) =>
% 88.68/26.82 ((
% 88.68/26.82 (setminusER) =>
% 88.68/26.82 ((
% 88.68/26.82 (setminusSubset2) =>
% 88.68/26.82 ((
% 88.68/26.82 (setminusERneg) =>
% 88.68/26.82 ((
% 88.68/26.82 (setminusELneg) =>
% 88.68/26.82 ((
% 88.68/26.82 (setminusILneg) =>
% 88.68/26.82 ((
% 88.68/26.82 (setminusIRneg) =>
% 88.68/26.82 ((
% 88.68/26.82 (setminusLsub) =>
% 88.68/26.82 ((
% 88.68/26.82 (setminusSubset1) =>
% 88.68/26.82 ((
% 88.68/26.82 (symdiffE) =>
% 88.68/26.82 ((
% 88.68/26.82 (symdiffI1) =>
% 88.68/26.82 ((
% 88.68/26.82 (symdiffI2) =>
% 88.68/26.82 ((
% 88.68/26.82 (symdiffIneg1) =>
% 88.68/26.82 ((
% 88.68/26.82 (symdiffIneg2) =>
% 88.68/26.82 ((
% 88.68/26.82 (secondinupair) =>
% 88.68/26.82 ((
% 88.68/26.82 (setukpairIL) =>
% 88.68/26.82 ((
% 88.68/26.82 (setukpairIR) =>
% 88.68/26.82 ((
% 88.68/26.82 (kpairiskpair) =>
% 88.68/26.82 ((
% 88.68/26.82 (kpairp) =>
% 88.68/26.82 ((
% 88.68/26.82 (singletonsubset) =>
% 88.68/26.82 ((
% 88.68/26.82 (singletoninpowerset) =>
% 88.68/26.82 ((
% 88.68/26.82 (singletoninpowunion) =>
% 88.68/26.82 ((
% 88.68/26.82 (upairset2E) =>
% 88.68/26.82 ((
% 88.68/26.82 (upairsubunion) =>
% 88.68/26.82 ((
% 88.68/26.82 (upairinpowunion) =>
% 88.68/26.82 ((
% 88.68/26.82 (ubforcartprodlem1) =>
% 88.68/26.82 ((
% 88.68/26.82 (ubforcartprodlem2) =>
% 88.68/26.82 ((
% 88.68/26.82 (ubforcartprodlem3) =>
% 88.68/26.82 ((
% 88.68/26.82 (cartprodpairin) =>
% 88.68/26.82 ((
% 88.68/26.82 (cartprodmempair1) =>
% 88.68/26.82 ((
% 88.68/26.82 (cartprodmempair) =>
% 88.68/26.82 ((
% 88.68/26.82 (setunionE2) =>
% 88.68/26.82 ((
% 88.68/26.82 (setunionsingleton1) =>
% 88.68/26.82 ((
% 88.68/26.82 (setunionsingleton2) =>
% 88.68/26.82 ((
% 88.68/26.82 (setunionsingleton) =>
% 88.68/26.82 ((
% 88.68/26.82 (singletonprop) =>
% 88.68/26.82 ((
% 88.68/26.82 (ex1E1) =>
% 88.68/26.82 ((
% 88.68/26.82 (ex1I) =>
% 88.68/26.82 ((
% 88.68/26.82 (ex1I2) =>
% 88.68/26.82 ((
% 88.68/26.82 (singletonsuniq) =>
% 88.68/26.82 ((
% 88.68/26.82 (setukpairinjL1) =>
% 88.68/26.82 ((
% 88.68/26.82 (kfstsingleton) =>
% 88.68/26.82 ((
% 88.68/26.82 (theprop) =>
% 88.68/26.82 ((
% 88.68/26.82 (kfstpairEq) =>
% 88.68/26.82 ((
% 88.68/26.82 (cartprodfstin) =>
% 88.68/26.82 ((
% 88.68/26.82 (setukpairinjL2) =>
% 88.68/26.82 ((
% 88.68/26.82 (setukpairinjL) =>
% 88.68/26.82 ((
% 88.68/26.82 (setukpairinjR11) =>
% 88.68/26.82 ((
% 88.68/26.82 (setukpairinjR12) =>
% 88.68/26.82 ((
% 88.68/26.82 (setukpairinjR1) =>
% 88.68/26.82 ((
% 88.68/26.82 (upairequniteq) =>
% 88.68/26.82 ((
% 88.68/26.82 (setukpairinjR2) =>
% 88.68/26.82 ((
% 88.68/26.82 (setukpairinjR) =>
% 88.68/26.82 ((
% 88.68/26.82 (ksndsingleton) =>
% 88.68/26.82 ((
% 88.68/26.82 (ksndpairEq) =>
% 88.68/26.82 ((
% 88.68/26.82 (kpairsurjEq) =>
% 88.68/26.82 ((
% 88.68/26.82 (cartprodsndin) =>
% 88.68/26.82 ((
% 88.68/26.82 (cartprodpairmemEL) =>
% 88.68/26.82 ((
% 88.68/26.82 (cartprodpairmemER) =>
% 88.68/26.82 ((
% 88.68/26.82 (cartprodmempaircEq) =>
% 88.68/26.82 ((
% 88.68/26.82 (cartprodfstpairEq) =>
% 88.68/26.82 ((
% 88.68/26.82 (cartprodsndpairEq) =>
% 88.68/26.82 ((
% 88.68/26.82 (cartprodpairsurjEq) =>
% 88.68/26.82 ((
% 88.68/26.82 (dpsetconstrI) =>
% 88.68/26.82 ((
% 88.68/26.84 (dpsetconstrSub) =>
% 88.68/26.84 ((
% 88.68/26.84 (setOfPairsIsBReln) =>
% 88.68/26.84 ((
% 88.68/26.84 (dpsetconstrERa) =>
% 88.68/26.84 ((
% 88.68/26.84 (dpsetconstrEL1) =>
% 88.68/26.84 ((
% 88.68/26.84 (dpsetconstrEL2) =>
% 88.68/26.84 ((
% 88.68/26.84 (dpsetconstrER) =>
% 88.68/26.84 ((
% 88.68/26.84 (funcImageSingleton) =>
% 88.68/26.84 ((
% 88.68/26.84 (apProp) =>
% 88.68/26.84 ((
% 88.68/26.84 (app) =>
% 88.68/26.84 ((
% 88.68/26.84 (infuncsetfunc) =>
% 88.68/26.84 ((
% 88.68/26.84 (ap2p) =>
% 88.68/26.84 ((
% 88.68/26.84 (funcinfuncset) =>
% 88.68/26.84 ((
% 88.68/26.84 (lamProp) =>
% 88.68/26.84 ((
% 88.68/26.84 (lamp) =>
% 88.68/26.84 ((
% 88.68/26.84 (lam2p) =>
% 88.68/26.84 ((
% 88.68/26.84 (brelnall1) =>
% 88.68/26.84 ((
% 88.68/26.84 (brelnall2) =>
% 88.68/26.84 ((
% 88.68/26.84 (!!) @ (
% 88.68/26.84 (('#B') @ (
% 88.68/26.84 !!) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#S') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#S') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 =>))) @
% 88.68/26.84 ex1)))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 !!))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#S') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#B') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#S') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 =>))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#C') @ in)))))))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 !!))))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#C') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#B') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#B') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#S') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 =>))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#C') @ in)))))))))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#S') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#S') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#B'))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 =>))))))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#C') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#B') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#S') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 =>))))))) @
% 88.68/26.84 (
% 88.68/26.84 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 88.68/26.84 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl408])).
% 88.68/26.84 thf(zip_derived_cl428, plain,
% 88.68/26.84 (~ (((exuE2) =>
% 88.68/26.84 (((nonemptyImpWitness) =>
% 88.68/26.84 (((uniqinunit) =>
% 88.68/26.84 (((notinsingleton) =>
% 88.68/26.84 (((eqinunit) =>
% 88.68/26.84 (((singletonsswitch) =>
% 88.68/26.84 (((upairsetE) =>
% 88.68/26.84 (((upairsetIL) =>
% 88.68/26.84 (((upairsetIR) =>
% 88.68/26.84 (((emptyE1) =>
% 88.68/26.84 (((vacuousDall) =>
% 88.68/26.84 (((quantDeMorgan1) =>
% 88.68/26.84 (((quantDeMorgan2) =>
% 88.68/26.84 (((quantDeMorgan3) =>
% 88.68/26.84 (((quantDeMorgan4) =>
% 88.68/26.84 (((prop2setI) =>
% 88.68/26.84 (((prop2set2propI) =>
% 88.68/26.84 (((notdexE) =>
% 88.68/26.84 (((notdallE) =>
% 88.68/26.84 (((exuI1) =>
% 88.68/26.84 (((exuI3) =>
% 88.68/26.84 (((exuI2) =>
% 88.68/26.84 (((inCongP) =>
% 88.68/26.84 (((in__Cong) =>
% 88.68/26.84 (((exuE3u) =>
% 88.68/26.84 (((exu__Cong) =>
% 88.68/26.84 (((setadjoin__Cong) =>
% 88.68/26.84 (((powerset__Cong) =>
% 88.68/26.84 (((setunion__Cong) =>
% 88.68/26.84 (((exuEu) =>
% 88.68/26.84 ((
% 88.68/26.84 (descr__Cong) =>
% 88.68/26.84 ((
% 88.68/26.84 (dsetconstr__Cong) =>
% 88.68/26.84 ((
% 88.68/26.84 (subsetI1) =>
% 88.68/26.84 ((
% 88.68/26.84 (eqimpsubset2) =>
% 88.68/26.84 ((
% 88.68/26.84 (eqimpsubset1) =>
% 88.68/26.84 ((
% 88.68/26.84 (subsetI2) =>
% 88.68/26.84 ((
% 88.68/26.84 (emptysetsubset) =>
% 88.68/26.84 ((
% 88.68/26.84 (subsetE) =>
% 88.68/26.84 ((
% 88.68/26.84 (subsetE2) =>
% 88.68/26.84 ((
% 88.68/26.84 (notsubsetI) =>
% 88.68/26.84 ((
% 88.68/26.84 (notequalI1) =>
% 88.68/26.84 ((
% 88.68/26.84 (notequalI2) =>
% 88.68/26.84 ((
% 88.68/26.84 (subsetRefl) =>
% 88.68/26.84 ((
% 88.68/26.84 (subsetTrans) =>
% 88.68/26.84 ((
% 88.68/26.84 (setadjoinSub) =>
% 88.68/26.84 ((
% 88.68/26.84 (setadjoinSub2) =>
% 88.68/26.84 ((
% 88.68/26.84 (subset2powerset) =>
% 88.68/26.84 ((
% 88.68/26.84 (setextsub) =>
% 88.68/26.84 ((
% 88.68/26.84 (subsetemptysetimpeq) =>
% 88.68/26.84 ((
% 88.68/26.84 (powersetI1) =>
% 88.68/26.84 ((
% 88.68/26.84 (powersetE1) =>
% 88.68/26.84 ((
% 88.68/26.84 (inPowerset) =>
% 88.68/26.84 ((
% 88.68/26.84 (powersetsubset) =>
% 88.68/26.84 ((
% 88.68/26.84 (sepInPowerset) =>
% 88.68/26.84 ((
% 88.68/26.84 (sepSubset) =>
% 88.68/26.84 ((
% 88.68/26.84 (binunionIL) =>
% 88.68/26.84 ((
% 88.68/26.84 (upairset2IR) =>
% 88.68/26.84 ((
% 88.68/26.84 (binunionIR) =>
% 88.68/26.84 ((
% 88.68/26.84 (binunionEcases) =>
% 88.68/26.84 ((
% 88.68/26.84 (binunionE) =>
% 88.68/26.84 ((
% 88.68/26.84 (binunionLsub) =>
% 88.68/26.84 ((
% 88.68/26.84 (binunionRsub) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectI) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectSubset5) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectEL) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectLsub) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectSubset2) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectSubset3) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectER) =>
% 88.68/26.84 ((
% 88.68/26.84 (disjointsetsI1) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectRsub) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectSubset4) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectSubset1) =>
% 88.68/26.84 ((
% 88.68/26.84 (bs114d) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusI) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusEL) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusER) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusSubset2) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusERneg) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusELneg) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusILneg) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusIRneg) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusLsub) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusSubset1) =>
% 88.68/26.84 ((
% 88.68/26.84 (symdiffE) =>
% 88.68/26.84 ((
% 88.68/26.84 (symdiffI1) =>
% 88.68/26.84 ((
% 88.68/26.84 (symdiffI2) =>
% 88.68/26.84 ((
% 88.68/26.84 (symdiffIneg1) =>
% 88.68/26.84 ((
% 88.68/26.84 (symdiffIneg2) =>
% 88.68/26.84 ((
% 88.68/26.84 (secondinupair) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairIL) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairIR) =>
% 88.68/26.84 ((
% 88.68/26.84 (kpairiskpair) =>
% 88.68/26.84 ((
% 88.68/26.84 (kpairp) =>
% 88.68/26.84 ((
% 88.68/26.84 (singletonsubset) =>
% 88.68/26.84 ((
% 88.68/26.84 (singletoninpowerset) =>
% 88.68/26.84 ((
% 88.68/26.84 (singletoninpowunion) =>
% 88.68/26.84 ((
% 88.68/26.84 (upairset2E) =>
% 88.68/26.84 ((
% 88.68/26.84 (upairsubunion) =>
% 88.68/26.84 ((
% 88.68/26.84 (upairinpowunion) =>
% 88.68/26.84 ((
% 88.68/26.84 (ubforcartprodlem1) =>
% 88.68/26.84 ((
% 88.68/26.84 (ubforcartprodlem2) =>
% 88.68/26.84 ((
% 88.68/26.84 (ubforcartprodlem3) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodpairin) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodmempair1) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodmempair) =>
% 88.68/26.84 ((
% 88.68/26.84 (setunionE2) =>
% 88.68/26.84 ((
% 88.68/26.84 (setunionsingleton1) =>
% 88.68/26.84 ((
% 88.68/26.84 (setunionsingleton2) =>
% 88.68/26.84 ((
% 88.68/26.84 (setunionsingleton) =>
% 88.68/26.84 ((
% 88.68/26.84 (singletonprop) =>
% 88.68/26.84 ((
% 88.68/26.84 (ex1E1) =>
% 88.68/26.84 ((
% 88.68/26.84 (ex1I) =>
% 88.68/26.84 ((
% 88.68/26.84 (ex1I2) =>
% 88.68/26.84 ((
% 88.68/26.84 (singletonsuniq) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairinjL1) =>
% 88.68/26.84 ((
% 88.68/26.84 (kfstsingleton) =>
% 88.68/26.84 ((
% 88.68/26.84 (theprop) =>
% 88.68/26.84 ((
% 88.68/26.84 (kfstpairEq) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodfstin) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairinjL2) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairinjL) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairinjR11) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairinjR12) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairinjR1) =>
% 88.68/26.84 ((
% 88.68/26.84 (upairequniteq) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairinjR2) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairinjR) =>
% 88.68/26.84 ((
% 88.68/26.84 (ksndsingleton) =>
% 88.68/26.84 ((
% 88.68/26.84 (ksndpairEq) =>
% 88.68/26.84 ((
% 88.68/26.84 (kpairsurjEq) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodsndin) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodpairmemEL) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodpairmemER) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodmempaircEq) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodfstpairEq) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodsndpairEq) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodpairsurjEq) =>
% 88.68/26.84 ((
% 88.68/26.84 (dpsetconstrI) =>
% 88.68/26.84 ((
% 88.68/26.84 (dpsetconstrSub) =>
% 88.68/26.84 ((
% 88.68/26.84 (setOfPairsIsBReln) =>
% 88.68/26.84 ((
% 88.68/26.84 (dpsetconstrERa) =>
% 88.68/26.84 ((
% 88.68/26.84 (dpsetconstrEL1) =>
% 88.68/26.84 ((
% 88.68/26.84 (dpsetconstrEL2) =>
% 88.68/26.84 ((
% 88.68/26.84 (dpsetconstrER) =>
% 88.68/26.84 ((
% 88.68/26.84 (funcImageSingleton) =>
% 88.68/26.84 ((
% 88.68/26.84 (apProp) =>
% 88.68/26.84 ((
% 88.68/26.84 (app) =>
% 88.68/26.84 ((
% 88.68/26.84 (infuncsetfunc) =>
% 88.68/26.84 ((
% 88.68/26.84 (ap2p) =>
% 88.68/26.84 ((
% 88.68/26.84 (funcinfuncset) =>
% 88.68/26.84 ((
% 88.68/26.84 (lamProp) =>
% 88.68/26.84 ((
% 88.68/26.84 (lamp) =>
% 88.68/26.84 ((
% 88.68/26.84 (lam2p) =>
% 88.68/26.84 ((
% 88.68/26.84 (brelnall1) =>
% 88.68/26.84 ((
% 88.68/26.84 (brelnall2) =>
% 88.68/26.84 ((
% 88.68/26.84 (!!) @ (
% 88.68/26.84 (('#B') @ (
% 88.68/26.84 !!) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#S') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#S') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 =>))) @
% 88.68/26.84 ex1)))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 !!))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#S') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#B') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#S') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 =>))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#C') @ in)))))))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 !!))))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#C') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#B') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#B') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#S') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 =>))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#C') @ in)))))))))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#S') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#S') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#B'))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 =>))))))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#C') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#B') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#S') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 =>))))))) @
% 88.68/26.84 (
% 88.68/26.84 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 88.68/26.84 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl417])).
% 88.68/26.84 thf(zip_derived_cl439, plain,
% 88.68/26.84 (~ (((nonemptyImpWitness) =>
% 88.68/26.84 (((uniqinunit) =>
% 88.68/26.84 (((notinsingleton) =>
% 88.68/26.84 (((eqinunit) =>
% 88.68/26.84 (((singletonsswitch) =>
% 88.68/26.84 (((upairsetE) =>
% 88.68/26.84 (((upairsetIL) =>
% 88.68/26.84 (((upairsetIR) =>
% 88.68/26.84 (((emptyE1) =>
% 88.68/26.84 (((vacuousDall) =>
% 88.68/26.84 (((quantDeMorgan1) =>
% 88.68/26.84 (((quantDeMorgan2) =>
% 88.68/26.84 (((quantDeMorgan3) =>
% 88.68/26.84 (((quantDeMorgan4) =>
% 88.68/26.84 (((prop2setI) =>
% 88.68/26.84 (((prop2set2propI) =>
% 88.68/26.84 (((notdexE) =>
% 88.68/26.84 (((notdallE) =>
% 88.68/26.84 (((exuI1) =>
% 88.68/26.84 (((exuI3) =>
% 88.68/26.84 (((exuI2) =>
% 88.68/26.84 (((inCongP) =>
% 88.68/26.84 (((in__Cong) =>
% 88.68/26.84 (((exuE3u) =>
% 88.68/26.84 (((exu__Cong) =>
% 88.68/26.84 (((setadjoin__Cong) =>
% 88.68/26.84 (((powerset__Cong) =>
% 88.68/26.84 (((setunion__Cong) =>
% 88.68/26.84 (((exuEu) =>
% 88.68/26.84 (((descr__Cong) =>
% 88.68/26.84 ((
% 88.68/26.84 (dsetconstr__Cong) =>
% 88.68/26.84 ((
% 88.68/26.84 (subsetI1) =>
% 88.68/26.84 ((
% 88.68/26.84 (eqimpsubset2) =>
% 88.68/26.84 ((
% 88.68/26.84 (eqimpsubset1) =>
% 88.68/26.84 ((
% 88.68/26.84 (subsetI2) =>
% 88.68/26.84 ((
% 88.68/26.84 (emptysetsubset) =>
% 88.68/26.84 ((
% 88.68/26.84 (subsetE) =>
% 88.68/26.84 ((
% 88.68/26.84 (subsetE2) =>
% 88.68/26.84 ((
% 88.68/26.84 (notsubsetI) =>
% 88.68/26.84 ((
% 88.68/26.84 (notequalI1) =>
% 88.68/26.84 ((
% 88.68/26.84 (notequalI2) =>
% 88.68/26.84 ((
% 88.68/26.84 (subsetRefl) =>
% 88.68/26.84 ((
% 88.68/26.84 (subsetTrans) =>
% 88.68/26.84 ((
% 88.68/26.84 (setadjoinSub) =>
% 88.68/26.84 ((
% 88.68/26.84 (setadjoinSub2) =>
% 88.68/26.84 ((
% 88.68/26.84 (subset2powerset) =>
% 88.68/26.84 ((
% 88.68/26.84 (setextsub) =>
% 88.68/26.84 ((
% 88.68/26.84 (subsetemptysetimpeq) =>
% 88.68/26.84 ((
% 88.68/26.84 (powersetI1) =>
% 88.68/26.84 ((
% 88.68/26.84 (powersetE1) =>
% 88.68/26.84 ((
% 88.68/26.84 (inPowerset) =>
% 88.68/26.84 ((
% 88.68/26.84 (powersetsubset) =>
% 88.68/26.84 ((
% 88.68/26.84 (sepInPowerset) =>
% 88.68/26.84 ((
% 88.68/26.84 (sepSubset) =>
% 88.68/26.84 ((
% 88.68/26.84 (binunionIL) =>
% 88.68/26.84 ((
% 88.68/26.84 (upairset2IR) =>
% 88.68/26.84 ((
% 88.68/26.84 (binunionIR) =>
% 88.68/26.84 ((
% 88.68/26.84 (binunionEcases) =>
% 88.68/26.84 ((
% 88.68/26.84 (binunionE) =>
% 88.68/26.84 ((
% 88.68/26.84 (binunionLsub) =>
% 88.68/26.84 ((
% 88.68/26.84 (binunionRsub) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectI) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectSubset5) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectEL) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectLsub) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectSubset2) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectSubset3) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectER) =>
% 88.68/26.84 ((
% 88.68/26.84 (disjointsetsI1) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectRsub) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectSubset4) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectSubset1) =>
% 88.68/26.84 ((
% 88.68/26.84 (bs114d) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusI) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusEL) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusER) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusSubset2) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusERneg) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusELneg) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusILneg) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusIRneg) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusLsub) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusSubset1) =>
% 88.68/26.84 ((
% 88.68/26.84 (symdiffE) =>
% 88.68/26.84 ((
% 88.68/26.84 (symdiffI1) =>
% 88.68/26.84 ((
% 88.68/26.84 (symdiffI2) =>
% 88.68/26.84 ((
% 88.68/26.84 (symdiffIneg1) =>
% 88.68/26.84 ((
% 88.68/26.84 (symdiffIneg2) =>
% 88.68/26.84 ((
% 88.68/26.84 (secondinupair) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairIL) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairIR) =>
% 88.68/26.84 ((
% 88.68/26.84 (kpairiskpair) =>
% 88.68/26.84 ((
% 88.68/26.84 (kpairp) =>
% 88.68/26.84 ((
% 88.68/26.84 (singletonsubset) =>
% 88.68/26.84 ((
% 88.68/26.84 (singletoninpowerset) =>
% 88.68/26.84 ((
% 88.68/26.84 (singletoninpowunion) =>
% 88.68/26.84 ((
% 88.68/26.84 (upairset2E) =>
% 88.68/26.84 ((
% 88.68/26.84 (upairsubunion) =>
% 88.68/26.84 ((
% 88.68/26.84 (upairinpowunion) =>
% 88.68/26.84 ((
% 88.68/26.84 (ubforcartprodlem1) =>
% 88.68/26.84 ((
% 88.68/26.84 (ubforcartprodlem2) =>
% 88.68/26.84 ((
% 88.68/26.84 (ubforcartprodlem3) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodpairin) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodmempair1) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodmempair) =>
% 88.68/26.84 ((
% 88.68/26.84 (setunionE2) =>
% 88.68/26.84 ((
% 88.68/26.84 (setunionsingleton1) =>
% 88.68/26.84 ((
% 88.68/26.84 (setunionsingleton2) =>
% 88.68/26.84 ((
% 88.68/26.84 (setunionsingleton) =>
% 88.68/26.84 ((
% 88.68/26.84 (singletonprop) =>
% 88.68/26.84 ((
% 88.68/26.84 (ex1E1) =>
% 88.68/26.84 ((
% 88.68/26.84 (ex1I) =>
% 88.68/26.84 ((
% 88.68/26.84 (ex1I2) =>
% 88.68/26.84 ((
% 88.68/26.84 (singletonsuniq) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairinjL1) =>
% 88.68/26.84 ((
% 88.68/26.84 (kfstsingleton) =>
% 88.68/26.84 ((
% 88.68/26.84 (theprop) =>
% 88.68/26.84 ((
% 88.68/26.84 (kfstpairEq) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodfstin) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairinjL2) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairinjL) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairinjR11) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairinjR12) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairinjR1) =>
% 88.68/26.84 ((
% 88.68/26.84 (upairequniteq) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairinjR2) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairinjR) =>
% 88.68/26.84 ((
% 88.68/26.84 (ksndsingleton) =>
% 88.68/26.84 ((
% 88.68/26.84 (ksndpairEq) =>
% 88.68/26.84 ((
% 88.68/26.84 (kpairsurjEq) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodsndin) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodpairmemEL) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodpairmemER) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodmempaircEq) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodfstpairEq) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodsndpairEq) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodpairsurjEq) =>
% 88.68/26.84 ((
% 88.68/26.84 (dpsetconstrI) =>
% 88.68/26.84 ((
% 88.68/26.84 (dpsetconstrSub) =>
% 88.68/26.84 ((
% 88.68/26.84 (setOfPairsIsBReln) =>
% 88.68/26.84 ((
% 88.68/26.84 (dpsetconstrERa) =>
% 88.68/26.84 ((
% 88.68/26.84 (dpsetconstrEL1) =>
% 88.68/26.84 ((
% 88.68/26.84 (dpsetconstrEL2) =>
% 88.68/26.84 ((
% 88.68/26.84 (dpsetconstrER) =>
% 88.68/26.84 ((
% 88.68/26.84 (funcImageSingleton) =>
% 88.68/26.84 ((
% 88.68/26.84 (apProp) =>
% 88.68/26.84 ((
% 88.68/26.84 (app) =>
% 88.68/26.84 ((
% 88.68/26.84 (infuncsetfunc) =>
% 88.68/26.84 ((
% 88.68/26.84 (ap2p) =>
% 88.68/26.84 ((
% 88.68/26.84 (funcinfuncset) =>
% 88.68/26.84 ((
% 88.68/26.84 (lamProp) =>
% 88.68/26.84 ((
% 88.68/26.84 (lamp) =>
% 88.68/26.84 ((
% 88.68/26.84 (lam2p) =>
% 88.68/26.84 ((
% 88.68/26.84 (brelnall1) =>
% 88.68/26.84 ((
% 88.68/26.84 (brelnall2) =>
% 88.68/26.84 ((
% 88.68/26.84 (!!) @ (
% 88.68/26.84 (('#B') @ (
% 88.68/26.84 !!) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#S') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#S') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 =>))) @
% 88.68/26.84 ex1)))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 !!))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#S') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#B') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#S') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 =>))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#C') @ in)))))))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 !!))))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#C') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#B') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#B') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#S') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 =>))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#C') @ in)))))))))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#S') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#S') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#B'))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 =>))))))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#C') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#B') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#S') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 =>))))))) @
% 88.68/26.84 (
% 88.68/26.84 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 88.68/26.84 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl428])).
% 88.68/26.84 thf(zip_derived_cl449, plain,
% 88.68/26.84 (~ (((uniqinunit) =>
% 88.68/26.84 (((notinsingleton) =>
% 88.68/26.84 (((eqinunit) =>
% 88.68/26.84 (((singletonsswitch) =>
% 88.68/26.84 (((upairsetE) =>
% 88.68/26.84 (((upairsetIL) =>
% 88.68/26.84 (((upairsetIR) =>
% 88.68/26.84 (((emptyE1) =>
% 88.68/26.84 (((vacuousDall) =>
% 88.68/26.84 (((quantDeMorgan1) =>
% 88.68/26.84 (((quantDeMorgan2) =>
% 88.68/26.84 (((quantDeMorgan3) =>
% 88.68/26.84 (((quantDeMorgan4) =>
% 88.68/26.84 (((prop2setI) =>
% 88.68/26.84 (((prop2set2propI) =>
% 88.68/26.84 (((notdexE) =>
% 88.68/26.84 (((notdallE) =>
% 88.68/26.84 (((exuI1) =>
% 88.68/26.84 (((exuI3) =>
% 88.68/26.84 (((exuI2) =>
% 88.68/26.84 (((inCongP) =>
% 88.68/26.84 (((in__Cong) =>
% 88.68/26.84 (((exuE3u) =>
% 88.68/26.84 (((exu__Cong) =>
% 88.68/26.84 (((setadjoin__Cong) =>
% 88.68/26.84 (((powerset__Cong) =>
% 88.68/26.84 (((setunion__Cong) =>
% 88.68/26.84 (((exuEu) =>
% 88.68/26.84 (((descr__Cong) =>
% 88.68/26.84 (((dsetconstr__Cong) =>
% 88.68/26.84 ((
% 88.68/26.84 (subsetI1) =>
% 88.68/26.84 ((
% 88.68/26.84 (eqimpsubset2) =>
% 88.68/26.84 ((
% 88.68/26.84 (eqimpsubset1) =>
% 88.68/26.84 ((
% 88.68/26.84 (subsetI2) =>
% 88.68/26.84 ((
% 88.68/26.84 (emptysetsubset) =>
% 88.68/26.84 ((
% 88.68/26.84 (subsetE) =>
% 88.68/26.84 ((
% 88.68/26.84 (subsetE2) =>
% 88.68/26.84 ((
% 88.68/26.84 (notsubsetI) =>
% 88.68/26.84 ((
% 88.68/26.84 (notequalI1) =>
% 88.68/26.84 ((
% 88.68/26.84 (notequalI2) =>
% 88.68/26.84 ((
% 88.68/26.84 (subsetRefl) =>
% 88.68/26.84 ((
% 88.68/26.84 (subsetTrans) =>
% 88.68/26.84 ((
% 88.68/26.84 (setadjoinSub) =>
% 88.68/26.84 ((
% 88.68/26.84 (setadjoinSub2) =>
% 88.68/26.84 ((
% 88.68/26.84 (subset2powerset) =>
% 88.68/26.84 ((
% 88.68/26.84 (setextsub) =>
% 88.68/26.84 ((
% 88.68/26.84 (subsetemptysetimpeq) =>
% 88.68/26.84 ((
% 88.68/26.84 (powersetI1) =>
% 88.68/26.84 ((
% 88.68/26.84 (powersetE1) =>
% 88.68/26.84 ((
% 88.68/26.84 (inPowerset) =>
% 88.68/26.84 ((
% 88.68/26.84 (powersetsubset) =>
% 88.68/26.84 ((
% 88.68/26.84 (sepInPowerset) =>
% 88.68/26.84 ((
% 88.68/26.84 (sepSubset) =>
% 88.68/26.84 ((
% 88.68/26.84 (binunionIL) =>
% 88.68/26.84 ((
% 88.68/26.84 (upairset2IR) =>
% 88.68/26.84 ((
% 88.68/26.84 (binunionIR) =>
% 88.68/26.84 ((
% 88.68/26.84 (binunionEcases) =>
% 88.68/26.84 ((
% 88.68/26.84 (binunionE) =>
% 88.68/26.84 ((
% 88.68/26.84 (binunionLsub) =>
% 88.68/26.84 ((
% 88.68/26.84 (binunionRsub) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectI) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectSubset5) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectEL) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectLsub) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectSubset2) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectSubset3) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectER) =>
% 88.68/26.84 ((
% 88.68/26.84 (disjointsetsI1) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectRsub) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectSubset4) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectSubset1) =>
% 88.68/26.84 ((
% 88.68/26.84 (bs114d) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusI) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusEL) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusER) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusSubset2) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusERneg) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusELneg) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusILneg) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusIRneg) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusLsub) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusSubset1) =>
% 88.68/26.84 ((
% 88.68/26.84 (symdiffE) =>
% 88.68/26.84 ((
% 88.68/26.84 (symdiffI1) =>
% 88.68/26.84 ((
% 88.68/26.84 (symdiffI2) =>
% 88.68/26.84 ((
% 88.68/26.84 (symdiffIneg1) =>
% 88.68/26.84 ((
% 88.68/26.84 (symdiffIneg2) =>
% 88.68/26.84 ((
% 88.68/26.84 (secondinupair) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairIL) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairIR) =>
% 88.68/26.84 ((
% 88.68/26.84 (kpairiskpair) =>
% 88.68/26.84 ((
% 88.68/26.84 (kpairp) =>
% 88.68/26.84 ((
% 88.68/26.84 (singletonsubset) =>
% 88.68/26.84 ((
% 88.68/26.84 (singletoninpowerset) =>
% 88.68/26.84 ((
% 88.68/26.84 (singletoninpowunion) =>
% 88.68/26.84 ((
% 88.68/26.84 (upairset2E) =>
% 88.68/26.84 ((
% 88.68/26.84 (upairsubunion) =>
% 88.68/26.84 ((
% 88.68/26.84 (upairinpowunion) =>
% 88.68/26.84 ((
% 88.68/26.84 (ubforcartprodlem1) =>
% 88.68/26.84 ((
% 88.68/26.84 (ubforcartprodlem2) =>
% 88.68/26.84 ((
% 88.68/26.84 (ubforcartprodlem3) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodpairin) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodmempair1) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodmempair) =>
% 88.68/26.84 ((
% 88.68/26.84 (setunionE2) =>
% 88.68/26.84 ((
% 88.68/26.84 (setunionsingleton1) =>
% 88.68/26.84 ((
% 88.68/26.84 (setunionsingleton2) =>
% 88.68/26.84 ((
% 88.68/26.84 (setunionsingleton) =>
% 88.68/26.84 ((
% 88.68/26.84 (singletonprop) =>
% 88.68/26.84 ((
% 88.68/26.84 (ex1E1) =>
% 88.68/26.84 ((
% 88.68/26.84 (ex1I) =>
% 88.68/26.84 ((
% 88.68/26.84 (ex1I2) =>
% 88.68/26.84 ((
% 88.68/26.84 (singletonsuniq) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairinjL1) =>
% 88.68/26.84 ((
% 88.68/26.84 (kfstsingleton) =>
% 88.68/26.84 ((
% 88.68/26.84 (theprop) =>
% 88.68/26.84 ((
% 88.68/26.84 (kfstpairEq) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodfstin) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairinjL2) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairinjL) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairinjR11) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairinjR12) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairinjR1) =>
% 88.68/26.84 ((
% 88.68/26.84 (upairequniteq) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairinjR2) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairinjR) =>
% 88.68/26.84 ((
% 88.68/26.84 (ksndsingleton) =>
% 88.68/26.84 ((
% 88.68/26.84 (ksndpairEq) =>
% 88.68/26.84 ((
% 88.68/26.84 (kpairsurjEq) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodsndin) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodpairmemEL) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodpairmemER) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodmempaircEq) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodfstpairEq) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodsndpairEq) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodpairsurjEq) =>
% 88.68/26.84 ((
% 88.68/26.84 (dpsetconstrI) =>
% 88.68/26.84 ((
% 88.68/26.84 (dpsetconstrSub) =>
% 88.68/26.84 ((
% 88.68/26.84 (setOfPairsIsBReln) =>
% 88.68/26.84 ((
% 88.68/26.84 (dpsetconstrERa) =>
% 88.68/26.84 ((
% 88.68/26.84 (dpsetconstrEL1) =>
% 88.68/26.84 ((
% 88.68/26.84 (dpsetconstrEL2) =>
% 88.68/26.84 ((
% 88.68/26.84 (dpsetconstrER) =>
% 88.68/26.84 ((
% 88.68/26.84 (funcImageSingleton) =>
% 88.68/26.84 ((
% 88.68/26.84 (apProp) =>
% 88.68/26.84 ((
% 88.68/26.84 (app) =>
% 88.68/26.84 ((
% 88.68/26.84 (infuncsetfunc) =>
% 88.68/26.84 ((
% 88.68/26.84 (ap2p) =>
% 88.68/26.84 ((
% 88.68/26.84 (funcinfuncset) =>
% 88.68/26.84 ((
% 88.68/26.84 (lamProp) =>
% 88.68/26.84 ((
% 88.68/26.84 (lamp) =>
% 88.68/26.84 ((
% 88.68/26.84 (lam2p) =>
% 88.68/26.84 ((
% 88.68/26.84 (brelnall1) =>
% 88.68/26.84 ((
% 88.68/26.84 (brelnall2) =>
% 88.68/26.84 ((
% 88.68/26.84 (!!) @ (
% 88.68/26.84 (('#B') @ (
% 88.68/26.84 !!) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#S') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#S') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 =>))) @
% 88.68/26.84 ex1)))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 !!))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#S') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#B') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#S') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 =>))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#C') @ in)))))))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 !!))))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#C') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#B') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#B') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#S') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 =>))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#C') @ in)))))))))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#S') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#S') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#B'))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 =>))))))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#C') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#B') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#S') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 =>))))))) @
% 88.68/26.84 (
% 88.68/26.84 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 88.68/26.84 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl439])).
% 88.68/26.84 thf(zip_derived_cl458, plain,
% 88.68/26.84 (~ (((notinsingleton) =>
% 88.68/26.84 (((eqinunit) =>
% 88.68/26.84 (((singletonsswitch) =>
% 88.68/26.84 (((upairsetE) =>
% 88.68/26.84 (((upairsetIL) =>
% 88.68/26.84 (((upairsetIR) =>
% 88.68/26.84 (((emptyE1) =>
% 88.68/26.84 (((vacuousDall) =>
% 88.68/26.84 (((quantDeMorgan1) =>
% 88.68/26.84 (((quantDeMorgan2) =>
% 88.68/26.84 (((quantDeMorgan3) =>
% 88.68/26.84 (((quantDeMorgan4) =>
% 88.68/26.84 (((prop2setI) =>
% 88.68/26.84 (((prop2set2propI) =>
% 88.68/26.84 (((notdexE) =>
% 88.68/26.84 (((notdallE) =>
% 88.68/26.84 (((exuI1) =>
% 88.68/26.84 (((exuI3) =>
% 88.68/26.84 (((exuI2) =>
% 88.68/26.84 (((inCongP) =>
% 88.68/26.84 (((in__Cong) =>
% 88.68/26.84 (((exuE3u) =>
% 88.68/26.84 (((exu__Cong) =>
% 88.68/26.84 (((setadjoin__Cong) =>
% 88.68/26.84 (((powerset__Cong) =>
% 88.68/26.84 (((setunion__Cong) =>
% 88.68/26.84 (((exuEu) =>
% 88.68/26.84 (((descr__Cong) =>
% 88.68/26.84 (((dsetconstr__Cong) =>
% 88.68/26.84 (((subsetI1) =>
% 88.68/26.84 ((
% 88.68/26.84 (eqimpsubset2) =>
% 88.68/26.84 ((
% 88.68/26.84 (eqimpsubset1) =>
% 88.68/26.84 ((
% 88.68/26.84 (subsetI2) =>
% 88.68/26.84 ((
% 88.68/26.84 (emptysetsubset) =>
% 88.68/26.84 ((
% 88.68/26.84 (subsetE) =>
% 88.68/26.84 ((
% 88.68/26.84 (subsetE2) =>
% 88.68/26.84 ((
% 88.68/26.84 (notsubsetI) =>
% 88.68/26.84 ((
% 88.68/26.84 (notequalI1) =>
% 88.68/26.84 ((
% 88.68/26.84 (notequalI2) =>
% 88.68/26.84 ((
% 88.68/26.84 (subsetRefl) =>
% 88.68/26.84 ((
% 88.68/26.84 (subsetTrans) =>
% 88.68/26.84 ((
% 88.68/26.84 (setadjoinSub) =>
% 88.68/26.84 ((
% 88.68/26.84 (setadjoinSub2) =>
% 88.68/26.84 ((
% 88.68/26.84 (subset2powerset) =>
% 88.68/26.84 ((
% 88.68/26.84 (setextsub) =>
% 88.68/26.84 ((
% 88.68/26.84 (subsetemptysetimpeq) =>
% 88.68/26.84 ((
% 88.68/26.84 (powersetI1) =>
% 88.68/26.84 ((
% 88.68/26.84 (powersetE1) =>
% 88.68/26.84 ((
% 88.68/26.84 (inPowerset) =>
% 88.68/26.84 ((
% 88.68/26.84 (powersetsubset) =>
% 88.68/26.84 ((
% 88.68/26.84 (sepInPowerset) =>
% 88.68/26.84 ((
% 88.68/26.84 (sepSubset) =>
% 88.68/26.84 ((
% 88.68/26.84 (binunionIL) =>
% 88.68/26.84 ((
% 88.68/26.84 (upairset2IR) =>
% 88.68/26.84 ((
% 88.68/26.84 (binunionIR) =>
% 88.68/26.84 ((
% 88.68/26.84 (binunionEcases) =>
% 88.68/26.84 ((
% 88.68/26.84 (binunionE) =>
% 88.68/26.84 ((
% 88.68/26.84 (binunionLsub) =>
% 88.68/26.84 ((
% 88.68/26.84 (binunionRsub) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectI) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectSubset5) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectEL) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectLsub) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectSubset2) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectSubset3) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectER) =>
% 88.68/26.84 ((
% 88.68/26.84 (disjointsetsI1) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectRsub) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectSubset4) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectSubset1) =>
% 88.68/26.84 ((
% 88.68/26.84 (bs114d) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusI) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusEL) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusER) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusSubset2) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusERneg) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusELneg) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusILneg) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusIRneg) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusLsub) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusSubset1) =>
% 88.68/26.84 ((
% 88.68/26.84 (symdiffE) =>
% 88.68/26.84 ((
% 88.68/26.84 (symdiffI1) =>
% 88.68/26.84 ((
% 88.68/26.84 (symdiffI2) =>
% 88.68/26.84 ((
% 88.68/26.84 (symdiffIneg1) =>
% 88.68/26.84 ((
% 88.68/26.84 (symdiffIneg2) =>
% 88.68/26.84 ((
% 88.68/26.84 (secondinupair) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairIL) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairIR) =>
% 88.68/26.84 ((
% 88.68/26.84 (kpairiskpair) =>
% 88.68/26.84 ((
% 88.68/26.84 (kpairp) =>
% 88.68/26.84 ((
% 88.68/26.84 (singletonsubset) =>
% 88.68/26.84 ((
% 88.68/26.84 (singletoninpowerset) =>
% 88.68/26.84 ((
% 88.68/26.84 (singletoninpowunion) =>
% 88.68/26.84 ((
% 88.68/26.84 (upairset2E) =>
% 88.68/26.84 ((
% 88.68/26.84 (upairsubunion) =>
% 88.68/26.84 ((
% 88.68/26.84 (upairinpowunion) =>
% 88.68/26.84 ((
% 88.68/26.84 (ubforcartprodlem1) =>
% 88.68/26.84 ((
% 88.68/26.84 (ubforcartprodlem2) =>
% 88.68/26.84 ((
% 88.68/26.84 (ubforcartprodlem3) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodpairin) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodmempair1) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodmempair) =>
% 88.68/26.84 ((
% 88.68/26.84 (setunionE2) =>
% 88.68/26.84 ((
% 88.68/26.84 (setunionsingleton1) =>
% 88.68/26.84 ((
% 88.68/26.84 (setunionsingleton2) =>
% 88.68/26.84 ((
% 88.68/26.84 (setunionsingleton) =>
% 88.68/26.84 ((
% 88.68/26.84 (singletonprop) =>
% 88.68/26.84 ((
% 88.68/26.84 (ex1E1) =>
% 88.68/26.84 ((
% 88.68/26.84 (ex1I) =>
% 88.68/26.84 ((
% 88.68/26.84 (ex1I2) =>
% 88.68/26.84 ((
% 88.68/26.84 (singletonsuniq) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairinjL1) =>
% 88.68/26.84 ((
% 88.68/26.84 (kfstsingleton) =>
% 88.68/26.84 ((
% 88.68/26.84 (theprop) =>
% 88.68/26.84 ((
% 88.68/26.84 (kfstpairEq) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodfstin) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairinjL2) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairinjL) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairinjR11) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairinjR12) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairinjR1) =>
% 88.68/26.84 ((
% 88.68/26.84 (upairequniteq) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairinjR2) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairinjR) =>
% 88.68/26.84 ((
% 88.68/26.84 (ksndsingleton) =>
% 88.68/26.84 ((
% 88.68/26.84 (ksndpairEq) =>
% 88.68/26.84 ((
% 88.68/26.84 (kpairsurjEq) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodsndin) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodpairmemEL) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodpairmemER) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodmempaircEq) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodfstpairEq) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodsndpairEq) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodpairsurjEq) =>
% 88.68/26.84 ((
% 88.68/26.84 (dpsetconstrI) =>
% 88.68/26.84 ((
% 88.68/26.84 (dpsetconstrSub) =>
% 88.68/26.84 ((
% 88.68/26.84 (setOfPairsIsBReln) =>
% 88.68/26.84 ((
% 88.68/26.84 (dpsetconstrERa) =>
% 88.68/26.84 ((
% 88.68/26.84 (dpsetconstrEL1) =>
% 88.68/26.84 ((
% 88.68/26.84 (dpsetconstrEL2) =>
% 88.68/26.84 ((
% 88.68/26.84 (dpsetconstrER) =>
% 88.68/26.84 ((
% 88.68/26.84 (funcImageSingleton) =>
% 88.68/26.84 ((
% 88.68/26.84 (apProp) =>
% 88.68/26.84 ((
% 88.68/26.84 (app) =>
% 88.68/26.84 ((
% 88.68/26.84 (infuncsetfunc) =>
% 88.68/26.84 ((
% 88.68/26.84 (ap2p) =>
% 88.68/26.84 ((
% 88.68/26.84 (funcinfuncset) =>
% 88.68/26.84 ((
% 88.68/26.84 (lamProp) =>
% 88.68/26.84 ((
% 88.68/26.84 (lamp) =>
% 88.68/26.84 ((
% 88.68/26.84 (lam2p) =>
% 88.68/26.84 ((
% 88.68/26.84 (brelnall1) =>
% 88.68/26.84 ((
% 88.68/26.84 (brelnall2) =>
% 88.68/26.84 ((
% 88.68/26.84 (!!) @ (
% 88.68/26.84 (('#B') @ (
% 88.68/26.84 !!) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#S') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#S') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 =>))) @
% 88.68/26.84 ex1)))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 !!))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#S') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#B') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#S') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 =>))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#C') @ in)))))))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 !!))))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#C') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#B') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#B') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#S') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 =>))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#C') @ in)))))))))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#S') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#S') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#B'))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 =>))))))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#C') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#B') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#S') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 =>))))))) @
% 88.68/26.84 (
% 88.68/26.84 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 88.68/26.84 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl449])).
% 88.68/26.84 thf(zip_derived_cl467, plain,
% 88.68/26.84 (~ (((eqinunit) =>
% 88.68/26.84 (((singletonsswitch) =>
% 88.68/26.84 (((upairsetE) =>
% 88.68/26.84 (((upairsetIL) =>
% 88.68/26.84 (((upairsetIR) =>
% 88.68/26.84 (((emptyE1) =>
% 88.68/26.84 (((vacuousDall) =>
% 88.68/26.84 (((quantDeMorgan1) =>
% 88.68/26.84 (((quantDeMorgan2) =>
% 88.68/26.84 (((quantDeMorgan3) =>
% 88.68/26.84 (((quantDeMorgan4) =>
% 88.68/26.84 (((prop2setI) =>
% 88.68/26.84 (((prop2set2propI) =>
% 88.68/26.84 (((notdexE) =>
% 88.68/26.84 (((notdallE) =>
% 88.68/26.84 (((exuI1) =>
% 88.68/26.84 (((exuI3) =>
% 88.68/26.84 (((exuI2) =>
% 88.68/26.84 (((inCongP) =>
% 88.68/26.84 (((in__Cong) =>
% 88.68/26.84 (((exuE3u) =>
% 88.68/26.84 (((exu__Cong) =>
% 88.68/26.84 (((setadjoin__Cong) =>
% 88.68/26.84 (((powerset__Cong) =>
% 88.68/26.84 (((setunion__Cong) =>
% 88.68/26.84 (((exuEu) =>
% 88.68/26.84 (((descr__Cong) =>
% 88.68/26.84 (((dsetconstr__Cong) =>
% 88.68/26.84 (((subsetI1) =>
% 88.68/26.84 (((eqimpsubset2) =>
% 88.68/26.84 ((
% 88.68/26.84 (eqimpsubset1) =>
% 88.68/26.84 ((
% 88.68/26.84 (subsetI2) =>
% 88.68/26.84 ((
% 88.68/26.84 (emptysetsubset) =>
% 88.68/26.84 ((
% 88.68/26.84 (subsetE) =>
% 88.68/26.84 ((
% 88.68/26.84 (subsetE2) =>
% 88.68/26.84 ((
% 88.68/26.84 (notsubsetI) =>
% 88.68/26.84 ((
% 88.68/26.84 (notequalI1) =>
% 88.68/26.84 ((
% 88.68/26.84 (notequalI2) =>
% 88.68/26.84 ((
% 88.68/26.84 (subsetRefl) =>
% 88.68/26.84 ((
% 88.68/26.84 (subsetTrans) =>
% 88.68/26.84 ((
% 88.68/26.84 (setadjoinSub) =>
% 88.68/26.84 ((
% 88.68/26.84 (setadjoinSub2) =>
% 88.68/26.84 ((
% 88.68/26.84 (subset2powerset) =>
% 88.68/26.84 ((
% 88.68/26.84 (setextsub) =>
% 88.68/26.84 ((
% 88.68/26.84 (subsetemptysetimpeq) =>
% 88.68/26.84 ((
% 88.68/26.84 (powersetI1) =>
% 88.68/26.84 ((
% 88.68/26.84 (powersetE1) =>
% 88.68/26.84 ((
% 88.68/26.84 (inPowerset) =>
% 88.68/26.84 ((
% 88.68/26.84 (powersetsubset) =>
% 88.68/26.84 ((
% 88.68/26.84 (sepInPowerset) =>
% 88.68/26.84 ((
% 88.68/26.84 (sepSubset) =>
% 88.68/26.84 ((
% 88.68/26.84 (binunionIL) =>
% 88.68/26.84 ((
% 88.68/26.84 (upairset2IR) =>
% 88.68/26.84 ((
% 88.68/26.84 (binunionIR) =>
% 88.68/26.84 ((
% 88.68/26.84 (binunionEcases) =>
% 88.68/26.84 ((
% 88.68/26.84 (binunionE) =>
% 88.68/26.84 ((
% 88.68/26.84 (binunionLsub) =>
% 88.68/26.84 ((
% 88.68/26.84 (binunionRsub) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectI) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectSubset5) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectEL) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectLsub) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectSubset2) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectSubset3) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectER) =>
% 88.68/26.84 ((
% 88.68/26.84 (disjointsetsI1) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectRsub) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectSubset4) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectSubset1) =>
% 88.68/26.84 ((
% 88.68/26.84 (bs114d) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusI) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusEL) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusER) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusSubset2) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusERneg) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusELneg) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusILneg) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusIRneg) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusLsub) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusSubset1) =>
% 88.68/26.84 ((
% 88.68/26.84 (symdiffE) =>
% 88.68/26.84 ((
% 88.68/26.84 (symdiffI1) =>
% 88.68/26.84 ((
% 88.68/26.84 (symdiffI2) =>
% 88.68/26.84 ((
% 88.68/26.84 (symdiffIneg1) =>
% 88.68/26.84 ((
% 88.68/26.84 (symdiffIneg2) =>
% 88.68/26.84 ((
% 88.68/26.84 (secondinupair) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairIL) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairIR) =>
% 88.68/26.84 ((
% 88.68/26.84 (kpairiskpair) =>
% 88.68/26.84 ((
% 88.68/26.84 (kpairp) =>
% 88.68/26.84 ((
% 88.68/26.84 (singletonsubset) =>
% 88.68/26.84 ((
% 88.68/26.84 (singletoninpowerset) =>
% 88.68/26.84 ((
% 88.68/26.84 (singletoninpowunion) =>
% 88.68/26.84 ((
% 88.68/26.84 (upairset2E) =>
% 88.68/26.84 ((
% 88.68/26.84 (upairsubunion) =>
% 88.68/26.84 ((
% 88.68/26.84 (upairinpowunion) =>
% 88.68/26.84 ((
% 88.68/26.84 (ubforcartprodlem1) =>
% 88.68/26.84 ((
% 88.68/26.84 (ubforcartprodlem2) =>
% 88.68/26.84 ((
% 88.68/26.84 (ubforcartprodlem3) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodpairin) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodmempair1) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodmempair) =>
% 88.68/26.84 ((
% 88.68/26.84 (setunionE2) =>
% 88.68/26.84 ((
% 88.68/26.84 (setunionsingleton1) =>
% 88.68/26.84 ((
% 88.68/26.84 (setunionsingleton2) =>
% 88.68/26.84 ((
% 88.68/26.84 (setunionsingleton) =>
% 88.68/26.84 ((
% 88.68/26.84 (singletonprop) =>
% 88.68/26.84 ((
% 88.68/26.84 (ex1E1) =>
% 88.68/26.84 ((
% 88.68/26.84 (ex1I) =>
% 88.68/26.84 ((
% 88.68/26.84 (ex1I2) =>
% 88.68/26.84 ((
% 88.68/26.84 (singletonsuniq) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairinjL1) =>
% 88.68/26.84 ((
% 88.68/26.84 (kfstsingleton) =>
% 88.68/26.84 ((
% 88.68/26.84 (theprop) =>
% 88.68/26.84 ((
% 88.68/26.84 (kfstpairEq) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodfstin) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairinjL2) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairinjL) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairinjR11) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairinjR12) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairinjR1) =>
% 88.68/26.84 ((
% 88.68/26.84 (upairequniteq) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairinjR2) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairinjR) =>
% 88.68/26.84 ((
% 88.68/26.84 (ksndsingleton) =>
% 88.68/26.84 ((
% 88.68/26.84 (ksndpairEq) =>
% 88.68/26.84 ((
% 88.68/26.84 (kpairsurjEq) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodsndin) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodpairmemEL) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodpairmemER) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodmempaircEq) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodfstpairEq) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodsndpairEq) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodpairsurjEq) =>
% 88.68/26.84 ((
% 88.68/26.84 (dpsetconstrI) =>
% 88.68/26.84 ((
% 88.68/26.84 (dpsetconstrSub) =>
% 88.68/26.84 ((
% 88.68/26.84 (setOfPairsIsBReln) =>
% 88.68/26.84 ((
% 88.68/26.84 (dpsetconstrERa) =>
% 88.68/26.84 ((
% 88.68/26.84 (dpsetconstrEL1) =>
% 88.68/26.84 ((
% 88.68/26.84 (dpsetconstrEL2) =>
% 88.68/26.84 ((
% 88.68/26.84 (dpsetconstrER) =>
% 88.68/26.84 ((
% 88.68/26.84 (funcImageSingleton) =>
% 88.68/26.84 ((
% 88.68/26.84 (apProp) =>
% 88.68/26.84 ((
% 88.68/26.84 (app) =>
% 88.68/26.84 ((
% 88.68/26.84 (infuncsetfunc) =>
% 88.68/26.84 ((
% 88.68/26.84 (ap2p) =>
% 88.68/26.84 ((
% 88.68/26.84 (funcinfuncset) =>
% 88.68/26.84 ((
% 88.68/26.84 (lamProp) =>
% 88.68/26.84 ((
% 88.68/26.84 (lamp) =>
% 88.68/26.84 ((
% 88.68/26.84 (lam2p) =>
% 88.68/26.84 ((
% 88.68/26.84 (brelnall1) =>
% 88.68/26.84 ((
% 88.68/26.84 (brelnall2) =>
% 88.68/26.84 ((
% 88.68/26.84 (!!) @ (
% 88.68/26.84 (('#B') @ (
% 88.68/26.84 !!) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#S') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#S') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 =>))) @
% 88.68/26.84 ex1)))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 !!))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#S') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#B') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#S') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 =>))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#C') @ in)))))))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 !!))))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#C') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#B') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#B') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#S') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 =>))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#C') @ in)))))))))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#S') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#S') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#B'))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 =>))))))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#C') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#B') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#S') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 =>))))))) @
% 88.68/26.84 (
% 88.68/26.84 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 88.68/26.84 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl458])).
% 88.68/26.84 thf(zip_derived_cl475, plain,
% 88.68/26.84 (~ (((singletonsswitch) =>
% 88.68/26.84 (((upairsetE) =>
% 88.68/26.84 (((upairsetIL) =>
% 88.68/26.84 (((upairsetIR) =>
% 88.68/26.84 (((emptyE1) =>
% 88.68/26.84 (((vacuousDall) =>
% 88.68/26.84 (((quantDeMorgan1) =>
% 88.68/26.84 (((quantDeMorgan2) =>
% 88.68/26.84 (((quantDeMorgan3) =>
% 88.68/26.84 (((quantDeMorgan4) =>
% 88.68/26.84 (((prop2setI) =>
% 88.68/26.84 (((prop2set2propI) =>
% 88.68/26.84 (((notdexE) =>
% 88.68/26.84 (((notdallE) =>
% 88.68/26.84 (((exuI1) =>
% 88.68/26.84 (((exuI3) =>
% 88.68/26.84 (((exuI2) =>
% 88.68/26.84 (((inCongP) =>
% 88.68/26.84 (((in__Cong) =>
% 88.68/26.84 (((exuE3u) =>
% 88.68/26.84 (((exu__Cong) =>
% 88.68/26.84 (((setadjoin__Cong) =>
% 88.68/26.84 (((powerset__Cong) =>
% 88.68/26.84 (((setunion__Cong) =>
% 88.68/26.84 (((exuEu) =>
% 88.68/26.84 (((descr__Cong) =>
% 88.68/26.84 (((dsetconstr__Cong) =>
% 88.68/26.84 (((subsetI1) =>
% 88.68/26.84 (((eqimpsubset2) =>
% 88.68/26.84 (((eqimpsubset1) =>
% 88.68/26.84 ((
% 88.68/26.84 (subsetI2) =>
% 88.68/26.84 ((
% 88.68/26.84 (emptysetsubset) =>
% 88.68/26.84 ((
% 88.68/26.84 (subsetE) =>
% 88.68/26.84 ((
% 88.68/26.84 (subsetE2) =>
% 88.68/26.84 ((
% 88.68/26.84 (notsubsetI) =>
% 88.68/26.84 ((
% 88.68/26.84 (notequalI1) =>
% 88.68/26.84 ((
% 88.68/26.84 (notequalI2) =>
% 88.68/26.84 ((
% 88.68/26.84 (subsetRefl) =>
% 88.68/26.84 ((
% 88.68/26.84 (subsetTrans) =>
% 88.68/26.84 ((
% 88.68/26.84 (setadjoinSub) =>
% 88.68/26.84 ((
% 88.68/26.84 (setadjoinSub2) =>
% 88.68/26.84 ((
% 88.68/26.84 (subset2powerset) =>
% 88.68/26.84 ((
% 88.68/26.84 (setextsub) =>
% 88.68/26.84 ((
% 88.68/26.84 (subsetemptysetimpeq) =>
% 88.68/26.84 ((
% 88.68/26.84 (powersetI1) =>
% 88.68/26.84 ((
% 88.68/26.84 (powersetE1) =>
% 88.68/26.84 ((
% 88.68/26.84 (inPowerset) =>
% 88.68/26.84 ((
% 88.68/26.84 (powersetsubset) =>
% 88.68/26.84 ((
% 88.68/26.84 (sepInPowerset) =>
% 88.68/26.84 ((
% 88.68/26.84 (sepSubset) =>
% 88.68/26.84 ((
% 88.68/26.84 (binunionIL) =>
% 88.68/26.84 ((
% 88.68/26.84 (upairset2IR) =>
% 88.68/26.84 ((
% 88.68/26.84 (binunionIR) =>
% 88.68/26.84 ((
% 88.68/26.84 (binunionEcases) =>
% 88.68/26.84 ((
% 88.68/26.84 (binunionE) =>
% 88.68/26.84 ((
% 88.68/26.84 (binunionLsub) =>
% 88.68/26.84 ((
% 88.68/26.84 (binunionRsub) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectI) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectSubset5) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectEL) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectLsub) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectSubset2) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectSubset3) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectER) =>
% 88.68/26.84 ((
% 88.68/26.84 (disjointsetsI1) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectRsub) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectSubset4) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectSubset1) =>
% 88.68/26.84 ((
% 88.68/26.84 (bs114d) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusI) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusEL) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusER) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusSubset2) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusERneg) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusELneg) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusILneg) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusIRneg) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusLsub) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusSubset1) =>
% 88.68/26.84 ((
% 88.68/26.84 (symdiffE) =>
% 88.68/26.84 ((
% 88.68/26.84 (symdiffI1) =>
% 88.68/26.84 ((
% 88.68/26.84 (symdiffI2) =>
% 88.68/26.84 ((
% 88.68/26.84 (symdiffIneg1) =>
% 88.68/26.84 ((
% 88.68/26.84 (symdiffIneg2) =>
% 88.68/26.84 ((
% 88.68/26.84 (secondinupair) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairIL) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairIR) =>
% 88.68/26.84 ((
% 88.68/26.84 (kpairiskpair) =>
% 88.68/26.84 ((
% 88.68/26.84 (kpairp) =>
% 88.68/26.84 ((
% 88.68/26.84 (singletonsubset) =>
% 88.68/26.84 ((
% 88.68/26.84 (singletoninpowerset) =>
% 88.68/26.84 ((
% 88.68/26.84 (singletoninpowunion) =>
% 88.68/26.84 ((
% 88.68/26.84 (upairset2E) =>
% 88.68/26.84 ((
% 88.68/26.84 (upairsubunion) =>
% 88.68/26.84 ((
% 88.68/26.84 (upairinpowunion) =>
% 88.68/26.84 ((
% 88.68/26.84 (ubforcartprodlem1) =>
% 88.68/26.84 ((
% 88.68/26.84 (ubforcartprodlem2) =>
% 88.68/26.84 ((
% 88.68/26.84 (ubforcartprodlem3) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodpairin) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodmempair1) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodmempair) =>
% 88.68/26.84 ((
% 88.68/26.84 (setunionE2) =>
% 88.68/26.84 ((
% 88.68/26.84 (setunionsingleton1) =>
% 88.68/26.84 ((
% 88.68/26.84 (setunionsingleton2) =>
% 88.68/26.84 ((
% 88.68/26.84 (setunionsingleton) =>
% 88.68/26.84 ((
% 88.68/26.84 (singletonprop) =>
% 88.68/26.84 ((
% 88.68/26.84 (ex1E1) =>
% 88.68/26.84 ((
% 88.68/26.84 (ex1I) =>
% 88.68/26.84 ((
% 88.68/26.84 (ex1I2) =>
% 88.68/26.84 ((
% 88.68/26.84 (singletonsuniq) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairinjL1) =>
% 88.68/26.84 ((
% 88.68/26.84 (kfstsingleton) =>
% 88.68/26.84 ((
% 88.68/26.84 (theprop) =>
% 88.68/26.84 ((
% 88.68/26.84 (kfstpairEq) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodfstin) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairinjL2) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairinjL) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairinjR11) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairinjR12) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairinjR1) =>
% 88.68/26.84 ((
% 88.68/26.84 (upairequniteq) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairinjR2) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairinjR) =>
% 88.68/26.84 ((
% 88.68/26.84 (ksndsingleton) =>
% 88.68/26.84 ((
% 88.68/26.84 (ksndpairEq) =>
% 88.68/26.84 ((
% 88.68/26.84 (kpairsurjEq) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodsndin) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodpairmemEL) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodpairmemER) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodmempaircEq) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodfstpairEq) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodsndpairEq) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodpairsurjEq) =>
% 88.68/26.84 ((
% 88.68/26.84 (dpsetconstrI) =>
% 88.68/26.84 ((
% 88.68/26.84 (dpsetconstrSub) =>
% 88.68/26.84 ((
% 88.68/26.84 (setOfPairsIsBReln) =>
% 88.68/26.84 ((
% 88.68/26.84 (dpsetconstrERa) =>
% 88.68/26.84 ((
% 88.68/26.84 (dpsetconstrEL1) =>
% 88.68/26.84 ((
% 88.68/26.84 (dpsetconstrEL2) =>
% 88.68/26.84 ((
% 88.68/26.84 (dpsetconstrER) =>
% 88.68/26.84 ((
% 88.68/26.84 (funcImageSingleton) =>
% 88.68/26.84 ((
% 88.68/26.84 (apProp) =>
% 88.68/26.84 ((
% 88.68/26.84 (app) =>
% 88.68/26.84 ((
% 88.68/26.84 (infuncsetfunc) =>
% 88.68/26.84 ((
% 88.68/26.84 (ap2p) =>
% 88.68/26.84 ((
% 88.68/26.84 (funcinfuncset) =>
% 88.68/26.84 ((
% 88.68/26.84 (lamProp) =>
% 88.68/26.84 ((
% 88.68/26.84 (lamp) =>
% 88.68/26.84 ((
% 88.68/26.84 (lam2p) =>
% 88.68/26.84 ((
% 88.68/26.84 (brelnall1) =>
% 88.68/26.84 ((
% 88.68/26.84 (brelnall2) =>
% 88.68/26.84 ((
% 88.68/26.84 (!!) @ (
% 88.68/26.84 (('#B') @ (
% 88.68/26.84 !!) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#S') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#S') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 =>))) @
% 88.68/26.84 ex1)))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 !!))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#S') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#B') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#S') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 =>))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#C') @ in)))))))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 !!))))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#C') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#B') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#B') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#S') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 =>))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#C') @ in)))))))))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#S') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#S') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#B'))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 =>))))))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#C') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#B') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#S') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 =>))))))) @
% 88.68/26.84 (
% 88.68/26.84 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 88.68/26.84 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl467])).
% 88.68/26.84 thf(zip_derived_cl485, plain,
% 88.68/26.84 (~ (((upairsetE) =>
% 88.68/26.84 (((upairsetIL) =>
% 88.68/26.84 (((upairsetIR) =>
% 88.68/26.84 (((emptyE1) =>
% 88.68/26.84 (((vacuousDall) =>
% 88.68/26.84 (((quantDeMorgan1) =>
% 88.68/26.84 (((quantDeMorgan2) =>
% 88.68/26.84 (((quantDeMorgan3) =>
% 88.68/26.84 (((quantDeMorgan4) =>
% 88.68/26.84 (((prop2setI) =>
% 88.68/26.84 (((prop2set2propI) =>
% 88.68/26.84 (((notdexE) =>
% 88.68/26.84 (((notdallE) =>
% 88.68/26.84 (((exuI1) =>
% 88.68/26.84 (((exuI3) =>
% 88.68/26.84 (((exuI2) =>
% 88.68/26.84 (((inCongP) =>
% 88.68/26.84 (((in__Cong) =>
% 88.68/26.84 (((exuE3u) =>
% 88.68/26.84 (((exu__Cong) =>
% 88.68/26.84 (((setadjoin__Cong) =>
% 88.68/26.84 (((powerset__Cong) =>
% 88.68/26.84 (((setunion__Cong) =>
% 88.68/26.84 (((exuEu) =>
% 88.68/26.84 (((descr__Cong) =>
% 88.68/26.84 (((dsetconstr__Cong) =>
% 88.68/26.84 (((subsetI1) =>
% 88.68/26.84 (((eqimpsubset2) =>
% 88.68/26.84 (((eqimpsubset1) =>
% 88.68/26.84 (((subsetI2) =>
% 88.68/26.84 ((
% 88.68/26.84 (emptysetsubset) =>
% 88.68/26.84 ((
% 88.68/26.84 (subsetE) =>
% 88.68/26.84 ((
% 88.68/26.84 (subsetE2) =>
% 88.68/26.84 ((
% 88.68/26.84 (notsubsetI) =>
% 88.68/26.84 ((
% 88.68/26.84 (notequalI1) =>
% 88.68/26.84 ((
% 88.68/26.84 (notequalI2) =>
% 88.68/26.84 ((
% 88.68/26.84 (subsetRefl) =>
% 88.68/26.84 ((
% 88.68/26.84 (subsetTrans) =>
% 88.68/26.84 ((
% 88.68/26.84 (setadjoinSub) =>
% 88.68/26.84 ((
% 88.68/26.84 (setadjoinSub2) =>
% 88.68/26.84 ((
% 88.68/26.84 (subset2powerset) =>
% 88.68/26.84 ((
% 88.68/26.84 (setextsub) =>
% 88.68/26.84 ((
% 88.68/26.84 (subsetemptysetimpeq) =>
% 88.68/26.84 ((
% 88.68/26.84 (powersetI1) =>
% 88.68/26.84 ((
% 88.68/26.84 (powersetE1) =>
% 88.68/26.84 ((
% 88.68/26.84 (inPowerset) =>
% 88.68/26.84 ((
% 88.68/26.84 (powersetsubset) =>
% 88.68/26.84 ((
% 88.68/26.84 (sepInPowerset) =>
% 88.68/26.84 ((
% 88.68/26.84 (sepSubset) =>
% 88.68/26.84 ((
% 88.68/26.84 (binunionIL) =>
% 88.68/26.84 ((
% 88.68/26.84 (upairset2IR) =>
% 88.68/26.84 ((
% 88.68/26.84 (binunionIR) =>
% 88.68/26.84 ((
% 88.68/26.84 (binunionEcases) =>
% 88.68/26.84 ((
% 88.68/26.84 (binunionE) =>
% 88.68/26.84 ((
% 88.68/26.84 (binunionLsub) =>
% 88.68/26.84 ((
% 88.68/26.84 (binunionRsub) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectI) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectSubset5) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectEL) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectLsub) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectSubset2) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectSubset3) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectER) =>
% 88.68/26.84 ((
% 88.68/26.84 (disjointsetsI1) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectRsub) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectSubset4) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectSubset1) =>
% 88.68/26.84 ((
% 88.68/26.84 (bs114d) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusI) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusEL) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusER) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusSubset2) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusERneg) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusELneg) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusILneg) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusIRneg) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusLsub) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusSubset1) =>
% 88.68/26.84 ((
% 88.68/26.84 (symdiffE) =>
% 88.68/26.84 ((
% 88.68/26.84 (symdiffI1) =>
% 88.68/26.84 ((
% 88.68/26.84 (symdiffI2) =>
% 88.68/26.84 ((
% 88.68/26.84 (symdiffIneg1) =>
% 88.68/26.84 ((
% 88.68/26.84 (symdiffIneg2) =>
% 88.68/26.84 ((
% 88.68/26.84 (secondinupair) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairIL) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairIR) =>
% 88.68/26.84 ((
% 88.68/26.84 (kpairiskpair) =>
% 88.68/26.84 ((
% 88.68/26.84 (kpairp) =>
% 88.68/26.84 ((
% 88.68/26.84 (singletonsubset) =>
% 88.68/26.84 ((
% 88.68/26.84 (singletoninpowerset) =>
% 88.68/26.84 ((
% 88.68/26.84 (singletoninpowunion) =>
% 88.68/26.84 ((
% 88.68/26.84 (upairset2E) =>
% 88.68/26.84 ((
% 88.68/26.84 (upairsubunion) =>
% 88.68/26.84 ((
% 88.68/26.84 (upairinpowunion) =>
% 88.68/26.84 ((
% 88.68/26.84 (ubforcartprodlem1) =>
% 88.68/26.84 ((
% 88.68/26.84 (ubforcartprodlem2) =>
% 88.68/26.84 ((
% 88.68/26.84 (ubforcartprodlem3) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodpairin) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodmempair1) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodmempair) =>
% 88.68/26.84 ((
% 88.68/26.84 (setunionE2) =>
% 88.68/26.84 ((
% 88.68/26.84 (setunionsingleton1) =>
% 88.68/26.84 ((
% 88.68/26.84 (setunionsingleton2) =>
% 88.68/26.84 ((
% 88.68/26.84 (setunionsingleton) =>
% 88.68/26.84 ((
% 88.68/26.84 (singletonprop) =>
% 88.68/26.84 ((
% 88.68/26.84 (ex1E1) =>
% 88.68/26.84 ((
% 88.68/26.84 (ex1I) =>
% 88.68/26.84 ((
% 88.68/26.84 (ex1I2) =>
% 88.68/26.84 ((
% 88.68/26.84 (singletonsuniq) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairinjL1) =>
% 88.68/26.84 ((
% 88.68/26.84 (kfstsingleton) =>
% 88.68/26.84 ((
% 88.68/26.84 (theprop) =>
% 88.68/26.84 ((
% 88.68/26.84 (kfstpairEq) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodfstin) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairinjL2) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairinjL) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairinjR11) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairinjR12) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairinjR1) =>
% 88.68/26.84 ((
% 88.68/26.84 (upairequniteq) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairinjR2) =>
% 88.68/26.84 ((
% 88.68/26.84 (setukpairinjR) =>
% 88.68/26.84 ((
% 88.68/26.84 (ksndsingleton) =>
% 88.68/26.84 ((
% 88.68/26.84 (ksndpairEq) =>
% 88.68/26.84 ((
% 88.68/26.84 (kpairsurjEq) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodsndin) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodpairmemEL) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodpairmemER) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodmempaircEq) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodfstpairEq) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodsndpairEq) =>
% 88.68/26.84 ((
% 88.68/26.84 (cartprodpairsurjEq) =>
% 88.68/26.84 ((
% 88.68/26.84 (dpsetconstrI) =>
% 88.68/26.84 ((
% 88.68/26.84 (dpsetconstrSub) =>
% 88.68/26.84 ((
% 88.68/26.84 (setOfPairsIsBReln) =>
% 88.68/26.84 ((
% 88.68/26.84 (dpsetconstrERa) =>
% 88.68/26.84 ((
% 88.68/26.84 (dpsetconstrEL1) =>
% 88.68/26.84 ((
% 88.68/26.84 (dpsetconstrEL2) =>
% 88.68/26.84 ((
% 88.68/26.84 (dpsetconstrER) =>
% 88.68/26.84 ((
% 88.68/26.84 (funcImageSingleton) =>
% 88.68/26.84 ((
% 88.68/26.84 (apProp) =>
% 88.68/26.84 ((
% 88.68/26.84 (app) =>
% 88.68/26.84 ((
% 88.68/26.84 (infuncsetfunc) =>
% 88.68/26.84 ((
% 88.68/26.84 (ap2p) =>
% 88.68/26.84 ((
% 88.68/26.84 (funcinfuncset) =>
% 88.68/26.84 ((
% 88.68/26.84 (lamProp) =>
% 88.68/26.84 ((
% 88.68/26.84 (lamp) =>
% 88.68/26.84 ((
% 88.68/26.84 (lam2p) =>
% 88.68/26.84 ((
% 88.68/26.84 (brelnall1) =>
% 88.68/26.84 ((
% 88.68/26.84 (brelnall2) =>
% 88.68/26.84 ((
% 88.68/26.84 (!!) @ (
% 88.68/26.84 (('#B') @ (
% 88.68/26.84 !!) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#S') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#S') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 =>))) @
% 88.68/26.84 ex1)))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 !!))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#S') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#B') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#S') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 =>))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#C') @ in)))))))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 !!))))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#C') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#B') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#B') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#S') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 =>))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#C') @ in)))))))))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#S') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#S') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#B'))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 =>))))))) @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#C') @ (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#B') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 '#S') @
% 88.68/26.84 (
% 88.68/26.84 (
% 88.68/26.84 ('#B') @ (
% 88.68/26.84 =>))))))) @
% 88.68/26.84 (
% 88.68/26.84 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 88.68/26.84 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl475])).
% 88.68/26.84 thf(zip_derived_cl496, plain,
% 88.68/26.84 (~ (((upairsetIL) =>
% 88.68/26.84 (((upairsetIR) =>
% 88.68/26.84 (((emptyE1) =>
% 88.68/26.84 (((vacuousDall) =>
% 88.68/26.84 (((quantDeMorgan1) =>
% 88.68/26.84 (((quantDeMorgan2) =>
% 88.68/26.84 (((quantDeMorgan3) =>
% 88.68/26.84 (((quantDeMorgan4) =>
% 88.68/26.84 (((prop2setI) =>
% 88.68/26.84 (((prop2set2propI) =>
% 88.68/26.84 (((notdexE) =>
% 88.68/26.84 (((notdallE) =>
% 88.68/26.84 (((exuI1) =>
% 88.68/26.84 (((exuI3) =>
% 88.68/26.84 (((exuI2) =>
% 88.68/26.84 (((inCongP) =>
% 88.68/26.84 (((in__Cong) =>
% 88.68/26.84 (((exuE3u) =>
% 88.68/26.84 (((exu__Cong) =>
% 88.68/26.84 (((setadjoin__Cong) =>
% 88.68/26.84 (((powerset__Cong) =>
% 88.68/26.84 (((setunion__Cong) =>
% 88.68/26.84 (((exuEu) =>
% 88.68/26.84 (((descr__Cong) =>
% 88.68/26.84 (((dsetconstr__Cong) =>
% 88.68/26.84 (((subsetI1) =>
% 88.68/26.84 (((eqimpsubset2) =>
% 88.68/26.84 (((eqimpsubset1) =>
% 88.68/26.84 (((subsetI2) =>
% 88.68/26.84 (((emptysetsubset) =>
% 88.68/26.84 ((
% 88.68/26.84 (subsetE) =>
% 88.68/26.84 ((
% 88.68/26.84 (subsetE2) =>
% 88.68/26.84 ((
% 88.68/26.84 (notsubsetI) =>
% 88.68/26.84 ((
% 88.68/26.84 (notequalI1) =>
% 88.68/26.84 ((
% 88.68/26.84 (notequalI2) =>
% 88.68/26.84 ((
% 88.68/26.84 (subsetRefl) =>
% 88.68/26.84 ((
% 88.68/26.84 (subsetTrans) =>
% 88.68/26.84 ((
% 88.68/26.84 (setadjoinSub) =>
% 88.68/26.84 ((
% 88.68/26.84 (setadjoinSub2) =>
% 88.68/26.84 ((
% 88.68/26.84 (subset2powerset) =>
% 88.68/26.84 ((
% 88.68/26.84 (setextsub) =>
% 88.68/26.84 ((
% 88.68/26.84 (subsetemptysetimpeq) =>
% 88.68/26.84 ((
% 88.68/26.84 (powersetI1) =>
% 88.68/26.84 ((
% 88.68/26.84 (powersetE1) =>
% 88.68/26.84 ((
% 88.68/26.84 (inPowerset) =>
% 88.68/26.84 ((
% 88.68/26.84 (powersetsubset) =>
% 88.68/26.84 ((
% 88.68/26.84 (sepInPowerset) =>
% 88.68/26.84 ((
% 88.68/26.84 (sepSubset) =>
% 88.68/26.84 ((
% 88.68/26.84 (binunionIL) =>
% 88.68/26.84 ((
% 88.68/26.84 (upairset2IR) =>
% 88.68/26.84 ((
% 88.68/26.84 (binunionIR) =>
% 88.68/26.84 ((
% 88.68/26.84 (binunionEcases) =>
% 88.68/26.84 ((
% 88.68/26.84 (binunionE) =>
% 88.68/26.84 ((
% 88.68/26.84 (binunionLsub) =>
% 88.68/26.84 ((
% 88.68/26.84 (binunionRsub) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectI) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectSubset5) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectEL) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectLsub) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectSubset2) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectSubset3) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectER) =>
% 88.68/26.84 ((
% 88.68/26.84 (disjointsetsI1) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectRsub) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectSubset4) =>
% 88.68/26.84 ((
% 88.68/26.84 (binintersectSubset1) =>
% 88.68/26.84 ((
% 88.68/26.84 (bs114d) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusI) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusEL) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusER) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusSubset2) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusERneg) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusELneg) =>
% 88.68/26.84 ((
% 88.68/26.84 (setminusILneg) =>
% 88.68/26.85 ((
% 88.68/26.85 (setminusIRneg) =>
% 88.68/26.85 ((
% 88.68/26.85 (setminusLsub) =>
% 88.68/26.85 ((
% 88.68/26.85 (setminusSubset1) =>
% 88.68/26.85 ((
% 88.68/26.85 (symdiffE) =>
% 88.68/26.85 ((
% 88.68/26.85 (symdiffI1) =>
% 88.68/26.85 ((
% 88.68/26.85 (symdiffI2) =>
% 88.68/26.85 ((
% 88.68/26.85 (symdiffIneg1) =>
% 88.68/26.85 ((
% 88.68/26.85 (symdiffIneg2) =>
% 88.68/26.85 ((
% 88.68/26.85 (secondinupair) =>
% 88.68/26.85 ((
% 88.68/26.85 (setukpairIL) =>
% 88.68/26.85 ((
% 88.68/26.85 (setukpairIR) =>
% 88.68/26.85 ((
% 88.68/26.85 (kpairiskpair) =>
% 88.68/26.85 ((
% 88.68/26.85 (kpairp) =>
% 88.68/26.85 ((
% 88.68/26.85 (singletonsubset) =>
% 88.68/26.85 ((
% 88.68/26.85 (singletoninpowerset) =>
% 88.68/26.85 ((
% 88.68/26.85 (singletoninpowunion) =>
% 88.68/26.85 ((
% 88.68/26.85 (upairset2E) =>
% 88.68/26.85 ((
% 88.68/26.85 (upairsubunion) =>
% 88.68/26.85 ((
% 88.68/26.85 (upairinpowunion) =>
% 88.68/26.85 ((
% 88.68/26.85 (ubforcartprodlem1) =>
% 88.68/26.85 ((
% 88.68/26.85 (ubforcartprodlem2) =>
% 88.68/26.85 ((
% 88.68/26.85 (ubforcartprodlem3) =>
% 88.68/26.85 ((
% 88.68/26.85 (cartprodpairin) =>
% 88.68/26.85 ((
% 88.68/26.85 (cartprodmempair1) =>
% 88.68/26.85 ((
% 88.68/26.85 (cartprodmempair) =>
% 88.68/26.85 ((
% 88.68/26.85 (setunionE2) =>
% 88.68/26.85 ((
% 88.68/26.85 (setunionsingleton1) =>
% 88.68/26.85 ((
% 88.68/26.85 (setunionsingleton2) =>
% 88.68/26.85 ((
% 88.68/26.85 (setunionsingleton) =>
% 88.68/26.85 ((
% 88.68/26.85 (singletonprop) =>
% 88.68/26.85 ((
% 88.68/26.85 (ex1E1) =>
% 88.68/26.85 ((
% 88.68/26.85 (ex1I) =>
% 88.68/26.85 ((
% 88.68/26.85 (ex1I2) =>
% 88.68/26.85 ((
% 88.68/26.85 (singletonsuniq) =>
% 88.68/26.85 ((
% 88.68/26.85 (setukpairinjL1) =>
% 88.68/26.85 ((
% 88.68/26.85 (kfstsingleton) =>
% 88.68/26.85 ((
% 88.68/26.85 (theprop) =>
% 88.68/26.85 ((
% 88.68/26.85 (kfstpairEq) =>
% 88.68/26.85 ((
% 88.68/26.85 (cartprodfstin) =>
% 88.68/26.85 ((
% 88.68/26.85 (setukpairinjL2) =>
% 88.68/26.85 ((
% 88.68/26.85 (setukpairinjL) =>
% 88.68/26.85 ((
% 88.68/26.85 (setukpairinjR11) =>
% 88.68/26.85 ((
% 88.68/26.85 (setukpairinjR12) =>
% 88.68/26.85 ((
% 88.68/26.85 (setukpairinjR1) =>
% 88.68/26.85 ((
% 88.68/26.85 (upairequniteq) =>
% 88.68/26.85 ((
% 88.68/26.85 (setukpairinjR2) =>
% 88.68/26.85 ((
% 88.68/26.85 (setukpairinjR) =>
% 88.68/26.85 ((
% 88.68/26.85 (ksndsingleton) =>
% 88.68/26.85 ((
% 88.68/26.85 (ksndpairEq) =>
% 88.68/26.85 ((
% 88.68/26.85 (kpairsurjEq) =>
% 88.68/26.85 ((
% 88.68/26.85 (cartprodsndin) =>
% 88.68/26.85 ((
% 88.68/26.85 (cartprodpairmemEL) =>
% 88.68/26.85 ((
% 88.68/26.85 (cartprodpairmemER) =>
% 88.68/26.85 ((
% 88.68/26.85 (cartprodmempaircEq) =>
% 88.68/26.85 ((
% 88.68/26.85 (cartprodfstpairEq) =>
% 88.68/26.85 ((
% 88.68/26.85 (cartprodsndpairEq) =>
% 88.68/26.85 ((
% 88.68/26.85 (cartprodpairsurjEq) =>
% 88.68/26.85 ((
% 88.68/26.85 (dpsetconstrI) =>
% 88.68/26.85 ((
% 88.68/26.85 (dpsetconstrSub) =>
% 88.68/26.85 ((
% 88.68/26.85 (setOfPairsIsBReln) =>
% 88.68/26.85 ((
% 88.68/26.85 (dpsetconstrERa) =>
% 88.68/26.85 ((
% 88.68/26.85 (dpsetconstrEL1) =>
% 88.68/26.85 ((
% 88.68/26.85 (dpsetconstrEL2) =>
% 88.68/26.85 ((
% 88.68/26.85 (dpsetconstrER) =>
% 88.68/26.85 ((
% 88.68/26.85 (funcImageSingleton) =>
% 88.68/26.85 ((
% 88.68/26.85 (apProp) =>
% 88.68/26.85 ((
% 88.68/26.85 (app) =>
% 88.68/26.85 ((
% 88.68/26.85 (infuncsetfunc) =>
% 88.68/26.85 ((
% 88.68/26.85 (ap2p) =>
% 88.68/26.85 ((
% 88.68/26.85 (funcinfuncset) =>
% 88.68/26.85 ((
% 88.68/26.85 (lamProp) =>
% 88.68/26.85 ((
% 88.68/26.85 (lamp) =>
% 88.68/26.85 ((
% 88.68/26.85 (lam2p) =>
% 88.68/26.85 ((
% 88.68/26.85 (brelnall1) =>
% 88.68/26.85 ((
% 88.68/26.85 (brelnall2) =>
% 88.68/26.85 ((
% 88.68/26.85 (!!) @ (
% 88.68/26.85 (('#B') @ (
% 88.68/26.85 !!) @
% 88.68/26.85 (
% 88.68/26.85 (
% 88.68/26.85 ('#S') @ (
% 88.68/26.85 (
% 88.68/26.85 ('#B') @ (
% 88.68/26.85 '#S') @
% 88.68/26.85 (
% 88.68/26.85 (
% 88.68/26.85 ('#B') @ (
% 88.68/26.85 (
% 88.68/26.85 ('#B') @ (
% 88.68/26.85 =>))) @
% 88.68/26.85 ex1)))) @
% 88.68/26.85 (
% 88.68/26.85 (
% 88.68/26.85 ('#B') @ (
% 88.68/26.85 (
% 88.68/26.85 ('#B') @ (
% 88.68/26.85 !!))) @
% 88.68/26.85 (
% 88.68/26.85 (
% 88.68/26.85 ('#S') @ (
% 88.68/26.85 (
% 88.68/26.85 ('#B') @ (
% 88.68/26.85 '#B') @
% 88.68/26.85 (
% 88.68/26.85 (
% 88.68/26.85 ('#B') @ (
% 88.68/26.85 '#S') @
% 88.68/26.85 (
% 88.68/26.85 (
% 88.68/26.85 ('#B') @ (
% 88.68/26.85 (
% 88.68/26.85 ('#B') @ (
% 88.68/26.85 =>))) @
% 88.68/26.85 (
% 88.68/26.85 (
% 88.68/26.85 ('#C') @ in)))))))) @
% 88.68/26.85 (
% 88.68/26.85 (
% 88.68/26.85 ('#B') @ (
% 88.68/26.85 (
% 88.68/26.85 ('#B') @ (
% 88.68/26.85 (
% 88.68/26.85 ('#B') @ (
% 88.68/26.85 !!))))) @
% 88.68/26.85 (
% 88.68/26.85 (
% 88.68/26.85 ('#C') @ (
% 88.68/26.85 (
% 88.68/26.85 ('#B') @ (
% 88.68/26.85 '#B') @
% 88.68/26.85 (
% 88.68/26.85 (
% 88.68/26.85 ('#B') @ (
% 88.68/26.85 '#B') @
% 88.68/26.85 (
% 88.68/26.85 (
% 88.68/26.85 ('#B') @ (
% 88.68/26.85 '#S') @
% 88.68/26.85 (
% 88.68/26.85 (
% 88.68/26.85 ('#B') @ (
% 88.68/26.85 (
% 88.68/26.85 ('#B') @ (
% 88.68/26.85 =>))) @
% 88.68/26.85 (
% 88.68/26.85 (
% 88.68/26.85 ('#C') @ in)))))))))) @
% 88.68/26.85 (
% 88.68/26.85 (
% 88.68/26.85 ('#S') @ (
% 88.68/26.85 (
% 88.68/26.85 ('#B') @ (
% 88.68/26.85 '#S') @
% 88.68/26.85 (
% 88.68/26.85 (
% 88.68/26.85 ('#B') @ (
% 88.68/26.85 (
% 88.68/26.85 ('#B') @ (
% 88.68/26.85 '#B'))) @
% 88.68/26.85 (
% 88.68/26.85 (
% 88.68/26.85 ('#B') @ (
% 88.68/26.85 =>))))))) @
% 88.68/26.85 (
% 88.68/26.85 (
% 88.68/26.85 ('#C') @ (
% 88.68/26.85 (
% 88.68/26.85 ('#B') @ (
% 88.68/26.85 '#B') @
% 88.68/26.85 (
% 88.68/26.85 (
% 88.68/26.85 ('#B') @ (
% 88.68/26.85 '#S') @
% 88.68/26.85 (
% 88.68/26.85 (
% 88.68/26.85 ('#B') @ (
% 88.68/26.85 =>))))))) @
% 88.68/26.85 (
% 88.68/26.85 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 88.68/26.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl485])).
% 88.68/26.85 thf(zip_derived_cl507, plain,
% 88.68/26.85 (~ (((upairsetIR) =>
% 88.68/26.85 (((emptyE1) =>
% 88.68/26.85 (((vacuousDall) =>
% 88.68/26.85 (((quantDeMorgan1) =>
% 88.68/26.85 (((quantDeMorgan2) =>
% 88.68/26.85 (((quantDeMorgan3) =>
% 88.68/26.85 (((quantDeMorgan4) =>
% 88.68/26.85 (((prop2setI) =>
% 88.68/26.85 (((prop2set2propI) =>
% 88.68/26.85 (((notdexE) =>
% 88.68/26.85 (((notdallE) =>
% 88.68/26.85 (((exuI1) =>
% 88.68/26.85 (((exuI3) =>
% 88.68/26.85 (((exuI2) =>
% 88.68/26.85 (((inCongP) =>
% 88.68/26.85 (((in__Cong) =>
% 88.68/26.85 (((exuE3u) =>
% 88.68/26.85 (((exu__Cong) =>
% 88.68/26.85 (((setadjoin__Cong) =>
% 88.68/26.85 (((powerset__Cong) =>
% 88.68/26.85 (((setunion__Cong) =>
% 88.68/26.85 (((exuEu) =>
% 88.68/26.85 (((descr__Cong) =>
% 88.68/26.85 (((dsetconstr__Cong) =>
% 88.68/26.85 (((subsetI1) =>
% 88.68/26.85 (((eqimpsubset2) =>
% 88.68/26.85 (((eqimpsubset1) =>
% 88.68/26.85 (((subsetI2) =>
% 88.68/26.85 (((emptysetsubset) =>
% 88.68/26.85 (((subsetE) =>
% 88.68/26.85 ((
% 88.68/26.85 (subsetE2) =>
% 88.68/26.85 ((
% 88.68/26.85 (notsubsetI) =>
% 88.68/26.85 ((
% 88.68/26.85 (notequalI1) =>
% 88.68/26.85 ((
% 88.68/26.85 (notequalI2) =>
% 88.68/26.85 ((
% 88.68/26.85 (subsetRefl) =>
% 88.68/26.85 ((
% 88.68/26.85 (subsetTrans) =>
% 88.68/26.85 ((
% 88.68/26.85 (setadjoinSub) =>
% 88.68/26.85 ((
% 88.68/26.85 (setadjoinSub2) =>
% 88.68/26.85 ((
% 88.68/26.85 (subset2powerset) =>
% 88.68/26.85 ((
% 88.68/26.85 (setextsub) =>
% 88.68/26.85 ((
% 88.68/26.85 (subsetemptysetimpeq) =>
% 88.68/26.85 ((
% 88.68/26.85 (powersetI1) =>
% 88.68/26.85 ((
% 88.68/26.85 (powersetE1) =>
% 88.68/26.85 ((
% 88.68/26.85 (inPowerset) =>
% 88.68/26.85 ((
% 88.68/26.85 (powersetsubset) =>
% 88.68/26.85 ((
% 88.68/26.85 (sepInPowerset) =>
% 88.68/26.85 ((
% 88.68/26.85 (sepSubset) =>
% 88.68/26.85 ((
% 88.68/26.85 (binunionIL) =>
% 88.68/26.85 ((
% 88.68/26.85 (upairset2IR) =>
% 88.68/26.85 ((
% 88.68/26.85 (binunionIR) =>
% 88.68/26.85 ((
% 88.68/26.85 (binunionEcases) =>
% 88.68/26.85 ((
% 88.68/26.85 (binunionE) =>
% 88.68/26.85 ((
% 88.68/26.85 (binunionLsub) =>
% 88.68/26.85 ((
% 88.68/26.85 (binunionRsub) =>
% 88.68/26.85 ((
% 88.68/26.85 (binintersectI) =>
% 88.68/26.85 ((
% 88.68/26.85 (binintersectSubset5) =>
% 88.68/26.85 ((
% 88.68/26.85 (binintersectEL) =>
% 88.68/26.85 ((
% 88.68/26.85 (binintersectLsub) =>
% 88.68/26.85 ((
% 88.68/26.85 (binintersectSubset2) =>
% 88.68/26.85 ((
% 88.68/26.85 (binintersectSubset3) =>
% 88.68/26.85 ((
% 88.68/26.85 (binintersectER) =>
% 88.68/26.85 ((
% 88.68/26.85 (disjointsetsI1) =>
% 88.68/26.85 ((
% 88.68/26.85 (binintersectRsub) =>
% 88.68/26.85 ((
% 88.68/26.85 (binintersectSubset4) =>
% 88.68/26.85 ((
% 88.68/26.85 (binintersectSubset1) =>
% 88.68/26.85 ((
% 88.68/26.85 (bs114d) =>
% 88.68/26.85 ((
% 88.68/26.85 (setminusI) =>
% 88.68/26.85 ((
% 88.68/26.85 (setminusEL) =>
% 88.68/26.85 ((
% 88.68/26.85 (setminusER) =>
% 88.68/26.85 ((
% 88.68/26.85 (setminusSubset2) =>
% 88.68/26.85 ((
% 88.68/26.85 (setminusERneg) =>
% 88.68/26.85 ((
% 88.68/26.85 (setminusELneg) =>
% 88.68/26.85 ((
% 88.68/26.85 (setminusILneg) =>
% 88.68/26.85 ((
% 88.68/26.85 (setminusIRneg) =>
% 88.68/26.85 ((
% 88.68/26.85 (setminusLsub) =>
% 88.68/26.85 ((
% 88.68/26.85 (setminusSubset1) =>
% 88.68/26.85 ((
% 88.68/26.85 (symdiffE) =>
% 88.68/26.85 ((
% 88.68/26.85 (symdiffI1) =>
% 88.68/26.85 ((
% 88.68/26.85 (symdiffI2) =>
% 88.68/26.85 ((
% 88.68/26.85 (symdiffIneg1) =>
% 88.68/26.85 ((
% 88.68/26.85 (symdiffIneg2) =>
% 88.68/26.85 ((
% 88.68/26.85 (secondinupair) =>
% 88.68/26.85 ((
% 88.68/26.85 (setukpairIL) =>
% 88.68/26.85 ((
% 88.68/26.85 (setukpairIR) =>
% 88.68/26.85 ((
% 88.68/26.85 (kpairiskpair) =>
% 88.68/26.85 ((
% 88.68/26.85 (kpairp) =>
% 88.68/26.85 ((
% 88.68/26.85 (singletonsubset) =>
% 88.68/26.85 ((
% 88.68/26.85 (singletoninpowerset) =>
% 88.68/26.85 ((
% 88.68/26.85 (singletoninpowunion) =>
% 88.68/26.85 ((
% 88.68/26.85 (upairset2E) =>
% 88.68/26.85 ((
% 88.68/26.85 (upairsubunion) =>
% 88.68/26.85 ((
% 88.68/26.85 (upairinpowunion) =>
% 88.68/26.85 ((
% 88.68/26.85 (ubforcartprodlem1) =>
% 88.68/26.85 ((
% 88.68/26.85 (ubforcartprodlem2) =>
% 88.68/26.85 ((
% 88.68/26.85 (ubforcartprodlem3) =>
% 88.68/26.85 ((
% 88.68/26.85 (cartprodpairin) =>
% 88.68/26.85 ((
% 88.68/26.85 (cartprodmempair1) =>
% 88.68/26.85 ((
% 88.68/26.85 (cartprodmempair) =>
% 88.68/26.85 ((
% 88.68/26.85 (setunionE2) =>
% 88.68/26.85 ((
% 88.68/26.85 (setunionsingleton1) =>
% 88.68/26.85 ((
% 88.68/26.85 (setunionsingleton2) =>
% 88.68/26.85 ((
% 88.68/26.85 (setunionsingleton) =>
% 88.68/26.85 ((
% 88.68/26.85 (singletonprop) =>
% 88.68/26.85 ((
% 88.68/26.85 (ex1E1) =>
% 88.68/26.85 ((
% 88.68/26.85 (ex1I) =>
% 88.68/26.85 ((
% 88.68/26.85 (ex1I2) =>
% 88.68/26.85 ((
% 88.68/26.85 (singletonsuniq) =>
% 88.68/26.85 ((
% 88.68/26.85 (setukpairinjL1) =>
% 88.68/26.85 ((
% 88.68/26.85 (kfstsingleton) =>
% 88.68/26.85 ((
% 88.68/26.85 (theprop) =>
% 88.68/26.85 ((
% 88.68/26.85 (kfstpairEq) =>
% 88.68/26.85 ((
% 88.68/26.85 (cartprodfstin) =>
% 88.68/26.85 ((
% 88.68/26.85 (setukpairinjL2) =>
% 88.68/26.85 ((
% 88.68/26.85 (setukpairinjL) =>
% 88.68/26.85 ((
% 88.68/26.85 (setukpairinjR11) =>
% 88.68/26.85 ((
% 88.68/26.85 (setukpairinjR12) =>
% 88.68/26.85 ((
% 88.68/26.85 (setukpairinjR1) =>
% 88.68/26.85 ((
% 88.68/26.85 (upairequniteq) =>
% 88.68/26.85 ((
% 88.68/26.85 (setukpairinjR2) =>
% 88.68/26.85 ((
% 88.68/26.85 (setukpairinjR) =>
% 88.68/26.85 ((
% 88.68/26.85 (ksndsingleton) =>
% 88.68/26.85 ((
% 88.68/26.85 (ksndpairEq) =>
% 88.68/26.85 ((
% 88.68/26.85 (kpairsurjEq) =>
% 88.68/26.85 ((
% 88.68/26.85 (cartprodsndin) =>
% 88.68/26.85 ((
% 88.68/26.85 (cartprodpairmemEL) =>
% 88.68/26.85 ((
% 88.68/26.85 (cartprodpairmemER) =>
% 88.68/26.85 ((
% 88.68/26.85 (cartprodmempaircEq) =>
% 88.68/26.85 ((
% 88.68/26.85 (cartprodfstpairEq) =>
% 88.68/26.85 ((
% 88.68/26.85 (cartprodsndpairEq) =>
% 88.68/26.85 ((
% 88.68/26.85 (cartprodpairsurjEq) =>
% 88.68/26.85 ((
% 88.68/26.85 (dpsetconstrI) =>
% 88.68/26.85 ((
% 88.68/26.85 (dpsetconstrSub) =>
% 88.68/26.85 ((
% 88.68/26.85 (setOfPairsIsBReln) =>
% 88.68/26.85 ((
% 88.68/26.85 (dpsetconstrERa) =>
% 88.68/26.85 ((
% 88.68/26.85 (dpsetconstrEL1) =>
% 88.68/26.85 ((
% 88.68/26.85 (dpsetconstrEL2) =>
% 88.68/26.85 ((
% 88.68/26.85 (dpsetconstrER) =>
% 88.68/26.85 ((
% 88.68/26.85 (funcImageSingleton) =>
% 88.68/26.85 ((
% 88.68/26.85 (apProp) =>
% 88.68/26.85 ((
% 88.68/26.85 (app) =>
% 88.68/26.85 ((
% 88.68/26.85 (infuncsetfunc) =>
% 88.68/26.85 ((
% 88.68/26.85 (ap2p) =>
% 88.68/26.85 ((
% 88.68/26.85 (funcinfuncset) =>
% 88.68/26.85 ((
% 88.68/26.85 (lamProp) =>
% 88.68/26.85 ((
% 88.68/26.85 (lamp) =>
% 88.68/26.85 ((
% 88.68/26.85 (lam2p) =>
% 88.68/26.85 ((
% 88.68/26.85 (brelnall1) =>
% 88.68/26.85 ((
% 88.68/26.85 (brelnall2) =>
% 88.68/26.85 ((
% 88.68/26.85 (!!) @ (
% 88.68/26.85 (('#B') @ (
% 88.68/26.85 !!) @
% 88.68/26.85 (
% 88.68/26.85 (
% 88.68/26.85 ('#S') @ (
% 88.68/26.85 (
% 88.68/26.85 ('#B') @ (
% 88.68/26.85 '#S') @
% 88.68/26.85 (
% 88.68/26.85 (
% 88.68/26.85 ('#B') @ (
% 88.68/26.85 (
% 88.68/26.85 ('#B') @ (
% 88.68/26.85 =>))) @
% 88.68/26.85 ex1)))) @
% 88.68/26.85 (
% 88.68/26.85 (
% 88.68/26.85 ('#B') @ (
% 88.68/26.85 (
% 88.68/26.85 ('#B') @ (
% 88.68/26.85 !!))) @
% 88.68/26.85 (
% 88.68/26.85 (
% 88.68/26.85 ('#S') @ (
% 88.68/26.85 (
% 88.68/26.85 ('#B') @ (
% 88.68/26.85 '#B') @
% 88.68/26.85 (
% 88.68/26.85 (
% 88.68/26.85 ('#B') @ (
% 88.68/26.85 '#S') @
% 88.68/26.85 (
% 88.68/26.85 (
% 88.68/26.85 ('#B') @ (
% 88.68/26.85 (
% 88.68/26.85 ('#B') @ (
% 88.68/26.85 =>))) @
% 88.68/26.85 (
% 88.68/26.85 (
% 88.68/26.85 ('#C') @ in)))))))) @
% 88.68/26.85 (
% 88.68/26.85 (
% 88.68/26.85 ('#B') @ (
% 88.68/26.85 (
% 88.68/26.85 ('#B') @ (
% 88.68/26.85 (
% 88.68/26.85 ('#B') @ (
% 88.68/26.85 !!))))) @
% 88.68/26.85 (
% 88.68/26.85 (
% 88.68/26.85 ('#C') @ (
% 88.68/26.85 (
% 88.68/26.85 ('#B') @ (
% 88.68/26.85 '#B') @
% 88.68/26.85 (
% 88.68/26.85 (
% 88.68/26.85 ('#B') @ (
% 88.68/26.85 '#B') @
% 88.68/26.85 (
% 88.68/26.85 (
% 88.68/26.85 ('#B') @ (
% 88.68/26.85 '#S') @
% 88.68/26.85 (
% 88.68/26.85 (
% 88.68/26.85 ('#B') @ (
% 88.68/26.85 (
% 88.68/26.85 ('#B') @ (
% 88.68/26.85 =>))) @
% 88.68/26.85 (
% 88.68/26.85 (
% 88.68/26.85 ('#C') @ in)))))))))) @
% 88.68/26.85 (
% 88.68/26.85 (
% 88.68/26.85 ('#S') @ (
% 88.68/26.85 (
% 88.68/26.85 ('#B') @ (
% 88.68/26.85 '#S') @
% 88.68/26.85 (
% 88.68/26.85 (
% 88.68/26.85 ('#B') @ (
% 88.68/26.85 (
% 88.68/26.85 ('#B') @ (
% 88.68/26.85 '#B'))) @
% 88.68/26.85 (
% 88.68/26.85 (
% 88.68/26.85 ('#B') @ (
% 88.68/26.85 =>))))))) @
% 88.68/26.85 (
% 88.68/26.85 (
% 88.68/26.85 ('#C') @ (
% 88.68/26.85 (
% 88.68/26.85 ('#B') @ (
% 88.68/26.85 '#B') @
% 88.68/26.85 (
% 88.68/26.85 (
% 88.68/26.85 ('#B') @ (
% 88.68/26.85 '#S') @
% 88.68/26.85 (
% 88.68/26.85 (
% 88.68/26.85 ('#B') @ (
% 88.68/26.85 =>))))))) @
% 88.68/26.85 (
% 88.68/26.85 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 88.68/26.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl496])).
% 88.68/26.85 thf(zip_derived_cl517, plain,
% 88.68/26.85 (~ (((emptyE1) =>
% 88.68/26.85 (((vacuousDall) =>
% 88.68/26.85 (((quantDeMorgan1) =>
% 88.68/26.85 (((quantDeMorgan2) =>
% 88.68/26.85 (((quantDeMorgan3) =>
% 88.68/26.85 (((quantDeMorgan4) =>
% 88.68/26.85 (((prop2setI) =>
% 88.68/26.85 (((prop2set2propI) =>
% 88.68/26.85 (((notdexE) =>
% 88.68/26.85 (((notdallE) =>
% 88.68/26.85 (((exuI1) =>
% 88.68/26.85 (((exuI3) =>
% 88.68/26.85 (((exuI2) =>
% 88.68/26.85 (((inCongP) =>
% 88.68/26.85 (((in__Cong) =>
% 88.68/26.85 (((exuE3u) =>
% 88.68/26.85 (((exu__Cong) =>
% 88.68/26.85 (((setadjoin__Cong) =>
% 88.68/26.85 (((powerset__Cong) =>
% 88.68/26.85 (((setunion__Cong) =>
% 88.68/26.85 (((exuEu) =>
% 88.68/26.85 (((descr__Cong) =>
% 88.68/26.85 (((dsetconstr__Cong) =>
% 88.68/26.85 (((subsetI1) =>
% 88.68/26.85 (((eqimpsubset2) =>
% 88.68/26.85 (((eqimpsubset1) =>
% 88.68/26.85 (((subsetI2) =>
% 88.68/26.85 (((emptysetsubset) =>
% 88.68/26.85 (((subsetE) =>
% 88.68/26.85 (((subsetE2) =>
% 88.68/26.85 ((
% 88.68/26.85 (notsubsetI) =>
% 88.68/26.85 ((
% 88.68/26.85 (notequalI1) =>
% 88.68/26.85 ((
% 88.68/26.85 (notequalI2) =>
% 88.68/26.85 ((
% 88.68/26.85 (subsetRefl) =>
% 88.68/26.85 ((
% 88.68/26.85 (subsetTrans) =>
% 88.68/26.85 ((
% 88.68/26.85 (setadjoinSub) =>
% 88.68/26.85 ((
% 88.68/26.85 (setadjoinSub2) =>
% 88.68/26.85 ((
% 88.68/26.85 (subset2powerset) =>
% 88.68/26.85 ((
% 88.68/26.85 (setextsub) =>
% 88.68/26.85 ((
% 88.68/26.85 (subsetemptysetimpeq) =>
% 88.68/26.85 ((
% 88.68/26.85 (powersetI1) =>
% 88.68/26.85 ((
% 88.68/26.85 (powersetE1) =>
% 88.68/26.85 ((
% 88.68/26.85 (inPowerset) =>
% 88.68/26.85 ((
% 88.68/26.85 (powersetsubset) =>
% 88.68/26.85 ((
% 88.68/26.85 (sepInPowerset) =>
% 88.68/26.85 ((
% 88.68/26.85 (sepSubset) =>
% 88.68/26.85 ((
% 88.68/26.85 (binunionIL) =>
% 88.68/26.85 ((
% 88.68/26.85 (upairset2IR) =>
% 88.68/26.85 ((
% 88.68/26.85 (binunionIR) =>
% 88.68/26.85 ((
% 88.68/26.85 (binunionEcases) =>
% 88.68/26.85 ((
% 88.68/26.85 (binunionE) =>
% 88.68/26.85 ((
% 88.68/26.85 (binunionLsub) =>
% 88.68/26.85 ((
% 88.68/26.85 (binunionRsub) =>
% 88.68/26.85 ((
% 88.68/26.85 (binintersectI) =>
% 88.68/26.85 ((
% 88.68/26.85 (binintersectSubset5) =>
% 88.68/26.85 ((
% 88.68/26.85 (binintersectEL) =>
% 88.68/26.85 ((
% 88.68/26.85 (binintersectLsub) =>
% 88.68/26.85 ((
% 88.68/26.85 (binintersectSubset2) =>
% 88.68/26.85 ((
% 88.68/26.85 (binintersectSubset3) =>
% 88.68/26.85 ((
% 88.68/26.85 (binintersectER) =>
% 88.68/26.85 ((
% 88.68/26.85 (disjointsetsI1) =>
% 88.68/26.85 ((
% 88.68/26.85 (binintersectRsub) =>
% 88.68/26.85 ((
% 88.68/26.85 (binintersectSubset4) =>
% 88.68/26.85 ((
% 88.68/26.85 (binintersectSubset1) =>
% 88.68/26.85 ((
% 88.68/26.85 (bs114d) =>
% 88.68/26.85 ((
% 88.68/26.85 (setminusI) =>
% 88.68/26.85 ((
% 88.68/26.85 (setminusEL) =>
% 88.68/26.85 ((
% 88.68/26.85 (setminusER) =>
% 88.68/26.85 ((
% 88.68/26.85 (setminusSubset2) =>
% 88.68/26.85 ((
% 88.68/26.85 (setminusERneg) =>
% 88.68/26.85 ((
% 88.68/26.85 (setminusELneg) =>
% 88.68/26.85 ((
% 88.68/26.85 (setminusILneg) =>
% 88.68/26.85 ((
% 88.68/26.85 (setminusIRneg) =>
% 88.68/26.85 ((
% 88.68/26.85 (setminusLsub) =>
% 88.68/26.85 ((
% 88.68/26.85 (setminusSubset1) =>
% 88.68/26.85 ((
% 88.68/26.85 (symdiffE) =>
% 88.68/26.85 ((
% 88.68/26.85 (symdiffI1) =>
% 88.68/26.85 ((
% 88.68/26.85 (symdiffI2) =>
% 88.68/26.85 ((
% 88.68/26.85 (symdiffIneg1) =>
% 88.68/26.85 ((
% 88.68/26.85 (symdiffIneg2) =>
% 88.68/26.85 ((
% 88.68/26.85 (secondinupair) =>
% 88.68/26.85 ((
% 88.68/26.85 (setukpairIL) =>
% 88.68/26.85 ((
% 88.68/26.85 (setukpairIR) =>
% 88.68/26.85 ((
% 88.68/26.85 (kpairiskpair) =>
% 88.68/26.85 ((
% 88.68/26.85 (kpairp) =>
% 88.68/26.85 ((
% 88.68/26.85 (singletonsubset) =>
% 88.68/26.85 ((
% 88.68/26.85 (singletoninpowerset) =>
% 88.68/26.85 ((
% 88.68/26.85 (singletoninpowunion) =>
% 88.68/26.85 ((
% 88.68/26.85 (upairset2E) =>
% 88.68/26.85 ((
% 88.68/26.85 (upairsubunion) =>
% 88.68/26.85 ((
% 88.68/26.85 (upairinpowunion) =>
% 88.68/26.85 ((
% 88.68/26.85 (ubforcartprodlem1) =>
% 88.68/26.85 ((
% 88.68/26.85 (ubforcartprodlem2) =>
% 88.68/26.85 ((
% 88.68/26.85 (ubforcartprodlem3) =>
% 88.68/26.85 ((
% 88.68/26.85 (cartprodpairin) =>
% 88.68/26.85 ((
% 88.68/26.85 (cartprodmempair1) =>
% 88.68/26.85 ((
% 88.68/26.85 (cartprodmempair) =>
% 88.68/26.85 ((
% 88.68/26.85 (setunionE2) =>
% 88.68/26.85 ((
% 88.68/26.85 (setunionsingleton1) =>
% 88.68/26.85 ((
% 88.68/26.85 (setunionsingleton2) =>
% 88.68/26.85 ((
% 88.68/26.85 (setunionsingleton) =>
% 88.68/26.85 ((
% 88.68/26.85 (singletonprop) =>
% 88.68/26.85 ((
% 88.68/26.85 (ex1E1) =>
% 88.68/26.85 ((
% 88.68/26.85 (ex1I) =>
% 88.68/26.85 ((
% 88.68/26.85 (ex1I2) =>
% 88.68/26.85 ((
% 88.68/26.85 (singletonsuniq) =>
% 88.68/26.85 ((
% 88.68/26.85 (setukpairinjL1) =>
% 88.68/26.85 ((
% 88.68/26.85 (kfstsingleton) =>
% 88.68/26.85 ((
% 88.68/26.85 (theprop) =>
% 88.68/26.85 ((
% 88.68/26.85 (kfstpairEq) =>
% 88.68/26.85 ((
% 88.68/26.85 (cartprodfstin) =>
% 88.68/26.85 ((
% 88.68/26.85 (setukpairinjL2) =>
% 88.68/26.85 ((
% 88.68/26.85 (setukpairinjL) =>
% 88.68/26.85 ((
% 88.68/26.85 (setukpairinjR11) =>
% 88.68/26.85 ((
% 88.68/26.85 (setukpairinjR12) =>
% 88.68/26.85 ((
% 88.68/26.85 (setukpairinjR1) =>
% 88.68/26.85 ((
% 88.68/26.85 (upairequniteq) =>
% 88.68/26.85 ((
% 88.68/26.85 (setukpairinjR2) =>
% 88.68/26.85 ((
% 88.68/26.85 (setukpairinjR) =>
% 88.68/26.85 ((
% 88.68/26.85 (ksndsingleton) =>
% 88.68/26.85 ((
% 88.68/26.85 (ksndpairEq) =>
% 88.68/26.85 ((
% 88.68/26.85 (kpairsurjEq) =>
% 88.68/26.85 ((
% 88.68/26.85 (cartprodsndin) =>
% 88.68/26.85 ((
% 88.68/26.85 (cartprodpairmemEL) =>
% 88.68/26.85 ((
% 88.68/26.85 (cartprodpairmemER) =>
% 88.68/26.85 ((
% 88.68/26.85 (cartprodmempaircEq) =>
% 88.68/26.85 ((
% 88.68/26.85 (cartprodfstpairEq) =>
% 88.68/26.85 ((
% 88.68/26.85 (cartprodsndpairEq) =>
% 88.68/26.85 ((
% 88.68/26.85 (cartprodpairsurjEq) =>
% 88.68/26.85 ((
% 88.68/26.85 (dpsetconstrI) =>
% 88.68/26.85 ((
% 88.68/26.85 (dpsetconstrSub) =>
% 88.68/26.85 ((
% 88.68/26.85 (setOfPairsIsBReln) =>
% 88.68/26.85 ((
% 88.68/26.85 (dpsetconstrERa) =>
% 88.68/26.85 ((
% 88.68/26.85 (dpsetconstrEL1) =>
% 88.68/26.85 ((
% 88.68/26.85 (dpsetconstrEL2) =>
% 88.68/26.85 ((
% 88.68/26.85 (dpsetconstrER) =>
% 88.68/26.85 ((
% 88.68/26.85 (funcImageSingleton) =>
% 88.68/26.85 ((
% 88.68/26.85 (apProp) =>
% 88.68/26.85 ((
% 88.68/26.85 (app) =>
% 88.68/26.85 ((
% 88.68/26.85 (infuncsetfunc) =>
% 88.68/26.85 ((
% 88.68/26.85 (ap2p) =>
% 88.68/26.85 ((
% 88.68/26.85 (funcinfuncset) =>
% 88.68/26.85 ((
% 88.68/26.85 (lamProp) =>
% 88.68/26.85 ((
% 88.68/26.85 (lamp) =>
% 88.68/26.85 ((
% 88.68/26.85 (lam2p) =>
% 88.68/26.85 ((
% 88.68/26.85 (brelnall1) =>
% 88.68/26.85 ((
% 88.68/26.85 (brelnall2) =>
% 88.68/26.85 ((
% 88.68/26.85 (!!) @ (
% 88.68/26.85 (('#B') @ (
% 88.68/26.85 !!) @
% 88.68/26.85 (
% 88.68/26.85 (
% 88.68/26.85 ('#S') @ (
% 88.68/26.85 (
% 88.68/26.85 ('#B') @ (
% 89.02/26.85 '#S') @
% 89.02/26.85 (
% 89.02/26.85 (
% 89.02/26.85 ('#B') @ (
% 89.02/26.85 (
% 89.02/26.85 ('#B') @ (
% 89.02/26.85 =>))) @
% 89.02/26.85 ex1)))) @
% 89.02/26.85 (
% 89.02/26.85 (
% 89.02/26.85 ('#B') @ (
% 89.02/26.85 (
% 89.02/26.85 ('#B') @ (
% 89.02/26.85 !!))) @
% 89.02/26.85 (
% 89.02/26.85 (
% 89.02/26.85 ('#S') @ (
% 89.02/26.85 (
% 89.02/26.85 ('#B') @ (
% 89.02/26.85 '#B') @
% 89.02/26.85 (
% 89.02/26.85 (
% 89.02/26.85 ('#B') @ (
% 89.02/26.85 '#S') @
% 89.02/26.85 (
% 89.02/26.85 (
% 89.02/26.85 ('#B') @ (
% 89.02/26.85 (
% 89.02/26.85 ('#B') @ (
% 89.02/26.85 =>))) @
% 89.02/26.85 (
% 89.02/26.85 (
% 89.02/26.85 ('#C') @ in)))))))) @
% 89.02/26.85 (
% 89.02/26.85 (
% 89.02/26.85 ('#B') @ (
% 89.02/26.85 (
% 89.02/26.85 ('#B') @ (
% 89.02/26.85 (
% 89.02/26.85 ('#B') @ (
% 89.02/26.85 !!))))) @
% 89.02/26.85 (
% 89.02/26.85 (
% 89.02/26.85 ('#C') @ (
% 89.02/26.85 (
% 89.02/26.85 ('#B') @ (
% 89.02/26.85 '#B') @
% 89.02/26.85 (
% 89.02/26.85 (
% 89.02/26.85 ('#B') @ (
% 89.02/26.85 '#B') @
% 89.02/26.85 (
% 89.02/26.85 (
% 89.02/26.85 ('#B') @ (
% 89.02/26.85 '#S') @
% 89.02/26.85 (
% 89.02/26.85 (
% 89.02/26.85 ('#B') @ (
% 89.02/26.85 (
% 89.02/26.85 ('#B') @ (
% 89.02/26.85 =>))) @
% 89.02/26.85 (
% 89.02/26.85 (
% 89.02/26.85 ('#C') @ in)))))))))) @
% 89.02/26.85 (
% 89.02/26.85 (
% 89.02/26.85 ('#S') @ (
% 89.02/26.85 (
% 89.02/26.85 ('#B') @ (
% 89.02/26.85 '#S') @
% 89.02/26.85 (
% 89.02/26.85 (
% 89.02/26.85 ('#B') @ (
% 89.02/26.85 (
% 89.02/26.85 ('#B') @ (
% 89.02/26.85 '#B'))) @
% 89.02/26.85 (
% 89.02/26.85 (
% 89.02/26.85 ('#B') @ (
% 89.02/26.85 =>))))))) @
% 89.02/26.85 (
% 89.02/26.85 (
% 89.02/26.85 ('#C') @ (
% 89.02/26.85 (
% 89.02/26.85 ('#B') @ (
% 89.02/26.85 '#B') @
% 89.02/26.85 (
% 89.02/26.85 (
% 89.02/26.85 ('#B') @ (
% 89.02/26.85 '#S') @
% 89.02/26.85 (
% 89.02/26.85 (
% 89.02/26.85 ('#B') @ (
% 89.02/26.85 =>))))))) @
% 89.02/26.85 (
% 89.02/26.85 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.02/26.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl507])).
% 89.02/26.85 thf(zip_derived_cl528, plain,
% 89.02/26.85 (~ (((vacuousDall) =>
% 89.02/26.85 (((quantDeMorgan1) =>
% 89.02/26.85 (((quantDeMorgan2) =>
% 89.02/26.85 (((quantDeMorgan3) =>
% 89.02/26.85 (((quantDeMorgan4) =>
% 89.02/26.85 (((prop2setI) =>
% 89.02/26.85 (((prop2set2propI) =>
% 89.02/26.85 (((notdexE) =>
% 89.02/26.85 (((notdallE) =>
% 89.02/26.85 (((exuI1) =>
% 89.02/26.85 (((exuI3) =>
% 89.02/26.85 (((exuI2) =>
% 89.02/26.85 (((inCongP) =>
% 89.02/26.85 (((in__Cong) =>
% 89.02/26.85 (((exuE3u) =>
% 89.02/26.85 (((exu__Cong) =>
% 89.02/26.85 (((setadjoin__Cong) =>
% 89.02/26.85 (((powerset__Cong) =>
% 89.02/26.85 (((setunion__Cong) =>
% 89.02/26.85 (((exuEu) =>
% 89.02/26.85 (((descr__Cong) =>
% 89.02/26.85 (((dsetconstr__Cong) =>
% 89.02/26.85 (((subsetI1) =>
% 89.02/26.85 (((eqimpsubset2) =>
% 89.02/26.85 (((eqimpsubset1) =>
% 89.02/26.85 (((subsetI2) =>
% 89.02/26.85 (((emptysetsubset) =>
% 89.02/26.85 (((subsetE) =>
% 89.02/26.85 (((subsetE2) =>
% 89.02/26.85 (((notsubsetI) =>
% 89.02/26.85 ((
% 89.02/26.85 (notequalI1) =>
% 89.02/26.85 ((
% 89.02/26.85 (notequalI2) =>
% 89.02/26.85 ((
% 89.02/26.85 (subsetRefl) =>
% 89.02/26.85 ((
% 89.02/26.85 (subsetTrans) =>
% 89.02/26.85 ((
% 89.02/26.85 (setadjoinSub) =>
% 89.02/26.85 ((
% 89.02/26.85 (setadjoinSub2) =>
% 89.02/26.85 ((
% 89.02/26.85 (subset2powerset) =>
% 89.02/26.85 ((
% 89.02/26.85 (setextsub) =>
% 89.02/26.85 ((
% 89.02/26.85 (subsetemptysetimpeq) =>
% 89.02/26.85 ((
% 89.02/26.85 (powersetI1) =>
% 89.02/26.85 ((
% 89.02/26.85 (powersetE1) =>
% 89.02/26.85 ((
% 89.02/26.85 (inPowerset) =>
% 89.02/26.85 ((
% 89.02/26.85 (powersetsubset) =>
% 89.02/26.85 ((
% 89.02/26.85 (sepInPowerset) =>
% 89.02/26.85 ((
% 89.02/26.85 (sepSubset) =>
% 89.02/26.85 ((
% 89.02/26.85 (binunionIL) =>
% 89.02/26.85 ((
% 89.02/26.85 (upairset2IR) =>
% 89.02/26.85 ((
% 89.02/26.85 (binunionIR) =>
% 89.02/26.85 ((
% 89.02/26.85 (binunionEcases) =>
% 89.02/26.85 ((
% 89.02/26.85 (binunionE) =>
% 89.02/26.85 ((
% 89.02/26.85 (binunionLsub) =>
% 89.02/26.85 ((
% 89.02/26.85 (binunionRsub) =>
% 89.02/26.85 ((
% 89.02/26.85 (binintersectI) =>
% 89.02/26.85 ((
% 89.02/26.85 (binintersectSubset5) =>
% 89.02/26.85 ((
% 89.02/26.85 (binintersectEL) =>
% 89.02/26.85 ((
% 89.02/26.85 (binintersectLsub) =>
% 89.02/26.85 ((
% 89.02/26.85 (binintersectSubset2) =>
% 89.02/26.85 ((
% 89.02/26.85 (binintersectSubset3) =>
% 89.02/26.85 ((
% 89.02/26.85 (binintersectER) =>
% 89.02/26.85 ((
% 89.02/26.85 (disjointsetsI1) =>
% 89.02/26.85 ((
% 89.02/26.85 (binintersectRsub) =>
% 89.02/26.85 ((
% 89.02/26.85 (binintersectSubset4) =>
% 89.02/26.85 ((
% 89.02/26.85 (binintersectSubset1) =>
% 89.02/26.85 ((
% 89.02/26.85 (bs114d) =>
% 89.02/26.85 ((
% 89.02/26.85 (setminusI) =>
% 89.02/26.85 ((
% 89.02/26.85 (setminusEL) =>
% 89.02/26.85 ((
% 89.02/26.85 (setminusER) =>
% 89.02/26.85 ((
% 89.02/26.85 (setminusSubset2) =>
% 89.02/26.85 ((
% 89.02/26.85 (setminusERneg) =>
% 89.02/26.85 ((
% 89.02/26.85 (setminusELneg) =>
% 89.02/26.85 ((
% 89.02/26.85 (setminusILneg) =>
% 89.02/26.85 ((
% 89.02/26.85 (setminusIRneg) =>
% 89.02/26.85 ((
% 89.02/26.85 (setminusLsub) =>
% 89.02/26.85 ((
% 89.02/26.85 (setminusSubset1) =>
% 89.02/26.85 ((
% 89.02/26.85 (symdiffE) =>
% 89.02/26.85 ((
% 89.02/26.85 (symdiffI1) =>
% 89.02/26.85 ((
% 89.02/26.85 (symdiffI2) =>
% 89.02/26.85 ((
% 89.02/26.85 (symdiffIneg1) =>
% 89.02/26.85 ((
% 89.02/26.85 (symdiffIneg2) =>
% 89.02/26.85 ((
% 89.02/26.85 (secondinupair) =>
% 89.02/26.85 ((
% 89.02/26.85 (setukpairIL) =>
% 89.02/26.85 ((
% 89.02/26.85 (setukpairIR) =>
% 89.02/26.85 ((
% 89.02/26.85 (kpairiskpair) =>
% 89.02/26.85 ((
% 89.02/26.85 (kpairp) =>
% 89.02/26.85 ((
% 89.02/26.85 (singletonsubset) =>
% 89.02/26.85 ((
% 89.02/26.85 (singletoninpowerset) =>
% 89.02/26.85 ((
% 89.02/26.85 (singletoninpowunion) =>
% 89.02/26.85 ((
% 89.02/26.85 (upairset2E) =>
% 89.02/26.85 ((
% 89.02/26.85 (upairsubunion) =>
% 89.02/26.85 ((
% 89.02/26.85 (upairinpowunion) =>
% 89.02/26.85 ((
% 89.02/26.85 (ubforcartprodlem1) =>
% 89.02/26.85 ((
% 89.02/26.85 (ubforcartprodlem2) =>
% 89.02/26.85 ((
% 89.02/26.85 (ubforcartprodlem3) =>
% 89.02/26.85 ((
% 89.02/26.85 (cartprodpairin) =>
% 89.02/26.85 ((
% 89.02/26.85 (cartprodmempair1) =>
% 89.02/26.85 ((
% 89.02/26.85 (cartprodmempair) =>
% 89.02/26.85 ((
% 89.02/26.85 (setunionE2) =>
% 89.02/26.85 ((
% 89.02/26.85 (setunionsingleton1) =>
% 89.02/26.85 ((
% 89.02/26.85 (setunionsingleton2) =>
% 89.02/26.85 ((
% 89.02/26.85 (setunionsingleton) =>
% 89.02/26.85 ((
% 89.02/26.85 (singletonprop) =>
% 89.02/26.85 ((
% 89.02/26.85 (ex1E1) =>
% 89.02/26.85 ((
% 89.02/26.85 (ex1I) =>
% 89.02/26.85 ((
% 89.02/26.85 (ex1I2) =>
% 89.02/26.85 ((
% 89.02/26.85 (singletonsuniq) =>
% 89.02/26.85 ((
% 89.02/26.85 (setukpairinjL1) =>
% 89.02/26.85 ((
% 89.02/26.85 (kfstsingleton) =>
% 89.02/26.85 ((
% 89.02/26.85 (theprop) =>
% 89.02/26.85 ((
% 89.02/26.85 (kfstpairEq) =>
% 89.02/26.85 ((
% 89.02/26.85 (cartprodfstin) =>
% 89.02/26.85 ((
% 89.02/26.85 (setukpairinjL2) =>
% 89.02/26.85 ((
% 89.02/26.85 (setukpairinjL) =>
% 89.02/26.85 ((
% 89.02/26.85 (setukpairinjR11) =>
% 89.02/26.85 ((
% 89.02/26.85 (setukpairinjR12) =>
% 89.02/26.85 ((
% 89.02/26.85 (setukpairinjR1) =>
% 89.02/26.85 ((
% 89.02/26.85 (upairequniteq) =>
% 89.02/26.85 ((
% 89.02/26.85 (setukpairinjR2) =>
% 89.02/26.85 ((
% 89.02/26.85 (setukpairinjR) =>
% 89.02/26.85 ((
% 89.02/26.85 (ksndsingleton) =>
% 89.02/26.85 ((
% 89.02/26.85 (ksndpairEq) =>
% 89.02/26.85 ((
% 89.02/26.85 (kpairsurjEq) =>
% 89.02/26.85 ((
% 89.02/26.85 (cartprodsndin) =>
% 89.02/26.85 ((
% 89.02/26.85 (cartprodpairmemEL) =>
% 89.02/26.85 ((
% 89.02/26.85 (cartprodpairmemER) =>
% 89.02/26.85 ((
% 89.02/26.85 (cartprodmempaircEq) =>
% 89.02/26.85 ((
% 89.02/26.85 (cartprodfstpairEq) =>
% 89.02/26.85 ((
% 89.02/26.85 (cartprodsndpairEq) =>
% 89.02/26.85 ((
% 89.02/26.85 (cartprodpairsurjEq) =>
% 89.02/26.85 ((
% 89.02/26.85 (dpsetconstrI) =>
% 89.02/26.85 ((
% 89.02/26.85 (dpsetconstrSub) =>
% 89.02/26.85 ((
% 89.02/26.85 (setOfPairsIsBReln) =>
% 89.02/26.85 ((
% 89.02/26.85 (dpsetconstrERa) =>
% 89.02/26.85 ((
% 89.02/26.85 (dpsetconstrEL1) =>
% 89.02/26.85 ((
% 89.02/26.85 (dpsetconstrEL2) =>
% 89.02/26.85 ((
% 89.02/26.85 (dpsetconstrER) =>
% 89.02/26.85 ((
% 89.02/26.85 (funcImageSingleton) =>
% 89.02/26.85 ((
% 89.02/26.85 (apProp) =>
% 89.02/26.85 ((
% 89.02/26.85 (app) =>
% 89.02/26.85 ((
% 89.02/26.85 (infuncsetfunc) =>
% 89.02/26.85 ((
% 89.02/26.85 (ap2p) =>
% 89.02/26.85 ((
% 89.02/26.85 (funcinfuncset) =>
% 89.02/26.85 ((
% 89.02/26.85 (lamProp) =>
% 89.02/26.85 ((
% 89.02/26.85 (lamp) =>
% 89.02/26.85 ((
% 89.02/26.85 (lam2p) =>
% 89.02/26.85 ((
% 89.02/26.85 (brelnall1) =>
% 89.02/26.85 ((
% 89.02/26.85 (brelnall2) =>
% 89.02/26.85 ((
% 89.02/26.85 (!!) @ (
% 89.02/26.85 (('#B') @ (
% 89.02/26.85 !!) @
% 89.02/26.85 (
% 89.02/26.85 (
% 89.02/26.85 ('#S') @ (
% 89.02/26.85 (
% 89.02/26.85 ('#B') @ (
% 89.02/26.85 '#S') @
% 89.02/26.85 (
% 89.02/26.85 (
% 89.02/26.85 ('#B') @ (
% 89.02/26.85 (
% 89.02/26.85 ('#B') @ (
% 89.02/26.85 =>))) @
% 89.02/26.85 ex1)))) @
% 89.02/26.85 (
% 89.02/26.85 (
% 89.02/26.85 ('#B') @ (
% 89.02/26.85 (
% 89.02/26.85 ('#B') @ (
% 89.02/26.85 !!))) @
% 89.02/26.85 (
% 89.02/26.85 (
% 89.02/26.85 ('#S') @ (
% 89.02/26.85 (
% 89.02/26.85 ('#B') @ (
% 89.02/26.85 '#B') @
% 89.02/26.85 (
% 89.02/26.85 (
% 89.02/26.85 ('#B') @ (
% 89.02/26.85 '#S') @
% 89.02/26.85 (
% 89.02/26.85 (
% 89.02/26.85 ('#B') @ (
% 89.02/26.85 (
% 89.02/26.85 ('#B') @ (
% 89.02/26.85 =>))) @
% 89.02/26.85 (
% 89.02/26.85 (
% 89.02/26.85 ('#C') @ in)))))))) @
% 89.02/26.85 (
% 89.02/26.85 (
% 89.02/26.85 ('#B') @ (
% 89.02/26.85 (
% 89.02/26.85 ('#B') @ (
% 89.02/26.85 (
% 89.02/26.85 ('#B') @ (
% 89.02/26.85 !!))))) @
% 89.02/26.85 (
% 89.02/26.85 (
% 89.02/26.85 ('#C') @ (
% 89.02/26.85 (
% 89.02/26.85 ('#B') @ (
% 89.02/26.85 '#B') @
% 89.02/26.85 (
% 89.02/26.85 (
% 89.02/26.85 ('#B') @ (
% 89.02/26.85 '#B') @
% 89.02/26.85 (
% 89.02/26.85 (
% 89.02/26.85 ('#B') @ (
% 89.02/26.85 '#S') @
% 89.02/26.85 (
% 89.02/26.85 (
% 89.02/26.85 ('#B') @ (
% 89.02/26.85 (
% 89.02/26.85 ('#B') @ (
% 89.02/26.85 =>))) @
% 89.02/26.85 (
% 89.02/26.85 (
% 89.02/26.85 ('#C') @ in)))))))))) @
% 89.02/26.85 (
% 89.02/26.85 (
% 89.02/26.85 ('#S') @ (
% 89.02/26.85 (
% 89.02/26.85 ('#B') @ (
% 89.02/26.85 '#S') @
% 89.02/26.85 (
% 89.02/26.85 (
% 89.02/26.85 ('#B') @ (
% 89.02/26.85 (
% 89.02/26.85 ('#B') @ (
% 89.02/26.85 '#B'))) @
% 89.02/26.85 (
% 89.02/26.85 (
% 89.02/26.85 ('#B') @ (
% 89.02/26.85 =>))))))) @
% 89.02/26.85 (
% 89.02/26.85 (
% 89.02/26.85 ('#C') @ (
% 89.02/26.85 (
% 89.02/26.85 ('#B') @ (
% 89.02/26.85 '#B') @
% 89.02/26.85 (
% 89.02/26.85 (
% 89.02/26.85 ('#B') @ (
% 89.02/26.85 '#S') @
% 89.02/26.85 (
% 89.02/26.85 (
% 89.02/26.85 ('#B') @ (
% 89.02/26.85 =>))))))) @
% 89.02/26.85 (
% 89.02/26.85 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.02/26.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl517])).
% 89.02/26.85 thf(zip_derived_cl537, plain,
% 89.02/26.85 (~ (((quantDeMorgan1) =>
% 89.02/26.85 (((quantDeMorgan2) =>
% 89.02/26.85 (((quantDeMorgan3) =>
% 89.02/26.85 (((quantDeMorgan4) =>
% 89.02/26.85 (((prop2setI) =>
% 89.02/26.85 (((prop2set2propI) =>
% 89.02/26.85 (((notdexE) =>
% 89.02/26.85 (((notdallE) =>
% 89.02/26.85 (((exuI1) =>
% 89.02/26.85 (((exuI3) =>
% 89.02/26.85 (((exuI2) =>
% 89.02/26.85 (((inCongP) =>
% 89.02/26.85 (((in__Cong) =>
% 89.02/26.85 (((exuE3u) =>
% 89.02/26.85 (((exu__Cong) =>
% 89.02/26.85 (((setadjoin__Cong) =>
% 89.02/26.85 (((powerset__Cong) =>
% 89.02/26.85 (((setunion__Cong) =>
% 89.02/26.85 (((exuEu) =>
% 89.02/26.85 (((descr__Cong) =>
% 89.02/26.85 (((dsetconstr__Cong) =>
% 89.02/26.85 (((subsetI1) =>
% 89.02/26.85 (((eqimpsubset2) =>
% 89.02/26.85 (((eqimpsubset1) =>
% 89.02/26.85 (((subsetI2) =>
% 89.02/26.85 (((emptysetsubset) =>
% 89.02/26.85 (((subsetE) =>
% 89.02/26.85 (((subsetE2) =>
% 89.02/26.85 (((notsubsetI) =>
% 89.02/26.85 (((notequalI1) =>
% 89.02/26.85 ((
% 89.02/26.85 (notequalI2) =>
% 89.02/26.85 ((
% 89.02/26.85 (subsetRefl) =>
% 89.02/26.85 ((
% 89.02/26.85 (subsetTrans) =>
% 89.02/26.85 ((
% 89.02/26.85 (setadjoinSub) =>
% 89.02/26.85 ((
% 89.02/26.85 (setadjoinSub2) =>
% 89.02/26.85 ((
% 89.02/26.85 (subset2powerset) =>
% 89.02/26.85 ((
% 89.02/26.85 (setextsub) =>
% 89.02/26.85 ((
% 89.02/26.85 (subsetemptysetimpeq) =>
% 89.02/26.85 ((
% 89.02/26.85 (powersetI1) =>
% 89.02/26.85 ((
% 89.02/26.85 (powersetE1) =>
% 89.02/26.85 ((
% 89.02/26.85 (inPowerset) =>
% 89.02/26.85 ((
% 89.02/26.85 (powersetsubset) =>
% 89.02/26.85 ((
% 89.02/26.85 (sepInPowerset) =>
% 89.02/26.85 ((
% 89.02/26.85 (sepSubset) =>
% 89.02/26.85 ((
% 89.02/26.85 (binunionIL) =>
% 89.02/26.85 ((
% 89.02/26.85 (upairset2IR) =>
% 89.02/26.85 ((
% 89.02/26.85 (binunionIR) =>
% 89.02/26.85 ((
% 89.02/26.85 (binunionEcases) =>
% 89.02/26.85 ((
% 89.02/26.85 (binunionE) =>
% 89.02/26.85 ((
% 89.02/26.85 (binunionLsub) =>
% 89.02/26.85 ((
% 89.02/26.85 (binunionRsub) =>
% 89.02/26.85 ((
% 89.02/26.85 (binintersectI) =>
% 89.02/26.85 ((
% 89.02/26.85 (binintersectSubset5) =>
% 89.02/26.85 ((
% 89.02/26.85 (binintersectEL) =>
% 89.02/26.85 ((
% 89.02/26.85 (binintersectLsub) =>
% 89.02/26.85 ((
% 89.02/26.85 (binintersectSubset2) =>
% 89.02/26.85 ((
% 89.02/26.85 (binintersectSubset3) =>
% 89.02/26.85 ((
% 89.02/26.85 (binintersectER) =>
% 89.02/26.85 ((
% 89.02/26.85 (disjointsetsI1) =>
% 89.02/26.85 ((
% 89.02/26.85 (binintersectRsub) =>
% 89.02/26.85 ((
% 89.02/26.85 (binintersectSubset4) =>
% 89.02/26.85 ((
% 89.02/26.85 (binintersectSubset1) =>
% 89.02/26.85 ((
% 89.02/26.85 (bs114d) =>
% 89.02/26.85 ((
% 89.02/26.85 (setminusI) =>
% 89.02/26.85 ((
% 89.02/26.85 (setminusEL) =>
% 89.02/26.85 ((
% 89.02/26.85 (setminusER) =>
% 89.02/26.85 ((
% 89.02/26.85 (setminusSubset2) =>
% 89.02/26.85 ((
% 89.02/26.85 (setminusERneg) =>
% 89.02/26.85 ((
% 89.02/26.85 (setminusELneg) =>
% 89.02/26.85 ((
% 89.02/26.85 (setminusILneg) =>
% 89.02/26.85 ((
% 89.02/26.85 (setminusIRneg) =>
% 89.02/26.85 ((
% 89.02/26.85 (setminusLsub) =>
% 89.02/26.85 ((
% 89.02/26.85 (setminusSubset1) =>
% 89.02/26.85 ((
% 89.02/26.85 (symdiffE) =>
% 89.02/26.85 ((
% 89.02/26.85 (symdiffI1) =>
% 89.02/26.85 ((
% 89.02/26.85 (symdiffI2) =>
% 89.02/26.85 ((
% 89.02/26.85 (symdiffIneg1) =>
% 89.02/26.85 ((
% 89.02/26.85 (symdiffIneg2) =>
% 89.02/26.85 ((
% 89.02/26.85 (secondinupair) =>
% 89.02/26.85 ((
% 89.02/26.85 (setukpairIL) =>
% 89.02/26.85 ((
% 89.02/26.85 (setukpairIR) =>
% 89.02/26.86 ((
% 89.02/26.86 (kpairiskpair) =>
% 89.02/26.86 ((
% 89.02/26.86 (kpairp) =>
% 89.02/26.86 ((
% 89.02/26.86 (singletonsubset) =>
% 89.02/26.86 ((
% 89.02/26.86 (singletoninpowerset) =>
% 89.02/26.86 ((
% 89.02/26.86 (singletoninpowunion) =>
% 89.02/26.86 ((
% 89.02/26.86 (upairset2E) =>
% 89.02/26.86 ((
% 89.02/26.86 (upairsubunion) =>
% 89.02/26.86 ((
% 89.02/26.86 (upairinpowunion) =>
% 89.02/26.86 ((
% 89.02/26.86 (ubforcartprodlem1) =>
% 89.02/26.86 ((
% 89.02/26.86 (ubforcartprodlem2) =>
% 89.02/26.86 ((
% 89.02/26.86 (ubforcartprodlem3) =>
% 89.02/26.86 ((
% 89.02/26.86 (cartprodpairin) =>
% 89.02/26.86 ((
% 89.02/26.86 (cartprodmempair1) =>
% 89.02/26.86 ((
% 89.02/26.86 (cartprodmempair) =>
% 89.02/26.86 ((
% 89.02/26.86 (setunionE2) =>
% 89.02/26.86 ((
% 89.02/26.86 (setunionsingleton1) =>
% 89.02/26.86 ((
% 89.02/26.86 (setunionsingleton2) =>
% 89.02/26.86 ((
% 89.02/26.86 (setunionsingleton) =>
% 89.02/26.86 ((
% 89.02/26.86 (singletonprop) =>
% 89.02/26.86 ((
% 89.02/26.86 (ex1E1) =>
% 89.02/26.86 ((
% 89.02/26.86 (ex1I) =>
% 89.02/26.86 ((
% 89.02/26.86 (ex1I2) =>
% 89.02/26.86 ((
% 89.02/26.86 (singletonsuniq) =>
% 89.02/26.86 ((
% 89.02/26.86 (setukpairinjL1) =>
% 89.02/26.86 ((
% 89.02/26.86 (kfstsingleton) =>
% 89.02/26.86 ((
% 89.02/26.86 (theprop) =>
% 89.02/26.86 ((
% 89.02/26.86 (kfstpairEq) =>
% 89.02/26.86 ((
% 89.02/26.86 (cartprodfstin) =>
% 89.02/26.86 ((
% 89.02/26.86 (setukpairinjL2) =>
% 89.02/26.86 ((
% 89.02/26.86 (setukpairinjL) =>
% 89.02/26.86 ((
% 89.02/26.86 (setukpairinjR11) =>
% 89.02/26.86 ((
% 89.02/26.86 (setukpairinjR12) =>
% 89.02/26.86 ((
% 89.02/26.86 (setukpairinjR1) =>
% 89.02/26.86 ((
% 89.02/26.86 (upairequniteq) =>
% 89.02/26.86 ((
% 89.02/26.86 (setukpairinjR2) =>
% 89.02/26.86 ((
% 89.02/26.86 (setukpairinjR) =>
% 89.02/26.86 ((
% 89.02/26.86 (ksndsingleton) =>
% 89.02/26.86 ((
% 89.02/26.86 (ksndpairEq) =>
% 89.02/26.86 ((
% 89.02/26.86 (kpairsurjEq) =>
% 89.02/26.86 ((
% 89.02/26.86 (cartprodsndin) =>
% 89.02/26.86 ((
% 89.02/26.86 (cartprodpairmemEL) =>
% 89.02/26.86 ((
% 89.02/26.86 (cartprodpairmemER) =>
% 89.02/26.86 ((
% 89.02/26.86 (cartprodmempaircEq) =>
% 89.02/26.86 ((
% 89.02/26.86 (cartprodfstpairEq) =>
% 89.02/26.86 ((
% 89.02/26.86 (cartprodsndpairEq) =>
% 89.02/26.86 ((
% 89.02/26.86 (cartprodpairsurjEq) =>
% 89.02/26.86 ((
% 89.02/26.86 (dpsetconstrI) =>
% 89.02/26.86 ((
% 89.02/26.86 (dpsetconstrSub) =>
% 89.02/26.86 ((
% 89.02/26.86 (setOfPairsIsBReln) =>
% 89.02/26.86 ((
% 89.02/26.86 (dpsetconstrERa) =>
% 89.02/26.86 ((
% 89.02/26.86 (dpsetconstrEL1) =>
% 89.02/26.86 ((
% 89.02/26.86 (dpsetconstrEL2) =>
% 89.02/26.86 ((
% 89.02/26.86 (dpsetconstrER) =>
% 89.02/26.86 ((
% 89.02/26.86 (funcImageSingleton) =>
% 89.02/26.86 ((
% 89.02/26.86 (apProp) =>
% 89.02/26.86 ((
% 89.02/26.86 (app) =>
% 89.02/26.86 ((
% 89.02/26.86 (infuncsetfunc) =>
% 89.02/26.86 ((
% 89.02/26.86 (ap2p) =>
% 89.02/26.86 ((
% 89.02/26.86 (funcinfuncset) =>
% 89.02/26.86 ((
% 89.02/26.86 (lamProp) =>
% 89.02/26.86 ((
% 89.02/26.86 (lamp) =>
% 89.02/26.86 ((
% 89.02/26.86 (lam2p) =>
% 89.02/26.86 ((
% 89.02/26.86 (brelnall1) =>
% 89.02/26.86 ((
% 89.02/26.86 (brelnall2) =>
% 89.02/26.86 ((
% 89.02/26.86 (!!) @ (
% 89.02/26.86 (('#B') @ (
% 89.02/26.86 !!) @
% 89.02/26.86 (
% 89.02/26.86 (
% 89.02/26.86 ('#S') @ (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 '#S') @
% 89.02/26.86 (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 =>))) @
% 89.02/26.86 ex1)))) @
% 89.02/26.86 (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 !!))) @
% 89.02/26.86 (
% 89.02/26.86 (
% 89.02/26.86 ('#S') @ (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 '#B') @
% 89.02/26.86 (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 '#S') @
% 89.02/26.86 (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 =>))) @
% 89.02/26.86 (
% 89.02/26.86 (
% 89.02/26.86 ('#C') @ in)))))))) @
% 89.02/26.86 (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 !!))))) @
% 89.02/26.86 (
% 89.02/26.86 (
% 89.02/26.86 ('#C') @ (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 '#B') @
% 89.02/26.86 (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 '#B') @
% 89.02/26.86 (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 '#S') @
% 89.02/26.86 (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 =>))) @
% 89.02/26.86 (
% 89.02/26.86 (
% 89.02/26.86 ('#C') @ in)))))))))) @
% 89.02/26.86 (
% 89.02/26.86 (
% 89.02/26.86 ('#S') @ (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 '#S') @
% 89.02/26.86 (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 '#B'))) @
% 89.02/26.86 (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 =>))))))) @
% 89.02/26.86 (
% 89.02/26.86 (
% 89.02/26.86 ('#C') @ (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 '#B') @
% 89.02/26.86 (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 '#S') @
% 89.02/26.86 (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 =>))))))) @
% 89.02/26.86 (
% 89.02/26.86 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.02/26.86 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl528])).
% 89.02/26.86 thf(zip_derived_cl546, plain,
% 89.02/26.86 (~ (((quantDeMorgan2) =>
% 89.02/26.86 (((quantDeMorgan3) =>
% 89.02/26.86 (((quantDeMorgan4) =>
% 89.02/26.86 (((prop2setI) =>
% 89.02/26.86 (((prop2set2propI) =>
% 89.02/26.86 (((notdexE) =>
% 89.02/26.86 (((notdallE) =>
% 89.02/26.86 (((exuI1) =>
% 89.02/26.86 (((exuI3) =>
% 89.02/26.86 (((exuI2) =>
% 89.02/26.86 (((inCongP) =>
% 89.02/26.86 (((in__Cong) =>
% 89.02/26.86 (((exuE3u) =>
% 89.02/26.86 (((exu__Cong) =>
% 89.02/26.86 (((setadjoin__Cong) =>
% 89.02/26.86 (((powerset__Cong) =>
% 89.02/26.86 (((setunion__Cong) =>
% 89.02/26.86 (((exuEu) =>
% 89.02/26.86 (((descr__Cong) =>
% 89.02/26.86 (((dsetconstr__Cong) =>
% 89.02/26.86 (((subsetI1) =>
% 89.02/26.86 (((eqimpsubset2) =>
% 89.02/26.86 (((eqimpsubset1) =>
% 89.02/26.86 (((subsetI2) =>
% 89.02/26.86 (((emptysetsubset) =>
% 89.02/26.86 (((subsetE) =>
% 89.02/26.86 (((subsetE2) =>
% 89.02/26.86 (((notsubsetI) =>
% 89.02/26.86 (((notequalI1) =>
% 89.02/26.86 (((notequalI2) =>
% 89.02/26.86 ((
% 89.02/26.86 (subsetRefl) =>
% 89.02/26.86 ((
% 89.02/26.86 (subsetTrans) =>
% 89.02/26.86 ((
% 89.02/26.86 (setadjoinSub) =>
% 89.02/26.86 ((
% 89.02/26.86 (setadjoinSub2) =>
% 89.02/26.86 ((
% 89.02/26.86 (subset2powerset) =>
% 89.02/26.86 ((
% 89.02/26.86 (setextsub) =>
% 89.02/26.86 ((
% 89.02/26.86 (subsetemptysetimpeq) =>
% 89.02/26.86 ((
% 89.02/26.86 (powersetI1) =>
% 89.02/26.86 ((
% 89.02/26.86 (powersetE1) =>
% 89.02/26.86 ((
% 89.02/26.86 (inPowerset) =>
% 89.02/26.86 ((
% 89.02/26.86 (powersetsubset) =>
% 89.02/26.86 ((
% 89.02/26.86 (sepInPowerset) =>
% 89.02/26.86 ((
% 89.02/26.86 (sepSubset) =>
% 89.02/26.86 ((
% 89.02/26.86 (binunionIL) =>
% 89.02/26.86 ((
% 89.02/26.86 (upairset2IR) =>
% 89.02/26.86 ((
% 89.02/26.86 (binunionIR) =>
% 89.02/26.86 ((
% 89.02/26.86 (binunionEcases) =>
% 89.02/26.86 ((
% 89.02/26.86 (binunionE) =>
% 89.02/26.86 ((
% 89.02/26.86 (binunionLsub) =>
% 89.02/26.86 ((
% 89.02/26.86 (binunionRsub) =>
% 89.02/26.86 ((
% 89.02/26.86 (binintersectI) =>
% 89.02/26.86 ((
% 89.02/26.86 (binintersectSubset5) =>
% 89.02/26.86 ((
% 89.02/26.86 (binintersectEL) =>
% 89.02/26.86 ((
% 89.02/26.86 (binintersectLsub) =>
% 89.02/26.86 ((
% 89.02/26.86 (binintersectSubset2) =>
% 89.02/26.86 ((
% 89.02/26.86 (binintersectSubset3) =>
% 89.02/26.86 ((
% 89.02/26.86 (binintersectER) =>
% 89.02/26.86 ((
% 89.02/26.86 (disjointsetsI1) =>
% 89.02/26.86 ((
% 89.02/26.86 (binintersectRsub) =>
% 89.02/26.86 ((
% 89.02/26.86 (binintersectSubset4) =>
% 89.02/26.86 ((
% 89.02/26.86 (binintersectSubset1) =>
% 89.02/26.86 ((
% 89.02/26.86 (bs114d) =>
% 89.02/26.86 ((
% 89.02/26.86 (setminusI) =>
% 89.02/26.86 ((
% 89.02/26.86 (setminusEL) =>
% 89.02/26.86 ((
% 89.02/26.86 (setminusER) =>
% 89.02/26.86 ((
% 89.02/26.86 (setminusSubset2) =>
% 89.02/26.86 ((
% 89.02/26.86 (setminusERneg) =>
% 89.02/26.86 ((
% 89.02/26.86 (setminusELneg) =>
% 89.02/26.86 ((
% 89.02/26.86 (setminusILneg) =>
% 89.02/26.86 ((
% 89.02/26.86 (setminusIRneg) =>
% 89.02/26.86 ((
% 89.02/26.86 (setminusLsub) =>
% 89.02/26.86 ((
% 89.02/26.86 (setminusSubset1) =>
% 89.02/26.86 ((
% 89.02/26.86 (symdiffE) =>
% 89.02/26.86 ((
% 89.02/26.86 (symdiffI1) =>
% 89.02/26.86 ((
% 89.02/26.86 (symdiffI2) =>
% 89.02/26.86 ((
% 89.02/26.86 (symdiffIneg1) =>
% 89.02/26.86 ((
% 89.02/26.86 (symdiffIneg2) =>
% 89.02/26.86 ((
% 89.02/26.86 (secondinupair) =>
% 89.02/26.86 ((
% 89.02/26.86 (setukpairIL) =>
% 89.02/26.86 ((
% 89.02/26.86 (setukpairIR) =>
% 89.02/26.86 ((
% 89.02/26.86 (kpairiskpair) =>
% 89.02/26.86 ((
% 89.02/26.86 (kpairp) =>
% 89.02/26.86 ((
% 89.02/26.86 (singletonsubset) =>
% 89.02/26.86 ((
% 89.02/26.86 (singletoninpowerset) =>
% 89.02/26.86 ((
% 89.02/26.86 (singletoninpowunion) =>
% 89.02/26.86 ((
% 89.02/26.86 (upairset2E) =>
% 89.02/26.86 ((
% 89.02/26.86 (upairsubunion) =>
% 89.02/26.86 ((
% 89.02/26.86 (upairinpowunion) =>
% 89.02/26.86 ((
% 89.02/26.86 (ubforcartprodlem1) =>
% 89.02/26.86 ((
% 89.02/26.86 (ubforcartprodlem2) =>
% 89.02/26.86 ((
% 89.02/26.86 (ubforcartprodlem3) =>
% 89.02/26.86 ((
% 89.02/26.86 (cartprodpairin) =>
% 89.02/26.86 ((
% 89.02/26.86 (cartprodmempair1) =>
% 89.02/26.86 ((
% 89.02/26.86 (cartprodmempair) =>
% 89.02/26.86 ((
% 89.02/26.86 (setunionE2) =>
% 89.02/26.86 ((
% 89.02/26.86 (setunionsingleton1) =>
% 89.02/26.86 ((
% 89.02/26.86 (setunionsingleton2) =>
% 89.02/26.86 ((
% 89.02/26.86 (setunionsingleton) =>
% 89.02/26.86 ((
% 89.02/26.86 (singletonprop) =>
% 89.02/26.86 ((
% 89.02/26.86 (ex1E1) =>
% 89.02/26.86 ((
% 89.02/26.86 (ex1I) =>
% 89.02/26.86 ((
% 89.02/26.86 (ex1I2) =>
% 89.02/26.86 ((
% 89.02/26.86 (singletonsuniq) =>
% 89.02/26.86 ((
% 89.02/26.86 (setukpairinjL1) =>
% 89.02/26.86 ((
% 89.02/26.86 (kfstsingleton) =>
% 89.02/26.86 ((
% 89.02/26.86 (theprop) =>
% 89.02/26.86 ((
% 89.02/26.86 (kfstpairEq) =>
% 89.02/26.86 ((
% 89.02/26.86 (cartprodfstin) =>
% 89.02/26.86 ((
% 89.02/26.86 (setukpairinjL2) =>
% 89.02/26.86 ((
% 89.02/26.86 (setukpairinjL) =>
% 89.02/26.86 ((
% 89.02/26.86 (setukpairinjR11) =>
% 89.02/26.86 ((
% 89.02/26.86 (setukpairinjR12) =>
% 89.02/26.86 ((
% 89.02/26.86 (setukpairinjR1) =>
% 89.02/26.86 ((
% 89.02/26.86 (upairequniteq) =>
% 89.02/26.86 ((
% 89.02/26.86 (setukpairinjR2) =>
% 89.02/26.86 ((
% 89.02/26.86 (setukpairinjR) =>
% 89.02/26.86 ((
% 89.02/26.86 (ksndsingleton) =>
% 89.02/26.86 ((
% 89.02/26.86 (ksndpairEq) =>
% 89.02/26.86 ((
% 89.02/26.86 (kpairsurjEq) =>
% 89.02/26.86 ((
% 89.02/26.86 (cartprodsndin) =>
% 89.02/26.86 ((
% 89.02/26.86 (cartprodpairmemEL) =>
% 89.02/26.86 ((
% 89.02/26.86 (cartprodpairmemER) =>
% 89.02/26.86 ((
% 89.02/26.86 (cartprodmempaircEq) =>
% 89.02/26.86 ((
% 89.02/26.86 (cartprodfstpairEq) =>
% 89.02/26.86 ((
% 89.02/26.86 (cartprodsndpairEq) =>
% 89.02/26.86 ((
% 89.02/26.86 (cartprodpairsurjEq) =>
% 89.02/26.86 ((
% 89.02/26.86 (dpsetconstrI) =>
% 89.02/26.86 ((
% 89.02/26.86 (dpsetconstrSub) =>
% 89.02/26.86 ((
% 89.02/26.86 (setOfPairsIsBReln) =>
% 89.02/26.86 ((
% 89.02/26.86 (dpsetconstrERa) =>
% 89.02/26.86 ((
% 89.02/26.86 (dpsetconstrEL1) =>
% 89.02/26.86 ((
% 89.02/26.86 (dpsetconstrEL2) =>
% 89.02/26.86 ((
% 89.02/26.86 (dpsetconstrER) =>
% 89.02/26.86 ((
% 89.02/26.86 (funcImageSingleton) =>
% 89.02/26.86 ((
% 89.02/26.86 (apProp) =>
% 89.02/26.86 ((
% 89.02/26.86 (app) =>
% 89.02/26.86 ((
% 89.02/26.86 (infuncsetfunc) =>
% 89.02/26.86 ((
% 89.02/26.86 (ap2p) =>
% 89.02/26.86 ((
% 89.02/26.86 (funcinfuncset) =>
% 89.02/26.86 ((
% 89.02/26.86 (lamProp) =>
% 89.02/26.86 ((
% 89.02/26.86 (lamp) =>
% 89.02/26.86 ((
% 89.02/26.86 (lam2p) =>
% 89.02/26.86 ((
% 89.02/26.86 (brelnall1) =>
% 89.02/26.86 ((
% 89.02/26.86 (brelnall2) =>
% 89.02/26.86 ((
% 89.02/26.86 (!!) @ (
% 89.02/26.86 (('#B') @ (
% 89.02/26.86 !!) @
% 89.02/26.86 (
% 89.02/26.86 (
% 89.02/26.86 ('#S') @ (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 '#S') @
% 89.02/26.86 (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 =>))) @
% 89.02/26.86 ex1)))) @
% 89.02/26.86 (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 !!))) @
% 89.02/26.86 (
% 89.02/26.86 (
% 89.02/26.86 ('#S') @ (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 '#B') @
% 89.02/26.86 (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 '#S') @
% 89.02/26.86 (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 =>))) @
% 89.02/26.86 (
% 89.02/26.86 (
% 89.02/26.86 ('#C') @ in)))))))) @
% 89.02/26.86 (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 !!))))) @
% 89.02/26.86 (
% 89.02/26.86 (
% 89.02/26.86 ('#C') @ (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 '#B') @
% 89.02/26.86 (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 '#B') @
% 89.02/26.86 (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 '#S') @
% 89.02/26.86 (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 =>))) @
% 89.02/26.86 (
% 89.02/26.86 (
% 89.02/26.86 ('#C') @ in)))))))))) @
% 89.02/26.86 (
% 89.02/26.86 (
% 89.02/26.86 ('#S') @ (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 '#S') @
% 89.02/26.86 (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 '#B'))) @
% 89.02/26.86 (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 =>))))))) @
% 89.02/26.86 (
% 89.02/26.86 (
% 89.02/26.86 ('#C') @ (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 '#B') @
% 89.02/26.86 (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 '#S') @
% 89.02/26.86 (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 =>))))))) @
% 89.02/26.86 (
% 89.02/26.86 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.02/26.86 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl537])).
% 89.02/26.86 thf(zip_derived_cl553, plain,
% 89.02/26.86 (~ (((quantDeMorgan3) =>
% 89.02/26.86 (((quantDeMorgan4) =>
% 89.02/26.86 (((prop2setI) =>
% 89.02/26.86 (((prop2set2propI) =>
% 89.02/26.86 (((notdexE) =>
% 89.02/26.86 (((notdallE) =>
% 89.02/26.86 (((exuI1) =>
% 89.02/26.86 (((exuI3) =>
% 89.02/26.86 (((exuI2) =>
% 89.02/26.86 (((inCongP) =>
% 89.02/26.86 (((in__Cong) =>
% 89.02/26.86 (((exuE3u) =>
% 89.02/26.86 (((exu__Cong) =>
% 89.02/26.86 (((setadjoin__Cong) =>
% 89.02/26.86 (((powerset__Cong) =>
% 89.02/26.86 (((setunion__Cong) =>
% 89.02/26.86 (((exuEu) =>
% 89.02/26.86 (((descr__Cong) =>
% 89.02/26.86 (((dsetconstr__Cong) =>
% 89.02/26.86 (((subsetI1) =>
% 89.02/26.86 (((eqimpsubset2) =>
% 89.02/26.86 (((eqimpsubset1) =>
% 89.02/26.86 (((subsetI2) =>
% 89.02/26.86 (((emptysetsubset) =>
% 89.02/26.86 (((subsetE) =>
% 89.02/26.86 (((subsetE2) =>
% 89.02/26.86 (((notsubsetI) =>
% 89.02/26.86 (((notequalI1) =>
% 89.02/26.86 (((notequalI2) =>
% 89.02/26.86 (((subsetRefl) =>
% 89.02/26.86 ((
% 89.02/26.86 (subsetTrans) =>
% 89.02/26.86 ((
% 89.02/26.86 (setadjoinSub) =>
% 89.02/26.86 ((
% 89.02/26.86 (setadjoinSub2) =>
% 89.02/26.86 ((
% 89.02/26.86 (subset2powerset) =>
% 89.02/26.86 ((
% 89.02/26.86 (setextsub) =>
% 89.02/26.86 ((
% 89.02/26.86 (subsetemptysetimpeq) =>
% 89.02/26.86 ((
% 89.02/26.86 (powersetI1) =>
% 89.02/26.86 ((
% 89.02/26.86 (powersetE1) =>
% 89.02/26.86 ((
% 89.02/26.86 (inPowerset) =>
% 89.02/26.86 ((
% 89.02/26.86 (powersetsubset) =>
% 89.02/26.86 ((
% 89.02/26.86 (sepInPowerset) =>
% 89.02/26.86 ((
% 89.02/26.86 (sepSubset) =>
% 89.02/26.86 ((
% 89.02/26.86 (binunionIL) =>
% 89.02/26.86 ((
% 89.02/26.86 (upairset2IR) =>
% 89.02/26.86 ((
% 89.02/26.86 (binunionIR) =>
% 89.02/26.86 ((
% 89.02/26.86 (binunionEcases) =>
% 89.02/26.86 ((
% 89.02/26.86 (binunionE) =>
% 89.02/26.86 ((
% 89.02/26.86 (binunionLsub) =>
% 89.02/26.86 ((
% 89.02/26.86 (binunionRsub) =>
% 89.02/26.86 ((
% 89.02/26.86 (binintersectI) =>
% 89.02/26.86 ((
% 89.02/26.86 (binintersectSubset5) =>
% 89.02/26.86 ((
% 89.02/26.86 (binintersectEL) =>
% 89.02/26.86 ((
% 89.02/26.86 (binintersectLsub) =>
% 89.02/26.86 ((
% 89.02/26.86 (binintersectSubset2) =>
% 89.02/26.86 ((
% 89.02/26.86 (binintersectSubset3) =>
% 89.02/26.86 ((
% 89.02/26.86 (binintersectER) =>
% 89.02/26.86 ((
% 89.02/26.86 (disjointsetsI1) =>
% 89.02/26.86 ((
% 89.02/26.86 (binintersectRsub) =>
% 89.02/26.86 ((
% 89.02/26.86 (binintersectSubset4) =>
% 89.02/26.86 ((
% 89.02/26.86 (binintersectSubset1) =>
% 89.02/26.86 ((
% 89.02/26.86 (bs114d) =>
% 89.02/26.86 ((
% 89.02/26.86 (setminusI) =>
% 89.02/26.86 ((
% 89.02/26.86 (setminusEL) =>
% 89.02/26.86 ((
% 89.02/26.86 (setminusER) =>
% 89.02/26.86 ((
% 89.02/26.86 (setminusSubset2) =>
% 89.02/26.86 ((
% 89.02/26.86 (setminusERneg) =>
% 89.02/26.86 ((
% 89.02/26.86 (setminusELneg) =>
% 89.02/26.86 ((
% 89.02/26.86 (setminusILneg) =>
% 89.02/26.86 ((
% 89.02/26.86 (setminusIRneg) =>
% 89.02/26.86 ((
% 89.02/26.86 (setminusLsub) =>
% 89.02/26.86 ((
% 89.02/26.86 (setminusSubset1) =>
% 89.02/26.86 ((
% 89.02/26.86 (symdiffE) =>
% 89.02/26.86 ((
% 89.02/26.86 (symdiffI1) =>
% 89.02/26.86 ((
% 89.02/26.86 (symdiffI2) =>
% 89.02/26.86 ((
% 89.02/26.86 (symdiffIneg1) =>
% 89.02/26.86 ((
% 89.02/26.86 (symdiffIneg2) =>
% 89.02/26.86 ((
% 89.02/26.86 (secondinupair) =>
% 89.02/26.86 ((
% 89.02/26.86 (setukpairIL) =>
% 89.02/26.86 ((
% 89.02/26.86 (setukpairIR) =>
% 89.02/26.86 ((
% 89.02/26.86 (kpairiskpair) =>
% 89.02/26.86 ((
% 89.02/26.86 (kpairp) =>
% 89.02/26.86 ((
% 89.02/26.86 (singletonsubset) =>
% 89.02/26.86 ((
% 89.02/26.86 (singletoninpowerset) =>
% 89.02/26.86 ((
% 89.02/26.86 (singletoninpowunion) =>
% 89.02/26.86 ((
% 89.02/26.86 (upairset2E) =>
% 89.02/26.86 ((
% 89.02/26.86 (upairsubunion) =>
% 89.02/26.86 ((
% 89.02/26.86 (upairinpowunion) =>
% 89.02/26.86 ((
% 89.02/26.86 (ubforcartprodlem1) =>
% 89.02/26.86 ((
% 89.02/26.86 (ubforcartprodlem2) =>
% 89.02/26.86 ((
% 89.02/26.86 (ubforcartprodlem3) =>
% 89.02/26.86 ((
% 89.02/26.86 (cartprodpairin) =>
% 89.02/26.86 ((
% 89.02/26.86 (cartprodmempair1) =>
% 89.02/26.86 ((
% 89.02/26.86 (cartprodmempair) =>
% 89.02/26.86 ((
% 89.02/26.86 (setunionE2) =>
% 89.02/26.86 ((
% 89.02/26.86 (setunionsingleton1) =>
% 89.02/26.86 ((
% 89.02/26.86 (setunionsingleton2) =>
% 89.02/26.86 ((
% 89.02/26.86 (setunionsingleton) =>
% 89.02/26.86 ((
% 89.02/26.86 (singletonprop) =>
% 89.02/26.86 ((
% 89.02/26.86 (ex1E1) =>
% 89.02/26.86 ((
% 89.02/26.86 (ex1I) =>
% 89.02/26.86 ((
% 89.02/26.86 (ex1I2) =>
% 89.02/26.86 ((
% 89.02/26.86 (singletonsuniq) =>
% 89.02/26.86 ((
% 89.02/26.86 (setukpairinjL1) =>
% 89.02/26.86 ((
% 89.02/26.86 (kfstsingleton) =>
% 89.02/26.86 ((
% 89.02/26.86 (theprop) =>
% 89.02/26.86 ((
% 89.02/26.86 (kfstpairEq) =>
% 89.02/26.86 ((
% 89.02/26.86 (cartprodfstin) =>
% 89.02/26.86 ((
% 89.02/26.86 (setukpairinjL2) =>
% 89.02/26.86 ((
% 89.02/26.86 (setukpairinjL) =>
% 89.02/26.86 ((
% 89.02/26.86 (setukpairinjR11) =>
% 89.02/26.86 ((
% 89.02/26.86 (setukpairinjR12) =>
% 89.02/26.86 ((
% 89.02/26.86 (setukpairinjR1) =>
% 89.02/26.86 ((
% 89.02/26.86 (upairequniteq) =>
% 89.02/26.86 ((
% 89.02/26.86 (setukpairinjR2) =>
% 89.02/26.86 ((
% 89.02/26.86 (setukpairinjR) =>
% 89.02/26.86 ((
% 89.02/26.86 (ksndsingleton) =>
% 89.02/26.86 ((
% 89.02/26.86 (ksndpairEq) =>
% 89.02/26.86 ((
% 89.02/26.86 (kpairsurjEq) =>
% 89.02/26.86 ((
% 89.02/26.86 (cartprodsndin) =>
% 89.02/26.86 ((
% 89.02/26.86 (cartprodpairmemEL) =>
% 89.02/26.86 ((
% 89.02/26.86 (cartprodpairmemER) =>
% 89.02/26.86 ((
% 89.02/26.86 (cartprodmempaircEq) =>
% 89.02/26.86 ((
% 89.02/26.86 (cartprodfstpairEq) =>
% 89.02/26.86 ((
% 89.02/26.86 (cartprodsndpairEq) =>
% 89.02/26.86 ((
% 89.02/26.86 (cartprodpairsurjEq) =>
% 89.02/26.86 ((
% 89.02/26.86 (dpsetconstrI) =>
% 89.02/26.86 ((
% 89.02/26.86 (dpsetconstrSub) =>
% 89.02/26.86 ((
% 89.02/26.86 (setOfPairsIsBReln) =>
% 89.02/26.86 ((
% 89.02/26.86 (dpsetconstrERa) =>
% 89.02/26.86 ((
% 89.02/26.86 (dpsetconstrEL1) =>
% 89.02/26.86 ((
% 89.02/26.86 (dpsetconstrEL2) =>
% 89.02/26.86 ((
% 89.02/26.86 (dpsetconstrER) =>
% 89.02/26.86 ((
% 89.02/26.86 (funcImageSingleton) =>
% 89.02/26.86 ((
% 89.02/26.86 (apProp) =>
% 89.02/26.86 ((
% 89.02/26.86 (app) =>
% 89.02/26.86 ((
% 89.02/26.86 (infuncsetfunc) =>
% 89.02/26.86 ((
% 89.02/26.86 (ap2p) =>
% 89.02/26.86 ((
% 89.02/26.86 (funcinfuncset) =>
% 89.02/26.86 ((
% 89.02/26.86 (lamProp) =>
% 89.02/26.86 ((
% 89.02/26.86 (lamp) =>
% 89.02/26.86 ((
% 89.02/26.86 (lam2p) =>
% 89.02/26.86 ((
% 89.02/26.86 (brelnall1) =>
% 89.02/26.86 ((
% 89.02/26.86 (brelnall2) =>
% 89.02/26.86 ((
% 89.02/26.86 (!!) @ (
% 89.02/26.86 (('#B') @ (
% 89.02/26.86 !!) @
% 89.02/26.86 (
% 89.02/26.86 (
% 89.02/26.86 ('#S') @ (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 '#S') @
% 89.02/26.86 (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 =>))) @
% 89.02/26.86 ex1)))) @
% 89.02/26.86 (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 !!))) @
% 89.02/26.86 (
% 89.02/26.86 (
% 89.02/26.86 ('#S') @ (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 '#B') @
% 89.02/26.86 (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 '#S') @
% 89.02/26.86 (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 =>))) @
% 89.02/26.86 (
% 89.02/26.86 (
% 89.02/26.86 ('#C') @ in)))))))) @
% 89.02/26.86 (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 !!))))) @
% 89.02/26.86 (
% 89.02/26.86 (
% 89.02/26.86 ('#C') @ (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 '#B') @
% 89.02/26.86 (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 '#B') @
% 89.02/26.86 (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 '#S') @
% 89.02/26.86 (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 =>))) @
% 89.02/26.86 (
% 89.02/26.86 (
% 89.02/26.86 ('#C') @ in)))))))))) @
% 89.02/26.86 (
% 89.02/26.86 (
% 89.02/26.86 ('#S') @ (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 '#S') @
% 89.02/26.86 (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 '#B'))) @
% 89.02/26.86 (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 =>))))))) @
% 89.02/26.86 (
% 89.02/26.86 (
% 89.02/26.86 ('#C') @ (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 '#B') @
% 89.02/26.86 (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 '#S') @
% 89.02/26.86 (
% 89.02/26.86 (
% 89.02/26.86 ('#B') @ (
% 89.02/26.86 =>))))))) @
% 89.02/26.86 (
% 89.02/26.86 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.02/26.86 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl546])).
% 89.02/26.86 thf(zip_derived_cl561, plain,
% 89.02/26.86 (~ (((quantDeMorgan4) =>
% 89.02/26.86 (((prop2setI) =>
% 89.02/26.86 (((prop2set2propI) =>
% 89.02/26.86 (((notdexE) =>
% 89.02/26.86 (((notdallE) =>
% 89.02/26.86 (((exuI1) =>
% 89.02/26.86 (((exuI3) =>
% 89.02/26.86 (((exuI2) =>
% 89.02/26.86 (((inCongP) =>
% 89.02/26.86 (((in__Cong) =>
% 89.02/26.86 (((exuE3u) =>
% 89.02/26.86 (((exu__Cong) =>
% 89.02/26.86 (((setadjoin__Cong) =>
% 89.02/26.86 (((powerset__Cong) =>
% 89.02/26.86 (((setunion__Cong) =>
% 89.02/26.86 (((exuEu) =>
% 89.02/26.86 (((descr__Cong) =>
% 89.02/26.86 (((dsetconstr__Cong) =>
% 89.02/26.86 (((subsetI1) =>
% 89.02/26.86 (((eqimpsubset2) =>
% 89.02/26.86 (((eqimpsubset1) =>
% 89.02/26.86 (((subsetI2) =>
% 89.02/26.86 (((emptysetsubset) =>
% 89.02/26.86 (((subsetE) =>
% 89.02/26.86 (((subsetE2) =>
% 89.02/26.86 (((notsubsetI) =>
% 89.02/26.86 (((notequalI1) =>
% 89.02/26.86 (((notequalI2) =>
% 89.02/26.86 (((subsetRefl) =>
% 89.02/26.86 (((subsetTrans) =>
% 89.02/26.86 ((
% 89.02/26.86 (setadjoinSub) =>
% 89.02/26.86 ((
% 89.02/26.86 (setadjoinSub2) =>
% 89.02/26.86 ((
% 89.02/26.86 (subset2powerset) =>
% 89.02/26.86 ((
% 89.02/26.86 (setextsub) =>
% 89.02/26.86 ((
% 89.02/26.86 (subsetemptysetimpeq) =>
% 89.02/26.86 ((
% 89.02/26.86 (powersetI1) =>
% 89.02/26.86 ((
% 89.02/26.86 (powersetE1) =>
% 89.02/26.86 ((
% 89.02/26.86 (inPowerset) =>
% 89.02/26.86 ((
% 89.02/26.86 (powersetsubset) =>
% 89.02/26.86 ((
% 89.02/26.86 (sepInPowerset) =>
% 89.02/26.86 ((
% 89.02/26.86 (sepSubset) =>
% 89.02/26.86 ((
% 89.02/26.86 (binunionIL) =>
% 89.02/26.86 ((
% 89.02/26.86 (upairset2IR) =>
% 89.02/26.86 ((
% 89.02/26.86 (binunionIR) =>
% 89.02/26.86 ((
% 89.02/26.86 (binunionEcases) =>
% 89.02/26.86 ((
% 89.02/26.86 (binunionE) =>
% 89.02/26.86 ((
% 89.02/26.86 (binunionLsub) =>
% 89.02/26.86 ((
% 89.02/26.86 (binunionRsub) =>
% 89.02/26.86 ((
% 89.02/26.86 (binintersectI) =>
% 89.02/26.86 ((
% 89.02/26.86 (binintersectSubset5) =>
% 89.02/26.86 ((
% 89.02/26.86 (binintersectEL) =>
% 89.02/26.86 ((
% 89.02/26.86 (binintersectLsub) =>
% 89.02/26.86 ((
% 89.02/26.86 (binintersectSubset2) =>
% 89.02/26.86 ((
% 89.02/26.86 (binintersectSubset3) =>
% 89.02/26.86 ((
% 89.02/26.86 (binintersectER) =>
% 89.02/26.86 ((
% 89.02/26.86 (disjointsetsI1) =>
% 89.02/26.86 ((
% 89.02/26.86 (binintersectRsub) =>
% 89.02/26.86 ((
% 89.02/26.86 (binintersectSubset4) =>
% 89.02/26.86 ((
% 89.02/26.86 (binintersectSubset1) =>
% 89.02/26.86 ((
% 89.02/26.86 (bs114d) =>
% 89.02/26.86 ((
% 89.02/26.86 (setminusI) =>
% 89.02/26.86 ((
% 89.02/26.86 (setminusEL) =>
% 89.02/26.86 ((
% 89.02/26.86 (setminusER) =>
% 89.02/26.86 ((
% 89.02/26.86 (setminusSubset2) =>
% 89.02/26.86 ((
% 89.02/26.86 (setminusERneg) =>
% 89.02/26.86 ((
% 89.02/26.86 (setminusELneg) =>
% 89.02/26.86 ((
% 89.02/26.86 (setminusILneg) =>
% 89.02/26.86 ((
% 89.02/26.86 (setminusIRneg) =>
% 89.02/26.86 ((
% 89.02/26.86 (setminusLsub) =>
% 89.02/26.86 ((
% 89.02/26.86 (setminusSubset1) =>
% 89.02/26.86 ((
% 89.02/26.86 (symdiffE) =>
% 89.02/26.86 ((
% 89.02/26.86 (symdiffI1) =>
% 89.02/26.86 ((
% 89.02/26.86 (symdiffI2) =>
% 89.02/26.86 ((
% 89.02/26.86 (symdiffIneg1) =>
% 89.02/26.86 ((
% 89.02/26.86 (symdiffIneg2) =>
% 89.02/26.86 ((
% 89.02/26.86 (secondinupair) =>
% 89.02/26.86 ((
% 89.02/26.86 (setukpairIL) =>
% 89.02/26.86 ((
% 89.02/26.86 (setukpairIR) =>
% 89.02/26.86 ((
% 89.02/26.86 (kpairiskpair) =>
% 89.02/26.86 ((
% 89.02/26.86 (kpairp) =>
% 89.02/26.86 ((
% 89.02/26.86 (singletonsubset) =>
% 89.02/26.86 ((
% 89.02/26.86 (singletoninpowerset) =>
% 89.02/26.86 ((
% 89.02/26.86 (singletoninpowunion) =>
% 89.02/26.86 ((
% 89.02/26.86 (upairset2E) =>
% 89.02/26.86 ((
% 89.02/26.86 (upairsubunion) =>
% 89.02/26.86 ((
% 89.02/26.86 (upairinpowunion) =>
% 89.02/26.86 ((
% 89.02/26.86 (ubforcartprodlem1) =>
% 89.02/26.86 ((
% 89.02/26.86 (ubforcartprodlem2) =>
% 89.02/26.86 ((
% 89.02/26.86 (ubforcartprodlem3) =>
% 89.02/26.86 ((
% 89.02/26.86 (cartprodpairin) =>
% 89.02/26.86 ((
% 89.02/26.86 (cartprodmempair1) =>
% 89.02/26.86 ((
% 89.02/26.86 (cartprodmempair) =>
% 89.02/26.86 ((
% 89.02/26.86 (setunionE2) =>
% 89.02/26.86 ((
% 89.02/26.86 (setunionsingleton1) =>
% 89.02/26.86 ((
% 89.02/26.86 (setunionsingleton2) =>
% 89.02/26.86 ((
% 89.02/26.86 (setunionsingleton) =>
% 89.02/26.86 ((
% 89.02/26.86 (singletonprop) =>
% 89.02/26.86 ((
% 89.02/26.86 (ex1E1) =>
% 89.02/26.86 ((
% 89.02/26.86 (ex1I) =>
% 89.02/26.86 ((
% 89.02/26.86 (ex1I2) =>
% 89.02/26.86 ((
% 89.02/26.86 (singletonsuniq) =>
% 89.02/26.86 ((
% 89.02/26.86 (setukpairinjL1) =>
% 89.02/26.86 ((
% 89.02/26.86 (kfstsingleton) =>
% 89.02/26.86 ((
% 89.02/26.86 (theprop) =>
% 89.02/26.86 ((
% 89.02/26.86 (kfstpairEq) =>
% 89.02/26.86 ((
% 89.02/26.86 (cartprodfstin) =>
% 89.02/26.86 ((
% 89.02/26.86 (setukpairinjL2) =>
% 89.02/26.86 ((
% 89.02/26.86 (setukpairinjL) =>
% 89.02/26.86 ((
% 89.02/26.86 (setukpairinjR11) =>
% 89.02/26.86 ((
% 89.02/26.86 (setukpairinjR12) =>
% 89.02/26.86 ((
% 89.02/26.86 (setukpairinjR1) =>
% 89.02/26.86 ((
% 89.02/26.86 (upairequniteq) =>
% 89.02/26.86 ((
% 89.02/26.86 (setukpairinjR2) =>
% 89.02/26.86 ((
% 89.02/26.86 (setukpairinjR) =>
% 89.02/26.86 ((
% 89.02/26.86 (ksndsingleton) =>
% 89.02/26.86 ((
% 89.02/26.86 (ksndpairEq) =>
% 89.02/26.86 ((
% 89.02/26.86 (kpairsurjEq) =>
% 89.02/26.86 ((
% 89.02/26.86 (cartprodsndin) =>
% 89.02/26.86 ((
% 89.02/26.86 (cartprodpairmemEL) =>
% 89.02/26.86 ((
% 89.02/26.86 (cartprodpairmemER) =>
% 89.02/26.86 ((
% 89.02/26.86 (cartprodmempaircEq) =>
% 89.02/26.86 ((
% 89.02/26.87 (cartprodfstpairEq) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodsndpairEq) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodpairsurjEq) =>
% 89.02/26.87 ((
% 89.02/26.87 (dpsetconstrI) =>
% 89.02/26.87 ((
% 89.02/26.87 (dpsetconstrSub) =>
% 89.02/26.87 ((
% 89.02/26.87 (setOfPairsIsBReln) =>
% 89.02/26.87 ((
% 89.02/26.87 (dpsetconstrERa) =>
% 89.02/26.87 ((
% 89.02/26.87 (dpsetconstrEL1) =>
% 89.02/26.87 ((
% 89.02/26.87 (dpsetconstrEL2) =>
% 89.02/26.87 ((
% 89.02/26.87 (dpsetconstrER) =>
% 89.02/26.87 ((
% 89.02/26.87 (funcImageSingleton) =>
% 89.02/26.87 ((
% 89.02/26.87 (apProp) =>
% 89.02/26.87 ((
% 89.02/26.87 (app) =>
% 89.02/26.87 ((
% 89.02/26.87 (infuncsetfunc) =>
% 89.02/26.87 ((
% 89.02/26.87 (ap2p) =>
% 89.02/26.87 ((
% 89.02/26.87 (funcinfuncset) =>
% 89.02/26.87 ((
% 89.02/26.87 (lamProp) =>
% 89.02/26.87 ((
% 89.02/26.87 (lamp) =>
% 89.02/26.87 ((
% 89.02/26.87 (lam2p) =>
% 89.02/26.87 ((
% 89.02/26.87 (brelnall1) =>
% 89.02/26.87 ((
% 89.02/26.87 (brelnall2) =>
% 89.02/26.87 ((
% 89.02/26.87 (!!) @ (
% 89.02/26.87 (('#B') @ (
% 89.02/26.87 !!) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#S') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#S') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 =>))) @
% 89.02/26.87 ex1)))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 !!))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#S') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#B') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#S') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 =>))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#C') @ in)))))))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 !!))))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#C') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#B') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#B') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#S') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 =>))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#C') @ in)))))))))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#S') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#S') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#B'))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 =>))))))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#C') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#B') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#S') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 =>))))))) @
% 89.02/26.87 (
% 89.02/26.87 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.02/26.87 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl553])).
% 89.02/26.87 thf(zip_derived_cl570, plain,
% 89.02/26.87 (~ (((prop2setI) =>
% 89.02/26.87 (((prop2set2propI) =>
% 89.02/26.87 (((notdexE) =>
% 89.02/26.87 (((notdallE) =>
% 89.02/26.87 (((exuI1) =>
% 89.02/26.87 (((exuI3) =>
% 89.02/26.87 (((exuI2) =>
% 89.02/26.87 (((inCongP) =>
% 89.02/26.87 (((in__Cong) =>
% 89.02/26.87 (((exuE3u) =>
% 89.02/26.87 (((exu__Cong) =>
% 89.02/26.87 (((setadjoin__Cong) =>
% 89.02/26.87 (((powerset__Cong) =>
% 89.02/26.87 (((setunion__Cong) =>
% 89.02/26.87 (((exuEu) =>
% 89.02/26.87 (((descr__Cong) =>
% 89.02/26.87 (((dsetconstr__Cong) =>
% 89.02/26.87 (((subsetI1) =>
% 89.02/26.87 (((eqimpsubset2) =>
% 89.02/26.87 (((eqimpsubset1) =>
% 89.02/26.87 (((subsetI2) =>
% 89.02/26.87 (((emptysetsubset) =>
% 89.02/26.87 (((subsetE) =>
% 89.02/26.87 (((subsetE2) =>
% 89.02/26.87 (((notsubsetI) =>
% 89.02/26.87 (((notequalI1) =>
% 89.02/26.87 (((notequalI2) =>
% 89.02/26.87 (((subsetRefl) =>
% 89.02/26.87 (((subsetTrans) =>
% 89.02/26.87 (((setadjoinSub) =>
% 89.02/26.87 ((
% 89.02/26.87 (setadjoinSub2) =>
% 89.02/26.87 ((
% 89.02/26.87 (subset2powerset) =>
% 89.02/26.87 ((
% 89.02/26.87 (setextsub) =>
% 89.02/26.87 ((
% 89.02/26.87 (subsetemptysetimpeq) =>
% 89.02/26.87 ((
% 89.02/26.87 (powersetI1) =>
% 89.02/26.87 ((
% 89.02/26.87 (powersetE1) =>
% 89.02/26.87 ((
% 89.02/26.87 (inPowerset) =>
% 89.02/26.87 ((
% 89.02/26.87 (powersetsubset) =>
% 89.02/26.87 ((
% 89.02/26.87 (sepInPowerset) =>
% 89.02/26.87 ((
% 89.02/26.87 (sepSubset) =>
% 89.02/26.87 ((
% 89.02/26.87 (binunionIL) =>
% 89.02/26.87 ((
% 89.02/26.87 (upairset2IR) =>
% 89.02/26.87 ((
% 89.02/26.87 (binunionIR) =>
% 89.02/26.87 ((
% 89.02/26.87 (binunionEcases) =>
% 89.02/26.87 ((
% 89.02/26.87 (binunionE) =>
% 89.02/26.87 ((
% 89.02/26.87 (binunionLsub) =>
% 89.02/26.87 ((
% 89.02/26.87 (binunionRsub) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectI) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectSubset5) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectEL) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectLsub) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectSubset2) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectSubset3) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectER) =>
% 89.02/26.87 ((
% 89.02/26.87 (disjointsetsI1) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectRsub) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectSubset4) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectSubset1) =>
% 89.02/26.87 ((
% 89.02/26.87 (bs114d) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusI) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusEL) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusER) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusSubset2) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusERneg) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusELneg) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusILneg) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusIRneg) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusLsub) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusSubset1) =>
% 89.02/26.87 ((
% 89.02/26.87 (symdiffE) =>
% 89.02/26.87 ((
% 89.02/26.87 (symdiffI1) =>
% 89.02/26.87 ((
% 89.02/26.87 (symdiffI2) =>
% 89.02/26.87 ((
% 89.02/26.87 (symdiffIneg1) =>
% 89.02/26.87 ((
% 89.02/26.87 (symdiffIneg2) =>
% 89.02/26.87 ((
% 89.02/26.87 (secondinupair) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairIL) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairIR) =>
% 89.02/26.87 ((
% 89.02/26.87 (kpairiskpair) =>
% 89.02/26.87 ((
% 89.02/26.87 (kpairp) =>
% 89.02/26.87 ((
% 89.02/26.87 (singletonsubset) =>
% 89.02/26.87 ((
% 89.02/26.87 (singletoninpowerset) =>
% 89.02/26.87 ((
% 89.02/26.87 (singletoninpowunion) =>
% 89.02/26.87 ((
% 89.02/26.87 (upairset2E) =>
% 89.02/26.87 ((
% 89.02/26.87 (upairsubunion) =>
% 89.02/26.87 ((
% 89.02/26.87 (upairinpowunion) =>
% 89.02/26.87 ((
% 89.02/26.87 (ubforcartprodlem1) =>
% 89.02/26.87 ((
% 89.02/26.87 (ubforcartprodlem2) =>
% 89.02/26.87 ((
% 89.02/26.87 (ubforcartprodlem3) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodpairin) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodmempair1) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodmempair) =>
% 89.02/26.87 ((
% 89.02/26.87 (setunionE2) =>
% 89.02/26.87 ((
% 89.02/26.87 (setunionsingleton1) =>
% 89.02/26.87 ((
% 89.02/26.87 (setunionsingleton2) =>
% 89.02/26.87 ((
% 89.02/26.87 (setunionsingleton) =>
% 89.02/26.87 ((
% 89.02/26.87 (singletonprop) =>
% 89.02/26.87 ((
% 89.02/26.87 (ex1E1) =>
% 89.02/26.87 ((
% 89.02/26.87 (ex1I) =>
% 89.02/26.87 ((
% 89.02/26.87 (ex1I2) =>
% 89.02/26.87 ((
% 89.02/26.87 (singletonsuniq) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjL1) =>
% 89.02/26.87 ((
% 89.02/26.87 (kfstsingleton) =>
% 89.02/26.87 ((
% 89.02/26.87 (theprop) =>
% 89.02/26.87 ((
% 89.02/26.87 (kfstpairEq) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodfstin) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjL2) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjL) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjR11) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjR12) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjR1) =>
% 89.02/26.87 ((
% 89.02/26.87 (upairequniteq) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjR2) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjR) =>
% 89.02/26.87 ((
% 89.02/26.87 (ksndsingleton) =>
% 89.02/26.87 ((
% 89.02/26.87 (ksndpairEq) =>
% 89.02/26.87 ((
% 89.02/26.87 (kpairsurjEq) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodsndin) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodpairmemEL) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodpairmemER) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodmempaircEq) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodfstpairEq) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodsndpairEq) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodpairsurjEq) =>
% 89.02/26.87 ((
% 89.02/26.87 (dpsetconstrI) =>
% 89.02/26.87 ((
% 89.02/26.87 (dpsetconstrSub) =>
% 89.02/26.87 ((
% 89.02/26.87 (setOfPairsIsBReln) =>
% 89.02/26.87 ((
% 89.02/26.87 (dpsetconstrERa) =>
% 89.02/26.87 ((
% 89.02/26.87 (dpsetconstrEL1) =>
% 89.02/26.87 ((
% 89.02/26.87 (dpsetconstrEL2) =>
% 89.02/26.87 ((
% 89.02/26.87 (dpsetconstrER) =>
% 89.02/26.87 ((
% 89.02/26.87 (funcImageSingleton) =>
% 89.02/26.87 ((
% 89.02/26.87 (apProp) =>
% 89.02/26.87 ((
% 89.02/26.87 (app) =>
% 89.02/26.87 ((
% 89.02/26.87 (infuncsetfunc) =>
% 89.02/26.87 ((
% 89.02/26.87 (ap2p) =>
% 89.02/26.87 ((
% 89.02/26.87 (funcinfuncset) =>
% 89.02/26.87 ((
% 89.02/26.87 (lamProp) =>
% 89.02/26.87 ((
% 89.02/26.87 (lamp) =>
% 89.02/26.87 ((
% 89.02/26.87 (lam2p) =>
% 89.02/26.87 ((
% 89.02/26.87 (brelnall1) =>
% 89.02/26.87 ((
% 89.02/26.87 (brelnall2) =>
% 89.02/26.87 ((
% 89.02/26.87 (!!) @ (
% 89.02/26.87 (('#B') @ (
% 89.02/26.87 !!) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#S') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#S') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 =>))) @
% 89.02/26.87 ex1)))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 !!))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#S') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#B') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#S') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 =>))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#C') @ in)))))))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 !!))))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#C') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#B') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#B') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#S') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 =>))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#C') @ in)))))))))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#S') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#S') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#B'))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 =>))))))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#C') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#B') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#S') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 =>))))))) @
% 89.02/26.87 (
% 89.02/26.87 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.02/26.87 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl561])).
% 89.02/26.87 thf(zip_derived_cl578, plain,
% 89.02/26.87 (~ (((prop2set2propI) =>
% 89.02/26.87 (((notdexE) =>
% 89.02/26.87 (((notdallE) =>
% 89.02/26.87 (((exuI1) =>
% 89.02/26.87 (((exuI3) =>
% 89.02/26.87 (((exuI2) =>
% 89.02/26.87 (((inCongP) =>
% 89.02/26.87 (((in__Cong) =>
% 89.02/26.87 (((exuE3u) =>
% 89.02/26.87 (((exu__Cong) =>
% 89.02/26.87 (((setadjoin__Cong) =>
% 89.02/26.87 (((powerset__Cong) =>
% 89.02/26.87 (((setunion__Cong) =>
% 89.02/26.87 (((exuEu) =>
% 89.02/26.87 (((descr__Cong) =>
% 89.02/26.87 (((dsetconstr__Cong) =>
% 89.02/26.87 (((subsetI1) =>
% 89.02/26.87 (((eqimpsubset2) =>
% 89.02/26.87 (((eqimpsubset1) =>
% 89.02/26.87 (((subsetI2) =>
% 89.02/26.87 (((emptysetsubset) =>
% 89.02/26.87 (((subsetE) =>
% 89.02/26.87 (((subsetE2) =>
% 89.02/26.87 (((notsubsetI) =>
% 89.02/26.87 (((notequalI1) =>
% 89.02/26.87 (((notequalI2) =>
% 89.02/26.87 (((subsetRefl) =>
% 89.02/26.87 (((subsetTrans) =>
% 89.02/26.87 (((setadjoinSub) =>
% 89.02/26.87 (((setadjoinSub2) =>
% 89.02/26.87 ((
% 89.02/26.87 (subset2powerset) =>
% 89.02/26.87 ((
% 89.02/26.87 (setextsub) =>
% 89.02/26.87 ((
% 89.02/26.87 (subsetemptysetimpeq) =>
% 89.02/26.87 ((
% 89.02/26.87 (powersetI1) =>
% 89.02/26.87 ((
% 89.02/26.87 (powersetE1) =>
% 89.02/26.87 ((
% 89.02/26.87 (inPowerset) =>
% 89.02/26.87 ((
% 89.02/26.87 (powersetsubset) =>
% 89.02/26.87 ((
% 89.02/26.87 (sepInPowerset) =>
% 89.02/26.87 ((
% 89.02/26.87 (sepSubset) =>
% 89.02/26.87 ((
% 89.02/26.87 (binunionIL) =>
% 89.02/26.87 ((
% 89.02/26.87 (upairset2IR) =>
% 89.02/26.87 ((
% 89.02/26.87 (binunionIR) =>
% 89.02/26.87 ((
% 89.02/26.87 (binunionEcases) =>
% 89.02/26.87 ((
% 89.02/26.87 (binunionE) =>
% 89.02/26.87 ((
% 89.02/26.87 (binunionLsub) =>
% 89.02/26.87 ((
% 89.02/26.87 (binunionRsub) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectI) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectSubset5) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectEL) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectLsub) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectSubset2) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectSubset3) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectER) =>
% 89.02/26.87 ((
% 89.02/26.87 (disjointsetsI1) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectRsub) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectSubset4) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectSubset1) =>
% 89.02/26.87 ((
% 89.02/26.87 (bs114d) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusI) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusEL) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusER) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusSubset2) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusERneg) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusELneg) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusILneg) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusIRneg) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusLsub) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusSubset1) =>
% 89.02/26.87 ((
% 89.02/26.87 (symdiffE) =>
% 89.02/26.87 ((
% 89.02/26.87 (symdiffI1) =>
% 89.02/26.87 ((
% 89.02/26.87 (symdiffI2) =>
% 89.02/26.87 ((
% 89.02/26.87 (symdiffIneg1) =>
% 89.02/26.87 ((
% 89.02/26.87 (symdiffIneg2) =>
% 89.02/26.87 ((
% 89.02/26.87 (secondinupair) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairIL) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairIR) =>
% 89.02/26.87 ((
% 89.02/26.87 (kpairiskpair) =>
% 89.02/26.87 ((
% 89.02/26.87 (kpairp) =>
% 89.02/26.87 ((
% 89.02/26.87 (singletonsubset) =>
% 89.02/26.87 ((
% 89.02/26.87 (singletoninpowerset) =>
% 89.02/26.87 ((
% 89.02/26.87 (singletoninpowunion) =>
% 89.02/26.87 ((
% 89.02/26.87 (upairset2E) =>
% 89.02/26.87 ((
% 89.02/26.87 (upairsubunion) =>
% 89.02/26.87 ((
% 89.02/26.87 (upairinpowunion) =>
% 89.02/26.87 ((
% 89.02/26.87 (ubforcartprodlem1) =>
% 89.02/26.87 ((
% 89.02/26.87 (ubforcartprodlem2) =>
% 89.02/26.87 ((
% 89.02/26.87 (ubforcartprodlem3) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodpairin) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodmempair1) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodmempair) =>
% 89.02/26.87 ((
% 89.02/26.87 (setunionE2) =>
% 89.02/26.87 ((
% 89.02/26.87 (setunionsingleton1) =>
% 89.02/26.87 ((
% 89.02/26.87 (setunionsingleton2) =>
% 89.02/26.87 ((
% 89.02/26.87 (setunionsingleton) =>
% 89.02/26.87 ((
% 89.02/26.87 (singletonprop) =>
% 89.02/26.87 ((
% 89.02/26.87 (ex1E1) =>
% 89.02/26.87 ((
% 89.02/26.87 (ex1I) =>
% 89.02/26.87 ((
% 89.02/26.87 (ex1I2) =>
% 89.02/26.87 ((
% 89.02/26.87 (singletonsuniq) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjL1) =>
% 89.02/26.87 ((
% 89.02/26.87 (kfstsingleton) =>
% 89.02/26.87 ((
% 89.02/26.87 (theprop) =>
% 89.02/26.87 ((
% 89.02/26.87 (kfstpairEq) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodfstin) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjL2) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjL) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjR11) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjR12) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjR1) =>
% 89.02/26.87 ((
% 89.02/26.87 (upairequniteq) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjR2) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjR) =>
% 89.02/26.87 ((
% 89.02/26.87 (ksndsingleton) =>
% 89.02/26.87 ((
% 89.02/26.87 (ksndpairEq) =>
% 89.02/26.87 ((
% 89.02/26.87 (kpairsurjEq) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodsndin) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodpairmemEL) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodpairmemER) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodmempaircEq) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodfstpairEq) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodsndpairEq) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodpairsurjEq) =>
% 89.02/26.87 ((
% 89.02/26.87 (dpsetconstrI) =>
% 89.02/26.87 ((
% 89.02/26.87 (dpsetconstrSub) =>
% 89.02/26.87 ((
% 89.02/26.87 (setOfPairsIsBReln) =>
% 89.02/26.87 ((
% 89.02/26.87 (dpsetconstrERa) =>
% 89.02/26.87 ((
% 89.02/26.87 (dpsetconstrEL1) =>
% 89.02/26.87 ((
% 89.02/26.87 (dpsetconstrEL2) =>
% 89.02/26.87 ((
% 89.02/26.87 (dpsetconstrER) =>
% 89.02/26.87 ((
% 89.02/26.87 (funcImageSingleton) =>
% 89.02/26.87 ((
% 89.02/26.87 (apProp) =>
% 89.02/26.87 ((
% 89.02/26.87 (app) =>
% 89.02/26.87 ((
% 89.02/26.87 (infuncsetfunc) =>
% 89.02/26.87 ((
% 89.02/26.87 (ap2p) =>
% 89.02/26.87 ((
% 89.02/26.87 (funcinfuncset) =>
% 89.02/26.87 ((
% 89.02/26.87 (lamProp) =>
% 89.02/26.87 ((
% 89.02/26.87 (lamp) =>
% 89.02/26.87 ((
% 89.02/26.87 (lam2p) =>
% 89.02/26.87 ((
% 89.02/26.87 (brelnall1) =>
% 89.02/26.87 ((
% 89.02/26.87 (brelnall2) =>
% 89.02/26.87 ((
% 89.02/26.87 (!!) @ (
% 89.02/26.87 (('#B') @ (
% 89.02/26.87 !!) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#S') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#S') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 =>))) @
% 89.02/26.87 ex1)))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 !!))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#S') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#B') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#S') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 =>))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#C') @ in)))))))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 !!))))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#C') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#B') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#B') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#S') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 =>))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#C') @ in)))))))))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#S') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#S') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#B'))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 =>))))))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#C') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#B') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#S') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 =>))))))) @
% 89.02/26.87 (
% 89.02/26.87 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.02/26.87 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl570])).
% 89.02/26.87 thf(zip_derived_cl586, plain,
% 89.02/26.87 (~ (((notdexE) =>
% 89.02/26.87 (((notdallE) =>
% 89.02/26.87 (((exuI1) =>
% 89.02/26.87 (((exuI3) =>
% 89.02/26.87 (((exuI2) =>
% 89.02/26.87 (((inCongP) =>
% 89.02/26.87 (((in__Cong) =>
% 89.02/26.87 (((exuE3u) =>
% 89.02/26.87 (((exu__Cong) =>
% 89.02/26.87 (((setadjoin__Cong) =>
% 89.02/26.87 (((powerset__Cong) =>
% 89.02/26.87 (((setunion__Cong) =>
% 89.02/26.87 (((exuEu) =>
% 89.02/26.87 (((descr__Cong) =>
% 89.02/26.87 (((dsetconstr__Cong) =>
% 89.02/26.87 (((subsetI1) =>
% 89.02/26.87 (((eqimpsubset2) =>
% 89.02/26.87 (((eqimpsubset1) =>
% 89.02/26.87 (((subsetI2) =>
% 89.02/26.87 (((emptysetsubset) =>
% 89.02/26.87 (((subsetE) =>
% 89.02/26.87 (((subsetE2) =>
% 89.02/26.87 (((notsubsetI) =>
% 89.02/26.87 (((notequalI1) =>
% 89.02/26.87 (((notequalI2) =>
% 89.02/26.87 (((subsetRefl) =>
% 89.02/26.87 (((subsetTrans) =>
% 89.02/26.87 (((setadjoinSub) =>
% 89.02/26.87 (((setadjoinSub2) =>
% 89.02/26.87 (((subset2powerset) =>
% 89.02/26.87 ((
% 89.02/26.87 (setextsub) =>
% 89.02/26.87 ((
% 89.02/26.87 (subsetemptysetimpeq) =>
% 89.02/26.87 ((
% 89.02/26.87 (powersetI1) =>
% 89.02/26.87 ((
% 89.02/26.87 (powersetE1) =>
% 89.02/26.87 ((
% 89.02/26.87 (inPowerset) =>
% 89.02/26.87 ((
% 89.02/26.87 (powersetsubset) =>
% 89.02/26.87 ((
% 89.02/26.87 (sepInPowerset) =>
% 89.02/26.87 ((
% 89.02/26.87 (sepSubset) =>
% 89.02/26.87 ((
% 89.02/26.87 (binunionIL) =>
% 89.02/26.87 ((
% 89.02/26.87 (upairset2IR) =>
% 89.02/26.87 ((
% 89.02/26.87 (binunionIR) =>
% 89.02/26.87 ((
% 89.02/26.87 (binunionEcases) =>
% 89.02/26.87 ((
% 89.02/26.87 (binunionE) =>
% 89.02/26.87 ((
% 89.02/26.87 (binunionLsub) =>
% 89.02/26.87 ((
% 89.02/26.87 (binunionRsub) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectI) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectSubset5) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectEL) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectLsub) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectSubset2) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectSubset3) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectER) =>
% 89.02/26.87 ((
% 89.02/26.87 (disjointsetsI1) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectRsub) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectSubset4) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectSubset1) =>
% 89.02/26.87 ((
% 89.02/26.87 (bs114d) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusI) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusEL) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusER) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusSubset2) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusERneg) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusELneg) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusILneg) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusIRneg) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusLsub) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusSubset1) =>
% 89.02/26.87 ((
% 89.02/26.87 (symdiffE) =>
% 89.02/26.87 ((
% 89.02/26.87 (symdiffI1) =>
% 89.02/26.87 ((
% 89.02/26.87 (symdiffI2) =>
% 89.02/26.87 ((
% 89.02/26.87 (symdiffIneg1) =>
% 89.02/26.87 ((
% 89.02/26.87 (symdiffIneg2) =>
% 89.02/26.87 ((
% 89.02/26.87 (secondinupair) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairIL) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairIR) =>
% 89.02/26.87 ((
% 89.02/26.87 (kpairiskpair) =>
% 89.02/26.87 ((
% 89.02/26.87 (kpairp) =>
% 89.02/26.87 ((
% 89.02/26.87 (singletonsubset) =>
% 89.02/26.87 ((
% 89.02/26.87 (singletoninpowerset) =>
% 89.02/26.87 ((
% 89.02/26.87 (singletoninpowunion) =>
% 89.02/26.87 ((
% 89.02/26.87 (upairset2E) =>
% 89.02/26.87 ((
% 89.02/26.87 (upairsubunion) =>
% 89.02/26.87 ((
% 89.02/26.87 (upairinpowunion) =>
% 89.02/26.87 ((
% 89.02/26.87 (ubforcartprodlem1) =>
% 89.02/26.87 ((
% 89.02/26.87 (ubforcartprodlem2) =>
% 89.02/26.87 ((
% 89.02/26.87 (ubforcartprodlem3) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodpairin) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodmempair1) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodmempair) =>
% 89.02/26.87 ((
% 89.02/26.87 (setunionE2) =>
% 89.02/26.87 ((
% 89.02/26.87 (setunionsingleton1) =>
% 89.02/26.87 ((
% 89.02/26.87 (setunionsingleton2) =>
% 89.02/26.87 ((
% 89.02/26.87 (setunionsingleton) =>
% 89.02/26.87 ((
% 89.02/26.87 (singletonprop) =>
% 89.02/26.87 ((
% 89.02/26.87 (ex1E1) =>
% 89.02/26.87 ((
% 89.02/26.87 (ex1I) =>
% 89.02/26.87 ((
% 89.02/26.87 (ex1I2) =>
% 89.02/26.87 ((
% 89.02/26.87 (singletonsuniq) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjL1) =>
% 89.02/26.87 ((
% 89.02/26.87 (kfstsingleton) =>
% 89.02/26.87 ((
% 89.02/26.87 (theprop) =>
% 89.02/26.87 ((
% 89.02/26.87 (kfstpairEq) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodfstin) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjL2) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjL) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjR11) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjR12) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjR1) =>
% 89.02/26.87 ((
% 89.02/26.87 (upairequniteq) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjR2) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjR) =>
% 89.02/26.87 ((
% 89.02/26.87 (ksndsingleton) =>
% 89.02/26.87 ((
% 89.02/26.87 (ksndpairEq) =>
% 89.02/26.87 ((
% 89.02/26.87 (kpairsurjEq) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodsndin) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodpairmemEL) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodpairmemER) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodmempaircEq) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodfstpairEq) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodsndpairEq) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodpairsurjEq) =>
% 89.02/26.87 ((
% 89.02/26.87 (dpsetconstrI) =>
% 89.02/26.87 ((
% 89.02/26.87 (dpsetconstrSub) =>
% 89.02/26.87 ((
% 89.02/26.87 (setOfPairsIsBReln) =>
% 89.02/26.87 ((
% 89.02/26.87 (dpsetconstrERa) =>
% 89.02/26.87 ((
% 89.02/26.87 (dpsetconstrEL1) =>
% 89.02/26.87 ((
% 89.02/26.87 (dpsetconstrEL2) =>
% 89.02/26.87 ((
% 89.02/26.87 (dpsetconstrER) =>
% 89.02/26.87 ((
% 89.02/26.87 (funcImageSingleton) =>
% 89.02/26.87 ((
% 89.02/26.87 (apProp) =>
% 89.02/26.87 ((
% 89.02/26.87 (app) =>
% 89.02/26.87 ((
% 89.02/26.87 (infuncsetfunc) =>
% 89.02/26.87 ((
% 89.02/26.87 (ap2p) =>
% 89.02/26.87 ((
% 89.02/26.87 (funcinfuncset) =>
% 89.02/26.87 ((
% 89.02/26.87 (lamProp) =>
% 89.02/26.87 ((
% 89.02/26.87 (lamp) =>
% 89.02/26.87 ((
% 89.02/26.87 (lam2p) =>
% 89.02/26.87 ((
% 89.02/26.87 (brelnall1) =>
% 89.02/26.87 ((
% 89.02/26.87 (brelnall2) =>
% 89.02/26.87 ((
% 89.02/26.87 (!!) @ (
% 89.02/26.87 (('#B') @ (
% 89.02/26.87 !!) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#S') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#S') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 =>))) @
% 89.02/26.87 ex1)))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 !!))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#S') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#B') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#S') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 =>))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#C') @ in)))))))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 !!))))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#C') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#B') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#B') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#S') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 =>))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#C') @ in)))))))))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#S') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#S') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#B'))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 =>))))))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#C') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#B') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#S') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 =>))))))) @
% 89.02/26.87 (
% 89.02/26.87 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.02/26.87 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl578])).
% 89.02/26.87 thf(zip_derived_cl595, plain,
% 89.02/26.87 (~ (((notdallE) =>
% 89.02/26.87 (((exuI1) =>
% 89.02/26.87 (((exuI3) =>
% 89.02/26.87 (((exuI2) =>
% 89.02/26.87 (((inCongP) =>
% 89.02/26.87 (((in__Cong) =>
% 89.02/26.87 (((exuE3u) =>
% 89.02/26.87 (((exu__Cong) =>
% 89.02/26.87 (((setadjoin__Cong) =>
% 89.02/26.87 (((powerset__Cong) =>
% 89.02/26.87 (((setunion__Cong) =>
% 89.02/26.87 (((exuEu) =>
% 89.02/26.87 (((descr__Cong) =>
% 89.02/26.87 (((dsetconstr__Cong) =>
% 89.02/26.87 (((subsetI1) =>
% 89.02/26.87 (((eqimpsubset2) =>
% 89.02/26.87 (((eqimpsubset1) =>
% 89.02/26.87 (((subsetI2) =>
% 89.02/26.87 (((emptysetsubset) =>
% 89.02/26.87 (((subsetE) =>
% 89.02/26.87 (((subsetE2) =>
% 89.02/26.87 (((notsubsetI) =>
% 89.02/26.87 (((notequalI1) =>
% 89.02/26.87 (((notequalI2) =>
% 89.02/26.87 (((subsetRefl) =>
% 89.02/26.87 (((subsetTrans) =>
% 89.02/26.87 (((setadjoinSub) =>
% 89.02/26.87 (((setadjoinSub2) =>
% 89.02/26.87 (((subset2powerset) =>
% 89.02/26.87 (((setextsub) =>
% 89.02/26.87 ((
% 89.02/26.87 (subsetemptysetimpeq) =>
% 89.02/26.87 ((
% 89.02/26.87 (powersetI1) =>
% 89.02/26.87 ((
% 89.02/26.87 (powersetE1) =>
% 89.02/26.87 ((
% 89.02/26.87 (inPowerset) =>
% 89.02/26.87 ((
% 89.02/26.87 (powersetsubset) =>
% 89.02/26.87 ((
% 89.02/26.87 (sepInPowerset) =>
% 89.02/26.87 ((
% 89.02/26.87 (sepSubset) =>
% 89.02/26.87 ((
% 89.02/26.87 (binunionIL) =>
% 89.02/26.87 ((
% 89.02/26.87 (upairset2IR) =>
% 89.02/26.87 ((
% 89.02/26.87 (binunionIR) =>
% 89.02/26.87 ((
% 89.02/26.87 (binunionEcases) =>
% 89.02/26.87 ((
% 89.02/26.87 (binunionE) =>
% 89.02/26.87 ((
% 89.02/26.87 (binunionLsub) =>
% 89.02/26.87 ((
% 89.02/26.87 (binunionRsub) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectI) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectSubset5) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectEL) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectLsub) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectSubset2) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectSubset3) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectER) =>
% 89.02/26.87 ((
% 89.02/26.87 (disjointsetsI1) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectRsub) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectSubset4) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectSubset1) =>
% 89.02/26.87 ((
% 89.02/26.87 (bs114d) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusI) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusEL) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusER) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusSubset2) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusERneg) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusELneg) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusILneg) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusIRneg) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusLsub) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusSubset1) =>
% 89.02/26.87 ((
% 89.02/26.87 (symdiffE) =>
% 89.02/26.87 ((
% 89.02/26.87 (symdiffI1) =>
% 89.02/26.87 ((
% 89.02/26.87 (symdiffI2) =>
% 89.02/26.87 ((
% 89.02/26.87 (symdiffIneg1) =>
% 89.02/26.87 ((
% 89.02/26.87 (symdiffIneg2) =>
% 89.02/26.87 ((
% 89.02/26.87 (secondinupair) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairIL) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairIR) =>
% 89.02/26.87 ((
% 89.02/26.87 (kpairiskpair) =>
% 89.02/26.87 ((
% 89.02/26.87 (kpairp) =>
% 89.02/26.87 ((
% 89.02/26.87 (singletonsubset) =>
% 89.02/26.87 ((
% 89.02/26.87 (singletoninpowerset) =>
% 89.02/26.87 ((
% 89.02/26.87 (singletoninpowunion) =>
% 89.02/26.87 ((
% 89.02/26.87 (upairset2E) =>
% 89.02/26.87 ((
% 89.02/26.87 (upairsubunion) =>
% 89.02/26.87 ((
% 89.02/26.87 (upairinpowunion) =>
% 89.02/26.87 ((
% 89.02/26.87 (ubforcartprodlem1) =>
% 89.02/26.87 ((
% 89.02/26.87 (ubforcartprodlem2) =>
% 89.02/26.87 ((
% 89.02/26.87 (ubforcartprodlem3) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodpairin) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodmempair1) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodmempair) =>
% 89.02/26.87 ((
% 89.02/26.87 (setunionE2) =>
% 89.02/26.87 ((
% 89.02/26.87 (setunionsingleton1) =>
% 89.02/26.87 ((
% 89.02/26.87 (setunionsingleton2) =>
% 89.02/26.87 ((
% 89.02/26.87 (setunionsingleton) =>
% 89.02/26.87 ((
% 89.02/26.87 (singletonprop) =>
% 89.02/26.87 ((
% 89.02/26.87 (ex1E1) =>
% 89.02/26.87 ((
% 89.02/26.87 (ex1I) =>
% 89.02/26.87 ((
% 89.02/26.87 (ex1I2) =>
% 89.02/26.87 ((
% 89.02/26.87 (singletonsuniq) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjL1) =>
% 89.02/26.87 ((
% 89.02/26.87 (kfstsingleton) =>
% 89.02/26.87 ((
% 89.02/26.87 (theprop) =>
% 89.02/26.87 ((
% 89.02/26.87 (kfstpairEq) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodfstin) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjL2) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjL) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjR11) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjR12) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjR1) =>
% 89.02/26.87 ((
% 89.02/26.87 (upairequniteq) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjR2) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjR) =>
% 89.02/26.87 ((
% 89.02/26.87 (ksndsingleton) =>
% 89.02/26.87 ((
% 89.02/26.87 (ksndpairEq) =>
% 89.02/26.87 ((
% 89.02/26.87 (kpairsurjEq) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodsndin) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodpairmemEL) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodpairmemER) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodmempaircEq) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodfstpairEq) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodsndpairEq) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodpairsurjEq) =>
% 89.02/26.87 ((
% 89.02/26.87 (dpsetconstrI) =>
% 89.02/26.87 ((
% 89.02/26.87 (dpsetconstrSub) =>
% 89.02/26.87 ((
% 89.02/26.87 (setOfPairsIsBReln) =>
% 89.02/26.87 ((
% 89.02/26.87 (dpsetconstrERa) =>
% 89.02/26.87 ((
% 89.02/26.87 (dpsetconstrEL1) =>
% 89.02/26.87 ((
% 89.02/26.87 (dpsetconstrEL2) =>
% 89.02/26.87 ((
% 89.02/26.87 (dpsetconstrER) =>
% 89.02/26.87 ((
% 89.02/26.87 (funcImageSingleton) =>
% 89.02/26.87 ((
% 89.02/26.87 (apProp) =>
% 89.02/26.87 ((
% 89.02/26.87 (app) =>
% 89.02/26.87 ((
% 89.02/26.87 (infuncsetfunc) =>
% 89.02/26.87 ((
% 89.02/26.87 (ap2p) =>
% 89.02/26.87 ((
% 89.02/26.87 (funcinfuncset) =>
% 89.02/26.87 ((
% 89.02/26.87 (lamProp) =>
% 89.02/26.87 ((
% 89.02/26.87 (lamp) =>
% 89.02/26.87 ((
% 89.02/26.87 (lam2p) =>
% 89.02/26.87 ((
% 89.02/26.87 (brelnall1) =>
% 89.02/26.87 ((
% 89.02/26.87 (brelnall2) =>
% 89.02/26.87 ((
% 89.02/26.87 (!!) @ (
% 89.02/26.87 (('#B') @ (
% 89.02/26.87 !!) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#S') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#S') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 =>))) @
% 89.02/26.87 ex1)))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 !!))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#S') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#B') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#S') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 =>))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#C') @ in)))))))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 !!))))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#C') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#B') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#B') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#S') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 =>))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#C') @ in)))))))))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#S') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#S') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#B'))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 =>))))))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#C') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#B') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#S') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 =>))))))) @
% 89.02/26.87 (
% 89.02/26.87 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.02/26.87 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl586])).
% 89.02/26.87 thf(zip_derived_cl606, plain,
% 89.02/26.87 (~ (((exuI1) =>
% 89.02/26.87 (((exuI3) =>
% 89.02/26.87 (((exuI2) =>
% 89.02/26.87 (((inCongP) =>
% 89.02/26.87 (((in__Cong) =>
% 89.02/26.87 (((exuE3u) =>
% 89.02/26.87 (((exu__Cong) =>
% 89.02/26.87 (((setadjoin__Cong) =>
% 89.02/26.87 (((powerset__Cong) =>
% 89.02/26.87 (((setunion__Cong) =>
% 89.02/26.87 (((exuEu) =>
% 89.02/26.87 (((descr__Cong) =>
% 89.02/26.87 (((dsetconstr__Cong) =>
% 89.02/26.87 (((subsetI1) =>
% 89.02/26.87 (((eqimpsubset2) =>
% 89.02/26.87 (((eqimpsubset1) =>
% 89.02/26.87 (((subsetI2) =>
% 89.02/26.87 (((emptysetsubset) =>
% 89.02/26.87 (((subsetE) =>
% 89.02/26.87 (((subsetE2) =>
% 89.02/26.87 (((notsubsetI) =>
% 89.02/26.87 (((notequalI1) =>
% 89.02/26.87 (((notequalI2) =>
% 89.02/26.87 (((subsetRefl) =>
% 89.02/26.87 (((subsetTrans) =>
% 89.02/26.87 (((setadjoinSub) =>
% 89.02/26.87 (((setadjoinSub2) =>
% 89.02/26.87 (((subset2powerset) =>
% 89.02/26.87 (((setextsub) =>
% 89.02/26.87 (((subsetemptysetimpeq) =>
% 89.02/26.87 ((
% 89.02/26.87 (powersetI1) =>
% 89.02/26.87 ((
% 89.02/26.87 (powersetE1) =>
% 89.02/26.87 ((
% 89.02/26.87 (inPowerset) =>
% 89.02/26.87 ((
% 89.02/26.87 (powersetsubset) =>
% 89.02/26.87 ((
% 89.02/26.87 (sepInPowerset) =>
% 89.02/26.87 ((
% 89.02/26.87 (sepSubset) =>
% 89.02/26.87 ((
% 89.02/26.87 (binunionIL) =>
% 89.02/26.87 ((
% 89.02/26.87 (upairset2IR) =>
% 89.02/26.87 ((
% 89.02/26.87 (binunionIR) =>
% 89.02/26.87 ((
% 89.02/26.87 (binunionEcases) =>
% 89.02/26.87 ((
% 89.02/26.87 (binunionE) =>
% 89.02/26.87 ((
% 89.02/26.87 (binunionLsub) =>
% 89.02/26.87 ((
% 89.02/26.87 (binunionRsub) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectI) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectSubset5) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectEL) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectLsub) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectSubset2) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectSubset3) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectER) =>
% 89.02/26.87 ((
% 89.02/26.87 (disjointsetsI1) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectRsub) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectSubset4) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectSubset1) =>
% 89.02/26.87 ((
% 89.02/26.87 (bs114d) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusI) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusEL) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusER) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusSubset2) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusERneg) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusELneg) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusILneg) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusIRneg) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusLsub) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusSubset1) =>
% 89.02/26.87 ((
% 89.02/26.87 (symdiffE) =>
% 89.02/26.87 ((
% 89.02/26.87 (symdiffI1) =>
% 89.02/26.87 ((
% 89.02/26.87 (symdiffI2) =>
% 89.02/26.87 ((
% 89.02/26.87 (symdiffIneg1) =>
% 89.02/26.87 ((
% 89.02/26.87 (symdiffIneg2) =>
% 89.02/26.87 ((
% 89.02/26.87 (secondinupair) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairIL) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairIR) =>
% 89.02/26.87 ((
% 89.02/26.87 (kpairiskpair) =>
% 89.02/26.87 ((
% 89.02/26.87 (kpairp) =>
% 89.02/26.87 ((
% 89.02/26.87 (singletonsubset) =>
% 89.02/26.87 ((
% 89.02/26.87 (singletoninpowerset) =>
% 89.02/26.87 ((
% 89.02/26.87 (singletoninpowunion) =>
% 89.02/26.87 ((
% 89.02/26.87 (upairset2E) =>
% 89.02/26.87 ((
% 89.02/26.87 (upairsubunion) =>
% 89.02/26.87 ((
% 89.02/26.87 (upairinpowunion) =>
% 89.02/26.87 ((
% 89.02/26.87 (ubforcartprodlem1) =>
% 89.02/26.87 ((
% 89.02/26.87 (ubforcartprodlem2) =>
% 89.02/26.87 ((
% 89.02/26.87 (ubforcartprodlem3) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodpairin) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodmempair1) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodmempair) =>
% 89.02/26.87 ((
% 89.02/26.87 (setunionE2) =>
% 89.02/26.87 ((
% 89.02/26.87 (setunionsingleton1) =>
% 89.02/26.87 ((
% 89.02/26.87 (setunionsingleton2) =>
% 89.02/26.87 ((
% 89.02/26.87 (setunionsingleton) =>
% 89.02/26.87 ((
% 89.02/26.87 (singletonprop) =>
% 89.02/26.87 ((
% 89.02/26.87 (ex1E1) =>
% 89.02/26.87 ((
% 89.02/26.87 (ex1I) =>
% 89.02/26.87 ((
% 89.02/26.87 (ex1I2) =>
% 89.02/26.87 ((
% 89.02/26.87 (singletonsuniq) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjL1) =>
% 89.02/26.87 ((
% 89.02/26.87 (kfstsingleton) =>
% 89.02/26.87 ((
% 89.02/26.87 (theprop) =>
% 89.02/26.87 ((
% 89.02/26.87 (kfstpairEq) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodfstin) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjL2) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjL) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjR11) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjR12) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjR1) =>
% 89.02/26.87 ((
% 89.02/26.87 (upairequniteq) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjR2) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjR) =>
% 89.02/26.87 ((
% 89.02/26.87 (ksndsingleton) =>
% 89.02/26.87 ((
% 89.02/26.87 (ksndpairEq) =>
% 89.02/26.87 ((
% 89.02/26.87 (kpairsurjEq) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodsndin) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodpairmemEL) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodpairmemER) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodmempaircEq) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodfstpairEq) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodsndpairEq) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodpairsurjEq) =>
% 89.02/26.87 ((
% 89.02/26.87 (dpsetconstrI) =>
% 89.02/26.87 ((
% 89.02/26.87 (dpsetconstrSub) =>
% 89.02/26.87 ((
% 89.02/26.87 (setOfPairsIsBReln) =>
% 89.02/26.87 ((
% 89.02/26.87 (dpsetconstrERa) =>
% 89.02/26.87 ((
% 89.02/26.87 (dpsetconstrEL1) =>
% 89.02/26.87 ((
% 89.02/26.87 (dpsetconstrEL2) =>
% 89.02/26.87 ((
% 89.02/26.87 (dpsetconstrER) =>
% 89.02/26.87 ((
% 89.02/26.87 (funcImageSingleton) =>
% 89.02/26.87 ((
% 89.02/26.87 (apProp) =>
% 89.02/26.87 ((
% 89.02/26.87 (app) =>
% 89.02/26.87 ((
% 89.02/26.87 (infuncsetfunc) =>
% 89.02/26.87 ((
% 89.02/26.87 (ap2p) =>
% 89.02/26.87 ((
% 89.02/26.87 (funcinfuncset) =>
% 89.02/26.87 ((
% 89.02/26.87 (lamProp) =>
% 89.02/26.87 ((
% 89.02/26.87 (lamp) =>
% 89.02/26.87 ((
% 89.02/26.87 (lam2p) =>
% 89.02/26.87 ((
% 89.02/26.87 (brelnall1) =>
% 89.02/26.87 ((
% 89.02/26.87 (brelnall2) =>
% 89.02/26.87 ((
% 89.02/26.87 (!!) @ (
% 89.02/26.87 (('#B') @ (
% 89.02/26.87 !!) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#S') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#S') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 =>))) @
% 89.02/26.87 ex1)))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 !!))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#S') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#B') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#S') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 =>))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#C') @ in)))))))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 !!))))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#C') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#B') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#B') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#S') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 =>))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#C') @ in)))))))))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#S') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#S') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#B'))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 =>))))))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#C') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#B') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#S') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 =>))))))) @
% 89.02/26.87 (
% 89.02/26.87 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.02/26.87 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl595])).
% 89.02/26.87 thf(zip_derived_cl619, plain,
% 89.02/26.87 (~ (((exuI3) =>
% 89.02/26.87 (((exuI2) =>
% 89.02/26.87 (((inCongP) =>
% 89.02/26.87 (((in__Cong) =>
% 89.02/26.87 (((exuE3u) =>
% 89.02/26.87 (((exu__Cong) =>
% 89.02/26.87 (((setadjoin__Cong) =>
% 89.02/26.87 (((powerset__Cong) =>
% 89.02/26.87 (((setunion__Cong) =>
% 89.02/26.87 (((exuEu) =>
% 89.02/26.87 (((descr__Cong) =>
% 89.02/26.87 (((dsetconstr__Cong) =>
% 89.02/26.87 (((subsetI1) =>
% 89.02/26.87 (((eqimpsubset2) =>
% 89.02/26.87 (((eqimpsubset1) =>
% 89.02/26.87 (((subsetI2) =>
% 89.02/26.87 (((emptysetsubset) =>
% 89.02/26.87 (((subsetE) =>
% 89.02/26.87 (((subsetE2) =>
% 89.02/26.87 (((notsubsetI) =>
% 89.02/26.87 (((notequalI1) =>
% 89.02/26.87 (((notequalI2) =>
% 89.02/26.87 (((subsetRefl) =>
% 89.02/26.87 (((subsetTrans) =>
% 89.02/26.87 (((setadjoinSub) =>
% 89.02/26.87 (((setadjoinSub2) =>
% 89.02/26.87 (((subset2powerset) =>
% 89.02/26.87 (((setextsub) =>
% 89.02/26.87 (((subsetemptysetimpeq) =>
% 89.02/26.87 (((powersetI1) =>
% 89.02/26.87 ((
% 89.02/26.87 (powersetE1) =>
% 89.02/26.87 ((
% 89.02/26.87 (inPowerset) =>
% 89.02/26.87 ((
% 89.02/26.87 (powersetsubset) =>
% 89.02/26.87 ((
% 89.02/26.87 (sepInPowerset) =>
% 89.02/26.87 ((
% 89.02/26.87 (sepSubset) =>
% 89.02/26.87 ((
% 89.02/26.87 (binunionIL) =>
% 89.02/26.87 ((
% 89.02/26.87 (upairset2IR) =>
% 89.02/26.87 ((
% 89.02/26.87 (binunionIR) =>
% 89.02/26.87 ((
% 89.02/26.87 (binunionEcases) =>
% 89.02/26.87 ((
% 89.02/26.87 (binunionE) =>
% 89.02/26.87 ((
% 89.02/26.87 (binunionLsub) =>
% 89.02/26.87 ((
% 89.02/26.87 (binunionRsub) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectI) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectSubset5) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectEL) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectLsub) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectSubset2) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectSubset3) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectER) =>
% 89.02/26.87 ((
% 89.02/26.87 (disjointsetsI1) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectRsub) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectSubset4) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectSubset1) =>
% 89.02/26.87 ((
% 89.02/26.87 (bs114d) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusI) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusEL) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusER) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusSubset2) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusERneg) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusELneg) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusILneg) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusIRneg) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusLsub) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusSubset1) =>
% 89.02/26.87 ((
% 89.02/26.87 (symdiffE) =>
% 89.02/26.87 ((
% 89.02/26.87 (symdiffI1) =>
% 89.02/26.87 ((
% 89.02/26.87 (symdiffI2) =>
% 89.02/26.87 ((
% 89.02/26.87 (symdiffIneg1) =>
% 89.02/26.87 ((
% 89.02/26.87 (symdiffIneg2) =>
% 89.02/26.87 ((
% 89.02/26.87 (secondinupair) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairIL) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairIR) =>
% 89.02/26.87 ((
% 89.02/26.87 (kpairiskpair) =>
% 89.02/26.87 ((
% 89.02/26.87 (kpairp) =>
% 89.02/26.87 ((
% 89.02/26.87 (singletonsubset) =>
% 89.02/26.87 ((
% 89.02/26.87 (singletoninpowerset) =>
% 89.02/26.87 ((
% 89.02/26.87 (singletoninpowunion) =>
% 89.02/26.87 ((
% 89.02/26.87 (upairset2E) =>
% 89.02/26.87 ((
% 89.02/26.87 (upairsubunion) =>
% 89.02/26.87 ((
% 89.02/26.87 (upairinpowunion) =>
% 89.02/26.87 ((
% 89.02/26.87 (ubforcartprodlem1) =>
% 89.02/26.87 ((
% 89.02/26.87 (ubforcartprodlem2) =>
% 89.02/26.87 ((
% 89.02/26.87 (ubforcartprodlem3) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodpairin) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodmempair1) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodmempair) =>
% 89.02/26.87 ((
% 89.02/26.87 (setunionE2) =>
% 89.02/26.87 ((
% 89.02/26.87 (setunionsingleton1) =>
% 89.02/26.87 ((
% 89.02/26.87 (setunionsingleton2) =>
% 89.02/26.87 ((
% 89.02/26.87 (setunionsingleton) =>
% 89.02/26.87 ((
% 89.02/26.87 (singletonprop) =>
% 89.02/26.87 ((
% 89.02/26.87 (ex1E1) =>
% 89.02/26.87 ((
% 89.02/26.87 (ex1I) =>
% 89.02/26.87 ((
% 89.02/26.87 (ex1I2) =>
% 89.02/26.87 ((
% 89.02/26.87 (singletonsuniq) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjL1) =>
% 89.02/26.87 ((
% 89.02/26.87 (kfstsingleton) =>
% 89.02/26.87 ((
% 89.02/26.87 (theprop) =>
% 89.02/26.87 ((
% 89.02/26.87 (kfstpairEq) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodfstin) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjL2) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjL) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjR11) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjR12) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjR1) =>
% 89.02/26.87 ((
% 89.02/26.87 (upairequniteq) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjR2) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjR) =>
% 89.02/26.87 ((
% 89.02/26.87 (ksndsingleton) =>
% 89.02/26.87 ((
% 89.02/26.87 (ksndpairEq) =>
% 89.02/26.87 ((
% 89.02/26.87 (kpairsurjEq) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodsndin) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodpairmemEL) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodpairmemER) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodmempaircEq) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodfstpairEq) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodsndpairEq) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodpairsurjEq) =>
% 89.02/26.87 ((
% 89.02/26.87 (dpsetconstrI) =>
% 89.02/26.87 ((
% 89.02/26.87 (dpsetconstrSub) =>
% 89.02/26.87 ((
% 89.02/26.87 (setOfPairsIsBReln) =>
% 89.02/26.87 ((
% 89.02/26.87 (dpsetconstrERa) =>
% 89.02/26.87 ((
% 89.02/26.87 (dpsetconstrEL1) =>
% 89.02/26.87 ((
% 89.02/26.87 (dpsetconstrEL2) =>
% 89.02/26.87 ((
% 89.02/26.87 (dpsetconstrER) =>
% 89.02/26.87 ((
% 89.02/26.87 (funcImageSingleton) =>
% 89.02/26.87 ((
% 89.02/26.87 (apProp) =>
% 89.02/26.87 ((
% 89.02/26.87 (app) =>
% 89.02/26.87 ((
% 89.02/26.87 (infuncsetfunc) =>
% 89.02/26.87 ((
% 89.02/26.87 (ap2p) =>
% 89.02/26.87 ((
% 89.02/26.87 (funcinfuncset) =>
% 89.02/26.87 ((
% 89.02/26.87 (lamProp) =>
% 89.02/26.87 ((
% 89.02/26.87 (lamp) =>
% 89.02/26.87 ((
% 89.02/26.87 (lam2p) =>
% 89.02/26.87 ((
% 89.02/26.87 (brelnall1) =>
% 89.02/26.87 ((
% 89.02/26.87 (brelnall2) =>
% 89.02/26.87 ((
% 89.02/26.87 (!!) @ (
% 89.02/26.87 (('#B') @ (
% 89.02/26.87 !!) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#S') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#S') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 =>))) @
% 89.02/26.87 ex1)))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 !!))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#S') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#B') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#S') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 =>))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#C') @ in)))))))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 !!))))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#C') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#B') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#B') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#S') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 =>))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#C') @ in)))))))))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#S') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#S') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#B'))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 =>))))))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#C') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#B') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#S') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 =>))))))) @
% 89.02/26.87 (
% 89.02/26.87 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.02/26.87 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl606])).
% 89.02/26.87 thf(zip_derived_cl630, plain,
% 89.02/26.87 (~ (((exuI2) =>
% 89.02/26.87 (((inCongP) =>
% 89.02/26.87 (((in__Cong) =>
% 89.02/26.87 (((exuE3u) =>
% 89.02/26.87 (((exu__Cong) =>
% 89.02/26.87 (((setadjoin__Cong) =>
% 89.02/26.87 (((powerset__Cong) =>
% 89.02/26.87 (((setunion__Cong) =>
% 89.02/26.87 (((exuEu) =>
% 89.02/26.87 (((descr__Cong) =>
% 89.02/26.87 (((dsetconstr__Cong) =>
% 89.02/26.87 (((subsetI1) =>
% 89.02/26.87 (((eqimpsubset2) =>
% 89.02/26.87 (((eqimpsubset1) =>
% 89.02/26.87 (((subsetI2) =>
% 89.02/26.87 (((emptysetsubset) =>
% 89.02/26.87 (((subsetE) =>
% 89.02/26.87 (((subsetE2) =>
% 89.02/26.87 (((notsubsetI) =>
% 89.02/26.87 (((notequalI1) =>
% 89.02/26.87 (((notequalI2) =>
% 89.02/26.87 (((subsetRefl) =>
% 89.02/26.87 (((subsetTrans) =>
% 89.02/26.87 (((setadjoinSub) =>
% 89.02/26.87 (((setadjoinSub2) =>
% 89.02/26.87 (((subset2powerset) =>
% 89.02/26.87 (((setextsub) =>
% 89.02/26.87 (((subsetemptysetimpeq) =>
% 89.02/26.87 (((powersetI1) =>
% 89.02/26.87 (((powersetE1) =>
% 89.02/26.87 ((
% 89.02/26.87 (inPowerset) =>
% 89.02/26.87 ((
% 89.02/26.87 (powersetsubset) =>
% 89.02/26.87 ((
% 89.02/26.87 (sepInPowerset) =>
% 89.02/26.87 ((
% 89.02/26.87 (sepSubset) =>
% 89.02/26.87 ((
% 89.02/26.87 (binunionIL) =>
% 89.02/26.87 ((
% 89.02/26.87 (upairset2IR) =>
% 89.02/26.87 ((
% 89.02/26.87 (binunionIR) =>
% 89.02/26.87 ((
% 89.02/26.87 (binunionEcases) =>
% 89.02/26.87 ((
% 89.02/26.87 (binunionE) =>
% 89.02/26.87 ((
% 89.02/26.87 (binunionLsub) =>
% 89.02/26.87 ((
% 89.02/26.87 (binunionRsub) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectI) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectSubset5) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectEL) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectLsub) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectSubset2) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectSubset3) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectER) =>
% 89.02/26.87 ((
% 89.02/26.87 (disjointsetsI1) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectRsub) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectSubset4) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectSubset1) =>
% 89.02/26.87 ((
% 89.02/26.87 (bs114d) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusI) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusEL) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusER) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusSubset2) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusERneg) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusELneg) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusILneg) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusIRneg) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusLsub) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusSubset1) =>
% 89.02/26.87 ((
% 89.02/26.87 (symdiffE) =>
% 89.02/26.87 ((
% 89.02/26.87 (symdiffI1) =>
% 89.02/26.87 ((
% 89.02/26.87 (symdiffI2) =>
% 89.02/26.87 ((
% 89.02/26.87 (symdiffIneg1) =>
% 89.02/26.87 ((
% 89.02/26.87 (symdiffIneg2) =>
% 89.02/26.87 ((
% 89.02/26.87 (secondinupair) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairIL) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairIR) =>
% 89.02/26.87 ((
% 89.02/26.87 (kpairiskpair) =>
% 89.02/26.87 ((
% 89.02/26.87 (kpairp) =>
% 89.02/26.87 ((
% 89.02/26.87 (singletonsubset) =>
% 89.02/26.87 ((
% 89.02/26.87 (singletoninpowerset) =>
% 89.02/26.87 ((
% 89.02/26.87 (singletoninpowunion) =>
% 89.02/26.87 ((
% 89.02/26.87 (upairset2E) =>
% 89.02/26.87 ((
% 89.02/26.87 (upairsubunion) =>
% 89.02/26.87 ((
% 89.02/26.87 (upairinpowunion) =>
% 89.02/26.87 ((
% 89.02/26.87 (ubforcartprodlem1) =>
% 89.02/26.87 ((
% 89.02/26.87 (ubforcartprodlem2) =>
% 89.02/26.87 ((
% 89.02/26.87 (ubforcartprodlem3) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodpairin) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodmempair1) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodmempair) =>
% 89.02/26.87 ((
% 89.02/26.87 (setunionE2) =>
% 89.02/26.87 ((
% 89.02/26.87 (setunionsingleton1) =>
% 89.02/26.87 ((
% 89.02/26.87 (setunionsingleton2) =>
% 89.02/26.87 ((
% 89.02/26.87 (setunionsingleton) =>
% 89.02/26.87 ((
% 89.02/26.87 (singletonprop) =>
% 89.02/26.87 ((
% 89.02/26.87 (ex1E1) =>
% 89.02/26.87 ((
% 89.02/26.87 (ex1I) =>
% 89.02/26.87 ((
% 89.02/26.87 (ex1I2) =>
% 89.02/26.87 ((
% 89.02/26.87 (singletonsuniq) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjL1) =>
% 89.02/26.87 ((
% 89.02/26.87 (kfstsingleton) =>
% 89.02/26.87 ((
% 89.02/26.87 (theprop) =>
% 89.02/26.87 ((
% 89.02/26.87 (kfstpairEq) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodfstin) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjL2) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjL) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjR11) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjR12) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjR1) =>
% 89.02/26.87 ((
% 89.02/26.87 (upairequniteq) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjR2) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjR) =>
% 89.02/26.87 ((
% 89.02/26.87 (ksndsingleton) =>
% 89.02/26.87 ((
% 89.02/26.87 (ksndpairEq) =>
% 89.02/26.87 ((
% 89.02/26.87 (kpairsurjEq) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodsndin) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodpairmemEL) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodpairmemER) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodmempaircEq) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodfstpairEq) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodsndpairEq) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodpairsurjEq) =>
% 89.02/26.87 ((
% 89.02/26.87 (dpsetconstrI) =>
% 89.02/26.87 ((
% 89.02/26.87 (dpsetconstrSub) =>
% 89.02/26.87 ((
% 89.02/26.87 (setOfPairsIsBReln) =>
% 89.02/26.87 ((
% 89.02/26.87 (dpsetconstrERa) =>
% 89.02/26.87 ((
% 89.02/26.87 (dpsetconstrEL1) =>
% 89.02/26.87 ((
% 89.02/26.87 (dpsetconstrEL2) =>
% 89.02/26.87 ((
% 89.02/26.87 (dpsetconstrER) =>
% 89.02/26.87 ((
% 89.02/26.87 (funcImageSingleton) =>
% 89.02/26.87 ((
% 89.02/26.87 (apProp) =>
% 89.02/26.87 ((
% 89.02/26.87 (app) =>
% 89.02/26.87 ((
% 89.02/26.87 (infuncsetfunc) =>
% 89.02/26.87 ((
% 89.02/26.87 (ap2p) =>
% 89.02/26.87 ((
% 89.02/26.87 (funcinfuncset) =>
% 89.02/26.87 ((
% 89.02/26.87 (lamProp) =>
% 89.02/26.87 ((
% 89.02/26.87 (lamp) =>
% 89.02/26.87 ((
% 89.02/26.87 (lam2p) =>
% 89.02/26.87 ((
% 89.02/26.87 (brelnall1) =>
% 89.02/26.87 ((
% 89.02/26.87 (brelnall2) =>
% 89.02/26.87 ((
% 89.02/26.87 (!!) @ (
% 89.02/26.87 (('#B') @ (
% 89.02/26.87 !!) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#S') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#S') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 =>))) @
% 89.02/26.87 ex1)))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 !!))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#S') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#B') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#S') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 =>))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#C') @ in)))))))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 !!))))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#C') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#B') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#B') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#S') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 =>))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#C') @ in)))))))))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#S') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#S') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#B'))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 =>))))))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#C') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#B') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#S') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 =>))))))) @
% 89.02/26.87 (
% 89.02/26.87 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.02/26.87 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl619])).
% 89.02/26.87 thf(zip_derived_cl640, plain,
% 89.02/26.87 (~ (((inCongP) =>
% 89.02/26.87 (((in__Cong) =>
% 89.02/26.87 (((exuE3u) =>
% 89.02/26.87 (((exu__Cong) =>
% 89.02/26.87 (((setadjoin__Cong) =>
% 89.02/26.87 (((powerset__Cong) =>
% 89.02/26.87 (((setunion__Cong) =>
% 89.02/26.87 (((exuEu) =>
% 89.02/26.87 (((descr__Cong) =>
% 89.02/26.87 (((dsetconstr__Cong) =>
% 89.02/26.87 (((subsetI1) =>
% 89.02/26.87 (((eqimpsubset2) =>
% 89.02/26.87 (((eqimpsubset1) =>
% 89.02/26.87 (((subsetI2) =>
% 89.02/26.87 (((emptysetsubset) =>
% 89.02/26.87 (((subsetE) =>
% 89.02/26.87 (((subsetE2) =>
% 89.02/26.87 (((notsubsetI) =>
% 89.02/26.87 (((notequalI1) =>
% 89.02/26.87 (((notequalI2) =>
% 89.02/26.87 (((subsetRefl) =>
% 89.02/26.87 (((subsetTrans) =>
% 89.02/26.87 (((setadjoinSub) =>
% 89.02/26.87 (((setadjoinSub2) =>
% 89.02/26.87 (((subset2powerset) =>
% 89.02/26.87 (((setextsub) =>
% 89.02/26.87 (((subsetemptysetimpeq) =>
% 89.02/26.87 (((powersetI1) =>
% 89.02/26.87 (((powersetE1) =>
% 89.02/26.87 (((inPowerset) =>
% 89.02/26.87 ((
% 89.02/26.87 (powersetsubset) =>
% 89.02/26.87 ((
% 89.02/26.87 (sepInPowerset) =>
% 89.02/26.87 ((
% 89.02/26.87 (sepSubset) =>
% 89.02/26.87 ((
% 89.02/26.87 (binunionIL) =>
% 89.02/26.87 ((
% 89.02/26.87 (upairset2IR) =>
% 89.02/26.87 ((
% 89.02/26.87 (binunionIR) =>
% 89.02/26.87 ((
% 89.02/26.87 (binunionEcases) =>
% 89.02/26.87 ((
% 89.02/26.87 (binunionE) =>
% 89.02/26.87 ((
% 89.02/26.87 (binunionLsub) =>
% 89.02/26.87 ((
% 89.02/26.87 (binunionRsub) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectI) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectSubset5) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectEL) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectLsub) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectSubset2) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectSubset3) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectER) =>
% 89.02/26.87 ((
% 89.02/26.87 (disjointsetsI1) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectRsub) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectSubset4) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectSubset1) =>
% 89.02/26.87 ((
% 89.02/26.87 (bs114d) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusI) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusEL) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusER) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusSubset2) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusERneg) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusELneg) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusILneg) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusIRneg) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusLsub) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusSubset1) =>
% 89.02/26.87 ((
% 89.02/26.87 (symdiffE) =>
% 89.02/26.87 ((
% 89.02/26.87 (symdiffI1) =>
% 89.02/26.87 ((
% 89.02/26.87 (symdiffI2) =>
% 89.02/26.87 ((
% 89.02/26.87 (symdiffIneg1) =>
% 89.02/26.87 ((
% 89.02/26.87 (symdiffIneg2) =>
% 89.02/26.87 ((
% 89.02/26.87 (secondinupair) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairIL) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairIR) =>
% 89.02/26.87 ((
% 89.02/26.87 (kpairiskpair) =>
% 89.02/26.87 ((
% 89.02/26.87 (kpairp) =>
% 89.02/26.87 ((
% 89.02/26.87 (singletonsubset) =>
% 89.02/26.87 ((
% 89.02/26.87 (singletoninpowerset) =>
% 89.02/26.87 ((
% 89.02/26.87 (singletoninpowunion) =>
% 89.02/26.87 ((
% 89.02/26.87 (upairset2E) =>
% 89.02/26.87 ((
% 89.02/26.87 (upairsubunion) =>
% 89.02/26.87 ((
% 89.02/26.87 (upairinpowunion) =>
% 89.02/26.87 ((
% 89.02/26.87 (ubforcartprodlem1) =>
% 89.02/26.87 ((
% 89.02/26.87 (ubforcartprodlem2) =>
% 89.02/26.87 ((
% 89.02/26.87 (ubforcartprodlem3) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodpairin) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodmempair1) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodmempair) =>
% 89.02/26.87 ((
% 89.02/26.87 (setunionE2) =>
% 89.02/26.87 ((
% 89.02/26.87 (setunionsingleton1) =>
% 89.02/26.87 ((
% 89.02/26.87 (setunionsingleton2) =>
% 89.02/26.87 ((
% 89.02/26.87 (setunionsingleton) =>
% 89.02/26.87 ((
% 89.02/26.87 (singletonprop) =>
% 89.02/26.87 ((
% 89.02/26.87 (ex1E1) =>
% 89.02/26.87 ((
% 89.02/26.87 (ex1I) =>
% 89.02/26.87 ((
% 89.02/26.87 (ex1I2) =>
% 89.02/26.87 ((
% 89.02/26.87 (singletonsuniq) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjL1) =>
% 89.02/26.87 ((
% 89.02/26.87 (kfstsingleton) =>
% 89.02/26.87 ((
% 89.02/26.87 (theprop) =>
% 89.02/26.87 ((
% 89.02/26.87 (kfstpairEq) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodfstin) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjL2) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjL) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjR11) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjR12) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjR1) =>
% 89.02/26.87 ((
% 89.02/26.87 (upairequniteq) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjR2) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjR) =>
% 89.02/26.87 ((
% 89.02/26.87 (ksndsingleton) =>
% 89.02/26.87 ((
% 89.02/26.87 (ksndpairEq) =>
% 89.02/26.87 ((
% 89.02/26.87 (kpairsurjEq) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodsndin) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodpairmemEL) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodpairmemER) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodmempaircEq) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodfstpairEq) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodsndpairEq) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodpairsurjEq) =>
% 89.02/26.87 ((
% 89.02/26.87 (dpsetconstrI) =>
% 89.02/26.87 ((
% 89.02/26.87 (dpsetconstrSub) =>
% 89.02/26.87 ((
% 89.02/26.87 (setOfPairsIsBReln) =>
% 89.02/26.87 ((
% 89.02/26.87 (dpsetconstrERa) =>
% 89.02/26.87 ((
% 89.02/26.87 (dpsetconstrEL1) =>
% 89.02/26.87 ((
% 89.02/26.87 (dpsetconstrEL2) =>
% 89.02/26.87 ((
% 89.02/26.87 (dpsetconstrER) =>
% 89.02/26.87 ((
% 89.02/26.87 (funcImageSingleton) =>
% 89.02/26.87 ((
% 89.02/26.87 (apProp) =>
% 89.02/26.87 ((
% 89.02/26.87 (app) =>
% 89.02/26.87 ((
% 89.02/26.87 (infuncsetfunc) =>
% 89.02/26.87 ((
% 89.02/26.87 (ap2p) =>
% 89.02/26.87 ((
% 89.02/26.87 (funcinfuncset) =>
% 89.02/26.87 ((
% 89.02/26.87 (lamProp) =>
% 89.02/26.87 ((
% 89.02/26.87 (lamp) =>
% 89.02/26.87 ((
% 89.02/26.87 (lam2p) =>
% 89.02/26.87 ((
% 89.02/26.87 (brelnall1) =>
% 89.02/26.87 ((
% 89.02/26.87 (brelnall2) =>
% 89.02/26.87 ((
% 89.02/26.87 (!!) @ (
% 89.02/26.87 (('#B') @ (
% 89.02/26.87 !!) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#S') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#S') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 =>))) @
% 89.02/26.87 ex1)))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 !!))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#S') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#B') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#S') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 =>))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#C') @ in)))))))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 !!))))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#C') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#B') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#B') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#S') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 =>))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#C') @ in)))))))))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#S') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#S') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#B'))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 =>))))))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#C') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#B') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#S') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 =>))))))) @
% 89.02/26.87 (
% 89.02/26.87 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.02/26.87 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl630])).
% 89.02/26.87 thf(zip_derived_cl650, plain,
% 89.02/26.87 (~ (((in__Cong) =>
% 89.02/26.87 (((exuE3u) =>
% 89.02/26.87 (((exu__Cong) =>
% 89.02/26.87 (((setadjoin__Cong) =>
% 89.02/26.87 (((powerset__Cong) =>
% 89.02/26.87 (((setunion__Cong) =>
% 89.02/26.87 (((exuEu) =>
% 89.02/26.87 (((descr__Cong) =>
% 89.02/26.87 (((dsetconstr__Cong) =>
% 89.02/26.87 (((subsetI1) =>
% 89.02/26.87 (((eqimpsubset2) =>
% 89.02/26.87 (((eqimpsubset1) =>
% 89.02/26.87 (((subsetI2) =>
% 89.02/26.87 (((emptysetsubset) =>
% 89.02/26.87 (((subsetE) =>
% 89.02/26.87 (((subsetE2) =>
% 89.02/26.87 (((notsubsetI) =>
% 89.02/26.87 (((notequalI1) =>
% 89.02/26.87 (((notequalI2) =>
% 89.02/26.87 (((subsetRefl) =>
% 89.02/26.87 (((subsetTrans) =>
% 89.02/26.87 (((setadjoinSub) =>
% 89.02/26.87 (((setadjoinSub2) =>
% 89.02/26.87 (((subset2powerset) =>
% 89.02/26.87 (((setextsub) =>
% 89.02/26.87 (((subsetemptysetimpeq) =>
% 89.02/26.87 (((powersetI1) =>
% 89.02/26.87 (((powersetE1) =>
% 89.02/26.87 (((inPowerset) =>
% 89.02/26.87 (((powersetsubset) =>
% 89.02/26.87 ((
% 89.02/26.87 (sepInPowerset) =>
% 89.02/26.87 ((
% 89.02/26.87 (sepSubset) =>
% 89.02/26.87 ((
% 89.02/26.87 (binunionIL) =>
% 89.02/26.87 ((
% 89.02/26.87 (upairset2IR) =>
% 89.02/26.87 ((
% 89.02/26.87 (binunionIR) =>
% 89.02/26.87 ((
% 89.02/26.87 (binunionEcases) =>
% 89.02/26.87 ((
% 89.02/26.87 (binunionE) =>
% 89.02/26.87 ((
% 89.02/26.87 (binunionLsub) =>
% 89.02/26.87 ((
% 89.02/26.87 (binunionRsub) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectI) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectSubset5) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectEL) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectLsub) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectSubset2) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectSubset3) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectER) =>
% 89.02/26.87 ((
% 89.02/26.87 (disjointsetsI1) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectRsub) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectSubset4) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectSubset1) =>
% 89.02/26.87 ((
% 89.02/26.87 (bs114d) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusI) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusEL) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusER) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusSubset2) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusERneg) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusELneg) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusILneg) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusIRneg) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusLsub) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusSubset1) =>
% 89.02/26.87 ((
% 89.02/26.87 (symdiffE) =>
% 89.02/26.87 ((
% 89.02/26.87 (symdiffI1) =>
% 89.02/26.87 ((
% 89.02/26.87 (symdiffI2) =>
% 89.02/26.87 ((
% 89.02/26.87 (symdiffIneg1) =>
% 89.02/26.87 ((
% 89.02/26.87 (symdiffIneg2) =>
% 89.02/26.87 ((
% 89.02/26.87 (secondinupair) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairIL) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairIR) =>
% 89.02/26.87 ((
% 89.02/26.87 (kpairiskpair) =>
% 89.02/26.87 ((
% 89.02/26.87 (kpairp) =>
% 89.02/26.87 ((
% 89.02/26.87 (singletonsubset) =>
% 89.02/26.87 ((
% 89.02/26.87 (singletoninpowerset) =>
% 89.02/26.87 ((
% 89.02/26.87 (singletoninpowunion) =>
% 89.02/26.87 ((
% 89.02/26.87 (upairset2E) =>
% 89.02/26.87 ((
% 89.02/26.87 (upairsubunion) =>
% 89.02/26.87 ((
% 89.02/26.87 (upairinpowunion) =>
% 89.02/26.87 ((
% 89.02/26.87 (ubforcartprodlem1) =>
% 89.02/26.87 ((
% 89.02/26.87 (ubforcartprodlem2) =>
% 89.02/26.87 ((
% 89.02/26.87 (ubforcartprodlem3) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodpairin) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodmempair1) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodmempair) =>
% 89.02/26.87 ((
% 89.02/26.87 (setunionE2) =>
% 89.02/26.87 ((
% 89.02/26.87 (setunionsingleton1) =>
% 89.02/26.87 ((
% 89.02/26.87 (setunionsingleton2) =>
% 89.02/26.87 ((
% 89.02/26.87 (setunionsingleton) =>
% 89.02/26.87 ((
% 89.02/26.87 (singletonprop) =>
% 89.02/26.87 ((
% 89.02/26.87 (ex1E1) =>
% 89.02/26.87 ((
% 89.02/26.87 (ex1I) =>
% 89.02/26.87 ((
% 89.02/26.87 (ex1I2) =>
% 89.02/26.87 ((
% 89.02/26.87 (singletonsuniq) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjL1) =>
% 89.02/26.87 ((
% 89.02/26.87 (kfstsingleton) =>
% 89.02/26.87 ((
% 89.02/26.87 (theprop) =>
% 89.02/26.87 ((
% 89.02/26.87 (kfstpairEq) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodfstin) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjL2) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjL) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjR11) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjR12) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjR1) =>
% 89.02/26.87 ((
% 89.02/26.87 (upairequniteq) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjR2) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjR) =>
% 89.02/26.87 ((
% 89.02/26.87 (ksndsingleton) =>
% 89.02/26.87 ((
% 89.02/26.87 (ksndpairEq) =>
% 89.02/26.87 ((
% 89.02/26.87 (kpairsurjEq) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodsndin) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodpairmemEL) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodpairmemER) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodmempaircEq) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodfstpairEq) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodsndpairEq) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodpairsurjEq) =>
% 89.02/26.87 ((
% 89.02/26.87 (dpsetconstrI) =>
% 89.02/26.87 ((
% 89.02/26.87 (dpsetconstrSub) =>
% 89.02/26.87 ((
% 89.02/26.87 (setOfPairsIsBReln) =>
% 89.02/26.87 ((
% 89.02/26.87 (dpsetconstrERa) =>
% 89.02/26.87 ((
% 89.02/26.87 (dpsetconstrEL1) =>
% 89.02/26.87 ((
% 89.02/26.87 (dpsetconstrEL2) =>
% 89.02/26.87 ((
% 89.02/26.87 (dpsetconstrER) =>
% 89.02/26.87 ((
% 89.02/26.87 (funcImageSingleton) =>
% 89.02/26.87 ((
% 89.02/26.87 (apProp) =>
% 89.02/26.87 ((
% 89.02/26.87 (app) =>
% 89.02/26.87 ((
% 89.02/26.87 (infuncsetfunc) =>
% 89.02/26.87 ((
% 89.02/26.87 (ap2p) =>
% 89.02/26.87 ((
% 89.02/26.87 (funcinfuncset) =>
% 89.02/26.87 ((
% 89.02/26.87 (lamProp) =>
% 89.02/26.87 ((
% 89.02/26.87 (lamp) =>
% 89.02/26.87 ((
% 89.02/26.87 (lam2p) =>
% 89.02/26.87 ((
% 89.02/26.87 (brelnall1) =>
% 89.02/26.87 ((
% 89.02/26.87 (brelnall2) =>
% 89.02/26.87 ((
% 89.02/26.87 (!!) @ (
% 89.02/26.87 (('#B') @ (
% 89.02/26.87 !!) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#S') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#S') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 =>))) @
% 89.02/26.87 ex1)))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 !!))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#S') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#B') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#S') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 =>))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#C') @ in)))))))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 !!))))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#C') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#B') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#B') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#S') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 =>))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#C') @ in)))))))))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#S') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#S') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#B'))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 =>))))))) @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#C') @ (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#B') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 '#S') @
% 89.02/26.87 (
% 89.02/26.87 (
% 89.02/26.87 ('#B') @ (
% 89.02/26.87 =>))))))) @
% 89.02/26.87 (
% 89.02/26.87 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.02/26.87 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl640])).
% 89.02/26.87 thf(zip_derived_cl660, plain,
% 89.02/26.87 (~ (((exuE3u) =>
% 89.02/26.87 (((exu__Cong) =>
% 89.02/26.87 (((setadjoin__Cong) =>
% 89.02/26.87 (((powerset__Cong) =>
% 89.02/26.87 (((setunion__Cong) =>
% 89.02/26.87 (((exuEu) =>
% 89.02/26.87 (((descr__Cong) =>
% 89.02/26.87 (((dsetconstr__Cong) =>
% 89.02/26.87 (((subsetI1) =>
% 89.02/26.87 (((eqimpsubset2) =>
% 89.02/26.87 (((eqimpsubset1) =>
% 89.02/26.87 (((subsetI2) =>
% 89.02/26.87 (((emptysetsubset) =>
% 89.02/26.87 (((subsetE) =>
% 89.02/26.87 (((subsetE2) =>
% 89.02/26.87 (((notsubsetI) =>
% 89.02/26.87 (((notequalI1) =>
% 89.02/26.87 (((notequalI2) =>
% 89.02/26.87 (((subsetRefl) =>
% 89.02/26.87 (((subsetTrans) =>
% 89.02/26.87 (((setadjoinSub) =>
% 89.02/26.87 (((setadjoinSub2) =>
% 89.02/26.87 (((subset2powerset) =>
% 89.02/26.87 (((setextsub) =>
% 89.02/26.87 (((subsetemptysetimpeq) =>
% 89.02/26.87 (((powersetI1) =>
% 89.02/26.87 (((powersetE1) =>
% 89.02/26.87 (((inPowerset) =>
% 89.02/26.87 (((powersetsubset) =>
% 89.02/26.87 (((sepInPowerset) =>
% 89.02/26.87 ((
% 89.02/26.87 (sepSubset) =>
% 89.02/26.87 ((
% 89.02/26.87 (binunionIL) =>
% 89.02/26.87 ((
% 89.02/26.87 (upairset2IR) =>
% 89.02/26.87 ((
% 89.02/26.87 (binunionIR) =>
% 89.02/26.87 ((
% 89.02/26.87 (binunionEcases) =>
% 89.02/26.87 ((
% 89.02/26.87 (binunionE) =>
% 89.02/26.87 ((
% 89.02/26.87 (binunionLsub) =>
% 89.02/26.87 ((
% 89.02/26.87 (binunionRsub) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectI) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectSubset5) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectEL) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectLsub) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectSubset2) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectSubset3) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectER) =>
% 89.02/26.87 ((
% 89.02/26.87 (disjointsetsI1) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectRsub) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectSubset4) =>
% 89.02/26.87 ((
% 89.02/26.87 (binintersectSubset1) =>
% 89.02/26.87 ((
% 89.02/26.87 (bs114d) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusI) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusEL) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusER) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusSubset2) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusERneg) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusELneg) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusILneg) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusIRneg) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusLsub) =>
% 89.02/26.87 ((
% 89.02/26.87 (setminusSubset1) =>
% 89.02/26.87 ((
% 89.02/26.87 (symdiffE) =>
% 89.02/26.87 ((
% 89.02/26.87 (symdiffI1) =>
% 89.02/26.87 ((
% 89.02/26.87 (symdiffI2) =>
% 89.02/26.87 ((
% 89.02/26.87 (symdiffIneg1) =>
% 89.02/26.87 ((
% 89.02/26.87 (symdiffIneg2) =>
% 89.02/26.87 ((
% 89.02/26.87 (secondinupair) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairIL) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairIR) =>
% 89.02/26.87 ((
% 89.02/26.87 (kpairiskpair) =>
% 89.02/26.87 ((
% 89.02/26.87 (kpairp) =>
% 89.02/26.87 ((
% 89.02/26.87 (singletonsubset) =>
% 89.02/26.87 ((
% 89.02/26.87 (singletoninpowerset) =>
% 89.02/26.87 ((
% 89.02/26.87 (singletoninpowunion) =>
% 89.02/26.87 ((
% 89.02/26.87 (upairset2E) =>
% 89.02/26.87 ((
% 89.02/26.87 (upairsubunion) =>
% 89.02/26.87 ((
% 89.02/26.87 (upairinpowunion) =>
% 89.02/26.87 ((
% 89.02/26.87 (ubforcartprodlem1) =>
% 89.02/26.87 ((
% 89.02/26.87 (ubforcartprodlem2) =>
% 89.02/26.87 ((
% 89.02/26.87 (ubforcartprodlem3) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodpairin) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodmempair1) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodmempair) =>
% 89.02/26.87 ((
% 89.02/26.87 (setunionE2) =>
% 89.02/26.87 ((
% 89.02/26.87 (setunionsingleton1) =>
% 89.02/26.87 ((
% 89.02/26.87 (setunionsingleton2) =>
% 89.02/26.87 ((
% 89.02/26.87 (setunionsingleton) =>
% 89.02/26.87 ((
% 89.02/26.87 (singletonprop) =>
% 89.02/26.87 ((
% 89.02/26.87 (ex1E1) =>
% 89.02/26.87 ((
% 89.02/26.87 (ex1I) =>
% 89.02/26.87 ((
% 89.02/26.87 (ex1I2) =>
% 89.02/26.87 ((
% 89.02/26.87 (singletonsuniq) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjL1) =>
% 89.02/26.87 ((
% 89.02/26.87 (kfstsingleton) =>
% 89.02/26.87 ((
% 89.02/26.87 (theprop) =>
% 89.02/26.87 ((
% 89.02/26.87 (kfstpairEq) =>
% 89.02/26.87 ((
% 89.02/26.87 (cartprodfstin) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjL2) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjL) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjR11) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjR12) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjR1) =>
% 89.02/26.87 ((
% 89.02/26.87 (upairequniteq) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjR2) =>
% 89.02/26.87 ((
% 89.02/26.87 (setukpairinjR) =>
% 89.02/26.87 ((
% 89.16/26.89 (ksndsingleton) =>
% 89.16/26.89 ((
% 89.16/26.89 (ksndpairEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (kpairsurjEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodsndin) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodpairmemEL) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodpairmemER) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodmempaircEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodfstpairEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodsndpairEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodpairsurjEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (dpsetconstrI) =>
% 89.16/26.89 ((
% 89.16/26.89 (dpsetconstrSub) =>
% 89.16/26.89 ((
% 89.16/26.89 (setOfPairsIsBReln) =>
% 89.16/26.89 ((
% 89.16/26.89 (dpsetconstrERa) =>
% 89.16/26.89 ((
% 89.16/26.89 (dpsetconstrEL1) =>
% 89.16/26.89 ((
% 89.16/26.89 (dpsetconstrEL2) =>
% 89.16/26.89 ((
% 89.16/26.89 (dpsetconstrER) =>
% 89.16/26.89 ((
% 89.16/26.89 (funcImageSingleton) =>
% 89.16/26.89 ((
% 89.16/26.89 (apProp) =>
% 89.16/26.89 ((
% 89.16/26.89 (app) =>
% 89.16/26.89 ((
% 89.16/26.89 (infuncsetfunc) =>
% 89.16/26.89 ((
% 89.16/26.89 (ap2p) =>
% 89.16/26.89 ((
% 89.16/26.89 (funcinfuncset) =>
% 89.16/26.89 ((
% 89.16/26.89 (lamProp) =>
% 89.16/26.89 ((
% 89.16/26.89 (lamp) =>
% 89.16/26.89 ((
% 89.16/26.89 (lam2p) =>
% 89.16/26.89 ((
% 89.16/26.89 (brelnall1) =>
% 89.16/26.89 ((
% 89.16/26.89 (brelnall2) =>
% 89.16/26.89 ((
% 89.16/26.89 (!!) @ (
% 89.16/26.89 (('#B') @ (
% 89.16/26.89 !!) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#S') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#S') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 =>))) @
% 89.16/26.89 ex1)))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 !!))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#S') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#B') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#S') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 =>))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#C') @ in)))))))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 !!))))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#C') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#B') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#B') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#S') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 =>))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#C') @ in)))))))))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#S') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#S') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#B'))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 =>))))))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#C') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#B') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#S') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 =>))))))) @
% 89.16/26.89 (
% 89.16/26.89 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.16/26.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl650])).
% 89.16/26.89 thf(zip_derived_cl672, plain,
% 89.16/26.89 (~ (((exu__Cong) =>
% 89.16/26.89 (((setadjoin__Cong) =>
% 89.16/26.89 (((powerset__Cong) =>
% 89.16/26.89 (((setunion__Cong) =>
% 89.16/26.89 (((exuEu) =>
% 89.16/26.89 (((descr__Cong) =>
% 89.16/26.89 (((dsetconstr__Cong) =>
% 89.16/26.89 (((subsetI1) =>
% 89.16/26.89 (((eqimpsubset2) =>
% 89.16/26.89 (((eqimpsubset1) =>
% 89.16/26.89 (((subsetI2) =>
% 89.16/26.89 (((emptysetsubset) =>
% 89.16/26.89 (((subsetE) =>
% 89.16/26.89 (((subsetE2) =>
% 89.16/26.89 (((notsubsetI) =>
% 89.16/26.89 (((notequalI1) =>
% 89.16/26.89 (((notequalI2) =>
% 89.16/26.89 (((subsetRefl) =>
% 89.16/26.89 (((subsetTrans) =>
% 89.16/26.89 (((setadjoinSub) =>
% 89.16/26.89 (((setadjoinSub2) =>
% 89.16/26.89 (((subset2powerset) =>
% 89.16/26.89 (((setextsub) =>
% 89.16/26.89 (((subsetemptysetimpeq) =>
% 89.16/26.89 (((powersetI1) =>
% 89.16/26.89 (((powersetE1) =>
% 89.16/26.89 (((inPowerset) =>
% 89.16/26.89 (((powersetsubset) =>
% 89.16/26.89 (((sepInPowerset) =>
% 89.16/26.89 (((sepSubset) =>
% 89.16/26.89 ((
% 89.16/26.89 (binunionIL) =>
% 89.16/26.89 ((
% 89.16/26.89 (upairset2IR) =>
% 89.16/26.89 ((
% 89.16/26.89 (binunionIR) =>
% 89.16/26.89 ((
% 89.16/26.89 (binunionEcases) =>
% 89.16/26.89 ((
% 89.16/26.89 (binunionE) =>
% 89.16/26.89 ((
% 89.16/26.89 (binunionLsub) =>
% 89.16/26.89 ((
% 89.16/26.89 (binunionRsub) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectI) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectSubset5) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectEL) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectLsub) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectSubset2) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectSubset3) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectER) =>
% 89.16/26.89 ((
% 89.16/26.89 (disjointsetsI1) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectRsub) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectSubset4) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectSubset1) =>
% 89.16/26.89 ((
% 89.16/26.89 (bs114d) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusI) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusEL) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusER) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusSubset2) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusERneg) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusELneg) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusILneg) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusIRneg) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusLsub) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusSubset1) =>
% 89.16/26.89 ((
% 89.16/26.89 (symdiffE) =>
% 89.16/26.89 ((
% 89.16/26.89 (symdiffI1) =>
% 89.16/26.89 ((
% 89.16/26.89 (symdiffI2) =>
% 89.16/26.89 ((
% 89.16/26.89 (symdiffIneg1) =>
% 89.16/26.89 ((
% 89.16/26.89 (symdiffIneg2) =>
% 89.16/26.89 ((
% 89.16/26.89 (secondinupair) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairIL) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairIR) =>
% 89.16/26.89 ((
% 89.16/26.89 (kpairiskpair) =>
% 89.16/26.89 ((
% 89.16/26.89 (kpairp) =>
% 89.16/26.89 ((
% 89.16/26.89 (singletonsubset) =>
% 89.16/26.89 ((
% 89.16/26.89 (singletoninpowerset) =>
% 89.16/26.89 ((
% 89.16/26.89 (singletoninpowunion) =>
% 89.16/26.89 ((
% 89.16/26.89 (upairset2E) =>
% 89.16/26.89 ((
% 89.16/26.89 (upairsubunion) =>
% 89.16/26.89 ((
% 89.16/26.89 (upairinpowunion) =>
% 89.16/26.89 ((
% 89.16/26.89 (ubforcartprodlem1) =>
% 89.16/26.89 ((
% 89.16/26.89 (ubforcartprodlem2) =>
% 89.16/26.89 ((
% 89.16/26.89 (ubforcartprodlem3) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodpairin) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodmempair1) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodmempair) =>
% 89.16/26.89 ((
% 89.16/26.89 (setunionE2) =>
% 89.16/26.89 ((
% 89.16/26.89 (setunionsingleton1) =>
% 89.16/26.89 ((
% 89.16/26.89 (setunionsingleton2) =>
% 89.16/26.89 ((
% 89.16/26.89 (setunionsingleton) =>
% 89.16/26.89 ((
% 89.16/26.89 (singletonprop) =>
% 89.16/26.89 ((
% 89.16/26.89 (ex1E1) =>
% 89.16/26.89 ((
% 89.16/26.89 (ex1I) =>
% 89.16/26.89 ((
% 89.16/26.89 (ex1I2) =>
% 89.16/26.89 ((
% 89.16/26.89 (singletonsuniq) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjL1) =>
% 89.16/26.89 ((
% 89.16/26.89 (kfstsingleton) =>
% 89.16/26.89 ((
% 89.16/26.89 (theprop) =>
% 89.16/26.89 ((
% 89.16/26.89 (kfstpairEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodfstin) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjL2) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjL) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjR11) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjR12) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjR1) =>
% 89.16/26.89 ((
% 89.16/26.89 (upairequniteq) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjR2) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjR) =>
% 89.16/26.89 ((
% 89.16/26.89 (ksndsingleton) =>
% 89.16/26.89 ((
% 89.16/26.89 (ksndpairEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (kpairsurjEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodsndin) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodpairmemEL) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodpairmemER) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodmempaircEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodfstpairEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodsndpairEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodpairsurjEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (dpsetconstrI) =>
% 89.16/26.89 ((
% 89.16/26.89 (dpsetconstrSub) =>
% 89.16/26.89 ((
% 89.16/26.89 (setOfPairsIsBReln) =>
% 89.16/26.89 ((
% 89.16/26.89 (dpsetconstrERa) =>
% 89.16/26.89 ((
% 89.16/26.89 (dpsetconstrEL1) =>
% 89.16/26.89 ((
% 89.16/26.89 (dpsetconstrEL2) =>
% 89.16/26.89 ((
% 89.16/26.89 (dpsetconstrER) =>
% 89.16/26.89 ((
% 89.16/26.89 (funcImageSingleton) =>
% 89.16/26.89 ((
% 89.16/26.89 (apProp) =>
% 89.16/26.89 ((
% 89.16/26.89 (app) =>
% 89.16/26.89 ((
% 89.16/26.89 (infuncsetfunc) =>
% 89.16/26.89 ((
% 89.16/26.89 (ap2p) =>
% 89.16/26.89 ((
% 89.16/26.89 (funcinfuncset) =>
% 89.16/26.89 ((
% 89.16/26.89 (lamProp) =>
% 89.16/26.89 ((
% 89.16/26.89 (lamp) =>
% 89.16/26.89 ((
% 89.16/26.89 (lam2p) =>
% 89.16/26.89 ((
% 89.16/26.89 (brelnall1) =>
% 89.16/26.89 ((
% 89.16/26.89 (brelnall2) =>
% 89.16/26.89 ((
% 89.16/26.89 (!!) @ (
% 89.16/26.89 (('#B') @ (
% 89.16/26.89 !!) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#S') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#S') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 =>))) @
% 89.16/26.89 ex1)))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 !!))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#S') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#B') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#S') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 =>))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#C') @ in)))))))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 !!))))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#C') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#B') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#B') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#S') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 =>))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#C') @ in)))))))))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#S') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#S') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#B'))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 =>))))))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#C') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#B') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#S') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 =>))))))) @
% 89.16/26.89 (
% 89.16/26.89 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.16/26.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl660])).
% 89.16/26.89 thf(zip_derived_cl685, plain,
% 89.16/26.89 (~ (((setadjoin__Cong) =>
% 89.16/26.89 (((powerset__Cong) =>
% 89.16/26.89 (((setunion__Cong) =>
% 89.16/26.89 (((exuEu) =>
% 89.16/26.89 (((descr__Cong) =>
% 89.16/26.89 (((dsetconstr__Cong) =>
% 89.16/26.89 (((subsetI1) =>
% 89.16/26.89 (((eqimpsubset2) =>
% 89.16/26.89 (((eqimpsubset1) =>
% 89.16/26.89 (((subsetI2) =>
% 89.16/26.89 (((emptysetsubset) =>
% 89.16/26.89 (((subsetE) =>
% 89.16/26.89 (((subsetE2) =>
% 89.16/26.89 (((notsubsetI) =>
% 89.16/26.89 (((notequalI1) =>
% 89.16/26.89 (((notequalI2) =>
% 89.16/26.89 (((subsetRefl) =>
% 89.16/26.89 (((subsetTrans) =>
% 89.16/26.89 (((setadjoinSub) =>
% 89.16/26.89 (((setadjoinSub2) =>
% 89.16/26.89 (((subset2powerset) =>
% 89.16/26.89 (((setextsub) =>
% 89.16/26.89 (((subsetemptysetimpeq) =>
% 89.16/26.89 (((powersetI1) =>
% 89.16/26.89 (((powersetE1) =>
% 89.16/26.89 (((inPowerset) =>
% 89.16/26.89 (((powersetsubset) =>
% 89.16/26.89 (((sepInPowerset) =>
% 89.16/26.89 (((sepSubset) =>
% 89.16/26.89 (((binunionIL) =>
% 89.16/26.89 ((
% 89.16/26.89 (upairset2IR) =>
% 89.16/26.89 ((
% 89.16/26.89 (binunionIR) =>
% 89.16/26.89 ((
% 89.16/26.89 (binunionEcases) =>
% 89.16/26.89 ((
% 89.16/26.89 (binunionE) =>
% 89.16/26.89 ((
% 89.16/26.89 (binunionLsub) =>
% 89.16/26.89 ((
% 89.16/26.89 (binunionRsub) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectI) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectSubset5) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectEL) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectLsub) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectSubset2) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectSubset3) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectER) =>
% 89.16/26.89 ((
% 89.16/26.89 (disjointsetsI1) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectRsub) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectSubset4) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectSubset1) =>
% 89.16/26.89 ((
% 89.16/26.89 (bs114d) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusI) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusEL) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusER) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusSubset2) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusERneg) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusELneg) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusILneg) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusIRneg) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusLsub) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusSubset1) =>
% 89.16/26.89 ((
% 89.16/26.89 (symdiffE) =>
% 89.16/26.89 ((
% 89.16/26.89 (symdiffI1) =>
% 89.16/26.89 ((
% 89.16/26.89 (symdiffI2) =>
% 89.16/26.89 ((
% 89.16/26.89 (symdiffIneg1) =>
% 89.16/26.89 ((
% 89.16/26.89 (symdiffIneg2) =>
% 89.16/26.89 ((
% 89.16/26.89 (secondinupair) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairIL) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairIR) =>
% 89.16/26.89 ((
% 89.16/26.89 (kpairiskpair) =>
% 89.16/26.89 ((
% 89.16/26.89 (kpairp) =>
% 89.16/26.89 ((
% 89.16/26.89 (singletonsubset) =>
% 89.16/26.89 ((
% 89.16/26.89 (singletoninpowerset) =>
% 89.16/26.89 ((
% 89.16/26.89 (singletoninpowunion) =>
% 89.16/26.89 ((
% 89.16/26.89 (upairset2E) =>
% 89.16/26.89 ((
% 89.16/26.89 (upairsubunion) =>
% 89.16/26.89 ((
% 89.16/26.89 (upairinpowunion) =>
% 89.16/26.89 ((
% 89.16/26.89 (ubforcartprodlem1) =>
% 89.16/26.89 ((
% 89.16/26.89 (ubforcartprodlem2) =>
% 89.16/26.89 ((
% 89.16/26.89 (ubforcartprodlem3) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodpairin) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodmempair1) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodmempair) =>
% 89.16/26.89 ((
% 89.16/26.89 (setunionE2) =>
% 89.16/26.89 ((
% 89.16/26.89 (setunionsingleton1) =>
% 89.16/26.89 ((
% 89.16/26.89 (setunionsingleton2) =>
% 89.16/26.89 ((
% 89.16/26.89 (setunionsingleton) =>
% 89.16/26.89 ((
% 89.16/26.89 (singletonprop) =>
% 89.16/26.89 ((
% 89.16/26.89 (ex1E1) =>
% 89.16/26.89 ((
% 89.16/26.89 (ex1I) =>
% 89.16/26.89 ((
% 89.16/26.89 (ex1I2) =>
% 89.16/26.89 ((
% 89.16/26.89 (singletonsuniq) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjL1) =>
% 89.16/26.89 ((
% 89.16/26.89 (kfstsingleton) =>
% 89.16/26.89 ((
% 89.16/26.89 (theprop) =>
% 89.16/26.89 ((
% 89.16/26.89 (kfstpairEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodfstin) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjL2) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjL) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjR11) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjR12) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjR1) =>
% 89.16/26.89 ((
% 89.16/26.89 (upairequniteq) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjR2) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjR) =>
% 89.16/26.89 ((
% 89.16/26.89 (ksndsingleton) =>
% 89.16/26.89 ((
% 89.16/26.89 (ksndpairEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (kpairsurjEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodsndin) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodpairmemEL) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodpairmemER) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodmempaircEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodfstpairEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodsndpairEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodpairsurjEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (dpsetconstrI) =>
% 89.16/26.89 ((
% 89.16/26.89 (dpsetconstrSub) =>
% 89.16/26.89 ((
% 89.16/26.89 (setOfPairsIsBReln) =>
% 89.16/26.89 ((
% 89.16/26.89 (dpsetconstrERa) =>
% 89.16/26.89 ((
% 89.16/26.89 (dpsetconstrEL1) =>
% 89.16/26.89 ((
% 89.16/26.89 (dpsetconstrEL2) =>
% 89.16/26.89 ((
% 89.16/26.89 (dpsetconstrER) =>
% 89.16/26.89 ((
% 89.16/26.89 (funcImageSingleton) =>
% 89.16/26.89 ((
% 89.16/26.89 (apProp) =>
% 89.16/26.89 ((
% 89.16/26.89 (app) =>
% 89.16/26.89 ((
% 89.16/26.89 (infuncsetfunc) =>
% 89.16/26.89 ((
% 89.16/26.89 (ap2p) =>
% 89.16/26.89 ((
% 89.16/26.89 (funcinfuncset) =>
% 89.16/26.89 ((
% 89.16/26.89 (lamProp) =>
% 89.16/26.89 ((
% 89.16/26.89 (lamp) =>
% 89.16/26.89 ((
% 89.16/26.89 (lam2p) =>
% 89.16/26.89 ((
% 89.16/26.89 (brelnall1) =>
% 89.16/26.89 ((
% 89.16/26.89 (brelnall2) =>
% 89.16/26.89 ((
% 89.16/26.89 (!!) @ (
% 89.16/26.89 (('#B') @ (
% 89.16/26.89 !!) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#S') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#S') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 =>))) @
% 89.16/26.89 ex1)))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 !!))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#S') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#B') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#S') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 =>))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#C') @ in)))))))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 !!))))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#C') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#B') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#B') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#S') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 =>))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#C') @ in)))))))))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#S') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#S') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#B'))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 =>))))))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#C') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#B') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#S') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 =>))))))) @
% 89.16/26.89 (
% 89.16/26.89 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.16/26.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl672])).
% 89.16/26.89 thf(zip_derived_cl699, plain,
% 89.16/26.89 (~ (((powerset__Cong) =>
% 89.16/26.89 (((setunion__Cong) =>
% 89.16/26.89 (((exuEu) =>
% 89.16/26.89 (((descr__Cong) =>
% 89.16/26.89 (((dsetconstr__Cong) =>
% 89.16/26.89 (((subsetI1) =>
% 89.16/26.89 (((eqimpsubset2) =>
% 89.16/26.89 (((eqimpsubset1) =>
% 89.16/26.89 (((subsetI2) =>
% 89.16/26.89 (((emptysetsubset) =>
% 89.16/26.89 (((subsetE) =>
% 89.16/26.89 (((subsetE2) =>
% 89.16/26.89 (((notsubsetI) =>
% 89.16/26.89 (((notequalI1) =>
% 89.16/26.89 (((notequalI2) =>
% 89.16/26.89 (((subsetRefl) =>
% 89.16/26.89 (((subsetTrans) =>
% 89.16/26.89 (((setadjoinSub) =>
% 89.16/26.89 (((setadjoinSub2) =>
% 89.16/26.89 (((subset2powerset) =>
% 89.16/26.89 (((setextsub) =>
% 89.16/26.89 (((subsetemptysetimpeq) =>
% 89.16/26.89 (((powersetI1) =>
% 89.16/26.89 (((powersetE1) =>
% 89.16/26.89 (((inPowerset) =>
% 89.16/26.89 (((powersetsubset) =>
% 89.16/26.89 (((sepInPowerset) =>
% 89.16/26.89 (((sepSubset) =>
% 89.16/26.89 (((binunionIL) =>
% 89.16/26.89 (((upairset2IR) =>
% 89.16/26.89 ((
% 89.16/26.89 (binunionIR) =>
% 89.16/26.89 ((
% 89.16/26.89 (binunionEcases) =>
% 89.16/26.89 ((
% 89.16/26.89 (binunionE) =>
% 89.16/26.89 ((
% 89.16/26.89 (binunionLsub) =>
% 89.16/26.89 ((
% 89.16/26.89 (binunionRsub) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectI) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectSubset5) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectEL) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectLsub) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectSubset2) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectSubset3) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectER) =>
% 89.16/26.89 ((
% 89.16/26.89 (disjointsetsI1) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectRsub) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectSubset4) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectSubset1) =>
% 89.16/26.89 ((
% 89.16/26.89 (bs114d) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusI) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusEL) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusER) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusSubset2) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusERneg) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusELneg) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusILneg) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusIRneg) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusLsub) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusSubset1) =>
% 89.16/26.89 ((
% 89.16/26.89 (symdiffE) =>
% 89.16/26.89 ((
% 89.16/26.89 (symdiffI1) =>
% 89.16/26.89 ((
% 89.16/26.89 (symdiffI2) =>
% 89.16/26.89 ((
% 89.16/26.89 (symdiffIneg1) =>
% 89.16/26.89 ((
% 89.16/26.89 (symdiffIneg2) =>
% 89.16/26.89 ((
% 89.16/26.89 (secondinupair) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairIL) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairIR) =>
% 89.16/26.89 ((
% 89.16/26.89 (kpairiskpair) =>
% 89.16/26.89 ((
% 89.16/26.89 (kpairp) =>
% 89.16/26.89 ((
% 89.16/26.89 (singletonsubset) =>
% 89.16/26.89 ((
% 89.16/26.89 (singletoninpowerset) =>
% 89.16/26.89 ((
% 89.16/26.89 (singletoninpowunion) =>
% 89.16/26.89 ((
% 89.16/26.89 (upairset2E) =>
% 89.16/26.89 ((
% 89.16/26.89 (upairsubunion) =>
% 89.16/26.89 ((
% 89.16/26.89 (upairinpowunion) =>
% 89.16/26.89 ((
% 89.16/26.89 (ubforcartprodlem1) =>
% 89.16/26.89 ((
% 89.16/26.89 (ubforcartprodlem2) =>
% 89.16/26.89 ((
% 89.16/26.89 (ubforcartprodlem3) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodpairin) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodmempair1) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodmempair) =>
% 89.16/26.89 ((
% 89.16/26.89 (setunionE2) =>
% 89.16/26.89 ((
% 89.16/26.89 (setunionsingleton1) =>
% 89.16/26.89 ((
% 89.16/26.89 (setunionsingleton2) =>
% 89.16/26.89 ((
% 89.16/26.89 (setunionsingleton) =>
% 89.16/26.89 ((
% 89.16/26.89 (singletonprop) =>
% 89.16/26.89 ((
% 89.16/26.89 (ex1E1) =>
% 89.16/26.89 ((
% 89.16/26.89 (ex1I) =>
% 89.16/26.89 ((
% 89.16/26.89 (ex1I2) =>
% 89.16/26.89 ((
% 89.16/26.89 (singletonsuniq) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjL1) =>
% 89.16/26.89 ((
% 89.16/26.89 (kfstsingleton) =>
% 89.16/26.89 ((
% 89.16/26.89 (theprop) =>
% 89.16/26.89 ((
% 89.16/26.89 (kfstpairEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodfstin) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjL2) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjL) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjR11) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjR12) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjR1) =>
% 89.16/26.89 ((
% 89.16/26.89 (upairequniteq) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjR2) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjR) =>
% 89.16/26.89 ((
% 89.16/26.89 (ksndsingleton) =>
% 89.16/26.89 ((
% 89.16/26.89 (ksndpairEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (kpairsurjEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodsndin) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodpairmemEL) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodpairmemER) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodmempaircEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodfstpairEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodsndpairEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodpairsurjEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (dpsetconstrI) =>
% 89.16/26.89 ((
% 89.16/26.89 (dpsetconstrSub) =>
% 89.16/26.89 ((
% 89.16/26.89 (setOfPairsIsBReln) =>
% 89.16/26.89 ((
% 89.16/26.89 (dpsetconstrERa) =>
% 89.16/26.89 ((
% 89.16/26.89 (dpsetconstrEL1) =>
% 89.16/26.89 ((
% 89.16/26.89 (dpsetconstrEL2) =>
% 89.16/26.89 ((
% 89.16/26.89 (dpsetconstrER) =>
% 89.16/26.89 ((
% 89.16/26.89 (funcImageSingleton) =>
% 89.16/26.89 ((
% 89.16/26.89 (apProp) =>
% 89.16/26.89 ((
% 89.16/26.89 (app) =>
% 89.16/26.89 ((
% 89.16/26.89 (infuncsetfunc) =>
% 89.16/26.89 ((
% 89.16/26.89 (ap2p) =>
% 89.16/26.89 ((
% 89.16/26.89 (funcinfuncset) =>
% 89.16/26.89 ((
% 89.16/26.89 (lamProp) =>
% 89.16/26.89 ((
% 89.16/26.89 (lamp) =>
% 89.16/26.89 ((
% 89.16/26.89 (lam2p) =>
% 89.16/26.89 ((
% 89.16/26.89 (brelnall1) =>
% 89.16/26.89 ((
% 89.16/26.89 (brelnall2) =>
% 89.16/26.89 ((
% 89.16/26.89 (!!) @ (
% 89.16/26.89 (('#B') @ (
% 89.16/26.89 !!) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#S') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#S') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 =>))) @
% 89.16/26.89 ex1)))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 !!))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#S') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#B') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#S') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 =>))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#C') @ in)))))))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 !!))))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#C') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#B') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#B') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#S') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 =>))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#C') @ in)))))))))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#S') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#S') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#B'))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 =>))))))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#C') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#B') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#S') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 =>))))))) @
% 89.16/26.89 (
% 89.16/26.89 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.16/26.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl685])).
% 89.16/26.89 thf(zip_derived_cl714, plain,
% 89.16/26.89 (~ (((setunion__Cong) =>
% 89.16/26.89 (((exuEu) =>
% 89.16/26.89 (((descr__Cong) =>
% 89.16/26.89 (((dsetconstr__Cong) =>
% 89.16/26.89 (((subsetI1) =>
% 89.16/26.89 (((eqimpsubset2) =>
% 89.16/26.89 (((eqimpsubset1) =>
% 89.16/26.89 (((subsetI2) =>
% 89.16/26.89 (((emptysetsubset) =>
% 89.16/26.89 (((subsetE) =>
% 89.16/26.89 (((subsetE2) =>
% 89.16/26.89 (((notsubsetI) =>
% 89.16/26.89 (((notequalI1) =>
% 89.16/26.89 (((notequalI2) =>
% 89.16/26.89 (((subsetRefl) =>
% 89.16/26.89 (((subsetTrans) =>
% 89.16/26.89 (((setadjoinSub) =>
% 89.16/26.89 (((setadjoinSub2) =>
% 89.16/26.89 (((subset2powerset) =>
% 89.16/26.89 (((setextsub) =>
% 89.16/26.89 (((subsetemptysetimpeq) =>
% 89.16/26.89 (((powersetI1) =>
% 89.16/26.89 (((powersetE1) =>
% 89.16/26.89 (((inPowerset) =>
% 89.16/26.89 (((powersetsubset) =>
% 89.16/26.89 (((sepInPowerset) =>
% 89.16/26.89 (((sepSubset) =>
% 89.16/26.89 (((binunionIL) =>
% 89.16/26.89 (((upairset2IR) =>
% 89.16/26.89 (((binunionIR) =>
% 89.16/26.89 ((
% 89.16/26.89 (binunionEcases) =>
% 89.16/26.89 ((
% 89.16/26.89 (binunionE) =>
% 89.16/26.89 ((
% 89.16/26.89 (binunionLsub) =>
% 89.16/26.89 ((
% 89.16/26.89 (binunionRsub) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectI) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectSubset5) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectEL) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectLsub) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectSubset2) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectSubset3) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectER) =>
% 89.16/26.89 ((
% 89.16/26.89 (disjointsetsI1) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectRsub) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectSubset4) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectSubset1) =>
% 89.16/26.89 ((
% 89.16/26.89 (bs114d) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusI) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusEL) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusER) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusSubset2) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusERneg) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusELneg) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusILneg) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusIRneg) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusLsub) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusSubset1) =>
% 89.16/26.89 ((
% 89.16/26.89 (symdiffE) =>
% 89.16/26.89 ((
% 89.16/26.89 (symdiffI1) =>
% 89.16/26.89 ((
% 89.16/26.89 (symdiffI2) =>
% 89.16/26.89 ((
% 89.16/26.89 (symdiffIneg1) =>
% 89.16/26.89 ((
% 89.16/26.89 (symdiffIneg2) =>
% 89.16/26.89 ((
% 89.16/26.89 (secondinupair) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairIL) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairIR) =>
% 89.16/26.89 ((
% 89.16/26.89 (kpairiskpair) =>
% 89.16/26.89 ((
% 89.16/26.89 (kpairp) =>
% 89.16/26.89 ((
% 89.16/26.89 (singletonsubset) =>
% 89.16/26.89 ((
% 89.16/26.89 (singletoninpowerset) =>
% 89.16/26.89 ((
% 89.16/26.89 (singletoninpowunion) =>
% 89.16/26.89 ((
% 89.16/26.89 (upairset2E) =>
% 89.16/26.89 ((
% 89.16/26.89 (upairsubunion) =>
% 89.16/26.89 ((
% 89.16/26.89 (upairinpowunion) =>
% 89.16/26.89 ((
% 89.16/26.89 (ubforcartprodlem1) =>
% 89.16/26.89 ((
% 89.16/26.89 (ubforcartprodlem2) =>
% 89.16/26.89 ((
% 89.16/26.89 (ubforcartprodlem3) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodpairin) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodmempair1) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodmempair) =>
% 89.16/26.89 ((
% 89.16/26.89 (setunionE2) =>
% 89.16/26.89 ((
% 89.16/26.89 (setunionsingleton1) =>
% 89.16/26.89 ((
% 89.16/26.89 (setunionsingleton2) =>
% 89.16/26.89 ((
% 89.16/26.89 (setunionsingleton) =>
% 89.16/26.89 ((
% 89.16/26.89 (singletonprop) =>
% 89.16/26.89 ((
% 89.16/26.89 (ex1E1) =>
% 89.16/26.89 ((
% 89.16/26.89 (ex1I) =>
% 89.16/26.89 ((
% 89.16/26.89 (ex1I2) =>
% 89.16/26.89 ((
% 89.16/26.89 (singletonsuniq) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjL1) =>
% 89.16/26.89 ((
% 89.16/26.89 (kfstsingleton) =>
% 89.16/26.89 ((
% 89.16/26.89 (theprop) =>
% 89.16/26.89 ((
% 89.16/26.89 (kfstpairEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodfstin) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjL2) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjL) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjR11) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjR12) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjR1) =>
% 89.16/26.89 ((
% 89.16/26.89 (upairequniteq) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjR2) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjR) =>
% 89.16/26.89 ((
% 89.16/26.89 (ksndsingleton) =>
% 89.16/26.89 ((
% 89.16/26.89 (ksndpairEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (kpairsurjEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodsndin) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodpairmemEL) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodpairmemER) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodmempaircEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodfstpairEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodsndpairEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodpairsurjEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (dpsetconstrI) =>
% 89.16/26.89 ((
% 89.16/26.89 (dpsetconstrSub) =>
% 89.16/26.89 ((
% 89.16/26.89 (setOfPairsIsBReln) =>
% 89.16/26.89 ((
% 89.16/26.89 (dpsetconstrERa) =>
% 89.16/26.89 ((
% 89.16/26.89 (dpsetconstrEL1) =>
% 89.16/26.89 ((
% 89.16/26.89 (dpsetconstrEL2) =>
% 89.16/26.89 ((
% 89.16/26.89 (dpsetconstrER) =>
% 89.16/26.89 ((
% 89.16/26.89 (funcImageSingleton) =>
% 89.16/26.89 ((
% 89.16/26.89 (apProp) =>
% 89.16/26.89 ((
% 89.16/26.89 (app) =>
% 89.16/26.89 ((
% 89.16/26.89 (infuncsetfunc) =>
% 89.16/26.89 ((
% 89.16/26.89 (ap2p) =>
% 89.16/26.89 ((
% 89.16/26.89 (funcinfuncset) =>
% 89.16/26.89 ((
% 89.16/26.89 (lamProp) =>
% 89.16/26.89 ((
% 89.16/26.89 (lamp) =>
% 89.16/26.89 ((
% 89.16/26.89 (lam2p) =>
% 89.16/26.89 ((
% 89.16/26.89 (brelnall1) =>
% 89.16/26.89 ((
% 89.16/26.89 (brelnall2) =>
% 89.16/26.89 ((
% 89.16/26.89 (!!) @ (
% 89.16/26.89 (('#B') @ (
% 89.16/26.89 !!) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#S') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#S') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 =>))) @
% 89.16/26.89 ex1)))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 !!))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#S') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#B') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#S') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 =>))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#C') @ in)))))))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 !!))))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#C') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#B') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#B') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#S') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 =>))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#C') @ in)))))))))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#S') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#S') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#B'))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 =>))))))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#C') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#B') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#S') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 =>))))))) @
% 89.16/26.89 (
% 89.16/26.89 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.16/26.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl699])).
% 89.16/26.89 thf(zip_derived_cl731, plain,
% 89.16/26.89 (~ (((exuEu) =>
% 89.16/26.89 (((descr__Cong) =>
% 89.16/26.89 (((dsetconstr__Cong) =>
% 89.16/26.89 (((subsetI1) =>
% 89.16/26.89 (((eqimpsubset2) =>
% 89.16/26.89 (((eqimpsubset1) =>
% 89.16/26.89 (((subsetI2) =>
% 89.16/26.89 (((emptysetsubset) =>
% 89.16/26.89 (((subsetE) =>
% 89.16/26.89 (((subsetE2) =>
% 89.16/26.89 (((notsubsetI) =>
% 89.16/26.89 (((notequalI1) =>
% 89.16/26.89 (((notequalI2) =>
% 89.16/26.89 (((subsetRefl) =>
% 89.16/26.89 (((subsetTrans) =>
% 89.16/26.89 (((setadjoinSub) =>
% 89.16/26.89 (((setadjoinSub2) =>
% 89.16/26.89 (((subset2powerset) =>
% 89.16/26.89 (((setextsub) =>
% 89.16/26.89 (((subsetemptysetimpeq) =>
% 89.16/26.89 (((powersetI1) =>
% 89.16/26.89 (((powersetE1) =>
% 89.16/26.89 (((inPowerset) =>
% 89.16/26.89 (((powersetsubset) =>
% 89.16/26.89 (((sepInPowerset) =>
% 89.16/26.89 (((sepSubset) =>
% 89.16/26.89 (((binunionIL) =>
% 89.16/26.89 (((upairset2IR) =>
% 89.16/26.89 (((binunionIR) =>
% 89.16/26.89 (((binunionEcases) =>
% 89.16/26.89 ((
% 89.16/26.89 (binunionE) =>
% 89.16/26.89 ((
% 89.16/26.89 (binunionLsub) =>
% 89.16/26.89 ((
% 89.16/26.89 (binunionRsub) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectI) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectSubset5) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectEL) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectLsub) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectSubset2) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectSubset3) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectER) =>
% 89.16/26.89 ((
% 89.16/26.89 (disjointsetsI1) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectRsub) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectSubset4) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectSubset1) =>
% 89.16/26.89 ((
% 89.16/26.89 (bs114d) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusI) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusEL) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusER) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusSubset2) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusERneg) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusELneg) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusILneg) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusIRneg) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusLsub) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusSubset1) =>
% 89.16/26.89 ((
% 89.16/26.89 (symdiffE) =>
% 89.16/26.89 ((
% 89.16/26.89 (symdiffI1) =>
% 89.16/26.89 ((
% 89.16/26.89 (symdiffI2) =>
% 89.16/26.89 ((
% 89.16/26.89 (symdiffIneg1) =>
% 89.16/26.89 ((
% 89.16/26.89 (symdiffIneg2) =>
% 89.16/26.89 ((
% 89.16/26.89 (secondinupair) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairIL) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairIR) =>
% 89.16/26.89 ((
% 89.16/26.89 (kpairiskpair) =>
% 89.16/26.89 ((
% 89.16/26.89 (kpairp) =>
% 89.16/26.89 ((
% 89.16/26.89 (singletonsubset) =>
% 89.16/26.89 ((
% 89.16/26.89 (singletoninpowerset) =>
% 89.16/26.89 ((
% 89.16/26.89 (singletoninpowunion) =>
% 89.16/26.89 ((
% 89.16/26.89 (upairset2E) =>
% 89.16/26.89 ((
% 89.16/26.89 (upairsubunion) =>
% 89.16/26.89 ((
% 89.16/26.89 (upairinpowunion) =>
% 89.16/26.89 ((
% 89.16/26.89 (ubforcartprodlem1) =>
% 89.16/26.89 ((
% 89.16/26.89 (ubforcartprodlem2) =>
% 89.16/26.89 ((
% 89.16/26.89 (ubforcartprodlem3) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodpairin) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodmempair1) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodmempair) =>
% 89.16/26.89 ((
% 89.16/26.89 (setunionE2) =>
% 89.16/26.89 ((
% 89.16/26.89 (setunionsingleton1) =>
% 89.16/26.89 ((
% 89.16/26.89 (setunionsingleton2) =>
% 89.16/26.89 ((
% 89.16/26.89 (setunionsingleton) =>
% 89.16/26.89 ((
% 89.16/26.89 (singletonprop) =>
% 89.16/26.89 ((
% 89.16/26.89 (ex1E1) =>
% 89.16/26.89 ((
% 89.16/26.89 (ex1I) =>
% 89.16/26.89 ((
% 89.16/26.89 (ex1I2) =>
% 89.16/26.89 ((
% 89.16/26.89 (singletonsuniq) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjL1) =>
% 89.16/26.89 ((
% 89.16/26.89 (kfstsingleton) =>
% 89.16/26.89 ((
% 89.16/26.89 (theprop) =>
% 89.16/26.89 ((
% 89.16/26.89 (kfstpairEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodfstin) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjL2) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjL) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjR11) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjR12) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjR1) =>
% 89.16/26.89 ((
% 89.16/26.89 (upairequniteq) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjR2) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjR) =>
% 89.16/26.89 ((
% 89.16/26.89 (ksndsingleton) =>
% 89.16/26.89 ((
% 89.16/26.89 (ksndpairEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (kpairsurjEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodsndin) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodpairmemEL) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodpairmemER) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodmempaircEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodfstpairEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodsndpairEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodpairsurjEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (dpsetconstrI) =>
% 89.16/26.89 ((
% 89.16/26.89 (dpsetconstrSub) =>
% 89.16/26.89 ((
% 89.16/26.89 (setOfPairsIsBReln) =>
% 89.16/26.89 ((
% 89.16/26.89 (dpsetconstrERa) =>
% 89.16/26.89 ((
% 89.16/26.89 (dpsetconstrEL1) =>
% 89.16/26.89 ((
% 89.16/26.89 (dpsetconstrEL2) =>
% 89.16/26.89 ((
% 89.16/26.89 (dpsetconstrER) =>
% 89.16/26.89 ((
% 89.16/26.89 (funcImageSingleton) =>
% 89.16/26.89 ((
% 89.16/26.89 (apProp) =>
% 89.16/26.89 ((
% 89.16/26.89 (app) =>
% 89.16/26.89 ((
% 89.16/26.89 (infuncsetfunc) =>
% 89.16/26.89 ((
% 89.16/26.89 (ap2p) =>
% 89.16/26.89 ((
% 89.16/26.89 (funcinfuncset) =>
% 89.16/26.89 ((
% 89.16/26.89 (lamProp) =>
% 89.16/26.89 ((
% 89.16/26.89 (lamp) =>
% 89.16/26.89 ((
% 89.16/26.89 (lam2p) =>
% 89.16/26.89 ((
% 89.16/26.89 (brelnall1) =>
% 89.16/26.89 ((
% 89.16/26.89 (brelnall2) =>
% 89.16/26.89 ((
% 89.16/26.89 (!!) @ (
% 89.16/26.89 (('#B') @ (
% 89.16/26.89 !!) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#S') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#S') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 =>))) @
% 89.16/26.89 ex1)))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 !!))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#S') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#B') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#S') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 =>))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#C') @ in)))))))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 !!))))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#C') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#B') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#B') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#S') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 =>))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#C') @ in)))))))))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#S') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#S') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#B'))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 =>))))))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#C') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#B') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#S') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 =>))))))) @
% 89.16/26.89 (
% 89.16/26.89 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.16/26.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl714])).
% 89.16/26.89 thf(zip_derived_cl749, plain,
% 89.16/26.89 (~ (((descr__Cong) =>
% 89.16/26.89 (((dsetconstr__Cong) =>
% 89.16/26.89 (((subsetI1) =>
% 89.16/26.89 (((eqimpsubset2) =>
% 89.16/26.89 (((eqimpsubset1) =>
% 89.16/26.89 (((subsetI2) =>
% 89.16/26.89 (((emptysetsubset) =>
% 89.16/26.89 (((subsetE) =>
% 89.16/26.89 (((subsetE2) =>
% 89.16/26.89 (((notsubsetI) =>
% 89.16/26.89 (((notequalI1) =>
% 89.16/26.89 (((notequalI2) =>
% 89.16/26.89 (((subsetRefl) =>
% 89.16/26.89 (((subsetTrans) =>
% 89.16/26.89 (((setadjoinSub) =>
% 89.16/26.89 (((setadjoinSub2) =>
% 89.16/26.89 (((subset2powerset) =>
% 89.16/26.89 (((setextsub) =>
% 89.16/26.89 (((subsetemptysetimpeq) =>
% 89.16/26.89 (((powersetI1) =>
% 89.16/26.89 (((powersetE1) =>
% 89.16/26.89 (((inPowerset) =>
% 89.16/26.89 (((powersetsubset) =>
% 89.16/26.89 (((sepInPowerset) =>
% 89.16/26.89 (((sepSubset) =>
% 89.16/26.89 (((binunionIL) =>
% 89.16/26.89 (((upairset2IR) =>
% 89.16/26.89 (((binunionIR) =>
% 89.16/26.89 (((binunionEcases) =>
% 89.16/26.89 (((binunionE) =>
% 89.16/26.89 ((
% 89.16/26.89 (binunionLsub) =>
% 89.16/26.89 ((
% 89.16/26.89 (binunionRsub) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectI) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectSubset5) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectEL) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectLsub) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectSubset2) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectSubset3) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectER) =>
% 89.16/26.89 ((
% 89.16/26.89 (disjointsetsI1) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectRsub) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectSubset4) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectSubset1) =>
% 89.16/26.89 ((
% 89.16/26.89 (bs114d) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusI) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusEL) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusER) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusSubset2) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusERneg) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusELneg) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusILneg) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusIRneg) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusLsub) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusSubset1) =>
% 89.16/26.89 ((
% 89.16/26.89 (symdiffE) =>
% 89.16/26.89 ((
% 89.16/26.89 (symdiffI1) =>
% 89.16/26.89 ((
% 89.16/26.89 (symdiffI2) =>
% 89.16/26.89 ((
% 89.16/26.89 (symdiffIneg1) =>
% 89.16/26.89 ((
% 89.16/26.89 (symdiffIneg2) =>
% 89.16/26.89 ((
% 89.16/26.89 (secondinupair) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairIL) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairIR) =>
% 89.16/26.89 ((
% 89.16/26.89 (kpairiskpair) =>
% 89.16/26.89 ((
% 89.16/26.89 (kpairp) =>
% 89.16/26.89 ((
% 89.16/26.89 (singletonsubset) =>
% 89.16/26.89 ((
% 89.16/26.89 (singletoninpowerset) =>
% 89.16/26.89 ((
% 89.16/26.89 (singletoninpowunion) =>
% 89.16/26.89 ((
% 89.16/26.89 (upairset2E) =>
% 89.16/26.89 ((
% 89.16/26.89 (upairsubunion) =>
% 89.16/26.89 ((
% 89.16/26.89 (upairinpowunion) =>
% 89.16/26.89 ((
% 89.16/26.89 (ubforcartprodlem1) =>
% 89.16/26.89 ((
% 89.16/26.89 (ubforcartprodlem2) =>
% 89.16/26.89 ((
% 89.16/26.89 (ubforcartprodlem3) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodpairin) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodmempair1) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodmempair) =>
% 89.16/26.89 ((
% 89.16/26.89 (setunionE2) =>
% 89.16/26.89 ((
% 89.16/26.89 (setunionsingleton1) =>
% 89.16/26.89 ((
% 89.16/26.89 (setunionsingleton2) =>
% 89.16/26.89 ((
% 89.16/26.89 (setunionsingleton) =>
% 89.16/26.89 ((
% 89.16/26.89 (singletonprop) =>
% 89.16/26.89 ((
% 89.16/26.89 (ex1E1) =>
% 89.16/26.89 ((
% 89.16/26.89 (ex1I) =>
% 89.16/26.89 ((
% 89.16/26.89 (ex1I2) =>
% 89.16/26.89 ((
% 89.16/26.89 (singletonsuniq) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjL1) =>
% 89.16/26.89 ((
% 89.16/26.89 (kfstsingleton) =>
% 89.16/26.89 ((
% 89.16/26.89 (theprop) =>
% 89.16/26.89 ((
% 89.16/26.89 (kfstpairEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodfstin) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjL2) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjL) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjR11) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjR12) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjR1) =>
% 89.16/26.89 ((
% 89.16/26.89 (upairequniteq) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjR2) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjR) =>
% 89.16/26.89 ((
% 89.16/26.89 (ksndsingleton) =>
% 89.16/26.89 ((
% 89.16/26.89 (ksndpairEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (kpairsurjEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodsndin) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodpairmemEL) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodpairmemER) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodmempaircEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodfstpairEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodsndpairEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodpairsurjEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (dpsetconstrI) =>
% 89.16/26.89 ((
% 89.16/26.89 (dpsetconstrSub) =>
% 89.16/26.89 ((
% 89.16/26.89 (setOfPairsIsBReln) =>
% 89.16/26.89 ((
% 89.16/26.89 (dpsetconstrERa) =>
% 89.16/26.89 ((
% 89.16/26.89 (dpsetconstrEL1) =>
% 89.16/26.89 ((
% 89.16/26.89 (dpsetconstrEL2) =>
% 89.16/26.89 ((
% 89.16/26.89 (dpsetconstrER) =>
% 89.16/26.89 ((
% 89.16/26.89 (funcImageSingleton) =>
% 89.16/26.89 ((
% 89.16/26.89 (apProp) =>
% 89.16/26.89 ((
% 89.16/26.89 (app) =>
% 89.16/26.89 ((
% 89.16/26.89 (infuncsetfunc) =>
% 89.16/26.89 ((
% 89.16/26.89 (ap2p) =>
% 89.16/26.89 ((
% 89.16/26.89 (funcinfuncset) =>
% 89.16/26.89 ((
% 89.16/26.89 (lamProp) =>
% 89.16/26.89 ((
% 89.16/26.89 (lamp) =>
% 89.16/26.89 ((
% 89.16/26.89 (lam2p) =>
% 89.16/26.89 ((
% 89.16/26.89 (brelnall1) =>
% 89.16/26.89 ((
% 89.16/26.89 (brelnall2) =>
% 89.16/26.89 ((
% 89.16/26.89 (!!) @ (
% 89.16/26.89 (('#B') @ (
% 89.16/26.89 !!) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#S') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#S') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 =>))) @
% 89.16/26.89 ex1)))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 !!))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#S') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#B') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#S') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 =>))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#C') @ in)))))))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 !!))))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#C') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#B') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#B') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#S') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 =>))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#C') @ in)))))))))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#S') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#S') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#B'))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 =>))))))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#C') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#B') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#S') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 =>))))))) @
% 89.16/26.89 (
% 89.16/26.89 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.16/26.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl731])).
% 89.16/26.89 thf(zip_derived_cl769, plain,
% 89.16/26.89 (~ (((dsetconstr__Cong) =>
% 89.16/26.89 (((subsetI1) =>
% 89.16/26.89 (((eqimpsubset2) =>
% 89.16/26.89 (((eqimpsubset1) =>
% 89.16/26.89 (((subsetI2) =>
% 89.16/26.89 (((emptysetsubset) =>
% 89.16/26.89 (((subsetE) =>
% 89.16/26.89 (((subsetE2) =>
% 89.16/26.89 (((notsubsetI) =>
% 89.16/26.89 (((notequalI1) =>
% 89.16/26.89 (((notequalI2) =>
% 89.16/26.89 (((subsetRefl) =>
% 89.16/26.89 (((subsetTrans) =>
% 89.16/26.89 (((setadjoinSub) =>
% 89.16/26.89 (((setadjoinSub2) =>
% 89.16/26.89 (((subset2powerset) =>
% 89.16/26.89 (((setextsub) =>
% 89.16/26.89 (((subsetemptysetimpeq) =>
% 89.16/26.89 (((powersetI1) =>
% 89.16/26.89 (((powersetE1) =>
% 89.16/26.89 (((inPowerset) =>
% 89.16/26.89 (((powersetsubset) =>
% 89.16/26.89 (((sepInPowerset) =>
% 89.16/26.89 (((sepSubset) =>
% 89.16/26.89 (((binunionIL) =>
% 89.16/26.89 (((upairset2IR) =>
% 89.16/26.89 (((binunionIR) =>
% 89.16/26.89 (((binunionEcases) =>
% 89.16/26.89 (((binunionE) =>
% 89.16/26.89 (((binunionLsub) =>
% 89.16/26.89 ((
% 89.16/26.89 (binunionRsub) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectI) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectSubset5) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectEL) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectLsub) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectSubset2) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectSubset3) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectER) =>
% 89.16/26.89 ((
% 89.16/26.89 (disjointsetsI1) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectRsub) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectSubset4) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectSubset1) =>
% 89.16/26.89 ((
% 89.16/26.89 (bs114d) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusI) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusEL) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusER) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusSubset2) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusERneg) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusELneg) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusILneg) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusIRneg) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusLsub) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusSubset1) =>
% 89.16/26.89 ((
% 89.16/26.89 (symdiffE) =>
% 89.16/26.89 ((
% 89.16/26.89 (symdiffI1) =>
% 89.16/26.89 ((
% 89.16/26.89 (symdiffI2) =>
% 89.16/26.89 ((
% 89.16/26.89 (symdiffIneg1) =>
% 89.16/26.89 ((
% 89.16/26.89 (symdiffIneg2) =>
% 89.16/26.89 ((
% 89.16/26.89 (secondinupair) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairIL) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairIR) =>
% 89.16/26.89 ((
% 89.16/26.89 (kpairiskpair) =>
% 89.16/26.89 ((
% 89.16/26.89 (kpairp) =>
% 89.16/26.89 ((
% 89.16/26.89 (singletonsubset) =>
% 89.16/26.89 ((
% 89.16/26.89 (singletoninpowerset) =>
% 89.16/26.89 ((
% 89.16/26.89 (singletoninpowunion) =>
% 89.16/26.89 ((
% 89.16/26.89 (upairset2E) =>
% 89.16/26.89 ((
% 89.16/26.89 (upairsubunion) =>
% 89.16/26.89 ((
% 89.16/26.89 (upairinpowunion) =>
% 89.16/26.89 ((
% 89.16/26.89 (ubforcartprodlem1) =>
% 89.16/26.89 ((
% 89.16/26.89 (ubforcartprodlem2) =>
% 89.16/26.89 ((
% 89.16/26.89 (ubforcartprodlem3) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodpairin) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodmempair1) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodmempair) =>
% 89.16/26.89 ((
% 89.16/26.89 (setunionE2) =>
% 89.16/26.89 ((
% 89.16/26.89 (setunionsingleton1) =>
% 89.16/26.89 ((
% 89.16/26.89 (setunionsingleton2) =>
% 89.16/26.89 ((
% 89.16/26.89 (setunionsingleton) =>
% 89.16/26.89 ((
% 89.16/26.89 (singletonprop) =>
% 89.16/26.89 ((
% 89.16/26.89 (ex1E1) =>
% 89.16/26.89 ((
% 89.16/26.89 (ex1I) =>
% 89.16/26.89 ((
% 89.16/26.89 (ex1I2) =>
% 89.16/26.89 ((
% 89.16/26.89 (singletonsuniq) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjL1) =>
% 89.16/26.89 ((
% 89.16/26.89 (kfstsingleton) =>
% 89.16/26.89 ((
% 89.16/26.89 (theprop) =>
% 89.16/26.89 ((
% 89.16/26.89 (kfstpairEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodfstin) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjL2) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjL) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjR11) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjR12) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjR1) =>
% 89.16/26.89 ((
% 89.16/26.89 (upairequniteq) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjR2) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjR) =>
% 89.16/26.89 ((
% 89.16/26.89 (ksndsingleton) =>
% 89.16/26.89 ((
% 89.16/26.89 (ksndpairEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (kpairsurjEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodsndin) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodpairmemEL) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodpairmemER) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodmempaircEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodfstpairEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodsndpairEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodpairsurjEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (dpsetconstrI) =>
% 89.16/26.89 ((
% 89.16/26.89 (dpsetconstrSub) =>
% 89.16/26.89 ((
% 89.16/26.89 (setOfPairsIsBReln) =>
% 89.16/26.89 ((
% 89.16/26.89 (dpsetconstrERa) =>
% 89.16/26.89 ((
% 89.16/26.89 (dpsetconstrEL1) =>
% 89.16/26.89 ((
% 89.16/26.89 (dpsetconstrEL2) =>
% 89.16/26.89 ((
% 89.16/26.89 (dpsetconstrER) =>
% 89.16/26.89 ((
% 89.16/26.89 (funcImageSingleton) =>
% 89.16/26.89 ((
% 89.16/26.89 (apProp) =>
% 89.16/26.89 ((
% 89.16/26.89 (app) =>
% 89.16/26.89 ((
% 89.16/26.89 (infuncsetfunc) =>
% 89.16/26.89 ((
% 89.16/26.89 (ap2p) =>
% 89.16/26.89 ((
% 89.16/26.89 (funcinfuncset) =>
% 89.16/26.89 ((
% 89.16/26.89 (lamProp) =>
% 89.16/26.89 ((
% 89.16/26.89 (lamp) =>
% 89.16/26.89 ((
% 89.16/26.89 (lam2p) =>
% 89.16/26.89 ((
% 89.16/26.89 (brelnall1) =>
% 89.16/26.89 ((
% 89.16/26.89 (brelnall2) =>
% 89.16/26.89 ((
% 89.16/26.89 (!!) @ (
% 89.16/26.89 (('#B') @ (
% 89.16/26.89 !!) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#S') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#S') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 =>))) @
% 89.16/26.89 ex1)))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 !!))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#S') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#B') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#S') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 =>))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#C') @ in)))))))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 !!))))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#C') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#B') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#B') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#S') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 =>))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#C') @ in)))))))))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#S') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#S') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#B'))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 =>))))))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#C') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#B') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#S') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 =>))))))) @
% 89.16/26.89 (
% 89.16/26.89 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.16/26.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl749])).
% 89.16/26.89 thf(zip_derived_cl789, plain,
% 89.16/26.89 (~ (((subsetI1) =>
% 89.16/26.89 (((eqimpsubset2) =>
% 89.16/26.89 (((eqimpsubset1) =>
% 89.16/26.89 (((subsetI2) =>
% 89.16/26.89 (((emptysetsubset) =>
% 89.16/26.89 (((subsetE) =>
% 89.16/26.89 (((subsetE2) =>
% 89.16/26.89 (((notsubsetI) =>
% 89.16/26.89 (((notequalI1) =>
% 89.16/26.89 (((notequalI2) =>
% 89.16/26.89 (((subsetRefl) =>
% 89.16/26.89 (((subsetTrans) =>
% 89.16/26.89 (((setadjoinSub) =>
% 89.16/26.89 (((setadjoinSub2) =>
% 89.16/26.89 (((subset2powerset) =>
% 89.16/26.89 (((setextsub) =>
% 89.16/26.89 (((subsetemptysetimpeq) =>
% 89.16/26.89 (((powersetI1) =>
% 89.16/26.89 (((powersetE1) =>
% 89.16/26.89 (((inPowerset) =>
% 89.16/26.89 (((powersetsubset) =>
% 89.16/26.89 (((sepInPowerset) =>
% 89.16/26.89 (((sepSubset) =>
% 89.16/26.89 (((binunionIL) =>
% 89.16/26.89 (((upairset2IR) =>
% 89.16/26.89 (((binunionIR) =>
% 89.16/26.89 (((binunionEcases) =>
% 89.16/26.89 (((binunionE) =>
% 89.16/26.89 (((binunionLsub) =>
% 89.16/26.89 (((binunionRsub) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectI) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectSubset5) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectEL) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectLsub) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectSubset2) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectSubset3) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectER) =>
% 89.16/26.89 ((
% 89.16/26.89 (disjointsetsI1) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectRsub) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectSubset4) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectSubset1) =>
% 89.16/26.89 ((
% 89.16/26.89 (bs114d) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusI) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusEL) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusER) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusSubset2) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusERneg) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusELneg) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusILneg) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusIRneg) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusLsub) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusSubset1) =>
% 89.16/26.89 ((
% 89.16/26.89 (symdiffE) =>
% 89.16/26.89 ((
% 89.16/26.89 (symdiffI1) =>
% 89.16/26.89 ((
% 89.16/26.89 (symdiffI2) =>
% 89.16/26.89 ((
% 89.16/26.89 (symdiffIneg1) =>
% 89.16/26.89 ((
% 89.16/26.89 (symdiffIneg2) =>
% 89.16/26.89 ((
% 89.16/26.89 (secondinupair) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairIL) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairIR) =>
% 89.16/26.89 ((
% 89.16/26.89 (kpairiskpair) =>
% 89.16/26.89 ((
% 89.16/26.89 (kpairp) =>
% 89.16/26.89 ((
% 89.16/26.89 (singletonsubset) =>
% 89.16/26.89 ((
% 89.16/26.89 (singletoninpowerset) =>
% 89.16/26.89 ((
% 89.16/26.89 (singletoninpowunion) =>
% 89.16/26.89 ((
% 89.16/26.89 (upairset2E) =>
% 89.16/26.89 ((
% 89.16/26.89 (upairsubunion) =>
% 89.16/26.89 ((
% 89.16/26.89 (upairinpowunion) =>
% 89.16/26.89 ((
% 89.16/26.89 (ubforcartprodlem1) =>
% 89.16/26.89 ((
% 89.16/26.89 (ubforcartprodlem2) =>
% 89.16/26.89 ((
% 89.16/26.89 (ubforcartprodlem3) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodpairin) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodmempair1) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodmempair) =>
% 89.16/26.89 ((
% 89.16/26.89 (setunionE2) =>
% 89.16/26.89 ((
% 89.16/26.89 (setunionsingleton1) =>
% 89.16/26.89 ((
% 89.16/26.89 (setunionsingleton2) =>
% 89.16/26.89 ((
% 89.16/26.89 (setunionsingleton) =>
% 89.16/26.89 ((
% 89.16/26.89 (singletonprop) =>
% 89.16/26.89 ((
% 89.16/26.89 (ex1E1) =>
% 89.16/26.89 ((
% 89.16/26.89 (ex1I) =>
% 89.16/26.89 ((
% 89.16/26.89 (ex1I2) =>
% 89.16/26.89 ((
% 89.16/26.89 (singletonsuniq) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjL1) =>
% 89.16/26.89 ((
% 89.16/26.89 (kfstsingleton) =>
% 89.16/26.89 ((
% 89.16/26.89 (theprop) =>
% 89.16/26.89 ((
% 89.16/26.89 (kfstpairEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodfstin) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjL2) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjL) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjR11) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjR12) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjR1) =>
% 89.16/26.89 ((
% 89.16/26.89 (upairequniteq) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjR2) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjR) =>
% 89.16/26.89 ((
% 89.16/26.89 (ksndsingleton) =>
% 89.16/26.89 ((
% 89.16/26.89 (ksndpairEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (kpairsurjEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodsndin) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodpairmemEL) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodpairmemER) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodmempaircEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodfstpairEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodsndpairEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodpairsurjEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (dpsetconstrI) =>
% 89.16/26.89 ((
% 89.16/26.89 (dpsetconstrSub) =>
% 89.16/26.89 ((
% 89.16/26.89 (setOfPairsIsBReln) =>
% 89.16/26.89 ((
% 89.16/26.89 (dpsetconstrERa) =>
% 89.16/26.89 ((
% 89.16/26.89 (dpsetconstrEL1) =>
% 89.16/26.89 ((
% 89.16/26.89 (dpsetconstrEL2) =>
% 89.16/26.89 ((
% 89.16/26.89 (dpsetconstrER) =>
% 89.16/26.89 ((
% 89.16/26.89 (funcImageSingleton) =>
% 89.16/26.89 ((
% 89.16/26.89 (apProp) =>
% 89.16/26.89 ((
% 89.16/26.89 (app) =>
% 89.16/26.89 ((
% 89.16/26.89 (infuncsetfunc) =>
% 89.16/26.89 ((
% 89.16/26.89 (ap2p) =>
% 89.16/26.89 ((
% 89.16/26.89 (funcinfuncset) =>
% 89.16/26.89 ((
% 89.16/26.89 (lamProp) =>
% 89.16/26.89 ((
% 89.16/26.89 (lamp) =>
% 89.16/26.89 ((
% 89.16/26.89 (lam2p) =>
% 89.16/26.89 ((
% 89.16/26.89 (brelnall1) =>
% 89.16/26.89 ((
% 89.16/26.89 (brelnall2) =>
% 89.16/26.89 ((
% 89.16/26.89 (!!) @ (
% 89.16/26.89 (('#B') @ (
% 89.16/26.89 !!) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#S') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#S') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 =>))) @
% 89.16/26.89 ex1)))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 !!))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#S') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#B') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#S') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 =>))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#C') @ in)))))))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 !!))))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#C') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#B') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#B') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#S') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 =>))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#C') @ in)))))))))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#S') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#S') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#B'))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 =>))))))) @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#C') @ (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#B') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 '#S') @
% 89.16/26.89 (
% 89.16/26.89 (
% 89.16/26.89 ('#B') @ (
% 89.16/26.89 =>))))))) @
% 89.16/26.89 (
% 89.16/26.89 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.16/26.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl769])).
% 89.16/26.89 thf(zip_derived_cl807, plain,
% 89.16/26.89 (~ (((eqimpsubset2) =>
% 89.16/26.89 (((eqimpsubset1) =>
% 89.16/26.89 (((subsetI2) =>
% 89.16/26.89 (((emptysetsubset) =>
% 89.16/26.89 (((subsetE) =>
% 89.16/26.89 (((subsetE2) =>
% 89.16/26.89 (((notsubsetI) =>
% 89.16/26.89 (((notequalI1) =>
% 89.16/26.89 (((notequalI2) =>
% 89.16/26.89 (((subsetRefl) =>
% 89.16/26.89 (((subsetTrans) =>
% 89.16/26.89 (((setadjoinSub) =>
% 89.16/26.89 (((setadjoinSub2) =>
% 89.16/26.89 (((subset2powerset) =>
% 89.16/26.89 (((setextsub) =>
% 89.16/26.89 (((subsetemptysetimpeq) =>
% 89.16/26.89 (((powersetI1) =>
% 89.16/26.89 (((powersetE1) =>
% 89.16/26.89 (((inPowerset) =>
% 89.16/26.89 (((powersetsubset) =>
% 89.16/26.89 (((sepInPowerset) =>
% 89.16/26.89 (((sepSubset) =>
% 89.16/26.89 (((binunionIL) =>
% 89.16/26.89 (((upairset2IR) =>
% 89.16/26.89 (((binunionIR) =>
% 89.16/26.89 (((binunionEcases) =>
% 89.16/26.89 (((binunionE) =>
% 89.16/26.89 (((binunionLsub) =>
% 89.16/26.89 (((binunionRsub) =>
% 89.16/26.89 (((binintersectI) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectSubset5) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectEL) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectLsub) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectSubset2) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectSubset3) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectER) =>
% 89.16/26.89 ((
% 89.16/26.89 (disjointsetsI1) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectRsub) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectSubset4) =>
% 89.16/26.89 ((
% 89.16/26.89 (binintersectSubset1) =>
% 89.16/26.89 ((
% 89.16/26.89 (bs114d) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusI) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusEL) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusER) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusSubset2) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusERneg) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusELneg) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusILneg) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusIRneg) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusLsub) =>
% 89.16/26.89 ((
% 89.16/26.89 (setminusSubset1) =>
% 89.16/26.89 ((
% 89.16/26.89 (symdiffE) =>
% 89.16/26.89 ((
% 89.16/26.89 (symdiffI1) =>
% 89.16/26.89 ((
% 89.16/26.89 (symdiffI2) =>
% 89.16/26.89 ((
% 89.16/26.89 (symdiffIneg1) =>
% 89.16/26.89 ((
% 89.16/26.89 (symdiffIneg2) =>
% 89.16/26.89 ((
% 89.16/26.89 (secondinupair) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairIL) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairIR) =>
% 89.16/26.89 ((
% 89.16/26.89 (kpairiskpair) =>
% 89.16/26.89 ((
% 89.16/26.89 (kpairp) =>
% 89.16/26.89 ((
% 89.16/26.89 (singletonsubset) =>
% 89.16/26.89 ((
% 89.16/26.89 (singletoninpowerset) =>
% 89.16/26.89 ((
% 89.16/26.89 (singletoninpowunion) =>
% 89.16/26.89 ((
% 89.16/26.89 (upairset2E) =>
% 89.16/26.89 ((
% 89.16/26.89 (upairsubunion) =>
% 89.16/26.89 ((
% 89.16/26.89 (upairinpowunion) =>
% 89.16/26.89 ((
% 89.16/26.89 (ubforcartprodlem1) =>
% 89.16/26.89 ((
% 89.16/26.89 (ubforcartprodlem2) =>
% 89.16/26.89 ((
% 89.16/26.89 (ubforcartprodlem3) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodpairin) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodmempair1) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodmempair) =>
% 89.16/26.89 ((
% 89.16/26.89 (setunionE2) =>
% 89.16/26.89 ((
% 89.16/26.89 (setunionsingleton1) =>
% 89.16/26.89 ((
% 89.16/26.89 (setunionsingleton2) =>
% 89.16/26.89 ((
% 89.16/26.89 (setunionsingleton) =>
% 89.16/26.89 ((
% 89.16/26.89 (singletonprop) =>
% 89.16/26.89 ((
% 89.16/26.89 (ex1E1) =>
% 89.16/26.89 ((
% 89.16/26.89 (ex1I) =>
% 89.16/26.89 ((
% 89.16/26.89 (ex1I2) =>
% 89.16/26.89 ((
% 89.16/26.89 (singletonsuniq) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjL1) =>
% 89.16/26.89 ((
% 89.16/26.89 (kfstsingleton) =>
% 89.16/26.89 ((
% 89.16/26.89 (theprop) =>
% 89.16/26.89 ((
% 89.16/26.89 (kfstpairEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodfstin) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjL2) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjL) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjR11) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjR12) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjR1) =>
% 89.16/26.89 ((
% 89.16/26.89 (upairequniteq) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjR2) =>
% 89.16/26.89 ((
% 89.16/26.89 (setukpairinjR) =>
% 89.16/26.89 ((
% 89.16/26.89 (ksndsingleton) =>
% 89.16/26.89 ((
% 89.16/26.89 (ksndpairEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (kpairsurjEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodsndin) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodpairmemEL) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodpairmemER) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodmempaircEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodfstpairEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodsndpairEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (cartprodpairsurjEq) =>
% 89.16/26.89 ((
% 89.16/26.89 (dpsetconstrI) =>
% 89.16/26.89 ((
% 89.16/26.89 (dpsetconstrSub) =>
% 89.16/26.89 ((
% 89.16/26.89 (setOfPairsIsBReln) =>
% 89.16/26.89 ((
% 89.16/26.89 (dpsetconstrERa) =>
% 89.16/26.89 ((
% 89.16/26.89 (dpsetconstrEL1) =>
% 89.16/26.89 ((
% 89.16/26.89 (dpsetconstrEL2) =>
% 89.16/26.89 ((
% 89.16/26.89 (dpsetconstrER) =>
% 89.16/26.89 ((
% 89.16/26.89 (funcImageSingleton) =>
% 89.16/26.89 ((
% 89.16/26.89 (apProp) =>
% 89.16/26.89 ((
% 89.16/26.89 (app) =>
% 89.16/26.89 ((
% 89.16/26.89 (infuncsetfunc) =>
% 89.16/26.89 ((
% 89.16/26.89 (ap2p) =>
% 89.16/26.89 ((
% 89.16/26.89 (funcinfuncset) =>
% 89.16/26.89 ((
% 89.16/26.89 (lamProp) =>
% 89.16/26.90 ((
% 89.16/26.90 (lamp) =>
% 89.16/26.90 ((
% 89.16/26.90 (lam2p) =>
% 89.16/26.90 ((
% 89.16/26.90 (brelnall1) =>
% 89.16/26.90 ((
% 89.16/26.90 (brelnall2) =>
% 89.16/26.90 ((
% 89.16/26.90 (!!) @ (
% 89.16/26.90 (('#B') @ (
% 89.16/26.90 !!) @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#S') @ (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 '#S') @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 =>))) @
% 89.16/26.90 ex1)))) @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 !!))) @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#S') @ (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 '#B') @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 '#S') @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 =>))) @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#C') @ in)))))))) @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 !!))))) @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#C') @ (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 '#B') @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 '#B') @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 '#S') @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 =>))) @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#C') @ in)))))))))) @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#S') @ (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 '#S') @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 '#B'))) @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 =>))))))) @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#C') @ (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 '#B') @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 '#S') @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 =>))))))) @
% 89.16/26.90 (
% 89.16/26.90 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.16/26.90 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl789])).
% 89.16/26.90 thf(zip_derived_cl824, plain,
% 89.16/26.90 (~ (((eqimpsubset1) =>
% 89.16/26.90 (((subsetI2) =>
% 89.16/26.90 (((emptysetsubset) =>
% 89.16/26.90 (((subsetE) =>
% 89.16/26.90 (((subsetE2) =>
% 89.16/26.90 (((notsubsetI) =>
% 89.16/26.90 (((notequalI1) =>
% 89.16/26.90 (((notequalI2) =>
% 89.16/26.90 (((subsetRefl) =>
% 89.16/26.90 (((subsetTrans) =>
% 89.16/26.90 (((setadjoinSub) =>
% 89.16/26.90 (((setadjoinSub2) =>
% 89.16/26.90 (((subset2powerset) =>
% 89.16/26.90 (((setextsub) =>
% 89.16/26.90 (((subsetemptysetimpeq) =>
% 89.16/26.90 (((powersetI1) =>
% 89.16/26.90 (((powersetE1) =>
% 89.16/26.90 (((inPowerset) =>
% 89.16/26.90 (((powersetsubset) =>
% 89.16/26.90 (((sepInPowerset) =>
% 89.16/26.90 (((sepSubset) =>
% 89.16/26.90 (((binunionIL) =>
% 89.16/26.90 (((upairset2IR) =>
% 89.16/26.90 (((binunionIR) =>
% 89.16/26.90 (((binunionEcases) =>
% 89.16/26.90 (((binunionE) =>
% 89.16/26.90 (((binunionLsub) =>
% 89.16/26.90 (((binunionRsub) =>
% 89.16/26.90 (((binintersectI) =>
% 89.16/26.90 (((binintersectSubset5) =>
% 89.16/26.90 ((
% 89.16/26.90 (binintersectEL) =>
% 89.16/26.90 ((
% 89.16/26.90 (binintersectLsub) =>
% 89.16/26.90 ((
% 89.16/26.90 (binintersectSubset2) =>
% 89.16/26.90 ((
% 89.16/26.90 (binintersectSubset3) =>
% 89.16/26.90 ((
% 89.16/26.90 (binintersectER) =>
% 89.16/26.90 ((
% 89.16/26.90 (disjointsetsI1) =>
% 89.16/26.90 ((
% 89.16/26.90 (binintersectRsub) =>
% 89.16/26.90 ((
% 89.16/26.90 (binintersectSubset4) =>
% 89.16/26.90 ((
% 89.16/26.90 (binintersectSubset1) =>
% 89.16/26.90 ((
% 89.16/26.90 (bs114d) =>
% 89.16/26.90 ((
% 89.16/26.90 (setminusI) =>
% 89.16/26.90 ((
% 89.16/26.90 (setminusEL) =>
% 89.16/26.90 ((
% 89.16/26.90 (setminusER) =>
% 89.16/26.90 ((
% 89.16/26.90 (setminusSubset2) =>
% 89.16/26.90 ((
% 89.16/26.90 (setminusERneg) =>
% 89.16/26.90 ((
% 89.16/26.90 (setminusELneg) =>
% 89.16/26.90 ((
% 89.16/26.90 (setminusILneg) =>
% 89.16/26.90 ((
% 89.16/26.90 (setminusIRneg) =>
% 89.16/26.90 ((
% 89.16/26.90 (setminusLsub) =>
% 89.16/26.90 ((
% 89.16/26.90 (setminusSubset1) =>
% 89.16/26.90 ((
% 89.16/26.90 (symdiffE) =>
% 89.16/26.90 ((
% 89.16/26.90 (symdiffI1) =>
% 89.16/26.90 ((
% 89.16/26.90 (symdiffI2) =>
% 89.16/26.90 ((
% 89.16/26.90 (symdiffIneg1) =>
% 89.16/26.90 ((
% 89.16/26.90 (symdiffIneg2) =>
% 89.16/26.90 ((
% 89.16/26.90 (secondinupair) =>
% 89.16/26.90 ((
% 89.16/26.90 (setukpairIL) =>
% 89.16/26.90 ((
% 89.16/26.90 (setukpairIR) =>
% 89.16/26.90 ((
% 89.16/26.90 (kpairiskpair) =>
% 89.16/26.90 ((
% 89.16/26.90 (kpairp) =>
% 89.16/26.90 ((
% 89.16/26.90 (singletonsubset) =>
% 89.16/26.90 ((
% 89.16/26.90 (singletoninpowerset) =>
% 89.16/26.90 ((
% 89.16/26.90 (singletoninpowunion) =>
% 89.16/26.90 ((
% 89.16/26.90 (upairset2E) =>
% 89.16/26.90 ((
% 89.16/26.90 (upairsubunion) =>
% 89.16/26.90 ((
% 89.16/26.90 (upairinpowunion) =>
% 89.16/26.90 ((
% 89.16/26.90 (ubforcartprodlem1) =>
% 89.16/26.90 ((
% 89.16/26.90 (ubforcartprodlem2) =>
% 89.16/26.90 ((
% 89.16/26.90 (ubforcartprodlem3) =>
% 89.16/26.90 ((
% 89.16/26.90 (cartprodpairin) =>
% 89.16/26.90 ((
% 89.16/26.90 (cartprodmempair1) =>
% 89.16/26.90 ((
% 89.16/26.90 (cartprodmempair) =>
% 89.16/26.90 ((
% 89.16/26.90 (setunionE2) =>
% 89.16/26.90 ((
% 89.16/26.90 (setunionsingleton1) =>
% 89.16/26.90 ((
% 89.16/26.90 (setunionsingleton2) =>
% 89.16/26.90 ((
% 89.16/26.90 (setunionsingleton) =>
% 89.16/26.90 ((
% 89.16/26.90 (singletonprop) =>
% 89.16/26.90 ((
% 89.16/26.90 (ex1E1) =>
% 89.16/26.90 ((
% 89.16/26.90 (ex1I) =>
% 89.16/26.90 ((
% 89.16/26.90 (ex1I2) =>
% 89.16/26.90 ((
% 89.16/26.90 (singletonsuniq) =>
% 89.16/26.90 ((
% 89.16/26.90 (setukpairinjL1) =>
% 89.16/26.90 ((
% 89.16/26.90 (kfstsingleton) =>
% 89.16/26.90 ((
% 89.16/26.90 (theprop) =>
% 89.16/26.90 ((
% 89.16/26.90 (kfstpairEq) =>
% 89.16/26.90 ((
% 89.16/26.90 (cartprodfstin) =>
% 89.16/26.90 ((
% 89.16/26.90 (setukpairinjL2) =>
% 89.16/26.90 ((
% 89.16/26.90 (setukpairinjL) =>
% 89.16/26.90 ((
% 89.16/26.90 (setukpairinjR11) =>
% 89.16/26.90 ((
% 89.16/26.90 (setukpairinjR12) =>
% 89.16/26.90 ((
% 89.16/26.90 (setukpairinjR1) =>
% 89.16/26.90 ((
% 89.16/26.90 (upairequniteq) =>
% 89.16/26.90 ((
% 89.16/26.90 (setukpairinjR2) =>
% 89.16/26.90 ((
% 89.16/26.90 (setukpairinjR) =>
% 89.16/26.90 ((
% 89.16/26.90 (ksndsingleton) =>
% 89.16/26.90 ((
% 89.16/26.90 (ksndpairEq) =>
% 89.16/26.90 ((
% 89.16/26.90 (kpairsurjEq) =>
% 89.16/26.90 ((
% 89.16/26.90 (cartprodsndin) =>
% 89.16/26.90 ((
% 89.16/26.90 (cartprodpairmemEL) =>
% 89.16/26.90 ((
% 89.16/26.90 (cartprodpairmemER) =>
% 89.16/26.90 ((
% 89.16/26.90 (cartprodmempaircEq) =>
% 89.16/26.90 ((
% 89.16/26.90 (cartprodfstpairEq) =>
% 89.16/26.90 ((
% 89.16/26.90 (cartprodsndpairEq) =>
% 89.16/26.90 ((
% 89.16/26.90 (cartprodpairsurjEq) =>
% 89.16/26.90 ((
% 89.16/26.90 (dpsetconstrI) =>
% 89.16/26.90 ((
% 89.16/26.90 (dpsetconstrSub) =>
% 89.16/26.90 ((
% 89.16/26.90 (setOfPairsIsBReln) =>
% 89.16/26.90 ((
% 89.16/26.90 (dpsetconstrERa) =>
% 89.16/26.90 ((
% 89.16/26.90 (dpsetconstrEL1) =>
% 89.16/26.90 ((
% 89.16/26.90 (dpsetconstrEL2) =>
% 89.16/26.90 ((
% 89.16/26.90 (dpsetconstrER) =>
% 89.16/26.90 ((
% 89.16/26.90 (funcImageSingleton) =>
% 89.16/26.90 ((
% 89.16/26.90 (apProp) =>
% 89.16/26.90 ((
% 89.16/26.90 (app) =>
% 89.16/26.90 ((
% 89.16/26.90 (infuncsetfunc) =>
% 89.16/26.90 ((
% 89.16/26.90 (ap2p) =>
% 89.16/26.90 ((
% 89.16/26.90 (funcinfuncset) =>
% 89.16/26.90 ((
% 89.16/26.90 (lamProp) =>
% 89.16/26.90 ((
% 89.16/26.90 (lamp) =>
% 89.16/26.90 ((
% 89.16/26.90 (lam2p) =>
% 89.16/26.90 ((
% 89.16/26.90 (brelnall1) =>
% 89.16/26.90 ((
% 89.16/26.90 (brelnall2) =>
% 89.16/26.90 ((
% 89.16/26.90 (!!) @ (
% 89.16/26.90 (('#B') @ (
% 89.16/26.90 !!) @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#S') @ (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 '#S') @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 =>))) @
% 89.16/26.90 ex1)))) @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 !!))) @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#S') @ (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 '#B') @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 '#S') @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 =>))) @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#C') @ in)))))))) @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 !!))))) @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#C') @ (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 '#B') @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 '#B') @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 '#S') @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 =>))) @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#C') @ in)))))))))) @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#S') @ (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 '#S') @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 '#B'))) @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 =>))))))) @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#C') @ (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 '#B') @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 '#S') @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 =>))))))) @
% 89.16/26.90 (
% 89.16/26.90 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.16/26.90 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl807])).
% 89.16/26.90 thf(zip_derived_cl838, plain,
% 89.16/26.90 (~ (((subsetI2) =>
% 89.16/26.90 (((emptysetsubset) =>
% 89.16/26.90 (((subsetE) =>
% 89.16/26.90 (((subsetE2) =>
% 89.16/26.90 (((notsubsetI) =>
% 89.16/26.90 (((notequalI1) =>
% 89.16/26.90 (((notequalI2) =>
% 89.16/26.90 (((subsetRefl) =>
% 89.16/26.90 (((subsetTrans) =>
% 89.16/26.90 (((setadjoinSub) =>
% 89.16/26.90 (((setadjoinSub2) =>
% 89.16/26.90 (((subset2powerset) =>
% 89.16/26.90 (((setextsub) =>
% 89.16/26.90 (((subsetemptysetimpeq) =>
% 89.16/26.90 (((powersetI1) =>
% 89.16/26.90 (((powersetE1) =>
% 89.16/26.90 (((inPowerset) =>
% 89.16/26.90 (((powersetsubset) =>
% 89.16/26.90 (((sepInPowerset) =>
% 89.16/26.90 (((sepSubset) =>
% 89.16/26.90 (((binunionIL) =>
% 89.16/26.90 (((upairset2IR) =>
% 89.16/26.90 (((binunionIR) =>
% 89.16/26.90 (((binunionEcases) =>
% 89.16/26.90 (((binunionE) =>
% 89.16/26.90 (((binunionLsub) =>
% 89.16/26.90 (((binunionRsub) =>
% 89.16/26.90 (((binintersectI) =>
% 89.16/26.90 (((binintersectSubset5) =>
% 89.16/26.90 (((binintersectEL) =>
% 89.16/26.90 ((
% 89.16/26.90 (binintersectLsub) =>
% 89.16/26.90 ((
% 89.16/26.90 (binintersectSubset2) =>
% 89.16/26.90 ((
% 89.16/26.90 (binintersectSubset3) =>
% 89.16/26.90 ((
% 89.16/26.90 (binintersectER) =>
% 89.16/26.90 ((
% 89.16/26.90 (disjointsetsI1) =>
% 89.16/26.90 ((
% 89.16/26.90 (binintersectRsub) =>
% 89.16/26.90 ((
% 89.16/26.90 (binintersectSubset4) =>
% 89.16/26.90 ((
% 89.16/26.90 (binintersectSubset1) =>
% 89.16/26.90 ((
% 89.16/26.90 (bs114d) =>
% 89.16/26.90 ((
% 89.16/26.90 (setminusI) =>
% 89.16/26.90 ((
% 89.16/26.90 (setminusEL) =>
% 89.16/26.90 ((
% 89.16/26.90 (setminusER) =>
% 89.16/26.90 ((
% 89.16/26.90 (setminusSubset2) =>
% 89.16/26.90 ((
% 89.16/26.90 (setminusERneg) =>
% 89.16/26.90 ((
% 89.16/26.90 (setminusELneg) =>
% 89.16/26.90 ((
% 89.16/26.90 (setminusILneg) =>
% 89.16/26.90 ((
% 89.16/26.90 (setminusIRneg) =>
% 89.16/26.90 ((
% 89.16/26.90 (setminusLsub) =>
% 89.16/26.90 ((
% 89.16/26.90 (setminusSubset1) =>
% 89.16/26.90 ((
% 89.16/26.90 (symdiffE) =>
% 89.16/26.90 ((
% 89.16/26.90 (symdiffI1) =>
% 89.16/26.90 ((
% 89.16/26.90 (symdiffI2) =>
% 89.16/26.90 ((
% 89.16/26.90 (symdiffIneg1) =>
% 89.16/26.90 ((
% 89.16/26.90 (symdiffIneg2) =>
% 89.16/26.90 ((
% 89.16/26.90 (secondinupair) =>
% 89.16/26.90 ((
% 89.16/26.90 (setukpairIL) =>
% 89.16/26.90 ((
% 89.16/26.90 (setukpairIR) =>
% 89.16/26.90 ((
% 89.16/26.90 (kpairiskpair) =>
% 89.16/26.90 ((
% 89.16/26.90 (kpairp) =>
% 89.16/26.90 ((
% 89.16/26.90 (singletonsubset) =>
% 89.16/26.90 ((
% 89.16/26.90 (singletoninpowerset) =>
% 89.16/26.90 ((
% 89.16/26.90 (singletoninpowunion) =>
% 89.16/26.90 ((
% 89.16/26.90 (upairset2E) =>
% 89.16/26.90 ((
% 89.16/26.90 (upairsubunion) =>
% 89.16/26.90 ((
% 89.16/26.90 (upairinpowunion) =>
% 89.16/26.90 ((
% 89.16/26.90 (ubforcartprodlem1) =>
% 89.16/26.90 ((
% 89.16/26.90 (ubforcartprodlem2) =>
% 89.16/26.90 ((
% 89.16/26.90 (ubforcartprodlem3) =>
% 89.16/26.90 ((
% 89.16/26.90 (cartprodpairin) =>
% 89.16/26.90 ((
% 89.16/26.90 (cartprodmempair1) =>
% 89.16/26.90 ((
% 89.16/26.90 (cartprodmempair) =>
% 89.16/26.90 ((
% 89.16/26.90 (setunionE2) =>
% 89.16/26.90 ((
% 89.16/26.90 (setunionsingleton1) =>
% 89.16/26.90 ((
% 89.16/26.90 (setunionsingleton2) =>
% 89.16/26.90 ((
% 89.16/26.90 (setunionsingleton) =>
% 89.16/26.90 ((
% 89.16/26.90 (singletonprop) =>
% 89.16/26.90 ((
% 89.16/26.90 (ex1E1) =>
% 89.16/26.90 ((
% 89.16/26.90 (ex1I) =>
% 89.16/26.90 ((
% 89.16/26.90 (ex1I2) =>
% 89.16/26.90 ((
% 89.16/26.90 (singletonsuniq) =>
% 89.16/26.90 ((
% 89.16/26.90 (setukpairinjL1) =>
% 89.16/26.90 ((
% 89.16/26.90 (kfstsingleton) =>
% 89.16/26.90 ((
% 89.16/26.90 (theprop) =>
% 89.16/26.90 ((
% 89.16/26.90 (kfstpairEq) =>
% 89.16/26.90 ((
% 89.16/26.90 (cartprodfstin) =>
% 89.16/26.90 ((
% 89.16/26.90 (setukpairinjL2) =>
% 89.16/26.90 ((
% 89.16/26.90 (setukpairinjL) =>
% 89.16/26.90 ((
% 89.16/26.90 (setukpairinjR11) =>
% 89.16/26.90 ((
% 89.16/26.90 (setukpairinjR12) =>
% 89.16/26.90 ((
% 89.16/26.90 (setukpairinjR1) =>
% 89.16/26.90 ((
% 89.16/26.90 (upairequniteq) =>
% 89.16/26.90 ((
% 89.16/26.90 (setukpairinjR2) =>
% 89.16/26.90 ((
% 89.16/26.90 (setukpairinjR) =>
% 89.16/26.90 ((
% 89.16/26.90 (ksndsingleton) =>
% 89.16/26.90 ((
% 89.16/26.90 (ksndpairEq) =>
% 89.16/26.90 ((
% 89.16/26.90 (kpairsurjEq) =>
% 89.16/26.90 ((
% 89.16/26.90 (cartprodsndin) =>
% 89.16/26.90 ((
% 89.16/26.90 (cartprodpairmemEL) =>
% 89.16/26.90 ((
% 89.16/26.90 (cartprodpairmemER) =>
% 89.16/26.90 ((
% 89.16/26.90 (cartprodmempaircEq) =>
% 89.16/26.90 ((
% 89.16/26.90 (cartprodfstpairEq) =>
% 89.16/26.90 ((
% 89.16/26.90 (cartprodsndpairEq) =>
% 89.16/26.90 ((
% 89.16/26.90 (cartprodpairsurjEq) =>
% 89.16/26.90 ((
% 89.16/26.90 (dpsetconstrI) =>
% 89.16/26.90 ((
% 89.16/26.90 (dpsetconstrSub) =>
% 89.16/26.90 ((
% 89.16/26.90 (setOfPairsIsBReln) =>
% 89.16/26.90 ((
% 89.16/26.90 (dpsetconstrERa) =>
% 89.16/26.90 ((
% 89.16/26.90 (dpsetconstrEL1) =>
% 89.16/26.90 ((
% 89.16/26.90 (dpsetconstrEL2) =>
% 89.16/26.90 ((
% 89.16/26.90 (dpsetconstrER) =>
% 89.16/26.90 ((
% 89.16/26.90 (funcImageSingleton) =>
% 89.16/26.90 ((
% 89.16/26.90 (apProp) =>
% 89.16/26.90 ((
% 89.16/26.90 (app) =>
% 89.16/26.90 ((
% 89.16/26.90 (infuncsetfunc) =>
% 89.16/26.90 ((
% 89.16/26.90 (ap2p) =>
% 89.16/26.90 ((
% 89.16/26.90 (funcinfuncset) =>
% 89.16/26.90 ((
% 89.16/26.90 (lamProp) =>
% 89.16/26.90 ((
% 89.16/26.90 (lamp) =>
% 89.16/26.90 ((
% 89.16/26.90 (lam2p) =>
% 89.16/26.90 ((
% 89.16/26.90 (brelnall1) =>
% 89.16/26.90 ((
% 89.16/26.90 (brelnall2) =>
% 89.16/26.90 ((
% 89.16/26.90 (!!) @ (
% 89.16/26.90 (('#B') @ (
% 89.16/26.90 !!) @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#S') @ (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 '#S') @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 =>))) @
% 89.16/26.90 ex1)))) @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 !!))) @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#S') @ (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 '#B') @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 '#S') @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 =>))) @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#C') @ in)))))))) @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 !!))))) @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#C') @ (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 '#B') @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 '#B') @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 '#S') @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 =>))) @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#C') @ in)))))))))) @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#S') @ (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 '#S') @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 '#B'))) @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 =>))))))) @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#C') @ (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 '#B') @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 '#S') @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 =>))))))) @
% 89.16/26.90 (
% 89.16/26.90 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.16/26.90 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl824])).
% 89.16/26.90 thf(zip_derived_cl850, plain,
% 89.16/26.90 (~ (((emptysetsubset) =>
% 89.16/26.90 (((subsetE) =>
% 89.16/26.90 (((subsetE2) =>
% 89.16/26.90 (((notsubsetI) =>
% 89.16/26.90 (((notequalI1) =>
% 89.16/26.90 (((notequalI2) =>
% 89.16/26.90 (((subsetRefl) =>
% 89.16/26.90 (((subsetTrans) =>
% 89.16/26.90 (((setadjoinSub) =>
% 89.16/26.90 (((setadjoinSub2) =>
% 89.16/26.90 (((subset2powerset) =>
% 89.16/26.90 (((setextsub) =>
% 89.16/26.90 (((subsetemptysetimpeq) =>
% 89.16/26.90 (((powersetI1) =>
% 89.16/26.90 (((powersetE1) =>
% 89.16/26.90 (((inPowerset) =>
% 89.16/26.90 (((powersetsubset) =>
% 89.16/26.90 (((sepInPowerset) =>
% 89.16/26.90 (((sepSubset) =>
% 89.16/26.90 (((binunionIL) =>
% 89.16/26.90 (((upairset2IR) =>
% 89.16/26.90 (((binunionIR) =>
% 89.16/26.90 (((binunionEcases) =>
% 89.16/26.90 (((binunionE) =>
% 89.16/26.90 (((binunionLsub) =>
% 89.16/26.90 (((binunionRsub) =>
% 89.16/26.90 (((binintersectI) =>
% 89.16/26.90 (((binintersectSubset5) =>
% 89.16/26.90 (((binintersectEL) =>
% 89.16/26.90 (((binintersectLsub) =>
% 89.16/26.90 ((
% 89.16/26.90 (binintersectSubset2) =>
% 89.16/26.90 ((
% 89.16/26.90 (binintersectSubset3) =>
% 89.16/26.90 ((
% 89.16/26.90 (binintersectER) =>
% 89.16/26.90 ((
% 89.16/26.90 (disjointsetsI1) =>
% 89.16/26.90 ((
% 89.16/26.90 (binintersectRsub) =>
% 89.16/26.90 ((
% 89.16/26.90 (binintersectSubset4) =>
% 89.16/26.90 ((
% 89.16/26.90 (binintersectSubset1) =>
% 89.16/26.90 ((
% 89.16/26.90 (bs114d) =>
% 89.16/26.90 ((
% 89.16/26.90 (setminusI) =>
% 89.16/26.90 ((
% 89.16/26.90 (setminusEL) =>
% 89.16/26.90 ((
% 89.16/26.90 (setminusER) =>
% 89.16/26.90 ((
% 89.16/26.90 (setminusSubset2) =>
% 89.16/26.90 ((
% 89.16/26.90 (setminusERneg) =>
% 89.16/26.90 ((
% 89.16/26.90 (setminusELneg) =>
% 89.16/26.90 ((
% 89.16/26.90 (setminusILneg) =>
% 89.16/26.90 ((
% 89.16/26.90 (setminusIRneg) =>
% 89.16/26.90 ((
% 89.16/26.90 (setminusLsub) =>
% 89.16/26.90 ((
% 89.16/26.90 (setminusSubset1) =>
% 89.16/26.90 ((
% 89.16/26.90 (symdiffE) =>
% 89.16/26.90 ((
% 89.16/26.90 (symdiffI1) =>
% 89.16/26.90 ((
% 89.16/26.90 (symdiffI2) =>
% 89.16/26.90 ((
% 89.16/26.90 (symdiffIneg1) =>
% 89.16/26.90 ((
% 89.16/26.90 (symdiffIneg2) =>
% 89.16/26.90 ((
% 89.16/26.90 (secondinupair) =>
% 89.16/26.90 ((
% 89.16/26.90 (setukpairIL) =>
% 89.16/26.90 ((
% 89.16/26.90 (setukpairIR) =>
% 89.16/26.90 ((
% 89.16/26.90 (kpairiskpair) =>
% 89.16/26.90 ((
% 89.16/26.90 (kpairp) =>
% 89.16/26.90 ((
% 89.16/26.90 (singletonsubset) =>
% 89.16/26.90 ((
% 89.16/26.90 (singletoninpowerset) =>
% 89.16/26.90 ((
% 89.16/26.90 (singletoninpowunion) =>
% 89.16/26.90 ((
% 89.16/26.90 (upairset2E) =>
% 89.16/26.90 ((
% 89.16/26.90 (upairsubunion) =>
% 89.16/26.90 ((
% 89.16/26.90 (upairinpowunion) =>
% 89.16/26.90 ((
% 89.16/26.90 (ubforcartprodlem1) =>
% 89.16/26.90 ((
% 89.16/26.90 (ubforcartprodlem2) =>
% 89.16/26.90 ((
% 89.16/26.90 (ubforcartprodlem3) =>
% 89.16/26.90 ((
% 89.16/26.90 (cartprodpairin) =>
% 89.16/26.90 ((
% 89.16/26.90 (cartprodmempair1) =>
% 89.16/26.90 ((
% 89.16/26.90 (cartprodmempair) =>
% 89.16/26.90 ((
% 89.16/26.90 (setunionE2) =>
% 89.16/26.90 ((
% 89.16/26.90 (setunionsingleton1) =>
% 89.16/26.90 ((
% 89.16/26.90 (setunionsingleton2) =>
% 89.16/26.90 ((
% 89.16/26.90 (setunionsingleton) =>
% 89.16/26.90 ((
% 89.16/26.90 (singletonprop) =>
% 89.16/26.90 ((
% 89.16/26.90 (ex1E1) =>
% 89.16/26.90 ((
% 89.16/26.90 (ex1I) =>
% 89.16/26.90 ((
% 89.16/26.90 (ex1I2) =>
% 89.16/26.90 ((
% 89.16/26.90 (singletonsuniq) =>
% 89.16/26.90 ((
% 89.16/26.90 (setukpairinjL1) =>
% 89.16/26.90 ((
% 89.16/26.90 (kfstsingleton) =>
% 89.16/26.90 ((
% 89.16/26.90 (theprop) =>
% 89.16/26.90 ((
% 89.16/26.90 (kfstpairEq) =>
% 89.16/26.90 ((
% 89.16/26.90 (cartprodfstin) =>
% 89.16/26.90 ((
% 89.16/26.90 (setukpairinjL2) =>
% 89.16/26.90 ((
% 89.16/26.90 (setukpairinjL) =>
% 89.16/26.90 ((
% 89.16/26.90 (setukpairinjR11) =>
% 89.16/26.90 ((
% 89.16/26.90 (setukpairinjR12) =>
% 89.16/26.90 ((
% 89.16/26.90 (setukpairinjR1) =>
% 89.16/26.90 ((
% 89.16/26.90 (upairequniteq) =>
% 89.16/26.90 ((
% 89.16/26.90 (setukpairinjR2) =>
% 89.16/26.90 ((
% 89.16/26.90 (setukpairinjR) =>
% 89.16/26.90 ((
% 89.16/26.90 (ksndsingleton) =>
% 89.16/26.90 ((
% 89.16/26.90 (ksndpairEq) =>
% 89.16/26.90 ((
% 89.16/26.90 (kpairsurjEq) =>
% 89.16/26.90 ((
% 89.16/26.90 (cartprodsndin) =>
% 89.16/26.90 ((
% 89.16/26.90 (cartprodpairmemEL) =>
% 89.16/26.90 ((
% 89.16/26.90 (cartprodpairmemER) =>
% 89.16/26.90 ((
% 89.16/26.90 (cartprodmempaircEq) =>
% 89.16/26.90 ((
% 89.16/26.90 (cartprodfstpairEq) =>
% 89.16/26.90 ((
% 89.16/26.90 (cartprodsndpairEq) =>
% 89.16/26.90 ((
% 89.16/26.90 (cartprodpairsurjEq) =>
% 89.16/26.90 ((
% 89.16/26.90 (dpsetconstrI) =>
% 89.16/26.90 ((
% 89.16/26.90 (dpsetconstrSub) =>
% 89.16/26.90 ((
% 89.16/26.90 (setOfPairsIsBReln) =>
% 89.16/26.90 ((
% 89.16/26.90 (dpsetconstrERa) =>
% 89.16/26.90 ((
% 89.16/26.90 (dpsetconstrEL1) =>
% 89.16/26.90 ((
% 89.16/26.90 (dpsetconstrEL2) =>
% 89.16/26.90 ((
% 89.16/26.90 (dpsetconstrER) =>
% 89.16/26.90 ((
% 89.16/26.90 (funcImageSingleton) =>
% 89.16/26.90 ((
% 89.16/26.90 (apProp) =>
% 89.16/26.90 ((
% 89.16/26.90 (app) =>
% 89.16/26.90 ((
% 89.16/26.90 (infuncsetfunc) =>
% 89.16/26.90 ((
% 89.16/26.90 (ap2p) =>
% 89.16/26.90 ((
% 89.16/26.90 (funcinfuncset) =>
% 89.16/26.90 ((
% 89.16/26.90 (lamProp) =>
% 89.16/26.90 ((
% 89.16/26.90 (lamp) =>
% 89.16/26.90 ((
% 89.16/26.90 (lam2p) =>
% 89.16/26.90 ((
% 89.16/26.90 (brelnall1) =>
% 89.16/26.90 ((
% 89.16/26.90 (brelnall2) =>
% 89.16/26.90 ((
% 89.16/26.90 (!!) @ (
% 89.16/26.90 (('#B') @ (
% 89.16/26.90 !!) @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#S') @ (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 '#S') @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 =>))) @
% 89.16/26.90 ex1)))) @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 !!))) @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#S') @ (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 '#B') @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 '#S') @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 =>))) @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#C') @ in)))))))) @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 !!))))) @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#C') @ (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 '#B') @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 '#B') @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 '#S') @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 =>))) @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#C') @ in)))))))))) @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#S') @ (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 '#S') @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 '#B'))) @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 =>))))))) @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#C') @ (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 '#B') @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 '#S') @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 =>))))))) @
% 89.16/26.90 (
% 89.16/26.90 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.16/26.90 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl838])).
% 89.16/26.90 thf(zip_derived_cl863, plain,
% 89.16/26.90 (~ (((subsetE) =>
% 89.16/26.90 (((subsetE2) =>
% 89.16/26.90 (((notsubsetI) =>
% 89.16/26.90 (((notequalI1) =>
% 89.16/26.90 (((notequalI2) =>
% 89.16/26.90 (((subsetRefl) =>
% 89.16/26.90 (((subsetTrans) =>
% 89.16/26.90 (((setadjoinSub) =>
% 89.16/26.90 (((setadjoinSub2) =>
% 89.16/26.90 (((subset2powerset) =>
% 89.16/26.90 (((setextsub) =>
% 89.16/26.90 (((subsetemptysetimpeq) =>
% 89.16/26.90 (((powersetI1) =>
% 89.16/26.90 (((powersetE1) =>
% 89.16/26.90 (((inPowerset) =>
% 89.16/26.90 (((powersetsubset) =>
% 89.16/26.90 (((sepInPowerset) =>
% 89.16/26.90 (((sepSubset) =>
% 89.16/26.90 (((binunionIL) =>
% 89.16/26.90 (((upairset2IR) =>
% 89.16/26.90 (((binunionIR) =>
% 89.16/26.90 (((binunionEcases) =>
% 89.16/26.90 (((binunionE) =>
% 89.16/26.90 (((binunionLsub) =>
% 89.16/26.90 (((binunionRsub) =>
% 89.16/26.90 (((binintersectI) =>
% 89.16/26.90 (((binintersectSubset5) =>
% 89.16/26.90 (((binintersectEL) =>
% 89.16/26.90 (((binintersectLsub) =>
% 89.16/26.90 (((binintersectSubset2) =>
% 89.16/26.90 ((
% 89.16/26.90 (binintersectSubset3) =>
% 89.16/26.90 ((
% 89.16/26.90 (binintersectER) =>
% 89.16/26.90 ((
% 89.16/26.90 (disjointsetsI1) =>
% 89.16/26.90 ((
% 89.16/26.90 (binintersectRsub) =>
% 89.16/26.90 ((
% 89.16/26.90 (binintersectSubset4) =>
% 89.16/26.90 ((
% 89.16/26.90 (binintersectSubset1) =>
% 89.16/26.90 ((
% 89.16/26.90 (bs114d) =>
% 89.16/26.90 ((
% 89.16/26.90 (setminusI) =>
% 89.16/26.90 ((
% 89.16/26.90 (setminusEL) =>
% 89.16/26.90 ((
% 89.16/26.90 (setminusER) =>
% 89.16/26.90 ((
% 89.16/26.90 (setminusSubset2) =>
% 89.16/26.90 ((
% 89.16/26.90 (setminusERneg) =>
% 89.16/26.90 ((
% 89.16/26.90 (setminusELneg) =>
% 89.16/26.90 ((
% 89.16/26.90 (setminusILneg) =>
% 89.16/26.90 ((
% 89.16/26.90 (setminusIRneg) =>
% 89.16/26.90 ((
% 89.16/26.90 (setminusLsub) =>
% 89.16/26.90 ((
% 89.16/26.90 (setminusSubset1) =>
% 89.16/26.90 ((
% 89.16/26.90 (symdiffE) =>
% 89.16/26.90 ((
% 89.16/26.90 (symdiffI1) =>
% 89.16/26.90 ((
% 89.16/26.90 (symdiffI2) =>
% 89.16/26.90 ((
% 89.16/26.90 (symdiffIneg1) =>
% 89.16/26.90 ((
% 89.16/26.90 (symdiffIneg2) =>
% 89.16/26.90 ((
% 89.16/26.90 (secondinupair) =>
% 89.16/26.90 ((
% 89.16/26.90 (setukpairIL) =>
% 89.16/26.90 ((
% 89.16/26.90 (setukpairIR) =>
% 89.16/26.90 ((
% 89.16/26.90 (kpairiskpair) =>
% 89.16/26.90 ((
% 89.16/26.90 (kpairp) =>
% 89.16/26.90 ((
% 89.16/26.90 (singletonsubset) =>
% 89.16/26.90 ((
% 89.16/26.90 (singletoninpowerset) =>
% 89.16/26.90 ((
% 89.16/26.90 (singletoninpowunion) =>
% 89.16/26.90 ((
% 89.16/26.90 (upairset2E) =>
% 89.16/26.90 ((
% 89.16/26.90 (upairsubunion) =>
% 89.16/26.90 ((
% 89.16/26.90 (upairinpowunion) =>
% 89.16/26.90 ((
% 89.16/26.90 (ubforcartprodlem1) =>
% 89.16/26.90 ((
% 89.16/26.90 (ubforcartprodlem2) =>
% 89.16/26.90 ((
% 89.16/26.90 (ubforcartprodlem3) =>
% 89.16/26.90 ((
% 89.16/26.90 (cartprodpairin) =>
% 89.16/26.90 ((
% 89.16/26.90 (cartprodmempair1) =>
% 89.16/26.90 ((
% 89.16/26.90 (cartprodmempair) =>
% 89.16/26.90 ((
% 89.16/26.90 (setunionE2) =>
% 89.16/26.90 ((
% 89.16/26.90 (setunionsingleton1) =>
% 89.16/26.90 ((
% 89.16/26.90 (setunionsingleton2) =>
% 89.16/26.90 ((
% 89.16/26.90 (setunionsingleton) =>
% 89.16/26.90 ((
% 89.16/26.90 (singletonprop) =>
% 89.16/26.90 ((
% 89.16/26.90 (ex1E1) =>
% 89.16/26.90 ((
% 89.16/26.90 (ex1I) =>
% 89.16/26.90 ((
% 89.16/26.90 (ex1I2) =>
% 89.16/26.90 ((
% 89.16/26.90 (singletonsuniq) =>
% 89.16/26.90 ((
% 89.16/26.90 (setukpairinjL1) =>
% 89.16/26.90 ((
% 89.16/26.90 (kfstsingleton) =>
% 89.16/26.90 ((
% 89.16/26.90 (theprop) =>
% 89.16/26.90 ((
% 89.16/26.90 (kfstpairEq) =>
% 89.16/26.90 ((
% 89.16/26.90 (cartprodfstin) =>
% 89.16/26.90 ((
% 89.16/26.90 (setukpairinjL2) =>
% 89.16/26.90 ((
% 89.16/26.90 (setukpairinjL) =>
% 89.16/26.90 ((
% 89.16/26.90 (setukpairinjR11) =>
% 89.16/26.90 ((
% 89.16/26.90 (setukpairinjR12) =>
% 89.16/26.90 ((
% 89.16/26.90 (setukpairinjR1) =>
% 89.16/26.90 ((
% 89.16/26.90 (upairequniteq) =>
% 89.16/26.90 ((
% 89.16/26.90 (setukpairinjR2) =>
% 89.16/26.90 ((
% 89.16/26.90 (setukpairinjR) =>
% 89.16/26.90 ((
% 89.16/26.90 (ksndsingleton) =>
% 89.16/26.90 ((
% 89.16/26.90 (ksndpairEq) =>
% 89.16/26.90 ((
% 89.16/26.90 (kpairsurjEq) =>
% 89.16/26.90 ((
% 89.16/26.90 (cartprodsndin) =>
% 89.16/26.90 ((
% 89.16/26.90 (cartprodpairmemEL) =>
% 89.16/26.90 ((
% 89.16/26.90 (cartprodpairmemER) =>
% 89.16/26.90 ((
% 89.16/26.90 (cartprodmempaircEq) =>
% 89.16/26.90 ((
% 89.16/26.90 (cartprodfstpairEq) =>
% 89.16/26.90 ((
% 89.16/26.90 (cartprodsndpairEq) =>
% 89.16/26.90 ((
% 89.16/26.90 (cartprodpairsurjEq) =>
% 89.16/26.90 ((
% 89.16/26.90 (dpsetconstrI) =>
% 89.16/26.90 ((
% 89.16/26.90 (dpsetconstrSub) =>
% 89.16/26.90 ((
% 89.16/26.90 (setOfPairsIsBReln) =>
% 89.16/26.90 ((
% 89.16/26.90 (dpsetconstrERa) =>
% 89.16/26.90 ((
% 89.16/26.90 (dpsetconstrEL1) =>
% 89.16/26.90 ((
% 89.16/26.90 (dpsetconstrEL2) =>
% 89.16/26.90 ((
% 89.16/26.90 (dpsetconstrER) =>
% 89.16/26.90 ((
% 89.16/26.90 (funcImageSingleton) =>
% 89.16/26.90 ((
% 89.16/26.90 (apProp) =>
% 89.16/26.90 ((
% 89.16/26.90 (app) =>
% 89.16/26.90 ((
% 89.16/26.90 (infuncsetfunc) =>
% 89.16/26.90 ((
% 89.16/26.90 (ap2p) =>
% 89.16/26.90 ((
% 89.16/26.90 (funcinfuncset) =>
% 89.16/26.90 ((
% 89.16/26.90 (lamProp) =>
% 89.16/26.90 ((
% 89.16/26.90 (lamp) =>
% 89.16/26.90 ((
% 89.16/26.90 (lam2p) =>
% 89.16/26.90 ((
% 89.16/26.90 (brelnall1) =>
% 89.16/26.90 ((
% 89.16/26.90 (brelnall2) =>
% 89.16/26.90 ((
% 89.16/26.90 (!!) @ (
% 89.16/26.90 (('#B') @ (
% 89.16/26.90 !!) @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#S') @ (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 '#S') @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 =>))) @
% 89.16/26.90 ex1)))) @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 !!))) @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#S') @ (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 '#B') @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 '#S') @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 =>))) @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#C') @ in)))))))) @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 !!))))) @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#C') @ (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 '#B') @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 '#B') @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 '#S') @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 =>))) @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#C') @ in)))))))))) @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#S') @ (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 '#S') @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 '#B'))) @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 =>))))))) @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#C') @ (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 '#B') @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 '#S') @
% 89.16/26.90 (
% 89.16/26.90 (
% 89.16/26.90 ('#B') @ (
% 89.16/26.90 =>))))))) @
% 89.16/26.90 (
% 89.16/26.90 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.16/26.90 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl850])).
% 89.16/26.90 thf(zip_derived_cl878, plain,
% 89.16/26.90 (~ (((subsetE2) =>
% 89.16/26.90 (((notsubsetI) =>
% 89.16/26.90 (((notequalI1) =>
% 89.16/26.90 (((notequalI2) =>
% 89.16/26.90 (((subsetRefl) =>
% 89.16/26.90 (((subsetTrans) =>
% 89.16/26.90 (((setadjoinSub) =>
% 89.16/26.90 (((setadjoinSub2) =>
% 89.16/26.90 (((subset2powerset) =>
% 89.16/26.90 (((setextsub) =>
% 89.16/26.90 (((subsetemptysetimpeq) =>
% 89.16/26.90 (((powersetI1) =>
% 89.16/26.90 (((powersetE1) =>
% 89.16/26.90 (((inPowerset) =>
% 89.16/26.90 (((powersetsubset) =>
% 89.16/26.90 (((sepInPowerset) =>
% 89.16/26.90 (((sepSubset) =>
% 89.16/26.90 (((binunionIL) =>
% 89.16/26.90 (((upairset2IR) =>
% 89.16/26.90 (((binunionIR) =>
% 89.16/26.90 (((binunionEcases) =>
% 89.16/26.90 (((binunionE) =>
% 89.16/26.90 (((binunionLsub) =>
% 89.16/26.90 (((binunionRsub) =>
% 89.16/26.90 (((binintersectI) =>
% 89.16/26.90 (((binintersectSubset5) =>
% 89.16/26.90 (((binintersectEL) =>
% 89.16/26.90 (((binintersectLsub) =>
% 89.16/26.90 (((binintersectSubset2) =>
% 89.16/26.90 (((binintersectSubset3) =>
% 89.16/26.90 ((
% 89.16/26.90 (binintersectER) =>
% 89.16/26.90 ((
% 89.16/26.90 (disjointsetsI1) =>
% 89.16/26.90 ((
% 89.16/26.90 (binintersectRsub) =>
% 89.16/26.90 ((
% 89.16/26.90 (binintersectSubset4) =>
% 89.16/26.90 ((
% 89.16/26.90 (binintersectSubset1) =>
% 89.16/26.90 ((
% 89.16/26.90 (bs114d) =>
% 89.16/26.90 ((
% 89.16/26.90 (setminusI) =>
% 89.16/26.90 ((
% 89.16/26.90 (setminusEL) =>
% 89.16/26.90 ((
% 89.16/26.90 (setminusER) =>
% 89.16/26.90 ((
% 89.16/26.90 (setminusSubset2) =>
% 89.16/26.90 ((
% 89.16/26.90 (setminusERneg) =>
% 89.16/26.90 ((
% 89.16/26.90 (setminusELneg) =>
% 89.16/26.90 ((
% 89.16/26.90 (setminusILneg) =>
% 89.16/26.90 ((
% 89.16/26.90 (setminusIRneg) =>
% 89.16/26.90 ((
% 89.16/26.90 (setminusLsub) =>
% 89.16/26.90 ((
% 89.16/26.90 (setminusSubset1) =>
% 89.16/26.90 ((
% 89.16/26.90 (symdiffE) =>
% 89.16/26.90 ((
% 89.16/26.90 (symdiffI1) =>
% 89.16/26.90 ((
% 89.16/26.90 (symdiffI2) =>
% 89.16/26.90 ((
% 89.16/26.90 (symdiffIneg1) =>
% 89.16/26.90 ((
% 89.16/26.90 (symdiffIneg2) =>
% 89.16/26.90 ((
% 89.16/26.90 (secondinupair) =>
% 89.16/26.90 ((
% 89.16/26.90 (setukpairIL) =>
% 89.16/26.90 ((
% 89.16/26.90 (setukpairIR) =>
% 89.16/26.90 ((
% 89.16/26.90 (kpairiskpair) =>
% 89.16/26.90 ((
% 89.16/26.90 (kpairp) =>
% 89.16/26.90 ((
% 89.16/26.90 (singletonsubset) =>
% 89.16/26.90 ((
% 89.16/26.90 (singletoninpowerset) =>
% 89.16/26.90 ((
% 89.16/26.90 (singletoninpowunion) =>
% 89.16/26.90 ((
% 89.16/26.90 (upairset2E) =>
% 89.16/26.90 ((
% 89.16/26.90 (upairsubunion) =>
% 89.16/26.90 ((
% 89.16/26.90 (upairinpowunion) =>
% 89.16/26.90 ((
% 89.16/26.90 (ubforcartprodlem1) =>
% 89.16/26.90 ((
% 89.16/26.90 (ubforcartprodlem2) =>
% 89.16/26.90 ((
% 89.16/26.90 (ubforcartprodlem3) =>
% 89.16/26.90 ((
% 89.16/26.90 (cartprodpairin) =>
% 89.16/26.90 ((
% 89.16/26.90 (cartprodmempair1) =>
% 89.16/26.90 ((
% 89.16/26.90 (cartprodmempair) =>
% 89.16/26.90 ((
% 89.16/26.90 (setunionE2) =>
% 89.16/26.90 ((
% 89.16/26.90 (setunionsingleton1) =>
% 89.16/26.90 ((
% 89.16/26.90 (setunionsingleton2) =>
% 89.16/26.90 ((
% 89.16/26.90 (setunionsingleton) =>
% 89.16/26.90 ((
% 89.16/26.90 (singletonprop) =>
% 89.16/26.90 ((
% 89.16/26.90 (ex1E1) =>
% 89.16/26.90 ((
% 89.16/26.90 (ex1I) =>
% 89.16/26.90 ((
% 89.16/26.90 (ex1I2) =>
% 89.16/26.90 ((
% 89.16/26.90 (singletonsuniq) =>
% 89.16/26.90 ((
% 89.16/26.90 (setukpairinjL1) =>
% 89.16/26.90 ((
% 89.16/26.90 (kfstsingleton) =>
% 89.16/26.90 ((
% 89.16/26.90 (theprop) =>
% 89.16/26.90 ((
% 89.16/26.90 (kfstpairEq) =>
% 89.16/26.90 ((
% 89.16/26.90 (cartprodfstin) =>
% 89.16/26.90 ((
% 89.16/26.90 (setukpairinjL2) =>
% 89.16/26.90 ((
% 89.16/26.90 (setukpairinjL) =>
% 89.16/26.90 ((
% 89.16/26.90 (setukpairinjR11) =>
% 89.16/26.90 ((
% 89.16/26.90 (setukpairinjR12) =>
% 89.16/26.90 ((
% 89.16/26.90 (setukpairinjR1) =>
% 89.16/26.90 ((
% 89.16/26.90 (upairequniteq) =>
% 89.16/26.90 ((
% 89.16/26.90 (setukpairinjR2) =>
% 89.16/26.90 ((
% 89.16/26.90 (setukpairinjR) =>
% 89.16/26.90 ((
% 89.16/26.90 (ksndsingleton) =>
% 89.16/26.90 ((
% 89.16/26.90 (ksndpairEq) =>
% 89.16/26.90 ((
% 89.16/26.90 (kpairsurjEq) =>
% 89.16/26.90 ((
% 89.16/26.90 (cartprodsndin) =>
% 89.16/26.90 ((
% 89.16/26.90 (cartprodpairmemEL) =>
% 89.16/26.90 ((
% 89.16/26.90 (cartprodpairmemER) =>
% 89.16/26.90 ((
% 89.16/26.90 (cartprodmempaircEq) =>
% 89.16/26.90 ((
% 89.16/26.90 (cartprodfstpairEq) =>
% 89.16/26.90 ((
% 89.16/26.90 (cartprodsndpairEq) =>
% 89.16/26.90 ((
% 89.16/26.90 (cartprodpairsurjEq) =>
% 89.16/26.90 ((
% 89.16/26.90 (dpsetconstrI) =>
% 89.16/26.90 ((
% 89.16/26.90 (dpsetconstrSub) =>
% 89.16/26.90 ((
% 89.16/26.90 (setOfPairsIsBReln) =>
% 89.16/26.90 ((
% 89.16/26.90 (dpsetconstrERa) =>
% 89.16/26.90 ((
% 89.16/26.90 (dpsetconstrEL1) =>
% 89.16/26.90 ((
% 89.16/26.90 (dpsetconstrEL2) =>
% 89.16/26.90 ((
% 89.16/26.90 (dpsetconstrER) =>
% 89.16/26.90 ((
% 89.16/26.90 (funcImageSingleton) =>
% 89.16/26.90 ((
% 89.16/26.90 (apProp) =>
% 89.16/26.90 ((
% 89.16/26.90 (app) =>
% 89.16/26.90 ((
% 89.16/26.90 (infuncsetfunc) =>
% 89.16/26.90 ((
% 89.16/26.90 (ap2p) =>
% 89.16/26.90 ((
% 89.16/26.90 (funcinfuncset) =>
% 89.16/26.90 ((
% 89.16/26.90 (lamProp) =>
% 89.16/26.90 ((
% 89.16/26.90 (lamp) =>
% 89.16/26.90 ((
% 89.16/26.90 (lam2p) =>
% 89.16/26.90 ((
% 89.16/26.90 (brelnall1) =>
% 89.16/26.91 ((
% 89.16/26.91 (brelnall2) =>
% 89.16/26.91 ((
% 89.16/26.91 (!!) @ (
% 89.16/26.91 (('#B') @ (
% 89.16/26.91 !!) @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#S') @ (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 '#S') @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 =>))) @
% 89.16/26.91 ex1)))) @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 !!))) @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#S') @ (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 '#B') @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 '#S') @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 =>))) @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#C') @ in)))))))) @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 !!))))) @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#C') @ (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 '#B') @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 '#B') @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 '#S') @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 =>))) @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#C') @ in)))))))))) @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#S') @ (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 '#S') @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 '#B'))) @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 =>))))))) @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#C') @ (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 '#B') @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 '#S') @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 =>))))))) @
% 89.16/26.91 (
% 89.16/26.91 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.16/26.91 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl863])).
% 89.16/26.91 thf(zip_derived_cl896, plain,
% 89.16/26.91 (~ (((notsubsetI) =>
% 89.16/26.91 (((notequalI1) =>
% 89.16/26.91 (((notequalI2) =>
% 89.16/26.91 (((subsetRefl) =>
% 89.16/26.91 (((subsetTrans) =>
% 89.16/26.91 (((setadjoinSub) =>
% 89.16/26.91 (((setadjoinSub2) =>
% 89.16/26.91 (((subset2powerset) =>
% 89.16/26.91 (((setextsub) =>
% 89.16/26.91 (((subsetemptysetimpeq) =>
% 89.16/26.91 (((powersetI1) =>
% 89.16/26.91 (((powersetE1) =>
% 89.16/26.91 (((inPowerset) =>
% 89.16/26.91 (((powersetsubset) =>
% 89.16/26.91 (((sepInPowerset) =>
% 89.16/26.91 (((sepSubset) =>
% 89.16/26.91 (((binunionIL) =>
% 89.16/26.91 (((upairset2IR) =>
% 89.16/26.91 (((binunionIR) =>
% 89.16/26.91 (((binunionEcases) =>
% 89.16/26.91 (((binunionE) =>
% 89.16/26.91 (((binunionLsub) =>
% 89.16/26.91 (((binunionRsub) =>
% 89.16/26.91 (((binintersectI) =>
% 89.16/26.91 (((binintersectSubset5) =>
% 89.16/26.91 (((binintersectEL) =>
% 89.16/26.91 (((binintersectLsub) =>
% 89.16/26.91 (((binintersectSubset2) =>
% 89.16/26.91 (((binintersectSubset3) =>
% 89.16/26.91 (((binintersectER) =>
% 89.16/26.91 ((
% 89.16/26.91 (disjointsetsI1) =>
% 89.16/26.91 ((
% 89.16/26.91 (binintersectRsub) =>
% 89.16/26.91 ((
% 89.16/26.91 (binintersectSubset4) =>
% 89.16/26.91 ((
% 89.16/26.91 (binintersectSubset1) =>
% 89.16/26.91 ((
% 89.16/26.91 (bs114d) =>
% 89.16/26.91 ((
% 89.16/26.91 (setminusI) =>
% 89.16/26.91 ((
% 89.16/26.91 (setminusEL) =>
% 89.16/26.91 ((
% 89.16/26.91 (setminusER) =>
% 89.16/26.91 ((
% 89.16/26.91 (setminusSubset2) =>
% 89.16/26.91 ((
% 89.16/26.91 (setminusERneg) =>
% 89.16/26.91 ((
% 89.16/26.91 (setminusELneg) =>
% 89.16/26.91 ((
% 89.16/26.91 (setminusILneg) =>
% 89.16/26.91 ((
% 89.16/26.91 (setminusIRneg) =>
% 89.16/26.91 ((
% 89.16/26.91 (setminusLsub) =>
% 89.16/26.91 ((
% 89.16/26.91 (setminusSubset1) =>
% 89.16/26.91 ((
% 89.16/26.91 (symdiffE) =>
% 89.16/26.91 ((
% 89.16/26.91 (symdiffI1) =>
% 89.16/26.91 ((
% 89.16/26.91 (symdiffI2) =>
% 89.16/26.91 ((
% 89.16/26.91 (symdiffIneg1) =>
% 89.16/26.91 ((
% 89.16/26.91 (symdiffIneg2) =>
% 89.16/26.91 ((
% 89.16/26.91 (secondinupair) =>
% 89.16/26.91 ((
% 89.16/26.91 (setukpairIL) =>
% 89.16/26.91 ((
% 89.16/26.91 (setukpairIR) =>
% 89.16/26.91 ((
% 89.16/26.91 (kpairiskpair) =>
% 89.16/26.91 ((
% 89.16/26.91 (kpairp) =>
% 89.16/26.91 ((
% 89.16/26.91 (singletonsubset) =>
% 89.16/26.91 ((
% 89.16/26.91 (singletoninpowerset) =>
% 89.16/26.91 ((
% 89.16/26.91 (singletoninpowunion) =>
% 89.16/26.91 ((
% 89.16/26.91 (upairset2E) =>
% 89.16/26.91 ((
% 89.16/26.91 (upairsubunion) =>
% 89.16/26.91 ((
% 89.16/26.91 (upairinpowunion) =>
% 89.16/26.91 ((
% 89.16/26.91 (ubforcartprodlem1) =>
% 89.16/26.91 ((
% 89.16/26.91 (ubforcartprodlem2) =>
% 89.16/26.91 ((
% 89.16/26.91 (ubforcartprodlem3) =>
% 89.16/26.91 ((
% 89.16/26.91 (cartprodpairin) =>
% 89.16/26.91 ((
% 89.16/26.91 (cartprodmempair1) =>
% 89.16/26.91 ((
% 89.16/26.91 (cartprodmempair) =>
% 89.16/26.91 ((
% 89.16/26.91 (setunionE2) =>
% 89.16/26.91 ((
% 89.16/26.91 (setunionsingleton1) =>
% 89.16/26.91 ((
% 89.16/26.91 (setunionsingleton2) =>
% 89.16/26.91 ((
% 89.16/26.91 (setunionsingleton) =>
% 89.16/26.91 ((
% 89.16/26.91 (singletonprop) =>
% 89.16/26.91 ((
% 89.16/26.91 (ex1E1) =>
% 89.16/26.91 ((
% 89.16/26.91 (ex1I) =>
% 89.16/26.91 ((
% 89.16/26.91 (ex1I2) =>
% 89.16/26.91 ((
% 89.16/26.91 (singletonsuniq) =>
% 89.16/26.91 ((
% 89.16/26.91 (setukpairinjL1) =>
% 89.16/26.91 ((
% 89.16/26.91 (kfstsingleton) =>
% 89.16/26.91 ((
% 89.16/26.91 (theprop) =>
% 89.16/26.91 ((
% 89.16/26.91 (kfstpairEq) =>
% 89.16/26.91 ((
% 89.16/26.91 (cartprodfstin) =>
% 89.16/26.91 ((
% 89.16/26.91 (setukpairinjL2) =>
% 89.16/26.91 ((
% 89.16/26.91 (setukpairinjL) =>
% 89.16/26.91 ((
% 89.16/26.91 (setukpairinjR11) =>
% 89.16/26.91 ((
% 89.16/26.91 (setukpairinjR12) =>
% 89.16/26.91 ((
% 89.16/26.91 (setukpairinjR1) =>
% 89.16/26.91 ((
% 89.16/26.91 (upairequniteq) =>
% 89.16/26.91 ((
% 89.16/26.91 (setukpairinjR2) =>
% 89.16/26.91 ((
% 89.16/26.91 (setukpairinjR) =>
% 89.16/26.91 ((
% 89.16/26.91 (ksndsingleton) =>
% 89.16/26.91 ((
% 89.16/26.91 (ksndpairEq) =>
% 89.16/26.91 ((
% 89.16/26.91 (kpairsurjEq) =>
% 89.16/26.91 ((
% 89.16/26.91 (cartprodsndin) =>
% 89.16/26.91 ((
% 89.16/26.91 (cartprodpairmemEL) =>
% 89.16/26.91 ((
% 89.16/26.91 (cartprodpairmemER) =>
% 89.16/26.91 ((
% 89.16/26.91 (cartprodmempaircEq) =>
% 89.16/26.91 ((
% 89.16/26.91 (cartprodfstpairEq) =>
% 89.16/26.91 ((
% 89.16/26.91 (cartprodsndpairEq) =>
% 89.16/26.91 ((
% 89.16/26.91 (cartprodpairsurjEq) =>
% 89.16/26.91 ((
% 89.16/26.91 (dpsetconstrI) =>
% 89.16/26.91 ((
% 89.16/26.91 (dpsetconstrSub) =>
% 89.16/26.91 ((
% 89.16/26.91 (setOfPairsIsBReln) =>
% 89.16/26.91 ((
% 89.16/26.91 (dpsetconstrERa) =>
% 89.16/26.91 ((
% 89.16/26.91 (dpsetconstrEL1) =>
% 89.16/26.91 ((
% 89.16/26.91 (dpsetconstrEL2) =>
% 89.16/26.91 ((
% 89.16/26.91 (dpsetconstrER) =>
% 89.16/26.91 ((
% 89.16/26.91 (funcImageSingleton) =>
% 89.16/26.91 ((
% 89.16/26.91 (apProp) =>
% 89.16/26.91 ((
% 89.16/26.91 (app) =>
% 89.16/26.91 ((
% 89.16/26.91 (infuncsetfunc) =>
% 89.16/26.91 ((
% 89.16/26.91 (ap2p) =>
% 89.16/26.91 ((
% 89.16/26.91 (funcinfuncset) =>
% 89.16/26.91 ((
% 89.16/26.91 (lamProp) =>
% 89.16/26.91 ((
% 89.16/26.91 (lamp) =>
% 89.16/26.91 ((
% 89.16/26.91 (lam2p) =>
% 89.16/26.91 ((
% 89.16/26.91 (brelnall1) =>
% 89.16/26.91 ((
% 89.16/26.91 (brelnall2) =>
% 89.16/26.91 ((
% 89.16/26.91 (!!) @ (
% 89.16/26.91 (('#B') @ (
% 89.16/26.91 !!) @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#S') @ (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 '#S') @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 =>))) @
% 89.16/26.91 ex1)))) @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 !!))) @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#S') @ (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 '#B') @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 '#S') @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 =>))) @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#C') @ in)))))))) @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 !!))))) @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#C') @ (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 '#B') @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 '#B') @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 '#S') @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 =>))) @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#C') @ in)))))))))) @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#S') @ (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 '#S') @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 '#B'))) @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 =>))))))) @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#C') @ (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 '#B') @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 '#S') @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 =>))))))) @
% 89.16/26.91 (
% 89.16/26.91 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.16/26.91 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl878])).
% 89.16/26.91 thf(zip_derived_cl909, plain,
% 89.16/26.91 (~ (((notequalI1) =>
% 89.16/26.91 (((notequalI2) =>
% 89.16/26.91 (((subsetRefl) =>
% 89.16/26.91 (((subsetTrans) =>
% 89.16/26.91 (((setadjoinSub) =>
% 89.16/26.91 (((setadjoinSub2) =>
% 89.16/26.91 (((subset2powerset) =>
% 89.16/26.91 (((setextsub) =>
% 89.16/26.91 (((subsetemptysetimpeq) =>
% 89.16/26.91 (((powersetI1) =>
% 89.16/26.91 (((powersetE1) =>
% 89.16/26.91 (((inPowerset) =>
% 89.16/26.91 (((powersetsubset) =>
% 89.16/26.91 (((sepInPowerset) =>
% 89.16/26.91 (((sepSubset) =>
% 89.16/26.91 (((binunionIL) =>
% 89.16/26.91 (((upairset2IR) =>
% 89.16/26.91 (((binunionIR) =>
% 89.16/26.91 (((binunionEcases) =>
% 89.16/26.91 (((binunionE) =>
% 89.16/26.91 (((binunionLsub) =>
% 89.16/26.91 (((binunionRsub) =>
% 89.16/26.91 (((binintersectI) =>
% 89.16/26.91 (((binintersectSubset5) =>
% 89.16/26.91 (((binintersectEL) =>
% 89.16/26.91 (((binintersectLsub) =>
% 89.16/26.91 (((binintersectSubset2) =>
% 89.16/26.91 (((binintersectSubset3) =>
% 89.16/26.91 (((binintersectER) =>
% 89.16/26.91 (((disjointsetsI1) =>
% 89.16/26.91 ((
% 89.16/26.91 (binintersectRsub) =>
% 89.16/26.91 ((
% 89.16/26.91 (binintersectSubset4) =>
% 89.16/26.91 ((
% 89.16/26.91 (binintersectSubset1) =>
% 89.16/26.91 ((
% 89.16/26.91 (bs114d) =>
% 89.16/26.91 ((
% 89.16/26.91 (setminusI) =>
% 89.16/26.91 ((
% 89.16/26.91 (setminusEL) =>
% 89.16/26.91 ((
% 89.16/26.91 (setminusER) =>
% 89.16/26.91 ((
% 89.16/26.91 (setminusSubset2) =>
% 89.16/26.91 ((
% 89.16/26.91 (setminusERneg) =>
% 89.16/26.91 ((
% 89.16/26.91 (setminusELneg) =>
% 89.16/26.91 ((
% 89.16/26.91 (setminusILneg) =>
% 89.16/26.91 ((
% 89.16/26.91 (setminusIRneg) =>
% 89.16/26.91 ((
% 89.16/26.91 (setminusLsub) =>
% 89.16/26.91 ((
% 89.16/26.91 (setminusSubset1) =>
% 89.16/26.91 ((
% 89.16/26.91 (symdiffE) =>
% 89.16/26.91 ((
% 89.16/26.91 (symdiffI1) =>
% 89.16/26.91 ((
% 89.16/26.91 (symdiffI2) =>
% 89.16/26.91 ((
% 89.16/26.91 (symdiffIneg1) =>
% 89.16/26.91 ((
% 89.16/26.91 (symdiffIneg2) =>
% 89.16/26.91 ((
% 89.16/26.91 (secondinupair) =>
% 89.16/26.91 ((
% 89.16/26.91 (setukpairIL) =>
% 89.16/26.91 ((
% 89.16/26.91 (setukpairIR) =>
% 89.16/26.91 ((
% 89.16/26.91 (kpairiskpair) =>
% 89.16/26.91 ((
% 89.16/26.91 (kpairp) =>
% 89.16/26.91 ((
% 89.16/26.91 (singletonsubset) =>
% 89.16/26.91 ((
% 89.16/26.91 (singletoninpowerset) =>
% 89.16/26.91 ((
% 89.16/26.91 (singletoninpowunion) =>
% 89.16/26.91 ((
% 89.16/26.91 (upairset2E) =>
% 89.16/26.91 ((
% 89.16/26.91 (upairsubunion) =>
% 89.16/26.91 ((
% 89.16/26.91 (upairinpowunion) =>
% 89.16/26.91 ((
% 89.16/26.91 (ubforcartprodlem1) =>
% 89.16/26.91 ((
% 89.16/26.91 (ubforcartprodlem2) =>
% 89.16/26.91 ((
% 89.16/26.91 (ubforcartprodlem3) =>
% 89.16/26.91 ((
% 89.16/26.91 (cartprodpairin) =>
% 89.16/26.91 ((
% 89.16/26.91 (cartprodmempair1) =>
% 89.16/26.91 ((
% 89.16/26.91 (cartprodmempair) =>
% 89.16/26.91 ((
% 89.16/26.91 (setunionE2) =>
% 89.16/26.91 ((
% 89.16/26.91 (setunionsingleton1) =>
% 89.16/26.91 ((
% 89.16/26.91 (setunionsingleton2) =>
% 89.16/26.91 ((
% 89.16/26.91 (setunionsingleton) =>
% 89.16/26.91 ((
% 89.16/26.91 (singletonprop) =>
% 89.16/26.91 ((
% 89.16/26.91 (ex1E1) =>
% 89.16/26.91 ((
% 89.16/26.91 (ex1I) =>
% 89.16/26.91 ((
% 89.16/26.91 (ex1I2) =>
% 89.16/26.91 ((
% 89.16/26.91 (singletonsuniq) =>
% 89.16/26.91 ((
% 89.16/26.91 (setukpairinjL1) =>
% 89.16/26.91 ((
% 89.16/26.91 (kfstsingleton) =>
% 89.16/26.91 ((
% 89.16/26.91 (theprop) =>
% 89.16/26.91 ((
% 89.16/26.91 (kfstpairEq) =>
% 89.16/26.91 ((
% 89.16/26.91 (cartprodfstin) =>
% 89.16/26.91 ((
% 89.16/26.91 (setukpairinjL2) =>
% 89.16/26.91 ((
% 89.16/26.91 (setukpairinjL) =>
% 89.16/26.91 ((
% 89.16/26.91 (setukpairinjR11) =>
% 89.16/26.91 ((
% 89.16/26.91 (setukpairinjR12) =>
% 89.16/26.91 ((
% 89.16/26.91 (setukpairinjR1) =>
% 89.16/26.91 ((
% 89.16/26.91 (upairequniteq) =>
% 89.16/26.91 ((
% 89.16/26.91 (setukpairinjR2) =>
% 89.16/26.91 ((
% 89.16/26.91 (setukpairinjR) =>
% 89.16/26.91 ((
% 89.16/26.91 (ksndsingleton) =>
% 89.16/26.91 ((
% 89.16/26.91 (ksndpairEq) =>
% 89.16/26.91 ((
% 89.16/26.91 (kpairsurjEq) =>
% 89.16/26.91 ((
% 89.16/26.91 (cartprodsndin) =>
% 89.16/26.91 ((
% 89.16/26.91 (cartprodpairmemEL) =>
% 89.16/26.91 ((
% 89.16/26.91 (cartprodpairmemER) =>
% 89.16/26.91 ((
% 89.16/26.91 (cartprodmempaircEq) =>
% 89.16/26.91 ((
% 89.16/26.91 (cartprodfstpairEq) =>
% 89.16/26.91 ((
% 89.16/26.91 (cartprodsndpairEq) =>
% 89.16/26.91 ((
% 89.16/26.91 (cartprodpairsurjEq) =>
% 89.16/26.91 ((
% 89.16/26.91 (dpsetconstrI) =>
% 89.16/26.91 ((
% 89.16/26.91 (dpsetconstrSub) =>
% 89.16/26.91 ((
% 89.16/26.91 (setOfPairsIsBReln) =>
% 89.16/26.91 ((
% 89.16/26.91 (dpsetconstrERa) =>
% 89.16/26.91 ((
% 89.16/26.91 (dpsetconstrEL1) =>
% 89.16/26.91 ((
% 89.16/26.91 (dpsetconstrEL2) =>
% 89.16/26.91 ((
% 89.16/26.91 (dpsetconstrER) =>
% 89.16/26.91 ((
% 89.16/26.91 (funcImageSingleton) =>
% 89.16/26.91 ((
% 89.16/26.91 (apProp) =>
% 89.16/26.91 ((
% 89.16/26.91 (app) =>
% 89.16/26.91 ((
% 89.16/26.91 (infuncsetfunc) =>
% 89.16/26.91 ((
% 89.16/26.91 (ap2p) =>
% 89.16/26.91 ((
% 89.16/26.91 (funcinfuncset) =>
% 89.16/26.91 ((
% 89.16/26.91 (lamProp) =>
% 89.16/26.91 ((
% 89.16/26.91 (lamp) =>
% 89.16/26.91 ((
% 89.16/26.91 (lam2p) =>
% 89.16/26.91 ((
% 89.16/26.91 (brelnall1) =>
% 89.16/26.91 ((
% 89.16/26.91 (brelnall2) =>
% 89.16/26.91 ((
% 89.16/26.91 (!!) @ (
% 89.16/26.91 (('#B') @ (
% 89.16/26.91 !!) @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#S') @ (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 '#S') @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 =>))) @
% 89.16/26.91 ex1)))) @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 !!))) @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#S') @ (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 '#B') @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 '#S') @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 =>))) @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#C') @ in)))))))) @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 !!))))) @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#C') @ (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 '#B') @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 '#B') @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 '#S') @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 =>))) @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#C') @ in)))))))))) @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#S') @ (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 '#S') @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 '#B'))) @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 =>))))))) @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#C') @ (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 '#B') @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 '#S') @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 =>))))))) @
% 89.16/26.91 (
% 89.16/26.91 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.16/26.91 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl896])).
% 89.16/26.91 thf(zip_derived_cl924, plain,
% 89.16/26.91 (~ (((notequalI2) =>
% 89.16/26.91 (((subsetRefl) =>
% 89.16/26.91 (((subsetTrans) =>
% 89.16/26.91 (((setadjoinSub) =>
% 89.16/26.91 (((setadjoinSub2) =>
% 89.16/26.91 (((subset2powerset) =>
% 89.16/26.91 (((setextsub) =>
% 89.16/26.91 (((subsetemptysetimpeq) =>
% 89.16/26.91 (((powersetI1) =>
% 89.16/26.91 (((powersetE1) =>
% 89.16/26.91 (((inPowerset) =>
% 89.16/26.91 (((powersetsubset) =>
% 89.16/26.91 (((sepInPowerset) =>
% 89.16/26.91 (((sepSubset) =>
% 89.16/26.91 (((binunionIL) =>
% 89.16/26.91 (((upairset2IR) =>
% 89.16/26.91 (((binunionIR) =>
% 89.16/26.91 (((binunionEcases) =>
% 89.16/26.91 (((binunionE) =>
% 89.16/26.91 (((binunionLsub) =>
% 89.16/26.91 (((binunionRsub) =>
% 89.16/26.91 (((binintersectI) =>
% 89.16/26.91 (((binintersectSubset5) =>
% 89.16/26.91 (((binintersectEL) =>
% 89.16/26.91 (((binintersectLsub) =>
% 89.16/26.91 (((binintersectSubset2) =>
% 89.16/26.91 (((binintersectSubset3) =>
% 89.16/26.91 (((binintersectER) =>
% 89.16/26.91 (((disjointsetsI1) =>
% 89.16/26.91 (((binintersectRsub) =>
% 89.16/26.91 ((
% 89.16/26.91 (binintersectSubset4) =>
% 89.16/26.91 ((
% 89.16/26.91 (binintersectSubset1) =>
% 89.16/26.91 ((
% 89.16/26.91 (bs114d) =>
% 89.16/26.91 ((
% 89.16/26.91 (setminusI) =>
% 89.16/26.91 ((
% 89.16/26.91 (setminusEL) =>
% 89.16/26.91 ((
% 89.16/26.91 (setminusER) =>
% 89.16/26.91 ((
% 89.16/26.91 (setminusSubset2) =>
% 89.16/26.91 ((
% 89.16/26.91 (setminusERneg) =>
% 89.16/26.91 ((
% 89.16/26.91 (setminusELneg) =>
% 89.16/26.91 ((
% 89.16/26.91 (setminusILneg) =>
% 89.16/26.91 ((
% 89.16/26.91 (setminusIRneg) =>
% 89.16/26.91 ((
% 89.16/26.91 (setminusLsub) =>
% 89.16/26.91 ((
% 89.16/26.91 (setminusSubset1) =>
% 89.16/26.91 ((
% 89.16/26.91 (symdiffE) =>
% 89.16/26.91 ((
% 89.16/26.91 (symdiffI1) =>
% 89.16/26.91 ((
% 89.16/26.91 (symdiffI2) =>
% 89.16/26.91 ((
% 89.16/26.91 (symdiffIneg1) =>
% 89.16/26.91 ((
% 89.16/26.91 (symdiffIneg2) =>
% 89.16/26.91 ((
% 89.16/26.91 (secondinupair) =>
% 89.16/26.91 ((
% 89.16/26.91 (setukpairIL) =>
% 89.16/26.91 ((
% 89.16/26.91 (setukpairIR) =>
% 89.16/26.91 ((
% 89.16/26.91 (kpairiskpair) =>
% 89.16/26.91 ((
% 89.16/26.91 (kpairp) =>
% 89.16/26.91 ((
% 89.16/26.91 (singletonsubset) =>
% 89.16/26.91 ((
% 89.16/26.91 (singletoninpowerset) =>
% 89.16/26.91 ((
% 89.16/26.91 (singletoninpowunion) =>
% 89.16/26.91 ((
% 89.16/26.91 (upairset2E) =>
% 89.16/26.91 ((
% 89.16/26.91 (upairsubunion) =>
% 89.16/26.91 ((
% 89.16/26.91 (upairinpowunion) =>
% 89.16/26.91 ((
% 89.16/26.91 (ubforcartprodlem1) =>
% 89.16/26.91 ((
% 89.16/26.91 (ubforcartprodlem2) =>
% 89.16/26.91 ((
% 89.16/26.91 (ubforcartprodlem3) =>
% 89.16/26.91 ((
% 89.16/26.91 (cartprodpairin) =>
% 89.16/26.91 ((
% 89.16/26.91 (cartprodmempair1) =>
% 89.16/26.91 ((
% 89.16/26.91 (cartprodmempair) =>
% 89.16/26.91 ((
% 89.16/26.91 (setunionE2) =>
% 89.16/26.91 ((
% 89.16/26.91 (setunionsingleton1) =>
% 89.16/26.91 ((
% 89.16/26.91 (setunionsingleton2) =>
% 89.16/26.91 ((
% 89.16/26.91 (setunionsingleton) =>
% 89.16/26.91 ((
% 89.16/26.91 (singletonprop) =>
% 89.16/26.91 ((
% 89.16/26.91 (ex1E1) =>
% 89.16/26.91 ((
% 89.16/26.91 (ex1I) =>
% 89.16/26.91 ((
% 89.16/26.91 (ex1I2) =>
% 89.16/26.91 ((
% 89.16/26.91 (singletonsuniq) =>
% 89.16/26.91 ((
% 89.16/26.91 (setukpairinjL1) =>
% 89.16/26.91 ((
% 89.16/26.91 (kfstsingleton) =>
% 89.16/26.91 ((
% 89.16/26.91 (theprop) =>
% 89.16/26.91 ((
% 89.16/26.91 (kfstpairEq) =>
% 89.16/26.91 ((
% 89.16/26.91 (cartprodfstin) =>
% 89.16/26.91 ((
% 89.16/26.91 (setukpairinjL2) =>
% 89.16/26.91 ((
% 89.16/26.91 (setukpairinjL) =>
% 89.16/26.91 ((
% 89.16/26.91 (setukpairinjR11) =>
% 89.16/26.91 ((
% 89.16/26.91 (setukpairinjR12) =>
% 89.16/26.91 ((
% 89.16/26.91 (setukpairinjR1) =>
% 89.16/26.91 ((
% 89.16/26.91 (upairequniteq) =>
% 89.16/26.91 ((
% 89.16/26.91 (setukpairinjR2) =>
% 89.16/26.91 ((
% 89.16/26.91 (setukpairinjR) =>
% 89.16/26.91 ((
% 89.16/26.91 (ksndsingleton) =>
% 89.16/26.91 ((
% 89.16/26.91 (ksndpairEq) =>
% 89.16/26.91 ((
% 89.16/26.91 (kpairsurjEq) =>
% 89.16/26.91 ((
% 89.16/26.91 (cartprodsndin) =>
% 89.16/26.91 ((
% 89.16/26.91 (cartprodpairmemEL) =>
% 89.16/26.91 ((
% 89.16/26.91 (cartprodpairmemER) =>
% 89.16/26.91 ((
% 89.16/26.91 (cartprodmempaircEq) =>
% 89.16/26.91 ((
% 89.16/26.91 (cartprodfstpairEq) =>
% 89.16/26.91 ((
% 89.16/26.91 (cartprodsndpairEq) =>
% 89.16/26.91 ((
% 89.16/26.91 (cartprodpairsurjEq) =>
% 89.16/26.91 ((
% 89.16/26.91 (dpsetconstrI) =>
% 89.16/26.91 ((
% 89.16/26.91 (dpsetconstrSub) =>
% 89.16/26.91 ((
% 89.16/26.91 (setOfPairsIsBReln) =>
% 89.16/26.91 ((
% 89.16/26.91 (dpsetconstrERa) =>
% 89.16/26.91 ((
% 89.16/26.91 (dpsetconstrEL1) =>
% 89.16/26.91 ((
% 89.16/26.91 (dpsetconstrEL2) =>
% 89.16/26.91 ((
% 89.16/26.91 (dpsetconstrER) =>
% 89.16/26.91 ((
% 89.16/26.91 (funcImageSingleton) =>
% 89.16/26.91 ((
% 89.16/26.91 (apProp) =>
% 89.16/26.91 ((
% 89.16/26.91 (app) =>
% 89.16/26.91 ((
% 89.16/26.91 (infuncsetfunc) =>
% 89.16/26.91 ((
% 89.16/26.91 (ap2p) =>
% 89.16/26.91 ((
% 89.16/26.91 (funcinfuncset) =>
% 89.16/26.91 ((
% 89.16/26.91 (lamProp) =>
% 89.16/26.91 ((
% 89.16/26.91 (lamp) =>
% 89.16/26.91 ((
% 89.16/26.91 (lam2p) =>
% 89.16/26.91 ((
% 89.16/26.91 (brelnall1) =>
% 89.16/26.91 ((
% 89.16/26.91 (brelnall2) =>
% 89.16/26.91 ((
% 89.16/26.91 (!!) @ (
% 89.16/26.91 (('#B') @ (
% 89.16/26.91 !!) @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#S') @ (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 '#S') @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 =>))) @
% 89.16/26.91 ex1)))) @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 !!))) @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#S') @ (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 '#B') @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 '#S') @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 =>))) @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#C') @ in)))))))) @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 !!))))) @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#C') @ (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 '#B') @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 '#B') @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 '#S') @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 =>))) @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#C') @ in)))))))))) @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#S') @ (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 '#S') @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 '#B'))) @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 =>))))))) @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#C') @ (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 '#B') @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 '#S') @
% 89.16/26.91 (
% 89.16/26.91 (
% 89.16/26.91 ('#B') @ (
% 89.16/26.91 =>))))))) @
% 89.16/26.91 (
% 89.16/26.91 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.16/26.91 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl909])).
% 89.16/26.91 thf(zip_derived_cl938, plain,
% 89.16/26.91 (~ (((subsetRefl) =>
% 89.16/26.91 (((subsetTrans) =>
% 89.16/26.91 (((setadjoinSub) =>
% 89.16/26.91 (((setadjoinSub2) =>
% 89.16/26.91 (((subset2powerset) =>
% 89.16/26.91 (((setextsub) =>
% 89.16/26.91 (((subsetemptysetimpeq) =>
% 89.16/26.91 (((powersetI1) =>
% 89.16/26.91 (((powersetE1) =>
% 89.16/26.91 (((inPowerset) =>
% 89.16/26.91 (((powersetsubset) =>
% 89.16/26.91 (((sepInPowerset) =>
% 89.16/26.91 (((sepSubset) =>
% 89.16/26.91 (((binunionIL) =>
% 89.16/26.91 (((upairset2IR) =>
% 89.16/26.91 (((binunionIR) =>
% 89.16/26.91 (((binunionEcases) =>
% 89.16/26.91 (((binunionE) =>
% 89.16/26.91 (((binunionLsub) =>
% 89.16/26.91 (((binunionRsub) =>
% 89.16/26.91 (((binintersectI) =>
% 89.16/26.91 (((binintersectSubset5) =>
% 89.16/26.91 (((binintersectEL) =>
% 89.16/26.91 (((binintersectLsub) =>
% 89.16/26.91 (((binintersectSubset2) =>
% 89.16/26.91 (((binintersectSubset3) =>
% 89.16/26.91 (((binintersectER) =>
% 89.16/26.91 (((disjointsetsI1) =>
% 89.16/26.91 (((binintersectRsub) =>
% 89.16/26.91 (((binintersectSubset4) =>
% 89.16/26.91 ((
% 89.16/26.91 (binintersectSubset1) =>
% 89.16/26.91 ((
% 89.16/26.91 (bs114d) =>
% 89.16/26.91 ((
% 89.16/26.91 (setminusI) =>
% 89.16/26.91 ((
% 89.16/26.91 (setminusEL) =>
% 89.16/26.91 ((
% 89.16/26.91 (setminusER) =>
% 89.16/26.91 ((
% 89.16/26.91 (setminusSubset2) =>
% 89.16/26.91 ((
% 89.16/26.91 (setminusERneg) =>
% 89.16/26.91 ((
% 89.16/26.91 (setminusELneg) =>
% 89.16/26.91 ((
% 89.16/26.91 (setminusILneg) =>
% 89.16/26.91 ((
% 89.16/26.91 (setminusIRneg) =>
% 89.16/26.91 ((
% 89.16/26.91 (setminusLsub) =>
% 89.16/26.91 ((
% 89.16/26.91 (setminusSubset1) =>
% 89.16/26.91 ((
% 89.16/26.91 (symdiffE) =>
% 89.16/26.91 ((
% 89.16/26.91 (symdiffI1) =>
% 89.16/26.91 ((
% 89.16/26.91 (symdiffI2) =>
% 89.16/26.91 ((
% 89.16/26.91 (symdiffIneg1) =>
% 89.16/26.91 ((
% 89.16/26.91 (symdiffIneg2) =>
% 89.16/26.91 ((
% 89.16/26.91 (secondinupair) =>
% 89.16/26.91 ((
% 89.16/26.91 (setukpairIL) =>
% 89.16/26.91 ((
% 89.16/26.91 (setukpairIR) =>
% 89.16/26.91 ((
% 89.16/26.91 (kpairiskpair) =>
% 89.16/26.91 ((
% 89.16/26.91 (kpairp) =>
% 89.16/26.91 ((
% 89.16/26.91 (singletonsubset) =>
% 89.16/26.91 ((
% 89.16/26.91 (singletoninpowerset) =>
% 89.16/26.91 ((
% 89.16/26.91 (singletoninpowunion) =>
% 89.16/26.91 ((
% 89.16/26.91 (upairset2E) =>
% 89.16/26.91 ((
% 89.16/26.91 (upairsubunion) =>
% 89.16/26.91 ((
% 89.16/26.91 (upairinpowunion) =>
% 89.16/26.91 ((
% 89.16/26.91 (ubforcartprodlem1) =>
% 89.16/26.91 ((
% 89.16/26.91 (ubforcartprodlem2) =>
% 89.16/26.91 ((
% 89.16/26.91 (ubforcartprodlem3) =>
% 89.16/26.91 ((
% 89.16/26.91 (cartprodpairin) =>
% 89.16/26.91 ((
% 89.16/26.91 (cartprodmempair1) =>
% 89.16/26.91 ((
% 89.16/26.91 (cartprodmempair) =>
% 89.16/26.91 ((
% 89.16/26.91 (setunionE2) =>
% 89.16/26.91 ((
% 89.16/26.91 (setunionsingleton1) =>
% 89.16/26.91 ((
% 89.16/26.91 (setunionsingleton2) =>
% 89.16/26.91 ((
% 89.16/26.91 (setunionsingleton) =>
% 89.16/26.91 ((
% 89.16/26.91 (singletonprop) =>
% 89.16/26.91 ((
% 89.16/26.91 (ex1E1) =>
% 89.16/26.91 ((
% 89.16/26.91 (ex1I) =>
% 89.16/26.91 ((
% 89.16/26.91 (ex1I2) =>
% 89.16/26.91 ((
% 89.16/26.91 (singletonsuniq) =>
% 89.16/26.91 ((
% 89.16/26.91 (setukpairinjL1) =>
% 89.16/26.91 ((
% 89.16/26.91 (kfstsingleton) =>
% 89.16/26.91 ((
% 89.16/26.91 (theprop) =>
% 89.16/26.91 ((
% 89.16/26.91 (kfstpairEq) =>
% 89.16/26.91 ((
% 89.16/26.91 (cartprodfstin) =>
% 89.16/26.91 ((
% 89.16/26.91 (setukpairinjL2) =>
% 89.16/26.91 ((
% 89.16/26.91 (setukpairinjL) =>
% 89.16/26.91 ((
% 89.16/26.91 (setukpairinjR11) =>
% 89.16/26.91 ((
% 89.16/26.91 (setukpairinjR12) =>
% 89.16/26.91 ((
% 89.16/26.91 (setukpairinjR1) =>
% 89.16/26.91 ((
% 89.16/26.91 (upairequniteq) =>
% 89.16/26.91 ((
% 89.16/26.91 (setukpairinjR2) =>
% 89.16/26.91 ((
% 89.16/26.91 (setukpairinjR) =>
% 89.16/26.91 ((
% 89.16/26.91 (ksndsingleton) =>
% 89.16/26.91 ((
% 89.16/26.91 (ksndpairEq) =>
% 89.16/26.91 ((
% 89.16/26.91 (kpairsurjEq) =>
% 89.16/26.91 ((
% 89.16/26.91 (cartprodsndin) =>
% 89.16/26.91 ((
% 89.16/26.91 (cartprodpairmemEL) =>
% 89.16/26.91 ((
% 89.16/26.91 (cartprodpairmemER) =>
% 89.16/26.91 ((
% 89.16/26.91 (cartprodmempaircEq) =>
% 89.16/26.91 ((
% 89.16/26.91 (cartprodfstpairEq) =>
% 89.16/26.91 ((
% 89.16/26.91 (cartprodsndpairEq) =>
% 89.16/26.91 ((
% 89.16/26.91 (cartprodpairsurjEq) =>
% 89.16/26.91 ((
% 89.16/26.91 (dpsetconstrI) =>
% 89.16/26.91 ((
% 89.16/26.91 (dpsetconstrSub) =>
% 89.16/26.91 ((
% 89.16/26.91 (setOfPairsIsBReln) =>
% 89.16/26.91 ((
% 89.16/26.91 (dpsetconstrERa) =>
% 89.16/26.91 ((
% 89.16/26.91 (dpsetconstrEL1) =>
% 89.16/26.91 ((
% 89.16/26.91 (dpsetconstrEL2) =>
% 89.16/26.91 ((
% 89.16/26.92 (dpsetconstrER) =>
% 89.16/26.92 ((
% 89.16/26.92 (funcImageSingleton) =>
% 89.16/26.92 ((
% 89.16/26.92 (apProp) =>
% 89.16/26.92 ((
% 89.16/26.92 (app) =>
% 89.16/26.92 ((
% 89.16/26.92 (infuncsetfunc) =>
% 89.16/26.92 ((
% 89.16/26.92 (ap2p) =>
% 89.16/26.92 ((
% 89.16/26.92 (funcinfuncset) =>
% 89.16/26.92 ((
% 89.16/26.92 (lamProp) =>
% 89.16/26.92 ((
% 89.16/26.92 (lamp) =>
% 89.16/26.92 ((
% 89.16/26.92 (lam2p) =>
% 89.16/26.92 ((
% 89.16/26.92 (brelnall1) =>
% 89.16/26.92 ((
% 89.16/26.92 (brelnall2) =>
% 89.16/26.92 ((
% 89.16/26.92 (!!) @ (
% 89.16/26.92 (('#B') @ (
% 89.16/26.92 !!) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#S') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#S') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 =>))) @
% 89.16/26.92 ex1)))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 !!))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#S') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#B') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#S') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 =>))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#C') @ in)))))))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 !!))))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#C') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#B') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#B') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#S') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 =>))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#C') @ in)))))))))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#S') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#S') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#B'))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 =>))))))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#C') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#B') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#S') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 =>))))))) @
% 89.16/26.92 (
% 89.16/26.92 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.16/26.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl924])).
% 89.16/26.92 thf(zip_derived_cl952, plain,
% 89.16/26.92 (~ (((subsetTrans) =>
% 89.16/26.92 (((setadjoinSub) =>
% 89.16/26.92 (((setadjoinSub2) =>
% 89.16/26.92 (((subset2powerset) =>
% 89.16/26.92 (((setextsub) =>
% 89.16/26.92 (((subsetemptysetimpeq) =>
% 89.16/26.92 (((powersetI1) =>
% 89.16/26.92 (((powersetE1) =>
% 89.16/26.92 (((inPowerset) =>
% 89.16/26.92 (((powersetsubset) =>
% 89.16/26.92 (((sepInPowerset) =>
% 89.16/26.92 (((sepSubset) =>
% 89.16/26.92 (((binunionIL) =>
% 89.16/26.92 (((upairset2IR) =>
% 89.16/26.92 (((binunionIR) =>
% 89.16/26.92 (((binunionEcases) =>
% 89.16/26.92 (((binunionE) =>
% 89.16/26.92 (((binunionLsub) =>
% 89.16/26.92 (((binunionRsub) =>
% 89.16/26.92 (((binintersectI) =>
% 89.16/26.92 (((binintersectSubset5) =>
% 89.16/26.92 (((binintersectEL) =>
% 89.16/26.92 (((binintersectLsub) =>
% 89.16/26.92 (((binintersectSubset2) =>
% 89.16/26.92 (((binintersectSubset3) =>
% 89.16/26.92 (((binintersectER) =>
% 89.16/26.92 (((disjointsetsI1) =>
% 89.16/26.92 (((binintersectRsub) =>
% 89.16/26.92 (((binintersectSubset4) =>
% 89.16/26.92 (((binintersectSubset1) =>
% 89.16/26.92 ((
% 89.16/26.92 (bs114d) =>
% 89.16/26.92 ((
% 89.16/26.92 (setminusI) =>
% 89.16/26.92 ((
% 89.16/26.92 (setminusEL) =>
% 89.16/26.92 ((
% 89.16/26.92 (setminusER) =>
% 89.16/26.92 ((
% 89.16/26.92 (setminusSubset2) =>
% 89.16/26.92 ((
% 89.16/26.92 (setminusERneg) =>
% 89.16/26.92 ((
% 89.16/26.92 (setminusELneg) =>
% 89.16/26.92 ((
% 89.16/26.92 (setminusILneg) =>
% 89.16/26.92 ((
% 89.16/26.92 (setminusIRneg) =>
% 89.16/26.92 ((
% 89.16/26.92 (setminusLsub) =>
% 89.16/26.92 ((
% 89.16/26.92 (setminusSubset1) =>
% 89.16/26.92 ((
% 89.16/26.92 (symdiffE) =>
% 89.16/26.92 ((
% 89.16/26.92 (symdiffI1) =>
% 89.16/26.92 ((
% 89.16/26.92 (symdiffI2) =>
% 89.16/26.92 ((
% 89.16/26.92 (symdiffIneg1) =>
% 89.16/26.92 ((
% 89.16/26.92 (symdiffIneg2) =>
% 89.16/26.92 ((
% 89.16/26.92 (secondinupair) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairIL) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairIR) =>
% 89.16/26.92 ((
% 89.16/26.92 (kpairiskpair) =>
% 89.16/26.92 ((
% 89.16/26.92 (kpairp) =>
% 89.16/26.92 ((
% 89.16/26.92 (singletonsubset) =>
% 89.16/26.92 ((
% 89.16/26.92 (singletoninpowerset) =>
% 89.16/26.92 ((
% 89.16/26.92 (singletoninpowunion) =>
% 89.16/26.92 ((
% 89.16/26.92 (upairset2E) =>
% 89.16/26.92 ((
% 89.16/26.92 (upairsubunion) =>
% 89.16/26.92 ((
% 89.16/26.92 (upairinpowunion) =>
% 89.16/26.92 ((
% 89.16/26.92 (ubforcartprodlem1) =>
% 89.16/26.92 ((
% 89.16/26.92 (ubforcartprodlem2) =>
% 89.16/26.92 ((
% 89.16/26.92 (ubforcartprodlem3) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodpairin) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodmempair1) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodmempair) =>
% 89.16/26.92 ((
% 89.16/26.92 (setunionE2) =>
% 89.16/26.92 ((
% 89.16/26.92 (setunionsingleton1) =>
% 89.16/26.92 ((
% 89.16/26.92 (setunionsingleton2) =>
% 89.16/26.92 ((
% 89.16/26.92 (setunionsingleton) =>
% 89.16/26.92 ((
% 89.16/26.92 (singletonprop) =>
% 89.16/26.92 ((
% 89.16/26.92 (ex1E1) =>
% 89.16/26.92 ((
% 89.16/26.92 (ex1I) =>
% 89.16/26.92 ((
% 89.16/26.92 (ex1I2) =>
% 89.16/26.92 ((
% 89.16/26.92 (singletonsuniq) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjL1) =>
% 89.16/26.92 ((
% 89.16/26.92 (kfstsingleton) =>
% 89.16/26.92 ((
% 89.16/26.92 (theprop) =>
% 89.16/26.92 ((
% 89.16/26.92 (kfstpairEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodfstin) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjL2) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjL) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjR11) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjR12) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjR1) =>
% 89.16/26.92 ((
% 89.16/26.92 (upairequniteq) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjR2) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjR) =>
% 89.16/26.92 ((
% 89.16/26.92 (ksndsingleton) =>
% 89.16/26.92 ((
% 89.16/26.92 (ksndpairEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (kpairsurjEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodsndin) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodpairmemEL) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodpairmemER) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodmempaircEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodfstpairEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodsndpairEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodpairsurjEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (dpsetconstrI) =>
% 89.16/26.92 ((
% 89.16/26.92 (dpsetconstrSub) =>
% 89.16/26.92 ((
% 89.16/26.92 (setOfPairsIsBReln) =>
% 89.16/26.92 ((
% 89.16/26.92 (dpsetconstrERa) =>
% 89.16/26.92 ((
% 89.16/26.92 (dpsetconstrEL1) =>
% 89.16/26.92 ((
% 89.16/26.92 (dpsetconstrEL2) =>
% 89.16/26.92 ((
% 89.16/26.92 (dpsetconstrER) =>
% 89.16/26.92 ((
% 89.16/26.92 (funcImageSingleton) =>
% 89.16/26.92 ((
% 89.16/26.92 (apProp) =>
% 89.16/26.92 ((
% 89.16/26.92 (app) =>
% 89.16/26.92 ((
% 89.16/26.92 (infuncsetfunc) =>
% 89.16/26.92 ((
% 89.16/26.92 (ap2p) =>
% 89.16/26.92 ((
% 89.16/26.92 (funcinfuncset) =>
% 89.16/26.92 ((
% 89.16/26.92 (lamProp) =>
% 89.16/26.92 ((
% 89.16/26.92 (lamp) =>
% 89.16/26.92 ((
% 89.16/26.92 (lam2p) =>
% 89.16/26.92 ((
% 89.16/26.92 (brelnall1) =>
% 89.16/26.92 ((
% 89.16/26.92 (brelnall2) =>
% 89.16/26.92 ((
% 89.16/26.92 (!!) @ (
% 89.16/26.92 (('#B') @ (
% 89.16/26.92 !!) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#S') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#S') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 =>))) @
% 89.16/26.92 ex1)))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 !!))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#S') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#B') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#S') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 =>))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#C') @ in)))))))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 !!))))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#C') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#B') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#B') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#S') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 =>))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#C') @ in)))))))))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#S') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#S') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#B'))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 =>))))))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#C') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#B') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#S') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 =>))))))) @
% 89.16/26.92 (
% 89.16/26.92 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.16/26.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl938])).
% 89.16/26.92 thf(zip_derived_cl967, plain,
% 89.16/26.92 (~ (((setadjoinSub) =>
% 89.16/26.92 (((setadjoinSub2) =>
% 89.16/26.92 (((subset2powerset) =>
% 89.16/26.92 (((setextsub) =>
% 89.16/26.92 (((subsetemptysetimpeq) =>
% 89.16/26.92 (((powersetI1) =>
% 89.16/26.92 (((powersetE1) =>
% 89.16/26.92 (((inPowerset) =>
% 89.16/26.92 (((powersetsubset) =>
% 89.16/26.92 (((sepInPowerset) =>
% 89.16/26.92 (((sepSubset) =>
% 89.16/26.92 (((binunionIL) =>
% 89.16/26.92 (((upairset2IR) =>
% 89.16/26.92 (((binunionIR) =>
% 89.16/26.92 (((binunionEcases) =>
% 89.16/26.92 (((binunionE) =>
% 89.16/26.92 (((binunionLsub) =>
% 89.16/26.92 (((binunionRsub) =>
% 89.16/26.92 (((binintersectI) =>
% 89.16/26.92 (((binintersectSubset5) =>
% 89.16/26.92 (((binintersectEL) =>
% 89.16/26.92 (((binintersectLsub) =>
% 89.16/26.92 (((binintersectSubset2) =>
% 89.16/26.92 (((binintersectSubset3) =>
% 89.16/26.92 (((binintersectER) =>
% 89.16/26.92 (((disjointsetsI1) =>
% 89.16/26.92 (((binintersectRsub) =>
% 89.16/26.92 (((binintersectSubset4) =>
% 89.16/26.92 (((binintersectSubset1) =>
% 89.16/26.92 (((bs114d) =>
% 89.16/26.92 ((
% 89.16/26.92 (setminusI) =>
% 89.16/26.92 ((
% 89.16/26.92 (setminusEL) =>
% 89.16/26.92 ((
% 89.16/26.92 (setminusER) =>
% 89.16/26.92 ((
% 89.16/26.92 (setminusSubset2) =>
% 89.16/26.92 ((
% 89.16/26.92 (setminusERneg) =>
% 89.16/26.92 ((
% 89.16/26.92 (setminusELneg) =>
% 89.16/26.92 ((
% 89.16/26.92 (setminusILneg) =>
% 89.16/26.92 ((
% 89.16/26.92 (setminusIRneg) =>
% 89.16/26.92 ((
% 89.16/26.92 (setminusLsub) =>
% 89.16/26.92 ((
% 89.16/26.92 (setminusSubset1) =>
% 89.16/26.92 ((
% 89.16/26.92 (symdiffE) =>
% 89.16/26.92 ((
% 89.16/26.92 (symdiffI1) =>
% 89.16/26.92 ((
% 89.16/26.92 (symdiffI2) =>
% 89.16/26.92 ((
% 89.16/26.92 (symdiffIneg1) =>
% 89.16/26.92 ((
% 89.16/26.92 (symdiffIneg2) =>
% 89.16/26.92 ((
% 89.16/26.92 (secondinupair) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairIL) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairIR) =>
% 89.16/26.92 ((
% 89.16/26.92 (kpairiskpair) =>
% 89.16/26.92 ((
% 89.16/26.92 (kpairp) =>
% 89.16/26.92 ((
% 89.16/26.92 (singletonsubset) =>
% 89.16/26.92 ((
% 89.16/26.92 (singletoninpowerset) =>
% 89.16/26.92 ((
% 89.16/26.92 (singletoninpowunion) =>
% 89.16/26.92 ((
% 89.16/26.92 (upairset2E) =>
% 89.16/26.92 ((
% 89.16/26.92 (upairsubunion) =>
% 89.16/26.92 ((
% 89.16/26.92 (upairinpowunion) =>
% 89.16/26.92 ((
% 89.16/26.92 (ubforcartprodlem1) =>
% 89.16/26.92 ((
% 89.16/26.92 (ubforcartprodlem2) =>
% 89.16/26.92 ((
% 89.16/26.92 (ubforcartprodlem3) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodpairin) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodmempair1) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodmempair) =>
% 89.16/26.92 ((
% 89.16/26.92 (setunionE2) =>
% 89.16/26.92 ((
% 89.16/26.92 (setunionsingleton1) =>
% 89.16/26.92 ((
% 89.16/26.92 (setunionsingleton2) =>
% 89.16/26.92 ((
% 89.16/26.92 (setunionsingleton) =>
% 89.16/26.92 ((
% 89.16/26.92 (singletonprop) =>
% 89.16/26.92 ((
% 89.16/26.92 (ex1E1) =>
% 89.16/26.92 ((
% 89.16/26.92 (ex1I) =>
% 89.16/26.92 ((
% 89.16/26.92 (ex1I2) =>
% 89.16/26.92 ((
% 89.16/26.92 (singletonsuniq) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjL1) =>
% 89.16/26.92 ((
% 89.16/26.92 (kfstsingleton) =>
% 89.16/26.92 ((
% 89.16/26.92 (theprop) =>
% 89.16/26.92 ((
% 89.16/26.92 (kfstpairEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodfstin) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjL2) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjL) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjR11) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjR12) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjR1) =>
% 89.16/26.92 ((
% 89.16/26.92 (upairequniteq) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjR2) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjR) =>
% 89.16/26.92 ((
% 89.16/26.92 (ksndsingleton) =>
% 89.16/26.92 ((
% 89.16/26.92 (ksndpairEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (kpairsurjEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodsndin) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodpairmemEL) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodpairmemER) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodmempaircEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodfstpairEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodsndpairEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodpairsurjEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (dpsetconstrI) =>
% 89.16/26.92 ((
% 89.16/26.92 (dpsetconstrSub) =>
% 89.16/26.92 ((
% 89.16/26.92 (setOfPairsIsBReln) =>
% 89.16/26.92 ((
% 89.16/26.92 (dpsetconstrERa) =>
% 89.16/26.92 ((
% 89.16/26.92 (dpsetconstrEL1) =>
% 89.16/26.92 ((
% 89.16/26.92 (dpsetconstrEL2) =>
% 89.16/26.92 ((
% 89.16/26.92 (dpsetconstrER) =>
% 89.16/26.92 ((
% 89.16/26.92 (funcImageSingleton) =>
% 89.16/26.92 ((
% 89.16/26.92 (apProp) =>
% 89.16/26.92 ((
% 89.16/26.92 (app) =>
% 89.16/26.92 ((
% 89.16/26.92 (infuncsetfunc) =>
% 89.16/26.92 ((
% 89.16/26.92 (ap2p) =>
% 89.16/26.92 ((
% 89.16/26.92 (funcinfuncset) =>
% 89.16/26.92 ((
% 89.16/26.92 (lamProp) =>
% 89.16/26.92 ((
% 89.16/26.92 (lamp) =>
% 89.16/26.92 ((
% 89.16/26.92 (lam2p) =>
% 89.16/26.92 ((
% 89.16/26.92 (brelnall1) =>
% 89.16/26.92 ((
% 89.16/26.92 (brelnall2) =>
% 89.16/26.92 ((
% 89.16/26.92 (!!) @ (
% 89.16/26.92 (('#B') @ (
% 89.16/26.92 !!) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#S') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#S') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 =>))) @
% 89.16/26.92 ex1)))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 !!))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#S') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#B') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#S') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 =>))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#C') @ in)))))))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 !!))))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#C') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#B') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#B') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#S') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 =>))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#C') @ in)))))))))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#S') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#S') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#B'))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 =>))))))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#C') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#B') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#S') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 =>))))))) @
% 89.16/26.92 (
% 89.16/26.92 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.16/26.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl952])).
% 89.16/26.92 thf(zip_derived_cl984, plain,
% 89.16/26.92 (~ (((setadjoinSub2) =>
% 89.16/26.92 (((subset2powerset) =>
% 89.16/26.92 (((setextsub) =>
% 89.16/26.92 (((subsetemptysetimpeq) =>
% 89.16/26.92 (((powersetI1) =>
% 89.16/26.92 (((powersetE1) =>
% 89.16/26.92 (((inPowerset) =>
% 89.16/26.92 (((powersetsubset) =>
% 89.16/26.92 (((sepInPowerset) =>
% 89.16/26.92 (((sepSubset) =>
% 89.16/26.92 (((binunionIL) =>
% 89.16/26.92 (((upairset2IR) =>
% 89.16/26.92 (((binunionIR) =>
% 89.16/26.92 (((binunionEcases) =>
% 89.16/26.92 (((binunionE) =>
% 89.16/26.92 (((binunionLsub) =>
% 89.16/26.92 (((binunionRsub) =>
% 89.16/26.92 (((binintersectI) =>
% 89.16/26.92 (((binintersectSubset5) =>
% 89.16/26.92 (((binintersectEL) =>
% 89.16/26.92 (((binintersectLsub) =>
% 89.16/26.92 (((binintersectSubset2) =>
% 89.16/26.92 (((binintersectSubset3) =>
% 89.16/26.92 (((binintersectER) =>
% 89.16/26.92 (((disjointsetsI1) =>
% 89.16/26.92 (((binintersectRsub) =>
% 89.16/26.92 (((binintersectSubset4) =>
% 89.16/26.92 (((binintersectSubset1) =>
% 89.16/26.92 (((bs114d) =>
% 89.16/26.92 (((setminusI) =>
% 89.16/26.92 ((
% 89.16/26.92 (setminusEL) =>
% 89.16/26.92 ((
% 89.16/26.92 (setminusER) =>
% 89.16/26.92 ((
% 89.16/26.92 (setminusSubset2) =>
% 89.16/26.92 ((
% 89.16/26.92 (setminusERneg) =>
% 89.16/26.92 ((
% 89.16/26.92 (setminusELneg) =>
% 89.16/26.92 ((
% 89.16/26.92 (setminusILneg) =>
% 89.16/26.92 ((
% 89.16/26.92 (setminusIRneg) =>
% 89.16/26.92 ((
% 89.16/26.92 (setminusLsub) =>
% 89.16/26.92 ((
% 89.16/26.92 (setminusSubset1) =>
% 89.16/26.92 ((
% 89.16/26.92 (symdiffE) =>
% 89.16/26.92 ((
% 89.16/26.92 (symdiffI1) =>
% 89.16/26.92 ((
% 89.16/26.92 (symdiffI2) =>
% 89.16/26.92 ((
% 89.16/26.92 (symdiffIneg1) =>
% 89.16/26.92 ((
% 89.16/26.92 (symdiffIneg2) =>
% 89.16/26.92 ((
% 89.16/26.92 (secondinupair) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairIL) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairIR) =>
% 89.16/26.92 ((
% 89.16/26.92 (kpairiskpair) =>
% 89.16/26.92 ((
% 89.16/26.92 (kpairp) =>
% 89.16/26.92 ((
% 89.16/26.92 (singletonsubset) =>
% 89.16/26.92 ((
% 89.16/26.92 (singletoninpowerset) =>
% 89.16/26.92 ((
% 89.16/26.92 (singletoninpowunion) =>
% 89.16/26.92 ((
% 89.16/26.92 (upairset2E) =>
% 89.16/26.92 ((
% 89.16/26.92 (upairsubunion) =>
% 89.16/26.92 ((
% 89.16/26.92 (upairinpowunion) =>
% 89.16/26.92 ((
% 89.16/26.92 (ubforcartprodlem1) =>
% 89.16/26.92 ((
% 89.16/26.92 (ubforcartprodlem2) =>
% 89.16/26.92 ((
% 89.16/26.92 (ubforcartprodlem3) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodpairin) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodmempair1) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodmempair) =>
% 89.16/26.92 ((
% 89.16/26.92 (setunionE2) =>
% 89.16/26.92 ((
% 89.16/26.92 (setunionsingleton1) =>
% 89.16/26.92 ((
% 89.16/26.92 (setunionsingleton2) =>
% 89.16/26.92 ((
% 89.16/26.92 (setunionsingleton) =>
% 89.16/26.92 ((
% 89.16/26.92 (singletonprop) =>
% 89.16/26.92 ((
% 89.16/26.92 (ex1E1) =>
% 89.16/26.92 ((
% 89.16/26.92 (ex1I) =>
% 89.16/26.92 ((
% 89.16/26.92 (ex1I2) =>
% 89.16/26.92 ((
% 89.16/26.92 (singletonsuniq) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjL1) =>
% 89.16/26.92 ((
% 89.16/26.92 (kfstsingleton) =>
% 89.16/26.92 ((
% 89.16/26.92 (theprop) =>
% 89.16/26.92 ((
% 89.16/26.92 (kfstpairEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodfstin) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjL2) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjL) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjR11) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjR12) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjR1) =>
% 89.16/26.92 ((
% 89.16/26.92 (upairequniteq) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjR2) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjR) =>
% 89.16/26.92 ((
% 89.16/26.92 (ksndsingleton) =>
% 89.16/26.92 ((
% 89.16/26.92 (ksndpairEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (kpairsurjEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodsndin) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodpairmemEL) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodpairmemER) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodmempaircEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodfstpairEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodsndpairEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodpairsurjEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (dpsetconstrI) =>
% 89.16/26.92 ((
% 89.16/26.92 (dpsetconstrSub) =>
% 89.16/26.92 ((
% 89.16/26.92 (setOfPairsIsBReln) =>
% 89.16/26.92 ((
% 89.16/26.92 (dpsetconstrERa) =>
% 89.16/26.92 ((
% 89.16/26.92 (dpsetconstrEL1) =>
% 89.16/26.92 ((
% 89.16/26.92 (dpsetconstrEL2) =>
% 89.16/26.92 ((
% 89.16/26.92 (dpsetconstrER) =>
% 89.16/26.92 ((
% 89.16/26.92 (funcImageSingleton) =>
% 89.16/26.92 ((
% 89.16/26.92 (apProp) =>
% 89.16/26.92 ((
% 89.16/26.92 (app) =>
% 89.16/26.92 ((
% 89.16/26.92 (infuncsetfunc) =>
% 89.16/26.92 ((
% 89.16/26.92 (ap2p) =>
% 89.16/26.92 ((
% 89.16/26.92 (funcinfuncset) =>
% 89.16/26.92 ((
% 89.16/26.92 (lamProp) =>
% 89.16/26.92 ((
% 89.16/26.92 (lamp) =>
% 89.16/26.92 ((
% 89.16/26.92 (lam2p) =>
% 89.16/26.92 ((
% 89.16/26.92 (brelnall1) =>
% 89.16/26.92 ((
% 89.16/26.92 (brelnall2) =>
% 89.16/26.92 ((
% 89.16/26.92 (!!) @ (
% 89.16/26.92 (('#B') @ (
% 89.16/26.92 !!) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#S') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#S') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 =>))) @
% 89.16/26.92 ex1)))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 !!))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#S') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#B') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#S') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 =>))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#C') @ in)))))))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 !!))))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#C') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#B') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#B') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#S') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 =>))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#C') @ in)))))))))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#S') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#S') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#B'))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 =>))))))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#C') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#B') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#S') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 =>))))))) @
% 89.16/26.92 (
% 89.16/26.92 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.16/26.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl967])).
% 89.16/26.92 thf(zip_derived_cl1000, plain,
% 89.16/26.92 (~ (((subset2powerset) =>
% 89.16/26.92 (((setextsub) =>
% 89.16/26.92 (((subsetemptysetimpeq) =>
% 89.16/26.92 (((powersetI1) =>
% 89.16/26.92 (((powersetE1) =>
% 89.16/26.92 (((inPowerset) =>
% 89.16/26.92 (((powersetsubset) =>
% 89.16/26.92 (((sepInPowerset) =>
% 89.16/26.92 (((sepSubset) =>
% 89.16/26.92 (((binunionIL) =>
% 89.16/26.92 (((upairset2IR) =>
% 89.16/26.92 (((binunionIR) =>
% 89.16/26.92 (((binunionEcases) =>
% 89.16/26.92 (((binunionE) =>
% 89.16/26.92 (((binunionLsub) =>
% 89.16/26.92 (((binunionRsub) =>
% 89.16/26.92 (((binintersectI) =>
% 89.16/26.92 (((binintersectSubset5) =>
% 89.16/26.92 (((binintersectEL) =>
% 89.16/26.92 (((binintersectLsub) =>
% 89.16/26.92 (((binintersectSubset2) =>
% 89.16/26.92 (((binintersectSubset3) =>
% 89.16/26.92 (((binintersectER) =>
% 89.16/26.92 (((disjointsetsI1) =>
% 89.16/26.92 (((binintersectRsub) =>
% 89.16/26.92 (((binintersectSubset4) =>
% 89.16/26.92 (((binintersectSubset1) =>
% 89.16/26.92 (((bs114d) =>
% 89.16/26.92 (((setminusI) =>
% 89.16/26.92 (((setminusEL) =>
% 89.16/26.92 ((
% 89.16/26.92 (setminusER) =>
% 89.16/26.92 ((
% 89.16/26.92 (setminusSubset2) =>
% 89.16/26.92 ((
% 89.16/26.92 (setminusERneg) =>
% 89.16/26.92 ((
% 89.16/26.92 (setminusELneg) =>
% 89.16/26.92 ((
% 89.16/26.92 (setminusILneg) =>
% 89.16/26.92 ((
% 89.16/26.92 (setminusIRneg) =>
% 89.16/26.92 ((
% 89.16/26.92 (setminusLsub) =>
% 89.16/26.92 ((
% 89.16/26.92 (setminusSubset1) =>
% 89.16/26.92 ((
% 89.16/26.92 (symdiffE) =>
% 89.16/26.92 ((
% 89.16/26.92 (symdiffI1) =>
% 89.16/26.92 ((
% 89.16/26.92 (symdiffI2) =>
% 89.16/26.92 ((
% 89.16/26.92 (symdiffIneg1) =>
% 89.16/26.92 ((
% 89.16/26.92 (symdiffIneg2) =>
% 89.16/26.92 ((
% 89.16/26.92 (secondinupair) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairIL) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairIR) =>
% 89.16/26.92 ((
% 89.16/26.92 (kpairiskpair) =>
% 89.16/26.92 ((
% 89.16/26.92 (kpairp) =>
% 89.16/26.92 ((
% 89.16/26.92 (singletonsubset) =>
% 89.16/26.92 ((
% 89.16/26.92 (singletoninpowerset) =>
% 89.16/26.92 ((
% 89.16/26.92 (singletoninpowunion) =>
% 89.16/26.92 ((
% 89.16/26.92 (upairset2E) =>
% 89.16/26.92 ((
% 89.16/26.92 (upairsubunion) =>
% 89.16/26.92 ((
% 89.16/26.92 (upairinpowunion) =>
% 89.16/26.92 ((
% 89.16/26.92 (ubforcartprodlem1) =>
% 89.16/26.92 ((
% 89.16/26.92 (ubforcartprodlem2) =>
% 89.16/26.92 ((
% 89.16/26.92 (ubforcartprodlem3) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodpairin) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodmempair1) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodmempair) =>
% 89.16/26.92 ((
% 89.16/26.92 (setunionE2) =>
% 89.16/26.92 ((
% 89.16/26.92 (setunionsingleton1) =>
% 89.16/26.92 ((
% 89.16/26.92 (setunionsingleton2) =>
% 89.16/26.92 ((
% 89.16/26.92 (setunionsingleton) =>
% 89.16/26.92 ((
% 89.16/26.92 (singletonprop) =>
% 89.16/26.92 ((
% 89.16/26.92 (ex1E1) =>
% 89.16/26.92 ((
% 89.16/26.92 (ex1I) =>
% 89.16/26.92 ((
% 89.16/26.92 (ex1I2) =>
% 89.16/26.92 ((
% 89.16/26.92 (singletonsuniq) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjL1) =>
% 89.16/26.92 ((
% 89.16/26.92 (kfstsingleton) =>
% 89.16/26.92 ((
% 89.16/26.92 (theprop) =>
% 89.16/26.92 ((
% 89.16/26.92 (kfstpairEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodfstin) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjL2) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjL) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjR11) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjR12) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjR1) =>
% 89.16/26.92 ((
% 89.16/26.92 (upairequniteq) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjR2) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjR) =>
% 89.16/26.92 ((
% 89.16/26.92 (ksndsingleton) =>
% 89.16/26.92 ((
% 89.16/26.92 (ksndpairEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (kpairsurjEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodsndin) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodpairmemEL) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodpairmemER) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodmempaircEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodfstpairEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodsndpairEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodpairsurjEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (dpsetconstrI) =>
% 89.16/26.92 ((
% 89.16/26.92 (dpsetconstrSub) =>
% 89.16/26.92 ((
% 89.16/26.92 (setOfPairsIsBReln) =>
% 89.16/26.92 ((
% 89.16/26.92 (dpsetconstrERa) =>
% 89.16/26.92 ((
% 89.16/26.92 (dpsetconstrEL1) =>
% 89.16/26.92 ((
% 89.16/26.92 (dpsetconstrEL2) =>
% 89.16/26.92 ((
% 89.16/26.92 (dpsetconstrER) =>
% 89.16/26.92 ((
% 89.16/26.92 (funcImageSingleton) =>
% 89.16/26.92 ((
% 89.16/26.92 (apProp) =>
% 89.16/26.92 ((
% 89.16/26.92 (app) =>
% 89.16/26.92 ((
% 89.16/26.92 (infuncsetfunc) =>
% 89.16/26.92 ((
% 89.16/26.92 (ap2p) =>
% 89.16/26.92 ((
% 89.16/26.92 (funcinfuncset) =>
% 89.16/26.92 ((
% 89.16/26.92 (lamProp) =>
% 89.16/26.92 ((
% 89.16/26.92 (lamp) =>
% 89.16/26.92 ((
% 89.16/26.92 (lam2p) =>
% 89.16/26.92 ((
% 89.16/26.92 (brelnall1) =>
% 89.16/26.92 ((
% 89.16/26.92 (brelnall2) =>
% 89.16/26.92 ((
% 89.16/26.92 (!!) @ (
% 89.16/26.92 (('#B') @ (
% 89.16/26.92 !!) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#S') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#S') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 =>))) @
% 89.16/26.92 ex1)))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 !!))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#S') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#B') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#S') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 =>))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#C') @ in)))))))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 !!))))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#C') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#B') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#B') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#S') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 =>))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#C') @ in)))))))))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#S') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#S') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#B'))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 =>))))))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#C') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#B') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#S') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 =>))))))) @
% 89.16/26.92 (
% 89.16/26.92 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.16/26.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl984])).
% 89.16/26.92 thf(zip_derived_cl1015, plain,
% 89.16/26.92 (~ (((setextsub) =>
% 89.16/26.92 (((subsetemptysetimpeq) =>
% 89.16/26.92 (((powersetI1) =>
% 89.16/26.92 (((powersetE1) =>
% 89.16/26.92 (((inPowerset) =>
% 89.16/26.92 (((powersetsubset) =>
% 89.16/26.92 (((sepInPowerset) =>
% 89.16/26.92 (((sepSubset) =>
% 89.16/26.92 (((binunionIL) =>
% 89.16/26.92 (((upairset2IR) =>
% 89.16/26.92 (((binunionIR) =>
% 89.16/26.92 (((binunionEcases) =>
% 89.16/26.92 (((binunionE) =>
% 89.16/26.92 (((binunionLsub) =>
% 89.16/26.92 (((binunionRsub) =>
% 89.16/26.92 (((binintersectI) =>
% 89.16/26.92 (((binintersectSubset5) =>
% 89.16/26.92 (((binintersectEL) =>
% 89.16/26.92 (((binintersectLsub) =>
% 89.16/26.92 (((binintersectSubset2) =>
% 89.16/26.92 (((binintersectSubset3) =>
% 89.16/26.92 (((binintersectER) =>
% 89.16/26.92 (((disjointsetsI1) =>
% 89.16/26.92 (((binintersectRsub) =>
% 89.16/26.92 (((binintersectSubset4) =>
% 89.16/26.92 (((binintersectSubset1) =>
% 89.16/26.92 (((bs114d) =>
% 89.16/26.92 (((setminusI) =>
% 89.16/26.92 (((setminusEL) =>
% 89.16/26.92 (((setminusER) =>
% 89.16/26.92 ((
% 89.16/26.92 (setminusSubset2) =>
% 89.16/26.92 ((
% 89.16/26.92 (setminusERneg) =>
% 89.16/26.92 ((
% 89.16/26.92 (setminusELneg) =>
% 89.16/26.92 ((
% 89.16/26.92 (setminusILneg) =>
% 89.16/26.92 ((
% 89.16/26.92 (setminusIRneg) =>
% 89.16/26.92 ((
% 89.16/26.92 (setminusLsub) =>
% 89.16/26.92 ((
% 89.16/26.92 (setminusSubset1) =>
% 89.16/26.92 ((
% 89.16/26.92 (symdiffE) =>
% 89.16/26.92 ((
% 89.16/26.92 (symdiffI1) =>
% 89.16/26.92 ((
% 89.16/26.92 (symdiffI2) =>
% 89.16/26.92 ((
% 89.16/26.92 (symdiffIneg1) =>
% 89.16/26.92 ((
% 89.16/26.92 (symdiffIneg2) =>
% 89.16/26.92 ((
% 89.16/26.92 (secondinupair) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairIL) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairIR) =>
% 89.16/26.92 ((
% 89.16/26.92 (kpairiskpair) =>
% 89.16/26.92 ((
% 89.16/26.92 (kpairp) =>
% 89.16/26.92 ((
% 89.16/26.92 (singletonsubset) =>
% 89.16/26.92 ((
% 89.16/26.92 (singletoninpowerset) =>
% 89.16/26.92 ((
% 89.16/26.92 (singletoninpowunion) =>
% 89.16/26.92 ((
% 89.16/26.92 (upairset2E) =>
% 89.16/26.92 ((
% 89.16/26.92 (upairsubunion) =>
% 89.16/26.92 ((
% 89.16/26.92 (upairinpowunion) =>
% 89.16/26.92 ((
% 89.16/26.92 (ubforcartprodlem1) =>
% 89.16/26.92 ((
% 89.16/26.92 (ubforcartprodlem2) =>
% 89.16/26.92 ((
% 89.16/26.92 (ubforcartprodlem3) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodpairin) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodmempair1) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodmempair) =>
% 89.16/26.92 ((
% 89.16/26.92 (setunionE2) =>
% 89.16/26.92 ((
% 89.16/26.92 (setunionsingleton1) =>
% 89.16/26.92 ((
% 89.16/26.92 (setunionsingleton2) =>
% 89.16/26.92 ((
% 89.16/26.92 (setunionsingleton) =>
% 89.16/26.92 ((
% 89.16/26.92 (singletonprop) =>
% 89.16/26.92 ((
% 89.16/26.92 (ex1E1) =>
% 89.16/26.92 ((
% 89.16/26.92 (ex1I) =>
% 89.16/26.92 ((
% 89.16/26.92 (ex1I2) =>
% 89.16/26.92 ((
% 89.16/26.92 (singletonsuniq) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjL1) =>
% 89.16/26.92 ((
% 89.16/26.92 (kfstsingleton) =>
% 89.16/26.92 ((
% 89.16/26.92 (theprop) =>
% 89.16/26.92 ((
% 89.16/26.92 (kfstpairEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodfstin) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjL2) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjL) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjR11) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjR12) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjR1) =>
% 89.16/26.92 ((
% 89.16/26.92 (upairequniteq) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjR2) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjR) =>
% 89.16/26.92 ((
% 89.16/26.92 (ksndsingleton) =>
% 89.16/26.92 ((
% 89.16/26.92 (ksndpairEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (kpairsurjEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodsndin) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodpairmemEL) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodpairmemER) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodmempaircEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodfstpairEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodsndpairEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodpairsurjEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (dpsetconstrI) =>
% 89.16/26.92 ((
% 89.16/26.92 (dpsetconstrSub) =>
% 89.16/26.92 ((
% 89.16/26.92 (setOfPairsIsBReln) =>
% 89.16/26.92 ((
% 89.16/26.92 (dpsetconstrERa) =>
% 89.16/26.92 ((
% 89.16/26.92 (dpsetconstrEL1) =>
% 89.16/26.92 ((
% 89.16/26.92 (dpsetconstrEL2) =>
% 89.16/26.92 ((
% 89.16/26.92 (dpsetconstrER) =>
% 89.16/26.92 ((
% 89.16/26.92 (funcImageSingleton) =>
% 89.16/26.92 ((
% 89.16/26.92 (apProp) =>
% 89.16/26.92 ((
% 89.16/26.92 (app) =>
% 89.16/26.92 ((
% 89.16/26.92 (infuncsetfunc) =>
% 89.16/26.92 ((
% 89.16/26.92 (ap2p) =>
% 89.16/26.92 ((
% 89.16/26.92 (funcinfuncset) =>
% 89.16/26.92 ((
% 89.16/26.92 (lamProp) =>
% 89.16/26.92 ((
% 89.16/26.92 (lamp) =>
% 89.16/26.92 ((
% 89.16/26.92 (lam2p) =>
% 89.16/26.92 ((
% 89.16/26.92 (brelnall1) =>
% 89.16/26.92 ((
% 89.16/26.92 (brelnall2) =>
% 89.16/26.92 ((
% 89.16/26.92 (!!) @ (
% 89.16/26.92 (('#B') @ (
% 89.16/26.92 !!) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#S') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#S') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 =>))) @
% 89.16/26.92 ex1)))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 !!))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#S') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#B') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#S') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 =>))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#C') @ in)))))))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 !!))))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#C') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#B') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#B') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#S') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 =>))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#C') @ in)))))))))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#S') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#S') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#B'))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 =>))))))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#C') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#B') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#S') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 =>))))))) @
% 89.16/26.92 (
% 89.16/26.92 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.16/26.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1000])).
% 89.16/26.92 thf(zip_derived_cl1027, plain,
% 89.16/26.92 (~ (((subsetemptysetimpeq) =>
% 89.16/26.92 (((powersetI1) =>
% 89.16/26.92 (((powersetE1) =>
% 89.16/26.92 (((inPowerset) =>
% 89.16/26.92 (((powersetsubset) =>
% 89.16/26.92 (((sepInPowerset) =>
% 89.16/26.92 (((sepSubset) =>
% 89.16/26.92 (((binunionIL) =>
% 89.16/26.92 (((upairset2IR) =>
% 89.16/26.92 (((binunionIR) =>
% 89.16/26.92 (((binunionEcases) =>
% 89.16/26.92 (((binunionE) =>
% 89.16/26.92 (((binunionLsub) =>
% 89.16/26.92 (((binunionRsub) =>
% 89.16/26.92 (((binintersectI) =>
% 89.16/26.92 (((binintersectSubset5) =>
% 89.16/26.92 (((binintersectEL) =>
% 89.16/26.92 (((binintersectLsub) =>
% 89.16/26.92 (((binintersectSubset2) =>
% 89.16/26.92 (((binintersectSubset3) =>
% 89.16/26.92 (((binintersectER) =>
% 89.16/26.92 (((disjointsetsI1) =>
% 89.16/26.92 (((binintersectRsub) =>
% 89.16/26.92 (((binintersectSubset4) =>
% 89.16/26.92 (((binintersectSubset1) =>
% 89.16/26.92 (((bs114d) =>
% 89.16/26.92 (((setminusI) =>
% 89.16/26.92 (((setminusEL) =>
% 89.16/26.92 (((setminusER) =>
% 89.16/26.92 (((setminusSubset2) =>
% 89.16/26.92 ((
% 89.16/26.92 (setminusERneg) =>
% 89.16/26.92 ((
% 89.16/26.92 (setminusELneg) =>
% 89.16/26.92 ((
% 89.16/26.92 (setminusILneg) =>
% 89.16/26.92 ((
% 89.16/26.92 (setminusIRneg) =>
% 89.16/26.92 ((
% 89.16/26.92 (setminusLsub) =>
% 89.16/26.92 ((
% 89.16/26.92 (setminusSubset1) =>
% 89.16/26.92 ((
% 89.16/26.92 (symdiffE) =>
% 89.16/26.92 ((
% 89.16/26.92 (symdiffI1) =>
% 89.16/26.92 ((
% 89.16/26.92 (symdiffI2) =>
% 89.16/26.92 ((
% 89.16/26.92 (symdiffIneg1) =>
% 89.16/26.92 ((
% 89.16/26.92 (symdiffIneg2) =>
% 89.16/26.92 ((
% 89.16/26.92 (secondinupair) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairIL) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairIR) =>
% 89.16/26.92 ((
% 89.16/26.92 (kpairiskpair) =>
% 89.16/26.92 ((
% 89.16/26.92 (kpairp) =>
% 89.16/26.92 ((
% 89.16/26.92 (singletonsubset) =>
% 89.16/26.92 ((
% 89.16/26.92 (singletoninpowerset) =>
% 89.16/26.92 ((
% 89.16/26.92 (singletoninpowunion) =>
% 89.16/26.92 ((
% 89.16/26.92 (upairset2E) =>
% 89.16/26.92 ((
% 89.16/26.92 (upairsubunion) =>
% 89.16/26.92 ((
% 89.16/26.92 (upairinpowunion) =>
% 89.16/26.92 ((
% 89.16/26.92 (ubforcartprodlem1) =>
% 89.16/26.92 ((
% 89.16/26.92 (ubforcartprodlem2) =>
% 89.16/26.92 ((
% 89.16/26.92 (ubforcartprodlem3) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodpairin) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodmempair1) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodmempair) =>
% 89.16/26.92 ((
% 89.16/26.92 (setunionE2) =>
% 89.16/26.92 ((
% 89.16/26.92 (setunionsingleton1) =>
% 89.16/26.92 ((
% 89.16/26.92 (setunionsingleton2) =>
% 89.16/26.92 ((
% 89.16/26.92 (setunionsingleton) =>
% 89.16/26.92 ((
% 89.16/26.92 (singletonprop) =>
% 89.16/26.92 ((
% 89.16/26.92 (ex1E1) =>
% 89.16/26.92 ((
% 89.16/26.92 (ex1I) =>
% 89.16/26.92 ((
% 89.16/26.92 (ex1I2) =>
% 89.16/26.92 ((
% 89.16/26.92 (singletonsuniq) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjL1) =>
% 89.16/26.92 ((
% 89.16/26.92 (kfstsingleton) =>
% 89.16/26.92 ((
% 89.16/26.92 (theprop) =>
% 89.16/26.92 ((
% 89.16/26.92 (kfstpairEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodfstin) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjL2) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjL) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjR11) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjR12) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjR1) =>
% 89.16/26.92 ((
% 89.16/26.92 (upairequniteq) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjR2) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjR) =>
% 89.16/26.92 ((
% 89.16/26.92 (ksndsingleton) =>
% 89.16/26.92 ((
% 89.16/26.92 (ksndpairEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (kpairsurjEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodsndin) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodpairmemEL) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodpairmemER) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodmempaircEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodfstpairEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodsndpairEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodpairsurjEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (dpsetconstrI) =>
% 89.16/26.92 ((
% 89.16/26.92 (dpsetconstrSub) =>
% 89.16/26.92 ((
% 89.16/26.92 (setOfPairsIsBReln) =>
% 89.16/26.92 ((
% 89.16/26.92 (dpsetconstrERa) =>
% 89.16/26.92 ((
% 89.16/26.92 (dpsetconstrEL1) =>
% 89.16/26.92 ((
% 89.16/26.92 (dpsetconstrEL2) =>
% 89.16/26.92 ((
% 89.16/26.92 (dpsetconstrER) =>
% 89.16/26.92 ((
% 89.16/26.92 (funcImageSingleton) =>
% 89.16/26.92 ((
% 89.16/26.92 (apProp) =>
% 89.16/26.92 ((
% 89.16/26.92 (app) =>
% 89.16/26.92 ((
% 89.16/26.92 (infuncsetfunc) =>
% 89.16/26.92 ((
% 89.16/26.92 (ap2p) =>
% 89.16/26.92 ((
% 89.16/26.92 (funcinfuncset) =>
% 89.16/26.92 ((
% 89.16/26.92 (lamProp) =>
% 89.16/26.92 ((
% 89.16/26.92 (lamp) =>
% 89.16/26.92 ((
% 89.16/26.92 (lam2p) =>
% 89.16/26.92 ((
% 89.16/26.92 (brelnall1) =>
% 89.16/26.92 ((
% 89.16/26.92 (brelnall2) =>
% 89.16/26.92 ((
% 89.16/26.92 (!!) @ (
% 89.16/26.92 (('#B') @ (
% 89.16/26.92 !!) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#S') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#S') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 =>))) @
% 89.16/26.92 ex1)))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 !!))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#S') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#B') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#S') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 =>))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#C') @ in)))))))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 !!))))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#C') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#B') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#B') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#S') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 =>))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#C') @ in)))))))))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#S') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#S') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#B'))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 =>))))))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#C') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#B') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#S') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 =>))))))) @
% 89.16/26.92 (
% 89.16/26.92 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.16/26.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1015])).
% 89.16/26.92 thf(zip_derived_cl1039, plain,
% 89.16/26.92 (~ (((powersetI1) =>
% 89.16/26.92 (((powersetE1) =>
% 89.16/26.92 (((inPowerset) =>
% 89.16/26.92 (((powersetsubset) =>
% 89.16/26.92 (((sepInPowerset) =>
% 89.16/26.92 (((sepSubset) =>
% 89.16/26.92 (((binunionIL) =>
% 89.16/26.92 (((upairset2IR) =>
% 89.16/26.92 (((binunionIR) =>
% 89.16/26.92 (((binunionEcases) =>
% 89.16/26.92 (((binunionE) =>
% 89.16/26.92 (((binunionLsub) =>
% 89.16/26.92 (((binunionRsub) =>
% 89.16/26.92 (((binintersectI) =>
% 89.16/26.92 (((binintersectSubset5) =>
% 89.16/26.92 (((binintersectEL) =>
% 89.16/26.92 (((binintersectLsub) =>
% 89.16/26.92 (((binintersectSubset2) =>
% 89.16/26.92 (((binintersectSubset3) =>
% 89.16/26.92 (((binintersectER) =>
% 89.16/26.92 (((disjointsetsI1) =>
% 89.16/26.92 (((binintersectRsub) =>
% 89.16/26.92 (((binintersectSubset4) =>
% 89.16/26.92 (((binintersectSubset1) =>
% 89.16/26.92 (((bs114d) =>
% 89.16/26.92 (((setminusI) =>
% 89.16/26.92 (((setminusEL) =>
% 89.16/26.92 (((setminusER) =>
% 89.16/26.92 (((setminusSubset2) =>
% 89.16/26.92 (((setminusERneg) =>
% 89.16/26.92 ((
% 89.16/26.92 (setminusELneg) =>
% 89.16/26.92 ((
% 89.16/26.92 (setminusILneg) =>
% 89.16/26.92 ((
% 89.16/26.92 (setminusIRneg) =>
% 89.16/26.92 ((
% 89.16/26.92 (setminusLsub) =>
% 89.16/26.92 ((
% 89.16/26.92 (setminusSubset1) =>
% 89.16/26.92 ((
% 89.16/26.92 (symdiffE) =>
% 89.16/26.92 ((
% 89.16/26.92 (symdiffI1) =>
% 89.16/26.92 ((
% 89.16/26.92 (symdiffI2) =>
% 89.16/26.92 ((
% 89.16/26.92 (symdiffIneg1) =>
% 89.16/26.92 ((
% 89.16/26.92 (symdiffIneg2) =>
% 89.16/26.92 ((
% 89.16/26.92 (secondinupair) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairIL) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairIR) =>
% 89.16/26.92 ((
% 89.16/26.92 (kpairiskpair) =>
% 89.16/26.92 ((
% 89.16/26.92 (kpairp) =>
% 89.16/26.92 ((
% 89.16/26.92 (singletonsubset) =>
% 89.16/26.92 ((
% 89.16/26.92 (singletoninpowerset) =>
% 89.16/26.92 ((
% 89.16/26.92 (singletoninpowunion) =>
% 89.16/26.92 ((
% 89.16/26.92 (upairset2E) =>
% 89.16/26.92 ((
% 89.16/26.92 (upairsubunion) =>
% 89.16/26.92 ((
% 89.16/26.92 (upairinpowunion) =>
% 89.16/26.92 ((
% 89.16/26.92 (ubforcartprodlem1) =>
% 89.16/26.92 ((
% 89.16/26.92 (ubforcartprodlem2) =>
% 89.16/26.92 ((
% 89.16/26.92 (ubforcartprodlem3) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodpairin) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodmempair1) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodmempair) =>
% 89.16/26.92 ((
% 89.16/26.92 (setunionE2) =>
% 89.16/26.92 ((
% 89.16/26.92 (setunionsingleton1) =>
% 89.16/26.92 ((
% 89.16/26.92 (setunionsingleton2) =>
% 89.16/26.92 ((
% 89.16/26.92 (setunionsingleton) =>
% 89.16/26.92 ((
% 89.16/26.92 (singletonprop) =>
% 89.16/26.92 ((
% 89.16/26.92 (ex1E1) =>
% 89.16/26.92 ((
% 89.16/26.92 (ex1I) =>
% 89.16/26.92 ((
% 89.16/26.92 (ex1I2) =>
% 89.16/26.92 ((
% 89.16/26.92 (singletonsuniq) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjL1) =>
% 89.16/26.92 ((
% 89.16/26.92 (kfstsingleton) =>
% 89.16/26.92 ((
% 89.16/26.92 (theprop) =>
% 89.16/26.92 ((
% 89.16/26.92 (kfstpairEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodfstin) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjL2) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjL) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjR11) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjR12) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjR1) =>
% 89.16/26.92 ((
% 89.16/26.92 (upairequniteq) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjR2) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjR) =>
% 89.16/26.92 ((
% 89.16/26.92 (ksndsingleton) =>
% 89.16/26.92 ((
% 89.16/26.92 (ksndpairEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (kpairsurjEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodsndin) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodpairmemEL) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodpairmemER) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodmempaircEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodfstpairEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodsndpairEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodpairsurjEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (dpsetconstrI) =>
% 89.16/26.92 ((
% 89.16/26.92 (dpsetconstrSub) =>
% 89.16/26.92 ((
% 89.16/26.92 (setOfPairsIsBReln) =>
% 89.16/26.92 ((
% 89.16/26.92 (dpsetconstrERa) =>
% 89.16/26.92 ((
% 89.16/26.92 (dpsetconstrEL1) =>
% 89.16/26.92 ((
% 89.16/26.92 (dpsetconstrEL2) =>
% 89.16/26.92 ((
% 89.16/26.92 (dpsetconstrER) =>
% 89.16/26.92 ((
% 89.16/26.92 (funcImageSingleton) =>
% 89.16/26.92 ((
% 89.16/26.92 (apProp) =>
% 89.16/26.92 ((
% 89.16/26.92 (app) =>
% 89.16/26.92 ((
% 89.16/26.92 (infuncsetfunc) =>
% 89.16/26.92 ((
% 89.16/26.92 (ap2p) =>
% 89.16/26.92 ((
% 89.16/26.92 (funcinfuncset) =>
% 89.16/26.92 ((
% 89.16/26.92 (lamProp) =>
% 89.16/26.92 ((
% 89.16/26.92 (lamp) =>
% 89.16/26.92 ((
% 89.16/26.92 (lam2p) =>
% 89.16/26.92 ((
% 89.16/26.92 (brelnall1) =>
% 89.16/26.92 ((
% 89.16/26.92 (brelnall2) =>
% 89.16/26.92 ((
% 89.16/26.92 (!!) @ (
% 89.16/26.92 (('#B') @ (
% 89.16/26.92 !!) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#S') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#S') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 =>))) @
% 89.16/26.92 ex1)))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 !!))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#S') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#B') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#S') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 =>))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#C') @ in)))))))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 !!))))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#C') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#B') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#B') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#S') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 =>))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#C') @ in)))))))))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#S') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#S') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#B'))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 =>))))))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#C') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#B') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#S') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 =>))))))) @
% 89.16/26.92 (
% 89.16/26.92 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.16/26.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1027])).
% 89.16/26.92 thf(zip_derived_cl1055, plain,
% 89.16/26.92 (~ (((powersetE1) =>
% 89.16/26.92 (((inPowerset) =>
% 89.16/26.92 (((powersetsubset) =>
% 89.16/26.92 (((sepInPowerset) =>
% 89.16/26.92 (((sepSubset) =>
% 89.16/26.92 (((binunionIL) =>
% 89.16/26.92 (((upairset2IR) =>
% 89.16/26.92 (((binunionIR) =>
% 89.16/26.92 (((binunionEcases) =>
% 89.16/26.92 (((binunionE) =>
% 89.16/26.92 (((binunionLsub) =>
% 89.16/26.92 (((binunionRsub) =>
% 89.16/26.92 (((binintersectI) =>
% 89.16/26.92 (((binintersectSubset5) =>
% 89.16/26.92 (((binintersectEL) =>
% 89.16/26.92 (((binintersectLsub) =>
% 89.16/26.92 (((binintersectSubset2) =>
% 89.16/26.92 (((binintersectSubset3) =>
% 89.16/26.92 (((binintersectER) =>
% 89.16/26.92 (((disjointsetsI1) =>
% 89.16/26.92 (((binintersectRsub) =>
% 89.16/26.92 (((binintersectSubset4) =>
% 89.16/26.92 (((binintersectSubset1) =>
% 89.16/26.92 (((bs114d) =>
% 89.16/26.92 (((setminusI) =>
% 89.16/26.92 (((setminusEL) =>
% 89.16/26.92 (((setminusER) =>
% 89.16/26.92 (((setminusSubset2) =>
% 89.16/26.92 (((setminusERneg) =>
% 89.16/26.92 (((setminusELneg) =>
% 89.16/26.92 ((
% 89.16/26.92 (setminusILneg) =>
% 89.16/26.92 ((
% 89.16/26.92 (setminusIRneg) =>
% 89.16/26.92 ((
% 89.16/26.92 (setminusLsub) =>
% 89.16/26.92 ((
% 89.16/26.92 (setminusSubset1) =>
% 89.16/26.92 ((
% 89.16/26.92 (symdiffE) =>
% 89.16/26.92 ((
% 89.16/26.92 (symdiffI1) =>
% 89.16/26.92 ((
% 89.16/26.92 (symdiffI2) =>
% 89.16/26.92 ((
% 89.16/26.92 (symdiffIneg1) =>
% 89.16/26.92 ((
% 89.16/26.92 (symdiffIneg2) =>
% 89.16/26.92 ((
% 89.16/26.92 (secondinupair) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairIL) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairIR) =>
% 89.16/26.92 ((
% 89.16/26.92 (kpairiskpair) =>
% 89.16/26.92 ((
% 89.16/26.92 (kpairp) =>
% 89.16/26.92 ((
% 89.16/26.92 (singletonsubset) =>
% 89.16/26.92 ((
% 89.16/26.92 (singletoninpowerset) =>
% 89.16/26.92 ((
% 89.16/26.92 (singletoninpowunion) =>
% 89.16/26.92 ((
% 89.16/26.92 (upairset2E) =>
% 89.16/26.92 ((
% 89.16/26.92 (upairsubunion) =>
% 89.16/26.92 ((
% 89.16/26.92 (upairinpowunion) =>
% 89.16/26.92 ((
% 89.16/26.92 (ubforcartprodlem1) =>
% 89.16/26.92 ((
% 89.16/26.92 (ubforcartprodlem2) =>
% 89.16/26.92 ((
% 89.16/26.92 (ubforcartprodlem3) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodpairin) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodmempair1) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodmempair) =>
% 89.16/26.92 ((
% 89.16/26.92 (setunionE2) =>
% 89.16/26.92 ((
% 89.16/26.92 (setunionsingleton1) =>
% 89.16/26.92 ((
% 89.16/26.92 (setunionsingleton2) =>
% 89.16/26.92 ((
% 89.16/26.92 (setunionsingleton) =>
% 89.16/26.92 ((
% 89.16/26.92 (singletonprop) =>
% 89.16/26.92 ((
% 89.16/26.92 (ex1E1) =>
% 89.16/26.92 ((
% 89.16/26.92 (ex1I) =>
% 89.16/26.92 ((
% 89.16/26.92 (ex1I2) =>
% 89.16/26.92 ((
% 89.16/26.92 (singletonsuniq) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjL1) =>
% 89.16/26.92 ((
% 89.16/26.92 (kfstsingleton) =>
% 89.16/26.92 ((
% 89.16/26.92 (theprop) =>
% 89.16/26.92 ((
% 89.16/26.92 (kfstpairEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodfstin) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjL2) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjL) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjR11) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjR12) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjR1) =>
% 89.16/26.92 ((
% 89.16/26.92 (upairequniteq) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjR2) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjR) =>
% 89.16/26.92 ((
% 89.16/26.92 (ksndsingleton) =>
% 89.16/26.92 ((
% 89.16/26.92 (ksndpairEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (kpairsurjEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodsndin) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodpairmemEL) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodpairmemER) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodmempaircEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodfstpairEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodsndpairEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodpairsurjEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (dpsetconstrI) =>
% 89.16/26.92 ((
% 89.16/26.92 (dpsetconstrSub) =>
% 89.16/26.92 ((
% 89.16/26.92 (setOfPairsIsBReln) =>
% 89.16/26.92 ((
% 89.16/26.92 (dpsetconstrERa) =>
% 89.16/26.92 ((
% 89.16/26.92 (dpsetconstrEL1) =>
% 89.16/26.92 ((
% 89.16/26.92 (dpsetconstrEL2) =>
% 89.16/26.92 ((
% 89.16/26.92 (dpsetconstrER) =>
% 89.16/26.92 ((
% 89.16/26.92 (funcImageSingleton) =>
% 89.16/26.92 ((
% 89.16/26.92 (apProp) =>
% 89.16/26.92 ((
% 89.16/26.92 (app) =>
% 89.16/26.92 ((
% 89.16/26.92 (infuncsetfunc) =>
% 89.16/26.92 ((
% 89.16/26.92 (ap2p) =>
% 89.16/26.92 ((
% 89.16/26.92 (funcinfuncset) =>
% 89.16/26.92 ((
% 89.16/26.92 (lamProp) =>
% 89.16/26.92 ((
% 89.16/26.92 (lamp) =>
% 89.16/26.92 ((
% 89.16/26.92 (lam2p) =>
% 89.16/26.92 ((
% 89.16/26.92 (brelnall1) =>
% 89.16/26.92 ((
% 89.16/26.92 (brelnall2) =>
% 89.16/26.92 ((
% 89.16/26.92 (!!) @ (
% 89.16/26.92 (('#B') @ (
% 89.16/26.92 !!) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#S') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#S') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 =>))) @
% 89.16/26.92 ex1)))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 !!))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#S') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#B') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#S') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 =>))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#C') @ in)))))))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 !!))))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#C') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#B') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#B') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#S') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 =>))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#C') @ in)))))))))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#S') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#S') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#B'))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 =>))))))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#C') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#B') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#S') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 =>))))))) @
% 89.16/26.92 (
% 89.16/26.92 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.16/26.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1039])).
% 89.16/26.92 thf(zip_derived_cl1067, plain,
% 89.16/26.92 (~ (((inPowerset) =>
% 89.16/26.92 (((powersetsubset) =>
% 89.16/26.92 (((sepInPowerset) =>
% 89.16/26.92 (((sepSubset) =>
% 89.16/26.92 (((binunionIL) =>
% 89.16/26.92 (((upairset2IR) =>
% 89.16/26.92 (((binunionIR) =>
% 89.16/26.92 (((binunionEcases) =>
% 89.16/26.92 (((binunionE) =>
% 89.16/26.92 (((binunionLsub) =>
% 89.16/26.92 (((binunionRsub) =>
% 89.16/26.92 (((binintersectI) =>
% 89.16/26.92 (((binintersectSubset5) =>
% 89.16/26.92 (((binintersectEL) =>
% 89.16/26.92 (((binintersectLsub) =>
% 89.16/26.92 (((binintersectSubset2) =>
% 89.16/26.92 (((binintersectSubset3) =>
% 89.16/26.92 (((binintersectER) =>
% 89.16/26.92 (((disjointsetsI1) =>
% 89.16/26.92 (((binintersectRsub) =>
% 89.16/26.92 (((binintersectSubset4) =>
% 89.16/26.92 (((binintersectSubset1) =>
% 89.16/26.92 (((bs114d) =>
% 89.16/26.92 (((setminusI) =>
% 89.16/26.92 (((setminusEL) =>
% 89.16/26.92 (((setminusER) =>
% 89.16/26.92 (((setminusSubset2) =>
% 89.16/26.92 (((setminusERneg) =>
% 89.16/26.92 (((setminusELneg) =>
% 89.16/26.92 (((setminusILneg) =>
% 89.16/26.92 ((
% 89.16/26.92 (setminusIRneg) =>
% 89.16/26.92 ((
% 89.16/26.92 (setminusLsub) =>
% 89.16/26.92 ((
% 89.16/26.92 (setminusSubset1) =>
% 89.16/26.92 ((
% 89.16/26.92 (symdiffE) =>
% 89.16/26.92 ((
% 89.16/26.92 (symdiffI1) =>
% 89.16/26.92 ((
% 89.16/26.92 (symdiffI2) =>
% 89.16/26.92 ((
% 89.16/26.92 (symdiffIneg1) =>
% 89.16/26.92 ((
% 89.16/26.92 (symdiffIneg2) =>
% 89.16/26.92 ((
% 89.16/26.92 (secondinupair) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairIL) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairIR) =>
% 89.16/26.92 ((
% 89.16/26.92 (kpairiskpair) =>
% 89.16/26.92 ((
% 89.16/26.92 (kpairp) =>
% 89.16/26.92 ((
% 89.16/26.92 (singletonsubset) =>
% 89.16/26.92 ((
% 89.16/26.92 (singletoninpowerset) =>
% 89.16/26.92 ((
% 89.16/26.92 (singletoninpowunion) =>
% 89.16/26.92 ((
% 89.16/26.92 (upairset2E) =>
% 89.16/26.92 ((
% 89.16/26.92 (upairsubunion) =>
% 89.16/26.92 ((
% 89.16/26.92 (upairinpowunion) =>
% 89.16/26.92 ((
% 89.16/26.92 (ubforcartprodlem1) =>
% 89.16/26.92 ((
% 89.16/26.92 (ubforcartprodlem2) =>
% 89.16/26.92 ((
% 89.16/26.92 (ubforcartprodlem3) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodpairin) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodmempair1) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodmempair) =>
% 89.16/26.92 ((
% 89.16/26.92 (setunionE2) =>
% 89.16/26.92 ((
% 89.16/26.92 (setunionsingleton1) =>
% 89.16/26.92 ((
% 89.16/26.92 (setunionsingleton2) =>
% 89.16/26.92 ((
% 89.16/26.92 (setunionsingleton) =>
% 89.16/26.92 ((
% 89.16/26.92 (singletonprop) =>
% 89.16/26.92 ((
% 89.16/26.92 (ex1E1) =>
% 89.16/26.92 ((
% 89.16/26.92 (ex1I) =>
% 89.16/26.92 ((
% 89.16/26.92 (ex1I2) =>
% 89.16/26.92 ((
% 89.16/26.92 (singletonsuniq) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjL1) =>
% 89.16/26.92 ((
% 89.16/26.92 (kfstsingleton) =>
% 89.16/26.92 ((
% 89.16/26.92 (theprop) =>
% 89.16/26.92 ((
% 89.16/26.92 (kfstpairEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodfstin) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjL2) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjL) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjR11) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjR12) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjR1) =>
% 89.16/26.92 ((
% 89.16/26.92 (upairequniteq) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjR2) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjR) =>
% 89.16/26.92 ((
% 89.16/26.92 (ksndsingleton) =>
% 89.16/26.92 ((
% 89.16/26.92 (ksndpairEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (kpairsurjEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodsndin) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodpairmemEL) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodpairmemER) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodmempaircEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodfstpairEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodsndpairEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodpairsurjEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (dpsetconstrI) =>
% 89.16/26.92 ((
% 89.16/26.92 (dpsetconstrSub) =>
% 89.16/26.92 ((
% 89.16/26.92 (setOfPairsIsBReln) =>
% 89.16/26.92 ((
% 89.16/26.92 (dpsetconstrERa) =>
% 89.16/26.92 ((
% 89.16/26.92 (dpsetconstrEL1) =>
% 89.16/26.92 ((
% 89.16/26.92 (dpsetconstrEL2) =>
% 89.16/26.92 ((
% 89.16/26.92 (dpsetconstrER) =>
% 89.16/26.92 ((
% 89.16/26.92 (funcImageSingleton) =>
% 89.16/26.92 ((
% 89.16/26.92 (apProp) =>
% 89.16/26.92 ((
% 89.16/26.92 (app) =>
% 89.16/26.92 ((
% 89.16/26.92 (infuncsetfunc) =>
% 89.16/26.92 ((
% 89.16/26.92 (ap2p) =>
% 89.16/26.92 ((
% 89.16/26.92 (funcinfuncset) =>
% 89.16/26.92 ((
% 89.16/26.92 (lamProp) =>
% 89.16/26.92 ((
% 89.16/26.92 (lamp) =>
% 89.16/26.92 ((
% 89.16/26.92 (lam2p) =>
% 89.16/26.92 ((
% 89.16/26.92 (brelnall1) =>
% 89.16/26.92 ((
% 89.16/26.92 (brelnall2) =>
% 89.16/26.92 ((
% 89.16/26.92 (!!) @ (
% 89.16/26.92 (('#B') @ (
% 89.16/26.92 !!) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#S') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#S') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 =>))) @
% 89.16/26.92 ex1)))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 !!))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#S') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#B') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#S') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 =>))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#C') @ in)))))))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 !!))))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#C') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#B') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#B') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#S') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 =>))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#C') @ in)))))))))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#S') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#S') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#B'))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 =>))))))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#C') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#B') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#S') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 =>))))))) @
% 89.16/26.92 (
% 89.16/26.92 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.16/26.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1055])).
% 89.16/26.92 thf(zip_derived_cl1074, plain,
% 89.16/26.92 (~ (((powersetsubset) =>
% 89.16/26.92 (((sepInPowerset) =>
% 89.16/26.92 (((sepSubset) =>
% 89.16/26.92 (((binunionIL) =>
% 89.16/26.92 (((upairset2IR) =>
% 89.16/26.92 (((binunionIR) =>
% 89.16/26.92 (((binunionEcases) =>
% 89.16/26.92 (((binunionE) =>
% 89.16/26.92 (((binunionLsub) =>
% 89.16/26.92 (((binunionRsub) =>
% 89.16/26.92 (((binintersectI) =>
% 89.16/26.92 (((binintersectSubset5) =>
% 89.16/26.92 (((binintersectEL) =>
% 89.16/26.92 (((binintersectLsub) =>
% 89.16/26.92 (((binintersectSubset2) =>
% 89.16/26.92 (((binintersectSubset3) =>
% 89.16/26.92 (((binintersectER) =>
% 89.16/26.92 (((disjointsetsI1) =>
% 89.16/26.92 (((binintersectRsub) =>
% 89.16/26.92 (((binintersectSubset4) =>
% 89.16/26.92 (((binintersectSubset1) =>
% 89.16/26.92 (((bs114d) =>
% 89.16/26.92 (((setminusI) =>
% 89.16/26.92 (((setminusEL) =>
% 89.16/26.92 (((setminusER) =>
% 89.16/26.92 (((setminusSubset2) =>
% 89.16/26.92 (((setminusERneg) =>
% 89.16/26.92 (((setminusELneg) =>
% 89.16/26.92 (((setminusILneg) =>
% 89.16/26.92 (((setminusIRneg) =>
% 89.16/26.92 ((
% 89.16/26.92 (setminusLsub) =>
% 89.16/26.92 ((
% 89.16/26.92 (setminusSubset1) =>
% 89.16/26.92 ((
% 89.16/26.92 (symdiffE) =>
% 89.16/26.92 ((
% 89.16/26.92 (symdiffI1) =>
% 89.16/26.92 ((
% 89.16/26.92 (symdiffI2) =>
% 89.16/26.92 ((
% 89.16/26.92 (symdiffIneg1) =>
% 89.16/26.92 ((
% 89.16/26.92 (symdiffIneg2) =>
% 89.16/26.92 ((
% 89.16/26.92 (secondinupair) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairIL) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairIR) =>
% 89.16/26.92 ((
% 89.16/26.92 (kpairiskpair) =>
% 89.16/26.92 ((
% 89.16/26.92 (kpairp) =>
% 89.16/26.92 ((
% 89.16/26.92 (singletonsubset) =>
% 89.16/26.92 ((
% 89.16/26.92 (singletoninpowerset) =>
% 89.16/26.92 ((
% 89.16/26.92 (singletoninpowunion) =>
% 89.16/26.92 ((
% 89.16/26.92 (upairset2E) =>
% 89.16/26.92 ((
% 89.16/26.92 (upairsubunion) =>
% 89.16/26.92 ((
% 89.16/26.92 (upairinpowunion) =>
% 89.16/26.92 ((
% 89.16/26.92 (ubforcartprodlem1) =>
% 89.16/26.92 ((
% 89.16/26.92 (ubforcartprodlem2) =>
% 89.16/26.92 ((
% 89.16/26.92 (ubforcartprodlem3) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodpairin) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodmempair1) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodmempair) =>
% 89.16/26.92 ((
% 89.16/26.92 (setunionE2) =>
% 89.16/26.92 ((
% 89.16/26.92 (setunionsingleton1) =>
% 89.16/26.92 ((
% 89.16/26.92 (setunionsingleton2) =>
% 89.16/26.92 ((
% 89.16/26.92 (setunionsingleton) =>
% 89.16/26.92 ((
% 89.16/26.92 (singletonprop) =>
% 89.16/26.92 ((
% 89.16/26.92 (ex1E1) =>
% 89.16/26.92 ((
% 89.16/26.92 (ex1I) =>
% 89.16/26.92 ((
% 89.16/26.92 (ex1I2) =>
% 89.16/26.92 ((
% 89.16/26.92 (singletonsuniq) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjL1) =>
% 89.16/26.92 ((
% 89.16/26.92 (kfstsingleton) =>
% 89.16/26.92 ((
% 89.16/26.92 (theprop) =>
% 89.16/26.92 ((
% 89.16/26.92 (kfstpairEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodfstin) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjL2) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjL) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjR11) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjR12) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjR1) =>
% 89.16/26.92 ((
% 89.16/26.92 (upairequniteq) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjR2) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjR) =>
% 89.16/26.92 ((
% 89.16/26.92 (ksndsingleton) =>
% 89.16/26.92 ((
% 89.16/26.92 (ksndpairEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (kpairsurjEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodsndin) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodpairmemEL) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodpairmemER) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodmempaircEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodfstpairEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodsndpairEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodpairsurjEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (dpsetconstrI) =>
% 89.16/26.92 ((
% 89.16/26.92 (dpsetconstrSub) =>
% 89.16/26.92 ((
% 89.16/26.92 (setOfPairsIsBReln) =>
% 89.16/26.92 ((
% 89.16/26.92 (dpsetconstrERa) =>
% 89.16/26.92 ((
% 89.16/26.92 (dpsetconstrEL1) =>
% 89.16/26.92 ((
% 89.16/26.92 (dpsetconstrEL2) =>
% 89.16/26.92 ((
% 89.16/26.92 (dpsetconstrER) =>
% 89.16/26.92 ((
% 89.16/26.92 (funcImageSingleton) =>
% 89.16/26.92 ((
% 89.16/26.92 (apProp) =>
% 89.16/26.92 ((
% 89.16/26.92 (app) =>
% 89.16/26.92 ((
% 89.16/26.92 (infuncsetfunc) =>
% 89.16/26.92 ((
% 89.16/26.92 (ap2p) =>
% 89.16/26.92 ((
% 89.16/26.92 (funcinfuncset) =>
% 89.16/26.92 ((
% 89.16/26.92 (lamProp) =>
% 89.16/26.92 ((
% 89.16/26.92 (lamp) =>
% 89.16/26.92 ((
% 89.16/26.92 (lam2p) =>
% 89.16/26.92 ((
% 89.16/26.92 (brelnall1) =>
% 89.16/26.92 ((
% 89.16/26.92 (brelnall2) =>
% 89.16/26.92 ((
% 89.16/26.92 (!!) @ (
% 89.16/26.92 (('#B') @ (
% 89.16/26.92 !!) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#S') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#S') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 =>))) @
% 89.16/26.92 ex1)))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 !!))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#S') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#B') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#S') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 =>))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#C') @ in)))))))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 !!))))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#C') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#B') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#B') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#S') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 =>))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#C') @ in)))))))))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#S') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#S') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#B'))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 =>))))))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#C') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#B') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#S') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 =>))))))) @
% 89.16/26.92 (
% 89.16/26.92 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.16/26.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1067])).
% 89.16/26.92 thf(zip_derived_cl1082, plain,
% 89.16/26.92 (~ (((sepInPowerset) =>
% 89.16/26.92 (((sepSubset) =>
% 89.16/26.92 (((binunionIL) =>
% 89.16/26.92 (((upairset2IR) =>
% 89.16/26.92 (((binunionIR) =>
% 89.16/26.92 (((binunionEcases) =>
% 89.16/26.92 (((binunionE) =>
% 89.16/26.92 (((binunionLsub) =>
% 89.16/26.92 (((binunionRsub) =>
% 89.16/26.92 (((binintersectI) =>
% 89.16/26.92 (((binintersectSubset5) =>
% 89.16/26.92 (((binintersectEL) =>
% 89.16/26.92 (((binintersectLsub) =>
% 89.16/26.92 (((binintersectSubset2) =>
% 89.16/26.92 (((binintersectSubset3) =>
% 89.16/26.92 (((binintersectER) =>
% 89.16/26.92 (((disjointsetsI1) =>
% 89.16/26.92 (((binintersectRsub) =>
% 89.16/26.92 (((binintersectSubset4) =>
% 89.16/26.92 (((binintersectSubset1) =>
% 89.16/26.92 (((bs114d) =>
% 89.16/26.92 (((setminusI) =>
% 89.16/26.92 (((setminusEL) =>
% 89.16/26.92 (((setminusER) =>
% 89.16/26.92 (((setminusSubset2) =>
% 89.16/26.92 (((setminusERneg) =>
% 89.16/26.92 (((setminusELneg) =>
% 89.16/26.92 (((setminusILneg) =>
% 89.16/26.92 (((setminusIRneg) =>
% 89.16/26.92 (((setminusLsub) =>
% 89.16/26.92 ((
% 89.16/26.92 (setminusSubset1) =>
% 89.16/26.92 ((
% 89.16/26.92 (symdiffE) =>
% 89.16/26.92 ((
% 89.16/26.92 (symdiffI1) =>
% 89.16/26.92 ((
% 89.16/26.92 (symdiffI2) =>
% 89.16/26.92 ((
% 89.16/26.92 (symdiffIneg1) =>
% 89.16/26.92 ((
% 89.16/26.92 (symdiffIneg2) =>
% 89.16/26.92 ((
% 89.16/26.92 (secondinupair) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairIL) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairIR) =>
% 89.16/26.92 ((
% 89.16/26.92 (kpairiskpair) =>
% 89.16/26.92 ((
% 89.16/26.92 (kpairp) =>
% 89.16/26.92 ((
% 89.16/26.92 (singletonsubset) =>
% 89.16/26.92 ((
% 89.16/26.92 (singletoninpowerset) =>
% 89.16/26.92 ((
% 89.16/26.92 (singletoninpowunion) =>
% 89.16/26.92 ((
% 89.16/26.92 (upairset2E) =>
% 89.16/26.92 ((
% 89.16/26.92 (upairsubunion) =>
% 89.16/26.92 ((
% 89.16/26.92 (upairinpowunion) =>
% 89.16/26.92 ((
% 89.16/26.92 (ubforcartprodlem1) =>
% 89.16/26.92 ((
% 89.16/26.92 (ubforcartprodlem2) =>
% 89.16/26.92 ((
% 89.16/26.92 (ubforcartprodlem3) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodpairin) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodmempair1) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodmempair) =>
% 89.16/26.92 ((
% 89.16/26.92 (setunionE2) =>
% 89.16/26.92 ((
% 89.16/26.92 (setunionsingleton1) =>
% 89.16/26.92 ((
% 89.16/26.92 (setunionsingleton2) =>
% 89.16/26.92 ((
% 89.16/26.92 (setunionsingleton) =>
% 89.16/26.92 ((
% 89.16/26.92 (singletonprop) =>
% 89.16/26.92 ((
% 89.16/26.92 (ex1E1) =>
% 89.16/26.92 ((
% 89.16/26.92 (ex1I) =>
% 89.16/26.92 ((
% 89.16/26.92 (ex1I2) =>
% 89.16/26.92 ((
% 89.16/26.92 (singletonsuniq) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjL1) =>
% 89.16/26.92 ((
% 89.16/26.92 (kfstsingleton) =>
% 89.16/26.92 ((
% 89.16/26.92 (theprop) =>
% 89.16/26.92 ((
% 89.16/26.92 (kfstpairEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodfstin) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjL2) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjL) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjR11) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjR12) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjR1) =>
% 89.16/26.92 ((
% 89.16/26.92 (upairequniteq) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjR2) =>
% 89.16/26.92 ((
% 89.16/26.92 (setukpairinjR) =>
% 89.16/26.92 ((
% 89.16/26.92 (ksndsingleton) =>
% 89.16/26.92 ((
% 89.16/26.92 (ksndpairEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (kpairsurjEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodsndin) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodpairmemEL) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodpairmemER) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodmempaircEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodfstpairEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodsndpairEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (cartprodpairsurjEq) =>
% 89.16/26.92 ((
% 89.16/26.92 (dpsetconstrI) =>
% 89.16/26.92 ((
% 89.16/26.92 (dpsetconstrSub) =>
% 89.16/26.92 ((
% 89.16/26.92 (setOfPairsIsBReln) =>
% 89.16/26.92 ((
% 89.16/26.92 (dpsetconstrERa) =>
% 89.16/26.92 ((
% 89.16/26.92 (dpsetconstrEL1) =>
% 89.16/26.92 ((
% 89.16/26.92 (dpsetconstrEL2) =>
% 89.16/26.92 ((
% 89.16/26.92 (dpsetconstrER) =>
% 89.16/26.92 ((
% 89.16/26.92 (funcImageSingleton) =>
% 89.16/26.92 ((
% 89.16/26.92 (apProp) =>
% 89.16/26.92 ((
% 89.16/26.92 (app) =>
% 89.16/26.92 ((
% 89.16/26.92 (infuncsetfunc) =>
% 89.16/26.92 ((
% 89.16/26.92 (ap2p) =>
% 89.16/26.92 ((
% 89.16/26.92 (funcinfuncset) =>
% 89.16/26.92 ((
% 89.16/26.92 (lamProp) =>
% 89.16/26.92 ((
% 89.16/26.92 (lamp) =>
% 89.16/26.92 ((
% 89.16/26.92 (lam2p) =>
% 89.16/26.92 ((
% 89.16/26.92 (brelnall1) =>
% 89.16/26.92 ((
% 89.16/26.92 (brelnall2) =>
% 89.16/26.92 ((
% 89.16/26.92 (!!) @ (
% 89.16/26.92 (('#B') @ (
% 89.16/26.92 !!) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#S') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#S') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 =>))) @
% 89.16/26.92 ex1)))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 !!))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#S') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#B') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#S') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 =>))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#C') @ in)))))))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 !!))))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#C') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#B') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#B') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#S') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 =>))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#C') @ in)))))))))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#S') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#S') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#B'))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 =>))))))) @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#C') @ (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#B') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 '#S') @
% 89.16/26.92 (
% 89.16/26.92 (
% 89.16/26.92 ('#B') @ (
% 89.16/26.92 =>))))))) @
% 89.16/26.92 (
% 89.16/26.92 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.16/26.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1074])).
% 89.16/26.92 thf(zip_derived_cl1090, plain,
% 89.16/26.92 (~ (((sepSubset) =>
% 89.16/26.92 (((binunionIL) =>
% 89.16/26.92 (((upairset2IR) =>
% 89.16/26.92 (((binunionIR) =>
% 89.16/26.92 (((binunionEcases) =>
% 89.16/26.92 (((binunionE) =>
% 89.16/26.92 (((binunionLsub) =>
% 89.16/26.92 (((binunionRsub) =>
% 89.16/26.92 (((binintersectI) =>
% 89.16/26.92 (((binintersectSubset5) =>
% 89.16/26.92 (((binintersectEL) =>
% 89.16/26.92 (((binintersectLsub) =>
% 89.16/26.92 (((binintersectSubset2) =>
% 89.16/26.92 (((binintersectSubset3) =>
% 89.16/26.92 (((binintersectER) =>
% 89.16/26.92 (((disjointsetsI1) =>
% 89.16/26.92 (((binintersectRsub) =>
% 89.16/26.92 (((binintersectSubset4) =>
% 89.16/26.92 (((binintersectSubset1) =>
% 89.16/26.92 (((bs114d) =>
% 89.16/26.92 (((setminusI) =>
% 89.16/26.94 (((setminusEL) =>
% 89.16/26.94 (((setminusER) =>
% 89.16/26.94 (((setminusSubset2) =>
% 89.16/26.94 (((setminusERneg) =>
% 89.16/26.94 (((setminusELneg) =>
% 89.16/26.94 (((setminusILneg) =>
% 89.16/26.94 (((setminusIRneg) =>
% 89.16/26.94 (((setminusLsub) =>
% 89.16/26.94 (((setminusSubset1) =>
% 89.16/26.94 ((
% 89.16/26.94 (symdiffE) =>
% 89.16/26.94 ((
% 89.16/26.94 (symdiffI1) =>
% 89.16/26.94 ((
% 89.16/26.94 (symdiffI2) =>
% 89.16/26.94 ((
% 89.16/26.94 (symdiffIneg1) =>
% 89.16/26.94 ((
% 89.16/26.94 (symdiffIneg2) =>
% 89.16/26.94 ((
% 89.16/26.94 (secondinupair) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairIL) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairIR) =>
% 89.16/26.94 ((
% 89.16/26.94 (kpairiskpair) =>
% 89.16/26.94 ((
% 89.16/26.94 (kpairp) =>
% 89.16/26.94 ((
% 89.16/26.94 (singletonsubset) =>
% 89.16/26.94 ((
% 89.16/26.94 (singletoninpowerset) =>
% 89.16/26.94 ((
% 89.16/26.94 (singletoninpowunion) =>
% 89.16/26.94 ((
% 89.16/26.94 (upairset2E) =>
% 89.16/26.94 ((
% 89.16/26.94 (upairsubunion) =>
% 89.16/26.94 ((
% 89.16/26.94 (upairinpowunion) =>
% 89.16/26.94 ((
% 89.16/26.94 (ubforcartprodlem1) =>
% 89.16/26.94 ((
% 89.16/26.94 (ubforcartprodlem2) =>
% 89.16/26.94 ((
% 89.16/26.94 (ubforcartprodlem3) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodpairin) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodmempair1) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodmempair) =>
% 89.16/26.94 ((
% 89.16/26.94 (setunionE2) =>
% 89.16/26.94 ((
% 89.16/26.94 (setunionsingleton1) =>
% 89.16/26.94 ((
% 89.16/26.94 (setunionsingleton2) =>
% 89.16/26.94 ((
% 89.16/26.94 (setunionsingleton) =>
% 89.16/26.94 ((
% 89.16/26.94 (singletonprop) =>
% 89.16/26.94 ((
% 89.16/26.94 (ex1E1) =>
% 89.16/26.94 ((
% 89.16/26.94 (ex1I) =>
% 89.16/26.94 ((
% 89.16/26.94 (ex1I2) =>
% 89.16/26.94 ((
% 89.16/26.94 (singletonsuniq) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjL1) =>
% 89.16/26.94 ((
% 89.16/26.94 (kfstsingleton) =>
% 89.16/26.94 ((
% 89.16/26.94 (theprop) =>
% 89.16/26.94 ((
% 89.16/26.94 (kfstpairEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodfstin) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjL2) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjL) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjR11) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjR12) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjR1) =>
% 89.16/26.94 ((
% 89.16/26.94 (upairequniteq) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjR2) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjR) =>
% 89.16/26.94 ((
% 89.16/26.94 (ksndsingleton) =>
% 89.16/26.94 ((
% 89.16/26.94 (ksndpairEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (kpairsurjEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodsndin) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodpairmemEL) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodpairmemER) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodmempaircEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodfstpairEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodsndpairEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodpairsurjEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (dpsetconstrI) =>
% 89.16/26.94 ((
% 89.16/26.94 (dpsetconstrSub) =>
% 89.16/26.94 ((
% 89.16/26.94 (setOfPairsIsBReln) =>
% 89.16/26.94 ((
% 89.16/26.94 (dpsetconstrERa) =>
% 89.16/26.94 ((
% 89.16/26.94 (dpsetconstrEL1) =>
% 89.16/26.94 ((
% 89.16/26.94 (dpsetconstrEL2) =>
% 89.16/26.94 ((
% 89.16/26.94 (dpsetconstrER) =>
% 89.16/26.94 ((
% 89.16/26.94 (funcImageSingleton) =>
% 89.16/26.94 ((
% 89.16/26.94 (apProp) =>
% 89.16/26.94 ((
% 89.16/26.94 (app) =>
% 89.16/26.94 ((
% 89.16/26.94 (infuncsetfunc) =>
% 89.16/26.94 ((
% 89.16/26.94 (ap2p) =>
% 89.16/26.94 ((
% 89.16/26.94 (funcinfuncset) =>
% 89.16/26.94 ((
% 89.16/26.94 (lamProp) =>
% 89.16/26.94 ((
% 89.16/26.94 (lamp) =>
% 89.16/26.94 ((
% 89.16/26.94 (lam2p) =>
% 89.16/26.94 ((
% 89.16/26.94 (brelnall1) =>
% 89.16/26.94 ((
% 89.16/26.94 (brelnall2) =>
% 89.16/26.94 ((
% 89.16/26.94 (!!) @ (
% 89.16/26.94 (('#B') @ (
% 89.16/26.94 !!) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#S') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#S') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 =>))) @
% 89.16/26.94 ex1)))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 !!))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#S') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#B') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#S') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 =>))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#C') @ in)))))))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 !!))))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#C') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#B') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#B') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#S') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 =>))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#C') @ in)))))))))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#S') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#S') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#B'))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 =>))))))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#C') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#B') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#S') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 =>))))))) @
% 89.16/26.94 (
% 89.16/26.94 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.16/26.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1082])).
% 89.16/26.94 thf(zip_derived_cl1096, plain,
% 89.16/26.94 (~ (((binunionIL) =>
% 89.16/26.94 (((upairset2IR) =>
% 89.16/26.94 (((binunionIR) =>
% 89.16/26.94 (((binunionEcases) =>
% 89.16/26.94 (((binunionE) =>
% 89.16/26.94 (((binunionLsub) =>
% 89.16/26.94 (((binunionRsub) =>
% 89.16/26.94 (((binintersectI) =>
% 89.16/26.94 (((binintersectSubset5) =>
% 89.16/26.94 (((binintersectEL) =>
% 89.16/26.94 (((binintersectLsub) =>
% 89.16/26.94 (((binintersectSubset2) =>
% 89.16/26.94 (((binintersectSubset3) =>
% 89.16/26.94 (((binintersectER) =>
% 89.16/26.94 (((disjointsetsI1) =>
% 89.16/26.94 (((binintersectRsub) =>
% 89.16/26.94 (((binintersectSubset4) =>
% 89.16/26.94 (((binintersectSubset1) =>
% 89.16/26.94 (((bs114d) =>
% 89.16/26.94 (((setminusI) =>
% 89.16/26.94 (((setminusEL) =>
% 89.16/26.94 (((setminusER) =>
% 89.16/26.94 (((setminusSubset2) =>
% 89.16/26.94 (((setminusERneg) =>
% 89.16/26.94 (((setminusELneg) =>
% 89.16/26.94 (((setminusILneg) =>
% 89.16/26.94 (((setminusIRneg) =>
% 89.16/26.94 (((setminusLsub) =>
% 89.16/26.94 (((setminusSubset1) =>
% 89.16/26.94 (((symdiffE) =>
% 89.16/26.94 ((
% 89.16/26.94 (symdiffI1) =>
% 89.16/26.94 ((
% 89.16/26.94 (symdiffI2) =>
% 89.16/26.94 ((
% 89.16/26.94 (symdiffIneg1) =>
% 89.16/26.94 ((
% 89.16/26.94 (symdiffIneg2) =>
% 89.16/26.94 ((
% 89.16/26.94 (secondinupair) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairIL) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairIR) =>
% 89.16/26.94 ((
% 89.16/26.94 (kpairiskpair) =>
% 89.16/26.94 ((
% 89.16/26.94 (kpairp) =>
% 89.16/26.94 ((
% 89.16/26.94 (singletonsubset) =>
% 89.16/26.94 ((
% 89.16/26.94 (singletoninpowerset) =>
% 89.16/26.94 ((
% 89.16/26.94 (singletoninpowunion) =>
% 89.16/26.94 ((
% 89.16/26.94 (upairset2E) =>
% 89.16/26.94 ((
% 89.16/26.94 (upairsubunion) =>
% 89.16/26.94 ((
% 89.16/26.94 (upairinpowunion) =>
% 89.16/26.94 ((
% 89.16/26.94 (ubforcartprodlem1) =>
% 89.16/26.94 ((
% 89.16/26.94 (ubforcartprodlem2) =>
% 89.16/26.94 ((
% 89.16/26.94 (ubforcartprodlem3) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodpairin) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodmempair1) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodmempair) =>
% 89.16/26.94 ((
% 89.16/26.94 (setunionE2) =>
% 89.16/26.94 ((
% 89.16/26.94 (setunionsingleton1) =>
% 89.16/26.94 ((
% 89.16/26.94 (setunionsingleton2) =>
% 89.16/26.94 ((
% 89.16/26.94 (setunionsingleton) =>
% 89.16/26.94 ((
% 89.16/26.94 (singletonprop) =>
% 89.16/26.94 ((
% 89.16/26.94 (ex1E1) =>
% 89.16/26.94 ((
% 89.16/26.94 (ex1I) =>
% 89.16/26.94 ((
% 89.16/26.94 (ex1I2) =>
% 89.16/26.94 ((
% 89.16/26.94 (singletonsuniq) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjL1) =>
% 89.16/26.94 ((
% 89.16/26.94 (kfstsingleton) =>
% 89.16/26.94 ((
% 89.16/26.94 (theprop) =>
% 89.16/26.94 ((
% 89.16/26.94 (kfstpairEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodfstin) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjL2) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjL) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjR11) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjR12) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjR1) =>
% 89.16/26.94 ((
% 89.16/26.94 (upairequniteq) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjR2) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjR) =>
% 89.16/26.94 ((
% 89.16/26.94 (ksndsingleton) =>
% 89.16/26.94 ((
% 89.16/26.94 (ksndpairEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (kpairsurjEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodsndin) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodpairmemEL) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodpairmemER) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodmempaircEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodfstpairEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodsndpairEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodpairsurjEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (dpsetconstrI) =>
% 89.16/26.94 ((
% 89.16/26.94 (dpsetconstrSub) =>
% 89.16/26.94 ((
% 89.16/26.94 (setOfPairsIsBReln) =>
% 89.16/26.94 ((
% 89.16/26.94 (dpsetconstrERa) =>
% 89.16/26.94 ((
% 89.16/26.94 (dpsetconstrEL1) =>
% 89.16/26.94 ((
% 89.16/26.94 (dpsetconstrEL2) =>
% 89.16/26.94 ((
% 89.16/26.94 (dpsetconstrER) =>
% 89.16/26.94 ((
% 89.16/26.94 (funcImageSingleton) =>
% 89.16/26.94 ((
% 89.16/26.94 (apProp) =>
% 89.16/26.94 ((
% 89.16/26.94 (app) =>
% 89.16/26.94 ((
% 89.16/26.94 (infuncsetfunc) =>
% 89.16/26.94 ((
% 89.16/26.94 (ap2p) =>
% 89.16/26.94 ((
% 89.16/26.94 (funcinfuncset) =>
% 89.16/26.94 ((
% 89.16/26.94 (lamProp) =>
% 89.16/26.94 ((
% 89.16/26.94 (lamp) =>
% 89.16/26.94 ((
% 89.16/26.94 (lam2p) =>
% 89.16/26.94 ((
% 89.16/26.94 (brelnall1) =>
% 89.16/26.94 ((
% 89.16/26.94 (brelnall2) =>
% 89.16/26.94 ((
% 89.16/26.94 (!!) @ (
% 89.16/26.94 (('#B') @ (
% 89.16/26.94 !!) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#S') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#S') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 =>))) @
% 89.16/26.94 ex1)))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 !!))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#S') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#B') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#S') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 =>))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#C') @ in)))))))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 !!))))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#C') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#B') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#B') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#S') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 =>))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#C') @ in)))))))))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#S') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#S') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#B'))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 =>))))))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#C') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#B') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#S') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 =>))))))) @
% 89.16/26.94 (
% 89.16/26.94 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.16/26.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1090])).
% 89.16/26.94 thf(zip_derived_cl1102, plain,
% 89.16/26.94 (~ (((upairset2IR) =>
% 89.16/26.94 (((binunionIR) =>
% 89.16/26.94 (((binunionEcases) =>
% 89.16/26.94 (((binunionE) =>
% 89.16/26.94 (((binunionLsub) =>
% 89.16/26.94 (((binunionRsub) =>
% 89.16/26.94 (((binintersectI) =>
% 89.16/26.94 (((binintersectSubset5) =>
% 89.16/26.94 (((binintersectEL) =>
% 89.16/26.94 (((binintersectLsub) =>
% 89.16/26.94 (((binintersectSubset2) =>
% 89.16/26.94 (((binintersectSubset3) =>
% 89.16/26.94 (((binintersectER) =>
% 89.16/26.94 (((disjointsetsI1) =>
% 89.16/26.94 (((binintersectRsub) =>
% 89.16/26.94 (((binintersectSubset4) =>
% 89.16/26.94 (((binintersectSubset1) =>
% 89.16/26.94 (((bs114d) =>
% 89.16/26.94 (((setminusI) =>
% 89.16/26.94 (((setminusEL) =>
% 89.16/26.94 (((setminusER) =>
% 89.16/26.94 (((setminusSubset2) =>
% 89.16/26.94 (((setminusERneg) =>
% 89.16/26.94 (((setminusELneg) =>
% 89.16/26.94 (((setminusILneg) =>
% 89.16/26.94 (((setminusIRneg) =>
% 89.16/26.94 (((setminusLsub) =>
% 89.16/26.94 (((setminusSubset1) =>
% 89.16/26.94 (((symdiffE) =>
% 89.16/26.94 (((symdiffI1) =>
% 89.16/26.94 ((
% 89.16/26.94 (symdiffI2) =>
% 89.16/26.94 ((
% 89.16/26.94 (symdiffIneg1) =>
% 89.16/26.94 ((
% 89.16/26.94 (symdiffIneg2) =>
% 89.16/26.94 ((
% 89.16/26.94 (secondinupair) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairIL) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairIR) =>
% 89.16/26.94 ((
% 89.16/26.94 (kpairiskpair) =>
% 89.16/26.94 ((
% 89.16/26.94 (kpairp) =>
% 89.16/26.94 ((
% 89.16/26.94 (singletonsubset) =>
% 89.16/26.94 ((
% 89.16/26.94 (singletoninpowerset) =>
% 89.16/26.94 ((
% 89.16/26.94 (singletoninpowunion) =>
% 89.16/26.94 ((
% 89.16/26.94 (upairset2E) =>
% 89.16/26.94 ((
% 89.16/26.94 (upairsubunion) =>
% 89.16/26.94 ((
% 89.16/26.94 (upairinpowunion) =>
% 89.16/26.94 ((
% 89.16/26.94 (ubforcartprodlem1) =>
% 89.16/26.94 ((
% 89.16/26.94 (ubforcartprodlem2) =>
% 89.16/26.94 ((
% 89.16/26.94 (ubforcartprodlem3) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodpairin) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodmempair1) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodmempair) =>
% 89.16/26.94 ((
% 89.16/26.94 (setunionE2) =>
% 89.16/26.94 ((
% 89.16/26.94 (setunionsingleton1) =>
% 89.16/26.94 ((
% 89.16/26.94 (setunionsingleton2) =>
% 89.16/26.94 ((
% 89.16/26.94 (setunionsingleton) =>
% 89.16/26.94 ((
% 89.16/26.94 (singletonprop) =>
% 89.16/26.94 ((
% 89.16/26.94 (ex1E1) =>
% 89.16/26.94 ((
% 89.16/26.94 (ex1I) =>
% 89.16/26.94 ((
% 89.16/26.94 (ex1I2) =>
% 89.16/26.94 ((
% 89.16/26.94 (singletonsuniq) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjL1) =>
% 89.16/26.94 ((
% 89.16/26.94 (kfstsingleton) =>
% 89.16/26.94 ((
% 89.16/26.94 (theprop) =>
% 89.16/26.94 ((
% 89.16/26.94 (kfstpairEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodfstin) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjL2) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjL) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjR11) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjR12) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjR1) =>
% 89.16/26.94 ((
% 89.16/26.94 (upairequniteq) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjR2) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjR) =>
% 89.16/26.94 ((
% 89.16/26.94 (ksndsingleton) =>
% 89.16/26.94 ((
% 89.16/26.94 (ksndpairEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (kpairsurjEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodsndin) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodpairmemEL) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodpairmemER) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodmempaircEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodfstpairEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodsndpairEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodpairsurjEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (dpsetconstrI) =>
% 89.16/26.94 ((
% 89.16/26.94 (dpsetconstrSub) =>
% 89.16/26.94 ((
% 89.16/26.94 (setOfPairsIsBReln) =>
% 89.16/26.94 ((
% 89.16/26.94 (dpsetconstrERa) =>
% 89.16/26.94 ((
% 89.16/26.94 (dpsetconstrEL1) =>
% 89.16/26.94 ((
% 89.16/26.94 (dpsetconstrEL2) =>
% 89.16/26.94 ((
% 89.16/26.94 (dpsetconstrER) =>
% 89.16/26.94 ((
% 89.16/26.94 (funcImageSingleton) =>
% 89.16/26.94 ((
% 89.16/26.94 (apProp) =>
% 89.16/26.94 ((
% 89.16/26.94 (app) =>
% 89.16/26.94 ((
% 89.16/26.94 (infuncsetfunc) =>
% 89.16/26.94 ((
% 89.16/26.94 (ap2p) =>
% 89.16/26.94 ((
% 89.16/26.94 (funcinfuncset) =>
% 89.16/26.94 ((
% 89.16/26.94 (lamProp) =>
% 89.16/26.94 ((
% 89.16/26.94 (lamp) =>
% 89.16/26.94 ((
% 89.16/26.94 (lam2p) =>
% 89.16/26.94 ((
% 89.16/26.94 (brelnall1) =>
% 89.16/26.94 ((
% 89.16/26.94 (brelnall2) =>
% 89.16/26.94 ((
% 89.16/26.94 (!!) @ (
% 89.16/26.94 (('#B') @ (
% 89.16/26.94 !!) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#S') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#S') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 =>))) @
% 89.16/26.94 ex1)))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 !!))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#S') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#B') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#S') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 =>))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#C') @ in)))))))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 !!))))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#C') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#B') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#B') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#S') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 =>))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#C') @ in)))))))))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#S') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#S') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#B'))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 =>))))))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#C') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#B') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#S') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 =>))))))) @
% 89.16/26.94 (
% 89.16/26.94 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.16/26.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1096])).
% 89.16/26.94 thf(zip_derived_cl1109, plain,
% 89.16/26.94 (~ (((binunionIR) =>
% 89.16/26.94 (((binunionEcases) =>
% 89.16/26.94 (((binunionE) =>
% 89.16/26.94 (((binunionLsub) =>
% 89.16/26.94 (((binunionRsub) =>
% 89.16/26.94 (((binintersectI) =>
% 89.16/26.94 (((binintersectSubset5) =>
% 89.16/26.94 (((binintersectEL) =>
% 89.16/26.94 (((binintersectLsub) =>
% 89.16/26.94 (((binintersectSubset2) =>
% 89.16/26.94 (((binintersectSubset3) =>
% 89.16/26.94 (((binintersectER) =>
% 89.16/26.94 (((disjointsetsI1) =>
% 89.16/26.94 (((binintersectRsub) =>
% 89.16/26.94 (((binintersectSubset4) =>
% 89.16/26.94 (((binintersectSubset1) =>
% 89.16/26.94 (((bs114d) =>
% 89.16/26.94 (((setminusI) =>
% 89.16/26.94 (((setminusEL) =>
% 89.16/26.94 (((setminusER) =>
% 89.16/26.94 (((setminusSubset2) =>
% 89.16/26.94 (((setminusERneg) =>
% 89.16/26.94 (((setminusELneg) =>
% 89.16/26.94 (((setminusILneg) =>
% 89.16/26.94 (((setminusIRneg) =>
% 89.16/26.94 (((setminusLsub) =>
% 89.16/26.94 (((setminusSubset1) =>
% 89.16/26.94 (((symdiffE) =>
% 89.16/26.94 (((symdiffI1) =>
% 89.16/26.94 (((symdiffI2) =>
% 89.16/26.94 ((
% 89.16/26.94 (symdiffIneg1) =>
% 89.16/26.94 ((
% 89.16/26.94 (symdiffIneg2) =>
% 89.16/26.94 ((
% 89.16/26.94 (secondinupair) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairIL) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairIR) =>
% 89.16/26.94 ((
% 89.16/26.94 (kpairiskpair) =>
% 89.16/26.94 ((
% 89.16/26.94 (kpairp) =>
% 89.16/26.94 ((
% 89.16/26.94 (singletonsubset) =>
% 89.16/26.94 ((
% 89.16/26.94 (singletoninpowerset) =>
% 89.16/26.94 ((
% 89.16/26.94 (singletoninpowunion) =>
% 89.16/26.94 ((
% 89.16/26.94 (upairset2E) =>
% 89.16/26.94 ((
% 89.16/26.94 (upairsubunion) =>
% 89.16/26.94 ((
% 89.16/26.94 (upairinpowunion) =>
% 89.16/26.94 ((
% 89.16/26.94 (ubforcartprodlem1) =>
% 89.16/26.94 ((
% 89.16/26.94 (ubforcartprodlem2) =>
% 89.16/26.94 ((
% 89.16/26.94 (ubforcartprodlem3) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodpairin) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodmempair1) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodmempair) =>
% 89.16/26.94 ((
% 89.16/26.94 (setunionE2) =>
% 89.16/26.94 ((
% 89.16/26.94 (setunionsingleton1) =>
% 89.16/26.94 ((
% 89.16/26.94 (setunionsingleton2) =>
% 89.16/26.94 ((
% 89.16/26.94 (setunionsingleton) =>
% 89.16/26.94 ((
% 89.16/26.94 (singletonprop) =>
% 89.16/26.94 ((
% 89.16/26.94 (ex1E1) =>
% 89.16/26.94 ((
% 89.16/26.94 (ex1I) =>
% 89.16/26.94 ((
% 89.16/26.94 (ex1I2) =>
% 89.16/26.94 ((
% 89.16/26.94 (singletonsuniq) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjL1) =>
% 89.16/26.94 ((
% 89.16/26.94 (kfstsingleton) =>
% 89.16/26.94 ((
% 89.16/26.94 (theprop) =>
% 89.16/26.94 ((
% 89.16/26.94 (kfstpairEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodfstin) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjL2) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjL) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjR11) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjR12) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjR1) =>
% 89.16/26.94 ((
% 89.16/26.94 (upairequniteq) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjR2) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjR) =>
% 89.16/26.94 ((
% 89.16/26.94 (ksndsingleton) =>
% 89.16/26.94 ((
% 89.16/26.94 (ksndpairEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (kpairsurjEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodsndin) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodpairmemEL) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodpairmemER) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodmempaircEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodfstpairEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodsndpairEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodpairsurjEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (dpsetconstrI) =>
% 89.16/26.94 ((
% 89.16/26.94 (dpsetconstrSub) =>
% 89.16/26.94 ((
% 89.16/26.94 (setOfPairsIsBReln) =>
% 89.16/26.94 ((
% 89.16/26.94 (dpsetconstrERa) =>
% 89.16/26.94 ((
% 89.16/26.94 (dpsetconstrEL1) =>
% 89.16/26.94 ((
% 89.16/26.94 (dpsetconstrEL2) =>
% 89.16/26.94 ((
% 89.16/26.94 (dpsetconstrER) =>
% 89.16/26.94 ((
% 89.16/26.94 (funcImageSingleton) =>
% 89.16/26.94 ((
% 89.16/26.94 (apProp) =>
% 89.16/26.94 ((
% 89.16/26.94 (app) =>
% 89.16/26.94 ((
% 89.16/26.94 (infuncsetfunc) =>
% 89.16/26.94 ((
% 89.16/26.94 (ap2p) =>
% 89.16/26.94 ((
% 89.16/26.94 (funcinfuncset) =>
% 89.16/26.94 ((
% 89.16/26.94 (lamProp) =>
% 89.16/26.94 ((
% 89.16/26.94 (lamp) =>
% 89.16/26.94 ((
% 89.16/26.94 (lam2p) =>
% 89.16/26.94 ((
% 89.16/26.94 (brelnall1) =>
% 89.16/26.94 ((
% 89.16/26.94 (brelnall2) =>
% 89.16/26.94 ((
% 89.16/26.94 (!!) @ (
% 89.16/26.94 (('#B') @ (
% 89.16/26.94 !!) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#S') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#S') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 =>))) @
% 89.16/26.94 ex1)))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 !!))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#S') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#B') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#S') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 =>))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#C') @ in)))))))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 !!))))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#C') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#B') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#B') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#S') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 =>))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#C') @ in)))))))))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#S') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#S') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#B'))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 =>))))))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#C') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#B') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#S') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 =>))))))) @
% 89.16/26.94 (
% 89.16/26.94 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.16/26.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1102])).
% 89.16/26.94 thf(zip_derived_cl1115, plain,
% 89.16/26.94 (~ (((binunionEcases) =>
% 89.16/26.94 (((binunionE) =>
% 89.16/26.94 (((binunionLsub) =>
% 89.16/26.94 (((binunionRsub) =>
% 89.16/26.94 (((binintersectI) =>
% 89.16/26.94 (((binintersectSubset5) =>
% 89.16/26.94 (((binintersectEL) =>
% 89.16/26.94 (((binintersectLsub) =>
% 89.16/26.94 (((binintersectSubset2) =>
% 89.16/26.94 (((binintersectSubset3) =>
% 89.16/26.94 (((binintersectER) =>
% 89.16/26.94 (((disjointsetsI1) =>
% 89.16/26.94 (((binintersectRsub) =>
% 89.16/26.94 (((binintersectSubset4) =>
% 89.16/26.94 (((binintersectSubset1) =>
% 89.16/26.94 (((bs114d) =>
% 89.16/26.94 (((setminusI) =>
% 89.16/26.94 (((setminusEL) =>
% 89.16/26.94 (((setminusER) =>
% 89.16/26.94 (((setminusSubset2) =>
% 89.16/26.94 (((setminusERneg) =>
% 89.16/26.94 (((setminusELneg) =>
% 89.16/26.94 (((setminusILneg) =>
% 89.16/26.94 (((setminusIRneg) =>
% 89.16/26.94 (((setminusLsub) =>
% 89.16/26.94 (((setminusSubset1) =>
% 89.16/26.94 (((symdiffE) =>
% 89.16/26.94 (((symdiffI1) =>
% 89.16/26.94 (((symdiffI2) =>
% 89.16/26.94 (((symdiffIneg1) =>
% 89.16/26.94 ((
% 89.16/26.94 (symdiffIneg2) =>
% 89.16/26.94 ((
% 89.16/26.94 (secondinupair) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairIL) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairIR) =>
% 89.16/26.94 ((
% 89.16/26.94 (kpairiskpair) =>
% 89.16/26.94 ((
% 89.16/26.94 (kpairp) =>
% 89.16/26.94 ((
% 89.16/26.94 (singletonsubset) =>
% 89.16/26.94 ((
% 89.16/26.94 (singletoninpowerset) =>
% 89.16/26.94 ((
% 89.16/26.94 (singletoninpowunion) =>
% 89.16/26.94 ((
% 89.16/26.94 (upairset2E) =>
% 89.16/26.94 ((
% 89.16/26.94 (upairsubunion) =>
% 89.16/26.94 ((
% 89.16/26.94 (upairinpowunion) =>
% 89.16/26.94 ((
% 89.16/26.94 (ubforcartprodlem1) =>
% 89.16/26.94 ((
% 89.16/26.94 (ubforcartprodlem2) =>
% 89.16/26.94 ((
% 89.16/26.94 (ubforcartprodlem3) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodpairin) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodmempair1) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodmempair) =>
% 89.16/26.94 ((
% 89.16/26.94 (setunionE2) =>
% 89.16/26.94 ((
% 89.16/26.94 (setunionsingleton1) =>
% 89.16/26.94 ((
% 89.16/26.94 (setunionsingleton2) =>
% 89.16/26.94 ((
% 89.16/26.94 (setunionsingleton) =>
% 89.16/26.94 ((
% 89.16/26.94 (singletonprop) =>
% 89.16/26.94 ((
% 89.16/26.94 (ex1E1) =>
% 89.16/26.94 ((
% 89.16/26.94 (ex1I) =>
% 89.16/26.94 ((
% 89.16/26.94 (ex1I2) =>
% 89.16/26.94 ((
% 89.16/26.94 (singletonsuniq) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjL1) =>
% 89.16/26.94 ((
% 89.16/26.94 (kfstsingleton) =>
% 89.16/26.94 ((
% 89.16/26.94 (theprop) =>
% 89.16/26.94 ((
% 89.16/26.94 (kfstpairEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodfstin) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjL2) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjL) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjR11) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjR12) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjR1) =>
% 89.16/26.94 ((
% 89.16/26.94 (upairequniteq) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjR2) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjR) =>
% 89.16/26.94 ((
% 89.16/26.94 (ksndsingleton) =>
% 89.16/26.94 ((
% 89.16/26.94 (ksndpairEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (kpairsurjEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodsndin) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodpairmemEL) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodpairmemER) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodmempaircEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodfstpairEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodsndpairEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodpairsurjEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (dpsetconstrI) =>
% 89.16/26.94 ((
% 89.16/26.94 (dpsetconstrSub) =>
% 89.16/26.94 ((
% 89.16/26.94 (setOfPairsIsBReln) =>
% 89.16/26.94 ((
% 89.16/26.94 (dpsetconstrERa) =>
% 89.16/26.94 ((
% 89.16/26.94 (dpsetconstrEL1) =>
% 89.16/26.94 ((
% 89.16/26.94 (dpsetconstrEL2) =>
% 89.16/26.94 ((
% 89.16/26.94 (dpsetconstrER) =>
% 89.16/26.94 ((
% 89.16/26.94 (funcImageSingleton) =>
% 89.16/26.94 ((
% 89.16/26.94 (apProp) =>
% 89.16/26.94 ((
% 89.16/26.94 (app) =>
% 89.16/26.94 ((
% 89.16/26.94 (infuncsetfunc) =>
% 89.16/26.94 ((
% 89.16/26.94 (ap2p) =>
% 89.16/26.94 ((
% 89.16/26.94 (funcinfuncset) =>
% 89.16/26.94 ((
% 89.16/26.94 (lamProp) =>
% 89.16/26.94 ((
% 89.16/26.94 (lamp) =>
% 89.16/26.94 ((
% 89.16/26.94 (lam2p) =>
% 89.16/26.94 ((
% 89.16/26.94 (brelnall1) =>
% 89.16/26.94 ((
% 89.16/26.94 (brelnall2) =>
% 89.16/26.94 ((
% 89.16/26.94 (!!) @ (
% 89.16/26.94 (('#B') @ (
% 89.16/26.94 !!) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#S') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#S') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 =>))) @
% 89.16/26.94 ex1)))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 !!))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#S') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#B') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#S') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 =>))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#C') @ in)))))))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 !!))))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#C') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#B') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#B') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#S') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 =>))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#C') @ in)))))))))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#S') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#S') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#B'))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 =>))))))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#C') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#B') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#S') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 =>))))))) @
% 89.16/26.94 (
% 89.16/26.94 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.16/26.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1109])).
% 89.16/26.94 thf(zip_derived_cl1121, plain,
% 89.16/26.94 (~ (((binunionE) =>
% 89.16/26.94 (((binunionLsub) =>
% 89.16/26.94 (((binunionRsub) =>
% 89.16/26.94 (((binintersectI) =>
% 89.16/26.94 (((binintersectSubset5) =>
% 89.16/26.94 (((binintersectEL) =>
% 89.16/26.94 (((binintersectLsub) =>
% 89.16/26.94 (((binintersectSubset2) =>
% 89.16/26.94 (((binintersectSubset3) =>
% 89.16/26.94 (((binintersectER) =>
% 89.16/26.94 (((disjointsetsI1) =>
% 89.16/26.94 (((binintersectRsub) =>
% 89.16/26.94 (((binintersectSubset4) =>
% 89.16/26.94 (((binintersectSubset1) =>
% 89.16/26.94 (((bs114d) =>
% 89.16/26.94 (((setminusI) =>
% 89.16/26.94 (((setminusEL) =>
% 89.16/26.94 (((setminusER) =>
% 89.16/26.94 (((setminusSubset2) =>
% 89.16/26.94 (((setminusERneg) =>
% 89.16/26.94 (((setminusELneg) =>
% 89.16/26.94 (((setminusILneg) =>
% 89.16/26.94 (((setminusIRneg) =>
% 89.16/26.94 (((setminusLsub) =>
% 89.16/26.94 (((setminusSubset1) =>
% 89.16/26.94 (((symdiffE) =>
% 89.16/26.94 (((symdiffI1) =>
% 89.16/26.94 (((symdiffI2) =>
% 89.16/26.94 (((symdiffIneg1) =>
% 89.16/26.94 (((symdiffIneg2) =>
% 89.16/26.94 ((
% 89.16/26.94 (secondinupair) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairIL) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairIR) =>
% 89.16/26.94 ((
% 89.16/26.94 (kpairiskpair) =>
% 89.16/26.94 ((
% 89.16/26.94 (kpairp) =>
% 89.16/26.94 ((
% 89.16/26.94 (singletonsubset) =>
% 89.16/26.94 ((
% 89.16/26.94 (singletoninpowerset) =>
% 89.16/26.94 ((
% 89.16/26.94 (singletoninpowunion) =>
% 89.16/26.94 ((
% 89.16/26.94 (upairset2E) =>
% 89.16/26.94 ((
% 89.16/26.94 (upairsubunion) =>
% 89.16/26.94 ((
% 89.16/26.94 (upairinpowunion) =>
% 89.16/26.94 ((
% 89.16/26.94 (ubforcartprodlem1) =>
% 89.16/26.94 ((
% 89.16/26.94 (ubforcartprodlem2) =>
% 89.16/26.94 ((
% 89.16/26.94 (ubforcartprodlem3) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodpairin) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodmempair1) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodmempair) =>
% 89.16/26.94 ((
% 89.16/26.94 (setunionE2) =>
% 89.16/26.94 ((
% 89.16/26.94 (setunionsingleton1) =>
% 89.16/26.94 ((
% 89.16/26.94 (setunionsingleton2) =>
% 89.16/26.94 ((
% 89.16/26.94 (setunionsingleton) =>
% 89.16/26.94 ((
% 89.16/26.94 (singletonprop) =>
% 89.16/26.94 ((
% 89.16/26.94 (ex1E1) =>
% 89.16/26.94 ((
% 89.16/26.94 (ex1I) =>
% 89.16/26.94 ((
% 89.16/26.94 (ex1I2) =>
% 89.16/26.94 ((
% 89.16/26.94 (singletonsuniq) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjL1) =>
% 89.16/26.94 ((
% 89.16/26.94 (kfstsingleton) =>
% 89.16/26.94 ((
% 89.16/26.94 (theprop) =>
% 89.16/26.94 ((
% 89.16/26.94 (kfstpairEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodfstin) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjL2) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjL) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjR11) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjR12) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjR1) =>
% 89.16/26.94 ((
% 89.16/26.94 (upairequniteq) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjR2) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjR) =>
% 89.16/26.94 ((
% 89.16/26.94 (ksndsingleton) =>
% 89.16/26.94 ((
% 89.16/26.94 (ksndpairEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (kpairsurjEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodsndin) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodpairmemEL) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodpairmemER) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodmempaircEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodfstpairEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodsndpairEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodpairsurjEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (dpsetconstrI) =>
% 89.16/26.94 ((
% 89.16/26.94 (dpsetconstrSub) =>
% 89.16/26.94 ((
% 89.16/26.94 (setOfPairsIsBReln) =>
% 89.16/26.94 ((
% 89.16/26.94 (dpsetconstrERa) =>
% 89.16/26.94 ((
% 89.16/26.94 (dpsetconstrEL1) =>
% 89.16/26.94 ((
% 89.16/26.94 (dpsetconstrEL2) =>
% 89.16/26.94 ((
% 89.16/26.94 (dpsetconstrER) =>
% 89.16/26.94 ((
% 89.16/26.94 (funcImageSingleton) =>
% 89.16/26.94 ((
% 89.16/26.94 (apProp) =>
% 89.16/26.94 ((
% 89.16/26.94 (app) =>
% 89.16/26.94 ((
% 89.16/26.94 (infuncsetfunc) =>
% 89.16/26.94 ((
% 89.16/26.94 (ap2p) =>
% 89.16/26.94 ((
% 89.16/26.94 (funcinfuncset) =>
% 89.16/26.94 ((
% 89.16/26.94 (lamProp) =>
% 89.16/26.94 ((
% 89.16/26.94 (lamp) =>
% 89.16/26.94 ((
% 89.16/26.94 (lam2p) =>
% 89.16/26.94 ((
% 89.16/26.94 (brelnall1) =>
% 89.16/26.94 ((
% 89.16/26.94 (brelnall2) =>
% 89.16/26.94 ((
% 89.16/26.94 (!!) @ (
% 89.16/26.94 (('#B') @ (
% 89.16/26.94 !!) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#S') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#S') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 =>))) @
% 89.16/26.94 ex1)))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 !!))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#S') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#B') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#S') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 =>))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#C') @ in)))))))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 !!))))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#C') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#B') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#B') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#S') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 =>))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#C') @ in)))))))))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#S') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#S') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#B'))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 =>))))))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#C') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#B') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#S') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 =>))))))) @
% 89.16/26.94 (
% 89.16/26.94 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.16/26.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1115])).
% 89.16/26.94 thf(zip_derived_cl1128, plain,
% 89.16/26.94 (~ (((binunionLsub) =>
% 89.16/26.94 (((binunionRsub) =>
% 89.16/26.94 (((binintersectI) =>
% 89.16/26.94 (((binintersectSubset5) =>
% 89.16/26.94 (((binintersectEL) =>
% 89.16/26.94 (((binintersectLsub) =>
% 89.16/26.94 (((binintersectSubset2) =>
% 89.16/26.94 (((binintersectSubset3) =>
% 89.16/26.94 (((binintersectER) =>
% 89.16/26.94 (((disjointsetsI1) =>
% 89.16/26.94 (((binintersectRsub) =>
% 89.16/26.94 (((binintersectSubset4) =>
% 89.16/26.94 (((binintersectSubset1) =>
% 89.16/26.94 (((bs114d) =>
% 89.16/26.94 (((setminusI) =>
% 89.16/26.94 (((setminusEL) =>
% 89.16/26.94 (((setminusER) =>
% 89.16/26.94 (((setminusSubset2) =>
% 89.16/26.94 (((setminusERneg) =>
% 89.16/26.94 (((setminusELneg) =>
% 89.16/26.94 (((setminusILneg) =>
% 89.16/26.94 (((setminusIRneg) =>
% 89.16/26.94 (((setminusLsub) =>
% 89.16/26.94 (((setminusSubset1) =>
% 89.16/26.94 (((symdiffE) =>
% 89.16/26.94 (((symdiffI1) =>
% 89.16/26.94 (((symdiffI2) =>
% 89.16/26.94 (((symdiffIneg1) =>
% 89.16/26.94 (((symdiffIneg2) =>
% 89.16/26.94 (((secondinupair) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairIL) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairIR) =>
% 89.16/26.94 ((
% 89.16/26.94 (kpairiskpair) =>
% 89.16/26.94 ((
% 89.16/26.94 (kpairp) =>
% 89.16/26.94 ((
% 89.16/26.94 (singletonsubset) =>
% 89.16/26.94 ((
% 89.16/26.94 (singletoninpowerset) =>
% 89.16/26.94 ((
% 89.16/26.94 (singletoninpowunion) =>
% 89.16/26.94 ((
% 89.16/26.94 (upairset2E) =>
% 89.16/26.94 ((
% 89.16/26.94 (upairsubunion) =>
% 89.16/26.94 ((
% 89.16/26.94 (upairinpowunion) =>
% 89.16/26.94 ((
% 89.16/26.94 (ubforcartprodlem1) =>
% 89.16/26.94 ((
% 89.16/26.94 (ubforcartprodlem2) =>
% 89.16/26.94 ((
% 89.16/26.94 (ubforcartprodlem3) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodpairin) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodmempair1) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodmempair) =>
% 89.16/26.94 ((
% 89.16/26.94 (setunionE2) =>
% 89.16/26.94 ((
% 89.16/26.94 (setunionsingleton1) =>
% 89.16/26.94 ((
% 89.16/26.94 (setunionsingleton2) =>
% 89.16/26.94 ((
% 89.16/26.94 (setunionsingleton) =>
% 89.16/26.94 ((
% 89.16/26.94 (singletonprop) =>
% 89.16/26.94 ((
% 89.16/26.94 (ex1E1) =>
% 89.16/26.94 ((
% 89.16/26.94 (ex1I) =>
% 89.16/26.94 ((
% 89.16/26.94 (ex1I2) =>
% 89.16/26.94 ((
% 89.16/26.94 (singletonsuniq) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjL1) =>
% 89.16/26.94 ((
% 89.16/26.94 (kfstsingleton) =>
% 89.16/26.94 ((
% 89.16/26.94 (theprop) =>
% 89.16/26.94 ((
% 89.16/26.94 (kfstpairEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodfstin) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjL2) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjL) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjR11) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjR12) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjR1) =>
% 89.16/26.94 ((
% 89.16/26.94 (upairequniteq) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjR2) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjR) =>
% 89.16/26.94 ((
% 89.16/26.94 (ksndsingleton) =>
% 89.16/26.94 ((
% 89.16/26.94 (ksndpairEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (kpairsurjEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodsndin) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodpairmemEL) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodpairmemER) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodmempaircEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodfstpairEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodsndpairEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodpairsurjEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (dpsetconstrI) =>
% 89.16/26.94 ((
% 89.16/26.94 (dpsetconstrSub) =>
% 89.16/26.94 ((
% 89.16/26.94 (setOfPairsIsBReln) =>
% 89.16/26.94 ((
% 89.16/26.94 (dpsetconstrERa) =>
% 89.16/26.94 ((
% 89.16/26.94 (dpsetconstrEL1) =>
% 89.16/26.94 ((
% 89.16/26.94 (dpsetconstrEL2) =>
% 89.16/26.94 ((
% 89.16/26.94 (dpsetconstrER) =>
% 89.16/26.94 ((
% 89.16/26.94 (funcImageSingleton) =>
% 89.16/26.94 ((
% 89.16/26.94 (apProp) =>
% 89.16/26.94 ((
% 89.16/26.94 (app) =>
% 89.16/26.94 ((
% 89.16/26.94 (infuncsetfunc) =>
% 89.16/26.94 ((
% 89.16/26.94 (ap2p) =>
% 89.16/26.94 ((
% 89.16/26.94 (funcinfuncset) =>
% 89.16/26.94 ((
% 89.16/26.94 (lamProp) =>
% 89.16/26.94 ((
% 89.16/26.94 (lamp) =>
% 89.16/26.94 ((
% 89.16/26.94 (lam2p) =>
% 89.16/26.94 ((
% 89.16/26.94 (brelnall1) =>
% 89.16/26.94 ((
% 89.16/26.94 (brelnall2) =>
% 89.16/26.94 ((
% 89.16/26.94 (!!) @ (
% 89.16/26.94 (('#B') @ (
% 89.16/26.94 !!) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#S') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#S') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 =>))) @
% 89.16/26.94 ex1)))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 !!))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#S') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#B') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#S') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 =>))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#C') @ in)))))))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 !!))))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#C') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#B') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#B') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#S') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 =>))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#C') @ in)))))))))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#S') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#S') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#B'))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 =>))))))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#C') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#B') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#S') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 =>))))))) @
% 89.16/26.94 (
% 89.16/26.94 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.16/26.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1121])).
% 89.16/26.94 thf(zip_derived_cl1135, plain,
% 89.16/26.94 (~ (((binunionRsub) =>
% 89.16/26.94 (((binintersectI) =>
% 89.16/26.94 (((binintersectSubset5) =>
% 89.16/26.94 (((binintersectEL) =>
% 89.16/26.94 (((binintersectLsub) =>
% 89.16/26.94 (((binintersectSubset2) =>
% 89.16/26.94 (((binintersectSubset3) =>
% 89.16/26.94 (((binintersectER) =>
% 89.16/26.94 (((disjointsetsI1) =>
% 89.16/26.94 (((binintersectRsub) =>
% 89.16/26.94 (((binintersectSubset4) =>
% 89.16/26.94 (((binintersectSubset1) =>
% 89.16/26.94 (((bs114d) =>
% 89.16/26.94 (((setminusI) =>
% 89.16/26.94 (((setminusEL) =>
% 89.16/26.94 (((setminusER) =>
% 89.16/26.94 (((setminusSubset2) =>
% 89.16/26.94 (((setminusERneg) =>
% 89.16/26.94 (((setminusELneg) =>
% 89.16/26.94 (((setminusILneg) =>
% 89.16/26.94 (((setminusIRneg) =>
% 89.16/26.94 (((setminusLsub) =>
% 89.16/26.94 (((setminusSubset1) =>
% 89.16/26.94 (((symdiffE) =>
% 89.16/26.94 (((symdiffI1) =>
% 89.16/26.94 (((symdiffI2) =>
% 89.16/26.94 (((symdiffIneg1) =>
% 89.16/26.94 (((symdiffIneg2) =>
% 89.16/26.94 (((secondinupair) =>
% 89.16/26.94 (((setukpairIL) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairIR) =>
% 89.16/26.94 ((
% 89.16/26.94 (kpairiskpair) =>
% 89.16/26.94 ((
% 89.16/26.94 (kpairp) =>
% 89.16/26.94 ((
% 89.16/26.94 (singletonsubset) =>
% 89.16/26.94 ((
% 89.16/26.94 (singletoninpowerset) =>
% 89.16/26.94 ((
% 89.16/26.94 (singletoninpowunion) =>
% 89.16/26.94 ((
% 89.16/26.94 (upairset2E) =>
% 89.16/26.94 ((
% 89.16/26.94 (upairsubunion) =>
% 89.16/26.94 ((
% 89.16/26.94 (upairinpowunion) =>
% 89.16/26.94 ((
% 89.16/26.94 (ubforcartprodlem1) =>
% 89.16/26.94 ((
% 89.16/26.94 (ubforcartprodlem2) =>
% 89.16/26.94 ((
% 89.16/26.94 (ubforcartprodlem3) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodpairin) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodmempair1) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodmempair) =>
% 89.16/26.94 ((
% 89.16/26.94 (setunionE2) =>
% 89.16/26.94 ((
% 89.16/26.94 (setunionsingleton1) =>
% 89.16/26.94 ((
% 89.16/26.94 (setunionsingleton2) =>
% 89.16/26.94 ((
% 89.16/26.94 (setunionsingleton) =>
% 89.16/26.94 ((
% 89.16/26.94 (singletonprop) =>
% 89.16/26.94 ((
% 89.16/26.94 (ex1E1) =>
% 89.16/26.94 ((
% 89.16/26.94 (ex1I) =>
% 89.16/26.94 ((
% 89.16/26.94 (ex1I2) =>
% 89.16/26.94 ((
% 89.16/26.94 (singletonsuniq) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjL1) =>
% 89.16/26.94 ((
% 89.16/26.94 (kfstsingleton) =>
% 89.16/26.94 ((
% 89.16/26.94 (theprop) =>
% 89.16/26.94 ((
% 89.16/26.94 (kfstpairEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodfstin) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjL2) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjL) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjR11) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjR12) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjR1) =>
% 89.16/26.94 ((
% 89.16/26.94 (upairequniteq) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjR2) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjR) =>
% 89.16/26.94 ((
% 89.16/26.94 (ksndsingleton) =>
% 89.16/26.94 ((
% 89.16/26.94 (ksndpairEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (kpairsurjEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodsndin) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodpairmemEL) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodpairmemER) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodmempaircEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodfstpairEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodsndpairEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodpairsurjEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (dpsetconstrI) =>
% 89.16/26.94 ((
% 89.16/26.94 (dpsetconstrSub) =>
% 89.16/26.94 ((
% 89.16/26.94 (setOfPairsIsBReln) =>
% 89.16/26.94 ((
% 89.16/26.94 (dpsetconstrERa) =>
% 89.16/26.94 ((
% 89.16/26.94 (dpsetconstrEL1) =>
% 89.16/26.94 ((
% 89.16/26.94 (dpsetconstrEL2) =>
% 89.16/26.94 ((
% 89.16/26.94 (dpsetconstrER) =>
% 89.16/26.94 ((
% 89.16/26.94 (funcImageSingleton) =>
% 89.16/26.94 ((
% 89.16/26.94 (apProp) =>
% 89.16/26.94 ((
% 89.16/26.94 (app) =>
% 89.16/26.94 ((
% 89.16/26.94 (infuncsetfunc) =>
% 89.16/26.94 ((
% 89.16/26.94 (ap2p) =>
% 89.16/26.94 ((
% 89.16/26.94 (funcinfuncset) =>
% 89.16/26.94 ((
% 89.16/26.94 (lamProp) =>
% 89.16/26.94 ((
% 89.16/26.94 (lamp) =>
% 89.16/26.94 ((
% 89.16/26.94 (lam2p) =>
% 89.16/26.94 ((
% 89.16/26.94 (brelnall1) =>
% 89.16/26.94 ((
% 89.16/26.94 (brelnall2) =>
% 89.16/26.94 ((
% 89.16/26.94 (!!) @ (
% 89.16/26.94 (('#B') @ (
% 89.16/26.94 !!) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#S') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#S') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 =>))) @
% 89.16/26.94 ex1)))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 !!))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#S') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#B') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#S') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 =>))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#C') @ in)))))))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 !!))))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#C') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#B') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#B') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#S') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 =>))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#C') @ in)))))))))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#S') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#S') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#B'))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 =>))))))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#C') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#B') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#S') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 =>))))))) @
% 89.16/26.94 (
% 89.16/26.94 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.16/26.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1128])).
% 89.16/26.94 thf(zip_derived_cl1142, plain,
% 89.16/26.94 (~ (((binintersectI) =>
% 89.16/26.94 (((binintersectSubset5) =>
% 89.16/26.94 (((binintersectEL) =>
% 89.16/26.94 (((binintersectLsub) =>
% 89.16/26.94 (((binintersectSubset2) =>
% 89.16/26.94 (((binintersectSubset3) =>
% 89.16/26.94 (((binintersectER) =>
% 89.16/26.94 (((disjointsetsI1) =>
% 89.16/26.94 (((binintersectRsub) =>
% 89.16/26.94 (((binintersectSubset4) =>
% 89.16/26.94 (((binintersectSubset1) =>
% 89.16/26.94 (((bs114d) =>
% 89.16/26.94 (((setminusI) =>
% 89.16/26.94 (((setminusEL) =>
% 89.16/26.94 (((setminusER) =>
% 89.16/26.94 (((setminusSubset2) =>
% 89.16/26.94 (((setminusERneg) =>
% 89.16/26.94 (((setminusELneg) =>
% 89.16/26.94 (((setminusILneg) =>
% 89.16/26.94 (((setminusIRneg) =>
% 89.16/26.94 (((setminusLsub) =>
% 89.16/26.94 (((setminusSubset1) =>
% 89.16/26.94 (((symdiffE) =>
% 89.16/26.94 (((symdiffI1) =>
% 89.16/26.94 (((symdiffI2) =>
% 89.16/26.94 (((symdiffIneg1) =>
% 89.16/26.94 (((symdiffIneg2) =>
% 89.16/26.94 (((secondinupair) =>
% 89.16/26.94 (((setukpairIL) =>
% 89.16/26.94 (((setukpairIR) =>
% 89.16/26.94 ((
% 89.16/26.94 (kpairiskpair) =>
% 89.16/26.94 ((
% 89.16/26.94 (kpairp) =>
% 89.16/26.94 ((
% 89.16/26.94 (singletonsubset) =>
% 89.16/26.94 ((
% 89.16/26.94 (singletoninpowerset) =>
% 89.16/26.94 ((
% 89.16/26.94 (singletoninpowunion) =>
% 89.16/26.94 ((
% 89.16/26.94 (upairset2E) =>
% 89.16/26.94 ((
% 89.16/26.94 (upairsubunion) =>
% 89.16/26.94 ((
% 89.16/26.94 (upairinpowunion) =>
% 89.16/26.94 ((
% 89.16/26.94 (ubforcartprodlem1) =>
% 89.16/26.94 ((
% 89.16/26.94 (ubforcartprodlem2) =>
% 89.16/26.94 ((
% 89.16/26.94 (ubforcartprodlem3) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodpairin) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodmempair1) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodmempair) =>
% 89.16/26.94 ((
% 89.16/26.94 (setunionE2) =>
% 89.16/26.94 ((
% 89.16/26.94 (setunionsingleton1) =>
% 89.16/26.94 ((
% 89.16/26.94 (setunionsingleton2) =>
% 89.16/26.94 ((
% 89.16/26.94 (setunionsingleton) =>
% 89.16/26.94 ((
% 89.16/26.94 (singletonprop) =>
% 89.16/26.94 ((
% 89.16/26.94 (ex1E1) =>
% 89.16/26.94 ((
% 89.16/26.94 (ex1I) =>
% 89.16/26.94 ((
% 89.16/26.94 (ex1I2) =>
% 89.16/26.94 ((
% 89.16/26.94 (singletonsuniq) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjL1) =>
% 89.16/26.94 ((
% 89.16/26.94 (kfstsingleton) =>
% 89.16/26.94 ((
% 89.16/26.94 (theprop) =>
% 89.16/26.94 ((
% 89.16/26.94 (kfstpairEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodfstin) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjL2) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjL) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjR11) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjR12) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjR1) =>
% 89.16/26.94 ((
% 89.16/26.94 (upairequniteq) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjR2) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjR) =>
% 89.16/26.94 ((
% 89.16/26.94 (ksndsingleton) =>
% 89.16/26.94 ((
% 89.16/26.94 (ksndpairEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (kpairsurjEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodsndin) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodpairmemEL) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodpairmemER) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodmempaircEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodfstpairEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodsndpairEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodpairsurjEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (dpsetconstrI) =>
% 89.16/26.94 ((
% 89.16/26.94 (dpsetconstrSub) =>
% 89.16/26.94 ((
% 89.16/26.94 (setOfPairsIsBReln) =>
% 89.16/26.94 ((
% 89.16/26.94 (dpsetconstrERa) =>
% 89.16/26.94 ((
% 89.16/26.94 (dpsetconstrEL1) =>
% 89.16/26.94 ((
% 89.16/26.94 (dpsetconstrEL2) =>
% 89.16/26.94 ((
% 89.16/26.94 (dpsetconstrER) =>
% 89.16/26.94 ((
% 89.16/26.94 (funcImageSingleton) =>
% 89.16/26.94 ((
% 89.16/26.94 (apProp) =>
% 89.16/26.94 ((
% 89.16/26.94 (app) =>
% 89.16/26.94 ((
% 89.16/26.94 (infuncsetfunc) =>
% 89.16/26.94 ((
% 89.16/26.94 (ap2p) =>
% 89.16/26.94 ((
% 89.16/26.94 (funcinfuncset) =>
% 89.16/26.94 ((
% 89.16/26.94 (lamProp) =>
% 89.16/26.94 ((
% 89.16/26.94 (lamp) =>
% 89.16/26.94 ((
% 89.16/26.94 (lam2p) =>
% 89.16/26.94 ((
% 89.16/26.94 (brelnall1) =>
% 89.16/26.94 ((
% 89.16/26.94 (brelnall2) =>
% 89.16/26.94 ((
% 89.16/26.94 (!!) @ (
% 89.16/26.94 (('#B') @ (
% 89.16/26.94 !!) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#S') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#S') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 =>))) @
% 89.16/26.94 ex1)))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 !!))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#S') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#B') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#S') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 =>))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#C') @ in)))))))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 !!))))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#C') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#B') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#B') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#S') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 =>))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#C') @ in)))))))))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#S') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#S') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#B'))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 =>))))))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#C') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#B') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#S') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 =>))))))) @
% 89.16/26.94 (
% 89.16/26.94 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.16/26.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1135])).
% 89.16/26.94 thf(zip_derived_cl1150, plain,
% 89.16/26.94 (~ (((binintersectSubset5) =>
% 89.16/26.94 (((binintersectEL) =>
% 89.16/26.94 (((binintersectLsub) =>
% 89.16/26.94 (((binintersectSubset2) =>
% 89.16/26.94 (((binintersectSubset3) =>
% 89.16/26.94 (((binintersectER) =>
% 89.16/26.94 (((disjointsetsI1) =>
% 89.16/26.94 (((binintersectRsub) =>
% 89.16/26.94 (((binintersectSubset4) =>
% 89.16/26.94 (((binintersectSubset1) =>
% 89.16/26.94 (((bs114d) =>
% 89.16/26.94 (((setminusI) =>
% 89.16/26.94 (((setminusEL) =>
% 89.16/26.94 (((setminusER) =>
% 89.16/26.94 (((setminusSubset2) =>
% 89.16/26.94 (((setminusERneg) =>
% 89.16/26.94 (((setminusELneg) =>
% 89.16/26.94 (((setminusILneg) =>
% 89.16/26.94 (((setminusIRneg) =>
% 89.16/26.94 (((setminusLsub) =>
% 89.16/26.94 (((setminusSubset1) =>
% 89.16/26.94 (((symdiffE) =>
% 89.16/26.94 (((symdiffI1) =>
% 89.16/26.94 (((symdiffI2) =>
% 89.16/26.94 (((symdiffIneg1) =>
% 89.16/26.94 (((symdiffIneg2) =>
% 89.16/26.94 (((secondinupair) =>
% 89.16/26.94 (((setukpairIL) =>
% 89.16/26.94 (((setukpairIR) =>
% 89.16/26.94 (((kpairiskpair) =>
% 89.16/26.94 ((
% 89.16/26.94 (kpairp) =>
% 89.16/26.94 ((
% 89.16/26.94 (singletonsubset) =>
% 89.16/26.94 ((
% 89.16/26.94 (singletoninpowerset) =>
% 89.16/26.94 ((
% 89.16/26.94 (singletoninpowunion) =>
% 89.16/26.94 ((
% 89.16/26.94 (upairset2E) =>
% 89.16/26.94 ((
% 89.16/26.94 (upairsubunion) =>
% 89.16/26.94 ((
% 89.16/26.94 (upairinpowunion) =>
% 89.16/26.94 ((
% 89.16/26.94 (ubforcartprodlem1) =>
% 89.16/26.94 ((
% 89.16/26.94 (ubforcartprodlem2) =>
% 89.16/26.94 ((
% 89.16/26.94 (ubforcartprodlem3) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodpairin) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodmempair1) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodmempair) =>
% 89.16/26.94 ((
% 89.16/26.94 (setunionE2) =>
% 89.16/26.94 ((
% 89.16/26.94 (setunionsingleton1) =>
% 89.16/26.94 ((
% 89.16/26.94 (setunionsingleton2) =>
% 89.16/26.94 ((
% 89.16/26.94 (setunionsingleton) =>
% 89.16/26.94 ((
% 89.16/26.94 (singletonprop) =>
% 89.16/26.94 ((
% 89.16/26.94 (ex1E1) =>
% 89.16/26.94 ((
% 89.16/26.94 (ex1I) =>
% 89.16/26.94 ((
% 89.16/26.94 (ex1I2) =>
% 89.16/26.94 ((
% 89.16/26.94 (singletonsuniq) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjL1) =>
% 89.16/26.94 ((
% 89.16/26.94 (kfstsingleton) =>
% 89.16/26.94 ((
% 89.16/26.94 (theprop) =>
% 89.16/26.94 ((
% 89.16/26.94 (kfstpairEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodfstin) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjL2) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjL) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjR11) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjR12) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjR1) =>
% 89.16/26.94 ((
% 89.16/26.94 (upairequniteq) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjR2) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjR) =>
% 89.16/26.94 ((
% 89.16/26.94 (ksndsingleton) =>
% 89.16/26.94 ((
% 89.16/26.94 (ksndpairEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (kpairsurjEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodsndin) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodpairmemEL) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodpairmemER) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodmempaircEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodfstpairEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodsndpairEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodpairsurjEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (dpsetconstrI) =>
% 89.16/26.94 ((
% 89.16/26.94 (dpsetconstrSub) =>
% 89.16/26.94 ((
% 89.16/26.94 (setOfPairsIsBReln) =>
% 89.16/26.94 ((
% 89.16/26.94 (dpsetconstrERa) =>
% 89.16/26.94 ((
% 89.16/26.94 (dpsetconstrEL1) =>
% 89.16/26.94 ((
% 89.16/26.94 (dpsetconstrEL2) =>
% 89.16/26.94 ((
% 89.16/26.94 (dpsetconstrER) =>
% 89.16/26.94 ((
% 89.16/26.94 (funcImageSingleton) =>
% 89.16/26.94 ((
% 89.16/26.94 (apProp) =>
% 89.16/26.94 ((
% 89.16/26.94 (app) =>
% 89.16/26.94 ((
% 89.16/26.94 (infuncsetfunc) =>
% 89.16/26.94 ((
% 89.16/26.94 (ap2p) =>
% 89.16/26.94 ((
% 89.16/26.94 (funcinfuncset) =>
% 89.16/26.94 ((
% 89.16/26.94 (lamProp) =>
% 89.16/26.94 ((
% 89.16/26.94 (lamp) =>
% 89.16/26.94 ((
% 89.16/26.94 (lam2p) =>
% 89.16/26.94 ((
% 89.16/26.94 (brelnall1) =>
% 89.16/26.94 ((
% 89.16/26.94 (brelnall2) =>
% 89.16/26.94 ((
% 89.16/26.94 (!!) @ (
% 89.16/26.94 (('#B') @ (
% 89.16/26.94 !!) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#S') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#S') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 =>))) @
% 89.16/26.94 ex1)))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 !!))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#S') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#B') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#S') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 =>))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#C') @ in)))))))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 !!))))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#C') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#B') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#B') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#S') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 =>))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#C') @ in)))))))))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#S') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#S') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#B'))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 =>))))))) @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#C') @ (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#B') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 '#S') @
% 89.16/26.94 (
% 89.16/26.94 (
% 89.16/26.94 ('#B') @ (
% 89.16/26.94 =>))))))) @
% 89.16/26.94 (
% 89.16/26.94 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.16/26.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1142])).
% 89.16/26.94 thf(zip_derived_cl1158, plain,
% 89.16/26.94 (~ (((binintersectEL) =>
% 89.16/26.94 (((binintersectLsub) =>
% 89.16/26.94 (((binintersectSubset2) =>
% 89.16/26.94 (((binintersectSubset3) =>
% 89.16/26.94 (((binintersectER) =>
% 89.16/26.94 (((disjointsetsI1) =>
% 89.16/26.94 (((binintersectRsub) =>
% 89.16/26.94 (((binintersectSubset4) =>
% 89.16/26.94 (((binintersectSubset1) =>
% 89.16/26.94 (((bs114d) =>
% 89.16/26.94 (((setminusI) =>
% 89.16/26.94 (((setminusEL) =>
% 89.16/26.94 (((setminusER) =>
% 89.16/26.94 (((setminusSubset2) =>
% 89.16/26.94 (((setminusERneg) =>
% 89.16/26.94 (((setminusELneg) =>
% 89.16/26.94 (((setminusILneg) =>
% 89.16/26.94 (((setminusIRneg) =>
% 89.16/26.94 (((setminusLsub) =>
% 89.16/26.94 (((setminusSubset1) =>
% 89.16/26.94 (((symdiffE) =>
% 89.16/26.94 (((symdiffI1) =>
% 89.16/26.94 (((symdiffI2) =>
% 89.16/26.94 (((symdiffIneg1) =>
% 89.16/26.94 (((symdiffIneg2) =>
% 89.16/26.94 (((secondinupair) =>
% 89.16/26.94 (((setukpairIL) =>
% 89.16/26.94 (((setukpairIR) =>
% 89.16/26.94 (((kpairiskpair) =>
% 89.16/26.94 (((kpairp) =>
% 89.16/26.94 ((
% 89.16/26.94 (singletonsubset) =>
% 89.16/26.94 ((
% 89.16/26.94 (singletoninpowerset) =>
% 89.16/26.94 ((
% 89.16/26.94 (singletoninpowunion) =>
% 89.16/26.94 ((
% 89.16/26.94 (upairset2E) =>
% 89.16/26.94 ((
% 89.16/26.94 (upairsubunion) =>
% 89.16/26.94 ((
% 89.16/26.94 (upairinpowunion) =>
% 89.16/26.94 ((
% 89.16/26.94 (ubforcartprodlem1) =>
% 89.16/26.94 ((
% 89.16/26.94 (ubforcartprodlem2) =>
% 89.16/26.94 ((
% 89.16/26.94 (ubforcartprodlem3) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodpairin) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodmempair1) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodmempair) =>
% 89.16/26.94 ((
% 89.16/26.94 (setunionE2) =>
% 89.16/26.94 ((
% 89.16/26.94 (setunionsingleton1) =>
% 89.16/26.94 ((
% 89.16/26.94 (setunionsingleton2) =>
% 89.16/26.94 ((
% 89.16/26.94 (setunionsingleton) =>
% 89.16/26.94 ((
% 89.16/26.94 (singletonprop) =>
% 89.16/26.94 ((
% 89.16/26.94 (ex1E1) =>
% 89.16/26.94 ((
% 89.16/26.94 (ex1I) =>
% 89.16/26.94 ((
% 89.16/26.94 (ex1I2) =>
% 89.16/26.94 ((
% 89.16/26.94 (singletonsuniq) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjL1) =>
% 89.16/26.94 ((
% 89.16/26.94 (kfstsingleton) =>
% 89.16/26.94 ((
% 89.16/26.94 (theprop) =>
% 89.16/26.94 ((
% 89.16/26.94 (kfstpairEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodfstin) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjL2) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjL) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjR11) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjR12) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjR1) =>
% 89.16/26.94 ((
% 89.16/26.94 (upairequniteq) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjR2) =>
% 89.16/26.94 ((
% 89.16/26.94 (setukpairinjR) =>
% 89.16/26.94 ((
% 89.16/26.94 (ksndsingleton) =>
% 89.16/26.94 ((
% 89.16/26.94 (ksndpairEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (kpairsurjEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodsndin) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodpairmemEL) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodpairmemER) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodmempaircEq) =>
% 89.16/26.94 ((
% 89.16/26.94 (cartprodfstpairEq) =>
% 89.16/26.94 ((
% 89.16/26.95 (cartprodsndpairEq) =>
% 89.16/26.95 ((
% 89.16/26.95 (cartprodpairsurjEq) =>
% 89.16/26.95 ((
% 89.16/26.95 (dpsetconstrI) =>
% 89.16/26.95 ((
% 89.16/26.95 (dpsetconstrSub) =>
% 89.16/26.95 ((
% 89.16/26.95 (setOfPairsIsBReln) =>
% 89.16/26.95 ((
% 89.16/26.95 (dpsetconstrERa) =>
% 89.16/26.95 ((
% 89.16/26.95 (dpsetconstrEL1) =>
% 89.16/26.95 ((
% 89.16/26.95 (dpsetconstrEL2) =>
% 89.16/26.95 ((
% 89.16/26.95 (dpsetconstrER) =>
% 89.16/26.95 ((
% 89.16/26.95 (funcImageSingleton) =>
% 89.16/26.95 ((
% 89.16/26.95 (apProp) =>
% 89.16/26.95 ((
% 89.16/26.95 (app) =>
% 89.16/26.95 ((
% 89.16/26.95 (infuncsetfunc) =>
% 89.16/26.95 ((
% 89.16/26.95 (ap2p) =>
% 89.16/26.95 ((
% 89.16/26.95 (funcinfuncset) =>
% 89.16/26.95 ((
% 89.16/26.95 (lamProp) =>
% 89.16/26.95 ((
% 89.16/26.95 (lamp) =>
% 89.16/26.95 ((
% 89.16/26.95 (lam2p) =>
% 89.16/26.95 ((
% 89.16/26.95 (brelnall1) =>
% 89.16/26.95 ((
% 89.16/26.95 (brelnall2) =>
% 89.16/26.95 ((
% 89.16/26.95 (!!) @ (
% 89.16/26.95 (('#B') @ (
% 89.16/26.95 !!) @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#S') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 '#S') @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 =>))) @
% 89.16/26.95 ex1)))) @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 !!))) @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#S') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 '#B') @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 '#S') @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 =>))) @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#C') @ in)))))))) @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 !!))))) @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#C') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 '#B') @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 '#B') @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 '#S') @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 =>))) @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#C') @ in)))))))))) @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#S') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 '#S') @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 '#B'))) @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 =>))))))) @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#C') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 '#B') @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 '#S') @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 =>))))))) @
% 89.16/26.95 (
% 89.16/26.95 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.16/26.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1150])).
% 89.16/26.95 thf(zip_derived_cl1166, plain,
% 89.16/26.95 (~ (((binintersectLsub) =>
% 89.16/26.95 (((binintersectSubset2) =>
% 89.16/26.95 (((binintersectSubset3) =>
% 89.16/26.95 (((binintersectER) =>
% 89.16/26.95 (((disjointsetsI1) =>
% 89.16/26.95 (((binintersectRsub) =>
% 89.16/26.95 (((binintersectSubset4) =>
% 89.16/26.95 (((binintersectSubset1) =>
% 89.16/26.95 (((bs114d) =>
% 89.16/26.95 (((setminusI) =>
% 89.16/26.95 (((setminusEL) =>
% 89.16/26.95 (((setminusER) =>
% 89.16/26.95 (((setminusSubset2) =>
% 89.16/26.95 (((setminusERneg) =>
% 89.16/26.95 (((setminusELneg) =>
% 89.16/26.95 (((setminusILneg) =>
% 89.16/26.95 (((setminusIRneg) =>
% 89.16/26.95 (((setminusLsub) =>
% 89.16/26.95 (((setminusSubset1) =>
% 89.16/26.95 (((symdiffE) =>
% 89.16/26.95 (((symdiffI1) =>
% 89.16/26.95 (((symdiffI2) =>
% 89.16/26.95 (((symdiffIneg1) =>
% 89.16/26.95 (((symdiffIneg2) =>
% 89.16/26.95 (((secondinupair) =>
% 89.16/26.95 (((setukpairIL) =>
% 89.16/26.95 (((setukpairIR) =>
% 89.16/26.95 (((kpairiskpair) =>
% 89.16/26.95 (((kpairp) =>
% 89.16/26.95 (((singletonsubset) =>
% 89.16/26.95 ((
% 89.16/26.95 (singletoninpowerset) =>
% 89.16/26.95 ((
% 89.16/26.95 (singletoninpowunion) =>
% 89.16/26.95 ((
% 89.16/26.95 (upairset2E) =>
% 89.16/26.95 ((
% 89.16/26.95 (upairsubunion) =>
% 89.16/26.95 ((
% 89.16/26.95 (upairinpowunion) =>
% 89.16/26.95 ((
% 89.16/26.95 (ubforcartprodlem1) =>
% 89.16/26.95 ((
% 89.16/26.95 (ubforcartprodlem2) =>
% 89.16/26.95 ((
% 89.16/26.95 (ubforcartprodlem3) =>
% 89.16/26.95 ((
% 89.16/26.95 (cartprodpairin) =>
% 89.16/26.95 ((
% 89.16/26.95 (cartprodmempair1) =>
% 89.16/26.95 ((
% 89.16/26.95 (cartprodmempair) =>
% 89.16/26.95 ((
% 89.16/26.95 (setunionE2) =>
% 89.16/26.95 ((
% 89.16/26.95 (setunionsingleton1) =>
% 89.16/26.95 ((
% 89.16/26.95 (setunionsingleton2) =>
% 89.16/26.95 ((
% 89.16/26.95 (setunionsingleton) =>
% 89.16/26.95 ((
% 89.16/26.95 (singletonprop) =>
% 89.16/26.95 ((
% 89.16/26.95 (ex1E1) =>
% 89.16/26.95 ((
% 89.16/26.95 (ex1I) =>
% 89.16/26.95 ((
% 89.16/26.95 (ex1I2) =>
% 89.16/26.95 ((
% 89.16/26.95 (singletonsuniq) =>
% 89.16/26.95 ((
% 89.16/26.95 (setukpairinjL1) =>
% 89.16/26.95 ((
% 89.16/26.95 (kfstsingleton) =>
% 89.16/26.95 ((
% 89.16/26.95 (theprop) =>
% 89.16/26.95 ((
% 89.16/26.95 (kfstpairEq) =>
% 89.16/26.95 ((
% 89.16/26.95 (cartprodfstin) =>
% 89.16/26.95 ((
% 89.16/26.95 (setukpairinjL2) =>
% 89.16/26.95 ((
% 89.16/26.95 (setukpairinjL) =>
% 89.16/26.95 ((
% 89.16/26.95 (setukpairinjR11) =>
% 89.16/26.95 ((
% 89.16/26.95 (setukpairinjR12) =>
% 89.16/26.95 ((
% 89.16/26.95 (setukpairinjR1) =>
% 89.16/26.95 ((
% 89.16/26.95 (upairequniteq) =>
% 89.16/26.95 ((
% 89.16/26.95 (setukpairinjR2) =>
% 89.16/26.95 ((
% 89.16/26.95 (setukpairinjR) =>
% 89.16/26.95 ((
% 89.16/26.95 (ksndsingleton) =>
% 89.16/26.95 ((
% 89.16/26.95 (ksndpairEq) =>
% 89.16/26.95 ((
% 89.16/26.95 (kpairsurjEq) =>
% 89.16/26.95 ((
% 89.16/26.95 (cartprodsndin) =>
% 89.16/26.95 ((
% 89.16/26.95 (cartprodpairmemEL) =>
% 89.16/26.95 ((
% 89.16/26.95 (cartprodpairmemER) =>
% 89.16/26.95 ((
% 89.16/26.95 (cartprodmempaircEq) =>
% 89.16/26.95 ((
% 89.16/26.95 (cartprodfstpairEq) =>
% 89.16/26.95 ((
% 89.16/26.95 (cartprodsndpairEq) =>
% 89.16/26.95 ((
% 89.16/26.95 (cartprodpairsurjEq) =>
% 89.16/26.95 ((
% 89.16/26.95 (dpsetconstrI) =>
% 89.16/26.95 ((
% 89.16/26.95 (dpsetconstrSub) =>
% 89.16/26.95 ((
% 89.16/26.95 (setOfPairsIsBReln) =>
% 89.16/26.95 ((
% 89.16/26.95 (dpsetconstrERa) =>
% 89.16/26.95 ((
% 89.16/26.95 (dpsetconstrEL1) =>
% 89.16/26.95 ((
% 89.16/26.95 (dpsetconstrEL2) =>
% 89.16/26.95 ((
% 89.16/26.95 (dpsetconstrER) =>
% 89.16/26.95 ((
% 89.16/26.95 (funcImageSingleton) =>
% 89.16/26.95 ((
% 89.16/26.95 (apProp) =>
% 89.16/26.95 ((
% 89.16/26.95 (app) =>
% 89.16/26.95 ((
% 89.16/26.95 (infuncsetfunc) =>
% 89.16/26.95 ((
% 89.16/26.95 (ap2p) =>
% 89.16/26.95 ((
% 89.16/26.95 (funcinfuncset) =>
% 89.16/26.95 ((
% 89.16/26.95 (lamProp) =>
% 89.16/26.95 ((
% 89.16/26.95 (lamp) =>
% 89.16/26.95 ((
% 89.16/26.95 (lam2p) =>
% 89.16/26.95 ((
% 89.16/26.95 (brelnall1) =>
% 89.16/26.95 ((
% 89.16/26.95 (brelnall2) =>
% 89.16/26.95 ((
% 89.16/26.95 (!!) @ (
% 89.16/26.95 (('#B') @ (
% 89.16/26.95 !!) @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#S') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 '#S') @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 =>))) @
% 89.16/26.95 ex1)))) @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 !!))) @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#S') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 '#B') @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 '#S') @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 =>))) @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#C') @ in)))))))) @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 !!))))) @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#C') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 '#B') @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 '#B') @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 '#S') @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 =>))) @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#C') @ in)))))))))) @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#S') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 '#S') @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 '#B'))) @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 =>))))))) @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#C') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 '#B') @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 '#S') @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 =>))))))) @
% 89.16/26.95 (
% 89.16/26.95 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.16/26.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1158])).
% 89.16/26.95 thf(zip_derived_cl1174, plain,
% 89.16/26.95 (~ (((binintersectSubset2) =>
% 89.16/26.95 (((binintersectSubset3) =>
% 89.16/26.95 (((binintersectER) =>
% 89.16/26.95 (((disjointsetsI1) =>
% 89.16/26.95 (((binintersectRsub) =>
% 89.16/26.95 (((binintersectSubset4) =>
% 89.16/26.95 (((binintersectSubset1) =>
% 89.16/26.95 (((bs114d) =>
% 89.16/26.95 (((setminusI) =>
% 89.16/26.95 (((setminusEL) =>
% 89.16/26.95 (((setminusER) =>
% 89.16/26.95 (((setminusSubset2) =>
% 89.16/26.95 (((setminusERneg) =>
% 89.16/26.95 (((setminusELneg) =>
% 89.16/26.95 (((setminusILneg) =>
% 89.16/26.95 (((setminusIRneg) =>
% 89.16/26.95 (((setminusLsub) =>
% 89.16/26.95 (((setminusSubset1) =>
% 89.16/26.95 (((symdiffE) =>
% 89.16/26.95 (((symdiffI1) =>
% 89.16/26.95 (((symdiffI2) =>
% 89.16/26.95 (((symdiffIneg1) =>
% 89.16/26.95 (((symdiffIneg2) =>
% 89.16/26.95 (((secondinupair) =>
% 89.16/26.95 (((setukpairIL) =>
% 89.16/26.95 (((setukpairIR) =>
% 89.16/26.95 (((kpairiskpair) =>
% 89.16/26.95 (((kpairp) =>
% 89.16/26.95 (((singletonsubset) =>
% 89.16/26.95 (((singletoninpowerset) =>
% 89.16/26.95 ((
% 89.16/26.95 (singletoninpowunion) =>
% 89.16/26.95 ((
% 89.16/26.95 (upairset2E) =>
% 89.16/26.95 ((
% 89.16/26.95 (upairsubunion) =>
% 89.16/26.95 ((
% 89.16/26.95 (upairinpowunion) =>
% 89.16/26.95 ((
% 89.16/26.95 (ubforcartprodlem1) =>
% 89.16/26.95 ((
% 89.16/26.95 (ubforcartprodlem2) =>
% 89.16/26.95 ((
% 89.16/26.95 (ubforcartprodlem3) =>
% 89.16/26.95 ((
% 89.16/26.95 (cartprodpairin) =>
% 89.16/26.95 ((
% 89.16/26.95 (cartprodmempair1) =>
% 89.16/26.95 ((
% 89.16/26.95 (cartprodmempair) =>
% 89.16/26.95 ((
% 89.16/26.95 (setunionE2) =>
% 89.16/26.95 ((
% 89.16/26.95 (setunionsingleton1) =>
% 89.16/26.95 ((
% 89.16/26.95 (setunionsingleton2) =>
% 89.16/26.95 ((
% 89.16/26.95 (setunionsingleton) =>
% 89.16/26.95 ((
% 89.16/26.95 (singletonprop) =>
% 89.16/26.95 ((
% 89.16/26.95 (ex1E1) =>
% 89.16/26.95 ((
% 89.16/26.95 (ex1I) =>
% 89.16/26.95 ((
% 89.16/26.95 (ex1I2) =>
% 89.16/26.95 ((
% 89.16/26.95 (singletonsuniq) =>
% 89.16/26.95 ((
% 89.16/26.95 (setukpairinjL1) =>
% 89.16/26.95 ((
% 89.16/26.95 (kfstsingleton) =>
% 89.16/26.95 ((
% 89.16/26.95 (theprop) =>
% 89.16/26.95 ((
% 89.16/26.95 (kfstpairEq) =>
% 89.16/26.95 ((
% 89.16/26.95 (cartprodfstin) =>
% 89.16/26.95 ((
% 89.16/26.95 (setukpairinjL2) =>
% 89.16/26.95 ((
% 89.16/26.95 (setukpairinjL) =>
% 89.16/26.95 ((
% 89.16/26.95 (setukpairinjR11) =>
% 89.16/26.95 ((
% 89.16/26.95 (setukpairinjR12) =>
% 89.16/26.95 ((
% 89.16/26.95 (setukpairinjR1) =>
% 89.16/26.95 ((
% 89.16/26.95 (upairequniteq) =>
% 89.16/26.95 ((
% 89.16/26.95 (setukpairinjR2) =>
% 89.16/26.95 ((
% 89.16/26.95 (setukpairinjR) =>
% 89.16/26.95 ((
% 89.16/26.95 (ksndsingleton) =>
% 89.16/26.95 ((
% 89.16/26.95 (ksndpairEq) =>
% 89.16/26.95 ((
% 89.16/26.95 (kpairsurjEq) =>
% 89.16/26.95 ((
% 89.16/26.95 (cartprodsndin) =>
% 89.16/26.95 ((
% 89.16/26.95 (cartprodpairmemEL) =>
% 89.16/26.95 ((
% 89.16/26.95 (cartprodpairmemER) =>
% 89.16/26.95 ((
% 89.16/26.95 (cartprodmempaircEq) =>
% 89.16/26.95 ((
% 89.16/26.95 (cartprodfstpairEq) =>
% 89.16/26.95 ((
% 89.16/26.95 (cartprodsndpairEq) =>
% 89.16/26.95 ((
% 89.16/26.95 (cartprodpairsurjEq) =>
% 89.16/26.95 ((
% 89.16/26.95 (dpsetconstrI) =>
% 89.16/26.95 ((
% 89.16/26.95 (dpsetconstrSub) =>
% 89.16/26.95 ((
% 89.16/26.95 (setOfPairsIsBReln) =>
% 89.16/26.95 ((
% 89.16/26.95 (dpsetconstrERa) =>
% 89.16/26.95 ((
% 89.16/26.95 (dpsetconstrEL1) =>
% 89.16/26.95 ((
% 89.16/26.95 (dpsetconstrEL2) =>
% 89.16/26.95 ((
% 89.16/26.95 (dpsetconstrER) =>
% 89.16/26.95 ((
% 89.16/26.95 (funcImageSingleton) =>
% 89.16/26.95 ((
% 89.16/26.95 (apProp) =>
% 89.16/26.95 ((
% 89.16/26.95 (app) =>
% 89.16/26.95 ((
% 89.16/26.95 (infuncsetfunc) =>
% 89.16/26.95 ((
% 89.16/26.95 (ap2p) =>
% 89.16/26.95 ((
% 89.16/26.95 (funcinfuncset) =>
% 89.16/26.95 ((
% 89.16/26.95 (lamProp) =>
% 89.16/26.95 ((
% 89.16/26.95 (lamp) =>
% 89.16/26.95 ((
% 89.16/26.95 (lam2p) =>
% 89.16/26.95 ((
% 89.16/26.95 (brelnall1) =>
% 89.16/26.95 ((
% 89.16/26.95 (brelnall2) =>
% 89.16/26.95 ((
% 89.16/26.95 (!!) @ (
% 89.16/26.95 (('#B') @ (
% 89.16/26.95 !!) @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#S') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 '#S') @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 =>))) @
% 89.16/26.95 ex1)))) @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 !!))) @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#S') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 '#B') @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 '#S') @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 =>))) @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#C') @ in)))))))) @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 !!))))) @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#C') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 '#B') @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 '#B') @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 '#S') @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 =>))) @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#C') @ in)))))))))) @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#S') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 '#S') @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 '#B'))) @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 =>))))))) @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#C') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 '#B') @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 '#S') @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 =>))))))) @
% 89.16/26.95 (
% 89.16/26.95 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.16/26.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1166])).
% 89.16/26.95 thf(zip_derived_cl1183, plain,
% 89.16/26.95 (~ (((binintersectSubset3) =>
% 89.16/26.95 (((binintersectER) =>
% 89.16/26.95 (((disjointsetsI1) =>
% 89.16/26.95 (((binintersectRsub) =>
% 89.16/26.95 (((binintersectSubset4) =>
% 89.16/26.95 (((binintersectSubset1) =>
% 89.16/26.95 (((bs114d) =>
% 89.16/26.95 (((setminusI) =>
% 89.16/26.95 (((setminusEL) =>
% 89.16/26.95 (((setminusER) =>
% 89.16/26.95 (((setminusSubset2) =>
% 89.16/26.95 (((setminusERneg) =>
% 89.16/26.95 (((setminusELneg) =>
% 89.16/26.95 (((setminusILneg) =>
% 89.16/26.95 (((setminusIRneg) =>
% 89.16/26.95 (((setminusLsub) =>
% 89.16/26.95 (((setminusSubset1) =>
% 89.16/26.95 (((symdiffE) =>
% 89.16/26.95 (((symdiffI1) =>
% 89.16/26.95 (((symdiffI2) =>
% 89.16/26.95 (((symdiffIneg1) =>
% 89.16/26.95 (((symdiffIneg2) =>
% 89.16/26.95 (((secondinupair) =>
% 89.16/26.95 (((setukpairIL) =>
% 89.16/26.95 (((setukpairIR) =>
% 89.16/26.95 (((kpairiskpair) =>
% 89.16/26.95 (((kpairp) =>
% 89.16/26.95 (((singletonsubset) =>
% 89.16/26.95 (((singletoninpowerset) =>
% 89.16/26.95 (((singletoninpowunion) =>
% 89.16/26.95 ((
% 89.16/26.95 (upairset2E) =>
% 89.16/26.95 ((
% 89.16/26.95 (upairsubunion) =>
% 89.16/26.95 ((
% 89.16/26.95 (upairinpowunion) =>
% 89.16/26.95 ((
% 89.16/26.95 (ubforcartprodlem1) =>
% 89.16/26.95 ((
% 89.16/26.95 (ubforcartprodlem2) =>
% 89.16/26.95 ((
% 89.16/26.95 (ubforcartprodlem3) =>
% 89.16/26.95 ((
% 89.16/26.95 (cartprodpairin) =>
% 89.16/26.95 ((
% 89.16/26.95 (cartprodmempair1) =>
% 89.16/26.95 ((
% 89.16/26.95 (cartprodmempair) =>
% 89.16/26.95 ((
% 89.16/26.95 (setunionE2) =>
% 89.16/26.95 ((
% 89.16/26.95 (setunionsingleton1) =>
% 89.16/26.95 ((
% 89.16/26.95 (setunionsingleton2) =>
% 89.16/26.95 ((
% 89.16/26.95 (setunionsingleton) =>
% 89.16/26.95 ((
% 89.16/26.95 (singletonprop) =>
% 89.16/26.95 ((
% 89.16/26.95 (ex1E1) =>
% 89.16/26.95 ((
% 89.16/26.95 (ex1I) =>
% 89.16/26.95 ((
% 89.16/26.95 (ex1I2) =>
% 89.16/26.95 ((
% 89.16/26.95 (singletonsuniq) =>
% 89.16/26.95 ((
% 89.16/26.95 (setukpairinjL1) =>
% 89.16/26.95 ((
% 89.16/26.95 (kfstsingleton) =>
% 89.16/26.95 ((
% 89.16/26.95 (theprop) =>
% 89.16/26.95 ((
% 89.16/26.95 (kfstpairEq) =>
% 89.16/26.95 ((
% 89.16/26.95 (cartprodfstin) =>
% 89.16/26.95 ((
% 89.16/26.95 (setukpairinjL2) =>
% 89.16/26.95 ((
% 89.16/26.95 (setukpairinjL) =>
% 89.16/26.95 ((
% 89.16/26.95 (setukpairinjR11) =>
% 89.16/26.95 ((
% 89.16/26.95 (setukpairinjR12) =>
% 89.16/26.95 ((
% 89.16/26.95 (setukpairinjR1) =>
% 89.16/26.95 ((
% 89.16/26.95 (upairequniteq) =>
% 89.16/26.95 ((
% 89.16/26.95 (setukpairinjR2) =>
% 89.16/26.95 ((
% 89.16/26.95 (setukpairinjR) =>
% 89.16/26.95 ((
% 89.16/26.95 (ksndsingleton) =>
% 89.16/26.95 ((
% 89.16/26.95 (ksndpairEq) =>
% 89.16/26.95 ((
% 89.16/26.95 (kpairsurjEq) =>
% 89.16/26.95 ((
% 89.16/26.95 (cartprodsndin) =>
% 89.16/26.95 ((
% 89.16/26.95 (cartprodpairmemEL) =>
% 89.16/26.95 ((
% 89.16/26.95 (cartprodpairmemER) =>
% 89.16/26.95 ((
% 89.16/26.95 (cartprodmempaircEq) =>
% 89.16/26.95 ((
% 89.16/26.95 (cartprodfstpairEq) =>
% 89.16/26.95 ((
% 89.16/26.95 (cartprodsndpairEq) =>
% 89.16/26.95 ((
% 89.16/26.95 (cartprodpairsurjEq) =>
% 89.16/26.95 ((
% 89.16/26.95 (dpsetconstrI) =>
% 89.16/26.95 ((
% 89.16/26.95 (dpsetconstrSub) =>
% 89.16/26.95 ((
% 89.16/26.95 (setOfPairsIsBReln) =>
% 89.16/26.95 ((
% 89.16/26.95 (dpsetconstrERa) =>
% 89.16/26.95 ((
% 89.16/26.95 (dpsetconstrEL1) =>
% 89.16/26.95 ((
% 89.16/26.95 (dpsetconstrEL2) =>
% 89.16/26.95 ((
% 89.16/26.95 (dpsetconstrER) =>
% 89.16/26.95 ((
% 89.16/26.95 (funcImageSingleton) =>
% 89.16/26.95 ((
% 89.16/26.95 (apProp) =>
% 89.16/26.95 ((
% 89.16/26.95 (app) =>
% 89.16/26.95 ((
% 89.16/26.95 (infuncsetfunc) =>
% 89.16/26.95 ((
% 89.16/26.95 (ap2p) =>
% 89.16/26.95 ((
% 89.16/26.95 (funcinfuncset) =>
% 89.16/26.95 ((
% 89.16/26.95 (lamProp) =>
% 89.16/26.95 ((
% 89.16/26.95 (lamp) =>
% 89.16/26.95 ((
% 89.16/26.95 (lam2p) =>
% 89.16/26.95 ((
% 89.16/26.95 (brelnall1) =>
% 89.16/26.95 ((
% 89.16/26.95 (brelnall2) =>
% 89.16/26.95 ((
% 89.16/26.95 (!!) @ (
% 89.16/26.95 (('#B') @ (
% 89.16/26.95 !!) @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#S') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 '#S') @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 =>))) @
% 89.16/26.95 ex1)))) @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 !!))) @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#S') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 '#B') @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 '#S') @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 =>))) @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#C') @ in)))))))) @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 !!))))) @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#C') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 '#B') @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 '#B') @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 '#S') @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 =>))) @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#C') @ in)))))))))) @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#S') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 '#S') @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 '#B'))) @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 =>))))))) @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#C') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 '#B') @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 '#S') @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 =>))))))) @
% 89.16/26.95 (
% 89.16/26.95 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.16/26.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1174])).
% 89.16/26.95 thf(zip_derived_cl1193, plain,
% 89.16/26.95 (~ (((binintersectER) =>
% 89.16/26.95 (((disjointsetsI1) =>
% 89.16/26.95 (((binintersectRsub) =>
% 89.16/26.95 (((binintersectSubset4) =>
% 89.16/26.95 (((binintersectSubset1) =>
% 89.16/26.95 (((bs114d) =>
% 89.16/26.95 (((setminusI) =>
% 89.16/26.95 (((setminusEL) =>
% 89.16/26.95 (((setminusER) =>
% 89.16/26.95 (((setminusSubset2) =>
% 89.16/26.95 (((setminusERneg) =>
% 89.16/26.95 (((setminusELneg) =>
% 89.16/26.95 (((setminusILneg) =>
% 89.16/26.95 (((setminusIRneg) =>
% 89.16/26.95 (((setminusLsub) =>
% 89.16/26.95 (((setminusSubset1) =>
% 89.16/26.95 (((symdiffE) =>
% 89.16/26.95 (((symdiffI1) =>
% 89.16/26.95 (((symdiffI2) =>
% 89.16/26.95 (((symdiffIneg1) =>
% 89.16/26.95 (((symdiffIneg2) =>
% 89.16/26.95 (((secondinupair) =>
% 89.16/26.95 (((setukpairIL) =>
% 89.16/26.95 (((setukpairIR) =>
% 89.16/26.95 (((kpairiskpair) =>
% 89.16/26.95 (((kpairp) =>
% 89.16/26.95 (((singletonsubset) =>
% 89.16/26.95 (((singletoninpowerset) =>
% 89.16/26.95 (((singletoninpowunion) =>
% 89.16/26.95 (((upairset2E) =>
% 89.16/26.95 ((
% 89.16/26.95 (upairsubunion) =>
% 89.16/26.95 ((
% 89.16/26.95 (upairinpowunion) =>
% 89.16/26.95 ((
% 89.16/26.95 (ubforcartprodlem1) =>
% 89.16/26.95 ((
% 89.16/26.95 (ubforcartprodlem2) =>
% 89.16/26.95 ((
% 89.16/26.95 (ubforcartprodlem3) =>
% 89.16/26.95 ((
% 89.16/26.95 (cartprodpairin) =>
% 89.16/26.95 ((
% 89.16/26.95 (cartprodmempair1) =>
% 89.16/26.95 ((
% 89.16/26.95 (cartprodmempair) =>
% 89.16/26.95 ((
% 89.16/26.95 (setunionE2) =>
% 89.16/26.95 ((
% 89.16/26.95 (setunionsingleton1) =>
% 89.16/26.95 ((
% 89.16/26.95 (setunionsingleton2) =>
% 89.16/26.95 ((
% 89.16/26.95 (setunionsingleton) =>
% 89.16/26.95 ((
% 89.16/26.95 (singletonprop) =>
% 89.16/26.95 ((
% 89.16/26.95 (ex1E1) =>
% 89.16/26.95 ((
% 89.16/26.95 (ex1I) =>
% 89.16/26.95 ((
% 89.16/26.95 (ex1I2) =>
% 89.16/26.95 ((
% 89.16/26.95 (singletonsuniq) =>
% 89.16/26.95 ((
% 89.16/26.95 (setukpairinjL1) =>
% 89.16/26.95 ((
% 89.16/26.95 (kfstsingleton) =>
% 89.16/26.95 ((
% 89.16/26.95 (theprop) =>
% 89.16/26.95 ((
% 89.16/26.95 (kfstpairEq) =>
% 89.16/26.95 ((
% 89.16/26.95 (cartprodfstin) =>
% 89.16/26.95 ((
% 89.16/26.95 (setukpairinjL2) =>
% 89.16/26.95 ((
% 89.16/26.95 (setukpairinjL) =>
% 89.16/26.95 ((
% 89.16/26.95 (setukpairinjR11) =>
% 89.16/26.95 ((
% 89.16/26.95 (setukpairinjR12) =>
% 89.16/26.95 ((
% 89.16/26.95 (setukpairinjR1) =>
% 89.16/26.95 ((
% 89.16/26.95 (upairequniteq) =>
% 89.16/26.95 ((
% 89.16/26.95 (setukpairinjR2) =>
% 89.16/26.95 ((
% 89.16/26.95 (setukpairinjR) =>
% 89.16/26.95 ((
% 89.16/26.95 (ksndsingleton) =>
% 89.16/26.95 ((
% 89.16/26.95 (ksndpairEq) =>
% 89.16/26.95 ((
% 89.16/26.95 (kpairsurjEq) =>
% 89.16/26.95 ((
% 89.16/26.95 (cartprodsndin) =>
% 89.16/26.95 ((
% 89.16/26.95 (cartprodpairmemEL) =>
% 89.16/26.95 ((
% 89.16/26.95 (cartprodpairmemER) =>
% 89.16/26.95 ((
% 89.16/26.95 (cartprodmempaircEq) =>
% 89.16/26.95 ((
% 89.16/26.95 (cartprodfstpairEq) =>
% 89.16/26.95 ((
% 89.16/26.95 (cartprodsndpairEq) =>
% 89.16/26.95 ((
% 89.16/26.95 (cartprodpairsurjEq) =>
% 89.16/26.95 ((
% 89.16/26.95 (dpsetconstrI) =>
% 89.16/26.95 ((
% 89.16/26.95 (dpsetconstrSub) =>
% 89.16/26.95 ((
% 89.16/26.95 (setOfPairsIsBReln) =>
% 89.16/26.95 ((
% 89.16/26.95 (dpsetconstrERa) =>
% 89.16/26.95 ((
% 89.16/26.95 (dpsetconstrEL1) =>
% 89.16/26.95 ((
% 89.16/26.95 (dpsetconstrEL2) =>
% 89.16/26.95 ((
% 89.16/26.95 (dpsetconstrER) =>
% 89.16/26.95 ((
% 89.16/26.95 (funcImageSingleton) =>
% 89.16/26.95 ((
% 89.16/26.95 (apProp) =>
% 89.16/26.95 ((
% 89.16/26.95 (app) =>
% 89.16/26.95 ((
% 89.16/26.95 (infuncsetfunc) =>
% 89.16/26.95 ((
% 89.16/26.95 (ap2p) =>
% 89.16/26.95 ((
% 89.16/26.95 (funcinfuncset) =>
% 89.16/26.95 ((
% 89.16/26.95 (lamProp) =>
% 89.16/26.95 ((
% 89.16/26.95 (lamp) =>
% 89.16/26.95 ((
% 89.16/26.95 (lam2p) =>
% 89.16/26.95 ((
% 89.16/26.95 (brelnall1) =>
% 89.16/26.95 ((
% 89.16/26.95 (brelnall2) =>
% 89.16/26.95 ((
% 89.16/26.95 (!!) @ (
% 89.16/26.95 (('#B') @ (
% 89.16/26.95 !!) @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#S') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 '#S') @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 =>))) @
% 89.16/26.95 ex1)))) @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 !!))) @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#S') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 '#B') @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 '#S') @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 =>))) @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#C') @ in)))))))) @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 !!))))) @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#C') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 '#B') @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 '#B') @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 '#S') @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 =>))) @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#C') @ in)))))))))) @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#S') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 '#S') @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 '#B'))) @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 =>))))))) @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#C') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 '#B') @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 '#S') @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 =>))))))) @
% 89.16/26.95 (
% 89.16/26.95 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.16/26.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1183])).
% 89.16/26.95 thf(zip_derived_cl1206, plain,
% 89.16/26.95 (~ (((disjointsetsI1) =>
% 89.16/26.95 (((binintersectRsub) =>
% 89.16/26.95 (((binintersectSubset4) =>
% 89.16/26.95 (((binintersectSubset1) =>
% 89.16/26.95 (((bs114d) =>
% 89.16/26.95 (((setminusI) =>
% 89.16/26.95 (((setminusEL) =>
% 89.16/26.95 (((setminusER) =>
% 89.16/26.95 (((setminusSubset2) =>
% 89.16/26.95 (((setminusERneg) =>
% 89.16/26.95 (((setminusELneg) =>
% 89.16/26.95 (((setminusILneg) =>
% 89.16/26.95 (((setminusIRneg) =>
% 89.16/26.95 (((setminusLsub) =>
% 89.16/26.95 (((setminusSubset1) =>
% 89.16/26.95 (((symdiffE) =>
% 89.16/26.95 (((symdiffI1) =>
% 89.16/26.95 (((symdiffI2) =>
% 89.16/26.95 (((symdiffIneg1) =>
% 89.16/26.95 (((symdiffIneg2) =>
% 89.16/26.95 (((secondinupair) =>
% 89.16/26.95 (((setukpairIL) =>
% 89.16/26.95 (((setukpairIR) =>
% 89.16/26.95 (((kpairiskpair) =>
% 89.16/26.95 (((kpairp) =>
% 89.16/26.95 (((singletonsubset) =>
% 89.16/26.95 (((singletoninpowerset) =>
% 89.16/26.95 (((singletoninpowunion) =>
% 89.16/26.95 (((upairset2E) =>
% 89.16/26.95 (((upairsubunion) =>
% 89.16/26.95 ((
% 89.16/26.95 (upairinpowunion) =>
% 89.16/26.95 ((
% 89.16/26.95 (ubforcartprodlem1) =>
% 89.16/26.95 ((
% 89.16/26.95 (ubforcartprodlem2) =>
% 89.16/26.95 ((
% 89.16/26.95 (ubforcartprodlem3) =>
% 89.16/26.95 ((
% 89.16/26.95 (cartprodpairin) =>
% 89.16/26.95 ((
% 89.16/26.95 (cartprodmempair1) =>
% 89.16/26.95 ((
% 89.16/26.95 (cartprodmempair) =>
% 89.16/26.95 ((
% 89.16/26.95 (setunionE2) =>
% 89.16/26.95 ((
% 89.16/26.95 (setunionsingleton1) =>
% 89.16/26.95 ((
% 89.16/26.95 (setunionsingleton2) =>
% 89.16/26.95 ((
% 89.16/26.95 (setunionsingleton) =>
% 89.16/26.95 ((
% 89.16/26.95 (singletonprop) =>
% 89.16/26.95 ((
% 89.16/26.95 (ex1E1) =>
% 89.16/26.95 ((
% 89.16/26.95 (ex1I) =>
% 89.16/26.95 ((
% 89.16/26.95 (ex1I2) =>
% 89.16/26.95 ((
% 89.16/26.95 (singletonsuniq) =>
% 89.16/26.95 ((
% 89.16/26.95 (setukpairinjL1) =>
% 89.16/26.95 ((
% 89.16/26.95 (kfstsingleton) =>
% 89.16/26.95 ((
% 89.16/26.95 (theprop) =>
% 89.16/26.95 ((
% 89.16/26.95 (kfstpairEq) =>
% 89.16/26.95 ((
% 89.16/26.95 (cartprodfstin) =>
% 89.16/26.95 ((
% 89.16/26.95 (setukpairinjL2) =>
% 89.16/26.95 ((
% 89.16/26.95 (setukpairinjL) =>
% 89.16/26.95 ((
% 89.16/26.95 (setukpairinjR11) =>
% 89.16/26.95 ((
% 89.16/26.95 (setukpairinjR12) =>
% 89.16/26.95 ((
% 89.16/26.95 (setukpairinjR1) =>
% 89.16/26.95 ((
% 89.16/26.95 (upairequniteq) =>
% 89.16/26.95 ((
% 89.16/26.95 (setukpairinjR2) =>
% 89.16/26.95 ((
% 89.16/26.95 (setukpairinjR) =>
% 89.16/26.95 ((
% 89.16/26.95 (ksndsingleton) =>
% 89.16/26.95 ((
% 89.16/26.95 (ksndpairEq) =>
% 89.16/26.95 ((
% 89.16/26.95 (kpairsurjEq) =>
% 89.16/26.95 ((
% 89.16/26.95 (cartprodsndin) =>
% 89.16/26.95 ((
% 89.16/26.95 (cartprodpairmemEL) =>
% 89.16/26.95 ((
% 89.16/26.95 (cartprodpairmemER) =>
% 89.16/26.95 ((
% 89.16/26.95 (cartprodmempaircEq) =>
% 89.16/26.95 ((
% 89.16/26.95 (cartprodfstpairEq) =>
% 89.16/26.95 ((
% 89.16/26.95 (cartprodsndpairEq) =>
% 89.16/26.95 ((
% 89.16/26.95 (cartprodpairsurjEq) =>
% 89.16/26.95 ((
% 89.16/26.95 (dpsetconstrI) =>
% 89.16/26.95 ((
% 89.16/26.95 (dpsetconstrSub) =>
% 89.16/26.95 ((
% 89.16/26.95 (setOfPairsIsBReln) =>
% 89.16/26.95 ((
% 89.16/26.95 (dpsetconstrERa) =>
% 89.16/26.95 ((
% 89.16/26.95 (dpsetconstrEL1) =>
% 89.16/26.95 ((
% 89.16/26.95 (dpsetconstrEL2) =>
% 89.16/26.95 ((
% 89.16/26.95 (dpsetconstrER) =>
% 89.16/26.95 ((
% 89.16/26.95 (funcImageSingleton) =>
% 89.16/26.95 ((
% 89.16/26.95 (apProp) =>
% 89.16/26.95 ((
% 89.16/26.95 (app) =>
% 89.16/26.95 ((
% 89.16/26.95 (infuncsetfunc) =>
% 89.16/26.95 ((
% 89.16/26.95 (ap2p) =>
% 89.16/26.95 ((
% 89.16/26.95 (funcinfuncset) =>
% 89.16/26.95 ((
% 89.16/26.95 (lamProp) =>
% 89.16/26.95 ((
% 89.16/26.95 (lamp) =>
% 89.16/26.95 ((
% 89.16/26.95 (lam2p) =>
% 89.16/26.95 ((
% 89.16/26.95 (brelnall1) =>
% 89.16/26.95 ((
% 89.16/26.95 (brelnall2) =>
% 89.16/26.95 ((
% 89.16/26.95 (!!) @ (
% 89.16/26.95 (('#B') @ (
% 89.16/26.95 !!) @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#S') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 '#S') @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 =>))) @
% 89.16/26.95 ex1)))) @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 !!))) @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#S') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 '#B') @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 '#S') @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 =>))) @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#C') @ in)))))))) @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 !!))))) @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#C') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 '#B') @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 '#B') @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 '#S') @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 =>))) @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#C') @ in)))))))))) @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#S') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 '#S') @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 '#B'))) @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 =>))))))) @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#C') @ (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 '#B') @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 '#S') @
% 89.16/26.95 (
% 89.16/26.95 (
% 89.16/26.95 ('#B') @ (
% 89.16/26.95 =>))))))) @
% 89.16/26.95 (
% 89.16/26.95 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.16/26.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1193])).
% 89.16/26.95 thf(zip_derived_cl1216, plain,
% 89.16/26.95 (~ (((binintersectRsub) =>
% 89.16/26.95 (((binintersectSubset4) =>
% 89.16/26.95 (((binintersectSubset1) =>
% 89.16/26.95 (((bs114d) =>
% 89.16/26.95 (((setminusI) =>
% 89.16/26.95 (((setminusEL) =>
% 89.16/26.95 (((setminusER) =>
% 89.16/26.95 (((setminusSubset2) =>
% 89.16/26.95 (((setminusERneg) =>
% 89.16/26.95 (((setminusELneg) =>
% 89.16/26.95 (((setminusILneg) =>
% 89.16/26.95 (((setminusIRneg) =>
% 89.16/26.95 (((setminusLsub) =>
% 89.16/26.95 (((setminusSubset1) =>
% 89.16/26.95 (((symdiffE) =>
% 89.16/26.95 (((symdiffI1) =>
% 89.16/26.95 (((symdiffI2) =>
% 89.16/26.95 (((symdiffIneg1) =>
% 89.16/26.95 (((symdiffIneg2) =>
% 89.16/26.95 (((secondinupair) =>
% 89.16/26.95 (((setukpairIL) =>
% 89.16/26.95 (((setukpairIR) =>
% 89.16/26.95 (((kpairiskpair) =>
% 89.16/26.95 (((kpairp) =>
% 89.16/26.95 (((singletonsubset) =>
% 89.16/26.95 (((singletoninpowerset) =>
% 89.16/26.95 (((singletoninpowunion) =>
% 89.16/26.95 (((upairset2E) =>
% 89.16/26.95 (((upairsubunion) =>
% 89.16/26.95 (((upairinpowunion) =>
% 89.16/26.95 ((
% 89.16/26.95 (ubforcartprodlem1) =>
% 89.16/26.95 ((
% 89.16/26.95 (ubforcartprodlem2) =>
% 89.16/26.95 ((
% 89.16/26.95 (ubforcartprodlem3) =>
% 89.16/26.95 ((
% 89.16/26.95 (cartprodpairin) =>
% 89.16/26.95 ((
% 89.16/26.95 (cartprodmempair1) =>
% 89.16/26.95 ((
% 89.16/26.95 (cartprodmempair) =>
% 89.16/26.95 ((
% 89.16/26.95 (setunionE2) =>
% 89.16/26.95 ((
% 89.16/26.95 (setunionsingleton1) =>
% 89.16/26.95 ((
% 89.16/26.95 (setunionsingleton2) =>
% 89.16/26.95 ((
% 89.16/26.95 (setunionsingleton) =>
% 89.16/26.95 ((
% 89.16/26.95 (singletonprop) =>
% 89.16/26.95 ((
% 89.16/26.95 (ex1E1) =>
% 89.16/26.95 ((
% 89.16/26.95 (ex1I) =>
% 89.16/26.95 ((
% 89.16/26.95 (ex1I2) =>
% 89.16/26.95 ((
% 89.16/26.95 (singletonsuniq) =>
% 89.16/26.95 ((
% 89.16/26.95 (setukpairinjL1) =>
% 89.16/26.95 ((
% 89.16/26.95 (kfstsingleton) =>
% 89.16/26.95 ((
% 89.16/26.95 (theprop) =>
% 89.16/26.95 ((
% 89.16/26.95 (kfstpairEq) =>
% 89.16/26.95 ((
% 89.16/26.95 (cartprodfstin) =>
% 89.16/26.95 ((
% 89.16/26.95 (setukpairinjL2) =>
% 89.16/26.95 ((
% 89.16/26.95 (setukpairinjL) =>
% 89.16/26.95 ((
% 89.16/26.95 (setukpairinjR11) =>
% 89.16/26.95 ((
% 89.16/26.95 (setukpairinjR12) =>
% 89.16/26.95 ((
% 89.16/26.95 (setukpairinjR1) =>
% 89.16/26.95 ((
% 89.16/26.95 (upairequniteq) =>
% 89.16/26.95 ((
% 89.16/26.95 (setukpairinjR2) =>
% 89.16/26.95 ((
% 89.16/26.95 (setukpairinjR) =>
% 89.16/26.95 ((
% 89.16/26.95 (ksndsingleton) =>
% 89.16/26.95 ((
% 89.16/26.95 (ksndpairEq) =>
% 89.16/26.95 ((
% 89.16/26.95 (kpairsurjEq) =>
% 89.16/26.95 ((
% 89.16/26.95 (cartprodsndin) =>
% 89.16/26.95 ((
% 89.16/26.95 (cartprodpairmemEL) =>
% 89.16/26.95 ((
% 89.16/26.95 (cartprodpairmemER) =>
% 89.16/26.95 ((
% 89.16/26.95 (cartprodmempaircEq) =>
% 89.16/26.95 ((
% 89.16/26.95 (cartprodfstpairEq) =>
% 89.16/26.95 ((
% 89.16/26.95 (cartprodsndpairEq) =>
% 89.16/26.95 ((
% 89.16/26.95 (cartprodpairsurjEq) =>
% 89.16/26.95 ((
% 89.16/26.95 (dpsetconstrI) =>
% 89.16/26.95 ((
% 89.16/26.95 (dpsetconstrSub) =>
% 89.16/26.95 ((
% 89.16/26.95 (setOfPairsIsBReln) =>
% 89.16/26.95 ((
% 89.16/26.95 (dpsetconstrERa) =>
% 89.16/26.95 ((
% 89.16/26.95 (dpsetconstrEL1) =>
% 89.16/26.95 ((
% 89.16/26.95 (dpsetconstrEL2) =>
% 89.16/26.95 ((
% 89.16/26.95 (dpsetconstrER) =>
% 89.16/26.95 ((
% 89.16/26.95 (funcImageSingleton) =>
% 89.16/26.95 ((
% 89.16/26.95 (apProp) =>
% 89.16/26.95 ((
% 89.16/26.95 (app) =>
% 89.16/26.95 ((
% 89.16/26.95 (infuncsetfunc) =>
% 89.16/26.95 ((
% 89.16/26.95 (ap2p) =>
% 89.16/26.95 ((
% 89.16/26.95 (funcinfuncset) =>
% 89.16/26.95 ((
% 89.16/26.95 (lamProp) =>
% 89.16/26.95 ((
% 89.16/26.95 (lamp) =>
% 89.16/26.95 ((
% 89.16/26.95 (lam2p) =>
% 89.16/26.95 ((
% 89.16/26.95 (brelnall1) =>
% 89.16/26.95 ((
% 89.16/26.95 (brelnall2) =>
% 89.16/26.95 ((
% 89.16/26.95 (!!) @ (
% 89.16/26.95 (('#B') @ (
% 89.40/26.96 !!) @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#S') @ (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 '#S') @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 =>))) @
% 89.40/26.96 ex1)))) @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 !!))) @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#S') @ (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 '#B') @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 '#S') @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 =>))) @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#C') @ in)))))))) @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 !!))))) @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#C') @ (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 '#B') @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 '#B') @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 '#S') @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 =>))) @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#C') @ in)))))))))) @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#S') @ (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 '#S') @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 '#B'))) @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 =>))))))) @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#C') @ (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 '#B') @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 '#S') @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 =>))))))) @
% 89.40/26.96 (
% 89.40/26.96 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.40/26.96 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1206])).
% 89.40/26.96 thf(zip_derived_cl1223, plain,
% 89.40/26.96 (~ (((binintersectSubset4) =>
% 89.40/26.96 (((binintersectSubset1) =>
% 89.40/26.96 (((bs114d) =>
% 89.40/26.96 (((setminusI) =>
% 89.40/26.96 (((setminusEL) =>
% 89.40/26.96 (((setminusER) =>
% 89.40/26.96 (((setminusSubset2) =>
% 89.40/26.96 (((setminusERneg) =>
% 89.40/26.96 (((setminusELneg) =>
% 89.40/26.96 (((setminusILneg) =>
% 89.40/26.96 (((setminusIRneg) =>
% 89.40/26.96 (((setminusLsub) =>
% 89.40/26.96 (((setminusSubset1) =>
% 89.40/26.96 (((symdiffE) =>
% 89.40/26.96 (((symdiffI1) =>
% 89.40/26.96 (((symdiffI2) =>
% 89.40/26.96 (((symdiffIneg1) =>
% 89.40/26.96 (((symdiffIneg2) =>
% 89.40/26.96 (((secondinupair) =>
% 89.40/26.96 (((setukpairIL) =>
% 89.40/26.96 (((setukpairIR) =>
% 89.40/26.96 (((kpairiskpair) =>
% 89.40/26.96 (((kpairp) =>
% 89.40/26.96 (((singletonsubset) =>
% 89.40/26.96 (((singletoninpowerset) =>
% 89.40/26.96 (((singletoninpowunion) =>
% 89.40/26.96 (((upairset2E) =>
% 89.40/26.96 (((upairsubunion) =>
% 89.40/26.96 (((upairinpowunion) =>
% 89.40/26.96 (((ubforcartprodlem1) =>
% 89.40/26.96 ((
% 89.40/26.96 (ubforcartprodlem2) =>
% 89.40/26.96 ((
% 89.40/26.96 (ubforcartprodlem3) =>
% 89.40/26.96 ((
% 89.40/26.96 (cartprodpairin) =>
% 89.40/26.96 ((
% 89.40/26.96 (cartprodmempair1) =>
% 89.40/26.96 ((
% 89.40/26.96 (cartprodmempair) =>
% 89.40/26.96 ((
% 89.40/26.96 (setunionE2) =>
% 89.40/26.96 ((
% 89.40/26.96 (setunionsingleton1) =>
% 89.40/26.96 ((
% 89.40/26.96 (setunionsingleton2) =>
% 89.40/26.96 ((
% 89.40/26.96 (setunionsingleton) =>
% 89.40/26.96 ((
% 89.40/26.96 (singletonprop) =>
% 89.40/26.96 ((
% 89.40/26.96 (ex1E1) =>
% 89.40/26.96 ((
% 89.40/26.96 (ex1I) =>
% 89.40/26.96 ((
% 89.40/26.96 (ex1I2) =>
% 89.40/26.96 ((
% 89.40/26.96 (singletonsuniq) =>
% 89.40/26.96 ((
% 89.40/26.96 (setukpairinjL1) =>
% 89.40/26.96 ((
% 89.40/26.96 (kfstsingleton) =>
% 89.40/26.96 ((
% 89.40/26.96 (theprop) =>
% 89.40/26.96 ((
% 89.40/26.96 (kfstpairEq) =>
% 89.40/26.96 ((
% 89.40/26.96 (cartprodfstin) =>
% 89.40/26.96 ((
% 89.40/26.96 (setukpairinjL2) =>
% 89.40/26.96 ((
% 89.40/26.96 (setukpairinjL) =>
% 89.40/26.96 ((
% 89.40/26.96 (setukpairinjR11) =>
% 89.40/26.96 ((
% 89.40/26.96 (setukpairinjR12) =>
% 89.40/26.96 ((
% 89.40/26.96 (setukpairinjR1) =>
% 89.40/26.96 ((
% 89.40/26.96 (upairequniteq) =>
% 89.40/26.96 ((
% 89.40/26.96 (setukpairinjR2) =>
% 89.40/26.96 ((
% 89.40/26.96 (setukpairinjR) =>
% 89.40/26.96 ((
% 89.40/26.96 (ksndsingleton) =>
% 89.40/26.96 ((
% 89.40/26.96 (ksndpairEq) =>
% 89.40/26.96 ((
% 89.40/26.96 (kpairsurjEq) =>
% 89.40/26.96 ((
% 89.40/26.96 (cartprodsndin) =>
% 89.40/26.96 ((
% 89.40/26.96 (cartprodpairmemEL) =>
% 89.40/26.96 ((
% 89.40/26.96 (cartprodpairmemER) =>
% 89.40/26.96 ((
% 89.40/26.96 (cartprodmempaircEq) =>
% 89.40/26.96 ((
% 89.40/26.96 (cartprodfstpairEq) =>
% 89.40/26.96 ((
% 89.40/26.96 (cartprodsndpairEq) =>
% 89.40/26.96 ((
% 89.40/26.96 (cartprodpairsurjEq) =>
% 89.40/26.96 ((
% 89.40/26.96 (dpsetconstrI) =>
% 89.40/26.96 ((
% 89.40/26.96 (dpsetconstrSub) =>
% 89.40/26.96 ((
% 89.40/26.96 (setOfPairsIsBReln) =>
% 89.40/26.96 ((
% 89.40/26.96 (dpsetconstrERa) =>
% 89.40/26.96 ((
% 89.40/26.96 (dpsetconstrEL1) =>
% 89.40/26.96 ((
% 89.40/26.96 (dpsetconstrEL2) =>
% 89.40/26.96 ((
% 89.40/26.96 (dpsetconstrER) =>
% 89.40/26.96 ((
% 89.40/26.96 (funcImageSingleton) =>
% 89.40/26.96 ((
% 89.40/26.96 (apProp) =>
% 89.40/26.96 ((
% 89.40/26.96 (app) =>
% 89.40/26.96 ((
% 89.40/26.96 (infuncsetfunc) =>
% 89.40/26.96 ((
% 89.40/26.96 (ap2p) =>
% 89.40/26.96 ((
% 89.40/26.96 (funcinfuncset) =>
% 89.40/26.96 ((
% 89.40/26.96 (lamProp) =>
% 89.40/26.96 ((
% 89.40/26.96 (lamp) =>
% 89.40/26.96 ((
% 89.40/26.96 (lam2p) =>
% 89.40/26.96 ((
% 89.40/26.96 (brelnall1) =>
% 89.40/26.96 ((
% 89.40/26.96 (brelnall2) =>
% 89.40/26.96 ((
% 89.40/26.96 (!!) @ (
% 89.40/26.96 (('#B') @ (
% 89.40/26.96 !!) @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#S') @ (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 '#S') @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 =>))) @
% 89.40/26.96 ex1)))) @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 !!))) @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#S') @ (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 '#B') @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 '#S') @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 =>))) @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#C') @ in)))))))) @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 !!))))) @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#C') @ (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 '#B') @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 '#B') @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 '#S') @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 =>))) @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#C') @ in)))))))))) @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#S') @ (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 '#S') @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 '#B'))) @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 =>))))))) @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#C') @ (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 '#B') @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 '#S') @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 =>))))))) @
% 89.40/26.96 (
% 89.40/26.96 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.40/26.96 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1216])).
% 89.40/26.96 thf(zip_derived_cl1231, plain,
% 89.40/26.96 (~ (((binintersectSubset1) =>
% 89.40/26.96 (((bs114d) =>
% 89.40/26.96 (((setminusI) =>
% 89.40/26.96 (((setminusEL) =>
% 89.40/26.96 (((setminusER) =>
% 89.40/26.96 (((setminusSubset2) =>
% 89.40/26.96 (((setminusERneg) =>
% 89.40/26.96 (((setminusELneg) =>
% 89.40/26.96 (((setminusILneg) =>
% 89.40/26.96 (((setminusIRneg) =>
% 89.40/26.96 (((setminusLsub) =>
% 89.40/26.96 (((setminusSubset1) =>
% 89.40/26.96 (((symdiffE) =>
% 89.40/26.96 (((symdiffI1) =>
% 89.40/26.96 (((symdiffI2) =>
% 89.40/26.96 (((symdiffIneg1) =>
% 89.40/26.96 (((symdiffIneg2) =>
% 89.40/26.96 (((secondinupair) =>
% 89.40/26.96 (((setukpairIL) =>
% 89.40/26.96 (((setukpairIR) =>
% 89.40/26.96 (((kpairiskpair) =>
% 89.40/26.96 (((kpairp) =>
% 89.40/26.96 (((singletonsubset) =>
% 89.40/26.96 (((singletoninpowerset) =>
% 89.40/26.96 (((singletoninpowunion) =>
% 89.40/26.96 (((upairset2E) =>
% 89.40/26.96 (((upairsubunion) =>
% 89.40/26.96 (((upairinpowunion) =>
% 89.40/26.96 (((ubforcartprodlem1) =>
% 89.40/26.96 (((ubforcartprodlem2) =>
% 89.40/26.96 ((
% 89.40/26.96 (ubforcartprodlem3) =>
% 89.40/26.96 ((
% 89.40/26.96 (cartprodpairin) =>
% 89.40/26.96 ((
% 89.40/26.96 (cartprodmempair1) =>
% 89.40/26.96 ((
% 89.40/26.96 (cartprodmempair) =>
% 89.40/26.96 ((
% 89.40/26.96 (setunionE2) =>
% 89.40/26.96 ((
% 89.40/26.96 (setunionsingleton1) =>
% 89.40/26.96 ((
% 89.40/26.96 (setunionsingleton2) =>
% 89.40/26.96 ((
% 89.40/26.96 (setunionsingleton) =>
% 89.40/26.96 ((
% 89.40/26.96 (singletonprop) =>
% 89.40/26.96 ((
% 89.40/26.96 (ex1E1) =>
% 89.40/26.96 ((
% 89.40/26.96 (ex1I) =>
% 89.40/26.96 ((
% 89.40/26.96 (ex1I2) =>
% 89.40/26.96 ((
% 89.40/26.96 (singletonsuniq) =>
% 89.40/26.96 ((
% 89.40/26.96 (setukpairinjL1) =>
% 89.40/26.96 ((
% 89.40/26.96 (kfstsingleton) =>
% 89.40/26.96 ((
% 89.40/26.96 (theprop) =>
% 89.40/26.96 ((
% 89.40/26.96 (kfstpairEq) =>
% 89.40/26.96 ((
% 89.40/26.96 (cartprodfstin) =>
% 89.40/26.96 ((
% 89.40/26.96 (setukpairinjL2) =>
% 89.40/26.96 ((
% 89.40/26.96 (setukpairinjL) =>
% 89.40/26.96 ((
% 89.40/26.96 (setukpairinjR11) =>
% 89.40/26.96 ((
% 89.40/26.96 (setukpairinjR12) =>
% 89.40/26.96 ((
% 89.40/26.96 (setukpairinjR1) =>
% 89.40/26.96 ((
% 89.40/26.96 (upairequniteq) =>
% 89.40/26.96 ((
% 89.40/26.96 (setukpairinjR2) =>
% 89.40/26.96 ((
% 89.40/26.96 (setukpairinjR) =>
% 89.40/26.96 ((
% 89.40/26.96 (ksndsingleton) =>
% 89.40/26.96 ((
% 89.40/26.96 (ksndpairEq) =>
% 89.40/26.96 ((
% 89.40/26.96 (kpairsurjEq) =>
% 89.40/26.96 ((
% 89.40/26.96 (cartprodsndin) =>
% 89.40/26.96 ((
% 89.40/26.96 (cartprodpairmemEL) =>
% 89.40/26.96 ((
% 89.40/26.96 (cartprodpairmemER) =>
% 89.40/26.96 ((
% 89.40/26.96 (cartprodmempaircEq) =>
% 89.40/26.96 ((
% 89.40/26.96 (cartprodfstpairEq) =>
% 89.40/26.96 ((
% 89.40/26.96 (cartprodsndpairEq) =>
% 89.40/26.96 ((
% 89.40/26.96 (cartprodpairsurjEq) =>
% 89.40/26.96 ((
% 89.40/26.96 (dpsetconstrI) =>
% 89.40/26.96 ((
% 89.40/26.96 (dpsetconstrSub) =>
% 89.40/26.96 ((
% 89.40/26.96 (setOfPairsIsBReln) =>
% 89.40/26.96 ((
% 89.40/26.96 (dpsetconstrERa) =>
% 89.40/26.96 ((
% 89.40/26.96 (dpsetconstrEL1) =>
% 89.40/26.96 ((
% 89.40/26.96 (dpsetconstrEL2) =>
% 89.40/26.96 ((
% 89.40/26.96 (dpsetconstrER) =>
% 89.40/26.96 ((
% 89.40/26.96 (funcImageSingleton) =>
% 89.40/26.96 ((
% 89.40/26.96 (apProp) =>
% 89.40/26.96 ((
% 89.40/26.96 (app) =>
% 89.40/26.96 ((
% 89.40/26.96 (infuncsetfunc) =>
% 89.40/26.96 ((
% 89.40/26.96 (ap2p) =>
% 89.40/26.96 ((
% 89.40/26.96 (funcinfuncset) =>
% 89.40/26.96 ((
% 89.40/26.96 (lamProp) =>
% 89.40/26.96 ((
% 89.40/26.96 (lamp) =>
% 89.40/26.96 ((
% 89.40/26.96 (lam2p) =>
% 89.40/26.96 ((
% 89.40/26.96 (brelnall1) =>
% 89.40/26.96 ((
% 89.40/26.96 (brelnall2) =>
% 89.40/26.96 ((
% 89.40/26.96 (!!) @ (
% 89.40/26.96 (('#B') @ (
% 89.40/26.96 !!) @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#S') @ (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 '#S') @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 =>))) @
% 89.40/26.96 ex1)))) @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 !!))) @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#S') @ (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 '#B') @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 '#S') @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 =>))) @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#C') @ in)))))))) @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 !!))))) @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#C') @ (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 '#B') @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 '#B') @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 '#S') @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 =>))) @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#C') @ in)))))))))) @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#S') @ (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 '#S') @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 '#B'))) @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 =>))))))) @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#C') @ (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 '#B') @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 '#S') @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 =>))))))) @
% 89.40/26.96 (
% 89.40/26.96 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.40/26.96 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1223])).
% 89.40/26.96 thf(zip_derived_cl1239, plain,
% 89.40/26.96 (~ (((bs114d) =>
% 89.40/26.96 (((setminusI) =>
% 89.40/26.96 (((setminusEL) =>
% 89.40/26.96 (((setminusER) =>
% 89.40/26.96 (((setminusSubset2) =>
% 89.40/26.96 (((setminusERneg) =>
% 89.40/26.96 (((setminusELneg) =>
% 89.40/26.96 (((setminusILneg) =>
% 89.40/26.96 (((setminusIRneg) =>
% 89.40/26.96 (((setminusLsub) =>
% 89.40/26.96 (((setminusSubset1) =>
% 89.40/26.96 (((symdiffE) =>
% 89.40/26.96 (((symdiffI1) =>
% 89.40/26.96 (((symdiffI2) =>
% 89.40/26.96 (((symdiffIneg1) =>
% 89.40/26.96 (((symdiffIneg2) =>
% 89.40/26.96 (((secondinupair) =>
% 89.40/26.96 (((setukpairIL) =>
% 89.40/26.96 (((setukpairIR) =>
% 89.40/26.96 (((kpairiskpair) =>
% 89.40/26.96 (((kpairp) =>
% 89.40/26.96 (((singletonsubset) =>
% 89.40/26.96 (((singletoninpowerset) =>
% 89.40/26.96 (((singletoninpowunion) =>
% 89.40/26.96 (((upairset2E) =>
% 89.40/26.96 (((upairsubunion) =>
% 89.40/26.96 (((upairinpowunion) =>
% 89.40/26.96 (((ubforcartprodlem1) =>
% 89.40/26.96 (((ubforcartprodlem2) =>
% 89.40/26.96 (((ubforcartprodlem3) =>
% 89.40/26.96 ((
% 89.40/26.96 (cartprodpairin) =>
% 89.40/26.96 ((
% 89.40/26.96 (cartprodmempair1) =>
% 89.40/26.96 ((
% 89.40/26.96 (cartprodmempair) =>
% 89.40/26.96 ((
% 89.40/26.96 (setunionE2) =>
% 89.40/26.96 ((
% 89.40/26.96 (setunionsingleton1) =>
% 89.40/26.96 ((
% 89.40/26.96 (setunionsingleton2) =>
% 89.40/26.96 ((
% 89.40/26.96 (setunionsingleton) =>
% 89.40/26.96 ((
% 89.40/26.96 (singletonprop) =>
% 89.40/26.96 ((
% 89.40/26.96 (ex1E1) =>
% 89.40/26.96 ((
% 89.40/26.96 (ex1I) =>
% 89.40/26.96 ((
% 89.40/26.96 (ex1I2) =>
% 89.40/26.96 ((
% 89.40/26.96 (singletonsuniq) =>
% 89.40/26.96 ((
% 89.40/26.96 (setukpairinjL1) =>
% 89.40/26.96 ((
% 89.40/26.96 (kfstsingleton) =>
% 89.40/26.96 ((
% 89.40/26.96 (theprop) =>
% 89.40/26.96 ((
% 89.40/26.96 (kfstpairEq) =>
% 89.40/26.96 ((
% 89.40/26.96 (cartprodfstin) =>
% 89.40/26.96 ((
% 89.40/26.96 (setukpairinjL2) =>
% 89.40/26.96 ((
% 89.40/26.96 (setukpairinjL) =>
% 89.40/26.96 ((
% 89.40/26.96 (setukpairinjR11) =>
% 89.40/26.96 ((
% 89.40/26.96 (setukpairinjR12) =>
% 89.40/26.96 ((
% 89.40/26.96 (setukpairinjR1) =>
% 89.40/26.96 ((
% 89.40/26.96 (upairequniteq) =>
% 89.40/26.96 ((
% 89.40/26.96 (setukpairinjR2) =>
% 89.40/26.96 ((
% 89.40/26.96 (setukpairinjR) =>
% 89.40/26.96 ((
% 89.40/26.96 (ksndsingleton) =>
% 89.40/26.96 ((
% 89.40/26.96 (ksndpairEq) =>
% 89.40/26.96 ((
% 89.40/26.96 (kpairsurjEq) =>
% 89.40/26.96 ((
% 89.40/26.96 (cartprodsndin) =>
% 89.40/26.96 ((
% 89.40/26.96 (cartprodpairmemEL) =>
% 89.40/26.96 ((
% 89.40/26.96 (cartprodpairmemER) =>
% 89.40/26.96 ((
% 89.40/26.96 (cartprodmempaircEq) =>
% 89.40/26.96 ((
% 89.40/26.96 (cartprodfstpairEq) =>
% 89.40/26.96 ((
% 89.40/26.96 (cartprodsndpairEq) =>
% 89.40/26.96 ((
% 89.40/26.96 (cartprodpairsurjEq) =>
% 89.40/26.96 ((
% 89.40/26.96 (dpsetconstrI) =>
% 89.40/26.96 ((
% 89.40/26.96 (dpsetconstrSub) =>
% 89.40/26.96 ((
% 89.40/26.96 (setOfPairsIsBReln) =>
% 89.40/26.96 ((
% 89.40/26.96 (dpsetconstrERa) =>
% 89.40/26.96 ((
% 89.40/26.96 (dpsetconstrEL1) =>
% 89.40/26.96 ((
% 89.40/26.96 (dpsetconstrEL2) =>
% 89.40/26.96 ((
% 89.40/26.96 (dpsetconstrER) =>
% 89.40/26.96 ((
% 89.40/26.96 (funcImageSingleton) =>
% 89.40/26.96 ((
% 89.40/26.96 (apProp) =>
% 89.40/26.96 ((
% 89.40/26.96 (app) =>
% 89.40/26.96 ((
% 89.40/26.96 (infuncsetfunc) =>
% 89.40/26.96 ((
% 89.40/26.96 (ap2p) =>
% 89.40/26.96 ((
% 89.40/26.96 (funcinfuncset) =>
% 89.40/26.96 ((
% 89.40/26.96 (lamProp) =>
% 89.40/26.96 ((
% 89.40/26.96 (lamp) =>
% 89.40/26.96 ((
% 89.40/26.96 (lam2p) =>
% 89.40/26.96 ((
% 89.40/26.96 (brelnall1) =>
% 89.40/26.96 ((
% 89.40/26.96 (brelnall2) =>
% 89.40/26.96 ((
% 89.40/26.96 (!!) @ (
% 89.40/26.96 (('#B') @ (
% 89.40/26.96 !!) @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#S') @ (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 '#S') @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 =>))) @
% 89.40/26.96 ex1)))) @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 !!))) @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#S') @ (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 '#B') @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 '#S') @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 =>))) @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#C') @ in)))))))) @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 !!))))) @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#C') @ (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 '#B') @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 '#B') @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 '#S') @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 =>))) @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#C') @ in)))))))))) @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#S') @ (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 '#S') @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 '#B'))) @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 =>))))))) @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#C') @ (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 '#B') @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 '#S') @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 =>))))))) @
% 89.40/26.96 (
% 89.40/26.96 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.40/26.96 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1231])).
% 89.40/26.96 thf(zip_derived_cl1247, plain,
% 89.40/26.96 (~ (((setminusI) =>
% 89.40/26.96 (((setminusEL) =>
% 89.40/26.96 (((setminusER) =>
% 89.40/26.96 (((setminusSubset2) =>
% 89.40/26.96 (((setminusERneg) =>
% 89.40/26.96 (((setminusELneg) =>
% 89.40/26.96 (((setminusILneg) =>
% 89.40/26.96 (((setminusIRneg) =>
% 89.40/26.96 (((setminusLsub) =>
% 89.40/26.96 (((setminusSubset1) =>
% 89.40/26.96 (((symdiffE) =>
% 89.40/26.96 (((symdiffI1) =>
% 89.40/26.96 (((symdiffI2) =>
% 89.40/26.96 (((symdiffIneg1) =>
% 89.40/26.96 (((symdiffIneg2) =>
% 89.40/26.96 (((secondinupair) =>
% 89.40/26.96 (((setukpairIL) =>
% 89.40/26.96 (((setukpairIR) =>
% 89.40/26.96 (((kpairiskpair) =>
% 89.40/26.96 (((kpairp) =>
% 89.40/26.96 (((singletonsubset) =>
% 89.40/26.96 (((singletoninpowerset) =>
% 89.40/26.96 (((singletoninpowunion) =>
% 89.40/26.96 (((upairset2E) =>
% 89.40/26.96 (((upairsubunion) =>
% 89.40/26.96 (((upairinpowunion) =>
% 89.40/26.96 (((ubforcartprodlem1) =>
% 89.40/26.96 (((ubforcartprodlem2) =>
% 89.40/26.96 (((ubforcartprodlem3) =>
% 89.40/26.96 (((cartprodpairin) =>
% 89.40/26.96 ((
% 89.40/26.96 (cartprodmempair1) =>
% 89.40/26.96 ((
% 89.40/26.96 (cartprodmempair) =>
% 89.40/26.96 ((
% 89.40/26.96 (setunionE2) =>
% 89.40/26.96 ((
% 89.40/26.96 (setunionsingleton1) =>
% 89.40/26.96 ((
% 89.40/26.96 (setunionsingleton2) =>
% 89.40/26.96 ((
% 89.40/26.96 (setunionsingleton) =>
% 89.40/26.96 ((
% 89.40/26.96 (singletonprop) =>
% 89.40/26.96 ((
% 89.40/26.96 (ex1E1) =>
% 89.40/26.96 ((
% 89.40/26.96 (ex1I) =>
% 89.40/26.96 ((
% 89.40/26.96 (ex1I2) =>
% 89.40/26.96 ((
% 89.40/26.96 (singletonsuniq) =>
% 89.40/26.96 ((
% 89.40/26.96 (setukpairinjL1) =>
% 89.40/26.96 ((
% 89.40/26.96 (kfstsingleton) =>
% 89.40/26.96 ((
% 89.40/26.96 (theprop) =>
% 89.40/26.96 ((
% 89.40/26.96 (kfstpairEq) =>
% 89.40/26.96 ((
% 89.40/26.96 (cartprodfstin) =>
% 89.40/26.96 ((
% 89.40/26.96 (setukpairinjL2) =>
% 89.40/26.96 ((
% 89.40/26.96 (setukpairinjL) =>
% 89.40/26.96 ((
% 89.40/26.96 (setukpairinjR11) =>
% 89.40/26.96 ((
% 89.40/26.96 (setukpairinjR12) =>
% 89.40/26.96 ((
% 89.40/26.96 (setukpairinjR1) =>
% 89.40/26.96 ((
% 89.40/26.96 (upairequniteq) =>
% 89.40/26.96 ((
% 89.40/26.96 (setukpairinjR2) =>
% 89.40/26.96 ((
% 89.40/26.96 (setukpairinjR) =>
% 89.40/26.96 ((
% 89.40/26.96 (ksndsingleton) =>
% 89.40/26.96 ((
% 89.40/26.96 (ksndpairEq) =>
% 89.40/26.96 ((
% 89.40/26.96 (kpairsurjEq) =>
% 89.40/26.96 ((
% 89.40/26.96 (cartprodsndin) =>
% 89.40/26.96 ((
% 89.40/26.96 (cartprodpairmemEL) =>
% 89.40/26.96 ((
% 89.40/26.96 (cartprodpairmemER) =>
% 89.40/26.96 ((
% 89.40/26.96 (cartprodmempaircEq) =>
% 89.40/26.96 ((
% 89.40/26.96 (cartprodfstpairEq) =>
% 89.40/26.96 ((
% 89.40/26.96 (cartprodsndpairEq) =>
% 89.40/26.96 ((
% 89.40/26.96 (cartprodpairsurjEq) =>
% 89.40/26.96 ((
% 89.40/26.96 (dpsetconstrI) =>
% 89.40/26.96 ((
% 89.40/26.96 (dpsetconstrSub) =>
% 89.40/26.96 ((
% 89.40/26.96 (setOfPairsIsBReln) =>
% 89.40/26.96 ((
% 89.40/26.96 (dpsetconstrERa) =>
% 89.40/26.96 ((
% 89.40/26.96 (dpsetconstrEL1) =>
% 89.40/26.96 ((
% 89.40/26.96 (dpsetconstrEL2) =>
% 89.40/26.96 ((
% 89.40/26.96 (dpsetconstrER) =>
% 89.40/26.96 ((
% 89.40/26.96 (funcImageSingleton) =>
% 89.40/26.96 ((
% 89.40/26.96 (apProp) =>
% 89.40/26.96 ((
% 89.40/26.96 (app) =>
% 89.40/26.96 ((
% 89.40/26.96 (infuncsetfunc) =>
% 89.40/26.96 ((
% 89.40/26.96 (ap2p) =>
% 89.40/26.96 ((
% 89.40/26.96 (funcinfuncset) =>
% 89.40/26.96 ((
% 89.40/26.96 (lamProp) =>
% 89.40/26.96 ((
% 89.40/26.96 (lamp) =>
% 89.40/26.96 ((
% 89.40/26.96 (lam2p) =>
% 89.40/26.96 ((
% 89.40/26.96 (brelnall1) =>
% 89.40/26.96 ((
% 89.40/26.96 (brelnall2) =>
% 89.40/26.96 ((
% 89.40/26.96 (!!) @ (
% 89.40/26.96 (('#B') @ (
% 89.40/26.96 !!) @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#S') @ (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 '#S') @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 =>))) @
% 89.40/26.96 ex1)))) @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 !!))) @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#S') @ (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 '#B') @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 '#S') @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 =>))) @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#C') @ in)))))))) @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 !!))))) @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#C') @ (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 '#B') @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 '#B') @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 '#S') @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 =>))) @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#C') @ in)))))))))) @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#S') @ (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 '#S') @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 '#B'))) @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 =>))))))) @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#C') @ (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 '#B') @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 '#S') @
% 89.40/26.96 (
% 89.40/26.96 (
% 89.40/26.96 ('#B') @ (
% 89.40/26.96 =>))))))) @
% 89.40/26.96 (
% 89.40/26.96 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.40/26.96 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1239])).
% 89.40/26.96 thf(zip_derived_cl1255, plain,
% 89.40/26.96 (~ (((setminusEL) =>
% 89.40/26.96 (((setminusER) =>
% 89.40/26.96 (((setminusSubset2) =>
% 89.40/26.96 (((setminusERneg) =>
% 89.40/26.96 (((setminusELneg) =>
% 89.40/26.96 (((setminusILneg) =>
% 89.40/26.96 (((setminusIRneg) =>
% 89.40/26.96 (((setminusLsub) =>
% 89.40/26.96 (((setminusSubset1) =>
% 89.40/26.96 (((symdiffE) =>
% 89.40/26.96 (((symdiffI1) =>
% 89.40/26.96 (((symdiffI2) =>
% 89.40/26.96 (((symdiffIneg1) =>
% 89.40/26.96 (((symdiffIneg2) =>
% 89.40/26.96 (((secondinupair) =>
% 89.40/26.96 (((setukpairIL) =>
% 89.40/26.96 (((setukpairIR) =>
% 89.40/26.96 (((kpairiskpair) =>
% 89.40/26.96 (((kpairp) =>
% 89.40/26.96 (((singletonsubset) =>
% 89.40/26.96 (((singletoninpowerset) =>
% 89.40/26.96 (((singletoninpowunion) =>
% 89.40/26.96 (((upairset2E) =>
% 89.40/26.96 (((upairsubunion) =>
% 89.40/26.96 (((upairinpowunion) =>
% 89.40/26.96 (((ubforcartprodlem1) =>
% 89.40/26.96 (((ubforcartprodlem2) =>
% 89.40/26.96 (((ubforcartprodlem3) =>
% 89.40/26.96 (((cartprodpairin) =>
% 89.40/26.96 (((cartprodmempair1) =>
% 89.40/26.96 ((
% 89.40/26.96 (cartprodmempair) =>
% 89.40/26.96 ((
% 89.40/26.96 (setunionE2) =>
% 89.40/26.96 ((
% 89.40/26.96 (setunionsingleton1) =>
% 89.40/26.96 ((
% 89.40/26.96 (setunionsingleton2) =>
% 89.40/26.96 ((
% 89.40/26.96 (setunionsingleton) =>
% 89.40/26.96 ((
% 89.40/26.96 (singletonprop) =>
% 89.40/26.96 ((
% 89.40/26.96 (ex1E1) =>
% 89.40/26.96 ((
% 89.40/26.96 (ex1I) =>
% 89.40/26.96 ((
% 89.40/26.96 (ex1I2) =>
% 89.40/26.96 ((
% 89.40/26.96 (singletonsuniq) =>
% 89.40/26.96 ((
% 89.40/26.96 (setukpairinjL1) =>
% 89.40/26.96 ((
% 89.40/26.96 (kfstsingleton) =>
% 89.40/26.96 ((
% 89.40/26.96 (theprop) =>
% 89.40/26.96 ((
% 89.40/26.96 (kfstpairEq) =>
% 89.40/26.96 ((
% 89.40/26.96 (cartprodfstin) =>
% 89.40/26.96 ((
% 89.40/26.96 (setukpairinjL2) =>
% 89.40/26.96 ((
% 89.40/26.96 (setukpairinjL) =>
% 89.40/26.96 ((
% 89.40/26.96 (setukpairinjR11) =>
% 89.40/26.96 ((
% 89.40/26.96 (setukpairinjR12) =>
% 89.40/26.96 ((
% 89.40/26.96 (setukpairinjR1) =>
% 89.40/26.96 ((
% 89.40/26.96 (upairequniteq) =>
% 89.40/26.96 ((
% 89.40/26.96 (setukpairinjR2) =>
% 89.40/26.96 ((
% 89.40/26.96 (setukpairinjR) =>
% 89.40/26.96 ((
% 89.40/26.96 (ksndsingleton) =>
% 89.40/26.96 ((
% 89.40/26.96 (ksndpairEq) =>
% 89.40/26.97 ((
% 89.40/26.97 (kpairsurjEq) =>
% 89.40/26.97 ((
% 89.40/26.97 (cartprodsndin) =>
% 89.40/26.97 ((
% 89.40/26.97 (cartprodpairmemEL) =>
% 89.40/26.97 ((
% 89.40/26.97 (cartprodpairmemER) =>
% 89.40/26.97 ((
% 89.40/26.97 (cartprodmempaircEq) =>
% 89.40/26.97 ((
% 89.40/26.97 (cartprodfstpairEq) =>
% 89.40/26.97 ((
% 89.40/26.97 (cartprodsndpairEq) =>
% 89.40/26.97 ((
% 89.40/26.97 (cartprodpairsurjEq) =>
% 89.40/26.97 ((
% 89.40/26.97 (dpsetconstrI) =>
% 89.40/26.97 ((
% 89.40/26.97 (dpsetconstrSub) =>
% 89.40/26.97 ((
% 89.40/26.97 (setOfPairsIsBReln) =>
% 89.40/26.97 ((
% 89.40/26.97 (dpsetconstrERa) =>
% 89.40/26.97 ((
% 89.40/26.97 (dpsetconstrEL1) =>
% 89.40/26.97 ((
% 89.40/26.97 (dpsetconstrEL2) =>
% 89.40/26.97 ((
% 89.40/26.97 (dpsetconstrER) =>
% 89.40/26.97 ((
% 89.40/26.97 (funcImageSingleton) =>
% 89.40/26.97 ((
% 89.40/26.97 (apProp) =>
% 89.40/26.97 ((
% 89.40/26.97 (app) =>
% 89.40/26.97 ((
% 89.40/26.97 (infuncsetfunc) =>
% 89.40/26.97 ((
% 89.40/26.97 (ap2p) =>
% 89.40/26.97 ((
% 89.40/26.97 (funcinfuncset) =>
% 89.40/26.97 ((
% 89.40/26.97 (lamProp) =>
% 89.40/26.97 ((
% 89.40/26.97 (lamp) =>
% 89.40/26.97 ((
% 89.40/26.97 (lam2p) =>
% 89.40/26.97 ((
% 89.40/26.97 (brelnall1) =>
% 89.40/26.97 ((
% 89.40/26.97 (brelnall2) =>
% 89.40/26.97 ((
% 89.40/26.97 (!!) @ (
% 89.40/26.97 (('#B') @ (
% 89.40/26.97 !!) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#S') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#S') @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 =>))) @
% 89.40/26.97 ex1)))) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 !!))) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#S') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#B') @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#S') @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 =>))) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#C') @ in)))))))) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 !!))))) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#C') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#B') @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#B') @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#S') @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 =>))) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#C') @ in)))))))))) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#S') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#S') @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#B'))) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 =>))))))) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#C') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#B') @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#S') @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 =>))))))) @
% 89.40/26.97 (
% 89.40/26.97 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.40/26.97 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1247])).
% 89.40/26.97 thf(zip_derived_cl1264, plain,
% 89.40/26.97 (~ (((setminusER) =>
% 89.40/26.97 (((setminusSubset2) =>
% 89.40/26.97 (((setminusERneg) =>
% 89.40/26.97 (((setminusELneg) =>
% 89.40/26.97 (((setminusILneg) =>
% 89.40/26.97 (((setminusIRneg) =>
% 89.40/26.97 (((setminusLsub) =>
% 89.40/26.97 (((setminusSubset1) =>
% 89.40/26.97 (((symdiffE) =>
% 89.40/26.97 (((symdiffI1) =>
% 89.40/26.97 (((symdiffI2) =>
% 89.40/26.97 (((symdiffIneg1) =>
% 89.40/26.97 (((symdiffIneg2) =>
% 89.40/26.97 (((secondinupair) =>
% 89.40/26.97 (((setukpairIL) =>
% 89.40/26.97 (((setukpairIR) =>
% 89.40/26.97 (((kpairiskpair) =>
% 89.40/26.97 (((kpairp) =>
% 89.40/26.97 (((singletonsubset) =>
% 89.40/26.97 (((singletoninpowerset) =>
% 89.40/26.97 (((singletoninpowunion) =>
% 89.40/26.97 (((upairset2E) =>
% 89.40/26.97 (((upairsubunion) =>
% 89.40/26.97 (((upairinpowunion) =>
% 89.40/26.97 (((ubforcartprodlem1) =>
% 89.40/26.97 (((ubforcartprodlem2) =>
% 89.40/26.97 (((ubforcartprodlem3) =>
% 89.40/26.97 (((cartprodpairin) =>
% 89.40/26.97 (((cartprodmempair1) =>
% 89.40/26.97 (((cartprodmempair) =>
% 89.40/26.97 ((
% 89.40/26.97 (setunionE2) =>
% 89.40/26.97 ((
% 89.40/26.97 (setunionsingleton1) =>
% 89.40/26.97 ((
% 89.40/26.97 (setunionsingleton2) =>
% 89.40/26.97 ((
% 89.40/26.97 (setunionsingleton) =>
% 89.40/26.97 ((
% 89.40/26.97 (singletonprop) =>
% 89.40/26.97 ((
% 89.40/26.97 (ex1E1) =>
% 89.40/26.97 ((
% 89.40/26.97 (ex1I) =>
% 89.40/26.97 ((
% 89.40/26.97 (ex1I2) =>
% 89.40/26.97 ((
% 89.40/26.97 (singletonsuniq) =>
% 89.40/26.97 ((
% 89.40/26.97 (setukpairinjL1) =>
% 89.40/26.97 ((
% 89.40/26.97 (kfstsingleton) =>
% 89.40/26.97 ((
% 89.40/26.97 (theprop) =>
% 89.40/26.97 ((
% 89.40/26.97 (kfstpairEq) =>
% 89.40/26.97 ((
% 89.40/26.97 (cartprodfstin) =>
% 89.40/26.97 ((
% 89.40/26.97 (setukpairinjL2) =>
% 89.40/26.97 ((
% 89.40/26.97 (setukpairinjL) =>
% 89.40/26.97 ((
% 89.40/26.97 (setukpairinjR11) =>
% 89.40/26.97 ((
% 89.40/26.97 (setukpairinjR12) =>
% 89.40/26.97 ((
% 89.40/26.97 (setukpairinjR1) =>
% 89.40/26.97 ((
% 89.40/26.97 (upairequniteq) =>
% 89.40/26.97 ((
% 89.40/26.97 (setukpairinjR2) =>
% 89.40/26.97 ((
% 89.40/26.97 (setukpairinjR) =>
% 89.40/26.97 ((
% 89.40/26.97 (ksndsingleton) =>
% 89.40/26.97 ((
% 89.40/26.97 (ksndpairEq) =>
% 89.40/26.97 ((
% 89.40/26.97 (kpairsurjEq) =>
% 89.40/26.97 ((
% 89.40/26.97 (cartprodsndin) =>
% 89.40/26.97 ((
% 89.40/26.97 (cartprodpairmemEL) =>
% 89.40/26.97 ((
% 89.40/26.97 (cartprodpairmemER) =>
% 89.40/26.97 ((
% 89.40/26.97 (cartprodmempaircEq) =>
% 89.40/26.97 ((
% 89.40/26.97 (cartprodfstpairEq) =>
% 89.40/26.97 ((
% 89.40/26.97 (cartprodsndpairEq) =>
% 89.40/26.97 ((
% 89.40/26.97 (cartprodpairsurjEq) =>
% 89.40/26.97 ((
% 89.40/26.97 (dpsetconstrI) =>
% 89.40/26.97 ((
% 89.40/26.97 (dpsetconstrSub) =>
% 89.40/26.97 ((
% 89.40/26.97 (setOfPairsIsBReln) =>
% 89.40/26.97 ((
% 89.40/26.97 (dpsetconstrERa) =>
% 89.40/26.97 ((
% 89.40/26.97 (dpsetconstrEL1) =>
% 89.40/26.97 ((
% 89.40/26.97 (dpsetconstrEL2) =>
% 89.40/26.97 ((
% 89.40/26.97 (dpsetconstrER) =>
% 89.40/26.97 ((
% 89.40/26.97 (funcImageSingleton) =>
% 89.40/26.97 ((
% 89.40/26.97 (apProp) =>
% 89.40/26.97 ((
% 89.40/26.97 (app) =>
% 89.40/26.97 ((
% 89.40/26.97 (infuncsetfunc) =>
% 89.40/26.97 ((
% 89.40/26.97 (ap2p) =>
% 89.40/26.97 ((
% 89.40/26.97 (funcinfuncset) =>
% 89.40/26.97 ((
% 89.40/26.97 (lamProp) =>
% 89.40/26.97 ((
% 89.40/26.97 (lamp) =>
% 89.40/26.97 ((
% 89.40/26.97 (lam2p) =>
% 89.40/26.97 ((
% 89.40/26.97 (brelnall1) =>
% 89.40/26.97 ((
% 89.40/26.97 (brelnall2) =>
% 89.40/26.97 ((
% 89.40/26.97 (!!) @ (
% 89.40/26.97 (('#B') @ (
% 89.40/26.97 !!) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#S') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#S') @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 =>))) @
% 89.40/26.97 ex1)))) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 !!))) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#S') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#B') @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#S') @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 =>))) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#C') @ in)))))))) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 !!))))) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#C') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#B') @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#B') @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#S') @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 =>))) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#C') @ in)))))))))) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#S') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#S') @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#B'))) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 =>))))))) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#C') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#B') @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#S') @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 =>))))))) @
% 89.40/26.97 (
% 89.40/26.97 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.40/26.97 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1255])).
% 89.40/26.97 thf(zip_derived_cl1272, plain,
% 89.40/26.97 (~ (((setminusSubset2) =>
% 89.40/26.97 (((setminusERneg) =>
% 89.40/26.97 (((setminusELneg) =>
% 89.40/26.97 (((setminusILneg) =>
% 89.40/26.97 (((setminusIRneg) =>
% 89.40/26.97 (((setminusLsub) =>
% 89.40/26.97 (((setminusSubset1) =>
% 89.40/26.97 (((symdiffE) =>
% 89.40/26.97 (((symdiffI1) =>
% 89.40/26.97 (((symdiffI2) =>
% 89.40/26.97 (((symdiffIneg1) =>
% 89.40/26.97 (((symdiffIneg2) =>
% 89.40/26.97 (((secondinupair) =>
% 89.40/26.97 (((setukpairIL) =>
% 89.40/26.97 (((setukpairIR) =>
% 89.40/26.97 (((kpairiskpair) =>
% 89.40/26.97 (((kpairp) =>
% 89.40/26.97 (((singletonsubset) =>
% 89.40/26.97 (((singletoninpowerset) =>
% 89.40/26.97 (((singletoninpowunion) =>
% 89.40/26.97 (((upairset2E) =>
% 89.40/26.97 (((upairsubunion) =>
% 89.40/26.97 (((upairinpowunion) =>
% 89.40/26.97 (((ubforcartprodlem1) =>
% 89.40/26.97 (((ubforcartprodlem2) =>
% 89.40/26.97 (((ubforcartprodlem3) =>
% 89.40/26.97 (((cartprodpairin) =>
% 89.40/26.97 (((cartprodmempair1) =>
% 89.40/26.97 (((cartprodmempair) =>
% 89.40/26.97 (((setunionE2) =>
% 89.40/26.97 ((
% 89.40/26.97 (setunionsingleton1) =>
% 89.40/26.97 ((
% 89.40/26.97 (setunionsingleton2) =>
% 89.40/26.97 ((
% 89.40/26.97 (setunionsingleton) =>
% 89.40/26.97 ((
% 89.40/26.97 (singletonprop) =>
% 89.40/26.97 ((
% 89.40/26.97 (ex1E1) =>
% 89.40/26.97 ((
% 89.40/26.97 (ex1I) =>
% 89.40/26.97 ((
% 89.40/26.97 (ex1I2) =>
% 89.40/26.97 ((
% 89.40/26.97 (singletonsuniq) =>
% 89.40/26.97 ((
% 89.40/26.97 (setukpairinjL1) =>
% 89.40/26.97 ((
% 89.40/26.97 (kfstsingleton) =>
% 89.40/26.97 ((
% 89.40/26.97 (theprop) =>
% 89.40/26.97 ((
% 89.40/26.97 (kfstpairEq) =>
% 89.40/26.97 ((
% 89.40/26.97 (cartprodfstin) =>
% 89.40/26.97 ((
% 89.40/26.97 (setukpairinjL2) =>
% 89.40/26.97 ((
% 89.40/26.97 (setukpairinjL) =>
% 89.40/26.97 ((
% 89.40/26.97 (setukpairinjR11) =>
% 89.40/26.97 ((
% 89.40/26.97 (setukpairinjR12) =>
% 89.40/26.97 ((
% 89.40/26.97 (setukpairinjR1) =>
% 89.40/26.97 ((
% 89.40/26.97 (upairequniteq) =>
% 89.40/26.97 ((
% 89.40/26.97 (setukpairinjR2) =>
% 89.40/26.97 ((
% 89.40/26.97 (setukpairinjR) =>
% 89.40/26.97 ((
% 89.40/26.97 (ksndsingleton) =>
% 89.40/26.97 ((
% 89.40/26.97 (ksndpairEq) =>
% 89.40/26.97 ((
% 89.40/26.97 (kpairsurjEq) =>
% 89.40/26.97 ((
% 89.40/26.97 (cartprodsndin) =>
% 89.40/26.97 ((
% 89.40/26.97 (cartprodpairmemEL) =>
% 89.40/26.97 ((
% 89.40/26.97 (cartprodpairmemER) =>
% 89.40/26.97 ((
% 89.40/26.97 (cartprodmempaircEq) =>
% 89.40/26.97 ((
% 89.40/26.97 (cartprodfstpairEq) =>
% 89.40/26.97 ((
% 89.40/26.97 (cartprodsndpairEq) =>
% 89.40/26.97 ((
% 89.40/26.97 (cartprodpairsurjEq) =>
% 89.40/26.97 ((
% 89.40/26.97 (dpsetconstrI) =>
% 89.40/26.97 ((
% 89.40/26.97 (dpsetconstrSub) =>
% 89.40/26.97 ((
% 89.40/26.97 (setOfPairsIsBReln) =>
% 89.40/26.97 ((
% 89.40/26.97 (dpsetconstrERa) =>
% 89.40/26.97 ((
% 89.40/26.97 (dpsetconstrEL1) =>
% 89.40/26.97 ((
% 89.40/26.97 (dpsetconstrEL2) =>
% 89.40/26.97 ((
% 89.40/26.97 (dpsetconstrER) =>
% 89.40/26.97 ((
% 89.40/26.97 (funcImageSingleton) =>
% 89.40/26.97 ((
% 89.40/26.97 (apProp) =>
% 89.40/26.97 ((
% 89.40/26.97 (app) =>
% 89.40/26.97 ((
% 89.40/26.97 (infuncsetfunc) =>
% 89.40/26.97 ((
% 89.40/26.97 (ap2p) =>
% 89.40/26.97 ((
% 89.40/26.97 (funcinfuncset) =>
% 89.40/26.97 ((
% 89.40/26.97 (lamProp) =>
% 89.40/26.97 ((
% 89.40/26.97 (lamp) =>
% 89.40/26.97 ((
% 89.40/26.97 (lam2p) =>
% 89.40/26.97 ((
% 89.40/26.97 (brelnall1) =>
% 89.40/26.97 ((
% 89.40/26.97 (brelnall2) =>
% 89.40/26.97 ((
% 89.40/26.97 (!!) @ (
% 89.40/26.97 (('#B') @ (
% 89.40/26.97 !!) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#S') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#S') @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 =>))) @
% 89.40/26.97 ex1)))) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 !!))) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#S') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#B') @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#S') @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 =>))) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#C') @ in)))))))) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 !!))))) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#C') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#B') @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#B') @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#S') @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 =>))) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#C') @ in)))))))))) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#S') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#S') @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#B'))) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 =>))))))) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#C') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#B') @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#S') @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 =>))))))) @
% 89.40/26.97 (
% 89.40/26.97 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.40/26.97 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1264])).
% 89.40/26.97 thf(zip_derived_cl1280, plain,
% 89.40/26.97 (~ (((setminusERneg) =>
% 89.40/26.97 (((setminusELneg) =>
% 89.40/26.97 (((setminusILneg) =>
% 89.40/26.97 (((setminusIRneg) =>
% 89.40/26.97 (((setminusLsub) =>
% 89.40/26.97 (((setminusSubset1) =>
% 89.40/26.97 (((symdiffE) =>
% 89.40/26.97 (((symdiffI1) =>
% 89.40/26.97 (((symdiffI2) =>
% 89.40/26.97 (((symdiffIneg1) =>
% 89.40/26.97 (((symdiffIneg2) =>
% 89.40/26.97 (((secondinupair) =>
% 89.40/26.97 (((setukpairIL) =>
% 89.40/26.97 (((setukpairIR) =>
% 89.40/26.97 (((kpairiskpair) =>
% 89.40/26.97 (((kpairp) =>
% 89.40/26.97 (((singletonsubset) =>
% 89.40/26.97 (((singletoninpowerset) =>
% 89.40/26.97 (((singletoninpowunion) =>
% 89.40/26.97 (((upairset2E) =>
% 89.40/26.97 (((upairsubunion) =>
% 89.40/26.97 (((upairinpowunion) =>
% 89.40/26.97 (((ubforcartprodlem1) =>
% 89.40/26.97 (((ubforcartprodlem2) =>
% 89.40/26.97 (((ubforcartprodlem3) =>
% 89.40/26.97 (((cartprodpairin) =>
% 89.40/26.97 (((cartprodmempair1) =>
% 89.40/26.97 (((cartprodmempair) =>
% 89.40/26.97 (((setunionE2) =>
% 89.40/26.97 (((setunionsingleton1) =>
% 89.40/26.97 ((
% 89.40/26.97 (setunionsingleton2) =>
% 89.40/26.97 ((
% 89.40/26.97 (setunionsingleton) =>
% 89.40/26.97 ((
% 89.40/26.97 (singletonprop) =>
% 89.40/26.97 ((
% 89.40/26.97 (ex1E1) =>
% 89.40/26.97 ((
% 89.40/26.97 (ex1I) =>
% 89.40/26.97 ((
% 89.40/26.97 (ex1I2) =>
% 89.40/26.97 ((
% 89.40/26.97 (singletonsuniq) =>
% 89.40/26.97 ((
% 89.40/26.97 (setukpairinjL1) =>
% 89.40/26.97 ((
% 89.40/26.97 (kfstsingleton) =>
% 89.40/26.97 ((
% 89.40/26.97 (theprop) =>
% 89.40/26.97 ((
% 89.40/26.97 (kfstpairEq) =>
% 89.40/26.97 ((
% 89.40/26.97 (cartprodfstin) =>
% 89.40/26.97 ((
% 89.40/26.97 (setukpairinjL2) =>
% 89.40/26.97 ((
% 89.40/26.97 (setukpairinjL) =>
% 89.40/26.97 ((
% 89.40/26.97 (setukpairinjR11) =>
% 89.40/26.97 ((
% 89.40/26.97 (setukpairinjR12) =>
% 89.40/26.97 ((
% 89.40/26.97 (setukpairinjR1) =>
% 89.40/26.97 ((
% 89.40/26.97 (upairequniteq) =>
% 89.40/26.97 ((
% 89.40/26.97 (setukpairinjR2) =>
% 89.40/26.97 ((
% 89.40/26.97 (setukpairinjR) =>
% 89.40/26.97 ((
% 89.40/26.97 (ksndsingleton) =>
% 89.40/26.97 ((
% 89.40/26.97 (ksndpairEq) =>
% 89.40/26.97 ((
% 89.40/26.97 (kpairsurjEq) =>
% 89.40/26.97 ((
% 89.40/26.97 (cartprodsndin) =>
% 89.40/26.97 ((
% 89.40/26.97 (cartprodpairmemEL) =>
% 89.40/26.97 ((
% 89.40/26.97 (cartprodpairmemER) =>
% 89.40/26.97 ((
% 89.40/26.97 (cartprodmempaircEq) =>
% 89.40/26.97 ((
% 89.40/26.97 (cartprodfstpairEq) =>
% 89.40/26.97 ((
% 89.40/26.97 (cartprodsndpairEq) =>
% 89.40/26.97 ((
% 89.40/26.97 (cartprodpairsurjEq) =>
% 89.40/26.97 ((
% 89.40/26.97 (dpsetconstrI) =>
% 89.40/26.97 ((
% 89.40/26.97 (dpsetconstrSub) =>
% 89.40/26.97 ((
% 89.40/26.97 (setOfPairsIsBReln) =>
% 89.40/26.97 ((
% 89.40/26.97 (dpsetconstrERa) =>
% 89.40/26.97 ((
% 89.40/26.97 (dpsetconstrEL1) =>
% 89.40/26.97 ((
% 89.40/26.97 (dpsetconstrEL2) =>
% 89.40/26.97 ((
% 89.40/26.97 (dpsetconstrER) =>
% 89.40/26.97 ((
% 89.40/26.97 (funcImageSingleton) =>
% 89.40/26.97 ((
% 89.40/26.97 (apProp) =>
% 89.40/26.97 ((
% 89.40/26.97 (app) =>
% 89.40/26.97 ((
% 89.40/26.97 (infuncsetfunc) =>
% 89.40/26.97 ((
% 89.40/26.97 (ap2p) =>
% 89.40/26.97 ((
% 89.40/26.97 (funcinfuncset) =>
% 89.40/26.97 ((
% 89.40/26.97 (lamProp) =>
% 89.40/26.97 ((
% 89.40/26.97 (lamp) =>
% 89.40/26.97 ((
% 89.40/26.97 (lam2p) =>
% 89.40/26.97 ((
% 89.40/26.97 (brelnall1) =>
% 89.40/26.97 ((
% 89.40/26.97 (brelnall2) =>
% 89.40/26.97 ((
% 89.40/26.97 (!!) @ (
% 89.40/26.97 (('#B') @ (
% 89.40/26.97 !!) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#S') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#S') @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 =>))) @
% 89.40/26.97 ex1)))) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 !!))) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#S') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#B') @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#S') @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 =>))) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#C') @ in)))))))) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 !!))))) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#C') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#B') @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#B') @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#S') @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 =>))) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#C') @ in)))))))))) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#S') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#S') @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#B'))) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 =>))))))) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#C') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#B') @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#S') @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 =>))))))) @
% 89.40/26.97 (
% 89.40/26.97 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.40/26.97 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1272])).
% 89.40/26.97 thf(zip_derived_cl1288, plain,
% 89.40/26.97 (~ (((setminusELneg) =>
% 89.40/26.97 (((setminusILneg) =>
% 89.40/26.97 (((setminusIRneg) =>
% 89.40/26.97 (((setminusLsub) =>
% 89.40/26.97 (((setminusSubset1) =>
% 89.40/26.97 (((symdiffE) =>
% 89.40/26.97 (((symdiffI1) =>
% 89.40/26.97 (((symdiffI2) =>
% 89.40/26.97 (((symdiffIneg1) =>
% 89.40/26.97 (((symdiffIneg2) =>
% 89.40/26.97 (((secondinupair) =>
% 89.40/26.97 (((setukpairIL) =>
% 89.40/26.97 (((setukpairIR) =>
% 89.40/26.97 (((kpairiskpair) =>
% 89.40/26.97 (((kpairp) =>
% 89.40/26.97 (((singletonsubset) =>
% 89.40/26.97 (((singletoninpowerset) =>
% 89.40/26.97 (((singletoninpowunion) =>
% 89.40/26.97 (((upairset2E) =>
% 89.40/26.97 (((upairsubunion) =>
% 89.40/26.97 (((upairinpowunion) =>
% 89.40/26.97 (((ubforcartprodlem1) =>
% 89.40/26.97 (((ubforcartprodlem2) =>
% 89.40/26.97 (((ubforcartprodlem3) =>
% 89.40/26.97 (((cartprodpairin) =>
% 89.40/26.97 (((cartprodmempair1) =>
% 89.40/26.97 (((cartprodmempair) =>
% 89.40/26.97 (((setunionE2) =>
% 89.40/26.97 (((setunionsingleton1) =>
% 89.40/26.97 (((setunionsingleton2) =>
% 89.40/26.97 ((
% 89.40/26.97 (setunionsingleton) =>
% 89.40/26.97 ((
% 89.40/26.97 (singletonprop) =>
% 89.40/26.97 ((
% 89.40/26.97 (ex1E1) =>
% 89.40/26.97 ((
% 89.40/26.97 (ex1I) =>
% 89.40/26.97 ((
% 89.40/26.97 (ex1I2) =>
% 89.40/26.97 ((
% 89.40/26.97 (singletonsuniq) =>
% 89.40/26.97 ((
% 89.40/26.97 (setukpairinjL1) =>
% 89.40/26.97 ((
% 89.40/26.97 (kfstsingleton) =>
% 89.40/26.97 ((
% 89.40/26.97 (theprop) =>
% 89.40/26.97 ((
% 89.40/26.97 (kfstpairEq) =>
% 89.40/26.97 ((
% 89.40/26.97 (cartprodfstin) =>
% 89.40/26.97 ((
% 89.40/26.97 (setukpairinjL2) =>
% 89.40/26.97 ((
% 89.40/26.97 (setukpairinjL) =>
% 89.40/26.97 ((
% 89.40/26.97 (setukpairinjR11) =>
% 89.40/26.97 ((
% 89.40/26.97 (setukpairinjR12) =>
% 89.40/26.97 ((
% 89.40/26.97 (setukpairinjR1) =>
% 89.40/26.97 ((
% 89.40/26.97 (upairequniteq) =>
% 89.40/26.97 ((
% 89.40/26.97 (setukpairinjR2) =>
% 89.40/26.97 ((
% 89.40/26.97 (setukpairinjR) =>
% 89.40/26.97 ((
% 89.40/26.97 (ksndsingleton) =>
% 89.40/26.97 ((
% 89.40/26.97 (ksndpairEq) =>
% 89.40/26.97 ((
% 89.40/26.97 (kpairsurjEq) =>
% 89.40/26.97 ((
% 89.40/26.97 (cartprodsndin) =>
% 89.40/26.97 ((
% 89.40/26.97 (cartprodpairmemEL) =>
% 89.40/26.97 ((
% 89.40/26.97 (cartprodpairmemER) =>
% 89.40/26.97 ((
% 89.40/26.97 (cartprodmempaircEq) =>
% 89.40/26.97 ((
% 89.40/26.97 (cartprodfstpairEq) =>
% 89.40/26.97 ((
% 89.40/26.97 (cartprodsndpairEq) =>
% 89.40/26.97 ((
% 89.40/26.97 (cartprodpairsurjEq) =>
% 89.40/26.97 ((
% 89.40/26.97 (dpsetconstrI) =>
% 89.40/26.97 ((
% 89.40/26.97 (dpsetconstrSub) =>
% 89.40/26.97 ((
% 89.40/26.97 (setOfPairsIsBReln) =>
% 89.40/26.97 ((
% 89.40/26.97 (dpsetconstrERa) =>
% 89.40/26.97 ((
% 89.40/26.97 (dpsetconstrEL1) =>
% 89.40/26.97 ((
% 89.40/26.97 (dpsetconstrEL2) =>
% 89.40/26.97 ((
% 89.40/26.97 (dpsetconstrER) =>
% 89.40/26.97 ((
% 89.40/26.97 (funcImageSingleton) =>
% 89.40/26.97 ((
% 89.40/26.97 (apProp) =>
% 89.40/26.97 ((
% 89.40/26.97 (app) =>
% 89.40/26.97 ((
% 89.40/26.97 (infuncsetfunc) =>
% 89.40/26.97 ((
% 89.40/26.97 (ap2p) =>
% 89.40/26.97 ((
% 89.40/26.97 (funcinfuncset) =>
% 89.40/26.97 ((
% 89.40/26.97 (lamProp) =>
% 89.40/26.97 ((
% 89.40/26.97 (lamp) =>
% 89.40/26.97 ((
% 89.40/26.97 (lam2p) =>
% 89.40/26.97 ((
% 89.40/26.97 (brelnall1) =>
% 89.40/26.97 ((
% 89.40/26.97 (brelnall2) =>
% 89.40/26.97 ((
% 89.40/26.97 (!!) @ (
% 89.40/26.97 (('#B') @ (
% 89.40/26.97 !!) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#S') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#S') @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 =>))) @
% 89.40/26.97 ex1)))) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 !!))) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#S') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#B') @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#S') @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 =>))) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#C') @ in)))))))) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 !!))))) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#C') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#B') @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#B') @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#S') @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 =>))) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#C') @ in)))))))))) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#S') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#S') @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#B'))) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 =>))))))) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#C') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#B') @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#S') @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 =>))))))) @
% 89.40/26.97 (
% 89.40/26.97 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.40/26.97 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1280])).
% 89.40/26.97 thf(zip_derived_cl1296, plain,
% 89.40/26.97 (~ (((setminusILneg) =>
% 89.40/26.97 (((setminusIRneg) =>
% 89.40/26.97 (((setminusLsub) =>
% 89.40/26.97 (((setminusSubset1) =>
% 89.40/26.97 (((symdiffE) =>
% 89.40/26.97 (((symdiffI1) =>
% 89.40/26.97 (((symdiffI2) =>
% 89.40/26.97 (((symdiffIneg1) =>
% 89.40/26.97 (((symdiffIneg2) =>
% 89.40/26.97 (((secondinupair) =>
% 89.40/26.97 (((setukpairIL) =>
% 89.40/26.97 (((setukpairIR) =>
% 89.40/26.97 (((kpairiskpair) =>
% 89.40/26.97 (((kpairp) =>
% 89.40/26.97 (((singletonsubset) =>
% 89.40/26.97 (((singletoninpowerset) =>
% 89.40/26.97 (((singletoninpowunion) =>
% 89.40/26.97 (((upairset2E) =>
% 89.40/26.97 (((upairsubunion) =>
% 89.40/26.97 (((upairinpowunion) =>
% 89.40/26.97 (((ubforcartprodlem1) =>
% 89.40/26.97 (((ubforcartprodlem2) =>
% 89.40/26.97 (((ubforcartprodlem3) =>
% 89.40/26.97 (((cartprodpairin) =>
% 89.40/26.97 (((cartprodmempair1) =>
% 89.40/26.97 (((cartprodmempair) =>
% 89.40/26.97 (((setunionE2) =>
% 89.40/26.97 (((setunionsingleton1) =>
% 89.40/26.97 (((setunionsingleton2) =>
% 89.40/26.97 (((setunionsingleton) =>
% 89.40/26.97 ((
% 89.40/26.97 (singletonprop) =>
% 89.40/26.97 ((
% 89.40/26.97 (ex1E1) =>
% 89.40/26.97 ((
% 89.40/26.97 (ex1I) =>
% 89.40/26.97 ((
% 89.40/26.97 (ex1I2) =>
% 89.40/26.97 ((
% 89.40/26.97 (singletonsuniq) =>
% 89.40/26.97 ((
% 89.40/26.97 (setukpairinjL1) =>
% 89.40/26.97 ((
% 89.40/26.97 (kfstsingleton) =>
% 89.40/26.97 ((
% 89.40/26.97 (theprop) =>
% 89.40/26.97 ((
% 89.40/26.97 (kfstpairEq) =>
% 89.40/26.97 ((
% 89.40/26.97 (cartprodfstin) =>
% 89.40/26.97 ((
% 89.40/26.97 (setukpairinjL2) =>
% 89.40/26.97 ((
% 89.40/26.97 (setukpairinjL) =>
% 89.40/26.97 ((
% 89.40/26.97 (setukpairinjR11) =>
% 89.40/26.97 ((
% 89.40/26.97 (setukpairinjR12) =>
% 89.40/26.97 ((
% 89.40/26.97 (setukpairinjR1) =>
% 89.40/26.97 ((
% 89.40/26.97 (upairequniteq) =>
% 89.40/26.97 ((
% 89.40/26.97 (setukpairinjR2) =>
% 89.40/26.97 ((
% 89.40/26.97 (setukpairinjR) =>
% 89.40/26.97 ((
% 89.40/26.97 (ksndsingleton) =>
% 89.40/26.97 ((
% 89.40/26.97 (ksndpairEq) =>
% 89.40/26.97 ((
% 89.40/26.97 (kpairsurjEq) =>
% 89.40/26.97 ((
% 89.40/26.97 (cartprodsndin) =>
% 89.40/26.97 ((
% 89.40/26.97 (cartprodpairmemEL) =>
% 89.40/26.97 ((
% 89.40/26.97 (cartprodpairmemER) =>
% 89.40/26.97 ((
% 89.40/26.97 (cartprodmempaircEq) =>
% 89.40/26.97 ((
% 89.40/26.97 (cartprodfstpairEq) =>
% 89.40/26.97 ((
% 89.40/26.97 (cartprodsndpairEq) =>
% 89.40/26.97 ((
% 89.40/26.97 (cartprodpairsurjEq) =>
% 89.40/26.97 ((
% 89.40/26.97 (dpsetconstrI) =>
% 89.40/26.97 ((
% 89.40/26.97 (dpsetconstrSub) =>
% 89.40/26.97 ((
% 89.40/26.97 (setOfPairsIsBReln) =>
% 89.40/26.97 ((
% 89.40/26.97 (dpsetconstrERa) =>
% 89.40/26.97 ((
% 89.40/26.97 (dpsetconstrEL1) =>
% 89.40/26.97 ((
% 89.40/26.97 (dpsetconstrEL2) =>
% 89.40/26.97 ((
% 89.40/26.97 (dpsetconstrER) =>
% 89.40/26.97 ((
% 89.40/26.97 (funcImageSingleton) =>
% 89.40/26.97 ((
% 89.40/26.97 (apProp) =>
% 89.40/26.97 ((
% 89.40/26.97 (app) =>
% 89.40/26.97 ((
% 89.40/26.97 (infuncsetfunc) =>
% 89.40/26.97 ((
% 89.40/26.97 (ap2p) =>
% 89.40/26.97 ((
% 89.40/26.97 (funcinfuncset) =>
% 89.40/26.97 ((
% 89.40/26.97 (lamProp) =>
% 89.40/26.97 ((
% 89.40/26.97 (lamp) =>
% 89.40/26.97 ((
% 89.40/26.97 (lam2p) =>
% 89.40/26.97 ((
% 89.40/26.97 (brelnall1) =>
% 89.40/26.97 ((
% 89.40/26.97 (brelnall2) =>
% 89.40/26.97 ((
% 89.40/26.97 (!!) @ (
% 89.40/26.97 (('#B') @ (
% 89.40/26.97 !!) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#S') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#S') @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 =>))) @
% 89.40/26.97 ex1)))) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 !!))) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#S') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#B') @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#S') @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 =>))) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#C') @ in)))))))) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 !!))))) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#C') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#B') @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#B') @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#S') @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 =>))) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#C') @ in)))))))))) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#S') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#S') @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#B'))) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 =>))))))) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#C') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#B') @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#S') @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 =>))))))) @
% 89.40/26.97 (
% 89.40/26.97 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.40/26.97 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1288])).
% 89.40/26.97 thf(zip_derived_cl1305, plain,
% 89.40/26.97 (~ (((setminusIRneg) =>
% 89.40/26.97 (((setminusLsub) =>
% 89.40/26.97 (((setminusSubset1) =>
% 89.40/26.97 (((symdiffE) =>
% 89.40/26.97 (((symdiffI1) =>
% 89.40/26.97 (((symdiffI2) =>
% 89.40/26.97 (((symdiffIneg1) =>
% 89.40/26.97 (((symdiffIneg2) =>
% 89.40/26.97 (((secondinupair) =>
% 89.40/26.97 (((setukpairIL) =>
% 89.40/26.97 (((setukpairIR) =>
% 89.40/26.97 (((kpairiskpair) =>
% 89.40/26.97 (((kpairp) =>
% 89.40/26.97 (((singletonsubset) =>
% 89.40/26.97 (((singletoninpowerset) =>
% 89.40/26.97 (((singletoninpowunion) =>
% 89.40/26.97 (((upairset2E) =>
% 89.40/26.97 (((upairsubunion) =>
% 89.40/26.97 (((upairinpowunion) =>
% 89.40/26.97 (((ubforcartprodlem1) =>
% 89.40/26.97 (((ubforcartprodlem2) =>
% 89.40/26.97 (((ubforcartprodlem3) =>
% 89.40/26.97 (((cartprodpairin) =>
% 89.40/26.97 (((cartprodmempair1) =>
% 89.40/26.97 (((cartprodmempair) =>
% 89.40/26.97 (((setunionE2) =>
% 89.40/26.97 (((setunionsingleton1) =>
% 89.40/26.97 (((setunionsingleton2) =>
% 89.40/26.97 (((setunionsingleton) =>
% 89.40/26.97 (((singletonprop) =>
% 89.40/26.97 ((
% 89.40/26.97 (ex1E1) =>
% 89.40/26.97 ((
% 89.40/26.97 (ex1I) =>
% 89.40/26.97 ((
% 89.40/26.97 (ex1I2) =>
% 89.40/26.97 ((
% 89.40/26.97 (singletonsuniq) =>
% 89.40/26.97 ((
% 89.40/26.97 (setukpairinjL1) =>
% 89.40/26.97 ((
% 89.40/26.97 (kfstsingleton) =>
% 89.40/26.97 ((
% 89.40/26.97 (theprop) =>
% 89.40/26.97 ((
% 89.40/26.97 (kfstpairEq) =>
% 89.40/26.97 ((
% 89.40/26.97 (cartprodfstin) =>
% 89.40/26.97 ((
% 89.40/26.97 (setukpairinjL2) =>
% 89.40/26.97 ((
% 89.40/26.97 (setukpairinjL) =>
% 89.40/26.97 ((
% 89.40/26.97 (setukpairinjR11) =>
% 89.40/26.97 ((
% 89.40/26.97 (setukpairinjR12) =>
% 89.40/26.97 ((
% 89.40/26.97 (setukpairinjR1) =>
% 89.40/26.97 ((
% 89.40/26.97 (upairequniteq) =>
% 89.40/26.97 ((
% 89.40/26.97 (setukpairinjR2) =>
% 89.40/26.97 ((
% 89.40/26.97 (setukpairinjR) =>
% 89.40/26.97 ((
% 89.40/26.97 (ksndsingleton) =>
% 89.40/26.97 ((
% 89.40/26.97 (ksndpairEq) =>
% 89.40/26.97 ((
% 89.40/26.97 (kpairsurjEq) =>
% 89.40/26.97 ((
% 89.40/26.97 (cartprodsndin) =>
% 89.40/26.97 ((
% 89.40/26.97 (cartprodpairmemEL) =>
% 89.40/26.97 ((
% 89.40/26.97 (cartprodpairmemER) =>
% 89.40/26.97 ((
% 89.40/26.97 (cartprodmempaircEq) =>
% 89.40/26.97 ((
% 89.40/26.97 (cartprodfstpairEq) =>
% 89.40/26.97 ((
% 89.40/26.97 (cartprodsndpairEq) =>
% 89.40/26.97 ((
% 89.40/26.97 (cartprodpairsurjEq) =>
% 89.40/26.97 ((
% 89.40/26.97 (dpsetconstrI) =>
% 89.40/26.97 ((
% 89.40/26.97 (dpsetconstrSub) =>
% 89.40/26.97 ((
% 89.40/26.97 (setOfPairsIsBReln) =>
% 89.40/26.97 ((
% 89.40/26.97 (dpsetconstrERa) =>
% 89.40/26.97 ((
% 89.40/26.97 (dpsetconstrEL1) =>
% 89.40/26.97 ((
% 89.40/26.97 (dpsetconstrEL2) =>
% 89.40/26.97 ((
% 89.40/26.97 (dpsetconstrER) =>
% 89.40/26.97 ((
% 89.40/26.97 (funcImageSingleton) =>
% 89.40/26.97 ((
% 89.40/26.97 (apProp) =>
% 89.40/26.97 ((
% 89.40/26.97 (app) =>
% 89.40/26.97 ((
% 89.40/26.97 (infuncsetfunc) =>
% 89.40/26.97 ((
% 89.40/26.97 (ap2p) =>
% 89.40/26.97 ((
% 89.40/26.97 (funcinfuncset) =>
% 89.40/26.97 ((
% 89.40/26.97 (lamProp) =>
% 89.40/26.97 ((
% 89.40/26.97 (lamp) =>
% 89.40/26.97 ((
% 89.40/26.97 (lam2p) =>
% 89.40/26.97 ((
% 89.40/26.97 (brelnall1) =>
% 89.40/26.97 ((
% 89.40/26.97 (brelnall2) =>
% 89.40/26.97 ((
% 89.40/26.97 (!!) @ (
% 89.40/26.97 (('#B') @ (
% 89.40/26.97 !!) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#S') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#S') @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 =>))) @
% 89.40/26.97 ex1)))) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 !!))) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#S') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#B') @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#S') @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 =>))) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#C') @ in)))))))) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 !!))))) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#C') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#B') @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#B') @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#S') @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 =>))) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#C') @ in)))))))))) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#S') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#S') @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#B'))) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 =>))))))) @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#C') @ (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#B') @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.40/26.97 '#S') @
% 89.40/26.97 (
% 89.40/26.97 (
% 89.40/26.97 ('#B') @ (
% 89.45/26.97 =>))))))) @
% 89.45/26.97 (
% 89.45/26.97 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.45/26.97 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1296])).
% 89.45/26.97 thf(zip_derived_cl1313, plain,
% 89.45/26.97 (~ (((setminusLsub) =>
% 89.45/26.97 (((setminusSubset1) =>
% 89.45/26.97 (((symdiffE) =>
% 89.45/26.97 (((symdiffI1) =>
% 89.45/26.97 (((symdiffI2) =>
% 89.45/26.97 (((symdiffIneg1) =>
% 89.45/26.97 (((symdiffIneg2) =>
% 89.45/26.97 (((secondinupair) =>
% 89.45/26.97 (((setukpairIL) =>
% 89.45/26.97 (((setukpairIR) =>
% 89.45/26.97 (((kpairiskpair) =>
% 89.45/26.97 (((kpairp) =>
% 89.45/26.97 (((singletonsubset) =>
% 89.45/26.97 (((singletoninpowerset) =>
% 89.45/26.97 (((singletoninpowunion) =>
% 89.45/26.97 (((upairset2E) =>
% 89.45/26.97 (((upairsubunion) =>
% 89.45/26.97 (((upairinpowunion) =>
% 89.45/26.97 (((ubforcartprodlem1) =>
% 89.45/26.97 (((ubforcartprodlem2) =>
% 89.45/26.97 (((ubforcartprodlem3) =>
% 89.45/26.97 (((cartprodpairin) =>
% 89.45/26.97 (((cartprodmempair1) =>
% 89.45/26.97 (((cartprodmempair) =>
% 89.45/26.97 (((setunionE2) =>
% 89.45/26.97 (((setunionsingleton1) =>
% 89.45/26.97 (((setunionsingleton2) =>
% 89.45/26.97 (((setunionsingleton) =>
% 89.45/26.97 (((singletonprop) =>
% 89.45/26.97 (((ex1E1) =>
% 89.45/26.97 ((
% 89.45/26.97 (ex1I) =>
% 89.45/26.97 ((
% 89.45/26.97 (ex1I2) =>
% 89.45/26.97 ((
% 89.45/26.97 (singletonsuniq) =>
% 89.45/26.97 ((
% 89.45/26.97 (setukpairinjL1) =>
% 89.45/26.97 ((
% 89.45/26.97 (kfstsingleton) =>
% 89.45/26.97 ((
% 89.45/26.97 (theprop) =>
% 89.45/26.97 ((
% 89.45/26.97 (kfstpairEq) =>
% 89.45/26.97 ((
% 89.45/26.97 (cartprodfstin) =>
% 89.45/26.97 ((
% 89.45/26.97 (setukpairinjL2) =>
% 89.45/26.97 ((
% 89.45/26.97 (setukpairinjL) =>
% 89.45/26.97 ((
% 89.45/26.97 (setukpairinjR11) =>
% 89.45/26.97 ((
% 89.45/26.97 (setukpairinjR12) =>
% 89.45/26.97 ((
% 89.45/26.97 (setukpairinjR1) =>
% 89.45/26.97 ((
% 89.45/26.97 (upairequniteq) =>
% 89.45/26.97 ((
% 89.45/26.97 (setukpairinjR2) =>
% 89.45/26.97 ((
% 89.45/26.97 (setukpairinjR) =>
% 89.45/26.97 ((
% 89.45/26.97 (ksndsingleton) =>
% 89.45/26.97 ((
% 89.45/26.97 (ksndpairEq) =>
% 89.45/26.97 ((
% 89.45/26.97 (kpairsurjEq) =>
% 89.45/26.97 ((
% 89.45/26.97 (cartprodsndin) =>
% 89.45/26.97 ((
% 89.45/26.97 (cartprodpairmemEL) =>
% 89.45/26.97 ((
% 89.45/26.97 (cartprodpairmemER) =>
% 89.45/26.97 ((
% 89.45/26.97 (cartprodmempaircEq) =>
% 89.45/26.97 ((
% 89.45/26.97 (cartprodfstpairEq) =>
% 89.45/26.97 ((
% 89.45/26.97 (cartprodsndpairEq) =>
% 89.45/26.97 ((
% 89.45/26.97 (cartprodpairsurjEq) =>
% 89.45/26.97 ((
% 89.45/26.97 (dpsetconstrI) =>
% 89.45/26.97 ((
% 89.45/26.97 (dpsetconstrSub) =>
% 89.45/26.97 ((
% 89.45/26.97 (setOfPairsIsBReln) =>
% 89.45/26.97 ((
% 89.45/26.97 (dpsetconstrERa) =>
% 89.45/26.97 ((
% 89.45/26.97 (dpsetconstrEL1) =>
% 89.45/26.97 ((
% 89.45/26.97 (dpsetconstrEL2) =>
% 89.45/26.97 ((
% 89.45/26.97 (dpsetconstrER) =>
% 89.45/26.97 ((
% 89.45/26.97 (funcImageSingleton) =>
% 89.45/26.97 ((
% 89.45/26.97 (apProp) =>
% 89.45/26.97 ((
% 89.45/26.97 (app) =>
% 89.45/26.97 ((
% 89.45/26.97 (infuncsetfunc) =>
% 89.45/26.97 ((
% 89.45/26.97 (ap2p) =>
% 89.45/26.97 ((
% 89.45/26.97 (funcinfuncset) =>
% 89.45/26.97 ((
% 89.45/26.97 (lamProp) =>
% 89.45/26.97 ((
% 89.45/26.97 (lamp) =>
% 89.45/26.97 ((
% 89.45/26.97 (lam2p) =>
% 89.45/26.97 ((
% 89.45/26.97 (brelnall1) =>
% 89.45/26.97 ((
% 89.45/26.97 (brelnall2) =>
% 89.45/26.97 ((
% 89.45/26.97 (!!) @ (
% 89.45/26.97 (('#B') @ (
% 89.45/26.97 !!) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#S') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#S') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 =>))) @
% 89.45/26.97 ex1)))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 !!))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#S') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#B') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#S') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 =>))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#C') @ in)))))))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 !!))))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#C') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#B') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#B') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#S') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 =>))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#C') @ in)))))))))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#S') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#S') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#B'))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 =>))))))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#C') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#B') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#S') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 =>))))))) @
% 89.45/26.97 (
% 89.45/26.97 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.45/26.97 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1305])).
% 89.45/26.97 thf(zip_derived_cl1321, plain,
% 89.45/26.97 (~ (((setminusSubset1) =>
% 89.45/26.97 (((symdiffE) =>
% 89.45/26.97 (((symdiffI1) =>
% 89.45/26.97 (((symdiffI2) =>
% 89.45/26.97 (((symdiffIneg1) =>
% 89.45/26.97 (((symdiffIneg2) =>
% 89.45/26.97 (((secondinupair) =>
% 89.45/26.97 (((setukpairIL) =>
% 89.45/26.97 (((setukpairIR) =>
% 89.45/26.97 (((kpairiskpair) =>
% 89.45/26.97 (((kpairp) =>
% 89.45/26.97 (((singletonsubset) =>
% 89.45/26.97 (((singletoninpowerset) =>
% 89.45/26.97 (((singletoninpowunion) =>
% 89.45/26.97 (((upairset2E) =>
% 89.45/26.97 (((upairsubunion) =>
% 89.45/26.97 (((upairinpowunion) =>
% 89.45/26.97 (((ubforcartprodlem1) =>
% 89.45/26.97 (((ubforcartprodlem2) =>
% 89.45/26.97 (((ubforcartprodlem3) =>
% 89.45/26.97 (((cartprodpairin) =>
% 89.45/26.97 (((cartprodmempair1) =>
% 89.45/26.97 (((cartprodmempair) =>
% 89.45/26.97 (((setunionE2) =>
% 89.45/26.97 (((setunionsingleton1) =>
% 89.45/26.97 (((setunionsingleton2) =>
% 89.45/26.97 (((setunionsingleton) =>
% 89.45/26.97 (((singletonprop) =>
% 89.45/26.97 (((ex1E1) =>
% 89.45/26.97 (((ex1I) =>
% 89.45/26.97 ((
% 89.45/26.97 (ex1I2) =>
% 89.45/26.97 ((
% 89.45/26.97 (singletonsuniq) =>
% 89.45/26.97 ((
% 89.45/26.97 (setukpairinjL1) =>
% 89.45/26.97 ((
% 89.45/26.97 (kfstsingleton) =>
% 89.45/26.97 ((
% 89.45/26.97 (theprop) =>
% 89.45/26.97 ((
% 89.45/26.97 (kfstpairEq) =>
% 89.45/26.97 ((
% 89.45/26.97 (cartprodfstin) =>
% 89.45/26.97 ((
% 89.45/26.97 (setukpairinjL2) =>
% 89.45/26.97 ((
% 89.45/26.97 (setukpairinjL) =>
% 89.45/26.97 ((
% 89.45/26.97 (setukpairinjR11) =>
% 89.45/26.97 ((
% 89.45/26.97 (setukpairinjR12) =>
% 89.45/26.97 ((
% 89.45/26.97 (setukpairinjR1) =>
% 89.45/26.97 ((
% 89.45/26.97 (upairequniteq) =>
% 89.45/26.97 ((
% 89.45/26.97 (setukpairinjR2) =>
% 89.45/26.97 ((
% 89.45/26.97 (setukpairinjR) =>
% 89.45/26.97 ((
% 89.45/26.97 (ksndsingleton) =>
% 89.45/26.97 ((
% 89.45/26.97 (ksndpairEq) =>
% 89.45/26.97 ((
% 89.45/26.97 (kpairsurjEq) =>
% 89.45/26.97 ((
% 89.45/26.97 (cartprodsndin) =>
% 89.45/26.97 ((
% 89.45/26.97 (cartprodpairmemEL) =>
% 89.45/26.97 ((
% 89.45/26.97 (cartprodpairmemER) =>
% 89.45/26.97 ((
% 89.45/26.97 (cartprodmempaircEq) =>
% 89.45/26.97 ((
% 89.45/26.97 (cartprodfstpairEq) =>
% 89.45/26.97 ((
% 89.45/26.97 (cartprodsndpairEq) =>
% 89.45/26.97 ((
% 89.45/26.97 (cartprodpairsurjEq) =>
% 89.45/26.97 ((
% 89.45/26.97 (dpsetconstrI) =>
% 89.45/26.97 ((
% 89.45/26.97 (dpsetconstrSub) =>
% 89.45/26.97 ((
% 89.45/26.97 (setOfPairsIsBReln) =>
% 89.45/26.97 ((
% 89.45/26.97 (dpsetconstrERa) =>
% 89.45/26.97 ((
% 89.45/26.97 (dpsetconstrEL1) =>
% 89.45/26.97 ((
% 89.45/26.97 (dpsetconstrEL2) =>
% 89.45/26.97 ((
% 89.45/26.97 (dpsetconstrER) =>
% 89.45/26.97 ((
% 89.45/26.97 (funcImageSingleton) =>
% 89.45/26.97 ((
% 89.45/26.97 (apProp) =>
% 89.45/26.97 ((
% 89.45/26.97 (app) =>
% 89.45/26.97 ((
% 89.45/26.97 (infuncsetfunc) =>
% 89.45/26.97 ((
% 89.45/26.97 (ap2p) =>
% 89.45/26.97 ((
% 89.45/26.97 (funcinfuncset) =>
% 89.45/26.97 ((
% 89.45/26.97 (lamProp) =>
% 89.45/26.97 ((
% 89.45/26.97 (lamp) =>
% 89.45/26.97 ((
% 89.45/26.97 (lam2p) =>
% 89.45/26.97 ((
% 89.45/26.97 (brelnall1) =>
% 89.45/26.97 ((
% 89.45/26.97 (brelnall2) =>
% 89.45/26.97 ((
% 89.45/26.97 (!!) @ (
% 89.45/26.97 (('#B') @ (
% 89.45/26.97 !!) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#S') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#S') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 =>))) @
% 89.45/26.97 ex1)))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 !!))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#S') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#B') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#S') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 =>))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#C') @ in)))))))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 !!))))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#C') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#B') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#B') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#S') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 =>))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#C') @ in)))))))))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#S') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#S') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#B'))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 =>))))))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#C') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#B') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#S') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 =>))))))) @
% 89.45/26.97 (
% 89.45/26.97 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.45/26.97 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1313])).
% 89.45/26.97 thf(zip_derived_cl1329, plain,
% 89.45/26.97 (~ (((symdiffE) =>
% 89.45/26.97 (((symdiffI1) =>
% 89.45/26.97 (((symdiffI2) =>
% 89.45/26.97 (((symdiffIneg1) =>
% 89.45/26.97 (((symdiffIneg2) =>
% 89.45/26.97 (((secondinupair) =>
% 89.45/26.97 (((setukpairIL) =>
% 89.45/26.97 (((setukpairIR) =>
% 89.45/26.97 (((kpairiskpair) =>
% 89.45/26.97 (((kpairp) =>
% 89.45/26.97 (((singletonsubset) =>
% 89.45/26.97 (((singletoninpowerset) =>
% 89.45/26.97 (((singletoninpowunion) =>
% 89.45/26.97 (((upairset2E) =>
% 89.45/26.97 (((upairsubunion) =>
% 89.45/26.97 (((upairinpowunion) =>
% 89.45/26.97 (((ubforcartprodlem1) =>
% 89.45/26.97 (((ubforcartprodlem2) =>
% 89.45/26.97 (((ubforcartprodlem3) =>
% 89.45/26.97 (((cartprodpairin) =>
% 89.45/26.97 (((cartprodmempair1) =>
% 89.45/26.97 (((cartprodmempair) =>
% 89.45/26.97 (((setunionE2) =>
% 89.45/26.97 (((setunionsingleton1) =>
% 89.45/26.97 (((setunionsingleton2) =>
% 89.45/26.97 (((setunionsingleton) =>
% 89.45/26.97 (((singletonprop) =>
% 89.45/26.97 (((ex1E1) =>
% 89.45/26.97 (((ex1I) =>
% 89.45/26.97 (((ex1I2) =>
% 89.45/26.97 ((
% 89.45/26.97 (singletonsuniq) =>
% 89.45/26.97 ((
% 89.45/26.97 (setukpairinjL1) =>
% 89.45/26.97 ((
% 89.45/26.97 (kfstsingleton) =>
% 89.45/26.97 ((
% 89.45/26.97 (theprop) =>
% 89.45/26.97 ((
% 89.45/26.97 (kfstpairEq) =>
% 89.45/26.97 ((
% 89.45/26.97 (cartprodfstin) =>
% 89.45/26.97 ((
% 89.45/26.97 (setukpairinjL2) =>
% 89.45/26.97 ((
% 89.45/26.97 (setukpairinjL) =>
% 89.45/26.97 ((
% 89.45/26.97 (setukpairinjR11) =>
% 89.45/26.97 ((
% 89.45/26.97 (setukpairinjR12) =>
% 89.45/26.97 ((
% 89.45/26.97 (setukpairinjR1) =>
% 89.45/26.97 ((
% 89.45/26.97 (upairequniteq) =>
% 89.45/26.97 ((
% 89.45/26.97 (setukpairinjR2) =>
% 89.45/26.97 ((
% 89.45/26.97 (setukpairinjR) =>
% 89.45/26.97 ((
% 89.45/26.97 (ksndsingleton) =>
% 89.45/26.97 ((
% 89.45/26.97 (ksndpairEq) =>
% 89.45/26.97 ((
% 89.45/26.97 (kpairsurjEq) =>
% 89.45/26.97 ((
% 89.45/26.97 (cartprodsndin) =>
% 89.45/26.97 ((
% 89.45/26.97 (cartprodpairmemEL) =>
% 89.45/26.97 ((
% 89.45/26.97 (cartprodpairmemER) =>
% 89.45/26.97 ((
% 89.45/26.97 (cartprodmempaircEq) =>
% 89.45/26.97 ((
% 89.45/26.97 (cartprodfstpairEq) =>
% 89.45/26.97 ((
% 89.45/26.97 (cartprodsndpairEq) =>
% 89.45/26.97 ((
% 89.45/26.97 (cartprodpairsurjEq) =>
% 89.45/26.97 ((
% 89.45/26.97 (dpsetconstrI) =>
% 89.45/26.97 ((
% 89.45/26.97 (dpsetconstrSub) =>
% 89.45/26.97 ((
% 89.45/26.97 (setOfPairsIsBReln) =>
% 89.45/26.97 ((
% 89.45/26.97 (dpsetconstrERa) =>
% 89.45/26.97 ((
% 89.45/26.97 (dpsetconstrEL1) =>
% 89.45/26.97 ((
% 89.45/26.97 (dpsetconstrEL2) =>
% 89.45/26.97 ((
% 89.45/26.97 (dpsetconstrER) =>
% 89.45/26.97 ((
% 89.45/26.97 (funcImageSingleton) =>
% 89.45/26.97 ((
% 89.45/26.97 (apProp) =>
% 89.45/26.97 ((
% 89.45/26.97 (app) =>
% 89.45/26.97 ((
% 89.45/26.97 (infuncsetfunc) =>
% 89.45/26.97 ((
% 89.45/26.97 (ap2p) =>
% 89.45/26.97 ((
% 89.45/26.97 (funcinfuncset) =>
% 89.45/26.97 ((
% 89.45/26.97 (lamProp) =>
% 89.45/26.97 ((
% 89.45/26.97 (lamp) =>
% 89.45/26.97 ((
% 89.45/26.97 (lam2p) =>
% 89.45/26.97 ((
% 89.45/26.97 (brelnall1) =>
% 89.45/26.97 ((
% 89.45/26.97 (brelnall2) =>
% 89.45/26.97 ((
% 89.45/26.97 (!!) @ (
% 89.45/26.97 (('#B') @ (
% 89.45/26.97 !!) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#S') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#S') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 =>))) @
% 89.45/26.97 ex1)))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 !!))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#S') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#B') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#S') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 =>))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#C') @ in)))))))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 !!))))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#C') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#B') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#B') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#S') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 =>))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#C') @ in)))))))))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#S') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#S') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#B'))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 =>))))))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#C') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#B') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#S') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 =>))))))) @
% 89.45/26.97 (
% 89.45/26.97 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.45/26.97 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1321])).
% 89.45/26.97 thf(zip_derived_cl1338, plain,
% 89.45/26.97 (~ (((symdiffI1) =>
% 89.45/26.97 (((symdiffI2) =>
% 89.45/26.97 (((symdiffIneg1) =>
% 89.45/26.97 (((symdiffIneg2) =>
% 89.45/26.97 (((secondinupair) =>
% 89.45/26.97 (((setukpairIL) =>
% 89.45/26.97 (((setukpairIR) =>
% 89.45/26.97 (((kpairiskpair) =>
% 89.45/26.97 (((kpairp) =>
% 89.45/26.97 (((singletonsubset) =>
% 89.45/26.97 (((singletoninpowerset) =>
% 89.45/26.97 (((singletoninpowunion) =>
% 89.45/26.97 (((upairset2E) =>
% 89.45/26.97 (((upairsubunion) =>
% 89.45/26.97 (((upairinpowunion) =>
% 89.45/26.97 (((ubforcartprodlem1) =>
% 89.45/26.97 (((ubforcartprodlem2) =>
% 89.45/26.97 (((ubforcartprodlem3) =>
% 89.45/26.97 (((cartprodpairin) =>
% 89.45/26.97 (((cartprodmempair1) =>
% 89.45/26.97 (((cartprodmempair) =>
% 89.45/26.97 (((setunionE2) =>
% 89.45/26.97 (((setunionsingleton1) =>
% 89.45/26.97 (((setunionsingleton2) =>
% 89.45/26.97 (((setunionsingleton) =>
% 89.45/26.97 (((singletonprop) =>
% 89.45/26.97 (((ex1E1) =>
% 89.45/26.97 (((ex1I) =>
% 89.45/26.97 (((ex1I2) =>
% 89.45/26.97 (((singletonsuniq) =>
% 89.45/26.97 ((
% 89.45/26.97 (setukpairinjL1) =>
% 89.45/26.97 ((
% 89.45/26.97 (kfstsingleton) =>
% 89.45/26.97 ((
% 89.45/26.97 (theprop) =>
% 89.45/26.97 ((
% 89.45/26.97 (kfstpairEq) =>
% 89.45/26.97 ((
% 89.45/26.97 (cartprodfstin) =>
% 89.45/26.97 ((
% 89.45/26.97 (setukpairinjL2) =>
% 89.45/26.97 ((
% 89.45/26.97 (setukpairinjL) =>
% 89.45/26.97 ((
% 89.45/26.97 (setukpairinjR11) =>
% 89.45/26.97 ((
% 89.45/26.97 (setukpairinjR12) =>
% 89.45/26.97 ((
% 89.45/26.97 (setukpairinjR1) =>
% 89.45/26.97 ((
% 89.45/26.97 (upairequniteq) =>
% 89.45/26.97 ((
% 89.45/26.97 (setukpairinjR2) =>
% 89.45/26.97 ((
% 89.45/26.97 (setukpairinjR) =>
% 89.45/26.97 ((
% 89.45/26.97 (ksndsingleton) =>
% 89.45/26.97 ((
% 89.45/26.97 (ksndpairEq) =>
% 89.45/26.97 ((
% 89.45/26.97 (kpairsurjEq) =>
% 89.45/26.97 ((
% 89.45/26.97 (cartprodsndin) =>
% 89.45/26.97 ((
% 89.45/26.97 (cartprodpairmemEL) =>
% 89.45/26.97 ((
% 89.45/26.97 (cartprodpairmemER) =>
% 89.45/26.97 ((
% 89.45/26.97 (cartprodmempaircEq) =>
% 89.45/26.97 ((
% 89.45/26.97 (cartprodfstpairEq) =>
% 89.45/26.97 ((
% 89.45/26.97 (cartprodsndpairEq) =>
% 89.45/26.97 ((
% 89.45/26.97 (cartprodpairsurjEq) =>
% 89.45/26.97 ((
% 89.45/26.97 (dpsetconstrI) =>
% 89.45/26.97 ((
% 89.45/26.97 (dpsetconstrSub) =>
% 89.45/26.97 ((
% 89.45/26.97 (setOfPairsIsBReln) =>
% 89.45/26.97 ((
% 89.45/26.97 (dpsetconstrERa) =>
% 89.45/26.97 ((
% 89.45/26.97 (dpsetconstrEL1) =>
% 89.45/26.97 ((
% 89.45/26.97 (dpsetconstrEL2) =>
% 89.45/26.97 ((
% 89.45/26.97 (dpsetconstrER) =>
% 89.45/26.97 ((
% 89.45/26.97 (funcImageSingleton) =>
% 89.45/26.97 ((
% 89.45/26.97 (apProp) =>
% 89.45/26.97 ((
% 89.45/26.97 (app) =>
% 89.45/26.97 ((
% 89.45/26.97 (infuncsetfunc) =>
% 89.45/26.97 ((
% 89.45/26.97 (ap2p) =>
% 89.45/26.97 ((
% 89.45/26.97 (funcinfuncset) =>
% 89.45/26.97 ((
% 89.45/26.97 (lamProp) =>
% 89.45/26.97 ((
% 89.45/26.97 (lamp) =>
% 89.45/26.97 ((
% 89.45/26.97 (lam2p) =>
% 89.45/26.97 ((
% 89.45/26.97 (brelnall1) =>
% 89.45/26.97 ((
% 89.45/26.97 (brelnall2) =>
% 89.45/26.97 ((
% 89.45/26.97 (!!) @ (
% 89.45/26.97 (('#B') @ (
% 89.45/26.97 !!) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#S') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#S') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 =>))) @
% 89.45/26.97 ex1)))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 !!))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#S') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#B') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#S') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 =>))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#C') @ in)))))))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 !!))))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#C') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#B') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#B') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#S') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 =>))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#C') @ in)))))))))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#S') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#S') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#B'))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 =>))))))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#C') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#B') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#S') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 =>))))))) @
% 89.45/26.97 (
% 89.45/26.97 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.45/26.97 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1329])).
% 89.45/26.97 thf(zip_derived_cl1347, plain,
% 89.45/26.97 (~ (((symdiffI2) =>
% 89.45/26.97 (((symdiffIneg1) =>
% 89.45/26.97 (((symdiffIneg2) =>
% 89.45/26.97 (((secondinupair) =>
% 89.45/26.97 (((setukpairIL) =>
% 89.45/26.97 (((setukpairIR) =>
% 89.45/26.97 (((kpairiskpair) =>
% 89.45/26.97 (((kpairp) =>
% 89.45/26.97 (((singletonsubset) =>
% 89.45/26.97 (((singletoninpowerset) =>
% 89.45/26.97 (((singletoninpowunion) =>
% 89.45/26.97 (((upairset2E) =>
% 89.45/26.97 (((upairsubunion) =>
% 89.45/26.97 (((upairinpowunion) =>
% 89.45/26.97 (((ubforcartprodlem1) =>
% 89.45/26.97 (((ubforcartprodlem2) =>
% 89.45/26.97 (((ubforcartprodlem3) =>
% 89.45/26.97 (((cartprodpairin) =>
% 89.45/26.97 (((cartprodmempair1) =>
% 89.45/26.97 (((cartprodmempair) =>
% 89.45/26.97 (((setunionE2) =>
% 89.45/26.97 (((setunionsingleton1) =>
% 89.45/26.97 (((setunionsingleton2) =>
% 89.45/26.97 (((setunionsingleton) =>
% 89.45/26.97 (((singletonprop) =>
% 89.45/26.97 (((ex1E1) =>
% 89.45/26.97 (((ex1I) =>
% 89.45/26.97 (((ex1I2) =>
% 89.45/26.97 (((singletonsuniq) =>
% 89.45/26.97 (((setukpairinjL1) =>
% 89.45/26.97 ((
% 89.45/26.97 (kfstsingleton) =>
% 89.45/26.97 ((
% 89.45/26.97 (theprop) =>
% 89.45/26.97 ((
% 89.45/26.97 (kfstpairEq) =>
% 89.45/26.97 ((
% 89.45/26.97 (cartprodfstin) =>
% 89.45/26.97 ((
% 89.45/26.97 (setukpairinjL2) =>
% 89.45/26.97 ((
% 89.45/26.97 (setukpairinjL) =>
% 89.45/26.97 ((
% 89.45/26.97 (setukpairinjR11) =>
% 89.45/26.97 ((
% 89.45/26.97 (setukpairinjR12) =>
% 89.45/26.97 ((
% 89.45/26.97 (setukpairinjR1) =>
% 89.45/26.97 ((
% 89.45/26.97 (upairequniteq) =>
% 89.45/26.97 ((
% 89.45/26.97 (setukpairinjR2) =>
% 89.45/26.97 ((
% 89.45/26.97 (setukpairinjR) =>
% 89.45/26.97 ((
% 89.45/26.97 (ksndsingleton) =>
% 89.45/26.97 ((
% 89.45/26.97 (ksndpairEq) =>
% 89.45/26.97 ((
% 89.45/26.97 (kpairsurjEq) =>
% 89.45/26.97 ((
% 89.45/26.97 (cartprodsndin) =>
% 89.45/26.97 ((
% 89.45/26.97 (cartprodpairmemEL) =>
% 89.45/26.97 ((
% 89.45/26.97 (cartprodpairmemER) =>
% 89.45/26.97 ((
% 89.45/26.97 (cartprodmempaircEq) =>
% 89.45/26.97 ((
% 89.45/26.97 (cartprodfstpairEq) =>
% 89.45/26.97 ((
% 89.45/26.97 (cartprodsndpairEq) =>
% 89.45/26.97 ((
% 89.45/26.97 (cartprodpairsurjEq) =>
% 89.45/26.97 ((
% 89.45/26.97 (dpsetconstrI) =>
% 89.45/26.97 ((
% 89.45/26.97 (dpsetconstrSub) =>
% 89.45/26.97 ((
% 89.45/26.97 (setOfPairsIsBReln) =>
% 89.45/26.97 ((
% 89.45/26.97 (dpsetconstrERa) =>
% 89.45/26.97 ((
% 89.45/26.97 (dpsetconstrEL1) =>
% 89.45/26.97 ((
% 89.45/26.97 (dpsetconstrEL2) =>
% 89.45/26.97 ((
% 89.45/26.97 (dpsetconstrER) =>
% 89.45/26.97 ((
% 89.45/26.97 (funcImageSingleton) =>
% 89.45/26.97 ((
% 89.45/26.97 (apProp) =>
% 89.45/26.97 ((
% 89.45/26.97 (app) =>
% 89.45/26.97 ((
% 89.45/26.97 (infuncsetfunc) =>
% 89.45/26.97 ((
% 89.45/26.97 (ap2p) =>
% 89.45/26.97 ((
% 89.45/26.97 (funcinfuncset) =>
% 89.45/26.97 ((
% 89.45/26.97 (lamProp) =>
% 89.45/26.97 ((
% 89.45/26.97 (lamp) =>
% 89.45/26.97 ((
% 89.45/26.97 (lam2p) =>
% 89.45/26.97 ((
% 89.45/26.97 (brelnall1) =>
% 89.45/26.97 ((
% 89.45/26.97 (brelnall2) =>
% 89.45/26.97 ((
% 89.45/26.97 (!!) @ (
% 89.45/26.97 (('#B') @ (
% 89.45/26.97 !!) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#S') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#S') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 =>))) @
% 89.45/26.97 ex1)))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 !!))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#S') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#B') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#S') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 =>))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#C') @ in)))))))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 !!))))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#C') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#B') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#B') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#S') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 =>))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#C') @ in)))))))))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#S') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#S') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#B'))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 =>))))))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#C') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#B') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#S') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 =>))))))) @
% 89.45/26.97 (
% 89.45/26.97 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.45/26.97 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1338])).
% 89.45/26.97 thf(zip_derived_cl1354, plain,
% 89.45/26.97 (~ (((symdiffIneg1) =>
% 89.45/26.97 (((symdiffIneg2) =>
% 89.45/26.97 (((secondinupair) =>
% 89.45/26.97 (((setukpairIL) =>
% 89.45/26.97 (((setukpairIR) =>
% 89.45/26.97 (((kpairiskpair) =>
% 89.45/26.97 (((kpairp) =>
% 89.45/26.97 (((singletonsubset) =>
% 89.45/26.97 (((singletoninpowerset) =>
% 89.45/26.97 (((singletoninpowunion) =>
% 89.45/26.97 (((upairset2E) =>
% 89.45/26.97 (((upairsubunion) =>
% 89.45/26.97 (((upairinpowunion) =>
% 89.45/26.97 (((ubforcartprodlem1) =>
% 89.45/26.97 (((ubforcartprodlem2) =>
% 89.45/26.97 (((ubforcartprodlem3) =>
% 89.45/26.97 (((cartprodpairin) =>
% 89.45/26.97 (((cartprodmempair1) =>
% 89.45/26.97 (((cartprodmempair) =>
% 89.45/26.97 (((setunionE2) =>
% 89.45/26.97 (((setunionsingleton1) =>
% 89.45/26.97 (((setunionsingleton2) =>
% 89.45/26.97 (((setunionsingleton) =>
% 89.45/26.97 (((singletonprop) =>
% 89.45/26.97 (((ex1E1) =>
% 89.45/26.97 (((ex1I) =>
% 89.45/26.97 (((ex1I2) =>
% 89.45/26.97 (((singletonsuniq) =>
% 89.45/26.97 (((setukpairinjL1) =>
% 89.45/26.97 (((kfstsingleton) =>
% 89.45/26.97 ((
% 89.45/26.97 (theprop) =>
% 89.45/26.97 ((
% 89.45/26.97 (kfstpairEq) =>
% 89.45/26.97 ((
% 89.45/26.97 (cartprodfstin) =>
% 89.45/26.97 ((
% 89.45/26.97 (setukpairinjL2) =>
% 89.45/26.97 ((
% 89.45/26.97 (setukpairinjL) =>
% 89.45/26.97 ((
% 89.45/26.97 (setukpairinjR11) =>
% 89.45/26.97 ((
% 89.45/26.97 (setukpairinjR12) =>
% 89.45/26.97 ((
% 89.45/26.97 (setukpairinjR1) =>
% 89.45/26.97 ((
% 89.45/26.97 (upairequniteq) =>
% 89.45/26.97 ((
% 89.45/26.97 (setukpairinjR2) =>
% 89.45/26.97 ((
% 89.45/26.97 (setukpairinjR) =>
% 89.45/26.97 ((
% 89.45/26.97 (ksndsingleton) =>
% 89.45/26.97 ((
% 89.45/26.97 (ksndpairEq) =>
% 89.45/26.97 ((
% 89.45/26.97 (kpairsurjEq) =>
% 89.45/26.97 ((
% 89.45/26.97 (cartprodsndin) =>
% 89.45/26.97 ((
% 89.45/26.97 (cartprodpairmemEL) =>
% 89.45/26.97 ((
% 89.45/26.97 (cartprodpairmemER) =>
% 89.45/26.97 ((
% 89.45/26.97 (cartprodmempaircEq) =>
% 89.45/26.97 ((
% 89.45/26.97 (cartprodfstpairEq) =>
% 89.45/26.97 ((
% 89.45/26.97 (cartprodsndpairEq) =>
% 89.45/26.97 ((
% 89.45/26.97 (cartprodpairsurjEq) =>
% 89.45/26.97 ((
% 89.45/26.97 (dpsetconstrI) =>
% 89.45/26.97 ((
% 89.45/26.97 (dpsetconstrSub) =>
% 89.45/26.97 ((
% 89.45/26.97 (setOfPairsIsBReln) =>
% 89.45/26.97 ((
% 89.45/26.97 (dpsetconstrERa) =>
% 89.45/26.97 ((
% 89.45/26.97 (dpsetconstrEL1) =>
% 89.45/26.97 ((
% 89.45/26.97 (dpsetconstrEL2) =>
% 89.45/26.97 ((
% 89.45/26.97 (dpsetconstrER) =>
% 89.45/26.97 ((
% 89.45/26.97 (funcImageSingleton) =>
% 89.45/26.97 ((
% 89.45/26.97 (apProp) =>
% 89.45/26.97 ((
% 89.45/26.97 (app) =>
% 89.45/26.97 ((
% 89.45/26.97 (infuncsetfunc) =>
% 89.45/26.97 ((
% 89.45/26.97 (ap2p) =>
% 89.45/26.97 ((
% 89.45/26.97 (funcinfuncset) =>
% 89.45/26.97 ((
% 89.45/26.97 (lamProp) =>
% 89.45/26.97 ((
% 89.45/26.97 (lamp) =>
% 89.45/26.97 ((
% 89.45/26.97 (lam2p) =>
% 89.45/26.97 ((
% 89.45/26.97 (brelnall1) =>
% 89.45/26.97 ((
% 89.45/26.97 (brelnall2) =>
% 89.45/26.97 ((
% 89.45/26.97 (!!) @ (
% 89.45/26.97 (('#B') @ (
% 89.45/26.97 !!) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#S') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#S') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 =>))) @
% 89.45/26.97 ex1)))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 !!))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#S') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#B') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#S') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 =>))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#C') @ in)))))))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 !!))))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#C') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#B') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#B') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#S') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 =>))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#C') @ in)))))))))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#S') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#S') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#B'))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 =>))))))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#C') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#B') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#S') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 =>))))))) @
% 89.45/26.97 (
% 89.45/26.97 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.45/26.97 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1347])).
% 89.45/26.97 thf(zip_derived_cl1361, plain,
% 89.45/26.97 (~ (((symdiffIneg2) =>
% 89.45/26.97 (((secondinupair) =>
% 89.45/26.97 (((setukpairIL) =>
% 89.45/26.97 (((setukpairIR) =>
% 89.45/26.97 (((kpairiskpair) =>
% 89.45/26.97 (((kpairp) =>
% 89.45/26.97 (((singletonsubset) =>
% 89.45/26.97 (((singletoninpowerset) =>
% 89.45/26.97 (((singletoninpowunion) =>
% 89.45/26.97 (((upairset2E) =>
% 89.45/26.97 (((upairsubunion) =>
% 89.45/26.97 (((upairinpowunion) =>
% 89.45/26.97 (((ubforcartprodlem1) =>
% 89.45/26.97 (((ubforcartprodlem2) =>
% 89.45/26.97 (((ubforcartprodlem3) =>
% 89.45/26.97 (((cartprodpairin) =>
% 89.45/26.97 (((cartprodmempair1) =>
% 89.45/26.97 (((cartprodmempair) =>
% 89.45/26.97 (((setunionE2) =>
% 89.45/26.97 (((setunionsingleton1) =>
% 89.45/26.97 (((setunionsingleton2) =>
% 89.45/26.97 (((setunionsingleton) =>
% 89.45/26.97 (((singletonprop) =>
% 89.45/26.97 (((ex1E1) =>
% 89.45/26.97 (((ex1I) =>
% 89.45/26.97 (((ex1I2) =>
% 89.45/26.97 (((singletonsuniq) =>
% 89.45/26.97 (((setukpairinjL1) =>
% 89.45/26.97 (((kfstsingleton) =>
% 89.45/26.97 (((theprop) =>
% 89.45/26.97 ((
% 89.45/26.97 (kfstpairEq) =>
% 89.45/26.97 ((
% 89.45/26.97 (cartprodfstin) =>
% 89.45/26.97 ((
% 89.45/26.97 (setukpairinjL2) =>
% 89.45/26.97 ((
% 89.45/26.97 (setukpairinjL) =>
% 89.45/26.97 ((
% 89.45/26.97 (setukpairinjR11) =>
% 89.45/26.97 ((
% 89.45/26.97 (setukpairinjR12) =>
% 89.45/26.97 ((
% 89.45/26.97 (setukpairinjR1) =>
% 89.45/26.97 ((
% 89.45/26.97 (upairequniteq) =>
% 89.45/26.97 ((
% 89.45/26.97 (setukpairinjR2) =>
% 89.45/26.97 ((
% 89.45/26.97 (setukpairinjR) =>
% 89.45/26.97 ((
% 89.45/26.97 (ksndsingleton) =>
% 89.45/26.97 ((
% 89.45/26.97 (ksndpairEq) =>
% 89.45/26.97 ((
% 89.45/26.97 (kpairsurjEq) =>
% 89.45/26.97 ((
% 89.45/26.97 (cartprodsndin) =>
% 89.45/26.97 ((
% 89.45/26.97 (cartprodpairmemEL) =>
% 89.45/26.97 ((
% 89.45/26.97 (cartprodpairmemER) =>
% 89.45/26.97 ((
% 89.45/26.97 (cartprodmempaircEq) =>
% 89.45/26.97 ((
% 89.45/26.97 (cartprodfstpairEq) =>
% 89.45/26.97 ((
% 89.45/26.97 (cartprodsndpairEq) =>
% 89.45/26.97 ((
% 89.45/26.97 (cartprodpairsurjEq) =>
% 89.45/26.97 ((
% 89.45/26.97 (dpsetconstrI) =>
% 89.45/26.97 ((
% 89.45/26.97 (dpsetconstrSub) =>
% 89.45/26.97 ((
% 89.45/26.97 (setOfPairsIsBReln) =>
% 89.45/26.97 ((
% 89.45/26.97 (dpsetconstrERa) =>
% 89.45/26.97 ((
% 89.45/26.97 (dpsetconstrEL1) =>
% 89.45/26.97 ((
% 89.45/26.97 (dpsetconstrEL2) =>
% 89.45/26.97 ((
% 89.45/26.97 (dpsetconstrER) =>
% 89.45/26.97 ((
% 89.45/26.97 (funcImageSingleton) =>
% 89.45/26.97 ((
% 89.45/26.97 (apProp) =>
% 89.45/26.97 ((
% 89.45/26.97 (app) =>
% 89.45/26.97 ((
% 89.45/26.97 (infuncsetfunc) =>
% 89.45/26.97 ((
% 89.45/26.97 (ap2p) =>
% 89.45/26.97 ((
% 89.45/26.97 (funcinfuncset) =>
% 89.45/26.97 ((
% 89.45/26.97 (lamProp) =>
% 89.45/26.97 ((
% 89.45/26.97 (lamp) =>
% 89.45/26.97 ((
% 89.45/26.97 (lam2p) =>
% 89.45/26.97 ((
% 89.45/26.97 (brelnall1) =>
% 89.45/26.97 ((
% 89.45/26.97 (brelnall2) =>
% 89.45/26.97 ((
% 89.45/26.97 (!!) @ (
% 89.45/26.97 (('#B') @ (
% 89.45/26.97 !!) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#S') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#S') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 =>))) @
% 89.45/26.97 ex1)))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 !!))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#S') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#B') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#S') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 =>))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#C') @ in)))))))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 !!))))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#C') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#B') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#B') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#S') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 =>))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#C') @ in)))))))))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#S') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#S') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#B'))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 =>))))))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#C') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#B') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#S') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 =>))))))) @
% 89.45/26.97 (
% 89.45/26.97 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.45/26.97 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1354])).
% 89.45/26.97 thf(zip_derived_cl1369, plain,
% 89.45/26.97 (~ (((secondinupair) =>
% 89.45/26.97 (((setukpairIL) =>
% 89.45/26.97 (((setukpairIR) =>
% 89.45/26.97 (((kpairiskpair) =>
% 89.45/26.97 (((kpairp) =>
% 89.45/26.97 (((singletonsubset) =>
% 89.45/26.97 (((singletoninpowerset) =>
% 89.45/26.97 (((singletoninpowunion) =>
% 89.45/26.97 (((upairset2E) =>
% 89.45/26.97 (((upairsubunion) =>
% 89.45/26.97 (((upairinpowunion) =>
% 89.45/26.97 (((ubforcartprodlem1) =>
% 89.45/26.97 (((ubforcartprodlem2) =>
% 89.45/26.97 (((ubforcartprodlem3) =>
% 89.45/26.97 (((cartprodpairin) =>
% 89.45/26.97 (((cartprodmempair1) =>
% 89.45/26.97 (((cartprodmempair) =>
% 89.45/26.97 (((setunionE2) =>
% 89.45/26.97 (((setunionsingleton1) =>
% 89.45/26.97 (((setunionsingleton2) =>
% 89.45/26.97 (((setunionsingleton) =>
% 89.45/26.97 (((singletonprop) =>
% 89.45/26.97 (((ex1E1) =>
% 89.45/26.97 (((ex1I) =>
% 89.45/26.97 (((ex1I2) =>
% 89.45/26.97 (((singletonsuniq) =>
% 89.45/26.97 (((setukpairinjL1) =>
% 89.45/26.97 (((kfstsingleton) =>
% 89.45/26.97 (((theprop) =>
% 89.45/26.97 (((kfstpairEq) =>
% 89.45/26.97 ((
% 89.45/26.97 (cartprodfstin) =>
% 89.45/26.97 ((
% 89.45/26.97 (setukpairinjL2) =>
% 89.45/26.97 ((
% 89.45/26.97 (setukpairinjL) =>
% 89.45/26.97 ((
% 89.45/26.97 (setukpairinjR11) =>
% 89.45/26.97 ((
% 89.45/26.97 (setukpairinjR12) =>
% 89.45/26.97 ((
% 89.45/26.97 (setukpairinjR1) =>
% 89.45/26.97 ((
% 89.45/26.97 (upairequniteq) =>
% 89.45/26.97 ((
% 89.45/26.97 (setukpairinjR2) =>
% 89.45/26.97 ((
% 89.45/26.97 (setukpairinjR) =>
% 89.45/26.97 ((
% 89.45/26.97 (ksndsingleton) =>
% 89.45/26.97 ((
% 89.45/26.97 (ksndpairEq) =>
% 89.45/26.97 ((
% 89.45/26.97 (kpairsurjEq) =>
% 89.45/26.97 ((
% 89.45/26.97 (cartprodsndin) =>
% 89.45/26.97 ((
% 89.45/26.97 (cartprodpairmemEL) =>
% 89.45/26.97 ((
% 89.45/26.97 (cartprodpairmemER) =>
% 89.45/26.97 ((
% 89.45/26.97 (cartprodmempaircEq) =>
% 89.45/26.97 ((
% 89.45/26.97 (cartprodfstpairEq) =>
% 89.45/26.97 ((
% 89.45/26.97 (cartprodsndpairEq) =>
% 89.45/26.97 ((
% 89.45/26.97 (cartprodpairsurjEq) =>
% 89.45/26.97 ((
% 89.45/26.97 (dpsetconstrI) =>
% 89.45/26.97 ((
% 89.45/26.97 (dpsetconstrSub) =>
% 89.45/26.97 ((
% 89.45/26.97 (setOfPairsIsBReln) =>
% 89.45/26.97 ((
% 89.45/26.97 (dpsetconstrERa) =>
% 89.45/26.97 ((
% 89.45/26.97 (dpsetconstrEL1) =>
% 89.45/26.97 ((
% 89.45/26.97 (dpsetconstrEL2) =>
% 89.45/26.97 ((
% 89.45/26.97 (dpsetconstrER) =>
% 89.45/26.97 ((
% 89.45/26.97 (funcImageSingleton) =>
% 89.45/26.97 ((
% 89.45/26.97 (apProp) =>
% 89.45/26.97 ((
% 89.45/26.97 (app) =>
% 89.45/26.97 ((
% 89.45/26.97 (infuncsetfunc) =>
% 89.45/26.97 ((
% 89.45/26.97 (ap2p) =>
% 89.45/26.97 ((
% 89.45/26.97 (funcinfuncset) =>
% 89.45/26.97 ((
% 89.45/26.97 (lamProp) =>
% 89.45/26.97 ((
% 89.45/26.97 (lamp) =>
% 89.45/26.97 ((
% 89.45/26.97 (lam2p) =>
% 89.45/26.97 ((
% 89.45/26.97 (brelnall1) =>
% 89.45/26.97 ((
% 89.45/26.97 (brelnall2) =>
% 89.45/26.97 ((
% 89.45/26.97 (!!) @ (
% 89.45/26.97 (('#B') @ (
% 89.45/26.97 !!) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#S') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#S') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 =>))) @
% 89.45/26.97 ex1)))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 !!))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#S') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#B') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#S') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 =>))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#C') @ in)))))))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 !!))))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#C') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#B') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#B') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#S') @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 =>))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#C') @ in)))))))))) @
% 89.45/26.97 (
% 89.45/26.97 (
% 89.45/26.97 ('#S') @ (
% 89.45/26.97 (
% 89.45/26.97 ('#B') @ (
% 89.45/26.97 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B'))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))))))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#C') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))))))) @
% 89.45/26.99 (
% 89.45/26.99 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.45/26.99 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1361])).
% 89.45/26.99 thf(zip_derived_cl1377, plain,
% 89.45/26.99 (~ (((setukpairIL) =>
% 89.45/26.99 (((setukpairIR) =>
% 89.45/26.99 (((kpairiskpair) =>
% 89.45/26.99 (((kpairp) =>
% 89.45/26.99 (((singletonsubset) =>
% 89.45/26.99 (((singletoninpowerset) =>
% 89.45/26.99 (((singletoninpowunion) =>
% 89.45/26.99 (((upairset2E) =>
% 89.45/26.99 (((upairsubunion) =>
% 89.45/26.99 (((upairinpowunion) =>
% 89.45/26.99 (((ubforcartprodlem1) =>
% 89.45/26.99 (((ubforcartprodlem2) =>
% 89.45/26.99 (((ubforcartprodlem3) =>
% 89.45/26.99 (((cartprodpairin) =>
% 89.45/26.99 (((cartprodmempair1) =>
% 89.45/26.99 (((cartprodmempair) =>
% 89.45/26.99 (((setunionE2) =>
% 89.45/26.99 (((setunionsingleton1) =>
% 89.45/26.99 (((setunionsingleton2) =>
% 89.45/26.99 (((setunionsingleton) =>
% 89.45/26.99 (((singletonprop) =>
% 89.45/26.99 (((ex1E1) =>
% 89.45/26.99 (((ex1I) =>
% 89.45/26.99 (((ex1I2) =>
% 89.45/26.99 (((singletonsuniq) =>
% 89.45/26.99 (((setukpairinjL1) =>
% 89.45/26.99 (((kfstsingleton) =>
% 89.45/26.99 (((theprop) =>
% 89.45/26.99 (((kfstpairEq) =>
% 89.45/26.99 (((cartprodfstin) =>
% 89.45/26.99 ((
% 89.45/26.99 (setukpairinjL2) =>
% 89.45/26.99 ((
% 89.45/26.99 (setukpairinjL) =>
% 89.45/26.99 ((
% 89.45/26.99 (setukpairinjR11) =>
% 89.45/26.99 ((
% 89.45/26.99 (setukpairinjR12) =>
% 89.45/26.99 ((
% 89.45/26.99 (setukpairinjR1) =>
% 89.45/26.99 ((
% 89.45/26.99 (upairequniteq) =>
% 89.45/26.99 ((
% 89.45/26.99 (setukpairinjR2) =>
% 89.45/26.99 ((
% 89.45/26.99 (setukpairinjR) =>
% 89.45/26.99 ((
% 89.45/26.99 (ksndsingleton) =>
% 89.45/26.99 ((
% 89.45/26.99 (ksndpairEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (kpairsurjEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodsndin) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodpairmemEL) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodpairmemER) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodmempaircEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodfstpairEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodsndpairEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodpairsurjEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrI) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrSub) =>
% 89.45/26.99 ((
% 89.45/26.99 (setOfPairsIsBReln) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrERa) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrEL1) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrEL2) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrER) =>
% 89.45/26.99 ((
% 89.45/26.99 (funcImageSingleton) =>
% 89.45/26.99 ((
% 89.45/26.99 (apProp) =>
% 89.45/26.99 ((
% 89.45/26.99 (app) =>
% 89.45/26.99 ((
% 89.45/26.99 (infuncsetfunc) =>
% 89.45/26.99 ((
% 89.45/26.99 (ap2p) =>
% 89.45/26.99 ((
% 89.45/26.99 (funcinfuncset) =>
% 89.45/26.99 ((
% 89.45/26.99 (lamProp) =>
% 89.45/26.99 ((
% 89.45/26.99 (lamp) =>
% 89.45/26.99 ((
% 89.45/26.99 (lam2p) =>
% 89.45/26.99 ((
% 89.45/26.99 (brelnall1) =>
% 89.45/26.99 ((
% 89.45/26.99 (brelnall2) =>
% 89.45/26.99 ((
% 89.45/26.99 (!!) @ (
% 89.45/26.99 (('#B') @ (
% 89.45/26.99 !!) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#S') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))) @
% 89.45/26.99 ex1)))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 !!))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#S') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#C') @ in)))))))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 !!))))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#C') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#C') @ in)))))))))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#S') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B'))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))))))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#C') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))))))) @
% 89.45/26.99 (
% 89.45/26.99 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.45/26.99 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1369])).
% 89.45/26.99 thf(zip_derived_cl1386, plain,
% 89.45/26.99 (~ (((setukpairIR) =>
% 89.45/26.99 (((kpairiskpair) =>
% 89.45/26.99 (((kpairp) =>
% 89.45/26.99 (((singletonsubset) =>
% 89.45/26.99 (((singletoninpowerset) =>
% 89.45/26.99 (((singletoninpowunion) =>
% 89.45/26.99 (((upairset2E) =>
% 89.45/26.99 (((upairsubunion) =>
% 89.45/26.99 (((upairinpowunion) =>
% 89.45/26.99 (((ubforcartprodlem1) =>
% 89.45/26.99 (((ubforcartprodlem2) =>
% 89.45/26.99 (((ubforcartprodlem3) =>
% 89.45/26.99 (((cartprodpairin) =>
% 89.45/26.99 (((cartprodmempair1) =>
% 89.45/26.99 (((cartprodmempair) =>
% 89.45/26.99 (((setunionE2) =>
% 89.45/26.99 (((setunionsingleton1) =>
% 89.45/26.99 (((setunionsingleton2) =>
% 89.45/26.99 (((setunionsingleton) =>
% 89.45/26.99 (((singletonprop) =>
% 89.45/26.99 (((ex1E1) =>
% 89.45/26.99 (((ex1I) =>
% 89.45/26.99 (((ex1I2) =>
% 89.45/26.99 (((singletonsuniq) =>
% 89.45/26.99 (((setukpairinjL1) =>
% 89.45/26.99 (((kfstsingleton) =>
% 89.45/26.99 (((theprop) =>
% 89.45/26.99 (((kfstpairEq) =>
% 89.45/26.99 (((cartprodfstin) =>
% 89.45/26.99 (((setukpairinjL2) =>
% 89.45/26.99 ((
% 89.45/26.99 (setukpairinjL) =>
% 89.45/26.99 ((
% 89.45/26.99 (setukpairinjR11) =>
% 89.45/26.99 ((
% 89.45/26.99 (setukpairinjR12) =>
% 89.45/26.99 ((
% 89.45/26.99 (setukpairinjR1) =>
% 89.45/26.99 ((
% 89.45/26.99 (upairequniteq) =>
% 89.45/26.99 ((
% 89.45/26.99 (setukpairinjR2) =>
% 89.45/26.99 ((
% 89.45/26.99 (setukpairinjR) =>
% 89.45/26.99 ((
% 89.45/26.99 (ksndsingleton) =>
% 89.45/26.99 ((
% 89.45/26.99 (ksndpairEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (kpairsurjEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodsndin) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodpairmemEL) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodpairmemER) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodmempaircEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodfstpairEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodsndpairEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodpairsurjEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrI) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrSub) =>
% 89.45/26.99 ((
% 89.45/26.99 (setOfPairsIsBReln) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrERa) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrEL1) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrEL2) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrER) =>
% 89.45/26.99 ((
% 89.45/26.99 (funcImageSingleton) =>
% 89.45/26.99 ((
% 89.45/26.99 (apProp) =>
% 89.45/26.99 ((
% 89.45/26.99 (app) =>
% 89.45/26.99 ((
% 89.45/26.99 (infuncsetfunc) =>
% 89.45/26.99 ((
% 89.45/26.99 (ap2p) =>
% 89.45/26.99 ((
% 89.45/26.99 (funcinfuncset) =>
% 89.45/26.99 ((
% 89.45/26.99 (lamProp) =>
% 89.45/26.99 ((
% 89.45/26.99 (lamp) =>
% 89.45/26.99 ((
% 89.45/26.99 (lam2p) =>
% 89.45/26.99 ((
% 89.45/26.99 (brelnall1) =>
% 89.45/26.99 ((
% 89.45/26.99 (brelnall2) =>
% 89.45/26.99 ((
% 89.45/26.99 (!!) @ (
% 89.45/26.99 (('#B') @ (
% 89.45/26.99 !!) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#S') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))) @
% 89.45/26.99 ex1)))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 !!))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#S') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#C') @ in)))))))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 !!))))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#C') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#C') @ in)))))))))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#S') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B'))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))))))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#C') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))))))) @
% 89.45/26.99 (
% 89.45/26.99 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.45/26.99 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1377])).
% 89.45/26.99 thf(zip_derived_cl1396, plain,
% 89.45/26.99 (~ (((kpairiskpair) =>
% 89.45/26.99 (((kpairp) =>
% 89.45/26.99 (((singletonsubset) =>
% 89.45/26.99 (((singletoninpowerset) =>
% 89.45/26.99 (((singletoninpowunion) =>
% 89.45/26.99 (((upairset2E) =>
% 89.45/26.99 (((upairsubunion) =>
% 89.45/26.99 (((upairinpowunion) =>
% 89.45/26.99 (((ubforcartprodlem1) =>
% 89.45/26.99 (((ubforcartprodlem2) =>
% 89.45/26.99 (((ubforcartprodlem3) =>
% 89.45/26.99 (((cartprodpairin) =>
% 89.45/26.99 (((cartprodmempair1) =>
% 89.45/26.99 (((cartprodmempair) =>
% 89.45/26.99 (((setunionE2) =>
% 89.45/26.99 (((setunionsingleton1) =>
% 89.45/26.99 (((setunionsingleton2) =>
% 89.45/26.99 (((setunionsingleton) =>
% 89.45/26.99 (((singletonprop) =>
% 89.45/26.99 (((ex1E1) =>
% 89.45/26.99 (((ex1I) =>
% 89.45/26.99 (((ex1I2) =>
% 89.45/26.99 (((singletonsuniq) =>
% 89.45/26.99 (((setukpairinjL1) =>
% 89.45/26.99 (((kfstsingleton) =>
% 89.45/26.99 (((theprop) =>
% 89.45/26.99 (((kfstpairEq) =>
% 89.45/26.99 (((cartprodfstin) =>
% 89.45/26.99 (((setukpairinjL2) =>
% 89.45/26.99 (((setukpairinjL) =>
% 89.45/26.99 ((
% 89.45/26.99 (setukpairinjR11) =>
% 89.45/26.99 ((
% 89.45/26.99 (setukpairinjR12) =>
% 89.45/26.99 ((
% 89.45/26.99 (setukpairinjR1) =>
% 89.45/26.99 ((
% 89.45/26.99 (upairequniteq) =>
% 89.45/26.99 ((
% 89.45/26.99 (setukpairinjR2) =>
% 89.45/26.99 ((
% 89.45/26.99 (setukpairinjR) =>
% 89.45/26.99 ((
% 89.45/26.99 (ksndsingleton) =>
% 89.45/26.99 ((
% 89.45/26.99 (ksndpairEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (kpairsurjEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodsndin) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodpairmemEL) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodpairmemER) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodmempaircEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodfstpairEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodsndpairEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodpairsurjEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrI) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrSub) =>
% 89.45/26.99 ((
% 89.45/26.99 (setOfPairsIsBReln) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrERa) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrEL1) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrEL2) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrER) =>
% 89.45/26.99 ((
% 89.45/26.99 (funcImageSingleton) =>
% 89.45/26.99 ((
% 89.45/26.99 (apProp) =>
% 89.45/26.99 ((
% 89.45/26.99 (app) =>
% 89.45/26.99 ((
% 89.45/26.99 (infuncsetfunc) =>
% 89.45/26.99 ((
% 89.45/26.99 (ap2p) =>
% 89.45/26.99 ((
% 89.45/26.99 (funcinfuncset) =>
% 89.45/26.99 ((
% 89.45/26.99 (lamProp) =>
% 89.45/26.99 ((
% 89.45/26.99 (lamp) =>
% 89.45/26.99 ((
% 89.45/26.99 (lam2p) =>
% 89.45/26.99 ((
% 89.45/26.99 (brelnall1) =>
% 89.45/26.99 ((
% 89.45/26.99 (brelnall2) =>
% 89.45/26.99 ((
% 89.45/26.99 (!!) @ (
% 89.45/26.99 (('#B') @ (
% 89.45/26.99 !!) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#S') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))) @
% 89.45/26.99 ex1)))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 !!))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#S') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#C') @ in)))))))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 !!))))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#C') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#C') @ in)))))))))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#S') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B'))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))))))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#C') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))))))) @
% 89.45/26.99 (
% 89.45/26.99 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.45/26.99 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1386])).
% 89.45/26.99 thf(zip_derived_cl1407, plain,
% 89.45/26.99 (~ (((kpairp) =>
% 89.45/26.99 (((singletonsubset) =>
% 89.45/26.99 (((singletoninpowerset) =>
% 89.45/26.99 (((singletoninpowunion) =>
% 89.45/26.99 (((upairset2E) =>
% 89.45/26.99 (((upairsubunion) =>
% 89.45/26.99 (((upairinpowunion) =>
% 89.45/26.99 (((ubforcartprodlem1) =>
% 89.45/26.99 (((ubforcartprodlem2) =>
% 89.45/26.99 (((ubforcartprodlem3) =>
% 89.45/26.99 (((cartprodpairin) =>
% 89.45/26.99 (((cartprodmempair1) =>
% 89.45/26.99 (((cartprodmempair) =>
% 89.45/26.99 (((setunionE2) =>
% 89.45/26.99 (((setunionsingleton1) =>
% 89.45/26.99 (((setunionsingleton2) =>
% 89.45/26.99 (((setunionsingleton) =>
% 89.45/26.99 (((singletonprop) =>
% 89.45/26.99 (((ex1E1) =>
% 89.45/26.99 (((ex1I) =>
% 89.45/26.99 (((ex1I2) =>
% 89.45/26.99 (((singletonsuniq) =>
% 89.45/26.99 (((setukpairinjL1) =>
% 89.45/26.99 (((kfstsingleton) =>
% 89.45/26.99 (((theprop) =>
% 89.45/26.99 (((kfstpairEq) =>
% 89.45/26.99 (((cartprodfstin) =>
% 89.45/26.99 (((setukpairinjL2) =>
% 89.45/26.99 (((setukpairinjL) =>
% 89.45/26.99 (((setukpairinjR11) =>
% 89.45/26.99 ((
% 89.45/26.99 (setukpairinjR12) =>
% 89.45/26.99 ((
% 89.45/26.99 (setukpairinjR1) =>
% 89.45/26.99 ((
% 89.45/26.99 (upairequniteq) =>
% 89.45/26.99 ((
% 89.45/26.99 (setukpairinjR2) =>
% 89.45/26.99 ((
% 89.45/26.99 (setukpairinjR) =>
% 89.45/26.99 ((
% 89.45/26.99 (ksndsingleton) =>
% 89.45/26.99 ((
% 89.45/26.99 (ksndpairEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (kpairsurjEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodsndin) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodpairmemEL) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodpairmemER) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodmempaircEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodfstpairEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodsndpairEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodpairsurjEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrI) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrSub) =>
% 89.45/26.99 ((
% 89.45/26.99 (setOfPairsIsBReln) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrERa) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrEL1) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrEL2) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrER) =>
% 89.45/26.99 ((
% 89.45/26.99 (funcImageSingleton) =>
% 89.45/26.99 ((
% 89.45/26.99 (apProp) =>
% 89.45/26.99 ((
% 89.45/26.99 (app) =>
% 89.45/26.99 ((
% 89.45/26.99 (infuncsetfunc) =>
% 89.45/26.99 ((
% 89.45/26.99 (ap2p) =>
% 89.45/26.99 ((
% 89.45/26.99 (funcinfuncset) =>
% 89.45/26.99 ((
% 89.45/26.99 (lamProp) =>
% 89.45/26.99 ((
% 89.45/26.99 (lamp) =>
% 89.45/26.99 ((
% 89.45/26.99 (lam2p) =>
% 89.45/26.99 ((
% 89.45/26.99 (brelnall1) =>
% 89.45/26.99 ((
% 89.45/26.99 (brelnall2) =>
% 89.45/26.99 ((
% 89.45/26.99 (!!) @ (
% 89.45/26.99 (('#B') @ (
% 89.45/26.99 !!) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#S') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))) @
% 89.45/26.99 ex1)))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 !!))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#S') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#C') @ in)))))))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 !!))))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#C') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#C') @ in)))))))))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#S') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B'))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))))))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#C') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))))))) @
% 89.45/26.99 (
% 89.45/26.99 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.45/26.99 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1396])).
% 89.45/26.99 thf(zip_derived_cl1420, plain,
% 89.45/26.99 (~ (((singletonsubset) =>
% 89.45/26.99 (((singletoninpowerset) =>
% 89.45/26.99 (((singletoninpowunion) =>
% 89.45/26.99 (((upairset2E) =>
% 89.45/26.99 (((upairsubunion) =>
% 89.45/26.99 (((upairinpowunion) =>
% 89.45/26.99 (((ubforcartprodlem1) =>
% 89.45/26.99 (((ubforcartprodlem2) =>
% 89.45/26.99 (((ubforcartprodlem3) =>
% 89.45/26.99 (((cartprodpairin) =>
% 89.45/26.99 (((cartprodmempair1) =>
% 89.45/26.99 (((cartprodmempair) =>
% 89.45/26.99 (((setunionE2) =>
% 89.45/26.99 (((setunionsingleton1) =>
% 89.45/26.99 (((setunionsingleton2) =>
% 89.45/26.99 (((setunionsingleton) =>
% 89.45/26.99 (((singletonprop) =>
% 89.45/26.99 (((ex1E1) =>
% 89.45/26.99 (((ex1I) =>
% 89.45/26.99 (((ex1I2) =>
% 89.45/26.99 (((singletonsuniq) =>
% 89.45/26.99 (((setukpairinjL1) =>
% 89.45/26.99 (((kfstsingleton) =>
% 89.45/26.99 (((theprop) =>
% 89.45/26.99 (((kfstpairEq) =>
% 89.45/26.99 (((cartprodfstin) =>
% 89.45/26.99 (((setukpairinjL2) =>
% 89.45/26.99 (((setukpairinjL) =>
% 89.45/26.99 (((setukpairinjR11) =>
% 89.45/26.99 (((setukpairinjR12) =>
% 89.45/26.99 ((
% 89.45/26.99 (setukpairinjR1) =>
% 89.45/26.99 ((
% 89.45/26.99 (upairequniteq) =>
% 89.45/26.99 ((
% 89.45/26.99 (setukpairinjR2) =>
% 89.45/26.99 ((
% 89.45/26.99 (setukpairinjR) =>
% 89.45/26.99 ((
% 89.45/26.99 (ksndsingleton) =>
% 89.45/26.99 ((
% 89.45/26.99 (ksndpairEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (kpairsurjEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodsndin) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodpairmemEL) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodpairmemER) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodmempaircEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodfstpairEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodsndpairEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodpairsurjEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrI) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrSub) =>
% 89.45/26.99 ((
% 89.45/26.99 (setOfPairsIsBReln) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrERa) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrEL1) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrEL2) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrER) =>
% 89.45/26.99 ((
% 89.45/26.99 (funcImageSingleton) =>
% 89.45/26.99 ((
% 89.45/26.99 (apProp) =>
% 89.45/26.99 ((
% 89.45/26.99 (app) =>
% 89.45/26.99 ((
% 89.45/26.99 (infuncsetfunc) =>
% 89.45/26.99 ((
% 89.45/26.99 (ap2p) =>
% 89.45/26.99 ((
% 89.45/26.99 (funcinfuncset) =>
% 89.45/26.99 ((
% 89.45/26.99 (lamProp) =>
% 89.45/26.99 ((
% 89.45/26.99 (lamp) =>
% 89.45/26.99 ((
% 89.45/26.99 (lam2p) =>
% 89.45/26.99 ((
% 89.45/26.99 (brelnall1) =>
% 89.45/26.99 ((
% 89.45/26.99 (brelnall2) =>
% 89.45/26.99 ((
% 89.45/26.99 (!!) @ (
% 89.45/26.99 (('#B') @ (
% 89.45/26.99 !!) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#S') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))) @
% 89.45/26.99 ex1)))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 !!))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#S') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#C') @ in)))))))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 !!))))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#C') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#C') @ in)))))))))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#S') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B'))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))))))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#C') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))))))) @
% 89.45/26.99 (
% 89.45/26.99 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.45/26.99 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1407])).
% 89.45/26.99 thf(zip_derived_cl1433, plain,
% 89.45/26.99 (~ (((singletoninpowerset) =>
% 89.45/26.99 (((singletoninpowunion) =>
% 89.45/26.99 (((upairset2E) =>
% 89.45/26.99 (((upairsubunion) =>
% 89.45/26.99 (((upairinpowunion) =>
% 89.45/26.99 (((ubforcartprodlem1) =>
% 89.45/26.99 (((ubforcartprodlem2) =>
% 89.45/26.99 (((ubforcartprodlem3) =>
% 89.45/26.99 (((cartprodpairin) =>
% 89.45/26.99 (((cartprodmempair1) =>
% 89.45/26.99 (((cartprodmempair) =>
% 89.45/26.99 (((setunionE2) =>
% 89.45/26.99 (((setunionsingleton1) =>
% 89.45/26.99 (((setunionsingleton2) =>
% 89.45/26.99 (((setunionsingleton) =>
% 89.45/26.99 (((singletonprop) =>
% 89.45/26.99 (((ex1E1) =>
% 89.45/26.99 (((ex1I) =>
% 89.45/26.99 (((ex1I2) =>
% 89.45/26.99 (((singletonsuniq) =>
% 89.45/26.99 (((setukpairinjL1) =>
% 89.45/26.99 (((kfstsingleton) =>
% 89.45/26.99 (((theprop) =>
% 89.45/26.99 (((kfstpairEq) =>
% 89.45/26.99 (((cartprodfstin) =>
% 89.45/26.99 (((setukpairinjL2) =>
% 89.45/26.99 (((setukpairinjL) =>
% 89.45/26.99 (((setukpairinjR11) =>
% 89.45/26.99 (((setukpairinjR12) =>
% 89.45/26.99 (((setukpairinjR1) =>
% 89.45/26.99 ((
% 89.45/26.99 (upairequniteq) =>
% 89.45/26.99 ((
% 89.45/26.99 (setukpairinjR2) =>
% 89.45/26.99 ((
% 89.45/26.99 (setukpairinjR) =>
% 89.45/26.99 ((
% 89.45/26.99 (ksndsingleton) =>
% 89.45/26.99 ((
% 89.45/26.99 (ksndpairEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (kpairsurjEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodsndin) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodpairmemEL) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodpairmemER) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodmempaircEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodfstpairEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodsndpairEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodpairsurjEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrI) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrSub) =>
% 89.45/26.99 ((
% 89.45/26.99 (setOfPairsIsBReln) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrERa) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrEL1) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrEL2) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrER) =>
% 89.45/26.99 ((
% 89.45/26.99 (funcImageSingleton) =>
% 89.45/26.99 ((
% 89.45/26.99 (apProp) =>
% 89.45/26.99 ((
% 89.45/26.99 (app) =>
% 89.45/26.99 ((
% 89.45/26.99 (infuncsetfunc) =>
% 89.45/26.99 ((
% 89.45/26.99 (ap2p) =>
% 89.45/26.99 ((
% 89.45/26.99 (funcinfuncset) =>
% 89.45/26.99 ((
% 89.45/26.99 (lamProp) =>
% 89.45/26.99 ((
% 89.45/26.99 (lamp) =>
% 89.45/26.99 ((
% 89.45/26.99 (lam2p) =>
% 89.45/26.99 ((
% 89.45/26.99 (brelnall1) =>
% 89.45/26.99 ((
% 89.45/26.99 (brelnall2) =>
% 89.45/26.99 ((
% 89.45/26.99 (!!) @ (
% 89.45/26.99 (('#B') @ (
% 89.45/26.99 !!) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#S') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))) @
% 89.45/26.99 ex1)))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 !!))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#S') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#C') @ in)))))))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 !!))))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#C') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#C') @ in)))))))))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#S') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B'))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))))))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#C') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))))))) @
% 89.45/26.99 (
% 89.45/26.99 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.45/26.99 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1420])).
% 89.45/26.99 thf(zip_derived_cl1444, plain,
% 89.45/26.99 (~ (((singletoninpowunion) =>
% 89.45/26.99 (((upairset2E) =>
% 89.45/26.99 (((upairsubunion) =>
% 89.45/26.99 (((upairinpowunion) =>
% 89.45/26.99 (((ubforcartprodlem1) =>
% 89.45/26.99 (((ubforcartprodlem2) =>
% 89.45/26.99 (((ubforcartprodlem3) =>
% 89.45/26.99 (((cartprodpairin) =>
% 89.45/26.99 (((cartprodmempair1) =>
% 89.45/26.99 (((cartprodmempair) =>
% 89.45/26.99 (((setunionE2) =>
% 89.45/26.99 (((setunionsingleton1) =>
% 89.45/26.99 (((setunionsingleton2) =>
% 89.45/26.99 (((setunionsingleton) =>
% 89.45/26.99 (((singletonprop) =>
% 89.45/26.99 (((ex1E1) =>
% 89.45/26.99 (((ex1I) =>
% 89.45/26.99 (((ex1I2) =>
% 89.45/26.99 (((singletonsuniq) =>
% 89.45/26.99 (((setukpairinjL1) =>
% 89.45/26.99 (((kfstsingleton) =>
% 89.45/26.99 (((theprop) =>
% 89.45/26.99 (((kfstpairEq) =>
% 89.45/26.99 (((cartprodfstin) =>
% 89.45/26.99 (((setukpairinjL2) =>
% 89.45/26.99 (((setukpairinjL) =>
% 89.45/26.99 (((setukpairinjR11) =>
% 89.45/26.99 (((setukpairinjR12) =>
% 89.45/26.99 (((setukpairinjR1) =>
% 89.45/26.99 (((upairequniteq) =>
% 89.45/26.99 ((
% 89.45/26.99 (setukpairinjR2) =>
% 89.45/26.99 ((
% 89.45/26.99 (setukpairinjR) =>
% 89.45/26.99 ((
% 89.45/26.99 (ksndsingleton) =>
% 89.45/26.99 ((
% 89.45/26.99 (ksndpairEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (kpairsurjEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodsndin) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodpairmemEL) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodpairmemER) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodmempaircEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodfstpairEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodsndpairEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodpairsurjEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrI) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrSub) =>
% 89.45/26.99 ((
% 89.45/26.99 (setOfPairsIsBReln) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrERa) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrEL1) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrEL2) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrER) =>
% 89.45/26.99 ((
% 89.45/26.99 (funcImageSingleton) =>
% 89.45/26.99 ((
% 89.45/26.99 (apProp) =>
% 89.45/26.99 ((
% 89.45/26.99 (app) =>
% 89.45/26.99 ((
% 89.45/26.99 (infuncsetfunc) =>
% 89.45/26.99 ((
% 89.45/26.99 (ap2p) =>
% 89.45/26.99 ((
% 89.45/26.99 (funcinfuncset) =>
% 89.45/26.99 ((
% 89.45/26.99 (lamProp) =>
% 89.45/26.99 ((
% 89.45/26.99 (lamp) =>
% 89.45/26.99 ((
% 89.45/26.99 (lam2p) =>
% 89.45/26.99 ((
% 89.45/26.99 (brelnall1) =>
% 89.45/26.99 ((
% 89.45/26.99 (brelnall2) =>
% 89.45/26.99 ((
% 89.45/26.99 (!!) @ (
% 89.45/26.99 (('#B') @ (
% 89.45/26.99 !!) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#S') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))) @
% 89.45/26.99 ex1)))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 !!))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#S') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#C') @ in)))))))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 !!))))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#C') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#C') @ in)))))))))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#S') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B'))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))))))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#C') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))))))) @
% 89.45/26.99 (
% 89.45/26.99 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.45/26.99 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1433])).
% 89.45/26.99 thf(zip_derived_cl1452, plain,
% 89.45/26.99 (~ (((upairset2E) =>
% 89.45/26.99 (((upairsubunion) =>
% 89.45/26.99 (((upairinpowunion) =>
% 89.45/26.99 (((ubforcartprodlem1) =>
% 89.45/26.99 (((ubforcartprodlem2) =>
% 89.45/26.99 (((ubforcartprodlem3) =>
% 89.45/26.99 (((cartprodpairin) =>
% 89.45/26.99 (((cartprodmempair1) =>
% 89.45/26.99 (((cartprodmempair) =>
% 89.45/26.99 (((setunionE2) =>
% 89.45/26.99 (((setunionsingleton1) =>
% 89.45/26.99 (((setunionsingleton2) =>
% 89.45/26.99 (((setunionsingleton) =>
% 89.45/26.99 (((singletonprop) =>
% 89.45/26.99 (((ex1E1) =>
% 89.45/26.99 (((ex1I) =>
% 89.45/26.99 (((ex1I2) =>
% 89.45/26.99 (((singletonsuniq) =>
% 89.45/26.99 (((setukpairinjL1) =>
% 89.45/26.99 (((kfstsingleton) =>
% 89.45/26.99 (((theprop) =>
% 89.45/26.99 (((kfstpairEq) =>
% 89.45/26.99 (((cartprodfstin) =>
% 89.45/26.99 (((setukpairinjL2) =>
% 89.45/26.99 (((setukpairinjL) =>
% 89.45/26.99 (((setukpairinjR11) =>
% 89.45/26.99 (((setukpairinjR12) =>
% 89.45/26.99 (((setukpairinjR1) =>
% 89.45/26.99 (((upairequniteq) =>
% 89.45/26.99 (((setukpairinjR2) =>
% 89.45/26.99 ((
% 89.45/26.99 (setukpairinjR) =>
% 89.45/26.99 ((
% 89.45/26.99 (ksndsingleton) =>
% 89.45/26.99 ((
% 89.45/26.99 (ksndpairEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (kpairsurjEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodsndin) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodpairmemEL) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodpairmemER) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodmempaircEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodfstpairEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodsndpairEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodpairsurjEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrI) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrSub) =>
% 89.45/26.99 ((
% 89.45/26.99 (setOfPairsIsBReln) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrERa) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrEL1) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrEL2) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrER) =>
% 89.45/26.99 ((
% 89.45/26.99 (funcImageSingleton) =>
% 89.45/26.99 ((
% 89.45/26.99 (apProp) =>
% 89.45/26.99 ((
% 89.45/26.99 (app) =>
% 89.45/26.99 ((
% 89.45/26.99 (infuncsetfunc) =>
% 89.45/26.99 ((
% 89.45/26.99 (ap2p) =>
% 89.45/26.99 ((
% 89.45/26.99 (funcinfuncset) =>
% 89.45/26.99 ((
% 89.45/26.99 (lamProp) =>
% 89.45/26.99 ((
% 89.45/26.99 (lamp) =>
% 89.45/26.99 ((
% 89.45/26.99 (lam2p) =>
% 89.45/26.99 ((
% 89.45/26.99 (brelnall1) =>
% 89.45/26.99 ((
% 89.45/26.99 (brelnall2) =>
% 89.45/26.99 ((
% 89.45/26.99 (!!) @ (
% 89.45/26.99 (('#B') @ (
% 89.45/26.99 !!) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#S') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))) @
% 89.45/26.99 ex1)))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 !!))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#S') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#C') @ in)))))))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 !!))))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#C') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#C') @ in)))))))))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#S') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B'))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))))))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#C') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))))))) @
% 89.45/26.99 (
% 89.45/26.99 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.45/26.99 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1444])).
% 89.45/26.99 thf(zip_derived_cl1459, plain,
% 89.45/26.99 (~ (((upairsubunion) =>
% 89.45/26.99 (((upairinpowunion) =>
% 89.45/26.99 (((ubforcartprodlem1) =>
% 89.45/26.99 (((ubforcartprodlem2) =>
% 89.45/26.99 (((ubforcartprodlem3) =>
% 89.45/26.99 (((cartprodpairin) =>
% 89.45/26.99 (((cartprodmempair1) =>
% 89.45/26.99 (((cartprodmempair) =>
% 89.45/26.99 (((setunionE2) =>
% 89.45/26.99 (((setunionsingleton1) =>
% 89.45/26.99 (((setunionsingleton2) =>
% 89.45/26.99 (((setunionsingleton) =>
% 89.45/26.99 (((singletonprop) =>
% 89.45/26.99 (((ex1E1) =>
% 89.45/26.99 (((ex1I) =>
% 89.45/26.99 (((ex1I2) =>
% 89.45/26.99 (((singletonsuniq) =>
% 89.45/26.99 (((setukpairinjL1) =>
% 89.45/26.99 (((kfstsingleton) =>
% 89.45/26.99 (((theprop) =>
% 89.45/26.99 (((kfstpairEq) =>
% 89.45/26.99 (((cartprodfstin) =>
% 89.45/26.99 (((setukpairinjL2) =>
% 89.45/26.99 (((setukpairinjL) =>
% 89.45/26.99 (((setukpairinjR11) =>
% 89.45/26.99 (((setukpairinjR12) =>
% 89.45/26.99 (((setukpairinjR1) =>
% 89.45/26.99 (((upairequniteq) =>
% 89.45/26.99 (((setukpairinjR2) =>
% 89.45/26.99 (((setukpairinjR) =>
% 89.45/26.99 ((
% 89.45/26.99 (ksndsingleton) =>
% 89.45/26.99 ((
% 89.45/26.99 (ksndpairEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (kpairsurjEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodsndin) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodpairmemEL) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodpairmemER) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodmempaircEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodfstpairEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodsndpairEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodpairsurjEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrI) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrSub) =>
% 89.45/26.99 ((
% 89.45/26.99 (setOfPairsIsBReln) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrERa) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrEL1) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrEL2) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrER) =>
% 89.45/26.99 ((
% 89.45/26.99 (funcImageSingleton) =>
% 89.45/26.99 ((
% 89.45/26.99 (apProp) =>
% 89.45/26.99 ((
% 89.45/26.99 (app) =>
% 89.45/26.99 ((
% 89.45/26.99 (infuncsetfunc) =>
% 89.45/26.99 ((
% 89.45/26.99 (ap2p) =>
% 89.45/26.99 ((
% 89.45/26.99 (funcinfuncset) =>
% 89.45/26.99 ((
% 89.45/26.99 (lamProp) =>
% 89.45/26.99 ((
% 89.45/26.99 (lamp) =>
% 89.45/26.99 ((
% 89.45/26.99 (lam2p) =>
% 89.45/26.99 ((
% 89.45/26.99 (brelnall1) =>
% 89.45/26.99 ((
% 89.45/26.99 (brelnall2) =>
% 89.45/26.99 ((
% 89.45/26.99 (!!) @ (
% 89.45/26.99 (('#B') @ (
% 89.45/26.99 !!) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#S') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))) @
% 89.45/26.99 ex1)))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 !!))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#S') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#C') @ in)))))))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 !!))))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#C') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#C') @ in)))))))))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#S') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B'))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))))))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#C') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))))))) @
% 89.45/26.99 (
% 89.45/26.99 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.45/26.99 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1452])).
% 89.45/26.99 thf(zip_derived_cl1466, plain,
% 89.45/26.99 (~ (((upairinpowunion) =>
% 89.45/26.99 (((ubforcartprodlem1) =>
% 89.45/26.99 (((ubforcartprodlem2) =>
% 89.45/26.99 (((ubforcartprodlem3) =>
% 89.45/26.99 (((cartprodpairin) =>
% 89.45/26.99 (((cartprodmempair1) =>
% 89.45/26.99 (((cartprodmempair) =>
% 89.45/26.99 (((setunionE2) =>
% 89.45/26.99 (((setunionsingleton1) =>
% 89.45/26.99 (((setunionsingleton2) =>
% 89.45/26.99 (((setunionsingleton) =>
% 89.45/26.99 (((singletonprop) =>
% 89.45/26.99 (((ex1E1) =>
% 89.45/26.99 (((ex1I) =>
% 89.45/26.99 (((ex1I2) =>
% 89.45/26.99 (((singletonsuniq) =>
% 89.45/26.99 (((setukpairinjL1) =>
% 89.45/26.99 (((kfstsingleton) =>
% 89.45/26.99 (((theprop) =>
% 89.45/26.99 (((kfstpairEq) =>
% 89.45/26.99 (((cartprodfstin) =>
% 89.45/26.99 (((setukpairinjL2) =>
% 89.45/26.99 (((setukpairinjL) =>
% 89.45/26.99 (((setukpairinjR11) =>
% 89.45/26.99 (((setukpairinjR12) =>
% 89.45/26.99 (((setukpairinjR1) =>
% 89.45/26.99 (((upairequniteq) =>
% 89.45/26.99 (((setukpairinjR2) =>
% 89.45/26.99 (((setukpairinjR) =>
% 89.45/26.99 (((ksndsingleton) =>
% 89.45/26.99 ((
% 89.45/26.99 (ksndpairEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (kpairsurjEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodsndin) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodpairmemEL) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodpairmemER) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodmempaircEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodfstpairEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodsndpairEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodpairsurjEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrI) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrSub) =>
% 89.45/26.99 ((
% 89.45/26.99 (setOfPairsIsBReln) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrERa) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrEL1) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrEL2) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrER) =>
% 89.45/26.99 ((
% 89.45/26.99 (funcImageSingleton) =>
% 89.45/26.99 ((
% 89.45/26.99 (apProp) =>
% 89.45/26.99 ((
% 89.45/26.99 (app) =>
% 89.45/26.99 ((
% 89.45/26.99 (infuncsetfunc) =>
% 89.45/26.99 ((
% 89.45/26.99 (ap2p) =>
% 89.45/26.99 ((
% 89.45/26.99 (funcinfuncset) =>
% 89.45/26.99 ((
% 89.45/26.99 (lamProp) =>
% 89.45/26.99 ((
% 89.45/26.99 (lamp) =>
% 89.45/26.99 ((
% 89.45/26.99 (lam2p) =>
% 89.45/26.99 ((
% 89.45/26.99 (brelnall1) =>
% 89.45/26.99 ((
% 89.45/26.99 (brelnall2) =>
% 89.45/26.99 ((
% 89.45/26.99 (!!) @ (
% 89.45/26.99 (('#B') @ (
% 89.45/26.99 !!) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#S') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))) @
% 89.45/26.99 ex1)))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 !!))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#S') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#C') @ in)))))))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 !!))))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#C') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#C') @ in)))))))))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#S') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B'))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))))))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#C') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))))))) @
% 89.45/26.99 (
% 89.45/26.99 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.45/26.99 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1459])).
% 89.45/26.99 thf(zip_derived_cl1473, plain,
% 89.45/26.99 (~ (((ubforcartprodlem1) =>
% 89.45/26.99 (((ubforcartprodlem2) =>
% 89.45/26.99 (((ubforcartprodlem3) =>
% 89.45/26.99 (((cartprodpairin) =>
% 89.45/26.99 (((cartprodmempair1) =>
% 89.45/26.99 (((cartprodmempair) =>
% 89.45/26.99 (((setunionE2) =>
% 89.45/26.99 (((setunionsingleton1) =>
% 89.45/26.99 (((setunionsingleton2) =>
% 89.45/26.99 (((setunionsingleton) =>
% 89.45/26.99 (((singletonprop) =>
% 89.45/26.99 (((ex1E1) =>
% 89.45/26.99 (((ex1I) =>
% 89.45/26.99 (((ex1I2) =>
% 89.45/26.99 (((singletonsuniq) =>
% 89.45/26.99 (((setukpairinjL1) =>
% 89.45/26.99 (((kfstsingleton) =>
% 89.45/26.99 (((theprop) =>
% 89.45/26.99 (((kfstpairEq) =>
% 89.45/26.99 (((cartprodfstin) =>
% 89.45/26.99 (((setukpairinjL2) =>
% 89.45/26.99 (((setukpairinjL) =>
% 89.45/26.99 (((setukpairinjR11) =>
% 89.45/26.99 (((setukpairinjR12) =>
% 89.45/26.99 (((setukpairinjR1) =>
% 89.45/26.99 (((upairequniteq) =>
% 89.45/26.99 (((setukpairinjR2) =>
% 89.45/26.99 (((setukpairinjR) =>
% 89.45/26.99 (((ksndsingleton) =>
% 89.45/26.99 (((ksndpairEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (kpairsurjEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodsndin) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodpairmemEL) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodpairmemER) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodmempaircEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodfstpairEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodsndpairEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodpairsurjEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrI) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrSub) =>
% 89.45/26.99 ((
% 89.45/26.99 (setOfPairsIsBReln) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrERa) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrEL1) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrEL2) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrER) =>
% 89.45/26.99 ((
% 89.45/26.99 (funcImageSingleton) =>
% 89.45/26.99 ((
% 89.45/26.99 (apProp) =>
% 89.45/26.99 ((
% 89.45/26.99 (app) =>
% 89.45/26.99 ((
% 89.45/26.99 (infuncsetfunc) =>
% 89.45/26.99 ((
% 89.45/26.99 (ap2p) =>
% 89.45/26.99 ((
% 89.45/26.99 (funcinfuncset) =>
% 89.45/26.99 ((
% 89.45/26.99 (lamProp) =>
% 89.45/26.99 ((
% 89.45/26.99 (lamp) =>
% 89.45/26.99 ((
% 89.45/26.99 (lam2p) =>
% 89.45/26.99 ((
% 89.45/26.99 (brelnall1) =>
% 89.45/26.99 ((
% 89.45/26.99 (brelnall2) =>
% 89.45/26.99 ((
% 89.45/26.99 (!!) @ (
% 89.45/26.99 (('#B') @ (
% 89.45/26.99 !!) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#S') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))) @
% 89.45/26.99 ex1)))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 !!))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#S') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#C') @ in)))))))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 !!))))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#C') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#C') @ in)))))))))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#S') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B'))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))))))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#C') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))))))) @
% 89.45/26.99 (
% 89.45/26.99 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.45/26.99 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1466])).
% 89.45/26.99 thf(zip_derived_cl1480, plain,
% 89.45/26.99 (~ (((ubforcartprodlem2) =>
% 89.45/26.99 (((ubforcartprodlem3) =>
% 89.45/26.99 (((cartprodpairin) =>
% 89.45/26.99 (((cartprodmempair1) =>
% 89.45/26.99 (((cartprodmempair) =>
% 89.45/26.99 (((setunionE2) =>
% 89.45/26.99 (((setunionsingleton1) =>
% 89.45/26.99 (((setunionsingleton2) =>
% 89.45/26.99 (((setunionsingleton) =>
% 89.45/26.99 (((singletonprop) =>
% 89.45/26.99 (((ex1E1) =>
% 89.45/26.99 (((ex1I) =>
% 89.45/26.99 (((ex1I2) =>
% 89.45/26.99 (((singletonsuniq) =>
% 89.45/26.99 (((setukpairinjL1) =>
% 89.45/26.99 (((kfstsingleton) =>
% 89.45/26.99 (((theprop) =>
% 89.45/26.99 (((kfstpairEq) =>
% 89.45/26.99 (((cartprodfstin) =>
% 89.45/26.99 (((setukpairinjL2) =>
% 89.45/26.99 (((setukpairinjL) =>
% 89.45/26.99 (((setukpairinjR11) =>
% 89.45/26.99 (((setukpairinjR12) =>
% 89.45/26.99 (((setukpairinjR1) =>
% 89.45/26.99 (((upairequniteq) =>
% 89.45/26.99 (((setukpairinjR2) =>
% 89.45/26.99 (((setukpairinjR) =>
% 89.45/26.99 (((ksndsingleton) =>
% 89.45/26.99 (((ksndpairEq) =>
% 89.45/26.99 (((kpairsurjEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodsndin) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodpairmemEL) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodpairmemER) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodmempaircEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodfstpairEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodsndpairEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodpairsurjEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrI) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrSub) =>
% 89.45/26.99 ((
% 89.45/26.99 (setOfPairsIsBReln) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrERa) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrEL1) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrEL2) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrER) =>
% 89.45/26.99 ((
% 89.45/26.99 (funcImageSingleton) =>
% 89.45/26.99 ((
% 89.45/26.99 (apProp) =>
% 89.45/26.99 ((
% 89.45/26.99 (app) =>
% 89.45/26.99 ((
% 89.45/26.99 (infuncsetfunc) =>
% 89.45/26.99 ((
% 89.45/26.99 (ap2p) =>
% 89.45/26.99 ((
% 89.45/26.99 (funcinfuncset) =>
% 89.45/26.99 ((
% 89.45/26.99 (lamProp) =>
% 89.45/26.99 ((
% 89.45/26.99 (lamp) =>
% 89.45/26.99 ((
% 89.45/26.99 (lam2p) =>
% 89.45/26.99 ((
% 89.45/26.99 (brelnall1) =>
% 89.45/26.99 ((
% 89.45/26.99 (brelnall2) =>
% 89.45/26.99 ((
% 89.45/26.99 (!!) @ (
% 89.45/26.99 (('#B') @ (
% 89.45/26.99 !!) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#S') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))) @
% 89.45/26.99 ex1)))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 !!))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#S') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#C') @ in)))))))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 !!))))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#C') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#C') @ in)))))))))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#S') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B'))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))))))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#C') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))))))) @
% 89.45/26.99 (
% 89.45/26.99 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.45/26.99 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1473])).
% 89.45/26.99 thf(zip_derived_cl1488, plain,
% 89.45/26.99 (~ (((ubforcartprodlem3) =>
% 89.45/26.99 (((cartprodpairin) =>
% 89.45/26.99 (((cartprodmempair1) =>
% 89.45/26.99 (((cartprodmempair) =>
% 89.45/26.99 (((setunionE2) =>
% 89.45/26.99 (((setunionsingleton1) =>
% 89.45/26.99 (((setunionsingleton2) =>
% 89.45/26.99 (((setunionsingleton) =>
% 89.45/26.99 (((singletonprop) =>
% 89.45/26.99 (((ex1E1) =>
% 89.45/26.99 (((ex1I) =>
% 89.45/26.99 (((ex1I2) =>
% 89.45/26.99 (((singletonsuniq) =>
% 89.45/26.99 (((setukpairinjL1) =>
% 89.45/26.99 (((kfstsingleton) =>
% 89.45/26.99 (((theprop) =>
% 89.45/26.99 (((kfstpairEq) =>
% 89.45/26.99 (((cartprodfstin) =>
% 89.45/26.99 (((setukpairinjL2) =>
% 89.45/26.99 (((setukpairinjL) =>
% 89.45/26.99 (((setukpairinjR11) =>
% 89.45/26.99 (((setukpairinjR12) =>
% 89.45/26.99 (((setukpairinjR1) =>
% 89.45/26.99 (((upairequniteq) =>
% 89.45/26.99 (((setukpairinjR2) =>
% 89.45/26.99 (((setukpairinjR) =>
% 89.45/26.99 (((ksndsingleton) =>
% 89.45/26.99 (((ksndpairEq) =>
% 89.45/26.99 (((kpairsurjEq) =>
% 89.45/26.99 (((cartprodsndin) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodpairmemEL) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodpairmemER) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodmempaircEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodfstpairEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodsndpairEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodpairsurjEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrI) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrSub) =>
% 89.45/26.99 ((
% 89.45/26.99 (setOfPairsIsBReln) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrERa) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrEL1) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrEL2) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrER) =>
% 89.45/26.99 ((
% 89.45/26.99 (funcImageSingleton) =>
% 89.45/26.99 ((
% 89.45/26.99 (apProp) =>
% 89.45/26.99 ((
% 89.45/26.99 (app) =>
% 89.45/26.99 ((
% 89.45/26.99 (infuncsetfunc) =>
% 89.45/26.99 ((
% 89.45/26.99 (ap2p) =>
% 89.45/26.99 ((
% 89.45/26.99 (funcinfuncset) =>
% 89.45/26.99 ((
% 89.45/26.99 (lamProp) =>
% 89.45/26.99 ((
% 89.45/26.99 (lamp) =>
% 89.45/26.99 ((
% 89.45/26.99 (lam2p) =>
% 89.45/26.99 ((
% 89.45/26.99 (brelnall1) =>
% 89.45/26.99 ((
% 89.45/26.99 (brelnall2) =>
% 89.45/26.99 ((
% 89.45/26.99 (!!) @ (
% 89.45/26.99 (('#B') @ (
% 89.45/26.99 !!) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#S') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))) @
% 89.45/26.99 ex1)))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 !!))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#S') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#C') @ in)))))))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 !!))))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#C') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#C') @ in)))))))))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#S') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B'))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))))))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#C') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))))))) @
% 89.45/26.99 (
% 89.45/26.99 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.45/26.99 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1480])).
% 89.45/26.99 thf(zip_derived_cl1496, plain,
% 89.45/26.99 (~ (((cartprodpairin) =>
% 89.45/26.99 (((cartprodmempair1) =>
% 89.45/26.99 (((cartprodmempair) =>
% 89.45/26.99 (((setunionE2) =>
% 89.45/26.99 (((setunionsingleton1) =>
% 89.45/26.99 (((setunionsingleton2) =>
% 89.45/26.99 (((setunionsingleton) =>
% 89.45/26.99 (((singletonprop) =>
% 89.45/26.99 (((ex1E1) =>
% 89.45/26.99 (((ex1I) =>
% 89.45/26.99 (((ex1I2) =>
% 89.45/26.99 (((singletonsuniq) =>
% 89.45/26.99 (((setukpairinjL1) =>
% 89.45/26.99 (((kfstsingleton) =>
% 89.45/26.99 (((theprop) =>
% 89.45/26.99 (((kfstpairEq) =>
% 89.45/26.99 (((cartprodfstin) =>
% 89.45/26.99 (((setukpairinjL2) =>
% 89.45/26.99 (((setukpairinjL) =>
% 89.45/26.99 (((setukpairinjR11) =>
% 89.45/26.99 (((setukpairinjR12) =>
% 89.45/26.99 (((setukpairinjR1) =>
% 89.45/26.99 (((upairequniteq) =>
% 89.45/26.99 (((setukpairinjR2) =>
% 89.45/26.99 (((setukpairinjR) =>
% 89.45/26.99 (((ksndsingleton) =>
% 89.45/26.99 (((ksndpairEq) =>
% 89.45/26.99 (((kpairsurjEq) =>
% 89.45/26.99 (((cartprodsndin) =>
% 89.45/26.99 (((cartprodpairmemEL) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodpairmemER) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodmempaircEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodfstpairEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodsndpairEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodpairsurjEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrI) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrSub) =>
% 89.45/26.99 ((
% 89.45/26.99 (setOfPairsIsBReln) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrERa) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrEL1) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrEL2) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrER) =>
% 89.45/26.99 ((
% 89.45/26.99 (funcImageSingleton) =>
% 89.45/26.99 ((
% 89.45/26.99 (apProp) =>
% 89.45/26.99 ((
% 89.45/26.99 (app) =>
% 89.45/26.99 ((
% 89.45/26.99 (infuncsetfunc) =>
% 89.45/26.99 ((
% 89.45/26.99 (ap2p) =>
% 89.45/26.99 ((
% 89.45/26.99 (funcinfuncset) =>
% 89.45/26.99 ((
% 89.45/26.99 (lamProp) =>
% 89.45/26.99 ((
% 89.45/26.99 (lamp) =>
% 89.45/26.99 ((
% 89.45/26.99 (lam2p) =>
% 89.45/26.99 ((
% 89.45/26.99 (brelnall1) =>
% 89.45/26.99 ((
% 89.45/26.99 (brelnall2) =>
% 89.45/26.99 ((
% 89.45/26.99 (!!) @ (
% 89.45/26.99 (('#B') @ (
% 89.45/26.99 !!) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#S') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))) @
% 89.45/26.99 ex1)))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 !!))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#S') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#C') @ in)))))))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 !!))))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#C') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#C') @ in)))))))))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#S') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B'))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))))))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#C') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))))))) @
% 89.45/26.99 (
% 89.45/26.99 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.45/26.99 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1488])).
% 89.45/26.99 thf(zip_derived_cl1505, plain,
% 89.45/26.99 (~ (((cartprodmempair1) =>
% 89.45/26.99 (((cartprodmempair) =>
% 89.45/26.99 (((setunionE2) =>
% 89.45/26.99 (((setunionsingleton1) =>
% 89.45/26.99 (((setunionsingleton2) =>
% 89.45/26.99 (((setunionsingleton) =>
% 89.45/26.99 (((singletonprop) =>
% 89.45/26.99 (((ex1E1) =>
% 89.45/26.99 (((ex1I) =>
% 89.45/26.99 (((ex1I2) =>
% 89.45/26.99 (((singletonsuniq) =>
% 89.45/26.99 (((setukpairinjL1) =>
% 89.45/26.99 (((kfstsingleton) =>
% 89.45/26.99 (((theprop) =>
% 89.45/26.99 (((kfstpairEq) =>
% 89.45/26.99 (((cartprodfstin) =>
% 89.45/26.99 (((setukpairinjL2) =>
% 89.45/26.99 (((setukpairinjL) =>
% 89.45/26.99 (((setukpairinjR11) =>
% 89.45/26.99 (((setukpairinjR12) =>
% 89.45/26.99 (((setukpairinjR1) =>
% 89.45/26.99 (((upairequniteq) =>
% 89.45/26.99 (((setukpairinjR2) =>
% 89.45/26.99 (((setukpairinjR) =>
% 89.45/26.99 (((ksndsingleton) =>
% 89.45/26.99 (((ksndpairEq) =>
% 89.45/26.99 (((kpairsurjEq) =>
% 89.45/26.99 (((cartprodsndin) =>
% 89.45/26.99 (((cartprodpairmemEL) =>
% 89.45/26.99 (((cartprodpairmemER) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodmempaircEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodfstpairEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodsndpairEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodpairsurjEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrI) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrSub) =>
% 89.45/26.99 ((
% 89.45/26.99 (setOfPairsIsBReln) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrERa) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrEL1) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrEL2) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrER) =>
% 89.45/26.99 ((
% 89.45/26.99 (funcImageSingleton) =>
% 89.45/26.99 ((
% 89.45/26.99 (apProp) =>
% 89.45/26.99 ((
% 89.45/26.99 (app) =>
% 89.45/26.99 ((
% 89.45/26.99 (infuncsetfunc) =>
% 89.45/26.99 ((
% 89.45/26.99 (ap2p) =>
% 89.45/26.99 ((
% 89.45/26.99 (funcinfuncset) =>
% 89.45/26.99 ((
% 89.45/26.99 (lamProp) =>
% 89.45/26.99 ((
% 89.45/26.99 (lamp) =>
% 89.45/26.99 ((
% 89.45/26.99 (lam2p) =>
% 89.45/26.99 ((
% 89.45/26.99 (brelnall1) =>
% 89.45/26.99 ((
% 89.45/26.99 (brelnall2) =>
% 89.45/26.99 ((
% 89.45/26.99 (!!) @ (
% 89.45/26.99 (('#B') @ (
% 89.45/26.99 !!) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#S') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))) @
% 89.45/26.99 ex1)))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 !!))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#S') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#C') @ in)))))))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 !!))))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#C') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#C') @ in)))))))))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#S') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B'))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))))))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#C') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))))))) @
% 89.45/26.99 (
% 89.45/26.99 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.45/26.99 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1496])).
% 89.45/26.99 thf(zip_derived_cl1515, plain,
% 89.45/26.99 (~ (((cartprodmempair) =>
% 89.45/26.99 (((setunionE2) =>
% 89.45/26.99 (((setunionsingleton1) =>
% 89.45/26.99 (((setunionsingleton2) =>
% 89.45/26.99 (((setunionsingleton) =>
% 89.45/26.99 (((singletonprop) =>
% 89.45/26.99 (((ex1E1) =>
% 89.45/26.99 (((ex1I) =>
% 89.45/26.99 (((ex1I2) =>
% 89.45/26.99 (((singletonsuniq) =>
% 89.45/26.99 (((setukpairinjL1) =>
% 89.45/26.99 (((kfstsingleton) =>
% 89.45/26.99 (((theprop) =>
% 89.45/26.99 (((kfstpairEq) =>
% 89.45/26.99 (((cartprodfstin) =>
% 89.45/26.99 (((setukpairinjL2) =>
% 89.45/26.99 (((setukpairinjL) =>
% 89.45/26.99 (((setukpairinjR11) =>
% 89.45/26.99 (((setukpairinjR12) =>
% 89.45/26.99 (((setukpairinjR1) =>
% 89.45/26.99 (((upairequniteq) =>
% 89.45/26.99 (((setukpairinjR2) =>
% 89.45/26.99 (((setukpairinjR) =>
% 89.45/26.99 (((ksndsingleton) =>
% 89.45/26.99 (((ksndpairEq) =>
% 89.45/26.99 (((kpairsurjEq) =>
% 89.45/26.99 (((cartprodsndin) =>
% 89.45/26.99 (((cartprodpairmemEL) =>
% 89.45/26.99 (((cartprodpairmemER) =>
% 89.45/26.99 (((cartprodmempaircEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodfstpairEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodsndpairEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (cartprodpairsurjEq) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrI) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrSub) =>
% 89.45/26.99 ((
% 89.45/26.99 (setOfPairsIsBReln) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrERa) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrEL1) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrEL2) =>
% 89.45/26.99 ((
% 89.45/26.99 (dpsetconstrER) =>
% 89.45/26.99 ((
% 89.45/26.99 (funcImageSingleton) =>
% 89.45/26.99 ((
% 89.45/26.99 (apProp) =>
% 89.45/26.99 ((
% 89.45/26.99 (app) =>
% 89.45/26.99 ((
% 89.45/26.99 (infuncsetfunc) =>
% 89.45/26.99 ((
% 89.45/26.99 (ap2p) =>
% 89.45/26.99 ((
% 89.45/26.99 (funcinfuncset) =>
% 89.45/26.99 ((
% 89.45/26.99 (lamProp) =>
% 89.45/26.99 ((
% 89.45/26.99 (lamp) =>
% 89.45/26.99 ((
% 89.45/26.99 (lam2p) =>
% 89.45/26.99 ((
% 89.45/26.99 (brelnall1) =>
% 89.45/26.99 ((
% 89.45/26.99 (brelnall2) =>
% 89.45/26.99 ((
% 89.45/26.99 (!!) @ (
% 89.45/26.99 (('#B') @ (
% 89.45/26.99 !!) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#S') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))) @
% 89.45/26.99 ex1)))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 !!))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#S') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#B') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 '#S') @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 =>))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#C') @ in)))))))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/26.99 !!))))) @
% 89.45/26.99 (
% 89.45/26.99 (
% 89.45/26.99 ('#C') @ (
% 89.45/26.99 (
% 89.45/26.99 ('#B') @ (
% 89.45/27.00 '#B') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#B') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#S') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 =>))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#C') @ in)))))))))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#S') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#S') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#B'))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 =>))))))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#C') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#B') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#S') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 =>))))))) @
% 89.45/27.00 (
% 89.45/27.00 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.45/27.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1505])).
% 89.45/27.00 thf(zip_derived_cl1525, plain,
% 89.45/27.00 (~ (((setunionE2) =>
% 89.45/27.00 (((setunionsingleton1) =>
% 89.45/27.00 (((setunionsingleton2) =>
% 89.45/27.00 (((setunionsingleton) =>
% 89.45/27.00 (((singletonprop) =>
% 89.45/27.00 (((ex1E1) =>
% 89.45/27.00 (((ex1I) =>
% 89.45/27.00 (((ex1I2) =>
% 89.45/27.00 (((singletonsuniq) =>
% 89.45/27.00 (((setukpairinjL1) =>
% 89.45/27.00 (((kfstsingleton) =>
% 89.45/27.00 (((theprop) =>
% 89.45/27.00 (((kfstpairEq) =>
% 89.45/27.00 (((cartprodfstin) =>
% 89.45/27.00 (((setukpairinjL2) =>
% 89.45/27.00 (((setukpairinjL) =>
% 89.45/27.00 (((setukpairinjR11) =>
% 89.45/27.00 (((setukpairinjR12) =>
% 89.45/27.00 (((setukpairinjR1) =>
% 89.45/27.00 (((upairequniteq) =>
% 89.45/27.00 (((setukpairinjR2) =>
% 89.45/27.00 (((setukpairinjR) =>
% 89.45/27.00 (((ksndsingleton) =>
% 89.45/27.00 (((ksndpairEq) =>
% 89.45/27.00 (((kpairsurjEq) =>
% 89.45/27.00 (((cartprodsndin) =>
% 89.45/27.00 (((cartprodpairmemEL) =>
% 89.45/27.00 (((cartprodpairmemER) =>
% 89.45/27.00 (((cartprodmempaircEq) =>
% 89.45/27.00 (((cartprodfstpairEq) =>
% 89.45/27.00 ((
% 89.45/27.00 (cartprodsndpairEq) =>
% 89.45/27.00 ((
% 89.45/27.00 (cartprodpairsurjEq) =>
% 89.45/27.00 ((
% 89.45/27.00 (dpsetconstrI) =>
% 89.45/27.00 ((
% 89.45/27.00 (dpsetconstrSub) =>
% 89.45/27.00 ((
% 89.45/27.00 (setOfPairsIsBReln) =>
% 89.45/27.00 ((
% 89.45/27.00 (dpsetconstrERa) =>
% 89.45/27.00 ((
% 89.45/27.00 (dpsetconstrEL1) =>
% 89.45/27.00 ((
% 89.45/27.00 (dpsetconstrEL2) =>
% 89.45/27.00 ((
% 89.45/27.00 (dpsetconstrER) =>
% 89.45/27.00 ((
% 89.45/27.00 (funcImageSingleton) =>
% 89.45/27.00 ((
% 89.45/27.00 (apProp) =>
% 89.45/27.00 ((
% 89.45/27.00 (app) =>
% 89.45/27.00 ((
% 89.45/27.00 (infuncsetfunc) =>
% 89.45/27.00 ((
% 89.45/27.00 (ap2p) =>
% 89.45/27.00 ((
% 89.45/27.00 (funcinfuncset) =>
% 89.45/27.00 ((
% 89.45/27.00 (lamProp) =>
% 89.45/27.00 ((
% 89.45/27.00 (lamp) =>
% 89.45/27.00 ((
% 89.45/27.00 (lam2p) =>
% 89.45/27.00 ((
% 89.45/27.00 (brelnall1) =>
% 89.45/27.00 ((
% 89.45/27.00 (brelnall2) =>
% 89.45/27.00 ((
% 89.45/27.00 (!!) @ (
% 89.45/27.00 (('#B') @ (
% 89.45/27.00 !!) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#S') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#S') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 =>))) @
% 89.45/27.00 ex1)))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 !!))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#S') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#B') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#S') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 =>))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#C') @ in)))))))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 !!))))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#C') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#B') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#B') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#S') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 =>))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#C') @ in)))))))))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#S') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#S') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#B'))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 =>))))))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#C') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#B') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#S') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 =>))))))) @
% 89.45/27.00 (
% 89.45/27.00 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.45/27.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1515])).
% 89.45/27.00 thf(zip_derived_cl1535, plain,
% 89.45/27.00 (~ (((setunionsingleton1) =>
% 89.45/27.00 (((setunionsingleton2) =>
% 89.45/27.00 (((setunionsingleton) =>
% 89.45/27.00 (((singletonprop) =>
% 89.45/27.00 (((ex1E1) =>
% 89.45/27.00 (((ex1I) =>
% 89.45/27.00 (((ex1I2) =>
% 89.45/27.00 (((singletonsuniq) =>
% 89.45/27.00 (((setukpairinjL1) =>
% 89.45/27.00 (((kfstsingleton) =>
% 89.45/27.00 (((theprop) =>
% 89.45/27.00 (((kfstpairEq) =>
% 89.45/27.00 (((cartprodfstin) =>
% 89.45/27.00 (((setukpairinjL2) =>
% 89.45/27.00 (((setukpairinjL) =>
% 89.45/27.00 (((setukpairinjR11) =>
% 89.45/27.00 (((setukpairinjR12) =>
% 89.45/27.00 (((setukpairinjR1) =>
% 89.45/27.00 (((upairequniteq) =>
% 89.45/27.00 (((setukpairinjR2) =>
% 89.45/27.00 (((setukpairinjR) =>
% 89.45/27.00 (((ksndsingleton) =>
% 89.45/27.00 (((ksndpairEq) =>
% 89.45/27.00 (((kpairsurjEq) =>
% 89.45/27.00 (((cartprodsndin) =>
% 89.45/27.00 (((cartprodpairmemEL) =>
% 89.45/27.00 (((cartprodpairmemER) =>
% 89.45/27.00 (((cartprodmempaircEq) =>
% 89.45/27.00 (((cartprodfstpairEq) =>
% 89.45/27.00 (((cartprodsndpairEq) =>
% 89.45/27.00 ((
% 89.45/27.00 (cartprodpairsurjEq) =>
% 89.45/27.00 ((
% 89.45/27.00 (dpsetconstrI) =>
% 89.45/27.00 ((
% 89.45/27.00 (dpsetconstrSub) =>
% 89.45/27.00 ((
% 89.45/27.00 (setOfPairsIsBReln) =>
% 89.45/27.00 ((
% 89.45/27.00 (dpsetconstrERa) =>
% 89.45/27.00 ((
% 89.45/27.00 (dpsetconstrEL1) =>
% 89.45/27.00 ((
% 89.45/27.00 (dpsetconstrEL2) =>
% 89.45/27.00 ((
% 89.45/27.00 (dpsetconstrER) =>
% 89.45/27.00 ((
% 89.45/27.00 (funcImageSingleton) =>
% 89.45/27.00 ((
% 89.45/27.00 (apProp) =>
% 89.45/27.00 ((
% 89.45/27.00 (app) =>
% 89.45/27.00 ((
% 89.45/27.00 (infuncsetfunc) =>
% 89.45/27.00 ((
% 89.45/27.00 (ap2p) =>
% 89.45/27.00 ((
% 89.45/27.00 (funcinfuncset) =>
% 89.45/27.00 ((
% 89.45/27.00 (lamProp) =>
% 89.45/27.00 ((
% 89.45/27.00 (lamp) =>
% 89.45/27.00 ((
% 89.45/27.00 (lam2p) =>
% 89.45/27.00 ((
% 89.45/27.00 (brelnall1) =>
% 89.45/27.00 ((
% 89.45/27.00 (brelnall2) =>
% 89.45/27.00 ((
% 89.45/27.00 (!!) @ (
% 89.45/27.00 (('#B') @ (
% 89.45/27.00 !!) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#S') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#S') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 =>))) @
% 89.45/27.00 ex1)))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 !!))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#S') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#B') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#S') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 =>))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#C') @ in)))))))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 !!))))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#C') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#B') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#B') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#S') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 =>))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#C') @ in)))))))))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#S') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#S') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#B'))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 =>))))))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#C') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#B') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#S') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 =>))))))) @
% 89.45/27.00 (
% 89.45/27.00 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.45/27.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1525])).
% 89.45/27.00 thf(zip_derived_cl1545, plain,
% 89.45/27.00 (~ (((setunionsingleton2) =>
% 89.45/27.00 (((setunionsingleton) =>
% 89.45/27.00 (((singletonprop) =>
% 89.45/27.00 (((ex1E1) =>
% 89.45/27.00 (((ex1I) =>
% 89.45/27.00 (((ex1I2) =>
% 89.45/27.00 (((singletonsuniq) =>
% 89.45/27.00 (((setukpairinjL1) =>
% 89.45/27.00 (((kfstsingleton) =>
% 89.45/27.00 (((theprop) =>
% 89.45/27.00 (((kfstpairEq) =>
% 89.45/27.00 (((cartprodfstin) =>
% 89.45/27.00 (((setukpairinjL2) =>
% 89.45/27.00 (((setukpairinjL) =>
% 89.45/27.00 (((setukpairinjR11) =>
% 89.45/27.00 (((setukpairinjR12) =>
% 89.45/27.00 (((setukpairinjR1) =>
% 89.45/27.00 (((upairequniteq) =>
% 89.45/27.00 (((setukpairinjR2) =>
% 89.45/27.00 (((setukpairinjR) =>
% 89.45/27.00 (((ksndsingleton) =>
% 89.45/27.00 (((ksndpairEq) =>
% 89.45/27.00 (((kpairsurjEq) =>
% 89.45/27.00 (((cartprodsndin) =>
% 89.45/27.00 (((cartprodpairmemEL) =>
% 89.45/27.00 (((cartprodpairmemER) =>
% 89.45/27.00 (((cartprodmempaircEq) =>
% 89.45/27.00 (((cartprodfstpairEq) =>
% 89.45/27.00 (((cartprodsndpairEq) =>
% 89.45/27.00 (((cartprodpairsurjEq) =>
% 89.45/27.00 ((
% 89.45/27.00 (dpsetconstrI) =>
% 89.45/27.00 ((
% 89.45/27.00 (dpsetconstrSub) =>
% 89.45/27.00 ((
% 89.45/27.00 (setOfPairsIsBReln) =>
% 89.45/27.00 ((
% 89.45/27.00 (dpsetconstrERa) =>
% 89.45/27.00 ((
% 89.45/27.00 (dpsetconstrEL1) =>
% 89.45/27.00 ((
% 89.45/27.00 (dpsetconstrEL2) =>
% 89.45/27.00 ((
% 89.45/27.00 (dpsetconstrER) =>
% 89.45/27.00 ((
% 89.45/27.00 (funcImageSingleton) =>
% 89.45/27.00 ((
% 89.45/27.00 (apProp) =>
% 89.45/27.00 ((
% 89.45/27.00 (app) =>
% 89.45/27.00 ((
% 89.45/27.00 (infuncsetfunc) =>
% 89.45/27.00 ((
% 89.45/27.00 (ap2p) =>
% 89.45/27.00 ((
% 89.45/27.00 (funcinfuncset) =>
% 89.45/27.00 ((
% 89.45/27.00 (lamProp) =>
% 89.45/27.00 ((
% 89.45/27.00 (lamp) =>
% 89.45/27.00 ((
% 89.45/27.00 (lam2p) =>
% 89.45/27.00 ((
% 89.45/27.00 (brelnall1) =>
% 89.45/27.00 ((
% 89.45/27.00 (brelnall2) =>
% 89.45/27.00 ((
% 89.45/27.00 (!!) @ (
% 89.45/27.00 (('#B') @ (
% 89.45/27.00 !!) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#S') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#S') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 =>))) @
% 89.45/27.00 ex1)))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 !!))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#S') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#B') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#S') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 =>))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#C') @ in)))))))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 !!))))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#C') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#B') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#B') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#S') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 =>))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#C') @ in)))))))))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#S') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#S') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#B'))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 =>))))))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#C') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#B') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#S') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 =>))))))) @
% 89.45/27.00 (
% 89.45/27.00 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.45/27.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1535])).
% 89.45/27.00 thf(zip_derived_cl1555, plain,
% 89.45/27.00 (~ (((setunionsingleton) =>
% 89.45/27.00 (((singletonprop) =>
% 89.45/27.00 (((ex1E1) =>
% 89.45/27.00 (((ex1I) =>
% 89.45/27.00 (((ex1I2) =>
% 89.45/27.00 (((singletonsuniq) =>
% 89.45/27.00 (((setukpairinjL1) =>
% 89.45/27.00 (((kfstsingleton) =>
% 89.45/27.00 (((theprop) =>
% 89.45/27.00 (((kfstpairEq) =>
% 89.45/27.00 (((cartprodfstin) =>
% 89.45/27.00 (((setukpairinjL2) =>
% 89.45/27.00 (((setukpairinjL) =>
% 89.45/27.00 (((setukpairinjR11) =>
% 89.45/27.00 (((setukpairinjR12) =>
% 89.45/27.00 (((setukpairinjR1) =>
% 89.45/27.00 (((upairequniteq) =>
% 89.45/27.00 (((setukpairinjR2) =>
% 89.45/27.00 (((setukpairinjR) =>
% 89.45/27.00 (((ksndsingleton) =>
% 89.45/27.00 (((ksndpairEq) =>
% 89.45/27.00 (((kpairsurjEq) =>
% 89.45/27.00 (((cartprodsndin) =>
% 89.45/27.00 (((cartprodpairmemEL) =>
% 89.45/27.00 (((cartprodpairmemER) =>
% 89.45/27.00 (((cartprodmempaircEq) =>
% 89.45/27.00 (((cartprodfstpairEq) =>
% 89.45/27.00 (((cartprodsndpairEq) =>
% 89.45/27.00 (((cartprodpairsurjEq) =>
% 89.45/27.00 (((dpsetconstrI) =>
% 89.45/27.00 ((
% 89.45/27.00 (dpsetconstrSub) =>
% 89.45/27.00 ((
% 89.45/27.00 (setOfPairsIsBReln) =>
% 89.45/27.00 ((
% 89.45/27.00 (dpsetconstrERa) =>
% 89.45/27.00 ((
% 89.45/27.00 (dpsetconstrEL1) =>
% 89.45/27.00 ((
% 89.45/27.00 (dpsetconstrEL2) =>
% 89.45/27.00 ((
% 89.45/27.00 (dpsetconstrER) =>
% 89.45/27.00 ((
% 89.45/27.00 (funcImageSingleton) =>
% 89.45/27.00 ((
% 89.45/27.00 (apProp) =>
% 89.45/27.00 ((
% 89.45/27.00 (app) =>
% 89.45/27.00 ((
% 89.45/27.00 (infuncsetfunc) =>
% 89.45/27.00 ((
% 89.45/27.00 (ap2p) =>
% 89.45/27.00 ((
% 89.45/27.00 (funcinfuncset) =>
% 89.45/27.00 ((
% 89.45/27.00 (lamProp) =>
% 89.45/27.00 ((
% 89.45/27.00 (lamp) =>
% 89.45/27.00 ((
% 89.45/27.00 (lam2p) =>
% 89.45/27.00 ((
% 89.45/27.00 (brelnall1) =>
% 89.45/27.00 ((
% 89.45/27.00 (brelnall2) =>
% 89.45/27.00 ((
% 89.45/27.00 (!!) @ (
% 89.45/27.00 (('#B') @ (
% 89.45/27.00 !!) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#S') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#S') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 =>))) @
% 89.45/27.00 ex1)))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 !!))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#S') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#B') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#S') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 =>))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#C') @ in)))))))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 !!))))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#C') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#B') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#B') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#S') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 =>))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#C') @ in)))))))))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#S') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#S') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#B'))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 =>))))))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#C') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#B') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#S') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 =>))))))) @
% 89.45/27.00 (
% 89.45/27.00 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.45/27.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1545])).
% 89.45/27.00 thf(zip_derived_cl1565, plain,
% 89.45/27.00 (~ (((singletonprop) =>
% 89.45/27.00 (((ex1E1) =>
% 89.45/27.00 (((ex1I) =>
% 89.45/27.00 (((ex1I2) =>
% 89.45/27.00 (((singletonsuniq) =>
% 89.45/27.00 (((setukpairinjL1) =>
% 89.45/27.00 (((kfstsingleton) =>
% 89.45/27.00 (((theprop) =>
% 89.45/27.00 (((kfstpairEq) =>
% 89.45/27.00 (((cartprodfstin) =>
% 89.45/27.00 (((setukpairinjL2) =>
% 89.45/27.00 (((setukpairinjL) =>
% 89.45/27.00 (((setukpairinjR11) =>
% 89.45/27.00 (((setukpairinjR12) =>
% 89.45/27.00 (((setukpairinjR1) =>
% 89.45/27.00 (((upairequniteq) =>
% 89.45/27.00 (((setukpairinjR2) =>
% 89.45/27.00 (((setukpairinjR) =>
% 89.45/27.00 (((ksndsingleton) =>
% 89.45/27.00 (((ksndpairEq) =>
% 89.45/27.00 (((kpairsurjEq) =>
% 89.45/27.00 (((cartprodsndin) =>
% 89.45/27.00 (((cartprodpairmemEL) =>
% 89.45/27.00 (((cartprodpairmemER) =>
% 89.45/27.00 (((cartprodmempaircEq) =>
% 89.45/27.00 (((cartprodfstpairEq) =>
% 89.45/27.00 (((cartprodsndpairEq) =>
% 89.45/27.00 (((cartprodpairsurjEq) =>
% 89.45/27.00 (((dpsetconstrI) =>
% 89.45/27.00 (((dpsetconstrSub) =>
% 89.45/27.00 ((
% 89.45/27.00 (setOfPairsIsBReln) =>
% 89.45/27.00 ((
% 89.45/27.00 (dpsetconstrERa) =>
% 89.45/27.00 ((
% 89.45/27.00 (dpsetconstrEL1) =>
% 89.45/27.00 ((
% 89.45/27.00 (dpsetconstrEL2) =>
% 89.45/27.00 ((
% 89.45/27.00 (dpsetconstrER) =>
% 89.45/27.00 ((
% 89.45/27.00 (funcImageSingleton) =>
% 89.45/27.00 ((
% 89.45/27.00 (apProp) =>
% 89.45/27.00 ((
% 89.45/27.00 (app) =>
% 89.45/27.00 ((
% 89.45/27.00 (infuncsetfunc) =>
% 89.45/27.00 ((
% 89.45/27.00 (ap2p) =>
% 89.45/27.00 ((
% 89.45/27.00 (funcinfuncset) =>
% 89.45/27.00 ((
% 89.45/27.00 (lamProp) =>
% 89.45/27.00 ((
% 89.45/27.00 (lamp) =>
% 89.45/27.00 ((
% 89.45/27.00 (lam2p) =>
% 89.45/27.00 ((
% 89.45/27.00 (brelnall1) =>
% 89.45/27.00 ((
% 89.45/27.00 (brelnall2) =>
% 89.45/27.00 ((
% 89.45/27.00 (!!) @ (
% 89.45/27.00 (('#B') @ (
% 89.45/27.00 !!) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#S') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#S') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 =>))) @
% 89.45/27.00 ex1)))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 !!))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#S') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#B') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#S') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 =>))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#C') @ in)))))))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 !!))))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#C') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#B') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#B') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#S') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 =>))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#C') @ in)))))))))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#S') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#S') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#B'))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 =>))))))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#C') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#B') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#S') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 =>))))))) @
% 89.45/27.00 (
% 89.45/27.00 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.45/27.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1555])).
% 89.45/27.00 thf(zip_derived_cl1574, plain,
% 89.45/27.00 (~ (((ex1E1) =>
% 89.45/27.00 (((ex1I) =>
% 89.45/27.00 (((ex1I2) =>
% 89.45/27.00 (((singletonsuniq) =>
% 89.45/27.00 (((setukpairinjL1) =>
% 89.45/27.00 (((kfstsingleton) =>
% 89.45/27.00 (((theprop) =>
% 89.45/27.00 (((kfstpairEq) =>
% 89.45/27.00 (((cartprodfstin) =>
% 89.45/27.00 (((setukpairinjL2) =>
% 89.45/27.00 (((setukpairinjL) =>
% 89.45/27.00 (((setukpairinjR11) =>
% 89.45/27.00 (((setukpairinjR12) =>
% 89.45/27.00 (((setukpairinjR1) =>
% 89.45/27.00 (((upairequniteq) =>
% 89.45/27.00 (((setukpairinjR2) =>
% 89.45/27.00 (((setukpairinjR) =>
% 89.45/27.00 (((ksndsingleton) =>
% 89.45/27.00 (((ksndpairEq) =>
% 89.45/27.00 (((kpairsurjEq) =>
% 89.45/27.00 (((cartprodsndin) =>
% 89.45/27.00 (((cartprodpairmemEL) =>
% 89.45/27.00 (((cartprodpairmemER) =>
% 89.45/27.00 (((cartprodmempaircEq) =>
% 89.45/27.00 (((cartprodfstpairEq) =>
% 89.45/27.00 (((cartprodsndpairEq) =>
% 89.45/27.00 (((cartprodpairsurjEq) =>
% 89.45/27.00 (((dpsetconstrI) =>
% 89.45/27.00 (((dpsetconstrSub) =>
% 89.45/27.00 (((setOfPairsIsBReln) =>
% 89.45/27.00 ((
% 89.45/27.00 (dpsetconstrERa) =>
% 89.45/27.00 ((
% 89.45/27.00 (dpsetconstrEL1) =>
% 89.45/27.00 ((
% 89.45/27.00 (dpsetconstrEL2) =>
% 89.45/27.00 ((
% 89.45/27.00 (dpsetconstrER) =>
% 89.45/27.00 ((
% 89.45/27.00 (funcImageSingleton) =>
% 89.45/27.00 ((
% 89.45/27.00 (apProp) =>
% 89.45/27.00 ((
% 89.45/27.00 (app) =>
% 89.45/27.00 ((
% 89.45/27.00 (infuncsetfunc) =>
% 89.45/27.00 ((
% 89.45/27.00 (ap2p) =>
% 89.45/27.00 ((
% 89.45/27.00 (funcinfuncset) =>
% 89.45/27.00 ((
% 89.45/27.00 (lamProp) =>
% 89.45/27.00 ((
% 89.45/27.00 (lamp) =>
% 89.45/27.00 ((
% 89.45/27.00 (lam2p) =>
% 89.45/27.00 ((
% 89.45/27.00 (brelnall1) =>
% 89.45/27.00 ((
% 89.45/27.00 (brelnall2) =>
% 89.45/27.00 ((
% 89.45/27.00 (!!) @ (
% 89.45/27.00 (('#B') @ (
% 89.45/27.00 !!) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#S') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#S') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 =>))) @
% 89.45/27.00 ex1)))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 !!))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#S') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#B') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#S') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 =>))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#C') @ in)))))))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 !!))))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#C') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#B') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#B') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#S') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 =>))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#C') @ in)))))))))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#S') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#S') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#B'))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 =>))))))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#C') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#B') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#S') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 =>))))))) @
% 89.45/27.00 (
% 89.45/27.00 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.45/27.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1565])).
% 89.45/27.00 thf(zip_derived_cl1582, plain,
% 89.45/27.00 (~ (((ex1I) =>
% 89.45/27.00 (((ex1I2) =>
% 89.45/27.00 (((singletonsuniq) =>
% 89.45/27.00 (((setukpairinjL1) =>
% 89.45/27.00 (((kfstsingleton) =>
% 89.45/27.00 (((theprop) =>
% 89.45/27.00 (((kfstpairEq) =>
% 89.45/27.00 (((cartprodfstin) =>
% 89.45/27.00 (((setukpairinjL2) =>
% 89.45/27.00 (((setukpairinjL) =>
% 89.45/27.00 (((setukpairinjR11) =>
% 89.45/27.00 (((setukpairinjR12) =>
% 89.45/27.00 (((setukpairinjR1) =>
% 89.45/27.00 (((upairequniteq) =>
% 89.45/27.00 (((setukpairinjR2) =>
% 89.45/27.00 (((setukpairinjR) =>
% 89.45/27.00 (((ksndsingleton) =>
% 89.45/27.00 (((ksndpairEq) =>
% 89.45/27.00 (((kpairsurjEq) =>
% 89.45/27.00 (((cartprodsndin) =>
% 89.45/27.00 (((cartprodpairmemEL) =>
% 89.45/27.00 (((cartprodpairmemER) =>
% 89.45/27.00 (((cartprodmempaircEq) =>
% 89.45/27.00 (((cartprodfstpairEq) =>
% 89.45/27.00 (((cartprodsndpairEq) =>
% 89.45/27.00 (((cartprodpairsurjEq) =>
% 89.45/27.00 (((dpsetconstrI) =>
% 89.45/27.00 (((dpsetconstrSub) =>
% 89.45/27.00 (((setOfPairsIsBReln) =>
% 89.45/27.00 (((dpsetconstrERa) =>
% 89.45/27.00 ((
% 89.45/27.00 (dpsetconstrEL1) =>
% 89.45/27.00 ((
% 89.45/27.00 (dpsetconstrEL2) =>
% 89.45/27.00 ((
% 89.45/27.00 (dpsetconstrER) =>
% 89.45/27.00 ((
% 89.45/27.00 (funcImageSingleton) =>
% 89.45/27.00 ((
% 89.45/27.00 (apProp) =>
% 89.45/27.00 ((
% 89.45/27.00 (app) =>
% 89.45/27.00 ((
% 89.45/27.00 (infuncsetfunc) =>
% 89.45/27.00 ((
% 89.45/27.00 (ap2p) =>
% 89.45/27.00 ((
% 89.45/27.00 (funcinfuncset) =>
% 89.45/27.00 ((
% 89.45/27.00 (lamProp) =>
% 89.45/27.00 ((
% 89.45/27.00 (lamp) =>
% 89.45/27.00 ((
% 89.45/27.00 (lam2p) =>
% 89.45/27.00 ((
% 89.45/27.00 (brelnall1) =>
% 89.45/27.00 ((
% 89.45/27.00 (brelnall2) =>
% 89.45/27.00 ((
% 89.45/27.00 (!!) @ (
% 89.45/27.00 (('#B') @ (
% 89.45/27.00 !!) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#S') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#S') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 =>))) @
% 89.45/27.00 ex1)))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 !!))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#S') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#B') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#S') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 =>))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#C') @ in)))))))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 !!))))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#C') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#B') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#B') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#S') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 =>))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#C') @ in)))))))))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#S') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#S') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#B'))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 =>))))))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#C') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#B') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#S') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 =>))))))) @
% 89.45/27.00 (
% 89.45/27.00 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.45/27.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1574])).
% 89.45/27.00 thf(zip_derived_cl1591, plain,
% 89.45/27.00 (~ (((ex1I2) =>
% 89.45/27.00 (((singletonsuniq) =>
% 89.45/27.00 (((setukpairinjL1) =>
% 89.45/27.00 (((kfstsingleton) =>
% 89.45/27.00 (((theprop) =>
% 89.45/27.00 (((kfstpairEq) =>
% 89.45/27.00 (((cartprodfstin) =>
% 89.45/27.00 (((setukpairinjL2) =>
% 89.45/27.00 (((setukpairinjL) =>
% 89.45/27.00 (((setukpairinjR11) =>
% 89.45/27.00 (((setukpairinjR12) =>
% 89.45/27.00 (((setukpairinjR1) =>
% 89.45/27.00 (((upairequniteq) =>
% 89.45/27.00 (((setukpairinjR2) =>
% 89.45/27.00 (((setukpairinjR) =>
% 89.45/27.00 (((ksndsingleton) =>
% 89.45/27.00 (((ksndpairEq) =>
% 89.45/27.00 (((kpairsurjEq) =>
% 89.45/27.00 (((cartprodsndin) =>
% 89.45/27.00 (((cartprodpairmemEL) =>
% 89.45/27.00 (((cartprodpairmemER) =>
% 89.45/27.00 (((cartprodmempaircEq) =>
% 89.45/27.00 (((cartprodfstpairEq) =>
% 89.45/27.00 (((cartprodsndpairEq) =>
% 89.45/27.00 (((cartprodpairsurjEq) =>
% 89.45/27.00 (((dpsetconstrI) =>
% 89.45/27.00 (((dpsetconstrSub) =>
% 89.45/27.00 (((setOfPairsIsBReln) =>
% 89.45/27.00 (((dpsetconstrERa) =>
% 89.45/27.00 (((dpsetconstrEL1) =>
% 89.45/27.00 ((
% 89.45/27.00 (dpsetconstrEL2) =>
% 89.45/27.00 ((
% 89.45/27.00 (dpsetconstrER) =>
% 89.45/27.00 ((
% 89.45/27.00 (funcImageSingleton) =>
% 89.45/27.00 ((
% 89.45/27.00 (apProp) =>
% 89.45/27.00 ((
% 89.45/27.00 (app) =>
% 89.45/27.00 ((
% 89.45/27.00 (infuncsetfunc) =>
% 89.45/27.00 ((
% 89.45/27.00 (ap2p) =>
% 89.45/27.00 ((
% 89.45/27.00 (funcinfuncset) =>
% 89.45/27.00 ((
% 89.45/27.00 (lamProp) =>
% 89.45/27.00 ((
% 89.45/27.00 (lamp) =>
% 89.45/27.00 ((
% 89.45/27.00 (lam2p) =>
% 89.45/27.00 ((
% 89.45/27.00 (brelnall1) =>
% 89.45/27.00 ((
% 89.45/27.00 (brelnall2) =>
% 89.45/27.00 ((
% 89.45/27.00 (!!) @ (
% 89.45/27.00 (('#B') @ (
% 89.45/27.00 !!) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#S') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#S') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 =>))) @
% 89.45/27.00 ex1)))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 !!))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#S') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#B') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#S') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 =>))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#C') @ in)))))))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 !!))))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#C') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#B') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#B') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#S') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 =>))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#C') @ in)))))))))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#S') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#S') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#B'))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 =>))))))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#C') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#B') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#S') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 =>))))))) @
% 89.45/27.00 (
% 89.45/27.00 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.45/27.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1582])).
% 89.45/27.00 thf(zip_derived_cl1599, plain,
% 89.45/27.00 (~ (((singletonsuniq) =>
% 89.45/27.00 (((setukpairinjL1) =>
% 89.45/27.00 (((kfstsingleton) =>
% 89.45/27.00 (((theprop) =>
% 89.45/27.00 (((kfstpairEq) =>
% 89.45/27.00 (((cartprodfstin) =>
% 89.45/27.00 (((setukpairinjL2) =>
% 89.45/27.00 (((setukpairinjL) =>
% 89.45/27.00 (((setukpairinjR11) =>
% 89.45/27.00 (((setukpairinjR12) =>
% 89.45/27.00 (((setukpairinjR1) =>
% 89.45/27.00 (((upairequniteq) =>
% 89.45/27.00 (((setukpairinjR2) =>
% 89.45/27.00 (((setukpairinjR) =>
% 89.45/27.00 (((ksndsingleton) =>
% 89.45/27.00 (((ksndpairEq) =>
% 89.45/27.00 (((kpairsurjEq) =>
% 89.45/27.00 (((cartprodsndin) =>
% 89.45/27.00 (((cartprodpairmemEL) =>
% 89.45/27.00 (((cartprodpairmemER) =>
% 89.45/27.00 (((cartprodmempaircEq) =>
% 89.45/27.00 (((cartprodfstpairEq) =>
% 89.45/27.00 (((cartprodsndpairEq) =>
% 89.45/27.00 (((cartprodpairsurjEq) =>
% 89.45/27.00 (((dpsetconstrI) =>
% 89.45/27.00 (((dpsetconstrSub) =>
% 89.45/27.00 (((setOfPairsIsBReln) =>
% 89.45/27.00 (((dpsetconstrERa) =>
% 89.45/27.00 (((dpsetconstrEL1) =>
% 89.45/27.00 (((dpsetconstrEL2) =>
% 89.45/27.00 ((
% 89.45/27.00 (dpsetconstrER) =>
% 89.45/27.00 ((
% 89.45/27.00 (funcImageSingleton) =>
% 89.45/27.00 ((
% 89.45/27.00 (apProp) =>
% 89.45/27.00 ((
% 89.45/27.00 (app) =>
% 89.45/27.00 ((
% 89.45/27.00 (infuncsetfunc) =>
% 89.45/27.00 ((
% 89.45/27.00 (ap2p) =>
% 89.45/27.00 ((
% 89.45/27.00 (funcinfuncset) =>
% 89.45/27.00 ((
% 89.45/27.00 (lamProp) =>
% 89.45/27.00 ((
% 89.45/27.00 (lamp) =>
% 89.45/27.00 ((
% 89.45/27.00 (lam2p) =>
% 89.45/27.00 ((
% 89.45/27.00 (brelnall1) =>
% 89.45/27.00 ((
% 89.45/27.00 (brelnall2) =>
% 89.45/27.00 ((
% 89.45/27.00 (!!) @ (
% 89.45/27.00 (('#B') @ (
% 89.45/27.00 !!) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#S') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#S') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 =>))) @
% 89.45/27.00 ex1)))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 !!))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#S') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#B') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#S') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 =>))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#C') @ in)))))))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 !!))))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#C') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#B') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#B') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#S') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 =>))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#C') @ in)))))))))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#S') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#S') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#B'))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 =>))))))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#C') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#B') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#S') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 =>))))))) @
% 89.45/27.00 (
% 89.45/27.00 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.45/27.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1591])).
% 89.45/27.00 thf(zip_derived_cl1607, plain,
% 89.45/27.00 (~ (((setukpairinjL1) =>
% 89.45/27.00 (((kfstsingleton) =>
% 89.45/27.00 (((theprop) =>
% 89.45/27.00 (((kfstpairEq) =>
% 89.45/27.00 (((cartprodfstin) =>
% 89.45/27.00 (((setukpairinjL2) =>
% 89.45/27.00 (((setukpairinjL) =>
% 89.45/27.00 (((setukpairinjR11) =>
% 89.45/27.00 (((setukpairinjR12) =>
% 89.45/27.00 (((setukpairinjR1) =>
% 89.45/27.00 (((upairequniteq) =>
% 89.45/27.00 (((setukpairinjR2) =>
% 89.45/27.00 (((setukpairinjR) =>
% 89.45/27.00 (((ksndsingleton) =>
% 89.45/27.00 (((ksndpairEq) =>
% 89.45/27.00 (((kpairsurjEq) =>
% 89.45/27.00 (((cartprodsndin) =>
% 89.45/27.00 (((cartprodpairmemEL) =>
% 89.45/27.00 (((cartprodpairmemER) =>
% 89.45/27.00 (((cartprodmempaircEq) =>
% 89.45/27.00 (((cartprodfstpairEq) =>
% 89.45/27.00 (((cartprodsndpairEq) =>
% 89.45/27.00 (((cartprodpairsurjEq) =>
% 89.45/27.00 (((dpsetconstrI) =>
% 89.45/27.00 (((dpsetconstrSub) =>
% 89.45/27.00 (((setOfPairsIsBReln) =>
% 89.45/27.00 (((dpsetconstrERa) =>
% 89.45/27.00 (((dpsetconstrEL1) =>
% 89.45/27.00 (((dpsetconstrEL2) =>
% 89.45/27.00 (((dpsetconstrER) =>
% 89.45/27.00 ((
% 89.45/27.00 (funcImageSingleton) =>
% 89.45/27.00 ((
% 89.45/27.00 (apProp) =>
% 89.45/27.00 ((
% 89.45/27.00 (app) =>
% 89.45/27.00 ((
% 89.45/27.00 (infuncsetfunc) =>
% 89.45/27.00 ((
% 89.45/27.00 (ap2p) =>
% 89.45/27.00 ((
% 89.45/27.00 (funcinfuncset) =>
% 89.45/27.00 ((
% 89.45/27.00 (lamProp) =>
% 89.45/27.00 ((
% 89.45/27.00 (lamp) =>
% 89.45/27.00 ((
% 89.45/27.00 (lam2p) =>
% 89.45/27.00 ((
% 89.45/27.00 (brelnall1) =>
% 89.45/27.00 ((
% 89.45/27.00 (brelnall2) =>
% 89.45/27.00 ((
% 89.45/27.00 (!!) @ (
% 89.45/27.00 (('#B') @ (
% 89.45/27.00 !!) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#S') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#S') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 =>))) @
% 89.45/27.00 ex1)))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 !!))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#S') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#B') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#S') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 =>))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#C') @ in)))))))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 !!))))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#C') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#B') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#B') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 '#S') @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.00 =>))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#C') @ in)))))))))) @
% 89.45/27.00 (
% 89.45/27.00 (
% 89.45/27.00 ('#S') @ (
% 89.45/27.00 (
% 89.45/27.00 ('#B') @ (
% 89.45/27.01 '#S') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#B'))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 =>))))))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#C') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#B') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#S') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 =>))))))) @
% 89.45/27.01 (
% 89.45/27.01 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.45/27.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1599])).
% 89.45/27.01 thf(zip_derived_cl1616, plain,
% 89.45/27.01 (~ (((kfstsingleton) =>
% 89.45/27.01 (((theprop) =>
% 89.45/27.01 (((kfstpairEq) =>
% 89.45/27.01 (((cartprodfstin) =>
% 89.45/27.01 (((setukpairinjL2) =>
% 89.45/27.01 (((setukpairinjL) =>
% 89.45/27.01 (((setukpairinjR11) =>
% 89.45/27.01 (((setukpairinjR12) =>
% 89.45/27.01 (((setukpairinjR1) =>
% 89.45/27.01 (((upairequniteq) =>
% 89.45/27.01 (((setukpairinjR2) =>
% 89.45/27.01 (((setukpairinjR) =>
% 89.45/27.01 (((ksndsingleton) =>
% 89.45/27.01 (((ksndpairEq) =>
% 89.45/27.01 (((kpairsurjEq) =>
% 89.45/27.01 (((cartprodsndin) =>
% 89.45/27.01 (((cartprodpairmemEL) =>
% 89.45/27.01 (((cartprodpairmemER) =>
% 89.45/27.01 (((cartprodmempaircEq) =>
% 89.45/27.01 (((cartprodfstpairEq) =>
% 89.45/27.01 (((cartprodsndpairEq) =>
% 89.45/27.01 (((cartprodpairsurjEq) =>
% 89.45/27.01 (((dpsetconstrI) =>
% 89.45/27.01 (((dpsetconstrSub) =>
% 89.45/27.01 (((setOfPairsIsBReln) =>
% 89.45/27.01 (((dpsetconstrERa) =>
% 89.45/27.01 (((dpsetconstrEL1) =>
% 89.45/27.01 (((dpsetconstrEL2) =>
% 89.45/27.01 (((dpsetconstrER) =>
% 89.45/27.01 (((funcImageSingleton) =>
% 89.45/27.01 ((
% 89.45/27.01 (apProp) =>
% 89.45/27.01 ((
% 89.45/27.01 (app) =>
% 89.45/27.01 ((
% 89.45/27.01 (infuncsetfunc) =>
% 89.45/27.01 ((
% 89.45/27.01 (ap2p) =>
% 89.45/27.01 ((
% 89.45/27.01 (funcinfuncset) =>
% 89.45/27.01 ((
% 89.45/27.01 (lamProp) =>
% 89.45/27.01 ((
% 89.45/27.01 (lamp) =>
% 89.45/27.01 ((
% 89.45/27.01 (lam2p) =>
% 89.45/27.01 ((
% 89.45/27.01 (brelnall1) =>
% 89.45/27.01 ((
% 89.45/27.01 (brelnall2) =>
% 89.45/27.01 ((
% 89.45/27.01 (!!) @ (
% 89.45/27.01 (('#B') @ (
% 89.45/27.01 !!) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#S') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#S') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 =>))) @
% 89.45/27.01 ex1)))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 !!))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#S') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#B') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#S') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 =>))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#C') @ in)))))))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 !!))))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#C') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#B') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#B') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#S') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 =>))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#C') @ in)))))))))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#S') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#S') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#B'))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 =>))))))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#C') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#B') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#S') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 =>))))))) @
% 89.45/27.01 (
% 89.45/27.01 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.45/27.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1607])).
% 89.45/27.01 thf(zip_derived_cl1627, plain,
% 89.45/27.01 (~ (((theprop) =>
% 89.45/27.01 (((kfstpairEq) =>
% 89.45/27.01 (((cartprodfstin) =>
% 89.45/27.01 (((setukpairinjL2) =>
% 89.45/27.01 (((setukpairinjL) =>
% 89.45/27.01 (((setukpairinjR11) =>
% 89.45/27.01 (((setukpairinjR12) =>
% 89.45/27.01 (((setukpairinjR1) =>
% 89.45/27.01 (((upairequniteq) =>
% 89.45/27.01 (((setukpairinjR2) =>
% 89.45/27.01 (((setukpairinjR) =>
% 89.45/27.01 (((ksndsingleton) =>
% 89.45/27.01 (((ksndpairEq) =>
% 89.45/27.01 (((kpairsurjEq) =>
% 89.45/27.01 (((cartprodsndin) =>
% 89.45/27.01 (((cartprodpairmemEL) =>
% 89.45/27.01 (((cartprodpairmemER) =>
% 89.45/27.01 (((cartprodmempaircEq) =>
% 89.45/27.01 (((cartprodfstpairEq) =>
% 89.45/27.01 (((cartprodsndpairEq) =>
% 89.45/27.01 (((cartprodpairsurjEq) =>
% 89.45/27.01 (((dpsetconstrI) =>
% 89.45/27.01 (((dpsetconstrSub) =>
% 89.45/27.01 (((setOfPairsIsBReln) =>
% 89.45/27.01 (((dpsetconstrERa) =>
% 89.45/27.01 (((dpsetconstrEL1) =>
% 89.45/27.01 (((dpsetconstrEL2) =>
% 89.45/27.01 (((dpsetconstrER) =>
% 89.45/27.01 (((funcImageSingleton) =>
% 89.45/27.01 (((apProp) =>
% 89.45/27.01 ((
% 89.45/27.01 (app) =>
% 89.45/27.01 ((
% 89.45/27.01 (infuncsetfunc) =>
% 89.45/27.01 ((
% 89.45/27.01 (ap2p) =>
% 89.45/27.01 ((
% 89.45/27.01 (funcinfuncset) =>
% 89.45/27.01 ((
% 89.45/27.01 (lamProp) =>
% 89.45/27.01 ((
% 89.45/27.01 (lamp) =>
% 89.45/27.01 ((
% 89.45/27.01 (lam2p) =>
% 89.45/27.01 ((
% 89.45/27.01 (brelnall1) =>
% 89.45/27.01 ((
% 89.45/27.01 (brelnall2) =>
% 89.45/27.01 ((
% 89.45/27.01 (!!) @ (
% 89.45/27.01 (('#B') @ (
% 89.45/27.01 !!) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#S') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#S') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 =>))) @
% 89.45/27.01 ex1)))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 !!))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#S') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#B') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#S') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 =>))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#C') @ in)))))))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 !!))))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#C') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#B') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#B') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#S') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 =>))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#C') @ in)))))))))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#S') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#S') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#B'))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 =>))))))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#C') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#B') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#S') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 =>))))))) @
% 89.45/27.01 (
% 89.45/27.01 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.45/27.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1616])).
% 89.45/27.01 thf(zip_derived_cl1640, plain,
% 89.45/27.01 (~ (((kfstpairEq) =>
% 89.45/27.01 (((cartprodfstin) =>
% 89.45/27.01 (((setukpairinjL2) =>
% 89.45/27.01 (((setukpairinjL) =>
% 89.45/27.01 (((setukpairinjR11) =>
% 89.45/27.01 (((setukpairinjR12) =>
% 89.45/27.01 (((setukpairinjR1) =>
% 89.45/27.01 (((upairequniteq) =>
% 89.45/27.01 (((setukpairinjR2) =>
% 89.45/27.01 (((setukpairinjR) =>
% 89.45/27.01 (((ksndsingleton) =>
% 89.45/27.01 (((ksndpairEq) =>
% 89.45/27.01 (((kpairsurjEq) =>
% 89.45/27.01 (((cartprodsndin) =>
% 89.45/27.01 (((cartprodpairmemEL) =>
% 89.45/27.01 (((cartprodpairmemER) =>
% 89.45/27.01 (((cartprodmempaircEq) =>
% 89.45/27.01 (((cartprodfstpairEq) =>
% 89.45/27.01 (((cartprodsndpairEq) =>
% 89.45/27.01 (((cartprodpairsurjEq) =>
% 89.45/27.01 (((dpsetconstrI) =>
% 89.45/27.01 (((dpsetconstrSub) =>
% 89.45/27.01 (((setOfPairsIsBReln) =>
% 89.45/27.01 (((dpsetconstrERa) =>
% 89.45/27.01 (((dpsetconstrEL1) =>
% 89.45/27.01 (((dpsetconstrEL2) =>
% 89.45/27.01 (((dpsetconstrER) =>
% 89.45/27.01 (((funcImageSingleton) =>
% 89.45/27.01 (((apProp) =>
% 89.45/27.01 (((app) =>
% 89.45/27.01 ((
% 89.45/27.01 (infuncsetfunc) =>
% 89.45/27.01 ((
% 89.45/27.01 (ap2p) =>
% 89.45/27.01 ((
% 89.45/27.01 (funcinfuncset) =>
% 89.45/27.01 ((
% 89.45/27.01 (lamProp) =>
% 89.45/27.01 ((
% 89.45/27.01 (lamp) =>
% 89.45/27.01 ((
% 89.45/27.01 (lam2p) =>
% 89.45/27.01 ((
% 89.45/27.01 (brelnall1) =>
% 89.45/27.01 ((
% 89.45/27.01 (brelnall2) =>
% 89.45/27.01 ((
% 89.45/27.01 (!!) @ (
% 89.45/27.01 (('#B') @ (
% 89.45/27.01 !!) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#S') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#S') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 =>))) @
% 89.45/27.01 ex1)))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 !!))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#S') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#B') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#S') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 =>))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#C') @ in)))))))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 !!))))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#C') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#B') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#B') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#S') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 =>))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#C') @ in)))))))))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#S') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#S') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#B'))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 =>))))))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#C') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#B') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#S') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 =>))))))) @
% 89.45/27.01 (
% 89.45/27.01 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.45/27.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1627])).
% 89.45/27.01 thf(zip_derived_cl1653, plain,
% 89.45/27.01 (~ (((cartprodfstin) =>
% 89.45/27.01 (((setukpairinjL2) =>
% 89.45/27.01 (((setukpairinjL) =>
% 89.45/27.01 (((setukpairinjR11) =>
% 89.45/27.01 (((setukpairinjR12) =>
% 89.45/27.01 (((setukpairinjR1) =>
% 89.45/27.01 (((upairequniteq) =>
% 89.45/27.01 (((setukpairinjR2) =>
% 89.45/27.01 (((setukpairinjR) =>
% 89.45/27.01 (((ksndsingleton) =>
% 89.45/27.01 (((ksndpairEq) =>
% 89.45/27.01 (((kpairsurjEq) =>
% 89.45/27.01 (((cartprodsndin) =>
% 89.45/27.01 (((cartprodpairmemEL) =>
% 89.45/27.01 (((cartprodpairmemER) =>
% 89.45/27.01 (((cartprodmempaircEq) =>
% 89.45/27.01 (((cartprodfstpairEq) =>
% 89.45/27.01 (((cartprodsndpairEq) =>
% 89.45/27.01 (((cartprodpairsurjEq) =>
% 89.45/27.01 (((dpsetconstrI) =>
% 89.45/27.01 (((dpsetconstrSub) =>
% 89.45/27.01 (((setOfPairsIsBReln) =>
% 89.45/27.01 (((dpsetconstrERa) =>
% 89.45/27.01 (((dpsetconstrEL1) =>
% 89.45/27.01 (((dpsetconstrEL2) =>
% 89.45/27.01 (((dpsetconstrER) =>
% 89.45/27.01 (((funcImageSingleton) =>
% 89.45/27.01 (((apProp) =>
% 89.45/27.01 (((app) =>
% 89.45/27.01 (((infuncsetfunc) =>
% 89.45/27.01 ((
% 89.45/27.01 (ap2p) =>
% 89.45/27.01 ((
% 89.45/27.01 (funcinfuncset) =>
% 89.45/27.01 ((
% 89.45/27.01 (lamProp) =>
% 89.45/27.01 ((
% 89.45/27.01 (lamp) =>
% 89.45/27.01 ((
% 89.45/27.01 (lam2p) =>
% 89.45/27.01 ((
% 89.45/27.01 (brelnall1) =>
% 89.45/27.01 ((
% 89.45/27.01 (brelnall2) =>
% 89.45/27.01 ((
% 89.45/27.01 (!!) @ (
% 89.45/27.01 (('#B') @ (
% 89.45/27.01 !!) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#S') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#S') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 =>))) @
% 89.45/27.01 ex1)))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 !!))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#S') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#B') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#S') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 =>))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#C') @ in)))))))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 !!))))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#C') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#B') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#B') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#S') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 =>))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#C') @ in)))))))))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#S') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#S') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#B'))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 =>))))))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#C') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#B') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#S') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 =>))))))) @
% 89.45/27.01 (
% 89.45/27.01 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.45/27.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1640])).
% 89.45/27.01 thf(zip_derived_cl1671, plain,
% 89.45/27.01 (~ (((setukpairinjL2) =>
% 89.45/27.01 (((setukpairinjL) =>
% 89.45/27.01 (((setukpairinjR11) =>
% 89.45/27.01 (((setukpairinjR12) =>
% 89.45/27.01 (((setukpairinjR1) =>
% 89.45/27.01 (((upairequniteq) =>
% 89.45/27.01 (((setukpairinjR2) =>
% 89.45/27.01 (((setukpairinjR) =>
% 89.45/27.01 (((ksndsingleton) =>
% 89.45/27.01 (((ksndpairEq) =>
% 89.45/27.01 (((kpairsurjEq) =>
% 89.45/27.01 (((cartprodsndin) =>
% 89.45/27.01 (((cartprodpairmemEL) =>
% 89.45/27.01 (((cartprodpairmemER) =>
% 89.45/27.01 (((cartprodmempaircEq) =>
% 89.45/27.01 (((cartprodfstpairEq) =>
% 89.45/27.01 (((cartprodsndpairEq) =>
% 89.45/27.01 (((cartprodpairsurjEq) =>
% 89.45/27.01 (((dpsetconstrI) =>
% 89.45/27.01 (((dpsetconstrSub) =>
% 89.45/27.01 (((setOfPairsIsBReln) =>
% 89.45/27.01 (((dpsetconstrERa) =>
% 89.45/27.01 (((dpsetconstrEL1) =>
% 89.45/27.01 (((dpsetconstrEL2) =>
% 89.45/27.01 (((dpsetconstrER) =>
% 89.45/27.01 (((funcImageSingleton) =>
% 89.45/27.01 (((apProp) =>
% 89.45/27.01 (((app) =>
% 89.45/27.01 (((infuncsetfunc) =>
% 89.45/27.01 (((ap2p) =>
% 89.45/27.01 ((
% 89.45/27.01 (funcinfuncset) =>
% 89.45/27.01 ((
% 89.45/27.01 (lamProp) =>
% 89.45/27.01 ((
% 89.45/27.01 (lamp) =>
% 89.45/27.01 ((
% 89.45/27.01 (lam2p) =>
% 89.45/27.01 ((
% 89.45/27.01 (brelnall1) =>
% 89.45/27.01 ((
% 89.45/27.01 (brelnall2) =>
% 89.45/27.01 ((
% 89.45/27.01 (!!) @ (
% 89.45/27.01 (('#B') @ (
% 89.45/27.01 !!) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#S') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#S') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 =>))) @
% 89.45/27.01 ex1)))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 !!))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#S') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#B') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#S') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 =>))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#C') @ in)))))))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 !!))))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#C') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#B') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#B') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#S') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 =>))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#C') @ in)))))))))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#S') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#S') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#B'))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 =>))))))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#C') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#B') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#S') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 =>))))))) @
% 89.45/27.01 (
% 89.45/27.01 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.45/27.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1653])).
% 89.45/27.01 thf(zip_derived_cl1690, plain,
% 89.45/27.01 (~ (((setukpairinjL) =>
% 89.45/27.01 (((setukpairinjR11) =>
% 89.45/27.01 (((setukpairinjR12) =>
% 89.45/27.01 (((setukpairinjR1) =>
% 89.45/27.01 (((upairequniteq) =>
% 89.45/27.01 (((setukpairinjR2) =>
% 89.45/27.01 (((setukpairinjR) =>
% 89.45/27.01 (((ksndsingleton) =>
% 89.45/27.01 (((ksndpairEq) =>
% 89.45/27.01 (((kpairsurjEq) =>
% 89.45/27.01 (((cartprodsndin) =>
% 89.45/27.01 (((cartprodpairmemEL) =>
% 89.45/27.01 (((cartprodpairmemER) =>
% 89.45/27.01 (((cartprodmempaircEq) =>
% 89.45/27.01 (((cartprodfstpairEq) =>
% 89.45/27.01 (((cartprodsndpairEq) =>
% 89.45/27.01 (((cartprodpairsurjEq) =>
% 89.45/27.01 (((dpsetconstrI) =>
% 89.45/27.01 (((dpsetconstrSub) =>
% 89.45/27.01 (((setOfPairsIsBReln) =>
% 89.45/27.01 (((dpsetconstrERa) =>
% 89.45/27.01 (((dpsetconstrEL1) =>
% 89.45/27.01 (((dpsetconstrEL2) =>
% 89.45/27.01 (((dpsetconstrER) =>
% 89.45/27.01 (((funcImageSingleton) =>
% 89.45/27.01 (((apProp) =>
% 89.45/27.01 (((app) =>
% 89.45/27.01 (((infuncsetfunc) =>
% 89.45/27.01 (((ap2p) =>
% 89.45/27.01 (((funcinfuncset) =>
% 89.45/27.01 ((
% 89.45/27.01 (lamProp) =>
% 89.45/27.01 ((
% 89.45/27.01 (lamp) =>
% 89.45/27.01 ((
% 89.45/27.01 (lam2p) =>
% 89.45/27.01 ((
% 89.45/27.01 (brelnall1) =>
% 89.45/27.01 ((
% 89.45/27.01 (brelnall2) =>
% 89.45/27.01 ((
% 89.45/27.01 (!!) @ (
% 89.45/27.01 (('#B') @ (
% 89.45/27.01 !!) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#S') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#S') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 =>))) @
% 89.45/27.01 ex1)))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 !!))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#S') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#B') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#S') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 =>))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#C') @ in)))))))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 !!))))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#C') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#B') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#B') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#S') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 =>))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#C') @ in)))))))))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#S') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#S') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#B'))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 =>))))))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#C') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#B') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#S') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 =>))))))) @
% 89.45/27.01 (
% 89.45/27.01 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.45/27.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1671])).
% 89.45/27.01 thf(zip_derived_cl1714, plain,
% 89.45/27.01 (~ (((setukpairinjR11) =>
% 89.45/27.01 (((setukpairinjR12) =>
% 89.45/27.01 (((setukpairinjR1) =>
% 89.45/27.01 (((upairequniteq) =>
% 89.45/27.01 (((setukpairinjR2) =>
% 89.45/27.01 (((setukpairinjR) =>
% 89.45/27.01 (((ksndsingleton) =>
% 89.45/27.01 (((ksndpairEq) =>
% 89.45/27.01 (((kpairsurjEq) =>
% 89.45/27.01 (((cartprodsndin) =>
% 89.45/27.01 (((cartprodpairmemEL) =>
% 89.45/27.01 (((cartprodpairmemER) =>
% 89.45/27.01 (((cartprodmempaircEq) =>
% 89.45/27.01 (((cartprodfstpairEq) =>
% 89.45/27.01 (((cartprodsndpairEq) =>
% 89.45/27.01 (((cartprodpairsurjEq) =>
% 89.45/27.01 (((dpsetconstrI) =>
% 89.45/27.01 (((dpsetconstrSub) =>
% 89.45/27.01 (((setOfPairsIsBReln) =>
% 89.45/27.01 (((dpsetconstrERa) =>
% 89.45/27.01 (((dpsetconstrEL1) =>
% 89.45/27.01 (((dpsetconstrEL2) =>
% 89.45/27.01 (((dpsetconstrER) =>
% 89.45/27.01 (((funcImageSingleton) =>
% 89.45/27.01 (((apProp) =>
% 89.45/27.01 (((app) =>
% 89.45/27.01 (((infuncsetfunc) =>
% 89.45/27.01 (((ap2p) =>
% 89.45/27.01 (((funcinfuncset) =>
% 89.45/27.01 (((lamProp) =>
% 89.45/27.01 ((
% 89.45/27.01 (lamp) =>
% 89.45/27.01 ((
% 89.45/27.01 (lam2p) =>
% 89.45/27.01 ((
% 89.45/27.01 (brelnall1) =>
% 89.45/27.01 ((
% 89.45/27.01 (brelnall2) =>
% 89.45/27.01 ((
% 89.45/27.01 (!!) @ (
% 89.45/27.01 (('#B') @ (
% 89.45/27.01 !!) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#S') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#S') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 =>))) @
% 89.45/27.01 ex1)))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 !!))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#S') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#B') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#S') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 =>))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#C') @ in)))))))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 !!))))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#C') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#B') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#B') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#S') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 =>))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#C') @ in)))))))))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#S') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#S') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#B'))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 =>))))))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#C') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#B') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#S') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 =>))))))) @
% 89.45/27.01 (
% 89.45/27.01 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.45/27.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1690])).
% 89.45/27.01 thf(zip_derived_cl1740, plain,
% 89.45/27.01 (~ (((setukpairinjR12) =>
% 89.45/27.01 (((setukpairinjR1) =>
% 89.45/27.01 (((upairequniteq) =>
% 89.45/27.01 (((setukpairinjR2) =>
% 89.45/27.01 (((setukpairinjR) =>
% 89.45/27.01 (((ksndsingleton) =>
% 89.45/27.01 (((ksndpairEq) =>
% 89.45/27.01 (((kpairsurjEq) =>
% 89.45/27.01 (((cartprodsndin) =>
% 89.45/27.01 (((cartprodpairmemEL) =>
% 89.45/27.01 (((cartprodpairmemER) =>
% 89.45/27.01 (((cartprodmempaircEq) =>
% 89.45/27.01 (((cartprodfstpairEq) =>
% 89.45/27.01 (((cartprodsndpairEq) =>
% 89.45/27.01 (((cartprodpairsurjEq) =>
% 89.45/27.01 (((dpsetconstrI) =>
% 89.45/27.01 (((dpsetconstrSub) =>
% 89.45/27.01 (((setOfPairsIsBReln) =>
% 89.45/27.01 (((dpsetconstrERa) =>
% 89.45/27.01 (((dpsetconstrEL1) =>
% 89.45/27.01 (((dpsetconstrEL2) =>
% 89.45/27.01 (((dpsetconstrER) =>
% 89.45/27.01 (((funcImageSingleton) =>
% 89.45/27.01 (((apProp) =>
% 89.45/27.01 (((app) =>
% 89.45/27.01 (((infuncsetfunc) =>
% 89.45/27.01 (((ap2p) =>
% 89.45/27.01 (((funcinfuncset) =>
% 89.45/27.01 (((lamProp) =>
% 89.45/27.01 (((lamp) =>
% 89.45/27.01 ((
% 89.45/27.01 (lam2p) =>
% 89.45/27.01 ((
% 89.45/27.01 (brelnall1) =>
% 89.45/27.01 ((
% 89.45/27.01 (brelnall2) =>
% 89.45/27.01 ((
% 89.45/27.01 (!!) @ (
% 89.45/27.01 (('#B') @ (
% 89.45/27.01 !!) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#S') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#S') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 =>))) @
% 89.45/27.01 ex1)))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 !!))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#S') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#B') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 '#S') @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 =>))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#C') @ in)))))))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 (
% 89.45/27.01 ('#B') @ (
% 89.45/27.01 !!))))) @
% 89.45/27.01 (
% 89.45/27.01 (
% 89.45/27.01 ('#C') @ (
% 89.45/27.01 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#C') @ in)))))))))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#S') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B'))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))))))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#C') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))))))) @
% 89.45/27.02 (
% 89.45/27.02 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.45/27.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1714])).
% 89.45/27.02 thf(zip_derived_cl1767, plain,
% 89.45/27.02 (~ (((setukpairinjR1) =>
% 89.45/27.02 (((upairequniteq) =>
% 89.45/27.02 (((setukpairinjR2) =>
% 89.45/27.02 (((setukpairinjR) =>
% 89.45/27.02 (((ksndsingleton) =>
% 89.45/27.02 (((ksndpairEq) =>
% 89.45/27.02 (((kpairsurjEq) =>
% 89.45/27.02 (((cartprodsndin) =>
% 89.45/27.02 (((cartprodpairmemEL) =>
% 89.45/27.02 (((cartprodpairmemER) =>
% 89.45/27.02 (((cartprodmempaircEq) =>
% 89.45/27.02 (((cartprodfstpairEq) =>
% 89.45/27.02 (((cartprodsndpairEq) =>
% 89.45/27.02 (((cartprodpairsurjEq) =>
% 89.45/27.02 (((dpsetconstrI) =>
% 89.45/27.02 (((dpsetconstrSub) =>
% 89.45/27.02 (((setOfPairsIsBReln) =>
% 89.45/27.02 (((dpsetconstrERa) =>
% 89.45/27.02 (((dpsetconstrEL1) =>
% 89.45/27.02 (((dpsetconstrEL2) =>
% 89.45/27.02 (((dpsetconstrER) =>
% 89.45/27.02 (((funcImageSingleton) =>
% 89.45/27.02 (((apProp) =>
% 89.45/27.02 (((app) =>
% 89.45/27.02 (((infuncsetfunc) =>
% 89.45/27.02 (((ap2p) =>
% 89.45/27.02 (((funcinfuncset) =>
% 89.45/27.02 (((lamProp) =>
% 89.45/27.02 (((lamp) =>
% 89.45/27.02 (((lam2p) =>
% 89.45/27.02 ((
% 89.45/27.02 (brelnall1) =>
% 89.45/27.02 ((
% 89.45/27.02 (brelnall2) =>
% 89.45/27.02 ((
% 89.45/27.02 (!!) @ (
% 89.45/27.02 (('#B') @ (
% 89.45/27.02 !!) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#S') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))) @
% 89.45/27.02 ex1)))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 !!))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#S') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#C') @ in)))))))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 !!))))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#C') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#C') @ in)))))))))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#S') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B'))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))))))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#C') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))))))) @
% 89.45/27.02 (
% 89.45/27.02 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.45/27.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1740])).
% 89.45/27.02 thf(zip_derived_cl1798, plain,
% 89.45/27.02 (~ (((upairequniteq) =>
% 89.45/27.02 (((setukpairinjR2) =>
% 89.45/27.02 (((setukpairinjR) =>
% 89.45/27.02 (((ksndsingleton) =>
% 89.45/27.02 (((ksndpairEq) =>
% 89.45/27.02 (((kpairsurjEq) =>
% 89.45/27.02 (((cartprodsndin) =>
% 89.45/27.02 (((cartprodpairmemEL) =>
% 89.45/27.02 (((cartprodpairmemER) =>
% 89.45/27.02 (((cartprodmempaircEq) =>
% 89.45/27.02 (((cartprodfstpairEq) =>
% 89.45/27.02 (((cartprodsndpairEq) =>
% 89.45/27.02 (((cartprodpairsurjEq) =>
% 89.45/27.02 (((dpsetconstrI) =>
% 89.45/27.02 (((dpsetconstrSub) =>
% 89.45/27.02 (((setOfPairsIsBReln) =>
% 89.45/27.02 (((dpsetconstrERa) =>
% 89.45/27.02 (((dpsetconstrEL1) =>
% 89.45/27.02 (((dpsetconstrEL2) =>
% 89.45/27.02 (((dpsetconstrER) =>
% 89.45/27.02 (((funcImageSingleton) =>
% 89.45/27.02 (((apProp) =>
% 89.45/27.02 (((app) =>
% 89.45/27.02 (((infuncsetfunc) =>
% 89.45/27.02 (((ap2p) =>
% 89.45/27.02 (((funcinfuncset) =>
% 89.45/27.02 (((lamProp) =>
% 89.45/27.02 (((lamp) =>
% 89.45/27.02 (((lam2p) =>
% 89.45/27.02 (((brelnall1) =>
% 89.45/27.02 ((
% 89.45/27.02 (brelnall2) =>
% 89.45/27.02 ((
% 89.45/27.02 (!!) @ (
% 89.45/27.02 (('#B') @ (
% 89.45/27.02 !!) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#S') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))) @
% 89.45/27.02 ex1)))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 !!))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#S') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#C') @ in)))))))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 !!))))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#C') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#C') @ in)))))))))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#S') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B'))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))))))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#C') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))))))) @
% 89.45/27.02 (
% 89.45/27.02 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.45/27.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1767])).
% 89.45/27.02 thf(zip_derived_cl1826, plain,
% 89.45/27.02 (~ (((setukpairinjR2) =>
% 89.45/27.02 (((setukpairinjR) =>
% 89.45/27.02 (((ksndsingleton) =>
% 89.45/27.02 (((ksndpairEq) =>
% 89.45/27.02 (((kpairsurjEq) =>
% 89.45/27.02 (((cartprodsndin) =>
% 89.45/27.02 (((cartprodpairmemEL) =>
% 89.45/27.02 (((cartprodpairmemER) =>
% 89.45/27.02 (((cartprodmempaircEq) =>
% 89.45/27.02 (((cartprodfstpairEq) =>
% 89.45/27.02 (((cartprodsndpairEq) =>
% 89.45/27.02 (((cartprodpairsurjEq) =>
% 89.45/27.02 (((dpsetconstrI) =>
% 89.45/27.02 (((dpsetconstrSub) =>
% 89.45/27.02 (((setOfPairsIsBReln) =>
% 89.45/27.02 (((dpsetconstrERa) =>
% 89.45/27.02 (((dpsetconstrEL1) =>
% 89.45/27.02 (((dpsetconstrEL2) =>
% 89.45/27.02 (((dpsetconstrER) =>
% 89.45/27.02 (((funcImageSingleton) =>
% 89.45/27.02 (((apProp) =>
% 89.45/27.02 (((app) =>
% 89.45/27.02 (((infuncsetfunc) =>
% 89.45/27.02 (((ap2p) =>
% 89.45/27.02 (((funcinfuncset) =>
% 89.45/27.02 (((lamProp) =>
% 89.45/27.02 (((lamp) =>
% 89.45/27.02 (((lam2p) =>
% 89.45/27.02 (((brelnall1) =>
% 89.45/27.02 (((brelnall2) =>
% 89.45/27.02 ((
% 89.45/27.02 (!!) @ (
% 89.45/27.02 (('#B') @ (
% 89.45/27.02 !!) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#S') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))) @
% 89.45/27.02 ex1)))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 !!))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#S') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#C') @ in)))))))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 !!))))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#C') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#C') @ in)))))))))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#S') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B'))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))))))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#C') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))))))) @
% 89.45/27.02 (
% 89.45/27.02 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.45/27.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1798])).
% 89.45/27.02 thf(zip_derived_cl1850, plain,
% 89.45/27.02 (~ (((setukpairinjR) =>
% 89.45/27.02 (((ksndsingleton) =>
% 89.45/27.02 (((ksndpairEq) =>
% 89.45/27.02 (((kpairsurjEq) =>
% 89.45/27.02 (((cartprodsndin) =>
% 89.45/27.02 (((cartprodpairmemEL) =>
% 89.45/27.02 (((cartprodpairmemER) =>
% 89.45/27.02 (((cartprodmempaircEq) =>
% 89.45/27.02 (((cartprodfstpairEq) =>
% 89.45/27.02 (((cartprodsndpairEq) =>
% 89.45/27.02 (((cartprodpairsurjEq) =>
% 89.45/27.02 (((dpsetconstrI) =>
% 89.45/27.02 (((dpsetconstrSub) =>
% 89.45/27.02 (((setOfPairsIsBReln) =>
% 89.45/27.02 (((dpsetconstrERa) =>
% 89.45/27.02 (((dpsetconstrEL1) =>
% 89.45/27.02 (((dpsetconstrEL2) =>
% 89.45/27.02 (((dpsetconstrER) =>
% 89.45/27.02 (((funcImageSingleton) =>
% 89.45/27.02 (((apProp) =>
% 89.45/27.02 (((app) =>
% 89.45/27.02 (((infuncsetfunc) =>
% 89.45/27.02 (((ap2p) =>
% 89.45/27.02 (((funcinfuncset) =>
% 89.45/27.02 (((lamProp) =>
% 89.45/27.02 (((lamp) =>
% 89.45/27.02 (((lam2p) =>
% 89.45/27.02 (((brelnall1) =>
% 89.45/27.02 (((brelnall2) =>
% 89.45/27.02 (((!!) @ (
% 89.45/27.02 (('#B') @ (
% 89.45/27.02 !!) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#S') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))) @
% 89.45/27.02 ex1)))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 !!))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#S') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#C') @ in)))))))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 !!))))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#C') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#C') @ in)))))))))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#S') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B'))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))))))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#C') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))))))) @
% 89.45/27.02 (
% 89.45/27.02 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.45/27.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1826])).
% 89.45/27.02 thf(zip_derived_cl1869, plain,
% 89.45/27.02 (~ (((ksndsingleton) =>
% 89.45/27.02 (((ksndpairEq) =>
% 89.45/27.02 (((kpairsurjEq) =>
% 89.45/27.02 (((cartprodsndin) =>
% 89.45/27.02 (((cartprodpairmemEL) =>
% 89.45/27.02 (((cartprodpairmemER) =>
% 89.45/27.02 (((cartprodmempaircEq) =>
% 89.45/27.02 (((cartprodfstpairEq) =>
% 89.45/27.02 (((cartprodsndpairEq) =>
% 89.45/27.02 (((cartprodpairsurjEq) =>
% 89.45/27.02 (((dpsetconstrI) =>
% 89.45/27.02 (((dpsetconstrSub) =>
% 89.45/27.02 (((setOfPairsIsBReln) =>
% 89.45/27.02 (((dpsetconstrERa) =>
% 89.45/27.02 (((dpsetconstrEL1) =>
% 89.45/27.02 (((dpsetconstrEL2) =>
% 89.45/27.02 (((dpsetconstrER) =>
% 89.45/27.02 (((funcImageSingleton) =>
% 89.45/27.02 (((apProp) =>
% 89.45/27.02 (((app) =>
% 89.45/27.02 (((infuncsetfunc) =>
% 89.45/27.02 (((ap2p) =>
% 89.45/27.02 (((funcinfuncset) =>
% 89.45/27.02 (((lamProp) =>
% 89.45/27.02 (((lamp) =>
% 89.45/27.02 (((lam2p) =>
% 89.45/27.02 (((brelnall1) =>
% 89.45/27.02 (((brelnall2) =>
% 89.45/27.02 (((!!) @ (
% 89.45/27.02 (('#B') @ (
% 89.45/27.02 !!) @
% 89.45/27.02 ((('#S') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))) @
% 89.45/27.02 ex1)))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 !!))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#S') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#C') @ in)))))))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 !!))))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#C') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#C') @ in)))))))))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#S') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B'))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))))))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#C') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))))))) @
% 89.45/27.02 (
% 89.45/27.02 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.45/27.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1850])).
% 89.45/27.02 thf(zip_derived_cl1886, plain,
% 89.45/27.02 (~ (((ksndpairEq) =>
% 89.45/27.02 (((kpairsurjEq) =>
% 89.45/27.02 (((cartprodsndin) =>
% 89.45/27.02 (((cartprodpairmemEL) =>
% 89.45/27.02 (((cartprodpairmemER) =>
% 89.45/27.02 (((cartprodmempaircEq) =>
% 89.45/27.02 (((cartprodfstpairEq) =>
% 89.45/27.02 (((cartprodsndpairEq) =>
% 89.45/27.02 (((cartprodpairsurjEq) =>
% 89.45/27.02 (((dpsetconstrI) =>
% 89.45/27.02 (((dpsetconstrSub) =>
% 89.45/27.02 (((setOfPairsIsBReln) =>
% 89.45/27.02 (((dpsetconstrERa) =>
% 89.45/27.02 (((dpsetconstrEL1) =>
% 89.45/27.02 (((dpsetconstrEL2) =>
% 89.45/27.02 (((dpsetconstrER) =>
% 89.45/27.02 (((funcImageSingleton) =>
% 89.45/27.02 (((apProp) =>
% 89.45/27.02 (((app) =>
% 89.45/27.02 (((infuncsetfunc) =>
% 89.45/27.02 (((ap2p) =>
% 89.45/27.02 (((funcinfuncset) =>
% 89.45/27.02 (((lamProp) =>
% 89.45/27.02 (((lamp) =>
% 89.45/27.02 (((lam2p) =>
% 89.45/27.02 (((brelnall1) =>
% 89.45/27.02 (((brelnall2) =>
% 89.45/27.02 (((!!) @ (
% 89.45/27.02 (('#B') @ (
% 89.45/27.02 !!) @
% 89.45/27.02 ((('#S') @ (
% 89.45/27.02 (('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 ((
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))) @
% 89.45/27.02 ex1)))) @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 !!))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#S') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#C') @ in)))))))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 !!))))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#C') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#C') @ in)))))))))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#S') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B'))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))))))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#C') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))))))) @
% 89.45/27.02 (
% 89.45/27.02 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.45/27.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1869])).
% 89.45/27.02 thf(zip_derived_cl1898, plain,
% 89.45/27.02 (~ (((kpairsurjEq) =>
% 89.45/27.02 (((cartprodsndin) =>
% 89.45/27.02 (((cartprodpairmemEL) =>
% 89.45/27.02 (((cartprodpairmemER) =>
% 89.45/27.02 (((cartprodmempaircEq) =>
% 89.45/27.02 (((cartprodfstpairEq) =>
% 89.45/27.02 (((cartprodsndpairEq) =>
% 89.45/27.02 (((cartprodpairsurjEq) =>
% 89.45/27.02 (((dpsetconstrI) =>
% 89.45/27.02 (((dpsetconstrSub) =>
% 89.45/27.02 (((setOfPairsIsBReln) =>
% 89.45/27.02 (((dpsetconstrERa) =>
% 89.45/27.02 (((dpsetconstrEL1) =>
% 89.45/27.02 (((dpsetconstrEL2) =>
% 89.45/27.02 (((dpsetconstrER) =>
% 89.45/27.02 (((funcImageSingleton) =>
% 89.45/27.02 (((apProp) =>
% 89.45/27.02 (((app) =>
% 89.45/27.02 (((infuncsetfunc) =>
% 89.45/27.02 (((ap2p) =>
% 89.45/27.02 (((funcinfuncset) =>
% 89.45/27.02 (((lamProp) =>
% 89.45/27.02 (((lamp) =>
% 89.45/27.02 (((lam2p) =>
% 89.45/27.02 (((brelnall1) =>
% 89.45/27.02 (((brelnall2) =>
% 89.45/27.02 (((!!) @ (
% 89.45/27.02 (('#B') @ (
% 89.45/27.02 !!) @
% 89.45/27.02 ((('#S') @ (
% 89.45/27.02 (('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 (('#B') @ (
% 89.45/27.02 =>))) @
% 89.45/27.02 ex1)))) @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 (('#B') @ (
% 89.45/27.02 !!))) @
% 89.45/27.02 ((('#S') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#C') @ in)))))))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 !!))))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#C') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#C') @ in)))))))))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#S') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B'))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))))))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#C') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))))))) @
% 89.45/27.02 (
% 89.45/27.02 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.45/27.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1886])).
% 89.45/27.02 thf(zip_derived_cl1907, plain,
% 89.45/27.02 (~ (((cartprodsndin) =>
% 89.45/27.02 (((cartprodpairmemEL) =>
% 89.45/27.02 (((cartprodpairmemER) =>
% 89.45/27.02 (((cartprodmempaircEq) =>
% 89.45/27.02 (((cartprodfstpairEq) =>
% 89.45/27.02 (((cartprodsndpairEq) =>
% 89.45/27.02 (((cartprodpairsurjEq) =>
% 89.45/27.02 (((dpsetconstrI) =>
% 89.45/27.02 (((dpsetconstrSub) =>
% 89.45/27.02 (((setOfPairsIsBReln) =>
% 89.45/27.02 (((dpsetconstrERa) =>
% 89.45/27.02 (((dpsetconstrEL1) =>
% 89.45/27.02 (((dpsetconstrEL2) =>
% 89.45/27.02 (((dpsetconstrER) =>
% 89.45/27.02 (((funcImageSingleton) =>
% 89.45/27.02 (((apProp) =>
% 89.45/27.02 (((app) =>
% 89.45/27.02 (((infuncsetfunc) =>
% 89.45/27.02 (((ap2p) =>
% 89.45/27.02 (((funcinfuncset) =>
% 89.45/27.02 (((lamProp) =>
% 89.45/27.02 (((lamp) =>
% 89.45/27.02 (((lam2p) =>
% 89.45/27.02 (((brelnall1) =>
% 89.45/27.02 (((brelnall2) =>
% 89.45/27.02 (((!!) @ ((('#B') @ (
% 89.45/27.02 !!) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#S') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))) @
% 89.45/27.02 ex1)))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 !!))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#S') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#C') @ in)))))))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 !!))))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#C') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#C') @ in)))))))))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#S') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B'))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))))))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#C') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))))))) @
% 89.45/27.02 (
% 89.45/27.02 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.45/27.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1898])).
% 89.45/27.02 thf(zip_derived_cl1918, plain,
% 89.45/27.02 (~ (((cartprodpairmemEL) =>
% 89.45/27.02 (((cartprodpairmemER) =>
% 89.45/27.02 (((cartprodmempaircEq) =>
% 89.45/27.02 (((cartprodfstpairEq) =>
% 89.45/27.02 (((cartprodsndpairEq) =>
% 89.45/27.02 (((cartprodpairsurjEq) =>
% 89.45/27.02 (((dpsetconstrI) =>
% 89.45/27.02 (((dpsetconstrSub) =>
% 89.45/27.02 (((setOfPairsIsBReln) =>
% 89.45/27.02 (((dpsetconstrERa) =>
% 89.45/27.02 (((dpsetconstrEL1) =>
% 89.45/27.02 (((dpsetconstrEL2) =>
% 89.45/27.02 (((dpsetconstrER) =>
% 89.45/27.02 (((funcImageSingleton) =>
% 89.45/27.02 (((apProp) =>
% 89.45/27.02 (((app) =>
% 89.45/27.02 (((infuncsetfunc) =>
% 89.45/27.02 (((ap2p) =>
% 89.45/27.02 (((funcinfuncset) =>
% 89.45/27.02 (((lamProp) =>
% 89.45/27.02 (((lamp) =>
% 89.45/27.02 (((lam2p) =>
% 89.45/27.02 (((brelnall1) =>
% 89.45/27.02 (((brelnall2) =>
% 89.45/27.02 (((!!) @ ((('#B') @ (
% 89.45/27.02 !!) @
% 89.45/27.02 ((('#S') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))) @
% 89.45/27.02 ex1)))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 !!))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#S') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#C') @ in)))))))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 !!))))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#C') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#C') @ in)))))))))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#S') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B'))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))))))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#C') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))))))) @
% 89.45/27.02 (
% 89.45/27.02 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.45/27.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1907])).
% 89.45/27.02 thf(zip_derived_cl1928, plain,
% 89.45/27.02 (~ (((cartprodpairmemER) =>
% 89.45/27.02 (((cartprodmempaircEq) =>
% 89.45/27.02 (((cartprodfstpairEq) =>
% 89.45/27.02 (((cartprodsndpairEq) =>
% 89.45/27.02 (((cartprodpairsurjEq) =>
% 89.45/27.02 (((dpsetconstrI) =>
% 89.45/27.02 (((dpsetconstrSub) =>
% 89.45/27.02 (((setOfPairsIsBReln) =>
% 89.45/27.02 (((dpsetconstrERa) =>
% 89.45/27.02 (((dpsetconstrEL1) =>
% 89.45/27.02 (((dpsetconstrEL2) =>
% 89.45/27.02 (((dpsetconstrER) =>
% 89.45/27.02 (((funcImageSingleton) =>
% 89.45/27.02 (((apProp) =>
% 89.45/27.02 (((app) =>
% 89.45/27.02 (((infuncsetfunc) =>
% 89.45/27.02 (((ap2p) =>
% 89.45/27.02 (((funcinfuncset) =>
% 89.45/27.02 (((lamProp) =>
% 89.45/27.02 (((lamp) =>
% 89.45/27.02 (((lam2p) =>
% 89.45/27.02 (((brelnall1) =>
% 89.45/27.02 (((brelnall2) =>
% 89.45/27.02 (((!!) @ ((('#B') @ (
% 89.45/27.02 !!) @
% 89.45/27.02 ((('#S') @ (
% 89.45/27.02 (('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 ((
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))) @
% 89.45/27.02 ex1)))) @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 !!))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#S') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#C') @ in)))))))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 !!))))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#C') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#C') @ in)))))))))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#S') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B'))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))))))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#C') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))))))) @
% 89.45/27.02 (
% 89.45/27.02 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.45/27.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1918])).
% 89.45/27.02 thf(zip_derived_cl1939, plain,
% 89.45/27.02 (~ (((cartprodmempaircEq) =>
% 89.45/27.02 (((cartprodfstpairEq) =>
% 89.45/27.02 (((cartprodsndpairEq) =>
% 89.45/27.02 (((cartprodpairsurjEq) =>
% 89.45/27.02 (((dpsetconstrI) =>
% 89.45/27.02 (((dpsetconstrSub) =>
% 89.45/27.02 (((setOfPairsIsBReln) =>
% 89.45/27.02 (((dpsetconstrERa) =>
% 89.45/27.02 (((dpsetconstrEL1) =>
% 89.45/27.02 (((dpsetconstrEL2) =>
% 89.45/27.02 (((dpsetconstrER) =>
% 89.45/27.02 (((funcImageSingleton) =>
% 89.45/27.02 (((apProp) =>
% 89.45/27.02 (((app) =>
% 89.45/27.02 (((infuncsetfunc) =>
% 89.45/27.02 (((ap2p) =>
% 89.45/27.02 (((funcinfuncset) =>
% 89.45/27.02 (((lamProp) =>
% 89.45/27.02 (((lamp) =>
% 89.45/27.02 (((lam2p) =>
% 89.45/27.02 (((brelnall1) =>
% 89.45/27.02 (((brelnall2) =>
% 89.45/27.02 (((!!) @ ((('#B') @ (
% 89.45/27.02 !!) @
% 89.45/27.02 ((('#S') @ (
% 89.45/27.02 (('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 (('#B') @ (
% 89.45/27.02 =>))) @
% 89.45/27.02 ex1)))) @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 (('#B') @ (
% 89.45/27.02 !!))) @
% 89.45/27.02 ((('#S') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#C') @ in)))))))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 !!))))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#C') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#C') @ in)))))))))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#S') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B'))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))))))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#C') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))))))) @
% 89.45/27.02 (
% 89.45/27.02 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.45/27.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1928])).
% 89.45/27.02 thf(zip_derived_cl1949, plain,
% 89.45/27.02 (~ (((cartprodfstpairEq) =>
% 89.45/27.02 (((cartprodsndpairEq) =>
% 89.45/27.02 (((cartprodpairsurjEq) =>
% 89.45/27.02 (((dpsetconstrI) =>
% 89.45/27.02 (((dpsetconstrSub) =>
% 89.45/27.02 (((setOfPairsIsBReln) =>
% 89.45/27.02 (((dpsetconstrERa) =>
% 89.45/27.02 (((dpsetconstrEL1) =>
% 89.45/27.02 (((dpsetconstrEL2) =>
% 89.45/27.02 (((dpsetconstrER) =>
% 89.45/27.02 (((funcImageSingleton) =>
% 89.45/27.02 (((apProp) =>
% 89.45/27.02 (((app) =>
% 89.45/27.02 (((infuncsetfunc) =>
% 89.45/27.02 (((ap2p) =>
% 89.45/27.02 (((funcinfuncset) =>
% 89.45/27.02 (((lamProp) =>
% 89.45/27.02 (((lamp) =>
% 89.45/27.02 (((lam2p) =>
% 89.45/27.02 (((brelnall1) =>
% 89.45/27.02 (((brelnall2) =>
% 89.45/27.02 (((!!) @ ((('#B') @ (
% 89.45/27.02 !!) @
% 89.45/27.02 ((('#S') @ (
% 89.45/27.02 (('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 (('#B') @ (
% 89.45/27.02 =>))) @
% 89.45/27.02 ex1)))) @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 (('#B') @ (
% 89.45/27.02 !!))) @
% 89.45/27.02 ((('#S') @ (
% 89.45/27.02 (('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 ((
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#C') @ in)))))))) @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 !!))))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#C') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#C') @ in)))))))))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#S') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B'))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))))))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#C') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))))))) @
% 89.45/27.02 (
% 89.45/27.02 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.45/27.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1939])).
% 89.45/27.02 thf(zip_derived_cl1957, plain,
% 89.45/27.02 (~ (((cartprodsndpairEq) =>
% 89.45/27.02 (((cartprodpairsurjEq) =>
% 89.45/27.02 (((dpsetconstrI) =>
% 89.45/27.02 (((dpsetconstrSub) =>
% 89.45/27.02 (((setOfPairsIsBReln) =>
% 89.45/27.02 (((dpsetconstrERa) =>
% 89.45/27.02 (((dpsetconstrEL1) =>
% 89.45/27.02 (((dpsetconstrEL2) =>
% 89.45/27.02 (((dpsetconstrER) =>
% 89.45/27.02 (((funcImageSingleton) =>
% 89.45/27.02 (((apProp) =>
% 89.45/27.02 (((app) =>
% 89.45/27.02 (((infuncsetfunc) =>
% 89.45/27.02 (((ap2p) =>
% 89.45/27.02 (((funcinfuncset) =>
% 89.45/27.02 (((lamProp) =>
% 89.45/27.02 (((lamp) =>
% 89.45/27.02 (((lam2p) =>
% 89.45/27.02 (((brelnall1) =>
% 89.45/27.02 (((brelnall2) =>
% 89.45/27.02 (((!!) @ ((('#B') @ (!!) @
% 89.45/27.02 ((('#S') @ (
% 89.45/27.02 (('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 (('#B') @ (=>))) @
% 89.45/27.02 ex1)))) @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 (('#B') @ (!!))) @
% 89.45/27.02 ((('#S') @ (
% 89.45/27.02 (('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 ((
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#C') @ in)))))))) @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 (('#B') @ (
% 89.45/27.02 (('#B') @ (
% 89.45/27.02 !!))))) @
% 89.45/27.02 ((('#C') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#C') @ in)))))))))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#S') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B'))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))))))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#C') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))))))) @
% 89.45/27.02 (
% 89.45/27.02 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.45/27.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1949])).
% 89.45/27.02 thf(zip_derived_cl1965, plain,
% 89.45/27.02 (~ (((cartprodpairsurjEq) =>
% 89.45/27.02 (((dpsetconstrI) =>
% 89.45/27.02 (((dpsetconstrSub) =>
% 89.45/27.02 (((setOfPairsIsBReln) =>
% 89.45/27.02 (((dpsetconstrERa) =>
% 89.45/27.02 (((dpsetconstrEL1) =>
% 89.45/27.02 (((dpsetconstrEL2) =>
% 89.45/27.02 (((dpsetconstrER) =>
% 89.45/27.02 (((funcImageSingleton) =>
% 89.45/27.02 (((apProp) =>
% 89.45/27.02 (((app) =>
% 89.45/27.02 (((infuncsetfunc) =>
% 89.45/27.02 (((ap2p) =>
% 89.45/27.02 (((funcinfuncset) =>
% 89.45/27.02 (((lamProp) =>
% 89.45/27.02 (((lamp) =>
% 89.45/27.02 (((lam2p) =>
% 89.45/27.02 (((brelnall1) =>
% 89.45/27.02 (((brelnall2) =>
% 89.45/27.02 (((!!) @ ((('#B') @ (!!) @
% 89.45/27.02 ((('#S') @ ((
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))) @
% 89.45/27.02 ex1)))) @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 (('#B') @ (!!))) @
% 89.45/27.02 ((('#S') @ (
% 89.45/27.02 (('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 (('#B') @ (
% 89.45/27.02 =>))) @
% 89.45/27.02 ((
% 89.45/27.02 ('#C') @ in)))))))) @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 (('#B') @ (
% 89.45/27.02 (('#B') @ (
% 89.45/27.02 !!))))) @
% 89.45/27.02 ((('#C') @ (
% 89.45/27.02 (('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 ((
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#C') @ in)))))))))) @
% 89.45/27.02 ((('#S') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B'))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))))))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#C') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))))))) @
% 89.45/27.02 (
% 89.45/27.02 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.45/27.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1957])).
% 89.45/27.02 thf(zip_derived_cl1973, plain,
% 89.45/27.02 (~ (((dpsetconstrI) =>
% 89.45/27.02 (((dpsetconstrSub) =>
% 89.45/27.02 (((setOfPairsIsBReln) =>
% 89.45/27.02 (((dpsetconstrERa) =>
% 89.45/27.02 (((dpsetconstrEL1) =>
% 89.45/27.02 (((dpsetconstrEL2) =>
% 89.45/27.02 (((dpsetconstrER) =>
% 89.45/27.02 (((funcImageSingleton) =>
% 89.45/27.02 (((apProp) =>
% 89.45/27.02 (((app) =>
% 89.45/27.02 (((infuncsetfunc) =>
% 89.45/27.02 (((ap2p) =>
% 89.45/27.02 (((funcinfuncset) =>
% 89.45/27.02 (((lamProp) =>
% 89.45/27.02 (((lamp) =>
% 89.45/27.02 (((lam2p) =>
% 89.45/27.02 (((brelnall1) =>
% 89.45/27.02 (((brelnall2) =>
% 89.45/27.02 (((!!) @ ((('#B') @ (!!) @
% 89.45/27.02 ((('#S') @ ((('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 ((
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))) @
% 89.45/27.02 ex1)))) @
% 89.45/27.02 ((('#B') @ ((
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 !!))) @
% 89.45/27.02 ((('#S') @ (
% 89.45/27.02 (('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 (('#B') @ (
% 89.45/27.02 =>))) @
% 89.45/27.02 ((('#C') @ in)))))))) @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 (('#B') @ (
% 89.45/27.02 (('#B') @ (!!))))) @
% 89.45/27.02 ((('#C') @ (
% 89.45/27.02 (('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 ((
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#C') @ in)))))))))) @
% 89.45/27.02 ((('#S') @ (
% 89.45/27.02 (('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 ((
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B'))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))))))) @
% 89.45/27.02 ((('#C') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))))))) @
% 89.45/27.02 (
% 89.45/27.02 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.45/27.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1965])).
% 89.45/27.02 thf(zip_derived_cl1982, plain,
% 89.45/27.02 (~ (((dpsetconstrSub) =>
% 89.45/27.02 (((setOfPairsIsBReln) =>
% 89.45/27.02 (((dpsetconstrERa) =>
% 89.45/27.02 (((dpsetconstrEL1) =>
% 89.45/27.02 (((dpsetconstrEL2) =>
% 89.45/27.02 (((dpsetconstrER) =>
% 89.45/27.02 (((funcImageSingleton) =>
% 89.45/27.02 (((apProp) =>
% 89.45/27.02 (((app) =>
% 89.45/27.02 (((infuncsetfunc) =>
% 89.45/27.02 (((ap2p) =>
% 89.45/27.02 (((funcinfuncset) =>
% 89.45/27.02 (((lamProp) =>
% 89.45/27.02 (((lamp) =>
% 89.45/27.02 (((lam2p) =>
% 89.45/27.02 (((brelnall1) =>
% 89.45/27.02 (((brelnall2) =>
% 89.45/27.02 (((!!) @ ((('#B') @ (!!) @
% 89.45/27.02 ((('#S') @ ((('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 (('#B') @ (
% 89.45/27.02 =>))) @
% 89.45/27.02 ex1)))) @
% 89.45/27.02 ((('#B') @ ((('#B') @ (
% 89.45/27.02 !!))) @
% 89.45/27.02 ((('#S') @ ((
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#C') @ in)))))))) @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 (('#B') @ (
% 89.45/27.02 (('#B') @ (!!))))) @
% 89.45/27.02 ((('#C') @ (
% 89.45/27.02 (('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 ((
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#C') @ in)))))))))) @
% 89.45/27.02 ((('#S') @ (
% 89.45/27.02 (('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 (('#B') @ (
% 89.45/27.02 '#B'))) @
% 89.45/27.02 ((
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))))))) @
% 89.45/27.02 ((('#C') @ (
% 89.45/27.02 (('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 ((
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))))))) @
% 89.45/27.02 (=)))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.45/27.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1973])).
% 89.45/27.02 thf(zip_derived_cl1991, plain,
% 89.45/27.02 (~ (((setOfPairsIsBReln) =>
% 89.45/27.02 (((dpsetconstrERa) =>
% 89.45/27.02 (((dpsetconstrEL1) =>
% 89.45/27.02 (((dpsetconstrEL2) =>
% 89.45/27.02 (((dpsetconstrER) =>
% 89.45/27.02 (((funcImageSingleton) =>
% 89.45/27.02 (((apProp) =>
% 89.45/27.02 (((app) =>
% 89.45/27.02 (((infuncsetfunc) =>
% 89.45/27.02 (((ap2p) =>
% 89.45/27.02 (((funcinfuncset) =>
% 89.45/27.02 (((lamProp) =>
% 89.45/27.02 (((lamp) =>
% 89.45/27.02 (((lam2p) =>
% 89.45/27.02 (((brelnall1) =>
% 89.45/27.02 (((brelnall2) =>
% 89.45/27.02 (((!!) @ ((('#B') @ (!!) @
% 89.45/27.02 ((('#S') @ ((('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 (('#B') @ (
% 89.45/27.02 =>))) @
% 89.45/27.02 ex1)))) @
% 89.45/27.02 ((('#B') @ ((('#B') @ (
% 89.45/27.02 !!))) @
% 89.45/27.02 ((('#S') @ ((('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 ((
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#C') @ in)))))))) @
% 89.45/27.02 ((('#B') @ ((
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 !!))))) @
% 89.45/27.02 ((('#C') @ (
% 89.45/27.02 (('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 (('#B') @ (
% 89.45/27.02 =>))) @
% 89.45/27.02 ((
% 89.45/27.02 ('#C') @ in)))))))))) @
% 89.45/27.02 ((('#S') @ (
% 89.45/27.02 (('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 (('#B') @ (
% 89.45/27.02 '#B'))) @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 =>))))))) @
% 89.45/27.02 ((('#C') @ (
% 89.45/27.02 (('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 ((
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))))))) @
% 89.45/27.02 (=)))))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.45/27.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1982])).
% 89.45/27.02 thf(zip_derived_cl2000, plain,
% 89.45/27.02 (~ (((dpsetconstrERa) =>
% 89.45/27.02 (((dpsetconstrEL1) =>
% 89.45/27.02 (((dpsetconstrEL2) =>
% 89.45/27.02 (((dpsetconstrER) =>
% 89.45/27.02 (((funcImageSingleton) =>
% 89.45/27.02 (((apProp) =>
% 89.45/27.02 (((app) =>
% 89.45/27.02 (((infuncsetfunc) =>
% 89.45/27.02 (((ap2p) =>
% 89.45/27.02 (((funcinfuncset) =>
% 89.45/27.02 (((lamProp) =>
% 89.45/27.02 (((lamp) =>
% 89.45/27.02 (((lam2p) =>
% 89.45/27.02 (((brelnall1) =>
% 89.45/27.02 (((brelnall2) =>
% 89.45/27.02 (((!!) @ ((('#B') @ (!!) @
% 89.45/27.02 ((('#S') @ ((('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 (('#B') @ (=>))) @
% 89.45/27.02 ex1)))) @
% 89.45/27.02 ((('#B') @ ((('#B') @ (!!))) @
% 89.45/27.02 ((('#S') @ ((('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 ((
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#C') @ in)))))))) @
% 89.45/27.02 ((('#B') @ ((('#B') @ (
% 89.45/27.02 (('#B') @ (
% 89.45/27.02 !!))))) @
% 89.45/27.02 ((('#C') @ ((
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#C') @ in)))))))))) @
% 89.45/27.02 ((('#S') @ (
% 89.45/27.02 (('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 (('#B') @ (
% 89.45/27.02 '#B'))) @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 =>))))))) @
% 89.45/27.02 ((('#C') @ (
% 89.45/27.02 (('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 =>))))))) @
% 89.45/27.02 (=)))))))))))))))))))))))))))))))))))))))))))))))))),
% 89.45/27.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1991])).
% 89.45/27.02 thf(zip_derived_cl2010, plain,
% 89.45/27.02 (~ (((dpsetconstrEL1) =>
% 89.45/27.02 (((dpsetconstrEL2) =>
% 89.45/27.02 (((dpsetconstrER) =>
% 89.45/27.02 (((funcImageSingleton) =>
% 89.45/27.02 (((apProp) =>
% 89.45/27.02 (((app) =>
% 89.45/27.02 (((infuncsetfunc) =>
% 89.45/27.02 (((ap2p) =>
% 89.45/27.02 (((funcinfuncset) =>
% 89.45/27.02 (((lamProp) =>
% 89.45/27.02 (((lamp) =>
% 89.45/27.02 (((lam2p) =>
% 89.45/27.02 (((brelnall1) =>
% 89.45/27.02 (((brelnall2) =>
% 89.45/27.02 (((!!) @ ((('#B') @ (!!) @
% 89.45/27.02 ((('#S') @ ((('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 (('#B') @ (=>))) @
% 89.45/27.02 ex1)))) @
% 89.45/27.02 ((('#B') @ ((('#B') @ (!!))) @
% 89.45/27.02 ((('#S') @ ((('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 (('#B') @ (
% 89.45/27.02 =>))) @
% 89.45/27.02 ((
% 89.45/27.02 ('#C') @ in)))))))) @
% 89.45/27.02 ((('#B') @ ((('#B') @ (
% 89.45/27.02 (('#B') @ (
% 89.45/27.02 !!))))) @
% 89.45/27.02 ((('#C') @ ((('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 ((
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#C') @ in)))))))))) @
% 89.45/27.02 ((('#S') @ ((
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B'))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))))))) @
% 89.45/27.02 ((('#C') @ (
% 89.45/27.02 (('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 =>))))))) @
% 89.45/27.02 (=)))))))))))))))))))))))))))))))))))))))))))))))),
% 89.45/27.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2000])).
% 89.45/27.02 thf(zip_derived_cl2020, plain,
% 89.45/27.02 (~ (((dpsetconstrEL2) =>
% 89.45/27.02 (((dpsetconstrER) =>
% 89.45/27.02 (((funcImageSingleton) =>
% 89.45/27.02 (((apProp) =>
% 89.45/27.02 (((app) =>
% 89.45/27.02 (((infuncsetfunc) =>
% 89.45/27.02 (((ap2p) =>
% 89.45/27.02 (((funcinfuncset) =>
% 89.45/27.02 (((lamProp) =>
% 89.45/27.02 (((lamp) =>
% 89.45/27.02 (((lam2p) =>
% 89.45/27.02 (((brelnall1) =>
% 89.45/27.02 (((brelnall2) =>
% 89.45/27.02 (((!!) @ ((('#B') @ (!!) @
% 89.45/27.02 ((('#S') @ ((('#B') @ ('#S') @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 (('#B') @ (=>))) @
% 89.45/27.02 ex1)))) @
% 89.45/27.02 ((('#B') @ ((('#B') @ (!!))) @
% 89.45/27.02 ((('#S') @ ((('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 (('#B') @ (
% 89.45/27.02 =>))) @
% 89.45/27.02 ((('#C') @ in)))))))) @
% 89.45/27.02 ((('#B') @ ((('#B') @ (
% 89.45/27.02 (('#B') @ (!!))))) @
% 89.45/27.02 ((('#C') @ ((('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 ((
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#C') @ in)))))))))) @
% 89.45/27.02 ((('#S') @ ((('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 ((
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B'))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))))))) @
% 89.45/27.02 ((('#C') @ ((
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))))))) @
% 89.45/27.02 (=)))))))))))))))))))))))))))))))))))))))))))))),
% 89.45/27.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2010])).
% 89.45/27.02 thf(zip_derived_cl2031, plain,
% 89.45/27.02 (~ (((dpsetconstrER) =>
% 89.45/27.02 (((funcImageSingleton) =>
% 89.45/27.02 (((apProp) =>
% 89.45/27.02 (((app) =>
% 89.45/27.02 (((infuncsetfunc) =>
% 89.45/27.02 (((ap2p) =>
% 89.45/27.02 (((funcinfuncset) =>
% 89.45/27.02 (((lamProp) =>
% 89.45/27.02 (((lamp) =>
% 89.45/27.02 (((lam2p) =>
% 89.45/27.02 (((brelnall1) =>
% 89.45/27.02 (((brelnall2) =>
% 89.45/27.02 (((!!) @ ((('#B') @ (!!) @
% 89.45/27.02 ((('#S') @ ((('#B') @ ('#S') @
% 89.45/27.02 ((('#B') @ ((('#B') @ (
% 89.45/27.02 =>))) @
% 89.45/27.02 ex1)))) @
% 89.45/27.02 ((('#B') @ ((('#B') @ (!!))) @
% 89.45/27.02 ((('#S') @ ((('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 (('#B') @ (=>))) @
% 89.45/27.02 ((('#C') @ in)))))))) @
% 89.45/27.02 ((('#B') @ ((('#B') @ (
% 89.45/27.02 (('#B') @ (!!))))) @
% 89.45/27.02 ((('#C') @ ((('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 ((
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))) @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#C') @ in)))))))))) @
% 89.45/27.02 ((('#S') @ ((('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 (('#B') @ (
% 89.45/27.02 '#B'))) @
% 89.45/27.02 ((
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))))))) @
% 89.45/27.02 ((('#C') @ ((('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 ((
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 (
% 89.45/27.02 (
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))))))) @
% 89.45/27.02 (=)))))))))))))))))))))))))))))))))))))))))))),
% 89.45/27.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2020])).
% 89.45/27.02 thf(zip_derived_cl2040, plain,
% 89.45/27.02 (~ (((funcImageSingleton) =>
% 89.45/27.02 (((apProp) =>
% 89.45/27.02 (((app) =>
% 89.45/27.02 (((infuncsetfunc) =>
% 89.45/27.02 (((ap2p) =>
% 89.45/27.02 (((funcinfuncset) =>
% 89.45/27.02 (((lamProp) =>
% 89.45/27.02 (((lamp) =>
% 89.45/27.02 (((lam2p) =>
% 89.45/27.02 (((brelnall1) =>
% 89.45/27.02 (((brelnall2) =>
% 89.45/27.02 (((!!) @ ((('#B') @ (!!) @
% 89.45/27.02 ((('#S') @ ((('#B') @ ('#S') @
% 89.45/27.02 ((('#B') @ ((('#B') @ (
% 89.45/27.02 =>))) @
% 89.45/27.02 ex1)))) @
% 89.45/27.02 ((('#B') @ ((('#B') @ (!!))) @
% 89.45/27.02 ((('#S') @ ((('#B') @ ('#B') @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 (('#B') @ (=>))) @
% 89.45/27.02 ((('#C') @ in)))))))) @
% 89.45/27.02 ((('#B') @ ((('#B') @ (
% 89.45/27.02 (('#B') @ (!!))))) @
% 89.45/27.02 ((('#C') @ ((('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 (('#B') @ (
% 89.45/27.02 =>))) @
% 89.45/27.02 ((
% 89.45/27.02 ('#C') @ in)))))))))) @
% 89.45/27.02 ((('#S') @ ((('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 (('#B') @ (
% 89.45/27.02 '#B'))) @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 =>))))))) @
% 89.45/27.02 ((('#C') @ ((('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 ((
% 89.45/27.02 ('#B') @ (
% 89.45/27.02 =>))))))) @
% 89.45/27.02 (=)))))))))))))))))))))))))))))))))))))))))),
% 89.45/27.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2031])).
% 89.45/27.02 thf(zip_derived_cl2049, plain,
% 89.45/27.02 (~ (((apProp) =>
% 89.45/27.02 (((app) =>
% 89.45/27.02 (((infuncsetfunc) =>
% 89.45/27.02 (((ap2p) =>
% 89.45/27.02 (((funcinfuncset) =>
% 89.45/27.02 (((lamProp) =>
% 89.45/27.02 (((lamp) =>
% 89.45/27.02 (((lam2p) =>
% 89.45/27.02 (((brelnall1) =>
% 89.45/27.02 (((brelnall2) =>
% 89.45/27.02 (((!!) @ ((('#B') @ (!!) @
% 89.45/27.02 ((('#S') @ ((('#B') @ ('#S') @
% 89.45/27.02 ((('#B') @ ((('#B') @ (=>))) @
% 89.45/27.02 ex1)))) @
% 89.45/27.02 ((('#B') @ ((('#B') @ (!!))) @
% 89.45/27.02 ((('#S') @ ((('#B') @ ('#B') @
% 89.45/27.02 ((('#B') @ ('#S') @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 (('#B') @ (=>))) @
% 89.45/27.02 ((('#C') @ in)))))))) @
% 89.45/27.02 ((('#B') @ ((('#B') @ ((('#B') @ (
% 89.45/27.02 !!))))) @
% 89.45/27.02 ((('#C') @ ((('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 (('#B') @ (
% 89.45/27.02 =>))) @
% 89.45/27.02 ((('#C') @ in)))))))))) @
% 89.45/27.02 ((('#S') @ ((('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 (('#B') @ (
% 89.45/27.02 '#B'))) @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 =>))))))) @
% 89.45/27.02 ((('#C') @ ((('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 =>))))))) @
% 89.45/27.02 (=)))))))))))))))))))))))))))))))))))))))),
% 89.45/27.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2040])).
% 89.45/27.02 thf(zip_derived_cl2058, plain,
% 89.45/27.02 (~ (((app) =>
% 89.45/27.02 (((infuncsetfunc) =>
% 89.45/27.02 (((ap2p) =>
% 89.45/27.02 (((funcinfuncset) =>
% 89.45/27.02 (((lamProp) =>
% 89.45/27.02 (((lamp) =>
% 89.45/27.02 (((lam2p) =>
% 89.45/27.02 (((brelnall1) =>
% 89.45/27.02 (((brelnall2) =>
% 89.45/27.02 (((!!) @ ((('#B') @ (!!) @
% 89.45/27.02 ((('#S') @ ((('#B') @ ('#S') @
% 89.45/27.02 ((('#B') @ ((('#B') @ (=>))) @
% 89.45/27.02 ex1)))) @
% 89.45/27.02 ((('#B') @ ((('#B') @ (!!))) @
% 89.45/27.02 ((('#S') @ ((('#B') @ ('#B') @
% 89.45/27.02 ((('#B') @ ('#S') @
% 89.45/27.02 ((('#B') @ ((('#B') @ (
% 89.45/27.02 =>))) @
% 89.45/27.02 ((('#C') @ in)))))))) @
% 89.45/27.02 ((('#B') @ ((('#B') @ ((('#B') @ (
% 89.45/27.02 !!))))) @
% 89.45/27.02 ((('#C') @ ((('#B') @ ('#B') @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 (('#B') @ (=>))) @
% 89.45/27.02 ((('#C') @ in)))))))))) @
% 89.45/27.02 ((('#S') @ ((('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 (('#B') @ ('#B'))) @
% 89.45/27.02 ((('#B') @ (=>))))))) @
% 89.45/27.02 ((('#C') @ ((('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 =>))))))) @
% 89.45/27.02 (=)))))))))))))))))))))))))))))))))))))),
% 89.45/27.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2049])).
% 89.45/27.02 thf(zip_derived_cl2068, plain,
% 89.45/27.02 (~ (((infuncsetfunc) =>
% 89.45/27.02 (((ap2p) =>
% 89.45/27.02 (((funcinfuncset) =>
% 89.45/27.02 (((lamProp) =>
% 89.45/27.02 (((lamp) =>
% 89.45/27.02 (((lam2p) =>
% 89.45/27.02 (((brelnall1) =>
% 89.45/27.02 (((brelnall2) =>
% 89.45/27.02 (((!!) @ ((('#B') @ (!!) @
% 89.45/27.02 ((('#S') @ ((('#B') @ ('#S') @
% 89.45/27.02 ((('#B') @ ((('#B') @ (=>))) @
% 89.45/27.02 ex1)))) @
% 89.45/27.02 ((('#B') @ ((('#B') @ (!!))) @
% 89.45/27.02 ((('#S') @ ((('#B') @ ('#B') @
% 89.45/27.02 ((('#B') @ ('#S') @
% 89.45/27.02 ((('#B') @ ((('#B') @ (
% 89.45/27.02 =>))) @
% 89.45/27.02 ((('#C') @ in)))))))) @
% 89.45/27.02 ((('#B') @ ((('#B') @ ((('#B') @ (!!))))) @
% 89.45/27.02 ((('#C') @ ((('#B') @ ('#B') @
% 89.45/27.02 ((('#B') @ ('#B') @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 (('#B') @ (=>))) @
% 89.45/27.02 ((('#C') @ in)))))))))) @
% 89.45/27.02 ((('#S') @ ((('#B') @ ('#S') @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 (('#B') @ ('#B'))) @
% 89.45/27.02 ((('#B') @ (=>))))))) @
% 89.45/27.02 ((('#C') @ ((('#B') @ (
% 89.45/27.02 '#B') @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 ((('#B') @ (=>))))))) @
% 89.45/27.02 (=)))))))))))))))))))))))))))))))))))),
% 89.45/27.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2058])).
% 89.45/27.02 thf(zip_derived_cl2078, plain,
% 89.45/27.02 (~ (((ap2p) =>
% 89.45/27.02 (((funcinfuncset) =>
% 89.45/27.02 (((lamProp) =>
% 89.45/27.02 (((lamp) =>
% 89.45/27.02 (((lam2p) =>
% 89.45/27.02 (((brelnall1) =>
% 89.45/27.02 (((brelnall2) =>
% 89.45/27.02 (((!!) @ ((('#B') @ (!!) @
% 89.45/27.02 ((('#S') @ ((('#B') @ ('#S') @
% 89.45/27.02 ((('#B') @ ((('#B') @ (=>))) @
% 89.45/27.02 ex1)))) @
% 89.45/27.02 ((('#B') @ ((('#B') @ (!!))) @
% 89.45/27.02 ((('#S') @ ((('#B') @ ('#B') @
% 89.45/27.02 ((('#B') @ ('#S') @
% 89.45/27.02 ((('#B') @ ((('#B') @ (=>))) @
% 89.45/27.02 ((('#C') @ in)))))))) @
% 89.45/27.02 ((('#B') @ ((('#B') @ ((('#B') @ (!!))))) @
% 89.45/27.02 ((('#C') @ ((('#B') @ ('#B') @
% 89.45/27.02 ((('#B') @ ('#B') @
% 89.45/27.02 ((('#B') @ ('#S') @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 (('#B') @ (=>))) @
% 89.45/27.02 ((('#C') @ in)))))))))) @
% 89.45/27.02 ((('#S') @ ((('#B') @ ('#S') @
% 89.45/27.02 ((('#B') @ ((('#B') @ (
% 89.45/27.02 '#B'))) @
% 89.45/27.02 ((('#B') @ (=>))))))) @
% 89.45/27.02 ((('#C') @ ((('#B') @ ('#B') @
% 89.45/27.02 ((('#B') @ (
% 89.45/27.02 '#S') @
% 89.45/27.02 ((('#B') @ (=>))))))) @
% 89.45/27.02 (=)))))))))))))))))))))))))))))))))),
% 89.45/27.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2068])).
% 89.45/27.02 thf(zip_derived_cl2089, plain,
% 89.45/27.02 (~ (((funcinfuncset) =>
% 89.45/27.02 (((lamProp) =>
% 89.45/27.02 (((lamp) =>
% 89.45/27.02 (((lam2p) =>
% 89.45/27.02 (((brelnall1) =>
% 89.45/27.02 (((brelnall2) =>
% 89.45/27.02 (((!!) @ ((('#B') @ (!!) @
% 89.45/27.02 ((('#S') @ ((('#B') @ ('#S') @
% 89.45/27.02 ((('#B') @ ((('#B') @ (=>))) @ ex1)))) @
% 89.45/27.02 ((('#B') @ ((('#B') @ (!!))) @
% 89.45/27.02 ((('#S') @ ((('#B') @ ('#B') @
% 89.45/27.02 ((('#B') @ ('#S') @
% 89.45/27.02 ((('#B') @ ((('#B') @ (=>))) @
% 89.45/27.02 ((('#C') @ in)))))))) @
% 89.45/27.02 ((('#B') @ ((('#B') @ ((('#B') @ (!!))))) @
% 89.45/27.02 ((('#C') @ ((('#B') @ ('#B') @
% 89.45/27.02 ((('#B') @ ('#B') @
% 89.45/27.02 ((('#B') @ ('#S') @
% 89.45/27.02 ((('#B') @ ((('#B') @ (
% 89.45/27.02 =>))) @
% 89.45/27.02 ((('#C') @ in)))))))))) @
% 89.45/27.02 ((('#S') @ ((('#B') @ ('#S') @
% 89.45/27.02 ((('#B') @ ((('#B') @ (
% 89.45/27.02 '#B'))) @
% 89.45/27.02 ((('#B') @ (=>))))))) @
% 89.45/27.02 ((('#C') @ ((('#B') @ ('#B') @
% 89.45/27.02 ((('#B') @ ('#S') @
% 89.45/27.02 ((('#B') @ (=>))))))) @
% 89.45/27.02 (=)))))))))))))))))))))))))))))))),
% 89.45/27.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2078])).
% 89.45/27.02 thf(zip_derived_cl2100, plain,
% 89.45/27.02 (~ (((lamProp) =>
% 89.45/27.02 (((lamp) =>
% 89.45/27.02 (((lam2p) =>
% 89.45/27.02 (((brelnall1) =>
% 89.45/27.02 (((brelnall2) =>
% 89.45/27.02 (((!!) @ ((('#B') @ (!!) @
% 89.45/27.02 ((('#S') @ ((('#B') @ ('#S') @
% 89.45/27.02 ((('#B') @ ((('#B') @ (=>))) @ ex1)))) @
% 89.45/27.02 ((('#B') @ ((('#B') @ (!!))) @
% 89.45/27.02 ((('#S') @ ((('#B') @ ('#B') @
% 89.45/27.02 ((('#B') @ ('#S') @
% 89.45/27.02 ((('#B') @ ((('#B') @ (=>))) @
% 89.45/27.02 ((('#C') @ in)))))))) @
% 89.45/27.02 ((('#B') @ ((('#B') @ ((('#B') @ (!!))))) @
% 89.45/27.02 ((('#C') @ ((('#B') @ ('#B') @
% 89.45/27.02 ((('#B') @ ('#B') @
% 89.45/27.02 ((('#B') @ ('#S') @
% 89.45/27.02 ((('#B') @ ((('#B') @ (
% 89.45/27.02 =>))) @
% 89.45/27.02 ((('#C') @ in)))))))))) @
% 89.45/27.02 ((('#S') @ ((('#B') @ ('#S') @
% 89.45/27.02 ((('#B') @ ((('#B') @ (
% 89.45/27.02 '#B'))) @
% 89.45/27.02 ((('#B') @ (=>))))))) @
% 89.45/27.02 ((('#C') @ ((('#B') @ ('#B') @
% 89.45/27.02 ((('#B') @ ('#S') @
% 89.45/27.02 ((('#B') @ (=>))))))) @
% 89.45/27.02 (=)))))))))))))))))))))))))))))),
% 89.45/27.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2089])).
% 89.45/27.02 thf(zip_derived_cl2110, plain,
% 89.45/27.02 (~ (((lamp) =>
% 89.45/27.02 (((lam2p) =>
% 89.45/27.02 (((brelnall1) =>
% 89.45/27.02 (((brelnall2) =>
% 89.45/27.02 (((!!) @ ((('#B') @ (!!) @
% 89.45/27.02 ((('#S') @ ((('#B') @ ('#S') @
% 89.45/27.02 ((('#B') @ ((('#B') @ (=>))) @ ex1)))) @
% 89.45/27.02 ((('#B') @ ((('#B') @ (!!))) @
% 89.45/27.02 ((('#S') @ ((('#B') @ ('#B') @
% 89.45/27.02 ((('#B') @ ('#S') @
% 89.45/27.02 ((('#B') @ ((('#B') @ (=>))) @
% 89.45/27.02 ((('#C') @ in)))))))) @
% 89.45/27.02 ((('#B') @ ((('#B') @ ((('#B') @ (!!))))) @
% 89.45/27.02 ((('#C') @ ((('#B') @ ('#B') @
% 89.45/27.02 ((('#B') @ ('#B') @
% 89.45/27.02 ((('#B') @ ('#S') @
% 89.45/27.02 ((('#B') @ ((('#B') @ (=>))) @
% 89.45/27.02 ((('#C') @ in)))))))))) @
% 89.45/27.02 ((('#S') @ ((('#B') @ ('#S') @
% 89.45/27.02 ((('#B') @ ((('#B') @ ('#B'))) @
% 89.45/27.02 ((('#B') @ (=>))))))) @
% 89.45/27.02 ((('#C') @ ((('#B') @ ('#B') @
% 89.45/27.02 ((('#B') @ ('#S') @
% 89.45/27.02 ((('#B') @ (=>))))))) @
% 89.45/27.02 (=)))))))))))))))))))))))))))),
% 89.45/27.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2100])).
% 89.45/27.02 thf(zip_derived_cl2122, plain,
% 89.45/27.02 (~ (((lam2p) =>
% 89.45/27.02 (((brelnall1) =>
% 89.45/27.02 (((brelnall2) =>
% 89.45/27.02 (((!!) @ ((('#B') @ (!!) @
% 89.45/27.02 ((('#S') @ ((('#B') @ ('#S') @
% 89.45/27.02 ((('#B') @ ((('#B') @ (=>))) @ ex1)))) @
% 89.45/27.02 ((('#B') @ ((('#B') @ (!!))) @
% 89.45/27.02 ((('#S') @ ((('#B') @ ('#B') @
% 89.45/27.02 ((('#B') @ ('#S') @
% 89.45/27.02 ((('#B') @ ((('#B') @ (=>))) @
% 89.45/27.02 ((('#C') @ in)))))))) @
% 89.45/27.02 ((('#B') @ ((('#B') @ ((('#B') @ (!!))))) @
% 89.45/27.02 ((('#C') @ ((('#B') @ ('#B') @
% 89.45/27.02 ((('#B') @ ('#B') @
% 89.45/27.02 ((('#B') @ ('#S') @
% 89.45/27.02 ((('#B') @ ((('#B') @ (=>))) @
% 89.45/27.02 ((('#C') @ in)))))))))) @
% 89.45/27.02 ((('#S') @ ((('#B') @ ('#S') @
% 89.45/27.02 ((('#B') @ ((('#B') @ ('#B'))) @
% 89.45/27.02 ((('#B') @ (=>))))))) @
% 89.45/27.02 ((('#C') @ ((('#B') @ ('#B') @
% 89.45/27.02 ((('#B') @ ('#S') @
% 89.45/27.02 ((('#B') @ (=>))))))) @
% 89.45/27.02 (=)))))))))))))))))))))))))),
% 89.45/27.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2110])).
% 89.45/27.02 thf(zip_derived_cl2135, plain,
% 89.45/27.02 (~ (((brelnall1) =>
% 89.45/27.02 (((brelnall2) =>
% 89.45/27.02 (((!!) @ ((('#B') @ (!!) @
% 89.45/27.02 ((('#S') @ ((('#B') @ ('#S') @
% 89.45/27.02 ((('#B') @ ((('#B') @ (=>))) @ ex1)))) @
% 89.45/27.02 ((('#B') @ ((('#B') @ (!!))) @
% 89.45/27.02 ((('#S') @ ((('#B') @ ('#B') @
% 89.45/27.02 ((('#B') @ ('#S') @
% 89.45/27.02 ((('#B') @ ((('#B') @ (=>))) @
% 89.45/27.02 ((('#C') @ in)))))))) @
% 89.45/27.02 ((('#B') @ ((('#B') @ ((('#B') @ (!!))))) @
% 89.45/27.02 ((('#C') @ ((('#B') @ ('#B') @
% 89.45/27.02 ((('#B') @ ('#B') @
% 89.45/27.02 ((('#B') @ ('#S') @
% 89.45/27.02 ((('#B') @ ((('#B') @ (=>))) @
% 89.45/27.02 ((('#C') @ in)))))))))) @
% 89.45/27.02 ((('#S') @ ((('#B') @ ('#S') @
% 89.45/27.02 ((('#B') @ ((('#B') @ ('#B'))) @
% 89.45/27.02 ((('#B') @ (=>))))))) @
% 89.45/27.02 ((('#C') @ ((('#B') @ ('#B') @
% 89.45/27.02 ((('#B') @ ('#S') @
% 89.45/27.02 ((('#B') @ (=>))))))) @
% 89.45/27.02 (=)))))))))))))))))))))))),
% 89.45/27.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2122])).
% 89.45/27.02 thf(zip_derived_cl2151, plain,
% 89.45/27.02 (~ (((brelnall2) =>
% 89.45/27.02 (((!!) @ ((('#B') @ (!!) @
% 89.45/27.02 ((('#S') @ ((('#B') @ ('#S') @
% 89.45/27.02 ((('#B') @ ((('#B') @ (=>))) @ ex1)))) @
% 89.45/27.02 ((('#B') @ ((('#B') @ (!!))) @
% 89.45/27.02 ((('#S') @ ((('#B') @ ('#B') @
% 89.45/27.02 ((('#B') @ ('#S') @
% 89.45/27.02 ((('#B') @ ((('#B') @ (=>))) @
% 89.45/27.02 ((('#C') @ in)))))))) @
% 89.45/27.02 ((('#B') @ ((('#B') @ ((('#B') @ (!!))))) @
% 89.45/27.02 ((('#C') @ ((('#B') @ ('#B') @
% 89.45/27.02 ((('#B') @ ('#B') @
% 89.45/27.02 ((('#B') @ ('#S') @
% 89.45/27.02 ((('#B') @ ((('#B') @ (=>))) @
% 89.45/27.02 ((('#C') @ in)))))))))) @
% 89.45/27.02 ((('#S') @ ((('#B') @ ('#S') @
% 89.45/27.02 ((('#B') @ ((('#B') @ ('#B'))) @
% 89.45/27.02 ((('#B') @ (=>))))))) @
% 89.45/27.02 ((('#C') @ ((('#B') @ ('#B') @
% 89.45/27.02 ((('#B') @ ('#S') @
% 89.45/27.02 ((('#B') @ (=>))))))) @
% 89.45/27.02 (=)))))))))))))))))))))),
% 89.45/27.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2135])).
% 89.45/27.02 thf(zip_derived_cl2170, plain,
% 89.45/27.02 (~ (((!!) @ ((('#B') @ (!!) @
% 89.45/27.02 ((('#S') @ ((('#B') @ ('#S') @
% 89.45/27.02 ((('#B') @ ((('#B') @ (=>))) @ ex1)))) @
% 89.45/27.02 ((('#B') @ ((('#B') @ (!!))) @
% 89.45/27.02 ((('#S') @ ((('#B') @ ('#B') @
% 89.45/27.02 ((('#B') @ ('#S') @
% 89.45/27.02 ((('#B') @ ((('#B') @ (=>))) @
% 89.45/27.02 ((('#C') @ in)))))))) @
% 89.45/27.02 ((('#B') @ ((('#B') @ ((('#B') @ (!!))))) @
% 89.45/27.02 ((('#C') @ ((('#B') @ ('#B') @
% 89.45/27.02 ((('#B') @ ('#B') @
% 89.45/27.02 ((('#B') @ ('#S') @
% 89.45/27.02 ((('#B') @ ((('#B') @ (=>))) @
% 89.45/27.02 ((('#C') @ in)))))))))) @
% 89.45/27.02 ((('#S') @ ((('#B') @ ('#S') @
% 89.45/27.02 ((('#B') @ ((('#B') @ ('#B'))) @
% 89.45/27.02 ((('#B') @ (=>))))))) @
% 89.45/27.02 ((('#C') @ ((('#B') @ ('#B') @
% 89.45/27.02 ((('#B') @ ('#S') @
% 89.45/27.02 ((('#B') @ (=>))))))) @
% 89.45/27.02 (=)))))))))))))))))))),
% 89.45/27.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2151])).
% 89.45/27.02 thf(zip_derived_cl2189, plain,
% 89.45/27.02 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (ex1 @ '#sk37'))) @
% 89.45/27.02 ((('#B') @ (!!) @
% 89.45/27.02 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @
% 89.45/27.02 ((('#C') @ in @ '#sk37')))))) @
% 89.45/27.02 ((('#B') @ ((('#B') @ (!!))) @
% 89.45/27.02 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ (
% 89.45/27.02 =>) @
% 89.45/27.02 ((('#C') @ in @
% 89.45/27.02 '#sk37')))))))) @
% 89.45/27.02 ((('#S') @ ((('#B') @ ('#S') @
% 89.45/27.02 ((('#B') @ ((('#B') @ ('#B'))) @
% 89.45/27.02 ((('#B') @ (=>))))))) @
% 89.45/27.02 ((('#C') @ ((('#B') @ ('#B') @
% 89.45/27.02 ((('#B') @ ('#S') @
% 89.45/27.02 ((('#B') @ (=>))))))) @
% 89.45/27.02 (=)))))))))))))))))),
% 89.45/27.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl2170])).
% 89.45/27.02 thf(zip_derived_cl2209, plain,
% 89.45/27.02 (~ (((ex1 @ '#sk37' @ '#sk38') =>
% 89.45/27.02 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ '#sk37')))) @
% 89.45/27.02 ((('#B') @ (!!) @
% 89.45/27.02 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @
% 89.45/27.02 ((('#C') @ in @ '#sk37')))))) @
% 89.45/27.02 ((('#S') @ ((('#B') @ ('#B') @
% 89.45/27.02 ((('#B') @ (=>) @ '#sk38')))) @
% 89.45/27.02 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ '#sk38')))) @
% 89.45/27.02 (=)))))))))))))))),
% 89.45/27.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl2189])).
% 89.45/27.02 thf(ex1, axiom,(( ex1 @ (X0)@ (X1)) =
% 89.45/27.02 ((singleton @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0))))))).
% 89.45/27.02 thf('4', plain,
% 89.45/27.02 (![X1:( $i > $o ),X0:$i]:
% 89.45/27.02 ( ( ex1 @ X0 @ X1 ) =
% 89.45/27.02 ( singleton @ ( dsetconstr @ X0 @ ( ^[V_1:$i]: ( X1 @ V_1 ) ) ) ) )),
% 89.45/27.02 define([status(thm)])).
% 89.45/27.02 thf(zip_derived_cl2230, plain,
% 89.45/27.02 (~ (((singleton @ (dsetconstr @ '#sk37' @ '#sk38')) =>
% 89.45/27.02 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ '#sk37')))) @
% 89.45/27.02 ((('#B') @ (!!) @
% 89.45/27.02 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @
% 89.45/27.02 ((('#C') @ in @ '#sk37')))))) @
% 89.45/27.02 ((('#S') @ ((('#B') @ ('#B') @
% 89.45/27.02 ((('#B') @ (=>) @ '#sk38')))) @
% 89.45/27.02 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ '#sk38')))) @
% 89.45/27.02 (=)))))))))))))))),
% 89.45/27.02 inference('rw', [status(thm)], [zip_derived_cl2209, '4'])).
% 89.45/27.02 thf(zip_derived_cl2232, plain,
% 89.45/27.02 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ '#sk37')))) @
% 89.45/27.02 ((('#B') @ (!!) @
% 89.45/27.02 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @
% 89.45/27.02 ((('#C') @ in @ '#sk37')))))) @
% 89.45/27.02 ((('#S') @ ((('#B') @ ('#B') @
% 89.45/27.02 ((('#B') @ (=>) @ '#sk38')))) @
% 89.45/27.02 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ '#sk38')))) @
% 89.45/27.02 (=)))))))))))))),
% 89.45/27.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2230])).
% 89.45/27.02 thf(zip_derived_cl2255, plain,
% 89.45/27.02 (~ (((in @ ('#sk32' @ '#sk37' @ '#sk38') @ '#sk37') =>
% 89.45/27.02 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ '#sk37')))) @
% 89.45/27.02 ((('#B') @ (((=>) @ ('#sk38' @
% 89.45/27.02 ('#sk32' @ '#sk37' @ '#sk38')))) @
% 89.45/27.02 ((('#S') @ ((('#B') @ (=>) @ '#sk38')) @
% 89.45/27.02 ((($i) = ('#sk32' @ '#sk37' @ '#sk38')))))))))))))),
% 89.45/27.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl2232])).
% 89.45/27.02 thf(zip_derived_cl2278, plain,
% 89.45/27.02 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ '#sk37')))) @
% 89.45/27.02 ((('#B') @ (((=>) @ ('#sk38' @
% 89.45/27.02 ('#sk32' @ '#sk37' @ '#sk38')))) @
% 89.45/27.02 ((('#S') @ ((('#B') @ (=>) @ '#sk38')) @
% 89.45/27.02 ((($i) = ('#sk32' @ '#sk37' @ '#sk38')))))))))))),
% 89.45/27.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2255])).
% 89.45/27.02 thf(zip_derived_cl2295, plain,
% 89.45/27.02 (~ (((in @ ('#sk33' @ '#sk37' @ '#sk38') @ '#sk37') =>
% 89.45/27.02 ((('#sk38' @ ('#sk32' @ '#sk37' @ '#sk38')) =>
% 89.45/27.02 ((('#sk38' @ ('#sk33' @ '#sk37' @ '#sk38')) =>
% 89.45/27.02 ((('#sk32' @ '#sk37' @ '#sk38') = ('#sk33' @ '#sk37' @ '#sk38')))))))))),
% 89.45/27.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl2278])).
% 89.45/27.02 thf(zip_derived_cl2306, plain,
% 89.45/27.02 (~ ((('#sk38' @ ('#sk32' @ '#sk37' @ '#sk38')) =>
% 89.45/27.02 ((('#sk38' @ ('#sk33' @ '#sk37' @ '#sk38')) =>
% 89.45/27.02 ((('#sk32' @ '#sk37' @ '#sk38') = ('#sk33' @ '#sk37' @ '#sk38')))))))),
% 89.45/27.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2295])).
% 89.45/27.02 thf(zip_derived_cl2317, plain,
% 89.45/27.02 (~ ((('#sk38' @ ('#sk33' @ '#sk37' @ '#sk38')) =>
% 89.45/27.02 ((('#sk32' @ '#sk37' @ '#sk38') = ('#sk33' @ '#sk37' @ '#sk38')))))),
% 89.45/27.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2306])).
% 89.45/27.02 thf(zip_derived_cl2328, plain,
% 89.45/27.02 (~ ((('#sk32' @ '#sk37' @ '#sk38') = ('#sk33' @ '#sk37' @ '#sk38')))),
% 89.45/27.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2317])).
% 89.45/27.02 thf(zip_derived_cl2341, plain,
% 89.45/27.02 ((('#sk32' @ '#sk37' @ '#sk38') != ('#sk33' @ '#sk37' @ '#sk38'))),
% 89.45/27.02 inference('simplify nested equalities', [status(thm)],
% 89.45/27.02 [zip_derived_cl2328])).
% 89.45/27.02 thf(zip_derived_cl2277, plain,
% 89.45/27.02 ( (in @ ('#sk32' @ '#sk37' @ '#sk38') @ '#sk37')),
% 89.45/27.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2255])).
% 89.45/27.02 thf(zip_derived_cl2316, plain, ( ('#sk38' @ ('#sk32' @ '#sk37' @ '#sk38'))),
% 89.45/27.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2306])).
% 89.45/27.02 thf(zip_derived_cl2305, plain,
% 89.45/27.02 ( (in @ ('#sk33' @ '#sk37' @ '#sk38') @ '#sk37')),
% 89.45/27.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2295])).
% 89.45/27.02 thf(zip_derived_cl2231, plain,
% 89.45/27.02 ( (singleton @ (dsetconstr @ '#sk37' @ '#sk38'))),
% 89.45/27.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2230])).
% 89.45/27.02 thf(singleton, axiom, (singleton @ X0) =>
% 89.45/27.02 ((((??) @ (^[Y0 : $i]:
% 89.45/27.02 (((in @ Y0 @ X0) & (((X0) = (setadjoin @ Y0 @ emptyset))))))))
% 89.45/27.02 = ($true))).
% 89.45/27.02 thf('5', plain,
% 89.45/27.02 (![X0:$i]:
% 89.45/27.02 ( ( singleton @ X0 ) <=>
% 89.45/27.02 ( ?[X5:$i]:
% 89.45/27.02 ( ( in @ X5 @ X0 ) & ( ( X0 ) = ( setadjoin @ X5 @ emptyset ) ) ) ) )),
% 89.45/27.02 inference('rw.lit', [status(esa)], [singleton])).
% 89.45/27.02 thf(zip_derived_cl2254, plain,
% 89.45/27.02 ( (((??) @ (^[Y0 : $i]:
% 89.45/27.02 (((in @ Y0 @ (dsetconstr @ '#sk37' @ '#sk38')) &
% 89.45/27.02 (((dsetconstr @ '#sk37' @ '#sk38') = (setadjoin @ Y0 @
% 89.45/27.02 emptyset))))))))),
% 89.45/27.02 inference('rw_clause', [status(thm)], [zip_derived_cl2231, '5'])).
% 89.45/27.02 thf(zip_derived_cl2275, plain,
% 89.45/27.02 ( (((??) @ ((('#S') @ ((('#B') @ (&) @
% 89.45/27.02 ((('#C') @ in @ (dsetconstr @ '#sk37' @ '#sk38'))))) @
% 89.45/27.02 ((('#B') @ ((($i) = (dsetconstr @ '#sk37' @ '#sk38'))) @
% 89.45/27.02 ((('#C') @ setadjoin @ emptyset))))))))),
% 89.45/27.02 inference('comb-normalize', [status(thm)], [zip_derived_cl2254])).
% 89.45/27.02 thf(zip_derived_cl2276, plain,
% 89.45/27.02 ( (((in @ ('#sk34' @ '#sk37' @ '#sk38') @
% 89.45/27.02 (dsetconstr @ '#sk37' @ '#sk38')) &
% 89.45/27.02 (((dsetconstr @ '#sk37' @ '#sk38') = (setadjoin @
% 89.45/27.02 ('#sk34' @ '#sk37' @ '#sk38') @ emptyset)))))),
% 89.45/27.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl2275])).
% 89.45/27.02 thf(zip_derived_cl2294, plain,
% 89.45/27.02 ( (((dsetconstr @ '#sk37' @ '#sk38') = (setadjoin @
% 89.45/27.02 ('#sk34' @ '#sk37' @ '#sk38') @ emptyset)))),
% 89.45/27.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl2276])).
% 89.45/27.02 thf(zip_derived_cl2304, plain,
% 89.45/27.02 (((dsetconstr @ '#sk37' @ '#sk38')
% 89.45/27.02 = (setadjoin @ ('#sk34' @ '#sk37' @ '#sk38') @ emptyset))),
% 89.45/27.02 inference('simplify nested equalities', [status(thm)],
% 89.45/27.02 [zip_derived_cl2294])).
% 89.45/27.02 thf(zip_derived_cl2327, plain, ( ('#sk38' @ ('#sk33' @ '#sk37' @ '#sk38'))),
% 89.45/27.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2317])).
% 89.45/27.02 thf(zip_derived_cl457, plain, ( (uniqinunit)),
% 89.45/27.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl449])).
% 89.45/27.02 thf(uniqinunit, axiom, (uniqinunit) =>
% 89.45/27.02 ((((!!) @ (^[Y0 : $i]:
% 89.45/27.02 (((!!) @ (^[Y1 : $i]:
% 89.45/27.02 (((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) =>
% 89.45/27.02 (((Y0) = (Y1)))))))))))
% 89.45/27.02 = ($true))).
% 89.45/27.02 thf('6', plain,
% 89.45/27.02 (( uniqinunit ) <=>
% 89.45/27.02 ( ![X5:$i,X7:$i]:
% 89.45/27.02 ( ( in @ X5 @ ( setadjoin @ X7 @ emptyset ) ) => ( ( X5 ) = ( X7 ) ) ) )),
% 89.45/27.02 inference('rw.lit', [status(esa)], [uniqinunit])).
% 89.45/27.02 thf(zip_derived_cl465, plain,
% 89.45/27.02 ( (((!!) @ (^[Y0 : $i]:
% 89.45/27.02 (((!!) @ (^[Y1 : $i]:
% 89.45/27.02 (((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) =>
% 89.45/27.02 (((Y0) = (Y1)))))))))))),
% 89.45/27.02 inference('rw_clause', [status(thm)], [zip_derived_cl457, '6'])).
% 89.45/27.02 thf(zip_derived_cl471, plain,
% 89.45/27.02 ( (((!!) @ ((('#B') @ (!!) @
% 89.45/27.02 ((('#S') @ ((('#B') @ ('#S') @
% 89.45/27.02 ((('#B') @ ((('#B') @ (=>))) @
% 89.45/27.02 ((('#C') @ ((('#B') @ ('#B') @ in)) @
% 89.45/27.02 ((('#C') @ setadjoin @ emptyset)))))))) @
% 89.45/27.02 (=)))))))),
% 89.45/27.02 inference('comb-normalize', [status(thm)], [zip_derived_cl465])).
% 89.45/27.02 thf(zip_derived_cl472, plain,
% 89.45/27.02 (![X2 : $i]:
% 89.45/27.02 (((!!) @ ((('#S') @ ((('#B') @ (=>) @
% 89.45/27.02 ((('#B') @ (in @ X2) @
% 89.45/27.02 ((('#C') @ setadjoin @ emptyset)))))) @
% 89.45/27.02 ((($i) = (X2)))))))),
% 89.45/27.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl471])).
% 89.45/27.02 thf(zip_derived_cl480, plain,
% 89.45/27.02 (![X2 : $i, X4 : $i]:
% 89.45/27.02 (((in @ X2 @ (setadjoin @ X4 @ emptyset)) => (((X2) = (X4)))))),
% 89.45/27.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl472])).
% 89.45/27.02 thf(zip_derived_cl490, plain,
% 89.45/27.02 (![X2 : $i, X4 : $i]:
% 89.45/27.02 (~ (in @ X2 @ (setadjoin @ X4 @ emptyset)) | (((X2) = (X4))))),
% 89.45/27.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl480])).
% 89.45/27.02 thf(zip_derived_cl500, plain,
% 89.45/27.02 (![X2 : $i, X4 : $i]:
% 89.45/27.02 (~ (in @ X2 @ (setadjoin @ X4 @ emptyset)) | ((X2) = (X4)))),
% 89.45/27.02 inference('simplify nested equalities', [status(thm)],
% 89.45/27.02 [zip_derived_cl490])).
% 89.45/27.02 thf(zip_derived_cl263, plain, ( (setbeta)),
% 89.45/27.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl251])).
% 89.45/27.02 thf(setbeta, axiom, (setbeta) =>
% 89.45/27.02 ((((!!) @ (^[Y0 : $i]:
% 89.45/27.02 (((!!) @ (^[Y1 : $i > $o]:
% 89.45/27.02 (((!!) @ (^[Y2 : $i]:
% 89.45/27.02 (((in @ Y2 @ Y0) =>
% 89.45/27.02 (((in @ Y2 @
% 89.45/27.02 (dsetconstr @ Y0 @
% 89.45/27.02 (^[Y3 : $i]: (Y1 @ Y3)))) <=>
% 89.45/27.02 (Y1 @ Y2))))))))))))))
% 89.45/27.02 = ($true))).
% 89.45/27.02 thf('7', plain,
% 89.45/27.02 (( setbeta ) <=>
% 89.45/27.02 ( ![X5:$i,X7:( $i > $o ),X9:$i]:
% 89.45/27.02 ( ( in @ X9 @ X5 ) =>
% 89.45/27.02 ( ( in @ X9 @ ( dsetconstr @ X5 @ ( ^[V_1:$i]: ( X7 @ V_1 ) ) ) ) <=>
% 89.45/27.02 ( X7 @ X9 ) ) ) )),
% 89.45/27.02 inference('rw.lit', [status(esa)], [setbeta])).
% 89.45/27.02 thf(zip_derived_cl278, plain,
% 89.45/27.02 ( (((!!) @ (^[Y0 : $i]:
% 89.45/27.02 (((!!) @ (^[Y1 : $i > $o]:
% 89.45/27.02 (((!!) @ (^[Y2 : $i]:
% 89.45/27.02 (((in @ Y2 @ Y0) =>
% 89.45/27.02 (((in @ Y2 @
% 89.45/27.02 (dsetconstr @ Y0 @
% 89.45/27.02 (^[Y3 : $i]: (Y1 @ Y3)))) <=>
% 89.45/27.02 (Y1 @ Y2))))))))))))))),
% 89.45/27.02 inference('rw_clause', [status(thm)], [zip_derived_cl263, '7'])).
% 89.45/27.02 thf(zip_derived_cl289, plain,
% 89.45/27.02 ( (((!!) @ ((('#B') @ (!!) @
% 89.45/27.02 ((('#B') @ ((('#B') @ (!!))) @
% 89.45/27.02 ((('#S') @ ((('#B') @ ('#B') @
% 89.45/27.02 ((('#B') @ ('#S') @
% 89.45/27.02 ((('#B') @ ((('#B') @ (=>))) @
% 89.45/27.02 ((('#C') @ in)))))))) @
% 89.45/27.02 ((('#C') @ ((('#B') @ ('#S') @
% 89.45/27.02 ((('#B') @ ((('#B') @ ('#S'))) @
% 89.45/27.02 ((('#B') @ ((('#B') @ ((('#B') @ (<=>))))) @
% 89.45/27.02 ((('#B') @ ((('#B') @ ((('#C') @ in)))) @
% 89.45/27.02 dsetconstr)))))))) @
% 89.45/27.02 ('#I')))))))))))),
% 89.45/27.02 inference('comb-normalize', [status(thm)], [zip_derived_cl278])).
% 89.45/27.02 thf(zip_derived_cl290, plain,
% 89.45/27.02 (![X2 : $i]:
% 89.45/27.02 (((!!) @ ((('#B') @ (!!) @
% 89.45/27.02 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @
% 89.45/27.02 ((('#C') @ in @ X2)))))) @
% 89.45/27.02 ((('#S') @ ((('#B') @ ('#S') @
% 89.45/27.02 ((('#B') @ ((('#B') @ (<=>))) @
% 89.45/27.02 ((('#B') @ ((('#C') @ in)) @
% 89.45/27.02 (dsetconstr @ X2))))))) @
% 89.45/27.02 ('#I')))))))))),
% 89.45/27.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl289])).
% 89.45/27.02 thf(zip_derived_cl302, plain,
% 89.45/27.02 (![X2 : $i, X4 : $i > $o]:
% 89.45/27.02 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ in @ X2)))) @
% 89.45/27.02 ((('#S') @ ((('#B') @ (<=>) @
% 89.45/27.02 ((('#C') @ in @ (dsetconstr @ X2 @ X4))))) @
% 89.45/27.02 X4))))))),
% 89.45/27.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl290])).
% 89.45/27.02 thf(zip_derived_cl316, plain,
% 89.45/27.02 (![X2 : $i, X4 : $i > $o, X6 : $i]:
% 89.45/27.02 (((in @ X6 @ X2) =>
% 89.45/27.02 (((in @ X6 @ (dsetconstr @ X2 @ X4)) <=> (X4 @ X6)))))),
% 89.45/27.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl302])).
% 89.45/27.02 thf(zip_derived_cl330, plain,
% 89.45/27.02 (![X2 : $i, X4 : $i > $o, X6 : $i]:
% 89.45/27.02 (~ (in @ X6 @ X2)
% 89.45/27.02 | (((in @ X6 @ (dsetconstr @ X2 @ X4)) <=> (X4 @ X6))))),
% 89.45/27.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl316])).
% 89.45/27.02 thf(zip_derived_cl342, plain,
% 89.45/27.02 (![X2 : $i, X4 : $i > $o, X6 : $i]:
% 89.45/27.02 (~ (in @ X6 @ X2) | ((in @ X6 @ (dsetconstr @ X2 @ X4)) = (X4 @ X6)))),
% 89.45/27.02 inference('simplify nested equalities', [status(thm)],
% 89.45/27.02 [zip_derived_cl330])).
% 89.45/27.02 thf(zip_derived_cl2398, plain, ($false),
% 89.45/27.02 inference('eprover', [status(thm)],
% 89.45/27.02 [zip_derived_cl2341, zip_derived_cl2277, zip_derived_cl2316,
% 89.45/27.02 zip_derived_cl2305, zip_derived_cl2304, zip_derived_cl2327,
% 89.45/27.02 zip_derived_cl500, zip_derived_cl342])).
% 89.45/27.02
% 89.45/27.02 % SZS output end Refutation
% 89.45/27.02
% 89.45/27.02
% 89.45/27.02 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s
% 89.45/27.02 % Terminating...
% 90.16/27.23 % Runner terminated.
% 90.21/27.25 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------