%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU666^1 : 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.sxD6322V6L true
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 2 04:55:38 PM UTC 2025
% Result : Theorem 24.08s 6.29s
% Output : Refutation 24.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.22 % Problem : SEU666^1 : TPTP v9.2.0. Released v3.7.0.
% 0.06/0.22 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.sxD6322V6L true
% 0.09/0.45 % Computer : n010.cluster.edu
% 0.09/0.45 % Model : x86_64 x86_64
% 0.09/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.45 % Memory : 8042.1875MB
% 0.09/0.45 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.45 % CPULimit : 300
% 0.09/0.45 % WCLimit : 300
% 0.09/0.45 % DateTime : Wed Oct 1 16:03:08 EDT 2025
% 0.09/0.46 % CPUTime :
% 0.09/0.46 % Running portfolio for 300 s
% 0.09/0.46 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.46 % Number of cores: 8
% 0.13/0.46 % Python version: Python 3.6.8
% 0.13/0.48 % Running in HO mode
% 0.23/0.71 % Total configuration time : 828
% 0.23/0.71 % Estimated wc time : 1656
% 0.23/0.71 % Estimated cpu time (8 cpus) : 207.0
% 0.25/0.79 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.25/0.97 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.25/0.97 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.25/0.97 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.25/0.98 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.25/0.99 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.25/1.00 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.25/1.00 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 24.08/6.29 % Solved by lams/40_b.comb.sh.
% 24.08/6.29 % done 0 iterations in 5.029s
% 24.08/6.29 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 24.08/6.29 % SZS output start Refutation
% 24.08/6.29 thf(setadjoinAx_type, type, setadjoinAx: $o).
% 24.08/6.29 thf(cartprodmempaircEq_type, type, cartprodmempaircEq: $o).
% 24.08/6.29 thf(notdexE_type, type, notdexE: $o).
% 24.08/6.29 thf(setunionAx_type, type, setunionAx: $o).
% 24.08/6.29 thf(setminusELneg_type, type, setminusELneg: $o).
% 24.08/6.29 thf(kpairsurjEq_type, type, kpairsurjEq: $o).
% 24.08/6.29 thf(powersetE_type, type, powersetE: $o).
% 24.08/6.29 thf(omegaSAx_type, type, omegaSAx: $o).
% 24.08/6.29 thf(exuI1_type, type, exuI1: $o).
% 24.08/6.29 thf(exuI2_type, type, exuI2: $o).
% 24.08/6.29 thf(notequalI2_type, type, notequalI2: $o).
% 24.08/6.29 thf(kpairiskpair_type, type, kpairiskpair: $o).
% 24.08/6.29 thf(upairsubunion_type, type, upairsubunion: $o).
% 24.08/6.29 thf(powerset__Cong_type, type, powerset__Cong: $o).
% 24.08/6.29 thf(setminusILneg_type, type, setminusILneg: $o).
% 24.08/6.29 thf(wellorderingAx_type, type, wellorderingAx: $o).
% 24.08/6.29 thf(setadjoinSub2_type, type, setadjoinSub2: $o).
% 24.08/6.29 thf(binintersectSubset5_type, type, binintersectSubset5: $o).
% 24.08/6.29 thf(upairinpowunion_type, type, upairinpowunion: $o).
% 24.08/6.29 thf(setoftrueEq_type, type, setoftrueEq: $o).
% 24.08/6.29 thf(emptyset__Cong_type, type, emptyset__Cong: $o).
% 24.08/6.29 thf(cartprodpairmemER_type, type, cartprodpairmemER: $o).
% 24.08/6.29 thf(sepInPowerset_type, type, sepInPowerset: $o).
% 24.08/6.29 thf(setukpairIR_type, type, setukpairIR: $o).
% 24.08/6.29 thf(kpair_type, type, kpair: $i > $i > $i).
% 24.08/6.29 thf(binunionE_type, type, binunionE: $o).
% 24.08/6.29 thf(setext_type, type, setext: $o).
% 24.08/6.29 thf(emptyinPowerset_type, type, emptyinPowerset: $o).
% 24.08/6.29 thf(ubforcartprodlem1_type, type, ubforcartprodlem1: $o).
% 24.08/6.29 thf(setukpairinjR12_type, type, setukpairinjR12: $o).
% 24.08/6.29 thf(descr__Cong_type, type, descr__Cong: $o).
% 24.08/6.29 thf(binintersectSubset1_type, type, binintersectSubset1: $o).
% 24.08/6.29 thf(in_type, type, in: $i > $i > $o).
% 24.08/6.29 thf(cartprodfstpairEq_type, type, cartprodfstpairEq: $o).
% 24.08/6.29 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o).
% 24.08/6.29 thf(setadjoinIR_type, type, setadjoinIR: $o).
% 24.08/6.29 thf('#sk37_type', type, '#sk37': $i).
% 24.08/6.29 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o).
% 24.08/6.29 thf(symdiffI2_type, type, symdiffI2: $o).
% 24.08/6.29 thf(upairset2IR_type, type, upairset2IR: $o).
% 24.08/6.29 thf(subsetE_type, type, subsetE: $o).
% 24.08/6.29 thf(prop2set2propI_type, type, prop2set2propI: $o).
% 24.08/6.29 thf(dsetconstrEL_type, type, dsetconstrEL: $o).
% 24.08/6.29 thf(setbeta_type, type, setbeta: $o).
% 24.08/6.29 thf(eqinunit_type, type, eqinunit: $o).
% 24.08/6.29 thf(upairsetIL_type, type, upairsetIL: $o).
% 24.08/6.29 thf(powersetI1_type, type, powersetI1: $o).
% 24.08/6.29 thf(binintersectSubset3_type, type, binintersectSubset3: $o).
% 24.08/6.29 thf(setukpairinjR_type, type, setukpairinjR: $o).
% 24.08/6.29 thf(cartprodfstin_type, type, cartprodfstin: $o).
% 24.08/6.29 thf(setminusIRneg_type, type, setminusIRneg: $o).
% 24.08/6.29 thf(powersetAx_type, type, powersetAx: $o).
% 24.08/6.29 thf(singletonprop_type, type, singletonprop: $o).
% 24.08/6.29 thf(binintersectSubset4_type, type, binintersectSubset4: $o).
% 24.08/6.29 thf(singletoninpowunion_type, type, singletoninpowunion: $o).
% 24.08/6.29 thf(powersetI_type, type, powersetI: $o).
% 24.08/6.29 thf(cartprodmempair_type, type, cartprodmempair: $o).
% 24.08/6.29 thf(upairsetIR_type, type, upairsetIR: $o).
% 24.08/6.29 thf(cartprodsndpairEq_type, type, cartprodsndpairEq: $o).
% 24.08/6.29 thf(inCongP_type, type, inCongP: $o).
% 24.08/6.29 thf(setukpairinjL_type, type, setukpairinjL: $o).
% 24.08/6.29 thf(setadjoinSub_type, type, setadjoinSub: $o).
% 24.08/6.29 thf(exuE3e_type, type, exuE3e: $o).
% 24.08/6.29 thf(emptysetE_type, type, emptysetE: $o).
% 24.08/6.29 thf(upairequniteq_type, type, upairequniteq: $o).
% 24.08/6.29 thf(binintersectSubset2_type, type, binintersectSubset2: $o).
% 24.08/6.29 thf(setunionI_type, type, setunionI: $o).
% 24.08/6.29 thf(setunion__Cong_type, type, setunion__Cong: $o).
% 24.08/6.29 thf(prop2setI_type, type, prop2setI: $o).
% 24.08/6.29 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o).
% 24.08/6.29 thf(setminusER_type, type, setminusER: $o).
% 24.08/6.29 thf(exuE2_type, type, exuE2: $o).
% 24.08/6.29 thf(emptyset_type, type, emptyset: $i).
% 24.08/6.29 thf(powersetsubset_type, type, powersetsubset: $o).
% 24.08/6.29 thf(setukpairinjR1_type, type, setukpairinjR1: $o).
% 24.08/6.29 thf(subPowSU_type, type, subPowSU: $o).
% 24.08/6.29 thf(notequalI1_type, type, notequalI1: $o).
% 24.08/6.29 thf(notinemptyset_type, type, notinemptyset: $o).
% 24.08/6.29 thf(nonemptyI1_type, type, nonemptyI1: $o).
% 24.08/6.29 thf(subsetTrans_type, type, subsetTrans: $o).
% 24.08/6.29 thf(setukpairinjR2_type, type, setukpairinjR2: $o).
% 24.08/6.29 thf(kpairp_type, type, kpairp: $o).
% 24.08/6.29 thf(setminusI_type, type, setminusI: $o).
% 24.08/6.29 thf(binunionIL_type, type, binunionIL: $o).
% 24.08/6.29 thf(dpsetconstrI_type, type, dpsetconstrI: $o).
% 24.08/6.29 thf(setunionsingleton_type, type, setunionsingleton: $o).
% 24.08/6.29 thf(subsetE2_type, type, subsetE2: $o).
% 24.08/6.29 thf(singletonsswitch_type, type, singletonsswitch: $o).
% 24.08/6.29 thf(kfstpairEq_type, type, kfstpairEq: $o).
% 24.08/6.29 thf(ubforcartprodlem3_type, type, ubforcartprodlem3: $o).
% 24.08/6.29 thf(setextsub_type, type, setextsub: $o).
% 24.08/6.29 thf(binunionLsub_type, type, binunionLsub: $o).
% 24.08/6.29 thf(setunionsingleton1_type, type, setunionsingleton1: $o).
% 24.08/6.29 thf(emptysetsubset_type, type, emptysetsubset: $o).
% 24.08/6.29 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o).
% 24.08/6.29 thf(setunionE_type, type, setunionE: $o).
% 24.08/6.29 thf(setminusSubset1_type, type, setminusSubset1: $o).
% 24.08/6.29 thf(emptyinunitempty_type, type, emptyinunitempty: $o).
% 24.08/6.29 thf(binunionIR_type, type, binunionIR: $o).
% 24.08/6.29 thf(setadjoinE_type, type, setadjoinE: $o).
% 24.08/6.29 thf(cartprodpairmemEL_type, type, cartprodpairmemEL: $o).
% 24.08/6.29 thf(singletonsuniq_type, type, singletonsuniq: $o).
% 24.08/6.29 thf('#sk36_type', type, '#sk36': $i).
% 24.08/6.29 thf(setadjoinIL_type, type, setadjoinIL: $o).
% 24.08/6.29 thf(exuE1_type, type, exuE1: $o).
% 24.08/6.29 thf(ubforcartprodlem2_type, type, ubforcartprodlem2: $o).
% 24.08/6.29 thf(binintersectRsub_type, type, binintersectRsub: $o).
% 24.08/6.29 thf(setminusLsub_type, type, setminusLsub: $o).
% 24.08/6.29 thf(notinsingleton_type, type, notinsingleton: $o).
% 24.08/6.29 thf('#sk38_type', type, '#sk38': $i > $i > $o).
% 24.08/6.29 thf(eqimpsubset2_type, type, eqimpsubset2: $o).
% 24.08/6.29 thf(exuEu_type, type, exuEu: $o).
% 24.08/6.29 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o).
% 24.08/6.29 thf(ex1I2_type, type, ex1I2: $o).
% 24.08/6.29 thf(upairsetE_type, type, upairsetE: $o).
% 24.08/6.29 thf(omega0Ax_type, type, omega0Ax: $o).
% 24.08/6.29 thf(notsubsetI_type, type, notsubsetI: $o).
% 24.08/6.29 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o).
% 24.08/6.29 thf(setextAx_type, type, setextAx: $o).
% 24.08/6.29 thf(powersetE1_type, type, powersetE1: $o).
% 24.08/6.29 thf(bs114d_type, type, bs114d: $o).
% 24.08/6.29 thf(noeltsimpempty_type, type, noeltsimpempty: $o).
% 24.08/6.29 thf(binintersectLsub_type, type, binintersectLsub: $o).
% 24.08/6.29 thf(subsetI1_type, type, subsetI1: $o).
% 24.08/6.29 thf(symdiffE_type, type, symdiffE: $o).
% 24.08/6.29 thf(descrp_type, type, descrp: $o).
% 24.08/6.29 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o).
% 24.08/6.29 thf(foundationAx_type, type, foundationAx: $o).
% 24.08/6.29 thf(emptysetAx_type, type, emptysetAx: $o).
% 24.08/6.29 thf(emptyI_type, type, emptyI: $o).
% 24.08/6.29 thf(setadjoinOr_type, type, setadjoinOr: $o).
% 24.08/6.29 thf(binintersectEL_type, type, binintersectEL: $o).
% 24.08/6.29 thf(emptyE1_type, type, emptyE1: $o).
% 24.08/6.29 thf(emptyInPowerset_type, type, emptyInPowerset: $o).
% 24.08/6.29 thf(vacuousDall_type, type, vacuousDall: $o).
% 24.08/6.29 thf(dsetconstr_type, type, dsetconstr: $i > ($i > $o) > $i).
% 24.08/6.29 thf(dsetconstrER_type, type, dsetconstrER: $o).
% 24.08/6.29 thf(binintersectI_type, type, binintersectI: $o).
% 24.08/6.29 thf(cartprodpairin_type, type, cartprodpairin: $o).
% 24.08/6.29 thf(ex1I_type, type, ex1I: $o).
% 24.08/6.29 thf(cartprodmempair1_type, type, cartprodmempair1: $o).
% 24.08/6.29 thf(cartprodsndin_type, type, cartprodsndin: $o).
% 24.08/6.29 thf(setukpairinjR11_type, type, setukpairinjR11: $o).
% 24.08/6.29 thf(dpsetconstr_type, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 24.08/6.29 thf(symdiffI1_type, type, symdiffI1: $o).
% 24.08/6.29 thf(subsetI2_type, type, subsetI2: $o).
% 24.08/6.29 thf(symdiffIneg1_type, type, symdiffIneg1: $o).
% 24.08/6.29 thf(theprop_type, type, theprop: $o).
% 24.08/6.29 thf(setminusERneg_type, type, setminusERneg: $o).
% 24.08/6.29 thf(symdiffIneg2_type, type, symdiffIneg2: $o).
% 24.08/6.29 thf(omega__Cong_type, type, omega__Cong: $o).
% 24.08/6.29 thf(subsetRefl_type, type, subsetRefl: $o).
% 24.08/6.29 thf(uniqinunit_type, type, uniqinunit: $o).
% 24.08/6.29 thf(setminusSubset2_type, type, setminusSubset2: $o).
% 24.08/6.29 thf(prop2setE_type, type, prop2setE: $o).
% 24.08/6.29 thf(binunionEcases_type, type, binunionEcases: $o).
% 24.08/6.29 thf(omega_type, type, omega: $i).
% 24.08/6.29 thf(nonemptyI_type, type, nonemptyI: $o).
% 24.08/6.29 thf(disjointsetsI1_type, type, disjointsetsI1: $o).
% 24.08/6.29 thf(exuE3u_type, type, exuE3u: $o).
% 24.08/6.29 thf(setminusEL_type, type, setminusEL: $o).
% 24.08/6.29 thf(setunionsingleton2_type, type, setunionsingleton2: $o).
% 24.08/6.29 thf(sepSubset_type, type, sepSubset: $o).
% 24.08/6.29 thf(upairset2E_type, type, upairset2E: $o).
% 24.08/6.29 thf(eqimpsubset1_type, type, eqimpsubset1: $o).
% 24.08/6.29 thf(exuI3_type, type, exuI3: $o).
% 24.08/6.29 thf(notdallE_type, type, notdallE: $o).
% 24.08/6.29 thf(binintersectER_type, type, binintersectER: $o).
% 24.08/6.29 thf(ksndsingleton_type, type, ksndsingleton: $o).
% 24.08/6.29 thf(kfstsingleton_type, type, kfstsingleton: $o).
% 24.08/6.29 thf(dsetconstrI_type, type, dsetconstrI: $o).
% 24.08/6.29 thf(cartprodpairsurjEq_type, type, cartprodpairsurjEq: $o).
% 24.08/6.29 thf(setadjoin_type, type, setadjoin: $i > $i > $i).
% 24.08/6.29 thf(exu__Cong_type, type, exu__Cong: $o).
% 24.08/6.29 thf(ksndpairEq_type, type, ksndpairEq: $o).
% 24.08/6.29 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o).
% 24.08/6.29 thf(ex1E1_type, type, ex1E1: $o).
% 24.08/6.29 thf(secondinupair_type, type, secondinupair: $o).
% 24.08/6.29 thf(singletonsubset_type, type, singletonsubset: $o).
% 24.08/6.29 thf(singletoninpowerset_type, type, singletoninpowerset: $o).
% 24.08/6.29 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o).
% 24.08/6.29 thf(replAx_type, type, replAx: $o).
% 24.08/6.29 thf(nonemptyE1_type, type, nonemptyE1: $o).
% 24.08/6.29 thf(omegaIndAx_type, type, omegaIndAx: $o).
% 24.08/6.29 thf(setukpairIL_type, type, setukpairIL: $o).
% 24.08/6.29 thf(setunionE2_type, type, setunionE2: $o).
% 24.08/6.29 thf(inPowerset_type, type, inPowerset: $o).
% 24.08/6.29 thf(cartprod_type, type, cartprod: $i > $i > $i).
% 24.08/6.29 thf(subset_type, type, subset: $i > $i > $o).
% 24.08/6.29 thf(in__Cong_type, type, in__Cong: $o).
% 24.08/6.29 thf(setukpairinjL2_type, type, setukpairinjL2: $o).
% 24.08/6.29 thf(binunionRsub_type, type, binunionRsub: $o).
% 24.08/6.29 thf(subset2powerset_type, type, subset2powerset: $o).
% 24.08/6.29 thf(setukpairinjL1_type, type, setukpairinjL1: $o).
% 24.08/6.29 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)).
% 24.08/6.29 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)).
% 24.08/6.29 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)).
% 24.08/6.29 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)).
% 24.08/6.29 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)).
% 24.08/6.29 thf(dpsetconstrSub, conjecture,
% 24.08/6.29 (( setextAx ) =>
% 24.08/6.29 ( ( emptysetAx ) =>
% 24.08/6.29 ( ( setadjoinAx ) =>
% 24.08/6.29 ( ( powersetAx ) =>
% 24.08/6.29 ( ( setunionAx ) =>
% 24.08/6.29 ( ( omega0Ax ) =>
% 24.08/6.29 ( ( omegaSAx ) =>
% 24.08/6.29 ( ( omegaIndAx ) =>
% 24.08/6.29 ( ( replAx ) =>
% 24.08/6.29 ( ( foundationAx ) =>
% 24.08/6.29 ( ( wellorderingAx ) =>
% 24.08/6.29 ( ( descrp ) =>
% 24.08/6.29 ( ( dsetconstrI ) =>
% 24.08/6.29 ( ( dsetconstrEL ) =>
% 24.08/6.29 ( ( dsetconstrER ) =>
% 24.08/6.29 ( ( exuE1 ) =>
% 24.08/6.29 ( ( prop2setE ) =>
% 24.08/6.29 ( ( emptysetE ) =>
% 24.08/6.29 ( ( emptysetimpfalse ) =>
% 24.08/6.29 ( ( notinemptyset ) =>
% 24.08/6.29 ( ( exuE3e ) =>
% 24.08/6.29 ( ( setext ) =>
% 24.08/6.29 ( ( emptyI ) =>
% 24.08/6.29 ( ( noeltsimpempty ) =>
% 24.08/6.29 ( ( setbeta ) =>
% 24.08/6.29 ( ( nonemptyE1 ) =>
% 24.08/6.29 ( ( nonemptyI ) =>
% 24.08/6.29 ( ( nonemptyI1 ) =>
% 24.08/6.29 ( ( setadjoinIL ) =>
% 24.08/6.29 ( ( emptyinunitempty ) =>
% 24.08/6.29 ( ( setadjoinIR ) =>
% 24.08/6.29 ( ( setadjoinE ) =>
% 24.08/6.29 ( (
% 24.08/6.29 setadjoinOr ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 setoftrueEq ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 powersetI ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 emptyinPowerset ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 emptyInPowerset ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 powersetE ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 setunionI ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 setunionE ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 subPowSU ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 exuE2 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 nonemptyImpWitness ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 uniqinunit ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 notinsingleton ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 eqinunit ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 singletonsswitch ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 upairsetE ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 upairsetIL ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 upairsetIR ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 emptyE1 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 vacuousDall ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 quantDeMorgan1 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 quantDeMorgan2 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 quantDeMorgan3 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 quantDeMorgan4 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 prop2setI ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 prop2set2propI ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 notdexE ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 notdallE ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 exuI1 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 exuI3 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 exuI2 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 inCongP ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 in__Cong ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 exuE3u ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 exu__Cong ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 emptyset__Cong ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 setadjoin__Cong ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 powerset__Cong ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 setunion__Cong ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 omega__Cong ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 exuEu ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 descr__Cong ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 dsetconstr__Cong ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 subsetI1 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 eqimpsubset2 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 eqimpsubset1 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 subsetI2 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 emptysetsubset ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 subsetE ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 subsetE2 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 notsubsetI ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 notequalI1 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 notequalI2 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 subsetRefl ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 subsetTrans ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 setadjoinSub ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 setadjoinSub2 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 subset2powerset ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 setextsub ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 subsetemptysetimpeq ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 powersetI1 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 powersetE1 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 inPowerset ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 powersetsubset ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 sepInPowerset ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 sepSubset ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 binunionIL ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 upairset2IR ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 binunionIR ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 binunionEcases ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 binunionE ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 binunionLsub ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 binunionRsub ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 binintersectI ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 binintersectSubset5 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 binintersectEL ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 binintersectLsub ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 binintersectSubset2 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 binintersectSubset3 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 binintersectER ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 disjointsetsI1 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 binintersectRsub ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 binintersectSubset4 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 binintersectSubset1 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 bs114d ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 setminusI ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 setminusEL ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 setminusER ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 setminusSubset2 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 setminusERneg ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 setminusELneg ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 setminusILneg ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 setminusIRneg ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 setminusLsub ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 setminusSubset1 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 symdiffE ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 symdiffI1 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 symdiffI2 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 symdiffIneg1 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 symdiffIneg2 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 secondinupair ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 setukpairIL ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 setukpairIR ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 kpairiskpair ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 kpairp ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 singletonsubset ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 singletoninpowerset ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 singletoninpowunion ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 upairset2E ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 upairsubunion ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 upairinpowunion ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 ubforcartprodlem1 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 ubforcartprodlem2 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 ubforcartprodlem3 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 cartprodpairin ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 cartprodmempair1 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 cartprodmempair ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 setunionE2 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 setunionsingleton1 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 setunionsingleton2 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 setunionsingleton ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 singletonprop ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 ex1E1 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 ex1I ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 ex1I2 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 singletonsuniq ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 setukpairinjL1 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 kfstsingleton ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 theprop ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 kfstpairEq ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 cartprodfstin ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 setukpairinjL2 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 setukpairinjL ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 setukpairinjR11 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 setukpairinjR12 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 setukpairinjR1 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 upairequniteq ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 setukpairinjR2 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 setukpairinjR ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 ksndsingleton ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 ksndpairEq ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 kpairsurjEq ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 cartprodsndin ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 cartprodpairmemEL ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 cartprodpairmemER ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 cartprodmempaircEq ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 cartprodfstpairEq ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 cartprodsndpairEq ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 cartprodpairsurjEq ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 dpsetconstrI ) =>
% 24.08/6.29 (
% 24.08/6.29 ![
% 24.08/6.29 A:$i,B:$i,
% 24.08/6.29 Xphi:(
% 24.08/6.29 $i > $i >
% 24.08/6.29 $o )]:
% 24.08/6.29 (
% 24.08/6.29 subset @
% 24.08/6.29 (
% 24.08/6.29 dpsetconstr
% 24.08/6.29 @
% 24.08/6.29 A @ B @
% 24.08/6.29 (
% 24.08/6.29 ^[
% 24.08/6.29 Xx:$i,
% 24.08/6.29 Xy:$i]:
% 24.08/6.29 (
% 24.08/6.29 Xphi @
% 24.08/6.29 Xx @ Xy ) ) ) @
% 24.08/6.29 (
% 24.08/6.29 cartprod @
% 24.08/6.29 A @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 24.08/6.29 thf(zf_stmt_0, negated_conjecture,
% 24.08/6.29 (~( ( setextAx ) =>
% 24.08/6.29 ( ( emptysetAx ) =>
% 24.08/6.29 ( ( setadjoinAx ) =>
% 24.08/6.29 ( ( powersetAx ) =>
% 24.08/6.29 ( ( setunionAx ) =>
% 24.08/6.29 ( ( omega0Ax ) =>
% 24.08/6.29 ( ( omegaSAx ) =>
% 24.08/6.29 ( ( omegaIndAx ) =>
% 24.08/6.29 ( ( replAx ) =>
% 24.08/6.29 ( ( foundationAx ) =>
% 24.08/6.29 ( ( wellorderingAx ) =>
% 24.08/6.29 ( ( descrp ) =>
% 24.08/6.29 ( ( dsetconstrI ) =>
% 24.08/6.29 ( ( dsetconstrEL ) =>
% 24.08/6.29 ( ( dsetconstrER ) =>
% 24.08/6.29 ( ( exuE1 ) =>
% 24.08/6.29 ( ( prop2setE ) =>
% 24.08/6.29 ( ( emptysetE ) =>
% 24.08/6.29 ( ( emptysetimpfalse ) =>
% 24.08/6.29 ( ( notinemptyset ) =>
% 24.08/6.29 ( ( exuE3e ) =>
% 24.08/6.29 ( ( setext ) =>
% 24.08/6.29 ( ( emptyI ) =>
% 24.08/6.29 ( ( noeltsimpempty ) =>
% 24.08/6.29 ( ( setbeta ) =>
% 24.08/6.29 ( ( nonemptyE1 ) =>
% 24.08/6.29 ( ( nonemptyI ) =>
% 24.08/6.29 ( ( nonemptyI1 ) =>
% 24.08/6.29 ( ( setadjoinIL ) =>
% 24.08/6.29 ( ( emptyinunitempty ) =>
% 24.08/6.29 ( ( setadjoinIR ) =>
% 24.08/6.29 ( (
% 24.08/6.29 setadjoinE ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 setadjoinOr ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 setoftrueEq ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 powersetI ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 emptyinPowerset ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 emptyInPowerset ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 powersetE ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 setunionI ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 setunionE ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 subPowSU ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 exuE2 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 nonemptyImpWitness ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 uniqinunit ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 notinsingleton ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 eqinunit ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 singletonsswitch ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 upairsetE ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 upairsetIL ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 upairsetIR ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 emptyE1 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 vacuousDall ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 quantDeMorgan1 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 quantDeMorgan2 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 quantDeMorgan3 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 quantDeMorgan4 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 prop2setI ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 prop2set2propI ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 notdexE ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 notdallE ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 exuI1 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 exuI3 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 exuI2 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 inCongP ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 in__Cong ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 exuE3u ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 exu__Cong ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 emptyset__Cong ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 setadjoin__Cong ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 powerset__Cong ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 setunion__Cong ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 omega__Cong ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 exuEu ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 descr__Cong ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 dsetconstr__Cong ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 subsetI1 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 eqimpsubset2 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 eqimpsubset1 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 subsetI2 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 emptysetsubset ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 subsetE ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 subsetE2 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 notsubsetI ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 notequalI1 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 notequalI2 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 subsetRefl ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 subsetTrans ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 setadjoinSub ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 setadjoinSub2 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 subset2powerset ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 setextsub ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 subsetemptysetimpeq ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 powersetI1 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 powersetE1 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 inPowerset ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 powersetsubset ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 sepInPowerset ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 sepSubset ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 binunionIL ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 upairset2IR ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 binunionIR ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 binunionEcases ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 binunionE ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 binunionLsub ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 binunionRsub ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 binintersectI ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 binintersectSubset5 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 binintersectEL ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 binintersectLsub ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 binintersectSubset2 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 binintersectSubset3 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 binintersectER ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 disjointsetsI1 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 binintersectRsub ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 binintersectSubset4 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 binintersectSubset1 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 bs114d ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 setminusI ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 setminusEL ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 setminusER ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 setminusSubset2 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 setminusERneg ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 setminusELneg ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 setminusILneg ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 setminusIRneg ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 setminusLsub ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 setminusSubset1 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 symdiffE ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 symdiffI1 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 symdiffI2 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 symdiffIneg1 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 symdiffIneg2 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 secondinupair ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 setukpairIL ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 setukpairIR ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 kpairiskpair ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 kpairp ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 singletonsubset ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 singletoninpowerset ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 singletoninpowunion ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 upairset2E ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 upairsubunion ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 upairinpowunion ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 ubforcartprodlem1 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 ubforcartprodlem2 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 ubforcartprodlem3 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 cartprodpairin ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 cartprodmempair1 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 cartprodmempair ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 setunionE2 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 setunionsingleton1 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 setunionsingleton2 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 setunionsingleton ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 singletonprop ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 ex1E1 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 ex1I ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 ex1I2 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 singletonsuniq ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 setukpairinjL1 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 kfstsingleton ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 theprop ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 kfstpairEq ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 cartprodfstin ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 setukpairinjL2 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 setukpairinjL ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 setukpairinjR11 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 setukpairinjR12 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 setukpairinjR1 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 upairequniteq ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 setukpairinjR2 ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 setukpairinjR ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 ksndsingleton ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 ksndpairEq ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 kpairsurjEq ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 cartprodsndin ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 cartprodpairmemEL ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 cartprodpairmemER ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 cartprodmempaircEq ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 cartprodfstpairEq ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 cartprodsndpairEq ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 cartprodpairsurjEq ) =>
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 dpsetconstrI ) =>
% 24.08/6.29 (
% 24.08/6.29 ![
% 24.08/6.29 A:$i,
% 24.08/6.29 B:$i,
% 24.08/6.29 Xphi:(
% 24.08/6.29 $i > $i >
% 24.08/6.29 $o )]:
% 24.08/6.29 (
% 24.08/6.29 subset @
% 24.08/6.29 (
% 24.08/6.29 dpsetconstr
% 24.08/6.29 @
% 24.08/6.29 A @ B @
% 24.08/6.29 (
% 24.08/6.29 ^[
% 24.08/6.29 Xx:$i,
% 24.08/6.29 Xy:$i]:
% 24.08/6.29 (
% 24.08/6.29 Xphi @
% 24.08/6.29 Xx @ Xy ) ) ) @
% 24.08/6.29 (
% 24.08/6.29 cartprod
% 24.08/6.29 @
% 24.08/6.29 A @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 24.08/6.29 inference('cnf.neg', [status(esa)], [dpsetconstrSub])).
% 24.08/6.29 thf(zip_derived_cl0, plain,
% 24.08/6.29 (~ (((setextAx) =>
% 24.08/6.29 (((emptysetAx) =>
% 24.08/6.29 (((setadjoinAx) =>
% 24.08/6.29 (((powersetAx) =>
% 24.08/6.29 (((setunionAx) =>
% 24.08/6.29 (((omega0Ax) =>
% 24.08/6.29 (((omegaSAx) =>
% 24.08/6.29 (((omegaIndAx) =>
% 24.08/6.29 (((replAx) =>
% 24.08/6.29 (((foundationAx) =>
% 24.08/6.29 (((wellorderingAx) =>
% 24.08/6.29 (((descrp) =>
% 24.08/6.29 (((dsetconstrI) =>
% 24.08/6.29 (((dsetconstrEL) =>
% 24.08/6.29 (((dsetconstrER) =>
% 24.08/6.29 (((exuE1) =>
% 24.08/6.29 (((prop2setE) =>
% 24.08/6.29 (((emptysetE) =>
% 24.08/6.29 (((emptysetimpfalse) =>
% 24.08/6.29 (((notinemptyset) =>
% 24.08/6.29 (((exuE3e) =>
% 24.08/6.29 (((setext) =>
% 24.08/6.29 (((emptyI) =>
% 24.08/6.29 (((noeltsimpempty) =>
% 24.08/6.29 (((setbeta) =>
% 24.08/6.29 (((nonemptyE1) =>
% 24.08/6.29 (((nonemptyI) =>
% 24.08/6.29 (((nonemptyI1) =>
% 24.08/6.29 (((setadjoinIL) =>
% 24.08/6.29 (((emptyinunitempty) =>
% 24.08/6.29 ((
% 24.08/6.29 (setadjoinIR) =>
% 24.08/6.29 ((
% 24.08/6.29 (setadjoinE) =>
% 24.08/6.29 ((
% 24.08/6.29 (setadjoinOr) =>
% 24.08/6.29 ((
% 24.08/6.29 (setoftrueEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (powersetI) =>
% 24.08/6.29 ((
% 24.08/6.29 (emptyinPowerset) =>
% 24.08/6.29 ((
% 24.08/6.29 (emptyInPowerset) =>
% 24.08/6.29 ((
% 24.08/6.29 (powersetE) =>
% 24.08/6.29 ((
% 24.08/6.29 (setunionI) =>
% 24.08/6.29 ((
% 24.08/6.29 (setunionE) =>
% 24.08/6.29 ((
% 24.08/6.29 (subPowSU) =>
% 24.08/6.29 ((
% 24.08/6.29 (exuE2) =>
% 24.08/6.29 ((
% 24.08/6.29 (nonemptyImpWitness) =>
% 24.08/6.29 ((
% 24.08/6.29 (uniqinunit) =>
% 24.08/6.29 ((
% 24.08/6.29 (notinsingleton) =>
% 24.08/6.29 ((
% 24.08/6.29 (eqinunit) =>
% 24.08/6.29 ((
% 24.08/6.29 (singletonsswitch) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairsetE) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairsetIL) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairsetIR) =>
% 24.08/6.29 ((
% 24.08/6.29 (emptyE1) =>
% 24.08/6.29 ((
% 24.08/6.29 (vacuousDall) =>
% 24.08/6.29 ((
% 24.08/6.29 (quantDeMorgan1) =>
% 24.08/6.29 ((
% 24.08/6.29 (quantDeMorgan2) =>
% 24.08/6.29 ((
% 24.08/6.29 (quantDeMorgan3) =>
% 24.08/6.29 ((
% 24.08/6.29 (quantDeMorgan4) =>
% 24.08/6.29 ((
% 24.08/6.29 (prop2setI) =>
% 24.08/6.29 ((
% 24.08/6.29 (prop2set2propI) =>
% 24.08/6.29 ((
% 24.08/6.29 (notdexE) =>
% 24.08/6.29 ((
% 24.08/6.29 (notdallE) =>
% 24.08/6.29 ((
% 24.08/6.29 (exuI1) =>
% 24.08/6.29 ((
% 24.08/6.29 (exuI3) =>
% 24.08/6.29 ((
% 24.08/6.29 (exuI2) =>
% 24.08/6.29 ((
% 24.08/6.29 (inCongP) =>
% 24.08/6.29 ((
% 24.08/6.29 (in__Cong) =>
% 24.08/6.29 ((
% 24.08/6.29 (exuE3u) =>
% 24.08/6.29 ((
% 24.08/6.29 (exu__Cong) =>
% 24.08/6.29 ((
% 24.08/6.29 (emptyset__Cong) =>
% 24.08/6.29 ((
% 24.08/6.29 (setadjoin__Cong) =>
% 24.08/6.29 ((
% 24.08/6.29 (powerset__Cong) =>
% 24.08/6.29 ((
% 24.08/6.29 (setunion__Cong) =>
% 24.08/6.29 ((
% 24.08/6.29 (omega__Cong) =>
% 24.08/6.29 ((
% 24.08/6.29 (exuEu) =>
% 24.08/6.29 ((
% 24.08/6.29 (descr__Cong) =>
% 24.08/6.29 ((
% 24.08/6.29 (dsetconstr__Cong) =>
% 24.08/6.29 ((
% 24.08/6.29 (subsetI1) =>
% 24.08/6.29 ((
% 24.08/6.29 (eqimpsubset2) =>
% 24.08/6.29 ((
% 24.08/6.29 (eqimpsubset1) =>
% 24.08/6.29 ((
% 24.08/6.29 (subsetI2) =>
% 24.08/6.29 ((
% 24.08/6.29 (emptysetsubset) =>
% 24.08/6.29 ((
% 24.08/6.29 (subsetE) =>
% 24.08/6.29 ((
% 24.08/6.29 (subsetE2) =>
% 24.08/6.29 ((
% 24.08/6.29 (notsubsetI) =>
% 24.08/6.29 ((
% 24.08/6.29 (notequalI1) =>
% 24.08/6.29 ((
% 24.08/6.29 (notequalI2) =>
% 24.08/6.29 ((
% 24.08/6.29 (subsetRefl) =>
% 24.08/6.29 ((
% 24.08/6.29 (subsetTrans) =>
% 24.08/6.29 ((
% 24.08/6.29 (setadjoinSub) =>
% 24.08/6.29 ((
% 24.08/6.29 (setadjoinSub2) =>
% 24.08/6.29 ((
% 24.08/6.29 (subset2powerset) =>
% 24.08/6.29 ((
% 24.08/6.29 (setextsub) =>
% 24.08/6.29 ((
% 24.08/6.29 (subsetemptysetimpeq) =>
% 24.08/6.29 ((
% 24.08/6.29 (powersetI1) =>
% 24.08/6.29 ((
% 24.08/6.29 (powersetE1) =>
% 24.08/6.29 ((
% 24.08/6.29 (inPowerset) =>
% 24.08/6.29 ((
% 24.08/6.29 (powersetsubset) =>
% 24.08/6.29 ((
% 24.08/6.29 (sepInPowerset) =>
% 24.08/6.29 ((
% 24.08/6.29 (sepSubset) =>
% 24.08/6.29 ((
% 24.08/6.29 (binunionIL) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairset2IR) =>
% 24.08/6.29 ((
% 24.08/6.29 (binunionIR) =>
% 24.08/6.29 ((
% 24.08/6.29 (binunionEcases) =>
% 24.08/6.29 ((
% 24.08/6.29 (binunionE) =>
% 24.08/6.29 ((
% 24.08/6.29 (binunionLsub) =>
% 24.08/6.29 ((
% 24.08/6.29 (binunionRsub) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectI) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectSubset5) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectEL) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectLsub) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectSubset2) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectSubset3) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectER) =>
% 24.08/6.29 ((
% 24.08/6.29 (disjointsetsI1) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectRsub) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectSubset4) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectSubset1) =>
% 24.08/6.29 ((
% 24.08/6.29 (bs114d) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusI) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusEL) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusER) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusSubset2) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusERneg) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusELneg) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusILneg) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusIRneg) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusLsub) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusSubset1) =>
% 24.08/6.29 ((
% 24.08/6.29 (symdiffE) =>
% 24.08/6.29 ((
% 24.08/6.29 (symdiffI1) =>
% 24.08/6.29 ((
% 24.08/6.29 (symdiffI2) =>
% 24.08/6.29 ((
% 24.08/6.29 (symdiffIneg1) =>
% 24.08/6.29 ((
% 24.08/6.29 (symdiffIneg2) =>
% 24.08/6.29 ((
% 24.08/6.29 (secondinupair) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairIL) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairIR) =>
% 24.08/6.29 ((
% 24.08/6.29 (kpairiskpair) =>
% 24.08/6.29 ((
% 24.08/6.29 (kpairp) =>
% 24.08/6.29 ((
% 24.08/6.29 (singletonsubset) =>
% 24.08/6.29 ((
% 24.08/6.29 (singletoninpowerset) =>
% 24.08/6.29 ((
% 24.08/6.29 (singletoninpowunion) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairset2E) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairsubunion) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairinpowunion) =>
% 24.08/6.29 ((
% 24.08/6.29 (ubforcartprodlem1) =>
% 24.08/6.29 ((
% 24.08/6.29 (ubforcartprodlem2) =>
% 24.08/6.29 ((
% 24.08/6.29 (ubforcartprodlem3) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodpairin) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodmempair1) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodmempair) =>
% 24.08/6.29 ((
% 24.08/6.29 (setunionE2) =>
% 24.08/6.29 ((
% 24.08/6.29 (setunionsingleton1) =>
% 24.08/6.29 ((
% 24.08/6.29 (setunionsingleton2) =>
% 24.08/6.29 ((
% 24.08/6.29 (setunionsingleton) =>
% 24.08/6.29 ((
% 24.08/6.29 (singletonprop) =>
% 24.08/6.29 ((
% 24.08/6.29 (ex1E1) =>
% 24.08/6.29 ((
% 24.08/6.29 (ex1I) =>
% 24.08/6.29 ((
% 24.08/6.29 (ex1I2) =>
% 24.08/6.29 ((
% 24.08/6.29 (singletonsuniq) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjL1) =>
% 24.08/6.29 ((
% 24.08/6.29 (kfstsingleton) =>
% 24.08/6.29 ((
% 24.08/6.29 (theprop) =>
% 24.08/6.29 ((
% 24.08/6.29 (kfstpairEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodfstin) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjL2) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjL) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjR11) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjR12) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjR1) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairequniteq) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjR2) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjR) =>
% 24.08/6.29 ((
% 24.08/6.29 (ksndsingleton) =>
% 24.08/6.29 ((
% 24.08/6.29 (ksndpairEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (kpairsurjEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodsndin) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodpairmemEL) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodpairmemER) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodmempaircEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodfstpairEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodsndpairEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodpairsurjEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (dpsetconstrI) =>
% 24.08/6.29 ((
% 24.08/6.29 (!!) @ (
% 24.08/6.29 ^[Y0 : $i]:
% 24.08/6.29 ((
% 24.08/6.29 (!!) @ (
% 24.08/6.29 ^[Y1 : $i]:
% 24.08/6.29 ((
% 24.08/6.29 (!!) @ (
% 24.08/6.29 ^[Y2 :
% 24.08/6.29 $i > $i > $o]:
% 24.08/6.29 (subset @
% 24.08/6.29 (dpsetconstr @
% 24.08/6.29 Y0 @
% 24.08/6.29 Y1 @
% 24.08/6.29 (^[Y3 : $i,
% 24.08/6.29 Y4 : $i]:
% 24.08/6.29 (Y2 @
% 24.08/6.29 Y3 @ Y4))) @
% 24.08/6.29 (cartprod @
% 24.08/6.29 Y0 @ Y1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.08/6.29 inference('cnf', [status(esa)], [zf_stmt_0])).
% 24.08/6.29 thf(zip_derived_cl1, plain,
% 24.08/6.29 (~ (((setextAx) =>
% 24.08/6.29 (((emptysetAx) =>
% 24.08/6.29 (((setadjoinAx) =>
% 24.08/6.29 (((powersetAx) =>
% 24.08/6.29 (((setunionAx) =>
% 24.08/6.29 (((omega0Ax) =>
% 24.08/6.29 (((omegaSAx) =>
% 24.08/6.29 (((omegaIndAx) =>
% 24.08/6.29 (((replAx) =>
% 24.08/6.29 (((foundationAx) =>
% 24.08/6.29 (((wellorderingAx) =>
% 24.08/6.29 (((descrp) =>
% 24.08/6.29 (((dsetconstrI) =>
% 24.08/6.29 (((dsetconstrEL) =>
% 24.08/6.29 (((dsetconstrER) =>
% 24.08/6.29 (((exuE1) =>
% 24.08/6.29 (((prop2setE) =>
% 24.08/6.29 (((emptysetE) =>
% 24.08/6.29 (((emptysetimpfalse) =>
% 24.08/6.29 (((notinemptyset) =>
% 24.08/6.29 (((exuE3e) =>
% 24.08/6.29 (((setext) =>
% 24.08/6.29 (((emptyI) =>
% 24.08/6.29 (((noeltsimpempty) =>
% 24.08/6.29 (((setbeta) =>
% 24.08/6.29 (((nonemptyE1) =>
% 24.08/6.29 (((nonemptyI) =>
% 24.08/6.29 (((nonemptyI1) =>
% 24.08/6.29 (((setadjoinIL) =>
% 24.08/6.29 (((emptyinunitempty) =>
% 24.08/6.29 ((
% 24.08/6.29 (setadjoinIR) =>
% 24.08/6.29 ((
% 24.08/6.29 (setadjoinE) =>
% 24.08/6.29 ((
% 24.08/6.29 (setadjoinOr) =>
% 24.08/6.29 ((
% 24.08/6.29 (setoftrueEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (powersetI) =>
% 24.08/6.29 ((
% 24.08/6.29 (emptyinPowerset) =>
% 24.08/6.29 ((
% 24.08/6.29 (emptyInPowerset) =>
% 24.08/6.29 ((
% 24.08/6.29 (powersetE) =>
% 24.08/6.29 ((
% 24.08/6.29 (setunionI) =>
% 24.08/6.29 ((
% 24.08/6.29 (setunionE) =>
% 24.08/6.29 ((
% 24.08/6.29 (subPowSU) =>
% 24.08/6.29 ((
% 24.08/6.29 (exuE2) =>
% 24.08/6.29 ((
% 24.08/6.29 (nonemptyImpWitness) =>
% 24.08/6.29 ((
% 24.08/6.29 (uniqinunit) =>
% 24.08/6.29 ((
% 24.08/6.29 (notinsingleton) =>
% 24.08/6.29 ((
% 24.08/6.29 (eqinunit) =>
% 24.08/6.29 ((
% 24.08/6.29 (singletonsswitch) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairsetE) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairsetIL) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairsetIR) =>
% 24.08/6.29 ((
% 24.08/6.29 (emptyE1) =>
% 24.08/6.29 ((
% 24.08/6.29 (vacuousDall) =>
% 24.08/6.29 ((
% 24.08/6.29 (quantDeMorgan1) =>
% 24.08/6.29 ((
% 24.08/6.29 (quantDeMorgan2) =>
% 24.08/6.29 ((
% 24.08/6.29 (quantDeMorgan3) =>
% 24.08/6.29 ((
% 24.08/6.29 (quantDeMorgan4) =>
% 24.08/6.29 ((
% 24.08/6.29 (prop2setI) =>
% 24.08/6.29 ((
% 24.08/6.29 (prop2set2propI) =>
% 24.08/6.29 ((
% 24.08/6.29 (notdexE) =>
% 24.08/6.29 ((
% 24.08/6.29 (notdallE) =>
% 24.08/6.29 ((
% 24.08/6.29 (exuI1) =>
% 24.08/6.29 ((
% 24.08/6.29 (exuI3) =>
% 24.08/6.29 ((
% 24.08/6.29 (exuI2) =>
% 24.08/6.29 ((
% 24.08/6.29 (inCongP) =>
% 24.08/6.29 ((
% 24.08/6.29 (in__Cong) =>
% 24.08/6.29 ((
% 24.08/6.29 (exuE3u) =>
% 24.08/6.29 ((
% 24.08/6.29 (exu__Cong) =>
% 24.08/6.29 ((
% 24.08/6.29 (emptyset__Cong) =>
% 24.08/6.29 ((
% 24.08/6.29 (setadjoin__Cong) =>
% 24.08/6.29 ((
% 24.08/6.29 (powerset__Cong) =>
% 24.08/6.29 ((
% 24.08/6.29 (setunion__Cong) =>
% 24.08/6.29 ((
% 24.08/6.29 (omega__Cong) =>
% 24.08/6.29 ((
% 24.08/6.29 (exuEu) =>
% 24.08/6.29 ((
% 24.08/6.29 (descr__Cong) =>
% 24.08/6.29 ((
% 24.08/6.29 (dsetconstr__Cong) =>
% 24.08/6.29 ((
% 24.08/6.29 (subsetI1) =>
% 24.08/6.29 ((
% 24.08/6.29 (eqimpsubset2) =>
% 24.08/6.29 ((
% 24.08/6.29 (eqimpsubset1) =>
% 24.08/6.29 ((
% 24.08/6.29 (subsetI2) =>
% 24.08/6.29 ((
% 24.08/6.29 (emptysetsubset) =>
% 24.08/6.29 ((
% 24.08/6.29 (subsetE) =>
% 24.08/6.29 ((
% 24.08/6.29 (subsetE2) =>
% 24.08/6.29 ((
% 24.08/6.29 (notsubsetI) =>
% 24.08/6.29 ((
% 24.08/6.29 (notequalI1) =>
% 24.08/6.29 ((
% 24.08/6.29 (notequalI2) =>
% 24.08/6.29 ((
% 24.08/6.29 (subsetRefl) =>
% 24.08/6.29 ((
% 24.08/6.29 (subsetTrans) =>
% 24.08/6.29 ((
% 24.08/6.29 (setadjoinSub) =>
% 24.08/6.29 ((
% 24.08/6.29 (setadjoinSub2) =>
% 24.08/6.29 ((
% 24.08/6.29 (subset2powerset) =>
% 24.08/6.29 ((
% 24.08/6.29 (setextsub) =>
% 24.08/6.29 ((
% 24.08/6.29 (subsetemptysetimpeq) =>
% 24.08/6.29 ((
% 24.08/6.29 (powersetI1) =>
% 24.08/6.29 ((
% 24.08/6.29 (powersetE1) =>
% 24.08/6.29 ((
% 24.08/6.29 (inPowerset) =>
% 24.08/6.29 ((
% 24.08/6.29 (powersetsubset) =>
% 24.08/6.29 ((
% 24.08/6.29 (sepInPowerset) =>
% 24.08/6.29 ((
% 24.08/6.29 (sepSubset) =>
% 24.08/6.29 ((
% 24.08/6.29 (binunionIL) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairset2IR) =>
% 24.08/6.29 ((
% 24.08/6.29 (binunionIR) =>
% 24.08/6.29 ((
% 24.08/6.29 (binunionEcases) =>
% 24.08/6.29 ((
% 24.08/6.29 (binunionE) =>
% 24.08/6.29 ((
% 24.08/6.29 (binunionLsub) =>
% 24.08/6.29 ((
% 24.08/6.29 (binunionRsub) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectI) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectSubset5) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectEL) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectLsub) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectSubset2) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectSubset3) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectER) =>
% 24.08/6.29 ((
% 24.08/6.29 (disjointsetsI1) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectRsub) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectSubset4) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectSubset1) =>
% 24.08/6.29 ((
% 24.08/6.29 (bs114d) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusI) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusEL) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusER) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusSubset2) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusERneg) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusELneg) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusILneg) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusIRneg) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusLsub) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusSubset1) =>
% 24.08/6.29 ((
% 24.08/6.29 (symdiffE) =>
% 24.08/6.29 ((
% 24.08/6.29 (symdiffI1) =>
% 24.08/6.29 ((
% 24.08/6.29 (symdiffI2) =>
% 24.08/6.29 ((
% 24.08/6.29 (symdiffIneg1) =>
% 24.08/6.29 ((
% 24.08/6.29 (symdiffIneg2) =>
% 24.08/6.29 ((
% 24.08/6.29 (secondinupair) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairIL) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairIR) =>
% 24.08/6.29 ((
% 24.08/6.29 (kpairiskpair) =>
% 24.08/6.29 ((
% 24.08/6.29 (kpairp) =>
% 24.08/6.29 ((
% 24.08/6.29 (singletonsubset) =>
% 24.08/6.29 ((
% 24.08/6.29 (singletoninpowerset) =>
% 24.08/6.29 ((
% 24.08/6.29 (singletoninpowunion) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairset2E) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairsubunion) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairinpowunion) =>
% 24.08/6.29 ((
% 24.08/6.29 (ubforcartprodlem1) =>
% 24.08/6.29 ((
% 24.08/6.29 (ubforcartprodlem2) =>
% 24.08/6.29 ((
% 24.08/6.29 (ubforcartprodlem3) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodpairin) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodmempair1) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodmempair) =>
% 24.08/6.29 ((
% 24.08/6.29 (setunionE2) =>
% 24.08/6.29 ((
% 24.08/6.29 (setunionsingleton1) =>
% 24.08/6.29 ((
% 24.08/6.29 (setunionsingleton2) =>
% 24.08/6.29 ((
% 24.08/6.29 (setunionsingleton) =>
% 24.08/6.29 ((
% 24.08/6.29 (singletonprop) =>
% 24.08/6.29 ((
% 24.08/6.29 (ex1E1) =>
% 24.08/6.29 ((
% 24.08/6.29 (ex1I) =>
% 24.08/6.29 ((
% 24.08/6.29 (ex1I2) =>
% 24.08/6.29 ((
% 24.08/6.29 (singletonsuniq) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjL1) =>
% 24.08/6.29 ((
% 24.08/6.29 (kfstsingleton) =>
% 24.08/6.29 ((
% 24.08/6.29 (theprop) =>
% 24.08/6.29 ((
% 24.08/6.29 (kfstpairEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodfstin) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjL2) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjL) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjR11) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjR12) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjR1) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairequniteq) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjR2) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjR) =>
% 24.08/6.29 ((
% 24.08/6.29 (ksndsingleton) =>
% 24.08/6.29 ((
% 24.08/6.29 (ksndpairEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (kpairsurjEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodsndin) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodpairmemEL) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodpairmemER) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodmempaircEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodfstpairEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodsndpairEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodpairsurjEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (dpsetconstrI) =>
% 24.08/6.29 ((
% 24.08/6.29 (!!) @ (
% 24.08/6.29 (('#B') @ (
% 24.08/6.29 !!) @
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 ('#B') @ (
% 24.08/6.29 (
% 24.08/6.29 ('#B') @ (
% 24.08/6.29 !!))) @
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 ('#S') @ (
% 24.08/6.29 (
% 24.08/6.29 ('#B') @ (
% 24.08/6.29 '#S') @
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 ('#B') @ (
% 24.08/6.29 (
% 24.08/6.29 ('#B') @ (
% 24.08/6.29 '#C'))) @
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 ('#B') @ (
% 24.08/6.29 (
% 24.08/6.29 ('#B') @ (
% 24.08/6.29 (
% 24.08/6.29 ('#B') @ subset)))) @
% 24.08/6.29 dpsetconstr)))))) @
% 24.08/6.29 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.08/6.29 inference('lams2combs', [status(thm)], [zip_derived_cl0])).
% 24.08/6.29 thf(omega0Ax, axiom,(( omega0Ax ) = ((in @ emptyset @ omega)))).
% 24.08/6.29 thf('0', plain, (( omega0Ax ) = ( in @ emptyset @ omega )),
% 24.08/6.29 define([status(thm)])).
% 24.08/6.29 thf(emptyinunitempty, axiom,(( emptyinunitempty ) =
% 24.08/6.29 ((in @ emptyset @ (setadjoin @ emptyset @ emptyset))))).
% 24.08/6.29 thf('1', plain,
% 24.08/6.29 (( emptyinunitempty ) =
% 24.08/6.29 ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )),
% 24.08/6.29 define([status(thm)])).
% 24.08/6.29 thf(emptyset__Cong, axiom,(( emptyset__Cong ) =
% 24.08/6.29 ((((emptyset) = (emptyset)))))).
% 24.08/6.29 thf('2', plain, (( emptyset__Cong ) = ( ( emptyset ) = ( emptyset ) )),
% 24.08/6.29 define([status(thm)])).
% 24.08/6.29 thf(omega__Cong, axiom,(( omega__Cong ) = ((((omega) = (omega)))))).
% 24.08/6.29 thf('3', plain, (( omega__Cong ) = ( ( omega ) = ( omega ) )),
% 24.08/6.29 define([status(thm)])).
% 24.08/6.29 thf(zip_derived_cl2, plain,
% 24.08/6.29 (~ (((setextAx) =>
% 24.08/6.29 (((emptysetAx) =>
% 24.08/6.29 (((setadjoinAx) =>
% 24.08/6.29 (((powersetAx) =>
% 24.08/6.29 (((setunionAx) =>
% 24.08/6.29 (((in @ emptyset @ omega) =>
% 24.08/6.29 (((omegaSAx) =>
% 24.08/6.29 (((omegaIndAx) =>
% 24.08/6.29 (((replAx) =>
% 24.08/6.29 (((foundationAx) =>
% 24.08/6.29 (((wellorderingAx) =>
% 24.08/6.29 (((descrp) =>
% 24.08/6.29 (((dsetconstrI) =>
% 24.08/6.29 (((dsetconstrEL) =>
% 24.08/6.29 (((dsetconstrER) =>
% 24.08/6.29 (((exuE1) =>
% 24.08/6.29 (((prop2setE) =>
% 24.08/6.29 (((emptysetE) =>
% 24.08/6.29 (((emptysetimpfalse) =>
% 24.08/6.29 (((notinemptyset) =>
% 24.08/6.29 (((exuE3e) =>
% 24.08/6.29 (((setext) =>
% 24.08/6.29 (((emptyI) =>
% 24.08/6.29 (((noeltsimpempty) =>
% 24.08/6.29 (((setbeta) =>
% 24.08/6.29 (((nonemptyE1) =>
% 24.08/6.29 (((nonemptyI) =>
% 24.08/6.29 (((nonemptyI1) =>
% 24.08/6.29 (((setadjoinIL) =>
% 24.08/6.29 (((in @
% 24.08/6.29 emptyset @
% 24.08/6.29 (setadjoin @
% 24.08/6.29 emptyset @
% 24.08/6.29 emptyset)) =>
% 24.08/6.29 ((
% 24.08/6.29 (setadjoinIR) =>
% 24.08/6.29 ((
% 24.08/6.29 (setadjoinE) =>
% 24.08/6.29 ((
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% 24.08/6.29 ((
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% 24.08/6.29 ((
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% 24.08/6.29 ((
% 24.08/6.29 (setukpairIL) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairIR) =>
% 24.08/6.29 ((
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% 24.08/6.29 ((
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% 24.08/6.29 ((
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% 24.08/6.29 (upairsubunion) =>
% 24.08/6.29 ((
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% 24.08/6.29 (ubforcartprodlem1) =>
% 24.08/6.29 ((
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% 24.08/6.29 ((
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% 24.08/6.29 ((
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% 24.08/6.29 ((
% 24.08/6.29 (cartprodmempair1) =>
% 24.08/6.29 ((
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% 24.08/6.29 (setunionE2) =>
% 24.08/6.29 ((
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% 24.08/6.29 ((
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% 24.08/6.29 ((
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% 24.08/6.29 ((
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% 24.08/6.29 ((
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% 24.08/6.29 ((
% 24.08/6.29 (ex1I) =>
% 24.08/6.29 ((
% 24.08/6.29 (ex1I2) =>
% 24.08/6.29 ((
% 24.08/6.29 (singletonsuniq) =>
% 24.08/6.29 ((
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% 24.08/6.29 ((
% 24.08/6.29 (kfstsingleton) =>
% 24.08/6.29 ((
% 24.08/6.29 (theprop) =>
% 24.08/6.29 ((
% 24.08/6.29 (kfstpairEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodfstin) =>
% 24.08/6.29 ((
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% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjL) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjR11) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjR12) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjR1) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairequniteq) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjR2) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjR) =>
% 24.08/6.29 ((
% 24.08/6.29 (ksndsingleton) =>
% 24.08/6.29 ((
% 24.08/6.29 (ksndpairEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (kpairsurjEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodsndin) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodpairmemEL) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodpairmemER) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodmempaircEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodfstpairEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodsndpairEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodpairsurjEq) =>
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% 24.08/6.29 ((
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% 24.08/6.29 (
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% 24.08/6.29 inference('rw', [status(thm)], [zip_derived_cl1, '0', '1', '2', '3'])).
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% 24.08/6.29 ((
% 24.08/6.29 (symdiffIneg1) =>
% 24.08/6.29 ((
% 24.08/6.29 (symdiffIneg2) =>
% 24.08/6.29 ((
% 24.08/6.29 (secondinupair) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairIL) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairIR) =>
% 24.08/6.29 ((
% 24.08/6.29 (kpairiskpair) =>
% 24.08/6.29 ((
% 24.08/6.29 (kpairp) =>
% 24.08/6.29 ((
% 24.08/6.29 (singletonsubset) =>
% 24.08/6.29 ((
% 24.08/6.29 (singletoninpowerset) =>
% 24.08/6.29 ((
% 24.08/6.29 (singletoninpowunion) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairset2E) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairsubunion) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairinpowunion) =>
% 24.08/6.29 ((
% 24.08/6.29 (ubforcartprodlem1) =>
% 24.08/6.29 ((
% 24.08/6.29 (ubforcartprodlem2) =>
% 24.08/6.29 ((
% 24.08/6.29 (ubforcartprodlem3) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodpairin) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodmempair1) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodmempair) =>
% 24.08/6.29 ((
% 24.08/6.29 (setunionE2) =>
% 24.08/6.29 ((
% 24.08/6.29 (setunionsingleton1) =>
% 24.08/6.29 ((
% 24.08/6.29 (setunionsingleton2) =>
% 24.08/6.29 ((
% 24.08/6.29 (setunionsingleton) =>
% 24.08/6.29 ((
% 24.08/6.29 (singletonprop) =>
% 24.08/6.29 ((
% 24.08/6.29 (ex1E1) =>
% 24.08/6.29 ((
% 24.08/6.29 (ex1I) =>
% 24.08/6.29 ((
% 24.08/6.29 (ex1I2) =>
% 24.08/6.29 ((
% 24.08/6.29 (singletonsuniq) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjL1) =>
% 24.08/6.29 ((
% 24.08/6.29 (kfstsingleton) =>
% 24.08/6.29 ((
% 24.08/6.29 (theprop) =>
% 24.08/6.29 ((
% 24.08/6.29 (kfstpairEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodfstin) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjL2) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjL) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjR11) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjR12) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjR1) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairequniteq) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjR2) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjR) =>
% 24.08/6.29 ((
% 24.08/6.29 (ksndsingleton) =>
% 24.08/6.29 ((
% 24.08/6.29 (ksndpairEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (kpairsurjEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodsndin) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodpairmemEL) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodpairmemER) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodmempaircEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodfstpairEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodsndpairEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodpairsurjEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (dpsetconstrI) =>
% 24.08/6.29 ((
% 24.08/6.29 (!!) @ (
% 24.08/6.29 (('#B') @ (
% 24.08/6.29 !!) @
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 ('#B') @ (
% 24.08/6.29 (
% 24.08/6.29 ('#B') @ (
% 24.08/6.29 !!))) @
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 ('#S') @ (
% 24.08/6.29 (
% 24.08/6.29 ('#B') @ (
% 24.08/6.29 '#S') @
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 ('#B') @ (
% 24.08/6.29 (
% 24.08/6.29 ('#B') @ (
% 24.08/6.29 '#C'))) @
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 ('#B') @ (
% 24.08/6.29 (
% 24.08/6.29 ('#B') @ (
% 24.08/6.29 (
% 24.08/6.29 ('#B') @ subset)))) @
% 24.08/6.29 dpsetconstr)))))) @
% 24.08/6.29 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.08/6.29 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl2])).
% 24.08/6.29 thf(zip_derived_cl5, plain,
% 24.08/6.29 (~ (((emptysetAx) =>
% 24.08/6.29 (((setadjoinAx) =>
% 24.08/6.29 (((powersetAx) =>
% 24.08/6.29 (((setunionAx) =>
% 24.08/6.29 (((in @ emptyset @ omega) =>
% 24.08/6.29 (((omegaSAx) =>
% 24.08/6.29 (((omegaIndAx) =>
% 24.08/6.29 (((replAx) =>
% 24.08/6.29 (((foundationAx) =>
% 24.08/6.29 (((wellorderingAx) =>
% 24.08/6.29 (((descrp) =>
% 24.08/6.29 (((dsetconstrI) =>
% 24.08/6.29 (((dsetconstrEL) =>
% 24.08/6.29 (((dsetconstrER) =>
% 24.08/6.29 (((exuE1) =>
% 24.08/6.29 (((prop2setE) =>
% 24.08/6.29 (((emptysetE) =>
% 24.08/6.29 (((emptysetimpfalse) =>
% 24.08/6.29 (((notinemptyset) =>
% 24.08/6.29 (((exuE3e) =>
% 24.08/6.29 (((setext) =>
% 24.08/6.29 (((emptyI) =>
% 24.08/6.29 (((noeltsimpempty) =>
% 24.08/6.29 (((setbeta) =>
% 24.08/6.29 (((nonemptyE1) =>
% 24.08/6.29 (((nonemptyI) =>
% 24.08/6.29 (((nonemptyI1) =>
% 24.08/6.29 (((setadjoinIL) =>
% 24.08/6.29 (((in @
% 24.08/6.29 emptyset @
% 24.08/6.29 (setadjoin @
% 24.08/6.29 emptyset @
% 24.08/6.29 emptyset)) =>
% 24.08/6.29 (((setadjoinIR) =>
% 24.08/6.29 ((
% 24.08/6.29 (setadjoinE) =>
% 24.08/6.29 ((
% 24.08/6.29 (setadjoinOr) =>
% 24.08/6.29 ((
% 24.08/6.29 (setoftrueEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (powersetI) =>
% 24.08/6.29 ((
% 24.08/6.29 (emptyinPowerset) =>
% 24.08/6.29 ((
% 24.08/6.29 (emptyInPowerset) =>
% 24.08/6.29 ((
% 24.08/6.29 (powersetE) =>
% 24.08/6.29 ((
% 24.08/6.29 (setunionI) =>
% 24.08/6.29 ((
% 24.08/6.29 (setunionE) =>
% 24.08/6.29 ((
% 24.08/6.29 (subPowSU) =>
% 24.08/6.29 ((
% 24.08/6.29 (exuE2) =>
% 24.08/6.29 ((
% 24.08/6.29 (nonemptyImpWitness) =>
% 24.08/6.29 ((
% 24.08/6.29 (uniqinunit) =>
% 24.08/6.29 ((
% 24.08/6.29 (notinsingleton) =>
% 24.08/6.29 ((
% 24.08/6.29 (eqinunit) =>
% 24.08/6.29 ((
% 24.08/6.29 (singletonsswitch) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairsetE) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairsetIL) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairsetIR) =>
% 24.08/6.29 ((
% 24.08/6.29 (emptyE1) =>
% 24.08/6.29 ((
% 24.08/6.29 (vacuousDall) =>
% 24.08/6.29 ((
% 24.08/6.29 (quantDeMorgan1) =>
% 24.08/6.29 ((
% 24.08/6.29 (quantDeMorgan2) =>
% 24.08/6.29 ((
% 24.08/6.29 (quantDeMorgan3) =>
% 24.08/6.29 ((
% 24.08/6.29 (quantDeMorgan4) =>
% 24.08/6.29 ((
% 24.08/6.29 (prop2setI) =>
% 24.08/6.29 ((
% 24.08/6.29 (prop2set2propI) =>
% 24.08/6.29 ((
% 24.08/6.29 (notdexE) =>
% 24.08/6.29 ((
% 24.08/6.29 (notdallE) =>
% 24.08/6.29 ((
% 24.08/6.29 (exuI1) =>
% 24.08/6.29 ((
% 24.08/6.29 (exuI3) =>
% 24.08/6.29 ((
% 24.08/6.29 (exuI2) =>
% 24.08/6.29 ((
% 24.08/6.29 (inCongP) =>
% 24.08/6.29 ((
% 24.08/6.29 (in__Cong) =>
% 24.08/6.29 ((
% 24.08/6.29 (exuE3u) =>
% 24.08/6.29 ((
% 24.08/6.29 (exu__Cong) =>
% 24.08/6.29 ((
% 24.08/6.29 (setadjoin__Cong) =>
% 24.08/6.29 ((
% 24.08/6.29 (powerset__Cong) =>
% 24.08/6.29 ((
% 24.08/6.29 (setunion__Cong) =>
% 24.08/6.29 ((
% 24.08/6.29 (exuEu) =>
% 24.08/6.29 ((
% 24.08/6.29 (descr__Cong) =>
% 24.08/6.29 ((
% 24.08/6.29 (dsetconstr__Cong) =>
% 24.08/6.29 ((
% 24.08/6.29 (subsetI1) =>
% 24.08/6.29 ((
% 24.08/6.29 (eqimpsubset2) =>
% 24.08/6.29 ((
% 24.08/6.29 (eqimpsubset1) =>
% 24.08/6.29 ((
% 24.08/6.29 (subsetI2) =>
% 24.08/6.29 ((
% 24.08/6.29 (emptysetsubset) =>
% 24.08/6.29 ((
% 24.08/6.29 (subsetE) =>
% 24.08/6.29 ((
% 24.08/6.29 (subsetE2) =>
% 24.08/6.29 ((
% 24.08/6.29 (notsubsetI) =>
% 24.08/6.29 ((
% 24.08/6.29 (notequalI1) =>
% 24.08/6.29 ((
% 24.08/6.29 (notequalI2) =>
% 24.08/6.29 ((
% 24.08/6.29 (subsetRefl) =>
% 24.08/6.29 ((
% 24.08/6.29 (subsetTrans) =>
% 24.08/6.29 ((
% 24.08/6.29 (setadjoinSub) =>
% 24.08/6.29 ((
% 24.08/6.29 (setadjoinSub2) =>
% 24.08/6.29 ((
% 24.08/6.29 (subset2powerset) =>
% 24.08/6.29 ((
% 24.08/6.29 (setextsub) =>
% 24.08/6.29 ((
% 24.08/6.29 (subsetemptysetimpeq) =>
% 24.08/6.29 ((
% 24.08/6.29 (powersetI1) =>
% 24.08/6.29 ((
% 24.08/6.29 (powersetE1) =>
% 24.08/6.29 ((
% 24.08/6.29 (inPowerset) =>
% 24.08/6.29 ((
% 24.08/6.29 (powersetsubset) =>
% 24.08/6.29 ((
% 24.08/6.29 (sepInPowerset) =>
% 24.08/6.29 ((
% 24.08/6.29 (sepSubset) =>
% 24.08/6.29 ((
% 24.08/6.29 (binunionIL) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairset2IR) =>
% 24.08/6.29 ((
% 24.08/6.29 (binunionIR) =>
% 24.08/6.29 ((
% 24.08/6.29 (binunionEcases) =>
% 24.08/6.29 ((
% 24.08/6.29 (binunionE) =>
% 24.08/6.29 ((
% 24.08/6.29 (binunionLsub) =>
% 24.08/6.29 ((
% 24.08/6.29 (binunionRsub) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectI) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectSubset5) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectEL) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectLsub) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectSubset2) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectSubset3) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectER) =>
% 24.08/6.29 ((
% 24.08/6.29 (disjointsetsI1) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectRsub) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectSubset4) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectSubset1) =>
% 24.08/6.29 ((
% 24.08/6.29 (bs114d) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusI) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusEL) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusER) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusSubset2) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusERneg) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusELneg) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusILneg) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusIRneg) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusLsub) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusSubset1) =>
% 24.08/6.29 ((
% 24.08/6.29 (symdiffE) =>
% 24.08/6.29 ((
% 24.08/6.29 (symdiffI1) =>
% 24.08/6.29 ((
% 24.08/6.29 (symdiffI2) =>
% 24.08/6.29 ((
% 24.08/6.29 (symdiffIneg1) =>
% 24.08/6.29 ((
% 24.08/6.29 (symdiffIneg2) =>
% 24.08/6.29 ((
% 24.08/6.29 (secondinupair) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairIL) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairIR) =>
% 24.08/6.29 ((
% 24.08/6.29 (kpairiskpair) =>
% 24.08/6.29 ((
% 24.08/6.29 (kpairp) =>
% 24.08/6.29 ((
% 24.08/6.29 (singletonsubset) =>
% 24.08/6.29 ((
% 24.08/6.29 (singletoninpowerset) =>
% 24.08/6.29 ((
% 24.08/6.29 (singletoninpowunion) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairset2E) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairsubunion) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairinpowunion) =>
% 24.08/6.29 ((
% 24.08/6.29 (ubforcartprodlem1) =>
% 24.08/6.29 ((
% 24.08/6.29 (ubforcartprodlem2) =>
% 24.08/6.29 ((
% 24.08/6.29 (ubforcartprodlem3) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodpairin) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodmempair1) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodmempair) =>
% 24.08/6.29 ((
% 24.08/6.29 (setunionE2) =>
% 24.08/6.29 ((
% 24.08/6.29 (setunionsingleton1) =>
% 24.08/6.29 ((
% 24.08/6.29 (setunionsingleton2) =>
% 24.08/6.29 ((
% 24.08/6.29 (setunionsingleton) =>
% 24.08/6.29 ((
% 24.08/6.29 (singletonprop) =>
% 24.08/6.29 ((
% 24.08/6.29 (ex1E1) =>
% 24.08/6.29 ((
% 24.08/6.29 (ex1I) =>
% 24.08/6.29 ((
% 24.08/6.29 (ex1I2) =>
% 24.08/6.29 ((
% 24.08/6.29 (singletonsuniq) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjL1) =>
% 24.08/6.29 ((
% 24.08/6.29 (kfstsingleton) =>
% 24.08/6.29 ((
% 24.08/6.29 (theprop) =>
% 24.08/6.29 ((
% 24.08/6.29 (kfstpairEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodfstin) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjL2) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjL) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjR11) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjR12) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjR1) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairequniteq) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjR2) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjR) =>
% 24.08/6.29 ((
% 24.08/6.29 (ksndsingleton) =>
% 24.08/6.29 ((
% 24.08/6.29 (ksndpairEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (kpairsurjEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodsndin) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodpairmemEL) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodpairmemER) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodmempaircEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodfstpairEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodsndpairEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodpairsurjEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (dpsetconstrI) =>
% 24.08/6.29 ((
% 24.08/6.29 (!!) @ (
% 24.08/6.29 (('#B') @ (
% 24.08/6.29 !!) @
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 ('#B') @ (
% 24.08/6.29 (
% 24.08/6.29 ('#B') @ (
% 24.08/6.29 !!))) @
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 ('#S') @ (
% 24.08/6.29 (
% 24.08/6.29 ('#B') @ (
% 24.08/6.29 '#S') @
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 ('#B') @ (
% 24.08/6.29 (
% 24.08/6.29 ('#B') @ (
% 24.08/6.29 '#C'))) @
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 ('#B') @ (
% 24.08/6.29 (
% 24.08/6.29 ('#B') @ (
% 24.08/6.29 (
% 24.08/6.29 ('#B') @ subset)))) @
% 24.08/6.29 dpsetconstr)))))) @
% 24.08/6.29 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.08/6.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3])).
% 24.08/6.29 thf(zip_derived_cl8, plain,
% 24.08/6.29 (~ (((setadjoinAx) =>
% 24.08/6.29 (((powersetAx) =>
% 24.08/6.29 (((setunionAx) =>
% 24.08/6.29 (((in @ emptyset @ omega) =>
% 24.08/6.29 (((omegaSAx) =>
% 24.08/6.29 (((omegaIndAx) =>
% 24.08/6.29 (((replAx) =>
% 24.08/6.29 (((foundationAx) =>
% 24.08/6.29 (((wellorderingAx) =>
% 24.08/6.29 (((descrp) =>
% 24.08/6.29 (((dsetconstrI) =>
% 24.08/6.29 (((dsetconstrEL) =>
% 24.08/6.29 (((dsetconstrER) =>
% 24.08/6.29 (((exuE1) =>
% 24.08/6.29 (((prop2setE) =>
% 24.08/6.29 (((emptysetE) =>
% 24.08/6.29 (((emptysetimpfalse) =>
% 24.08/6.29 (((notinemptyset) =>
% 24.08/6.29 (((exuE3e) =>
% 24.08/6.29 (((setext) =>
% 24.08/6.29 (((emptyI) =>
% 24.08/6.29 (((noeltsimpempty) =>
% 24.08/6.29 (((setbeta) =>
% 24.08/6.29 (((nonemptyE1) =>
% 24.08/6.29 (((nonemptyI) =>
% 24.08/6.29 (((nonemptyI1) =>
% 24.08/6.29 (((setadjoinIL) =>
% 24.08/6.29 (((in @
% 24.08/6.29 emptyset @
% 24.08/6.29 (setadjoin @
% 24.08/6.29 emptyset @
% 24.08/6.29 emptyset)) =>
% 24.08/6.29 (((setadjoinIR) =>
% 24.08/6.29 (((setadjoinE) =>
% 24.08/6.29 ((
% 24.08/6.29 (setadjoinOr) =>
% 24.08/6.29 ((
% 24.08/6.29 (setoftrueEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (powersetI) =>
% 24.08/6.29 ((
% 24.08/6.29 (emptyinPowerset) =>
% 24.08/6.29 ((
% 24.08/6.29 (emptyInPowerset) =>
% 24.08/6.29 ((
% 24.08/6.29 (powersetE) =>
% 24.08/6.29 ((
% 24.08/6.29 (setunionI) =>
% 24.08/6.29 ((
% 24.08/6.29 (setunionE) =>
% 24.08/6.29 ((
% 24.08/6.29 (subPowSU) =>
% 24.08/6.29 ((
% 24.08/6.29 (exuE2) =>
% 24.08/6.29 ((
% 24.08/6.29 (nonemptyImpWitness) =>
% 24.08/6.29 ((
% 24.08/6.29 (uniqinunit) =>
% 24.08/6.29 ((
% 24.08/6.29 (notinsingleton) =>
% 24.08/6.29 ((
% 24.08/6.29 (eqinunit) =>
% 24.08/6.29 ((
% 24.08/6.29 (singletonsswitch) =>
% 24.08/6.29 ((
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% 24.08/6.29 ((
% 24.08/6.29 (upairsetIL) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairsetIR) =>
% 24.08/6.29 ((
% 24.08/6.29 (emptyE1) =>
% 24.08/6.29 ((
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% 24.08/6.29 ((
% 24.08/6.29 (quantDeMorgan1) =>
% 24.08/6.29 ((
% 24.08/6.29 (quantDeMorgan2) =>
% 24.08/6.29 ((
% 24.08/6.29 (quantDeMorgan3) =>
% 24.08/6.29 ((
% 24.08/6.29 (quantDeMorgan4) =>
% 24.08/6.29 ((
% 24.08/6.29 (prop2setI) =>
% 24.08/6.29 ((
% 24.08/6.29 (prop2set2propI) =>
% 24.08/6.29 ((
% 24.08/6.29 (notdexE) =>
% 24.08/6.29 ((
% 24.08/6.29 (notdallE) =>
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% 24.08/6.29 ((
% 24.08/6.29 (exuI3) =>
% 24.08/6.29 ((
% 24.08/6.29 (exuI2) =>
% 24.08/6.29 ((
% 24.08/6.29 (inCongP) =>
% 24.08/6.29 ((
% 24.08/6.29 (in__Cong) =>
% 24.08/6.29 ((
% 24.08/6.29 (exuE3u) =>
% 24.08/6.29 ((
% 24.08/6.29 (exu__Cong) =>
% 24.08/6.29 ((
% 24.08/6.29 (setadjoin__Cong) =>
% 24.08/6.29 ((
% 24.08/6.29 (powerset__Cong) =>
% 24.08/6.29 ((
% 24.08/6.29 (setunion__Cong) =>
% 24.08/6.29 ((
% 24.08/6.29 (exuEu) =>
% 24.08/6.29 ((
% 24.08/6.29 (descr__Cong) =>
% 24.08/6.29 ((
% 24.08/6.29 (dsetconstr__Cong) =>
% 24.08/6.29 ((
% 24.08/6.29 (subsetI1) =>
% 24.08/6.29 ((
% 24.08/6.29 (eqimpsubset2) =>
% 24.08/6.29 ((
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% 24.08/6.29 ((
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% 24.08/6.29 ((
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% 24.08/6.29 ((
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% 24.08/6.29 ((
% 24.08/6.29 (notequalI1) =>
% 24.08/6.29 ((
% 24.08/6.29 (notequalI2) =>
% 24.08/6.29 ((
% 24.08/6.29 (subsetRefl) =>
% 24.08/6.29 ((
% 24.08/6.29 (subsetTrans) =>
% 24.08/6.29 ((
% 24.08/6.29 (setadjoinSub) =>
% 24.08/6.29 ((
% 24.08/6.29 (setadjoinSub2) =>
% 24.08/6.29 ((
% 24.08/6.29 (subset2powerset) =>
% 24.08/6.29 ((
% 24.08/6.29 (setextsub) =>
% 24.08/6.29 ((
% 24.08/6.29 (subsetemptysetimpeq) =>
% 24.08/6.29 ((
% 24.08/6.29 (powersetI1) =>
% 24.08/6.29 ((
% 24.08/6.29 (powersetE1) =>
% 24.08/6.29 ((
% 24.08/6.29 (inPowerset) =>
% 24.08/6.29 ((
% 24.08/6.29 (powersetsubset) =>
% 24.08/6.29 ((
% 24.08/6.29 (sepInPowerset) =>
% 24.08/6.29 ((
% 24.08/6.29 (sepSubset) =>
% 24.08/6.29 ((
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% 24.08/6.29 ((
% 24.08/6.29 (upairset2IR) =>
% 24.08/6.29 ((
% 24.08/6.29 (binunionIR) =>
% 24.08/6.29 ((
% 24.08/6.29 (binunionEcases) =>
% 24.08/6.29 ((
% 24.08/6.29 (binunionE) =>
% 24.08/6.29 ((
% 24.08/6.29 (binunionLsub) =>
% 24.08/6.29 ((
% 24.08/6.29 (binunionRsub) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectI) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectSubset5) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectEL) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectLsub) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectSubset2) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectSubset3) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectER) =>
% 24.08/6.29 ((
% 24.08/6.29 (disjointsetsI1) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectRsub) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectSubset4) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectSubset1) =>
% 24.08/6.29 ((
% 24.08/6.29 (bs114d) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusI) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusEL) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusER) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusSubset2) =>
% 24.08/6.29 ((
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% 24.08/6.29 ((
% 24.08/6.29 (setminusELneg) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusILneg) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusIRneg) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusLsub) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusSubset1) =>
% 24.08/6.29 ((
% 24.08/6.29 (symdiffE) =>
% 24.08/6.29 ((
% 24.08/6.29 (symdiffI1) =>
% 24.08/6.29 ((
% 24.08/6.29 (symdiffI2) =>
% 24.08/6.29 ((
% 24.08/6.29 (symdiffIneg1) =>
% 24.08/6.29 ((
% 24.08/6.29 (symdiffIneg2) =>
% 24.08/6.29 ((
% 24.08/6.29 (secondinupair) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairIL) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairIR) =>
% 24.08/6.29 ((
% 24.08/6.29 (kpairiskpair) =>
% 24.08/6.29 ((
% 24.08/6.29 (kpairp) =>
% 24.08/6.29 ((
% 24.08/6.29 (singletonsubset) =>
% 24.08/6.29 ((
% 24.08/6.29 (singletoninpowerset) =>
% 24.08/6.29 ((
% 24.08/6.29 (singletoninpowunion) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairset2E) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairsubunion) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairinpowunion) =>
% 24.08/6.29 ((
% 24.08/6.29 (ubforcartprodlem1) =>
% 24.08/6.29 ((
% 24.08/6.29 (ubforcartprodlem2) =>
% 24.08/6.29 ((
% 24.08/6.29 (ubforcartprodlem3) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodpairin) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodmempair1) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodmempair) =>
% 24.08/6.29 ((
% 24.08/6.29 (setunionE2) =>
% 24.08/6.29 ((
% 24.08/6.29 (setunionsingleton1) =>
% 24.08/6.29 ((
% 24.08/6.29 (setunionsingleton2) =>
% 24.08/6.29 ((
% 24.08/6.29 (setunionsingleton) =>
% 24.08/6.29 ((
% 24.08/6.29 (singletonprop) =>
% 24.08/6.29 ((
% 24.08/6.29 (ex1E1) =>
% 24.08/6.29 ((
% 24.08/6.29 (ex1I) =>
% 24.08/6.29 ((
% 24.08/6.29 (ex1I2) =>
% 24.08/6.29 ((
% 24.08/6.29 (singletonsuniq) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjL1) =>
% 24.08/6.29 ((
% 24.08/6.29 (kfstsingleton) =>
% 24.08/6.29 ((
% 24.08/6.29 (theprop) =>
% 24.08/6.29 ((
% 24.08/6.29 (kfstpairEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodfstin) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjL2) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjL) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjR11) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjR12) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjR1) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairequniteq) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjR2) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjR) =>
% 24.08/6.29 ((
% 24.08/6.29 (ksndsingleton) =>
% 24.08/6.29 ((
% 24.08/6.29 (ksndpairEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (kpairsurjEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodsndin) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodpairmemEL) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodpairmemER) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodmempaircEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodfstpairEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodsndpairEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodpairsurjEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (dpsetconstrI) =>
% 24.08/6.29 ((
% 24.08/6.29 (!!) @ (
% 24.08/6.29 (('#B') @ (
% 24.08/6.29 !!) @
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 ('#B') @ (
% 24.08/6.29 (
% 24.08/6.29 ('#B') @ (
% 24.08/6.29 !!))) @
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 ('#S') @ (
% 24.08/6.29 (
% 24.08/6.29 ('#B') @ (
% 24.08/6.29 '#S') @
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 ('#B') @ (
% 24.08/6.29 (
% 24.08/6.29 ('#B') @ (
% 24.08/6.29 '#C'))) @
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 ('#B') @ (
% 24.08/6.29 (
% 24.08/6.29 ('#B') @ (
% 24.08/6.29 (
% 24.08/6.29 ('#B') @ subset)))) @
% 24.08/6.29 dpsetconstr)))))) @
% 24.08/6.29 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.08/6.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5])).
% 24.08/6.29 thf(zip_derived_cl13, plain,
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% 24.08/6.29 (((setunionAx) =>
% 24.08/6.29 (((in @ emptyset @ omega) =>
% 24.08/6.29 (((omegaSAx) =>
% 24.08/6.29 (((omegaIndAx) =>
% 24.08/6.29 (((replAx) =>
% 24.08/6.29 (((foundationAx) =>
% 24.08/6.29 (((wellorderingAx) =>
% 24.08/6.29 (((descrp) =>
% 24.08/6.29 (((dsetconstrI) =>
% 24.08/6.29 (((dsetconstrEL) =>
% 24.08/6.29 (((dsetconstrER) =>
% 24.08/6.29 (((exuE1) =>
% 24.08/6.29 (((prop2setE) =>
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% 24.08/6.29 (((emptysetimpfalse) =>
% 24.08/6.29 (((notinemptyset) =>
% 24.08/6.29 (((exuE3e) =>
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% 24.08/6.29 (((noeltsimpempty) =>
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% 24.08/6.29 (((nonemptyI) =>
% 24.08/6.29 (((nonemptyI1) =>
% 24.08/6.29 (((setadjoinIL) =>
% 24.08/6.29 (((in @
% 24.08/6.29 emptyset @
% 24.08/6.29 (setadjoin @
% 24.08/6.29 emptyset @
% 24.08/6.29 emptyset)) =>
% 24.08/6.29 (((setadjoinIR) =>
% 24.08/6.29 (((setadjoinE) =>
% 24.08/6.29 (((setadjoinOr) =>
% 24.08/6.29 ((
% 24.08/6.29 (setoftrueEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (powersetI) =>
% 24.08/6.29 ((
% 24.08/6.29 (emptyinPowerset) =>
% 24.08/6.29 ((
% 24.08/6.29 (emptyInPowerset) =>
% 24.08/6.29 ((
% 24.08/6.29 (powersetE) =>
% 24.08/6.29 ((
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% 24.08/6.29 ((
% 24.08/6.29 (setunionE) =>
% 24.08/6.29 ((
% 24.08/6.29 (subPowSU) =>
% 24.08/6.29 ((
% 24.08/6.29 (exuE2) =>
% 24.08/6.29 ((
% 24.08/6.29 (nonemptyImpWitness) =>
% 24.08/6.29 ((
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% 24.08/6.29 ((
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% 24.08/6.29 ((
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% 24.08/6.29 ((
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% 24.08/6.29 ((
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% 24.08/6.29 ((
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% 24.08/6.29 ((
% 24.08/6.29 (upairsetIR) =>
% 24.08/6.29 ((
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% 24.08/6.29 (quantDeMorgan4) =>
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% 24.08/6.29 ((
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% 24.08/6.29 ((
% 24.08/6.29 (exuI3) =>
% 24.08/6.29 ((
% 24.08/6.29 (exuI2) =>
% 24.08/6.29 ((
% 24.08/6.29 (inCongP) =>
% 24.08/6.29 ((
% 24.08/6.29 (in__Cong) =>
% 24.08/6.29 ((
% 24.08/6.29 (exuE3u) =>
% 24.08/6.29 ((
% 24.08/6.29 (exu__Cong) =>
% 24.08/6.29 ((
% 24.08/6.29 (setadjoin__Cong) =>
% 24.08/6.29 ((
% 24.08/6.29 (powerset__Cong) =>
% 24.08/6.29 ((
% 24.08/6.29 (setunion__Cong) =>
% 24.08/6.29 ((
% 24.08/6.29 (exuEu) =>
% 24.08/6.29 ((
% 24.08/6.29 (descr__Cong) =>
% 24.08/6.29 ((
% 24.08/6.29 (dsetconstr__Cong) =>
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% 24.08/6.29 ((
% 24.08/6.29 (eqimpsubset2) =>
% 24.08/6.29 ((
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% 24.08/6.29 ((
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% 24.08/6.29 ((
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% 24.08/6.29 (subsetE2) =>
% 24.08/6.29 ((
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% 24.08/6.29 ((
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% 24.08/6.29 ((
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% 24.08/6.29 ((
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% 24.08/6.29 ((
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% 24.08/6.29 ((
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% 24.08/6.29 ((
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% 24.08/6.29 ((
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% 24.08/6.29 ((
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% 24.08/6.29 ((
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% 24.08/6.29 ((
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% 24.08/6.29 ((
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% 24.08/6.29 ((
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% 24.08/6.29 ((
% 24.08/6.29 (binunionLsub) =>
% 24.08/6.29 ((
% 24.08/6.29 (binunionRsub) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectI) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectSubset5) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectEL) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectLsub) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectSubset2) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectSubset3) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectER) =>
% 24.08/6.29 ((
% 24.08/6.29 (disjointsetsI1) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectRsub) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectSubset4) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectSubset1) =>
% 24.08/6.29 ((
% 24.08/6.29 (bs114d) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusI) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusEL) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusER) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusSubset2) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusERneg) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusELneg) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusILneg) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusIRneg) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusLsub) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusSubset1) =>
% 24.08/6.29 ((
% 24.08/6.29 (symdiffE) =>
% 24.08/6.29 ((
% 24.08/6.29 (symdiffI1) =>
% 24.08/6.29 ((
% 24.08/6.29 (symdiffI2) =>
% 24.08/6.29 ((
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% 24.08/6.29 ((
% 24.08/6.29 (symdiffIneg2) =>
% 24.08/6.29 ((
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% 24.08/6.29 ((
% 24.08/6.29 (setukpairIL) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairIR) =>
% 24.08/6.29 ((
% 24.08/6.29 (kpairiskpair) =>
% 24.08/6.29 ((
% 24.08/6.29 (kpairp) =>
% 24.08/6.29 ((
% 24.08/6.29 (singletonsubset) =>
% 24.08/6.29 ((
% 24.08/6.29 (singletoninpowerset) =>
% 24.08/6.29 ((
% 24.08/6.29 (singletoninpowunion) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairset2E) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairsubunion) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairinpowunion) =>
% 24.08/6.29 ((
% 24.08/6.29 (ubforcartprodlem1) =>
% 24.08/6.29 ((
% 24.08/6.29 (ubforcartprodlem2) =>
% 24.08/6.29 ((
% 24.08/6.29 (ubforcartprodlem3) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodpairin) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodmempair1) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodmempair) =>
% 24.08/6.29 ((
% 24.08/6.29 (setunionE2) =>
% 24.08/6.29 ((
% 24.08/6.29 (setunionsingleton1) =>
% 24.08/6.29 ((
% 24.08/6.29 (setunionsingleton2) =>
% 24.08/6.29 ((
% 24.08/6.29 (setunionsingleton) =>
% 24.08/6.29 ((
% 24.08/6.29 (singletonprop) =>
% 24.08/6.29 ((
% 24.08/6.29 (ex1E1) =>
% 24.08/6.29 ((
% 24.08/6.29 (ex1I) =>
% 24.08/6.29 ((
% 24.08/6.29 (ex1I2) =>
% 24.08/6.29 ((
% 24.08/6.29 (singletonsuniq) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjL1) =>
% 24.08/6.29 ((
% 24.08/6.29 (kfstsingleton) =>
% 24.08/6.29 ((
% 24.08/6.29 (theprop) =>
% 24.08/6.29 ((
% 24.08/6.29 (kfstpairEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodfstin) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjL2) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjL) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjR11) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjR12) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjR1) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairequniteq) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjR2) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjR) =>
% 24.08/6.29 ((
% 24.08/6.29 (ksndsingleton) =>
% 24.08/6.29 ((
% 24.08/6.29 (ksndpairEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (kpairsurjEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodsndin) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodpairmemEL) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodpairmemER) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodmempaircEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodfstpairEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodsndpairEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodpairsurjEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (dpsetconstrI) =>
% 24.08/6.29 ((
% 24.08/6.29 (!!) @ (
% 24.08/6.29 (('#B') @ (
% 24.08/6.29 !!) @
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 ('#B') @ (
% 24.08/6.29 (
% 24.08/6.29 ('#B') @ (
% 24.08/6.29 !!))) @
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 ('#S') @ (
% 24.08/6.29 (
% 24.08/6.29 ('#B') @ (
% 24.08/6.29 '#S') @
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 ('#B') @ (
% 24.08/6.29 (
% 24.08/6.29 ('#B') @ (
% 24.08/6.29 '#C'))) @
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 ('#B') @ (
% 24.08/6.29 (
% 24.08/6.29 ('#B') @ (
% 24.08/6.29 (
% 24.08/6.29 ('#B') @ subset)))) @
% 24.08/6.29 dpsetconstr)))))) @
% 24.08/6.29 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.08/6.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl8])).
% 24.08/6.29 thf(zip_derived_cl19, plain,
% 24.08/6.29 (~ (((setunionAx) =>
% 24.08/6.29 (((in @ emptyset @ omega) =>
% 24.08/6.29 (((omegaSAx) =>
% 24.08/6.29 (((omegaIndAx) =>
% 24.08/6.29 (((replAx) =>
% 24.08/6.29 (((foundationAx) =>
% 24.08/6.29 (((wellorderingAx) =>
% 24.08/6.29 (((descrp) =>
% 24.08/6.29 (((dsetconstrI) =>
% 24.08/6.29 (((dsetconstrEL) =>
% 24.08/6.29 (((dsetconstrER) =>
% 24.08/6.29 (((exuE1) =>
% 24.08/6.29 (((prop2setE) =>
% 24.08/6.29 (((emptysetE) =>
% 24.08/6.29 (((emptysetimpfalse) =>
% 24.08/6.29 (((notinemptyset) =>
% 24.08/6.29 (((exuE3e) =>
% 24.08/6.29 (((setext) =>
% 24.08/6.29 (((emptyI) =>
% 24.08/6.29 (((noeltsimpempty) =>
% 24.08/6.29 (((setbeta) =>
% 24.08/6.29 (((nonemptyE1) =>
% 24.08/6.29 (((nonemptyI) =>
% 24.08/6.29 (((nonemptyI1) =>
% 24.08/6.29 (((setadjoinIL) =>
% 24.08/6.29 (((in @ emptyset @
% 24.08/6.29 (setadjoin @
% 24.08/6.29 emptyset @
% 24.08/6.29 emptyset)) =>
% 24.08/6.29 (((setadjoinIR) =>
% 24.08/6.29 (((setadjoinE) =>
% 24.08/6.29 (((setadjoinOr) =>
% 24.08/6.29 (((setoftrueEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (powersetI) =>
% 24.08/6.29 ((
% 24.08/6.29 (emptyinPowerset) =>
% 24.08/6.29 ((
% 24.08/6.29 (emptyInPowerset) =>
% 24.08/6.29 ((
% 24.08/6.29 (powersetE) =>
% 24.08/6.29 ((
% 24.08/6.29 (setunionI) =>
% 24.08/6.29 ((
% 24.08/6.29 (setunionE) =>
% 24.08/6.29 ((
% 24.08/6.29 (subPowSU) =>
% 24.08/6.29 ((
% 24.08/6.29 (exuE2) =>
% 24.08/6.29 ((
% 24.08/6.29 (nonemptyImpWitness) =>
% 24.08/6.29 ((
% 24.08/6.29 (uniqinunit) =>
% 24.08/6.29 ((
% 24.08/6.29 (notinsingleton) =>
% 24.08/6.29 ((
% 24.08/6.29 (eqinunit) =>
% 24.08/6.29 ((
% 24.08/6.29 (singletonsswitch) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairsetE) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairsetIL) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairsetIR) =>
% 24.08/6.29 ((
% 24.08/6.29 (emptyE1) =>
% 24.08/6.29 ((
% 24.08/6.29 (vacuousDall) =>
% 24.08/6.29 ((
% 24.08/6.29 (quantDeMorgan1) =>
% 24.08/6.29 ((
% 24.08/6.29 (quantDeMorgan2) =>
% 24.08/6.29 ((
% 24.08/6.29 (quantDeMorgan3) =>
% 24.08/6.29 ((
% 24.08/6.29 (quantDeMorgan4) =>
% 24.08/6.29 ((
% 24.08/6.29 (prop2setI) =>
% 24.08/6.29 ((
% 24.08/6.29 (prop2set2propI) =>
% 24.08/6.29 ((
% 24.08/6.29 (notdexE) =>
% 24.08/6.29 ((
% 24.08/6.29 (notdallE) =>
% 24.08/6.29 ((
% 24.08/6.29 (exuI1) =>
% 24.08/6.29 ((
% 24.08/6.29 (exuI3) =>
% 24.08/6.29 ((
% 24.08/6.29 (exuI2) =>
% 24.08/6.29 ((
% 24.08/6.29 (inCongP) =>
% 24.08/6.29 ((
% 24.08/6.29 (in__Cong) =>
% 24.08/6.29 ((
% 24.08/6.29 (exuE3u) =>
% 24.08/6.29 ((
% 24.08/6.29 (exu__Cong) =>
% 24.08/6.29 ((
% 24.08/6.29 (setadjoin__Cong) =>
% 24.08/6.29 ((
% 24.08/6.29 (powerset__Cong) =>
% 24.08/6.29 ((
% 24.08/6.29 (setunion__Cong) =>
% 24.08/6.29 ((
% 24.08/6.29 (exuEu) =>
% 24.08/6.29 ((
% 24.08/6.29 (descr__Cong) =>
% 24.08/6.29 ((
% 24.08/6.29 (dsetconstr__Cong) =>
% 24.08/6.29 ((
% 24.08/6.29 (subsetI1) =>
% 24.08/6.29 ((
% 24.08/6.29 (eqimpsubset2) =>
% 24.08/6.29 ((
% 24.08/6.29 (eqimpsubset1) =>
% 24.08/6.29 ((
% 24.08/6.29 (subsetI2) =>
% 24.08/6.29 ((
% 24.08/6.29 (emptysetsubset) =>
% 24.08/6.29 ((
% 24.08/6.29 (subsetE) =>
% 24.08/6.29 ((
% 24.08/6.29 (subsetE2) =>
% 24.08/6.29 ((
% 24.08/6.29 (notsubsetI) =>
% 24.08/6.29 ((
% 24.08/6.29 (notequalI1) =>
% 24.08/6.29 ((
% 24.08/6.29 (notequalI2) =>
% 24.08/6.29 ((
% 24.08/6.29 (subsetRefl) =>
% 24.08/6.29 ((
% 24.08/6.29 (subsetTrans) =>
% 24.08/6.29 ((
% 24.08/6.29 (setadjoinSub) =>
% 24.08/6.29 ((
% 24.08/6.29 (setadjoinSub2) =>
% 24.08/6.29 ((
% 24.08/6.29 (subset2powerset) =>
% 24.08/6.29 ((
% 24.08/6.29 (setextsub) =>
% 24.08/6.29 ((
% 24.08/6.29 (subsetemptysetimpeq) =>
% 24.08/6.29 ((
% 24.08/6.29 (powersetI1) =>
% 24.08/6.29 ((
% 24.08/6.29 (powersetE1) =>
% 24.08/6.29 ((
% 24.08/6.29 (inPowerset) =>
% 24.08/6.29 ((
% 24.08/6.29 (powersetsubset) =>
% 24.08/6.29 ((
% 24.08/6.29 (sepInPowerset) =>
% 24.08/6.29 ((
% 24.08/6.29 (sepSubset) =>
% 24.08/6.29 ((
% 24.08/6.29 (binunionIL) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairset2IR) =>
% 24.08/6.29 ((
% 24.08/6.29 (binunionIR) =>
% 24.08/6.29 ((
% 24.08/6.29 (binunionEcases) =>
% 24.08/6.29 ((
% 24.08/6.29 (binunionE) =>
% 24.08/6.29 ((
% 24.08/6.29 (binunionLsub) =>
% 24.08/6.29 ((
% 24.08/6.29 (binunionRsub) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectI) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectSubset5) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectEL) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectLsub) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectSubset2) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectSubset3) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectER) =>
% 24.08/6.29 ((
% 24.08/6.29 (disjointsetsI1) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectRsub) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectSubset4) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectSubset1) =>
% 24.08/6.29 ((
% 24.08/6.29 (bs114d) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusI) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusEL) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusER) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusSubset2) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusERneg) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusELneg) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusILneg) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusIRneg) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusLsub) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusSubset1) =>
% 24.08/6.29 ((
% 24.08/6.29 (symdiffE) =>
% 24.08/6.29 ((
% 24.08/6.29 (symdiffI1) =>
% 24.08/6.29 ((
% 24.08/6.29 (symdiffI2) =>
% 24.08/6.29 ((
% 24.08/6.29 (symdiffIneg1) =>
% 24.08/6.29 ((
% 24.08/6.29 (symdiffIneg2) =>
% 24.08/6.29 ((
% 24.08/6.29 (secondinupair) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairIL) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairIR) =>
% 24.08/6.29 ((
% 24.08/6.29 (kpairiskpair) =>
% 24.08/6.29 ((
% 24.08/6.29 (kpairp) =>
% 24.08/6.29 ((
% 24.08/6.29 (singletonsubset) =>
% 24.08/6.29 ((
% 24.08/6.29 (singletoninpowerset) =>
% 24.08/6.29 ((
% 24.08/6.29 (singletoninpowunion) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairset2E) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairsubunion) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairinpowunion) =>
% 24.08/6.29 ((
% 24.08/6.29 (ubforcartprodlem1) =>
% 24.08/6.29 ((
% 24.08/6.29 (ubforcartprodlem2) =>
% 24.08/6.29 ((
% 24.08/6.29 (ubforcartprodlem3) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodpairin) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodmempair1) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodmempair) =>
% 24.08/6.29 ((
% 24.08/6.29 (setunionE2) =>
% 24.08/6.29 ((
% 24.08/6.29 (setunionsingleton1) =>
% 24.08/6.29 ((
% 24.08/6.29 (setunionsingleton2) =>
% 24.08/6.29 ((
% 24.08/6.29 (setunionsingleton) =>
% 24.08/6.29 ((
% 24.08/6.29 (singletonprop) =>
% 24.08/6.29 ((
% 24.08/6.29 (ex1E1) =>
% 24.08/6.29 ((
% 24.08/6.29 (ex1I) =>
% 24.08/6.29 ((
% 24.08/6.29 (ex1I2) =>
% 24.08/6.29 ((
% 24.08/6.29 (singletonsuniq) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjL1) =>
% 24.08/6.29 ((
% 24.08/6.29 (kfstsingleton) =>
% 24.08/6.29 ((
% 24.08/6.29 (theprop) =>
% 24.08/6.29 ((
% 24.08/6.29 (kfstpairEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodfstin) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjL2) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjL) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjR11) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjR12) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjR1) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairequniteq) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjR2) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjR) =>
% 24.08/6.29 ((
% 24.08/6.29 (ksndsingleton) =>
% 24.08/6.29 ((
% 24.08/6.29 (ksndpairEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (kpairsurjEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodsndin) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodpairmemEL) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodpairmemER) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodmempaircEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodfstpairEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodsndpairEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodpairsurjEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (dpsetconstrI) =>
% 24.08/6.29 ((
% 24.08/6.29 (!!) @ (
% 24.08/6.29 (('#B') @ (
% 24.08/6.29 !!) @
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 ('#B') @ (
% 24.08/6.29 (
% 24.08/6.29 ('#B') @ (
% 24.08/6.29 !!))) @
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 ('#S') @ (
% 24.08/6.29 (
% 24.08/6.29 ('#B') @ (
% 24.08/6.29 '#S') @
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 ('#B') @ (
% 24.08/6.29 (
% 24.08/6.29 ('#B') @ (
% 24.08/6.29 '#C'))) @
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 ('#B') @ (
% 24.08/6.29 (
% 24.08/6.29 ('#B') @ (
% 24.08/6.29 (
% 24.08/6.29 ('#B') @ subset)))) @
% 24.08/6.29 dpsetconstr)))))) @
% 24.08/6.29 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.08/6.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl13])).
% 24.08/6.29 thf(zip_derived_cl25, plain,
% 24.08/6.29 (~ (((in @ emptyset @ omega) =>
% 24.08/6.29 (((omegaSAx) =>
% 24.08/6.29 (((omegaIndAx) =>
% 24.08/6.29 (((replAx) =>
% 24.08/6.29 (((foundationAx) =>
% 24.08/6.29 (((wellorderingAx) =>
% 24.08/6.29 (((descrp) =>
% 24.08/6.29 (((dsetconstrI) =>
% 24.08/6.29 (((dsetconstrEL) =>
% 24.08/6.29 (((dsetconstrER) =>
% 24.08/6.29 (((exuE1) =>
% 24.08/6.29 (((prop2setE) =>
% 24.08/6.29 (((emptysetE) =>
% 24.08/6.29 (((emptysetimpfalse) =>
% 24.08/6.29 (((notinemptyset) =>
% 24.08/6.29 (((exuE3e) =>
% 24.08/6.29 (((setext) =>
% 24.08/6.29 (((emptyI) =>
% 24.08/6.29 (((noeltsimpempty) =>
% 24.08/6.29 (((setbeta) =>
% 24.08/6.29 (((nonemptyE1) =>
% 24.08/6.29 (((nonemptyI) =>
% 24.08/6.29 (((nonemptyI1) =>
% 24.08/6.29 (((setadjoinIL) =>
% 24.08/6.29 (((in @ emptyset @
% 24.08/6.29 (setadjoin @
% 24.08/6.29 emptyset @ emptyset)) =>
% 24.08/6.29 (((setadjoinIR) =>
% 24.08/6.29 (((setadjoinE) =>
% 24.08/6.29 (((setadjoinOr) =>
% 24.08/6.29 (((setoftrueEq) =>
% 24.08/6.29 (((powersetI) =>
% 24.08/6.29 ((
% 24.08/6.29 (emptyinPowerset) =>
% 24.08/6.29 ((
% 24.08/6.29 (emptyInPowerset) =>
% 24.08/6.29 ((
% 24.08/6.29 (powersetE) =>
% 24.08/6.29 ((
% 24.08/6.29 (setunionI) =>
% 24.08/6.29 ((
% 24.08/6.29 (setunionE) =>
% 24.08/6.29 ((
% 24.08/6.29 (subPowSU) =>
% 24.08/6.29 ((
% 24.08/6.29 (exuE2) =>
% 24.08/6.29 ((
% 24.08/6.29 (nonemptyImpWitness) =>
% 24.08/6.29 ((
% 24.08/6.29 (uniqinunit) =>
% 24.08/6.29 ((
% 24.08/6.29 (notinsingleton) =>
% 24.08/6.29 ((
% 24.08/6.29 (eqinunit) =>
% 24.08/6.29 ((
% 24.08/6.29 (singletonsswitch) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairsetE) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairsetIL) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairsetIR) =>
% 24.08/6.29 ((
% 24.08/6.29 (emptyE1) =>
% 24.08/6.29 ((
% 24.08/6.29 (vacuousDall) =>
% 24.08/6.29 ((
% 24.08/6.29 (quantDeMorgan1) =>
% 24.08/6.29 ((
% 24.08/6.29 (quantDeMorgan2) =>
% 24.08/6.29 ((
% 24.08/6.29 (quantDeMorgan3) =>
% 24.08/6.29 ((
% 24.08/6.29 (quantDeMorgan4) =>
% 24.08/6.29 ((
% 24.08/6.29 (prop2setI) =>
% 24.08/6.29 ((
% 24.08/6.29 (prop2set2propI) =>
% 24.08/6.29 ((
% 24.08/6.29 (notdexE) =>
% 24.08/6.29 ((
% 24.08/6.29 (notdallE) =>
% 24.08/6.29 ((
% 24.08/6.29 (exuI1) =>
% 24.08/6.29 ((
% 24.08/6.29 (exuI3) =>
% 24.08/6.29 ((
% 24.08/6.29 (exuI2) =>
% 24.08/6.29 ((
% 24.08/6.29 (inCongP) =>
% 24.08/6.29 ((
% 24.08/6.29 (in__Cong) =>
% 24.08/6.29 ((
% 24.08/6.29 (exuE3u) =>
% 24.08/6.29 ((
% 24.08/6.29 (exu__Cong) =>
% 24.08/6.29 ((
% 24.08/6.29 (setadjoin__Cong) =>
% 24.08/6.29 ((
% 24.08/6.29 (powerset__Cong) =>
% 24.08/6.29 ((
% 24.08/6.29 (setunion__Cong) =>
% 24.08/6.29 ((
% 24.08/6.29 (exuEu) =>
% 24.08/6.29 ((
% 24.08/6.29 (descr__Cong) =>
% 24.08/6.29 ((
% 24.08/6.29 (dsetconstr__Cong) =>
% 24.08/6.29 ((
% 24.08/6.29 (subsetI1) =>
% 24.08/6.29 ((
% 24.08/6.29 (eqimpsubset2) =>
% 24.08/6.29 ((
% 24.08/6.29 (eqimpsubset1) =>
% 24.08/6.29 ((
% 24.08/6.29 (subsetI2) =>
% 24.08/6.29 ((
% 24.08/6.29 (emptysetsubset) =>
% 24.08/6.29 ((
% 24.08/6.29 (subsetE) =>
% 24.08/6.29 ((
% 24.08/6.29 (subsetE2) =>
% 24.08/6.29 ((
% 24.08/6.29 (notsubsetI) =>
% 24.08/6.29 ((
% 24.08/6.29 (notequalI1) =>
% 24.08/6.29 ((
% 24.08/6.29 (notequalI2) =>
% 24.08/6.29 ((
% 24.08/6.29 (subsetRefl) =>
% 24.08/6.29 ((
% 24.08/6.29 (subsetTrans) =>
% 24.08/6.29 ((
% 24.08/6.29 (setadjoinSub) =>
% 24.08/6.29 ((
% 24.08/6.29 (setadjoinSub2) =>
% 24.08/6.29 ((
% 24.08/6.29 (subset2powerset) =>
% 24.08/6.29 ((
% 24.08/6.29 (setextsub) =>
% 24.08/6.29 ((
% 24.08/6.29 (subsetemptysetimpeq) =>
% 24.08/6.29 ((
% 24.08/6.29 (powersetI1) =>
% 24.08/6.29 ((
% 24.08/6.29 (powersetE1) =>
% 24.08/6.29 ((
% 24.08/6.29 (inPowerset) =>
% 24.08/6.29 ((
% 24.08/6.29 (powersetsubset) =>
% 24.08/6.29 ((
% 24.08/6.29 (sepInPowerset) =>
% 24.08/6.29 ((
% 24.08/6.29 (sepSubset) =>
% 24.08/6.29 ((
% 24.08/6.29 (binunionIL) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairset2IR) =>
% 24.08/6.29 ((
% 24.08/6.29 (binunionIR) =>
% 24.08/6.29 ((
% 24.08/6.29 (binunionEcases) =>
% 24.08/6.29 ((
% 24.08/6.29 (binunionE) =>
% 24.08/6.29 ((
% 24.08/6.29 (binunionLsub) =>
% 24.08/6.29 ((
% 24.08/6.29 (binunionRsub) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectI) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectSubset5) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectEL) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectLsub) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectSubset2) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectSubset3) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectER) =>
% 24.08/6.29 ((
% 24.08/6.29 (disjointsetsI1) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectRsub) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectSubset4) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectSubset1) =>
% 24.08/6.29 ((
% 24.08/6.29 (bs114d) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusI) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusEL) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusER) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusSubset2) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusERneg) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusELneg) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusILneg) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusIRneg) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusLsub) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusSubset1) =>
% 24.08/6.29 ((
% 24.08/6.29 (symdiffE) =>
% 24.08/6.29 ((
% 24.08/6.29 (symdiffI1) =>
% 24.08/6.29 ((
% 24.08/6.29 (symdiffI2) =>
% 24.08/6.29 ((
% 24.08/6.29 (symdiffIneg1) =>
% 24.08/6.29 ((
% 24.08/6.29 (symdiffIneg2) =>
% 24.08/6.29 ((
% 24.08/6.29 (secondinupair) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairIL) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairIR) =>
% 24.08/6.29 ((
% 24.08/6.29 (kpairiskpair) =>
% 24.08/6.29 ((
% 24.08/6.29 (kpairp) =>
% 24.08/6.29 ((
% 24.08/6.29 (singletonsubset) =>
% 24.08/6.29 ((
% 24.08/6.29 (singletoninpowerset) =>
% 24.08/6.29 ((
% 24.08/6.29 (singletoninpowunion) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairset2E) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairsubunion) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairinpowunion) =>
% 24.08/6.29 ((
% 24.08/6.29 (ubforcartprodlem1) =>
% 24.08/6.29 ((
% 24.08/6.29 (ubforcartprodlem2) =>
% 24.08/6.29 ((
% 24.08/6.29 (ubforcartprodlem3) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodpairin) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodmempair1) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodmempair) =>
% 24.08/6.29 ((
% 24.08/6.29 (setunionE2) =>
% 24.08/6.29 ((
% 24.08/6.29 (setunionsingleton1) =>
% 24.08/6.29 ((
% 24.08/6.29 (setunionsingleton2) =>
% 24.08/6.29 ((
% 24.08/6.29 (setunionsingleton) =>
% 24.08/6.29 ((
% 24.08/6.29 (singletonprop) =>
% 24.08/6.29 ((
% 24.08/6.29 (ex1E1) =>
% 24.08/6.29 ((
% 24.08/6.29 (ex1I) =>
% 24.08/6.29 ((
% 24.08/6.29 (ex1I2) =>
% 24.08/6.29 ((
% 24.08/6.29 (singletonsuniq) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjL1) =>
% 24.08/6.29 ((
% 24.08/6.29 (kfstsingleton) =>
% 24.08/6.29 ((
% 24.08/6.29 (theprop) =>
% 24.08/6.29 ((
% 24.08/6.29 (kfstpairEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodfstin) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjL2) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjL) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjR11) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjR12) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjR1) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairequniteq) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjR2) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjR) =>
% 24.08/6.29 ((
% 24.08/6.29 (ksndsingleton) =>
% 24.08/6.29 ((
% 24.08/6.29 (ksndpairEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (kpairsurjEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodsndin) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodpairmemEL) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodpairmemER) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodmempaircEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodfstpairEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodsndpairEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodpairsurjEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (dpsetconstrI) =>
% 24.08/6.29 ((
% 24.08/6.29 (!!) @ (
% 24.08/6.29 (('#B') @ (
% 24.08/6.29 !!) @
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 ('#B') @ (
% 24.08/6.29 (
% 24.08/6.29 ('#B') @ (
% 24.08/6.29 !!))) @
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 ('#S') @ (
% 24.08/6.29 (
% 24.08/6.29 ('#B') @ (
% 24.08/6.29 '#S') @
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 ('#B') @ (
% 24.08/6.29 (
% 24.08/6.29 ('#B') @ (
% 24.08/6.29 '#C'))) @
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 ('#B') @ (
% 24.08/6.29 (
% 24.08/6.29 ('#B') @ (
% 24.08/6.29 (
% 24.08/6.29 ('#B') @ subset)))) @
% 24.08/6.29 dpsetconstr)))))) @
% 24.08/6.29 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.08/6.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl19])).
% 24.08/6.29 thf(zip_derived_cl33, plain,
% 24.08/6.29 (~ (((omegaSAx) =>
% 24.08/6.29 (((omegaIndAx) =>
% 24.08/6.29 (((replAx) =>
% 24.08/6.29 (((foundationAx) =>
% 24.08/6.29 (((wellorderingAx) =>
% 24.08/6.29 (((descrp) =>
% 24.08/6.29 (((dsetconstrI) =>
% 24.08/6.29 (((dsetconstrEL) =>
% 24.08/6.29 (((dsetconstrER) =>
% 24.08/6.29 (((exuE1) =>
% 24.08/6.29 (((prop2setE) =>
% 24.08/6.29 (((emptysetE) =>
% 24.08/6.29 (((emptysetimpfalse) =>
% 24.08/6.29 (((notinemptyset) =>
% 24.08/6.29 (((exuE3e) =>
% 24.08/6.29 (((setext) =>
% 24.08/6.29 (((emptyI) =>
% 24.08/6.29 (((noeltsimpempty) =>
% 24.08/6.29 (((setbeta) =>
% 24.08/6.29 (((nonemptyE1) =>
% 24.08/6.29 (((nonemptyI) =>
% 24.08/6.29 (((nonemptyI1) =>
% 24.08/6.29 (((setadjoinIL) =>
% 24.08/6.29 (((in @ emptyset @
% 24.08/6.29 (setadjoin @
% 24.08/6.29 emptyset @ emptyset)) =>
% 24.08/6.29 (((setadjoinIR) =>
% 24.08/6.29 (((setadjoinE) =>
% 24.08/6.29 (((setadjoinOr) =>
% 24.08/6.29 (((setoftrueEq) =>
% 24.08/6.29 (((powersetI) =>
% 24.08/6.29 (((emptyinPowerset) =>
% 24.08/6.29 ((
% 24.08/6.29 (emptyInPowerset) =>
% 24.08/6.29 ((
% 24.08/6.29 (powersetE) =>
% 24.08/6.29 ((
% 24.08/6.29 (setunionI) =>
% 24.08/6.29 ((
% 24.08/6.29 (setunionE) =>
% 24.08/6.29 ((
% 24.08/6.29 (subPowSU) =>
% 24.08/6.29 ((
% 24.08/6.29 (exuE2) =>
% 24.08/6.29 ((
% 24.08/6.29 (nonemptyImpWitness) =>
% 24.08/6.29 ((
% 24.08/6.29 (uniqinunit) =>
% 24.08/6.29 ((
% 24.08/6.29 (notinsingleton) =>
% 24.08/6.29 ((
% 24.08/6.29 (eqinunit) =>
% 24.08/6.29 ((
% 24.08/6.29 (singletonsswitch) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairsetE) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairsetIL) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairsetIR) =>
% 24.08/6.29 ((
% 24.08/6.29 (emptyE1) =>
% 24.08/6.29 ((
% 24.08/6.29 (vacuousDall) =>
% 24.08/6.29 ((
% 24.08/6.29 (quantDeMorgan1) =>
% 24.08/6.29 ((
% 24.08/6.29 (quantDeMorgan2) =>
% 24.08/6.29 ((
% 24.08/6.29 (quantDeMorgan3) =>
% 24.08/6.29 ((
% 24.08/6.29 (quantDeMorgan4) =>
% 24.08/6.29 ((
% 24.08/6.29 (prop2setI) =>
% 24.08/6.29 ((
% 24.08/6.29 (prop2set2propI) =>
% 24.08/6.29 ((
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% 24.08/6.29 ((
% 24.08/6.29 (notdallE) =>
% 24.08/6.29 ((
% 24.08/6.29 (exuI1) =>
% 24.08/6.29 ((
% 24.08/6.29 (exuI3) =>
% 24.08/6.29 ((
% 24.08/6.29 (exuI2) =>
% 24.08/6.29 ((
% 24.08/6.29 (inCongP) =>
% 24.08/6.29 ((
% 24.08/6.29 (in__Cong) =>
% 24.08/6.29 ((
% 24.08/6.29 (exuE3u) =>
% 24.08/6.29 ((
% 24.08/6.29 (exu__Cong) =>
% 24.08/6.29 ((
% 24.08/6.29 (setadjoin__Cong) =>
% 24.08/6.29 ((
% 24.08/6.29 (powerset__Cong) =>
% 24.08/6.29 ((
% 24.08/6.29 (setunion__Cong) =>
% 24.08/6.29 ((
% 24.08/6.29 (exuEu) =>
% 24.08/6.29 ((
% 24.08/6.29 (descr__Cong) =>
% 24.08/6.29 ((
% 24.08/6.29 (dsetconstr__Cong) =>
% 24.08/6.29 ((
% 24.08/6.29 (subsetI1) =>
% 24.08/6.29 ((
% 24.08/6.29 (eqimpsubset2) =>
% 24.08/6.29 ((
% 24.08/6.29 (eqimpsubset1) =>
% 24.08/6.29 ((
% 24.08/6.29 (subsetI2) =>
% 24.08/6.29 ((
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% 24.08/6.29 ((
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% 24.08/6.29 ((
% 24.08/6.29 (subsetE2) =>
% 24.08/6.29 ((
% 24.08/6.29 (notsubsetI) =>
% 24.08/6.29 ((
% 24.08/6.29 (notequalI1) =>
% 24.08/6.29 ((
% 24.08/6.29 (notequalI2) =>
% 24.08/6.29 ((
% 24.08/6.29 (subsetRefl) =>
% 24.08/6.29 ((
% 24.08/6.29 (subsetTrans) =>
% 24.08/6.29 ((
% 24.08/6.29 (setadjoinSub) =>
% 24.08/6.29 ((
% 24.08/6.29 (setadjoinSub2) =>
% 24.08/6.29 ((
% 24.08/6.29 (subset2powerset) =>
% 24.08/6.29 ((
% 24.08/6.29 (setextsub) =>
% 24.08/6.29 ((
% 24.08/6.29 (subsetemptysetimpeq) =>
% 24.08/6.29 ((
% 24.08/6.29 (powersetI1) =>
% 24.08/6.29 ((
% 24.08/6.29 (powersetE1) =>
% 24.08/6.29 ((
% 24.08/6.29 (inPowerset) =>
% 24.08/6.29 ((
% 24.08/6.29 (powersetsubset) =>
% 24.08/6.29 ((
% 24.08/6.29 (sepInPowerset) =>
% 24.08/6.29 ((
% 24.08/6.29 (sepSubset) =>
% 24.08/6.29 ((
% 24.08/6.29 (binunionIL) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairset2IR) =>
% 24.08/6.29 ((
% 24.08/6.29 (binunionIR) =>
% 24.08/6.29 ((
% 24.08/6.29 (binunionEcases) =>
% 24.08/6.29 ((
% 24.08/6.29 (binunionE) =>
% 24.08/6.29 ((
% 24.08/6.29 (binunionLsub) =>
% 24.08/6.29 ((
% 24.08/6.29 (binunionRsub) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectI) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectSubset5) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectEL) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectLsub) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectSubset2) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectSubset3) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectER) =>
% 24.08/6.29 ((
% 24.08/6.29 (disjointsetsI1) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectRsub) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectSubset4) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectSubset1) =>
% 24.08/6.29 ((
% 24.08/6.29 (bs114d) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusI) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusEL) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusER) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusSubset2) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusERneg) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusELneg) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusILneg) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusIRneg) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusLsub) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusSubset1) =>
% 24.08/6.29 ((
% 24.08/6.29 (symdiffE) =>
% 24.08/6.29 ((
% 24.08/6.29 (symdiffI1) =>
% 24.08/6.29 ((
% 24.08/6.29 (symdiffI2) =>
% 24.08/6.29 ((
% 24.08/6.29 (symdiffIneg1) =>
% 24.08/6.29 ((
% 24.08/6.29 (symdiffIneg2) =>
% 24.08/6.29 ((
% 24.08/6.29 (secondinupair) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairIL) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairIR) =>
% 24.08/6.29 ((
% 24.08/6.29 (kpairiskpair) =>
% 24.08/6.29 ((
% 24.08/6.29 (kpairp) =>
% 24.08/6.29 ((
% 24.08/6.29 (singletonsubset) =>
% 24.08/6.29 ((
% 24.08/6.29 (singletoninpowerset) =>
% 24.08/6.29 ((
% 24.08/6.29 (singletoninpowunion) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairset2E) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairsubunion) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairinpowunion) =>
% 24.08/6.29 ((
% 24.08/6.29 (ubforcartprodlem1) =>
% 24.08/6.29 ((
% 24.08/6.29 (ubforcartprodlem2) =>
% 24.08/6.29 ((
% 24.08/6.29 (ubforcartprodlem3) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodpairin) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodmempair1) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodmempair) =>
% 24.08/6.29 ((
% 24.08/6.29 (setunionE2) =>
% 24.08/6.29 ((
% 24.08/6.29 (setunionsingleton1) =>
% 24.08/6.29 ((
% 24.08/6.29 (setunionsingleton2) =>
% 24.08/6.29 ((
% 24.08/6.29 (setunionsingleton) =>
% 24.08/6.29 ((
% 24.08/6.29 (singletonprop) =>
% 24.08/6.29 ((
% 24.08/6.29 (ex1E1) =>
% 24.08/6.29 ((
% 24.08/6.29 (ex1I) =>
% 24.08/6.29 ((
% 24.08/6.29 (ex1I2) =>
% 24.08/6.29 ((
% 24.08/6.29 (singletonsuniq) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjL1) =>
% 24.08/6.29 ((
% 24.08/6.29 (kfstsingleton) =>
% 24.08/6.29 ((
% 24.08/6.29 (theprop) =>
% 24.08/6.29 ((
% 24.08/6.29 (kfstpairEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodfstin) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjL2) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjL) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjR11) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjR12) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjR1) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairequniteq) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjR2) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjR) =>
% 24.08/6.29 ((
% 24.08/6.29 (ksndsingleton) =>
% 24.08/6.29 ((
% 24.08/6.29 (ksndpairEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (kpairsurjEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodsndin) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodpairmemEL) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodpairmemER) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodmempaircEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodfstpairEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodsndpairEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodpairsurjEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (dpsetconstrI) =>
% 24.08/6.29 ((
% 24.08/6.29 (!!) @ (
% 24.08/6.29 (('#B') @ (
% 24.08/6.29 !!) @
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 ('#B') @ (
% 24.08/6.29 (
% 24.08/6.29 ('#B') @ (
% 24.08/6.29 !!))) @
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 ('#S') @ (
% 24.08/6.29 (
% 24.08/6.29 ('#B') @ (
% 24.08/6.29 '#S') @
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 ('#B') @ (
% 24.08/6.29 (
% 24.08/6.29 ('#B') @ (
% 24.08/6.29 '#C'))) @
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 ('#B') @ (
% 24.08/6.29 (
% 24.08/6.29 ('#B') @ (
% 24.08/6.29 (
% 24.08/6.29 ('#B') @ subset)))) @
% 24.08/6.29 dpsetconstr)))))) @
% 24.08/6.29 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.08/6.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl25])).
% 24.08/6.29 thf(zip_derived_cl40, plain,
% 24.08/6.29 (~ (((omegaIndAx) =>
% 24.08/6.29 (((replAx) =>
% 24.08/6.29 (((foundationAx) =>
% 24.08/6.29 (((wellorderingAx) =>
% 24.08/6.29 (((descrp) =>
% 24.08/6.29 (((dsetconstrI) =>
% 24.08/6.29 (((dsetconstrEL) =>
% 24.08/6.29 (((dsetconstrER) =>
% 24.08/6.29 (((exuE1) =>
% 24.08/6.29 (((prop2setE) =>
% 24.08/6.29 (((emptysetE) =>
% 24.08/6.29 (((emptysetimpfalse) =>
% 24.08/6.29 (((notinemptyset) =>
% 24.08/6.29 (((exuE3e) =>
% 24.08/6.29 (((setext) =>
% 24.08/6.29 (((emptyI) =>
% 24.08/6.29 (((noeltsimpempty) =>
% 24.08/6.29 (((setbeta) =>
% 24.08/6.29 (((nonemptyE1) =>
% 24.08/6.29 (((nonemptyI) =>
% 24.08/6.29 (((nonemptyI1) =>
% 24.08/6.29 (((setadjoinIL) =>
% 24.08/6.29 (((in @ emptyset @
% 24.08/6.29 (setadjoin @ emptyset @
% 24.08/6.29 emptyset)) =>
% 24.08/6.29 (((setadjoinIR) =>
% 24.08/6.29 (((setadjoinE) =>
% 24.08/6.29 (((setadjoinOr) =>
% 24.08/6.29 (((setoftrueEq) =>
% 24.08/6.29 (((powersetI) =>
% 24.08/6.29 (((emptyinPowerset) =>
% 24.08/6.29 (((emptyInPowerset) =>
% 24.08/6.29 ((
% 24.08/6.29 (powersetE) =>
% 24.08/6.29 ((
% 24.08/6.29 (setunionI) =>
% 24.08/6.29 ((
% 24.08/6.29 (setunionE) =>
% 24.08/6.29 ((
% 24.08/6.29 (subPowSU) =>
% 24.08/6.29 ((
% 24.08/6.29 (exuE2) =>
% 24.08/6.29 ((
% 24.08/6.29 (nonemptyImpWitness) =>
% 24.08/6.29 ((
% 24.08/6.29 (uniqinunit) =>
% 24.08/6.29 ((
% 24.08/6.29 (notinsingleton) =>
% 24.08/6.29 ((
% 24.08/6.29 (eqinunit) =>
% 24.08/6.29 ((
% 24.08/6.29 (singletonsswitch) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairsetE) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairsetIL) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairsetIR) =>
% 24.08/6.29 ((
% 24.08/6.29 (emptyE1) =>
% 24.08/6.29 ((
% 24.08/6.29 (vacuousDall) =>
% 24.08/6.29 ((
% 24.08/6.29 (quantDeMorgan1) =>
% 24.08/6.29 ((
% 24.08/6.29 (quantDeMorgan2) =>
% 24.08/6.29 ((
% 24.08/6.29 (quantDeMorgan3) =>
% 24.08/6.29 ((
% 24.08/6.29 (quantDeMorgan4) =>
% 24.08/6.29 ((
% 24.08/6.29 (prop2setI) =>
% 24.08/6.29 ((
% 24.08/6.29 (prop2set2propI) =>
% 24.08/6.29 ((
% 24.08/6.29 (notdexE) =>
% 24.08/6.29 ((
% 24.08/6.29 (notdallE) =>
% 24.08/6.29 ((
% 24.08/6.29 (exuI1) =>
% 24.08/6.29 ((
% 24.08/6.29 (exuI3) =>
% 24.08/6.29 ((
% 24.08/6.29 (exuI2) =>
% 24.08/6.29 ((
% 24.08/6.29 (inCongP) =>
% 24.08/6.29 ((
% 24.08/6.29 (in__Cong) =>
% 24.08/6.29 ((
% 24.08/6.29 (exuE3u) =>
% 24.08/6.29 ((
% 24.08/6.29 (exu__Cong) =>
% 24.08/6.29 ((
% 24.08/6.29 (setadjoin__Cong) =>
% 24.08/6.29 ((
% 24.08/6.29 (powerset__Cong) =>
% 24.08/6.29 ((
% 24.08/6.29 (setunion__Cong) =>
% 24.08/6.29 ((
% 24.08/6.29 (exuEu) =>
% 24.08/6.29 ((
% 24.08/6.29 (descr__Cong) =>
% 24.08/6.29 ((
% 24.08/6.29 (dsetconstr__Cong) =>
% 24.08/6.29 ((
% 24.08/6.29 (subsetI1) =>
% 24.08/6.29 ((
% 24.08/6.29 (eqimpsubset2) =>
% 24.08/6.29 ((
% 24.08/6.29 (eqimpsubset1) =>
% 24.08/6.29 ((
% 24.08/6.29 (subsetI2) =>
% 24.08/6.29 ((
% 24.08/6.29 (emptysetsubset) =>
% 24.08/6.29 ((
% 24.08/6.29 (subsetE) =>
% 24.08/6.29 ((
% 24.08/6.29 (subsetE2) =>
% 24.08/6.29 ((
% 24.08/6.29 (notsubsetI) =>
% 24.08/6.29 ((
% 24.08/6.29 (notequalI1) =>
% 24.08/6.29 ((
% 24.08/6.29 (notequalI2) =>
% 24.08/6.29 ((
% 24.08/6.29 (subsetRefl) =>
% 24.08/6.29 ((
% 24.08/6.29 (subsetTrans) =>
% 24.08/6.29 ((
% 24.08/6.29 (setadjoinSub) =>
% 24.08/6.29 ((
% 24.08/6.29 (setadjoinSub2) =>
% 24.08/6.29 ((
% 24.08/6.29 (subset2powerset) =>
% 24.08/6.29 ((
% 24.08/6.29 (setextsub) =>
% 24.08/6.29 ((
% 24.08/6.29 (subsetemptysetimpeq) =>
% 24.08/6.29 ((
% 24.08/6.29 (powersetI1) =>
% 24.08/6.29 ((
% 24.08/6.29 (powersetE1) =>
% 24.08/6.29 ((
% 24.08/6.29 (inPowerset) =>
% 24.08/6.29 ((
% 24.08/6.29 (powersetsubset) =>
% 24.08/6.29 ((
% 24.08/6.29 (sepInPowerset) =>
% 24.08/6.29 ((
% 24.08/6.29 (sepSubset) =>
% 24.08/6.29 ((
% 24.08/6.29 (binunionIL) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairset2IR) =>
% 24.08/6.29 ((
% 24.08/6.29 (binunionIR) =>
% 24.08/6.29 ((
% 24.08/6.29 (binunionEcases) =>
% 24.08/6.29 ((
% 24.08/6.29 (binunionE) =>
% 24.08/6.29 ((
% 24.08/6.29 (binunionLsub) =>
% 24.08/6.29 ((
% 24.08/6.29 (binunionRsub) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectI) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectSubset5) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectEL) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectLsub) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectSubset2) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectSubset3) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectER) =>
% 24.08/6.29 ((
% 24.08/6.29 (disjointsetsI1) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectRsub) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectSubset4) =>
% 24.08/6.29 ((
% 24.08/6.29 (binintersectSubset1) =>
% 24.08/6.29 ((
% 24.08/6.29 (bs114d) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusI) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusEL) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusER) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusSubset2) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusERneg) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusELneg) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusILneg) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusIRneg) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusLsub) =>
% 24.08/6.29 ((
% 24.08/6.29 (setminusSubset1) =>
% 24.08/6.29 ((
% 24.08/6.29 (symdiffE) =>
% 24.08/6.29 ((
% 24.08/6.29 (symdiffI1) =>
% 24.08/6.29 ((
% 24.08/6.29 (symdiffI2) =>
% 24.08/6.29 ((
% 24.08/6.29 (symdiffIneg1) =>
% 24.08/6.29 ((
% 24.08/6.29 (symdiffIneg2) =>
% 24.08/6.29 ((
% 24.08/6.29 (secondinupair) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairIL) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairIR) =>
% 24.08/6.29 ((
% 24.08/6.29 (kpairiskpair) =>
% 24.08/6.29 ((
% 24.08/6.29 (kpairp) =>
% 24.08/6.29 ((
% 24.08/6.29 (singletonsubset) =>
% 24.08/6.29 ((
% 24.08/6.29 (singletoninpowerset) =>
% 24.08/6.29 ((
% 24.08/6.29 (singletoninpowunion) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairset2E) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairsubunion) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairinpowunion) =>
% 24.08/6.29 ((
% 24.08/6.29 (ubforcartprodlem1) =>
% 24.08/6.29 ((
% 24.08/6.29 (ubforcartprodlem2) =>
% 24.08/6.29 ((
% 24.08/6.29 (ubforcartprodlem3) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodpairin) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodmempair1) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodmempair) =>
% 24.08/6.29 ((
% 24.08/6.29 (setunionE2) =>
% 24.08/6.29 ((
% 24.08/6.29 (setunionsingleton1) =>
% 24.08/6.29 ((
% 24.08/6.29 (setunionsingleton2) =>
% 24.08/6.29 ((
% 24.08/6.29 (setunionsingleton) =>
% 24.08/6.29 ((
% 24.08/6.29 (singletonprop) =>
% 24.08/6.29 ((
% 24.08/6.29 (ex1E1) =>
% 24.08/6.29 ((
% 24.08/6.29 (ex1I) =>
% 24.08/6.29 ((
% 24.08/6.29 (ex1I2) =>
% 24.08/6.29 ((
% 24.08/6.29 (singletonsuniq) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjL1) =>
% 24.08/6.29 ((
% 24.08/6.29 (kfstsingleton) =>
% 24.08/6.29 ((
% 24.08/6.29 (theprop) =>
% 24.08/6.29 ((
% 24.08/6.29 (kfstpairEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodfstin) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjL2) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjL) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjR11) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjR12) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjR1) =>
% 24.08/6.29 ((
% 24.08/6.29 (upairequniteq) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjR2) =>
% 24.08/6.29 ((
% 24.08/6.29 (setukpairinjR) =>
% 24.08/6.29 ((
% 24.08/6.29 (ksndsingleton) =>
% 24.08/6.29 ((
% 24.08/6.29 (ksndpairEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (kpairsurjEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodsndin) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodpairmemEL) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodpairmemER) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodmempaircEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodfstpairEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodsndpairEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (cartprodpairsurjEq) =>
% 24.08/6.29 ((
% 24.08/6.29 (dpsetconstrI) =>
% 24.08/6.29 ((
% 24.08/6.29 (!!) @ (
% 24.08/6.29 (('#B') @ (
% 24.08/6.29 !!) @
% 24.08/6.29 (
% 24.08/6.29 (
% 24.08/6.29 ('#B') @ (
% 24.08/6.29 (
% 24.08/6.29 ('#B') @ (
% 24.08/6.29 !!))) @
% 24.08/6.29 (
% 24.08/6.30 (
% 24.08/6.30 ('#S') @ (
% 24.08/6.30 (
% 24.08/6.30 ('#B') @ (
% 24.08/6.30 '#S') @
% 24.08/6.30 (
% 24.08/6.30 (
% 24.08/6.30 ('#B') @ (
% 24.08/6.30 (
% 24.08/6.30 ('#B') @ (
% 24.08/6.30 '#C'))) @
% 24.08/6.30 (
% 24.08/6.30 (
% 24.08/6.30 ('#B') @ (
% 24.08/6.30 (
% 24.08/6.30 ('#B') @ (
% 24.08/6.30 (
% 24.08/6.30 ('#B') @ subset)))) @
% 24.08/6.30 dpsetconstr)))))) @
% 24.08/6.30 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.08/6.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl33])).
% 24.08/6.30 thf(zip_derived_cl46, plain,
% 24.08/6.30 (~ (((replAx) =>
% 24.08/6.30 (((foundationAx) =>
% 24.08/6.30 (((wellorderingAx) =>
% 24.08/6.30 (((descrp) =>
% 24.08/6.30 (((dsetconstrI) =>
% 24.08/6.30 (((dsetconstrEL) =>
% 24.08/6.30 (((dsetconstrER) =>
% 24.08/6.30 (((exuE1) =>
% 24.08/6.30 (((prop2setE) =>
% 24.08/6.30 (((emptysetE) =>
% 24.08/6.30 (((emptysetimpfalse) =>
% 24.08/6.30 (((notinemptyset) =>
% 24.08/6.30 (((exuE3e) =>
% 24.08/6.30 (((setext) =>
% 24.08/6.30 (((emptyI) =>
% 24.08/6.30 (((noeltsimpempty) =>
% 24.08/6.30 (((setbeta) =>
% 24.08/6.30 (((nonemptyE1) =>
% 24.08/6.30 (((nonemptyI) =>
% 24.08/6.30 (((nonemptyI1) =>
% 24.08/6.30 (((setadjoinIL) =>
% 24.08/6.30 (((in @ emptyset @
% 24.08/6.30 (setadjoin @ emptyset @
% 24.08/6.30 emptyset)) =>
% 24.08/6.30 (((setadjoinIR) =>
% 24.08/6.30 (((setadjoinE) =>
% 24.08/6.30 (((setadjoinOr) =>
% 24.08/6.30 (((setoftrueEq) =>
% 24.08/6.30 (((powersetI) =>
% 24.08/6.30 (((emptyinPowerset) =>
% 24.08/6.30 (((emptyInPowerset) =>
% 24.08/6.30 (((powersetE) =>
% 24.08/6.30 ((
% 24.08/6.30 (setunionI) =>
% 24.08/6.30 ((
% 24.08/6.30 (setunionE) =>
% 24.08/6.30 ((
% 24.08/6.30 (subPowSU) =>
% 24.08/6.30 ((
% 24.08/6.30 (exuE2) =>
% 24.08/6.30 ((
% 24.08/6.30 (nonemptyImpWitness) =>
% 24.08/6.30 ((
% 24.08/6.30 (uniqinunit) =>
% 24.08/6.30 ((
% 24.08/6.30 (notinsingleton) =>
% 24.08/6.30 ((
% 24.08/6.30 (eqinunit) =>
% 24.08/6.30 ((
% 24.08/6.30 (singletonsswitch) =>
% 24.08/6.30 ((
% 24.08/6.30 (upairsetE) =>
% 24.08/6.30 ((
% 24.08/6.30 (upairsetIL) =>
% 24.08/6.30 ((
% 24.08/6.30 (upairsetIR) =>
% 24.08/6.30 ((
% 24.08/6.30 (emptyE1) =>
% 24.08/6.30 ((
% 24.08/6.30 (vacuousDall) =>
% 24.08/6.30 ((
% 24.08/6.30 (quantDeMorgan1) =>
% 24.08/6.30 ((
% 24.08/6.30 (quantDeMorgan2) =>
% 24.08/6.30 ((
% 24.08/6.30 (quantDeMorgan3) =>
% 24.08/6.30 ((
% 24.08/6.30 (quantDeMorgan4) =>
% 24.08/6.30 ((
% 24.08/6.30 (prop2setI) =>
% 24.08/6.30 ((
% 24.08/6.30 (prop2set2propI) =>
% 24.08/6.30 ((
% 24.08/6.30 (notdexE) =>
% 24.08/6.30 ((
% 24.08/6.30 (notdallE) =>
% 24.08/6.30 ((
% 24.08/6.30 (exuI1) =>
% 24.08/6.30 ((
% 24.08/6.30 (exuI3) =>
% 24.08/6.30 ((
% 24.08/6.30 (exuI2) =>
% 24.08/6.30 ((
% 24.08/6.30 (inCongP) =>
% 24.08/6.30 ((
% 24.08/6.30 (in__Cong) =>
% 24.08/6.30 ((
% 24.08/6.30 (exuE3u) =>
% 24.08/6.30 ((
% 24.08/6.30 (exu__Cong) =>
% 24.08/6.30 ((
% 24.08/6.30 (setadjoin__Cong) =>
% 24.08/6.30 ((
% 24.08/6.30 (powerset__Cong) =>
% 24.08/6.30 ((
% 24.08/6.30 (setunion__Cong) =>
% 24.08/6.30 ((
% 24.08/6.30 (exuEu) =>
% 24.08/6.30 ((
% 24.08/6.30 (descr__Cong) =>
% 24.08/6.30 ((
% 24.08/6.30 (dsetconstr__Cong) =>
% 24.08/6.30 ((
% 24.08/6.30 (subsetI1) =>
% 24.08/6.30 ((
% 24.08/6.30 (eqimpsubset2) =>
% 24.08/6.30 ((
% 24.08/6.30 (eqimpsubset1) =>
% 24.08/6.30 ((
% 24.08/6.30 (subsetI2) =>
% 24.08/6.30 ((
% 24.08/6.30 (emptysetsubset) =>
% 24.08/6.30 ((
% 24.08/6.30 (subsetE) =>
% 24.08/6.30 ((
% 24.08/6.30 (subsetE2) =>
% 24.08/6.30 ((
% 24.08/6.30 (notsubsetI) =>
% 24.08/6.30 ((
% 24.08/6.30 (notequalI1) =>
% 24.08/6.30 ((
% 24.08/6.30 (notequalI2) =>
% 24.08/6.30 ((
% 24.08/6.30 (subsetRefl) =>
% 24.08/6.30 ((
% 24.08/6.30 (subsetTrans) =>
% 24.08/6.30 ((
% 24.08/6.30 (setadjoinSub) =>
% 24.08/6.30 ((
% 24.08/6.30 (setadjoinSub2) =>
% 24.08/6.30 ((
% 24.08/6.30 (subset2powerset) =>
% 24.08/6.30 ((
% 24.08/6.30 (setextsub) =>
% 24.08/6.30 ((
% 24.08/6.30 (subsetemptysetimpeq) =>
% 24.08/6.30 ((
% 24.08/6.30 (powersetI1) =>
% 24.08/6.30 ((
% 24.08/6.30 (powersetE1) =>
% 24.08/6.30 ((
% 24.08/6.30 (inPowerset) =>
% 24.08/6.30 ((
% 24.08/6.30 (powersetsubset) =>
% 24.08/6.30 ((
% 24.08/6.30 (sepInPowerset) =>
% 24.08/6.30 ((
% 24.08/6.30 (sepSubset) =>
% 24.08/6.30 ((
% 24.08/6.30 (binunionIL) =>
% 24.08/6.30 ((
% 24.08/6.30 (upairset2IR) =>
% 24.08/6.30 ((
% 24.08/6.30 (binunionIR) =>
% 24.08/6.30 ((
% 24.08/6.30 (binunionEcases) =>
% 24.08/6.30 ((
% 24.08/6.30 (binunionE) =>
% 24.08/6.30 ((
% 24.08/6.30 (binunionLsub) =>
% 24.08/6.30 ((
% 24.08/6.30 (binunionRsub) =>
% 24.08/6.30 ((
% 24.08/6.30 (binintersectI) =>
% 24.08/6.30 ((
% 24.08/6.30 (binintersectSubset5) =>
% 24.08/6.30 ((
% 24.08/6.30 (binintersectEL) =>
% 24.08/6.30 ((
% 24.08/6.30 (binintersectLsub) =>
% 24.08/6.30 ((
% 24.08/6.30 (binintersectSubset2) =>
% 24.08/6.30 ((
% 24.08/6.30 (binintersectSubset3) =>
% 24.08/6.30 ((
% 24.08/6.30 (binintersectER) =>
% 24.08/6.30 ((
% 24.08/6.30 (disjointsetsI1) =>
% 24.08/6.30 ((
% 24.08/6.30 (binintersectRsub) =>
% 24.08/6.30 ((
% 24.08/6.30 (binintersectSubset4) =>
% 24.08/6.30 ((
% 24.08/6.30 (binintersectSubset1) =>
% 24.08/6.30 ((
% 24.08/6.30 (bs114d) =>
% 24.08/6.30 ((
% 24.08/6.30 (setminusI) =>
% 24.08/6.30 ((
% 24.08/6.30 (setminusEL) =>
% 24.08/6.30 ((
% 24.08/6.30 (setminusER) =>
% 24.08/6.30 ((
% 24.08/6.30 (setminusSubset2) =>
% 24.08/6.30 ((
% 24.08/6.30 (setminusERneg) =>
% 24.08/6.30 ((
% 24.08/6.30 (setminusELneg) =>
% 24.08/6.30 ((
% 24.08/6.30 (setminusILneg) =>
% 24.08/6.30 ((
% 24.08/6.30 (setminusIRneg) =>
% 24.08/6.30 ((
% 24.08/6.30 (setminusLsub) =>
% 24.08/6.30 ((
% 24.08/6.30 (setminusSubset1) =>
% 24.08/6.30 ((
% 24.08/6.30 (symdiffE) =>
% 24.08/6.30 ((
% 24.08/6.30 (symdiffI1) =>
% 24.08/6.30 ((
% 24.08/6.30 (symdiffI2) =>
% 24.08/6.30 ((
% 24.08/6.30 (symdiffIneg1) =>
% 24.08/6.30 ((
% 24.08/6.30 (symdiffIneg2) =>
% 24.08/6.30 ((
% 24.08/6.30 (secondinupair) =>
% 24.08/6.30 ((
% 24.08/6.30 (setukpairIL) =>
% 24.08/6.30 ((
% 24.08/6.30 (setukpairIR) =>
% 24.08/6.30 ((
% 24.08/6.30 (kpairiskpair) =>
% 24.08/6.30 ((
% 24.08/6.30 (kpairp) =>
% 24.08/6.30 ((
% 24.08/6.30 (singletonsubset) =>
% 24.08/6.30 ((
% 24.08/6.30 (singletoninpowerset) =>
% 24.08/6.30 ((
% 24.08/6.30 (singletoninpowunion) =>
% 24.08/6.30 ((
% 24.08/6.30 (upairset2E) =>
% 24.08/6.30 ((
% 24.08/6.30 (upairsubunion) =>
% 24.08/6.30 ((
% 24.08/6.30 (upairinpowunion) =>
% 24.08/6.30 ((
% 24.08/6.30 (ubforcartprodlem1) =>
% 24.08/6.30 ((
% 24.08/6.30 (ubforcartprodlem2) =>
% 24.08/6.30 ((
% 24.08/6.30 (ubforcartprodlem3) =>
% 24.08/6.30 ((
% 24.08/6.30 (cartprodpairin) =>
% 24.08/6.30 ((
% 24.08/6.30 (cartprodmempair1) =>
% 24.08/6.30 ((
% 24.08/6.30 (cartprodmempair) =>
% 24.08/6.30 ((
% 24.08/6.30 (setunionE2) =>
% 24.08/6.30 ((
% 24.08/6.30 (setunionsingleton1) =>
% 24.08/6.30 ((
% 24.08/6.30 (setunionsingleton2) =>
% 24.08/6.30 ((
% 24.08/6.30 (setunionsingleton) =>
% 24.08/6.30 ((
% 24.08/6.30 (singletonprop) =>
% 24.08/6.30 ((
% 24.08/6.30 (ex1E1) =>
% 24.08/6.30 ((
% 24.08/6.30 (ex1I) =>
% 24.08/6.30 ((
% 24.08/6.30 (ex1I2) =>
% 24.08/6.30 ((
% 24.08/6.30 (singletonsuniq) =>
% 24.08/6.30 ((
% 24.08/6.30 (setukpairinjL1) =>
% 24.08/6.30 ((
% 24.08/6.30 (kfstsingleton) =>
% 24.08/6.30 ((
% 24.08/6.30 (theprop) =>
% 24.08/6.30 ((
% 24.08/6.30 (kfstpairEq) =>
% 24.08/6.30 ((
% 24.08/6.30 (cartprodfstin) =>
% 24.08/6.30 ((
% 24.08/6.30 (setukpairinjL2) =>
% 24.08/6.30 ((
% 24.08/6.30 (setukpairinjL) =>
% 24.08/6.30 ((
% 24.08/6.30 (setukpairinjR11) =>
% 24.08/6.30 ((
% 24.08/6.30 (setukpairinjR12) =>
% 24.08/6.30 ((
% 24.08/6.30 (setukpairinjR1) =>
% 24.08/6.30 ((
% 24.08/6.30 (upairequniteq) =>
% 24.08/6.30 ((
% 24.08/6.30 (setukpairinjR2) =>
% 24.08/6.30 ((
% 24.08/6.30 (setukpairinjR) =>
% 24.08/6.30 ((
% 24.08/6.30 (ksndsingleton) =>
% 24.08/6.30 ((
% 24.08/6.30 (ksndpairEq) =>
% 24.08/6.30 ((
% 24.08/6.30 (kpairsurjEq) =>
% 24.08/6.30 ((
% 24.08/6.30 (cartprodsndin) =>
% 24.08/6.30 ((
% 24.08/6.30 (cartprodpairmemEL) =>
% 24.08/6.30 ((
% 24.08/6.30 (cartprodpairmemER) =>
% 24.08/6.30 ((
% 24.08/6.30 (cartprodmempaircEq) =>
% 24.08/6.30 ((
% 24.08/6.30 (cartprodfstpairEq) =>
% 24.08/6.30 ((
% 24.08/6.30 (cartprodsndpairEq) =>
% 24.08/6.30 ((
% 24.08/6.30 (cartprodpairsurjEq) =>
% 24.08/6.30 ((
% 24.08/6.30 (dpsetconstrI) =>
% 24.08/6.30 ((
% 24.08/6.30 (!!) @ (
% 24.08/6.30 (('#B') @ (
% 24.08/6.30 !!) @
% 24.08/6.30 (
% 24.08/6.30 (
% 24.08/6.30 ('#B') @ (
% 24.08/6.30 (
% 24.08/6.30 ('#B') @ (
% 24.08/6.30 !!))) @
% 24.08/6.30 (
% 24.08/6.30 (
% 24.08/6.30 ('#S') @ (
% 24.08/6.30 (
% 24.08/6.30 ('#B') @ (
% 24.08/6.30 '#S') @
% 24.08/6.30 (
% 24.08/6.30 (
% 24.08/6.30 ('#B') @ (
% 24.08/6.30 (
% 24.08/6.30 ('#B') @ (
% 24.08/6.30 '#C'))) @
% 24.08/6.30 (
% 24.08/6.30 (
% 24.08/6.30 ('#B') @ (
% 24.08/6.30 (
% 24.08/6.30 ('#B') @ (
% 24.08/6.30 (
% 24.08/6.30 ('#B') @ subset)))) @
% 24.08/6.30 dpsetconstr)))))) @
% 24.08/6.30 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.08/6.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl40])).
% 24.08/6.30 thf(zip_derived_cl52, plain,
% 24.08/6.30 (~ (((foundationAx) =>
% 24.08/6.30 (((wellorderingAx) =>
% 24.08/6.30 (((descrp) =>
% 24.08/6.30 (((dsetconstrI) =>
% 24.08/6.30 (((dsetconstrEL) =>
% 24.08/6.30 (((dsetconstrER) =>
% 24.08/6.30 (((exuE1) =>
% 24.08/6.30 (((prop2setE) =>
% 24.08/6.30 (((emptysetE) =>
% 24.08/6.30 (((emptysetimpfalse) =>
% 24.08/6.30 (((notinemptyset) =>
% 24.08/6.30 (((exuE3e) =>
% 24.08/6.30 (((setext) =>
% 24.08/6.30 (((emptyI) =>
% 24.08/6.30 (((noeltsimpempty) =>
% 24.08/6.30 (((setbeta) =>
% 24.08/6.30 (((nonemptyE1) =>
% 24.08/6.30 (((nonemptyI) =>
% 24.08/6.30 (((nonemptyI1) =>
% 24.08/6.30 (((setadjoinIL) =>
% 24.08/6.30 (((in @ emptyset @
% 24.08/6.30 (setadjoin @ emptyset @
% 24.08/6.30 emptyset)) =>
% 24.08/6.30 (((setadjoinIR) =>
% 24.08/6.30 (((setadjoinE) =>
% 24.08/6.30 (((setadjoinOr) =>
% 24.08/6.30 (((setoftrueEq) =>
% 24.08/6.30 (((powersetI) =>
% 24.08/6.30 (((emptyinPowerset) =>
% 24.08/6.30 (((emptyInPowerset) =>
% 24.08/6.30 (((powersetE) =>
% 24.08/6.30 (((setunionI) =>
% 24.08/6.30 ((
% 24.08/6.30 (setunionE) =>
% 24.08/6.30 ((
% 24.08/6.30 (subPowSU) =>
% 24.08/6.30 ((
% 24.08/6.30 (exuE2) =>
% 24.08/6.30 ((
% 24.08/6.30 (nonemptyImpWitness) =>
% 24.08/6.30 ((
% 24.08/6.30 (uniqinunit) =>
% 24.08/6.30 ((
% 24.08/6.30 (notinsingleton) =>
% 24.08/6.30 ((
% 24.08/6.30 (eqinunit) =>
% 24.08/6.30 ((
% 24.08/6.30 (singletonsswitch) =>
% 24.08/6.30 ((
% 24.08/6.30 (upairsetE) =>
% 24.08/6.30 ((
% 24.08/6.30 (upairsetIL) =>
% 24.08/6.30 ((
% 24.08/6.30 (upairsetIR) =>
% 24.08/6.30 ((
% 24.08/6.30 (emptyE1) =>
% 24.08/6.30 ((
% 24.08/6.30 (vacuousDall) =>
% 24.08/6.30 ((
% 24.08/6.30 (quantDeMorgan1) =>
% 24.08/6.30 ((
% 24.08/6.30 (quantDeMorgan2) =>
% 24.08/6.30 ((
% 24.08/6.30 (quantDeMorgan3) =>
% 24.08/6.30 ((
% 24.08/6.30 (quantDeMorgan4) =>
% 24.08/6.30 ((
% 24.08/6.30 (prop2setI) =>
% 24.08/6.30 ((
% 24.08/6.30 (prop2set2propI) =>
% 24.08/6.30 ((
% 24.08/6.30 (notdexE) =>
% 24.08/6.30 ((
% 24.08/6.30 (notdallE) =>
% 24.08/6.30 ((
% 24.08/6.30 (exuI1) =>
% 24.08/6.30 ((
% 24.08/6.30 (exuI3) =>
% 24.08/6.30 ((
% 24.08/6.30 (exuI2) =>
% 24.08/6.30 ((
% 24.08/6.30 (inCongP) =>
% 24.08/6.30 ((
% 24.08/6.30 (in__Cong) =>
% 24.08/6.30 ((
% 24.08/6.30 (exuE3u) =>
% 24.08/6.30 ((
% 24.08/6.30 (exu__Cong) =>
% 24.08/6.30 ((
% 24.08/6.30 (setadjoin__Cong) =>
% 24.08/6.30 ((
% 24.08/6.30 (powerset__Cong) =>
% 24.08/6.30 ((
% 24.08/6.30 (setunion__Cong) =>
% 24.08/6.30 ((
% 24.08/6.30 (exuEu) =>
% 24.08/6.30 ((
% 24.08/6.30 (descr__Cong) =>
% 24.08/6.30 ((
% 24.08/6.30 (dsetconstr__Cong) =>
% 24.08/6.30 ((
% 24.08/6.30 (subsetI1) =>
% 24.08/6.30 ((
% 24.08/6.30 (eqimpsubset2) =>
% 24.08/6.30 ((
% 24.08/6.30 (eqimpsubset1) =>
% 24.08/6.30 ((
% 24.08/6.30 (subsetI2) =>
% 24.08/6.30 ((
% 24.08/6.30 (emptysetsubset) =>
% 24.08/6.30 ((
% 24.08/6.30 (subsetE) =>
% 24.08/6.30 ((
% 24.08/6.30 (subsetE2) =>
% 24.08/6.30 ((
% 24.08/6.30 (notsubsetI) =>
% 24.08/6.30 ((
% 24.08/6.30 (notequalI1) =>
% 24.08/6.30 ((
% 24.08/6.30 (notequalI2) =>
% 24.08/6.30 ((
% 24.08/6.30 (subsetRefl) =>
% 24.08/6.30 ((
% 24.08/6.30 (subsetTrans) =>
% 24.08/6.30 ((
% 24.08/6.30 (setadjoinSub) =>
% 24.08/6.30 ((
% 24.08/6.30 (setadjoinSub2) =>
% 24.08/6.30 ((
% 24.08/6.30 (subset2powerset) =>
% 24.08/6.30 ((
% 24.08/6.30 (setextsub) =>
% 24.08/6.30 ((
% 24.08/6.30 (subsetemptysetimpeq) =>
% 24.08/6.30 ((
% 24.08/6.30 (powersetI1) =>
% 24.08/6.30 ((
% 24.08/6.30 (powersetE1) =>
% 24.08/6.30 ((
% 24.08/6.30 (inPowerset) =>
% 24.08/6.30 ((
% 24.08/6.30 (powersetsubset) =>
% 24.08/6.30 ((
% 24.08/6.30 (sepInPowerset) =>
% 24.08/6.30 ((
% 24.08/6.30 (sepSubset) =>
% 24.08/6.30 ((
% 24.08/6.30 (binunionIL) =>
% 24.08/6.30 ((
% 24.08/6.30 (upairset2IR) =>
% 24.08/6.30 ((
% 24.08/6.30 (binunionIR) =>
% 24.08/6.30 ((
% 24.08/6.30 (binunionEcases) =>
% 24.08/6.30 ((
% 24.08/6.30 (binunionE) =>
% 24.08/6.30 ((
% 24.08/6.30 (binunionLsub) =>
% 24.08/6.30 ((
% 24.08/6.30 (binunionRsub) =>
% 24.08/6.30 ((
% 24.08/6.30 (binintersectI) =>
% 24.08/6.30 ((
% 24.08/6.30 (binintersectSubset5) =>
% 24.08/6.30 ((
% 24.08/6.30 (binintersectEL) =>
% 24.08/6.30 ((
% 24.08/6.30 (binintersectLsub) =>
% 24.08/6.30 ((
% 24.08/6.30 (binintersectSubset2) =>
% 24.08/6.30 ((
% 24.08/6.30 (binintersectSubset3) =>
% 24.08/6.30 ((
% 24.08/6.30 (binintersectER) =>
% 24.08/6.30 ((
% 24.08/6.30 (disjointsetsI1) =>
% 24.08/6.30 ((
% 24.08/6.30 (binintersectRsub) =>
% 24.08/6.30 ((
% 24.08/6.30 (binintersectSubset4) =>
% 24.08/6.30 ((
% 24.08/6.30 (binintersectSubset1) =>
% 24.08/6.30 ((
% 24.08/6.30 (bs114d) =>
% 24.08/6.30 ((
% 24.08/6.30 (setminusI) =>
% 24.08/6.30 ((
% 24.08/6.30 (setminusEL) =>
% 24.08/6.30 ((
% 24.08/6.30 (setminusER) =>
% 24.08/6.30 ((
% 24.08/6.30 (setminusSubset2) =>
% 24.08/6.30 ((
% 24.08/6.30 (setminusERneg) =>
% 24.08/6.30 ((
% 24.08/6.30 (setminusELneg) =>
% 24.08/6.30 ((
% 24.08/6.30 (setminusILneg) =>
% 24.08/6.30 ((
% 24.08/6.30 (setminusIRneg) =>
% 24.08/6.30 ((
% 24.08/6.30 (setminusLsub) =>
% 24.08/6.30 ((
% 24.08/6.30 (setminusSubset1) =>
% 24.08/6.30 ((
% 24.08/6.30 (symdiffE) =>
% 24.08/6.30 ((
% 24.08/6.30 (symdiffI1) =>
% 24.08/6.30 ((
% 24.08/6.30 (symdiffI2) =>
% 24.08/6.30 ((
% 24.08/6.30 (symdiffIneg1) =>
% 24.08/6.30 ((
% 24.08/6.30 (symdiffIneg2) =>
% 24.08/6.30 ((
% 24.08/6.30 (secondinupair) =>
% 24.08/6.30 ((
% 24.08/6.30 (setukpairIL) =>
% 24.08/6.30 ((
% 24.08/6.30 (setukpairIR) =>
% 24.08/6.30 ((
% 24.08/6.30 (kpairiskpair) =>
% 24.08/6.30 ((
% 24.08/6.30 (kpairp) =>
% 24.08/6.30 ((
% 24.08/6.30 (singletonsubset) =>
% 24.08/6.30 ((
% 24.08/6.30 (singletoninpowerset) =>
% 24.08/6.30 ((
% 24.08/6.30 (singletoninpowunion) =>
% 24.08/6.30 ((
% 24.08/6.30 (upairset2E) =>
% 24.08/6.30 ((
% 24.08/6.30 (upairsubunion) =>
% 24.08/6.30 ((
% 24.08/6.30 (upairinpowunion) =>
% 24.08/6.30 ((
% 24.08/6.30 (ubforcartprodlem1) =>
% 24.08/6.30 ((
% 24.08/6.30 (ubforcartprodlem2) =>
% 24.08/6.30 ((
% 24.08/6.30 (ubforcartprodlem3) =>
% 24.08/6.30 ((
% 24.08/6.30 (cartprodpairin) =>
% 24.08/6.30 ((
% 24.08/6.30 (cartprodmempair1) =>
% 24.08/6.30 ((
% 24.08/6.30 (cartprodmempair) =>
% 24.08/6.30 ((
% 24.08/6.30 (setunionE2) =>
% 24.08/6.30 ((
% 24.08/6.30 (setunionsingleton1) =>
% 24.08/6.30 ((
% 24.08/6.30 (setunionsingleton2) =>
% 24.08/6.30 ((
% 24.08/6.30 (setunionsingleton) =>
% 24.08/6.30 ((
% 24.08/6.30 (singletonprop) =>
% 24.08/6.30 ((
% 24.08/6.30 (ex1E1) =>
% 24.08/6.30 ((
% 24.08/6.30 (ex1I) =>
% 24.08/6.30 ((
% 24.08/6.30 (ex1I2) =>
% 24.08/6.30 ((
% 24.08/6.30 (singletonsuniq) =>
% 24.08/6.30 ((
% 24.08/6.30 (setukpairinjL1) =>
% 24.08/6.30 ((
% 24.08/6.30 (kfstsingleton) =>
% 24.08/6.30 ((
% 24.08/6.30 (theprop) =>
% 24.08/6.30 ((
% 24.08/6.30 (kfstpairEq) =>
% 24.08/6.30 ((
% 24.08/6.30 (cartprodfstin) =>
% 24.08/6.30 ((
% 24.08/6.30 (setukpairinjL2) =>
% 24.08/6.30 ((
% 24.08/6.30 (setukpairinjL) =>
% 24.08/6.30 ((
% 24.08/6.30 (setukpairinjR11) =>
% 24.08/6.30 ((
% 24.08/6.30 (setukpairinjR12) =>
% 24.08/6.30 ((
% 24.08/6.30 (setukpairinjR1) =>
% 24.08/6.30 ((
% 24.08/6.30 (upairequniteq) =>
% 24.08/6.30 ((
% 24.08/6.30 (setukpairinjR2) =>
% 24.08/6.30 ((
% 24.08/6.30 (setukpairinjR) =>
% 24.08/6.30 ((
% 24.08/6.30 (ksndsingleton) =>
% 24.08/6.30 ((
% 24.08/6.30 (ksndpairEq) =>
% 24.08/6.30 ((
% 24.08/6.30 (kpairsurjEq) =>
% 24.08/6.30 ((
% 24.08/6.30 (cartprodsndin) =>
% 24.08/6.30 ((
% 24.08/6.30 (cartprodpairmemEL) =>
% 24.08/6.30 ((
% 24.08/6.30 (cartprodpairmemER) =>
% 24.08/6.30 ((
% 24.08/6.30 (cartprodmempaircEq) =>
% 24.08/6.30 ((
% 24.08/6.30 (cartprodfstpairEq) =>
% 24.08/6.30 ((
% 24.08/6.30 (cartprodsndpairEq) =>
% 24.08/6.30 ((
% 24.08/6.30 (cartprodpairsurjEq) =>
% 24.08/6.30 ((
% 24.08/6.30 (dpsetconstrI) =>
% 24.08/6.30 ((
% 24.08/6.30 (!!) @ (
% 24.08/6.30 (('#B') @ (
% 24.08/6.30 !!) @
% 24.08/6.30 (
% 24.08/6.30 (
% 24.08/6.30 ('#B') @ (
% 24.08/6.30 (
% 24.08/6.30 ('#B') @ (
% 24.08/6.30 !!))) @
% 24.08/6.30 (
% 24.08/6.30 (
% 24.08/6.30 ('#S') @ (
% 24.08/6.30 (
% 24.08/6.30 ('#B') @ (
% 24.08/6.30 '#S') @
% 24.08/6.30 (
% 24.08/6.30 (
% 24.08/6.30 ('#B') @ (
% 24.08/6.30 (
% 24.08/6.30 ('#B') @ (
% 24.08/6.30 '#C'))) @
% 24.08/6.30 (
% 24.08/6.30 (
% 24.08/6.30 ('#B') @ (
% 24.08/6.30 (
% 24.08/6.30 ('#B') @ (
% 24.08/6.30 (
% 24.08/6.30 ('#B') @ subset)))) @
% 24.08/6.30 dpsetconstr)))))) @
% 24.08/6.30 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.08/6.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl46])).
% 24.08/6.30 thf(zip_derived_cl58, plain,
% 24.08/6.30 (~ (((wellorderingAx) =>
% 24.08/6.30 (((descrp) =>
% 24.08/6.30 (((dsetconstrI) =>
% 24.08/6.30 (((dsetconstrEL) =>
% 24.08/6.30 (((dsetconstrER) =>
% 24.08/6.30 (((exuE1) =>
% 24.08/6.30 (((prop2setE) =>
% 24.08/6.30 (((emptysetE) =>
% 24.08/6.30 (((emptysetimpfalse) =>
% 24.08/6.30 (((notinemptyset) =>
% 24.08/6.30 (((exuE3e) =>
% 24.08/6.30 (((setext) =>
% 24.08/6.30 (((emptyI) =>
% 24.08/6.30 (((noeltsimpempty) =>
% 24.08/6.30 (((setbeta) =>
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% 24.08/6.30 (((nonemptyI) =>
% 24.08/6.30 (((nonemptyI1) =>
% 24.08/6.30 (((setadjoinIL) =>
% 24.08/6.30 (((in @ emptyset @
% 24.08/6.30 (setadjoin @ emptyset @
% 24.08/6.30 emptyset)) =>
% 24.08/6.30 (((setadjoinIR) =>
% 24.08/6.30 (((setadjoinE) =>
% 24.08/6.30 (((setadjoinOr) =>
% 24.08/6.30 (((setoftrueEq) =>
% 24.08/6.30 (((powersetI) =>
% 24.08/6.30 (((emptyinPowerset) =>
% 24.08/6.30 (((emptyInPowerset) =>
% 24.08/6.30 (((powersetE) =>
% 24.08/6.30 (((setunionI) =>
% 24.08/6.30 (((setunionE) =>
% 24.08/6.30 ((
% 24.08/6.30 (subPowSU) =>
% 24.08/6.30 ((
% 24.08/6.30 (exuE2) =>
% 24.08/6.30 ((
% 24.08/6.30 (nonemptyImpWitness) =>
% 24.08/6.30 ((
% 24.08/6.30 (uniqinunit) =>
% 24.08/6.30 ((
% 24.08/6.30 (notinsingleton) =>
% 24.08/6.30 ((
% 24.08/6.30 (eqinunit) =>
% 24.08/6.30 ((
% 24.08/6.30 (singletonsswitch) =>
% 24.08/6.30 ((
% 24.08/6.30 (upairsetE) =>
% 24.08/6.30 ((
% 24.08/6.30 (upairsetIL) =>
% 24.08/6.30 ((
% 24.08/6.30 (upairsetIR) =>
% 24.08/6.30 ((
% 24.08/6.30 (emptyE1) =>
% 24.08/6.30 ((
% 24.08/6.30 (vacuousDall) =>
% 24.08/6.30 ((
% 24.08/6.30 (quantDeMorgan1) =>
% 24.08/6.30 ((
% 24.08/6.30 (quantDeMorgan2) =>
% 24.08/6.30 ((
% 24.08/6.30 (quantDeMorgan3) =>
% 24.08/6.30 ((
% 24.08/6.30 (quantDeMorgan4) =>
% 24.08/6.30 ((
% 24.08/6.30 (prop2setI) =>
% 24.08/6.30 ((
% 24.08/6.30 (prop2set2propI) =>
% 24.08/6.30 ((
% 24.08/6.30 (notdexE) =>
% 24.08/6.30 ((
% 24.08/6.30 (notdallE) =>
% 24.08/6.30 ((
% 24.08/6.30 (exuI1) =>
% 24.08/6.30 ((
% 24.08/6.30 (exuI3) =>
% 24.08/6.30 ((
% 24.08/6.30 (exuI2) =>
% 24.08/6.30 ((
% 24.08/6.30 (inCongP) =>
% 24.08/6.30 ((
% 24.08/6.30 (in__Cong) =>
% 24.08/6.30 ((
% 24.08/6.30 (exuE3u) =>
% 24.08/6.30 ((
% 24.08/6.30 (exu__Cong) =>
% 24.08/6.30 ((
% 24.08/6.30 (setadjoin__Cong) =>
% 24.08/6.30 ((
% 24.08/6.30 (powerset__Cong) =>
% 24.08/6.30 ((
% 24.08/6.30 (setunion__Cong) =>
% 24.08/6.30 ((
% 24.08/6.30 (exuEu) =>
% 24.08/6.30 ((
% 24.08/6.30 (descr__Cong) =>
% 24.08/6.30 ((
% 24.08/6.30 (dsetconstr__Cong) =>
% 24.08/6.30 ((
% 24.08/6.30 (subsetI1) =>
% 24.08/6.30 ((
% 24.08/6.30 (eqimpsubset2) =>
% 24.08/6.30 ((
% 24.08/6.30 (eqimpsubset1) =>
% 24.08/6.30 ((
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% 24.08/6.30 ((
% 24.08/6.30 (emptysetsubset) =>
% 24.08/6.30 ((
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% 24.08/6.30 ((
% 24.08/6.30 (subsetE2) =>
% 24.08/6.30 ((
% 24.08/6.30 (notsubsetI) =>
% 24.08/6.30 ((
% 24.08/6.30 (notequalI1) =>
% 24.08/6.30 ((
% 24.08/6.30 (notequalI2) =>
% 24.08/6.30 ((
% 24.08/6.30 (subsetRefl) =>
% 24.08/6.30 ((
% 24.08/6.30 (subsetTrans) =>
% 24.08/6.30 ((
% 24.08/6.30 (setadjoinSub) =>
% 24.08/6.30 ((
% 24.08/6.30 (setadjoinSub2) =>
% 24.08/6.30 ((
% 24.08/6.30 (subset2powerset) =>
% 24.08/6.30 ((
% 24.08/6.30 (setextsub) =>
% 24.08/6.30 ((
% 24.08/6.30 (subsetemptysetimpeq) =>
% 24.08/6.30 ((
% 24.08/6.30 (powersetI1) =>
% 24.08/6.30 ((
% 24.08/6.30 (powersetE1) =>
% 24.08/6.30 ((
% 24.08/6.30 (inPowerset) =>
% 24.08/6.30 ((
% 24.08/6.30 (powersetsubset) =>
% 24.08/6.30 ((
% 24.08/6.30 (sepInPowerset) =>
% 24.08/6.30 ((
% 24.08/6.30 (sepSubset) =>
% 24.08/6.30 ((
% 24.08/6.30 (binunionIL) =>
% 24.08/6.30 ((
% 24.08/6.30 (upairset2IR) =>
% 24.08/6.30 ((
% 24.08/6.30 (binunionIR) =>
% 24.08/6.30 ((
% 24.08/6.30 (binunionEcases) =>
% 24.08/6.30 ((
% 24.08/6.30 (binunionE) =>
% 24.08/6.30 ((
% 24.08/6.30 (binunionLsub) =>
% 24.08/6.30 ((
% 24.08/6.30 (binunionRsub) =>
% 24.08/6.30 ((
% 24.08/6.30 (binintersectI) =>
% 24.08/6.30 ((
% 24.08/6.30 (binintersectSubset5) =>
% 24.08/6.30 ((
% 24.08/6.30 (binintersectEL) =>
% 24.08/6.30 ((
% 24.08/6.30 (binintersectLsub) =>
% 24.08/6.30 ((
% 24.08/6.30 (binintersectSubset2) =>
% 24.08/6.30 ((
% 24.08/6.30 (binintersectSubset3) =>
% 24.08/6.30 ((
% 24.08/6.30 (binintersectER) =>
% 24.08/6.30 ((
% 24.08/6.30 (disjointsetsI1) =>
% 24.08/6.30 ((
% 24.08/6.30 (binintersectRsub) =>
% 24.08/6.30 ((
% 24.08/6.30 (binintersectSubset4) =>
% 24.08/6.30 ((
% 24.08/6.30 (binintersectSubset1) =>
% 24.08/6.30 ((
% 24.08/6.30 (bs114d) =>
% 24.08/6.30 ((
% 24.08/6.30 (setminusI) =>
% 24.08/6.30 ((
% 24.08/6.30 (setminusEL) =>
% 24.08/6.30 ((
% 24.08/6.30 (setminusER) =>
% 24.08/6.30 ((
% 24.08/6.30 (setminusSubset2) =>
% 24.08/6.30 ((
% 24.08/6.30 (setminusERneg) =>
% 24.08/6.30 ((
% 24.08/6.30 (setminusELneg) =>
% 24.08/6.30 ((
% 24.08/6.30 (setminusILneg) =>
% 24.08/6.30 ((
% 24.08/6.30 (setminusIRneg) =>
% 24.08/6.30 ((
% 24.08/6.30 (setminusLsub) =>
% 24.08/6.30 ((
% 24.08/6.30 (setminusSubset1) =>
% 24.08/6.30 ((
% 24.08/6.30 (symdiffE) =>
% 24.08/6.30 ((
% 24.08/6.30 (symdiffI1) =>
% 24.08/6.30 ((
% 24.08/6.30 (symdiffI2) =>
% 24.08/6.30 ((
% 24.08/6.30 (symdiffIneg1) =>
% 24.08/6.30 ((
% 24.08/6.30 (symdiffIneg2) =>
% 24.08/6.30 ((
% 24.08/6.30 (secondinupair) =>
% 24.08/6.30 ((
% 24.08/6.30 (setukpairIL) =>
% 24.08/6.30 ((
% 24.08/6.30 (setukpairIR) =>
% 24.08/6.30 ((
% 24.08/6.30 (kpairiskpair) =>
% 24.08/6.30 ((
% 24.08/6.30 (kpairp) =>
% 24.08/6.30 ((
% 24.08/6.30 (singletonsubset) =>
% 24.08/6.30 ((
% 24.08/6.30 (singletoninpowerset) =>
% 24.08/6.30 ((
% 24.08/6.30 (singletoninpowunion) =>
% 24.08/6.30 ((
% 24.08/6.30 (upairset2E) =>
% 24.08/6.30 ((
% 24.08/6.30 (upairsubunion) =>
% 24.08/6.30 ((
% 24.08/6.30 (upairinpowunion) =>
% 24.08/6.30 ((
% 24.08/6.30 (ubforcartprodlem1) =>
% 24.08/6.30 ((
% 24.08/6.30 (ubforcartprodlem2) =>
% 24.08/6.30 ((
% 24.08/6.30 (ubforcartprodlem3) =>
% 24.08/6.30 ((
% 24.08/6.30 (cartprodpairin) =>
% 24.08/6.30 ((
% 24.08/6.30 (cartprodmempair1) =>
% 24.08/6.30 ((
% 24.08/6.30 (cartprodmempair) =>
% 24.08/6.30 ((
% 24.08/6.30 (setunionE2) =>
% 24.08/6.30 ((
% 24.08/6.30 (setunionsingleton1) =>
% 24.08/6.30 ((
% 24.08/6.30 (setunionsingleton2) =>
% 24.08/6.30 ((
% 24.08/6.30 (setunionsingleton) =>
% 24.08/6.30 ((
% 24.08/6.30 (singletonprop) =>
% 24.08/6.30 ((
% 24.08/6.30 (ex1E1) =>
% 24.08/6.30 ((
% 24.08/6.30 (ex1I) =>
% 24.08/6.30 ((
% 24.08/6.30 (ex1I2) =>
% 24.08/6.30 ((
% 24.08/6.30 (singletonsuniq) =>
% 24.08/6.30 ((
% 24.08/6.30 (setukpairinjL1) =>
% 24.08/6.30 ((
% 24.08/6.30 (kfstsingleton) =>
% 24.08/6.30 ((
% 24.08/6.30 (theprop) =>
% 24.08/6.30 ((
% 24.08/6.30 (kfstpairEq) =>
% 24.08/6.30 ((
% 24.08/6.30 (cartprodfstin) =>
% 24.08/6.30 ((
% 24.08/6.30 (setukpairinjL2) =>
% 24.08/6.30 ((
% 24.08/6.30 (setukpairinjL) =>
% 24.08/6.30 ((
% 24.08/6.30 (setukpairinjR11) =>
% 24.08/6.30 ((
% 24.08/6.30 (setukpairinjR12) =>
% 24.08/6.30 ((
% 24.08/6.30 (setukpairinjR1) =>
% 24.08/6.30 ((
% 24.08/6.30 (upairequniteq) =>
% 24.08/6.30 ((
% 24.08/6.30 (setukpairinjR2) =>
% 24.08/6.30 ((
% 24.08/6.30 (setukpairinjR) =>
% 24.08/6.30 ((
% 24.08/6.30 (ksndsingleton) =>
% 24.08/6.30 ((
% 24.08/6.30 (ksndpairEq) =>
% 24.08/6.30 ((
% 24.08/6.30 (kpairsurjEq) =>
% 24.08/6.30 ((
% 24.08/6.30 (cartprodsndin) =>
% 24.08/6.30 ((
% 24.08/6.30 (cartprodpairmemEL) =>
% 24.08/6.30 ((
% 24.08/6.30 (cartprodpairmemER) =>
% 24.08/6.30 ((
% 24.08/6.30 (cartprodmempaircEq) =>
% 24.08/6.30 ((
% 24.08/6.30 (cartprodfstpairEq) =>
% 24.08/6.30 ((
% 24.08/6.30 (cartprodsndpairEq) =>
% 24.08/6.30 ((
% 24.08/6.30 (cartprodpairsurjEq) =>
% 24.08/6.30 ((
% 24.08/6.30 (dpsetconstrI) =>
% 24.08/6.30 ((
% 24.08/6.30 (!!) @ (
% 24.08/6.30 (('#B') @ (
% 24.08/6.30 !!) @
% 24.08/6.30 (
% 24.08/6.30 (
% 24.08/6.30 ('#B') @ (
% 24.08/6.30 (
% 24.08/6.30 ('#B') @ (
% 24.08/6.30 !!))) @
% 24.08/6.30 (
% 24.08/6.30 (
% 24.08/6.30 ('#S') @ (
% 24.08/6.30 (
% 24.08/6.30 ('#B') @ (
% 24.08/6.30 '#S') @
% 24.08/6.30 (
% 24.08/6.30 (
% 24.08/6.30 ('#B') @ (
% 24.33/6.31 (
% 24.33/6.31 ('#B') @ (
% 24.33/6.31 '#C'))) @
% 24.33/6.31 (
% 24.33/6.31 (
% 24.33/6.31 ('#B') @ (
% 24.33/6.31 (
% 24.33/6.31 ('#B') @ (
% 24.33/6.31 (
% 24.33/6.31 ('#B') @ subset)))) @
% 24.33/6.31 dpsetconstr)))))) @
% 24.33/6.31 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.33/6.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl52])).
% 24.33/6.31 thf(zip_derived_cl64, plain,
% 24.33/6.31 (~ (((descrp) =>
% 24.33/6.31 (((dsetconstrI) =>
% 24.33/6.31 (((dsetconstrEL) =>
% 24.33/6.31 (((dsetconstrER) =>
% 24.33/6.31 (((exuE1) =>
% 24.33/6.31 (((prop2setE) =>
% 24.33/6.31 (((emptysetE) =>
% 24.33/6.31 (((emptysetimpfalse) =>
% 24.33/6.31 (((notinemptyset) =>
% 24.33/6.31 (((exuE3e) =>
% 24.33/6.31 (((setext) =>
% 24.33/6.31 (((emptyI) =>
% 24.33/6.31 (((noeltsimpempty) =>
% 24.33/6.31 (((setbeta) =>
% 24.33/6.31 (((nonemptyE1) =>
% 24.33/6.31 (((nonemptyI) =>
% 24.33/6.31 (((nonemptyI1) =>
% 24.33/6.31 (((setadjoinIL) =>
% 24.33/6.31 (((in @ emptyset @
% 24.33/6.31 (setadjoin @ emptyset @ emptyset)) =>
% 24.33/6.31 (((setadjoinIR) =>
% 24.33/6.31 (((setadjoinE) =>
% 24.33/6.31 (((setadjoinOr) =>
% 24.33/6.31 (((setoftrueEq) =>
% 24.33/6.31 (((powersetI) =>
% 24.33/6.31 (((emptyinPowerset) =>
% 24.33/6.31 (((emptyInPowerset) =>
% 24.33/6.31 (((powersetE) =>
% 24.33/6.31 (((setunionI) =>
% 24.33/6.31 (((setunionE) =>
% 24.33/6.31 (((subPowSU) =>
% 24.33/6.31 ((
% 24.33/6.31 (exuE2) =>
% 24.33/6.31 ((
% 24.33/6.31 (nonemptyImpWitness) =>
% 24.33/6.31 ((
% 24.33/6.31 (uniqinunit) =>
% 24.33/6.31 ((
% 24.33/6.31 (notinsingleton) =>
% 24.33/6.31 ((
% 24.33/6.31 (eqinunit) =>
% 24.33/6.31 ((
% 24.33/6.31 (singletonsswitch) =>
% 24.33/6.31 ((
% 24.33/6.31 (upairsetE) =>
% 24.33/6.31 ((
% 24.33/6.31 (upairsetIL) =>
% 24.33/6.31 ((
% 24.33/6.31 (upairsetIR) =>
% 24.33/6.31 ((
% 24.33/6.31 (emptyE1) =>
% 24.33/6.31 ((
% 24.33/6.31 (vacuousDall) =>
% 24.33/6.31 ((
% 24.33/6.31 (quantDeMorgan1) =>
% 24.33/6.31 ((
% 24.33/6.31 (quantDeMorgan2) =>
% 24.33/6.31 ((
% 24.33/6.31 (quantDeMorgan3) =>
% 24.33/6.31 ((
% 24.33/6.31 (quantDeMorgan4) =>
% 24.33/6.31 ((
% 24.33/6.31 (prop2setI) =>
% 24.33/6.31 ((
% 24.33/6.31 (prop2set2propI) =>
% 24.33/6.31 ((
% 24.33/6.31 (notdexE) =>
% 24.33/6.31 ((
% 24.33/6.31 (notdallE) =>
% 24.33/6.31 ((
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% 24.33/6.31 ((
% 24.33/6.31 (exuI3) =>
% 24.33/6.31 ((
% 24.33/6.31 (exuI2) =>
% 24.33/6.31 ((
% 24.33/6.31 (inCongP) =>
% 24.33/6.31 ((
% 24.33/6.31 (in__Cong) =>
% 24.33/6.31 ((
% 24.33/6.31 (exuE3u) =>
% 24.33/6.31 ((
% 24.33/6.31 (exu__Cong) =>
% 24.33/6.31 ((
% 24.33/6.31 (setadjoin__Cong) =>
% 24.33/6.31 ((
% 24.33/6.31 (powerset__Cong) =>
% 24.33/6.31 ((
% 24.33/6.31 (setunion__Cong) =>
% 24.33/6.31 ((
% 24.33/6.31 (exuEu) =>
% 24.33/6.31 ((
% 24.33/6.31 (descr__Cong) =>
% 24.33/6.31 ((
% 24.33/6.31 (dsetconstr__Cong) =>
% 24.33/6.31 ((
% 24.33/6.31 (subsetI1) =>
% 24.33/6.31 ((
% 24.33/6.31 (eqimpsubset2) =>
% 24.33/6.31 ((
% 24.33/6.31 (eqimpsubset1) =>
% 24.33/6.31 ((
% 24.33/6.31 (subsetI2) =>
% 24.33/6.31 ((
% 24.33/6.31 (emptysetsubset) =>
% 24.33/6.31 ((
% 24.33/6.31 (subsetE) =>
% 24.33/6.31 ((
% 24.33/6.31 (subsetE2) =>
% 24.33/6.31 ((
% 24.33/6.31 (notsubsetI) =>
% 24.33/6.31 ((
% 24.33/6.31 (notequalI1) =>
% 24.33/6.31 ((
% 24.33/6.31 (notequalI2) =>
% 24.33/6.31 ((
% 24.33/6.31 (subsetRefl) =>
% 24.33/6.31 ((
% 24.33/6.31 (subsetTrans) =>
% 24.33/6.31 ((
% 24.33/6.31 (setadjoinSub) =>
% 24.33/6.31 ((
% 24.33/6.31 (setadjoinSub2) =>
% 24.33/6.31 ((
% 24.33/6.31 (subset2powerset) =>
% 24.33/6.31 ((
% 24.33/6.31 (setextsub) =>
% 24.33/6.31 ((
% 24.33/6.31 (subsetemptysetimpeq) =>
% 24.33/6.31 ((
% 24.33/6.31 (powersetI1) =>
% 24.33/6.31 ((
% 24.33/6.31 (powersetE1) =>
% 24.33/6.31 ((
% 24.33/6.31 (inPowerset) =>
% 24.33/6.31 ((
% 24.33/6.31 (powersetsubset) =>
% 24.33/6.31 ((
% 24.33/6.31 (sepInPowerset) =>
% 24.33/6.31 ((
% 24.33/6.31 (sepSubset) =>
% 24.33/6.31 ((
% 24.33/6.31 (binunionIL) =>
% 24.33/6.31 ((
% 24.33/6.31 (upairset2IR) =>
% 24.33/6.31 ((
% 24.33/6.31 (binunionIR) =>
% 24.33/6.31 ((
% 24.33/6.31 (binunionEcases) =>
% 24.33/6.31 ((
% 24.33/6.31 (binunionE) =>
% 24.33/6.31 ((
% 24.33/6.31 (binunionLsub) =>
% 24.33/6.31 ((
% 24.33/6.31 (binunionRsub) =>
% 24.33/6.31 ((
% 24.33/6.31 (binintersectI) =>
% 24.33/6.31 ((
% 24.33/6.31 (binintersectSubset5) =>
% 24.33/6.31 ((
% 24.33/6.31 (binintersectEL) =>
% 24.33/6.31 ((
% 24.33/6.31 (binintersectLsub) =>
% 24.33/6.31 ((
% 24.33/6.31 (binintersectSubset2) =>
% 24.33/6.31 ((
% 24.33/6.31 (binintersectSubset3) =>
% 24.33/6.31 ((
% 24.33/6.31 (binintersectER) =>
% 24.33/6.31 ((
% 24.33/6.31 (disjointsetsI1) =>
% 24.33/6.31 ((
% 24.33/6.31 (binintersectRsub) =>
% 24.33/6.31 ((
% 24.33/6.31 (binintersectSubset4) =>
% 24.33/6.31 ((
% 24.33/6.31 (binintersectSubset1) =>
% 24.33/6.31 ((
% 24.33/6.31 (bs114d) =>
% 24.33/6.31 ((
% 24.33/6.31 (setminusI) =>
% 24.33/6.31 ((
% 24.33/6.31 (setminusEL) =>
% 24.33/6.31 ((
% 24.33/6.31 (setminusER) =>
% 24.33/6.31 ((
% 24.33/6.31 (setminusSubset2) =>
% 24.33/6.31 ((
% 24.33/6.31 (setminusERneg) =>
% 24.33/6.31 ((
% 24.33/6.31 (setminusELneg) =>
% 24.33/6.31 ((
% 24.33/6.31 (setminusILneg) =>
% 24.33/6.31 ((
% 24.33/6.31 (setminusIRneg) =>
% 24.33/6.31 ((
% 24.33/6.31 (setminusLsub) =>
% 24.33/6.31 ((
% 24.33/6.31 (setminusSubset1) =>
% 24.33/6.31 ((
% 24.33/6.31 (symdiffE) =>
% 24.33/6.31 ((
% 24.33/6.31 (symdiffI1) =>
% 24.33/6.31 ((
% 24.33/6.31 (symdiffI2) =>
% 24.33/6.31 ((
% 24.33/6.31 (symdiffIneg1) =>
% 24.33/6.31 ((
% 24.33/6.31 (symdiffIneg2) =>
% 24.33/6.31 ((
% 24.33/6.31 (secondinupair) =>
% 24.33/6.31 ((
% 24.33/6.31 (setukpairIL) =>
% 24.33/6.31 ((
% 24.33/6.31 (setukpairIR) =>
% 24.33/6.31 ((
% 24.33/6.31 (kpairiskpair) =>
% 24.33/6.31 ((
% 24.33/6.31 (kpairp) =>
% 24.33/6.31 ((
% 24.33/6.31 (singletonsubset) =>
% 24.33/6.31 ((
% 24.33/6.31 (singletoninpowerset) =>
% 24.33/6.31 ((
% 24.33/6.31 (singletoninpowunion) =>
% 24.33/6.31 ((
% 24.33/6.31 (upairset2E) =>
% 24.33/6.31 ((
% 24.33/6.31 (upairsubunion) =>
% 24.33/6.31 ((
% 24.33/6.31 (upairinpowunion) =>
% 24.33/6.31 ((
% 24.33/6.31 (ubforcartprodlem1) =>
% 24.33/6.31 ((
% 24.33/6.31 (ubforcartprodlem2) =>
% 24.33/6.31 ((
% 24.33/6.31 (ubforcartprodlem3) =>
% 24.33/6.31 ((
% 24.33/6.31 (cartprodpairin) =>
% 24.33/6.31 ((
% 24.33/6.31 (cartprodmempair1) =>
% 24.33/6.31 ((
% 24.33/6.31 (cartprodmempair) =>
% 24.33/6.31 ((
% 24.33/6.31 (setunionE2) =>
% 24.33/6.31 ((
% 24.33/6.31 (setunionsingleton1) =>
% 24.33/6.31 ((
% 24.33/6.31 (setunionsingleton2) =>
% 24.33/6.31 ((
% 24.33/6.31 (setunionsingleton) =>
% 24.33/6.31 ((
% 24.33/6.31 (singletonprop) =>
% 24.33/6.31 ((
% 24.33/6.31 (ex1E1) =>
% 24.33/6.31 ((
% 24.33/6.31 (ex1I) =>
% 24.33/6.31 ((
% 24.33/6.31 (ex1I2) =>
% 24.33/6.31 ((
% 24.33/6.31 (singletonsuniq) =>
% 24.33/6.31 ((
% 24.33/6.31 (setukpairinjL1) =>
% 24.33/6.31 ((
% 24.33/6.31 (kfstsingleton) =>
% 24.33/6.31 ((
% 24.33/6.31 (theprop) =>
% 24.33/6.31 ((
% 24.33/6.31 (kfstpairEq) =>
% 24.33/6.31 ((
% 24.33/6.31 (cartprodfstin) =>
% 24.33/6.31 ((
% 24.33/6.31 (setukpairinjL2) =>
% 24.33/6.31 ((
% 24.33/6.31 (setukpairinjL) =>
% 24.33/6.31 ((
% 24.33/6.31 (setukpairinjR11) =>
% 24.33/6.31 ((
% 24.33/6.31 (setukpairinjR12) =>
% 24.33/6.31 ((
% 24.33/6.31 (setukpairinjR1) =>
% 24.33/6.31 ((
% 24.33/6.31 (upairequniteq) =>
% 24.33/6.31 ((
% 24.33/6.31 (setukpairinjR2) =>
% 24.33/6.31 ((
% 24.33/6.31 (setukpairinjR) =>
% 24.33/6.31 ((
% 24.33/6.31 (ksndsingleton) =>
% 24.33/6.31 ((
% 24.33/6.31 (ksndpairEq) =>
% 24.33/6.31 ((
% 24.33/6.31 (kpairsurjEq) =>
% 24.33/6.31 ((
% 24.33/6.31 (cartprodsndin) =>
% 24.33/6.31 ((
% 24.33/6.31 (cartprodpairmemEL) =>
% 24.33/6.31 ((
% 24.33/6.31 (cartprodpairmemER) =>
% 24.33/6.31 ((
% 24.33/6.31 (cartprodmempaircEq) =>
% 24.33/6.31 ((
% 24.33/6.31 (cartprodfstpairEq) =>
% 24.33/6.31 ((
% 24.33/6.31 (cartprodsndpairEq) =>
% 24.33/6.31 ((
% 24.33/6.31 (cartprodpairsurjEq) =>
% 24.33/6.31 ((
% 24.33/6.31 (dpsetconstrI) =>
% 24.33/6.31 ((
% 24.33/6.31 (!!) @ (
% 24.33/6.31 (('#B') @ (
% 24.33/6.31 !!) @
% 24.33/6.31 (
% 24.33/6.31 (
% 24.33/6.31 ('#B') @ (
% 24.33/6.31 (
% 24.33/6.31 ('#B') @ (
% 24.33/6.31 !!))) @
% 24.33/6.31 (
% 24.33/6.31 (
% 24.33/6.31 ('#S') @ (
% 24.33/6.31 (
% 24.33/6.31 ('#B') @ (
% 24.33/6.31 '#S') @
% 24.33/6.31 (
% 24.33/6.31 (
% 24.33/6.31 ('#B') @ (
% 24.33/6.31 (
% 24.33/6.31 ('#B') @ (
% 24.33/6.31 '#C'))) @
% 24.33/6.31 (
% 24.33/6.31 (
% 24.33/6.31 ('#B') @ (
% 24.33/6.31 (
% 24.33/6.31 ('#B') @ (
% 24.33/6.31 (
% 24.33/6.31 ('#B') @ subset)))) @
% 24.33/6.31 dpsetconstr)))))) @
% 24.33/6.31 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.33/6.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl58])).
% 24.33/6.31 thf(zip_derived_cl71, plain,
% 24.33/6.31 (~ (((dsetconstrI) =>
% 24.33/6.31 (((dsetconstrEL) =>
% 24.33/6.31 (((dsetconstrER) =>
% 24.33/6.31 (((exuE1) =>
% 24.33/6.31 (((prop2setE) =>
% 24.33/6.31 (((emptysetE) =>
% 24.33/6.31 (((emptysetimpfalse) =>
% 24.33/6.31 (((notinemptyset) =>
% 24.33/6.31 (((exuE3e) =>
% 24.33/6.31 (((setext) =>
% 24.33/6.31 (((emptyI) =>
% 24.33/6.31 (((noeltsimpempty) =>
% 24.33/6.31 (((setbeta) =>
% 24.33/6.31 (((nonemptyE1) =>
% 24.33/6.31 (((nonemptyI) =>
% 24.33/6.31 (((nonemptyI1) =>
% 24.33/6.31 (((setadjoinIL) =>
% 24.33/6.31 (((in @ emptyset @
% 24.33/6.31 (setadjoin @ emptyset @ emptyset)) =>
% 24.33/6.31 (((setadjoinIR) =>
% 24.33/6.31 (((setadjoinE) =>
% 24.33/6.31 (((setadjoinOr) =>
% 24.33/6.31 (((setoftrueEq) =>
% 24.33/6.31 (((powersetI) =>
% 24.33/6.31 (((emptyinPowerset) =>
% 24.33/6.31 (((emptyInPowerset) =>
% 24.33/6.31 (((powersetE) =>
% 24.33/6.31 (((setunionI) =>
% 24.33/6.31 (((setunionE) =>
% 24.33/6.31 (((subPowSU) =>
% 24.33/6.31 (((exuE2) =>
% 24.33/6.31 ((
% 24.33/6.31 (nonemptyImpWitness) =>
% 24.33/6.31 ((
% 24.33/6.31 (uniqinunit) =>
% 24.33/6.31 ((
% 24.33/6.31 (notinsingleton) =>
% 24.33/6.31 ((
% 24.33/6.31 (eqinunit) =>
% 24.33/6.31 ((
% 24.33/6.31 (singletonsswitch) =>
% 24.33/6.31 ((
% 24.33/6.31 (upairsetE) =>
% 24.33/6.31 ((
% 24.33/6.31 (upairsetIL) =>
% 24.33/6.31 ((
% 24.33/6.31 (upairsetIR) =>
% 24.33/6.31 ((
% 24.33/6.31 (emptyE1) =>
% 24.33/6.31 ((
% 24.33/6.31 (vacuousDall) =>
% 24.33/6.31 ((
% 24.33/6.31 (quantDeMorgan1) =>
% 24.33/6.31 ((
% 24.33/6.31 (quantDeMorgan2) =>
% 24.33/6.31 ((
% 24.33/6.31 (quantDeMorgan3) =>
% 24.33/6.31 ((
% 24.33/6.31 (quantDeMorgan4) =>
% 24.33/6.31 ((
% 24.33/6.31 (prop2setI) =>
% 24.33/6.31 ((
% 24.33/6.31 (prop2set2propI) =>
% 24.33/6.31 ((
% 24.33/6.31 (notdexE) =>
% 24.33/6.31 ((
% 24.33/6.31 (notdallE) =>
% 24.33/6.31 ((
% 24.33/6.31 (exuI1) =>
% 24.33/6.31 ((
% 24.33/6.31 (exuI3) =>
% 24.33/6.31 ((
% 24.33/6.31 (exuI2) =>
% 24.33/6.31 ((
% 24.33/6.31 (inCongP) =>
% 24.33/6.31 ((
% 24.33/6.31 (in__Cong) =>
% 24.33/6.31 ((
% 24.33/6.31 (exuE3u) =>
% 24.33/6.31 ((
% 24.33/6.31 (exu__Cong) =>
% 24.33/6.31 ((
% 24.33/6.31 (setadjoin__Cong) =>
% 24.33/6.31 ((
% 24.33/6.31 (powerset__Cong) =>
% 24.33/6.31 ((
% 24.33/6.31 (setunion__Cong) =>
% 24.33/6.31 ((
% 24.33/6.31 (exuEu) =>
% 24.33/6.31 ((
% 24.33/6.31 (descr__Cong) =>
% 24.33/6.31 ((
% 24.33/6.31 (dsetconstr__Cong) =>
% 24.33/6.31 ((
% 24.33/6.31 (subsetI1) =>
% 24.33/6.31 ((
% 24.33/6.31 (eqimpsubset2) =>
% 24.33/6.31 ((
% 24.33/6.31 (eqimpsubset1) =>
% 24.33/6.31 ((
% 24.33/6.31 (subsetI2) =>
% 24.33/6.31 ((
% 24.33/6.31 (emptysetsubset) =>
% 24.33/6.31 ((
% 24.33/6.31 (subsetE) =>
% 24.33/6.31 ((
% 24.33/6.31 (subsetE2) =>
% 24.33/6.31 ((
% 24.33/6.31 (notsubsetI) =>
% 24.33/6.31 ((
% 24.33/6.31 (notequalI1) =>
% 24.33/6.31 ((
% 24.33/6.31 (notequalI2) =>
% 24.33/6.31 ((
% 24.33/6.31 (subsetRefl) =>
% 24.33/6.31 ((
% 24.33/6.31 (subsetTrans) =>
% 24.33/6.31 ((
% 24.33/6.31 (setadjoinSub) =>
% 24.33/6.31 ((
% 24.33/6.31 (setadjoinSub2) =>
% 24.33/6.31 ((
% 24.33/6.31 (subset2powerset) =>
% 24.33/6.31 ((
% 24.33/6.31 (setextsub) =>
% 24.33/6.31 ((
% 24.33/6.31 (subsetemptysetimpeq) =>
% 24.33/6.31 ((
% 24.33/6.31 (powersetI1) =>
% 24.33/6.31 ((
% 24.33/6.31 (powersetE1) =>
% 24.33/6.31 ((
% 24.33/6.31 (inPowerset) =>
% 24.33/6.31 ((
% 24.33/6.31 (powersetsubset) =>
% 24.33/6.31 ((
% 24.33/6.31 (sepInPowerset) =>
% 24.33/6.31 ((
% 24.33/6.31 (sepSubset) =>
% 24.33/6.31 ((
% 24.33/6.31 (binunionIL) =>
% 24.33/6.31 ((
% 24.33/6.31 (upairset2IR) =>
% 24.33/6.31 ((
% 24.33/6.31 (binunionIR) =>
% 24.33/6.31 ((
% 24.33/6.31 (binunionEcases) =>
% 24.33/6.31 ((
% 24.33/6.31 (binunionE) =>
% 24.33/6.31 ((
% 24.33/6.31 (binunionLsub) =>
% 24.33/6.31 ((
% 24.33/6.31 (binunionRsub) =>
% 24.33/6.31 ((
% 24.33/6.31 (binintersectI) =>
% 24.33/6.31 ((
% 24.33/6.31 (binintersectSubset5) =>
% 24.33/6.31 ((
% 24.33/6.31 (binintersectEL) =>
% 24.33/6.31 ((
% 24.33/6.31 (binintersectLsub) =>
% 24.33/6.31 ((
% 24.33/6.31 (binintersectSubset2) =>
% 24.33/6.31 ((
% 24.33/6.31 (binintersectSubset3) =>
% 24.33/6.31 ((
% 24.33/6.31 (binintersectER) =>
% 24.33/6.31 ((
% 24.33/6.31 (disjointsetsI1) =>
% 24.33/6.31 ((
% 24.33/6.31 (binintersectRsub) =>
% 24.33/6.31 ((
% 24.33/6.31 (binintersectSubset4) =>
% 24.33/6.31 ((
% 24.33/6.31 (binintersectSubset1) =>
% 24.33/6.31 ((
% 24.33/6.31 (bs114d) =>
% 24.33/6.31 ((
% 24.33/6.31 (setminusI) =>
% 24.33/6.31 ((
% 24.33/6.31 (setminusEL) =>
% 24.33/6.31 ((
% 24.33/6.31 (setminusER) =>
% 24.33/6.31 ((
% 24.33/6.31 (setminusSubset2) =>
% 24.33/6.31 ((
% 24.33/6.31 (setminusERneg) =>
% 24.33/6.31 ((
% 24.33/6.31 (setminusELneg) =>
% 24.33/6.31 ((
% 24.33/6.31 (setminusILneg) =>
% 24.33/6.31 ((
% 24.33/6.31 (setminusIRneg) =>
% 24.33/6.31 ((
% 24.33/6.31 (setminusLsub) =>
% 24.33/6.31 ((
% 24.33/6.31 (setminusSubset1) =>
% 24.33/6.31 ((
% 24.33/6.31 (symdiffE) =>
% 24.33/6.31 ((
% 24.33/6.31 (symdiffI1) =>
% 24.33/6.31 ((
% 24.33/6.31 (symdiffI2) =>
% 24.33/6.31 ((
% 24.33/6.31 (symdiffIneg1) =>
% 24.33/6.31 ((
% 24.33/6.31 (symdiffIneg2) =>
% 24.33/6.31 ((
% 24.33/6.31 (secondinupair) =>
% 24.33/6.31 ((
% 24.33/6.31 (setukpairIL) =>
% 24.33/6.31 ((
% 24.33/6.31 (setukpairIR) =>
% 24.33/6.31 ((
% 24.33/6.31 (kpairiskpair) =>
% 24.33/6.31 ((
% 24.33/6.31 (kpairp) =>
% 24.33/6.31 ((
% 24.33/6.31 (singletonsubset) =>
% 24.33/6.31 ((
% 24.33/6.31 (singletoninpowerset) =>
% 24.33/6.31 ((
% 24.33/6.31 (singletoninpowunion) =>
% 24.33/6.31 ((
% 24.33/6.31 (upairset2E) =>
% 24.33/6.31 ((
% 24.33/6.31 (upairsubunion) =>
% 24.33/6.31 ((
% 24.33/6.31 (upairinpowunion) =>
% 24.33/6.31 ((
% 24.33/6.31 (ubforcartprodlem1) =>
% 24.33/6.31 ((
% 24.33/6.31 (ubforcartprodlem2) =>
% 24.33/6.31 ((
% 24.33/6.31 (ubforcartprodlem3) =>
% 24.33/6.31 ((
% 24.33/6.31 (cartprodpairin) =>
% 24.33/6.31 ((
% 24.33/6.31 (cartprodmempair1) =>
% 24.33/6.31 ((
% 24.33/6.31 (cartprodmempair) =>
% 24.33/6.31 ((
% 24.33/6.31 (setunionE2) =>
% 24.33/6.31 ((
% 24.33/6.31 (setunionsingleton1) =>
% 24.33/6.31 ((
% 24.33/6.31 (setunionsingleton2) =>
% 24.33/6.31 ((
% 24.33/6.31 (setunionsingleton) =>
% 24.33/6.31 ((
% 24.33/6.31 (singletonprop) =>
% 24.33/6.31 ((
% 24.33/6.31 (ex1E1) =>
% 24.33/6.31 ((
% 24.33/6.31 (ex1I) =>
% 24.33/6.31 ((
% 24.33/6.31 (ex1I2) =>
% 24.33/6.31 ((
% 24.33/6.31 (singletonsuniq) =>
% 24.33/6.31 ((
% 24.33/6.31 (setukpairinjL1) =>
% 24.33/6.31 ((
% 24.33/6.31 (kfstsingleton) =>
% 24.33/6.31 ((
% 24.33/6.31 (theprop) =>
% 24.33/6.31 ((
% 24.33/6.31 (kfstpairEq) =>
% 24.33/6.31 ((
% 24.33/6.31 (cartprodfstin) =>
% 24.33/6.31 ((
% 24.33/6.31 (setukpairinjL2) =>
% 24.33/6.31 ((
% 24.33/6.31 (setukpairinjL) =>
% 24.33/6.31 ((
% 24.33/6.31 (setukpairinjR11) =>
% 24.33/6.31 ((
% 24.33/6.31 (setukpairinjR12) =>
% 24.33/6.31 ((
% 24.33/6.31 (setukpairinjR1) =>
% 24.33/6.31 ((
% 24.33/6.31 (upairequniteq) =>
% 24.33/6.31 ((
% 24.33/6.31 (setukpairinjR2) =>
% 24.33/6.31 ((
% 24.33/6.31 (setukpairinjR) =>
% 24.33/6.31 ((
% 24.33/6.31 (ksndsingleton) =>
% 24.33/6.31 ((
% 24.33/6.31 (ksndpairEq) =>
% 24.33/6.31 ((
% 24.33/6.31 (kpairsurjEq) =>
% 24.33/6.31 ((
% 24.33/6.31 (cartprodsndin) =>
% 24.33/6.31 ((
% 24.33/6.31 (cartprodpairmemEL) =>
% 24.33/6.31 ((
% 24.33/6.31 (cartprodpairmemER) =>
% 24.33/6.31 ((
% 24.33/6.31 (cartprodmempaircEq) =>
% 24.33/6.31 ((
% 24.33/6.31 (cartprodfstpairEq) =>
% 24.33/6.31 ((
% 24.33/6.31 (cartprodsndpairEq) =>
% 24.33/6.31 ((
% 24.33/6.31 (cartprodpairsurjEq) =>
% 24.33/6.31 ((
% 24.33/6.31 (dpsetconstrI) =>
% 24.33/6.31 ((
% 24.33/6.31 (!!) @ (
% 24.33/6.31 (('#B') @ (
% 24.33/6.31 !!) @
% 24.33/6.31 (
% 24.33/6.31 (
% 24.33/6.31 ('#B') @ (
% 24.33/6.31 (
% 24.33/6.31 ('#B') @ (
% 24.33/6.31 !!))) @
% 24.33/6.31 (
% 24.33/6.31 (
% 24.33/6.31 ('#S') @ (
% 24.33/6.31 (
% 24.33/6.31 ('#B') @ (
% 24.33/6.31 '#S') @
% 24.33/6.31 (
% 24.33/6.31 (
% 24.33/6.31 ('#B') @ (
% 24.33/6.31 (
% 24.33/6.31 ('#B') @ (
% 24.33/6.31 '#C'))) @
% 24.33/6.31 (
% 24.33/6.31 (
% 24.33/6.31 ('#B') @ (
% 24.33/6.31 (
% 24.33/6.31 ('#B') @ (
% 24.33/6.31 (
% 24.33/6.31 ('#B') @ subset)))) @
% 24.33/6.31 dpsetconstr)))))) @
% 24.33/6.31 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.33/6.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl64])).
% 24.33/6.31 thf(zip_derived_cl79, plain,
% 24.33/6.31 (~ (((dsetconstrEL) =>
% 24.33/6.31 (((dsetconstrER) =>
% 24.33/6.31 (((exuE1) =>
% 24.33/6.31 (((prop2setE) =>
% 24.33/6.31 (((emptysetE) =>
% 24.33/6.31 (((emptysetimpfalse) =>
% 24.33/6.31 (((notinemptyset) =>
% 24.33/6.31 (((exuE3e) =>
% 24.33/6.31 (((setext) =>
% 24.33/6.31 (((emptyI) =>
% 24.33/6.31 (((noeltsimpempty) =>
% 24.33/6.31 (((setbeta) =>
% 24.33/6.31 (((nonemptyE1) =>
% 24.33/6.31 (((nonemptyI) =>
% 24.33/6.31 (((nonemptyI1) =>
% 24.33/6.31 (((setadjoinIL) =>
% 24.33/6.31 (((in @ emptyset @
% 24.33/6.31 (setadjoin @ emptyset @ emptyset)) =>
% 24.33/6.31 (((setadjoinIR) =>
% 24.33/6.31 (((setadjoinE) =>
% 24.33/6.31 (((setadjoinOr) =>
% 24.33/6.31 (((setoftrueEq) =>
% 24.33/6.31 (((powersetI) =>
% 24.33/6.31 (((emptyinPowerset) =>
% 24.33/6.31 (((emptyInPowerset) =>
% 24.33/6.31 (((powersetE) =>
% 24.33/6.31 (((setunionI) =>
% 24.33/6.31 (((setunionE) =>
% 24.33/6.31 (((subPowSU) =>
% 24.33/6.31 (((exuE2) =>
% 24.33/6.31 (((nonemptyImpWitness) =>
% 24.33/6.31 ((
% 24.33/6.31 (uniqinunit) =>
% 24.33/6.31 ((
% 24.33/6.31 (notinsingleton) =>
% 24.33/6.31 ((
% 24.33/6.31 (eqinunit) =>
% 24.33/6.31 ((
% 24.33/6.31 (singletonsswitch) =>
% 24.33/6.31 ((
% 24.33/6.31 (upairsetE) =>
% 24.33/6.31 ((
% 24.33/6.31 (upairsetIL) =>
% 24.33/6.31 ((
% 24.33/6.31 (upairsetIR) =>
% 24.33/6.31 ((
% 24.33/6.31 (emptyE1) =>
% 24.33/6.31 ((
% 24.33/6.31 (vacuousDall) =>
% 24.33/6.31 ((
% 24.33/6.31 (quantDeMorgan1) =>
% 24.33/6.31 ((
% 24.33/6.31 (quantDeMorgan2) =>
% 24.33/6.31 ((
% 24.33/6.31 (quantDeMorgan3) =>
% 24.33/6.31 ((
% 24.33/6.31 (quantDeMorgan4) =>
% 24.33/6.31 ((
% 24.33/6.31 (prop2setI) =>
% 24.33/6.31 ((
% 24.33/6.31 (prop2set2propI) =>
% 24.33/6.31 ((
% 24.33/6.31 (notdexE) =>
% 24.33/6.31 ((
% 24.33/6.31 (notdallE) =>
% 24.33/6.31 ((
% 24.33/6.31 (exuI1) =>
% 24.33/6.31 ((
% 24.33/6.31 (exuI3) =>
% 24.33/6.31 ((
% 24.33/6.31 (exuI2) =>
% 24.33/6.31 ((
% 24.33/6.31 (inCongP) =>
% 24.33/6.31 ((
% 24.33/6.31 (in__Cong) =>
% 24.33/6.31 ((
% 24.33/6.31 (exuE3u) =>
% 24.33/6.31 ((
% 24.33/6.31 (exu__Cong) =>
% 24.33/6.31 ((
% 24.33/6.31 (setadjoin__Cong) =>
% 24.33/6.31 ((
% 24.33/6.31 (powerset__Cong) =>
% 24.33/6.31 ((
% 24.33/6.31 (setunion__Cong) =>
% 24.33/6.31 ((
% 24.33/6.31 (exuEu) =>
% 24.33/6.31 ((
% 24.33/6.31 (descr__Cong) =>
% 24.33/6.31 ((
% 24.33/6.31 (dsetconstr__Cong) =>
% 24.33/6.31 ((
% 24.33/6.31 (subsetI1) =>
% 24.33/6.31 ((
% 24.33/6.31 (eqimpsubset2) =>
% 24.33/6.31 ((
% 24.33/6.31 (eqimpsubset1) =>
% 24.33/6.31 ((
% 24.33/6.31 (subsetI2) =>
% 24.33/6.31 ((
% 24.33/6.31 (emptysetsubset) =>
% 24.33/6.31 ((
% 24.33/6.31 (subsetE) =>
% 24.33/6.31 ((
% 24.33/6.31 (subsetE2) =>
% 24.33/6.31 ((
% 24.33/6.31 (notsubsetI) =>
% 24.33/6.31 ((
% 24.33/6.31 (notequalI1) =>
% 24.33/6.31 ((
% 24.33/6.31 (notequalI2) =>
% 24.33/6.31 ((
% 24.33/6.31 (subsetRefl) =>
% 24.33/6.31 ((
% 24.33/6.31 (subsetTrans) =>
% 24.33/6.31 ((
% 24.33/6.31 (setadjoinSub) =>
% 24.33/6.31 ((
% 24.33/6.31 (setadjoinSub2) =>
% 24.33/6.31 ((
% 24.33/6.31 (subset2powerset) =>
% 24.33/6.31 ((
% 24.33/6.31 (setextsub) =>
% 24.33/6.31 ((
% 24.33/6.31 (subsetemptysetimpeq) =>
% 24.33/6.31 ((
% 24.33/6.31 (powersetI1) =>
% 24.33/6.31 ((
% 24.33/6.31 (powersetE1) =>
% 24.33/6.31 ((
% 24.33/6.31 (inPowerset) =>
% 24.33/6.31 ((
% 24.33/6.31 (powersetsubset) =>
% 24.33/6.31 ((
% 24.33/6.31 (sepInPowerset) =>
% 24.33/6.31 ((
% 24.33/6.31 (sepSubset) =>
% 24.33/6.31 ((
% 24.33/6.31 (binunionIL) =>
% 24.33/6.31 ((
% 24.33/6.31 (upairset2IR) =>
% 24.33/6.31 ((
% 24.33/6.31 (binunionIR) =>
% 24.33/6.31 ((
% 24.33/6.31 (binunionEcases) =>
% 24.33/6.31 ((
% 24.33/6.31 (binunionE) =>
% 24.33/6.31 ((
% 24.33/6.31 (binunionLsub) =>
% 24.33/6.31 ((
% 24.33/6.31 (binunionRsub) =>
% 24.33/6.31 ((
% 24.33/6.31 (binintersectI) =>
% 24.33/6.31 ((
% 24.33/6.31 (binintersectSubset5) =>
% 24.33/6.31 ((
% 24.33/6.31 (binintersectEL) =>
% 24.33/6.31 ((
% 24.33/6.31 (binintersectLsub) =>
% 24.33/6.31 ((
% 24.33/6.31 (binintersectSubset2) =>
% 24.33/6.31 ((
% 24.33/6.31 (binintersectSubset3) =>
% 24.33/6.31 ((
% 24.33/6.31 (binintersectER) =>
% 24.33/6.31 ((
% 24.33/6.31 (disjointsetsI1) =>
% 24.33/6.31 ((
% 24.33/6.31 (binintersectRsub) =>
% 24.33/6.31 ((
% 24.33/6.31 (binintersectSubset4) =>
% 24.33/6.31 ((
% 24.33/6.31 (binintersectSubset1) =>
% 24.33/6.31 ((
% 24.33/6.31 (bs114d) =>
% 24.33/6.31 ((
% 24.33/6.31 (setminusI) =>
% 24.33/6.31 ((
% 24.33/6.31 (setminusEL) =>
% 24.33/6.31 ((
% 24.33/6.31 (setminusER) =>
% 24.33/6.31 ((
% 24.33/6.31 (setminusSubset2) =>
% 24.33/6.31 ((
% 24.33/6.31 (setminusERneg) =>
% 24.33/6.31 ((
% 24.33/6.31 (setminusELneg) =>
% 24.33/6.31 ((
% 24.33/6.31 (setminusILneg) =>
% 24.33/6.31 ((
% 24.33/6.31 (setminusIRneg) =>
% 24.33/6.31 ((
% 24.33/6.31 (setminusLsub) =>
% 24.33/6.31 ((
% 24.33/6.31 (setminusSubset1) =>
% 24.33/6.31 ((
% 24.33/6.31 (symdiffE) =>
% 24.33/6.31 ((
% 24.33/6.31 (symdiffI1) =>
% 24.33/6.31 ((
% 24.33/6.31 (symdiffI2) =>
% 24.33/6.31 ((
% 24.33/6.31 (symdiffIneg1) =>
% 24.33/6.31 ((
% 24.33/6.31 (symdiffIneg2) =>
% 24.33/6.31 ((
% 24.33/6.31 (secondinupair) =>
% 24.33/6.31 ((
% 24.33/6.31 (setukpairIL) =>
% 24.33/6.31 ((
% 24.33/6.31 (setukpairIR) =>
% 24.33/6.31 ((
% 24.33/6.31 (kpairiskpair) =>
% 24.33/6.31 ((
% 24.33/6.31 (kpairp) =>
% 24.33/6.31 ((
% 24.33/6.31 (singletonsubset) =>
% 24.33/6.31 ((
% 24.33/6.31 (singletoninpowerset) =>
% 24.33/6.31 ((
% 24.33/6.31 (singletoninpowunion) =>
% 24.33/6.31 ((
% 24.33/6.31 (upairset2E) =>
% 24.33/6.31 ((
% 24.33/6.31 (upairsubunion) =>
% 24.33/6.31 ((
% 24.33/6.31 (upairinpowunion) =>
% 24.33/6.31 ((
% 24.33/6.31 (ubforcartprodlem1) =>
% 24.33/6.31 ((
% 24.33/6.31 (ubforcartprodlem2) =>
% 24.33/6.31 ((
% 24.33/6.31 (ubforcartprodlem3) =>
% 24.33/6.31 ((
% 24.33/6.31 (cartprodpairin) =>
% 24.33/6.31 ((
% 24.33/6.31 (cartprodmempair1) =>
% 24.33/6.31 ((
% 24.33/6.31 (cartprodmempair) =>
% 24.33/6.31 ((
% 24.33/6.31 (setunionE2) =>
% 24.33/6.31 ((
% 24.33/6.31 (setunionsingleton1) =>
% 24.33/6.31 ((
% 24.33/6.31 (setunionsingleton2) =>
% 24.33/6.31 ((
% 24.33/6.31 (setunionsingleton) =>
% 24.33/6.31 ((
% 24.33/6.31 (singletonprop) =>
% 24.33/6.31 ((
% 24.33/6.31 (ex1E1) =>
% 24.33/6.31 ((
% 24.33/6.31 (ex1I) =>
% 24.33/6.31 ((
% 24.33/6.31 (ex1I2) =>
% 24.33/6.31 ((
% 24.33/6.31 (singletonsuniq) =>
% 24.33/6.31 ((
% 24.33/6.31 (setukpairinjL1) =>
% 24.33/6.31 ((
% 24.33/6.31 (kfstsingleton) =>
% 24.33/6.31 ((
% 24.33/6.31 (theprop) =>
% 24.33/6.31 ((
% 24.33/6.31 (kfstpairEq) =>
% 24.33/6.31 ((
% 24.33/6.31 (cartprodfstin) =>
% 24.33/6.31 ((
% 24.33/6.31 (setukpairinjL2) =>
% 24.33/6.31 ((
% 24.33/6.31 (setukpairinjL) =>
% 24.33/6.31 ((
% 24.33/6.31 (setukpairinjR11) =>
% 24.33/6.31 ((
% 24.33/6.31 (setukpairinjR12) =>
% 24.33/6.31 ((
% 24.33/6.31 (setukpairinjR1) =>
% 24.33/6.31 ((
% 24.33/6.31 (upairequniteq) =>
% 24.33/6.31 ((
% 24.33/6.31 (setukpairinjR2) =>
% 24.33/6.31 ((
% 24.33/6.31 (setukpairinjR) =>
% 24.33/6.31 ((
% 24.33/6.31 (ksndsingleton) =>
% 24.33/6.31 ((
% 24.33/6.31 (ksndpairEq) =>
% 24.33/6.31 ((
% 24.33/6.31 (kpairsurjEq) =>
% 24.33/6.31 ((
% 24.33/6.31 (cartprodsndin) =>
% 24.33/6.31 ((
% 24.33/6.31 (cartprodpairmemEL) =>
% 24.33/6.31 ((
% 24.33/6.31 (cartprodpairmemER) =>
% 24.33/6.31 ((
% 24.33/6.31 (cartprodmempaircEq) =>
% 24.33/6.31 ((
% 24.33/6.31 (cartprodfstpairEq) =>
% 24.33/6.31 ((
% 24.33/6.31 (cartprodsndpairEq) =>
% 24.33/6.31 ((
% 24.33/6.31 (cartprodpairsurjEq) =>
% 24.33/6.31 ((
% 24.33/6.31 (dpsetconstrI) =>
% 24.33/6.31 ((
% 24.33/6.31 (!!) @ (
% 24.33/6.31 (('#B') @ (
% 24.33/6.31 !!) @
% 24.33/6.31 (
% 24.33/6.31 (
% 24.33/6.31 ('#B') @ (
% 24.33/6.31 (
% 24.33/6.31 ('#B') @ (
% 24.33/6.31 !!))) @
% 24.33/6.31 (
% 24.33/6.31 (
% 24.33/6.31 ('#S') @ (
% 24.33/6.31 (
% 24.33/6.31 ('#B') @ (
% 24.33/6.31 '#S') @
% 24.33/6.31 (
% 24.33/6.31 (
% 24.33/6.31 ('#B') @ (
% 24.33/6.31 (
% 24.33/6.31 ('#B') @ (
% 24.33/6.31 '#C'))) @
% 24.33/6.31 (
% 24.33/6.31 (
% 24.33/6.31 ('#B') @ (
% 24.33/6.31 (
% 24.33/6.31 ('#B') @ (
% 24.33/6.31 (
% 24.33/6.31 ('#B') @ subset)))) @
% 24.33/6.31 dpsetconstr)))))) @
% 24.33/6.31 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.33/6.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl71])).
% 24.33/6.31 thf(zip_derived_cl89, plain,
% 24.33/6.31 (~ (((dsetconstrER) =>
% 24.33/6.31 (((exuE1) =>
% 24.33/6.31 (((prop2setE) =>
% 24.33/6.31 (((emptysetE) =>
% 24.33/6.31 (((emptysetimpfalse) =>
% 24.33/6.31 (((notinemptyset) =>
% 24.33/6.31 (((exuE3e) =>
% 24.33/6.31 (((setext) =>
% 24.33/6.31 (((emptyI) =>
% 24.33/6.31 (((noeltsimpempty) =>
% 24.33/6.31 (((setbeta) =>
% 24.33/6.31 (((nonemptyE1) =>
% 24.33/6.31 (((nonemptyI) =>
% 24.33/6.31 (((nonemptyI1) =>
% 24.33/6.31 (((setadjoinIL) =>
% 24.33/6.31 (((in @ emptyset @
% 24.33/6.31 (setadjoin @ emptyset @ emptyset)) =>
% 24.33/6.31 (((setadjoinIR) =>
% 24.33/6.31 (((setadjoinE) =>
% 24.33/6.31 (((setadjoinOr) =>
% 24.33/6.31 (((setoftrueEq) =>
% 24.33/6.31 (((powersetI) =>
% 24.33/6.31 (((emptyinPowerset) =>
% 24.33/6.31 (((emptyInPowerset) =>
% 24.33/6.31 (((powersetE) =>
% 24.33/6.31 (((setunionI) =>
% 24.33/6.31 (((setunionE) =>
% 24.33/6.31 (((subPowSU) =>
% 24.33/6.31 (((exuE2) =>
% 24.33/6.31 (((nonemptyImpWitness) =>
% 24.33/6.31 (((uniqinunit) =>
% 24.33/6.31 ((
% 24.33/6.31 (notinsingleton) =>
% 24.33/6.31 ((
% 24.33/6.31 (eqinunit) =>
% 24.33/6.31 ((
% 24.33/6.31 (singletonsswitch) =>
% 24.33/6.31 ((
% 24.33/6.31 (upairsetE) =>
% 24.33/6.31 ((
% 24.33/6.31 (upairsetIL) =>
% 24.33/6.31 ((
% 24.33/6.31 (upairsetIR) =>
% 24.33/6.31 ((
% 24.33/6.31 (emptyE1) =>
% 24.33/6.31 ((
% 24.33/6.31 (vacuousDall) =>
% 24.33/6.31 ((
% 24.33/6.31 (quantDeMorgan1) =>
% 24.33/6.31 ((
% 24.33/6.31 (quantDeMorgan2) =>
% 24.33/6.31 ((
% 24.33/6.31 (quantDeMorgan3) =>
% 24.33/6.31 ((
% 24.33/6.31 (quantDeMorgan4) =>
% 24.33/6.31 ((
% 24.33/6.31 (prop2setI) =>
% 24.33/6.31 ((
% 24.33/6.31 (prop2set2propI) =>
% 24.33/6.31 ((
% 24.33/6.31 (notdexE) =>
% 24.33/6.31 ((
% 24.33/6.31 (notdallE) =>
% 24.33/6.31 ((
% 24.33/6.31 (exuI1) =>
% 24.33/6.31 ((
% 24.33/6.31 (exuI3) =>
% 24.33/6.31 ((
% 24.33/6.31 (exuI2) =>
% 24.33/6.31 ((
% 24.33/6.31 (inCongP) =>
% 24.33/6.31 ((
% 24.33/6.31 (in__Cong) =>
% 24.33/6.31 ((
% 24.33/6.31 (exuE3u) =>
% 24.33/6.31 ((
% 24.33/6.31 (exu__Cong) =>
% 24.33/6.31 ((
% 24.33/6.31 (setadjoin__Cong) =>
% 24.33/6.31 ((
% 24.33/6.31 (powerset__Cong) =>
% 24.33/6.31 ((
% 24.33/6.31 (setunion__Cong) =>
% 24.33/6.31 ((
% 24.33/6.31 (exuEu) =>
% 24.33/6.31 ((
% 24.33/6.31 (descr__Cong) =>
% 24.33/6.31 ((
% 24.33/6.31 (dsetconstr__Cong) =>
% 24.33/6.31 ((
% 24.33/6.31 (subsetI1) =>
% 24.33/6.31 ((
% 24.33/6.31 (eqimpsubset2) =>
% 24.33/6.31 ((
% 24.33/6.31 (eqimpsubset1) =>
% 24.33/6.31 ((
% 24.33/6.31 (subsetI2) =>
% 24.33/6.31 ((
% 24.33/6.31 (emptysetsubset) =>
% 24.33/6.31 ((
% 24.33/6.31 (subsetE) =>
% 24.33/6.31 ((
% 24.33/6.31 (subsetE2) =>
% 24.33/6.31 ((
% 24.33/6.31 (notsubsetI) =>
% 24.33/6.31 ((
% 24.33/6.31 (notequalI1) =>
% 24.33/6.31 ((
% 24.33/6.31 (notequalI2) =>
% 24.33/6.31 ((
% 24.33/6.31 (subsetRefl) =>
% 24.33/6.31 ((
% 24.33/6.31 (subsetTrans) =>
% 24.33/6.31 ((
% 24.33/6.31 (setadjoinSub) =>
% 24.33/6.31 ((
% 24.33/6.31 (setadjoinSub2) =>
% 24.33/6.31 ((
% 24.33/6.31 (subset2powerset) =>
% 24.33/6.31 ((
% 24.33/6.31 (setextsub) =>
% 24.33/6.31 ((
% 24.33/6.31 (subsetemptysetimpeq) =>
% 24.33/6.31 ((
% 24.33/6.31 (powersetI1) =>
% 24.33/6.31 ((
% 24.33/6.31 (powersetE1) =>
% 24.33/6.31 ((
% 24.33/6.31 (inPowerset) =>
% 24.33/6.31 ((
% 24.33/6.31 (powersetsubset) =>
% 24.33/6.31 ((
% 24.33/6.31 (sepInPowerset) =>
% 24.33/6.31 ((
% 24.33/6.31 (sepSubset) =>
% 24.33/6.31 ((
% 24.33/6.31 (binunionIL) =>
% 24.33/6.31 ((
% 24.33/6.31 (upairset2IR) =>
% 24.33/6.31 ((
% 24.33/6.31 (binunionIR) =>
% 24.33/6.31 ((
% 24.33/6.31 (binunionEcases) =>
% 24.33/6.31 ((
% 24.33/6.31 (binunionE) =>
% 24.33/6.31 ((
% 24.33/6.31 (binunionLsub) =>
% 24.33/6.31 ((
% 24.33/6.31 (binunionRsub) =>
% 24.33/6.31 ((
% 24.33/6.31 (binintersectI) =>
% 24.33/6.31 ((
% 24.33/6.31 (binintersectSubset5) =>
% 24.33/6.31 ((
% 24.33/6.31 (binintersectEL) =>
% 24.33/6.31 ((
% 24.33/6.31 (binintersectLsub) =>
% 24.33/6.31 ((
% 24.33/6.31 (binintersectSubset2) =>
% 24.33/6.31 ((
% 24.33/6.31 (binintersectSubset3) =>
% 24.33/6.31 ((
% 24.33/6.31 (binintersectER) =>
% 24.33/6.31 ((
% 24.33/6.31 (disjointsetsI1) =>
% 24.33/6.31 ((
% 24.33/6.31 (binintersectRsub) =>
% 24.33/6.31 ((
% 24.33/6.31 (binintersectSubset4) =>
% 24.33/6.31 ((
% 24.33/6.31 (binintersectSubset1) =>
% 24.33/6.31 ((
% 24.33/6.31 (bs114d) =>
% 24.33/6.31 ((
% 24.33/6.31 (setminusI) =>
% 24.33/6.31 ((
% 24.33/6.31 (setminusEL) =>
% 24.33/6.31 ((
% 24.33/6.31 (setminusER) =>
% 24.33/6.31 ((
% 24.33/6.31 (setminusSubset2) =>
% 24.33/6.31 ((
% 24.33/6.31 (setminusERneg) =>
% 24.33/6.31 ((
% 24.33/6.31 (setminusELneg) =>
% 24.33/6.31 ((
% 24.33/6.31 (setminusILneg) =>
% 24.33/6.31 ((
% 24.33/6.31 (setminusIRneg) =>
% 24.33/6.31 ((
% 24.33/6.31 (setminusLsub) =>
% 24.33/6.31 ((
% 24.33/6.31 (setminusSubset1) =>
% 24.33/6.31 ((
% 24.33/6.31 (symdiffE) =>
% 24.33/6.31 ((
% 24.33/6.31 (symdiffI1) =>
% 24.33/6.31 ((
% 24.33/6.31 (symdiffI2) =>
% 24.33/6.31 ((
% 24.33/6.31 (symdiffIneg1) =>
% 24.33/6.31 ((
% 24.33/6.31 (symdiffIneg2) =>
% 24.33/6.31 ((
% 24.33/6.31 (secondinupair) =>
% 24.33/6.31 ((
% 24.33/6.31 (setukpairIL) =>
% 24.33/6.31 ((
% 24.33/6.31 (setukpairIR) =>
% 24.33/6.31 ((
% 24.33/6.31 (kpairiskpair) =>
% 24.33/6.31 ((
% 24.33/6.31 (kpairp) =>
% 24.33/6.31 ((
% 24.33/6.31 (singletonsubset) =>
% 24.33/6.31 ((
% 24.33/6.31 (singletoninpowerset) =>
% 24.33/6.31 ((
% 24.33/6.31 (singletoninpowunion) =>
% 24.33/6.31 ((
% 24.33/6.31 (upairset2E) =>
% 24.33/6.31 ((
% 24.33/6.31 (upairsubunion) =>
% 24.33/6.31 ((
% 24.33/6.31 (upairinpowunion) =>
% 24.33/6.31 ((
% 24.33/6.31 (ubforcartprodlem1) =>
% 24.33/6.31 ((
% 24.33/6.31 (ubforcartprodlem2) =>
% 24.33/6.31 ((
% 24.33/6.31 (ubforcartprodlem3) =>
% 24.33/6.31 ((
% 24.33/6.31 (cartprodpairin) =>
% 24.33/6.31 ((
% 24.33/6.31 (cartprodmempair1) =>
% 24.33/6.31 ((
% 24.33/6.31 (cartprodmempair) =>
% 24.33/6.31 ((
% 24.33/6.31 (setunionE2) =>
% 24.33/6.31 ((
% 24.33/6.31 (setunionsingleton1) =>
% 24.33/6.31 ((
% 24.33/6.31 (setunionsingleton2) =>
% 24.33/6.31 ((
% 24.33/6.31 (setunionsingleton) =>
% 24.33/6.31 ((
% 24.33/6.31 (singletonprop) =>
% 24.33/6.31 ((
% 24.33/6.31 (ex1E1) =>
% 24.33/6.31 ((
% 24.33/6.31 (ex1I) =>
% 24.33/6.31 ((
% 24.33/6.31 (ex1I2) =>
% 24.33/6.31 ((
% 24.33/6.31 (singletonsuniq) =>
% 24.33/6.31 ((
% 24.33/6.31 (setukpairinjL1) =>
% 24.33/6.31 ((
% 24.33/6.31 (kfstsingleton) =>
% 24.33/6.31 ((
% 24.33/6.31 (theprop) =>
% 24.33/6.31 ((
% 24.33/6.31 (kfstpairEq) =>
% 24.33/6.31 ((
% 24.33/6.31 (cartprodfstin) =>
% 24.33/6.31 ((
% 24.33/6.31 (setukpairinjL2) =>
% 24.33/6.31 ((
% 24.33/6.31 (setukpairinjL) =>
% 24.33/6.31 ((
% 24.33/6.31 (setukpairinjR11) =>
% 24.33/6.31 ((
% 24.33/6.31 (setukpairinjR12) =>
% 24.33/6.31 ((
% 24.33/6.31 (setukpairinjR1) =>
% 24.33/6.31 ((
% 24.33/6.31 (upairequniteq) =>
% 24.33/6.31 ((
% 24.33/6.31 (setukpairinjR2) =>
% 24.33/6.31 ((
% 24.33/6.31 (setukpairinjR) =>
% 24.33/6.31 ((
% 24.33/6.31 (ksndsingleton) =>
% 24.33/6.31 ((
% 24.33/6.31 (ksndpairEq) =>
% 24.33/6.31 ((
% 24.33/6.31 (kpairsurjEq) =>
% 24.33/6.31 ((
% 24.33/6.31 (cartprodsndin) =>
% 24.33/6.31 ((
% 24.33/6.31 (cartprodpairmemEL) =>
% 24.33/6.31 ((
% 24.33/6.31 (cartprodpairmemER) =>
% 24.33/6.31 ((
% 24.33/6.31 (cartprodmempaircEq) =>
% 24.33/6.31 ((
% 24.33/6.31 (cartprodfstpairEq) =>
% 24.33/6.31 ((
% 24.33/6.31 (cartprodsndpairEq) =>
% 24.33/6.31 ((
% 24.33/6.31 (cartprodpairsurjEq) =>
% 24.33/6.31 ((
% 24.33/6.31 (dpsetconstrI) =>
% 24.33/6.31 ((
% 24.33/6.31 (!!) @ (
% 24.33/6.31 (('#B') @ (
% 24.33/6.31 !!) @
% 24.33/6.31 (
% 24.33/6.31 (
% 24.33/6.31 ('#B') @ (
% 24.33/6.31 (
% 24.33/6.31 ('#B') @ (
% 24.33/6.31 !!))) @
% 24.33/6.31 (
% 24.33/6.31 (
% 24.33/6.31 ('#S') @ (
% 24.33/6.31 (
% 24.33/6.31 ('#B') @ (
% 24.33/6.31 '#S') @
% 24.33/6.31 (
% 24.33/6.31 (
% 24.33/6.31 ('#B') @ (
% 24.33/6.31 (
% 24.33/6.31 ('#B') @ (
% 24.33/6.31 '#C'))) @
% 24.33/6.31 (
% 24.33/6.31 (
% 24.33/6.31 ('#B') @ (
% 24.33/6.31 (
% 24.33/6.31 ('#B') @ (
% 24.33/6.31 (
% 24.33/6.31 ('#B') @ subset)))) @
% 24.33/6.31 dpsetconstr)))))) @
% 24.33/6.31 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.33/6.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl79])).
% 24.33/6.31 thf(zip_derived_cl105, plain,
% 24.33/6.31 (~ (((exuE1) =>
% 24.33/6.31 (((prop2setE) =>
% 24.33/6.31 (((emptysetE) =>
% 24.33/6.31 (((emptysetimpfalse) =>
% 24.33/6.31 (((notinemptyset) =>
% 24.33/6.31 (((exuE3e) =>
% 24.33/6.31 (((setext) =>
% 24.33/6.31 (((emptyI) =>
% 24.33/6.31 (((noeltsimpempty) =>
% 24.33/6.31 (((setbeta) =>
% 24.33/6.31 (((nonemptyE1) =>
% 24.33/6.31 (((nonemptyI) =>
% 24.33/6.31 (((nonemptyI1) =>
% 24.33/6.31 (((setadjoinIL) =>
% 24.33/6.31 (((in @ emptyset @
% 24.33/6.31 (setadjoin @ emptyset @ emptyset)) =>
% 24.33/6.31 (((setadjoinIR) =>
% 24.33/6.31 (((setadjoinE) =>
% 24.33/6.31 (((setadjoinOr) =>
% 24.33/6.31 (((setoftrueEq) =>
% 24.33/6.31 (((powersetI) =>
% 24.33/6.31 (((emptyinPowerset) =>
% 24.33/6.31 (((emptyInPowerset) =>
% 24.33/6.31 (((powersetE) =>
% 24.33/6.31 (((setunionI) =>
% 24.33/6.31 (((setunionE) =>
% 24.33/6.31 (((subPowSU) =>
% 24.33/6.31 (((exuE2) =>
% 24.33/6.31 (((nonemptyImpWitness) =>
% 24.33/6.31 (((uniqinunit) =>
% 24.33/6.31 (((notinsingleton) =>
% 24.33/6.31 ((
% 24.33/6.31 (eqinunit) =>
% 24.33/6.31 ((
% 24.33/6.31 (singletonsswitch) =>
% 24.33/6.31 ((
% 24.33/6.31 (upairsetE) =>
% 24.33/6.31 ((
% 24.33/6.31 (upairsetIL) =>
% 24.33/6.31 ((
% 24.33/6.31 (upairsetIR) =>
% 24.33/6.31 ((
% 24.33/6.31 (emptyE1) =>
% 24.33/6.31 ((
% 24.33/6.31 (vacuousDall) =>
% 24.33/6.31 ((
% 24.33/6.31 (quantDeMorgan1) =>
% 24.33/6.31 ((
% 24.33/6.31 (quantDeMorgan2) =>
% 24.33/6.31 ((
% 24.33/6.31 (quantDeMorgan3) =>
% 24.33/6.31 ((
% 24.33/6.31 (quantDeMorgan4) =>
% 24.33/6.31 ((
% 24.33/6.31 (prop2setI) =>
% 24.33/6.31 ((
% 24.33/6.31 (prop2set2propI) =>
% 24.33/6.31 ((
% 24.33/6.31 (notdexE) =>
% 24.33/6.31 ((
% 24.33/6.31 (notdallE) =>
% 24.33/6.31 ((
% 24.33/6.31 (exuI1) =>
% 24.33/6.31 ((
% 24.33/6.31 (exuI3) =>
% 24.33/6.31 ((
% 24.33/6.31 (exuI2) =>
% 24.33/6.31 ((
% 24.33/6.31 (inCongP) =>
% 24.33/6.31 ((
% 24.33/6.31 (in__Cong) =>
% 24.33/6.31 ((
% 24.33/6.31 (exuE3u) =>
% 24.33/6.31 ((
% 24.33/6.31 (exu__Cong) =>
% 24.33/6.31 ((
% 24.33/6.31 (setadjoin__Cong) =>
% 24.33/6.31 ((
% 24.33/6.31 (powerset__Cong) =>
% 24.33/6.31 ((
% 24.33/6.31 (setunion__Cong) =>
% 24.33/6.31 ((
% 24.33/6.31 (exuEu) =>
% 24.33/6.31 ((
% 24.33/6.31 (descr__Cong) =>
% 24.33/6.31 ((
% 24.33/6.31 (dsetconstr__Cong) =>
% 24.33/6.31 ((
% 24.33/6.31 (subsetI1) =>
% 24.33/6.31 ((
% 24.33/6.31 (eqimpsubset2) =>
% 24.33/6.31 ((
% 24.33/6.31 (eqimpsubset1) =>
% 24.33/6.31 ((
% 24.33/6.31 (subsetI2) =>
% 24.33/6.31 ((
% 24.33/6.31 (emptysetsubset) =>
% 24.33/6.31 ((
% 24.33/6.31 (subsetE) =>
% 24.33/6.31 ((
% 24.33/6.31 (subsetE2) =>
% 24.33/6.31 ((
% 24.33/6.31 (notsubsetI) =>
% 24.33/6.31 ((
% 24.33/6.31 (notequalI1) =>
% 24.33/6.31 ((
% 24.33/6.31 (notequalI2) =>
% 24.33/6.31 ((
% 24.33/6.31 (subsetRefl) =>
% 24.33/6.31 ((
% 24.33/6.31 (subsetTrans) =>
% 24.33/6.31 ((
% 24.33/6.31 (setadjoinSub) =>
% 24.33/6.31 ((
% 24.33/6.31 (setadjoinSub2) =>
% 24.33/6.31 ((
% 24.33/6.31 (subset2powerset) =>
% 24.33/6.31 ((
% 24.33/6.31 (setextsub) =>
% 24.33/6.31 ((
% 24.33/6.31 (subsetemptysetimpeq) =>
% 24.33/6.31 ((
% 24.33/6.31 (powersetI1) =>
% 24.33/6.31 ((
% 24.33/6.31 (powersetE1) =>
% 24.33/6.31 ((
% 24.33/6.31 (inPowerset) =>
% 24.33/6.31 ((
% 24.33/6.31 (powersetsubset) =>
% 24.33/6.31 ((
% 24.33/6.31 (sepInPowerset) =>
% 24.33/6.31 ((
% 24.33/6.31 (sepSubset) =>
% 24.33/6.31 ((
% 24.33/6.31 (binunionIL) =>
% 24.33/6.31 ((
% 24.33/6.31 (upairset2IR) =>
% 24.33/6.31 ((
% 24.33/6.31 (binunionIR) =>
% 24.33/6.31 ((
% 24.33/6.31 (binunionEcases) =>
% 24.33/6.31 ((
% 24.33/6.31 (binunionE) =>
% 24.33/6.31 ((
% 24.33/6.31 (binunionLsub) =>
% 24.33/6.31 ((
% 24.33/6.31 (binunionRsub) =>
% 24.33/6.31 ((
% 24.33/6.31 (binintersectI) =>
% 24.33/6.31 ((
% 24.33/6.31 (binintersectSubset5) =>
% 24.33/6.31 ((
% 24.33/6.31 (binintersectEL) =>
% 24.33/6.31 ((
% 24.33/6.31 (binintersectLsub) =>
% 24.33/6.31 ((
% 24.33/6.31 (binintersectSubset2) =>
% 24.33/6.31 ((
% 24.33/6.31 (binintersectSubset3) =>
% 24.33/6.31 ((
% 24.33/6.31 (binintersectER) =>
% 24.33/6.31 ((
% 24.33/6.31 (disjointsetsI1) =>
% 24.33/6.31 ((
% 24.33/6.31 (binintersectRsub) =>
% 24.33/6.31 ((
% 24.33/6.31 (binintersectSubset4) =>
% 24.33/6.31 ((
% 24.33/6.31 (binintersectSubset1) =>
% 24.33/6.31 ((
% 24.33/6.31 (bs114d) =>
% 24.33/6.31 ((
% 24.33/6.31 (setminusI) =>
% 24.33/6.31 ((
% 24.33/6.31 (setminusEL) =>
% 24.33/6.31 ((
% 24.33/6.31 (setminusER) =>
% 24.33/6.31 ((
% 24.33/6.31 (setminusSubset2) =>
% 24.33/6.31 ((
% 24.33/6.31 (setminusERneg) =>
% 24.33/6.31 ((
% 24.33/6.31 (setminusELneg) =>
% 24.33/6.31 ((
% 24.33/6.31 (setminusILneg) =>
% 24.33/6.31 ((
% 24.33/6.31 (setminusIRneg) =>
% 24.33/6.31 ((
% 24.33/6.31 (setminusLsub) =>
% 24.33/6.31 ((
% 24.33/6.31 (setminusSubset1) =>
% 24.33/6.31 ((
% 24.33/6.31 (symdiffE) =>
% 24.33/6.31 ((
% 24.33/6.31 (symdiffI1) =>
% 24.33/6.31 ((
% 24.33/6.31 (symdiffI2) =>
% 24.33/6.31 ((
% 24.33/6.31 (symdiffIneg1) =>
% 24.33/6.31 ((
% 24.33/6.31 (symdiffIneg2) =>
% 24.33/6.31 ((
% 24.33/6.31 (secondinupair) =>
% 24.33/6.31 ((
% 24.33/6.31 (setukpairIL) =>
% 24.33/6.31 ((
% 24.33/6.31 (setukpairIR) =>
% 24.33/6.31 ((
% 24.33/6.31 (kpairiskpair) =>
% 24.33/6.31 ((
% 24.33/6.31 (kpairp) =>
% 24.33/6.31 ((
% 24.33/6.31 (singletonsubset) =>
% 24.33/6.31 ((
% 24.33/6.31 (singletoninpowerset) =>
% 24.33/6.31 ((
% 24.33/6.31 (singletoninpowunion) =>
% 24.33/6.31 ((
% 24.33/6.31 (upairset2E) =>
% 24.33/6.31 ((
% 24.33/6.31 (upairsubunion) =>
% 24.33/6.31 ((
% 24.33/6.31 (upairinpowunion) =>
% 24.33/6.31 ((
% 24.33/6.31 (ubforcartprodlem1) =>
% 24.33/6.31 ((
% 24.33/6.31 (ubforcartprodlem2) =>
% 24.33/6.31 ((
% 24.33/6.31 (ubforcartprodlem3) =>
% 24.33/6.31 ((
% 24.33/6.31 (cartprodpairin) =>
% 24.33/6.31 ((
% 24.33/6.31 (cartprodmempair1) =>
% 24.33/6.31 ((
% 24.33/6.31 (cartprodmempair) =>
% 24.33/6.31 ((
% 24.33/6.31 (setunionE2) =>
% 24.33/6.31 ((
% 24.33/6.31 (setunionsingleton1) =>
% 24.33/6.31 ((
% 24.33/6.31 (setunionsingleton2) =>
% 24.33/6.31 ((
% 24.33/6.31 (setunionsingleton) =>
% 24.33/6.31 ((
% 24.33/6.31 (singletonprop) =>
% 24.33/6.31 ((
% 24.33/6.31 (ex1E1) =>
% 24.33/6.31 ((
% 24.33/6.31 (ex1I) =>
% 24.33/6.31 ((
% 24.33/6.31 (ex1I2) =>
% 24.33/6.31 ((
% 24.33/6.31 (singletonsuniq) =>
% 24.33/6.31 ((
% 24.33/6.31 (setukpairinjL1) =>
% 24.33/6.31 ((
% 24.33/6.31 (kfstsingleton) =>
% 24.33/6.31 ((
% 24.33/6.31 (theprop) =>
% 24.33/6.31 ((
% 24.33/6.31 (kfstpairEq) =>
% 24.33/6.31 ((
% 24.33/6.31 (cartprodfstin) =>
% 24.33/6.31 ((
% 24.33/6.31 (setukpairinjL2) =>
% 24.33/6.31 ((
% 24.33/6.31 (setukpairinjL) =>
% 24.33/6.31 ((
% 24.33/6.31 (setukpairinjR11) =>
% 24.33/6.31 ((
% 24.33/6.31 (setukpairinjR12) =>
% 24.33/6.31 ((
% 24.33/6.31 (setukpairinjR1) =>
% 24.33/6.31 ((
% 24.33/6.31 (upairequniteq) =>
% 24.33/6.31 ((
% 24.33/6.31 (setukpairinjR2) =>
% 24.33/6.31 ((
% 24.33/6.31 (setukpairinjR) =>
% 24.33/6.31 ((
% 24.33/6.31 (ksndsingleton) =>
% 24.33/6.31 ((
% 24.33/6.31 (ksndpairEq) =>
% 24.33/6.31 ((
% 24.33/6.31 (kpairsurjEq) =>
% 24.33/6.31 ((
% 24.33/6.31 (cartprodsndin) =>
% 24.33/6.31 ((
% 24.33/6.31 (cartprodpairmemEL) =>
% 24.33/6.31 ((
% 24.33/6.31 (cartprodpairmemER) =>
% 24.33/6.31 ((
% 24.33/6.31 (cartprodmempaircEq) =>
% 24.33/6.31 ((
% 24.33/6.31 (cartprodfstpairEq) =>
% 24.33/6.31 ((
% 24.33/6.31 (cartprodsndpairEq) =>
% 24.33/6.31 ((
% 24.33/6.31 (cartprodpairsurjEq) =>
% 24.33/6.31 ((
% 24.33/6.31 (dpsetconstrI) =>
% 24.33/6.31 ((
% 24.33/6.31 (!!) @ (
% 24.33/6.31 (('#B') @ (
% 24.33/6.31 !!) @
% 24.33/6.31 (
% 24.33/6.31 (
% 24.33/6.31 ('#B') @ (
% 24.33/6.31 (
% 24.33/6.31 ('#B') @ (
% 24.33/6.31 !!))) @
% 24.33/6.31 (
% 24.33/6.31 (
% 24.33/6.31 ('#S') @ (
% 24.33/6.31 (
% 24.33/6.31 ('#B') @ (
% 24.33/6.31 '#S') @
% 24.33/6.31 (
% 24.33/6.31 (
% 24.33/6.31 ('#B') @ (
% 24.33/6.31 (
% 24.33/6.31 ('#B') @ (
% 24.33/6.31 '#C'))) @
% 24.33/6.31 (
% 24.33/6.31 (
% 24.33/6.31 ('#B') @ (
% 24.33/6.31 (
% 24.33/6.31 ('#B') @ (
% 24.33/6.31 (
% 24.33/6.31 ('#B') @ subset)))) @
% 24.33/6.31 dpsetconstr)))))) @
% 24.33/6.31 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.33/6.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl89])).
% 24.33/6.31 thf(zip_derived_cl123, plain,
% 24.33/6.31 (~ (((prop2setE) =>
% 24.33/6.31 (((emptysetE) =>
% 24.33/6.31 (((emptysetimpfalse) =>
% 24.33/6.31 (((notinemptyset) =>
% 24.33/6.31 (((exuE3e) =>
% 24.33/6.31 (((setext) =>
% 24.33/6.31 (((emptyI) =>
% 24.33/6.31 (((noeltsimpempty) =>
% 24.33/6.31 (((setbeta) =>
% 24.33/6.31 (((nonemptyE1) =>
% 24.33/6.31 (((nonemptyI) =>
% 24.33/6.31 (((nonemptyI1) =>
% 24.33/6.31 (((setadjoinIL) =>
% 24.33/6.31 (((in @ emptyset @
% 24.33/6.31 (setadjoin @ emptyset @ emptyset)) =>
% 24.33/6.31 (((setadjoinIR) =>
% 24.33/6.31 (((setadjoinE) =>
% 24.33/6.31 (((setadjoinOr) =>
% 24.33/6.31 (((setoftrueEq) =>
% 24.33/6.31 (((powersetI) =>
% 24.33/6.31 (((emptyinPowerset) =>
% 24.33/6.31 (((emptyInPowerset) =>
% 24.33/6.31 (((powersetE) =>
% 24.33/6.31 (((setunionI) =>
% 24.33/6.31 (((setunionE) =>
% 24.33/6.31 (((subPowSU) =>
% 24.33/6.31 (((exuE2) =>
% 24.33/6.31 (((nonemptyImpWitness) =>
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% 24.33/6.31 (((notinsingleton) =>
% 24.33/6.31 (((eqinunit) =>
% 24.33/6.31 ((
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% 24.33/6.31 ((
% 24.33/6.31 (upairsetE) =>
% 24.33/6.31 ((
% 24.33/6.31 (upairsetIL) =>
% 24.33/6.31 ((
% 24.33/6.31 (upairsetIR) =>
% 24.33/6.31 ((
% 24.33/6.31 (emptyE1) =>
% 24.33/6.31 ((
% 24.33/6.31 (vacuousDall) =>
% 24.33/6.31 ((
% 24.33/6.31 (quantDeMorgan1) =>
% 24.33/6.31 ((
% 24.33/6.31 (quantDeMorgan2) =>
% 24.33/6.31 ((
% 24.33/6.32 (quantDeMorgan3) =>
% 24.33/6.32 ((
% 24.33/6.32 (quantDeMorgan4) =>
% 24.33/6.32 ((
% 24.33/6.32 (prop2setI) =>
% 24.33/6.32 ((
% 24.33/6.32 (prop2set2propI) =>
% 24.33/6.32 ((
% 24.33/6.32 (notdexE) =>
% 24.33/6.32 ((
% 24.33/6.32 (notdallE) =>
% 24.33/6.32 ((
% 24.33/6.32 (exuI1) =>
% 24.33/6.32 ((
% 24.33/6.32 (exuI3) =>
% 24.33/6.32 ((
% 24.33/6.32 (exuI2) =>
% 24.33/6.32 ((
% 24.33/6.32 (inCongP) =>
% 24.33/6.32 ((
% 24.33/6.32 (in__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (exuE3u) =>
% 24.33/6.32 ((
% 24.33/6.32 (exu__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (setadjoin__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (powerset__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (setunion__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (exuEu) =>
% 24.33/6.32 ((
% 24.33/6.32 (descr__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (dsetconstr__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetI1) =>
% 24.33/6.32 ((
% 24.33/6.32 (eqimpsubset2) =>
% 24.33/6.32 ((
% 24.33/6.32 (eqimpsubset1) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetI2) =>
% 24.33/6.32 ((
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% 24.33/6.32 ((
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% 24.33/6.32 ((
% 24.33/6.32 (subsetE2) =>
% 24.33/6.32 ((
% 24.33/6.32 (notsubsetI) =>
% 24.33/6.32 ((
% 24.33/6.32 (notequalI1) =>
% 24.33/6.32 ((
% 24.33/6.32 (notequalI2) =>
% 24.33/6.32 ((
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% 24.33/6.32 ((
% 24.33/6.32 (subsetTrans) =>
% 24.33/6.32 ((
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% 24.33/6.32 ((
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% 24.33/6.32 ((
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% 24.33/6.32 ((
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% 24.33/6.32 ((
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% 24.33/6.32 ((
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% 24.33/6.32 ((
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% 24.33/6.32 ((
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% 24.33/6.32 ((
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% 24.33/6.32 ((
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% 24.33/6.32 ((
% 24.33/6.32 (upairset2IR) =>
% 24.33/6.32 ((
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% 24.33/6.32 ((
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% 24.33/6.32 ((
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% 24.33/6.32 ((
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% 24.33/6.32 ((
% 24.33/6.32 (binunionRsub) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectI) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectSubset5) =>
% 24.33/6.32 ((
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% 24.33/6.32 ((
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% 24.33/6.32 ((
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% 24.33/6.32 ((
% 24.33/6.32 (binintersectSubset3) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectER) =>
% 24.33/6.32 ((
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% 24.33/6.32 ((
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% 24.33/6.32 ((
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% 24.33/6.32 ((
% 24.33/6.32 (binintersectSubset1) =>
% 24.33/6.32 ((
% 24.33/6.32 (bs114d) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusI) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusEL) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusER) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusSubset2) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusERneg) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusELneg) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusILneg) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusIRneg) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusLsub) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusSubset1) =>
% 24.33/6.32 ((
% 24.33/6.32 (symdiffE) =>
% 24.33/6.32 ((
% 24.33/6.32 (symdiffI1) =>
% 24.33/6.32 ((
% 24.33/6.32 (symdiffI2) =>
% 24.33/6.32 ((
% 24.33/6.32 (symdiffIneg1) =>
% 24.33/6.32 ((
% 24.33/6.32 (symdiffIneg2) =>
% 24.33/6.32 ((
% 24.33/6.32 (secondinupair) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairIL) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairIR) =>
% 24.33/6.32 ((
% 24.33/6.32 (kpairiskpair) =>
% 24.33/6.32 ((
% 24.33/6.32 (kpairp) =>
% 24.33/6.32 ((
% 24.33/6.32 (singletonsubset) =>
% 24.33/6.32 ((
% 24.33/6.32 (singletoninpowerset) =>
% 24.33/6.32 ((
% 24.33/6.32 (singletoninpowunion) =>
% 24.33/6.32 ((
% 24.33/6.32 (upairset2E) =>
% 24.33/6.32 ((
% 24.33/6.32 (upairsubunion) =>
% 24.33/6.32 ((
% 24.33/6.32 (upairinpowunion) =>
% 24.33/6.32 ((
% 24.33/6.32 (ubforcartprodlem1) =>
% 24.33/6.32 ((
% 24.33/6.32 (ubforcartprodlem2) =>
% 24.33/6.32 ((
% 24.33/6.32 (ubforcartprodlem3) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodpairin) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodmempair1) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodmempair) =>
% 24.33/6.32 ((
% 24.33/6.32 (setunionE2) =>
% 24.33/6.32 ((
% 24.33/6.32 (setunionsingleton1) =>
% 24.33/6.32 ((
% 24.33/6.32 (setunionsingleton2) =>
% 24.33/6.32 ((
% 24.33/6.32 (setunionsingleton) =>
% 24.33/6.32 ((
% 24.33/6.32 (singletonprop) =>
% 24.33/6.32 ((
% 24.33/6.32 (ex1E1) =>
% 24.33/6.32 ((
% 24.33/6.32 (ex1I) =>
% 24.33/6.32 ((
% 24.33/6.32 (ex1I2) =>
% 24.33/6.32 ((
% 24.33/6.32 (singletonsuniq) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjL1) =>
% 24.33/6.32 ((
% 24.33/6.32 (kfstsingleton) =>
% 24.33/6.32 ((
% 24.33/6.32 (theprop) =>
% 24.33/6.32 ((
% 24.33/6.32 (kfstpairEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodfstin) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjL2) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjL) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjR11) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjR12) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjR1) =>
% 24.33/6.32 ((
% 24.33/6.32 (upairequniteq) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjR2) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjR) =>
% 24.33/6.32 ((
% 24.33/6.32 (ksndsingleton) =>
% 24.33/6.32 ((
% 24.33/6.32 (ksndpairEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (kpairsurjEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodsndin) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodpairmemEL) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodpairmemER) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodmempaircEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodfstpairEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodsndpairEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodpairsurjEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (dpsetconstrI) =>
% 24.33/6.32 ((
% 24.33/6.32 (!!) @ (
% 24.33/6.32 (('#B') @ (
% 24.33/6.32 !!) @
% 24.33/6.32 (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 !!))) @
% 24.33/6.32 (
% 24.33/6.32 (
% 24.33/6.32 ('#S') @ (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 '#S') @
% 24.33/6.32 (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 '#C'))) @
% 24.33/6.32 (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ subset)))) @
% 24.33/6.32 dpsetconstr)))))) @
% 24.33/6.32 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.33/6.32 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl105])).
% 24.33/6.32 thf(zip_derived_cl142, plain,
% 24.33/6.32 (~ (((emptysetE) =>
% 24.33/6.32 (((emptysetimpfalse) =>
% 24.33/6.32 (((notinemptyset) =>
% 24.33/6.32 (((exuE3e) =>
% 24.33/6.32 (((setext) =>
% 24.33/6.32 (((emptyI) =>
% 24.33/6.32 (((noeltsimpempty) =>
% 24.33/6.32 (((setbeta) =>
% 24.33/6.32 (((nonemptyE1) =>
% 24.33/6.32 (((nonemptyI) =>
% 24.33/6.32 (((nonemptyI1) =>
% 24.33/6.32 (((setadjoinIL) =>
% 24.33/6.32 (((in @ emptyset @
% 24.33/6.32 (setadjoin @ emptyset @ emptyset)) =>
% 24.33/6.32 (((setadjoinIR) =>
% 24.33/6.32 (((setadjoinE) =>
% 24.33/6.32 (((setadjoinOr) =>
% 24.33/6.32 (((setoftrueEq) =>
% 24.33/6.32 (((powersetI) =>
% 24.33/6.32 (((emptyinPowerset) =>
% 24.33/6.32 (((emptyInPowerset) =>
% 24.33/6.32 (((powersetE) =>
% 24.33/6.32 (((setunionI) =>
% 24.33/6.32 (((setunionE) =>
% 24.33/6.32 (((subPowSU) =>
% 24.33/6.32 (((exuE2) =>
% 24.33/6.32 (((nonemptyImpWitness) =>
% 24.33/6.32 (((uniqinunit) =>
% 24.33/6.32 (((notinsingleton) =>
% 24.33/6.32 (((eqinunit) =>
% 24.33/6.32 (((singletonsswitch) =>
% 24.33/6.32 ((
% 24.33/6.32 (upairsetE) =>
% 24.33/6.32 ((
% 24.33/6.32 (upairsetIL) =>
% 24.33/6.32 ((
% 24.33/6.32 (upairsetIR) =>
% 24.33/6.32 ((
% 24.33/6.32 (emptyE1) =>
% 24.33/6.32 ((
% 24.33/6.32 (vacuousDall) =>
% 24.33/6.32 ((
% 24.33/6.32 (quantDeMorgan1) =>
% 24.33/6.32 ((
% 24.33/6.32 (quantDeMorgan2) =>
% 24.33/6.32 ((
% 24.33/6.32 (quantDeMorgan3) =>
% 24.33/6.32 ((
% 24.33/6.32 (quantDeMorgan4) =>
% 24.33/6.32 ((
% 24.33/6.32 (prop2setI) =>
% 24.33/6.32 ((
% 24.33/6.32 (prop2set2propI) =>
% 24.33/6.32 ((
% 24.33/6.32 (notdexE) =>
% 24.33/6.32 ((
% 24.33/6.32 (notdallE) =>
% 24.33/6.32 ((
% 24.33/6.32 (exuI1) =>
% 24.33/6.32 ((
% 24.33/6.32 (exuI3) =>
% 24.33/6.32 ((
% 24.33/6.32 (exuI2) =>
% 24.33/6.32 ((
% 24.33/6.32 (inCongP) =>
% 24.33/6.32 ((
% 24.33/6.32 (in__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (exuE3u) =>
% 24.33/6.32 ((
% 24.33/6.32 (exu__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (setadjoin__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (powerset__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (setunion__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (exuEu) =>
% 24.33/6.32 ((
% 24.33/6.32 (descr__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (dsetconstr__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetI1) =>
% 24.33/6.32 ((
% 24.33/6.32 (eqimpsubset2) =>
% 24.33/6.32 ((
% 24.33/6.32 (eqimpsubset1) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetI2) =>
% 24.33/6.32 ((
% 24.33/6.32 (emptysetsubset) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetE) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetE2) =>
% 24.33/6.32 ((
% 24.33/6.32 (notsubsetI) =>
% 24.33/6.32 ((
% 24.33/6.32 (notequalI1) =>
% 24.33/6.32 ((
% 24.33/6.32 (notequalI2) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetRefl) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetTrans) =>
% 24.33/6.32 ((
% 24.33/6.32 (setadjoinSub) =>
% 24.33/6.32 ((
% 24.33/6.32 (setadjoinSub2) =>
% 24.33/6.32 ((
% 24.33/6.32 (subset2powerset) =>
% 24.33/6.32 ((
% 24.33/6.32 (setextsub) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetemptysetimpeq) =>
% 24.33/6.32 ((
% 24.33/6.32 (powersetI1) =>
% 24.33/6.32 ((
% 24.33/6.32 (powersetE1) =>
% 24.33/6.32 ((
% 24.33/6.32 (inPowerset) =>
% 24.33/6.32 ((
% 24.33/6.32 (powersetsubset) =>
% 24.33/6.32 ((
% 24.33/6.32 (sepInPowerset) =>
% 24.33/6.32 ((
% 24.33/6.32 (sepSubset) =>
% 24.33/6.32 ((
% 24.33/6.32 (binunionIL) =>
% 24.33/6.32 ((
% 24.33/6.32 (upairset2IR) =>
% 24.33/6.32 ((
% 24.33/6.32 (binunionIR) =>
% 24.33/6.32 ((
% 24.33/6.32 (binunionEcases) =>
% 24.33/6.32 ((
% 24.33/6.32 (binunionE) =>
% 24.33/6.32 ((
% 24.33/6.32 (binunionLsub) =>
% 24.33/6.32 ((
% 24.33/6.32 (binunionRsub) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectI) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectSubset5) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectEL) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectLsub) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectSubset2) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectSubset3) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectER) =>
% 24.33/6.32 ((
% 24.33/6.32 (disjointsetsI1) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectRsub) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectSubset4) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectSubset1) =>
% 24.33/6.32 ((
% 24.33/6.32 (bs114d) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusI) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusEL) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusER) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusSubset2) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusERneg) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusELneg) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusILneg) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusIRneg) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusLsub) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusSubset1) =>
% 24.33/6.32 ((
% 24.33/6.32 (symdiffE) =>
% 24.33/6.32 ((
% 24.33/6.32 (symdiffI1) =>
% 24.33/6.32 ((
% 24.33/6.32 (symdiffI2) =>
% 24.33/6.32 ((
% 24.33/6.32 (symdiffIneg1) =>
% 24.33/6.32 ((
% 24.33/6.32 (symdiffIneg2) =>
% 24.33/6.32 ((
% 24.33/6.32 (secondinupair) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairIL) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairIR) =>
% 24.33/6.32 ((
% 24.33/6.32 (kpairiskpair) =>
% 24.33/6.32 ((
% 24.33/6.32 (kpairp) =>
% 24.33/6.32 ((
% 24.33/6.32 (singletonsubset) =>
% 24.33/6.32 ((
% 24.33/6.32 (singletoninpowerset) =>
% 24.33/6.32 ((
% 24.33/6.32 (singletoninpowunion) =>
% 24.33/6.32 ((
% 24.33/6.32 (upairset2E) =>
% 24.33/6.32 ((
% 24.33/6.32 (upairsubunion) =>
% 24.33/6.32 ((
% 24.33/6.32 (upairinpowunion) =>
% 24.33/6.32 ((
% 24.33/6.32 (ubforcartprodlem1) =>
% 24.33/6.32 ((
% 24.33/6.32 (ubforcartprodlem2) =>
% 24.33/6.32 ((
% 24.33/6.32 (ubforcartprodlem3) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodpairin) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodmempair1) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodmempair) =>
% 24.33/6.32 ((
% 24.33/6.32 (setunionE2) =>
% 24.33/6.32 ((
% 24.33/6.32 (setunionsingleton1) =>
% 24.33/6.32 ((
% 24.33/6.32 (setunionsingleton2) =>
% 24.33/6.32 ((
% 24.33/6.32 (setunionsingleton) =>
% 24.33/6.32 ((
% 24.33/6.32 (singletonprop) =>
% 24.33/6.32 ((
% 24.33/6.32 (ex1E1) =>
% 24.33/6.32 ((
% 24.33/6.32 (ex1I) =>
% 24.33/6.32 ((
% 24.33/6.32 (ex1I2) =>
% 24.33/6.32 ((
% 24.33/6.32 (singletonsuniq) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjL1) =>
% 24.33/6.32 ((
% 24.33/6.32 (kfstsingleton) =>
% 24.33/6.32 ((
% 24.33/6.32 (theprop) =>
% 24.33/6.32 ((
% 24.33/6.32 (kfstpairEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodfstin) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjL2) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjL) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjR11) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjR12) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjR1) =>
% 24.33/6.32 ((
% 24.33/6.32 (upairequniteq) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjR2) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjR) =>
% 24.33/6.32 ((
% 24.33/6.32 (ksndsingleton) =>
% 24.33/6.32 ((
% 24.33/6.32 (ksndpairEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (kpairsurjEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodsndin) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodpairmemEL) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodpairmemER) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodmempaircEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodfstpairEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodsndpairEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodpairsurjEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (dpsetconstrI) =>
% 24.33/6.32 ((
% 24.33/6.32 (!!) @ (
% 24.33/6.32 (('#B') @ (
% 24.33/6.32 !!) @
% 24.33/6.32 (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 !!))) @
% 24.33/6.32 (
% 24.33/6.32 (
% 24.33/6.32 ('#S') @ (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 '#S') @
% 24.33/6.32 (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 '#C'))) @
% 24.33/6.32 (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ subset)))) @
% 24.33/6.32 dpsetconstr)))))) @
% 24.33/6.32 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.33/6.32 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl123])).
% 24.33/6.32 thf(zip_derived_cl158, plain,
% 24.33/6.32 (~ (((emptysetimpfalse) =>
% 24.33/6.32 (((notinemptyset) =>
% 24.33/6.32 (((exuE3e) =>
% 24.33/6.32 (((setext) =>
% 24.33/6.32 (((emptyI) =>
% 24.33/6.32 (((noeltsimpempty) =>
% 24.33/6.32 (((setbeta) =>
% 24.33/6.32 (((nonemptyE1) =>
% 24.33/6.32 (((nonemptyI) =>
% 24.33/6.32 (((nonemptyI1) =>
% 24.33/6.32 (((setadjoinIL) =>
% 24.33/6.32 (((in @ emptyset @
% 24.33/6.32 (setadjoin @ emptyset @ emptyset)) =>
% 24.33/6.32 (((setadjoinIR) =>
% 24.33/6.32 (((setadjoinE) =>
% 24.33/6.32 (((setadjoinOr) =>
% 24.33/6.32 (((setoftrueEq) =>
% 24.33/6.32 (((powersetI) =>
% 24.33/6.32 (((emptyinPowerset) =>
% 24.33/6.32 (((emptyInPowerset) =>
% 24.33/6.32 (((powersetE) =>
% 24.33/6.32 (((setunionI) =>
% 24.33/6.32 (((setunionE) =>
% 24.33/6.32 (((subPowSU) =>
% 24.33/6.32 (((exuE2) =>
% 24.33/6.32 (((nonemptyImpWitness) =>
% 24.33/6.32 (((uniqinunit) =>
% 24.33/6.32 (((notinsingleton) =>
% 24.33/6.32 (((eqinunit) =>
% 24.33/6.32 (((singletonsswitch) =>
% 24.33/6.32 (((upairsetE) =>
% 24.33/6.32 ((
% 24.33/6.32 (upairsetIL) =>
% 24.33/6.32 ((
% 24.33/6.32 (upairsetIR) =>
% 24.33/6.32 ((
% 24.33/6.32 (emptyE1) =>
% 24.33/6.32 ((
% 24.33/6.32 (vacuousDall) =>
% 24.33/6.32 ((
% 24.33/6.32 (quantDeMorgan1) =>
% 24.33/6.32 ((
% 24.33/6.32 (quantDeMorgan2) =>
% 24.33/6.32 ((
% 24.33/6.32 (quantDeMorgan3) =>
% 24.33/6.32 ((
% 24.33/6.32 (quantDeMorgan4) =>
% 24.33/6.32 ((
% 24.33/6.32 (prop2setI) =>
% 24.33/6.32 ((
% 24.33/6.32 (prop2set2propI) =>
% 24.33/6.32 ((
% 24.33/6.32 (notdexE) =>
% 24.33/6.32 ((
% 24.33/6.32 (notdallE) =>
% 24.33/6.32 ((
% 24.33/6.32 (exuI1) =>
% 24.33/6.32 ((
% 24.33/6.32 (exuI3) =>
% 24.33/6.32 ((
% 24.33/6.32 (exuI2) =>
% 24.33/6.32 ((
% 24.33/6.32 (inCongP) =>
% 24.33/6.32 ((
% 24.33/6.32 (in__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (exuE3u) =>
% 24.33/6.32 ((
% 24.33/6.32 (exu__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (setadjoin__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (powerset__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (setunion__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (exuEu) =>
% 24.33/6.32 ((
% 24.33/6.32 (descr__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (dsetconstr__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetI1) =>
% 24.33/6.32 ((
% 24.33/6.32 (eqimpsubset2) =>
% 24.33/6.32 ((
% 24.33/6.32 (eqimpsubset1) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetI2) =>
% 24.33/6.32 ((
% 24.33/6.32 (emptysetsubset) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetE) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetE2) =>
% 24.33/6.32 ((
% 24.33/6.32 (notsubsetI) =>
% 24.33/6.32 ((
% 24.33/6.32 (notequalI1) =>
% 24.33/6.32 ((
% 24.33/6.32 (notequalI2) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetRefl) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetTrans) =>
% 24.33/6.32 ((
% 24.33/6.32 (setadjoinSub) =>
% 24.33/6.32 ((
% 24.33/6.32 (setadjoinSub2) =>
% 24.33/6.32 ((
% 24.33/6.32 (subset2powerset) =>
% 24.33/6.32 ((
% 24.33/6.32 (setextsub) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetemptysetimpeq) =>
% 24.33/6.32 ((
% 24.33/6.32 (powersetI1) =>
% 24.33/6.32 ((
% 24.33/6.32 (powersetE1) =>
% 24.33/6.32 ((
% 24.33/6.32 (inPowerset) =>
% 24.33/6.32 ((
% 24.33/6.32 (powersetsubset) =>
% 24.33/6.32 ((
% 24.33/6.32 (sepInPowerset) =>
% 24.33/6.32 ((
% 24.33/6.32 (sepSubset) =>
% 24.33/6.32 ((
% 24.33/6.32 (binunionIL) =>
% 24.33/6.32 ((
% 24.33/6.32 (upairset2IR) =>
% 24.33/6.32 ((
% 24.33/6.32 (binunionIR) =>
% 24.33/6.32 ((
% 24.33/6.32 (binunionEcases) =>
% 24.33/6.32 ((
% 24.33/6.32 (binunionE) =>
% 24.33/6.32 ((
% 24.33/6.32 (binunionLsub) =>
% 24.33/6.32 ((
% 24.33/6.32 (binunionRsub) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectI) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectSubset5) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectEL) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectLsub) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectSubset2) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectSubset3) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectER) =>
% 24.33/6.32 ((
% 24.33/6.32 (disjointsetsI1) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectRsub) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectSubset4) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectSubset1) =>
% 24.33/6.32 ((
% 24.33/6.32 (bs114d) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusI) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusEL) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusER) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusSubset2) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusERneg) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusELneg) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusILneg) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusIRneg) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusLsub) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusSubset1) =>
% 24.33/6.32 ((
% 24.33/6.32 (symdiffE) =>
% 24.33/6.32 ((
% 24.33/6.32 (symdiffI1) =>
% 24.33/6.32 ((
% 24.33/6.32 (symdiffI2) =>
% 24.33/6.32 ((
% 24.33/6.32 (symdiffIneg1) =>
% 24.33/6.32 ((
% 24.33/6.32 (symdiffIneg2) =>
% 24.33/6.32 ((
% 24.33/6.32 (secondinupair) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairIL) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairIR) =>
% 24.33/6.32 ((
% 24.33/6.32 (kpairiskpair) =>
% 24.33/6.32 ((
% 24.33/6.32 (kpairp) =>
% 24.33/6.32 ((
% 24.33/6.32 (singletonsubset) =>
% 24.33/6.32 ((
% 24.33/6.32 (singletoninpowerset) =>
% 24.33/6.32 ((
% 24.33/6.32 (singletoninpowunion) =>
% 24.33/6.32 ((
% 24.33/6.32 (upairset2E) =>
% 24.33/6.32 ((
% 24.33/6.32 (upairsubunion) =>
% 24.33/6.32 ((
% 24.33/6.32 (upairinpowunion) =>
% 24.33/6.32 ((
% 24.33/6.32 (ubforcartprodlem1) =>
% 24.33/6.32 ((
% 24.33/6.32 (ubforcartprodlem2) =>
% 24.33/6.32 ((
% 24.33/6.32 (ubforcartprodlem3) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodpairin) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodmempair1) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodmempair) =>
% 24.33/6.32 ((
% 24.33/6.32 (setunionE2) =>
% 24.33/6.32 ((
% 24.33/6.32 (setunionsingleton1) =>
% 24.33/6.32 ((
% 24.33/6.32 (setunionsingleton2) =>
% 24.33/6.32 ((
% 24.33/6.32 (setunionsingleton) =>
% 24.33/6.32 ((
% 24.33/6.32 (singletonprop) =>
% 24.33/6.32 ((
% 24.33/6.32 (ex1E1) =>
% 24.33/6.32 ((
% 24.33/6.32 (ex1I) =>
% 24.33/6.32 ((
% 24.33/6.32 (ex1I2) =>
% 24.33/6.32 ((
% 24.33/6.32 (singletonsuniq) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjL1) =>
% 24.33/6.32 ((
% 24.33/6.32 (kfstsingleton) =>
% 24.33/6.32 ((
% 24.33/6.32 (theprop) =>
% 24.33/6.32 ((
% 24.33/6.32 (kfstpairEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodfstin) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjL2) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjL) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjR11) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjR12) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjR1) =>
% 24.33/6.32 ((
% 24.33/6.32 (upairequniteq) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjR2) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjR) =>
% 24.33/6.32 ((
% 24.33/6.32 (ksndsingleton) =>
% 24.33/6.32 ((
% 24.33/6.32 (ksndpairEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (kpairsurjEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodsndin) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodpairmemEL) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodpairmemER) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodmempaircEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodfstpairEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodsndpairEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodpairsurjEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (dpsetconstrI) =>
% 24.33/6.32 ((
% 24.33/6.32 (!!) @ (
% 24.33/6.32 (('#B') @ (
% 24.33/6.32 !!) @
% 24.33/6.32 (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 !!))) @
% 24.33/6.32 (
% 24.33/6.32 (
% 24.33/6.32 ('#S') @ (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 '#S') @
% 24.33/6.32 (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 '#C'))) @
% 24.33/6.32 (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ subset)))) @
% 24.33/6.32 dpsetconstr)))))) @
% 24.33/6.32 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.33/6.32 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl142])).
% 24.33/6.32 thf(zip_derived_cl174, plain,
% 24.33/6.32 (~ (((notinemptyset) =>
% 24.33/6.32 (((exuE3e) =>
% 24.33/6.32 (((setext) =>
% 24.33/6.32 (((emptyI) =>
% 24.33/6.32 (((noeltsimpempty) =>
% 24.33/6.32 (((setbeta) =>
% 24.33/6.32 (((nonemptyE1) =>
% 24.33/6.32 (((nonemptyI) =>
% 24.33/6.32 (((nonemptyI1) =>
% 24.33/6.32 (((setadjoinIL) =>
% 24.33/6.32 (((in @ emptyset @
% 24.33/6.32 (setadjoin @ emptyset @ emptyset)) =>
% 24.33/6.32 (((setadjoinIR) =>
% 24.33/6.32 (((setadjoinE) =>
% 24.33/6.32 (((setadjoinOr) =>
% 24.33/6.32 (((setoftrueEq) =>
% 24.33/6.32 (((powersetI) =>
% 24.33/6.32 (((emptyinPowerset) =>
% 24.33/6.32 (((emptyInPowerset) =>
% 24.33/6.32 (((powersetE) =>
% 24.33/6.32 (((setunionI) =>
% 24.33/6.32 (((setunionE) =>
% 24.33/6.32 (((subPowSU) =>
% 24.33/6.32 (((exuE2) =>
% 24.33/6.32 (((nonemptyImpWitness) =>
% 24.33/6.32 (((uniqinunit) =>
% 24.33/6.32 (((notinsingleton) =>
% 24.33/6.32 (((eqinunit) =>
% 24.33/6.32 (((singletonsswitch) =>
% 24.33/6.32 (((upairsetE) =>
% 24.33/6.32 (((upairsetIL) =>
% 24.33/6.32 ((
% 24.33/6.32 (upairsetIR) =>
% 24.33/6.32 ((
% 24.33/6.32 (emptyE1) =>
% 24.33/6.32 ((
% 24.33/6.32 (vacuousDall) =>
% 24.33/6.32 ((
% 24.33/6.32 (quantDeMorgan1) =>
% 24.33/6.32 ((
% 24.33/6.32 (quantDeMorgan2) =>
% 24.33/6.32 ((
% 24.33/6.32 (quantDeMorgan3) =>
% 24.33/6.32 ((
% 24.33/6.32 (quantDeMorgan4) =>
% 24.33/6.32 ((
% 24.33/6.32 (prop2setI) =>
% 24.33/6.32 ((
% 24.33/6.32 (prop2set2propI) =>
% 24.33/6.32 ((
% 24.33/6.32 (notdexE) =>
% 24.33/6.32 ((
% 24.33/6.32 (notdallE) =>
% 24.33/6.32 ((
% 24.33/6.32 (exuI1) =>
% 24.33/6.32 ((
% 24.33/6.32 (exuI3) =>
% 24.33/6.32 ((
% 24.33/6.32 (exuI2) =>
% 24.33/6.32 ((
% 24.33/6.32 (inCongP) =>
% 24.33/6.32 ((
% 24.33/6.32 (in__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (exuE3u) =>
% 24.33/6.32 ((
% 24.33/6.32 (exu__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (setadjoin__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (powerset__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (setunion__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (exuEu) =>
% 24.33/6.32 ((
% 24.33/6.32 (descr__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (dsetconstr__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetI1) =>
% 24.33/6.32 ((
% 24.33/6.32 (eqimpsubset2) =>
% 24.33/6.32 ((
% 24.33/6.32 (eqimpsubset1) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetI2) =>
% 24.33/6.32 ((
% 24.33/6.32 (emptysetsubset) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetE) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetE2) =>
% 24.33/6.32 ((
% 24.33/6.32 (notsubsetI) =>
% 24.33/6.32 ((
% 24.33/6.32 (notequalI1) =>
% 24.33/6.32 ((
% 24.33/6.32 (notequalI2) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetRefl) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetTrans) =>
% 24.33/6.32 ((
% 24.33/6.32 (setadjoinSub) =>
% 24.33/6.32 ((
% 24.33/6.32 (setadjoinSub2) =>
% 24.33/6.32 ((
% 24.33/6.32 (subset2powerset) =>
% 24.33/6.32 ((
% 24.33/6.32 (setextsub) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetemptysetimpeq) =>
% 24.33/6.32 ((
% 24.33/6.32 (powersetI1) =>
% 24.33/6.32 ((
% 24.33/6.32 (powersetE1) =>
% 24.33/6.32 ((
% 24.33/6.32 (inPowerset) =>
% 24.33/6.32 ((
% 24.33/6.32 (powersetsubset) =>
% 24.33/6.32 ((
% 24.33/6.32 (sepInPowerset) =>
% 24.33/6.32 ((
% 24.33/6.32 (sepSubset) =>
% 24.33/6.32 ((
% 24.33/6.32 (binunionIL) =>
% 24.33/6.32 ((
% 24.33/6.32 (upairset2IR) =>
% 24.33/6.32 ((
% 24.33/6.32 (binunionIR) =>
% 24.33/6.32 ((
% 24.33/6.32 (binunionEcases) =>
% 24.33/6.32 ((
% 24.33/6.32 (binunionE) =>
% 24.33/6.32 ((
% 24.33/6.32 (binunionLsub) =>
% 24.33/6.32 ((
% 24.33/6.32 (binunionRsub) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectI) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectSubset5) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectEL) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectLsub) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectSubset2) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectSubset3) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectER) =>
% 24.33/6.32 ((
% 24.33/6.32 (disjointsetsI1) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectRsub) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectSubset4) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectSubset1) =>
% 24.33/6.32 ((
% 24.33/6.32 (bs114d) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusI) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusEL) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusER) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusSubset2) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusERneg) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusELneg) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusILneg) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusIRneg) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusLsub) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusSubset1) =>
% 24.33/6.32 ((
% 24.33/6.32 (symdiffE) =>
% 24.33/6.32 ((
% 24.33/6.32 (symdiffI1) =>
% 24.33/6.32 ((
% 24.33/6.32 (symdiffI2) =>
% 24.33/6.32 ((
% 24.33/6.32 (symdiffIneg1) =>
% 24.33/6.32 ((
% 24.33/6.32 (symdiffIneg2) =>
% 24.33/6.32 ((
% 24.33/6.32 (secondinupair) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairIL) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairIR) =>
% 24.33/6.32 ((
% 24.33/6.32 (kpairiskpair) =>
% 24.33/6.32 ((
% 24.33/6.32 (kpairp) =>
% 24.33/6.32 ((
% 24.33/6.32 (singletonsubset) =>
% 24.33/6.32 ((
% 24.33/6.32 (singletoninpowerset) =>
% 24.33/6.32 ((
% 24.33/6.32 (singletoninpowunion) =>
% 24.33/6.32 ((
% 24.33/6.32 (upairset2E) =>
% 24.33/6.32 ((
% 24.33/6.32 (upairsubunion) =>
% 24.33/6.32 ((
% 24.33/6.32 (upairinpowunion) =>
% 24.33/6.32 ((
% 24.33/6.32 (ubforcartprodlem1) =>
% 24.33/6.32 ((
% 24.33/6.32 (ubforcartprodlem2) =>
% 24.33/6.32 ((
% 24.33/6.32 (ubforcartprodlem3) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodpairin) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodmempair1) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodmempair) =>
% 24.33/6.32 ((
% 24.33/6.32 (setunionE2) =>
% 24.33/6.32 ((
% 24.33/6.32 (setunionsingleton1) =>
% 24.33/6.32 ((
% 24.33/6.32 (setunionsingleton2) =>
% 24.33/6.32 ((
% 24.33/6.32 (setunionsingleton) =>
% 24.33/6.32 ((
% 24.33/6.32 (singletonprop) =>
% 24.33/6.32 ((
% 24.33/6.32 (ex1E1) =>
% 24.33/6.32 ((
% 24.33/6.32 (ex1I) =>
% 24.33/6.32 ((
% 24.33/6.32 (ex1I2) =>
% 24.33/6.32 ((
% 24.33/6.32 (singletonsuniq) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjL1) =>
% 24.33/6.32 ((
% 24.33/6.32 (kfstsingleton) =>
% 24.33/6.32 ((
% 24.33/6.32 (theprop) =>
% 24.33/6.32 ((
% 24.33/6.32 (kfstpairEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodfstin) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjL2) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjL) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjR11) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjR12) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjR1) =>
% 24.33/6.32 ((
% 24.33/6.32 (upairequniteq) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjR2) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjR) =>
% 24.33/6.32 ((
% 24.33/6.32 (ksndsingleton) =>
% 24.33/6.32 ((
% 24.33/6.32 (ksndpairEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (kpairsurjEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodsndin) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodpairmemEL) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodpairmemER) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodmempaircEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodfstpairEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodsndpairEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodpairsurjEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (dpsetconstrI) =>
% 24.33/6.32 ((
% 24.33/6.32 (!!) @ (
% 24.33/6.32 (('#B') @ (
% 24.33/6.32 !!) @
% 24.33/6.32 (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 !!))) @
% 24.33/6.32 (
% 24.33/6.32 (
% 24.33/6.32 ('#S') @ (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 '#S') @
% 24.33/6.32 (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 '#C'))) @
% 24.33/6.32 (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ subset)))) @
% 24.33/6.32 dpsetconstr)))))) @
% 24.33/6.32 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.33/6.32 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl158])).
% 24.33/6.32 thf(zip_derived_cl189, plain,
% 24.33/6.32 (~ (((exuE3e) =>
% 24.33/6.32 (((setext) =>
% 24.33/6.32 (((emptyI) =>
% 24.33/6.32 (((noeltsimpempty) =>
% 24.33/6.32 (((setbeta) =>
% 24.33/6.32 (((nonemptyE1) =>
% 24.33/6.32 (((nonemptyI) =>
% 24.33/6.32 (((nonemptyI1) =>
% 24.33/6.32 (((setadjoinIL) =>
% 24.33/6.32 (((in @ emptyset @
% 24.33/6.32 (setadjoin @ emptyset @ emptyset)) =>
% 24.33/6.32 (((setadjoinIR) =>
% 24.33/6.32 (((setadjoinE) =>
% 24.33/6.32 (((setadjoinOr) =>
% 24.33/6.32 (((setoftrueEq) =>
% 24.33/6.32 (((powersetI) =>
% 24.33/6.32 (((emptyinPowerset) =>
% 24.33/6.32 (((emptyInPowerset) =>
% 24.33/6.32 (((powersetE) =>
% 24.33/6.32 (((setunionI) =>
% 24.33/6.32 (((setunionE) =>
% 24.33/6.32 (((subPowSU) =>
% 24.33/6.32 (((exuE2) =>
% 24.33/6.32 (((nonemptyImpWitness) =>
% 24.33/6.32 (((uniqinunit) =>
% 24.33/6.32 (((notinsingleton) =>
% 24.33/6.32 (((eqinunit) =>
% 24.33/6.32 (((singletonsswitch) =>
% 24.33/6.32 (((upairsetE) =>
% 24.33/6.32 (((upairsetIL) =>
% 24.33/6.32 (((upairsetIR) =>
% 24.33/6.32 ((
% 24.33/6.32 (emptyE1) =>
% 24.33/6.32 ((
% 24.33/6.32 (vacuousDall) =>
% 24.33/6.32 ((
% 24.33/6.32 (quantDeMorgan1) =>
% 24.33/6.32 ((
% 24.33/6.32 (quantDeMorgan2) =>
% 24.33/6.32 ((
% 24.33/6.32 (quantDeMorgan3) =>
% 24.33/6.32 ((
% 24.33/6.32 (quantDeMorgan4) =>
% 24.33/6.32 ((
% 24.33/6.32 (prop2setI) =>
% 24.33/6.32 ((
% 24.33/6.32 (prop2set2propI) =>
% 24.33/6.32 ((
% 24.33/6.32 (notdexE) =>
% 24.33/6.32 ((
% 24.33/6.32 (notdallE) =>
% 24.33/6.32 ((
% 24.33/6.32 (exuI1) =>
% 24.33/6.32 ((
% 24.33/6.32 (exuI3) =>
% 24.33/6.32 ((
% 24.33/6.32 (exuI2) =>
% 24.33/6.32 ((
% 24.33/6.32 (inCongP) =>
% 24.33/6.32 ((
% 24.33/6.32 (in__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (exuE3u) =>
% 24.33/6.32 ((
% 24.33/6.32 (exu__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (setadjoin__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (powerset__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (setunion__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (exuEu) =>
% 24.33/6.32 ((
% 24.33/6.32 (descr__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (dsetconstr__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetI1) =>
% 24.33/6.32 ((
% 24.33/6.32 (eqimpsubset2) =>
% 24.33/6.32 ((
% 24.33/6.32 (eqimpsubset1) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetI2) =>
% 24.33/6.32 ((
% 24.33/6.32 (emptysetsubset) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetE) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetE2) =>
% 24.33/6.32 ((
% 24.33/6.32 (notsubsetI) =>
% 24.33/6.32 ((
% 24.33/6.32 (notequalI1) =>
% 24.33/6.32 ((
% 24.33/6.32 (notequalI2) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetRefl) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetTrans) =>
% 24.33/6.32 ((
% 24.33/6.32 (setadjoinSub) =>
% 24.33/6.32 ((
% 24.33/6.32 (setadjoinSub2) =>
% 24.33/6.32 ((
% 24.33/6.32 (subset2powerset) =>
% 24.33/6.32 ((
% 24.33/6.32 (setextsub) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetemptysetimpeq) =>
% 24.33/6.32 ((
% 24.33/6.32 (powersetI1) =>
% 24.33/6.32 ((
% 24.33/6.32 (powersetE1) =>
% 24.33/6.32 ((
% 24.33/6.32 (inPowerset) =>
% 24.33/6.32 ((
% 24.33/6.32 (powersetsubset) =>
% 24.33/6.32 ((
% 24.33/6.32 (sepInPowerset) =>
% 24.33/6.32 ((
% 24.33/6.32 (sepSubset) =>
% 24.33/6.32 ((
% 24.33/6.32 (binunionIL) =>
% 24.33/6.32 ((
% 24.33/6.32 (upairset2IR) =>
% 24.33/6.32 ((
% 24.33/6.32 (binunionIR) =>
% 24.33/6.32 ((
% 24.33/6.32 (binunionEcases) =>
% 24.33/6.32 ((
% 24.33/6.32 (binunionE) =>
% 24.33/6.32 ((
% 24.33/6.32 (binunionLsub) =>
% 24.33/6.32 ((
% 24.33/6.32 (binunionRsub) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectI) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectSubset5) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectEL) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectLsub) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectSubset2) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectSubset3) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectER) =>
% 24.33/6.32 ((
% 24.33/6.32 (disjointsetsI1) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectRsub) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectSubset4) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectSubset1) =>
% 24.33/6.32 ((
% 24.33/6.32 (bs114d) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusI) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusEL) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusER) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusSubset2) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusERneg) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusELneg) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusILneg) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusIRneg) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusLsub) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusSubset1) =>
% 24.33/6.32 ((
% 24.33/6.32 (symdiffE) =>
% 24.33/6.32 ((
% 24.33/6.32 (symdiffI1) =>
% 24.33/6.32 ((
% 24.33/6.32 (symdiffI2) =>
% 24.33/6.32 ((
% 24.33/6.32 (symdiffIneg1) =>
% 24.33/6.32 ((
% 24.33/6.32 (symdiffIneg2) =>
% 24.33/6.32 ((
% 24.33/6.32 (secondinupair) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairIL) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairIR) =>
% 24.33/6.32 ((
% 24.33/6.32 (kpairiskpair) =>
% 24.33/6.32 ((
% 24.33/6.32 (kpairp) =>
% 24.33/6.32 ((
% 24.33/6.32 (singletonsubset) =>
% 24.33/6.32 ((
% 24.33/6.32 (singletoninpowerset) =>
% 24.33/6.32 ((
% 24.33/6.32 (singletoninpowunion) =>
% 24.33/6.32 ((
% 24.33/6.32 (upairset2E) =>
% 24.33/6.32 ((
% 24.33/6.32 (upairsubunion) =>
% 24.33/6.32 ((
% 24.33/6.32 (upairinpowunion) =>
% 24.33/6.32 ((
% 24.33/6.32 (ubforcartprodlem1) =>
% 24.33/6.32 ((
% 24.33/6.32 (ubforcartprodlem2) =>
% 24.33/6.32 ((
% 24.33/6.32 (ubforcartprodlem3) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodpairin) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodmempair1) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodmempair) =>
% 24.33/6.32 ((
% 24.33/6.32 (setunionE2) =>
% 24.33/6.32 ((
% 24.33/6.32 (setunionsingleton1) =>
% 24.33/6.32 ((
% 24.33/6.32 (setunionsingleton2) =>
% 24.33/6.32 ((
% 24.33/6.32 (setunionsingleton) =>
% 24.33/6.32 ((
% 24.33/6.32 (singletonprop) =>
% 24.33/6.32 ((
% 24.33/6.32 (ex1E1) =>
% 24.33/6.32 ((
% 24.33/6.32 (ex1I) =>
% 24.33/6.32 ((
% 24.33/6.32 (ex1I2) =>
% 24.33/6.32 ((
% 24.33/6.32 (singletonsuniq) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjL1) =>
% 24.33/6.32 ((
% 24.33/6.32 (kfstsingleton) =>
% 24.33/6.32 ((
% 24.33/6.32 (theprop) =>
% 24.33/6.32 ((
% 24.33/6.32 (kfstpairEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodfstin) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjL2) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjL) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjR11) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjR12) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjR1) =>
% 24.33/6.32 ((
% 24.33/6.32 (upairequniteq) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjR2) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjR) =>
% 24.33/6.32 ((
% 24.33/6.32 (ksndsingleton) =>
% 24.33/6.32 ((
% 24.33/6.32 (ksndpairEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (kpairsurjEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodsndin) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodpairmemEL) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodpairmemER) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodmempaircEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodfstpairEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodsndpairEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodpairsurjEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (dpsetconstrI) =>
% 24.33/6.32 ((
% 24.33/6.32 (!!) @ (
% 24.33/6.32 (('#B') @ (
% 24.33/6.32 !!) @
% 24.33/6.32 (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 !!))) @
% 24.33/6.32 (
% 24.33/6.32 (
% 24.33/6.32 ('#S') @ (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 '#S') @
% 24.33/6.32 (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 '#C'))) @
% 24.33/6.32 (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ subset)))) @
% 24.33/6.32 dpsetconstr)))))) @
% 24.33/6.32 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.33/6.32 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl174])).
% 24.33/6.32 thf(zip_derived_cl206, plain,
% 24.33/6.32 (~ (((setext) =>
% 24.33/6.32 (((emptyI) =>
% 24.33/6.32 (((noeltsimpempty) =>
% 24.33/6.32 (((setbeta) =>
% 24.33/6.32 (((nonemptyE1) =>
% 24.33/6.32 (((nonemptyI) =>
% 24.33/6.32 (((nonemptyI1) =>
% 24.33/6.32 (((setadjoinIL) =>
% 24.33/6.32 (((in @ emptyset @
% 24.33/6.32 (setadjoin @ emptyset @ emptyset)) =>
% 24.33/6.32 (((setadjoinIR) =>
% 24.33/6.32 (((setadjoinE) =>
% 24.33/6.32 (((setadjoinOr) =>
% 24.33/6.32 (((setoftrueEq) =>
% 24.33/6.32 (((powersetI) =>
% 24.33/6.32 (((emptyinPowerset) =>
% 24.33/6.32 (((emptyInPowerset) =>
% 24.33/6.32 (((powersetE) =>
% 24.33/6.32 (((setunionI) =>
% 24.33/6.32 (((setunionE) =>
% 24.33/6.32 (((subPowSU) =>
% 24.33/6.32 (((exuE2) =>
% 24.33/6.32 (((nonemptyImpWitness) =>
% 24.33/6.32 (((uniqinunit) =>
% 24.33/6.32 (((notinsingleton) =>
% 24.33/6.32 (((eqinunit) =>
% 24.33/6.32 (((singletonsswitch) =>
% 24.33/6.32 (((upairsetE) =>
% 24.33/6.32 (((upairsetIL) =>
% 24.33/6.32 (((upairsetIR) =>
% 24.33/6.32 (((emptyE1) =>
% 24.33/6.32 ((
% 24.33/6.32 (vacuousDall) =>
% 24.33/6.32 ((
% 24.33/6.32 (quantDeMorgan1) =>
% 24.33/6.32 ((
% 24.33/6.32 (quantDeMorgan2) =>
% 24.33/6.32 ((
% 24.33/6.32 (quantDeMorgan3) =>
% 24.33/6.32 ((
% 24.33/6.32 (quantDeMorgan4) =>
% 24.33/6.32 ((
% 24.33/6.32 (prop2setI) =>
% 24.33/6.32 ((
% 24.33/6.32 (prop2set2propI) =>
% 24.33/6.32 ((
% 24.33/6.32 (notdexE) =>
% 24.33/6.32 ((
% 24.33/6.32 (notdallE) =>
% 24.33/6.32 ((
% 24.33/6.32 (exuI1) =>
% 24.33/6.32 ((
% 24.33/6.32 (exuI3) =>
% 24.33/6.32 ((
% 24.33/6.32 (exuI2) =>
% 24.33/6.32 ((
% 24.33/6.32 (inCongP) =>
% 24.33/6.32 ((
% 24.33/6.32 (in__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (exuE3u) =>
% 24.33/6.32 ((
% 24.33/6.32 (exu__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (setadjoin__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (powerset__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (setunion__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (exuEu) =>
% 24.33/6.32 ((
% 24.33/6.32 (descr__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (dsetconstr__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetI1) =>
% 24.33/6.32 ((
% 24.33/6.32 (eqimpsubset2) =>
% 24.33/6.32 ((
% 24.33/6.32 (eqimpsubset1) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetI2) =>
% 24.33/6.32 ((
% 24.33/6.32 (emptysetsubset) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetE) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetE2) =>
% 24.33/6.32 ((
% 24.33/6.32 (notsubsetI) =>
% 24.33/6.32 ((
% 24.33/6.32 (notequalI1) =>
% 24.33/6.32 ((
% 24.33/6.32 (notequalI2) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetRefl) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetTrans) =>
% 24.33/6.32 ((
% 24.33/6.32 (setadjoinSub) =>
% 24.33/6.32 ((
% 24.33/6.32 (setadjoinSub2) =>
% 24.33/6.32 ((
% 24.33/6.32 (subset2powerset) =>
% 24.33/6.32 ((
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% 24.33/6.32 ((
% 24.33/6.32 (subsetemptysetimpeq) =>
% 24.33/6.32 ((
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% 24.33/6.32 ((
% 24.33/6.32 (powersetE1) =>
% 24.33/6.32 ((
% 24.33/6.32 (inPowerset) =>
% 24.33/6.32 ((
% 24.33/6.32 (powersetsubset) =>
% 24.33/6.32 ((
% 24.33/6.32 (sepInPowerset) =>
% 24.33/6.32 ((
% 24.33/6.32 (sepSubset) =>
% 24.33/6.32 ((
% 24.33/6.32 (binunionIL) =>
% 24.33/6.32 ((
% 24.33/6.32 (upairset2IR) =>
% 24.33/6.32 ((
% 24.33/6.32 (binunionIR) =>
% 24.33/6.32 ((
% 24.33/6.32 (binunionEcases) =>
% 24.33/6.32 ((
% 24.33/6.32 (binunionE) =>
% 24.33/6.32 ((
% 24.33/6.32 (binunionLsub) =>
% 24.33/6.32 ((
% 24.33/6.32 (binunionRsub) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectI) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectSubset5) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectEL) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectLsub) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectSubset2) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectSubset3) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectER) =>
% 24.33/6.32 ((
% 24.33/6.32 (disjointsetsI1) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectRsub) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectSubset4) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectSubset1) =>
% 24.33/6.32 ((
% 24.33/6.32 (bs114d) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusI) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusEL) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusER) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusSubset2) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusERneg) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusELneg) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusILneg) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusIRneg) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusLsub) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusSubset1) =>
% 24.33/6.32 ((
% 24.33/6.32 (symdiffE) =>
% 24.33/6.32 ((
% 24.33/6.32 (symdiffI1) =>
% 24.33/6.32 ((
% 24.33/6.32 (symdiffI2) =>
% 24.33/6.32 ((
% 24.33/6.32 (symdiffIneg1) =>
% 24.33/6.32 ((
% 24.33/6.32 (symdiffIneg2) =>
% 24.33/6.32 ((
% 24.33/6.32 (secondinupair) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairIL) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairIR) =>
% 24.33/6.32 ((
% 24.33/6.32 (kpairiskpair) =>
% 24.33/6.32 ((
% 24.33/6.32 (kpairp) =>
% 24.33/6.32 ((
% 24.33/6.32 (singletonsubset) =>
% 24.33/6.32 ((
% 24.33/6.32 (singletoninpowerset) =>
% 24.33/6.32 ((
% 24.33/6.32 (singletoninpowunion) =>
% 24.33/6.32 ((
% 24.33/6.32 (upairset2E) =>
% 24.33/6.32 ((
% 24.33/6.32 (upairsubunion) =>
% 24.33/6.32 ((
% 24.33/6.32 (upairinpowunion) =>
% 24.33/6.32 ((
% 24.33/6.32 (ubforcartprodlem1) =>
% 24.33/6.32 ((
% 24.33/6.32 (ubforcartprodlem2) =>
% 24.33/6.32 ((
% 24.33/6.32 (ubforcartprodlem3) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodpairin) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodmempair1) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodmempair) =>
% 24.33/6.32 ((
% 24.33/6.32 (setunionE2) =>
% 24.33/6.32 ((
% 24.33/6.32 (setunionsingleton1) =>
% 24.33/6.32 ((
% 24.33/6.32 (setunionsingleton2) =>
% 24.33/6.32 ((
% 24.33/6.32 (setunionsingleton) =>
% 24.33/6.32 ((
% 24.33/6.32 (singletonprop) =>
% 24.33/6.32 ((
% 24.33/6.32 (ex1E1) =>
% 24.33/6.32 ((
% 24.33/6.32 (ex1I) =>
% 24.33/6.32 ((
% 24.33/6.32 (ex1I2) =>
% 24.33/6.32 ((
% 24.33/6.32 (singletonsuniq) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjL1) =>
% 24.33/6.32 ((
% 24.33/6.32 (kfstsingleton) =>
% 24.33/6.32 ((
% 24.33/6.32 (theprop) =>
% 24.33/6.32 ((
% 24.33/6.32 (kfstpairEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodfstin) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjL2) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjL) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjR11) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjR12) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjR1) =>
% 24.33/6.32 ((
% 24.33/6.32 (upairequniteq) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjR2) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjR) =>
% 24.33/6.32 ((
% 24.33/6.32 (ksndsingleton) =>
% 24.33/6.32 ((
% 24.33/6.32 (ksndpairEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (kpairsurjEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodsndin) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodpairmemEL) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodpairmemER) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodmempaircEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodfstpairEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodsndpairEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodpairsurjEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (dpsetconstrI) =>
% 24.33/6.32 ((
% 24.33/6.32 (!!) @ (
% 24.33/6.32 (('#B') @ (
% 24.33/6.32 !!) @
% 24.33/6.32 (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 !!))) @
% 24.33/6.32 (
% 24.33/6.32 (
% 24.33/6.32 ('#S') @ (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 '#S') @
% 24.33/6.32 (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 '#C'))) @
% 24.33/6.32 (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ subset)))) @
% 24.33/6.32 dpsetconstr)))))) @
% 24.33/6.32 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.33/6.32 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl189])).
% 24.33/6.32 thf(zip_derived_cl222, plain,
% 24.33/6.32 (~ (((emptyI) =>
% 24.33/6.32 (((noeltsimpempty) =>
% 24.33/6.32 (((setbeta) =>
% 24.33/6.32 (((nonemptyE1) =>
% 24.33/6.32 (((nonemptyI) =>
% 24.33/6.32 (((nonemptyI1) =>
% 24.33/6.32 (((setadjoinIL) =>
% 24.33/6.32 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 24.33/6.32 (((setadjoinIR) =>
% 24.33/6.32 (((setadjoinE) =>
% 24.33/6.32 (((setadjoinOr) =>
% 24.33/6.32 (((setoftrueEq) =>
% 24.33/6.32 (((powersetI) =>
% 24.33/6.32 (((emptyinPowerset) =>
% 24.33/6.32 (((emptyInPowerset) =>
% 24.33/6.32 (((powersetE) =>
% 24.33/6.32 (((setunionI) =>
% 24.33/6.32 (((setunionE) =>
% 24.33/6.32 (((subPowSU) =>
% 24.33/6.32 (((exuE2) =>
% 24.33/6.32 (((nonemptyImpWitness) =>
% 24.33/6.32 (((uniqinunit) =>
% 24.33/6.32 (((notinsingleton) =>
% 24.33/6.32 (((eqinunit) =>
% 24.33/6.32 (((singletonsswitch) =>
% 24.33/6.32 (((upairsetE) =>
% 24.33/6.32 (((upairsetIL) =>
% 24.33/6.32 (((upairsetIR) =>
% 24.33/6.32 (((emptyE1) =>
% 24.33/6.32 (((vacuousDall) =>
% 24.33/6.32 ((
% 24.33/6.32 (quantDeMorgan1) =>
% 24.33/6.32 ((
% 24.33/6.32 (quantDeMorgan2) =>
% 24.33/6.32 ((
% 24.33/6.32 (quantDeMorgan3) =>
% 24.33/6.32 ((
% 24.33/6.32 (quantDeMorgan4) =>
% 24.33/6.32 ((
% 24.33/6.32 (prop2setI) =>
% 24.33/6.32 ((
% 24.33/6.32 (prop2set2propI) =>
% 24.33/6.32 ((
% 24.33/6.32 (notdexE) =>
% 24.33/6.32 ((
% 24.33/6.32 (notdallE) =>
% 24.33/6.32 ((
% 24.33/6.32 (exuI1) =>
% 24.33/6.32 ((
% 24.33/6.32 (exuI3) =>
% 24.33/6.32 ((
% 24.33/6.32 (exuI2) =>
% 24.33/6.32 ((
% 24.33/6.32 (inCongP) =>
% 24.33/6.32 ((
% 24.33/6.32 (in__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (exuE3u) =>
% 24.33/6.32 ((
% 24.33/6.32 (exu__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (setadjoin__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (powerset__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (setunion__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (exuEu) =>
% 24.33/6.32 ((
% 24.33/6.32 (descr__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (dsetconstr__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetI1) =>
% 24.33/6.32 ((
% 24.33/6.32 (eqimpsubset2) =>
% 24.33/6.32 ((
% 24.33/6.32 (eqimpsubset1) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetI2) =>
% 24.33/6.32 ((
% 24.33/6.32 (emptysetsubset) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetE) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetE2) =>
% 24.33/6.32 ((
% 24.33/6.32 (notsubsetI) =>
% 24.33/6.32 ((
% 24.33/6.32 (notequalI1) =>
% 24.33/6.32 ((
% 24.33/6.32 (notequalI2) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetRefl) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetTrans) =>
% 24.33/6.32 ((
% 24.33/6.32 (setadjoinSub) =>
% 24.33/6.32 ((
% 24.33/6.32 (setadjoinSub2) =>
% 24.33/6.32 ((
% 24.33/6.32 (subset2powerset) =>
% 24.33/6.32 ((
% 24.33/6.32 (setextsub) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetemptysetimpeq) =>
% 24.33/6.32 ((
% 24.33/6.32 (powersetI1) =>
% 24.33/6.32 ((
% 24.33/6.32 (powersetE1) =>
% 24.33/6.32 ((
% 24.33/6.32 (inPowerset) =>
% 24.33/6.32 ((
% 24.33/6.32 (powersetsubset) =>
% 24.33/6.32 ((
% 24.33/6.32 (sepInPowerset) =>
% 24.33/6.32 ((
% 24.33/6.32 (sepSubset) =>
% 24.33/6.32 ((
% 24.33/6.32 (binunionIL) =>
% 24.33/6.32 ((
% 24.33/6.32 (upairset2IR) =>
% 24.33/6.32 ((
% 24.33/6.32 (binunionIR) =>
% 24.33/6.32 ((
% 24.33/6.32 (binunionEcases) =>
% 24.33/6.32 ((
% 24.33/6.32 (binunionE) =>
% 24.33/6.32 ((
% 24.33/6.32 (binunionLsub) =>
% 24.33/6.32 ((
% 24.33/6.32 (binunionRsub) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectI) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectSubset5) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectEL) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectLsub) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectSubset2) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectSubset3) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectER) =>
% 24.33/6.32 ((
% 24.33/6.32 (disjointsetsI1) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectRsub) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectSubset4) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectSubset1) =>
% 24.33/6.32 ((
% 24.33/6.32 (bs114d) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusI) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusEL) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusER) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusSubset2) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusERneg) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusELneg) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusILneg) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusIRneg) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusLsub) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusSubset1) =>
% 24.33/6.32 ((
% 24.33/6.32 (symdiffE) =>
% 24.33/6.32 ((
% 24.33/6.32 (symdiffI1) =>
% 24.33/6.32 ((
% 24.33/6.32 (symdiffI2) =>
% 24.33/6.32 ((
% 24.33/6.32 (symdiffIneg1) =>
% 24.33/6.32 ((
% 24.33/6.32 (symdiffIneg2) =>
% 24.33/6.32 ((
% 24.33/6.32 (secondinupair) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairIL) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairIR) =>
% 24.33/6.32 ((
% 24.33/6.32 (kpairiskpair) =>
% 24.33/6.32 ((
% 24.33/6.32 (kpairp) =>
% 24.33/6.32 ((
% 24.33/6.32 (singletonsubset) =>
% 24.33/6.32 ((
% 24.33/6.32 (singletoninpowerset) =>
% 24.33/6.32 ((
% 24.33/6.32 (singletoninpowunion) =>
% 24.33/6.32 ((
% 24.33/6.32 (upairset2E) =>
% 24.33/6.32 ((
% 24.33/6.32 (upairsubunion) =>
% 24.33/6.32 ((
% 24.33/6.32 (upairinpowunion) =>
% 24.33/6.32 ((
% 24.33/6.32 (ubforcartprodlem1) =>
% 24.33/6.32 ((
% 24.33/6.32 (ubforcartprodlem2) =>
% 24.33/6.32 ((
% 24.33/6.32 (ubforcartprodlem3) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodpairin) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodmempair1) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodmempair) =>
% 24.33/6.32 ((
% 24.33/6.32 (setunionE2) =>
% 24.33/6.32 ((
% 24.33/6.32 (setunionsingleton1) =>
% 24.33/6.32 ((
% 24.33/6.32 (setunionsingleton2) =>
% 24.33/6.32 ((
% 24.33/6.32 (setunionsingleton) =>
% 24.33/6.32 ((
% 24.33/6.32 (singletonprop) =>
% 24.33/6.32 ((
% 24.33/6.32 (ex1E1) =>
% 24.33/6.32 ((
% 24.33/6.32 (ex1I) =>
% 24.33/6.32 ((
% 24.33/6.32 (ex1I2) =>
% 24.33/6.32 ((
% 24.33/6.32 (singletonsuniq) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjL1) =>
% 24.33/6.32 ((
% 24.33/6.32 (kfstsingleton) =>
% 24.33/6.32 ((
% 24.33/6.32 (theprop) =>
% 24.33/6.32 ((
% 24.33/6.32 (kfstpairEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodfstin) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjL2) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjL) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjR11) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjR12) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjR1) =>
% 24.33/6.32 ((
% 24.33/6.32 (upairequniteq) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjR2) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjR) =>
% 24.33/6.32 ((
% 24.33/6.32 (ksndsingleton) =>
% 24.33/6.32 ((
% 24.33/6.32 (ksndpairEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (kpairsurjEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodsndin) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodpairmemEL) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodpairmemER) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodmempaircEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodfstpairEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodsndpairEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodpairsurjEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (dpsetconstrI) =>
% 24.33/6.32 ((
% 24.33/6.32 (!!) @ (
% 24.33/6.32 (('#B') @ (
% 24.33/6.32 !!) @
% 24.33/6.32 (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 !!))) @
% 24.33/6.32 (
% 24.33/6.32 (
% 24.33/6.32 ('#S') @ (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 '#S') @
% 24.33/6.32 (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 '#C'))) @
% 24.33/6.32 (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ subset)))) @
% 24.33/6.32 dpsetconstr)))))) @
% 24.33/6.32 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.33/6.32 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl206])).
% 24.33/6.32 thf(zip_derived_cl236, plain,
% 24.33/6.32 (~ (((noeltsimpempty) =>
% 24.33/6.32 (((setbeta) =>
% 24.33/6.32 (((nonemptyE1) =>
% 24.33/6.32 (((nonemptyI) =>
% 24.33/6.32 (((nonemptyI1) =>
% 24.33/6.32 (((setadjoinIL) =>
% 24.33/6.32 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 24.33/6.32 (((setadjoinIR) =>
% 24.33/6.32 (((setadjoinE) =>
% 24.33/6.32 (((setadjoinOr) =>
% 24.33/6.32 (((setoftrueEq) =>
% 24.33/6.32 (((powersetI) =>
% 24.33/6.32 (((emptyinPowerset) =>
% 24.33/6.32 (((emptyInPowerset) =>
% 24.33/6.32 (((powersetE) =>
% 24.33/6.32 (((setunionI) =>
% 24.33/6.32 (((setunionE) =>
% 24.33/6.32 (((subPowSU) =>
% 24.33/6.32 (((exuE2) =>
% 24.33/6.32 (((nonemptyImpWitness) =>
% 24.33/6.32 (((uniqinunit) =>
% 24.33/6.32 (((notinsingleton) =>
% 24.33/6.32 (((eqinunit) =>
% 24.33/6.32 (((singletonsswitch) =>
% 24.33/6.32 (((upairsetE) =>
% 24.33/6.32 (((upairsetIL) =>
% 24.33/6.32 (((upairsetIR) =>
% 24.33/6.32 (((emptyE1) =>
% 24.33/6.32 (((vacuousDall) =>
% 24.33/6.32 (((quantDeMorgan1) =>
% 24.33/6.32 ((
% 24.33/6.32 (quantDeMorgan2) =>
% 24.33/6.32 ((
% 24.33/6.32 (quantDeMorgan3) =>
% 24.33/6.32 ((
% 24.33/6.32 (quantDeMorgan4) =>
% 24.33/6.32 ((
% 24.33/6.32 (prop2setI) =>
% 24.33/6.32 ((
% 24.33/6.32 (prop2set2propI) =>
% 24.33/6.32 ((
% 24.33/6.32 (notdexE) =>
% 24.33/6.32 ((
% 24.33/6.32 (notdallE) =>
% 24.33/6.32 ((
% 24.33/6.32 (exuI1) =>
% 24.33/6.32 ((
% 24.33/6.32 (exuI3) =>
% 24.33/6.32 ((
% 24.33/6.32 (exuI2) =>
% 24.33/6.32 ((
% 24.33/6.32 (inCongP) =>
% 24.33/6.32 ((
% 24.33/6.32 (in__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (exuE3u) =>
% 24.33/6.32 ((
% 24.33/6.32 (exu__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (setadjoin__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (powerset__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (setunion__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (exuEu) =>
% 24.33/6.32 ((
% 24.33/6.32 (descr__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (dsetconstr__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetI1) =>
% 24.33/6.32 ((
% 24.33/6.32 (eqimpsubset2) =>
% 24.33/6.32 ((
% 24.33/6.32 (eqimpsubset1) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetI2) =>
% 24.33/6.32 ((
% 24.33/6.32 (emptysetsubset) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetE) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetE2) =>
% 24.33/6.32 ((
% 24.33/6.32 (notsubsetI) =>
% 24.33/6.32 ((
% 24.33/6.32 (notequalI1) =>
% 24.33/6.32 ((
% 24.33/6.32 (notequalI2) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetRefl) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetTrans) =>
% 24.33/6.32 ((
% 24.33/6.32 (setadjoinSub) =>
% 24.33/6.32 ((
% 24.33/6.32 (setadjoinSub2) =>
% 24.33/6.32 ((
% 24.33/6.32 (subset2powerset) =>
% 24.33/6.32 ((
% 24.33/6.32 (setextsub) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetemptysetimpeq) =>
% 24.33/6.32 ((
% 24.33/6.32 (powersetI1) =>
% 24.33/6.32 ((
% 24.33/6.32 (powersetE1) =>
% 24.33/6.32 ((
% 24.33/6.32 (inPowerset) =>
% 24.33/6.32 ((
% 24.33/6.32 (powersetsubset) =>
% 24.33/6.32 ((
% 24.33/6.32 (sepInPowerset) =>
% 24.33/6.32 ((
% 24.33/6.32 (sepSubset) =>
% 24.33/6.32 ((
% 24.33/6.32 (binunionIL) =>
% 24.33/6.32 ((
% 24.33/6.32 (upairset2IR) =>
% 24.33/6.32 ((
% 24.33/6.32 (binunionIR) =>
% 24.33/6.32 ((
% 24.33/6.32 (binunionEcases) =>
% 24.33/6.32 ((
% 24.33/6.32 (binunionE) =>
% 24.33/6.32 ((
% 24.33/6.32 (binunionLsub) =>
% 24.33/6.32 ((
% 24.33/6.32 (binunionRsub) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectI) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectSubset5) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectEL) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectLsub) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectSubset2) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectSubset3) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectER) =>
% 24.33/6.32 ((
% 24.33/6.32 (disjointsetsI1) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectRsub) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectSubset4) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectSubset1) =>
% 24.33/6.32 ((
% 24.33/6.32 (bs114d) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusI) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusEL) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusER) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusSubset2) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusERneg) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusELneg) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusILneg) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusIRneg) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusLsub) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusSubset1) =>
% 24.33/6.32 ((
% 24.33/6.32 (symdiffE) =>
% 24.33/6.32 ((
% 24.33/6.32 (symdiffI1) =>
% 24.33/6.32 ((
% 24.33/6.32 (symdiffI2) =>
% 24.33/6.32 ((
% 24.33/6.32 (symdiffIneg1) =>
% 24.33/6.32 ((
% 24.33/6.32 (symdiffIneg2) =>
% 24.33/6.32 ((
% 24.33/6.32 (secondinupair) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairIL) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairIR) =>
% 24.33/6.32 ((
% 24.33/6.32 (kpairiskpair) =>
% 24.33/6.32 ((
% 24.33/6.32 (kpairp) =>
% 24.33/6.32 ((
% 24.33/6.32 (singletonsubset) =>
% 24.33/6.32 ((
% 24.33/6.32 (singletoninpowerset) =>
% 24.33/6.32 ((
% 24.33/6.32 (singletoninpowunion) =>
% 24.33/6.32 ((
% 24.33/6.32 (upairset2E) =>
% 24.33/6.32 ((
% 24.33/6.32 (upairsubunion) =>
% 24.33/6.32 ((
% 24.33/6.32 (upairinpowunion) =>
% 24.33/6.32 ((
% 24.33/6.32 (ubforcartprodlem1) =>
% 24.33/6.32 ((
% 24.33/6.32 (ubforcartprodlem2) =>
% 24.33/6.32 ((
% 24.33/6.32 (ubforcartprodlem3) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodpairin) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodmempair1) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodmempair) =>
% 24.33/6.32 ((
% 24.33/6.32 (setunionE2) =>
% 24.33/6.32 ((
% 24.33/6.32 (setunionsingleton1) =>
% 24.33/6.32 ((
% 24.33/6.32 (setunionsingleton2) =>
% 24.33/6.32 ((
% 24.33/6.32 (setunionsingleton) =>
% 24.33/6.32 ((
% 24.33/6.32 (singletonprop) =>
% 24.33/6.32 ((
% 24.33/6.32 (ex1E1) =>
% 24.33/6.32 ((
% 24.33/6.32 (ex1I) =>
% 24.33/6.32 ((
% 24.33/6.32 (ex1I2) =>
% 24.33/6.32 ((
% 24.33/6.32 (singletonsuniq) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjL1) =>
% 24.33/6.32 ((
% 24.33/6.32 (kfstsingleton) =>
% 24.33/6.32 ((
% 24.33/6.32 (theprop) =>
% 24.33/6.32 ((
% 24.33/6.32 (kfstpairEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodfstin) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjL2) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjL) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjR11) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjR12) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjR1) =>
% 24.33/6.32 ((
% 24.33/6.32 (upairequniteq) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjR2) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjR) =>
% 24.33/6.32 ((
% 24.33/6.32 (ksndsingleton) =>
% 24.33/6.32 ((
% 24.33/6.32 (ksndpairEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (kpairsurjEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodsndin) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodpairmemEL) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodpairmemER) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodmempaircEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodfstpairEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodsndpairEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodpairsurjEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (dpsetconstrI) =>
% 24.33/6.32 ((
% 24.33/6.32 (!!) @ (
% 24.33/6.32 (('#B') @ (
% 24.33/6.32 !!) @
% 24.33/6.32 (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 !!))) @
% 24.33/6.32 (
% 24.33/6.32 (
% 24.33/6.32 ('#S') @ (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 '#S') @
% 24.33/6.32 (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 '#C'))) @
% 24.33/6.32 (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ subset)))) @
% 24.33/6.32 dpsetconstr)))))) @
% 24.33/6.32 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.33/6.32 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl222])).
% 24.33/6.32 thf(zip_derived_cl251, plain,
% 24.33/6.32 (~ (((setbeta) =>
% 24.33/6.32 (((nonemptyE1) =>
% 24.33/6.32 (((nonemptyI) =>
% 24.33/6.32 (((nonemptyI1) =>
% 24.33/6.32 (((setadjoinIL) =>
% 24.33/6.32 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 24.33/6.32 (((setadjoinIR) =>
% 24.33/6.32 (((setadjoinE) =>
% 24.33/6.32 (((setadjoinOr) =>
% 24.33/6.32 (((setoftrueEq) =>
% 24.33/6.32 (((powersetI) =>
% 24.33/6.32 (((emptyinPowerset) =>
% 24.33/6.32 (((emptyInPowerset) =>
% 24.33/6.32 (((powersetE) =>
% 24.33/6.32 (((setunionI) =>
% 24.33/6.32 (((setunionE) =>
% 24.33/6.32 (((subPowSU) =>
% 24.33/6.32 (((exuE2) =>
% 24.33/6.32 (((nonemptyImpWitness) =>
% 24.33/6.32 (((uniqinunit) =>
% 24.33/6.32 (((notinsingleton) =>
% 24.33/6.32 (((eqinunit) =>
% 24.33/6.32 (((singletonsswitch) =>
% 24.33/6.32 (((upairsetE) =>
% 24.33/6.32 (((upairsetIL) =>
% 24.33/6.32 (((upairsetIR) =>
% 24.33/6.32 (((emptyE1) =>
% 24.33/6.32 (((vacuousDall) =>
% 24.33/6.32 (((quantDeMorgan1) =>
% 24.33/6.32 (((quantDeMorgan2) =>
% 24.33/6.32 ((
% 24.33/6.32 (quantDeMorgan3) =>
% 24.33/6.32 ((
% 24.33/6.32 (quantDeMorgan4) =>
% 24.33/6.32 ((
% 24.33/6.32 (prop2setI) =>
% 24.33/6.32 ((
% 24.33/6.32 (prop2set2propI) =>
% 24.33/6.32 ((
% 24.33/6.32 (notdexE) =>
% 24.33/6.32 ((
% 24.33/6.32 (notdallE) =>
% 24.33/6.32 ((
% 24.33/6.32 (exuI1) =>
% 24.33/6.32 ((
% 24.33/6.32 (exuI3) =>
% 24.33/6.32 ((
% 24.33/6.32 (exuI2) =>
% 24.33/6.32 ((
% 24.33/6.32 (inCongP) =>
% 24.33/6.32 ((
% 24.33/6.32 (in__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (exuE3u) =>
% 24.33/6.32 ((
% 24.33/6.32 (exu__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (setadjoin__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (powerset__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (setunion__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (exuEu) =>
% 24.33/6.32 ((
% 24.33/6.32 (descr__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (dsetconstr__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetI1) =>
% 24.33/6.32 ((
% 24.33/6.32 (eqimpsubset2) =>
% 24.33/6.32 ((
% 24.33/6.32 (eqimpsubset1) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetI2) =>
% 24.33/6.32 ((
% 24.33/6.32 (emptysetsubset) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetE) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetE2) =>
% 24.33/6.32 ((
% 24.33/6.32 (notsubsetI) =>
% 24.33/6.32 ((
% 24.33/6.32 (notequalI1) =>
% 24.33/6.32 ((
% 24.33/6.32 (notequalI2) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetRefl) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetTrans) =>
% 24.33/6.32 ((
% 24.33/6.32 (setadjoinSub) =>
% 24.33/6.32 ((
% 24.33/6.32 (setadjoinSub2) =>
% 24.33/6.32 ((
% 24.33/6.32 (subset2powerset) =>
% 24.33/6.32 ((
% 24.33/6.32 (setextsub) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetemptysetimpeq) =>
% 24.33/6.32 ((
% 24.33/6.32 (powersetI1) =>
% 24.33/6.32 ((
% 24.33/6.32 (powersetE1) =>
% 24.33/6.32 ((
% 24.33/6.32 (inPowerset) =>
% 24.33/6.32 ((
% 24.33/6.32 (powersetsubset) =>
% 24.33/6.32 ((
% 24.33/6.32 (sepInPowerset) =>
% 24.33/6.32 ((
% 24.33/6.32 (sepSubset) =>
% 24.33/6.32 ((
% 24.33/6.32 (binunionIL) =>
% 24.33/6.32 ((
% 24.33/6.32 (upairset2IR) =>
% 24.33/6.32 ((
% 24.33/6.32 (binunionIR) =>
% 24.33/6.32 ((
% 24.33/6.32 (binunionEcases) =>
% 24.33/6.32 ((
% 24.33/6.32 (binunionE) =>
% 24.33/6.32 ((
% 24.33/6.32 (binunionLsub) =>
% 24.33/6.32 ((
% 24.33/6.32 (binunionRsub) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectI) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectSubset5) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectEL) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectLsub) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectSubset2) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectSubset3) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectER) =>
% 24.33/6.32 ((
% 24.33/6.32 (disjointsetsI1) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectRsub) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectSubset4) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectSubset1) =>
% 24.33/6.32 ((
% 24.33/6.32 (bs114d) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusI) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusEL) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusER) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusSubset2) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusERneg) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusELneg) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusILneg) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusIRneg) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusLsub) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusSubset1) =>
% 24.33/6.32 ((
% 24.33/6.32 (symdiffE) =>
% 24.33/6.32 ((
% 24.33/6.32 (symdiffI1) =>
% 24.33/6.32 ((
% 24.33/6.32 (symdiffI2) =>
% 24.33/6.32 ((
% 24.33/6.32 (symdiffIneg1) =>
% 24.33/6.32 ((
% 24.33/6.32 (symdiffIneg2) =>
% 24.33/6.32 ((
% 24.33/6.32 (secondinupair) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairIL) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairIR) =>
% 24.33/6.32 ((
% 24.33/6.32 (kpairiskpair) =>
% 24.33/6.32 ((
% 24.33/6.32 (kpairp) =>
% 24.33/6.32 ((
% 24.33/6.32 (singletonsubset) =>
% 24.33/6.32 ((
% 24.33/6.32 (singletoninpowerset) =>
% 24.33/6.32 ((
% 24.33/6.32 (singletoninpowunion) =>
% 24.33/6.32 ((
% 24.33/6.32 (upairset2E) =>
% 24.33/6.32 ((
% 24.33/6.32 (upairsubunion) =>
% 24.33/6.32 ((
% 24.33/6.32 (upairinpowunion) =>
% 24.33/6.32 ((
% 24.33/6.32 (ubforcartprodlem1) =>
% 24.33/6.32 ((
% 24.33/6.32 (ubforcartprodlem2) =>
% 24.33/6.32 ((
% 24.33/6.32 (ubforcartprodlem3) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodpairin) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodmempair1) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodmempair) =>
% 24.33/6.32 ((
% 24.33/6.32 (setunionE2) =>
% 24.33/6.32 ((
% 24.33/6.32 (setunionsingleton1) =>
% 24.33/6.32 ((
% 24.33/6.32 (setunionsingleton2) =>
% 24.33/6.32 ((
% 24.33/6.32 (setunionsingleton) =>
% 24.33/6.32 ((
% 24.33/6.32 (singletonprop) =>
% 24.33/6.32 ((
% 24.33/6.32 (ex1E1) =>
% 24.33/6.32 ((
% 24.33/6.32 (ex1I) =>
% 24.33/6.32 ((
% 24.33/6.32 (ex1I2) =>
% 24.33/6.32 ((
% 24.33/6.32 (singletonsuniq) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjL1) =>
% 24.33/6.32 ((
% 24.33/6.32 (kfstsingleton) =>
% 24.33/6.32 ((
% 24.33/6.32 (theprop) =>
% 24.33/6.32 ((
% 24.33/6.32 (kfstpairEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodfstin) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjL2) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjL) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjR11) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjR12) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjR1) =>
% 24.33/6.32 ((
% 24.33/6.32 (upairequniteq) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjR2) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjR) =>
% 24.33/6.32 ((
% 24.33/6.32 (ksndsingleton) =>
% 24.33/6.32 ((
% 24.33/6.32 (ksndpairEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (kpairsurjEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodsndin) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodpairmemEL) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodpairmemER) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodmempaircEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodfstpairEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodsndpairEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodpairsurjEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (dpsetconstrI) =>
% 24.33/6.32 ((
% 24.33/6.32 (!!) @ (
% 24.33/6.32 (('#B') @ (
% 24.33/6.32 !!) @
% 24.33/6.32 (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 !!))) @
% 24.33/6.32 (
% 24.33/6.32 (
% 24.33/6.32 ('#S') @ (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 '#S') @
% 24.33/6.32 (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 '#C'))) @
% 24.33/6.32 (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ subset)))) @
% 24.33/6.32 dpsetconstr)))))) @
% 24.33/6.32 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.33/6.32 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl236])).
% 24.33/6.32 thf(zip_derived_cl264, plain,
% 24.33/6.32 (~ (((nonemptyE1) =>
% 24.33/6.32 (((nonemptyI) =>
% 24.33/6.32 (((nonemptyI1) =>
% 24.33/6.32 (((setadjoinIL) =>
% 24.33/6.32 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 24.33/6.32 (((setadjoinIR) =>
% 24.33/6.32 (((setadjoinE) =>
% 24.33/6.32 (((setadjoinOr) =>
% 24.33/6.32 (((setoftrueEq) =>
% 24.33/6.32 (((powersetI) =>
% 24.33/6.32 (((emptyinPowerset) =>
% 24.33/6.32 (((emptyInPowerset) =>
% 24.33/6.32 (((powersetE) =>
% 24.33/6.32 (((setunionI) =>
% 24.33/6.32 (((setunionE) =>
% 24.33/6.32 (((subPowSU) =>
% 24.33/6.32 (((exuE2) =>
% 24.33/6.32 (((nonemptyImpWitness) =>
% 24.33/6.32 (((uniqinunit) =>
% 24.33/6.32 (((notinsingleton) =>
% 24.33/6.32 (((eqinunit) =>
% 24.33/6.32 (((singletonsswitch) =>
% 24.33/6.32 (((upairsetE) =>
% 24.33/6.32 (((upairsetIL) =>
% 24.33/6.32 (((upairsetIR) =>
% 24.33/6.32 (((emptyE1) =>
% 24.33/6.32 (((vacuousDall) =>
% 24.33/6.32 (((quantDeMorgan1) =>
% 24.33/6.32 (((quantDeMorgan2) =>
% 24.33/6.32 (((quantDeMorgan3) =>
% 24.33/6.32 ((
% 24.33/6.32 (quantDeMorgan4) =>
% 24.33/6.32 ((
% 24.33/6.32 (prop2setI) =>
% 24.33/6.32 ((
% 24.33/6.32 (prop2set2propI) =>
% 24.33/6.32 ((
% 24.33/6.32 (notdexE) =>
% 24.33/6.32 ((
% 24.33/6.32 (notdallE) =>
% 24.33/6.32 ((
% 24.33/6.32 (exuI1) =>
% 24.33/6.32 ((
% 24.33/6.32 (exuI3) =>
% 24.33/6.32 ((
% 24.33/6.32 (exuI2) =>
% 24.33/6.32 ((
% 24.33/6.32 (inCongP) =>
% 24.33/6.32 ((
% 24.33/6.32 (in__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (exuE3u) =>
% 24.33/6.32 ((
% 24.33/6.32 (exu__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (setadjoin__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (powerset__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (setunion__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (exuEu) =>
% 24.33/6.32 ((
% 24.33/6.32 (descr__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (dsetconstr__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetI1) =>
% 24.33/6.32 ((
% 24.33/6.32 (eqimpsubset2) =>
% 24.33/6.32 ((
% 24.33/6.32 (eqimpsubset1) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetI2) =>
% 24.33/6.32 ((
% 24.33/6.32 (emptysetsubset) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetE) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetE2) =>
% 24.33/6.32 ((
% 24.33/6.32 (notsubsetI) =>
% 24.33/6.32 ((
% 24.33/6.32 (notequalI1) =>
% 24.33/6.32 ((
% 24.33/6.32 (notequalI2) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetRefl) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetTrans) =>
% 24.33/6.32 ((
% 24.33/6.32 (setadjoinSub) =>
% 24.33/6.32 ((
% 24.33/6.32 (setadjoinSub2) =>
% 24.33/6.32 ((
% 24.33/6.32 (subset2powerset) =>
% 24.33/6.32 ((
% 24.33/6.32 (setextsub) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetemptysetimpeq) =>
% 24.33/6.32 ((
% 24.33/6.32 (powersetI1) =>
% 24.33/6.32 ((
% 24.33/6.32 (powersetE1) =>
% 24.33/6.32 ((
% 24.33/6.32 (inPowerset) =>
% 24.33/6.32 ((
% 24.33/6.32 (powersetsubset) =>
% 24.33/6.32 ((
% 24.33/6.32 (sepInPowerset) =>
% 24.33/6.32 ((
% 24.33/6.32 (sepSubset) =>
% 24.33/6.32 ((
% 24.33/6.32 (binunionIL) =>
% 24.33/6.32 ((
% 24.33/6.32 (upairset2IR) =>
% 24.33/6.32 ((
% 24.33/6.32 (binunionIR) =>
% 24.33/6.32 ((
% 24.33/6.32 (binunionEcases) =>
% 24.33/6.32 ((
% 24.33/6.32 (binunionE) =>
% 24.33/6.32 ((
% 24.33/6.32 (binunionLsub) =>
% 24.33/6.32 ((
% 24.33/6.32 (binunionRsub) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectI) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectSubset5) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectEL) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectLsub) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectSubset2) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectSubset3) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectER) =>
% 24.33/6.32 ((
% 24.33/6.32 (disjointsetsI1) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectRsub) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectSubset4) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectSubset1) =>
% 24.33/6.32 ((
% 24.33/6.32 (bs114d) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusI) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusEL) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusER) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusSubset2) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusERneg) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusELneg) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusILneg) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusIRneg) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusLsub) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusSubset1) =>
% 24.33/6.32 ((
% 24.33/6.32 (symdiffE) =>
% 24.33/6.32 ((
% 24.33/6.32 (symdiffI1) =>
% 24.33/6.32 ((
% 24.33/6.32 (symdiffI2) =>
% 24.33/6.32 ((
% 24.33/6.32 (symdiffIneg1) =>
% 24.33/6.32 ((
% 24.33/6.32 (symdiffIneg2) =>
% 24.33/6.32 ((
% 24.33/6.32 (secondinupair) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairIL) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairIR) =>
% 24.33/6.32 ((
% 24.33/6.32 (kpairiskpair) =>
% 24.33/6.32 ((
% 24.33/6.32 (kpairp) =>
% 24.33/6.32 ((
% 24.33/6.32 (singletonsubset) =>
% 24.33/6.32 ((
% 24.33/6.32 (singletoninpowerset) =>
% 24.33/6.32 ((
% 24.33/6.32 (singletoninpowunion) =>
% 24.33/6.32 ((
% 24.33/6.32 (upairset2E) =>
% 24.33/6.32 ((
% 24.33/6.32 (upairsubunion) =>
% 24.33/6.32 ((
% 24.33/6.32 (upairinpowunion) =>
% 24.33/6.32 ((
% 24.33/6.32 (ubforcartprodlem1) =>
% 24.33/6.32 ((
% 24.33/6.32 (ubforcartprodlem2) =>
% 24.33/6.32 ((
% 24.33/6.32 (ubforcartprodlem3) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodpairin) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodmempair1) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodmempair) =>
% 24.33/6.32 ((
% 24.33/6.32 (setunionE2) =>
% 24.33/6.32 ((
% 24.33/6.32 (setunionsingleton1) =>
% 24.33/6.32 ((
% 24.33/6.32 (setunionsingleton2) =>
% 24.33/6.32 ((
% 24.33/6.32 (setunionsingleton) =>
% 24.33/6.32 ((
% 24.33/6.32 (singletonprop) =>
% 24.33/6.32 ((
% 24.33/6.32 (ex1E1) =>
% 24.33/6.32 ((
% 24.33/6.32 (ex1I) =>
% 24.33/6.32 ((
% 24.33/6.32 (ex1I2) =>
% 24.33/6.32 ((
% 24.33/6.32 (singletonsuniq) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjL1) =>
% 24.33/6.32 ((
% 24.33/6.32 (kfstsingleton) =>
% 24.33/6.32 ((
% 24.33/6.32 (theprop) =>
% 24.33/6.32 ((
% 24.33/6.32 (kfstpairEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodfstin) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjL2) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjL) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjR11) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjR12) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjR1) =>
% 24.33/6.32 ((
% 24.33/6.32 (upairequniteq) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjR2) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjR) =>
% 24.33/6.32 ((
% 24.33/6.32 (ksndsingleton) =>
% 24.33/6.32 ((
% 24.33/6.32 (ksndpairEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (kpairsurjEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodsndin) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodpairmemEL) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodpairmemER) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodmempaircEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodfstpairEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodsndpairEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodpairsurjEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (dpsetconstrI) =>
% 24.33/6.32 ((
% 24.33/6.32 (!!) @ (
% 24.33/6.32 (('#B') @ (
% 24.33/6.32 !!) @
% 24.33/6.32 (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 !!))) @
% 24.33/6.32 (
% 24.33/6.32 (
% 24.33/6.32 ('#S') @ (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 '#S') @
% 24.33/6.32 (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 '#C'))) @
% 24.33/6.32 (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ subset)))) @
% 24.33/6.32 dpsetconstr)))))) @
% 24.33/6.32 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.33/6.32 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl251])).
% 24.33/6.32 thf(zip_derived_cl280, plain,
% 24.33/6.32 (~ (((nonemptyI) =>
% 24.33/6.32 (((nonemptyI1) =>
% 24.33/6.32 (((setadjoinIL) =>
% 24.33/6.32 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 24.33/6.32 (((setadjoinIR) =>
% 24.33/6.32 (((setadjoinE) =>
% 24.33/6.32 (((setadjoinOr) =>
% 24.33/6.32 (((setoftrueEq) =>
% 24.33/6.32 (((powersetI) =>
% 24.33/6.32 (((emptyinPowerset) =>
% 24.33/6.32 (((emptyInPowerset) =>
% 24.33/6.32 (((powersetE) =>
% 24.33/6.32 (((setunionI) =>
% 24.33/6.32 (((setunionE) =>
% 24.33/6.32 (((subPowSU) =>
% 24.33/6.32 (((exuE2) =>
% 24.33/6.32 (((nonemptyImpWitness) =>
% 24.33/6.32 (((uniqinunit) =>
% 24.33/6.32 (((notinsingleton) =>
% 24.33/6.32 (((eqinunit) =>
% 24.33/6.32 (((singletonsswitch) =>
% 24.33/6.32 (((upairsetE) =>
% 24.33/6.32 (((upairsetIL) =>
% 24.33/6.32 (((upairsetIR) =>
% 24.33/6.32 (((emptyE1) =>
% 24.33/6.32 (((vacuousDall) =>
% 24.33/6.32 (((quantDeMorgan1) =>
% 24.33/6.32 (((quantDeMorgan2) =>
% 24.33/6.32 (((quantDeMorgan3) =>
% 24.33/6.32 (((quantDeMorgan4) =>
% 24.33/6.32 ((
% 24.33/6.32 (prop2setI) =>
% 24.33/6.32 ((
% 24.33/6.32 (prop2set2propI) =>
% 24.33/6.32 ((
% 24.33/6.32 (notdexE) =>
% 24.33/6.32 ((
% 24.33/6.32 (notdallE) =>
% 24.33/6.32 ((
% 24.33/6.32 (exuI1) =>
% 24.33/6.32 ((
% 24.33/6.32 (exuI3) =>
% 24.33/6.32 ((
% 24.33/6.32 (exuI2) =>
% 24.33/6.32 ((
% 24.33/6.32 (inCongP) =>
% 24.33/6.32 ((
% 24.33/6.32 (in__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (exuE3u) =>
% 24.33/6.32 ((
% 24.33/6.32 (exu__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (setadjoin__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (powerset__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (setunion__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (exuEu) =>
% 24.33/6.32 ((
% 24.33/6.32 (descr__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (dsetconstr__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetI1) =>
% 24.33/6.32 ((
% 24.33/6.32 (eqimpsubset2) =>
% 24.33/6.32 ((
% 24.33/6.32 (eqimpsubset1) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetI2) =>
% 24.33/6.32 ((
% 24.33/6.32 (emptysetsubset) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetE) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetE2) =>
% 24.33/6.32 ((
% 24.33/6.32 (notsubsetI) =>
% 24.33/6.32 ((
% 24.33/6.32 (notequalI1) =>
% 24.33/6.32 ((
% 24.33/6.32 (notequalI2) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetRefl) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetTrans) =>
% 24.33/6.32 ((
% 24.33/6.32 (setadjoinSub) =>
% 24.33/6.32 ((
% 24.33/6.32 (setadjoinSub2) =>
% 24.33/6.32 ((
% 24.33/6.32 (subset2powerset) =>
% 24.33/6.32 ((
% 24.33/6.32 (setextsub) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetemptysetimpeq) =>
% 24.33/6.32 ((
% 24.33/6.32 (powersetI1) =>
% 24.33/6.32 ((
% 24.33/6.32 (powersetE1) =>
% 24.33/6.32 ((
% 24.33/6.32 (inPowerset) =>
% 24.33/6.32 ((
% 24.33/6.32 (powersetsubset) =>
% 24.33/6.32 ((
% 24.33/6.32 (sepInPowerset) =>
% 24.33/6.32 ((
% 24.33/6.32 (sepSubset) =>
% 24.33/6.32 ((
% 24.33/6.32 (binunionIL) =>
% 24.33/6.32 ((
% 24.33/6.32 (upairset2IR) =>
% 24.33/6.32 ((
% 24.33/6.32 (binunionIR) =>
% 24.33/6.32 ((
% 24.33/6.32 (binunionEcases) =>
% 24.33/6.32 ((
% 24.33/6.32 (binunionE) =>
% 24.33/6.32 ((
% 24.33/6.32 (binunionLsub) =>
% 24.33/6.32 ((
% 24.33/6.32 (binunionRsub) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectI) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectSubset5) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectEL) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectLsub) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectSubset2) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectSubset3) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectER) =>
% 24.33/6.32 ((
% 24.33/6.32 (disjointsetsI1) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectRsub) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectSubset4) =>
% 24.33/6.32 ((
% 24.33/6.32 (binintersectSubset1) =>
% 24.33/6.32 ((
% 24.33/6.32 (bs114d) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusI) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusEL) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusER) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusSubset2) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusERneg) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusELneg) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusILneg) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusIRneg) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusLsub) =>
% 24.33/6.32 ((
% 24.33/6.32 (setminusSubset1) =>
% 24.33/6.32 ((
% 24.33/6.32 (symdiffE) =>
% 24.33/6.32 ((
% 24.33/6.32 (symdiffI1) =>
% 24.33/6.32 ((
% 24.33/6.32 (symdiffI2) =>
% 24.33/6.32 ((
% 24.33/6.32 (symdiffIneg1) =>
% 24.33/6.32 ((
% 24.33/6.32 (symdiffIneg2) =>
% 24.33/6.32 ((
% 24.33/6.32 (secondinupair) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairIL) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairIR) =>
% 24.33/6.32 ((
% 24.33/6.32 (kpairiskpair) =>
% 24.33/6.32 ((
% 24.33/6.32 (kpairp) =>
% 24.33/6.32 ((
% 24.33/6.32 (singletonsubset) =>
% 24.33/6.32 ((
% 24.33/6.32 (singletoninpowerset) =>
% 24.33/6.32 ((
% 24.33/6.32 (singletoninpowunion) =>
% 24.33/6.32 ((
% 24.33/6.32 (upairset2E) =>
% 24.33/6.32 ((
% 24.33/6.32 (upairsubunion) =>
% 24.33/6.32 ((
% 24.33/6.32 (upairinpowunion) =>
% 24.33/6.32 ((
% 24.33/6.32 (ubforcartprodlem1) =>
% 24.33/6.32 ((
% 24.33/6.32 (ubforcartprodlem2) =>
% 24.33/6.32 ((
% 24.33/6.32 (ubforcartprodlem3) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodpairin) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodmempair1) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodmempair) =>
% 24.33/6.32 ((
% 24.33/6.32 (setunionE2) =>
% 24.33/6.32 ((
% 24.33/6.32 (setunionsingleton1) =>
% 24.33/6.32 ((
% 24.33/6.32 (setunionsingleton2) =>
% 24.33/6.32 ((
% 24.33/6.32 (setunionsingleton) =>
% 24.33/6.32 ((
% 24.33/6.32 (singletonprop) =>
% 24.33/6.32 ((
% 24.33/6.32 (ex1E1) =>
% 24.33/6.32 ((
% 24.33/6.32 (ex1I) =>
% 24.33/6.32 ((
% 24.33/6.32 (ex1I2) =>
% 24.33/6.32 ((
% 24.33/6.32 (singletonsuniq) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjL1) =>
% 24.33/6.32 ((
% 24.33/6.32 (kfstsingleton) =>
% 24.33/6.32 ((
% 24.33/6.32 (theprop) =>
% 24.33/6.32 ((
% 24.33/6.32 (kfstpairEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodfstin) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjL2) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjL) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjR11) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjR12) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjR1) =>
% 24.33/6.32 ((
% 24.33/6.32 (upairequniteq) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjR2) =>
% 24.33/6.32 ((
% 24.33/6.32 (setukpairinjR) =>
% 24.33/6.32 ((
% 24.33/6.32 (ksndsingleton) =>
% 24.33/6.32 ((
% 24.33/6.32 (ksndpairEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (kpairsurjEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodsndin) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodpairmemEL) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodpairmemER) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodmempaircEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodfstpairEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodsndpairEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (cartprodpairsurjEq) =>
% 24.33/6.32 ((
% 24.33/6.32 (dpsetconstrI) =>
% 24.33/6.32 ((
% 24.33/6.32 (!!) @ (
% 24.33/6.32 (('#B') @ (
% 24.33/6.32 !!) @
% 24.33/6.32 (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 !!))) @
% 24.33/6.32 (
% 24.33/6.32 (
% 24.33/6.32 ('#S') @ (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 '#S') @
% 24.33/6.32 (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 '#C'))) @
% 24.33/6.32 (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ (
% 24.33/6.32 (
% 24.33/6.32 ('#B') @ subset)))) @
% 24.33/6.32 dpsetconstr)))))) @
% 24.33/6.32 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.33/6.32 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl264])).
% 24.33/6.32 thf(zip_derived_cl293, plain,
% 24.33/6.32 (~ (((nonemptyI1) =>
% 24.33/6.32 (((setadjoinIL) =>
% 24.33/6.32 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 24.33/6.32 (((setadjoinIR) =>
% 24.33/6.32 (((setadjoinE) =>
% 24.33/6.32 (((setadjoinOr) =>
% 24.33/6.32 (((setoftrueEq) =>
% 24.33/6.32 (((powersetI) =>
% 24.33/6.32 (((emptyinPowerset) =>
% 24.33/6.32 (((emptyInPowerset) =>
% 24.33/6.32 (((powersetE) =>
% 24.33/6.32 (((setunionI) =>
% 24.33/6.32 (((setunionE) =>
% 24.33/6.32 (((subPowSU) =>
% 24.33/6.32 (((exuE2) =>
% 24.33/6.32 (((nonemptyImpWitness) =>
% 24.33/6.32 (((uniqinunit) =>
% 24.33/6.32 (((notinsingleton) =>
% 24.33/6.32 (((eqinunit) =>
% 24.33/6.32 (((singletonsswitch) =>
% 24.33/6.32 (((upairsetE) =>
% 24.33/6.32 (((upairsetIL) =>
% 24.33/6.32 (((upairsetIR) =>
% 24.33/6.32 (((emptyE1) =>
% 24.33/6.32 (((vacuousDall) =>
% 24.33/6.32 (((quantDeMorgan1) =>
% 24.33/6.32 (((quantDeMorgan2) =>
% 24.33/6.32 (((quantDeMorgan3) =>
% 24.33/6.32 (((quantDeMorgan4) =>
% 24.33/6.32 (((prop2setI) =>
% 24.33/6.32 ((
% 24.33/6.32 (prop2set2propI) =>
% 24.33/6.32 ((
% 24.33/6.32 (notdexE) =>
% 24.33/6.32 ((
% 24.33/6.32 (notdallE) =>
% 24.33/6.32 ((
% 24.33/6.32 (exuI1) =>
% 24.33/6.32 ((
% 24.33/6.32 (exuI3) =>
% 24.33/6.32 ((
% 24.33/6.32 (exuI2) =>
% 24.33/6.32 ((
% 24.33/6.32 (inCongP) =>
% 24.33/6.32 ((
% 24.33/6.32 (in__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (exuE3u) =>
% 24.33/6.32 ((
% 24.33/6.32 (exu__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (setadjoin__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (powerset__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (setunion__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (exuEu) =>
% 24.33/6.32 ((
% 24.33/6.32 (descr__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (dsetconstr__Cong) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetI1) =>
% 24.33/6.32 ((
% 24.33/6.32 (eqimpsubset2) =>
% 24.33/6.32 ((
% 24.33/6.32 (eqimpsubset1) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetI2) =>
% 24.33/6.32 ((
% 24.33/6.32 (emptysetsubset) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetE) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetE2) =>
% 24.33/6.32 ((
% 24.33/6.32 (notsubsetI) =>
% 24.33/6.32 ((
% 24.33/6.32 (notequalI1) =>
% 24.33/6.32 ((
% 24.33/6.32 (notequalI2) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetRefl) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetTrans) =>
% 24.33/6.32 ((
% 24.33/6.32 (setadjoinSub) =>
% 24.33/6.32 ((
% 24.33/6.32 (setadjoinSub2) =>
% 24.33/6.32 ((
% 24.33/6.32 (subset2powerset) =>
% 24.33/6.32 ((
% 24.33/6.32 (setextsub) =>
% 24.33/6.32 ((
% 24.33/6.32 (subsetemptysetimpeq) =>
% 24.33/6.32 ((
% 24.33/6.32 (powersetI1) =>
% 24.33/6.32 ((
% 24.33/6.32 (powersetE1) =>
% 24.33/6.32 ((
% 24.33/6.32 (inPowerset) =>
% 24.33/6.32 ((
% 24.33/6.32 (powersetsubset) =>
% 24.33/6.32 ((
% 24.33/6.32 (sepInPowerset) =>
% 24.33/6.32 ((
% 24.33/6.32 (sepSubset) =>
% 24.33/6.32 ((
% 24.33/6.32 (binunionIL) =>
% 24.33/6.32 ((
% 24.33/6.32 (upairset2IR) =>
% 24.33/6.32 ((
% 24.33/6.32 (binunionIR) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionEcases) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionE) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionLsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionRsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectI) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectSubset5) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectEL) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectLsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectSubset2) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectSubset3) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectER) =>
% 24.33/6.34 ((
% 24.33/6.34 (disjointsetsI1) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectRsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectSubset4) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectSubset1) =>
% 24.33/6.34 ((
% 24.33/6.34 (bs114d) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusI) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusEL) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusER) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusSubset2) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusERneg) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusELneg) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusILneg) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusIRneg) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusLsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusSubset1) =>
% 24.33/6.34 ((
% 24.33/6.34 (symdiffE) =>
% 24.33/6.34 ((
% 24.33/6.34 (symdiffI1) =>
% 24.33/6.34 ((
% 24.33/6.34 (symdiffI2) =>
% 24.33/6.34 ((
% 24.33/6.34 (symdiffIneg1) =>
% 24.33/6.34 ((
% 24.33/6.34 (symdiffIneg2) =>
% 24.33/6.34 ((
% 24.33/6.34 (secondinupair) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairIL) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairIR) =>
% 24.33/6.34 ((
% 24.33/6.34 (kpairiskpair) =>
% 24.33/6.34 ((
% 24.33/6.34 (kpairp) =>
% 24.33/6.34 ((
% 24.33/6.34 (singletonsubset) =>
% 24.33/6.34 ((
% 24.33/6.34 (singletoninpowerset) =>
% 24.33/6.34 ((
% 24.33/6.34 (singletoninpowunion) =>
% 24.33/6.34 ((
% 24.33/6.34 (upairset2E) =>
% 24.33/6.34 ((
% 24.33/6.34 (upairsubunion) =>
% 24.33/6.34 ((
% 24.33/6.34 (upairinpowunion) =>
% 24.33/6.34 ((
% 24.33/6.34 (ubforcartprodlem1) =>
% 24.33/6.34 ((
% 24.33/6.34 (ubforcartprodlem2) =>
% 24.33/6.34 ((
% 24.33/6.34 (ubforcartprodlem3) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodpairin) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodmempair1) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodmempair) =>
% 24.33/6.34 ((
% 24.33/6.34 (setunionE2) =>
% 24.33/6.34 ((
% 24.33/6.34 (setunionsingleton1) =>
% 24.33/6.34 ((
% 24.33/6.34 (setunionsingleton2) =>
% 24.33/6.34 ((
% 24.33/6.34 (setunionsingleton) =>
% 24.33/6.34 ((
% 24.33/6.34 (singletonprop) =>
% 24.33/6.34 ((
% 24.33/6.34 (ex1E1) =>
% 24.33/6.34 ((
% 24.33/6.34 (ex1I) =>
% 24.33/6.34 ((
% 24.33/6.34 (ex1I2) =>
% 24.33/6.34 ((
% 24.33/6.34 (singletonsuniq) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjL1) =>
% 24.33/6.34 ((
% 24.33/6.34 (kfstsingleton) =>
% 24.33/6.34 ((
% 24.33/6.34 (theprop) =>
% 24.33/6.34 ((
% 24.33/6.34 (kfstpairEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodfstin) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjL2) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjL) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjR11) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjR12) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjR1) =>
% 24.33/6.34 ((
% 24.33/6.34 (upairequniteq) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjR2) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjR) =>
% 24.33/6.34 ((
% 24.33/6.34 (ksndsingleton) =>
% 24.33/6.34 ((
% 24.33/6.34 (ksndpairEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (kpairsurjEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodsndin) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodpairmemEL) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodpairmemER) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodmempaircEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodfstpairEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodsndpairEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodpairsurjEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (dpsetconstrI) =>
% 24.33/6.34 ((
% 24.33/6.34 (!!) @ (
% 24.33/6.34 (('#B') @ (
% 24.33/6.34 !!) @
% 24.33/6.34 (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 !!))) @
% 24.33/6.34 (
% 24.33/6.34 (
% 24.33/6.34 ('#S') @ (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 '#S') @
% 24.33/6.34 (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 '#C'))) @
% 24.33/6.34 (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ subset)))) @
% 24.33/6.34 dpsetconstr)))))) @
% 24.33/6.34 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.33/6.34 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl280])).
% 24.33/6.34 thf(zip_derived_cl307, plain,
% 24.33/6.34 (~ (((setadjoinIL) =>
% 24.33/6.34 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 24.33/6.34 (((setadjoinIR) =>
% 24.33/6.34 (((setadjoinE) =>
% 24.33/6.34 (((setadjoinOr) =>
% 24.33/6.34 (((setoftrueEq) =>
% 24.33/6.34 (((powersetI) =>
% 24.33/6.34 (((emptyinPowerset) =>
% 24.33/6.34 (((emptyInPowerset) =>
% 24.33/6.34 (((powersetE) =>
% 24.33/6.34 (((setunionI) =>
% 24.33/6.34 (((setunionE) =>
% 24.33/6.34 (((subPowSU) =>
% 24.33/6.34 (((exuE2) =>
% 24.33/6.34 (((nonemptyImpWitness) =>
% 24.33/6.34 (((uniqinunit) =>
% 24.33/6.34 (((notinsingleton) =>
% 24.33/6.34 (((eqinunit) =>
% 24.33/6.34 (((singletonsswitch) =>
% 24.33/6.34 (((upairsetE) =>
% 24.33/6.34 (((upairsetIL) =>
% 24.33/6.34 (((upairsetIR) =>
% 24.33/6.34 (((emptyE1) =>
% 24.33/6.34 (((vacuousDall) =>
% 24.33/6.34 (((quantDeMorgan1) =>
% 24.33/6.34 (((quantDeMorgan2) =>
% 24.33/6.34 (((quantDeMorgan3) =>
% 24.33/6.34 (((quantDeMorgan4) =>
% 24.33/6.34 (((prop2setI) =>
% 24.33/6.34 (((prop2set2propI) =>
% 24.33/6.34 ((
% 24.33/6.34 (notdexE) =>
% 24.33/6.34 ((
% 24.33/6.34 (notdallE) =>
% 24.33/6.34 ((
% 24.33/6.34 (exuI1) =>
% 24.33/6.34 ((
% 24.33/6.34 (exuI3) =>
% 24.33/6.34 ((
% 24.33/6.34 (exuI2) =>
% 24.33/6.34 ((
% 24.33/6.34 (inCongP) =>
% 24.33/6.34 ((
% 24.33/6.34 (in__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (exuE3u) =>
% 24.33/6.34 ((
% 24.33/6.34 (exu__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (setadjoin__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (powerset__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (setunion__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (exuEu) =>
% 24.33/6.34 ((
% 24.33/6.34 (descr__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (dsetconstr__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetI1) =>
% 24.33/6.34 ((
% 24.33/6.34 (eqimpsubset2) =>
% 24.33/6.34 ((
% 24.33/6.34 (eqimpsubset1) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetI2) =>
% 24.33/6.34 ((
% 24.33/6.34 (emptysetsubset) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetE) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetE2) =>
% 24.33/6.34 ((
% 24.33/6.34 (notsubsetI) =>
% 24.33/6.34 ((
% 24.33/6.34 (notequalI1) =>
% 24.33/6.34 ((
% 24.33/6.34 (notequalI2) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetRefl) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetTrans) =>
% 24.33/6.34 ((
% 24.33/6.34 (setadjoinSub) =>
% 24.33/6.34 ((
% 24.33/6.34 (setadjoinSub2) =>
% 24.33/6.34 ((
% 24.33/6.34 (subset2powerset) =>
% 24.33/6.34 ((
% 24.33/6.34 (setextsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetemptysetimpeq) =>
% 24.33/6.34 ((
% 24.33/6.34 (powersetI1) =>
% 24.33/6.34 ((
% 24.33/6.34 (powersetE1) =>
% 24.33/6.34 ((
% 24.33/6.34 (inPowerset) =>
% 24.33/6.34 ((
% 24.33/6.34 (powersetsubset) =>
% 24.33/6.34 ((
% 24.33/6.34 (sepInPowerset) =>
% 24.33/6.34 ((
% 24.33/6.34 (sepSubset) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionIL) =>
% 24.33/6.34 ((
% 24.33/6.34 (upairset2IR) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionIR) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionEcases) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionE) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionLsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionRsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectI) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectSubset5) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectEL) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectLsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectSubset2) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectSubset3) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectER) =>
% 24.33/6.34 ((
% 24.33/6.34 (disjointsetsI1) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectRsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectSubset4) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectSubset1) =>
% 24.33/6.34 ((
% 24.33/6.34 (bs114d) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusI) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusEL) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusER) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusSubset2) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusERneg) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusELneg) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusILneg) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusIRneg) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusLsub) =>
% 24.33/6.34 ((
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% 24.33/6.34 ((
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% 24.33/6.34 ((
% 24.33/6.34 (symdiffI1) =>
% 24.33/6.34 ((
% 24.33/6.34 (symdiffI2) =>
% 24.33/6.34 ((
% 24.33/6.34 (symdiffIneg1) =>
% 24.33/6.34 ((
% 24.33/6.34 (symdiffIneg2) =>
% 24.33/6.34 ((
% 24.33/6.34 (secondinupair) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairIL) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairIR) =>
% 24.33/6.34 ((
% 24.33/6.34 (kpairiskpair) =>
% 24.33/6.34 ((
% 24.33/6.34 (kpairp) =>
% 24.33/6.34 ((
% 24.33/6.34 (singletonsubset) =>
% 24.33/6.34 ((
% 24.33/6.34 (singletoninpowerset) =>
% 24.33/6.34 ((
% 24.33/6.34 (singletoninpowunion) =>
% 24.33/6.34 ((
% 24.33/6.34 (upairset2E) =>
% 24.33/6.34 ((
% 24.33/6.34 (upairsubunion) =>
% 24.33/6.34 ((
% 24.33/6.34 (upairinpowunion) =>
% 24.33/6.34 ((
% 24.33/6.34 (ubforcartprodlem1) =>
% 24.33/6.34 ((
% 24.33/6.34 (ubforcartprodlem2) =>
% 24.33/6.34 ((
% 24.33/6.34 (ubforcartprodlem3) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodpairin) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodmempair1) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodmempair) =>
% 24.33/6.34 ((
% 24.33/6.34 (setunionE2) =>
% 24.33/6.34 ((
% 24.33/6.34 (setunionsingleton1) =>
% 24.33/6.34 ((
% 24.33/6.34 (setunionsingleton2) =>
% 24.33/6.34 ((
% 24.33/6.34 (setunionsingleton) =>
% 24.33/6.34 ((
% 24.33/6.34 (singletonprop) =>
% 24.33/6.34 ((
% 24.33/6.34 (ex1E1) =>
% 24.33/6.34 ((
% 24.33/6.34 (ex1I) =>
% 24.33/6.34 ((
% 24.33/6.34 (ex1I2) =>
% 24.33/6.34 ((
% 24.33/6.34 (singletonsuniq) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjL1) =>
% 24.33/6.34 ((
% 24.33/6.34 (kfstsingleton) =>
% 24.33/6.34 ((
% 24.33/6.34 (theprop) =>
% 24.33/6.34 ((
% 24.33/6.34 (kfstpairEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodfstin) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjL2) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjL) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjR11) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjR12) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjR1) =>
% 24.33/6.34 ((
% 24.33/6.34 (upairequniteq) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjR2) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjR) =>
% 24.33/6.34 ((
% 24.33/6.34 (ksndsingleton) =>
% 24.33/6.34 ((
% 24.33/6.34 (ksndpairEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (kpairsurjEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodsndin) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodpairmemEL) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodpairmemER) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodmempaircEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodfstpairEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodsndpairEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodpairsurjEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (dpsetconstrI) =>
% 24.33/6.34 ((
% 24.33/6.34 (!!) @ (
% 24.33/6.34 (('#B') @ (
% 24.33/6.34 !!) @
% 24.33/6.34 (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 !!))) @
% 24.33/6.34 (
% 24.33/6.34 (
% 24.33/6.34 ('#S') @ (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 '#S') @
% 24.33/6.34 (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 '#C'))) @
% 24.33/6.34 (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ subset)))) @
% 24.33/6.34 dpsetconstr)))))) @
% 24.33/6.34 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.33/6.34 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl293])).
% 24.33/6.34 thf(zip_derived_cl322, plain,
% 24.33/6.34 (~ (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 24.33/6.34 (((setadjoinIR) =>
% 24.33/6.34 (((setadjoinE) =>
% 24.33/6.34 (((setadjoinOr) =>
% 24.33/6.34 (((setoftrueEq) =>
% 24.33/6.34 (((powersetI) =>
% 24.33/6.34 (((emptyinPowerset) =>
% 24.33/6.34 (((emptyInPowerset) =>
% 24.33/6.34 (((powersetE) =>
% 24.33/6.34 (((setunionI) =>
% 24.33/6.34 (((setunionE) =>
% 24.33/6.34 (((subPowSU) =>
% 24.33/6.34 (((exuE2) =>
% 24.33/6.34 (((nonemptyImpWitness) =>
% 24.33/6.34 (((uniqinunit) =>
% 24.33/6.34 (((notinsingleton) =>
% 24.33/6.34 (((eqinunit) =>
% 24.33/6.34 (((singletonsswitch) =>
% 24.33/6.34 (((upairsetE) =>
% 24.33/6.34 (((upairsetIL) =>
% 24.33/6.34 (((upairsetIR) =>
% 24.33/6.34 (((emptyE1) =>
% 24.33/6.34 (((vacuousDall) =>
% 24.33/6.34 (((quantDeMorgan1) =>
% 24.33/6.34 (((quantDeMorgan2) =>
% 24.33/6.34 (((quantDeMorgan3) =>
% 24.33/6.34 (((quantDeMorgan4) =>
% 24.33/6.34 (((prop2setI) =>
% 24.33/6.34 (((prop2set2propI) =>
% 24.33/6.34 (((notdexE) =>
% 24.33/6.34 ((
% 24.33/6.34 (notdallE) =>
% 24.33/6.34 ((
% 24.33/6.34 (exuI1) =>
% 24.33/6.34 ((
% 24.33/6.34 (exuI3) =>
% 24.33/6.34 ((
% 24.33/6.34 (exuI2) =>
% 24.33/6.34 ((
% 24.33/6.34 (inCongP) =>
% 24.33/6.34 ((
% 24.33/6.34 (in__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (exuE3u) =>
% 24.33/6.34 ((
% 24.33/6.34 (exu__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (setadjoin__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (powerset__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (setunion__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (exuEu) =>
% 24.33/6.34 ((
% 24.33/6.34 (descr__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (dsetconstr__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetI1) =>
% 24.33/6.34 ((
% 24.33/6.34 (eqimpsubset2) =>
% 24.33/6.34 ((
% 24.33/6.34 (eqimpsubset1) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetI2) =>
% 24.33/6.34 ((
% 24.33/6.34 (emptysetsubset) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetE) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetE2) =>
% 24.33/6.34 ((
% 24.33/6.34 (notsubsetI) =>
% 24.33/6.34 ((
% 24.33/6.34 (notequalI1) =>
% 24.33/6.34 ((
% 24.33/6.34 (notequalI2) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetRefl) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetTrans) =>
% 24.33/6.34 ((
% 24.33/6.34 (setadjoinSub) =>
% 24.33/6.34 ((
% 24.33/6.34 (setadjoinSub2) =>
% 24.33/6.34 ((
% 24.33/6.34 (subset2powerset) =>
% 24.33/6.34 ((
% 24.33/6.34 (setextsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetemptysetimpeq) =>
% 24.33/6.34 ((
% 24.33/6.34 (powersetI1) =>
% 24.33/6.34 ((
% 24.33/6.34 (powersetE1) =>
% 24.33/6.34 ((
% 24.33/6.34 (inPowerset) =>
% 24.33/6.34 ((
% 24.33/6.34 (powersetsubset) =>
% 24.33/6.34 ((
% 24.33/6.34 (sepInPowerset) =>
% 24.33/6.34 ((
% 24.33/6.34 (sepSubset) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionIL) =>
% 24.33/6.34 ((
% 24.33/6.34 (upairset2IR) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionIR) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionEcases) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionE) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionLsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionRsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectI) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectSubset5) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectEL) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectLsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectSubset2) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectSubset3) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectER) =>
% 24.33/6.34 ((
% 24.33/6.34 (disjointsetsI1) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectRsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectSubset4) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectSubset1) =>
% 24.33/6.34 ((
% 24.33/6.34 (bs114d) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusI) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusEL) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusER) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusSubset2) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusERneg) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusELneg) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusILneg) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusIRneg) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusLsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusSubset1) =>
% 24.33/6.34 ((
% 24.33/6.34 (symdiffE) =>
% 24.33/6.34 ((
% 24.33/6.34 (symdiffI1) =>
% 24.33/6.34 ((
% 24.33/6.34 (symdiffI2) =>
% 24.33/6.34 ((
% 24.33/6.34 (symdiffIneg1) =>
% 24.33/6.34 ((
% 24.33/6.34 (symdiffIneg2) =>
% 24.33/6.34 ((
% 24.33/6.34 (secondinupair) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairIL) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairIR) =>
% 24.33/6.34 ((
% 24.33/6.34 (kpairiskpair) =>
% 24.33/6.34 ((
% 24.33/6.34 (kpairp) =>
% 24.33/6.34 ((
% 24.33/6.34 (singletonsubset) =>
% 24.33/6.34 ((
% 24.33/6.34 (singletoninpowerset) =>
% 24.33/6.34 ((
% 24.33/6.34 (singletoninpowunion) =>
% 24.33/6.34 ((
% 24.33/6.34 (upairset2E) =>
% 24.33/6.34 ((
% 24.33/6.34 (upairsubunion) =>
% 24.33/6.34 ((
% 24.33/6.34 (upairinpowunion) =>
% 24.33/6.34 ((
% 24.33/6.34 (ubforcartprodlem1) =>
% 24.33/6.34 ((
% 24.33/6.34 (ubforcartprodlem2) =>
% 24.33/6.34 ((
% 24.33/6.34 (ubforcartprodlem3) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodpairin) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodmempair1) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodmempair) =>
% 24.33/6.34 ((
% 24.33/6.34 (setunionE2) =>
% 24.33/6.34 ((
% 24.33/6.34 (setunionsingleton1) =>
% 24.33/6.34 ((
% 24.33/6.34 (setunionsingleton2) =>
% 24.33/6.34 ((
% 24.33/6.34 (setunionsingleton) =>
% 24.33/6.34 ((
% 24.33/6.34 (singletonprop) =>
% 24.33/6.34 ((
% 24.33/6.34 (ex1E1) =>
% 24.33/6.34 ((
% 24.33/6.34 (ex1I) =>
% 24.33/6.34 ((
% 24.33/6.34 (ex1I2) =>
% 24.33/6.34 ((
% 24.33/6.34 (singletonsuniq) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjL1) =>
% 24.33/6.34 ((
% 24.33/6.34 (kfstsingleton) =>
% 24.33/6.34 ((
% 24.33/6.34 (theprop) =>
% 24.33/6.34 ((
% 24.33/6.34 (kfstpairEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodfstin) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjL2) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjL) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjR11) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjR12) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjR1) =>
% 24.33/6.34 ((
% 24.33/6.34 (upairequniteq) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjR2) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjR) =>
% 24.33/6.34 ((
% 24.33/6.34 (ksndsingleton) =>
% 24.33/6.34 ((
% 24.33/6.34 (ksndpairEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (kpairsurjEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodsndin) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodpairmemEL) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodpairmemER) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodmempaircEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodfstpairEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodsndpairEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodpairsurjEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (dpsetconstrI) =>
% 24.33/6.34 ((
% 24.33/6.34 (!!) @ (
% 24.33/6.34 (('#B') @ (
% 24.33/6.34 !!) @
% 24.33/6.34 (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 !!))) @
% 24.33/6.34 (
% 24.33/6.34 (
% 24.33/6.34 ('#S') @ (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 '#S') @
% 24.33/6.34 (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 '#C'))) @
% 24.33/6.34 (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ subset)))) @
% 24.33/6.34 dpsetconstr)))))) @
% 24.33/6.34 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.33/6.34 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl307])).
% 24.33/6.34 thf(zip_derived_cl337, plain,
% 24.33/6.34 (~ (((setadjoinIR) =>
% 24.33/6.34 (((setadjoinE) =>
% 24.33/6.34 (((setadjoinOr) =>
% 24.33/6.34 (((setoftrueEq) =>
% 24.33/6.34 (((powersetI) =>
% 24.33/6.34 (((emptyinPowerset) =>
% 24.33/6.34 (((emptyInPowerset) =>
% 24.33/6.34 (((powersetE) =>
% 24.33/6.34 (((setunionI) =>
% 24.33/6.34 (((setunionE) =>
% 24.33/6.34 (((subPowSU) =>
% 24.33/6.34 (((exuE2) =>
% 24.33/6.34 (((nonemptyImpWitness) =>
% 24.33/6.34 (((uniqinunit) =>
% 24.33/6.34 (((notinsingleton) =>
% 24.33/6.34 (((eqinunit) =>
% 24.33/6.34 (((singletonsswitch) =>
% 24.33/6.34 (((upairsetE) =>
% 24.33/6.34 (((upairsetIL) =>
% 24.33/6.34 (((upairsetIR) =>
% 24.33/6.34 (((emptyE1) =>
% 24.33/6.34 (((vacuousDall) =>
% 24.33/6.34 (((quantDeMorgan1) =>
% 24.33/6.34 (((quantDeMorgan2) =>
% 24.33/6.34 (((quantDeMorgan3) =>
% 24.33/6.34 (((quantDeMorgan4) =>
% 24.33/6.34 (((prop2setI) =>
% 24.33/6.34 (((prop2set2propI) =>
% 24.33/6.34 (((notdexE) =>
% 24.33/6.34 (((notdallE) =>
% 24.33/6.34 ((
% 24.33/6.34 (exuI1) =>
% 24.33/6.34 ((
% 24.33/6.34 (exuI3) =>
% 24.33/6.34 ((
% 24.33/6.34 (exuI2) =>
% 24.33/6.34 ((
% 24.33/6.34 (inCongP) =>
% 24.33/6.34 ((
% 24.33/6.34 (in__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (exuE3u) =>
% 24.33/6.34 ((
% 24.33/6.34 (exu__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (setadjoin__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (powerset__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (setunion__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (exuEu) =>
% 24.33/6.34 ((
% 24.33/6.34 (descr__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (dsetconstr__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetI1) =>
% 24.33/6.34 ((
% 24.33/6.34 (eqimpsubset2) =>
% 24.33/6.34 ((
% 24.33/6.34 (eqimpsubset1) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetI2) =>
% 24.33/6.34 ((
% 24.33/6.34 (emptysetsubset) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetE) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetE2) =>
% 24.33/6.34 ((
% 24.33/6.34 (notsubsetI) =>
% 24.33/6.34 ((
% 24.33/6.34 (notequalI1) =>
% 24.33/6.34 ((
% 24.33/6.34 (notequalI2) =>
% 24.33/6.34 ((
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% 24.33/6.34 ((
% 24.33/6.34 (subsetTrans) =>
% 24.33/6.34 ((
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% 24.33/6.34 ((
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% 24.33/6.34 ((
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% 24.33/6.34 ((
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% 24.33/6.34 ((
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% 24.33/6.34 ((
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% 24.33/6.34 ((
% 24.33/6.34 (powersetE1) =>
% 24.33/6.34 ((
% 24.33/6.34 (inPowerset) =>
% 24.33/6.34 ((
% 24.33/6.34 (powersetsubset) =>
% 24.33/6.34 ((
% 24.33/6.34 (sepInPowerset) =>
% 24.33/6.34 ((
% 24.33/6.34 (sepSubset) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionIL) =>
% 24.33/6.34 ((
% 24.33/6.34 (upairset2IR) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionIR) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionEcases) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionE) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionLsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionRsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectI) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectSubset5) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectEL) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectLsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectSubset2) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectSubset3) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectER) =>
% 24.33/6.34 ((
% 24.33/6.34 (disjointsetsI1) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectRsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectSubset4) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectSubset1) =>
% 24.33/6.34 ((
% 24.33/6.34 (bs114d) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusI) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusEL) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusER) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusSubset2) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusERneg) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusELneg) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusILneg) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusIRneg) =>
% 24.33/6.34 ((
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% 24.33/6.34 ((
% 24.33/6.34 (setminusSubset1) =>
% 24.33/6.34 ((
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% 24.33/6.34 ((
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% 24.33/6.34 ((
% 24.33/6.34 (symdiffI2) =>
% 24.33/6.34 ((
% 24.33/6.34 (symdiffIneg1) =>
% 24.33/6.34 ((
% 24.33/6.34 (symdiffIneg2) =>
% 24.33/6.34 ((
% 24.33/6.34 (secondinupair) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairIL) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairIR) =>
% 24.33/6.34 ((
% 24.33/6.34 (kpairiskpair) =>
% 24.33/6.34 ((
% 24.33/6.34 (kpairp) =>
% 24.33/6.34 ((
% 24.33/6.34 (singletonsubset) =>
% 24.33/6.34 ((
% 24.33/6.34 (singletoninpowerset) =>
% 24.33/6.34 ((
% 24.33/6.34 (singletoninpowunion) =>
% 24.33/6.34 ((
% 24.33/6.34 (upairset2E) =>
% 24.33/6.34 ((
% 24.33/6.34 (upairsubunion) =>
% 24.33/6.34 ((
% 24.33/6.34 (upairinpowunion) =>
% 24.33/6.34 ((
% 24.33/6.34 (ubforcartprodlem1) =>
% 24.33/6.34 ((
% 24.33/6.34 (ubforcartprodlem2) =>
% 24.33/6.34 ((
% 24.33/6.34 (ubforcartprodlem3) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodpairin) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodmempair1) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodmempair) =>
% 24.33/6.34 ((
% 24.33/6.34 (setunionE2) =>
% 24.33/6.34 ((
% 24.33/6.34 (setunionsingleton1) =>
% 24.33/6.34 ((
% 24.33/6.34 (setunionsingleton2) =>
% 24.33/6.34 ((
% 24.33/6.34 (setunionsingleton) =>
% 24.33/6.34 ((
% 24.33/6.34 (singletonprop) =>
% 24.33/6.34 ((
% 24.33/6.34 (ex1E1) =>
% 24.33/6.34 ((
% 24.33/6.34 (ex1I) =>
% 24.33/6.34 ((
% 24.33/6.34 (ex1I2) =>
% 24.33/6.34 ((
% 24.33/6.34 (singletonsuniq) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjL1) =>
% 24.33/6.34 ((
% 24.33/6.34 (kfstsingleton) =>
% 24.33/6.34 ((
% 24.33/6.34 (theprop) =>
% 24.33/6.34 ((
% 24.33/6.34 (kfstpairEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodfstin) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjL2) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjL) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjR11) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjR12) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjR1) =>
% 24.33/6.34 ((
% 24.33/6.34 (upairequniteq) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjR2) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjR) =>
% 24.33/6.34 ((
% 24.33/6.34 (ksndsingleton) =>
% 24.33/6.34 ((
% 24.33/6.34 (ksndpairEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (kpairsurjEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodsndin) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodpairmemEL) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodpairmemER) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodmempaircEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodfstpairEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodsndpairEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodpairsurjEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (dpsetconstrI) =>
% 24.33/6.34 ((
% 24.33/6.34 (!!) @ (
% 24.33/6.34 (('#B') @ (
% 24.33/6.34 !!) @
% 24.33/6.34 (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 !!))) @
% 24.33/6.34 (
% 24.33/6.34 (
% 24.33/6.34 ('#S') @ (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 '#S') @
% 24.33/6.34 (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 '#C'))) @
% 24.33/6.34 (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ subset)))) @
% 24.33/6.34 dpsetconstr)))))) @
% 24.33/6.34 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.33/6.34 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl322])).
% 24.33/6.34 thf(zip_derived_cl349, plain,
% 24.33/6.34 (~ (((setadjoinE) =>
% 24.33/6.34 (((setadjoinOr) =>
% 24.33/6.34 (((setoftrueEq) =>
% 24.33/6.34 (((powersetI) =>
% 24.33/6.34 (((emptyinPowerset) =>
% 24.33/6.34 (((emptyInPowerset) =>
% 24.33/6.34 (((powersetE) =>
% 24.33/6.34 (((setunionI) =>
% 24.33/6.34 (((setunionE) =>
% 24.33/6.34 (((subPowSU) =>
% 24.33/6.34 (((exuE2) =>
% 24.33/6.34 (((nonemptyImpWitness) =>
% 24.33/6.34 (((uniqinunit) =>
% 24.33/6.34 (((notinsingleton) =>
% 24.33/6.34 (((eqinunit) =>
% 24.33/6.34 (((singletonsswitch) =>
% 24.33/6.34 (((upairsetE) =>
% 24.33/6.34 (((upairsetIL) =>
% 24.33/6.34 (((upairsetIR) =>
% 24.33/6.34 (((emptyE1) =>
% 24.33/6.34 (((vacuousDall) =>
% 24.33/6.34 (((quantDeMorgan1) =>
% 24.33/6.34 (((quantDeMorgan2) =>
% 24.33/6.34 (((quantDeMorgan3) =>
% 24.33/6.34 (((quantDeMorgan4) =>
% 24.33/6.34 (((prop2setI) =>
% 24.33/6.34 (((prop2set2propI) =>
% 24.33/6.34 (((notdexE) =>
% 24.33/6.34 (((notdallE) =>
% 24.33/6.34 (((exuI1) =>
% 24.33/6.34 ((
% 24.33/6.34 (exuI3) =>
% 24.33/6.34 ((
% 24.33/6.34 (exuI2) =>
% 24.33/6.34 ((
% 24.33/6.34 (inCongP) =>
% 24.33/6.34 ((
% 24.33/6.34 (in__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (exuE3u) =>
% 24.33/6.34 ((
% 24.33/6.34 (exu__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (setadjoin__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (powerset__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (setunion__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (exuEu) =>
% 24.33/6.34 ((
% 24.33/6.34 (descr__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (dsetconstr__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetI1) =>
% 24.33/6.34 ((
% 24.33/6.34 (eqimpsubset2) =>
% 24.33/6.34 ((
% 24.33/6.34 (eqimpsubset1) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetI2) =>
% 24.33/6.34 ((
% 24.33/6.34 (emptysetsubset) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetE) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetE2) =>
% 24.33/6.34 ((
% 24.33/6.34 (notsubsetI) =>
% 24.33/6.34 ((
% 24.33/6.34 (notequalI1) =>
% 24.33/6.34 ((
% 24.33/6.34 (notequalI2) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetRefl) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetTrans) =>
% 24.33/6.34 ((
% 24.33/6.34 (setadjoinSub) =>
% 24.33/6.34 ((
% 24.33/6.34 (setadjoinSub2) =>
% 24.33/6.34 ((
% 24.33/6.34 (subset2powerset) =>
% 24.33/6.34 ((
% 24.33/6.34 (setextsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetemptysetimpeq) =>
% 24.33/6.34 ((
% 24.33/6.34 (powersetI1) =>
% 24.33/6.34 ((
% 24.33/6.34 (powersetE1) =>
% 24.33/6.34 ((
% 24.33/6.34 (inPowerset) =>
% 24.33/6.34 ((
% 24.33/6.34 (powersetsubset) =>
% 24.33/6.34 ((
% 24.33/6.34 (sepInPowerset) =>
% 24.33/6.34 ((
% 24.33/6.34 (sepSubset) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionIL) =>
% 24.33/6.34 ((
% 24.33/6.34 (upairset2IR) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionIR) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionEcases) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionE) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionLsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionRsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectI) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectSubset5) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectEL) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectLsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectSubset2) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectSubset3) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectER) =>
% 24.33/6.34 ((
% 24.33/6.34 (disjointsetsI1) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectRsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectSubset4) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectSubset1) =>
% 24.33/6.34 ((
% 24.33/6.34 (bs114d) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusI) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusEL) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusER) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusSubset2) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusERneg) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusELneg) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusILneg) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusIRneg) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusLsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusSubset1) =>
% 24.33/6.34 ((
% 24.33/6.34 (symdiffE) =>
% 24.33/6.34 ((
% 24.33/6.34 (symdiffI1) =>
% 24.33/6.34 ((
% 24.33/6.34 (symdiffI2) =>
% 24.33/6.34 ((
% 24.33/6.34 (symdiffIneg1) =>
% 24.33/6.34 ((
% 24.33/6.34 (symdiffIneg2) =>
% 24.33/6.34 ((
% 24.33/6.34 (secondinupair) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairIL) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairIR) =>
% 24.33/6.34 ((
% 24.33/6.34 (kpairiskpair) =>
% 24.33/6.34 ((
% 24.33/6.34 (kpairp) =>
% 24.33/6.34 ((
% 24.33/6.34 (singletonsubset) =>
% 24.33/6.34 ((
% 24.33/6.34 (singletoninpowerset) =>
% 24.33/6.34 ((
% 24.33/6.34 (singletoninpowunion) =>
% 24.33/6.34 ((
% 24.33/6.34 (upairset2E) =>
% 24.33/6.34 ((
% 24.33/6.34 (upairsubunion) =>
% 24.33/6.34 ((
% 24.33/6.34 (upairinpowunion) =>
% 24.33/6.34 ((
% 24.33/6.34 (ubforcartprodlem1) =>
% 24.33/6.34 ((
% 24.33/6.34 (ubforcartprodlem2) =>
% 24.33/6.34 ((
% 24.33/6.34 (ubforcartprodlem3) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodpairin) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodmempair1) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodmempair) =>
% 24.33/6.34 ((
% 24.33/6.34 (setunionE2) =>
% 24.33/6.34 ((
% 24.33/6.34 (setunionsingleton1) =>
% 24.33/6.34 ((
% 24.33/6.34 (setunionsingleton2) =>
% 24.33/6.34 ((
% 24.33/6.34 (setunionsingleton) =>
% 24.33/6.34 ((
% 24.33/6.34 (singletonprop) =>
% 24.33/6.34 ((
% 24.33/6.34 (ex1E1) =>
% 24.33/6.34 ((
% 24.33/6.34 (ex1I) =>
% 24.33/6.34 ((
% 24.33/6.34 (ex1I2) =>
% 24.33/6.34 ((
% 24.33/6.34 (singletonsuniq) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjL1) =>
% 24.33/6.34 ((
% 24.33/6.34 (kfstsingleton) =>
% 24.33/6.34 ((
% 24.33/6.34 (theprop) =>
% 24.33/6.34 ((
% 24.33/6.34 (kfstpairEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodfstin) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjL2) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjL) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjR11) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjR12) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjR1) =>
% 24.33/6.34 ((
% 24.33/6.34 (upairequniteq) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjR2) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjR) =>
% 24.33/6.34 ((
% 24.33/6.34 (ksndsingleton) =>
% 24.33/6.34 ((
% 24.33/6.34 (ksndpairEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (kpairsurjEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodsndin) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodpairmemEL) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodpairmemER) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodmempaircEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodfstpairEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodsndpairEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodpairsurjEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (dpsetconstrI) =>
% 24.33/6.34 ((
% 24.33/6.34 (!!) @ (
% 24.33/6.34 (('#B') @ (
% 24.33/6.34 !!) @
% 24.33/6.34 (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 !!))) @
% 24.33/6.34 (
% 24.33/6.34 (
% 24.33/6.34 ('#S') @ (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 '#S') @
% 24.33/6.34 (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 '#C'))) @
% 24.33/6.34 (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ subset)))) @
% 24.33/6.34 dpsetconstr)))))) @
% 24.33/6.34 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.33/6.34 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl337])).
% 24.33/6.34 thf(zip_derived_cl355, plain,
% 24.33/6.34 (~ (((setadjoinOr) =>
% 24.33/6.34 (((setoftrueEq) =>
% 24.33/6.34 (((powersetI) =>
% 24.33/6.34 (((emptyinPowerset) =>
% 24.33/6.34 (((emptyInPowerset) =>
% 24.33/6.34 (((powersetE) =>
% 24.33/6.34 (((setunionI) =>
% 24.33/6.34 (((setunionE) =>
% 24.33/6.34 (((subPowSU) =>
% 24.33/6.34 (((exuE2) =>
% 24.33/6.34 (((nonemptyImpWitness) =>
% 24.33/6.34 (((uniqinunit) =>
% 24.33/6.34 (((notinsingleton) =>
% 24.33/6.34 (((eqinunit) =>
% 24.33/6.34 (((singletonsswitch) =>
% 24.33/6.34 (((upairsetE) =>
% 24.33/6.34 (((upairsetIL) =>
% 24.33/6.34 (((upairsetIR) =>
% 24.33/6.34 (((emptyE1) =>
% 24.33/6.34 (((vacuousDall) =>
% 24.33/6.34 (((quantDeMorgan1) =>
% 24.33/6.34 (((quantDeMorgan2) =>
% 24.33/6.34 (((quantDeMorgan3) =>
% 24.33/6.34 (((quantDeMorgan4) =>
% 24.33/6.34 (((prop2setI) =>
% 24.33/6.34 (((prop2set2propI) =>
% 24.33/6.34 (((notdexE) =>
% 24.33/6.34 (((notdallE) =>
% 24.33/6.34 (((exuI1) =>
% 24.33/6.34 (((exuI3) =>
% 24.33/6.34 ((
% 24.33/6.34 (exuI2) =>
% 24.33/6.34 ((
% 24.33/6.34 (inCongP) =>
% 24.33/6.34 ((
% 24.33/6.34 (in__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (exuE3u) =>
% 24.33/6.34 ((
% 24.33/6.34 (exu__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (setadjoin__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (powerset__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (setunion__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (exuEu) =>
% 24.33/6.34 ((
% 24.33/6.34 (descr__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (dsetconstr__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetI1) =>
% 24.33/6.34 ((
% 24.33/6.34 (eqimpsubset2) =>
% 24.33/6.34 ((
% 24.33/6.34 (eqimpsubset1) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetI2) =>
% 24.33/6.34 ((
% 24.33/6.34 (emptysetsubset) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetE) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetE2) =>
% 24.33/6.34 ((
% 24.33/6.34 (notsubsetI) =>
% 24.33/6.34 ((
% 24.33/6.34 (notequalI1) =>
% 24.33/6.34 ((
% 24.33/6.34 (notequalI2) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetRefl) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetTrans) =>
% 24.33/6.34 ((
% 24.33/6.34 (setadjoinSub) =>
% 24.33/6.34 ((
% 24.33/6.34 (setadjoinSub2) =>
% 24.33/6.34 ((
% 24.33/6.34 (subset2powerset) =>
% 24.33/6.34 ((
% 24.33/6.34 (setextsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetemptysetimpeq) =>
% 24.33/6.34 ((
% 24.33/6.34 (powersetI1) =>
% 24.33/6.34 ((
% 24.33/6.34 (powersetE1) =>
% 24.33/6.34 ((
% 24.33/6.34 (inPowerset) =>
% 24.33/6.34 ((
% 24.33/6.34 (powersetsubset) =>
% 24.33/6.34 ((
% 24.33/6.34 (sepInPowerset) =>
% 24.33/6.34 ((
% 24.33/6.34 (sepSubset) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionIL) =>
% 24.33/6.34 ((
% 24.33/6.34 (upairset2IR) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionIR) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionEcases) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionE) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionLsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionRsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectI) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectSubset5) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectEL) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectLsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectSubset2) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectSubset3) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectER) =>
% 24.33/6.34 ((
% 24.33/6.34 (disjointsetsI1) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectRsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectSubset4) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectSubset1) =>
% 24.33/6.34 ((
% 24.33/6.34 (bs114d) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusI) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusEL) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusER) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusSubset2) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusERneg) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusELneg) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusILneg) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusIRneg) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusLsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusSubset1) =>
% 24.33/6.34 ((
% 24.33/6.34 (symdiffE) =>
% 24.33/6.34 ((
% 24.33/6.34 (symdiffI1) =>
% 24.33/6.34 ((
% 24.33/6.34 (symdiffI2) =>
% 24.33/6.34 ((
% 24.33/6.34 (symdiffIneg1) =>
% 24.33/6.34 ((
% 24.33/6.34 (symdiffIneg2) =>
% 24.33/6.34 ((
% 24.33/6.34 (secondinupair) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairIL) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairIR) =>
% 24.33/6.34 ((
% 24.33/6.34 (kpairiskpair) =>
% 24.33/6.34 ((
% 24.33/6.34 (kpairp) =>
% 24.33/6.34 ((
% 24.33/6.34 (singletonsubset) =>
% 24.33/6.34 ((
% 24.33/6.34 (singletoninpowerset) =>
% 24.33/6.34 ((
% 24.33/6.34 (singletoninpowunion) =>
% 24.33/6.34 ((
% 24.33/6.34 (upairset2E) =>
% 24.33/6.34 ((
% 24.33/6.34 (upairsubunion) =>
% 24.33/6.34 ((
% 24.33/6.34 (upairinpowunion) =>
% 24.33/6.34 ((
% 24.33/6.34 (ubforcartprodlem1) =>
% 24.33/6.34 ((
% 24.33/6.34 (ubforcartprodlem2) =>
% 24.33/6.34 ((
% 24.33/6.34 (ubforcartprodlem3) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodpairin) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodmempair1) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodmempair) =>
% 24.33/6.34 ((
% 24.33/6.34 (setunionE2) =>
% 24.33/6.34 ((
% 24.33/6.34 (setunionsingleton1) =>
% 24.33/6.34 ((
% 24.33/6.34 (setunionsingleton2) =>
% 24.33/6.34 ((
% 24.33/6.34 (setunionsingleton) =>
% 24.33/6.34 ((
% 24.33/6.34 (singletonprop) =>
% 24.33/6.34 ((
% 24.33/6.34 (ex1E1) =>
% 24.33/6.34 ((
% 24.33/6.34 (ex1I) =>
% 24.33/6.34 ((
% 24.33/6.34 (ex1I2) =>
% 24.33/6.34 ((
% 24.33/6.34 (singletonsuniq) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjL1) =>
% 24.33/6.34 ((
% 24.33/6.34 (kfstsingleton) =>
% 24.33/6.34 ((
% 24.33/6.34 (theprop) =>
% 24.33/6.34 ((
% 24.33/6.34 (kfstpairEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodfstin) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjL2) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjL) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjR11) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjR12) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjR1) =>
% 24.33/6.34 ((
% 24.33/6.34 (upairequniteq) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjR2) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjR) =>
% 24.33/6.34 ((
% 24.33/6.34 (ksndsingleton) =>
% 24.33/6.34 ((
% 24.33/6.34 (ksndpairEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (kpairsurjEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodsndin) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodpairmemEL) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodpairmemER) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodmempaircEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodfstpairEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodsndpairEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodpairsurjEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (dpsetconstrI) =>
% 24.33/6.34 ((
% 24.33/6.34 (!!) @ (
% 24.33/6.34 (('#B') @ (
% 24.33/6.34 !!) @
% 24.33/6.34 (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 !!))) @
% 24.33/6.34 (
% 24.33/6.34 (
% 24.33/6.34 ('#S') @ (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 '#S') @
% 24.33/6.34 (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 '#C'))) @
% 24.33/6.34 (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ subset)))) @
% 24.33/6.34 dpsetconstr)))))) @
% 24.33/6.34 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.33/6.34 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl349])).
% 24.33/6.34 thf(zip_derived_cl362, plain,
% 24.33/6.34 (~ (((setoftrueEq) =>
% 24.33/6.34 (((powersetI) =>
% 24.33/6.34 (((emptyinPowerset) =>
% 24.33/6.34 (((emptyInPowerset) =>
% 24.33/6.34 (((powersetE) =>
% 24.33/6.34 (((setunionI) =>
% 24.33/6.34 (((setunionE) =>
% 24.33/6.34 (((subPowSU) =>
% 24.33/6.34 (((exuE2) =>
% 24.33/6.34 (((nonemptyImpWitness) =>
% 24.33/6.34 (((uniqinunit) =>
% 24.33/6.34 (((notinsingleton) =>
% 24.33/6.34 (((eqinunit) =>
% 24.33/6.34 (((singletonsswitch) =>
% 24.33/6.34 (((upairsetE) =>
% 24.33/6.34 (((upairsetIL) =>
% 24.33/6.34 (((upairsetIR) =>
% 24.33/6.34 (((emptyE1) =>
% 24.33/6.34 (((vacuousDall) =>
% 24.33/6.34 (((quantDeMorgan1) =>
% 24.33/6.34 (((quantDeMorgan2) =>
% 24.33/6.34 (((quantDeMorgan3) =>
% 24.33/6.34 (((quantDeMorgan4) =>
% 24.33/6.34 (((prop2setI) =>
% 24.33/6.34 (((prop2set2propI) =>
% 24.33/6.34 (((notdexE) =>
% 24.33/6.34 (((notdallE) =>
% 24.33/6.34 (((exuI1) =>
% 24.33/6.34 (((exuI3) =>
% 24.33/6.34 (((exuI2) =>
% 24.33/6.34 ((
% 24.33/6.34 (inCongP) =>
% 24.33/6.34 ((
% 24.33/6.34 (in__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (exuE3u) =>
% 24.33/6.34 ((
% 24.33/6.34 (exu__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (setadjoin__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (powerset__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (setunion__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (exuEu) =>
% 24.33/6.34 ((
% 24.33/6.34 (descr__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (dsetconstr__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetI1) =>
% 24.33/6.34 ((
% 24.33/6.34 (eqimpsubset2) =>
% 24.33/6.34 ((
% 24.33/6.34 (eqimpsubset1) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetI2) =>
% 24.33/6.34 ((
% 24.33/6.34 (emptysetsubset) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetE) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetE2) =>
% 24.33/6.34 ((
% 24.33/6.34 (notsubsetI) =>
% 24.33/6.34 ((
% 24.33/6.34 (notequalI1) =>
% 24.33/6.34 ((
% 24.33/6.34 (notequalI2) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetRefl) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetTrans) =>
% 24.33/6.34 ((
% 24.33/6.34 (setadjoinSub) =>
% 24.33/6.34 ((
% 24.33/6.34 (setadjoinSub2) =>
% 24.33/6.34 ((
% 24.33/6.34 (subset2powerset) =>
% 24.33/6.34 ((
% 24.33/6.34 (setextsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetemptysetimpeq) =>
% 24.33/6.34 ((
% 24.33/6.34 (powersetI1) =>
% 24.33/6.34 ((
% 24.33/6.34 (powersetE1) =>
% 24.33/6.34 ((
% 24.33/6.34 (inPowerset) =>
% 24.33/6.34 ((
% 24.33/6.34 (powersetsubset) =>
% 24.33/6.34 ((
% 24.33/6.34 (sepInPowerset) =>
% 24.33/6.34 ((
% 24.33/6.34 (sepSubset) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionIL) =>
% 24.33/6.34 ((
% 24.33/6.34 (upairset2IR) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionIR) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionEcases) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionE) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionLsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionRsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectI) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectSubset5) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectEL) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectLsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectSubset2) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectSubset3) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectER) =>
% 24.33/6.34 ((
% 24.33/6.34 (disjointsetsI1) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectRsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectSubset4) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectSubset1) =>
% 24.33/6.34 ((
% 24.33/6.34 (bs114d) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusI) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusEL) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusER) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusSubset2) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusERneg) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusELneg) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusILneg) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusIRneg) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusLsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusSubset1) =>
% 24.33/6.34 ((
% 24.33/6.34 (symdiffE) =>
% 24.33/6.34 ((
% 24.33/6.34 (symdiffI1) =>
% 24.33/6.34 ((
% 24.33/6.34 (symdiffI2) =>
% 24.33/6.34 ((
% 24.33/6.34 (symdiffIneg1) =>
% 24.33/6.34 ((
% 24.33/6.34 (symdiffIneg2) =>
% 24.33/6.34 ((
% 24.33/6.34 (secondinupair) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairIL) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairIR) =>
% 24.33/6.34 ((
% 24.33/6.34 (kpairiskpair) =>
% 24.33/6.34 ((
% 24.33/6.34 (kpairp) =>
% 24.33/6.34 ((
% 24.33/6.34 (singletonsubset) =>
% 24.33/6.34 ((
% 24.33/6.34 (singletoninpowerset) =>
% 24.33/6.34 ((
% 24.33/6.34 (singletoninpowunion) =>
% 24.33/6.34 ((
% 24.33/6.34 (upairset2E) =>
% 24.33/6.34 ((
% 24.33/6.34 (upairsubunion) =>
% 24.33/6.34 ((
% 24.33/6.34 (upairinpowunion) =>
% 24.33/6.34 ((
% 24.33/6.34 (ubforcartprodlem1) =>
% 24.33/6.34 ((
% 24.33/6.34 (ubforcartprodlem2) =>
% 24.33/6.34 ((
% 24.33/6.34 (ubforcartprodlem3) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodpairin) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodmempair1) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodmempair) =>
% 24.33/6.34 ((
% 24.33/6.34 (setunionE2) =>
% 24.33/6.34 ((
% 24.33/6.34 (setunionsingleton1) =>
% 24.33/6.34 ((
% 24.33/6.34 (setunionsingleton2) =>
% 24.33/6.34 ((
% 24.33/6.34 (setunionsingleton) =>
% 24.33/6.34 ((
% 24.33/6.34 (singletonprop) =>
% 24.33/6.34 ((
% 24.33/6.34 (ex1E1) =>
% 24.33/6.34 ((
% 24.33/6.34 (ex1I) =>
% 24.33/6.34 ((
% 24.33/6.34 (ex1I2) =>
% 24.33/6.34 ((
% 24.33/6.34 (singletonsuniq) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjL1) =>
% 24.33/6.34 ((
% 24.33/6.34 (kfstsingleton) =>
% 24.33/6.34 ((
% 24.33/6.34 (theprop) =>
% 24.33/6.34 ((
% 24.33/6.34 (kfstpairEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodfstin) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjL2) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjL) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjR11) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjR12) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjR1) =>
% 24.33/6.34 ((
% 24.33/6.34 (upairequniteq) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjR2) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjR) =>
% 24.33/6.34 ((
% 24.33/6.34 (ksndsingleton) =>
% 24.33/6.34 ((
% 24.33/6.34 (ksndpairEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (kpairsurjEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodsndin) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodpairmemEL) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodpairmemER) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodmempaircEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodfstpairEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodsndpairEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodpairsurjEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (dpsetconstrI) =>
% 24.33/6.34 ((
% 24.33/6.34 (!!) @ (
% 24.33/6.34 (('#B') @ (
% 24.33/6.34 !!) @
% 24.33/6.34 (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 !!))) @
% 24.33/6.34 (
% 24.33/6.34 (
% 24.33/6.34 ('#S') @ (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 '#S') @
% 24.33/6.34 (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 '#C'))) @
% 24.33/6.34 (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ subset)))) @
% 24.33/6.34 dpsetconstr)))))) @
% 24.33/6.34 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.33/6.34 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl355])).
% 24.33/6.34 thf(zip_derived_cl369, plain,
% 24.33/6.34 (~ (((powersetI) =>
% 24.33/6.34 (((emptyinPowerset) =>
% 24.33/6.34 (((emptyInPowerset) =>
% 24.33/6.34 (((powersetE) =>
% 24.33/6.34 (((setunionI) =>
% 24.33/6.34 (((setunionE) =>
% 24.33/6.34 (((subPowSU) =>
% 24.33/6.34 (((exuE2) =>
% 24.33/6.34 (((nonemptyImpWitness) =>
% 24.33/6.34 (((uniqinunit) =>
% 24.33/6.34 (((notinsingleton) =>
% 24.33/6.34 (((eqinunit) =>
% 24.33/6.34 (((singletonsswitch) =>
% 24.33/6.34 (((upairsetE) =>
% 24.33/6.34 (((upairsetIL) =>
% 24.33/6.34 (((upairsetIR) =>
% 24.33/6.34 (((emptyE1) =>
% 24.33/6.34 (((vacuousDall) =>
% 24.33/6.34 (((quantDeMorgan1) =>
% 24.33/6.34 (((quantDeMorgan2) =>
% 24.33/6.34 (((quantDeMorgan3) =>
% 24.33/6.34 (((quantDeMorgan4) =>
% 24.33/6.34 (((prop2setI) =>
% 24.33/6.34 (((prop2set2propI) =>
% 24.33/6.34 (((notdexE) =>
% 24.33/6.34 (((notdallE) =>
% 24.33/6.34 (((exuI1) =>
% 24.33/6.34 (((exuI3) =>
% 24.33/6.34 (((exuI2) =>
% 24.33/6.34 (((inCongP) =>
% 24.33/6.34 ((
% 24.33/6.34 (in__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (exuE3u) =>
% 24.33/6.34 ((
% 24.33/6.34 (exu__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (setadjoin__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (powerset__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (setunion__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (exuEu) =>
% 24.33/6.34 ((
% 24.33/6.34 (descr__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (dsetconstr__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetI1) =>
% 24.33/6.34 ((
% 24.33/6.34 (eqimpsubset2) =>
% 24.33/6.34 ((
% 24.33/6.34 (eqimpsubset1) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetI2) =>
% 24.33/6.34 ((
% 24.33/6.34 (emptysetsubset) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetE) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetE2) =>
% 24.33/6.34 ((
% 24.33/6.34 (notsubsetI) =>
% 24.33/6.34 ((
% 24.33/6.34 (notequalI1) =>
% 24.33/6.34 ((
% 24.33/6.34 (notequalI2) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetRefl) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetTrans) =>
% 24.33/6.34 ((
% 24.33/6.34 (setadjoinSub) =>
% 24.33/6.34 ((
% 24.33/6.34 (setadjoinSub2) =>
% 24.33/6.34 ((
% 24.33/6.34 (subset2powerset) =>
% 24.33/6.34 ((
% 24.33/6.34 (setextsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetemptysetimpeq) =>
% 24.33/6.34 ((
% 24.33/6.34 (powersetI1) =>
% 24.33/6.34 ((
% 24.33/6.34 (powersetE1) =>
% 24.33/6.34 ((
% 24.33/6.34 (inPowerset) =>
% 24.33/6.34 ((
% 24.33/6.34 (powersetsubset) =>
% 24.33/6.34 ((
% 24.33/6.34 (sepInPowerset) =>
% 24.33/6.34 ((
% 24.33/6.34 (sepSubset) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionIL) =>
% 24.33/6.34 ((
% 24.33/6.34 (upairset2IR) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionIR) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionEcases) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionE) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionLsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionRsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectI) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectSubset5) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectEL) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectLsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectSubset2) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectSubset3) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectER) =>
% 24.33/6.34 ((
% 24.33/6.34 (disjointsetsI1) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectRsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectSubset4) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectSubset1) =>
% 24.33/6.34 ((
% 24.33/6.34 (bs114d) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusI) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusEL) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusER) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusSubset2) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusERneg) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusELneg) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusILneg) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusIRneg) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusLsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusSubset1) =>
% 24.33/6.34 ((
% 24.33/6.34 (symdiffE) =>
% 24.33/6.34 ((
% 24.33/6.34 (symdiffI1) =>
% 24.33/6.34 ((
% 24.33/6.34 (symdiffI2) =>
% 24.33/6.34 ((
% 24.33/6.34 (symdiffIneg1) =>
% 24.33/6.34 ((
% 24.33/6.34 (symdiffIneg2) =>
% 24.33/6.34 ((
% 24.33/6.34 (secondinupair) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairIL) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairIR) =>
% 24.33/6.34 ((
% 24.33/6.34 (kpairiskpair) =>
% 24.33/6.34 ((
% 24.33/6.34 (kpairp) =>
% 24.33/6.34 ((
% 24.33/6.34 (singletonsubset) =>
% 24.33/6.34 ((
% 24.33/6.34 (singletoninpowerset) =>
% 24.33/6.34 ((
% 24.33/6.34 (singletoninpowunion) =>
% 24.33/6.34 ((
% 24.33/6.34 (upairset2E) =>
% 24.33/6.34 ((
% 24.33/6.34 (upairsubunion) =>
% 24.33/6.34 ((
% 24.33/6.34 (upairinpowunion) =>
% 24.33/6.34 ((
% 24.33/6.34 (ubforcartprodlem1) =>
% 24.33/6.34 ((
% 24.33/6.34 (ubforcartprodlem2) =>
% 24.33/6.34 ((
% 24.33/6.34 (ubforcartprodlem3) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodpairin) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodmempair1) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodmempair) =>
% 24.33/6.34 ((
% 24.33/6.34 (setunionE2) =>
% 24.33/6.34 ((
% 24.33/6.34 (setunionsingleton1) =>
% 24.33/6.34 ((
% 24.33/6.34 (setunionsingleton2) =>
% 24.33/6.34 ((
% 24.33/6.34 (setunionsingleton) =>
% 24.33/6.34 ((
% 24.33/6.34 (singletonprop) =>
% 24.33/6.34 ((
% 24.33/6.34 (ex1E1) =>
% 24.33/6.34 ((
% 24.33/6.34 (ex1I) =>
% 24.33/6.34 ((
% 24.33/6.34 (ex1I2) =>
% 24.33/6.34 ((
% 24.33/6.34 (singletonsuniq) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjL1) =>
% 24.33/6.34 ((
% 24.33/6.34 (kfstsingleton) =>
% 24.33/6.34 ((
% 24.33/6.34 (theprop) =>
% 24.33/6.34 ((
% 24.33/6.34 (kfstpairEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodfstin) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjL2) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjL) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjR11) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjR12) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjR1) =>
% 24.33/6.34 ((
% 24.33/6.34 (upairequniteq) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjR2) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjR) =>
% 24.33/6.34 ((
% 24.33/6.34 (ksndsingleton) =>
% 24.33/6.34 ((
% 24.33/6.34 (ksndpairEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (kpairsurjEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodsndin) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodpairmemEL) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodpairmemER) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodmempaircEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodfstpairEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodsndpairEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodpairsurjEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (dpsetconstrI) =>
% 24.33/6.34 ((
% 24.33/6.34 (!!) @ (
% 24.33/6.34 (('#B') @ (
% 24.33/6.34 !!) @
% 24.33/6.34 (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 !!))) @
% 24.33/6.34 (
% 24.33/6.34 (
% 24.33/6.34 ('#S') @ (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 '#S') @
% 24.33/6.34 (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 '#C'))) @
% 24.33/6.34 (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ subset)))) @
% 24.33/6.34 dpsetconstr)))))) @
% 24.33/6.34 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.33/6.34 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl362])).
% 24.33/6.34 thf(zip_derived_cl376, plain,
% 24.33/6.34 (~ (((emptyinPowerset) =>
% 24.33/6.34 (((emptyInPowerset) =>
% 24.33/6.34 (((powersetE) =>
% 24.33/6.34 (((setunionI) =>
% 24.33/6.34 (((setunionE) =>
% 24.33/6.34 (((subPowSU) =>
% 24.33/6.34 (((exuE2) =>
% 24.33/6.34 (((nonemptyImpWitness) =>
% 24.33/6.34 (((uniqinunit) =>
% 24.33/6.34 (((notinsingleton) =>
% 24.33/6.34 (((eqinunit) =>
% 24.33/6.34 (((singletonsswitch) =>
% 24.33/6.34 (((upairsetE) =>
% 24.33/6.34 (((upairsetIL) =>
% 24.33/6.34 (((upairsetIR) =>
% 24.33/6.34 (((emptyE1) =>
% 24.33/6.34 (((vacuousDall) =>
% 24.33/6.34 (((quantDeMorgan1) =>
% 24.33/6.34 (((quantDeMorgan2) =>
% 24.33/6.34 (((quantDeMorgan3) =>
% 24.33/6.34 (((quantDeMorgan4) =>
% 24.33/6.34 (((prop2setI) =>
% 24.33/6.34 (((prop2set2propI) =>
% 24.33/6.34 (((notdexE) =>
% 24.33/6.34 (((notdallE) =>
% 24.33/6.34 (((exuI1) =>
% 24.33/6.34 (((exuI3) =>
% 24.33/6.34 (((exuI2) =>
% 24.33/6.34 (((inCongP) =>
% 24.33/6.34 (((in__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (exuE3u) =>
% 24.33/6.34 ((
% 24.33/6.34 (exu__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (setadjoin__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (powerset__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (setunion__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (exuEu) =>
% 24.33/6.34 ((
% 24.33/6.34 (descr__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (dsetconstr__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetI1) =>
% 24.33/6.34 ((
% 24.33/6.34 (eqimpsubset2) =>
% 24.33/6.34 ((
% 24.33/6.34 (eqimpsubset1) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetI2) =>
% 24.33/6.34 ((
% 24.33/6.34 (emptysetsubset) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetE) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetE2) =>
% 24.33/6.34 ((
% 24.33/6.34 (notsubsetI) =>
% 24.33/6.34 ((
% 24.33/6.34 (notequalI1) =>
% 24.33/6.34 ((
% 24.33/6.34 (notequalI2) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetRefl) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetTrans) =>
% 24.33/6.34 ((
% 24.33/6.34 (setadjoinSub) =>
% 24.33/6.34 ((
% 24.33/6.34 (setadjoinSub2) =>
% 24.33/6.34 ((
% 24.33/6.34 (subset2powerset) =>
% 24.33/6.34 ((
% 24.33/6.34 (setextsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetemptysetimpeq) =>
% 24.33/6.34 ((
% 24.33/6.34 (powersetI1) =>
% 24.33/6.34 ((
% 24.33/6.34 (powersetE1) =>
% 24.33/6.34 ((
% 24.33/6.34 (inPowerset) =>
% 24.33/6.34 ((
% 24.33/6.34 (powersetsubset) =>
% 24.33/6.34 ((
% 24.33/6.34 (sepInPowerset) =>
% 24.33/6.34 ((
% 24.33/6.34 (sepSubset) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionIL) =>
% 24.33/6.34 ((
% 24.33/6.34 (upairset2IR) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionIR) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionEcases) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionE) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionLsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionRsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectI) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectSubset5) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectEL) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectLsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectSubset2) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectSubset3) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectER) =>
% 24.33/6.34 ((
% 24.33/6.34 (disjointsetsI1) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectRsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectSubset4) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectSubset1) =>
% 24.33/6.34 ((
% 24.33/6.34 (bs114d) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusI) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusEL) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusER) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusSubset2) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusERneg) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusELneg) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusILneg) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusIRneg) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusLsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusSubset1) =>
% 24.33/6.34 ((
% 24.33/6.34 (symdiffE) =>
% 24.33/6.34 ((
% 24.33/6.34 (symdiffI1) =>
% 24.33/6.34 ((
% 24.33/6.34 (symdiffI2) =>
% 24.33/6.34 ((
% 24.33/6.34 (symdiffIneg1) =>
% 24.33/6.34 ((
% 24.33/6.34 (symdiffIneg2) =>
% 24.33/6.34 ((
% 24.33/6.34 (secondinupair) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairIL) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairIR) =>
% 24.33/6.34 ((
% 24.33/6.34 (kpairiskpair) =>
% 24.33/6.34 ((
% 24.33/6.34 (kpairp) =>
% 24.33/6.34 ((
% 24.33/6.34 (singletonsubset) =>
% 24.33/6.34 ((
% 24.33/6.34 (singletoninpowerset) =>
% 24.33/6.34 ((
% 24.33/6.34 (singletoninpowunion) =>
% 24.33/6.34 ((
% 24.33/6.34 (upairset2E) =>
% 24.33/6.34 ((
% 24.33/6.34 (upairsubunion) =>
% 24.33/6.34 ((
% 24.33/6.34 (upairinpowunion) =>
% 24.33/6.34 ((
% 24.33/6.34 (ubforcartprodlem1) =>
% 24.33/6.34 ((
% 24.33/6.34 (ubforcartprodlem2) =>
% 24.33/6.34 ((
% 24.33/6.34 (ubforcartprodlem3) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodpairin) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodmempair1) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodmempair) =>
% 24.33/6.34 ((
% 24.33/6.34 (setunionE2) =>
% 24.33/6.34 ((
% 24.33/6.34 (setunionsingleton1) =>
% 24.33/6.34 ((
% 24.33/6.34 (setunionsingleton2) =>
% 24.33/6.34 ((
% 24.33/6.34 (setunionsingleton) =>
% 24.33/6.34 ((
% 24.33/6.34 (singletonprop) =>
% 24.33/6.34 ((
% 24.33/6.34 (ex1E1) =>
% 24.33/6.34 ((
% 24.33/6.34 (ex1I) =>
% 24.33/6.34 ((
% 24.33/6.34 (ex1I2) =>
% 24.33/6.34 ((
% 24.33/6.34 (singletonsuniq) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjL1) =>
% 24.33/6.34 ((
% 24.33/6.34 (kfstsingleton) =>
% 24.33/6.34 ((
% 24.33/6.34 (theprop) =>
% 24.33/6.34 ((
% 24.33/6.34 (kfstpairEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodfstin) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjL2) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjL) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjR11) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjR12) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjR1) =>
% 24.33/6.34 ((
% 24.33/6.34 (upairequniteq) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjR2) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjR) =>
% 24.33/6.34 ((
% 24.33/6.34 (ksndsingleton) =>
% 24.33/6.34 ((
% 24.33/6.34 (ksndpairEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (kpairsurjEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodsndin) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodpairmemEL) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodpairmemER) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodmempaircEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodfstpairEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodsndpairEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodpairsurjEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (dpsetconstrI) =>
% 24.33/6.34 ((
% 24.33/6.34 (!!) @ (
% 24.33/6.34 (('#B') @ (
% 24.33/6.34 !!) @
% 24.33/6.34 (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 !!))) @
% 24.33/6.34 (
% 24.33/6.34 (
% 24.33/6.34 ('#S') @ (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 '#S') @
% 24.33/6.34 (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 '#C'))) @
% 24.33/6.34 (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ subset)))) @
% 24.33/6.34 dpsetconstr)))))) @
% 24.33/6.34 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.33/6.34 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl369])).
% 24.33/6.34 thf(zip_derived_cl384, plain,
% 24.33/6.34 (~ (((emptyInPowerset) =>
% 24.33/6.34 (((powersetE) =>
% 24.33/6.34 (((setunionI) =>
% 24.33/6.34 (((setunionE) =>
% 24.33/6.34 (((subPowSU) =>
% 24.33/6.34 (((exuE2) =>
% 24.33/6.34 (((nonemptyImpWitness) =>
% 24.33/6.34 (((uniqinunit) =>
% 24.33/6.34 (((notinsingleton) =>
% 24.33/6.34 (((eqinunit) =>
% 24.33/6.34 (((singletonsswitch) =>
% 24.33/6.34 (((upairsetE) =>
% 24.33/6.34 (((upairsetIL) =>
% 24.33/6.34 (((upairsetIR) =>
% 24.33/6.34 (((emptyE1) =>
% 24.33/6.34 (((vacuousDall) =>
% 24.33/6.34 (((quantDeMorgan1) =>
% 24.33/6.34 (((quantDeMorgan2) =>
% 24.33/6.34 (((quantDeMorgan3) =>
% 24.33/6.34 (((quantDeMorgan4) =>
% 24.33/6.34 (((prop2setI) =>
% 24.33/6.34 (((prop2set2propI) =>
% 24.33/6.34 (((notdexE) =>
% 24.33/6.34 (((notdallE) =>
% 24.33/6.34 (((exuI1) =>
% 24.33/6.34 (((exuI3) =>
% 24.33/6.34 (((exuI2) =>
% 24.33/6.34 (((inCongP) =>
% 24.33/6.34 (((in__Cong) =>
% 24.33/6.34 (((exuE3u) =>
% 24.33/6.34 ((
% 24.33/6.34 (exu__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (setadjoin__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (powerset__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (setunion__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (exuEu) =>
% 24.33/6.34 ((
% 24.33/6.34 (descr__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (dsetconstr__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetI1) =>
% 24.33/6.34 ((
% 24.33/6.34 (eqimpsubset2) =>
% 24.33/6.34 ((
% 24.33/6.34 (eqimpsubset1) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetI2) =>
% 24.33/6.34 ((
% 24.33/6.34 (emptysetsubset) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetE) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetE2) =>
% 24.33/6.34 ((
% 24.33/6.34 (notsubsetI) =>
% 24.33/6.34 ((
% 24.33/6.34 (notequalI1) =>
% 24.33/6.34 ((
% 24.33/6.34 (notequalI2) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetRefl) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetTrans) =>
% 24.33/6.34 ((
% 24.33/6.34 (setadjoinSub) =>
% 24.33/6.34 ((
% 24.33/6.34 (setadjoinSub2) =>
% 24.33/6.34 ((
% 24.33/6.34 (subset2powerset) =>
% 24.33/6.34 ((
% 24.33/6.34 (setextsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetemptysetimpeq) =>
% 24.33/6.34 ((
% 24.33/6.34 (powersetI1) =>
% 24.33/6.34 ((
% 24.33/6.34 (powersetE1) =>
% 24.33/6.34 ((
% 24.33/6.34 (inPowerset) =>
% 24.33/6.34 ((
% 24.33/6.34 (powersetsubset) =>
% 24.33/6.34 ((
% 24.33/6.34 (sepInPowerset) =>
% 24.33/6.34 ((
% 24.33/6.34 (sepSubset) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionIL) =>
% 24.33/6.34 ((
% 24.33/6.34 (upairset2IR) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionIR) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionEcases) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionE) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionLsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionRsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectI) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectSubset5) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectEL) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectLsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectSubset2) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectSubset3) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectER) =>
% 24.33/6.34 ((
% 24.33/6.34 (disjointsetsI1) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectRsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectSubset4) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectSubset1) =>
% 24.33/6.34 ((
% 24.33/6.34 (bs114d) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusI) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusEL) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusER) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusSubset2) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusERneg) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusELneg) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusILneg) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusIRneg) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusLsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusSubset1) =>
% 24.33/6.34 ((
% 24.33/6.34 (symdiffE) =>
% 24.33/6.34 ((
% 24.33/6.34 (symdiffI1) =>
% 24.33/6.34 ((
% 24.33/6.34 (symdiffI2) =>
% 24.33/6.34 ((
% 24.33/6.34 (symdiffIneg1) =>
% 24.33/6.34 ((
% 24.33/6.34 (symdiffIneg2) =>
% 24.33/6.34 ((
% 24.33/6.34 (secondinupair) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairIL) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairIR) =>
% 24.33/6.34 ((
% 24.33/6.34 (kpairiskpair) =>
% 24.33/6.34 ((
% 24.33/6.34 (kpairp) =>
% 24.33/6.34 ((
% 24.33/6.34 (singletonsubset) =>
% 24.33/6.34 ((
% 24.33/6.34 (singletoninpowerset) =>
% 24.33/6.34 ((
% 24.33/6.34 (singletoninpowunion) =>
% 24.33/6.34 ((
% 24.33/6.34 (upairset2E) =>
% 24.33/6.34 ((
% 24.33/6.34 (upairsubunion) =>
% 24.33/6.34 ((
% 24.33/6.34 (upairinpowunion) =>
% 24.33/6.34 ((
% 24.33/6.34 (ubforcartprodlem1) =>
% 24.33/6.34 ((
% 24.33/6.34 (ubforcartprodlem2) =>
% 24.33/6.34 ((
% 24.33/6.34 (ubforcartprodlem3) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodpairin) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodmempair1) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodmempair) =>
% 24.33/6.34 ((
% 24.33/6.34 (setunionE2) =>
% 24.33/6.34 ((
% 24.33/6.34 (setunionsingleton1) =>
% 24.33/6.34 ((
% 24.33/6.34 (setunionsingleton2) =>
% 24.33/6.34 ((
% 24.33/6.34 (setunionsingleton) =>
% 24.33/6.34 ((
% 24.33/6.34 (singletonprop) =>
% 24.33/6.34 ((
% 24.33/6.34 (ex1E1) =>
% 24.33/6.34 ((
% 24.33/6.34 (ex1I) =>
% 24.33/6.34 ((
% 24.33/6.34 (ex1I2) =>
% 24.33/6.34 ((
% 24.33/6.34 (singletonsuniq) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjL1) =>
% 24.33/6.34 ((
% 24.33/6.34 (kfstsingleton) =>
% 24.33/6.34 ((
% 24.33/6.34 (theprop) =>
% 24.33/6.34 ((
% 24.33/6.34 (kfstpairEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodfstin) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjL2) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjL) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjR11) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjR12) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjR1) =>
% 24.33/6.34 ((
% 24.33/6.34 (upairequniteq) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjR2) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjR) =>
% 24.33/6.34 ((
% 24.33/6.34 (ksndsingleton) =>
% 24.33/6.34 ((
% 24.33/6.34 (ksndpairEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (kpairsurjEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodsndin) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodpairmemEL) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodpairmemER) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodmempaircEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodfstpairEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodsndpairEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodpairsurjEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (dpsetconstrI) =>
% 24.33/6.34 ((
% 24.33/6.34 (!!) @ (
% 24.33/6.34 (('#B') @ (
% 24.33/6.34 !!) @
% 24.33/6.34 (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 !!))) @
% 24.33/6.34 (
% 24.33/6.34 (
% 24.33/6.34 ('#S') @ (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 '#S') @
% 24.33/6.34 (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 '#C'))) @
% 24.33/6.34 (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ subset)))) @
% 24.33/6.34 dpsetconstr)))))) @
% 24.33/6.34 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.33/6.34 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl376])).
% 24.33/6.34 thf(zip_derived_cl392, plain,
% 24.33/6.34 (~ (((powersetE) =>
% 24.33/6.34 (((setunionI) =>
% 24.33/6.34 (((setunionE) =>
% 24.33/6.34 (((subPowSU) =>
% 24.33/6.34 (((exuE2) =>
% 24.33/6.34 (((nonemptyImpWitness) =>
% 24.33/6.34 (((uniqinunit) =>
% 24.33/6.34 (((notinsingleton) =>
% 24.33/6.34 (((eqinunit) =>
% 24.33/6.34 (((singletonsswitch) =>
% 24.33/6.34 (((upairsetE) =>
% 24.33/6.34 (((upairsetIL) =>
% 24.33/6.34 (((upairsetIR) =>
% 24.33/6.34 (((emptyE1) =>
% 24.33/6.34 (((vacuousDall) =>
% 24.33/6.34 (((quantDeMorgan1) =>
% 24.33/6.34 (((quantDeMorgan2) =>
% 24.33/6.34 (((quantDeMorgan3) =>
% 24.33/6.34 (((quantDeMorgan4) =>
% 24.33/6.34 (((prop2setI) =>
% 24.33/6.34 (((prop2set2propI) =>
% 24.33/6.34 (((notdexE) =>
% 24.33/6.34 (((notdallE) =>
% 24.33/6.34 (((exuI1) =>
% 24.33/6.34 (((exuI3) =>
% 24.33/6.34 (((exuI2) =>
% 24.33/6.34 (((inCongP) =>
% 24.33/6.34 (((in__Cong) =>
% 24.33/6.34 (((exuE3u) =>
% 24.33/6.34 (((exu__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (setadjoin__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (powerset__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (setunion__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (exuEu) =>
% 24.33/6.34 ((
% 24.33/6.34 (descr__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (dsetconstr__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetI1) =>
% 24.33/6.34 ((
% 24.33/6.34 (eqimpsubset2) =>
% 24.33/6.34 ((
% 24.33/6.34 (eqimpsubset1) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetI2) =>
% 24.33/6.34 ((
% 24.33/6.34 (emptysetsubset) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetE) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetE2) =>
% 24.33/6.34 ((
% 24.33/6.34 (notsubsetI) =>
% 24.33/6.34 ((
% 24.33/6.34 (notequalI1) =>
% 24.33/6.34 ((
% 24.33/6.34 (notequalI2) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetRefl) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetTrans) =>
% 24.33/6.34 ((
% 24.33/6.34 (setadjoinSub) =>
% 24.33/6.34 ((
% 24.33/6.34 (setadjoinSub2) =>
% 24.33/6.34 ((
% 24.33/6.34 (subset2powerset) =>
% 24.33/6.34 ((
% 24.33/6.34 (setextsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetemptysetimpeq) =>
% 24.33/6.34 ((
% 24.33/6.34 (powersetI1) =>
% 24.33/6.34 ((
% 24.33/6.34 (powersetE1) =>
% 24.33/6.34 ((
% 24.33/6.34 (inPowerset) =>
% 24.33/6.34 ((
% 24.33/6.34 (powersetsubset) =>
% 24.33/6.34 ((
% 24.33/6.34 (sepInPowerset) =>
% 24.33/6.34 ((
% 24.33/6.34 (sepSubset) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionIL) =>
% 24.33/6.34 ((
% 24.33/6.34 (upairset2IR) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionIR) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionEcases) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionE) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionLsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionRsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectI) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectSubset5) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectEL) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectLsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectSubset2) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectSubset3) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectER) =>
% 24.33/6.34 ((
% 24.33/6.34 (disjointsetsI1) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectRsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectSubset4) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectSubset1) =>
% 24.33/6.34 ((
% 24.33/6.34 (bs114d) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusI) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusEL) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusER) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusSubset2) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusERneg) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusELneg) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusILneg) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusIRneg) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusLsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusSubset1) =>
% 24.33/6.34 ((
% 24.33/6.34 (symdiffE) =>
% 24.33/6.34 ((
% 24.33/6.34 (symdiffI1) =>
% 24.33/6.34 ((
% 24.33/6.34 (symdiffI2) =>
% 24.33/6.34 ((
% 24.33/6.34 (symdiffIneg1) =>
% 24.33/6.34 ((
% 24.33/6.34 (symdiffIneg2) =>
% 24.33/6.34 ((
% 24.33/6.34 (secondinupair) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairIL) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairIR) =>
% 24.33/6.34 ((
% 24.33/6.34 (kpairiskpair) =>
% 24.33/6.34 ((
% 24.33/6.34 (kpairp) =>
% 24.33/6.34 ((
% 24.33/6.34 (singletonsubset) =>
% 24.33/6.34 ((
% 24.33/6.34 (singletoninpowerset) =>
% 24.33/6.34 ((
% 24.33/6.34 (singletoninpowunion) =>
% 24.33/6.34 ((
% 24.33/6.34 (upairset2E) =>
% 24.33/6.34 ((
% 24.33/6.34 (upairsubunion) =>
% 24.33/6.34 ((
% 24.33/6.34 (upairinpowunion) =>
% 24.33/6.34 ((
% 24.33/6.34 (ubforcartprodlem1) =>
% 24.33/6.34 ((
% 24.33/6.34 (ubforcartprodlem2) =>
% 24.33/6.34 ((
% 24.33/6.34 (ubforcartprodlem3) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodpairin) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodmempair1) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodmempair) =>
% 24.33/6.34 ((
% 24.33/6.34 (setunionE2) =>
% 24.33/6.34 ((
% 24.33/6.34 (setunionsingleton1) =>
% 24.33/6.34 ((
% 24.33/6.34 (setunionsingleton2) =>
% 24.33/6.34 ((
% 24.33/6.34 (setunionsingleton) =>
% 24.33/6.34 ((
% 24.33/6.34 (singletonprop) =>
% 24.33/6.34 ((
% 24.33/6.34 (ex1E1) =>
% 24.33/6.34 ((
% 24.33/6.34 (ex1I) =>
% 24.33/6.34 ((
% 24.33/6.34 (ex1I2) =>
% 24.33/6.34 ((
% 24.33/6.34 (singletonsuniq) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjL1) =>
% 24.33/6.34 ((
% 24.33/6.34 (kfstsingleton) =>
% 24.33/6.34 ((
% 24.33/6.34 (theprop) =>
% 24.33/6.34 ((
% 24.33/6.34 (kfstpairEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodfstin) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjL2) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjL) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjR11) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjR12) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjR1) =>
% 24.33/6.34 ((
% 24.33/6.34 (upairequniteq) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjR2) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjR) =>
% 24.33/6.34 ((
% 24.33/6.34 (ksndsingleton) =>
% 24.33/6.34 ((
% 24.33/6.34 (ksndpairEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (kpairsurjEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodsndin) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodpairmemEL) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodpairmemER) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodmempaircEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodfstpairEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodsndpairEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodpairsurjEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (dpsetconstrI) =>
% 24.33/6.34 ((
% 24.33/6.34 (!!) @ (
% 24.33/6.34 (('#B') @ (
% 24.33/6.34 !!) @
% 24.33/6.34 (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 !!))) @
% 24.33/6.34 (
% 24.33/6.34 (
% 24.33/6.34 ('#S') @ (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 '#S') @
% 24.33/6.34 (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 '#C'))) @
% 24.33/6.34 (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ subset)))) @
% 24.33/6.34 dpsetconstr)))))) @
% 24.33/6.34 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.33/6.34 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl384])).
% 24.33/6.34 thf(zip_derived_cl400, plain,
% 24.33/6.34 (~ (((setunionI) =>
% 24.33/6.34 (((setunionE) =>
% 24.33/6.34 (((subPowSU) =>
% 24.33/6.34 (((exuE2) =>
% 24.33/6.34 (((nonemptyImpWitness) =>
% 24.33/6.34 (((uniqinunit) =>
% 24.33/6.34 (((notinsingleton) =>
% 24.33/6.34 (((eqinunit) =>
% 24.33/6.34 (((singletonsswitch) =>
% 24.33/6.34 (((upairsetE) =>
% 24.33/6.34 (((upairsetIL) =>
% 24.33/6.34 (((upairsetIR) =>
% 24.33/6.34 (((emptyE1) =>
% 24.33/6.34 (((vacuousDall) =>
% 24.33/6.34 (((quantDeMorgan1) =>
% 24.33/6.34 (((quantDeMorgan2) =>
% 24.33/6.34 (((quantDeMorgan3) =>
% 24.33/6.34 (((quantDeMorgan4) =>
% 24.33/6.34 (((prop2setI) =>
% 24.33/6.34 (((prop2set2propI) =>
% 24.33/6.34 (((notdexE) =>
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% 24.33/6.34 (((exuI1) =>
% 24.33/6.34 (((exuI3) =>
% 24.33/6.34 (((exuI2) =>
% 24.33/6.34 (((inCongP) =>
% 24.33/6.34 (((in__Cong) =>
% 24.33/6.34 (((exuE3u) =>
% 24.33/6.34 (((exu__Cong) =>
% 24.33/6.34 (((setadjoin__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (powerset__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (setunion__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (exuEu) =>
% 24.33/6.34 ((
% 24.33/6.34 (descr__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (dsetconstr__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetI1) =>
% 24.33/6.34 ((
% 24.33/6.34 (eqimpsubset2) =>
% 24.33/6.34 ((
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% 24.33/6.34 ((
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% 24.33/6.34 (subsetE2) =>
% 24.33/6.34 ((
% 24.33/6.34 (notsubsetI) =>
% 24.33/6.34 ((
% 24.33/6.34 (notequalI1) =>
% 24.33/6.34 ((
% 24.33/6.34 (notequalI2) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetRefl) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetTrans) =>
% 24.33/6.34 ((
% 24.33/6.34 (setadjoinSub) =>
% 24.33/6.34 ((
% 24.33/6.34 (setadjoinSub2) =>
% 24.33/6.34 ((
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% 24.33/6.34 ((
% 24.33/6.34 (setextsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetemptysetimpeq) =>
% 24.33/6.34 ((
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% 24.33/6.34 ((
% 24.33/6.34 (powersetE1) =>
% 24.33/6.34 ((
% 24.33/6.34 (inPowerset) =>
% 24.33/6.34 ((
% 24.33/6.34 (powersetsubset) =>
% 24.33/6.34 ((
% 24.33/6.34 (sepInPowerset) =>
% 24.33/6.34 ((
% 24.33/6.34 (sepSubset) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionIL) =>
% 24.33/6.34 ((
% 24.33/6.34 (upairset2IR) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionIR) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionEcases) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionE) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionLsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionRsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectI) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectSubset5) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectEL) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectLsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectSubset2) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectSubset3) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectER) =>
% 24.33/6.34 ((
% 24.33/6.34 (disjointsetsI1) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectRsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectSubset4) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectSubset1) =>
% 24.33/6.34 ((
% 24.33/6.34 (bs114d) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusI) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusEL) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusER) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusSubset2) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusERneg) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusELneg) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusILneg) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusIRneg) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusLsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusSubset1) =>
% 24.33/6.34 ((
% 24.33/6.34 (symdiffE) =>
% 24.33/6.34 ((
% 24.33/6.34 (symdiffI1) =>
% 24.33/6.34 ((
% 24.33/6.34 (symdiffI2) =>
% 24.33/6.34 ((
% 24.33/6.34 (symdiffIneg1) =>
% 24.33/6.34 ((
% 24.33/6.34 (symdiffIneg2) =>
% 24.33/6.34 ((
% 24.33/6.34 (secondinupair) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairIL) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairIR) =>
% 24.33/6.34 ((
% 24.33/6.34 (kpairiskpair) =>
% 24.33/6.34 ((
% 24.33/6.34 (kpairp) =>
% 24.33/6.34 ((
% 24.33/6.34 (singletonsubset) =>
% 24.33/6.34 ((
% 24.33/6.34 (singletoninpowerset) =>
% 24.33/6.34 ((
% 24.33/6.34 (singletoninpowunion) =>
% 24.33/6.34 ((
% 24.33/6.34 (upairset2E) =>
% 24.33/6.34 ((
% 24.33/6.34 (upairsubunion) =>
% 24.33/6.34 ((
% 24.33/6.34 (upairinpowunion) =>
% 24.33/6.34 ((
% 24.33/6.34 (ubforcartprodlem1) =>
% 24.33/6.34 ((
% 24.33/6.34 (ubforcartprodlem2) =>
% 24.33/6.34 ((
% 24.33/6.34 (ubforcartprodlem3) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodpairin) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodmempair1) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodmempair) =>
% 24.33/6.34 ((
% 24.33/6.34 (setunionE2) =>
% 24.33/6.34 ((
% 24.33/6.34 (setunionsingleton1) =>
% 24.33/6.34 ((
% 24.33/6.34 (setunionsingleton2) =>
% 24.33/6.34 ((
% 24.33/6.34 (setunionsingleton) =>
% 24.33/6.34 ((
% 24.33/6.34 (singletonprop) =>
% 24.33/6.34 ((
% 24.33/6.34 (ex1E1) =>
% 24.33/6.34 ((
% 24.33/6.34 (ex1I) =>
% 24.33/6.34 ((
% 24.33/6.34 (ex1I2) =>
% 24.33/6.34 ((
% 24.33/6.34 (singletonsuniq) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjL1) =>
% 24.33/6.34 ((
% 24.33/6.34 (kfstsingleton) =>
% 24.33/6.34 ((
% 24.33/6.34 (theprop) =>
% 24.33/6.34 ((
% 24.33/6.34 (kfstpairEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodfstin) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjL2) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjL) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjR11) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjR12) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjR1) =>
% 24.33/6.34 ((
% 24.33/6.34 (upairequniteq) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjR2) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjR) =>
% 24.33/6.34 ((
% 24.33/6.34 (ksndsingleton) =>
% 24.33/6.34 ((
% 24.33/6.34 (ksndpairEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (kpairsurjEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodsndin) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodpairmemEL) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodpairmemER) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodmempaircEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodfstpairEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodsndpairEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodpairsurjEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (dpsetconstrI) =>
% 24.33/6.34 ((
% 24.33/6.34 (!!) @ (
% 24.33/6.34 (('#B') @ (
% 24.33/6.34 !!) @
% 24.33/6.34 (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 !!))) @
% 24.33/6.34 (
% 24.33/6.34 (
% 24.33/6.34 ('#S') @ (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 '#S') @
% 24.33/6.34 (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 '#C'))) @
% 24.33/6.34 (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ subset)))) @
% 24.33/6.34 dpsetconstr)))))) @
% 24.33/6.34 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.33/6.34 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl392])).
% 24.33/6.34 thf(zip_derived_cl408, plain,
% 24.33/6.34 (~ (((setunionE) =>
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% 24.33/6.34 (((exuE2) =>
% 24.33/6.34 (((nonemptyImpWitness) =>
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% 24.33/6.34 (((notinsingleton) =>
% 24.33/6.34 (((eqinunit) =>
% 24.33/6.34 (((singletonsswitch) =>
% 24.33/6.34 (((upairsetE) =>
% 24.33/6.34 (((upairsetIL) =>
% 24.33/6.34 (((upairsetIR) =>
% 24.33/6.34 (((emptyE1) =>
% 24.33/6.34 (((vacuousDall) =>
% 24.33/6.34 (((quantDeMorgan1) =>
% 24.33/6.34 (((quantDeMorgan2) =>
% 24.33/6.34 (((quantDeMorgan3) =>
% 24.33/6.34 (((quantDeMorgan4) =>
% 24.33/6.34 (((prop2setI) =>
% 24.33/6.34 (((prop2set2propI) =>
% 24.33/6.34 (((notdexE) =>
% 24.33/6.34 (((notdallE) =>
% 24.33/6.34 (((exuI1) =>
% 24.33/6.34 (((exuI3) =>
% 24.33/6.34 (((exuI2) =>
% 24.33/6.34 (((inCongP) =>
% 24.33/6.34 (((in__Cong) =>
% 24.33/6.34 (((exuE3u) =>
% 24.33/6.34 (((exu__Cong) =>
% 24.33/6.34 (((setadjoin__Cong) =>
% 24.33/6.34 (((powerset__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (setunion__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (exuEu) =>
% 24.33/6.34 ((
% 24.33/6.34 (descr__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (dsetconstr__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetI1) =>
% 24.33/6.34 ((
% 24.33/6.34 (eqimpsubset2) =>
% 24.33/6.34 ((
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% 24.33/6.34 ((
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% 24.33/6.34 ((
% 24.33/6.34 (subsetE2) =>
% 24.33/6.34 ((
% 24.33/6.34 (notsubsetI) =>
% 24.33/6.34 ((
% 24.33/6.34 (notequalI1) =>
% 24.33/6.34 ((
% 24.33/6.34 (notequalI2) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetRefl) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetTrans) =>
% 24.33/6.34 ((
% 24.33/6.34 (setadjoinSub) =>
% 24.33/6.34 ((
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% 24.33/6.34 ((
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% 24.33/6.34 ((
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% 24.33/6.34 ((
% 24.33/6.34 (sepSubset) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionIL) =>
% 24.33/6.34 ((
% 24.33/6.34 (upairset2IR) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionIR) =>
% 24.33/6.34 ((
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% 24.33/6.34 ((
% 24.33/6.34 (binunionE) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionLsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (binunionRsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectI) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectSubset5) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectEL) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectLsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectSubset2) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectSubset3) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectER) =>
% 24.33/6.34 ((
% 24.33/6.34 (disjointsetsI1) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectRsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectSubset4) =>
% 24.33/6.34 ((
% 24.33/6.34 (binintersectSubset1) =>
% 24.33/6.34 ((
% 24.33/6.34 (bs114d) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusI) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusEL) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusER) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusSubset2) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusERneg) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusELneg) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusILneg) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusIRneg) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusLsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (setminusSubset1) =>
% 24.33/6.34 ((
% 24.33/6.34 (symdiffE) =>
% 24.33/6.34 ((
% 24.33/6.34 (symdiffI1) =>
% 24.33/6.34 ((
% 24.33/6.34 (symdiffI2) =>
% 24.33/6.34 ((
% 24.33/6.34 (symdiffIneg1) =>
% 24.33/6.34 ((
% 24.33/6.34 (symdiffIneg2) =>
% 24.33/6.34 ((
% 24.33/6.34 (secondinupair) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairIL) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairIR) =>
% 24.33/6.34 ((
% 24.33/6.34 (kpairiskpair) =>
% 24.33/6.34 ((
% 24.33/6.34 (kpairp) =>
% 24.33/6.34 ((
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% 24.33/6.34 ((
% 24.33/6.34 (singletoninpowerset) =>
% 24.33/6.34 ((
% 24.33/6.34 (singletoninpowunion) =>
% 24.33/6.34 ((
% 24.33/6.34 (upairset2E) =>
% 24.33/6.34 ((
% 24.33/6.34 (upairsubunion) =>
% 24.33/6.34 ((
% 24.33/6.34 (upairinpowunion) =>
% 24.33/6.34 ((
% 24.33/6.34 (ubforcartprodlem1) =>
% 24.33/6.34 ((
% 24.33/6.34 (ubforcartprodlem2) =>
% 24.33/6.34 ((
% 24.33/6.34 (ubforcartprodlem3) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodpairin) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodmempair1) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodmempair) =>
% 24.33/6.34 ((
% 24.33/6.34 (setunionE2) =>
% 24.33/6.34 ((
% 24.33/6.34 (setunionsingleton1) =>
% 24.33/6.34 ((
% 24.33/6.34 (setunionsingleton2) =>
% 24.33/6.34 ((
% 24.33/6.34 (setunionsingleton) =>
% 24.33/6.34 ((
% 24.33/6.34 (singletonprop) =>
% 24.33/6.34 ((
% 24.33/6.34 (ex1E1) =>
% 24.33/6.34 ((
% 24.33/6.34 (ex1I) =>
% 24.33/6.34 ((
% 24.33/6.34 (ex1I2) =>
% 24.33/6.34 ((
% 24.33/6.34 (singletonsuniq) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjL1) =>
% 24.33/6.34 ((
% 24.33/6.34 (kfstsingleton) =>
% 24.33/6.34 ((
% 24.33/6.34 (theprop) =>
% 24.33/6.34 ((
% 24.33/6.34 (kfstpairEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodfstin) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjL2) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjL) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjR11) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjR12) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjR1) =>
% 24.33/6.34 ((
% 24.33/6.34 (upairequniteq) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjR2) =>
% 24.33/6.34 ((
% 24.33/6.34 (setukpairinjR) =>
% 24.33/6.34 ((
% 24.33/6.34 (ksndsingleton) =>
% 24.33/6.34 ((
% 24.33/6.34 (ksndpairEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (kpairsurjEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodsndin) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodpairmemEL) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodpairmemER) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodmempaircEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodfstpairEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodsndpairEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (cartprodpairsurjEq) =>
% 24.33/6.34 ((
% 24.33/6.34 (dpsetconstrI) =>
% 24.33/6.34 ((
% 24.33/6.34 (!!) @ (
% 24.33/6.34 (('#B') @ (
% 24.33/6.34 !!) @
% 24.33/6.34 (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 !!))) @
% 24.33/6.34 (
% 24.33/6.34 (
% 24.33/6.34 ('#S') @ (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 '#S') @
% 24.33/6.34 (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
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% 24.33/6.34 (
% 24.33/6.34 (
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% 24.33/6.34 (
% 24.33/6.34 ('#B') @ (
% 24.33/6.34 (
% 24.33/6.34 ('#B') @ subset)))) @
% 24.33/6.34 dpsetconstr)))))) @
% 24.33/6.34 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.33/6.34 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl400])).
% 24.33/6.34 thf(zip_derived_cl417, plain,
% 24.33/6.34 (~ (((subPowSU) =>
% 24.33/6.34 (((exuE2) =>
% 24.33/6.34 (((nonemptyImpWitness) =>
% 24.33/6.34 (((uniqinunit) =>
% 24.33/6.34 (((notinsingleton) =>
% 24.33/6.34 (((eqinunit) =>
% 24.33/6.34 (((singletonsswitch) =>
% 24.33/6.34 (((upairsetE) =>
% 24.33/6.34 (((upairsetIL) =>
% 24.33/6.34 (((upairsetIR) =>
% 24.33/6.34 (((emptyE1) =>
% 24.33/6.34 (((vacuousDall) =>
% 24.33/6.34 (((quantDeMorgan1) =>
% 24.33/6.34 (((quantDeMorgan2) =>
% 24.33/6.34 (((quantDeMorgan3) =>
% 24.33/6.34 (((quantDeMorgan4) =>
% 24.33/6.34 (((prop2setI) =>
% 24.33/6.34 (((prop2set2propI) =>
% 24.33/6.34 (((notdexE) =>
% 24.33/6.34 (((notdallE) =>
% 24.33/6.34 (((exuI1) =>
% 24.33/6.34 (((exuI3) =>
% 24.33/6.34 (((exuI2) =>
% 24.33/6.34 (((inCongP) =>
% 24.33/6.34 (((in__Cong) =>
% 24.33/6.34 (((exuE3u) =>
% 24.33/6.34 (((exu__Cong) =>
% 24.33/6.34 (((setadjoin__Cong) =>
% 24.33/6.34 (((powerset__Cong) =>
% 24.33/6.34 (((setunion__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (exuEu) =>
% 24.33/6.34 ((
% 24.33/6.34 (descr__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (dsetconstr__Cong) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetI1) =>
% 24.33/6.34 ((
% 24.33/6.34 (eqimpsubset2) =>
% 24.33/6.34 ((
% 24.33/6.34 (eqimpsubset1) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetI2) =>
% 24.33/6.34 ((
% 24.33/6.34 (emptysetsubset) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetE) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetE2) =>
% 24.33/6.34 ((
% 24.33/6.34 (notsubsetI) =>
% 24.33/6.34 ((
% 24.33/6.34 (notequalI1) =>
% 24.33/6.34 ((
% 24.33/6.34 (notequalI2) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetRefl) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetTrans) =>
% 24.33/6.34 ((
% 24.33/6.34 (setadjoinSub) =>
% 24.33/6.34 ((
% 24.33/6.34 (setadjoinSub2) =>
% 24.33/6.34 ((
% 24.33/6.34 (subset2powerset) =>
% 24.33/6.34 ((
% 24.33/6.34 (setextsub) =>
% 24.33/6.34 ((
% 24.33/6.34 (subsetemptysetimpeq) =>
% 24.33/6.34 ((
% 24.33/6.34 (powersetI1) =>
% 24.33/6.34 ((
% 24.33/6.34 (powersetE1) =>
% 24.33/6.34 ((
% 24.33/6.34 (inPowerset) =>
% 24.33/6.34 ((
% 24.33/6.34 (powersetsubset) =>
% 24.33/6.34 ((
% 24.33/6.35 (sepInPowerset) =>
% 24.33/6.35 ((
% 24.33/6.35 (sepSubset) =>
% 24.33/6.35 ((
% 24.33/6.35 (binunionIL) =>
% 24.33/6.35 ((
% 24.33/6.35 (upairset2IR) =>
% 24.33/6.35 ((
% 24.33/6.35 (binunionIR) =>
% 24.33/6.35 ((
% 24.33/6.35 (binunionEcases) =>
% 24.33/6.35 ((
% 24.33/6.35 (binunionE) =>
% 24.33/6.35 ((
% 24.33/6.35 (binunionLsub) =>
% 24.33/6.35 ((
% 24.33/6.35 (binunionRsub) =>
% 24.33/6.35 ((
% 24.33/6.35 (binintersectI) =>
% 24.33/6.35 ((
% 24.33/6.35 (binintersectSubset5) =>
% 24.33/6.35 ((
% 24.33/6.35 (binintersectEL) =>
% 24.33/6.35 ((
% 24.33/6.35 (binintersectLsub) =>
% 24.33/6.35 ((
% 24.33/6.35 (binintersectSubset2) =>
% 24.33/6.35 ((
% 24.33/6.35 (binintersectSubset3) =>
% 24.33/6.35 ((
% 24.33/6.35 (binintersectER) =>
% 24.33/6.35 ((
% 24.33/6.35 (disjointsetsI1) =>
% 24.33/6.35 ((
% 24.33/6.35 (binintersectRsub) =>
% 24.33/6.35 ((
% 24.33/6.35 (binintersectSubset4) =>
% 24.33/6.35 ((
% 24.33/6.35 (binintersectSubset1) =>
% 24.33/6.35 ((
% 24.33/6.35 (bs114d) =>
% 24.33/6.35 ((
% 24.33/6.35 (setminusI) =>
% 24.33/6.35 ((
% 24.33/6.35 (setminusEL) =>
% 24.33/6.35 ((
% 24.33/6.35 (setminusER) =>
% 24.33/6.35 ((
% 24.33/6.35 (setminusSubset2) =>
% 24.33/6.35 ((
% 24.33/6.35 (setminusERneg) =>
% 24.33/6.35 ((
% 24.33/6.35 (setminusELneg) =>
% 24.33/6.35 ((
% 24.33/6.35 (setminusILneg) =>
% 24.33/6.35 ((
% 24.33/6.35 (setminusIRneg) =>
% 24.33/6.35 ((
% 24.33/6.35 (setminusLsub) =>
% 24.33/6.35 ((
% 24.33/6.35 (setminusSubset1) =>
% 24.33/6.35 ((
% 24.33/6.35 (symdiffE) =>
% 24.33/6.35 ((
% 24.33/6.35 (symdiffI1) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffI2) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffIneg1) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffIneg2) =>
% 24.53/6.36 ((
% 24.53/6.36 (secondinupair) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairIL) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairIR) =>
% 24.53/6.36 ((
% 24.53/6.36 (kpairiskpair) =>
% 24.53/6.36 ((
% 24.53/6.36 (kpairp) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletonsubset) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletoninpowerset) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletoninpowunion) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairset2E) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairsubunion) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairinpowunion) =>
% 24.53/6.36 ((
% 24.53/6.36 (ubforcartprodlem1) =>
% 24.53/6.36 ((
% 24.53/6.36 (ubforcartprodlem2) =>
% 24.53/6.36 ((
% 24.53/6.36 (ubforcartprodlem3) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodpairin) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodmempair1) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodmempair) =>
% 24.53/6.36 ((
% 24.53/6.36 (setunionE2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setunionsingleton1) =>
% 24.53/6.36 ((
% 24.53/6.36 (setunionsingleton2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setunionsingleton) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletonprop) =>
% 24.53/6.36 ((
% 24.53/6.36 (ex1E1) =>
% 24.53/6.36 ((
% 24.53/6.36 (ex1I) =>
% 24.53/6.36 ((
% 24.53/6.36 (ex1I2) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletonsuniq) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjL1) =>
% 24.53/6.36 ((
% 24.53/6.36 (kfstsingleton) =>
% 24.53/6.36 ((
% 24.53/6.36 (theprop) =>
% 24.53/6.36 ((
% 24.53/6.36 (kfstpairEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodfstin) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjL2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjL) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR11) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR12) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR1) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairequniteq) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR) =>
% 24.53/6.36 ((
% 24.53/6.36 (ksndsingleton) =>
% 24.53/6.36 ((
% 24.53/6.36 (ksndpairEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (kpairsurjEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodsndin) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodpairmemEL) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodpairmemER) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodmempaircEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodfstpairEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodsndpairEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodpairsurjEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (dpsetconstrI) =>
% 24.53/6.36 ((
% 24.53/6.36 (!!) @ (
% 24.53/6.36 (('#B') @ (
% 24.53/6.36 !!) @
% 24.53/6.36 (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 !!))) @
% 24.53/6.36 (
% 24.53/6.36 (
% 24.53/6.36 ('#S') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 '#S') @
% 24.53/6.36 (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 '#C'))) @
% 24.53/6.36 (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ subset)))) @
% 24.53/6.36 dpsetconstr)))))) @
% 24.53/6.36 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl408])).
% 24.53/6.36 thf(zip_derived_cl428, plain,
% 24.53/6.36 (~ (((exuE2) =>
% 24.53/6.36 (((nonemptyImpWitness) =>
% 24.53/6.36 (((uniqinunit) =>
% 24.53/6.36 (((notinsingleton) =>
% 24.53/6.36 (((eqinunit) =>
% 24.53/6.36 (((singletonsswitch) =>
% 24.53/6.36 (((upairsetE) =>
% 24.53/6.36 (((upairsetIL) =>
% 24.53/6.36 (((upairsetIR) =>
% 24.53/6.36 (((emptyE1) =>
% 24.53/6.36 (((vacuousDall) =>
% 24.53/6.36 (((quantDeMorgan1) =>
% 24.53/6.36 (((quantDeMorgan2) =>
% 24.53/6.36 (((quantDeMorgan3) =>
% 24.53/6.36 (((quantDeMorgan4) =>
% 24.53/6.36 (((prop2setI) =>
% 24.53/6.36 (((prop2set2propI) =>
% 24.53/6.36 (((notdexE) =>
% 24.53/6.36 (((notdallE) =>
% 24.53/6.36 (((exuI1) =>
% 24.53/6.36 (((exuI3) =>
% 24.53/6.36 (((exuI2) =>
% 24.53/6.36 (((inCongP) =>
% 24.53/6.36 (((in__Cong) =>
% 24.53/6.36 (((exuE3u) =>
% 24.53/6.36 (((exu__Cong) =>
% 24.53/6.36 (((setadjoin__Cong) =>
% 24.53/6.36 (((powerset__Cong) =>
% 24.53/6.36 (((setunion__Cong) =>
% 24.53/6.36 (((exuEu) =>
% 24.53/6.36 ((
% 24.53/6.36 (descr__Cong) =>
% 24.53/6.36 ((
% 24.53/6.36 (dsetconstr__Cong) =>
% 24.53/6.36 ((
% 24.53/6.36 (subsetI1) =>
% 24.53/6.36 ((
% 24.53/6.36 (eqimpsubset2) =>
% 24.53/6.36 ((
% 24.53/6.36 (eqimpsubset1) =>
% 24.53/6.36 ((
% 24.53/6.36 (subsetI2) =>
% 24.53/6.36 ((
% 24.53/6.36 (emptysetsubset) =>
% 24.53/6.36 ((
% 24.53/6.36 (subsetE) =>
% 24.53/6.36 ((
% 24.53/6.36 (subsetE2) =>
% 24.53/6.36 ((
% 24.53/6.36 (notsubsetI) =>
% 24.53/6.36 ((
% 24.53/6.36 (notequalI1) =>
% 24.53/6.36 ((
% 24.53/6.36 (notequalI2) =>
% 24.53/6.36 ((
% 24.53/6.36 (subsetRefl) =>
% 24.53/6.36 ((
% 24.53/6.36 (subsetTrans) =>
% 24.53/6.36 ((
% 24.53/6.36 (setadjoinSub) =>
% 24.53/6.36 ((
% 24.53/6.36 (setadjoinSub2) =>
% 24.53/6.36 ((
% 24.53/6.36 (subset2powerset) =>
% 24.53/6.36 ((
% 24.53/6.36 (setextsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (subsetemptysetimpeq) =>
% 24.53/6.36 ((
% 24.53/6.36 (powersetI1) =>
% 24.53/6.36 ((
% 24.53/6.36 (powersetE1) =>
% 24.53/6.36 ((
% 24.53/6.36 (inPowerset) =>
% 24.53/6.36 ((
% 24.53/6.36 (powersetsubset) =>
% 24.53/6.36 ((
% 24.53/6.36 (sepInPowerset) =>
% 24.53/6.36 ((
% 24.53/6.36 (sepSubset) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionIL) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairset2IR) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionIR) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionEcases) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionE) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionLsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionRsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectI) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset5) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectEL) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectLsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset2) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset3) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectER) =>
% 24.53/6.36 ((
% 24.53/6.36 (disjointsetsI1) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectRsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset4) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset1) =>
% 24.53/6.36 ((
% 24.53/6.36 (bs114d) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusI) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusEL) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusER) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusSubset2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusERneg) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusELneg) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusILneg) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusIRneg) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusLsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusSubset1) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffE) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffI1) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffI2) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffIneg1) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffIneg2) =>
% 24.53/6.36 ((
% 24.53/6.36 (secondinupair) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairIL) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairIR) =>
% 24.53/6.36 ((
% 24.53/6.36 (kpairiskpair) =>
% 24.53/6.36 ((
% 24.53/6.36 (kpairp) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletonsubset) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletoninpowerset) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletoninpowunion) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairset2E) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairsubunion) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairinpowunion) =>
% 24.53/6.36 ((
% 24.53/6.36 (ubforcartprodlem1) =>
% 24.53/6.36 ((
% 24.53/6.36 (ubforcartprodlem2) =>
% 24.53/6.36 ((
% 24.53/6.36 (ubforcartprodlem3) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodpairin) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodmempair1) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodmempair) =>
% 24.53/6.36 ((
% 24.53/6.36 (setunionE2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setunionsingleton1) =>
% 24.53/6.36 ((
% 24.53/6.36 (setunionsingleton2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setunionsingleton) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletonprop) =>
% 24.53/6.36 ((
% 24.53/6.36 (ex1E1) =>
% 24.53/6.36 ((
% 24.53/6.36 (ex1I) =>
% 24.53/6.36 ((
% 24.53/6.36 (ex1I2) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletonsuniq) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjL1) =>
% 24.53/6.36 ((
% 24.53/6.36 (kfstsingleton) =>
% 24.53/6.36 ((
% 24.53/6.36 (theprop) =>
% 24.53/6.36 ((
% 24.53/6.36 (kfstpairEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodfstin) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjL2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjL) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR11) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR12) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR1) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairequniteq) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR) =>
% 24.53/6.36 ((
% 24.53/6.36 (ksndsingleton) =>
% 24.53/6.36 ((
% 24.53/6.36 (ksndpairEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (kpairsurjEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodsndin) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodpairmemEL) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodpairmemER) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodmempaircEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodfstpairEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodsndpairEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodpairsurjEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (dpsetconstrI) =>
% 24.53/6.36 ((
% 24.53/6.36 (!!) @ (
% 24.53/6.36 (('#B') @ (
% 24.53/6.36 !!) @
% 24.53/6.36 (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 !!))) @
% 24.53/6.36 (
% 24.53/6.36 (
% 24.53/6.36 ('#S') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 '#S') @
% 24.53/6.36 (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 '#C'))) @
% 24.53/6.36 (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ subset)))) @
% 24.53/6.36 dpsetconstr)))))) @
% 24.53/6.36 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl417])).
% 24.53/6.36 thf(zip_derived_cl439, plain,
% 24.53/6.36 (~ (((nonemptyImpWitness) =>
% 24.53/6.36 (((uniqinunit) =>
% 24.53/6.36 (((notinsingleton) =>
% 24.53/6.36 (((eqinunit) =>
% 24.53/6.36 (((singletonsswitch) =>
% 24.53/6.36 (((upairsetE) =>
% 24.53/6.36 (((upairsetIL) =>
% 24.53/6.36 (((upairsetIR) =>
% 24.53/6.36 (((emptyE1) =>
% 24.53/6.36 (((vacuousDall) =>
% 24.53/6.36 (((quantDeMorgan1) =>
% 24.53/6.36 (((quantDeMorgan2) =>
% 24.53/6.36 (((quantDeMorgan3) =>
% 24.53/6.36 (((quantDeMorgan4) =>
% 24.53/6.36 (((prop2setI) =>
% 24.53/6.36 (((prop2set2propI) =>
% 24.53/6.36 (((notdexE) =>
% 24.53/6.36 (((notdallE) =>
% 24.53/6.36 (((exuI1) =>
% 24.53/6.36 (((exuI3) =>
% 24.53/6.36 (((exuI2) =>
% 24.53/6.36 (((inCongP) =>
% 24.53/6.36 (((in__Cong) =>
% 24.53/6.36 (((exuE3u) =>
% 24.53/6.36 (((exu__Cong) =>
% 24.53/6.36 (((setadjoin__Cong) =>
% 24.53/6.36 (((powerset__Cong) =>
% 24.53/6.36 (((setunion__Cong) =>
% 24.53/6.36 (((exuEu) =>
% 24.53/6.36 (((descr__Cong) =>
% 24.53/6.36 ((
% 24.53/6.36 (dsetconstr__Cong) =>
% 24.53/6.36 ((
% 24.53/6.36 (subsetI1) =>
% 24.53/6.36 ((
% 24.53/6.36 (eqimpsubset2) =>
% 24.53/6.36 ((
% 24.53/6.36 (eqimpsubset1) =>
% 24.53/6.36 ((
% 24.53/6.36 (subsetI2) =>
% 24.53/6.36 ((
% 24.53/6.36 (emptysetsubset) =>
% 24.53/6.36 ((
% 24.53/6.36 (subsetE) =>
% 24.53/6.36 ((
% 24.53/6.36 (subsetE2) =>
% 24.53/6.36 ((
% 24.53/6.36 (notsubsetI) =>
% 24.53/6.36 ((
% 24.53/6.36 (notequalI1) =>
% 24.53/6.36 ((
% 24.53/6.36 (notequalI2) =>
% 24.53/6.36 ((
% 24.53/6.36 (subsetRefl) =>
% 24.53/6.36 ((
% 24.53/6.36 (subsetTrans) =>
% 24.53/6.36 ((
% 24.53/6.36 (setadjoinSub) =>
% 24.53/6.36 ((
% 24.53/6.36 (setadjoinSub2) =>
% 24.53/6.36 ((
% 24.53/6.36 (subset2powerset) =>
% 24.53/6.36 ((
% 24.53/6.36 (setextsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (subsetemptysetimpeq) =>
% 24.53/6.36 ((
% 24.53/6.36 (powersetI1) =>
% 24.53/6.36 ((
% 24.53/6.36 (powersetE1) =>
% 24.53/6.36 ((
% 24.53/6.36 (inPowerset) =>
% 24.53/6.36 ((
% 24.53/6.36 (powersetsubset) =>
% 24.53/6.36 ((
% 24.53/6.36 (sepInPowerset) =>
% 24.53/6.36 ((
% 24.53/6.36 (sepSubset) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionIL) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairset2IR) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionIR) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionEcases) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionE) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionLsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionRsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectI) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset5) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectEL) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectLsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset2) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset3) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectER) =>
% 24.53/6.36 ((
% 24.53/6.36 (disjointsetsI1) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectRsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset4) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset1) =>
% 24.53/6.36 ((
% 24.53/6.36 (bs114d) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusI) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusEL) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusER) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusSubset2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusERneg) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusELneg) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusILneg) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusIRneg) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusLsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusSubset1) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffE) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffI1) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffI2) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffIneg1) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffIneg2) =>
% 24.53/6.36 ((
% 24.53/6.36 (secondinupair) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairIL) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairIR) =>
% 24.53/6.36 ((
% 24.53/6.36 (kpairiskpair) =>
% 24.53/6.36 ((
% 24.53/6.36 (kpairp) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletonsubset) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletoninpowerset) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletoninpowunion) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairset2E) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairsubunion) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairinpowunion) =>
% 24.53/6.36 ((
% 24.53/6.36 (ubforcartprodlem1) =>
% 24.53/6.36 ((
% 24.53/6.36 (ubforcartprodlem2) =>
% 24.53/6.36 ((
% 24.53/6.36 (ubforcartprodlem3) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodpairin) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodmempair1) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodmempair) =>
% 24.53/6.36 ((
% 24.53/6.36 (setunionE2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setunionsingleton1) =>
% 24.53/6.36 ((
% 24.53/6.36 (setunionsingleton2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setunionsingleton) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletonprop) =>
% 24.53/6.36 ((
% 24.53/6.36 (ex1E1) =>
% 24.53/6.36 ((
% 24.53/6.36 (ex1I) =>
% 24.53/6.36 ((
% 24.53/6.36 (ex1I2) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletonsuniq) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjL1) =>
% 24.53/6.36 ((
% 24.53/6.36 (kfstsingleton) =>
% 24.53/6.36 ((
% 24.53/6.36 (theprop) =>
% 24.53/6.36 ((
% 24.53/6.36 (kfstpairEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodfstin) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjL2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjL) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR11) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR12) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR1) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairequniteq) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR) =>
% 24.53/6.36 ((
% 24.53/6.36 (ksndsingleton) =>
% 24.53/6.36 ((
% 24.53/6.36 (ksndpairEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (kpairsurjEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodsndin) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodpairmemEL) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodpairmemER) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodmempaircEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodfstpairEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodsndpairEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodpairsurjEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (dpsetconstrI) =>
% 24.53/6.36 ((
% 24.53/6.36 (!!) @ (
% 24.53/6.36 (('#B') @ (
% 24.53/6.36 !!) @
% 24.53/6.36 (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 !!))) @
% 24.53/6.36 (
% 24.53/6.36 (
% 24.53/6.36 ('#S') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 '#S') @
% 24.53/6.36 (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 '#C'))) @
% 24.53/6.36 (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ subset)))) @
% 24.53/6.36 dpsetconstr)))))) @
% 24.53/6.36 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl428])).
% 24.53/6.36 thf(zip_derived_cl449, plain,
% 24.53/6.36 (~ (((uniqinunit) =>
% 24.53/6.36 (((notinsingleton) =>
% 24.53/6.36 (((eqinunit) =>
% 24.53/6.36 (((singletonsswitch) =>
% 24.53/6.36 (((upairsetE) =>
% 24.53/6.36 (((upairsetIL) =>
% 24.53/6.36 (((upairsetIR) =>
% 24.53/6.36 (((emptyE1) =>
% 24.53/6.36 (((vacuousDall) =>
% 24.53/6.36 (((quantDeMorgan1) =>
% 24.53/6.36 (((quantDeMorgan2) =>
% 24.53/6.36 (((quantDeMorgan3) =>
% 24.53/6.36 (((quantDeMorgan4) =>
% 24.53/6.36 (((prop2setI) =>
% 24.53/6.36 (((prop2set2propI) =>
% 24.53/6.36 (((notdexE) =>
% 24.53/6.36 (((notdallE) =>
% 24.53/6.36 (((exuI1) =>
% 24.53/6.36 (((exuI3) =>
% 24.53/6.36 (((exuI2) =>
% 24.53/6.36 (((inCongP) =>
% 24.53/6.36 (((in__Cong) =>
% 24.53/6.36 (((exuE3u) =>
% 24.53/6.36 (((exu__Cong) =>
% 24.53/6.36 (((setadjoin__Cong) =>
% 24.53/6.36 (((powerset__Cong) =>
% 24.53/6.36 (((setunion__Cong) =>
% 24.53/6.36 (((exuEu) =>
% 24.53/6.36 (((descr__Cong) =>
% 24.53/6.36 (((dsetconstr__Cong) =>
% 24.53/6.36 ((
% 24.53/6.36 (subsetI1) =>
% 24.53/6.36 ((
% 24.53/6.36 (eqimpsubset2) =>
% 24.53/6.36 ((
% 24.53/6.36 (eqimpsubset1) =>
% 24.53/6.36 ((
% 24.53/6.36 (subsetI2) =>
% 24.53/6.36 ((
% 24.53/6.36 (emptysetsubset) =>
% 24.53/6.36 ((
% 24.53/6.36 (subsetE) =>
% 24.53/6.36 ((
% 24.53/6.36 (subsetE2) =>
% 24.53/6.36 ((
% 24.53/6.36 (notsubsetI) =>
% 24.53/6.36 ((
% 24.53/6.36 (notequalI1) =>
% 24.53/6.36 ((
% 24.53/6.36 (notequalI2) =>
% 24.53/6.36 ((
% 24.53/6.36 (subsetRefl) =>
% 24.53/6.36 ((
% 24.53/6.36 (subsetTrans) =>
% 24.53/6.36 ((
% 24.53/6.36 (setadjoinSub) =>
% 24.53/6.36 ((
% 24.53/6.36 (setadjoinSub2) =>
% 24.53/6.36 ((
% 24.53/6.36 (subset2powerset) =>
% 24.53/6.36 ((
% 24.53/6.36 (setextsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (subsetemptysetimpeq) =>
% 24.53/6.36 ((
% 24.53/6.36 (powersetI1) =>
% 24.53/6.36 ((
% 24.53/6.36 (powersetE1) =>
% 24.53/6.36 ((
% 24.53/6.36 (inPowerset) =>
% 24.53/6.36 ((
% 24.53/6.36 (powersetsubset) =>
% 24.53/6.36 ((
% 24.53/6.36 (sepInPowerset) =>
% 24.53/6.36 ((
% 24.53/6.36 (sepSubset) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionIL) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairset2IR) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionIR) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionEcases) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionE) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionLsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionRsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectI) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset5) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectEL) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectLsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset2) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset3) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectER) =>
% 24.53/6.36 ((
% 24.53/6.36 (disjointsetsI1) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectRsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset4) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset1) =>
% 24.53/6.36 ((
% 24.53/6.36 (bs114d) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusI) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusEL) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusER) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusSubset2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusERneg) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusELneg) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusILneg) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusIRneg) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusLsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusSubset1) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffE) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffI1) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffI2) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffIneg1) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffIneg2) =>
% 24.53/6.36 ((
% 24.53/6.36 (secondinupair) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairIL) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairIR) =>
% 24.53/6.36 ((
% 24.53/6.36 (kpairiskpair) =>
% 24.53/6.36 ((
% 24.53/6.36 (kpairp) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletonsubset) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletoninpowerset) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletoninpowunion) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairset2E) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairsubunion) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairinpowunion) =>
% 24.53/6.36 ((
% 24.53/6.36 (ubforcartprodlem1) =>
% 24.53/6.36 ((
% 24.53/6.36 (ubforcartprodlem2) =>
% 24.53/6.36 ((
% 24.53/6.36 (ubforcartprodlem3) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodpairin) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodmempair1) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodmempair) =>
% 24.53/6.36 ((
% 24.53/6.36 (setunionE2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setunionsingleton1) =>
% 24.53/6.36 ((
% 24.53/6.36 (setunionsingleton2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setunionsingleton) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletonprop) =>
% 24.53/6.36 ((
% 24.53/6.36 (ex1E1) =>
% 24.53/6.36 ((
% 24.53/6.36 (ex1I) =>
% 24.53/6.36 ((
% 24.53/6.36 (ex1I2) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletonsuniq) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjL1) =>
% 24.53/6.36 ((
% 24.53/6.36 (kfstsingleton) =>
% 24.53/6.36 ((
% 24.53/6.36 (theprop) =>
% 24.53/6.36 ((
% 24.53/6.36 (kfstpairEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodfstin) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjL2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjL) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR11) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR12) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR1) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairequniteq) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR) =>
% 24.53/6.36 ((
% 24.53/6.36 (ksndsingleton) =>
% 24.53/6.36 ((
% 24.53/6.36 (ksndpairEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (kpairsurjEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodsndin) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodpairmemEL) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodpairmemER) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodmempaircEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodfstpairEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodsndpairEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodpairsurjEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (dpsetconstrI) =>
% 24.53/6.36 ((
% 24.53/6.36 (!!) @ (
% 24.53/6.36 (('#B') @ (
% 24.53/6.36 !!) @
% 24.53/6.36 (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 !!))) @
% 24.53/6.36 (
% 24.53/6.36 (
% 24.53/6.36 ('#S') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 '#S') @
% 24.53/6.36 (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 '#C'))) @
% 24.53/6.36 (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ subset)))) @
% 24.53/6.36 dpsetconstr)))))) @
% 24.53/6.36 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl439])).
% 24.53/6.36 thf(zip_derived_cl458, plain,
% 24.53/6.36 (~ (((notinsingleton) =>
% 24.53/6.36 (((eqinunit) =>
% 24.53/6.36 (((singletonsswitch) =>
% 24.53/6.36 (((upairsetE) =>
% 24.53/6.36 (((upairsetIL) =>
% 24.53/6.36 (((upairsetIR) =>
% 24.53/6.36 (((emptyE1) =>
% 24.53/6.36 (((vacuousDall) =>
% 24.53/6.36 (((quantDeMorgan1) =>
% 24.53/6.36 (((quantDeMorgan2) =>
% 24.53/6.36 (((quantDeMorgan3) =>
% 24.53/6.36 (((quantDeMorgan4) =>
% 24.53/6.36 (((prop2setI) =>
% 24.53/6.36 (((prop2set2propI) =>
% 24.53/6.36 (((notdexE) =>
% 24.53/6.36 (((notdallE) =>
% 24.53/6.36 (((exuI1) =>
% 24.53/6.36 (((exuI3) =>
% 24.53/6.36 (((exuI2) =>
% 24.53/6.36 (((inCongP) =>
% 24.53/6.36 (((in__Cong) =>
% 24.53/6.36 (((exuE3u) =>
% 24.53/6.36 (((exu__Cong) =>
% 24.53/6.36 (((setadjoin__Cong) =>
% 24.53/6.36 (((powerset__Cong) =>
% 24.53/6.36 (((setunion__Cong) =>
% 24.53/6.36 (((exuEu) =>
% 24.53/6.36 (((descr__Cong) =>
% 24.53/6.36 (((dsetconstr__Cong) =>
% 24.53/6.36 (((subsetI1) =>
% 24.53/6.36 ((
% 24.53/6.36 (eqimpsubset2) =>
% 24.53/6.36 ((
% 24.53/6.36 (eqimpsubset1) =>
% 24.53/6.36 ((
% 24.53/6.36 (subsetI2) =>
% 24.53/6.36 ((
% 24.53/6.36 (emptysetsubset) =>
% 24.53/6.36 ((
% 24.53/6.36 (subsetE) =>
% 24.53/6.36 ((
% 24.53/6.36 (subsetE2) =>
% 24.53/6.36 ((
% 24.53/6.36 (notsubsetI) =>
% 24.53/6.36 ((
% 24.53/6.36 (notequalI1) =>
% 24.53/6.36 ((
% 24.53/6.36 (notequalI2) =>
% 24.53/6.36 ((
% 24.53/6.36 (subsetRefl) =>
% 24.53/6.36 ((
% 24.53/6.36 (subsetTrans) =>
% 24.53/6.36 ((
% 24.53/6.36 (setadjoinSub) =>
% 24.53/6.36 ((
% 24.53/6.36 (setadjoinSub2) =>
% 24.53/6.36 ((
% 24.53/6.36 (subset2powerset) =>
% 24.53/6.36 ((
% 24.53/6.36 (setextsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (subsetemptysetimpeq) =>
% 24.53/6.36 ((
% 24.53/6.36 (powersetI1) =>
% 24.53/6.36 ((
% 24.53/6.36 (powersetE1) =>
% 24.53/6.36 ((
% 24.53/6.36 (inPowerset) =>
% 24.53/6.36 ((
% 24.53/6.36 (powersetsubset) =>
% 24.53/6.36 ((
% 24.53/6.36 (sepInPowerset) =>
% 24.53/6.36 ((
% 24.53/6.36 (sepSubset) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionIL) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairset2IR) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionIR) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionEcases) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionE) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionLsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionRsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectI) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset5) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectEL) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectLsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset2) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset3) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectER) =>
% 24.53/6.36 ((
% 24.53/6.36 (disjointsetsI1) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectRsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset4) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset1) =>
% 24.53/6.36 ((
% 24.53/6.36 (bs114d) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusI) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusEL) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusER) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusSubset2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusERneg) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusELneg) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusILneg) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusIRneg) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusLsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusSubset1) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffE) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffI1) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffI2) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffIneg1) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffIneg2) =>
% 24.53/6.36 ((
% 24.53/6.36 (secondinupair) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairIL) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairIR) =>
% 24.53/6.36 ((
% 24.53/6.36 (kpairiskpair) =>
% 24.53/6.36 ((
% 24.53/6.36 (kpairp) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletonsubset) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletoninpowerset) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletoninpowunion) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairset2E) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairsubunion) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairinpowunion) =>
% 24.53/6.36 ((
% 24.53/6.36 (ubforcartprodlem1) =>
% 24.53/6.36 ((
% 24.53/6.36 (ubforcartprodlem2) =>
% 24.53/6.36 ((
% 24.53/6.36 (ubforcartprodlem3) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodpairin) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodmempair1) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodmempair) =>
% 24.53/6.36 ((
% 24.53/6.36 (setunionE2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setunionsingleton1) =>
% 24.53/6.36 ((
% 24.53/6.36 (setunionsingleton2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setunionsingleton) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletonprop) =>
% 24.53/6.36 ((
% 24.53/6.36 (ex1E1) =>
% 24.53/6.36 ((
% 24.53/6.36 (ex1I) =>
% 24.53/6.36 ((
% 24.53/6.36 (ex1I2) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletonsuniq) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjL1) =>
% 24.53/6.36 ((
% 24.53/6.36 (kfstsingleton) =>
% 24.53/6.36 ((
% 24.53/6.36 (theprop) =>
% 24.53/6.36 ((
% 24.53/6.36 (kfstpairEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodfstin) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjL2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjL) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR11) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR12) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR1) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairequniteq) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR) =>
% 24.53/6.36 ((
% 24.53/6.36 (ksndsingleton) =>
% 24.53/6.36 ((
% 24.53/6.36 (ksndpairEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (kpairsurjEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodsndin) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodpairmemEL) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodpairmemER) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodmempaircEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodfstpairEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodsndpairEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodpairsurjEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (dpsetconstrI) =>
% 24.53/6.36 ((
% 24.53/6.36 (!!) @ (
% 24.53/6.36 (('#B') @ (
% 24.53/6.36 !!) @
% 24.53/6.36 (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 !!))) @
% 24.53/6.36 (
% 24.53/6.36 (
% 24.53/6.36 ('#S') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 '#S') @
% 24.53/6.36 (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 '#C'))) @
% 24.53/6.36 (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ subset)))) @
% 24.53/6.36 dpsetconstr)))))) @
% 24.53/6.36 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl449])).
% 24.53/6.36 thf(zip_derived_cl467, plain,
% 24.53/6.36 (~ (((eqinunit) =>
% 24.53/6.36 (((singletonsswitch) =>
% 24.53/6.36 (((upairsetE) =>
% 24.53/6.36 (((upairsetIL) =>
% 24.53/6.36 (((upairsetIR) =>
% 24.53/6.36 (((emptyE1) =>
% 24.53/6.36 (((vacuousDall) =>
% 24.53/6.36 (((quantDeMorgan1) =>
% 24.53/6.36 (((quantDeMorgan2) =>
% 24.53/6.36 (((quantDeMorgan3) =>
% 24.53/6.36 (((quantDeMorgan4) =>
% 24.53/6.36 (((prop2setI) =>
% 24.53/6.36 (((prop2set2propI) =>
% 24.53/6.36 (((notdexE) =>
% 24.53/6.36 (((notdallE) =>
% 24.53/6.36 (((exuI1) =>
% 24.53/6.36 (((exuI3) =>
% 24.53/6.36 (((exuI2) =>
% 24.53/6.36 (((inCongP) =>
% 24.53/6.36 (((in__Cong) =>
% 24.53/6.36 (((exuE3u) =>
% 24.53/6.36 (((exu__Cong) =>
% 24.53/6.36 (((setadjoin__Cong) =>
% 24.53/6.36 (((powerset__Cong) =>
% 24.53/6.36 (((setunion__Cong) =>
% 24.53/6.36 (((exuEu) =>
% 24.53/6.36 (((descr__Cong) =>
% 24.53/6.36 (((dsetconstr__Cong) =>
% 24.53/6.36 (((subsetI1) =>
% 24.53/6.36 (((eqimpsubset2) =>
% 24.53/6.36 ((
% 24.53/6.36 (eqimpsubset1) =>
% 24.53/6.36 ((
% 24.53/6.36 (subsetI2) =>
% 24.53/6.36 ((
% 24.53/6.36 (emptysetsubset) =>
% 24.53/6.36 ((
% 24.53/6.36 (subsetE) =>
% 24.53/6.36 ((
% 24.53/6.36 (subsetE2) =>
% 24.53/6.36 ((
% 24.53/6.36 (notsubsetI) =>
% 24.53/6.36 ((
% 24.53/6.36 (notequalI1) =>
% 24.53/6.36 ((
% 24.53/6.36 (notequalI2) =>
% 24.53/6.36 ((
% 24.53/6.36 (subsetRefl) =>
% 24.53/6.36 ((
% 24.53/6.36 (subsetTrans) =>
% 24.53/6.36 ((
% 24.53/6.36 (setadjoinSub) =>
% 24.53/6.36 ((
% 24.53/6.36 (setadjoinSub2) =>
% 24.53/6.36 ((
% 24.53/6.36 (subset2powerset) =>
% 24.53/6.36 ((
% 24.53/6.36 (setextsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (subsetemptysetimpeq) =>
% 24.53/6.36 ((
% 24.53/6.36 (powersetI1) =>
% 24.53/6.36 ((
% 24.53/6.36 (powersetE1) =>
% 24.53/6.36 ((
% 24.53/6.36 (inPowerset) =>
% 24.53/6.36 ((
% 24.53/6.36 (powersetsubset) =>
% 24.53/6.36 ((
% 24.53/6.36 (sepInPowerset) =>
% 24.53/6.36 ((
% 24.53/6.36 (sepSubset) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionIL) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairset2IR) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionIR) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionEcases) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionE) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionLsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionRsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectI) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset5) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectEL) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectLsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset2) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset3) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectER) =>
% 24.53/6.36 ((
% 24.53/6.36 (disjointsetsI1) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectRsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset4) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset1) =>
% 24.53/6.36 ((
% 24.53/6.36 (bs114d) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusI) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusEL) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusER) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusSubset2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusERneg) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusELneg) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusILneg) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusIRneg) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusLsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusSubset1) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffE) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffI1) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffI2) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffIneg1) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffIneg2) =>
% 24.53/6.36 ((
% 24.53/6.36 (secondinupair) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairIL) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairIR) =>
% 24.53/6.36 ((
% 24.53/6.36 (kpairiskpair) =>
% 24.53/6.36 ((
% 24.53/6.36 (kpairp) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletonsubset) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletoninpowerset) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletoninpowunion) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairset2E) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairsubunion) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairinpowunion) =>
% 24.53/6.36 ((
% 24.53/6.36 (ubforcartprodlem1) =>
% 24.53/6.36 ((
% 24.53/6.36 (ubforcartprodlem2) =>
% 24.53/6.36 ((
% 24.53/6.36 (ubforcartprodlem3) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodpairin) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodmempair1) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodmempair) =>
% 24.53/6.36 ((
% 24.53/6.36 (setunionE2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setunionsingleton1) =>
% 24.53/6.36 ((
% 24.53/6.36 (setunionsingleton2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setunionsingleton) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletonprop) =>
% 24.53/6.36 ((
% 24.53/6.36 (ex1E1) =>
% 24.53/6.36 ((
% 24.53/6.36 (ex1I) =>
% 24.53/6.36 ((
% 24.53/6.36 (ex1I2) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletonsuniq) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjL1) =>
% 24.53/6.36 ((
% 24.53/6.36 (kfstsingleton) =>
% 24.53/6.36 ((
% 24.53/6.36 (theprop) =>
% 24.53/6.36 ((
% 24.53/6.36 (kfstpairEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodfstin) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjL2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjL) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR11) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR12) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR1) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairequniteq) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR) =>
% 24.53/6.36 ((
% 24.53/6.36 (ksndsingleton) =>
% 24.53/6.36 ((
% 24.53/6.36 (ksndpairEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (kpairsurjEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodsndin) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodpairmemEL) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodpairmemER) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodmempaircEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodfstpairEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodsndpairEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodpairsurjEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (dpsetconstrI) =>
% 24.53/6.36 ((
% 24.53/6.36 (!!) @ (
% 24.53/6.36 (('#B') @ (
% 24.53/6.36 !!) @
% 24.53/6.36 (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 !!))) @
% 24.53/6.36 (
% 24.53/6.36 (
% 24.53/6.36 ('#S') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 '#S') @
% 24.53/6.36 (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 '#C'))) @
% 24.53/6.36 (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ subset)))) @
% 24.53/6.36 dpsetconstr)))))) @
% 24.53/6.36 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl458])).
% 24.53/6.36 thf(zip_derived_cl475, plain,
% 24.53/6.36 (~ (((singletonsswitch) =>
% 24.53/6.36 (((upairsetE) =>
% 24.53/6.36 (((upairsetIL) =>
% 24.53/6.36 (((upairsetIR) =>
% 24.53/6.36 (((emptyE1) =>
% 24.53/6.36 (((vacuousDall) =>
% 24.53/6.36 (((quantDeMorgan1) =>
% 24.53/6.36 (((quantDeMorgan2) =>
% 24.53/6.36 (((quantDeMorgan3) =>
% 24.53/6.36 (((quantDeMorgan4) =>
% 24.53/6.36 (((prop2setI) =>
% 24.53/6.36 (((prop2set2propI) =>
% 24.53/6.36 (((notdexE) =>
% 24.53/6.36 (((notdallE) =>
% 24.53/6.36 (((exuI1) =>
% 24.53/6.36 (((exuI3) =>
% 24.53/6.36 (((exuI2) =>
% 24.53/6.36 (((inCongP) =>
% 24.53/6.36 (((in__Cong) =>
% 24.53/6.36 (((exuE3u) =>
% 24.53/6.36 (((exu__Cong) =>
% 24.53/6.36 (((setadjoin__Cong) =>
% 24.53/6.36 (((powerset__Cong) =>
% 24.53/6.36 (((setunion__Cong) =>
% 24.53/6.36 (((exuEu) =>
% 24.53/6.36 (((descr__Cong) =>
% 24.53/6.36 (((dsetconstr__Cong) =>
% 24.53/6.36 (((subsetI1) =>
% 24.53/6.36 (((eqimpsubset2) =>
% 24.53/6.36 (((eqimpsubset1) =>
% 24.53/6.36 ((
% 24.53/6.36 (subsetI2) =>
% 24.53/6.36 ((
% 24.53/6.36 (emptysetsubset) =>
% 24.53/6.36 ((
% 24.53/6.36 (subsetE) =>
% 24.53/6.36 ((
% 24.53/6.36 (subsetE2) =>
% 24.53/6.36 ((
% 24.53/6.36 (notsubsetI) =>
% 24.53/6.36 ((
% 24.53/6.36 (notequalI1) =>
% 24.53/6.36 ((
% 24.53/6.36 (notequalI2) =>
% 24.53/6.36 ((
% 24.53/6.36 (subsetRefl) =>
% 24.53/6.36 ((
% 24.53/6.36 (subsetTrans) =>
% 24.53/6.36 ((
% 24.53/6.36 (setadjoinSub) =>
% 24.53/6.36 ((
% 24.53/6.36 (setadjoinSub2) =>
% 24.53/6.36 ((
% 24.53/6.36 (subset2powerset) =>
% 24.53/6.36 ((
% 24.53/6.36 (setextsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (subsetemptysetimpeq) =>
% 24.53/6.36 ((
% 24.53/6.36 (powersetI1) =>
% 24.53/6.36 ((
% 24.53/6.36 (powersetE1) =>
% 24.53/6.36 ((
% 24.53/6.36 (inPowerset) =>
% 24.53/6.36 ((
% 24.53/6.36 (powersetsubset) =>
% 24.53/6.36 ((
% 24.53/6.36 (sepInPowerset) =>
% 24.53/6.36 ((
% 24.53/6.36 (sepSubset) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionIL) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairset2IR) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionIR) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionEcases) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionE) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionLsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionRsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectI) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset5) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectEL) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectLsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset2) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset3) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectER) =>
% 24.53/6.36 ((
% 24.53/6.36 (disjointsetsI1) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectRsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset4) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset1) =>
% 24.53/6.36 ((
% 24.53/6.36 (bs114d) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusI) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusEL) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusER) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusSubset2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusERneg) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusELneg) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusILneg) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusIRneg) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusLsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusSubset1) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffE) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffI1) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffI2) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffIneg1) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffIneg2) =>
% 24.53/6.36 ((
% 24.53/6.36 (secondinupair) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairIL) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairIR) =>
% 24.53/6.36 ((
% 24.53/6.36 (kpairiskpair) =>
% 24.53/6.36 ((
% 24.53/6.36 (kpairp) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletonsubset) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletoninpowerset) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletoninpowunion) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairset2E) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairsubunion) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairinpowunion) =>
% 24.53/6.36 ((
% 24.53/6.36 (ubforcartprodlem1) =>
% 24.53/6.36 ((
% 24.53/6.36 (ubforcartprodlem2) =>
% 24.53/6.36 ((
% 24.53/6.36 (ubforcartprodlem3) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodpairin) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodmempair1) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodmempair) =>
% 24.53/6.36 ((
% 24.53/6.36 (setunionE2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setunionsingleton1) =>
% 24.53/6.36 ((
% 24.53/6.36 (setunionsingleton2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setunionsingleton) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletonprop) =>
% 24.53/6.36 ((
% 24.53/6.36 (ex1E1) =>
% 24.53/6.36 ((
% 24.53/6.36 (ex1I) =>
% 24.53/6.36 ((
% 24.53/6.36 (ex1I2) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletonsuniq) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjL1) =>
% 24.53/6.36 ((
% 24.53/6.36 (kfstsingleton) =>
% 24.53/6.36 ((
% 24.53/6.36 (theprop) =>
% 24.53/6.36 ((
% 24.53/6.36 (kfstpairEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodfstin) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjL2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjL) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR11) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR12) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR1) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairequniteq) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR) =>
% 24.53/6.36 ((
% 24.53/6.36 (ksndsingleton) =>
% 24.53/6.36 ((
% 24.53/6.36 (ksndpairEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (kpairsurjEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodsndin) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodpairmemEL) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodpairmemER) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodmempaircEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodfstpairEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodsndpairEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodpairsurjEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (dpsetconstrI) =>
% 24.53/6.36 ((
% 24.53/6.36 (!!) @ (
% 24.53/6.36 (('#B') @ (
% 24.53/6.36 !!) @
% 24.53/6.36 (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 !!))) @
% 24.53/6.36 (
% 24.53/6.36 (
% 24.53/6.36 ('#S') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 '#S') @
% 24.53/6.36 (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 '#C'))) @
% 24.53/6.36 (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ subset)))) @
% 24.53/6.36 dpsetconstr)))))) @
% 24.53/6.36 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl467])).
% 24.53/6.36 thf(zip_derived_cl485, plain,
% 24.53/6.36 (~ (((upairsetE) =>
% 24.53/6.36 (((upairsetIL) =>
% 24.53/6.36 (((upairsetIR) =>
% 24.53/6.36 (((emptyE1) =>
% 24.53/6.36 (((vacuousDall) =>
% 24.53/6.36 (((quantDeMorgan1) =>
% 24.53/6.36 (((quantDeMorgan2) =>
% 24.53/6.36 (((quantDeMorgan3) =>
% 24.53/6.36 (((quantDeMorgan4) =>
% 24.53/6.36 (((prop2setI) =>
% 24.53/6.36 (((prop2set2propI) =>
% 24.53/6.36 (((notdexE) =>
% 24.53/6.36 (((notdallE) =>
% 24.53/6.36 (((exuI1) =>
% 24.53/6.36 (((exuI3) =>
% 24.53/6.36 (((exuI2) =>
% 24.53/6.36 (((inCongP) =>
% 24.53/6.36 (((in__Cong) =>
% 24.53/6.36 (((exuE3u) =>
% 24.53/6.36 (((exu__Cong) =>
% 24.53/6.36 (((setadjoin__Cong) =>
% 24.53/6.36 (((powerset__Cong) =>
% 24.53/6.36 (((setunion__Cong) =>
% 24.53/6.36 (((exuEu) =>
% 24.53/6.36 (((descr__Cong) =>
% 24.53/6.36 (((dsetconstr__Cong) =>
% 24.53/6.36 (((subsetI1) =>
% 24.53/6.36 (((eqimpsubset2) =>
% 24.53/6.36 (((eqimpsubset1) =>
% 24.53/6.36 (((subsetI2) =>
% 24.53/6.36 ((
% 24.53/6.36 (emptysetsubset) =>
% 24.53/6.36 ((
% 24.53/6.36 (subsetE) =>
% 24.53/6.36 ((
% 24.53/6.36 (subsetE2) =>
% 24.53/6.36 ((
% 24.53/6.36 (notsubsetI) =>
% 24.53/6.36 ((
% 24.53/6.36 (notequalI1) =>
% 24.53/6.36 ((
% 24.53/6.36 (notequalI2) =>
% 24.53/6.36 ((
% 24.53/6.36 (subsetRefl) =>
% 24.53/6.36 ((
% 24.53/6.36 (subsetTrans) =>
% 24.53/6.36 ((
% 24.53/6.36 (setadjoinSub) =>
% 24.53/6.36 ((
% 24.53/6.36 (setadjoinSub2) =>
% 24.53/6.36 ((
% 24.53/6.36 (subset2powerset) =>
% 24.53/6.36 ((
% 24.53/6.36 (setextsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (subsetemptysetimpeq) =>
% 24.53/6.36 ((
% 24.53/6.36 (powersetI1) =>
% 24.53/6.36 ((
% 24.53/6.36 (powersetE1) =>
% 24.53/6.36 ((
% 24.53/6.36 (inPowerset) =>
% 24.53/6.36 ((
% 24.53/6.36 (powersetsubset) =>
% 24.53/6.36 ((
% 24.53/6.36 (sepInPowerset) =>
% 24.53/6.36 ((
% 24.53/6.36 (sepSubset) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionIL) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairset2IR) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionIR) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionEcases) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionE) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionLsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionRsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectI) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset5) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectEL) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectLsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset2) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset3) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectER) =>
% 24.53/6.36 ((
% 24.53/6.36 (disjointsetsI1) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectRsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset4) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset1) =>
% 24.53/6.36 ((
% 24.53/6.36 (bs114d) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusI) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusEL) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusER) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusSubset2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusERneg) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusELneg) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusILneg) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusIRneg) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusLsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusSubset1) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffE) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffI1) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffI2) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffIneg1) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffIneg2) =>
% 24.53/6.36 ((
% 24.53/6.36 (secondinupair) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairIL) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairIR) =>
% 24.53/6.36 ((
% 24.53/6.36 (kpairiskpair) =>
% 24.53/6.36 ((
% 24.53/6.36 (kpairp) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletonsubset) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletoninpowerset) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletoninpowunion) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairset2E) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairsubunion) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairinpowunion) =>
% 24.53/6.36 ((
% 24.53/6.36 (ubforcartprodlem1) =>
% 24.53/6.36 ((
% 24.53/6.36 (ubforcartprodlem2) =>
% 24.53/6.36 ((
% 24.53/6.36 (ubforcartprodlem3) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodpairin) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodmempair1) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodmempair) =>
% 24.53/6.36 ((
% 24.53/6.36 (setunionE2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setunionsingleton1) =>
% 24.53/6.36 ((
% 24.53/6.36 (setunionsingleton2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setunionsingleton) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletonprop) =>
% 24.53/6.36 ((
% 24.53/6.36 (ex1E1) =>
% 24.53/6.36 ((
% 24.53/6.36 (ex1I) =>
% 24.53/6.36 ((
% 24.53/6.36 (ex1I2) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletonsuniq) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjL1) =>
% 24.53/6.36 ((
% 24.53/6.36 (kfstsingleton) =>
% 24.53/6.36 ((
% 24.53/6.36 (theprop) =>
% 24.53/6.36 ((
% 24.53/6.36 (kfstpairEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodfstin) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjL2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjL) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR11) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR12) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR1) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairequniteq) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR) =>
% 24.53/6.36 ((
% 24.53/6.36 (ksndsingleton) =>
% 24.53/6.36 ((
% 24.53/6.36 (ksndpairEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (kpairsurjEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodsndin) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodpairmemEL) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodpairmemER) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodmempaircEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodfstpairEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodsndpairEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodpairsurjEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (dpsetconstrI) =>
% 24.53/6.36 ((
% 24.53/6.36 (!!) @ (
% 24.53/6.36 (('#B') @ (
% 24.53/6.36 !!) @
% 24.53/6.36 (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 !!))) @
% 24.53/6.36 (
% 24.53/6.36 (
% 24.53/6.36 ('#S') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 '#S') @
% 24.53/6.36 (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 '#C'))) @
% 24.53/6.36 (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ subset)))) @
% 24.53/6.36 dpsetconstr)))))) @
% 24.53/6.36 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl475])).
% 24.53/6.36 thf(zip_derived_cl496, plain,
% 24.53/6.36 (~ (((upairsetIL) =>
% 24.53/6.36 (((upairsetIR) =>
% 24.53/6.36 (((emptyE1) =>
% 24.53/6.36 (((vacuousDall) =>
% 24.53/6.36 (((quantDeMorgan1) =>
% 24.53/6.36 (((quantDeMorgan2) =>
% 24.53/6.36 (((quantDeMorgan3) =>
% 24.53/6.36 (((quantDeMorgan4) =>
% 24.53/6.36 (((prop2setI) =>
% 24.53/6.36 (((prop2set2propI) =>
% 24.53/6.36 (((notdexE) =>
% 24.53/6.36 (((notdallE) =>
% 24.53/6.36 (((exuI1) =>
% 24.53/6.36 (((exuI3) =>
% 24.53/6.36 (((exuI2) =>
% 24.53/6.36 (((inCongP) =>
% 24.53/6.36 (((in__Cong) =>
% 24.53/6.36 (((exuE3u) =>
% 24.53/6.36 (((exu__Cong) =>
% 24.53/6.36 (((setadjoin__Cong) =>
% 24.53/6.36 (((powerset__Cong) =>
% 24.53/6.36 (((setunion__Cong) =>
% 24.53/6.36 (((exuEu) =>
% 24.53/6.36 (((descr__Cong) =>
% 24.53/6.36 (((dsetconstr__Cong) =>
% 24.53/6.36 (((subsetI1) =>
% 24.53/6.36 (((eqimpsubset2) =>
% 24.53/6.36 (((eqimpsubset1) =>
% 24.53/6.36 (((subsetI2) =>
% 24.53/6.36 (((emptysetsubset) =>
% 24.53/6.36 ((
% 24.53/6.36 (subsetE) =>
% 24.53/6.36 ((
% 24.53/6.36 (subsetE2) =>
% 24.53/6.36 ((
% 24.53/6.36 (notsubsetI) =>
% 24.53/6.36 ((
% 24.53/6.36 (notequalI1) =>
% 24.53/6.36 ((
% 24.53/6.36 (notequalI2) =>
% 24.53/6.36 ((
% 24.53/6.36 (subsetRefl) =>
% 24.53/6.36 ((
% 24.53/6.36 (subsetTrans) =>
% 24.53/6.36 ((
% 24.53/6.36 (setadjoinSub) =>
% 24.53/6.36 ((
% 24.53/6.36 (setadjoinSub2) =>
% 24.53/6.36 ((
% 24.53/6.36 (subset2powerset) =>
% 24.53/6.36 ((
% 24.53/6.36 (setextsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (subsetemptysetimpeq) =>
% 24.53/6.36 ((
% 24.53/6.36 (powersetI1) =>
% 24.53/6.36 ((
% 24.53/6.36 (powersetE1) =>
% 24.53/6.36 ((
% 24.53/6.36 (inPowerset) =>
% 24.53/6.36 ((
% 24.53/6.36 (powersetsubset) =>
% 24.53/6.36 ((
% 24.53/6.36 (sepInPowerset) =>
% 24.53/6.36 ((
% 24.53/6.36 (sepSubset) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionIL) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairset2IR) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionIR) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionEcases) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionE) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionLsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionRsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectI) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset5) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectEL) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectLsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset2) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset3) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectER) =>
% 24.53/6.36 ((
% 24.53/6.36 (disjointsetsI1) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectRsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset4) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset1) =>
% 24.53/6.36 ((
% 24.53/6.36 (bs114d) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusI) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusEL) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusER) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusSubset2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusERneg) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusELneg) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusILneg) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusIRneg) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusLsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusSubset1) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffE) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffI1) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffI2) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffIneg1) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffIneg2) =>
% 24.53/6.36 ((
% 24.53/6.36 (secondinupair) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairIL) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairIR) =>
% 24.53/6.36 ((
% 24.53/6.36 (kpairiskpair) =>
% 24.53/6.36 ((
% 24.53/6.36 (kpairp) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletonsubset) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletoninpowerset) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletoninpowunion) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairset2E) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairsubunion) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairinpowunion) =>
% 24.53/6.36 ((
% 24.53/6.36 (ubforcartprodlem1) =>
% 24.53/6.36 ((
% 24.53/6.36 (ubforcartprodlem2) =>
% 24.53/6.36 ((
% 24.53/6.36 (ubforcartprodlem3) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodpairin) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodmempair1) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodmempair) =>
% 24.53/6.36 ((
% 24.53/6.36 (setunionE2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setunionsingleton1) =>
% 24.53/6.36 ((
% 24.53/6.36 (setunionsingleton2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setunionsingleton) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletonprop) =>
% 24.53/6.36 ((
% 24.53/6.36 (ex1E1) =>
% 24.53/6.36 ((
% 24.53/6.36 (ex1I) =>
% 24.53/6.36 ((
% 24.53/6.36 (ex1I2) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletonsuniq) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjL1) =>
% 24.53/6.36 ((
% 24.53/6.36 (kfstsingleton) =>
% 24.53/6.36 ((
% 24.53/6.36 (theprop) =>
% 24.53/6.36 ((
% 24.53/6.36 (kfstpairEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodfstin) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjL2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjL) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR11) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR12) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR1) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairequniteq) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR) =>
% 24.53/6.36 ((
% 24.53/6.36 (ksndsingleton) =>
% 24.53/6.36 ((
% 24.53/6.36 (ksndpairEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (kpairsurjEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodsndin) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodpairmemEL) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodpairmemER) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodmempaircEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodfstpairEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodsndpairEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodpairsurjEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (dpsetconstrI) =>
% 24.53/6.36 ((
% 24.53/6.36 (!!) @ (
% 24.53/6.36 (('#B') @ (
% 24.53/6.36 !!) @
% 24.53/6.36 (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 !!))) @
% 24.53/6.36 (
% 24.53/6.36 (
% 24.53/6.36 ('#S') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 '#S') @
% 24.53/6.36 (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 '#C'))) @
% 24.53/6.36 (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ subset)))) @
% 24.53/6.36 dpsetconstr)))))) @
% 24.53/6.36 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl485])).
% 24.53/6.36 thf(zip_derived_cl507, plain,
% 24.53/6.36 (~ (((upairsetIR) =>
% 24.53/6.36 (((emptyE1) =>
% 24.53/6.36 (((vacuousDall) =>
% 24.53/6.36 (((quantDeMorgan1) =>
% 24.53/6.36 (((quantDeMorgan2) =>
% 24.53/6.36 (((quantDeMorgan3) =>
% 24.53/6.36 (((quantDeMorgan4) =>
% 24.53/6.36 (((prop2setI) =>
% 24.53/6.36 (((prop2set2propI) =>
% 24.53/6.36 (((notdexE) =>
% 24.53/6.36 (((notdallE) =>
% 24.53/6.36 (((exuI1) =>
% 24.53/6.36 (((exuI3) =>
% 24.53/6.36 (((exuI2) =>
% 24.53/6.36 (((inCongP) =>
% 24.53/6.36 (((in__Cong) =>
% 24.53/6.36 (((exuE3u) =>
% 24.53/6.36 (((exu__Cong) =>
% 24.53/6.36 (((setadjoin__Cong) =>
% 24.53/6.36 (((powerset__Cong) =>
% 24.53/6.36 (((setunion__Cong) =>
% 24.53/6.36 (((exuEu) =>
% 24.53/6.36 (((descr__Cong) =>
% 24.53/6.36 (((dsetconstr__Cong) =>
% 24.53/6.36 (((subsetI1) =>
% 24.53/6.36 (((eqimpsubset2) =>
% 24.53/6.36 (((eqimpsubset1) =>
% 24.53/6.36 (((subsetI2) =>
% 24.53/6.36 (((emptysetsubset) =>
% 24.53/6.36 (((subsetE) =>
% 24.53/6.36 ((
% 24.53/6.36 (subsetE2) =>
% 24.53/6.36 ((
% 24.53/6.36 (notsubsetI) =>
% 24.53/6.36 ((
% 24.53/6.36 (notequalI1) =>
% 24.53/6.36 ((
% 24.53/6.36 (notequalI2) =>
% 24.53/6.36 ((
% 24.53/6.36 (subsetRefl) =>
% 24.53/6.36 ((
% 24.53/6.36 (subsetTrans) =>
% 24.53/6.36 ((
% 24.53/6.36 (setadjoinSub) =>
% 24.53/6.36 ((
% 24.53/6.36 (setadjoinSub2) =>
% 24.53/6.36 ((
% 24.53/6.36 (subset2powerset) =>
% 24.53/6.36 ((
% 24.53/6.36 (setextsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (subsetemptysetimpeq) =>
% 24.53/6.36 ((
% 24.53/6.36 (powersetI1) =>
% 24.53/6.36 ((
% 24.53/6.36 (powersetE1) =>
% 24.53/6.36 ((
% 24.53/6.36 (inPowerset) =>
% 24.53/6.36 ((
% 24.53/6.36 (powersetsubset) =>
% 24.53/6.36 ((
% 24.53/6.36 (sepInPowerset) =>
% 24.53/6.36 ((
% 24.53/6.36 (sepSubset) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionIL) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairset2IR) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionIR) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionEcases) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionE) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionLsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionRsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectI) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset5) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectEL) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectLsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset2) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset3) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectER) =>
% 24.53/6.36 ((
% 24.53/6.36 (disjointsetsI1) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectRsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset4) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset1) =>
% 24.53/6.36 ((
% 24.53/6.36 (bs114d) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusI) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusEL) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusER) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusSubset2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusERneg) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusELneg) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusILneg) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusIRneg) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusLsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusSubset1) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffE) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffI1) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffI2) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffIneg1) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffIneg2) =>
% 24.53/6.36 ((
% 24.53/6.36 (secondinupair) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairIL) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairIR) =>
% 24.53/6.36 ((
% 24.53/6.36 (kpairiskpair) =>
% 24.53/6.36 ((
% 24.53/6.36 (kpairp) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletonsubset) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletoninpowerset) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletoninpowunion) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairset2E) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairsubunion) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairinpowunion) =>
% 24.53/6.36 ((
% 24.53/6.36 (ubforcartprodlem1) =>
% 24.53/6.36 ((
% 24.53/6.36 (ubforcartprodlem2) =>
% 24.53/6.36 ((
% 24.53/6.36 (ubforcartprodlem3) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodpairin) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodmempair1) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodmempair) =>
% 24.53/6.36 ((
% 24.53/6.36 (setunionE2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setunionsingleton1) =>
% 24.53/6.36 ((
% 24.53/6.36 (setunionsingleton2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setunionsingleton) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletonprop) =>
% 24.53/6.36 ((
% 24.53/6.36 (ex1E1) =>
% 24.53/6.36 ((
% 24.53/6.36 (ex1I) =>
% 24.53/6.36 ((
% 24.53/6.36 (ex1I2) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletonsuniq) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjL1) =>
% 24.53/6.36 ((
% 24.53/6.36 (kfstsingleton) =>
% 24.53/6.36 ((
% 24.53/6.36 (theprop) =>
% 24.53/6.36 ((
% 24.53/6.36 (kfstpairEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodfstin) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjL2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjL) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR11) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR12) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR1) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairequniteq) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR) =>
% 24.53/6.36 ((
% 24.53/6.36 (ksndsingleton) =>
% 24.53/6.36 ((
% 24.53/6.36 (ksndpairEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (kpairsurjEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodsndin) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodpairmemEL) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodpairmemER) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodmempaircEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodfstpairEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodsndpairEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodpairsurjEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (dpsetconstrI) =>
% 24.53/6.36 ((
% 24.53/6.36 (!!) @ (
% 24.53/6.36 (('#B') @ (
% 24.53/6.36 !!) @
% 24.53/6.36 (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 !!))) @
% 24.53/6.36 (
% 24.53/6.36 (
% 24.53/6.36 ('#S') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 '#S') @
% 24.53/6.36 (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 '#C'))) @
% 24.53/6.36 (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ subset)))) @
% 24.53/6.36 dpsetconstr)))))) @
% 24.53/6.36 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl496])).
% 24.53/6.36 thf(zip_derived_cl517, plain,
% 24.53/6.36 (~ (((emptyE1) =>
% 24.53/6.36 (((vacuousDall) =>
% 24.53/6.36 (((quantDeMorgan1) =>
% 24.53/6.36 (((quantDeMorgan2) =>
% 24.53/6.36 (((quantDeMorgan3) =>
% 24.53/6.36 (((quantDeMorgan4) =>
% 24.53/6.36 (((prop2setI) =>
% 24.53/6.36 (((prop2set2propI) =>
% 24.53/6.36 (((notdexE) =>
% 24.53/6.36 (((notdallE) =>
% 24.53/6.36 (((exuI1) =>
% 24.53/6.36 (((exuI3) =>
% 24.53/6.36 (((exuI2) =>
% 24.53/6.36 (((inCongP) =>
% 24.53/6.36 (((in__Cong) =>
% 24.53/6.36 (((exuE3u) =>
% 24.53/6.36 (((exu__Cong) =>
% 24.53/6.36 (((setadjoin__Cong) =>
% 24.53/6.36 (((powerset__Cong) =>
% 24.53/6.36 (((setunion__Cong) =>
% 24.53/6.36 (((exuEu) =>
% 24.53/6.36 (((descr__Cong) =>
% 24.53/6.36 (((dsetconstr__Cong) =>
% 24.53/6.36 (((subsetI1) =>
% 24.53/6.36 (((eqimpsubset2) =>
% 24.53/6.36 (((eqimpsubset1) =>
% 24.53/6.36 (((subsetI2) =>
% 24.53/6.36 (((emptysetsubset) =>
% 24.53/6.36 (((subsetE) =>
% 24.53/6.36 (((subsetE2) =>
% 24.53/6.36 ((
% 24.53/6.36 (notsubsetI) =>
% 24.53/6.36 ((
% 24.53/6.36 (notequalI1) =>
% 24.53/6.36 ((
% 24.53/6.36 (notequalI2) =>
% 24.53/6.36 ((
% 24.53/6.36 (subsetRefl) =>
% 24.53/6.36 ((
% 24.53/6.36 (subsetTrans) =>
% 24.53/6.36 ((
% 24.53/6.36 (setadjoinSub) =>
% 24.53/6.36 ((
% 24.53/6.36 (setadjoinSub2) =>
% 24.53/6.36 ((
% 24.53/6.36 (subset2powerset) =>
% 24.53/6.36 ((
% 24.53/6.36 (setextsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (subsetemptysetimpeq) =>
% 24.53/6.36 ((
% 24.53/6.36 (powersetI1) =>
% 24.53/6.36 ((
% 24.53/6.36 (powersetE1) =>
% 24.53/6.36 ((
% 24.53/6.36 (inPowerset) =>
% 24.53/6.36 ((
% 24.53/6.36 (powersetsubset) =>
% 24.53/6.36 ((
% 24.53/6.36 (sepInPowerset) =>
% 24.53/6.36 ((
% 24.53/6.36 (sepSubset) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionIL) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairset2IR) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionIR) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionEcases) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionE) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionLsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionRsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectI) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset5) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectEL) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectLsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset2) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset3) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectER) =>
% 24.53/6.36 ((
% 24.53/6.36 (disjointsetsI1) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectRsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset4) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset1) =>
% 24.53/6.36 ((
% 24.53/6.36 (bs114d) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusI) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusEL) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusER) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusSubset2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusERneg) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusELneg) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusILneg) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusIRneg) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusLsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusSubset1) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffE) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffI1) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffI2) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffIneg1) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffIneg2) =>
% 24.53/6.36 ((
% 24.53/6.36 (secondinupair) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairIL) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairIR) =>
% 24.53/6.36 ((
% 24.53/6.36 (kpairiskpair) =>
% 24.53/6.36 ((
% 24.53/6.36 (kpairp) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletonsubset) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletoninpowerset) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletoninpowunion) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairset2E) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairsubunion) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairinpowunion) =>
% 24.53/6.36 ((
% 24.53/6.36 (ubforcartprodlem1) =>
% 24.53/6.36 ((
% 24.53/6.36 (ubforcartprodlem2) =>
% 24.53/6.36 ((
% 24.53/6.36 (ubforcartprodlem3) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodpairin) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodmempair1) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodmempair) =>
% 24.53/6.36 ((
% 24.53/6.36 (setunionE2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setunionsingleton1) =>
% 24.53/6.36 ((
% 24.53/6.36 (setunionsingleton2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setunionsingleton) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletonprop) =>
% 24.53/6.36 ((
% 24.53/6.36 (ex1E1) =>
% 24.53/6.36 ((
% 24.53/6.36 (ex1I) =>
% 24.53/6.36 ((
% 24.53/6.36 (ex1I2) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletonsuniq) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjL1) =>
% 24.53/6.36 ((
% 24.53/6.36 (kfstsingleton) =>
% 24.53/6.36 ((
% 24.53/6.36 (theprop) =>
% 24.53/6.36 ((
% 24.53/6.36 (kfstpairEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodfstin) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjL2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjL) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR11) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR12) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR1) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairequniteq) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR) =>
% 24.53/6.36 ((
% 24.53/6.36 (ksndsingleton) =>
% 24.53/6.36 ((
% 24.53/6.36 (ksndpairEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (kpairsurjEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodsndin) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodpairmemEL) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodpairmemER) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodmempaircEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodfstpairEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodsndpairEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodpairsurjEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (dpsetconstrI) =>
% 24.53/6.36 ((
% 24.53/6.36 (!!) @ (
% 24.53/6.36 (('#B') @ (
% 24.53/6.36 !!) @
% 24.53/6.36 (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 !!))) @
% 24.53/6.36 (
% 24.53/6.36 (
% 24.53/6.36 ('#S') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 '#S') @
% 24.53/6.36 (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 '#C'))) @
% 24.53/6.36 (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ subset)))) @
% 24.53/6.36 dpsetconstr)))))) @
% 24.53/6.36 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl507])).
% 24.53/6.36 thf(zip_derived_cl528, plain,
% 24.53/6.36 (~ (((vacuousDall) =>
% 24.53/6.36 (((quantDeMorgan1) =>
% 24.53/6.36 (((quantDeMorgan2) =>
% 24.53/6.36 (((quantDeMorgan3) =>
% 24.53/6.36 (((quantDeMorgan4) =>
% 24.53/6.36 (((prop2setI) =>
% 24.53/6.36 (((prop2set2propI) =>
% 24.53/6.36 (((notdexE) =>
% 24.53/6.36 (((notdallE) =>
% 24.53/6.36 (((exuI1) =>
% 24.53/6.36 (((exuI3) =>
% 24.53/6.36 (((exuI2) =>
% 24.53/6.36 (((inCongP) =>
% 24.53/6.36 (((in__Cong) =>
% 24.53/6.36 (((exuE3u) =>
% 24.53/6.36 (((exu__Cong) =>
% 24.53/6.36 (((setadjoin__Cong) =>
% 24.53/6.36 (((powerset__Cong) =>
% 24.53/6.36 (((setunion__Cong) =>
% 24.53/6.36 (((exuEu) =>
% 24.53/6.36 (((descr__Cong) =>
% 24.53/6.36 (((dsetconstr__Cong) =>
% 24.53/6.36 (((subsetI1) =>
% 24.53/6.36 (((eqimpsubset2) =>
% 24.53/6.36 (((eqimpsubset1) =>
% 24.53/6.36 (((subsetI2) =>
% 24.53/6.36 (((emptysetsubset) =>
% 24.53/6.36 (((subsetE) =>
% 24.53/6.36 (((subsetE2) =>
% 24.53/6.36 (((notsubsetI) =>
% 24.53/6.36 ((
% 24.53/6.36 (notequalI1) =>
% 24.53/6.36 ((
% 24.53/6.36 (notequalI2) =>
% 24.53/6.36 ((
% 24.53/6.36 (subsetRefl) =>
% 24.53/6.36 ((
% 24.53/6.36 (subsetTrans) =>
% 24.53/6.36 ((
% 24.53/6.36 (setadjoinSub) =>
% 24.53/6.36 ((
% 24.53/6.36 (setadjoinSub2) =>
% 24.53/6.36 ((
% 24.53/6.36 (subset2powerset) =>
% 24.53/6.36 ((
% 24.53/6.36 (setextsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (subsetemptysetimpeq) =>
% 24.53/6.36 ((
% 24.53/6.36 (powersetI1) =>
% 24.53/6.36 ((
% 24.53/6.36 (powersetE1) =>
% 24.53/6.36 ((
% 24.53/6.36 (inPowerset) =>
% 24.53/6.36 ((
% 24.53/6.36 (powersetsubset) =>
% 24.53/6.36 ((
% 24.53/6.36 (sepInPowerset) =>
% 24.53/6.36 ((
% 24.53/6.36 (sepSubset) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionIL) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairset2IR) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionIR) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionEcases) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionE) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionLsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionRsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectI) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset5) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectEL) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectLsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset2) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset3) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectER) =>
% 24.53/6.36 ((
% 24.53/6.36 (disjointsetsI1) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectRsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset4) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset1) =>
% 24.53/6.36 ((
% 24.53/6.36 (bs114d) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusI) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusEL) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusER) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusSubset2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusERneg) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusELneg) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusILneg) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusIRneg) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusLsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusSubset1) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffE) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffI1) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffI2) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffIneg1) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffIneg2) =>
% 24.53/6.36 ((
% 24.53/6.36 (secondinupair) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairIL) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairIR) =>
% 24.53/6.36 ((
% 24.53/6.36 (kpairiskpair) =>
% 24.53/6.36 ((
% 24.53/6.36 (kpairp) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletonsubset) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletoninpowerset) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletoninpowunion) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairset2E) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairsubunion) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairinpowunion) =>
% 24.53/6.36 ((
% 24.53/6.36 (ubforcartprodlem1) =>
% 24.53/6.36 ((
% 24.53/6.36 (ubforcartprodlem2) =>
% 24.53/6.36 ((
% 24.53/6.36 (ubforcartprodlem3) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodpairin) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodmempair1) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodmempair) =>
% 24.53/6.36 ((
% 24.53/6.36 (setunionE2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setunionsingleton1) =>
% 24.53/6.36 ((
% 24.53/6.36 (setunionsingleton2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setunionsingleton) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletonprop) =>
% 24.53/6.36 ((
% 24.53/6.36 (ex1E1) =>
% 24.53/6.36 ((
% 24.53/6.36 (ex1I) =>
% 24.53/6.36 ((
% 24.53/6.36 (ex1I2) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletonsuniq) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjL1) =>
% 24.53/6.36 ((
% 24.53/6.36 (kfstsingleton) =>
% 24.53/6.36 ((
% 24.53/6.36 (theprop) =>
% 24.53/6.36 ((
% 24.53/6.36 (kfstpairEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodfstin) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjL2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjL) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR11) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR12) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR1) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairequniteq) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR) =>
% 24.53/6.36 ((
% 24.53/6.36 (ksndsingleton) =>
% 24.53/6.36 ((
% 24.53/6.36 (ksndpairEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (kpairsurjEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodsndin) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodpairmemEL) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodpairmemER) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodmempaircEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodfstpairEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodsndpairEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodpairsurjEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (dpsetconstrI) =>
% 24.53/6.36 ((
% 24.53/6.36 (!!) @ (
% 24.53/6.36 (('#B') @ (
% 24.53/6.36 !!) @
% 24.53/6.36 (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 !!))) @
% 24.53/6.36 (
% 24.53/6.36 (
% 24.53/6.36 ('#S') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 '#S') @
% 24.53/6.36 (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 '#C'))) @
% 24.53/6.36 (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ subset)))) @
% 24.53/6.36 dpsetconstr)))))) @
% 24.53/6.36 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl517])).
% 24.53/6.36 thf(zip_derived_cl537, plain,
% 24.53/6.36 (~ (((quantDeMorgan1) =>
% 24.53/6.36 (((quantDeMorgan2) =>
% 24.53/6.36 (((quantDeMorgan3) =>
% 24.53/6.36 (((quantDeMorgan4) =>
% 24.53/6.36 (((prop2setI) =>
% 24.53/6.36 (((prop2set2propI) =>
% 24.53/6.36 (((notdexE) =>
% 24.53/6.36 (((notdallE) =>
% 24.53/6.36 (((exuI1) =>
% 24.53/6.36 (((exuI3) =>
% 24.53/6.36 (((exuI2) =>
% 24.53/6.36 (((inCongP) =>
% 24.53/6.36 (((in__Cong) =>
% 24.53/6.36 (((exuE3u) =>
% 24.53/6.36 (((exu__Cong) =>
% 24.53/6.36 (((setadjoin__Cong) =>
% 24.53/6.36 (((powerset__Cong) =>
% 24.53/6.36 (((setunion__Cong) =>
% 24.53/6.36 (((exuEu) =>
% 24.53/6.36 (((descr__Cong) =>
% 24.53/6.36 (((dsetconstr__Cong) =>
% 24.53/6.36 (((subsetI1) =>
% 24.53/6.36 (((eqimpsubset2) =>
% 24.53/6.36 (((eqimpsubset1) =>
% 24.53/6.36 (((subsetI2) =>
% 24.53/6.36 (((emptysetsubset) =>
% 24.53/6.36 (((subsetE) =>
% 24.53/6.36 (((subsetE2) =>
% 24.53/6.36 (((notsubsetI) =>
% 24.53/6.36 (((notequalI1) =>
% 24.53/6.36 ((
% 24.53/6.36 (notequalI2) =>
% 24.53/6.36 ((
% 24.53/6.36 (subsetRefl) =>
% 24.53/6.36 ((
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% 24.53/6.36 ((
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% 24.53/6.36 ((
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% 24.53/6.36 ((
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% 24.53/6.36 ((
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% 24.53/6.36 ((
% 24.53/6.36 (subsetemptysetimpeq) =>
% 24.53/6.36 ((
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% 24.53/6.36 ((
% 24.53/6.36 (powersetE1) =>
% 24.53/6.36 ((
% 24.53/6.36 (inPowerset) =>
% 24.53/6.36 ((
% 24.53/6.36 (powersetsubset) =>
% 24.53/6.36 ((
% 24.53/6.36 (sepInPowerset) =>
% 24.53/6.36 ((
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% 24.53/6.36 ((
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% 24.53/6.36 ((
% 24.53/6.36 (upairset2IR) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionIR) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionEcases) =>
% 24.53/6.36 ((
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% 24.53/6.36 ((
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% 24.53/6.36 ((
% 24.53/6.36 (binunionRsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectI) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset5) =>
% 24.53/6.36 ((
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% 24.53/6.36 ((
% 24.53/6.36 (binintersectLsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset2) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset3) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectER) =>
% 24.53/6.36 ((
% 24.53/6.36 (disjointsetsI1) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectRsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset4) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset1) =>
% 24.53/6.36 ((
% 24.53/6.36 (bs114d) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusI) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusEL) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusER) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusSubset2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusERneg) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusELneg) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusILneg) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusIRneg) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusLsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusSubset1) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffE) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffI1) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffI2) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffIneg1) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffIneg2) =>
% 24.53/6.36 ((
% 24.53/6.36 (secondinupair) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairIL) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairIR) =>
% 24.53/6.36 ((
% 24.53/6.36 (kpairiskpair) =>
% 24.53/6.36 ((
% 24.53/6.36 (kpairp) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletonsubset) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletoninpowerset) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletoninpowunion) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairset2E) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairsubunion) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairinpowunion) =>
% 24.53/6.36 ((
% 24.53/6.36 (ubforcartprodlem1) =>
% 24.53/6.36 ((
% 24.53/6.36 (ubforcartprodlem2) =>
% 24.53/6.36 ((
% 24.53/6.36 (ubforcartprodlem3) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodpairin) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodmempair1) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodmempair) =>
% 24.53/6.36 ((
% 24.53/6.36 (setunionE2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setunionsingleton1) =>
% 24.53/6.36 ((
% 24.53/6.36 (setunionsingleton2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setunionsingleton) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletonprop) =>
% 24.53/6.36 ((
% 24.53/6.36 (ex1E1) =>
% 24.53/6.36 ((
% 24.53/6.36 (ex1I) =>
% 24.53/6.36 ((
% 24.53/6.36 (ex1I2) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletonsuniq) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjL1) =>
% 24.53/6.36 ((
% 24.53/6.36 (kfstsingleton) =>
% 24.53/6.36 ((
% 24.53/6.36 (theprop) =>
% 24.53/6.36 ((
% 24.53/6.36 (kfstpairEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodfstin) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjL2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjL) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR11) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR12) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR1) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairequniteq) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR) =>
% 24.53/6.36 ((
% 24.53/6.36 (ksndsingleton) =>
% 24.53/6.36 ((
% 24.53/6.36 (ksndpairEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (kpairsurjEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodsndin) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodpairmemEL) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodpairmemER) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodmempaircEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodfstpairEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodsndpairEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodpairsurjEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (dpsetconstrI) =>
% 24.53/6.36 ((
% 24.53/6.36 (!!) @ (
% 24.53/6.36 (('#B') @ (
% 24.53/6.36 !!) @
% 24.53/6.36 (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 !!))) @
% 24.53/6.36 (
% 24.53/6.36 (
% 24.53/6.36 ('#S') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 '#S') @
% 24.53/6.36 (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 '#C'))) @
% 24.53/6.36 (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ subset)))) @
% 24.53/6.36 dpsetconstr)))))) @
% 24.53/6.36 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl528])).
% 24.53/6.36 thf(zip_derived_cl546, plain,
% 24.53/6.36 (~ (((quantDeMorgan2) =>
% 24.53/6.36 (((quantDeMorgan3) =>
% 24.53/6.36 (((quantDeMorgan4) =>
% 24.53/6.36 (((prop2setI) =>
% 24.53/6.36 (((prop2set2propI) =>
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% 24.53/6.36 (((notdallE) =>
% 24.53/6.36 (((exuI1) =>
% 24.53/6.36 (((exuI3) =>
% 24.53/6.36 (((exuI2) =>
% 24.53/6.36 (((inCongP) =>
% 24.53/6.36 (((in__Cong) =>
% 24.53/6.36 (((exuE3u) =>
% 24.53/6.36 (((exu__Cong) =>
% 24.53/6.36 (((setadjoin__Cong) =>
% 24.53/6.36 (((powerset__Cong) =>
% 24.53/6.36 (((setunion__Cong) =>
% 24.53/6.36 (((exuEu) =>
% 24.53/6.36 (((descr__Cong) =>
% 24.53/6.36 (((dsetconstr__Cong) =>
% 24.53/6.36 (((subsetI1) =>
% 24.53/6.36 (((eqimpsubset2) =>
% 24.53/6.36 (((eqimpsubset1) =>
% 24.53/6.36 (((subsetI2) =>
% 24.53/6.36 (((emptysetsubset) =>
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% 24.53/6.36 (((subsetE2) =>
% 24.53/6.36 (((notsubsetI) =>
% 24.53/6.36 (((notequalI1) =>
% 24.53/6.36 (((notequalI2) =>
% 24.53/6.36 ((
% 24.53/6.36 (subsetRefl) =>
% 24.53/6.36 ((
% 24.53/6.36 (subsetTrans) =>
% 24.53/6.36 ((
% 24.53/6.36 (setadjoinSub) =>
% 24.53/6.36 ((
% 24.53/6.36 (setadjoinSub2) =>
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% 24.53/6.36 ((
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% 24.53/6.36 ((
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% 24.53/6.36 ((
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% 24.53/6.36 ((
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% 24.53/6.36 ((
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% 24.53/6.36 ((
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% 24.53/6.36 ((
% 24.53/6.36 (binunionRsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectI) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset5) =>
% 24.53/6.36 ((
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% 24.53/6.36 ((
% 24.53/6.36 (binintersectLsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset2) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset3) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectER) =>
% 24.53/6.36 ((
% 24.53/6.36 (disjointsetsI1) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectRsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset4) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset1) =>
% 24.53/6.36 ((
% 24.53/6.36 (bs114d) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusI) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusEL) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusER) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusSubset2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusERneg) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusELneg) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusILneg) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusIRneg) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusLsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusSubset1) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffE) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffI1) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffI2) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffIneg1) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffIneg2) =>
% 24.53/6.36 ((
% 24.53/6.36 (secondinupair) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairIL) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairIR) =>
% 24.53/6.36 ((
% 24.53/6.36 (kpairiskpair) =>
% 24.53/6.36 ((
% 24.53/6.36 (kpairp) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletonsubset) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletoninpowerset) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletoninpowunion) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairset2E) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairsubunion) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairinpowunion) =>
% 24.53/6.36 ((
% 24.53/6.36 (ubforcartprodlem1) =>
% 24.53/6.36 ((
% 24.53/6.36 (ubforcartprodlem2) =>
% 24.53/6.36 ((
% 24.53/6.36 (ubforcartprodlem3) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodpairin) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodmempair1) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodmempair) =>
% 24.53/6.36 ((
% 24.53/6.36 (setunionE2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setunionsingleton1) =>
% 24.53/6.36 ((
% 24.53/6.36 (setunionsingleton2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setunionsingleton) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletonprop) =>
% 24.53/6.36 ((
% 24.53/6.36 (ex1E1) =>
% 24.53/6.36 ((
% 24.53/6.36 (ex1I) =>
% 24.53/6.36 ((
% 24.53/6.36 (ex1I2) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletonsuniq) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjL1) =>
% 24.53/6.36 ((
% 24.53/6.36 (kfstsingleton) =>
% 24.53/6.36 ((
% 24.53/6.36 (theprop) =>
% 24.53/6.36 ((
% 24.53/6.36 (kfstpairEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodfstin) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjL2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjL) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR11) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR12) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR1) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairequniteq) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairinjR) =>
% 24.53/6.36 ((
% 24.53/6.36 (ksndsingleton) =>
% 24.53/6.36 ((
% 24.53/6.36 (ksndpairEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (kpairsurjEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodsndin) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodpairmemEL) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodpairmemER) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodmempaircEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodfstpairEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodsndpairEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodpairsurjEq) =>
% 24.53/6.36 ((
% 24.53/6.36 (dpsetconstrI) =>
% 24.53/6.36 ((
% 24.53/6.36 (!!) @ (
% 24.53/6.36 (('#B') @ (
% 24.53/6.36 !!) @
% 24.53/6.36 (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
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% 24.53/6.36 (
% 24.53/6.36 (
% 24.53/6.36 ('#S') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 '#S') @
% 24.53/6.36 (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 '#C'))) @
% 24.53/6.36 (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ (
% 24.53/6.36 (
% 24.53/6.36 ('#B') @ subset)))) @
% 24.53/6.36 dpsetconstr)))))) @
% 24.53/6.36 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.36 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl537])).
% 24.53/6.36 thf(zip_derived_cl553, plain,
% 24.53/6.36 (~ (((quantDeMorgan3) =>
% 24.53/6.36 (((quantDeMorgan4) =>
% 24.53/6.36 (((prop2setI) =>
% 24.53/6.36 (((prop2set2propI) =>
% 24.53/6.36 (((notdexE) =>
% 24.53/6.36 (((notdallE) =>
% 24.53/6.36 (((exuI1) =>
% 24.53/6.36 (((exuI3) =>
% 24.53/6.36 (((exuI2) =>
% 24.53/6.36 (((inCongP) =>
% 24.53/6.36 (((in__Cong) =>
% 24.53/6.36 (((exuE3u) =>
% 24.53/6.36 (((exu__Cong) =>
% 24.53/6.36 (((setadjoin__Cong) =>
% 24.53/6.36 (((powerset__Cong) =>
% 24.53/6.36 (((setunion__Cong) =>
% 24.53/6.36 (((exuEu) =>
% 24.53/6.36 (((descr__Cong) =>
% 24.53/6.36 (((dsetconstr__Cong) =>
% 24.53/6.36 (((subsetI1) =>
% 24.53/6.36 (((eqimpsubset2) =>
% 24.53/6.36 (((eqimpsubset1) =>
% 24.53/6.36 (((subsetI2) =>
% 24.53/6.36 (((emptysetsubset) =>
% 24.53/6.36 (((subsetE) =>
% 24.53/6.36 (((subsetE2) =>
% 24.53/6.36 (((notsubsetI) =>
% 24.53/6.36 (((notequalI1) =>
% 24.53/6.36 (((notequalI2) =>
% 24.53/6.36 (((subsetRefl) =>
% 24.53/6.36 ((
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% 24.53/6.36 ((
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% 24.53/6.36 ((
% 24.53/6.36 (setadjoinSub2) =>
% 24.53/6.36 ((
% 24.53/6.36 (subset2powerset) =>
% 24.53/6.36 ((
% 24.53/6.36 (setextsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (subsetemptysetimpeq) =>
% 24.53/6.36 ((
% 24.53/6.36 (powersetI1) =>
% 24.53/6.36 ((
% 24.53/6.36 (powersetE1) =>
% 24.53/6.36 ((
% 24.53/6.36 (inPowerset) =>
% 24.53/6.36 ((
% 24.53/6.36 (powersetsubset) =>
% 24.53/6.36 ((
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% 24.53/6.36 ((
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% 24.53/6.36 ((
% 24.53/6.36 (upairset2IR) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionIR) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionEcases) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionE) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionLsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (binunionRsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectI) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset5) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectEL) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectLsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset2) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset3) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectER) =>
% 24.53/6.36 ((
% 24.53/6.36 (disjointsetsI1) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectRsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset4) =>
% 24.53/6.36 ((
% 24.53/6.36 (binintersectSubset1) =>
% 24.53/6.36 ((
% 24.53/6.36 (bs114d) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusI) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusEL) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusER) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusSubset2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusERneg) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusELneg) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusILneg) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusIRneg) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusLsub) =>
% 24.53/6.36 ((
% 24.53/6.36 (setminusSubset1) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffE) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffI1) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffI2) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffIneg1) =>
% 24.53/6.36 ((
% 24.53/6.36 (symdiffIneg2) =>
% 24.53/6.36 ((
% 24.53/6.36 (secondinupair) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairIL) =>
% 24.53/6.36 ((
% 24.53/6.36 (setukpairIR) =>
% 24.53/6.36 ((
% 24.53/6.36 (kpairiskpair) =>
% 24.53/6.36 ((
% 24.53/6.36 (kpairp) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletonsubset) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletoninpowerset) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletoninpowunion) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairset2E) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairsubunion) =>
% 24.53/6.36 ((
% 24.53/6.36 (upairinpowunion) =>
% 24.53/6.36 ((
% 24.53/6.36 (ubforcartprodlem1) =>
% 24.53/6.36 ((
% 24.53/6.36 (ubforcartprodlem2) =>
% 24.53/6.36 ((
% 24.53/6.36 (ubforcartprodlem3) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodpairin) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodmempair1) =>
% 24.53/6.36 ((
% 24.53/6.36 (cartprodmempair) =>
% 24.53/6.36 ((
% 24.53/6.36 (setunionE2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setunionsingleton1) =>
% 24.53/6.36 ((
% 24.53/6.36 (setunionsingleton2) =>
% 24.53/6.36 ((
% 24.53/6.36 (setunionsingleton) =>
% 24.53/6.36 ((
% 24.53/6.36 (singletonprop) =>
% 24.53/6.36 ((
% 24.53/6.36 (ex1E1) =>
% 24.53/6.36 ((
% 24.53/6.36 (ex1I) =>
% 24.53/6.36 ((
% 24.53/6.36 (ex1I2) =>
% 24.53/6.37 ((
% 24.53/6.37 (singletonsuniq) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjL1) =>
% 24.53/6.37 ((
% 24.53/6.37 (kfstsingleton) =>
% 24.53/6.37 ((
% 24.53/6.37 (theprop) =>
% 24.53/6.37 ((
% 24.53/6.37 (kfstpairEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodfstin) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjL2) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjL) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjR11) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjR12) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjR1) =>
% 24.53/6.37 ((
% 24.53/6.37 (upairequniteq) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjR2) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjR) =>
% 24.53/6.37 ((
% 24.53/6.37 (ksndsingleton) =>
% 24.53/6.37 ((
% 24.53/6.37 (ksndpairEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (kpairsurjEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodsndin) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodpairmemEL) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodpairmemER) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodmempaircEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodfstpairEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodsndpairEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodpairsurjEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (dpsetconstrI) =>
% 24.53/6.37 ((
% 24.53/6.37 (!!) @ (
% 24.53/6.37 (('#B') @ (
% 24.53/6.37 !!) @
% 24.53/6.37 (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 !!))) @
% 24.53/6.37 (
% 24.53/6.37 (
% 24.53/6.37 ('#S') @ (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 '#S') @
% 24.53/6.37 (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 '#C'))) @
% 24.53/6.37 (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ subset)))) @
% 24.53/6.37 dpsetconstr)))))) @
% 24.53/6.37 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.37 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl546])).
% 24.53/6.37 thf(zip_derived_cl561, plain,
% 24.53/6.37 (~ (((quantDeMorgan4) =>
% 24.53/6.37 (((prop2setI) =>
% 24.53/6.37 (((prop2set2propI) =>
% 24.53/6.37 (((notdexE) =>
% 24.53/6.37 (((notdallE) =>
% 24.53/6.37 (((exuI1) =>
% 24.53/6.37 (((exuI3) =>
% 24.53/6.37 (((exuI2) =>
% 24.53/6.37 (((inCongP) =>
% 24.53/6.37 (((in__Cong) =>
% 24.53/6.37 (((exuE3u) =>
% 24.53/6.37 (((exu__Cong) =>
% 24.53/6.37 (((setadjoin__Cong) =>
% 24.53/6.37 (((powerset__Cong) =>
% 24.53/6.37 (((setunion__Cong) =>
% 24.53/6.37 (((exuEu) =>
% 24.53/6.37 (((descr__Cong) =>
% 24.53/6.37 (((dsetconstr__Cong) =>
% 24.53/6.37 (((subsetI1) =>
% 24.53/6.37 (((eqimpsubset2) =>
% 24.53/6.37 (((eqimpsubset1) =>
% 24.53/6.37 (((subsetI2) =>
% 24.53/6.37 (((emptysetsubset) =>
% 24.53/6.37 (((subsetE) =>
% 24.53/6.37 (((subsetE2) =>
% 24.53/6.37 (((notsubsetI) =>
% 24.53/6.37 (((notequalI1) =>
% 24.53/6.37 (((notequalI2) =>
% 24.53/6.37 (((subsetRefl) =>
% 24.53/6.37 (((subsetTrans) =>
% 24.53/6.37 ((
% 24.53/6.37 (setadjoinSub) =>
% 24.53/6.37 ((
% 24.53/6.37 (setadjoinSub2) =>
% 24.53/6.37 ((
% 24.53/6.37 (subset2powerset) =>
% 24.53/6.37 ((
% 24.53/6.37 (setextsub) =>
% 24.53/6.37 ((
% 24.53/6.37 (subsetemptysetimpeq) =>
% 24.53/6.37 ((
% 24.53/6.37 (powersetI1) =>
% 24.53/6.37 ((
% 24.53/6.37 (powersetE1) =>
% 24.53/6.37 ((
% 24.53/6.37 (inPowerset) =>
% 24.53/6.37 ((
% 24.53/6.37 (powersetsubset) =>
% 24.53/6.37 ((
% 24.53/6.37 (sepInPowerset) =>
% 24.53/6.37 ((
% 24.53/6.37 (sepSubset) =>
% 24.53/6.37 ((
% 24.53/6.37 (binunionIL) =>
% 24.53/6.37 ((
% 24.53/6.37 (upairset2IR) =>
% 24.53/6.37 ((
% 24.53/6.37 (binunionIR) =>
% 24.53/6.37 ((
% 24.53/6.37 (binunionEcases) =>
% 24.53/6.37 ((
% 24.53/6.37 (binunionE) =>
% 24.53/6.37 ((
% 24.53/6.37 (binunionLsub) =>
% 24.53/6.37 ((
% 24.53/6.37 (binunionRsub) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectI) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectSubset5) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectEL) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectLsub) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectSubset2) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectSubset3) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectER) =>
% 24.53/6.37 ((
% 24.53/6.37 (disjointsetsI1) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectRsub) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectSubset4) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectSubset1) =>
% 24.53/6.37 ((
% 24.53/6.37 (bs114d) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusI) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusEL) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusER) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusSubset2) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusERneg) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusELneg) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusILneg) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusIRneg) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusLsub) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusSubset1) =>
% 24.53/6.37 ((
% 24.53/6.37 (symdiffE) =>
% 24.53/6.37 ((
% 24.53/6.37 (symdiffI1) =>
% 24.53/6.37 ((
% 24.53/6.37 (symdiffI2) =>
% 24.53/6.37 ((
% 24.53/6.37 (symdiffIneg1) =>
% 24.53/6.37 ((
% 24.53/6.37 (symdiffIneg2) =>
% 24.53/6.37 ((
% 24.53/6.37 (secondinupair) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairIL) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairIR) =>
% 24.53/6.37 ((
% 24.53/6.37 (kpairiskpair) =>
% 24.53/6.37 ((
% 24.53/6.37 (kpairp) =>
% 24.53/6.37 ((
% 24.53/6.37 (singletonsubset) =>
% 24.53/6.37 ((
% 24.53/6.37 (singletoninpowerset) =>
% 24.53/6.37 ((
% 24.53/6.37 (singletoninpowunion) =>
% 24.53/6.37 ((
% 24.53/6.37 (upairset2E) =>
% 24.53/6.37 ((
% 24.53/6.37 (upairsubunion) =>
% 24.53/6.37 ((
% 24.53/6.37 (upairinpowunion) =>
% 24.53/6.37 ((
% 24.53/6.37 (ubforcartprodlem1) =>
% 24.53/6.37 ((
% 24.53/6.37 (ubforcartprodlem2) =>
% 24.53/6.37 ((
% 24.53/6.37 (ubforcartprodlem3) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodpairin) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodmempair1) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodmempair) =>
% 24.53/6.37 ((
% 24.53/6.37 (setunionE2) =>
% 24.53/6.37 ((
% 24.53/6.37 (setunionsingleton1) =>
% 24.53/6.37 ((
% 24.53/6.37 (setunionsingleton2) =>
% 24.53/6.37 ((
% 24.53/6.37 (setunionsingleton) =>
% 24.53/6.37 ((
% 24.53/6.37 (singletonprop) =>
% 24.53/6.37 ((
% 24.53/6.37 (ex1E1) =>
% 24.53/6.37 ((
% 24.53/6.37 (ex1I) =>
% 24.53/6.37 ((
% 24.53/6.37 (ex1I2) =>
% 24.53/6.37 ((
% 24.53/6.37 (singletonsuniq) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjL1) =>
% 24.53/6.37 ((
% 24.53/6.37 (kfstsingleton) =>
% 24.53/6.37 ((
% 24.53/6.37 (theprop) =>
% 24.53/6.37 ((
% 24.53/6.37 (kfstpairEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodfstin) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjL2) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjL) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjR11) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjR12) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjR1) =>
% 24.53/6.37 ((
% 24.53/6.37 (upairequniteq) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjR2) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjR) =>
% 24.53/6.37 ((
% 24.53/6.37 (ksndsingleton) =>
% 24.53/6.37 ((
% 24.53/6.37 (ksndpairEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (kpairsurjEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodsndin) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodpairmemEL) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodpairmemER) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodmempaircEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodfstpairEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodsndpairEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodpairsurjEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (dpsetconstrI) =>
% 24.53/6.37 ((
% 24.53/6.37 (!!) @ (
% 24.53/6.37 (('#B') @ (
% 24.53/6.37 !!) @
% 24.53/6.37 (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 !!))) @
% 24.53/6.37 (
% 24.53/6.37 (
% 24.53/6.37 ('#S') @ (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 '#S') @
% 24.53/6.37 (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 '#C'))) @
% 24.53/6.37 (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ subset)))) @
% 24.53/6.37 dpsetconstr)))))) @
% 24.53/6.37 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.37 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl553])).
% 24.53/6.37 thf(zip_derived_cl570, plain,
% 24.53/6.37 (~ (((prop2setI) =>
% 24.53/6.37 (((prop2set2propI) =>
% 24.53/6.37 (((notdexE) =>
% 24.53/6.37 (((notdallE) =>
% 24.53/6.37 (((exuI1) =>
% 24.53/6.37 (((exuI3) =>
% 24.53/6.37 (((exuI2) =>
% 24.53/6.37 (((inCongP) =>
% 24.53/6.37 (((in__Cong) =>
% 24.53/6.37 (((exuE3u) =>
% 24.53/6.37 (((exu__Cong) =>
% 24.53/6.37 (((setadjoin__Cong) =>
% 24.53/6.37 (((powerset__Cong) =>
% 24.53/6.37 (((setunion__Cong) =>
% 24.53/6.37 (((exuEu) =>
% 24.53/6.37 (((descr__Cong) =>
% 24.53/6.37 (((dsetconstr__Cong) =>
% 24.53/6.37 (((subsetI1) =>
% 24.53/6.37 (((eqimpsubset2) =>
% 24.53/6.37 (((eqimpsubset1) =>
% 24.53/6.37 (((subsetI2) =>
% 24.53/6.37 (((emptysetsubset) =>
% 24.53/6.37 (((subsetE) =>
% 24.53/6.37 (((subsetE2) =>
% 24.53/6.37 (((notsubsetI) =>
% 24.53/6.37 (((notequalI1) =>
% 24.53/6.37 (((notequalI2) =>
% 24.53/6.37 (((subsetRefl) =>
% 24.53/6.37 (((subsetTrans) =>
% 24.53/6.37 (((setadjoinSub) =>
% 24.53/6.37 ((
% 24.53/6.37 (setadjoinSub2) =>
% 24.53/6.37 ((
% 24.53/6.37 (subset2powerset) =>
% 24.53/6.37 ((
% 24.53/6.37 (setextsub) =>
% 24.53/6.37 ((
% 24.53/6.37 (subsetemptysetimpeq) =>
% 24.53/6.37 ((
% 24.53/6.37 (powersetI1) =>
% 24.53/6.37 ((
% 24.53/6.37 (powersetE1) =>
% 24.53/6.37 ((
% 24.53/6.37 (inPowerset) =>
% 24.53/6.37 ((
% 24.53/6.37 (powersetsubset) =>
% 24.53/6.37 ((
% 24.53/6.37 (sepInPowerset) =>
% 24.53/6.37 ((
% 24.53/6.37 (sepSubset) =>
% 24.53/6.37 ((
% 24.53/6.37 (binunionIL) =>
% 24.53/6.37 ((
% 24.53/6.37 (upairset2IR) =>
% 24.53/6.37 ((
% 24.53/6.37 (binunionIR) =>
% 24.53/6.37 ((
% 24.53/6.37 (binunionEcases) =>
% 24.53/6.37 ((
% 24.53/6.37 (binunionE) =>
% 24.53/6.37 ((
% 24.53/6.37 (binunionLsub) =>
% 24.53/6.37 ((
% 24.53/6.37 (binunionRsub) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectI) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectSubset5) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectEL) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectLsub) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectSubset2) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectSubset3) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectER) =>
% 24.53/6.37 ((
% 24.53/6.37 (disjointsetsI1) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectRsub) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectSubset4) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectSubset1) =>
% 24.53/6.37 ((
% 24.53/6.37 (bs114d) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusI) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusEL) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusER) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusSubset2) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusERneg) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusELneg) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusILneg) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusIRneg) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusLsub) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusSubset1) =>
% 24.53/6.37 ((
% 24.53/6.37 (symdiffE) =>
% 24.53/6.37 ((
% 24.53/6.37 (symdiffI1) =>
% 24.53/6.37 ((
% 24.53/6.37 (symdiffI2) =>
% 24.53/6.37 ((
% 24.53/6.37 (symdiffIneg1) =>
% 24.53/6.37 ((
% 24.53/6.37 (symdiffIneg2) =>
% 24.53/6.37 ((
% 24.53/6.37 (secondinupair) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairIL) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairIR) =>
% 24.53/6.37 ((
% 24.53/6.37 (kpairiskpair) =>
% 24.53/6.37 ((
% 24.53/6.37 (kpairp) =>
% 24.53/6.37 ((
% 24.53/6.37 (singletonsubset) =>
% 24.53/6.37 ((
% 24.53/6.37 (singletoninpowerset) =>
% 24.53/6.37 ((
% 24.53/6.37 (singletoninpowunion) =>
% 24.53/6.37 ((
% 24.53/6.37 (upairset2E) =>
% 24.53/6.37 ((
% 24.53/6.37 (upairsubunion) =>
% 24.53/6.37 ((
% 24.53/6.37 (upairinpowunion) =>
% 24.53/6.37 ((
% 24.53/6.37 (ubforcartprodlem1) =>
% 24.53/6.37 ((
% 24.53/6.37 (ubforcartprodlem2) =>
% 24.53/6.37 ((
% 24.53/6.37 (ubforcartprodlem3) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodpairin) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodmempair1) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodmempair) =>
% 24.53/6.37 ((
% 24.53/6.37 (setunionE2) =>
% 24.53/6.37 ((
% 24.53/6.37 (setunionsingleton1) =>
% 24.53/6.37 ((
% 24.53/6.37 (setunionsingleton2) =>
% 24.53/6.37 ((
% 24.53/6.37 (setunionsingleton) =>
% 24.53/6.37 ((
% 24.53/6.37 (singletonprop) =>
% 24.53/6.37 ((
% 24.53/6.37 (ex1E1) =>
% 24.53/6.37 ((
% 24.53/6.37 (ex1I) =>
% 24.53/6.37 ((
% 24.53/6.37 (ex1I2) =>
% 24.53/6.37 ((
% 24.53/6.37 (singletonsuniq) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjL1) =>
% 24.53/6.37 ((
% 24.53/6.37 (kfstsingleton) =>
% 24.53/6.37 ((
% 24.53/6.37 (theprop) =>
% 24.53/6.37 ((
% 24.53/6.37 (kfstpairEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodfstin) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjL2) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjL) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjR11) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjR12) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjR1) =>
% 24.53/6.37 ((
% 24.53/6.37 (upairequniteq) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjR2) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjR) =>
% 24.53/6.37 ((
% 24.53/6.37 (ksndsingleton) =>
% 24.53/6.37 ((
% 24.53/6.37 (ksndpairEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (kpairsurjEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodsndin) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodpairmemEL) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodpairmemER) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodmempaircEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodfstpairEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodsndpairEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodpairsurjEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (dpsetconstrI) =>
% 24.53/6.37 ((
% 24.53/6.37 (!!) @ (
% 24.53/6.37 (('#B') @ (
% 24.53/6.37 !!) @
% 24.53/6.37 (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 !!))) @
% 24.53/6.37 (
% 24.53/6.37 (
% 24.53/6.37 ('#S') @ (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 '#S') @
% 24.53/6.37 (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 '#C'))) @
% 24.53/6.37 (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ subset)))) @
% 24.53/6.37 dpsetconstr)))))) @
% 24.53/6.37 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.37 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl561])).
% 24.53/6.37 thf(zip_derived_cl578, plain,
% 24.53/6.37 (~ (((prop2set2propI) =>
% 24.53/6.37 (((notdexE) =>
% 24.53/6.37 (((notdallE) =>
% 24.53/6.37 (((exuI1) =>
% 24.53/6.37 (((exuI3) =>
% 24.53/6.37 (((exuI2) =>
% 24.53/6.37 (((inCongP) =>
% 24.53/6.37 (((in__Cong) =>
% 24.53/6.37 (((exuE3u) =>
% 24.53/6.37 (((exu__Cong) =>
% 24.53/6.37 (((setadjoin__Cong) =>
% 24.53/6.37 (((powerset__Cong) =>
% 24.53/6.37 (((setunion__Cong) =>
% 24.53/6.37 (((exuEu) =>
% 24.53/6.37 (((descr__Cong) =>
% 24.53/6.37 (((dsetconstr__Cong) =>
% 24.53/6.37 (((subsetI1) =>
% 24.53/6.37 (((eqimpsubset2) =>
% 24.53/6.37 (((eqimpsubset1) =>
% 24.53/6.37 (((subsetI2) =>
% 24.53/6.37 (((emptysetsubset) =>
% 24.53/6.37 (((subsetE) =>
% 24.53/6.37 (((subsetE2) =>
% 24.53/6.37 (((notsubsetI) =>
% 24.53/6.37 (((notequalI1) =>
% 24.53/6.37 (((notequalI2) =>
% 24.53/6.37 (((subsetRefl) =>
% 24.53/6.37 (((subsetTrans) =>
% 24.53/6.37 (((setadjoinSub) =>
% 24.53/6.37 (((setadjoinSub2) =>
% 24.53/6.37 ((
% 24.53/6.37 (subset2powerset) =>
% 24.53/6.37 ((
% 24.53/6.37 (setextsub) =>
% 24.53/6.37 ((
% 24.53/6.37 (subsetemptysetimpeq) =>
% 24.53/6.37 ((
% 24.53/6.37 (powersetI1) =>
% 24.53/6.37 ((
% 24.53/6.37 (powersetE1) =>
% 24.53/6.37 ((
% 24.53/6.37 (inPowerset) =>
% 24.53/6.37 ((
% 24.53/6.37 (powersetsubset) =>
% 24.53/6.37 ((
% 24.53/6.37 (sepInPowerset) =>
% 24.53/6.37 ((
% 24.53/6.37 (sepSubset) =>
% 24.53/6.37 ((
% 24.53/6.37 (binunionIL) =>
% 24.53/6.37 ((
% 24.53/6.37 (upairset2IR) =>
% 24.53/6.37 ((
% 24.53/6.37 (binunionIR) =>
% 24.53/6.37 ((
% 24.53/6.37 (binunionEcases) =>
% 24.53/6.37 ((
% 24.53/6.37 (binunionE) =>
% 24.53/6.37 ((
% 24.53/6.37 (binunionLsub) =>
% 24.53/6.37 ((
% 24.53/6.37 (binunionRsub) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectI) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectSubset5) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectEL) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectLsub) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectSubset2) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectSubset3) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectER) =>
% 24.53/6.37 ((
% 24.53/6.37 (disjointsetsI1) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectRsub) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectSubset4) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectSubset1) =>
% 24.53/6.37 ((
% 24.53/6.37 (bs114d) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusI) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusEL) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusER) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusSubset2) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusERneg) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusELneg) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusILneg) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusIRneg) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusLsub) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusSubset1) =>
% 24.53/6.37 ((
% 24.53/6.37 (symdiffE) =>
% 24.53/6.37 ((
% 24.53/6.37 (symdiffI1) =>
% 24.53/6.37 ((
% 24.53/6.37 (symdiffI2) =>
% 24.53/6.37 ((
% 24.53/6.37 (symdiffIneg1) =>
% 24.53/6.37 ((
% 24.53/6.37 (symdiffIneg2) =>
% 24.53/6.37 ((
% 24.53/6.37 (secondinupair) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairIL) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairIR) =>
% 24.53/6.37 ((
% 24.53/6.37 (kpairiskpair) =>
% 24.53/6.37 ((
% 24.53/6.37 (kpairp) =>
% 24.53/6.37 ((
% 24.53/6.37 (singletonsubset) =>
% 24.53/6.37 ((
% 24.53/6.37 (singletoninpowerset) =>
% 24.53/6.37 ((
% 24.53/6.37 (singletoninpowunion) =>
% 24.53/6.37 ((
% 24.53/6.37 (upairset2E) =>
% 24.53/6.37 ((
% 24.53/6.37 (upairsubunion) =>
% 24.53/6.37 ((
% 24.53/6.37 (upairinpowunion) =>
% 24.53/6.37 ((
% 24.53/6.37 (ubforcartprodlem1) =>
% 24.53/6.37 ((
% 24.53/6.37 (ubforcartprodlem2) =>
% 24.53/6.37 ((
% 24.53/6.37 (ubforcartprodlem3) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodpairin) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodmempair1) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodmempair) =>
% 24.53/6.37 ((
% 24.53/6.37 (setunionE2) =>
% 24.53/6.37 ((
% 24.53/6.37 (setunionsingleton1) =>
% 24.53/6.37 ((
% 24.53/6.37 (setunionsingleton2) =>
% 24.53/6.37 ((
% 24.53/6.37 (setunionsingleton) =>
% 24.53/6.37 ((
% 24.53/6.37 (singletonprop) =>
% 24.53/6.37 ((
% 24.53/6.37 (ex1E1) =>
% 24.53/6.37 ((
% 24.53/6.37 (ex1I) =>
% 24.53/6.37 ((
% 24.53/6.37 (ex1I2) =>
% 24.53/6.37 ((
% 24.53/6.37 (singletonsuniq) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjL1) =>
% 24.53/6.37 ((
% 24.53/6.37 (kfstsingleton) =>
% 24.53/6.37 ((
% 24.53/6.37 (theprop) =>
% 24.53/6.37 ((
% 24.53/6.37 (kfstpairEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodfstin) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjL2) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjL) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjR11) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjR12) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjR1) =>
% 24.53/6.37 ((
% 24.53/6.37 (upairequniteq) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjR2) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjR) =>
% 24.53/6.37 ((
% 24.53/6.37 (ksndsingleton) =>
% 24.53/6.37 ((
% 24.53/6.37 (ksndpairEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (kpairsurjEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodsndin) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodpairmemEL) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodpairmemER) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodmempaircEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodfstpairEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodsndpairEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodpairsurjEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (dpsetconstrI) =>
% 24.53/6.37 ((
% 24.53/6.37 (!!) @ (
% 24.53/6.37 (('#B') @ (
% 24.53/6.37 !!) @
% 24.53/6.37 (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 !!))) @
% 24.53/6.37 (
% 24.53/6.37 (
% 24.53/6.37 ('#S') @ (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 '#S') @
% 24.53/6.37 (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 '#C'))) @
% 24.53/6.37 (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ subset)))) @
% 24.53/6.37 dpsetconstr)))))) @
% 24.53/6.37 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.37 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl570])).
% 24.53/6.37 thf(zip_derived_cl586, plain,
% 24.53/6.37 (~ (((notdexE) =>
% 24.53/6.37 (((notdallE) =>
% 24.53/6.37 (((exuI1) =>
% 24.53/6.37 (((exuI3) =>
% 24.53/6.37 (((exuI2) =>
% 24.53/6.37 (((inCongP) =>
% 24.53/6.37 (((in__Cong) =>
% 24.53/6.37 (((exuE3u) =>
% 24.53/6.37 (((exu__Cong) =>
% 24.53/6.37 (((setadjoin__Cong) =>
% 24.53/6.37 (((powerset__Cong) =>
% 24.53/6.37 (((setunion__Cong) =>
% 24.53/6.37 (((exuEu) =>
% 24.53/6.37 (((descr__Cong) =>
% 24.53/6.37 (((dsetconstr__Cong) =>
% 24.53/6.37 (((subsetI1) =>
% 24.53/6.37 (((eqimpsubset2) =>
% 24.53/6.37 (((eqimpsubset1) =>
% 24.53/6.37 (((subsetI2) =>
% 24.53/6.37 (((emptysetsubset) =>
% 24.53/6.37 (((subsetE) =>
% 24.53/6.37 (((subsetE2) =>
% 24.53/6.37 (((notsubsetI) =>
% 24.53/6.37 (((notequalI1) =>
% 24.53/6.37 (((notequalI2) =>
% 24.53/6.37 (((subsetRefl) =>
% 24.53/6.37 (((subsetTrans) =>
% 24.53/6.37 (((setadjoinSub) =>
% 24.53/6.37 (((setadjoinSub2) =>
% 24.53/6.37 (((subset2powerset) =>
% 24.53/6.37 ((
% 24.53/6.37 (setextsub) =>
% 24.53/6.37 ((
% 24.53/6.37 (subsetemptysetimpeq) =>
% 24.53/6.37 ((
% 24.53/6.37 (powersetI1) =>
% 24.53/6.37 ((
% 24.53/6.37 (powersetE1) =>
% 24.53/6.37 ((
% 24.53/6.37 (inPowerset) =>
% 24.53/6.37 ((
% 24.53/6.37 (powersetsubset) =>
% 24.53/6.37 ((
% 24.53/6.37 (sepInPowerset) =>
% 24.53/6.37 ((
% 24.53/6.37 (sepSubset) =>
% 24.53/6.37 ((
% 24.53/6.37 (binunionIL) =>
% 24.53/6.37 ((
% 24.53/6.37 (upairset2IR) =>
% 24.53/6.37 ((
% 24.53/6.37 (binunionIR) =>
% 24.53/6.37 ((
% 24.53/6.37 (binunionEcases) =>
% 24.53/6.37 ((
% 24.53/6.37 (binunionE) =>
% 24.53/6.37 ((
% 24.53/6.37 (binunionLsub) =>
% 24.53/6.37 ((
% 24.53/6.37 (binunionRsub) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectI) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectSubset5) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectEL) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectLsub) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectSubset2) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectSubset3) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectER) =>
% 24.53/6.37 ((
% 24.53/6.37 (disjointsetsI1) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectRsub) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectSubset4) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectSubset1) =>
% 24.53/6.37 ((
% 24.53/6.37 (bs114d) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusI) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusEL) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusER) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusSubset2) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusERneg) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusELneg) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusILneg) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusIRneg) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusLsub) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusSubset1) =>
% 24.53/6.37 ((
% 24.53/6.37 (symdiffE) =>
% 24.53/6.37 ((
% 24.53/6.37 (symdiffI1) =>
% 24.53/6.37 ((
% 24.53/6.37 (symdiffI2) =>
% 24.53/6.37 ((
% 24.53/6.37 (symdiffIneg1) =>
% 24.53/6.37 ((
% 24.53/6.37 (symdiffIneg2) =>
% 24.53/6.37 ((
% 24.53/6.37 (secondinupair) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairIL) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairIR) =>
% 24.53/6.37 ((
% 24.53/6.37 (kpairiskpair) =>
% 24.53/6.37 ((
% 24.53/6.37 (kpairp) =>
% 24.53/6.37 ((
% 24.53/6.37 (singletonsubset) =>
% 24.53/6.37 ((
% 24.53/6.37 (singletoninpowerset) =>
% 24.53/6.37 ((
% 24.53/6.37 (singletoninpowunion) =>
% 24.53/6.37 ((
% 24.53/6.37 (upairset2E) =>
% 24.53/6.37 ((
% 24.53/6.37 (upairsubunion) =>
% 24.53/6.37 ((
% 24.53/6.37 (upairinpowunion) =>
% 24.53/6.37 ((
% 24.53/6.37 (ubforcartprodlem1) =>
% 24.53/6.37 ((
% 24.53/6.37 (ubforcartprodlem2) =>
% 24.53/6.37 ((
% 24.53/6.37 (ubforcartprodlem3) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodpairin) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodmempair1) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodmempair) =>
% 24.53/6.37 ((
% 24.53/6.37 (setunionE2) =>
% 24.53/6.37 ((
% 24.53/6.37 (setunionsingleton1) =>
% 24.53/6.37 ((
% 24.53/6.37 (setunionsingleton2) =>
% 24.53/6.37 ((
% 24.53/6.37 (setunionsingleton) =>
% 24.53/6.37 ((
% 24.53/6.37 (singletonprop) =>
% 24.53/6.37 ((
% 24.53/6.37 (ex1E1) =>
% 24.53/6.37 ((
% 24.53/6.37 (ex1I) =>
% 24.53/6.37 ((
% 24.53/6.37 (ex1I2) =>
% 24.53/6.37 ((
% 24.53/6.37 (singletonsuniq) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjL1) =>
% 24.53/6.37 ((
% 24.53/6.37 (kfstsingleton) =>
% 24.53/6.37 ((
% 24.53/6.37 (theprop) =>
% 24.53/6.37 ((
% 24.53/6.37 (kfstpairEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodfstin) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjL2) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjL) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjR11) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjR12) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjR1) =>
% 24.53/6.37 ((
% 24.53/6.37 (upairequniteq) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjR2) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjR) =>
% 24.53/6.37 ((
% 24.53/6.37 (ksndsingleton) =>
% 24.53/6.37 ((
% 24.53/6.37 (ksndpairEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (kpairsurjEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodsndin) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodpairmemEL) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodpairmemER) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodmempaircEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodfstpairEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodsndpairEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodpairsurjEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (dpsetconstrI) =>
% 24.53/6.37 ((
% 24.53/6.37 (!!) @ (
% 24.53/6.37 (('#B') @ (
% 24.53/6.37 !!) @
% 24.53/6.37 (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 !!))) @
% 24.53/6.37 (
% 24.53/6.37 (
% 24.53/6.37 ('#S') @ (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 '#S') @
% 24.53/6.37 (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 '#C'))) @
% 24.53/6.37 (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ subset)))) @
% 24.53/6.37 dpsetconstr)))))) @
% 24.53/6.37 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.37 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl578])).
% 24.53/6.37 thf(zip_derived_cl595, plain,
% 24.53/6.37 (~ (((notdallE) =>
% 24.53/6.37 (((exuI1) =>
% 24.53/6.37 (((exuI3) =>
% 24.53/6.37 (((exuI2) =>
% 24.53/6.37 (((inCongP) =>
% 24.53/6.37 (((in__Cong) =>
% 24.53/6.37 (((exuE3u) =>
% 24.53/6.37 (((exu__Cong) =>
% 24.53/6.37 (((setadjoin__Cong) =>
% 24.53/6.37 (((powerset__Cong) =>
% 24.53/6.37 (((setunion__Cong) =>
% 24.53/6.37 (((exuEu) =>
% 24.53/6.37 (((descr__Cong) =>
% 24.53/6.37 (((dsetconstr__Cong) =>
% 24.53/6.37 (((subsetI1) =>
% 24.53/6.37 (((eqimpsubset2) =>
% 24.53/6.37 (((eqimpsubset1) =>
% 24.53/6.37 (((subsetI2) =>
% 24.53/6.37 (((emptysetsubset) =>
% 24.53/6.37 (((subsetE) =>
% 24.53/6.37 (((subsetE2) =>
% 24.53/6.37 (((notsubsetI) =>
% 24.53/6.37 (((notequalI1) =>
% 24.53/6.37 (((notequalI2) =>
% 24.53/6.37 (((subsetRefl) =>
% 24.53/6.37 (((subsetTrans) =>
% 24.53/6.37 (((setadjoinSub) =>
% 24.53/6.37 (((setadjoinSub2) =>
% 24.53/6.37 (((subset2powerset) =>
% 24.53/6.37 (((setextsub) =>
% 24.53/6.37 ((
% 24.53/6.37 (subsetemptysetimpeq) =>
% 24.53/6.37 ((
% 24.53/6.37 (powersetI1) =>
% 24.53/6.37 ((
% 24.53/6.37 (powersetE1) =>
% 24.53/6.37 ((
% 24.53/6.37 (inPowerset) =>
% 24.53/6.37 ((
% 24.53/6.37 (powersetsubset) =>
% 24.53/6.37 ((
% 24.53/6.37 (sepInPowerset) =>
% 24.53/6.37 ((
% 24.53/6.37 (sepSubset) =>
% 24.53/6.37 ((
% 24.53/6.37 (binunionIL) =>
% 24.53/6.37 ((
% 24.53/6.37 (upairset2IR) =>
% 24.53/6.37 ((
% 24.53/6.37 (binunionIR) =>
% 24.53/6.37 ((
% 24.53/6.37 (binunionEcases) =>
% 24.53/6.37 ((
% 24.53/6.37 (binunionE) =>
% 24.53/6.37 ((
% 24.53/6.37 (binunionLsub) =>
% 24.53/6.37 ((
% 24.53/6.37 (binunionRsub) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectI) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectSubset5) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectEL) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectLsub) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectSubset2) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectSubset3) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectER) =>
% 24.53/6.37 ((
% 24.53/6.37 (disjointsetsI1) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectRsub) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectSubset4) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectSubset1) =>
% 24.53/6.37 ((
% 24.53/6.37 (bs114d) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusI) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusEL) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusER) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusSubset2) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusERneg) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusELneg) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusILneg) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusIRneg) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusLsub) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusSubset1) =>
% 24.53/6.37 ((
% 24.53/6.37 (symdiffE) =>
% 24.53/6.37 ((
% 24.53/6.37 (symdiffI1) =>
% 24.53/6.37 ((
% 24.53/6.37 (symdiffI2) =>
% 24.53/6.37 ((
% 24.53/6.37 (symdiffIneg1) =>
% 24.53/6.37 ((
% 24.53/6.37 (symdiffIneg2) =>
% 24.53/6.37 ((
% 24.53/6.37 (secondinupair) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairIL) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairIR) =>
% 24.53/6.37 ((
% 24.53/6.37 (kpairiskpair) =>
% 24.53/6.37 ((
% 24.53/6.37 (kpairp) =>
% 24.53/6.37 ((
% 24.53/6.37 (singletonsubset) =>
% 24.53/6.37 ((
% 24.53/6.37 (singletoninpowerset) =>
% 24.53/6.37 ((
% 24.53/6.37 (singletoninpowunion) =>
% 24.53/6.37 ((
% 24.53/6.37 (upairset2E) =>
% 24.53/6.37 ((
% 24.53/6.37 (upairsubunion) =>
% 24.53/6.37 ((
% 24.53/6.37 (upairinpowunion) =>
% 24.53/6.37 ((
% 24.53/6.37 (ubforcartprodlem1) =>
% 24.53/6.37 ((
% 24.53/6.37 (ubforcartprodlem2) =>
% 24.53/6.37 ((
% 24.53/6.37 (ubforcartprodlem3) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodpairin) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodmempair1) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodmempair) =>
% 24.53/6.37 ((
% 24.53/6.37 (setunionE2) =>
% 24.53/6.37 ((
% 24.53/6.37 (setunionsingleton1) =>
% 24.53/6.37 ((
% 24.53/6.37 (setunionsingleton2) =>
% 24.53/6.37 ((
% 24.53/6.37 (setunionsingleton) =>
% 24.53/6.37 ((
% 24.53/6.37 (singletonprop) =>
% 24.53/6.37 ((
% 24.53/6.37 (ex1E1) =>
% 24.53/6.37 ((
% 24.53/6.37 (ex1I) =>
% 24.53/6.37 ((
% 24.53/6.37 (ex1I2) =>
% 24.53/6.37 ((
% 24.53/6.37 (singletonsuniq) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjL1) =>
% 24.53/6.37 ((
% 24.53/6.37 (kfstsingleton) =>
% 24.53/6.37 ((
% 24.53/6.37 (theprop) =>
% 24.53/6.37 ((
% 24.53/6.37 (kfstpairEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodfstin) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjL2) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjL) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjR11) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjR12) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjR1) =>
% 24.53/6.37 ((
% 24.53/6.37 (upairequniteq) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjR2) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjR) =>
% 24.53/6.37 ((
% 24.53/6.37 (ksndsingleton) =>
% 24.53/6.37 ((
% 24.53/6.37 (ksndpairEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (kpairsurjEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodsndin) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodpairmemEL) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodpairmemER) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodmempaircEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodfstpairEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodsndpairEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodpairsurjEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (dpsetconstrI) =>
% 24.53/6.37 ((
% 24.53/6.37 (!!) @ (
% 24.53/6.37 (('#B') @ (
% 24.53/6.37 !!) @
% 24.53/6.37 (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 !!))) @
% 24.53/6.37 (
% 24.53/6.37 (
% 24.53/6.37 ('#S') @ (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 '#S') @
% 24.53/6.37 (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 '#C'))) @
% 24.53/6.37 (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ subset)))) @
% 24.53/6.37 dpsetconstr)))))) @
% 24.53/6.37 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.37 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl586])).
% 24.53/6.37 thf(zip_derived_cl606, plain,
% 24.53/6.37 (~ (((exuI1) =>
% 24.53/6.37 (((exuI3) =>
% 24.53/6.37 (((exuI2) =>
% 24.53/6.37 (((inCongP) =>
% 24.53/6.37 (((in__Cong) =>
% 24.53/6.37 (((exuE3u) =>
% 24.53/6.37 (((exu__Cong) =>
% 24.53/6.37 (((setadjoin__Cong) =>
% 24.53/6.37 (((powerset__Cong) =>
% 24.53/6.37 (((setunion__Cong) =>
% 24.53/6.37 (((exuEu) =>
% 24.53/6.37 (((descr__Cong) =>
% 24.53/6.37 (((dsetconstr__Cong) =>
% 24.53/6.37 (((subsetI1) =>
% 24.53/6.37 (((eqimpsubset2) =>
% 24.53/6.37 (((eqimpsubset1) =>
% 24.53/6.37 (((subsetI2) =>
% 24.53/6.37 (((emptysetsubset) =>
% 24.53/6.37 (((subsetE) =>
% 24.53/6.37 (((subsetE2) =>
% 24.53/6.37 (((notsubsetI) =>
% 24.53/6.37 (((notequalI1) =>
% 24.53/6.37 (((notequalI2) =>
% 24.53/6.37 (((subsetRefl) =>
% 24.53/6.37 (((subsetTrans) =>
% 24.53/6.37 (((setadjoinSub) =>
% 24.53/6.37 (((setadjoinSub2) =>
% 24.53/6.37 (((subset2powerset) =>
% 24.53/6.37 (((setextsub) =>
% 24.53/6.37 (((subsetemptysetimpeq) =>
% 24.53/6.37 ((
% 24.53/6.37 (powersetI1) =>
% 24.53/6.37 ((
% 24.53/6.37 (powersetE1) =>
% 24.53/6.37 ((
% 24.53/6.37 (inPowerset) =>
% 24.53/6.37 ((
% 24.53/6.37 (powersetsubset) =>
% 24.53/6.37 ((
% 24.53/6.37 (sepInPowerset) =>
% 24.53/6.37 ((
% 24.53/6.37 (sepSubset) =>
% 24.53/6.37 ((
% 24.53/6.37 (binunionIL) =>
% 24.53/6.37 ((
% 24.53/6.37 (upairset2IR) =>
% 24.53/6.37 ((
% 24.53/6.37 (binunionIR) =>
% 24.53/6.37 ((
% 24.53/6.37 (binunionEcases) =>
% 24.53/6.37 ((
% 24.53/6.37 (binunionE) =>
% 24.53/6.37 ((
% 24.53/6.37 (binunionLsub) =>
% 24.53/6.37 ((
% 24.53/6.37 (binunionRsub) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectI) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectSubset5) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectEL) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectLsub) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectSubset2) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectSubset3) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectER) =>
% 24.53/6.37 ((
% 24.53/6.37 (disjointsetsI1) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectRsub) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectSubset4) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectSubset1) =>
% 24.53/6.37 ((
% 24.53/6.37 (bs114d) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusI) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusEL) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusER) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusSubset2) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusERneg) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusELneg) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusILneg) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusIRneg) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusLsub) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusSubset1) =>
% 24.53/6.37 ((
% 24.53/6.37 (symdiffE) =>
% 24.53/6.37 ((
% 24.53/6.37 (symdiffI1) =>
% 24.53/6.37 ((
% 24.53/6.37 (symdiffI2) =>
% 24.53/6.37 ((
% 24.53/6.37 (symdiffIneg1) =>
% 24.53/6.37 ((
% 24.53/6.37 (symdiffIneg2) =>
% 24.53/6.37 ((
% 24.53/6.37 (secondinupair) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairIL) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairIR) =>
% 24.53/6.37 ((
% 24.53/6.37 (kpairiskpair) =>
% 24.53/6.37 ((
% 24.53/6.37 (kpairp) =>
% 24.53/6.37 ((
% 24.53/6.37 (singletonsubset) =>
% 24.53/6.37 ((
% 24.53/6.37 (singletoninpowerset) =>
% 24.53/6.37 ((
% 24.53/6.37 (singletoninpowunion) =>
% 24.53/6.37 ((
% 24.53/6.37 (upairset2E) =>
% 24.53/6.37 ((
% 24.53/6.37 (upairsubunion) =>
% 24.53/6.37 ((
% 24.53/6.37 (upairinpowunion) =>
% 24.53/6.37 ((
% 24.53/6.37 (ubforcartprodlem1) =>
% 24.53/6.37 ((
% 24.53/6.37 (ubforcartprodlem2) =>
% 24.53/6.37 ((
% 24.53/6.37 (ubforcartprodlem3) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodpairin) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodmempair1) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodmempair) =>
% 24.53/6.37 ((
% 24.53/6.37 (setunionE2) =>
% 24.53/6.37 ((
% 24.53/6.37 (setunionsingleton1) =>
% 24.53/6.37 ((
% 24.53/6.37 (setunionsingleton2) =>
% 24.53/6.37 ((
% 24.53/6.37 (setunionsingleton) =>
% 24.53/6.37 ((
% 24.53/6.37 (singletonprop) =>
% 24.53/6.37 ((
% 24.53/6.37 (ex1E1) =>
% 24.53/6.37 ((
% 24.53/6.37 (ex1I) =>
% 24.53/6.37 ((
% 24.53/6.37 (ex1I2) =>
% 24.53/6.37 ((
% 24.53/6.37 (singletonsuniq) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjL1) =>
% 24.53/6.37 ((
% 24.53/6.37 (kfstsingleton) =>
% 24.53/6.37 ((
% 24.53/6.37 (theprop) =>
% 24.53/6.37 ((
% 24.53/6.37 (kfstpairEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodfstin) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjL2) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjL) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjR11) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjR12) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjR1) =>
% 24.53/6.37 ((
% 24.53/6.37 (upairequniteq) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjR2) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjR) =>
% 24.53/6.37 ((
% 24.53/6.37 (ksndsingleton) =>
% 24.53/6.37 ((
% 24.53/6.37 (ksndpairEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (kpairsurjEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodsndin) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodpairmemEL) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodpairmemER) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodmempaircEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodfstpairEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodsndpairEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodpairsurjEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (dpsetconstrI) =>
% 24.53/6.37 ((
% 24.53/6.37 (!!) @ (
% 24.53/6.37 (('#B') @ (
% 24.53/6.37 !!) @
% 24.53/6.37 (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 !!))) @
% 24.53/6.37 (
% 24.53/6.37 (
% 24.53/6.37 ('#S') @ (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 '#S') @
% 24.53/6.37 (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 '#C'))) @
% 24.53/6.37 (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ subset)))) @
% 24.53/6.37 dpsetconstr)))))) @
% 24.53/6.37 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.37 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl595])).
% 24.53/6.37 thf(zip_derived_cl619, plain,
% 24.53/6.37 (~ (((exuI3) =>
% 24.53/6.37 (((exuI2) =>
% 24.53/6.37 (((inCongP) =>
% 24.53/6.37 (((in__Cong) =>
% 24.53/6.37 (((exuE3u) =>
% 24.53/6.37 (((exu__Cong) =>
% 24.53/6.37 (((setadjoin__Cong) =>
% 24.53/6.37 (((powerset__Cong) =>
% 24.53/6.37 (((setunion__Cong) =>
% 24.53/6.37 (((exuEu) =>
% 24.53/6.37 (((descr__Cong) =>
% 24.53/6.37 (((dsetconstr__Cong) =>
% 24.53/6.37 (((subsetI1) =>
% 24.53/6.37 (((eqimpsubset2) =>
% 24.53/6.37 (((eqimpsubset1) =>
% 24.53/6.37 (((subsetI2) =>
% 24.53/6.37 (((emptysetsubset) =>
% 24.53/6.37 (((subsetE) =>
% 24.53/6.37 (((subsetE2) =>
% 24.53/6.37 (((notsubsetI) =>
% 24.53/6.37 (((notequalI1) =>
% 24.53/6.37 (((notequalI2) =>
% 24.53/6.37 (((subsetRefl) =>
% 24.53/6.37 (((subsetTrans) =>
% 24.53/6.37 (((setadjoinSub) =>
% 24.53/6.37 (((setadjoinSub2) =>
% 24.53/6.37 (((subset2powerset) =>
% 24.53/6.37 (((setextsub) =>
% 24.53/6.37 (((subsetemptysetimpeq) =>
% 24.53/6.37 (((powersetI1) =>
% 24.53/6.37 ((
% 24.53/6.37 (powersetE1) =>
% 24.53/6.37 ((
% 24.53/6.37 (inPowerset) =>
% 24.53/6.37 ((
% 24.53/6.37 (powersetsubset) =>
% 24.53/6.37 ((
% 24.53/6.37 (sepInPowerset) =>
% 24.53/6.37 ((
% 24.53/6.37 (sepSubset) =>
% 24.53/6.37 ((
% 24.53/6.37 (binunionIL) =>
% 24.53/6.37 ((
% 24.53/6.37 (upairset2IR) =>
% 24.53/6.37 ((
% 24.53/6.37 (binunionIR) =>
% 24.53/6.37 ((
% 24.53/6.37 (binunionEcases) =>
% 24.53/6.37 ((
% 24.53/6.37 (binunionE) =>
% 24.53/6.37 ((
% 24.53/6.37 (binunionLsub) =>
% 24.53/6.37 ((
% 24.53/6.37 (binunionRsub) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectI) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectSubset5) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectEL) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectLsub) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectSubset2) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectSubset3) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectER) =>
% 24.53/6.37 ((
% 24.53/6.37 (disjointsetsI1) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectRsub) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectSubset4) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectSubset1) =>
% 24.53/6.37 ((
% 24.53/6.37 (bs114d) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusI) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusEL) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusER) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusSubset2) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusERneg) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusELneg) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusILneg) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusIRneg) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusLsub) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusSubset1) =>
% 24.53/6.37 ((
% 24.53/6.37 (symdiffE) =>
% 24.53/6.37 ((
% 24.53/6.37 (symdiffI1) =>
% 24.53/6.37 ((
% 24.53/6.37 (symdiffI2) =>
% 24.53/6.37 ((
% 24.53/6.37 (symdiffIneg1) =>
% 24.53/6.37 ((
% 24.53/6.37 (symdiffIneg2) =>
% 24.53/6.37 ((
% 24.53/6.37 (secondinupair) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairIL) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairIR) =>
% 24.53/6.37 ((
% 24.53/6.37 (kpairiskpair) =>
% 24.53/6.37 ((
% 24.53/6.37 (kpairp) =>
% 24.53/6.37 ((
% 24.53/6.37 (singletonsubset) =>
% 24.53/6.37 ((
% 24.53/6.37 (singletoninpowerset) =>
% 24.53/6.37 ((
% 24.53/6.37 (singletoninpowunion) =>
% 24.53/6.37 ((
% 24.53/6.37 (upairset2E) =>
% 24.53/6.37 ((
% 24.53/6.37 (upairsubunion) =>
% 24.53/6.37 ((
% 24.53/6.37 (upairinpowunion) =>
% 24.53/6.37 ((
% 24.53/6.37 (ubforcartprodlem1) =>
% 24.53/6.37 ((
% 24.53/6.37 (ubforcartprodlem2) =>
% 24.53/6.37 ((
% 24.53/6.37 (ubforcartprodlem3) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodpairin) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodmempair1) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodmempair) =>
% 24.53/6.37 ((
% 24.53/6.37 (setunionE2) =>
% 24.53/6.37 ((
% 24.53/6.37 (setunionsingleton1) =>
% 24.53/6.37 ((
% 24.53/6.37 (setunionsingleton2) =>
% 24.53/6.37 ((
% 24.53/6.37 (setunionsingleton) =>
% 24.53/6.37 ((
% 24.53/6.37 (singletonprop) =>
% 24.53/6.37 ((
% 24.53/6.37 (ex1E1) =>
% 24.53/6.37 ((
% 24.53/6.37 (ex1I) =>
% 24.53/6.37 ((
% 24.53/6.37 (ex1I2) =>
% 24.53/6.37 ((
% 24.53/6.37 (singletonsuniq) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjL1) =>
% 24.53/6.37 ((
% 24.53/6.37 (kfstsingleton) =>
% 24.53/6.37 ((
% 24.53/6.37 (theprop) =>
% 24.53/6.37 ((
% 24.53/6.37 (kfstpairEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodfstin) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjL2) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjL) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjR11) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjR12) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjR1) =>
% 24.53/6.37 ((
% 24.53/6.37 (upairequniteq) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjR2) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjR) =>
% 24.53/6.37 ((
% 24.53/6.37 (ksndsingleton) =>
% 24.53/6.37 ((
% 24.53/6.37 (ksndpairEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (kpairsurjEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodsndin) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodpairmemEL) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodpairmemER) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodmempaircEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodfstpairEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodsndpairEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodpairsurjEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (dpsetconstrI) =>
% 24.53/6.37 ((
% 24.53/6.37 (!!) @ (
% 24.53/6.37 (('#B') @ (
% 24.53/6.37 !!) @
% 24.53/6.37 (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 !!))) @
% 24.53/6.37 (
% 24.53/6.37 (
% 24.53/6.37 ('#S') @ (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 '#S') @
% 24.53/6.37 (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 '#C'))) @
% 24.53/6.37 (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ subset)))) @
% 24.53/6.37 dpsetconstr)))))) @
% 24.53/6.37 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.37 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl606])).
% 24.53/6.37 thf(zip_derived_cl630, plain,
% 24.53/6.37 (~ (((exuI2) =>
% 24.53/6.37 (((inCongP) =>
% 24.53/6.37 (((in__Cong) =>
% 24.53/6.37 (((exuE3u) =>
% 24.53/6.37 (((exu__Cong) =>
% 24.53/6.37 (((setadjoin__Cong) =>
% 24.53/6.37 (((powerset__Cong) =>
% 24.53/6.37 (((setunion__Cong) =>
% 24.53/6.37 (((exuEu) =>
% 24.53/6.37 (((descr__Cong) =>
% 24.53/6.37 (((dsetconstr__Cong) =>
% 24.53/6.37 (((subsetI1) =>
% 24.53/6.37 (((eqimpsubset2) =>
% 24.53/6.37 (((eqimpsubset1) =>
% 24.53/6.37 (((subsetI2) =>
% 24.53/6.37 (((emptysetsubset) =>
% 24.53/6.37 (((subsetE) =>
% 24.53/6.37 (((subsetE2) =>
% 24.53/6.37 (((notsubsetI) =>
% 24.53/6.37 (((notequalI1) =>
% 24.53/6.37 (((notequalI2) =>
% 24.53/6.37 (((subsetRefl) =>
% 24.53/6.37 (((subsetTrans) =>
% 24.53/6.37 (((setadjoinSub) =>
% 24.53/6.37 (((setadjoinSub2) =>
% 24.53/6.37 (((subset2powerset) =>
% 24.53/6.37 (((setextsub) =>
% 24.53/6.37 (((subsetemptysetimpeq) =>
% 24.53/6.37 (((powersetI1) =>
% 24.53/6.37 (((powersetE1) =>
% 24.53/6.37 ((
% 24.53/6.37 (inPowerset) =>
% 24.53/6.37 ((
% 24.53/6.37 (powersetsubset) =>
% 24.53/6.37 ((
% 24.53/6.37 (sepInPowerset) =>
% 24.53/6.37 ((
% 24.53/6.37 (sepSubset) =>
% 24.53/6.37 ((
% 24.53/6.37 (binunionIL) =>
% 24.53/6.37 ((
% 24.53/6.37 (upairset2IR) =>
% 24.53/6.37 ((
% 24.53/6.37 (binunionIR) =>
% 24.53/6.37 ((
% 24.53/6.37 (binunionEcases) =>
% 24.53/6.37 ((
% 24.53/6.37 (binunionE) =>
% 24.53/6.37 ((
% 24.53/6.37 (binunionLsub) =>
% 24.53/6.37 ((
% 24.53/6.37 (binunionRsub) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectI) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectSubset5) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectEL) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectLsub) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectSubset2) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectSubset3) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectER) =>
% 24.53/6.37 ((
% 24.53/6.37 (disjointsetsI1) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectRsub) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectSubset4) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectSubset1) =>
% 24.53/6.37 ((
% 24.53/6.37 (bs114d) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusI) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusEL) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusER) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusSubset2) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusERneg) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusELneg) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusILneg) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusIRneg) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusLsub) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusSubset1) =>
% 24.53/6.37 ((
% 24.53/6.37 (symdiffE) =>
% 24.53/6.37 ((
% 24.53/6.37 (symdiffI1) =>
% 24.53/6.37 ((
% 24.53/6.37 (symdiffI2) =>
% 24.53/6.37 ((
% 24.53/6.37 (symdiffIneg1) =>
% 24.53/6.37 ((
% 24.53/6.37 (symdiffIneg2) =>
% 24.53/6.37 ((
% 24.53/6.37 (secondinupair) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairIL) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairIR) =>
% 24.53/6.37 ((
% 24.53/6.37 (kpairiskpair) =>
% 24.53/6.37 ((
% 24.53/6.37 (kpairp) =>
% 24.53/6.37 ((
% 24.53/6.37 (singletonsubset) =>
% 24.53/6.37 ((
% 24.53/6.37 (singletoninpowerset) =>
% 24.53/6.37 ((
% 24.53/6.37 (singletoninpowunion) =>
% 24.53/6.37 ((
% 24.53/6.37 (upairset2E) =>
% 24.53/6.37 ((
% 24.53/6.37 (upairsubunion) =>
% 24.53/6.37 ((
% 24.53/6.37 (upairinpowunion) =>
% 24.53/6.37 ((
% 24.53/6.37 (ubforcartprodlem1) =>
% 24.53/6.37 ((
% 24.53/6.37 (ubforcartprodlem2) =>
% 24.53/6.37 ((
% 24.53/6.37 (ubforcartprodlem3) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodpairin) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodmempair1) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodmempair) =>
% 24.53/6.37 ((
% 24.53/6.37 (setunionE2) =>
% 24.53/6.37 ((
% 24.53/6.37 (setunionsingleton1) =>
% 24.53/6.37 ((
% 24.53/6.37 (setunionsingleton2) =>
% 24.53/6.37 ((
% 24.53/6.37 (setunionsingleton) =>
% 24.53/6.37 ((
% 24.53/6.37 (singletonprop) =>
% 24.53/6.37 ((
% 24.53/6.37 (ex1E1) =>
% 24.53/6.37 ((
% 24.53/6.37 (ex1I) =>
% 24.53/6.37 ((
% 24.53/6.37 (ex1I2) =>
% 24.53/6.37 ((
% 24.53/6.37 (singletonsuniq) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjL1) =>
% 24.53/6.37 ((
% 24.53/6.37 (kfstsingleton) =>
% 24.53/6.37 ((
% 24.53/6.37 (theprop) =>
% 24.53/6.37 ((
% 24.53/6.37 (kfstpairEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodfstin) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjL2) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjL) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjR11) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjR12) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjR1) =>
% 24.53/6.37 ((
% 24.53/6.37 (upairequniteq) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjR2) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjR) =>
% 24.53/6.37 ((
% 24.53/6.37 (ksndsingleton) =>
% 24.53/6.37 ((
% 24.53/6.37 (ksndpairEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (kpairsurjEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodsndin) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodpairmemEL) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodpairmemER) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodmempaircEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodfstpairEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodsndpairEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodpairsurjEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (dpsetconstrI) =>
% 24.53/6.37 ((
% 24.53/6.37 (!!) @ (
% 24.53/6.37 (('#B') @ (
% 24.53/6.37 !!) @
% 24.53/6.37 (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 !!))) @
% 24.53/6.37 (
% 24.53/6.37 (
% 24.53/6.37 ('#S') @ (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 '#S') @
% 24.53/6.37 (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 '#C'))) @
% 24.53/6.37 (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ subset)))) @
% 24.53/6.37 dpsetconstr)))))) @
% 24.53/6.37 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.37 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl619])).
% 24.53/6.37 thf(zip_derived_cl640, plain,
% 24.53/6.37 (~ (((inCongP) =>
% 24.53/6.37 (((in__Cong) =>
% 24.53/6.37 (((exuE3u) =>
% 24.53/6.37 (((exu__Cong) =>
% 24.53/6.37 (((setadjoin__Cong) =>
% 24.53/6.37 (((powerset__Cong) =>
% 24.53/6.37 (((setunion__Cong) =>
% 24.53/6.37 (((exuEu) =>
% 24.53/6.37 (((descr__Cong) =>
% 24.53/6.37 (((dsetconstr__Cong) =>
% 24.53/6.37 (((subsetI1) =>
% 24.53/6.37 (((eqimpsubset2) =>
% 24.53/6.37 (((eqimpsubset1) =>
% 24.53/6.37 (((subsetI2) =>
% 24.53/6.37 (((emptysetsubset) =>
% 24.53/6.37 (((subsetE) =>
% 24.53/6.37 (((subsetE2) =>
% 24.53/6.37 (((notsubsetI) =>
% 24.53/6.37 (((notequalI1) =>
% 24.53/6.37 (((notequalI2) =>
% 24.53/6.37 (((subsetRefl) =>
% 24.53/6.37 (((subsetTrans) =>
% 24.53/6.37 (((setadjoinSub) =>
% 24.53/6.37 (((setadjoinSub2) =>
% 24.53/6.37 (((subset2powerset) =>
% 24.53/6.37 (((setextsub) =>
% 24.53/6.37 (((subsetemptysetimpeq) =>
% 24.53/6.37 (((powersetI1) =>
% 24.53/6.37 (((powersetE1) =>
% 24.53/6.37 (((inPowerset) =>
% 24.53/6.37 ((
% 24.53/6.37 (powersetsubset) =>
% 24.53/6.37 ((
% 24.53/6.37 (sepInPowerset) =>
% 24.53/6.37 ((
% 24.53/6.37 (sepSubset) =>
% 24.53/6.37 ((
% 24.53/6.37 (binunionIL) =>
% 24.53/6.37 ((
% 24.53/6.37 (upairset2IR) =>
% 24.53/6.37 ((
% 24.53/6.37 (binunionIR) =>
% 24.53/6.37 ((
% 24.53/6.37 (binunionEcases) =>
% 24.53/6.37 ((
% 24.53/6.37 (binunionE) =>
% 24.53/6.37 ((
% 24.53/6.37 (binunionLsub) =>
% 24.53/6.37 ((
% 24.53/6.37 (binunionRsub) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectI) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectSubset5) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectEL) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectLsub) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectSubset2) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectSubset3) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectER) =>
% 24.53/6.37 ((
% 24.53/6.37 (disjointsetsI1) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectRsub) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectSubset4) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectSubset1) =>
% 24.53/6.37 ((
% 24.53/6.37 (bs114d) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusI) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusEL) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusER) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusSubset2) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusERneg) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusELneg) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusILneg) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusIRneg) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusLsub) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusSubset1) =>
% 24.53/6.37 ((
% 24.53/6.37 (symdiffE) =>
% 24.53/6.37 ((
% 24.53/6.37 (symdiffI1) =>
% 24.53/6.37 ((
% 24.53/6.37 (symdiffI2) =>
% 24.53/6.37 ((
% 24.53/6.37 (symdiffIneg1) =>
% 24.53/6.37 ((
% 24.53/6.37 (symdiffIneg2) =>
% 24.53/6.37 ((
% 24.53/6.37 (secondinupair) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairIL) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairIR) =>
% 24.53/6.37 ((
% 24.53/6.37 (kpairiskpair) =>
% 24.53/6.37 ((
% 24.53/6.37 (kpairp) =>
% 24.53/6.37 ((
% 24.53/6.37 (singletonsubset) =>
% 24.53/6.37 ((
% 24.53/6.37 (singletoninpowerset) =>
% 24.53/6.37 ((
% 24.53/6.37 (singletoninpowunion) =>
% 24.53/6.37 ((
% 24.53/6.37 (upairset2E) =>
% 24.53/6.37 ((
% 24.53/6.37 (upairsubunion) =>
% 24.53/6.37 ((
% 24.53/6.37 (upairinpowunion) =>
% 24.53/6.37 ((
% 24.53/6.37 (ubforcartprodlem1) =>
% 24.53/6.37 ((
% 24.53/6.37 (ubforcartprodlem2) =>
% 24.53/6.37 ((
% 24.53/6.37 (ubforcartprodlem3) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodpairin) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodmempair1) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodmempair) =>
% 24.53/6.37 ((
% 24.53/6.37 (setunionE2) =>
% 24.53/6.37 ((
% 24.53/6.37 (setunionsingleton1) =>
% 24.53/6.37 ((
% 24.53/6.37 (setunionsingleton2) =>
% 24.53/6.37 ((
% 24.53/6.37 (setunionsingleton) =>
% 24.53/6.37 ((
% 24.53/6.37 (singletonprop) =>
% 24.53/6.37 ((
% 24.53/6.37 (ex1E1) =>
% 24.53/6.37 ((
% 24.53/6.37 (ex1I) =>
% 24.53/6.37 ((
% 24.53/6.37 (ex1I2) =>
% 24.53/6.37 ((
% 24.53/6.37 (singletonsuniq) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjL1) =>
% 24.53/6.37 ((
% 24.53/6.37 (kfstsingleton) =>
% 24.53/6.37 ((
% 24.53/6.37 (theprop) =>
% 24.53/6.37 ((
% 24.53/6.37 (kfstpairEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodfstin) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjL2) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjL) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjR11) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjR12) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjR1) =>
% 24.53/6.37 ((
% 24.53/6.37 (upairequniteq) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjR2) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairinjR) =>
% 24.53/6.37 ((
% 24.53/6.37 (ksndsingleton) =>
% 24.53/6.37 ((
% 24.53/6.37 (ksndpairEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (kpairsurjEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodsndin) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodpairmemEL) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodpairmemER) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodmempaircEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodfstpairEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodsndpairEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (cartprodpairsurjEq) =>
% 24.53/6.37 ((
% 24.53/6.37 (dpsetconstrI) =>
% 24.53/6.37 ((
% 24.53/6.37 (!!) @ (
% 24.53/6.37 (('#B') @ (
% 24.53/6.37 !!) @
% 24.53/6.37 (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 !!))) @
% 24.53/6.37 (
% 24.53/6.37 (
% 24.53/6.37 ('#S') @ (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 '#S') @
% 24.53/6.37 (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 '#C'))) @
% 24.53/6.37 (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ (
% 24.53/6.37 (
% 24.53/6.37 ('#B') @ subset)))) @
% 24.53/6.37 dpsetconstr)))))) @
% 24.53/6.37 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.37 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl630])).
% 24.53/6.37 thf(zip_derived_cl650, plain,
% 24.53/6.37 (~ (((in__Cong) =>
% 24.53/6.37 (((exuE3u) =>
% 24.53/6.37 (((exu__Cong) =>
% 24.53/6.37 (((setadjoin__Cong) =>
% 24.53/6.37 (((powerset__Cong) =>
% 24.53/6.37 (((setunion__Cong) =>
% 24.53/6.37 (((exuEu) =>
% 24.53/6.37 (((descr__Cong) =>
% 24.53/6.37 (((dsetconstr__Cong) =>
% 24.53/6.37 (((subsetI1) =>
% 24.53/6.37 (((eqimpsubset2) =>
% 24.53/6.37 (((eqimpsubset1) =>
% 24.53/6.37 (((subsetI2) =>
% 24.53/6.37 (((emptysetsubset) =>
% 24.53/6.37 (((subsetE) =>
% 24.53/6.37 (((subsetE2) =>
% 24.53/6.37 (((notsubsetI) =>
% 24.53/6.37 (((notequalI1) =>
% 24.53/6.37 (((notequalI2) =>
% 24.53/6.37 (((subsetRefl) =>
% 24.53/6.37 (((subsetTrans) =>
% 24.53/6.37 (((setadjoinSub) =>
% 24.53/6.37 (((setadjoinSub2) =>
% 24.53/6.37 (((subset2powerset) =>
% 24.53/6.37 (((setextsub) =>
% 24.53/6.37 (((subsetemptysetimpeq) =>
% 24.53/6.37 (((powersetI1) =>
% 24.53/6.37 (((powersetE1) =>
% 24.53/6.37 (((inPowerset) =>
% 24.53/6.37 (((powersetsubset) =>
% 24.53/6.37 ((
% 24.53/6.37 (sepInPowerset) =>
% 24.53/6.37 ((
% 24.53/6.37 (sepSubset) =>
% 24.53/6.37 ((
% 24.53/6.37 (binunionIL) =>
% 24.53/6.37 ((
% 24.53/6.37 (upairset2IR) =>
% 24.53/6.37 ((
% 24.53/6.37 (binunionIR) =>
% 24.53/6.37 ((
% 24.53/6.37 (binunionEcases) =>
% 24.53/6.37 ((
% 24.53/6.37 (binunionE) =>
% 24.53/6.37 ((
% 24.53/6.37 (binunionLsub) =>
% 24.53/6.37 ((
% 24.53/6.37 (binunionRsub) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectI) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectSubset5) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectEL) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectLsub) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectSubset2) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectSubset3) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectER) =>
% 24.53/6.37 ((
% 24.53/6.37 (disjointsetsI1) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectRsub) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectSubset4) =>
% 24.53/6.37 ((
% 24.53/6.37 (binintersectSubset1) =>
% 24.53/6.37 ((
% 24.53/6.37 (bs114d) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusI) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusEL) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusER) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusSubset2) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusERneg) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusELneg) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusILneg) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusIRneg) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusLsub) =>
% 24.53/6.37 ((
% 24.53/6.37 (setminusSubset1) =>
% 24.53/6.37 ((
% 24.53/6.37 (symdiffE) =>
% 24.53/6.37 ((
% 24.53/6.37 (symdiffI1) =>
% 24.53/6.37 ((
% 24.53/6.37 (symdiffI2) =>
% 24.53/6.37 ((
% 24.53/6.37 (symdiffIneg1) =>
% 24.53/6.37 ((
% 24.53/6.37 (symdiffIneg2) =>
% 24.53/6.37 ((
% 24.53/6.37 (secondinupair) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairIL) =>
% 24.53/6.37 ((
% 24.53/6.37 (setukpairIR) =>
% 24.53/6.37 ((
% 24.53/6.37 (kpairiskpair) =>
% 24.53/6.37 ((
% 24.53/6.37 (kpairp) =>
% 24.53/6.37 ((
% 24.53/6.37 (singletonsubset) =>
% 24.53/6.37 ((
% 24.53/6.37 (singletoninpowerset) =>
% 24.53/6.37 ((
% 24.53/6.37 (singletoninpowunion) =>
% 24.53/6.37 ((
% 24.53/6.37 (upairset2E) =>
% 24.53/6.37 ((
% 24.53/6.37 (upairsubunion) =>
% 24.53/6.37 ((
% 24.53/6.37 (upairinpowunion) =>
% 24.53/6.37 ((
% 24.53/6.38 (ubforcartprodlem1) =>
% 24.53/6.38 ((
% 24.53/6.38 (ubforcartprodlem2) =>
% 24.53/6.38 ((
% 24.53/6.38 (ubforcartprodlem3) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodpairin) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodmempair1) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodmempair) =>
% 24.53/6.38 ((
% 24.53/6.38 (setunionE2) =>
% 24.53/6.38 ((
% 24.53/6.38 (setunionsingleton1) =>
% 24.53/6.38 ((
% 24.53/6.38 (setunionsingleton2) =>
% 24.53/6.38 ((
% 24.53/6.38 (setunionsingleton) =>
% 24.53/6.38 ((
% 24.53/6.38 (singletonprop) =>
% 24.53/6.38 ((
% 24.53/6.38 (ex1E1) =>
% 24.53/6.38 ((
% 24.53/6.38 (ex1I) =>
% 24.53/6.38 ((
% 24.53/6.38 (ex1I2) =>
% 24.53/6.38 ((
% 24.53/6.38 (singletonsuniq) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairinjL1) =>
% 24.53/6.38 ((
% 24.53/6.38 (kfstsingleton) =>
% 24.53/6.38 ((
% 24.53/6.38 (theprop) =>
% 24.53/6.38 ((
% 24.53/6.38 (kfstpairEq) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodfstin) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairinjL2) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairinjL) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairinjR11) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairinjR12) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairinjR1) =>
% 24.53/6.38 ((
% 24.53/6.38 (upairequniteq) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairinjR2) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairinjR) =>
% 24.53/6.38 ((
% 24.53/6.38 (ksndsingleton) =>
% 24.53/6.38 ((
% 24.53/6.38 (ksndpairEq) =>
% 24.53/6.38 ((
% 24.53/6.38 (kpairsurjEq) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodsndin) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodpairmemEL) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodpairmemER) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodmempaircEq) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodfstpairEq) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodsndpairEq) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodpairsurjEq) =>
% 24.53/6.38 ((
% 24.53/6.38 (dpsetconstrI) =>
% 24.53/6.38 ((
% 24.53/6.38 (!!) @ (
% 24.53/6.38 (('#B') @ (
% 24.53/6.38 !!) @
% 24.53/6.38 (
% 24.53/6.38 (
% 24.53/6.38 ('#B') @ (
% 24.53/6.38 (
% 24.53/6.38 ('#B') @ (
% 24.53/6.38 !!))) @
% 24.53/6.38 (
% 24.53/6.38 (
% 24.53/6.38 ('#S') @ (
% 24.53/6.38 (
% 24.53/6.38 ('#B') @ (
% 24.53/6.38 '#S') @
% 24.53/6.38 (
% 24.53/6.38 (
% 24.53/6.38 ('#B') @ (
% 24.53/6.38 (
% 24.53/6.38 ('#B') @ (
% 24.53/6.38 '#C'))) @
% 24.53/6.38 (
% 24.53/6.38 (
% 24.53/6.38 ('#B') @ (
% 24.53/6.38 (
% 24.53/6.38 ('#B') @ (
% 24.53/6.38 (
% 24.53/6.38 ('#B') @ subset)))) @
% 24.53/6.38 dpsetconstr)))))) @
% 24.53/6.38 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl640])).
% 24.53/6.38 thf(zip_derived_cl660, plain,
% 24.53/6.38 (~ (((exuE3u) =>
% 24.53/6.38 (((exu__Cong) =>
% 24.53/6.38 (((setadjoin__Cong) =>
% 24.53/6.38 (((powerset__Cong) =>
% 24.53/6.38 (((setunion__Cong) =>
% 24.53/6.38 (((exuEu) =>
% 24.53/6.38 (((descr__Cong) =>
% 24.53/6.38 (((dsetconstr__Cong) =>
% 24.53/6.38 (((subsetI1) =>
% 24.53/6.38 (((eqimpsubset2) =>
% 24.53/6.38 (((eqimpsubset1) =>
% 24.53/6.38 (((subsetI2) =>
% 24.53/6.38 (((emptysetsubset) =>
% 24.53/6.38 (((subsetE) =>
% 24.53/6.38 (((subsetE2) =>
% 24.53/6.38 (((notsubsetI) =>
% 24.53/6.38 (((notequalI1) =>
% 24.53/6.38 (((notequalI2) =>
% 24.53/6.38 (((subsetRefl) =>
% 24.53/6.38 (((subsetTrans) =>
% 24.53/6.38 (((setadjoinSub) =>
% 24.53/6.38 (((setadjoinSub2) =>
% 24.53/6.38 (((subset2powerset) =>
% 24.53/6.38 (((setextsub) =>
% 24.53/6.38 (((subsetemptysetimpeq) =>
% 24.53/6.38 (((powersetI1) =>
% 24.53/6.38 (((powersetE1) =>
% 24.53/6.38 (((inPowerset) =>
% 24.53/6.38 (((powersetsubset) =>
% 24.53/6.38 (((sepInPowerset) =>
% 24.53/6.38 ((
% 24.53/6.38 (sepSubset) =>
% 24.53/6.38 ((
% 24.53/6.38 (binunionIL) =>
% 24.53/6.38 ((
% 24.53/6.38 (upairset2IR) =>
% 24.53/6.38 ((
% 24.53/6.38 (binunionIR) =>
% 24.53/6.38 ((
% 24.53/6.38 (binunionEcases) =>
% 24.53/6.38 ((
% 24.53/6.38 (binunionE) =>
% 24.53/6.38 ((
% 24.53/6.38 (binunionLsub) =>
% 24.53/6.38 ((
% 24.53/6.38 (binunionRsub) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectI) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectSubset5) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectEL) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectLsub) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectSubset2) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectSubset3) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectER) =>
% 24.53/6.38 ((
% 24.53/6.38 (disjointsetsI1) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectRsub) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectSubset4) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectSubset1) =>
% 24.53/6.38 ((
% 24.53/6.38 (bs114d) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusI) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusEL) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusER) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusSubset2) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusERneg) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusELneg) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusILneg) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusIRneg) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusLsub) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusSubset1) =>
% 24.53/6.38 ((
% 24.53/6.38 (symdiffE) =>
% 24.53/6.38 ((
% 24.53/6.38 (symdiffI1) =>
% 24.53/6.38 ((
% 24.53/6.38 (symdiffI2) =>
% 24.53/6.38 ((
% 24.53/6.38 (symdiffIneg1) =>
% 24.53/6.38 ((
% 24.53/6.38 (symdiffIneg2) =>
% 24.53/6.38 ((
% 24.53/6.38 (secondinupair) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairIL) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairIR) =>
% 24.53/6.38 ((
% 24.53/6.38 (kpairiskpair) =>
% 24.53/6.38 ((
% 24.53/6.38 (kpairp) =>
% 24.53/6.38 ((
% 24.53/6.38 (singletonsubset) =>
% 24.53/6.38 ((
% 24.53/6.38 (singletoninpowerset) =>
% 24.53/6.38 ((
% 24.53/6.38 (singletoninpowunion) =>
% 24.53/6.38 ((
% 24.53/6.38 (upairset2E) =>
% 24.53/6.38 ((
% 24.53/6.38 (upairsubunion) =>
% 24.53/6.38 ((
% 24.53/6.38 (upairinpowunion) =>
% 24.53/6.38 ((
% 24.53/6.38 (ubforcartprodlem1) =>
% 24.53/6.38 ((
% 24.53/6.38 (ubforcartprodlem2) =>
% 24.53/6.38 ((
% 24.53/6.38 (ubforcartprodlem3) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodpairin) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodmempair1) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodmempair) =>
% 24.53/6.38 ((
% 24.53/6.38 (setunionE2) =>
% 24.53/6.38 ((
% 24.53/6.38 (setunionsingleton1) =>
% 24.53/6.38 ((
% 24.53/6.38 (setunionsingleton2) =>
% 24.53/6.38 ((
% 24.53/6.38 (setunionsingleton) =>
% 24.53/6.38 ((
% 24.53/6.38 (singletonprop) =>
% 24.53/6.38 ((
% 24.53/6.38 (ex1E1) =>
% 24.53/6.38 ((
% 24.53/6.38 (ex1I) =>
% 24.53/6.38 ((
% 24.53/6.38 (ex1I2) =>
% 24.53/6.38 ((
% 24.53/6.38 (singletonsuniq) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairinjL1) =>
% 24.53/6.38 ((
% 24.53/6.38 (kfstsingleton) =>
% 24.53/6.38 ((
% 24.53/6.38 (theprop) =>
% 24.53/6.38 ((
% 24.53/6.38 (kfstpairEq) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodfstin) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairinjL2) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairinjL) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairinjR11) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairinjR12) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairinjR1) =>
% 24.53/6.38 ((
% 24.53/6.38 (upairequniteq) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairinjR2) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairinjR) =>
% 24.53/6.38 ((
% 24.53/6.38 (ksndsingleton) =>
% 24.53/6.38 ((
% 24.53/6.38 (ksndpairEq) =>
% 24.53/6.38 ((
% 24.53/6.38 (kpairsurjEq) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodsndin) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodpairmemEL) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodpairmemER) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodmempaircEq) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodfstpairEq) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodsndpairEq) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodpairsurjEq) =>
% 24.53/6.38 ((
% 24.53/6.38 (dpsetconstrI) =>
% 24.53/6.38 ((
% 24.53/6.38 (!!) @ (
% 24.53/6.38 (('#B') @ (
% 24.53/6.38 !!) @
% 24.53/6.38 (
% 24.53/6.38 (
% 24.53/6.38 ('#B') @ (
% 24.53/6.38 (
% 24.53/6.38 ('#B') @ (
% 24.53/6.38 !!))) @
% 24.53/6.38 (
% 24.53/6.38 (
% 24.53/6.38 ('#S') @ (
% 24.53/6.38 (
% 24.53/6.38 ('#B') @ (
% 24.53/6.38 '#S') @
% 24.53/6.38 (
% 24.53/6.38 (
% 24.53/6.38 ('#B') @ (
% 24.53/6.38 (
% 24.53/6.38 ('#B') @ (
% 24.53/6.38 '#C'))) @
% 24.53/6.38 (
% 24.53/6.38 (
% 24.53/6.38 ('#B') @ (
% 24.53/6.38 (
% 24.53/6.38 ('#B') @ (
% 24.53/6.38 (
% 24.53/6.38 ('#B') @ subset)))) @
% 24.53/6.38 dpsetconstr)))))) @
% 24.53/6.38 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl650])).
% 24.53/6.38 thf(zip_derived_cl672, plain,
% 24.53/6.38 (~ (((exu__Cong) =>
% 24.53/6.38 (((setadjoin__Cong) =>
% 24.53/6.38 (((powerset__Cong) =>
% 24.53/6.38 (((setunion__Cong) =>
% 24.53/6.38 (((exuEu) =>
% 24.53/6.38 (((descr__Cong) =>
% 24.53/6.38 (((dsetconstr__Cong) =>
% 24.53/6.38 (((subsetI1) =>
% 24.53/6.38 (((eqimpsubset2) =>
% 24.53/6.38 (((eqimpsubset1) =>
% 24.53/6.38 (((subsetI2) =>
% 24.53/6.38 (((emptysetsubset) =>
% 24.53/6.38 (((subsetE) =>
% 24.53/6.38 (((subsetE2) =>
% 24.53/6.38 (((notsubsetI) =>
% 24.53/6.38 (((notequalI1) =>
% 24.53/6.38 (((notequalI2) =>
% 24.53/6.38 (((subsetRefl) =>
% 24.53/6.38 (((subsetTrans) =>
% 24.53/6.38 (((setadjoinSub) =>
% 24.53/6.38 (((setadjoinSub2) =>
% 24.53/6.38 (((subset2powerset) =>
% 24.53/6.38 (((setextsub) =>
% 24.53/6.38 (((subsetemptysetimpeq) =>
% 24.53/6.38 (((powersetI1) =>
% 24.53/6.38 (((powersetE1) =>
% 24.53/6.38 (((inPowerset) =>
% 24.53/6.38 (((powersetsubset) =>
% 24.53/6.38 (((sepInPowerset) =>
% 24.53/6.38 (((sepSubset) =>
% 24.53/6.38 ((
% 24.53/6.38 (binunionIL) =>
% 24.53/6.38 ((
% 24.53/6.38 (upairset2IR) =>
% 24.53/6.38 ((
% 24.53/6.38 (binunionIR) =>
% 24.53/6.38 ((
% 24.53/6.38 (binunionEcases) =>
% 24.53/6.38 ((
% 24.53/6.38 (binunionE) =>
% 24.53/6.38 ((
% 24.53/6.38 (binunionLsub) =>
% 24.53/6.38 ((
% 24.53/6.38 (binunionRsub) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectI) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectSubset5) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectEL) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectLsub) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectSubset2) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectSubset3) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectER) =>
% 24.53/6.38 ((
% 24.53/6.38 (disjointsetsI1) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectRsub) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectSubset4) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectSubset1) =>
% 24.53/6.38 ((
% 24.53/6.38 (bs114d) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusI) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusEL) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusER) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusSubset2) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusERneg) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusELneg) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusILneg) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusIRneg) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusLsub) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusSubset1) =>
% 24.53/6.38 ((
% 24.53/6.38 (symdiffE) =>
% 24.53/6.38 ((
% 24.53/6.38 (symdiffI1) =>
% 24.53/6.38 ((
% 24.53/6.38 (symdiffI2) =>
% 24.53/6.38 ((
% 24.53/6.38 (symdiffIneg1) =>
% 24.53/6.38 ((
% 24.53/6.38 (symdiffIneg2) =>
% 24.53/6.38 ((
% 24.53/6.38 (secondinupair) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairIL) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairIR) =>
% 24.53/6.38 ((
% 24.53/6.38 (kpairiskpair) =>
% 24.53/6.38 ((
% 24.53/6.38 (kpairp) =>
% 24.53/6.38 ((
% 24.53/6.38 (singletonsubset) =>
% 24.53/6.38 ((
% 24.53/6.38 (singletoninpowerset) =>
% 24.53/6.38 ((
% 24.53/6.38 (singletoninpowunion) =>
% 24.53/6.38 ((
% 24.53/6.38 (upairset2E) =>
% 24.53/6.38 ((
% 24.53/6.38 (upairsubunion) =>
% 24.53/6.38 ((
% 24.53/6.38 (upairinpowunion) =>
% 24.53/6.38 ((
% 24.53/6.38 (ubforcartprodlem1) =>
% 24.53/6.38 ((
% 24.53/6.38 (ubforcartprodlem2) =>
% 24.53/6.38 ((
% 24.53/6.38 (ubforcartprodlem3) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodpairin) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodmempair1) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodmempair) =>
% 24.53/6.38 ((
% 24.53/6.38 (setunionE2) =>
% 24.53/6.38 ((
% 24.53/6.38 (setunionsingleton1) =>
% 24.53/6.38 ((
% 24.53/6.38 (setunionsingleton2) =>
% 24.53/6.38 ((
% 24.53/6.38 (setunionsingleton) =>
% 24.53/6.38 ((
% 24.53/6.38 (singletonprop) =>
% 24.53/6.38 ((
% 24.53/6.38 (ex1E1) =>
% 24.53/6.38 ((
% 24.53/6.38 (ex1I) =>
% 24.53/6.38 ((
% 24.53/6.38 (ex1I2) =>
% 24.53/6.38 ((
% 24.53/6.38 (singletonsuniq) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairinjL1) =>
% 24.53/6.38 ((
% 24.53/6.38 (kfstsingleton) =>
% 24.53/6.38 ((
% 24.53/6.38 (theprop) =>
% 24.53/6.38 ((
% 24.53/6.38 (kfstpairEq) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodfstin) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairinjL2) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairinjL) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairinjR11) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairinjR12) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairinjR1) =>
% 24.53/6.38 ((
% 24.53/6.38 (upairequniteq) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairinjR2) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairinjR) =>
% 24.53/6.38 ((
% 24.53/6.38 (ksndsingleton) =>
% 24.53/6.38 ((
% 24.53/6.38 (ksndpairEq) =>
% 24.53/6.38 ((
% 24.53/6.38 (kpairsurjEq) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodsndin) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodpairmemEL) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodpairmemER) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodmempaircEq) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodfstpairEq) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodsndpairEq) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodpairsurjEq) =>
% 24.53/6.38 ((
% 24.53/6.38 (dpsetconstrI) =>
% 24.53/6.38 ((
% 24.53/6.38 (!!) @ (
% 24.53/6.38 (('#B') @ (
% 24.53/6.38 !!) @
% 24.53/6.38 (
% 24.53/6.38 (
% 24.53/6.38 ('#B') @ (
% 24.53/6.38 (
% 24.53/6.38 ('#B') @ (
% 24.53/6.38 !!))) @
% 24.53/6.38 (
% 24.53/6.38 (
% 24.53/6.38 ('#S') @ (
% 24.53/6.38 (
% 24.53/6.38 ('#B') @ (
% 24.53/6.38 '#S') @
% 24.53/6.38 (
% 24.53/6.38 (
% 24.53/6.38 ('#B') @ (
% 24.53/6.38 (
% 24.53/6.38 ('#B') @ (
% 24.53/6.38 '#C'))) @
% 24.53/6.38 (
% 24.53/6.38 (
% 24.53/6.38 ('#B') @ (
% 24.53/6.38 (
% 24.53/6.38 ('#B') @ (
% 24.53/6.38 (
% 24.53/6.38 ('#B') @ subset)))) @
% 24.53/6.38 dpsetconstr)))))) @
% 24.53/6.38 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl660])).
% 24.53/6.38 thf(zip_derived_cl685, plain,
% 24.53/6.38 (~ (((setadjoin__Cong) =>
% 24.53/6.38 (((powerset__Cong) =>
% 24.53/6.38 (((setunion__Cong) =>
% 24.53/6.38 (((exuEu) =>
% 24.53/6.38 (((descr__Cong) =>
% 24.53/6.38 (((dsetconstr__Cong) =>
% 24.53/6.38 (((subsetI1) =>
% 24.53/6.38 (((eqimpsubset2) =>
% 24.53/6.38 (((eqimpsubset1) =>
% 24.53/6.38 (((subsetI2) =>
% 24.53/6.38 (((emptysetsubset) =>
% 24.53/6.38 (((subsetE) =>
% 24.53/6.38 (((subsetE2) =>
% 24.53/6.38 (((notsubsetI) =>
% 24.53/6.38 (((notequalI1) =>
% 24.53/6.38 (((notequalI2) =>
% 24.53/6.38 (((subsetRefl) =>
% 24.53/6.38 (((subsetTrans) =>
% 24.53/6.38 (((setadjoinSub) =>
% 24.53/6.38 (((setadjoinSub2) =>
% 24.53/6.38 (((subset2powerset) =>
% 24.53/6.38 (((setextsub) =>
% 24.53/6.38 (((subsetemptysetimpeq) =>
% 24.53/6.38 (((powersetI1) =>
% 24.53/6.38 (((powersetE1) =>
% 24.53/6.38 (((inPowerset) =>
% 24.53/6.38 (((powersetsubset) =>
% 24.53/6.38 (((sepInPowerset) =>
% 24.53/6.38 (((sepSubset) =>
% 24.53/6.38 (((binunionIL) =>
% 24.53/6.38 ((
% 24.53/6.38 (upairset2IR) =>
% 24.53/6.38 ((
% 24.53/6.38 (binunionIR) =>
% 24.53/6.38 ((
% 24.53/6.38 (binunionEcases) =>
% 24.53/6.38 ((
% 24.53/6.38 (binunionE) =>
% 24.53/6.38 ((
% 24.53/6.38 (binunionLsub) =>
% 24.53/6.38 ((
% 24.53/6.38 (binunionRsub) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectI) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectSubset5) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectEL) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectLsub) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectSubset2) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectSubset3) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectER) =>
% 24.53/6.38 ((
% 24.53/6.38 (disjointsetsI1) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectRsub) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectSubset4) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectSubset1) =>
% 24.53/6.38 ((
% 24.53/6.38 (bs114d) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusI) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusEL) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusER) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusSubset2) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusERneg) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusELneg) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusILneg) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusIRneg) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusLsub) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusSubset1) =>
% 24.53/6.38 ((
% 24.53/6.38 (symdiffE) =>
% 24.53/6.38 ((
% 24.53/6.38 (symdiffI1) =>
% 24.53/6.38 ((
% 24.53/6.38 (symdiffI2) =>
% 24.53/6.38 ((
% 24.53/6.38 (symdiffIneg1) =>
% 24.53/6.38 ((
% 24.53/6.38 (symdiffIneg2) =>
% 24.53/6.38 ((
% 24.53/6.38 (secondinupair) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairIL) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairIR) =>
% 24.53/6.38 ((
% 24.53/6.38 (kpairiskpair) =>
% 24.53/6.38 ((
% 24.53/6.38 (kpairp) =>
% 24.53/6.38 ((
% 24.53/6.38 (singletonsubset) =>
% 24.53/6.38 ((
% 24.53/6.38 (singletoninpowerset) =>
% 24.53/6.38 ((
% 24.53/6.38 (singletoninpowunion) =>
% 24.53/6.38 ((
% 24.53/6.38 (upairset2E) =>
% 24.53/6.38 ((
% 24.53/6.38 (upairsubunion) =>
% 24.53/6.38 ((
% 24.53/6.38 (upairinpowunion) =>
% 24.53/6.38 ((
% 24.53/6.38 (ubforcartprodlem1) =>
% 24.53/6.38 ((
% 24.53/6.38 (ubforcartprodlem2) =>
% 24.53/6.38 ((
% 24.53/6.38 (ubforcartprodlem3) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodpairin) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodmempair1) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodmempair) =>
% 24.53/6.38 ((
% 24.53/6.38 (setunionE2) =>
% 24.53/6.38 ((
% 24.53/6.38 (setunionsingleton1) =>
% 24.53/6.38 ((
% 24.53/6.38 (setunionsingleton2) =>
% 24.53/6.38 ((
% 24.53/6.38 (setunionsingleton) =>
% 24.53/6.38 ((
% 24.53/6.38 (singletonprop) =>
% 24.53/6.38 ((
% 24.53/6.38 (ex1E1) =>
% 24.53/6.38 ((
% 24.53/6.38 (ex1I) =>
% 24.53/6.38 ((
% 24.53/6.38 (ex1I2) =>
% 24.53/6.38 ((
% 24.53/6.38 (singletonsuniq) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairinjL1) =>
% 24.53/6.38 ((
% 24.53/6.38 (kfstsingleton) =>
% 24.53/6.38 ((
% 24.53/6.38 (theprop) =>
% 24.53/6.38 ((
% 24.53/6.38 (kfstpairEq) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodfstin) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairinjL2) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairinjL) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairinjR11) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairinjR12) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairinjR1) =>
% 24.53/6.38 ((
% 24.53/6.38 (upairequniteq) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairinjR2) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairinjR) =>
% 24.53/6.38 ((
% 24.53/6.38 (ksndsingleton) =>
% 24.53/6.38 ((
% 24.53/6.38 (ksndpairEq) =>
% 24.53/6.38 ((
% 24.53/6.38 (kpairsurjEq) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodsndin) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodpairmemEL) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodpairmemER) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodmempaircEq) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodfstpairEq) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodsndpairEq) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodpairsurjEq) =>
% 24.53/6.38 ((
% 24.53/6.38 (dpsetconstrI) =>
% 24.53/6.38 ((
% 24.53/6.38 (!!) @ (
% 24.53/6.38 (('#B') @ (
% 24.53/6.38 !!) @
% 24.53/6.38 (
% 24.53/6.38 (
% 24.53/6.38 ('#B') @ (
% 24.53/6.38 (
% 24.53/6.38 ('#B') @ (
% 24.53/6.38 !!))) @
% 24.53/6.38 (
% 24.53/6.38 (
% 24.53/6.38 ('#S') @ (
% 24.53/6.38 (
% 24.53/6.38 ('#B') @ (
% 24.53/6.38 '#S') @
% 24.53/6.38 (
% 24.53/6.38 (
% 24.53/6.38 ('#B') @ (
% 24.53/6.38 (
% 24.53/6.38 ('#B') @ (
% 24.53/6.38 '#C'))) @
% 24.53/6.38 (
% 24.53/6.38 (
% 24.53/6.38 ('#B') @ (
% 24.53/6.38 (
% 24.53/6.38 ('#B') @ (
% 24.53/6.38 (
% 24.53/6.38 ('#B') @ subset)))) @
% 24.53/6.38 dpsetconstr)))))) @
% 24.53/6.38 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl672])).
% 24.53/6.38 thf(zip_derived_cl699, plain,
% 24.53/6.38 (~ (((powerset__Cong) =>
% 24.53/6.38 (((setunion__Cong) =>
% 24.53/6.38 (((exuEu) =>
% 24.53/6.38 (((descr__Cong) =>
% 24.53/6.38 (((dsetconstr__Cong) =>
% 24.53/6.38 (((subsetI1) =>
% 24.53/6.38 (((eqimpsubset2) =>
% 24.53/6.38 (((eqimpsubset1) =>
% 24.53/6.38 (((subsetI2) =>
% 24.53/6.38 (((emptysetsubset) =>
% 24.53/6.38 (((subsetE) =>
% 24.53/6.38 (((subsetE2) =>
% 24.53/6.38 (((notsubsetI) =>
% 24.53/6.38 (((notequalI1) =>
% 24.53/6.38 (((notequalI2) =>
% 24.53/6.38 (((subsetRefl) =>
% 24.53/6.38 (((subsetTrans) =>
% 24.53/6.38 (((setadjoinSub) =>
% 24.53/6.38 (((setadjoinSub2) =>
% 24.53/6.38 (((subset2powerset) =>
% 24.53/6.38 (((setextsub) =>
% 24.53/6.38 (((subsetemptysetimpeq) =>
% 24.53/6.38 (((powersetI1) =>
% 24.53/6.38 (((powersetE1) =>
% 24.53/6.38 (((inPowerset) =>
% 24.53/6.38 (((powersetsubset) =>
% 24.53/6.38 (((sepInPowerset) =>
% 24.53/6.38 (((sepSubset) =>
% 24.53/6.38 (((binunionIL) =>
% 24.53/6.38 (((upairset2IR) =>
% 24.53/6.38 ((
% 24.53/6.38 (binunionIR) =>
% 24.53/6.38 ((
% 24.53/6.38 (binunionEcases) =>
% 24.53/6.38 ((
% 24.53/6.38 (binunionE) =>
% 24.53/6.38 ((
% 24.53/6.38 (binunionLsub) =>
% 24.53/6.38 ((
% 24.53/6.38 (binunionRsub) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectI) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectSubset5) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectEL) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectLsub) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectSubset2) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectSubset3) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectER) =>
% 24.53/6.38 ((
% 24.53/6.38 (disjointsetsI1) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectRsub) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectSubset4) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectSubset1) =>
% 24.53/6.38 ((
% 24.53/6.38 (bs114d) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusI) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusEL) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusER) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusSubset2) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusERneg) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusELneg) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusILneg) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusIRneg) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusLsub) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusSubset1) =>
% 24.53/6.38 ((
% 24.53/6.38 (symdiffE) =>
% 24.53/6.38 ((
% 24.53/6.38 (symdiffI1) =>
% 24.53/6.38 ((
% 24.53/6.38 (symdiffI2) =>
% 24.53/6.38 ((
% 24.53/6.38 (symdiffIneg1) =>
% 24.53/6.38 ((
% 24.53/6.38 (symdiffIneg2) =>
% 24.53/6.38 ((
% 24.53/6.38 (secondinupair) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairIL) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairIR) =>
% 24.53/6.38 ((
% 24.53/6.38 (kpairiskpair) =>
% 24.53/6.38 ((
% 24.53/6.38 (kpairp) =>
% 24.53/6.38 ((
% 24.53/6.38 (singletonsubset) =>
% 24.53/6.38 ((
% 24.53/6.38 (singletoninpowerset) =>
% 24.53/6.38 ((
% 24.53/6.38 (singletoninpowunion) =>
% 24.53/6.38 ((
% 24.53/6.38 (upairset2E) =>
% 24.53/6.38 ((
% 24.53/6.38 (upairsubunion) =>
% 24.53/6.38 ((
% 24.53/6.38 (upairinpowunion) =>
% 24.53/6.38 ((
% 24.53/6.38 (ubforcartprodlem1) =>
% 24.53/6.38 ((
% 24.53/6.38 (ubforcartprodlem2) =>
% 24.53/6.38 ((
% 24.53/6.38 (ubforcartprodlem3) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodpairin) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodmempair1) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodmempair) =>
% 24.53/6.38 ((
% 24.53/6.38 (setunionE2) =>
% 24.53/6.38 ((
% 24.53/6.38 (setunionsingleton1) =>
% 24.53/6.38 ((
% 24.53/6.38 (setunionsingleton2) =>
% 24.53/6.38 ((
% 24.53/6.38 (setunionsingleton) =>
% 24.53/6.38 ((
% 24.53/6.38 (singletonprop) =>
% 24.53/6.38 ((
% 24.53/6.38 (ex1E1) =>
% 24.53/6.38 ((
% 24.53/6.38 (ex1I) =>
% 24.53/6.38 ((
% 24.53/6.38 (ex1I2) =>
% 24.53/6.38 ((
% 24.53/6.38 (singletonsuniq) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairinjL1) =>
% 24.53/6.38 ((
% 24.53/6.38 (kfstsingleton) =>
% 24.53/6.38 ((
% 24.53/6.38 (theprop) =>
% 24.53/6.38 ((
% 24.53/6.38 (kfstpairEq) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodfstin) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairinjL2) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairinjL) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairinjR11) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairinjR12) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairinjR1) =>
% 24.53/6.38 ((
% 24.53/6.38 (upairequniteq) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairinjR2) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairinjR) =>
% 24.53/6.38 ((
% 24.53/6.38 (ksndsingleton) =>
% 24.53/6.38 ((
% 24.53/6.38 (ksndpairEq) =>
% 24.53/6.38 ((
% 24.53/6.38 (kpairsurjEq) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodsndin) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodpairmemEL) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodpairmemER) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodmempaircEq) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodfstpairEq) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodsndpairEq) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodpairsurjEq) =>
% 24.53/6.38 ((
% 24.53/6.38 (dpsetconstrI) =>
% 24.53/6.38 ((
% 24.53/6.38 (!!) @ (
% 24.53/6.38 (('#B') @ (
% 24.53/6.38 !!) @
% 24.53/6.38 (
% 24.53/6.38 (
% 24.53/6.38 ('#B') @ (
% 24.53/6.38 (
% 24.53/6.38 ('#B') @ (
% 24.53/6.38 !!))) @
% 24.53/6.38 (
% 24.53/6.38 (
% 24.53/6.38 ('#S') @ (
% 24.53/6.38 (
% 24.53/6.38 ('#B') @ (
% 24.53/6.38 '#S') @
% 24.53/6.38 (
% 24.53/6.38 (
% 24.53/6.38 ('#B') @ (
% 24.53/6.38 (
% 24.53/6.38 ('#B') @ (
% 24.53/6.38 '#C'))) @
% 24.53/6.38 (
% 24.53/6.38 (
% 24.53/6.38 ('#B') @ (
% 24.53/6.38 (
% 24.53/6.38 ('#B') @ (
% 24.53/6.38 (
% 24.53/6.38 ('#B') @ subset)))) @
% 24.53/6.38 dpsetconstr)))))) @
% 24.53/6.38 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl685])).
% 24.53/6.38 thf(zip_derived_cl714, plain,
% 24.53/6.38 (~ (((setunion__Cong) =>
% 24.53/6.38 (((exuEu) =>
% 24.53/6.38 (((descr__Cong) =>
% 24.53/6.38 (((dsetconstr__Cong) =>
% 24.53/6.38 (((subsetI1) =>
% 24.53/6.38 (((eqimpsubset2) =>
% 24.53/6.38 (((eqimpsubset1) =>
% 24.53/6.38 (((subsetI2) =>
% 24.53/6.38 (((emptysetsubset) =>
% 24.53/6.38 (((subsetE) =>
% 24.53/6.38 (((subsetE2) =>
% 24.53/6.38 (((notsubsetI) =>
% 24.53/6.38 (((notequalI1) =>
% 24.53/6.38 (((notequalI2) =>
% 24.53/6.38 (((subsetRefl) =>
% 24.53/6.38 (((subsetTrans) =>
% 24.53/6.38 (((setadjoinSub) =>
% 24.53/6.38 (((setadjoinSub2) =>
% 24.53/6.38 (((subset2powerset) =>
% 24.53/6.38 (((setextsub) =>
% 24.53/6.38 (((subsetemptysetimpeq) =>
% 24.53/6.38 (((powersetI1) =>
% 24.53/6.38 (((powersetE1) =>
% 24.53/6.38 (((inPowerset) =>
% 24.53/6.38 (((powersetsubset) =>
% 24.53/6.38 (((sepInPowerset) =>
% 24.53/6.38 (((sepSubset) =>
% 24.53/6.38 (((binunionIL) =>
% 24.53/6.38 (((upairset2IR) =>
% 24.53/6.38 (((binunionIR) =>
% 24.53/6.38 ((
% 24.53/6.38 (binunionEcases) =>
% 24.53/6.38 ((
% 24.53/6.38 (binunionE) =>
% 24.53/6.38 ((
% 24.53/6.38 (binunionLsub) =>
% 24.53/6.38 ((
% 24.53/6.38 (binunionRsub) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectI) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectSubset5) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectEL) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectLsub) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectSubset2) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectSubset3) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectER) =>
% 24.53/6.38 ((
% 24.53/6.38 (disjointsetsI1) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectRsub) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectSubset4) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectSubset1) =>
% 24.53/6.38 ((
% 24.53/6.38 (bs114d) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusI) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusEL) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusER) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusSubset2) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusERneg) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusELneg) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusILneg) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusIRneg) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusLsub) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusSubset1) =>
% 24.53/6.38 ((
% 24.53/6.38 (symdiffE) =>
% 24.53/6.38 ((
% 24.53/6.38 (symdiffI1) =>
% 24.53/6.38 ((
% 24.53/6.38 (symdiffI2) =>
% 24.53/6.38 ((
% 24.53/6.38 (symdiffIneg1) =>
% 24.53/6.38 ((
% 24.53/6.38 (symdiffIneg2) =>
% 24.53/6.38 ((
% 24.53/6.38 (secondinupair) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairIL) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairIR) =>
% 24.53/6.38 ((
% 24.53/6.38 (kpairiskpair) =>
% 24.53/6.38 ((
% 24.53/6.38 (kpairp) =>
% 24.53/6.38 ((
% 24.53/6.38 (singletonsubset) =>
% 24.53/6.38 ((
% 24.53/6.38 (singletoninpowerset) =>
% 24.53/6.38 ((
% 24.53/6.38 (singletoninpowunion) =>
% 24.53/6.38 ((
% 24.53/6.38 (upairset2E) =>
% 24.53/6.38 ((
% 24.53/6.38 (upairsubunion) =>
% 24.53/6.38 ((
% 24.53/6.38 (upairinpowunion) =>
% 24.53/6.38 ((
% 24.53/6.38 (ubforcartprodlem1) =>
% 24.53/6.38 ((
% 24.53/6.38 (ubforcartprodlem2) =>
% 24.53/6.38 ((
% 24.53/6.38 (ubforcartprodlem3) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodpairin) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodmempair1) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodmempair) =>
% 24.53/6.38 ((
% 24.53/6.38 (setunionE2) =>
% 24.53/6.38 ((
% 24.53/6.38 (setunionsingleton1) =>
% 24.53/6.38 ((
% 24.53/6.38 (setunionsingleton2) =>
% 24.53/6.38 ((
% 24.53/6.38 (setunionsingleton) =>
% 24.53/6.38 ((
% 24.53/6.38 (singletonprop) =>
% 24.53/6.38 ((
% 24.53/6.38 (ex1E1) =>
% 24.53/6.38 ((
% 24.53/6.38 (ex1I) =>
% 24.53/6.38 ((
% 24.53/6.38 (ex1I2) =>
% 24.53/6.38 ((
% 24.53/6.38 (singletonsuniq) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairinjL1) =>
% 24.53/6.38 ((
% 24.53/6.38 (kfstsingleton) =>
% 24.53/6.38 ((
% 24.53/6.38 (theprop) =>
% 24.53/6.38 ((
% 24.53/6.38 (kfstpairEq) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodfstin) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairinjL2) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairinjL) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairinjR11) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairinjR12) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairinjR1) =>
% 24.53/6.38 ((
% 24.53/6.38 (upairequniteq) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairinjR2) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairinjR) =>
% 24.53/6.38 ((
% 24.53/6.38 (ksndsingleton) =>
% 24.53/6.38 ((
% 24.53/6.38 (ksndpairEq) =>
% 24.53/6.38 ((
% 24.53/6.38 (kpairsurjEq) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodsndin) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodpairmemEL) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodpairmemER) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodmempaircEq) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodfstpairEq) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodsndpairEq) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodpairsurjEq) =>
% 24.53/6.38 ((
% 24.53/6.38 (dpsetconstrI) =>
% 24.53/6.38 ((
% 24.53/6.38 (!!) @ (
% 24.53/6.38 (('#B') @ (
% 24.53/6.38 !!) @
% 24.53/6.38 (
% 24.53/6.38 (
% 24.53/6.38 ('#B') @ (
% 24.53/6.38 (
% 24.53/6.38 ('#B') @ (
% 24.53/6.38 !!))) @
% 24.53/6.38 (
% 24.53/6.38 (
% 24.53/6.38 ('#S') @ (
% 24.53/6.38 (
% 24.53/6.38 ('#B') @ (
% 24.53/6.38 '#S') @
% 24.53/6.38 (
% 24.53/6.38 (
% 24.53/6.38 ('#B') @ (
% 24.53/6.38 (
% 24.53/6.38 ('#B') @ (
% 24.53/6.38 '#C'))) @
% 24.53/6.38 (
% 24.53/6.38 (
% 24.53/6.38 ('#B') @ (
% 24.53/6.38 (
% 24.53/6.38 ('#B') @ (
% 24.53/6.38 (
% 24.53/6.38 ('#B') @ subset)))) @
% 24.53/6.38 dpsetconstr)))))) @
% 24.53/6.38 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl699])).
% 24.53/6.38 thf(zip_derived_cl731, plain,
% 24.53/6.38 (~ (((exuEu) =>
% 24.53/6.38 (((descr__Cong) =>
% 24.53/6.38 (((dsetconstr__Cong) =>
% 24.53/6.38 (((subsetI1) =>
% 24.53/6.38 (((eqimpsubset2) =>
% 24.53/6.38 (((eqimpsubset1) =>
% 24.53/6.38 (((subsetI2) =>
% 24.53/6.38 (((emptysetsubset) =>
% 24.53/6.38 (((subsetE) =>
% 24.53/6.38 (((subsetE2) =>
% 24.53/6.38 (((notsubsetI) =>
% 24.53/6.38 (((notequalI1) =>
% 24.53/6.38 (((notequalI2) =>
% 24.53/6.38 (((subsetRefl) =>
% 24.53/6.38 (((subsetTrans) =>
% 24.53/6.38 (((setadjoinSub) =>
% 24.53/6.38 (((setadjoinSub2) =>
% 24.53/6.38 (((subset2powerset) =>
% 24.53/6.38 (((setextsub) =>
% 24.53/6.38 (((subsetemptysetimpeq) =>
% 24.53/6.38 (((powersetI1) =>
% 24.53/6.38 (((powersetE1) =>
% 24.53/6.38 (((inPowerset) =>
% 24.53/6.38 (((powersetsubset) =>
% 24.53/6.38 (((sepInPowerset) =>
% 24.53/6.38 (((sepSubset) =>
% 24.53/6.38 (((binunionIL) =>
% 24.53/6.38 (((upairset2IR) =>
% 24.53/6.38 (((binunionIR) =>
% 24.53/6.38 (((binunionEcases) =>
% 24.53/6.38 ((
% 24.53/6.38 (binunionE) =>
% 24.53/6.38 ((
% 24.53/6.38 (binunionLsub) =>
% 24.53/6.38 ((
% 24.53/6.38 (binunionRsub) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectI) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectSubset5) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectEL) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectLsub) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectSubset2) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectSubset3) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectER) =>
% 24.53/6.38 ((
% 24.53/6.38 (disjointsetsI1) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectRsub) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectSubset4) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectSubset1) =>
% 24.53/6.38 ((
% 24.53/6.38 (bs114d) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusI) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusEL) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusER) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusSubset2) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusERneg) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusELneg) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusILneg) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusIRneg) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusLsub) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusSubset1) =>
% 24.53/6.38 ((
% 24.53/6.38 (symdiffE) =>
% 24.53/6.38 ((
% 24.53/6.38 (symdiffI1) =>
% 24.53/6.38 ((
% 24.53/6.38 (symdiffI2) =>
% 24.53/6.38 ((
% 24.53/6.38 (symdiffIneg1) =>
% 24.53/6.38 ((
% 24.53/6.38 (symdiffIneg2) =>
% 24.53/6.38 ((
% 24.53/6.38 (secondinupair) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairIL) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairIR) =>
% 24.53/6.38 ((
% 24.53/6.38 (kpairiskpair) =>
% 24.53/6.38 ((
% 24.53/6.38 (kpairp) =>
% 24.53/6.38 ((
% 24.53/6.38 (singletonsubset) =>
% 24.53/6.38 ((
% 24.53/6.38 (singletoninpowerset) =>
% 24.53/6.38 ((
% 24.53/6.38 (singletoninpowunion) =>
% 24.53/6.38 ((
% 24.53/6.38 (upairset2E) =>
% 24.53/6.38 ((
% 24.53/6.38 (upairsubunion) =>
% 24.53/6.38 ((
% 24.53/6.38 (upairinpowunion) =>
% 24.53/6.38 ((
% 24.53/6.38 (ubforcartprodlem1) =>
% 24.53/6.38 ((
% 24.53/6.38 (ubforcartprodlem2) =>
% 24.53/6.38 ((
% 24.53/6.38 (ubforcartprodlem3) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodpairin) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodmempair1) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodmempair) =>
% 24.53/6.38 ((
% 24.53/6.38 (setunionE2) =>
% 24.53/6.38 ((
% 24.53/6.38 (setunionsingleton1) =>
% 24.53/6.38 ((
% 24.53/6.38 (setunionsingleton2) =>
% 24.53/6.38 ((
% 24.53/6.38 (setunionsingleton) =>
% 24.53/6.38 ((
% 24.53/6.38 (singletonprop) =>
% 24.53/6.38 ((
% 24.53/6.38 (ex1E1) =>
% 24.53/6.38 ((
% 24.53/6.38 (ex1I) =>
% 24.53/6.38 ((
% 24.53/6.38 (ex1I2) =>
% 24.53/6.38 ((
% 24.53/6.38 (singletonsuniq) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairinjL1) =>
% 24.53/6.38 ((
% 24.53/6.38 (kfstsingleton) =>
% 24.53/6.38 ((
% 24.53/6.38 (theprop) =>
% 24.53/6.38 ((
% 24.53/6.38 (kfstpairEq) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodfstin) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairinjL2) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairinjL) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairinjR11) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairinjR12) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairinjR1) =>
% 24.53/6.38 ((
% 24.53/6.38 (upairequniteq) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairinjR2) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairinjR) =>
% 24.53/6.38 ((
% 24.53/6.38 (ksndsingleton) =>
% 24.53/6.38 ((
% 24.53/6.38 (ksndpairEq) =>
% 24.53/6.38 ((
% 24.53/6.38 (kpairsurjEq) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodsndin) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodpairmemEL) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodpairmemER) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodmempaircEq) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodfstpairEq) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodsndpairEq) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodpairsurjEq) =>
% 24.53/6.38 ((
% 24.53/6.38 (dpsetconstrI) =>
% 24.53/6.38 ((
% 24.53/6.38 (!!) @ (
% 24.53/6.38 (('#B') @ (
% 24.53/6.38 !!) @
% 24.53/6.38 (
% 24.53/6.38 (
% 24.53/6.38 ('#B') @ (
% 24.53/6.38 (
% 24.53/6.38 ('#B') @ (
% 24.53/6.38 !!))) @
% 24.53/6.38 (
% 24.53/6.38 (
% 24.53/6.38 ('#S') @ (
% 24.53/6.38 (
% 24.53/6.38 ('#B') @ (
% 24.53/6.38 '#S') @
% 24.53/6.38 (
% 24.53/6.38 (
% 24.53/6.38 ('#B') @ (
% 24.53/6.38 (
% 24.53/6.38 ('#B') @ (
% 24.53/6.38 '#C'))) @
% 24.53/6.38 (
% 24.53/6.38 (
% 24.53/6.38 ('#B') @ (
% 24.53/6.38 (
% 24.53/6.38 ('#B') @ (
% 24.53/6.38 (
% 24.53/6.38 ('#B') @ subset)))) @
% 24.53/6.38 dpsetconstr)))))) @
% 24.53/6.38 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl714])).
% 24.53/6.38 thf(zip_derived_cl749, plain,
% 24.53/6.38 (~ (((descr__Cong) =>
% 24.53/6.38 (((dsetconstr__Cong) =>
% 24.53/6.38 (((subsetI1) =>
% 24.53/6.38 (((eqimpsubset2) =>
% 24.53/6.38 (((eqimpsubset1) =>
% 24.53/6.38 (((subsetI2) =>
% 24.53/6.38 (((emptysetsubset) =>
% 24.53/6.38 (((subsetE) =>
% 24.53/6.38 (((subsetE2) =>
% 24.53/6.38 (((notsubsetI) =>
% 24.53/6.38 (((notequalI1) =>
% 24.53/6.38 (((notequalI2) =>
% 24.53/6.38 (((subsetRefl) =>
% 24.53/6.38 (((subsetTrans) =>
% 24.53/6.38 (((setadjoinSub) =>
% 24.53/6.38 (((setadjoinSub2) =>
% 24.53/6.38 (((subset2powerset) =>
% 24.53/6.38 (((setextsub) =>
% 24.53/6.38 (((subsetemptysetimpeq) =>
% 24.53/6.38 (((powersetI1) =>
% 24.53/6.38 (((powersetE1) =>
% 24.53/6.38 (((inPowerset) =>
% 24.53/6.38 (((powersetsubset) =>
% 24.53/6.38 (((sepInPowerset) =>
% 24.53/6.38 (((sepSubset) =>
% 24.53/6.38 (((binunionIL) =>
% 24.53/6.38 (((upairset2IR) =>
% 24.53/6.38 (((binunionIR) =>
% 24.53/6.38 (((binunionEcases) =>
% 24.53/6.38 (((binunionE) =>
% 24.53/6.38 ((
% 24.53/6.38 (binunionLsub) =>
% 24.53/6.38 ((
% 24.53/6.38 (binunionRsub) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectI) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectSubset5) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectEL) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectLsub) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectSubset2) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectSubset3) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectER) =>
% 24.53/6.38 ((
% 24.53/6.38 (disjointsetsI1) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectRsub) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectSubset4) =>
% 24.53/6.38 ((
% 24.53/6.38 (binintersectSubset1) =>
% 24.53/6.38 ((
% 24.53/6.38 (bs114d) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusI) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusEL) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusER) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusSubset2) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusERneg) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusELneg) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusILneg) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusIRneg) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusLsub) =>
% 24.53/6.38 ((
% 24.53/6.38 (setminusSubset1) =>
% 24.53/6.38 ((
% 24.53/6.38 (symdiffE) =>
% 24.53/6.38 ((
% 24.53/6.38 (symdiffI1) =>
% 24.53/6.38 ((
% 24.53/6.38 (symdiffI2) =>
% 24.53/6.38 ((
% 24.53/6.38 (symdiffIneg1) =>
% 24.53/6.38 ((
% 24.53/6.38 (symdiffIneg2) =>
% 24.53/6.38 ((
% 24.53/6.38 (secondinupair) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairIL) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairIR) =>
% 24.53/6.38 ((
% 24.53/6.38 (kpairiskpair) =>
% 24.53/6.38 ((
% 24.53/6.38 (kpairp) =>
% 24.53/6.38 ((
% 24.53/6.38 (singletonsubset) =>
% 24.53/6.38 ((
% 24.53/6.38 (singletoninpowerset) =>
% 24.53/6.38 ((
% 24.53/6.38 (singletoninpowunion) =>
% 24.53/6.38 ((
% 24.53/6.38 (upairset2E) =>
% 24.53/6.38 ((
% 24.53/6.38 (upairsubunion) =>
% 24.53/6.38 ((
% 24.53/6.38 (upairinpowunion) =>
% 24.53/6.38 ((
% 24.53/6.38 (ubforcartprodlem1) =>
% 24.53/6.38 ((
% 24.53/6.38 (ubforcartprodlem2) =>
% 24.53/6.38 ((
% 24.53/6.38 (ubforcartprodlem3) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodpairin) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodmempair1) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodmempair) =>
% 24.53/6.38 ((
% 24.53/6.38 (setunionE2) =>
% 24.53/6.38 ((
% 24.53/6.38 (setunionsingleton1) =>
% 24.53/6.38 ((
% 24.53/6.38 (setunionsingleton2) =>
% 24.53/6.38 ((
% 24.53/6.38 (setunionsingleton) =>
% 24.53/6.38 ((
% 24.53/6.38 (singletonprop) =>
% 24.53/6.38 ((
% 24.53/6.38 (ex1E1) =>
% 24.53/6.38 ((
% 24.53/6.38 (ex1I) =>
% 24.53/6.38 ((
% 24.53/6.38 (ex1I2) =>
% 24.53/6.38 ((
% 24.53/6.38 (singletonsuniq) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairinjL1) =>
% 24.53/6.38 ((
% 24.53/6.38 (kfstsingleton) =>
% 24.53/6.38 ((
% 24.53/6.38 (theprop) =>
% 24.53/6.38 ((
% 24.53/6.38 (kfstpairEq) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodfstin) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairinjL2) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairinjL) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairinjR11) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairinjR12) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairinjR1) =>
% 24.53/6.38 ((
% 24.53/6.38 (upairequniteq) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairinjR2) =>
% 24.53/6.38 ((
% 24.53/6.38 (setukpairinjR) =>
% 24.53/6.38 ((
% 24.53/6.38 (ksndsingleton) =>
% 24.53/6.38 ((
% 24.53/6.38 (ksndpairEq) =>
% 24.53/6.38 ((
% 24.53/6.38 (kpairsurjEq) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodsndin) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodpairmemEL) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodpairmemER) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodmempaircEq) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodfstpairEq) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodsndpairEq) =>
% 24.53/6.38 ((
% 24.53/6.38 (cartprodpairsurjEq) =>
% 24.53/6.38 ((
% 24.53/6.38 (dpsetconstrI) =>
% 24.53/6.38 ((
% 24.53/6.38 (!!) @ (
% 24.53/6.38 (('#B') @ (
% 24.53/6.38 !!) @
% 24.53/6.38 (
% 24.53/6.38 (
% 24.53/6.38 ('#B') @ (
% 24.53/6.38 (
% 24.53/6.38 ('#B') @ (
% 24.53/6.38 !!))) @
% 24.53/6.38 (
% 24.53/6.38 (
% 24.53/6.38 ('#S') @ (
% 24.53/6.38 (
% 24.53/6.38 ('#B') @ (
% 24.53/6.38 '#S') @
% 24.53/6.38 (
% 24.53/6.38 (
% 24.53/6.38 ('#B') @ (
% 24.53/6.38 (
% 24.53/6.38 ('#B') @ (
% 24.53/6.38 '#C'))) @
% 24.53/6.38 (
% 24.53/6.38 (
% 24.53/6.38 ('#B') @ (
% 24.53/6.38 (
% 24.53/6.38 ('#B') @ (
% 24.53/6.38 (
% 24.53/6.38 ('#B') @ subset)))) @
% 24.53/6.38 dpsetconstr)))))) @
% 24.53/6.38 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl731])).
% 24.53/6.38 thf(zip_derived_cl769, plain,
% 24.53/6.38 (~ (((dsetconstr__Cong) =>
% 24.53/6.38 (((subsetI1) =>
% 24.53/6.38 (((eqimpsubset2) =>
% 24.53/6.38 (((eqimpsubset1) =>
% 24.53/6.38 (((subsetI2) =>
% 24.53/6.38 (((emptysetsubset) =>
% 24.53/6.38 (((subsetE) =>
% 24.53/6.38 (((subsetE2) =>
% 24.53/6.38 (((notsubsetI) =>
% 24.53/6.38 (((notequalI1) =>
% 24.53/6.38 (((notequalI2) =>
% 24.53/6.38 (((subsetRefl) =>
% 24.53/6.38 (((subsetTrans) =>
% 24.53/6.38 (((setadjoinSub) =>
% 24.53/6.38 (((setadjoinSub2) =>
% 24.53/6.38 (((subset2powerset) =>
% 24.53/6.38 (((setextsub) =>
% 24.53/6.38 (((subsetemptysetimpeq) =>
% 24.53/6.38 (((powersetI1) =>
% 24.53/6.38 (((powersetE1) =>
% 24.53/6.38 (((inPowerset) =>
% 24.53/6.38 (((powersetsubset) =>
% 24.53/6.38 (((sepInPowerset) =>
% 24.53/6.38 (((sepSubset) =>
% 24.53/6.38 (((binunionIL) =>
% 24.53/6.38 (((upairset2IR) =>
% 24.53/6.39 (((binunionIR) =>
% 24.53/6.39 (((binunionEcases) =>
% 24.53/6.39 (((binunionE) =>
% 24.53/6.39 (((binunionLsub) =>
% 24.53/6.39 ((
% 24.53/6.39 (binunionRsub) =>
% 24.53/6.39 ((
% 24.53/6.39 (binintersectI) =>
% 24.53/6.39 ((
% 24.53/6.39 (binintersectSubset5) =>
% 24.53/6.39 ((
% 24.53/6.39 (binintersectEL) =>
% 24.53/6.39 ((
% 24.53/6.39 (binintersectLsub) =>
% 24.53/6.39 ((
% 24.53/6.39 (binintersectSubset2) =>
% 24.53/6.39 ((
% 24.53/6.39 (binintersectSubset3) =>
% 24.53/6.39 ((
% 24.53/6.39 (binintersectER) =>
% 24.53/6.39 ((
% 24.53/6.39 (disjointsetsI1) =>
% 24.53/6.39 ((
% 24.53/6.39 (binintersectRsub) =>
% 24.53/6.39 ((
% 24.53/6.39 (binintersectSubset4) =>
% 24.53/6.39 ((
% 24.53/6.39 (binintersectSubset1) =>
% 24.53/6.39 ((
% 24.53/6.39 (bs114d) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusI) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusEL) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusER) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusSubset2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusERneg) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusELneg) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusILneg) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusIRneg) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusLsub) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusSubset1) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffE) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffI1) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffI2) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffIneg1) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffIneg2) =>
% 24.53/6.39 ((
% 24.53/6.39 (secondinupair) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairIL) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairIR) =>
% 24.53/6.39 ((
% 24.53/6.39 (kpairiskpair) =>
% 24.53/6.39 ((
% 24.53/6.39 (kpairp) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletonsubset) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletoninpowerset) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletoninpowunion) =>
% 24.53/6.39 ((
% 24.53/6.39 (upairset2E) =>
% 24.53/6.39 ((
% 24.53/6.39 (upairsubunion) =>
% 24.53/6.39 ((
% 24.53/6.39 (upairinpowunion) =>
% 24.53/6.39 ((
% 24.53/6.39 (ubforcartprodlem1) =>
% 24.53/6.39 ((
% 24.53/6.39 (ubforcartprodlem2) =>
% 24.53/6.39 ((
% 24.53/6.39 (ubforcartprodlem3) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodpairin) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodmempair1) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodmempair) =>
% 24.53/6.39 ((
% 24.53/6.39 (setunionE2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setunionsingleton1) =>
% 24.53/6.39 ((
% 24.53/6.39 (setunionsingleton2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setunionsingleton) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletonprop) =>
% 24.53/6.39 ((
% 24.53/6.39 (ex1E1) =>
% 24.53/6.39 ((
% 24.53/6.39 (ex1I) =>
% 24.53/6.39 ((
% 24.53/6.39 (ex1I2) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletonsuniq) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjL1) =>
% 24.53/6.39 ((
% 24.53/6.39 (kfstsingleton) =>
% 24.53/6.39 ((
% 24.53/6.39 (theprop) =>
% 24.53/6.39 ((
% 24.53/6.39 (kfstpairEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodfstin) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjL2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjL) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR11) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR12) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR1) =>
% 24.53/6.39 ((
% 24.53/6.39 (upairequniteq) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR) =>
% 24.53/6.39 ((
% 24.53/6.39 (ksndsingleton) =>
% 24.53/6.39 ((
% 24.53/6.39 (ksndpairEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (kpairsurjEq) =>
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% 24.53/6.39 (setminusELneg) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusILneg) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusIRneg) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusLsub) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusSubset1) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffE) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffI1) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffI2) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffIneg1) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffIneg2) =>
% 24.53/6.39 ((
% 24.53/6.39 (secondinupair) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairIL) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairIR) =>
% 24.53/6.39 ((
% 24.53/6.39 (kpairiskpair) =>
% 24.53/6.39 ((
% 24.53/6.39 (kpairp) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletonsubset) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletoninpowerset) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletoninpowunion) =>
% 24.53/6.39 ((
% 24.53/6.39 (upairset2E) =>
% 24.53/6.39 ((
% 24.53/6.39 (upairsubunion) =>
% 24.53/6.39 ((
% 24.53/6.39 (upairinpowunion) =>
% 24.53/6.39 ((
% 24.53/6.39 (ubforcartprodlem1) =>
% 24.53/6.39 ((
% 24.53/6.39 (ubforcartprodlem2) =>
% 24.53/6.39 ((
% 24.53/6.39 (ubforcartprodlem3) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodpairin) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodmempair1) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodmempair) =>
% 24.53/6.39 ((
% 24.53/6.39 (setunionE2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setunionsingleton1) =>
% 24.53/6.39 ((
% 24.53/6.39 (setunionsingleton2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setunionsingleton) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletonprop) =>
% 24.53/6.39 ((
% 24.53/6.39 (ex1E1) =>
% 24.53/6.39 ((
% 24.53/6.39 (ex1I) =>
% 24.53/6.39 ((
% 24.53/6.39 (ex1I2) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletonsuniq) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjL1) =>
% 24.53/6.39 ((
% 24.53/6.39 (kfstsingleton) =>
% 24.53/6.39 ((
% 24.53/6.39 (theprop) =>
% 24.53/6.39 ((
% 24.53/6.39 (kfstpairEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodfstin) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjL2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjL) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR11) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR12) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR1) =>
% 24.53/6.39 ((
% 24.53/6.39 (upairequniteq) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR) =>
% 24.53/6.39 ((
% 24.53/6.39 (ksndsingleton) =>
% 24.53/6.39 ((
% 24.53/6.39 (ksndpairEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (kpairsurjEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodsndin) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodpairmemEL) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodpairmemER) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodmempaircEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodfstpairEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodsndpairEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodpairsurjEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (dpsetconstrI) =>
% 24.53/6.39 ((
% 24.53/6.39 (!!) @ (
% 24.53/6.39 (('#B') @ (
% 24.53/6.39 !!) @
% 24.53/6.39 (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 !!))) @
% 24.53/6.39 (
% 24.53/6.39 (
% 24.53/6.39 ('#S') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 '#S') @
% 24.53/6.39 (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 '#C'))) @
% 24.53/6.39 (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ subset)))) @
% 24.53/6.39 dpsetconstr)))))) @
% 24.53/6.39 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl807])).
% 24.53/6.39 thf(zip_derived_cl838, plain,
% 24.53/6.39 (~ (((subsetI2) =>
% 24.53/6.39 (((emptysetsubset) =>
% 24.53/6.39 (((subsetE) =>
% 24.53/6.39 (((subsetE2) =>
% 24.53/6.39 (((notsubsetI) =>
% 24.53/6.39 (((notequalI1) =>
% 24.53/6.39 (((notequalI2) =>
% 24.53/6.39 (((subsetRefl) =>
% 24.53/6.39 (((subsetTrans) =>
% 24.53/6.39 (((setadjoinSub) =>
% 24.53/6.39 (((setadjoinSub2) =>
% 24.53/6.39 (((subset2powerset) =>
% 24.53/6.39 (((setextsub) =>
% 24.53/6.39 (((subsetemptysetimpeq) =>
% 24.53/6.39 (((powersetI1) =>
% 24.53/6.39 (((powersetE1) =>
% 24.53/6.39 (((inPowerset) =>
% 24.53/6.39 (((powersetsubset) =>
% 24.53/6.39 (((sepInPowerset) =>
% 24.53/6.39 (((sepSubset) =>
% 24.53/6.39 (((binunionIL) =>
% 24.53/6.39 (((upairset2IR) =>
% 24.53/6.39 (((binunionIR) =>
% 24.53/6.39 (((binunionEcases) =>
% 24.53/6.39 (((binunionE) =>
% 24.53/6.39 (((binunionLsub) =>
% 24.53/6.39 (((binunionRsub) =>
% 24.53/6.39 (((binintersectI) =>
% 24.53/6.39 (((binintersectSubset5) =>
% 24.53/6.39 (((binintersectEL) =>
% 24.53/6.39 ((
% 24.53/6.39 (binintersectLsub) =>
% 24.53/6.39 ((
% 24.53/6.39 (binintersectSubset2) =>
% 24.53/6.39 ((
% 24.53/6.39 (binintersectSubset3) =>
% 24.53/6.39 ((
% 24.53/6.39 (binintersectER) =>
% 24.53/6.39 ((
% 24.53/6.39 (disjointsetsI1) =>
% 24.53/6.39 ((
% 24.53/6.39 (binintersectRsub) =>
% 24.53/6.39 ((
% 24.53/6.39 (binintersectSubset4) =>
% 24.53/6.39 ((
% 24.53/6.39 (binintersectSubset1) =>
% 24.53/6.39 ((
% 24.53/6.39 (bs114d) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusI) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusEL) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusER) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusSubset2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusERneg) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusELneg) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusILneg) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusIRneg) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusLsub) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusSubset1) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffE) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffI1) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffI2) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffIneg1) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffIneg2) =>
% 24.53/6.39 ((
% 24.53/6.39 (secondinupair) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairIL) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairIR) =>
% 24.53/6.39 ((
% 24.53/6.39 (kpairiskpair) =>
% 24.53/6.39 ((
% 24.53/6.39 (kpairp) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletonsubset) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletoninpowerset) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletoninpowunion) =>
% 24.53/6.39 ((
% 24.53/6.39 (upairset2E) =>
% 24.53/6.39 ((
% 24.53/6.39 (upairsubunion) =>
% 24.53/6.39 ((
% 24.53/6.39 (upairinpowunion) =>
% 24.53/6.39 ((
% 24.53/6.39 (ubforcartprodlem1) =>
% 24.53/6.39 ((
% 24.53/6.39 (ubforcartprodlem2) =>
% 24.53/6.39 ((
% 24.53/6.39 (ubforcartprodlem3) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodpairin) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodmempair1) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodmempair) =>
% 24.53/6.39 ((
% 24.53/6.39 (setunionE2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setunionsingleton1) =>
% 24.53/6.39 ((
% 24.53/6.39 (setunionsingleton2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setunionsingleton) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletonprop) =>
% 24.53/6.39 ((
% 24.53/6.39 (ex1E1) =>
% 24.53/6.39 ((
% 24.53/6.39 (ex1I) =>
% 24.53/6.39 ((
% 24.53/6.39 (ex1I2) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletonsuniq) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjL1) =>
% 24.53/6.39 ((
% 24.53/6.39 (kfstsingleton) =>
% 24.53/6.39 ((
% 24.53/6.39 (theprop) =>
% 24.53/6.39 ((
% 24.53/6.39 (kfstpairEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodfstin) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjL2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjL) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR11) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR12) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR1) =>
% 24.53/6.39 ((
% 24.53/6.39 (upairequniteq) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR) =>
% 24.53/6.39 ((
% 24.53/6.39 (ksndsingleton) =>
% 24.53/6.39 ((
% 24.53/6.39 (ksndpairEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (kpairsurjEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodsndin) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodpairmemEL) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodpairmemER) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodmempaircEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodfstpairEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodsndpairEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodpairsurjEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (dpsetconstrI) =>
% 24.53/6.39 ((
% 24.53/6.39 (!!) @ (
% 24.53/6.39 (('#B') @ (
% 24.53/6.39 !!) @
% 24.53/6.39 (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 !!))) @
% 24.53/6.39 (
% 24.53/6.39 (
% 24.53/6.39 ('#S') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 '#S') @
% 24.53/6.39 (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 '#C'))) @
% 24.53/6.39 (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ subset)))) @
% 24.53/6.39 dpsetconstr)))))) @
% 24.53/6.39 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl824])).
% 24.53/6.39 thf(zip_derived_cl850, plain,
% 24.53/6.39 (~ (((emptysetsubset) =>
% 24.53/6.39 (((subsetE) =>
% 24.53/6.39 (((subsetE2) =>
% 24.53/6.39 (((notsubsetI) =>
% 24.53/6.39 (((notequalI1) =>
% 24.53/6.39 (((notequalI2) =>
% 24.53/6.39 (((subsetRefl) =>
% 24.53/6.39 (((subsetTrans) =>
% 24.53/6.39 (((setadjoinSub) =>
% 24.53/6.39 (((setadjoinSub2) =>
% 24.53/6.39 (((subset2powerset) =>
% 24.53/6.39 (((setextsub) =>
% 24.53/6.39 (((subsetemptysetimpeq) =>
% 24.53/6.39 (((powersetI1) =>
% 24.53/6.39 (((powersetE1) =>
% 24.53/6.39 (((inPowerset) =>
% 24.53/6.39 (((powersetsubset) =>
% 24.53/6.39 (((sepInPowerset) =>
% 24.53/6.39 (((sepSubset) =>
% 24.53/6.39 (((binunionIL) =>
% 24.53/6.39 (((upairset2IR) =>
% 24.53/6.39 (((binunionIR) =>
% 24.53/6.39 (((binunionEcases) =>
% 24.53/6.39 (((binunionE) =>
% 24.53/6.39 (((binunionLsub) =>
% 24.53/6.39 (((binunionRsub) =>
% 24.53/6.39 (((binintersectI) =>
% 24.53/6.39 (((binintersectSubset5) =>
% 24.53/6.39 (((binintersectEL) =>
% 24.53/6.39 (((binintersectLsub) =>
% 24.53/6.39 ((
% 24.53/6.39 (binintersectSubset2) =>
% 24.53/6.39 ((
% 24.53/6.39 (binintersectSubset3) =>
% 24.53/6.39 ((
% 24.53/6.39 (binintersectER) =>
% 24.53/6.39 ((
% 24.53/6.39 (disjointsetsI1) =>
% 24.53/6.39 ((
% 24.53/6.39 (binintersectRsub) =>
% 24.53/6.39 ((
% 24.53/6.39 (binintersectSubset4) =>
% 24.53/6.39 ((
% 24.53/6.39 (binintersectSubset1) =>
% 24.53/6.39 ((
% 24.53/6.39 (bs114d) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusI) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusEL) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusER) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusSubset2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusERneg) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusELneg) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusILneg) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusIRneg) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusLsub) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusSubset1) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffE) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffI1) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffI2) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffIneg1) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffIneg2) =>
% 24.53/6.39 ((
% 24.53/6.39 (secondinupair) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairIL) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairIR) =>
% 24.53/6.39 ((
% 24.53/6.39 (kpairiskpair) =>
% 24.53/6.39 ((
% 24.53/6.39 (kpairp) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletonsubset) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletoninpowerset) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletoninpowunion) =>
% 24.53/6.39 ((
% 24.53/6.39 (upairset2E) =>
% 24.53/6.39 ((
% 24.53/6.39 (upairsubunion) =>
% 24.53/6.39 ((
% 24.53/6.39 (upairinpowunion) =>
% 24.53/6.39 ((
% 24.53/6.39 (ubforcartprodlem1) =>
% 24.53/6.39 ((
% 24.53/6.39 (ubforcartprodlem2) =>
% 24.53/6.39 ((
% 24.53/6.39 (ubforcartprodlem3) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodpairin) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodmempair1) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodmempair) =>
% 24.53/6.39 ((
% 24.53/6.39 (setunionE2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setunionsingleton1) =>
% 24.53/6.39 ((
% 24.53/6.39 (setunionsingleton2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setunionsingleton) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletonprop) =>
% 24.53/6.39 ((
% 24.53/6.39 (ex1E1) =>
% 24.53/6.39 ((
% 24.53/6.39 (ex1I) =>
% 24.53/6.39 ((
% 24.53/6.39 (ex1I2) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletonsuniq) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjL1) =>
% 24.53/6.39 ((
% 24.53/6.39 (kfstsingleton) =>
% 24.53/6.39 ((
% 24.53/6.39 (theprop) =>
% 24.53/6.39 ((
% 24.53/6.39 (kfstpairEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodfstin) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjL2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjL) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR11) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR12) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR1) =>
% 24.53/6.39 ((
% 24.53/6.39 (upairequniteq) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR) =>
% 24.53/6.39 ((
% 24.53/6.39 (ksndsingleton) =>
% 24.53/6.39 ((
% 24.53/6.39 (ksndpairEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (kpairsurjEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodsndin) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodpairmemEL) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodpairmemER) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodmempaircEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodfstpairEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodsndpairEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodpairsurjEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (dpsetconstrI) =>
% 24.53/6.39 ((
% 24.53/6.39 (!!) @ (
% 24.53/6.39 (('#B') @ (
% 24.53/6.39 !!) @
% 24.53/6.39 (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
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% 24.53/6.39 (
% 24.53/6.39 (
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% 24.53/6.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl838])).
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% 24.53/6.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl850])).
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% 24.53/6.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl863])).
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% 24.53/6.39 ((
% 24.53/6.39 (setminusIRneg) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusLsub) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusSubset1) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffE) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffI1) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffI2) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffIneg1) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffIneg2) =>
% 24.53/6.39 ((
% 24.53/6.39 (secondinupair) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairIL) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairIR) =>
% 24.53/6.39 ((
% 24.53/6.39 (kpairiskpair) =>
% 24.53/6.39 ((
% 24.53/6.39 (kpairp) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletonsubset) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletoninpowerset) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletoninpowunion) =>
% 24.53/6.39 ((
% 24.53/6.39 (upairset2E) =>
% 24.53/6.39 ((
% 24.53/6.39 (upairsubunion) =>
% 24.53/6.39 ((
% 24.53/6.39 (upairinpowunion) =>
% 24.53/6.39 ((
% 24.53/6.39 (ubforcartprodlem1) =>
% 24.53/6.39 ((
% 24.53/6.39 (ubforcartprodlem2) =>
% 24.53/6.39 ((
% 24.53/6.39 (ubforcartprodlem3) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodpairin) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodmempair1) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodmempair) =>
% 24.53/6.39 ((
% 24.53/6.39 (setunionE2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setunionsingleton1) =>
% 24.53/6.39 ((
% 24.53/6.39 (setunionsingleton2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setunionsingleton) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletonprop) =>
% 24.53/6.39 ((
% 24.53/6.39 (ex1E1) =>
% 24.53/6.39 ((
% 24.53/6.39 (ex1I) =>
% 24.53/6.39 ((
% 24.53/6.39 (ex1I2) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletonsuniq) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjL1) =>
% 24.53/6.39 ((
% 24.53/6.39 (kfstsingleton) =>
% 24.53/6.39 ((
% 24.53/6.39 (theprop) =>
% 24.53/6.39 ((
% 24.53/6.39 (kfstpairEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodfstin) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjL2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjL) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR11) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR12) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR1) =>
% 24.53/6.39 ((
% 24.53/6.39 (upairequniteq) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR) =>
% 24.53/6.39 ((
% 24.53/6.39 (ksndsingleton) =>
% 24.53/6.39 ((
% 24.53/6.39 (ksndpairEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (kpairsurjEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodsndin) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodpairmemEL) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodpairmemER) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodmempaircEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodfstpairEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodsndpairEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodpairsurjEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (dpsetconstrI) =>
% 24.53/6.39 ((
% 24.53/6.39 (!!) @ (
% 24.53/6.39 (('#B') @ (
% 24.53/6.39 !!) @
% 24.53/6.39 (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 !!))) @
% 24.53/6.39 (
% 24.53/6.39 (
% 24.53/6.39 ('#S') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 '#S') @
% 24.53/6.39 (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 '#C'))) @
% 24.53/6.39 (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ subset)))) @
% 24.53/6.39 dpsetconstr)))))) @
% 24.53/6.39 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl924])).
% 24.53/6.39 thf(zip_derived_cl952, plain,
% 24.53/6.39 (~ (((subsetTrans) =>
% 24.53/6.39 (((setadjoinSub) =>
% 24.53/6.39 (((setadjoinSub2) =>
% 24.53/6.39 (((subset2powerset) =>
% 24.53/6.39 (((setextsub) =>
% 24.53/6.39 (((subsetemptysetimpeq) =>
% 24.53/6.39 (((powersetI1) =>
% 24.53/6.39 (((powersetE1) =>
% 24.53/6.39 (((inPowerset) =>
% 24.53/6.39 (((powersetsubset) =>
% 24.53/6.39 (((sepInPowerset) =>
% 24.53/6.39 (((sepSubset) =>
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% 24.53/6.39 (((upairset2IR) =>
% 24.53/6.39 (((binunionIR) =>
% 24.53/6.39 (((binunionEcases) =>
% 24.53/6.39 (((binunionE) =>
% 24.53/6.39 (((binunionLsub) =>
% 24.53/6.39 (((binunionRsub) =>
% 24.53/6.39 (((binintersectI) =>
% 24.53/6.39 (((binintersectSubset5) =>
% 24.53/6.39 (((binintersectEL) =>
% 24.53/6.39 (((binintersectLsub) =>
% 24.53/6.39 (((binintersectSubset2) =>
% 24.53/6.39 (((binintersectSubset3) =>
% 24.53/6.39 (((binintersectER) =>
% 24.53/6.39 (((disjointsetsI1) =>
% 24.53/6.39 (((binintersectRsub) =>
% 24.53/6.39 (((binintersectSubset4) =>
% 24.53/6.39 (((binintersectSubset1) =>
% 24.53/6.39 ((
% 24.53/6.39 (bs114d) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusI) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusEL) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusER) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusSubset2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusERneg) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusELneg) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusILneg) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusIRneg) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusLsub) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusSubset1) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffE) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffI1) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffI2) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffIneg1) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffIneg2) =>
% 24.53/6.39 ((
% 24.53/6.39 (secondinupair) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairIL) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairIR) =>
% 24.53/6.39 ((
% 24.53/6.39 (kpairiskpair) =>
% 24.53/6.39 ((
% 24.53/6.39 (kpairp) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletonsubset) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletoninpowerset) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletoninpowunion) =>
% 24.53/6.39 ((
% 24.53/6.39 (upairset2E) =>
% 24.53/6.39 ((
% 24.53/6.39 (upairsubunion) =>
% 24.53/6.39 ((
% 24.53/6.39 (upairinpowunion) =>
% 24.53/6.39 ((
% 24.53/6.39 (ubforcartprodlem1) =>
% 24.53/6.39 ((
% 24.53/6.39 (ubforcartprodlem2) =>
% 24.53/6.39 ((
% 24.53/6.39 (ubforcartprodlem3) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodpairin) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodmempair1) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodmempair) =>
% 24.53/6.39 ((
% 24.53/6.39 (setunionE2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setunionsingleton1) =>
% 24.53/6.39 ((
% 24.53/6.39 (setunionsingleton2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setunionsingleton) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletonprop) =>
% 24.53/6.39 ((
% 24.53/6.39 (ex1E1) =>
% 24.53/6.39 ((
% 24.53/6.39 (ex1I) =>
% 24.53/6.39 ((
% 24.53/6.39 (ex1I2) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletonsuniq) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjL1) =>
% 24.53/6.39 ((
% 24.53/6.39 (kfstsingleton) =>
% 24.53/6.39 ((
% 24.53/6.39 (theprop) =>
% 24.53/6.39 ((
% 24.53/6.39 (kfstpairEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodfstin) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjL2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjL) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR11) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR12) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR1) =>
% 24.53/6.39 ((
% 24.53/6.39 (upairequniteq) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR) =>
% 24.53/6.39 ((
% 24.53/6.39 (ksndsingleton) =>
% 24.53/6.39 ((
% 24.53/6.39 (ksndpairEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (kpairsurjEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodsndin) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodpairmemEL) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodpairmemER) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodmempaircEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodfstpairEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodsndpairEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodpairsurjEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (dpsetconstrI) =>
% 24.53/6.39 ((
% 24.53/6.39 (!!) @ (
% 24.53/6.39 (('#B') @ (
% 24.53/6.39 !!) @
% 24.53/6.39 (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 !!))) @
% 24.53/6.39 (
% 24.53/6.39 (
% 24.53/6.39 ('#S') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 '#S') @
% 24.53/6.39 (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 '#C'))) @
% 24.53/6.39 (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ subset)))) @
% 24.53/6.39 dpsetconstr)))))) @
% 24.53/6.39 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl938])).
% 24.53/6.39 thf(zip_derived_cl967, plain,
% 24.53/6.39 (~ (((setadjoinSub) =>
% 24.53/6.39 (((setadjoinSub2) =>
% 24.53/6.39 (((subset2powerset) =>
% 24.53/6.39 (((setextsub) =>
% 24.53/6.39 (((subsetemptysetimpeq) =>
% 24.53/6.39 (((powersetI1) =>
% 24.53/6.39 (((powersetE1) =>
% 24.53/6.39 (((inPowerset) =>
% 24.53/6.39 (((powersetsubset) =>
% 24.53/6.39 (((sepInPowerset) =>
% 24.53/6.39 (((sepSubset) =>
% 24.53/6.39 (((binunionIL) =>
% 24.53/6.39 (((upairset2IR) =>
% 24.53/6.39 (((binunionIR) =>
% 24.53/6.39 (((binunionEcases) =>
% 24.53/6.39 (((binunionE) =>
% 24.53/6.39 (((binunionLsub) =>
% 24.53/6.39 (((binunionRsub) =>
% 24.53/6.39 (((binintersectI) =>
% 24.53/6.39 (((binintersectSubset5) =>
% 24.53/6.39 (((binintersectEL) =>
% 24.53/6.39 (((binintersectLsub) =>
% 24.53/6.39 (((binintersectSubset2) =>
% 24.53/6.39 (((binintersectSubset3) =>
% 24.53/6.39 (((binintersectER) =>
% 24.53/6.39 (((disjointsetsI1) =>
% 24.53/6.39 (((binintersectRsub) =>
% 24.53/6.39 (((binintersectSubset4) =>
% 24.53/6.39 (((binintersectSubset1) =>
% 24.53/6.39 (((bs114d) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusI) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusEL) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusER) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusSubset2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusERneg) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusELneg) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusILneg) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusIRneg) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusLsub) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusSubset1) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffE) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffI1) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffI2) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffIneg1) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffIneg2) =>
% 24.53/6.39 ((
% 24.53/6.39 (secondinupair) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairIL) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairIR) =>
% 24.53/6.39 ((
% 24.53/6.39 (kpairiskpair) =>
% 24.53/6.39 ((
% 24.53/6.39 (kpairp) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletonsubset) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletoninpowerset) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletoninpowunion) =>
% 24.53/6.39 ((
% 24.53/6.39 (upairset2E) =>
% 24.53/6.39 ((
% 24.53/6.39 (upairsubunion) =>
% 24.53/6.39 ((
% 24.53/6.39 (upairinpowunion) =>
% 24.53/6.39 ((
% 24.53/6.39 (ubforcartprodlem1) =>
% 24.53/6.39 ((
% 24.53/6.39 (ubforcartprodlem2) =>
% 24.53/6.39 ((
% 24.53/6.39 (ubforcartprodlem3) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodpairin) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodmempair1) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodmempair) =>
% 24.53/6.39 ((
% 24.53/6.39 (setunionE2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setunionsingleton1) =>
% 24.53/6.39 ((
% 24.53/6.39 (setunionsingleton2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setunionsingleton) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletonprop) =>
% 24.53/6.39 ((
% 24.53/6.39 (ex1E1) =>
% 24.53/6.39 ((
% 24.53/6.39 (ex1I) =>
% 24.53/6.39 ((
% 24.53/6.39 (ex1I2) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletonsuniq) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjL1) =>
% 24.53/6.39 ((
% 24.53/6.39 (kfstsingleton) =>
% 24.53/6.39 ((
% 24.53/6.39 (theprop) =>
% 24.53/6.39 ((
% 24.53/6.39 (kfstpairEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodfstin) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjL2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjL) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR11) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR12) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR1) =>
% 24.53/6.39 ((
% 24.53/6.39 (upairequniteq) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR) =>
% 24.53/6.39 ((
% 24.53/6.39 (ksndsingleton) =>
% 24.53/6.39 ((
% 24.53/6.39 (ksndpairEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (kpairsurjEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodsndin) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodpairmemEL) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodpairmemER) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodmempaircEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodfstpairEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodsndpairEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodpairsurjEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (dpsetconstrI) =>
% 24.53/6.39 ((
% 24.53/6.39 (!!) @ (
% 24.53/6.39 (('#B') @ (
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% 24.53/6.39 (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
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% 24.53/6.39 (
% 24.53/6.39 (
% 24.53/6.39 ('#S') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 '#S') @
% 24.53/6.39 (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
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% 24.53/6.39 (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ subset)))) @
% 24.53/6.39 dpsetconstr)))))) @
% 24.53/6.39 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl952])).
% 24.53/6.39 thf(zip_derived_cl984, plain,
% 24.53/6.39 (~ (((setadjoinSub2) =>
% 24.53/6.39 (((subset2powerset) =>
% 24.53/6.39 (((setextsub) =>
% 24.53/6.39 (((subsetemptysetimpeq) =>
% 24.53/6.39 (((powersetI1) =>
% 24.53/6.39 (((powersetE1) =>
% 24.53/6.39 (((inPowerset) =>
% 24.53/6.39 (((powersetsubset) =>
% 24.53/6.39 (((sepInPowerset) =>
% 24.53/6.39 (((sepSubset) =>
% 24.53/6.39 (((binunionIL) =>
% 24.53/6.39 (((upairset2IR) =>
% 24.53/6.39 (((binunionIR) =>
% 24.53/6.39 (((binunionEcases) =>
% 24.53/6.39 (((binunionE) =>
% 24.53/6.39 (((binunionLsub) =>
% 24.53/6.39 (((binunionRsub) =>
% 24.53/6.39 (((binintersectI) =>
% 24.53/6.39 (((binintersectSubset5) =>
% 24.53/6.39 (((binintersectEL) =>
% 24.53/6.39 (((binintersectLsub) =>
% 24.53/6.39 (((binintersectSubset2) =>
% 24.53/6.39 (((binintersectSubset3) =>
% 24.53/6.39 (((binintersectER) =>
% 24.53/6.39 (((disjointsetsI1) =>
% 24.53/6.39 (((binintersectRsub) =>
% 24.53/6.39 (((binintersectSubset4) =>
% 24.53/6.39 (((binintersectSubset1) =>
% 24.53/6.39 (((bs114d) =>
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% 24.53/6.39 ((
% 24.53/6.39 (setminusEL) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusER) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusSubset2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusERneg) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusELneg) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusILneg) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusIRneg) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusLsub) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusSubset1) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffE) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffI1) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffI2) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffIneg1) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffIneg2) =>
% 24.53/6.39 ((
% 24.53/6.39 (secondinupair) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairIL) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairIR) =>
% 24.53/6.39 ((
% 24.53/6.39 (kpairiskpair) =>
% 24.53/6.39 ((
% 24.53/6.39 (kpairp) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletonsubset) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletoninpowerset) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletoninpowunion) =>
% 24.53/6.39 ((
% 24.53/6.39 (upairset2E) =>
% 24.53/6.39 ((
% 24.53/6.39 (upairsubunion) =>
% 24.53/6.39 ((
% 24.53/6.39 (upairinpowunion) =>
% 24.53/6.39 ((
% 24.53/6.39 (ubforcartprodlem1) =>
% 24.53/6.39 ((
% 24.53/6.39 (ubforcartprodlem2) =>
% 24.53/6.39 ((
% 24.53/6.39 (ubforcartprodlem3) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodpairin) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodmempair1) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodmempair) =>
% 24.53/6.39 ((
% 24.53/6.39 (setunionE2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setunionsingleton1) =>
% 24.53/6.39 ((
% 24.53/6.39 (setunionsingleton2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setunionsingleton) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletonprop) =>
% 24.53/6.39 ((
% 24.53/6.39 (ex1E1) =>
% 24.53/6.39 ((
% 24.53/6.39 (ex1I) =>
% 24.53/6.39 ((
% 24.53/6.39 (ex1I2) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletonsuniq) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjL1) =>
% 24.53/6.39 ((
% 24.53/6.39 (kfstsingleton) =>
% 24.53/6.39 ((
% 24.53/6.39 (theprop) =>
% 24.53/6.39 ((
% 24.53/6.39 (kfstpairEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodfstin) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjL2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjL) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR11) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR12) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR1) =>
% 24.53/6.39 ((
% 24.53/6.39 (upairequniteq) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR) =>
% 24.53/6.39 ((
% 24.53/6.39 (ksndsingleton) =>
% 24.53/6.39 ((
% 24.53/6.39 (ksndpairEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (kpairsurjEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodsndin) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodpairmemEL) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodpairmemER) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodmempaircEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodfstpairEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodsndpairEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodpairsurjEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (dpsetconstrI) =>
% 24.53/6.39 ((
% 24.53/6.39 (!!) @ (
% 24.53/6.39 (('#B') @ (
% 24.53/6.39 !!) @
% 24.53/6.39 (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 !!))) @
% 24.53/6.39 (
% 24.53/6.39 (
% 24.53/6.39 ('#S') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 '#S') @
% 24.53/6.39 (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 '#C'))) @
% 24.53/6.39 (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ subset)))) @
% 24.53/6.39 dpsetconstr)))))) @
% 24.53/6.39 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl967])).
% 24.53/6.39 thf(zip_derived_cl1000, plain,
% 24.53/6.39 (~ (((subset2powerset) =>
% 24.53/6.39 (((setextsub) =>
% 24.53/6.39 (((subsetemptysetimpeq) =>
% 24.53/6.39 (((powersetI1) =>
% 24.53/6.39 (((powersetE1) =>
% 24.53/6.39 (((inPowerset) =>
% 24.53/6.39 (((powersetsubset) =>
% 24.53/6.39 (((sepInPowerset) =>
% 24.53/6.39 (((sepSubset) =>
% 24.53/6.39 (((binunionIL) =>
% 24.53/6.39 (((upairset2IR) =>
% 24.53/6.39 (((binunionIR) =>
% 24.53/6.39 (((binunionEcases) =>
% 24.53/6.39 (((binunionE) =>
% 24.53/6.39 (((binunionLsub) =>
% 24.53/6.39 (((binunionRsub) =>
% 24.53/6.39 (((binintersectI) =>
% 24.53/6.39 (((binintersectSubset5) =>
% 24.53/6.39 (((binintersectEL) =>
% 24.53/6.39 (((binintersectLsub) =>
% 24.53/6.39 (((binintersectSubset2) =>
% 24.53/6.39 (((binintersectSubset3) =>
% 24.53/6.39 (((binintersectER) =>
% 24.53/6.39 (((disjointsetsI1) =>
% 24.53/6.39 (((binintersectRsub) =>
% 24.53/6.39 (((binintersectSubset4) =>
% 24.53/6.39 (((binintersectSubset1) =>
% 24.53/6.39 (((bs114d) =>
% 24.53/6.39 (((setminusI) =>
% 24.53/6.39 (((setminusEL) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusER) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusSubset2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusERneg) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusELneg) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusILneg) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusIRneg) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusLsub) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusSubset1) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffE) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffI1) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffI2) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffIneg1) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffIneg2) =>
% 24.53/6.39 ((
% 24.53/6.39 (secondinupair) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairIL) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairIR) =>
% 24.53/6.39 ((
% 24.53/6.39 (kpairiskpair) =>
% 24.53/6.39 ((
% 24.53/6.39 (kpairp) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletonsubset) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletoninpowerset) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletoninpowunion) =>
% 24.53/6.39 ((
% 24.53/6.39 (upairset2E) =>
% 24.53/6.39 ((
% 24.53/6.39 (upairsubunion) =>
% 24.53/6.39 ((
% 24.53/6.39 (upairinpowunion) =>
% 24.53/6.39 ((
% 24.53/6.39 (ubforcartprodlem1) =>
% 24.53/6.39 ((
% 24.53/6.39 (ubforcartprodlem2) =>
% 24.53/6.39 ((
% 24.53/6.39 (ubforcartprodlem3) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodpairin) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodmempair1) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodmempair) =>
% 24.53/6.39 ((
% 24.53/6.39 (setunionE2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setunionsingleton1) =>
% 24.53/6.39 ((
% 24.53/6.39 (setunionsingleton2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setunionsingleton) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletonprop) =>
% 24.53/6.39 ((
% 24.53/6.39 (ex1E1) =>
% 24.53/6.39 ((
% 24.53/6.39 (ex1I) =>
% 24.53/6.39 ((
% 24.53/6.39 (ex1I2) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletonsuniq) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjL1) =>
% 24.53/6.39 ((
% 24.53/6.39 (kfstsingleton) =>
% 24.53/6.39 ((
% 24.53/6.39 (theprop) =>
% 24.53/6.39 ((
% 24.53/6.39 (kfstpairEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodfstin) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjL2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjL) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR11) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR12) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR1) =>
% 24.53/6.39 ((
% 24.53/6.39 (upairequniteq) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR) =>
% 24.53/6.39 ((
% 24.53/6.39 (ksndsingleton) =>
% 24.53/6.39 ((
% 24.53/6.39 (ksndpairEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (kpairsurjEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodsndin) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodpairmemEL) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodpairmemER) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodmempaircEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodfstpairEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodsndpairEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodpairsurjEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (dpsetconstrI) =>
% 24.53/6.39 ((
% 24.53/6.39 (!!) @ (
% 24.53/6.39 (('#B') @ (
% 24.53/6.39 !!) @
% 24.53/6.39 (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 !!))) @
% 24.53/6.39 (
% 24.53/6.39 (
% 24.53/6.39 ('#S') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 '#S') @
% 24.53/6.39 (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 '#C'))) @
% 24.53/6.39 (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ subset)))) @
% 24.53/6.39 dpsetconstr)))))) @
% 24.53/6.39 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl984])).
% 24.53/6.39 thf(zip_derived_cl1015, plain,
% 24.53/6.39 (~ (((setextsub) =>
% 24.53/6.39 (((subsetemptysetimpeq) =>
% 24.53/6.39 (((powersetI1) =>
% 24.53/6.39 (((powersetE1) =>
% 24.53/6.39 (((inPowerset) =>
% 24.53/6.39 (((powersetsubset) =>
% 24.53/6.39 (((sepInPowerset) =>
% 24.53/6.39 (((sepSubset) =>
% 24.53/6.39 (((binunionIL) =>
% 24.53/6.39 (((upairset2IR) =>
% 24.53/6.39 (((binunionIR) =>
% 24.53/6.39 (((binunionEcases) =>
% 24.53/6.39 (((binunionE) =>
% 24.53/6.39 (((binunionLsub) =>
% 24.53/6.39 (((binunionRsub) =>
% 24.53/6.39 (((binintersectI) =>
% 24.53/6.39 (((binintersectSubset5) =>
% 24.53/6.39 (((binintersectEL) =>
% 24.53/6.39 (((binintersectLsub) =>
% 24.53/6.39 (((binintersectSubset2) =>
% 24.53/6.39 (((binintersectSubset3) =>
% 24.53/6.39 (((binintersectER) =>
% 24.53/6.39 (((disjointsetsI1) =>
% 24.53/6.39 (((binintersectRsub) =>
% 24.53/6.39 (((binintersectSubset4) =>
% 24.53/6.39 (((binintersectSubset1) =>
% 24.53/6.39 (((bs114d) =>
% 24.53/6.39 (((setminusI) =>
% 24.53/6.39 (((setminusEL) =>
% 24.53/6.39 (((setminusER) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusSubset2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusERneg) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusELneg) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusILneg) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusIRneg) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusLsub) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusSubset1) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffE) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffI1) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffI2) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffIneg1) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffIneg2) =>
% 24.53/6.39 ((
% 24.53/6.39 (secondinupair) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairIL) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairIR) =>
% 24.53/6.39 ((
% 24.53/6.39 (kpairiskpair) =>
% 24.53/6.39 ((
% 24.53/6.39 (kpairp) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletonsubset) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletoninpowerset) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletoninpowunion) =>
% 24.53/6.39 ((
% 24.53/6.39 (upairset2E) =>
% 24.53/6.39 ((
% 24.53/6.39 (upairsubunion) =>
% 24.53/6.39 ((
% 24.53/6.39 (upairinpowunion) =>
% 24.53/6.39 ((
% 24.53/6.39 (ubforcartprodlem1) =>
% 24.53/6.39 ((
% 24.53/6.39 (ubforcartprodlem2) =>
% 24.53/6.39 ((
% 24.53/6.39 (ubforcartprodlem3) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodpairin) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodmempair1) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodmempair) =>
% 24.53/6.39 ((
% 24.53/6.39 (setunionE2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setunionsingleton1) =>
% 24.53/6.39 ((
% 24.53/6.39 (setunionsingleton2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setunionsingleton) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletonprop) =>
% 24.53/6.39 ((
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% 24.53/6.39 ((
% 24.53/6.39 (ex1I) =>
% 24.53/6.39 ((
% 24.53/6.39 (ex1I2) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletonsuniq) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjL1) =>
% 24.53/6.39 ((
% 24.53/6.39 (kfstsingleton) =>
% 24.53/6.39 ((
% 24.53/6.39 (theprop) =>
% 24.53/6.39 ((
% 24.53/6.39 (kfstpairEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodfstin) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjL2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjL) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR11) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR12) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR1) =>
% 24.53/6.39 ((
% 24.53/6.39 (upairequniteq) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR) =>
% 24.53/6.39 ((
% 24.53/6.39 (ksndsingleton) =>
% 24.53/6.39 ((
% 24.53/6.39 (ksndpairEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (kpairsurjEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodsndin) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodpairmemEL) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodpairmemER) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodmempaircEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodfstpairEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodsndpairEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodpairsurjEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (dpsetconstrI) =>
% 24.53/6.39 ((
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% 24.53/6.39 ('#B') @ (
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% 24.53/6.39 (
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% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 '#C'))) @
% 24.53/6.39 (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ subset)))) @
% 24.53/6.39 dpsetconstr)))))) @
% 24.53/6.39 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1000])).
% 24.53/6.39 thf(zip_derived_cl1027, plain,
% 24.53/6.39 (~ (((subsetemptysetimpeq) =>
% 24.53/6.39 (((powersetI1) =>
% 24.53/6.39 (((powersetE1) =>
% 24.53/6.39 (((inPowerset) =>
% 24.53/6.39 (((powersetsubset) =>
% 24.53/6.39 (((sepInPowerset) =>
% 24.53/6.39 (((sepSubset) =>
% 24.53/6.39 (((binunionIL) =>
% 24.53/6.39 (((upairset2IR) =>
% 24.53/6.39 (((binunionIR) =>
% 24.53/6.39 (((binunionEcases) =>
% 24.53/6.39 (((binunionE) =>
% 24.53/6.39 (((binunionLsub) =>
% 24.53/6.39 (((binunionRsub) =>
% 24.53/6.39 (((binintersectI) =>
% 24.53/6.39 (((binintersectSubset5) =>
% 24.53/6.39 (((binintersectEL) =>
% 24.53/6.39 (((binintersectLsub) =>
% 24.53/6.39 (((binintersectSubset2) =>
% 24.53/6.39 (((binintersectSubset3) =>
% 24.53/6.39 (((binintersectER) =>
% 24.53/6.39 (((disjointsetsI1) =>
% 24.53/6.39 (((binintersectRsub) =>
% 24.53/6.39 (((binintersectSubset4) =>
% 24.53/6.39 (((binintersectSubset1) =>
% 24.53/6.39 (((bs114d) =>
% 24.53/6.39 (((setminusI) =>
% 24.53/6.39 (((setminusEL) =>
% 24.53/6.39 (((setminusER) =>
% 24.53/6.39 (((setminusSubset2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusERneg) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusELneg) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusILneg) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusIRneg) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusLsub) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusSubset1) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffE) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffI1) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffI2) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffIneg1) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffIneg2) =>
% 24.53/6.39 ((
% 24.53/6.39 (secondinupair) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairIL) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairIR) =>
% 24.53/6.39 ((
% 24.53/6.39 (kpairiskpair) =>
% 24.53/6.39 ((
% 24.53/6.39 (kpairp) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletonsubset) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletoninpowerset) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletoninpowunion) =>
% 24.53/6.39 ((
% 24.53/6.39 (upairset2E) =>
% 24.53/6.39 ((
% 24.53/6.39 (upairsubunion) =>
% 24.53/6.39 ((
% 24.53/6.39 (upairinpowunion) =>
% 24.53/6.39 ((
% 24.53/6.39 (ubforcartprodlem1) =>
% 24.53/6.39 ((
% 24.53/6.39 (ubforcartprodlem2) =>
% 24.53/6.39 ((
% 24.53/6.39 (ubforcartprodlem3) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodpairin) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodmempair1) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodmempair) =>
% 24.53/6.39 ((
% 24.53/6.39 (setunionE2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setunionsingleton1) =>
% 24.53/6.39 ((
% 24.53/6.39 (setunionsingleton2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setunionsingleton) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletonprop) =>
% 24.53/6.39 ((
% 24.53/6.39 (ex1E1) =>
% 24.53/6.39 ((
% 24.53/6.39 (ex1I) =>
% 24.53/6.39 ((
% 24.53/6.39 (ex1I2) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletonsuniq) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjL1) =>
% 24.53/6.39 ((
% 24.53/6.39 (kfstsingleton) =>
% 24.53/6.39 ((
% 24.53/6.39 (theprop) =>
% 24.53/6.39 ((
% 24.53/6.39 (kfstpairEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodfstin) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjL2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjL) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR11) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR12) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR1) =>
% 24.53/6.39 ((
% 24.53/6.39 (upairequniteq) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR) =>
% 24.53/6.39 ((
% 24.53/6.39 (ksndsingleton) =>
% 24.53/6.39 ((
% 24.53/6.39 (ksndpairEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (kpairsurjEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodsndin) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodpairmemEL) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodpairmemER) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodmempaircEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodfstpairEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodsndpairEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodpairsurjEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (dpsetconstrI) =>
% 24.53/6.39 ((
% 24.53/6.39 (!!) @ (
% 24.53/6.39 (('#B') @ (
% 24.53/6.39 !!) @
% 24.53/6.39 (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 !!))) @
% 24.53/6.39 (
% 24.53/6.39 (
% 24.53/6.39 ('#S') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 '#S') @
% 24.53/6.39 (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 '#C'))) @
% 24.53/6.39 (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ subset)))) @
% 24.53/6.39 dpsetconstr)))))) @
% 24.53/6.39 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1015])).
% 24.53/6.39 thf(zip_derived_cl1039, plain,
% 24.53/6.39 (~ (((powersetI1) =>
% 24.53/6.39 (((powersetE1) =>
% 24.53/6.39 (((inPowerset) =>
% 24.53/6.39 (((powersetsubset) =>
% 24.53/6.39 (((sepInPowerset) =>
% 24.53/6.39 (((sepSubset) =>
% 24.53/6.39 (((binunionIL) =>
% 24.53/6.39 (((upairset2IR) =>
% 24.53/6.39 (((binunionIR) =>
% 24.53/6.39 (((binunionEcases) =>
% 24.53/6.39 (((binunionE) =>
% 24.53/6.39 (((binunionLsub) =>
% 24.53/6.39 (((binunionRsub) =>
% 24.53/6.39 (((binintersectI) =>
% 24.53/6.39 (((binintersectSubset5) =>
% 24.53/6.39 (((binintersectEL) =>
% 24.53/6.39 (((binintersectLsub) =>
% 24.53/6.39 (((binintersectSubset2) =>
% 24.53/6.39 (((binintersectSubset3) =>
% 24.53/6.39 (((binintersectER) =>
% 24.53/6.39 (((disjointsetsI1) =>
% 24.53/6.39 (((binintersectRsub) =>
% 24.53/6.39 (((binintersectSubset4) =>
% 24.53/6.39 (((binintersectSubset1) =>
% 24.53/6.39 (((bs114d) =>
% 24.53/6.39 (((setminusI) =>
% 24.53/6.39 (((setminusEL) =>
% 24.53/6.39 (((setminusER) =>
% 24.53/6.39 (((setminusSubset2) =>
% 24.53/6.39 (((setminusERneg) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusELneg) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusILneg) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusIRneg) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusLsub) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusSubset1) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffE) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffI1) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffI2) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffIneg1) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffIneg2) =>
% 24.53/6.39 ((
% 24.53/6.39 (secondinupair) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairIL) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairIR) =>
% 24.53/6.39 ((
% 24.53/6.39 (kpairiskpair) =>
% 24.53/6.39 ((
% 24.53/6.39 (kpairp) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletonsubset) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletoninpowerset) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletoninpowunion) =>
% 24.53/6.39 ((
% 24.53/6.39 (upairset2E) =>
% 24.53/6.39 ((
% 24.53/6.39 (upairsubunion) =>
% 24.53/6.39 ((
% 24.53/6.39 (upairinpowunion) =>
% 24.53/6.39 ((
% 24.53/6.39 (ubforcartprodlem1) =>
% 24.53/6.39 ((
% 24.53/6.39 (ubforcartprodlem2) =>
% 24.53/6.39 ((
% 24.53/6.39 (ubforcartprodlem3) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodpairin) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodmempair1) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodmempair) =>
% 24.53/6.39 ((
% 24.53/6.39 (setunionE2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setunionsingleton1) =>
% 24.53/6.39 ((
% 24.53/6.39 (setunionsingleton2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setunionsingleton) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletonprop) =>
% 24.53/6.39 ((
% 24.53/6.39 (ex1E1) =>
% 24.53/6.39 ((
% 24.53/6.39 (ex1I) =>
% 24.53/6.39 ((
% 24.53/6.39 (ex1I2) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletonsuniq) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjL1) =>
% 24.53/6.39 ((
% 24.53/6.39 (kfstsingleton) =>
% 24.53/6.39 ((
% 24.53/6.39 (theprop) =>
% 24.53/6.39 ((
% 24.53/6.39 (kfstpairEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodfstin) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjL2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjL) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR11) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR12) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR1) =>
% 24.53/6.39 ((
% 24.53/6.39 (upairequniteq) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR) =>
% 24.53/6.39 ((
% 24.53/6.39 (ksndsingleton) =>
% 24.53/6.39 ((
% 24.53/6.39 (ksndpairEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (kpairsurjEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodsndin) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodpairmemEL) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodpairmemER) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodmempaircEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodfstpairEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodsndpairEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodpairsurjEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (dpsetconstrI) =>
% 24.53/6.39 ((
% 24.53/6.39 (!!) @ (
% 24.53/6.39 (('#B') @ (
% 24.53/6.39 !!) @
% 24.53/6.39 (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 !!))) @
% 24.53/6.39 (
% 24.53/6.39 (
% 24.53/6.39 ('#S') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 '#S') @
% 24.53/6.39 (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 '#C'))) @
% 24.53/6.39 (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ subset)))) @
% 24.53/6.39 dpsetconstr)))))) @
% 24.53/6.39 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1027])).
% 24.53/6.39 thf(zip_derived_cl1055, plain,
% 24.53/6.39 (~ (((powersetE1) =>
% 24.53/6.39 (((inPowerset) =>
% 24.53/6.39 (((powersetsubset) =>
% 24.53/6.39 (((sepInPowerset) =>
% 24.53/6.39 (((sepSubset) =>
% 24.53/6.39 (((binunionIL) =>
% 24.53/6.39 (((upairset2IR) =>
% 24.53/6.39 (((binunionIR) =>
% 24.53/6.39 (((binunionEcases) =>
% 24.53/6.39 (((binunionE) =>
% 24.53/6.39 (((binunionLsub) =>
% 24.53/6.39 (((binunionRsub) =>
% 24.53/6.39 (((binintersectI) =>
% 24.53/6.39 (((binintersectSubset5) =>
% 24.53/6.39 (((binintersectEL) =>
% 24.53/6.39 (((binintersectLsub) =>
% 24.53/6.39 (((binintersectSubset2) =>
% 24.53/6.39 (((binintersectSubset3) =>
% 24.53/6.39 (((binintersectER) =>
% 24.53/6.39 (((disjointsetsI1) =>
% 24.53/6.39 (((binintersectRsub) =>
% 24.53/6.39 (((binintersectSubset4) =>
% 24.53/6.39 (((binintersectSubset1) =>
% 24.53/6.39 (((bs114d) =>
% 24.53/6.39 (((setminusI) =>
% 24.53/6.39 (((setminusEL) =>
% 24.53/6.39 (((setminusER) =>
% 24.53/6.39 (((setminusSubset2) =>
% 24.53/6.39 (((setminusERneg) =>
% 24.53/6.39 (((setminusELneg) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusILneg) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusIRneg) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusLsub) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusSubset1) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffE) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffI1) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffI2) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffIneg1) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffIneg2) =>
% 24.53/6.39 ((
% 24.53/6.39 (secondinupair) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairIL) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairIR) =>
% 24.53/6.39 ((
% 24.53/6.39 (kpairiskpair) =>
% 24.53/6.39 ((
% 24.53/6.39 (kpairp) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletonsubset) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletoninpowerset) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletoninpowunion) =>
% 24.53/6.39 ((
% 24.53/6.39 (upairset2E) =>
% 24.53/6.39 ((
% 24.53/6.39 (upairsubunion) =>
% 24.53/6.39 ((
% 24.53/6.39 (upairinpowunion) =>
% 24.53/6.39 ((
% 24.53/6.39 (ubforcartprodlem1) =>
% 24.53/6.39 ((
% 24.53/6.39 (ubforcartprodlem2) =>
% 24.53/6.39 ((
% 24.53/6.39 (ubforcartprodlem3) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodpairin) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodmempair1) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodmempair) =>
% 24.53/6.39 ((
% 24.53/6.39 (setunionE2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setunionsingleton1) =>
% 24.53/6.39 ((
% 24.53/6.39 (setunionsingleton2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setunionsingleton) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletonprop) =>
% 24.53/6.39 ((
% 24.53/6.39 (ex1E1) =>
% 24.53/6.39 ((
% 24.53/6.39 (ex1I) =>
% 24.53/6.39 ((
% 24.53/6.39 (ex1I2) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletonsuniq) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjL1) =>
% 24.53/6.39 ((
% 24.53/6.39 (kfstsingleton) =>
% 24.53/6.39 ((
% 24.53/6.39 (theprop) =>
% 24.53/6.39 ((
% 24.53/6.39 (kfstpairEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodfstin) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjL2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjL) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR11) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR12) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR1) =>
% 24.53/6.39 ((
% 24.53/6.39 (upairequniteq) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR) =>
% 24.53/6.39 ((
% 24.53/6.39 (ksndsingleton) =>
% 24.53/6.39 ((
% 24.53/6.39 (ksndpairEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (kpairsurjEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodsndin) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodpairmemEL) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodpairmemER) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodmempaircEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodfstpairEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodsndpairEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodpairsurjEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (dpsetconstrI) =>
% 24.53/6.39 ((
% 24.53/6.39 (!!) @ (
% 24.53/6.39 (('#B') @ (
% 24.53/6.39 !!) @
% 24.53/6.39 (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 !!))) @
% 24.53/6.39 (
% 24.53/6.39 (
% 24.53/6.39 ('#S') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 '#S') @
% 24.53/6.39 (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 '#C'))) @
% 24.53/6.39 (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ subset)))) @
% 24.53/6.39 dpsetconstr)))))) @
% 24.53/6.39 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1039])).
% 24.53/6.39 thf(zip_derived_cl1067, plain,
% 24.53/6.39 (~ (((inPowerset) =>
% 24.53/6.39 (((powersetsubset) =>
% 24.53/6.39 (((sepInPowerset) =>
% 24.53/6.39 (((sepSubset) =>
% 24.53/6.39 (((binunionIL) =>
% 24.53/6.39 (((upairset2IR) =>
% 24.53/6.39 (((binunionIR) =>
% 24.53/6.39 (((binunionEcases) =>
% 24.53/6.39 (((binunionE) =>
% 24.53/6.39 (((binunionLsub) =>
% 24.53/6.39 (((binunionRsub) =>
% 24.53/6.39 (((binintersectI) =>
% 24.53/6.39 (((binintersectSubset5) =>
% 24.53/6.39 (((binintersectEL) =>
% 24.53/6.39 (((binintersectLsub) =>
% 24.53/6.39 (((binintersectSubset2) =>
% 24.53/6.39 (((binintersectSubset3) =>
% 24.53/6.39 (((binintersectER) =>
% 24.53/6.39 (((disjointsetsI1) =>
% 24.53/6.39 (((binintersectRsub) =>
% 24.53/6.39 (((binintersectSubset4) =>
% 24.53/6.39 (((binintersectSubset1) =>
% 24.53/6.39 (((bs114d) =>
% 24.53/6.39 (((setminusI) =>
% 24.53/6.39 (((setminusEL) =>
% 24.53/6.39 (((setminusER) =>
% 24.53/6.39 (((setminusSubset2) =>
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% 24.53/6.39 (((setminusELneg) =>
% 24.53/6.39 (((setminusILneg) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusIRneg) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusLsub) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusSubset1) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffE) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffI1) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffI2) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffIneg1) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffIneg2) =>
% 24.53/6.39 ((
% 24.53/6.39 (secondinupair) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairIL) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairIR) =>
% 24.53/6.39 ((
% 24.53/6.39 (kpairiskpair) =>
% 24.53/6.39 ((
% 24.53/6.39 (kpairp) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletonsubset) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletoninpowerset) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletoninpowunion) =>
% 24.53/6.39 ((
% 24.53/6.39 (upairset2E) =>
% 24.53/6.39 ((
% 24.53/6.39 (upairsubunion) =>
% 24.53/6.39 ((
% 24.53/6.39 (upairinpowunion) =>
% 24.53/6.39 ((
% 24.53/6.39 (ubforcartprodlem1) =>
% 24.53/6.39 ((
% 24.53/6.39 (ubforcartprodlem2) =>
% 24.53/6.39 ((
% 24.53/6.39 (ubforcartprodlem3) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodpairin) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodmempair1) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodmempair) =>
% 24.53/6.39 ((
% 24.53/6.39 (setunionE2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setunionsingleton1) =>
% 24.53/6.39 ((
% 24.53/6.39 (setunionsingleton2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setunionsingleton) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletonprop) =>
% 24.53/6.39 ((
% 24.53/6.39 (ex1E1) =>
% 24.53/6.39 ((
% 24.53/6.39 (ex1I) =>
% 24.53/6.39 ((
% 24.53/6.39 (ex1I2) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletonsuniq) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjL1) =>
% 24.53/6.39 ((
% 24.53/6.39 (kfstsingleton) =>
% 24.53/6.39 ((
% 24.53/6.39 (theprop) =>
% 24.53/6.39 ((
% 24.53/6.39 (kfstpairEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodfstin) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjL2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjL) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR11) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR12) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR1) =>
% 24.53/6.39 ((
% 24.53/6.39 (upairequniteq) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR) =>
% 24.53/6.39 ((
% 24.53/6.39 (ksndsingleton) =>
% 24.53/6.39 ((
% 24.53/6.39 (ksndpairEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (kpairsurjEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodsndin) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodpairmemEL) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodpairmemER) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodmempaircEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodfstpairEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodsndpairEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodpairsurjEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (dpsetconstrI) =>
% 24.53/6.39 ((
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% 24.53/6.39 (('#B') @ (
% 24.53/6.39 !!) @
% 24.53/6.39 (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 !!))) @
% 24.53/6.39 (
% 24.53/6.39 (
% 24.53/6.39 ('#S') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 '#S') @
% 24.53/6.39 (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 '#C'))) @
% 24.53/6.39 (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ subset)))) @
% 24.53/6.39 dpsetconstr)))))) @
% 24.53/6.39 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1055])).
% 24.53/6.39 thf(zip_derived_cl1074, plain,
% 24.53/6.39 (~ (((powersetsubset) =>
% 24.53/6.39 (((sepInPowerset) =>
% 24.53/6.39 (((sepSubset) =>
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% 24.53/6.39 (((upairset2IR) =>
% 24.53/6.39 (((binunionIR) =>
% 24.53/6.39 (((binunionEcases) =>
% 24.53/6.39 (((binunionE) =>
% 24.53/6.39 (((binunionLsub) =>
% 24.53/6.39 (((binunionRsub) =>
% 24.53/6.39 (((binintersectI) =>
% 24.53/6.39 (((binintersectSubset5) =>
% 24.53/6.39 (((binintersectEL) =>
% 24.53/6.39 (((binintersectLsub) =>
% 24.53/6.39 (((binintersectSubset2) =>
% 24.53/6.39 (((binintersectSubset3) =>
% 24.53/6.39 (((binintersectER) =>
% 24.53/6.39 (((disjointsetsI1) =>
% 24.53/6.39 (((binintersectRsub) =>
% 24.53/6.39 (((binintersectSubset4) =>
% 24.53/6.39 (((binintersectSubset1) =>
% 24.53/6.39 (((bs114d) =>
% 24.53/6.39 (((setminusI) =>
% 24.53/6.39 (((setminusEL) =>
% 24.53/6.39 (((setminusER) =>
% 24.53/6.39 (((setminusSubset2) =>
% 24.53/6.39 (((setminusERneg) =>
% 24.53/6.39 (((setminusELneg) =>
% 24.53/6.39 (((setminusILneg) =>
% 24.53/6.39 (((setminusIRneg) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusLsub) =>
% 24.53/6.39 ((
% 24.53/6.39 (setminusSubset1) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffE) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffI1) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffI2) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffIneg1) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffIneg2) =>
% 24.53/6.39 ((
% 24.53/6.39 (secondinupair) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairIL) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairIR) =>
% 24.53/6.39 ((
% 24.53/6.39 (kpairiskpair) =>
% 24.53/6.39 ((
% 24.53/6.39 (kpairp) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletonsubset) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletoninpowerset) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletoninpowunion) =>
% 24.53/6.39 ((
% 24.53/6.39 (upairset2E) =>
% 24.53/6.39 ((
% 24.53/6.39 (upairsubunion) =>
% 24.53/6.39 ((
% 24.53/6.39 (upairinpowunion) =>
% 24.53/6.39 ((
% 24.53/6.39 (ubforcartprodlem1) =>
% 24.53/6.39 ((
% 24.53/6.39 (ubforcartprodlem2) =>
% 24.53/6.39 ((
% 24.53/6.39 (ubforcartprodlem3) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodpairin) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodmempair1) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodmempair) =>
% 24.53/6.39 ((
% 24.53/6.39 (setunionE2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setunionsingleton1) =>
% 24.53/6.39 ((
% 24.53/6.39 (setunionsingleton2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setunionsingleton) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletonprop) =>
% 24.53/6.39 ((
% 24.53/6.39 (ex1E1) =>
% 24.53/6.39 ((
% 24.53/6.39 (ex1I) =>
% 24.53/6.39 ((
% 24.53/6.39 (ex1I2) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletonsuniq) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjL1) =>
% 24.53/6.39 ((
% 24.53/6.39 (kfstsingleton) =>
% 24.53/6.39 ((
% 24.53/6.39 (theprop) =>
% 24.53/6.39 ((
% 24.53/6.39 (kfstpairEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodfstin) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjL2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjL) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR11) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR12) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR1) =>
% 24.53/6.39 ((
% 24.53/6.39 (upairequniteq) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR) =>
% 24.53/6.39 ((
% 24.53/6.39 (ksndsingleton) =>
% 24.53/6.39 ((
% 24.53/6.39 (ksndpairEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (kpairsurjEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodsndin) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodpairmemEL) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodpairmemER) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodmempaircEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodfstpairEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodsndpairEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodpairsurjEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (dpsetconstrI) =>
% 24.53/6.39 ((
% 24.53/6.39 (!!) @ (
% 24.53/6.39 (('#B') @ (
% 24.53/6.39 !!) @
% 24.53/6.39 (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
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% 24.53/6.39 (
% 24.53/6.39 (
% 24.53/6.39 ('#S') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
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% 24.53/6.39 (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
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% 24.53/6.39 (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ subset)))) @
% 24.53/6.39 dpsetconstr)))))) @
% 24.53/6.39 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1067])).
% 24.53/6.39 thf(zip_derived_cl1082, plain,
% 24.53/6.39 (~ (((sepInPowerset) =>
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% 24.53/6.39 (((upairset2IR) =>
% 24.53/6.39 (((binunionIR) =>
% 24.53/6.39 (((binunionEcases) =>
% 24.53/6.39 (((binunionE) =>
% 24.53/6.39 (((binunionLsub) =>
% 24.53/6.39 (((binunionRsub) =>
% 24.53/6.39 (((binintersectI) =>
% 24.53/6.39 (((binintersectSubset5) =>
% 24.53/6.39 (((binintersectEL) =>
% 24.53/6.39 (((binintersectLsub) =>
% 24.53/6.39 (((binintersectSubset2) =>
% 24.53/6.39 (((binintersectSubset3) =>
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% 24.53/6.39 (((disjointsetsI1) =>
% 24.53/6.39 (((binintersectRsub) =>
% 24.53/6.39 (((binintersectSubset4) =>
% 24.53/6.39 (((binintersectSubset1) =>
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% 24.53/6.39 (((setminusEL) =>
% 24.53/6.39 (((setminusER) =>
% 24.53/6.39 (((setminusSubset2) =>
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% 24.53/6.39 ((
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% 24.53/6.39 ((
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% 24.53/6.39 ((
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% 24.53/6.39 ((
% 24.53/6.39 (symdiffIneg2) =>
% 24.53/6.39 ((
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% 24.53/6.39 ((
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% 24.53/6.39 ((
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% 24.53/6.39 ((
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% 24.53/6.39 ((
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% 24.53/6.39 ((
% 24.53/6.39 (upairset2E) =>
% 24.53/6.39 ((
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% 24.53/6.39 ((
% 24.53/6.39 (upairinpowunion) =>
% 24.53/6.39 ((
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% 24.53/6.39 ((
% 24.53/6.39 (ubforcartprodlem2) =>
% 24.53/6.39 ((
% 24.53/6.39 (ubforcartprodlem3) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodpairin) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodmempair1) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodmempair) =>
% 24.53/6.39 ((
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% 24.53/6.39 ((
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% 24.53/6.39 ((
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% 24.53/6.39 ((
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% 24.53/6.39 ((
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% 24.53/6.39 ((
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% 24.53/6.39 ((
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% 24.53/6.39 ((
% 24.53/6.39 (cartprodpairmemER) =>
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% 24.53/6.39 ((
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% 24.53/6.39 ('#B') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 '#C'))) @
% 24.53/6.39 (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ subset)))) @
% 24.53/6.39 dpsetconstr)))))) @
% 24.53/6.39 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1074])).
% 24.53/6.39 thf(zip_derived_cl1090, plain,
% 24.53/6.39 (~ (((sepSubset) =>
% 24.53/6.39 (((binunionIL) =>
% 24.53/6.39 (((upairset2IR) =>
% 24.53/6.39 (((binunionIR) =>
% 24.53/6.39 (((binunionEcases) =>
% 24.53/6.39 (((binunionE) =>
% 24.53/6.39 (((binunionLsub) =>
% 24.53/6.39 (((binunionRsub) =>
% 24.53/6.39 (((binintersectI) =>
% 24.53/6.39 (((binintersectSubset5) =>
% 24.53/6.39 (((binintersectEL) =>
% 24.53/6.39 (((binintersectLsub) =>
% 24.53/6.39 (((binintersectSubset2) =>
% 24.53/6.39 (((binintersectSubset3) =>
% 24.53/6.39 (((binintersectER) =>
% 24.53/6.39 (((disjointsetsI1) =>
% 24.53/6.39 (((binintersectRsub) =>
% 24.53/6.39 (((binintersectSubset4) =>
% 24.53/6.39 (((binintersectSubset1) =>
% 24.53/6.39 (((bs114d) =>
% 24.53/6.39 (((setminusI) =>
% 24.53/6.39 (((setminusEL) =>
% 24.53/6.39 (((setminusER) =>
% 24.53/6.39 (((setminusSubset2) =>
% 24.53/6.39 (((setminusERneg) =>
% 24.53/6.39 (((setminusELneg) =>
% 24.53/6.39 (((setminusILneg) =>
% 24.53/6.39 (((setminusIRneg) =>
% 24.53/6.39 (((setminusLsub) =>
% 24.53/6.39 (((setminusSubset1) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffE) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffI1) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffI2) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffIneg1) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffIneg2) =>
% 24.53/6.39 ((
% 24.53/6.39 (secondinupair) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairIL) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairIR) =>
% 24.53/6.39 ((
% 24.53/6.39 (kpairiskpair) =>
% 24.53/6.39 ((
% 24.53/6.39 (kpairp) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletonsubset) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletoninpowerset) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletoninpowunion) =>
% 24.53/6.39 ((
% 24.53/6.39 (upairset2E) =>
% 24.53/6.39 ((
% 24.53/6.39 (upairsubunion) =>
% 24.53/6.39 ((
% 24.53/6.39 (upairinpowunion) =>
% 24.53/6.39 ((
% 24.53/6.39 (ubforcartprodlem1) =>
% 24.53/6.39 ((
% 24.53/6.39 (ubforcartprodlem2) =>
% 24.53/6.39 ((
% 24.53/6.39 (ubforcartprodlem3) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodpairin) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodmempair1) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodmempair) =>
% 24.53/6.39 ((
% 24.53/6.39 (setunionE2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setunionsingleton1) =>
% 24.53/6.39 ((
% 24.53/6.39 (setunionsingleton2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setunionsingleton) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletonprop) =>
% 24.53/6.39 ((
% 24.53/6.39 (ex1E1) =>
% 24.53/6.39 ((
% 24.53/6.39 (ex1I) =>
% 24.53/6.39 ((
% 24.53/6.39 (ex1I2) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletonsuniq) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjL1) =>
% 24.53/6.39 ((
% 24.53/6.39 (kfstsingleton) =>
% 24.53/6.39 ((
% 24.53/6.39 (theprop) =>
% 24.53/6.39 ((
% 24.53/6.39 (kfstpairEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodfstin) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjL2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjL) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR11) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR12) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR1) =>
% 24.53/6.39 ((
% 24.53/6.39 (upairequniteq) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR) =>
% 24.53/6.39 ((
% 24.53/6.39 (ksndsingleton) =>
% 24.53/6.39 ((
% 24.53/6.39 (ksndpairEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (kpairsurjEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodsndin) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodpairmemEL) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodpairmemER) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodmempaircEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodfstpairEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodsndpairEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodpairsurjEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (dpsetconstrI) =>
% 24.53/6.39 ((
% 24.53/6.39 (!!) @ (
% 24.53/6.39 (('#B') @ (
% 24.53/6.39 !!) @
% 24.53/6.39 (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 !!))) @
% 24.53/6.39 (
% 24.53/6.39 (
% 24.53/6.39 ('#S') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 '#S') @
% 24.53/6.39 (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 '#C'))) @
% 24.53/6.39 (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ subset)))) @
% 24.53/6.39 dpsetconstr)))))) @
% 24.53/6.39 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1082])).
% 24.53/6.39 thf(zip_derived_cl1096, plain,
% 24.53/6.39 (~ (((binunionIL) =>
% 24.53/6.39 (((upairset2IR) =>
% 24.53/6.39 (((binunionIR) =>
% 24.53/6.39 (((binunionEcases) =>
% 24.53/6.39 (((binunionE) =>
% 24.53/6.39 (((binunionLsub) =>
% 24.53/6.39 (((binunionRsub) =>
% 24.53/6.39 (((binintersectI) =>
% 24.53/6.39 (((binintersectSubset5) =>
% 24.53/6.39 (((binintersectEL) =>
% 24.53/6.39 (((binintersectLsub) =>
% 24.53/6.39 (((binintersectSubset2) =>
% 24.53/6.39 (((binintersectSubset3) =>
% 24.53/6.39 (((binintersectER) =>
% 24.53/6.39 (((disjointsetsI1) =>
% 24.53/6.39 (((binintersectRsub) =>
% 24.53/6.39 (((binintersectSubset4) =>
% 24.53/6.39 (((binintersectSubset1) =>
% 24.53/6.39 (((bs114d) =>
% 24.53/6.39 (((setminusI) =>
% 24.53/6.39 (((setminusEL) =>
% 24.53/6.39 (((setminusER) =>
% 24.53/6.39 (((setminusSubset2) =>
% 24.53/6.39 (((setminusERneg) =>
% 24.53/6.39 (((setminusELneg) =>
% 24.53/6.39 (((setminusILneg) =>
% 24.53/6.39 (((setminusIRneg) =>
% 24.53/6.39 (((setminusLsub) =>
% 24.53/6.39 (((setminusSubset1) =>
% 24.53/6.39 (((symdiffE) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffI1) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffI2) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffIneg1) =>
% 24.53/6.39 ((
% 24.53/6.39 (symdiffIneg2) =>
% 24.53/6.39 ((
% 24.53/6.39 (secondinupair) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairIL) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairIR) =>
% 24.53/6.39 ((
% 24.53/6.39 (kpairiskpair) =>
% 24.53/6.39 ((
% 24.53/6.39 (kpairp) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletonsubset) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletoninpowerset) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletoninpowunion) =>
% 24.53/6.39 ((
% 24.53/6.39 (upairset2E) =>
% 24.53/6.39 ((
% 24.53/6.39 (upairsubunion) =>
% 24.53/6.39 ((
% 24.53/6.39 (upairinpowunion) =>
% 24.53/6.39 ((
% 24.53/6.39 (ubforcartprodlem1) =>
% 24.53/6.39 ((
% 24.53/6.39 (ubforcartprodlem2) =>
% 24.53/6.39 ((
% 24.53/6.39 (ubforcartprodlem3) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodpairin) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodmempair1) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodmempair) =>
% 24.53/6.39 ((
% 24.53/6.39 (setunionE2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setunionsingleton1) =>
% 24.53/6.39 ((
% 24.53/6.39 (setunionsingleton2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setunionsingleton) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletonprop) =>
% 24.53/6.39 ((
% 24.53/6.39 (ex1E1) =>
% 24.53/6.39 ((
% 24.53/6.39 (ex1I) =>
% 24.53/6.39 ((
% 24.53/6.39 (ex1I2) =>
% 24.53/6.39 ((
% 24.53/6.39 (singletonsuniq) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjL1) =>
% 24.53/6.39 ((
% 24.53/6.39 (kfstsingleton) =>
% 24.53/6.39 ((
% 24.53/6.39 (theprop) =>
% 24.53/6.39 ((
% 24.53/6.39 (kfstpairEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodfstin) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjL2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjL) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR11) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR12) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR1) =>
% 24.53/6.39 ((
% 24.53/6.39 (upairequniteq) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR2) =>
% 24.53/6.39 ((
% 24.53/6.39 (setukpairinjR) =>
% 24.53/6.39 ((
% 24.53/6.39 (ksndsingleton) =>
% 24.53/6.39 ((
% 24.53/6.39 (ksndpairEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (kpairsurjEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodsndin) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodpairmemEL) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodpairmemER) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodmempaircEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodfstpairEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodsndpairEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (cartprodpairsurjEq) =>
% 24.53/6.39 ((
% 24.53/6.39 (dpsetconstrI) =>
% 24.53/6.39 ((
% 24.53/6.39 (!!) @ (
% 24.53/6.39 (('#B') @ (
% 24.53/6.39 !!) @
% 24.53/6.39 (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 !!))) @
% 24.53/6.39 (
% 24.53/6.39 (
% 24.53/6.39 ('#S') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 '#S') @
% 24.53/6.39 (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 '#C'))) @
% 24.53/6.39 (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ (
% 24.53/6.39 (
% 24.53/6.39 ('#B') @ subset)))) @
% 24.53/6.39 dpsetconstr)))))) @
% 24.53/6.39 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1090])).
% 24.53/6.39 thf(zip_derived_cl1102, plain,
% 24.53/6.39 (~ (((upairset2IR) =>
% 24.53/6.39 (((binunionIR) =>
% 24.53/6.39 (((binunionEcases) =>
% 24.53/6.39 (((binunionE) =>
% 24.53/6.39 (((binunionLsub) =>
% 24.53/6.39 (((binunionRsub) =>
% 24.53/6.39 (((binintersectI) =>
% 24.53/6.39 (((binintersectSubset5) =>
% 24.53/6.39 (((binintersectEL) =>
% 24.53/6.39 (((binintersectLsub) =>
% 24.53/6.39 (((binintersectSubset2) =>
% 24.53/6.39 (((binintersectSubset3) =>
% 24.53/6.39 (((binintersectER) =>
% 24.53/6.39 (((disjointsetsI1) =>
% 24.53/6.39 (((binintersectRsub) =>
% 24.53/6.39 (((binintersectSubset4) =>
% 24.53/6.39 (((binintersectSubset1) =>
% 24.53/6.40 (((bs114d) =>
% 24.53/6.40 (((setminusI) =>
% 24.53/6.40 (((setminusEL) =>
% 24.53/6.40 (((setminusER) =>
% 24.53/6.40 (((setminusSubset2) =>
% 24.53/6.40 (((setminusERneg) =>
% 24.53/6.40 (((setminusELneg) =>
% 24.53/6.40 (((setminusILneg) =>
% 24.53/6.40 (((setminusIRneg) =>
% 24.53/6.40 (((setminusLsub) =>
% 24.53/6.40 (((setminusSubset1) =>
% 24.53/6.40 (((symdiffE) =>
% 24.53/6.40 (((symdiffI1) =>
% 24.53/6.40 ((
% 24.53/6.40 (symdiffI2) =>
% 24.53/6.40 ((
% 24.53/6.40 (symdiffIneg1) =>
% 24.53/6.40 ((
% 24.53/6.40 (symdiffIneg2) =>
% 24.53/6.40 ((
% 24.53/6.40 (secondinupair) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairIL) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairIR) =>
% 24.53/6.40 ((
% 24.53/6.40 (kpairiskpair) =>
% 24.53/6.40 ((
% 24.53/6.40 (kpairp) =>
% 24.53/6.40 ((
% 24.53/6.40 (singletonsubset) =>
% 24.53/6.40 ((
% 24.53/6.40 (singletoninpowerset) =>
% 24.53/6.40 ((
% 24.53/6.40 (singletoninpowunion) =>
% 24.53/6.40 ((
% 24.53/6.40 (upairset2E) =>
% 24.53/6.40 ((
% 24.53/6.40 (upairsubunion) =>
% 24.53/6.40 ((
% 24.53/6.40 (upairinpowunion) =>
% 24.53/6.40 ((
% 24.53/6.40 (ubforcartprodlem1) =>
% 24.53/6.40 ((
% 24.53/6.40 (ubforcartprodlem2) =>
% 24.53/6.40 ((
% 24.53/6.40 (ubforcartprodlem3) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodpairin) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodmempair1) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodmempair) =>
% 24.53/6.40 ((
% 24.53/6.40 (setunionE2) =>
% 24.53/6.40 ((
% 24.53/6.40 (setunionsingleton1) =>
% 24.53/6.40 ((
% 24.53/6.40 (setunionsingleton2) =>
% 24.53/6.40 ((
% 24.53/6.40 (setunionsingleton) =>
% 24.53/6.40 ((
% 24.53/6.40 (singletonprop) =>
% 24.53/6.40 ((
% 24.53/6.40 (ex1E1) =>
% 24.53/6.40 ((
% 24.53/6.40 (ex1I) =>
% 24.53/6.40 ((
% 24.53/6.40 (ex1I2) =>
% 24.53/6.40 ((
% 24.53/6.40 (singletonsuniq) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjL1) =>
% 24.53/6.40 ((
% 24.53/6.40 (kfstsingleton) =>
% 24.53/6.40 ((
% 24.53/6.40 (theprop) =>
% 24.53/6.40 ((
% 24.53/6.40 (kfstpairEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodfstin) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjL2) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjL) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjR11) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjR12) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjR1) =>
% 24.53/6.40 ((
% 24.53/6.40 (upairequniteq) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjR2) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjR) =>
% 24.53/6.40 ((
% 24.53/6.40 (ksndsingleton) =>
% 24.53/6.40 ((
% 24.53/6.40 (ksndpairEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (kpairsurjEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodsndin) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodpairmemEL) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodpairmemER) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodmempaircEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodfstpairEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodsndpairEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodpairsurjEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (dpsetconstrI) =>
% 24.53/6.40 ((
% 24.53/6.40 (!!) @ (
% 24.53/6.40 (('#B') @ (
% 24.53/6.40 !!) @
% 24.53/6.40 (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 !!))) @
% 24.53/6.40 (
% 24.53/6.40 (
% 24.53/6.40 ('#S') @ (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 '#S') @
% 24.53/6.40 (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 '#C'))) @
% 24.53/6.40 (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ subset)))) @
% 24.53/6.40 dpsetconstr)))))) @
% 24.53/6.40 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1096])).
% 24.53/6.40 thf(zip_derived_cl1109, plain,
% 24.53/6.40 (~ (((binunionIR) =>
% 24.53/6.40 (((binunionEcases) =>
% 24.53/6.40 (((binunionE) =>
% 24.53/6.40 (((binunionLsub) =>
% 24.53/6.40 (((binunionRsub) =>
% 24.53/6.40 (((binintersectI) =>
% 24.53/6.40 (((binintersectSubset5) =>
% 24.53/6.40 (((binintersectEL) =>
% 24.53/6.40 (((binintersectLsub) =>
% 24.53/6.40 (((binintersectSubset2) =>
% 24.53/6.40 (((binintersectSubset3) =>
% 24.53/6.40 (((binintersectER) =>
% 24.53/6.40 (((disjointsetsI1) =>
% 24.53/6.40 (((binintersectRsub) =>
% 24.53/6.40 (((binintersectSubset4) =>
% 24.53/6.40 (((binintersectSubset1) =>
% 24.53/6.40 (((bs114d) =>
% 24.53/6.40 (((setminusI) =>
% 24.53/6.40 (((setminusEL) =>
% 24.53/6.40 (((setminusER) =>
% 24.53/6.40 (((setminusSubset2) =>
% 24.53/6.40 (((setminusERneg) =>
% 24.53/6.40 (((setminusELneg) =>
% 24.53/6.40 (((setminusILneg) =>
% 24.53/6.40 (((setminusIRneg) =>
% 24.53/6.40 (((setminusLsub) =>
% 24.53/6.40 (((setminusSubset1) =>
% 24.53/6.40 (((symdiffE) =>
% 24.53/6.40 (((symdiffI1) =>
% 24.53/6.40 (((symdiffI2) =>
% 24.53/6.40 ((
% 24.53/6.40 (symdiffIneg1) =>
% 24.53/6.40 ((
% 24.53/6.40 (symdiffIneg2) =>
% 24.53/6.40 ((
% 24.53/6.40 (secondinupair) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairIL) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairIR) =>
% 24.53/6.40 ((
% 24.53/6.40 (kpairiskpair) =>
% 24.53/6.40 ((
% 24.53/6.40 (kpairp) =>
% 24.53/6.40 ((
% 24.53/6.40 (singletonsubset) =>
% 24.53/6.40 ((
% 24.53/6.40 (singletoninpowerset) =>
% 24.53/6.40 ((
% 24.53/6.40 (singletoninpowunion) =>
% 24.53/6.40 ((
% 24.53/6.40 (upairset2E) =>
% 24.53/6.40 ((
% 24.53/6.40 (upairsubunion) =>
% 24.53/6.40 ((
% 24.53/6.40 (upairinpowunion) =>
% 24.53/6.40 ((
% 24.53/6.40 (ubforcartprodlem1) =>
% 24.53/6.40 ((
% 24.53/6.40 (ubforcartprodlem2) =>
% 24.53/6.40 ((
% 24.53/6.40 (ubforcartprodlem3) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodpairin) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodmempair1) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodmempair) =>
% 24.53/6.40 ((
% 24.53/6.40 (setunionE2) =>
% 24.53/6.40 ((
% 24.53/6.40 (setunionsingleton1) =>
% 24.53/6.40 ((
% 24.53/6.40 (setunionsingleton2) =>
% 24.53/6.40 ((
% 24.53/6.40 (setunionsingleton) =>
% 24.53/6.40 ((
% 24.53/6.40 (singletonprop) =>
% 24.53/6.40 ((
% 24.53/6.40 (ex1E1) =>
% 24.53/6.40 ((
% 24.53/6.40 (ex1I) =>
% 24.53/6.40 ((
% 24.53/6.40 (ex1I2) =>
% 24.53/6.40 ((
% 24.53/6.40 (singletonsuniq) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjL1) =>
% 24.53/6.40 ((
% 24.53/6.40 (kfstsingleton) =>
% 24.53/6.40 ((
% 24.53/6.40 (theprop) =>
% 24.53/6.40 ((
% 24.53/6.40 (kfstpairEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodfstin) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjL2) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjL) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjR11) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjR12) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjR1) =>
% 24.53/6.40 ((
% 24.53/6.40 (upairequniteq) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjR2) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjR) =>
% 24.53/6.40 ((
% 24.53/6.40 (ksndsingleton) =>
% 24.53/6.40 ((
% 24.53/6.40 (ksndpairEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (kpairsurjEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodsndin) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodpairmemEL) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodpairmemER) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodmempaircEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodfstpairEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodsndpairEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodpairsurjEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (dpsetconstrI) =>
% 24.53/6.40 ((
% 24.53/6.40 (!!) @ (
% 24.53/6.40 (('#B') @ (
% 24.53/6.40 !!) @
% 24.53/6.40 (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 !!))) @
% 24.53/6.40 (
% 24.53/6.40 (
% 24.53/6.40 ('#S') @ (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 '#S') @
% 24.53/6.40 (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 '#C'))) @
% 24.53/6.40 (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ subset)))) @
% 24.53/6.40 dpsetconstr)))))) @
% 24.53/6.40 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1102])).
% 24.53/6.40 thf(zip_derived_cl1115, plain,
% 24.53/6.40 (~ (((binunionEcases) =>
% 24.53/6.40 (((binunionE) =>
% 24.53/6.40 (((binunionLsub) =>
% 24.53/6.40 (((binunionRsub) =>
% 24.53/6.40 (((binintersectI) =>
% 24.53/6.40 (((binintersectSubset5) =>
% 24.53/6.40 (((binintersectEL) =>
% 24.53/6.40 (((binintersectLsub) =>
% 24.53/6.40 (((binintersectSubset2) =>
% 24.53/6.40 (((binintersectSubset3) =>
% 24.53/6.40 (((binintersectER) =>
% 24.53/6.40 (((disjointsetsI1) =>
% 24.53/6.40 (((binintersectRsub) =>
% 24.53/6.40 (((binintersectSubset4) =>
% 24.53/6.40 (((binintersectSubset1) =>
% 24.53/6.40 (((bs114d) =>
% 24.53/6.40 (((setminusI) =>
% 24.53/6.40 (((setminusEL) =>
% 24.53/6.40 (((setminusER) =>
% 24.53/6.40 (((setminusSubset2) =>
% 24.53/6.40 (((setminusERneg) =>
% 24.53/6.40 (((setminusELneg) =>
% 24.53/6.40 (((setminusILneg) =>
% 24.53/6.40 (((setminusIRneg) =>
% 24.53/6.40 (((setminusLsub) =>
% 24.53/6.40 (((setminusSubset1) =>
% 24.53/6.40 (((symdiffE) =>
% 24.53/6.40 (((symdiffI1) =>
% 24.53/6.40 (((symdiffI2) =>
% 24.53/6.40 (((symdiffIneg1) =>
% 24.53/6.40 ((
% 24.53/6.40 (symdiffIneg2) =>
% 24.53/6.40 ((
% 24.53/6.40 (secondinupair) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairIL) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairIR) =>
% 24.53/6.40 ((
% 24.53/6.40 (kpairiskpair) =>
% 24.53/6.40 ((
% 24.53/6.40 (kpairp) =>
% 24.53/6.40 ((
% 24.53/6.40 (singletonsubset) =>
% 24.53/6.40 ((
% 24.53/6.40 (singletoninpowerset) =>
% 24.53/6.40 ((
% 24.53/6.40 (singletoninpowunion) =>
% 24.53/6.40 ((
% 24.53/6.40 (upairset2E) =>
% 24.53/6.40 ((
% 24.53/6.40 (upairsubunion) =>
% 24.53/6.40 ((
% 24.53/6.40 (upairinpowunion) =>
% 24.53/6.40 ((
% 24.53/6.40 (ubforcartprodlem1) =>
% 24.53/6.40 ((
% 24.53/6.40 (ubforcartprodlem2) =>
% 24.53/6.40 ((
% 24.53/6.40 (ubforcartprodlem3) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodpairin) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodmempair1) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodmempair) =>
% 24.53/6.40 ((
% 24.53/6.40 (setunionE2) =>
% 24.53/6.40 ((
% 24.53/6.40 (setunionsingleton1) =>
% 24.53/6.40 ((
% 24.53/6.40 (setunionsingleton2) =>
% 24.53/6.40 ((
% 24.53/6.40 (setunionsingleton) =>
% 24.53/6.40 ((
% 24.53/6.40 (singletonprop) =>
% 24.53/6.40 ((
% 24.53/6.40 (ex1E1) =>
% 24.53/6.40 ((
% 24.53/6.40 (ex1I) =>
% 24.53/6.40 ((
% 24.53/6.40 (ex1I2) =>
% 24.53/6.40 ((
% 24.53/6.40 (singletonsuniq) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjL1) =>
% 24.53/6.40 ((
% 24.53/6.40 (kfstsingleton) =>
% 24.53/6.40 ((
% 24.53/6.40 (theprop) =>
% 24.53/6.40 ((
% 24.53/6.40 (kfstpairEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodfstin) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjL2) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjL) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjR11) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjR12) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjR1) =>
% 24.53/6.40 ((
% 24.53/6.40 (upairequniteq) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjR2) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjR) =>
% 24.53/6.40 ((
% 24.53/6.40 (ksndsingleton) =>
% 24.53/6.40 ((
% 24.53/6.40 (ksndpairEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (kpairsurjEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodsndin) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodpairmemEL) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodpairmemER) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodmempaircEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodfstpairEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodsndpairEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodpairsurjEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (dpsetconstrI) =>
% 24.53/6.40 ((
% 24.53/6.40 (!!) @ (
% 24.53/6.40 (('#B') @ (
% 24.53/6.40 !!) @
% 24.53/6.40 (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 !!))) @
% 24.53/6.40 (
% 24.53/6.40 (
% 24.53/6.40 ('#S') @ (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 '#S') @
% 24.53/6.40 (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 '#C'))) @
% 24.53/6.40 (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ subset)))) @
% 24.53/6.40 dpsetconstr)))))) @
% 24.53/6.40 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1109])).
% 24.53/6.40 thf(zip_derived_cl1121, plain,
% 24.53/6.40 (~ (((binunionE) =>
% 24.53/6.40 (((binunionLsub) =>
% 24.53/6.40 (((binunionRsub) =>
% 24.53/6.40 (((binintersectI) =>
% 24.53/6.40 (((binintersectSubset5) =>
% 24.53/6.40 (((binintersectEL) =>
% 24.53/6.40 (((binintersectLsub) =>
% 24.53/6.40 (((binintersectSubset2) =>
% 24.53/6.40 (((binintersectSubset3) =>
% 24.53/6.40 (((binintersectER) =>
% 24.53/6.40 (((disjointsetsI1) =>
% 24.53/6.40 (((binintersectRsub) =>
% 24.53/6.40 (((binintersectSubset4) =>
% 24.53/6.40 (((binintersectSubset1) =>
% 24.53/6.40 (((bs114d) =>
% 24.53/6.40 (((setminusI) =>
% 24.53/6.40 (((setminusEL) =>
% 24.53/6.40 (((setminusER) =>
% 24.53/6.40 (((setminusSubset2) =>
% 24.53/6.40 (((setminusERneg) =>
% 24.53/6.40 (((setminusELneg) =>
% 24.53/6.40 (((setminusILneg) =>
% 24.53/6.40 (((setminusIRneg) =>
% 24.53/6.40 (((setminusLsub) =>
% 24.53/6.40 (((setminusSubset1) =>
% 24.53/6.40 (((symdiffE) =>
% 24.53/6.40 (((symdiffI1) =>
% 24.53/6.40 (((symdiffI2) =>
% 24.53/6.40 (((symdiffIneg1) =>
% 24.53/6.40 (((symdiffIneg2) =>
% 24.53/6.40 ((
% 24.53/6.40 (secondinupair) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairIL) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairIR) =>
% 24.53/6.40 ((
% 24.53/6.40 (kpairiskpair) =>
% 24.53/6.40 ((
% 24.53/6.40 (kpairp) =>
% 24.53/6.40 ((
% 24.53/6.40 (singletonsubset) =>
% 24.53/6.40 ((
% 24.53/6.40 (singletoninpowerset) =>
% 24.53/6.40 ((
% 24.53/6.40 (singletoninpowunion) =>
% 24.53/6.40 ((
% 24.53/6.40 (upairset2E) =>
% 24.53/6.40 ((
% 24.53/6.40 (upairsubunion) =>
% 24.53/6.40 ((
% 24.53/6.40 (upairinpowunion) =>
% 24.53/6.40 ((
% 24.53/6.40 (ubforcartprodlem1) =>
% 24.53/6.40 ((
% 24.53/6.40 (ubforcartprodlem2) =>
% 24.53/6.40 ((
% 24.53/6.40 (ubforcartprodlem3) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodpairin) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodmempair1) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodmempair) =>
% 24.53/6.40 ((
% 24.53/6.40 (setunionE2) =>
% 24.53/6.40 ((
% 24.53/6.40 (setunionsingleton1) =>
% 24.53/6.40 ((
% 24.53/6.40 (setunionsingleton2) =>
% 24.53/6.40 ((
% 24.53/6.40 (setunionsingleton) =>
% 24.53/6.40 ((
% 24.53/6.40 (singletonprop) =>
% 24.53/6.40 ((
% 24.53/6.40 (ex1E1) =>
% 24.53/6.40 ((
% 24.53/6.40 (ex1I) =>
% 24.53/6.40 ((
% 24.53/6.40 (ex1I2) =>
% 24.53/6.40 ((
% 24.53/6.40 (singletonsuniq) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjL1) =>
% 24.53/6.40 ((
% 24.53/6.40 (kfstsingleton) =>
% 24.53/6.40 ((
% 24.53/6.40 (theprop) =>
% 24.53/6.40 ((
% 24.53/6.40 (kfstpairEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodfstin) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjL2) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjL) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjR11) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjR12) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjR1) =>
% 24.53/6.40 ((
% 24.53/6.40 (upairequniteq) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjR2) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjR) =>
% 24.53/6.40 ((
% 24.53/6.40 (ksndsingleton) =>
% 24.53/6.40 ((
% 24.53/6.40 (ksndpairEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (kpairsurjEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodsndin) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodpairmemEL) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodpairmemER) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodmempaircEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodfstpairEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodsndpairEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodpairsurjEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (dpsetconstrI) =>
% 24.53/6.40 ((
% 24.53/6.40 (!!) @ (
% 24.53/6.40 (('#B') @ (
% 24.53/6.40 !!) @
% 24.53/6.40 (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 !!))) @
% 24.53/6.40 (
% 24.53/6.40 (
% 24.53/6.40 ('#S') @ (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 '#S') @
% 24.53/6.40 (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 '#C'))) @
% 24.53/6.40 (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ subset)))) @
% 24.53/6.40 dpsetconstr)))))) @
% 24.53/6.40 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1115])).
% 24.53/6.40 thf(zip_derived_cl1128, plain,
% 24.53/6.40 (~ (((binunionLsub) =>
% 24.53/6.40 (((binunionRsub) =>
% 24.53/6.40 (((binintersectI) =>
% 24.53/6.40 (((binintersectSubset5) =>
% 24.53/6.40 (((binintersectEL) =>
% 24.53/6.40 (((binintersectLsub) =>
% 24.53/6.40 (((binintersectSubset2) =>
% 24.53/6.40 (((binintersectSubset3) =>
% 24.53/6.40 (((binintersectER) =>
% 24.53/6.40 (((disjointsetsI1) =>
% 24.53/6.40 (((binintersectRsub) =>
% 24.53/6.40 (((binintersectSubset4) =>
% 24.53/6.40 (((binintersectSubset1) =>
% 24.53/6.40 (((bs114d) =>
% 24.53/6.40 (((setminusI) =>
% 24.53/6.40 (((setminusEL) =>
% 24.53/6.40 (((setminusER) =>
% 24.53/6.40 (((setminusSubset2) =>
% 24.53/6.40 (((setminusERneg) =>
% 24.53/6.40 (((setminusELneg) =>
% 24.53/6.40 (((setminusILneg) =>
% 24.53/6.40 (((setminusIRneg) =>
% 24.53/6.40 (((setminusLsub) =>
% 24.53/6.40 (((setminusSubset1) =>
% 24.53/6.40 (((symdiffE) =>
% 24.53/6.40 (((symdiffI1) =>
% 24.53/6.40 (((symdiffI2) =>
% 24.53/6.40 (((symdiffIneg1) =>
% 24.53/6.40 (((symdiffIneg2) =>
% 24.53/6.40 (((secondinupair) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairIL) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairIR) =>
% 24.53/6.40 ((
% 24.53/6.40 (kpairiskpair) =>
% 24.53/6.40 ((
% 24.53/6.40 (kpairp) =>
% 24.53/6.40 ((
% 24.53/6.40 (singletonsubset) =>
% 24.53/6.40 ((
% 24.53/6.40 (singletoninpowerset) =>
% 24.53/6.40 ((
% 24.53/6.40 (singletoninpowunion) =>
% 24.53/6.40 ((
% 24.53/6.40 (upairset2E) =>
% 24.53/6.40 ((
% 24.53/6.40 (upairsubunion) =>
% 24.53/6.40 ((
% 24.53/6.40 (upairinpowunion) =>
% 24.53/6.40 ((
% 24.53/6.40 (ubforcartprodlem1) =>
% 24.53/6.40 ((
% 24.53/6.40 (ubforcartprodlem2) =>
% 24.53/6.40 ((
% 24.53/6.40 (ubforcartprodlem3) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodpairin) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodmempair1) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodmempair) =>
% 24.53/6.40 ((
% 24.53/6.40 (setunionE2) =>
% 24.53/6.40 ((
% 24.53/6.40 (setunionsingleton1) =>
% 24.53/6.40 ((
% 24.53/6.40 (setunionsingleton2) =>
% 24.53/6.40 ((
% 24.53/6.40 (setunionsingleton) =>
% 24.53/6.40 ((
% 24.53/6.40 (singletonprop) =>
% 24.53/6.40 ((
% 24.53/6.40 (ex1E1) =>
% 24.53/6.40 ((
% 24.53/6.40 (ex1I) =>
% 24.53/6.40 ((
% 24.53/6.40 (ex1I2) =>
% 24.53/6.40 ((
% 24.53/6.40 (singletonsuniq) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjL1) =>
% 24.53/6.40 ((
% 24.53/6.40 (kfstsingleton) =>
% 24.53/6.40 ((
% 24.53/6.40 (theprop) =>
% 24.53/6.40 ((
% 24.53/6.40 (kfstpairEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodfstin) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjL2) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjL) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjR11) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjR12) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjR1) =>
% 24.53/6.40 ((
% 24.53/6.40 (upairequniteq) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjR2) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjR) =>
% 24.53/6.40 ((
% 24.53/6.40 (ksndsingleton) =>
% 24.53/6.40 ((
% 24.53/6.40 (ksndpairEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (kpairsurjEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodsndin) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodpairmemEL) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodpairmemER) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodmempaircEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodfstpairEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodsndpairEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodpairsurjEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (dpsetconstrI) =>
% 24.53/6.40 ((
% 24.53/6.40 (!!) @ (
% 24.53/6.40 (('#B') @ (
% 24.53/6.40 !!) @
% 24.53/6.40 (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 !!))) @
% 24.53/6.40 (
% 24.53/6.40 (
% 24.53/6.40 ('#S') @ (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 '#S') @
% 24.53/6.40 (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 '#C'))) @
% 24.53/6.40 (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ subset)))) @
% 24.53/6.40 dpsetconstr)))))) @
% 24.53/6.40 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1121])).
% 24.53/6.40 thf(zip_derived_cl1135, plain,
% 24.53/6.40 (~ (((binunionRsub) =>
% 24.53/6.40 (((binintersectI) =>
% 24.53/6.40 (((binintersectSubset5) =>
% 24.53/6.40 (((binintersectEL) =>
% 24.53/6.40 (((binintersectLsub) =>
% 24.53/6.40 (((binintersectSubset2) =>
% 24.53/6.40 (((binintersectSubset3) =>
% 24.53/6.40 (((binintersectER) =>
% 24.53/6.40 (((disjointsetsI1) =>
% 24.53/6.40 (((binintersectRsub) =>
% 24.53/6.40 (((binintersectSubset4) =>
% 24.53/6.40 (((binintersectSubset1) =>
% 24.53/6.40 (((bs114d) =>
% 24.53/6.40 (((setminusI) =>
% 24.53/6.40 (((setminusEL) =>
% 24.53/6.40 (((setminusER) =>
% 24.53/6.40 (((setminusSubset2) =>
% 24.53/6.40 (((setminusERneg) =>
% 24.53/6.40 (((setminusELneg) =>
% 24.53/6.40 (((setminusILneg) =>
% 24.53/6.40 (((setminusIRneg) =>
% 24.53/6.40 (((setminusLsub) =>
% 24.53/6.40 (((setminusSubset1) =>
% 24.53/6.40 (((symdiffE) =>
% 24.53/6.40 (((symdiffI1) =>
% 24.53/6.40 (((symdiffI2) =>
% 24.53/6.40 (((symdiffIneg1) =>
% 24.53/6.40 (((symdiffIneg2) =>
% 24.53/6.40 (((secondinupair) =>
% 24.53/6.40 (((setukpairIL) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairIR) =>
% 24.53/6.40 ((
% 24.53/6.40 (kpairiskpair) =>
% 24.53/6.40 ((
% 24.53/6.40 (kpairp) =>
% 24.53/6.40 ((
% 24.53/6.40 (singletonsubset) =>
% 24.53/6.40 ((
% 24.53/6.40 (singletoninpowerset) =>
% 24.53/6.40 ((
% 24.53/6.40 (singletoninpowunion) =>
% 24.53/6.40 ((
% 24.53/6.40 (upairset2E) =>
% 24.53/6.40 ((
% 24.53/6.40 (upairsubunion) =>
% 24.53/6.40 ((
% 24.53/6.40 (upairinpowunion) =>
% 24.53/6.40 ((
% 24.53/6.40 (ubforcartprodlem1) =>
% 24.53/6.40 ((
% 24.53/6.40 (ubforcartprodlem2) =>
% 24.53/6.40 ((
% 24.53/6.40 (ubforcartprodlem3) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodpairin) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodmempair1) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodmempair) =>
% 24.53/6.40 ((
% 24.53/6.40 (setunionE2) =>
% 24.53/6.40 ((
% 24.53/6.40 (setunionsingleton1) =>
% 24.53/6.40 ((
% 24.53/6.40 (setunionsingleton2) =>
% 24.53/6.40 ((
% 24.53/6.40 (setunionsingleton) =>
% 24.53/6.40 ((
% 24.53/6.40 (singletonprop) =>
% 24.53/6.40 ((
% 24.53/6.40 (ex1E1) =>
% 24.53/6.40 ((
% 24.53/6.40 (ex1I) =>
% 24.53/6.40 ((
% 24.53/6.40 (ex1I2) =>
% 24.53/6.40 ((
% 24.53/6.40 (singletonsuniq) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjL1) =>
% 24.53/6.40 ((
% 24.53/6.40 (kfstsingleton) =>
% 24.53/6.40 ((
% 24.53/6.40 (theprop) =>
% 24.53/6.40 ((
% 24.53/6.40 (kfstpairEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodfstin) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjL2) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjL) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjR11) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjR12) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjR1) =>
% 24.53/6.40 ((
% 24.53/6.40 (upairequniteq) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjR2) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjR) =>
% 24.53/6.40 ((
% 24.53/6.40 (ksndsingleton) =>
% 24.53/6.40 ((
% 24.53/6.40 (ksndpairEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (kpairsurjEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodsndin) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodpairmemEL) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodpairmemER) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodmempaircEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodfstpairEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodsndpairEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodpairsurjEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (dpsetconstrI) =>
% 24.53/6.40 ((
% 24.53/6.40 (!!) @ (
% 24.53/6.40 (('#B') @ (
% 24.53/6.40 !!) @
% 24.53/6.40 (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 !!))) @
% 24.53/6.40 (
% 24.53/6.40 (
% 24.53/6.40 ('#S') @ (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 '#S') @
% 24.53/6.40 (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 '#C'))) @
% 24.53/6.40 (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ subset)))) @
% 24.53/6.40 dpsetconstr)))))) @
% 24.53/6.40 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1128])).
% 24.53/6.40 thf(zip_derived_cl1142, plain,
% 24.53/6.40 (~ (((binintersectI) =>
% 24.53/6.40 (((binintersectSubset5) =>
% 24.53/6.40 (((binintersectEL) =>
% 24.53/6.40 (((binintersectLsub) =>
% 24.53/6.40 (((binintersectSubset2) =>
% 24.53/6.40 (((binintersectSubset3) =>
% 24.53/6.40 (((binintersectER) =>
% 24.53/6.40 (((disjointsetsI1) =>
% 24.53/6.40 (((binintersectRsub) =>
% 24.53/6.40 (((binintersectSubset4) =>
% 24.53/6.40 (((binintersectSubset1) =>
% 24.53/6.40 (((bs114d) =>
% 24.53/6.40 (((setminusI) =>
% 24.53/6.40 (((setminusEL) =>
% 24.53/6.40 (((setminusER) =>
% 24.53/6.40 (((setminusSubset2) =>
% 24.53/6.40 (((setminusERneg) =>
% 24.53/6.40 (((setminusELneg) =>
% 24.53/6.40 (((setminusILneg) =>
% 24.53/6.40 (((setminusIRneg) =>
% 24.53/6.40 (((setminusLsub) =>
% 24.53/6.40 (((setminusSubset1) =>
% 24.53/6.40 (((symdiffE) =>
% 24.53/6.40 (((symdiffI1) =>
% 24.53/6.40 (((symdiffI2) =>
% 24.53/6.40 (((symdiffIneg1) =>
% 24.53/6.40 (((symdiffIneg2) =>
% 24.53/6.40 (((secondinupair) =>
% 24.53/6.40 (((setukpairIL) =>
% 24.53/6.40 (((setukpairIR) =>
% 24.53/6.40 ((
% 24.53/6.40 (kpairiskpair) =>
% 24.53/6.40 ((
% 24.53/6.40 (kpairp) =>
% 24.53/6.40 ((
% 24.53/6.40 (singletonsubset) =>
% 24.53/6.40 ((
% 24.53/6.40 (singletoninpowerset) =>
% 24.53/6.40 ((
% 24.53/6.40 (singletoninpowunion) =>
% 24.53/6.40 ((
% 24.53/6.40 (upairset2E) =>
% 24.53/6.40 ((
% 24.53/6.40 (upairsubunion) =>
% 24.53/6.40 ((
% 24.53/6.40 (upairinpowunion) =>
% 24.53/6.40 ((
% 24.53/6.40 (ubforcartprodlem1) =>
% 24.53/6.40 ((
% 24.53/6.40 (ubforcartprodlem2) =>
% 24.53/6.40 ((
% 24.53/6.40 (ubforcartprodlem3) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodpairin) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodmempair1) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodmempair) =>
% 24.53/6.40 ((
% 24.53/6.40 (setunionE2) =>
% 24.53/6.40 ((
% 24.53/6.40 (setunionsingleton1) =>
% 24.53/6.40 ((
% 24.53/6.40 (setunionsingleton2) =>
% 24.53/6.40 ((
% 24.53/6.40 (setunionsingleton) =>
% 24.53/6.40 ((
% 24.53/6.40 (singletonprop) =>
% 24.53/6.40 ((
% 24.53/6.40 (ex1E1) =>
% 24.53/6.40 ((
% 24.53/6.40 (ex1I) =>
% 24.53/6.40 ((
% 24.53/6.40 (ex1I2) =>
% 24.53/6.40 ((
% 24.53/6.40 (singletonsuniq) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjL1) =>
% 24.53/6.40 ((
% 24.53/6.40 (kfstsingleton) =>
% 24.53/6.40 ((
% 24.53/6.40 (theprop) =>
% 24.53/6.40 ((
% 24.53/6.40 (kfstpairEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodfstin) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjL2) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjL) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjR11) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjR12) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjR1) =>
% 24.53/6.40 ((
% 24.53/6.40 (upairequniteq) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjR2) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjR) =>
% 24.53/6.40 ((
% 24.53/6.40 (ksndsingleton) =>
% 24.53/6.40 ((
% 24.53/6.40 (ksndpairEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (kpairsurjEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodsndin) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodpairmemEL) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodpairmemER) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodmempaircEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodfstpairEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodsndpairEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodpairsurjEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (dpsetconstrI) =>
% 24.53/6.40 ((
% 24.53/6.40 (!!) @ (
% 24.53/6.40 (('#B') @ (
% 24.53/6.40 !!) @
% 24.53/6.40 (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 !!))) @
% 24.53/6.40 (
% 24.53/6.40 (
% 24.53/6.40 ('#S') @ (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 '#S') @
% 24.53/6.40 (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 '#C'))) @
% 24.53/6.40 (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ subset)))) @
% 24.53/6.40 dpsetconstr)))))) @
% 24.53/6.40 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1135])).
% 24.53/6.40 thf(zip_derived_cl1150, plain,
% 24.53/6.40 (~ (((binintersectSubset5) =>
% 24.53/6.40 (((binintersectEL) =>
% 24.53/6.40 (((binintersectLsub) =>
% 24.53/6.40 (((binintersectSubset2) =>
% 24.53/6.40 (((binintersectSubset3) =>
% 24.53/6.40 (((binintersectER) =>
% 24.53/6.40 (((disjointsetsI1) =>
% 24.53/6.40 (((binintersectRsub) =>
% 24.53/6.40 (((binintersectSubset4) =>
% 24.53/6.40 (((binintersectSubset1) =>
% 24.53/6.40 (((bs114d) =>
% 24.53/6.40 (((setminusI) =>
% 24.53/6.40 (((setminusEL) =>
% 24.53/6.40 (((setminusER) =>
% 24.53/6.40 (((setminusSubset2) =>
% 24.53/6.40 (((setminusERneg) =>
% 24.53/6.40 (((setminusELneg) =>
% 24.53/6.40 (((setminusILneg) =>
% 24.53/6.40 (((setminusIRneg) =>
% 24.53/6.40 (((setminusLsub) =>
% 24.53/6.40 (((setminusSubset1) =>
% 24.53/6.40 (((symdiffE) =>
% 24.53/6.40 (((symdiffI1) =>
% 24.53/6.40 (((symdiffI2) =>
% 24.53/6.40 (((symdiffIneg1) =>
% 24.53/6.40 (((symdiffIneg2) =>
% 24.53/6.40 (((secondinupair) =>
% 24.53/6.40 (((setukpairIL) =>
% 24.53/6.40 (((setukpairIR) =>
% 24.53/6.40 (((kpairiskpair) =>
% 24.53/6.40 ((
% 24.53/6.40 (kpairp) =>
% 24.53/6.40 ((
% 24.53/6.40 (singletonsubset) =>
% 24.53/6.40 ((
% 24.53/6.40 (singletoninpowerset) =>
% 24.53/6.40 ((
% 24.53/6.40 (singletoninpowunion) =>
% 24.53/6.40 ((
% 24.53/6.40 (upairset2E) =>
% 24.53/6.40 ((
% 24.53/6.40 (upairsubunion) =>
% 24.53/6.40 ((
% 24.53/6.40 (upairinpowunion) =>
% 24.53/6.40 ((
% 24.53/6.40 (ubforcartprodlem1) =>
% 24.53/6.40 ((
% 24.53/6.40 (ubforcartprodlem2) =>
% 24.53/6.40 ((
% 24.53/6.40 (ubforcartprodlem3) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodpairin) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodmempair1) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodmempair) =>
% 24.53/6.40 ((
% 24.53/6.40 (setunionE2) =>
% 24.53/6.40 ((
% 24.53/6.40 (setunionsingleton1) =>
% 24.53/6.40 ((
% 24.53/6.40 (setunionsingleton2) =>
% 24.53/6.40 ((
% 24.53/6.40 (setunionsingleton) =>
% 24.53/6.40 ((
% 24.53/6.40 (singletonprop) =>
% 24.53/6.40 ((
% 24.53/6.40 (ex1E1) =>
% 24.53/6.40 ((
% 24.53/6.40 (ex1I) =>
% 24.53/6.40 ((
% 24.53/6.40 (ex1I2) =>
% 24.53/6.40 ((
% 24.53/6.40 (singletonsuniq) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjL1) =>
% 24.53/6.40 ((
% 24.53/6.40 (kfstsingleton) =>
% 24.53/6.40 ((
% 24.53/6.40 (theprop) =>
% 24.53/6.40 ((
% 24.53/6.40 (kfstpairEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodfstin) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjL2) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjL) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjR11) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjR12) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjR1) =>
% 24.53/6.40 ((
% 24.53/6.40 (upairequniteq) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjR2) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjR) =>
% 24.53/6.40 ((
% 24.53/6.40 (ksndsingleton) =>
% 24.53/6.40 ((
% 24.53/6.40 (ksndpairEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (kpairsurjEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodsndin) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodpairmemEL) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodpairmemER) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodmempaircEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodfstpairEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodsndpairEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodpairsurjEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (dpsetconstrI) =>
% 24.53/6.40 ((
% 24.53/6.40 (!!) @ (
% 24.53/6.40 (('#B') @ (
% 24.53/6.40 !!) @
% 24.53/6.40 (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 !!))) @
% 24.53/6.40 (
% 24.53/6.40 (
% 24.53/6.40 ('#S') @ (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 '#S') @
% 24.53/6.40 (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 '#C'))) @
% 24.53/6.40 (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ subset)))) @
% 24.53/6.40 dpsetconstr)))))) @
% 24.53/6.40 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1142])).
% 24.53/6.40 thf(zip_derived_cl1158, plain,
% 24.53/6.40 (~ (((binintersectEL) =>
% 24.53/6.40 (((binintersectLsub) =>
% 24.53/6.40 (((binintersectSubset2) =>
% 24.53/6.40 (((binintersectSubset3) =>
% 24.53/6.40 (((binintersectER) =>
% 24.53/6.40 (((disjointsetsI1) =>
% 24.53/6.40 (((binintersectRsub) =>
% 24.53/6.40 (((binintersectSubset4) =>
% 24.53/6.40 (((binintersectSubset1) =>
% 24.53/6.40 (((bs114d) =>
% 24.53/6.40 (((setminusI) =>
% 24.53/6.40 (((setminusEL) =>
% 24.53/6.40 (((setminusER) =>
% 24.53/6.40 (((setminusSubset2) =>
% 24.53/6.40 (((setminusERneg) =>
% 24.53/6.40 (((setminusELneg) =>
% 24.53/6.40 (((setminusILneg) =>
% 24.53/6.40 (((setminusIRneg) =>
% 24.53/6.40 (((setminusLsub) =>
% 24.53/6.40 (((setminusSubset1) =>
% 24.53/6.40 (((symdiffE) =>
% 24.53/6.40 (((symdiffI1) =>
% 24.53/6.40 (((symdiffI2) =>
% 24.53/6.40 (((symdiffIneg1) =>
% 24.53/6.40 (((symdiffIneg2) =>
% 24.53/6.40 (((secondinupair) =>
% 24.53/6.40 (((setukpairIL) =>
% 24.53/6.40 (((setukpairIR) =>
% 24.53/6.40 (((kpairiskpair) =>
% 24.53/6.40 (((kpairp) =>
% 24.53/6.40 ((
% 24.53/6.40 (singletonsubset) =>
% 24.53/6.40 ((
% 24.53/6.40 (singletoninpowerset) =>
% 24.53/6.40 ((
% 24.53/6.40 (singletoninpowunion) =>
% 24.53/6.40 ((
% 24.53/6.40 (upairset2E) =>
% 24.53/6.40 ((
% 24.53/6.40 (upairsubunion) =>
% 24.53/6.40 ((
% 24.53/6.40 (upairinpowunion) =>
% 24.53/6.40 ((
% 24.53/6.40 (ubforcartprodlem1) =>
% 24.53/6.40 ((
% 24.53/6.40 (ubforcartprodlem2) =>
% 24.53/6.40 ((
% 24.53/6.40 (ubforcartprodlem3) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodpairin) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodmempair1) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodmempair) =>
% 24.53/6.40 ((
% 24.53/6.40 (setunionE2) =>
% 24.53/6.40 ((
% 24.53/6.40 (setunionsingleton1) =>
% 24.53/6.40 ((
% 24.53/6.40 (setunionsingleton2) =>
% 24.53/6.40 ((
% 24.53/6.40 (setunionsingleton) =>
% 24.53/6.40 ((
% 24.53/6.40 (singletonprop) =>
% 24.53/6.40 ((
% 24.53/6.40 (ex1E1) =>
% 24.53/6.40 ((
% 24.53/6.40 (ex1I) =>
% 24.53/6.40 ((
% 24.53/6.40 (ex1I2) =>
% 24.53/6.40 ((
% 24.53/6.40 (singletonsuniq) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjL1) =>
% 24.53/6.40 ((
% 24.53/6.40 (kfstsingleton) =>
% 24.53/6.40 ((
% 24.53/6.40 (theprop) =>
% 24.53/6.40 ((
% 24.53/6.40 (kfstpairEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodfstin) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjL2) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjL) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjR11) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjR12) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjR1) =>
% 24.53/6.40 ((
% 24.53/6.40 (upairequniteq) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjR2) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjR) =>
% 24.53/6.40 ((
% 24.53/6.40 (ksndsingleton) =>
% 24.53/6.40 ((
% 24.53/6.40 (ksndpairEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (kpairsurjEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodsndin) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodpairmemEL) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodpairmemER) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodmempaircEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodfstpairEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodsndpairEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodpairsurjEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (dpsetconstrI) =>
% 24.53/6.40 ((
% 24.53/6.40 (!!) @ (
% 24.53/6.40 (('#B') @ (
% 24.53/6.40 !!) @
% 24.53/6.40 (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 !!))) @
% 24.53/6.40 (
% 24.53/6.40 (
% 24.53/6.40 ('#S') @ (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 '#S') @
% 24.53/6.40 (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 '#C'))) @
% 24.53/6.40 (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ subset)))) @
% 24.53/6.40 dpsetconstr)))))) @
% 24.53/6.40 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1150])).
% 24.53/6.40 thf(zip_derived_cl1166, plain,
% 24.53/6.40 (~ (((binintersectLsub) =>
% 24.53/6.40 (((binintersectSubset2) =>
% 24.53/6.40 (((binintersectSubset3) =>
% 24.53/6.40 (((binintersectER) =>
% 24.53/6.40 (((disjointsetsI1) =>
% 24.53/6.40 (((binintersectRsub) =>
% 24.53/6.40 (((binintersectSubset4) =>
% 24.53/6.40 (((binintersectSubset1) =>
% 24.53/6.40 (((bs114d) =>
% 24.53/6.40 (((setminusI) =>
% 24.53/6.40 (((setminusEL) =>
% 24.53/6.40 (((setminusER) =>
% 24.53/6.40 (((setminusSubset2) =>
% 24.53/6.40 (((setminusERneg) =>
% 24.53/6.40 (((setminusELneg) =>
% 24.53/6.40 (((setminusILneg) =>
% 24.53/6.40 (((setminusIRneg) =>
% 24.53/6.40 (((setminusLsub) =>
% 24.53/6.40 (((setminusSubset1) =>
% 24.53/6.40 (((symdiffE) =>
% 24.53/6.40 (((symdiffI1) =>
% 24.53/6.40 (((symdiffI2) =>
% 24.53/6.40 (((symdiffIneg1) =>
% 24.53/6.40 (((symdiffIneg2) =>
% 24.53/6.40 (((secondinupair) =>
% 24.53/6.40 (((setukpairIL) =>
% 24.53/6.40 (((setukpairIR) =>
% 24.53/6.40 (((kpairiskpair) =>
% 24.53/6.40 (((kpairp) =>
% 24.53/6.40 (((singletonsubset) =>
% 24.53/6.40 ((
% 24.53/6.40 (singletoninpowerset) =>
% 24.53/6.40 ((
% 24.53/6.40 (singletoninpowunion) =>
% 24.53/6.40 ((
% 24.53/6.40 (upairset2E) =>
% 24.53/6.40 ((
% 24.53/6.40 (upairsubunion) =>
% 24.53/6.40 ((
% 24.53/6.40 (upairinpowunion) =>
% 24.53/6.40 ((
% 24.53/6.40 (ubforcartprodlem1) =>
% 24.53/6.40 ((
% 24.53/6.40 (ubforcartprodlem2) =>
% 24.53/6.40 ((
% 24.53/6.40 (ubforcartprodlem3) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodpairin) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodmempair1) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodmempair) =>
% 24.53/6.40 ((
% 24.53/6.40 (setunionE2) =>
% 24.53/6.40 ((
% 24.53/6.40 (setunionsingleton1) =>
% 24.53/6.40 ((
% 24.53/6.40 (setunionsingleton2) =>
% 24.53/6.40 ((
% 24.53/6.40 (setunionsingleton) =>
% 24.53/6.40 ((
% 24.53/6.40 (singletonprop) =>
% 24.53/6.40 ((
% 24.53/6.40 (ex1E1) =>
% 24.53/6.40 ((
% 24.53/6.40 (ex1I) =>
% 24.53/6.40 ((
% 24.53/6.40 (ex1I2) =>
% 24.53/6.40 ((
% 24.53/6.40 (singletonsuniq) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjL1) =>
% 24.53/6.40 ((
% 24.53/6.40 (kfstsingleton) =>
% 24.53/6.40 ((
% 24.53/6.40 (theprop) =>
% 24.53/6.40 ((
% 24.53/6.40 (kfstpairEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodfstin) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjL2) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjL) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjR11) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjR12) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjR1) =>
% 24.53/6.40 ((
% 24.53/6.40 (upairequniteq) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjR2) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjR) =>
% 24.53/6.40 ((
% 24.53/6.40 (ksndsingleton) =>
% 24.53/6.40 ((
% 24.53/6.40 (ksndpairEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (kpairsurjEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodsndin) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodpairmemEL) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodpairmemER) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodmempaircEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodfstpairEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodsndpairEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodpairsurjEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (dpsetconstrI) =>
% 24.53/6.40 ((
% 24.53/6.40 (!!) @ (
% 24.53/6.40 (('#B') @ (
% 24.53/6.40 !!) @
% 24.53/6.40 (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 !!))) @
% 24.53/6.40 (
% 24.53/6.40 (
% 24.53/6.40 ('#S') @ (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 '#S') @
% 24.53/6.40 (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 '#C'))) @
% 24.53/6.40 (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ subset)))) @
% 24.53/6.40 dpsetconstr)))))) @
% 24.53/6.40 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1158])).
% 24.53/6.40 thf(zip_derived_cl1174, plain,
% 24.53/6.40 (~ (((binintersectSubset2) =>
% 24.53/6.40 (((binintersectSubset3) =>
% 24.53/6.40 (((binintersectER) =>
% 24.53/6.40 (((disjointsetsI1) =>
% 24.53/6.40 (((binintersectRsub) =>
% 24.53/6.40 (((binintersectSubset4) =>
% 24.53/6.40 (((binintersectSubset1) =>
% 24.53/6.40 (((bs114d) =>
% 24.53/6.40 (((setminusI) =>
% 24.53/6.40 (((setminusEL) =>
% 24.53/6.40 (((setminusER) =>
% 24.53/6.40 (((setminusSubset2) =>
% 24.53/6.40 (((setminusERneg) =>
% 24.53/6.40 (((setminusELneg) =>
% 24.53/6.40 (((setminusILneg) =>
% 24.53/6.40 (((setminusIRneg) =>
% 24.53/6.40 (((setminusLsub) =>
% 24.53/6.40 (((setminusSubset1) =>
% 24.53/6.40 (((symdiffE) =>
% 24.53/6.40 (((symdiffI1) =>
% 24.53/6.40 (((symdiffI2) =>
% 24.53/6.40 (((symdiffIneg1) =>
% 24.53/6.40 (((symdiffIneg2) =>
% 24.53/6.40 (((secondinupair) =>
% 24.53/6.40 (((setukpairIL) =>
% 24.53/6.40 (((setukpairIR) =>
% 24.53/6.40 (((kpairiskpair) =>
% 24.53/6.40 (((kpairp) =>
% 24.53/6.40 (((singletonsubset) =>
% 24.53/6.40 (((singletoninpowerset) =>
% 24.53/6.40 ((
% 24.53/6.40 (singletoninpowunion) =>
% 24.53/6.40 ((
% 24.53/6.40 (upairset2E) =>
% 24.53/6.40 ((
% 24.53/6.40 (upairsubunion) =>
% 24.53/6.40 ((
% 24.53/6.40 (upairinpowunion) =>
% 24.53/6.40 ((
% 24.53/6.40 (ubforcartprodlem1) =>
% 24.53/6.40 ((
% 24.53/6.40 (ubforcartprodlem2) =>
% 24.53/6.40 ((
% 24.53/6.40 (ubforcartprodlem3) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodpairin) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodmempair1) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodmempair) =>
% 24.53/6.40 ((
% 24.53/6.40 (setunionE2) =>
% 24.53/6.40 ((
% 24.53/6.40 (setunionsingleton1) =>
% 24.53/6.40 ((
% 24.53/6.40 (setunionsingleton2) =>
% 24.53/6.40 ((
% 24.53/6.40 (setunionsingleton) =>
% 24.53/6.40 ((
% 24.53/6.40 (singletonprop) =>
% 24.53/6.40 ((
% 24.53/6.40 (ex1E1) =>
% 24.53/6.40 ((
% 24.53/6.40 (ex1I) =>
% 24.53/6.40 ((
% 24.53/6.40 (ex1I2) =>
% 24.53/6.40 ((
% 24.53/6.40 (singletonsuniq) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjL1) =>
% 24.53/6.40 ((
% 24.53/6.40 (kfstsingleton) =>
% 24.53/6.40 ((
% 24.53/6.40 (theprop) =>
% 24.53/6.40 ((
% 24.53/6.40 (kfstpairEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodfstin) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjL2) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjL) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjR11) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjR12) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjR1) =>
% 24.53/6.40 ((
% 24.53/6.40 (upairequniteq) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjR2) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjR) =>
% 24.53/6.40 ((
% 24.53/6.40 (ksndsingleton) =>
% 24.53/6.40 ((
% 24.53/6.40 (ksndpairEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (kpairsurjEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodsndin) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodpairmemEL) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodpairmemER) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodmempaircEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodfstpairEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodsndpairEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodpairsurjEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (dpsetconstrI) =>
% 24.53/6.40 ((
% 24.53/6.40 (!!) @ (
% 24.53/6.40 (('#B') @ (
% 24.53/6.40 !!) @
% 24.53/6.40 (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 !!))) @
% 24.53/6.40 (
% 24.53/6.40 (
% 24.53/6.40 ('#S') @ (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 '#S') @
% 24.53/6.40 (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 '#C'))) @
% 24.53/6.40 (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ subset)))) @
% 24.53/6.40 dpsetconstr)))))) @
% 24.53/6.40 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1166])).
% 24.53/6.40 thf(zip_derived_cl1183, plain,
% 24.53/6.40 (~ (((binintersectSubset3) =>
% 24.53/6.40 (((binintersectER) =>
% 24.53/6.40 (((disjointsetsI1) =>
% 24.53/6.40 (((binintersectRsub) =>
% 24.53/6.40 (((binintersectSubset4) =>
% 24.53/6.40 (((binintersectSubset1) =>
% 24.53/6.40 (((bs114d) =>
% 24.53/6.40 (((setminusI) =>
% 24.53/6.40 (((setminusEL) =>
% 24.53/6.40 (((setminusER) =>
% 24.53/6.40 (((setminusSubset2) =>
% 24.53/6.40 (((setminusERneg) =>
% 24.53/6.40 (((setminusELneg) =>
% 24.53/6.40 (((setminusILneg) =>
% 24.53/6.40 (((setminusIRneg) =>
% 24.53/6.40 (((setminusLsub) =>
% 24.53/6.40 (((setminusSubset1) =>
% 24.53/6.40 (((symdiffE) =>
% 24.53/6.40 (((symdiffI1) =>
% 24.53/6.40 (((symdiffI2) =>
% 24.53/6.40 (((symdiffIneg1) =>
% 24.53/6.40 (((symdiffIneg2) =>
% 24.53/6.40 (((secondinupair) =>
% 24.53/6.40 (((setukpairIL) =>
% 24.53/6.40 (((setukpairIR) =>
% 24.53/6.40 (((kpairiskpair) =>
% 24.53/6.40 (((kpairp) =>
% 24.53/6.40 (((singletonsubset) =>
% 24.53/6.40 (((singletoninpowerset) =>
% 24.53/6.40 (((singletoninpowunion) =>
% 24.53/6.40 ((
% 24.53/6.40 (upairset2E) =>
% 24.53/6.40 ((
% 24.53/6.40 (upairsubunion) =>
% 24.53/6.40 ((
% 24.53/6.40 (upairinpowunion) =>
% 24.53/6.40 ((
% 24.53/6.40 (ubforcartprodlem1) =>
% 24.53/6.40 ((
% 24.53/6.40 (ubforcartprodlem2) =>
% 24.53/6.40 ((
% 24.53/6.40 (ubforcartprodlem3) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodpairin) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodmempair1) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodmempair) =>
% 24.53/6.40 ((
% 24.53/6.40 (setunionE2) =>
% 24.53/6.40 ((
% 24.53/6.40 (setunionsingleton1) =>
% 24.53/6.40 ((
% 24.53/6.40 (setunionsingleton2) =>
% 24.53/6.40 ((
% 24.53/6.40 (setunionsingleton) =>
% 24.53/6.40 ((
% 24.53/6.40 (singletonprop) =>
% 24.53/6.40 ((
% 24.53/6.40 (ex1E1) =>
% 24.53/6.40 ((
% 24.53/6.40 (ex1I) =>
% 24.53/6.40 ((
% 24.53/6.40 (ex1I2) =>
% 24.53/6.40 ((
% 24.53/6.40 (singletonsuniq) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjL1) =>
% 24.53/6.40 ((
% 24.53/6.40 (kfstsingleton) =>
% 24.53/6.40 ((
% 24.53/6.40 (theprop) =>
% 24.53/6.40 ((
% 24.53/6.40 (kfstpairEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodfstin) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjL2) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjL) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjR11) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjR12) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjR1) =>
% 24.53/6.40 ((
% 24.53/6.40 (upairequniteq) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjR2) =>
% 24.53/6.40 ((
% 24.53/6.40 (setukpairinjR) =>
% 24.53/6.40 ((
% 24.53/6.40 (ksndsingleton) =>
% 24.53/6.40 ((
% 24.53/6.40 (ksndpairEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (kpairsurjEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodsndin) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodpairmemEL) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodpairmemER) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodmempaircEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodfstpairEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodsndpairEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (cartprodpairsurjEq) =>
% 24.53/6.40 ((
% 24.53/6.40 (dpsetconstrI) =>
% 24.53/6.40 ((
% 24.53/6.40 (!!) @ (
% 24.53/6.40 (('#B') @ (
% 24.53/6.40 !!) @
% 24.53/6.40 (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 !!))) @
% 24.53/6.40 (
% 24.53/6.40 (
% 24.53/6.40 ('#S') @ (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 '#S') @
% 24.53/6.40 (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 (
% 24.53/6.40 ('#B') @ (
% 24.53/6.40 '#C'))) @
% 24.53/6.40 (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ subset)))) @
% 24.53/6.41 dpsetconstr)))))) @
% 24.53/6.41 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1174])).
% 24.53/6.41 thf(zip_derived_cl1193, plain,
% 24.53/6.41 (~ (((binintersectER) =>
% 24.53/6.41 (((disjointsetsI1) =>
% 24.53/6.41 (((binintersectRsub) =>
% 24.53/6.41 (((binintersectSubset4) =>
% 24.53/6.41 (((binintersectSubset1) =>
% 24.53/6.41 (((bs114d) =>
% 24.53/6.41 (((setminusI) =>
% 24.53/6.41 (((setminusEL) =>
% 24.53/6.41 (((setminusER) =>
% 24.53/6.41 (((setminusSubset2) =>
% 24.53/6.41 (((setminusERneg) =>
% 24.53/6.41 (((setminusELneg) =>
% 24.53/6.41 (((setminusILneg) =>
% 24.53/6.41 (((setminusIRneg) =>
% 24.53/6.41 (((setminusLsub) =>
% 24.53/6.41 (((setminusSubset1) =>
% 24.53/6.41 (((symdiffE) =>
% 24.53/6.41 (((symdiffI1) =>
% 24.53/6.41 (((symdiffI2) =>
% 24.53/6.41 (((symdiffIneg1) =>
% 24.53/6.41 (((symdiffIneg2) =>
% 24.53/6.41 (((secondinupair) =>
% 24.53/6.41 (((setukpairIL) =>
% 24.53/6.41 (((setukpairIR) =>
% 24.53/6.41 (((kpairiskpair) =>
% 24.53/6.41 (((kpairp) =>
% 24.53/6.41 (((singletonsubset) =>
% 24.53/6.41 (((singletoninpowerset) =>
% 24.53/6.41 (((singletoninpowunion) =>
% 24.53/6.41 (((upairset2E) =>
% 24.53/6.41 ((
% 24.53/6.41 (upairsubunion) =>
% 24.53/6.41 ((
% 24.53/6.41 (upairinpowunion) =>
% 24.53/6.41 ((
% 24.53/6.41 (ubforcartprodlem1) =>
% 24.53/6.41 ((
% 24.53/6.41 (ubforcartprodlem2) =>
% 24.53/6.41 ((
% 24.53/6.41 (ubforcartprodlem3) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodpairin) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodmempair1) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodmempair) =>
% 24.53/6.41 ((
% 24.53/6.41 (setunionE2) =>
% 24.53/6.41 ((
% 24.53/6.41 (setunionsingleton1) =>
% 24.53/6.41 ((
% 24.53/6.41 (setunionsingleton2) =>
% 24.53/6.41 ((
% 24.53/6.41 (setunionsingleton) =>
% 24.53/6.41 ((
% 24.53/6.41 (singletonprop) =>
% 24.53/6.41 ((
% 24.53/6.41 (ex1E1) =>
% 24.53/6.41 ((
% 24.53/6.41 (ex1I) =>
% 24.53/6.41 ((
% 24.53/6.41 (ex1I2) =>
% 24.53/6.41 ((
% 24.53/6.41 (singletonsuniq) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjL1) =>
% 24.53/6.41 ((
% 24.53/6.41 (kfstsingleton) =>
% 24.53/6.41 ((
% 24.53/6.41 (theprop) =>
% 24.53/6.41 ((
% 24.53/6.41 (kfstpairEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodfstin) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjL2) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjL) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR11) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR12) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR1) =>
% 24.53/6.41 ((
% 24.53/6.41 (upairequniteq) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR2) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR) =>
% 24.53/6.41 ((
% 24.53/6.41 (ksndsingleton) =>
% 24.53/6.41 ((
% 24.53/6.41 (ksndpairEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (kpairsurjEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodsndin) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodpairmemEL) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodpairmemER) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodmempaircEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodfstpairEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodsndpairEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodpairsurjEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (dpsetconstrI) =>
% 24.53/6.41 ((
% 24.53/6.41 (!!) @ (
% 24.53/6.41 (('#B') @ (
% 24.53/6.41 !!) @
% 24.53/6.41 (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 !!))) @
% 24.53/6.41 (
% 24.53/6.41 (
% 24.53/6.41 ('#S') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 '#S') @
% 24.53/6.41 (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 '#C'))) @
% 24.53/6.41 (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ subset)))) @
% 24.53/6.41 dpsetconstr)))))) @
% 24.53/6.41 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1183])).
% 24.53/6.41 thf(zip_derived_cl1206, plain,
% 24.53/6.41 (~ (((disjointsetsI1) =>
% 24.53/6.41 (((binintersectRsub) =>
% 24.53/6.41 (((binintersectSubset4) =>
% 24.53/6.41 (((binintersectSubset1) =>
% 24.53/6.41 (((bs114d) =>
% 24.53/6.41 (((setminusI) =>
% 24.53/6.41 (((setminusEL) =>
% 24.53/6.41 (((setminusER) =>
% 24.53/6.41 (((setminusSubset2) =>
% 24.53/6.41 (((setminusERneg) =>
% 24.53/6.41 (((setminusELneg) =>
% 24.53/6.41 (((setminusILneg) =>
% 24.53/6.41 (((setminusIRneg) =>
% 24.53/6.41 (((setminusLsub) =>
% 24.53/6.41 (((setminusSubset1) =>
% 24.53/6.41 (((symdiffE) =>
% 24.53/6.41 (((symdiffI1) =>
% 24.53/6.41 (((symdiffI2) =>
% 24.53/6.41 (((symdiffIneg1) =>
% 24.53/6.41 (((symdiffIneg2) =>
% 24.53/6.41 (((secondinupair) =>
% 24.53/6.41 (((setukpairIL) =>
% 24.53/6.41 (((setukpairIR) =>
% 24.53/6.41 (((kpairiskpair) =>
% 24.53/6.41 (((kpairp) =>
% 24.53/6.41 (((singletonsubset) =>
% 24.53/6.41 (((singletoninpowerset) =>
% 24.53/6.41 (((singletoninpowunion) =>
% 24.53/6.41 (((upairset2E) =>
% 24.53/6.41 (((upairsubunion) =>
% 24.53/6.41 ((
% 24.53/6.41 (upairinpowunion) =>
% 24.53/6.41 ((
% 24.53/6.41 (ubforcartprodlem1) =>
% 24.53/6.41 ((
% 24.53/6.41 (ubforcartprodlem2) =>
% 24.53/6.41 ((
% 24.53/6.41 (ubforcartprodlem3) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodpairin) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodmempair1) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodmempair) =>
% 24.53/6.41 ((
% 24.53/6.41 (setunionE2) =>
% 24.53/6.41 ((
% 24.53/6.41 (setunionsingleton1) =>
% 24.53/6.41 ((
% 24.53/6.41 (setunionsingleton2) =>
% 24.53/6.41 ((
% 24.53/6.41 (setunionsingleton) =>
% 24.53/6.41 ((
% 24.53/6.41 (singletonprop) =>
% 24.53/6.41 ((
% 24.53/6.41 (ex1E1) =>
% 24.53/6.41 ((
% 24.53/6.41 (ex1I) =>
% 24.53/6.41 ((
% 24.53/6.41 (ex1I2) =>
% 24.53/6.41 ((
% 24.53/6.41 (singletonsuniq) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjL1) =>
% 24.53/6.41 ((
% 24.53/6.41 (kfstsingleton) =>
% 24.53/6.41 ((
% 24.53/6.41 (theprop) =>
% 24.53/6.41 ((
% 24.53/6.41 (kfstpairEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodfstin) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjL2) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjL) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR11) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR12) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR1) =>
% 24.53/6.41 ((
% 24.53/6.41 (upairequniteq) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR2) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR) =>
% 24.53/6.41 ((
% 24.53/6.41 (ksndsingleton) =>
% 24.53/6.41 ((
% 24.53/6.41 (ksndpairEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (kpairsurjEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodsndin) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodpairmemEL) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodpairmemER) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodmempaircEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodfstpairEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodsndpairEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodpairsurjEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (dpsetconstrI) =>
% 24.53/6.41 ((
% 24.53/6.41 (!!) @ (
% 24.53/6.41 (('#B') @ (
% 24.53/6.41 !!) @
% 24.53/6.41 (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 !!))) @
% 24.53/6.41 (
% 24.53/6.41 (
% 24.53/6.41 ('#S') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 '#S') @
% 24.53/6.41 (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 '#C'))) @
% 24.53/6.41 (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ subset)))) @
% 24.53/6.41 dpsetconstr)))))) @
% 24.53/6.41 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1193])).
% 24.53/6.41 thf(zip_derived_cl1216, plain,
% 24.53/6.41 (~ (((binintersectRsub) =>
% 24.53/6.41 (((binintersectSubset4) =>
% 24.53/6.41 (((binintersectSubset1) =>
% 24.53/6.41 (((bs114d) =>
% 24.53/6.41 (((setminusI) =>
% 24.53/6.41 (((setminusEL) =>
% 24.53/6.41 (((setminusER) =>
% 24.53/6.41 (((setminusSubset2) =>
% 24.53/6.41 (((setminusERneg) =>
% 24.53/6.41 (((setminusELneg) =>
% 24.53/6.41 (((setminusILneg) =>
% 24.53/6.41 (((setminusIRneg) =>
% 24.53/6.41 (((setminusLsub) =>
% 24.53/6.41 (((setminusSubset1) =>
% 24.53/6.41 (((symdiffE) =>
% 24.53/6.41 (((symdiffI1) =>
% 24.53/6.41 (((symdiffI2) =>
% 24.53/6.41 (((symdiffIneg1) =>
% 24.53/6.41 (((symdiffIneg2) =>
% 24.53/6.41 (((secondinupair) =>
% 24.53/6.41 (((setukpairIL) =>
% 24.53/6.41 (((setukpairIR) =>
% 24.53/6.41 (((kpairiskpair) =>
% 24.53/6.41 (((kpairp) =>
% 24.53/6.41 (((singletonsubset) =>
% 24.53/6.41 (((singletoninpowerset) =>
% 24.53/6.41 (((singletoninpowunion) =>
% 24.53/6.41 (((upairset2E) =>
% 24.53/6.41 (((upairsubunion) =>
% 24.53/6.41 (((upairinpowunion) =>
% 24.53/6.41 ((
% 24.53/6.41 (ubforcartprodlem1) =>
% 24.53/6.41 ((
% 24.53/6.41 (ubforcartprodlem2) =>
% 24.53/6.41 ((
% 24.53/6.41 (ubforcartprodlem3) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodpairin) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodmempair1) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodmempair) =>
% 24.53/6.41 ((
% 24.53/6.41 (setunionE2) =>
% 24.53/6.41 ((
% 24.53/6.41 (setunionsingleton1) =>
% 24.53/6.41 ((
% 24.53/6.41 (setunionsingleton2) =>
% 24.53/6.41 ((
% 24.53/6.41 (setunionsingleton) =>
% 24.53/6.41 ((
% 24.53/6.41 (singletonprop) =>
% 24.53/6.41 ((
% 24.53/6.41 (ex1E1) =>
% 24.53/6.41 ((
% 24.53/6.41 (ex1I) =>
% 24.53/6.41 ((
% 24.53/6.41 (ex1I2) =>
% 24.53/6.41 ((
% 24.53/6.41 (singletonsuniq) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjL1) =>
% 24.53/6.41 ((
% 24.53/6.41 (kfstsingleton) =>
% 24.53/6.41 ((
% 24.53/6.41 (theprop) =>
% 24.53/6.41 ((
% 24.53/6.41 (kfstpairEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodfstin) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjL2) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjL) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR11) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR12) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR1) =>
% 24.53/6.41 ((
% 24.53/6.41 (upairequniteq) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR2) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR) =>
% 24.53/6.41 ((
% 24.53/6.41 (ksndsingleton) =>
% 24.53/6.41 ((
% 24.53/6.41 (ksndpairEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (kpairsurjEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodsndin) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodpairmemEL) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodpairmemER) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodmempaircEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodfstpairEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodsndpairEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodpairsurjEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (dpsetconstrI) =>
% 24.53/6.41 ((
% 24.53/6.41 (!!) @ (
% 24.53/6.41 (('#B') @ (
% 24.53/6.41 !!) @
% 24.53/6.41 (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 !!))) @
% 24.53/6.41 (
% 24.53/6.41 (
% 24.53/6.41 ('#S') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 '#S') @
% 24.53/6.41 (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 '#C'))) @
% 24.53/6.41 (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ subset)))) @
% 24.53/6.41 dpsetconstr)))))) @
% 24.53/6.41 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1206])).
% 24.53/6.41 thf(zip_derived_cl1223, plain,
% 24.53/6.41 (~ (((binintersectSubset4) =>
% 24.53/6.41 (((binintersectSubset1) =>
% 24.53/6.41 (((bs114d) =>
% 24.53/6.41 (((setminusI) =>
% 24.53/6.41 (((setminusEL) =>
% 24.53/6.41 (((setminusER) =>
% 24.53/6.41 (((setminusSubset2) =>
% 24.53/6.41 (((setminusERneg) =>
% 24.53/6.41 (((setminusELneg) =>
% 24.53/6.41 (((setminusILneg) =>
% 24.53/6.41 (((setminusIRneg) =>
% 24.53/6.41 (((setminusLsub) =>
% 24.53/6.41 (((setminusSubset1) =>
% 24.53/6.41 (((symdiffE) =>
% 24.53/6.41 (((symdiffI1) =>
% 24.53/6.41 (((symdiffI2) =>
% 24.53/6.41 (((symdiffIneg1) =>
% 24.53/6.41 (((symdiffIneg2) =>
% 24.53/6.41 (((secondinupair) =>
% 24.53/6.41 (((setukpairIL) =>
% 24.53/6.41 (((setukpairIR) =>
% 24.53/6.41 (((kpairiskpair) =>
% 24.53/6.41 (((kpairp) =>
% 24.53/6.41 (((singletonsubset) =>
% 24.53/6.41 (((singletoninpowerset) =>
% 24.53/6.41 (((singletoninpowunion) =>
% 24.53/6.41 (((upairset2E) =>
% 24.53/6.41 (((upairsubunion) =>
% 24.53/6.41 (((upairinpowunion) =>
% 24.53/6.41 (((ubforcartprodlem1) =>
% 24.53/6.41 ((
% 24.53/6.41 (ubforcartprodlem2) =>
% 24.53/6.41 ((
% 24.53/6.41 (ubforcartprodlem3) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodpairin) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodmempair1) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodmempair) =>
% 24.53/6.41 ((
% 24.53/6.41 (setunionE2) =>
% 24.53/6.41 ((
% 24.53/6.41 (setunionsingleton1) =>
% 24.53/6.41 ((
% 24.53/6.41 (setunionsingleton2) =>
% 24.53/6.41 ((
% 24.53/6.41 (setunionsingleton) =>
% 24.53/6.41 ((
% 24.53/6.41 (singletonprop) =>
% 24.53/6.41 ((
% 24.53/6.41 (ex1E1) =>
% 24.53/6.41 ((
% 24.53/6.41 (ex1I) =>
% 24.53/6.41 ((
% 24.53/6.41 (ex1I2) =>
% 24.53/6.41 ((
% 24.53/6.41 (singletonsuniq) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjL1) =>
% 24.53/6.41 ((
% 24.53/6.41 (kfstsingleton) =>
% 24.53/6.41 ((
% 24.53/6.41 (theprop) =>
% 24.53/6.41 ((
% 24.53/6.41 (kfstpairEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodfstin) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjL2) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjL) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR11) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR12) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR1) =>
% 24.53/6.41 ((
% 24.53/6.41 (upairequniteq) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR2) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR) =>
% 24.53/6.41 ((
% 24.53/6.41 (ksndsingleton) =>
% 24.53/6.41 ((
% 24.53/6.41 (ksndpairEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (kpairsurjEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodsndin) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodpairmemEL) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodpairmemER) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodmempaircEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodfstpairEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodsndpairEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodpairsurjEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (dpsetconstrI) =>
% 24.53/6.41 ((
% 24.53/6.41 (!!) @ (
% 24.53/6.41 (('#B') @ (
% 24.53/6.41 !!) @
% 24.53/6.41 (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 !!))) @
% 24.53/6.41 (
% 24.53/6.41 (
% 24.53/6.41 ('#S') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 '#S') @
% 24.53/6.41 (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 '#C'))) @
% 24.53/6.41 (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ subset)))) @
% 24.53/6.41 dpsetconstr)))))) @
% 24.53/6.41 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1216])).
% 24.53/6.41 thf(zip_derived_cl1231, plain,
% 24.53/6.41 (~ (((binintersectSubset1) =>
% 24.53/6.41 (((bs114d) =>
% 24.53/6.41 (((setminusI) =>
% 24.53/6.41 (((setminusEL) =>
% 24.53/6.41 (((setminusER) =>
% 24.53/6.41 (((setminusSubset2) =>
% 24.53/6.41 (((setminusERneg) =>
% 24.53/6.41 (((setminusELneg) =>
% 24.53/6.41 (((setminusILneg) =>
% 24.53/6.41 (((setminusIRneg) =>
% 24.53/6.41 (((setminusLsub) =>
% 24.53/6.41 (((setminusSubset1) =>
% 24.53/6.41 (((symdiffE) =>
% 24.53/6.41 (((symdiffI1) =>
% 24.53/6.41 (((symdiffI2) =>
% 24.53/6.41 (((symdiffIneg1) =>
% 24.53/6.41 (((symdiffIneg2) =>
% 24.53/6.41 (((secondinupair) =>
% 24.53/6.41 (((setukpairIL) =>
% 24.53/6.41 (((setukpairIR) =>
% 24.53/6.41 (((kpairiskpair) =>
% 24.53/6.41 (((kpairp) =>
% 24.53/6.41 (((singletonsubset) =>
% 24.53/6.41 (((singletoninpowerset) =>
% 24.53/6.41 (((singletoninpowunion) =>
% 24.53/6.41 (((upairset2E) =>
% 24.53/6.41 (((upairsubunion) =>
% 24.53/6.41 (((upairinpowunion) =>
% 24.53/6.41 (((ubforcartprodlem1) =>
% 24.53/6.41 (((ubforcartprodlem2) =>
% 24.53/6.41 ((
% 24.53/6.41 (ubforcartprodlem3) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodpairin) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodmempair1) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodmempair) =>
% 24.53/6.41 ((
% 24.53/6.41 (setunionE2) =>
% 24.53/6.41 ((
% 24.53/6.41 (setunionsingleton1) =>
% 24.53/6.41 ((
% 24.53/6.41 (setunionsingleton2) =>
% 24.53/6.41 ((
% 24.53/6.41 (setunionsingleton) =>
% 24.53/6.41 ((
% 24.53/6.41 (singletonprop) =>
% 24.53/6.41 ((
% 24.53/6.41 (ex1E1) =>
% 24.53/6.41 ((
% 24.53/6.41 (ex1I) =>
% 24.53/6.41 ((
% 24.53/6.41 (ex1I2) =>
% 24.53/6.41 ((
% 24.53/6.41 (singletonsuniq) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjL1) =>
% 24.53/6.41 ((
% 24.53/6.41 (kfstsingleton) =>
% 24.53/6.41 ((
% 24.53/6.41 (theprop) =>
% 24.53/6.41 ((
% 24.53/6.41 (kfstpairEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodfstin) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjL2) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjL) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR11) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR12) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR1) =>
% 24.53/6.41 ((
% 24.53/6.41 (upairequniteq) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR2) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR) =>
% 24.53/6.41 ((
% 24.53/6.41 (ksndsingleton) =>
% 24.53/6.41 ((
% 24.53/6.41 (ksndpairEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (kpairsurjEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodsndin) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodpairmemEL) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodpairmemER) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodmempaircEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodfstpairEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodsndpairEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodpairsurjEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (dpsetconstrI) =>
% 24.53/6.41 ((
% 24.53/6.41 (!!) @ (
% 24.53/6.41 (('#B') @ (
% 24.53/6.41 !!) @
% 24.53/6.41 (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 !!))) @
% 24.53/6.41 (
% 24.53/6.41 (
% 24.53/6.41 ('#S') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 '#S') @
% 24.53/6.41 (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 '#C'))) @
% 24.53/6.41 (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ subset)))) @
% 24.53/6.41 dpsetconstr)))))) @
% 24.53/6.41 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1223])).
% 24.53/6.41 thf(zip_derived_cl1239, plain,
% 24.53/6.41 (~ (((bs114d) =>
% 24.53/6.41 (((setminusI) =>
% 24.53/6.41 (((setminusEL) =>
% 24.53/6.41 (((setminusER) =>
% 24.53/6.41 (((setminusSubset2) =>
% 24.53/6.41 (((setminusERneg) =>
% 24.53/6.41 (((setminusELneg) =>
% 24.53/6.41 (((setminusILneg) =>
% 24.53/6.41 (((setminusIRneg) =>
% 24.53/6.41 (((setminusLsub) =>
% 24.53/6.41 (((setminusSubset1) =>
% 24.53/6.41 (((symdiffE) =>
% 24.53/6.41 (((symdiffI1) =>
% 24.53/6.41 (((symdiffI2) =>
% 24.53/6.41 (((symdiffIneg1) =>
% 24.53/6.41 (((symdiffIneg2) =>
% 24.53/6.41 (((secondinupair) =>
% 24.53/6.41 (((setukpairIL) =>
% 24.53/6.41 (((setukpairIR) =>
% 24.53/6.41 (((kpairiskpair) =>
% 24.53/6.41 (((kpairp) =>
% 24.53/6.41 (((singletonsubset) =>
% 24.53/6.41 (((singletoninpowerset) =>
% 24.53/6.41 (((singletoninpowunion) =>
% 24.53/6.41 (((upairset2E) =>
% 24.53/6.41 (((upairsubunion) =>
% 24.53/6.41 (((upairinpowunion) =>
% 24.53/6.41 (((ubforcartprodlem1) =>
% 24.53/6.41 (((ubforcartprodlem2) =>
% 24.53/6.41 (((ubforcartprodlem3) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodpairin) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodmempair1) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodmempair) =>
% 24.53/6.41 ((
% 24.53/6.41 (setunionE2) =>
% 24.53/6.41 ((
% 24.53/6.41 (setunionsingleton1) =>
% 24.53/6.41 ((
% 24.53/6.41 (setunionsingleton2) =>
% 24.53/6.41 ((
% 24.53/6.41 (setunionsingleton) =>
% 24.53/6.41 ((
% 24.53/6.41 (singletonprop) =>
% 24.53/6.41 ((
% 24.53/6.41 (ex1E1) =>
% 24.53/6.41 ((
% 24.53/6.41 (ex1I) =>
% 24.53/6.41 ((
% 24.53/6.41 (ex1I2) =>
% 24.53/6.41 ((
% 24.53/6.41 (singletonsuniq) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjL1) =>
% 24.53/6.41 ((
% 24.53/6.41 (kfstsingleton) =>
% 24.53/6.41 ((
% 24.53/6.41 (theprop) =>
% 24.53/6.41 ((
% 24.53/6.41 (kfstpairEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodfstin) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjL2) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjL) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR11) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR12) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR1) =>
% 24.53/6.41 ((
% 24.53/6.41 (upairequniteq) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR2) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR) =>
% 24.53/6.41 ((
% 24.53/6.41 (ksndsingleton) =>
% 24.53/6.41 ((
% 24.53/6.41 (ksndpairEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (kpairsurjEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodsndin) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodpairmemEL) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodpairmemER) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodmempaircEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodfstpairEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodsndpairEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodpairsurjEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (dpsetconstrI) =>
% 24.53/6.41 ((
% 24.53/6.41 (!!) @ (
% 24.53/6.41 (('#B') @ (
% 24.53/6.41 !!) @
% 24.53/6.41 (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 !!))) @
% 24.53/6.41 (
% 24.53/6.41 (
% 24.53/6.41 ('#S') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 '#S') @
% 24.53/6.41 (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 '#C'))) @
% 24.53/6.41 (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ subset)))) @
% 24.53/6.41 dpsetconstr)))))) @
% 24.53/6.41 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1231])).
% 24.53/6.41 thf(zip_derived_cl1247, plain,
% 24.53/6.41 (~ (((setminusI) =>
% 24.53/6.41 (((setminusEL) =>
% 24.53/6.41 (((setminusER) =>
% 24.53/6.41 (((setminusSubset2) =>
% 24.53/6.41 (((setminusERneg) =>
% 24.53/6.41 (((setminusELneg) =>
% 24.53/6.41 (((setminusILneg) =>
% 24.53/6.41 (((setminusIRneg) =>
% 24.53/6.41 (((setminusLsub) =>
% 24.53/6.41 (((setminusSubset1) =>
% 24.53/6.41 (((symdiffE) =>
% 24.53/6.41 (((symdiffI1) =>
% 24.53/6.41 (((symdiffI2) =>
% 24.53/6.41 (((symdiffIneg1) =>
% 24.53/6.41 (((symdiffIneg2) =>
% 24.53/6.41 (((secondinupair) =>
% 24.53/6.41 (((setukpairIL) =>
% 24.53/6.41 (((setukpairIR) =>
% 24.53/6.41 (((kpairiskpair) =>
% 24.53/6.41 (((kpairp) =>
% 24.53/6.41 (((singletonsubset) =>
% 24.53/6.41 (((singletoninpowerset) =>
% 24.53/6.41 (((singletoninpowunion) =>
% 24.53/6.41 (((upairset2E) =>
% 24.53/6.41 (((upairsubunion) =>
% 24.53/6.41 (((upairinpowunion) =>
% 24.53/6.41 (((ubforcartprodlem1) =>
% 24.53/6.41 (((ubforcartprodlem2) =>
% 24.53/6.41 (((ubforcartprodlem3) =>
% 24.53/6.41 (((cartprodpairin) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodmempair1) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodmempair) =>
% 24.53/6.41 ((
% 24.53/6.41 (setunionE2) =>
% 24.53/6.41 ((
% 24.53/6.41 (setunionsingleton1) =>
% 24.53/6.41 ((
% 24.53/6.41 (setunionsingleton2) =>
% 24.53/6.41 ((
% 24.53/6.41 (setunionsingleton) =>
% 24.53/6.41 ((
% 24.53/6.41 (singletonprop) =>
% 24.53/6.41 ((
% 24.53/6.41 (ex1E1) =>
% 24.53/6.41 ((
% 24.53/6.41 (ex1I) =>
% 24.53/6.41 ((
% 24.53/6.41 (ex1I2) =>
% 24.53/6.41 ((
% 24.53/6.41 (singletonsuniq) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjL1) =>
% 24.53/6.41 ((
% 24.53/6.41 (kfstsingleton) =>
% 24.53/6.41 ((
% 24.53/6.41 (theprop) =>
% 24.53/6.41 ((
% 24.53/6.41 (kfstpairEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodfstin) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjL2) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjL) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR11) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR12) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR1) =>
% 24.53/6.41 ((
% 24.53/6.41 (upairequniteq) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR2) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR) =>
% 24.53/6.41 ((
% 24.53/6.41 (ksndsingleton) =>
% 24.53/6.41 ((
% 24.53/6.41 (ksndpairEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (kpairsurjEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodsndin) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodpairmemEL) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodpairmemER) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodmempaircEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodfstpairEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodsndpairEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodpairsurjEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (dpsetconstrI) =>
% 24.53/6.41 ((
% 24.53/6.41 (!!) @ (
% 24.53/6.41 (('#B') @ (
% 24.53/6.41 !!) @
% 24.53/6.41 (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 !!))) @
% 24.53/6.41 (
% 24.53/6.41 (
% 24.53/6.41 ('#S') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 '#S') @
% 24.53/6.41 (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 '#C'))) @
% 24.53/6.41 (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ subset)))) @
% 24.53/6.41 dpsetconstr)))))) @
% 24.53/6.41 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1239])).
% 24.53/6.41 thf(zip_derived_cl1255, plain,
% 24.53/6.41 (~ (((setminusEL) =>
% 24.53/6.41 (((setminusER) =>
% 24.53/6.41 (((setminusSubset2) =>
% 24.53/6.41 (((setminusERneg) =>
% 24.53/6.41 (((setminusELneg) =>
% 24.53/6.41 (((setminusILneg) =>
% 24.53/6.41 (((setminusIRneg) =>
% 24.53/6.41 (((setminusLsub) =>
% 24.53/6.41 (((setminusSubset1) =>
% 24.53/6.41 (((symdiffE) =>
% 24.53/6.41 (((symdiffI1) =>
% 24.53/6.41 (((symdiffI2) =>
% 24.53/6.41 (((symdiffIneg1) =>
% 24.53/6.41 (((symdiffIneg2) =>
% 24.53/6.41 (((secondinupair) =>
% 24.53/6.41 (((setukpairIL) =>
% 24.53/6.41 (((setukpairIR) =>
% 24.53/6.41 (((kpairiskpair) =>
% 24.53/6.41 (((kpairp) =>
% 24.53/6.41 (((singletonsubset) =>
% 24.53/6.41 (((singletoninpowerset) =>
% 24.53/6.41 (((singletoninpowunion) =>
% 24.53/6.41 (((upairset2E) =>
% 24.53/6.41 (((upairsubunion) =>
% 24.53/6.41 (((upairinpowunion) =>
% 24.53/6.41 (((ubforcartprodlem1) =>
% 24.53/6.41 (((ubforcartprodlem2) =>
% 24.53/6.41 (((ubforcartprodlem3) =>
% 24.53/6.41 (((cartprodpairin) =>
% 24.53/6.41 (((cartprodmempair1) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodmempair) =>
% 24.53/6.41 ((
% 24.53/6.41 (setunionE2) =>
% 24.53/6.41 ((
% 24.53/6.41 (setunionsingleton1) =>
% 24.53/6.41 ((
% 24.53/6.41 (setunionsingleton2) =>
% 24.53/6.41 ((
% 24.53/6.41 (setunionsingleton) =>
% 24.53/6.41 ((
% 24.53/6.41 (singletonprop) =>
% 24.53/6.41 ((
% 24.53/6.41 (ex1E1) =>
% 24.53/6.41 ((
% 24.53/6.41 (ex1I) =>
% 24.53/6.41 ((
% 24.53/6.41 (ex1I2) =>
% 24.53/6.41 ((
% 24.53/6.41 (singletonsuniq) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjL1) =>
% 24.53/6.41 ((
% 24.53/6.41 (kfstsingleton) =>
% 24.53/6.41 ((
% 24.53/6.41 (theprop) =>
% 24.53/6.41 ((
% 24.53/6.41 (kfstpairEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodfstin) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjL2) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjL) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR11) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR12) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR1) =>
% 24.53/6.41 ((
% 24.53/6.41 (upairequniteq) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR2) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR) =>
% 24.53/6.41 ((
% 24.53/6.41 (ksndsingleton) =>
% 24.53/6.41 ((
% 24.53/6.41 (ksndpairEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (kpairsurjEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodsndin) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodpairmemEL) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodpairmemER) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodmempaircEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodfstpairEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodsndpairEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodpairsurjEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (dpsetconstrI) =>
% 24.53/6.41 ((
% 24.53/6.41 (!!) @ (
% 24.53/6.41 (('#B') @ (
% 24.53/6.41 !!) @
% 24.53/6.41 (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 !!))) @
% 24.53/6.41 (
% 24.53/6.41 (
% 24.53/6.41 ('#S') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 '#S') @
% 24.53/6.41 (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 '#C'))) @
% 24.53/6.41 (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ subset)))) @
% 24.53/6.41 dpsetconstr)))))) @
% 24.53/6.41 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1247])).
% 24.53/6.41 thf(zip_derived_cl1264, plain,
% 24.53/6.41 (~ (((setminusER) =>
% 24.53/6.41 (((setminusSubset2) =>
% 24.53/6.41 (((setminusERneg) =>
% 24.53/6.41 (((setminusELneg) =>
% 24.53/6.41 (((setminusILneg) =>
% 24.53/6.41 (((setminusIRneg) =>
% 24.53/6.41 (((setminusLsub) =>
% 24.53/6.41 (((setminusSubset1) =>
% 24.53/6.41 (((symdiffE) =>
% 24.53/6.41 (((symdiffI1) =>
% 24.53/6.41 (((symdiffI2) =>
% 24.53/6.41 (((symdiffIneg1) =>
% 24.53/6.41 (((symdiffIneg2) =>
% 24.53/6.41 (((secondinupair) =>
% 24.53/6.41 (((setukpairIL) =>
% 24.53/6.41 (((setukpairIR) =>
% 24.53/6.41 (((kpairiskpair) =>
% 24.53/6.41 (((kpairp) =>
% 24.53/6.41 (((singletonsubset) =>
% 24.53/6.41 (((singletoninpowerset) =>
% 24.53/6.41 (((singletoninpowunion) =>
% 24.53/6.41 (((upairset2E) =>
% 24.53/6.41 (((upairsubunion) =>
% 24.53/6.41 (((upairinpowunion) =>
% 24.53/6.41 (((ubforcartprodlem1) =>
% 24.53/6.41 (((ubforcartprodlem2) =>
% 24.53/6.41 (((ubforcartprodlem3) =>
% 24.53/6.41 (((cartprodpairin) =>
% 24.53/6.41 (((cartprodmempair1) =>
% 24.53/6.41 (((cartprodmempair) =>
% 24.53/6.41 ((
% 24.53/6.41 (setunionE2) =>
% 24.53/6.41 ((
% 24.53/6.41 (setunionsingleton1) =>
% 24.53/6.41 ((
% 24.53/6.41 (setunionsingleton2) =>
% 24.53/6.41 ((
% 24.53/6.41 (setunionsingleton) =>
% 24.53/6.41 ((
% 24.53/6.41 (singletonprop) =>
% 24.53/6.41 ((
% 24.53/6.41 (ex1E1) =>
% 24.53/6.41 ((
% 24.53/6.41 (ex1I) =>
% 24.53/6.41 ((
% 24.53/6.41 (ex1I2) =>
% 24.53/6.41 ((
% 24.53/6.41 (singletonsuniq) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjL1) =>
% 24.53/6.41 ((
% 24.53/6.41 (kfstsingleton) =>
% 24.53/6.41 ((
% 24.53/6.41 (theprop) =>
% 24.53/6.41 ((
% 24.53/6.41 (kfstpairEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodfstin) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjL2) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjL) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR11) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR12) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR1) =>
% 24.53/6.41 ((
% 24.53/6.41 (upairequniteq) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR2) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR) =>
% 24.53/6.41 ((
% 24.53/6.41 (ksndsingleton) =>
% 24.53/6.41 ((
% 24.53/6.41 (ksndpairEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (kpairsurjEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodsndin) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodpairmemEL) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodpairmemER) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodmempaircEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodfstpairEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodsndpairEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodpairsurjEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (dpsetconstrI) =>
% 24.53/6.41 ((
% 24.53/6.41 (!!) @ (
% 24.53/6.41 (('#B') @ (
% 24.53/6.41 !!) @
% 24.53/6.41 (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 !!))) @
% 24.53/6.41 (
% 24.53/6.41 (
% 24.53/6.41 ('#S') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 '#S') @
% 24.53/6.41 (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 '#C'))) @
% 24.53/6.41 (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ subset)))) @
% 24.53/6.41 dpsetconstr)))))) @
% 24.53/6.41 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1255])).
% 24.53/6.41 thf(zip_derived_cl1272, plain,
% 24.53/6.41 (~ (((setminusSubset2) =>
% 24.53/6.41 (((setminusERneg) =>
% 24.53/6.41 (((setminusELneg) =>
% 24.53/6.41 (((setminusILneg) =>
% 24.53/6.41 (((setminusIRneg) =>
% 24.53/6.41 (((setminusLsub) =>
% 24.53/6.41 (((setminusSubset1) =>
% 24.53/6.41 (((symdiffE) =>
% 24.53/6.41 (((symdiffI1) =>
% 24.53/6.41 (((symdiffI2) =>
% 24.53/6.41 (((symdiffIneg1) =>
% 24.53/6.41 (((symdiffIneg2) =>
% 24.53/6.41 (((secondinupair) =>
% 24.53/6.41 (((setukpairIL) =>
% 24.53/6.41 (((setukpairIR) =>
% 24.53/6.41 (((kpairiskpair) =>
% 24.53/6.41 (((kpairp) =>
% 24.53/6.41 (((singletonsubset) =>
% 24.53/6.41 (((singletoninpowerset) =>
% 24.53/6.41 (((singletoninpowunion) =>
% 24.53/6.41 (((upairset2E) =>
% 24.53/6.41 (((upairsubunion) =>
% 24.53/6.41 (((upairinpowunion) =>
% 24.53/6.41 (((ubforcartprodlem1) =>
% 24.53/6.41 (((ubforcartprodlem2) =>
% 24.53/6.41 (((ubforcartprodlem3) =>
% 24.53/6.41 (((cartprodpairin) =>
% 24.53/6.41 (((cartprodmempair1) =>
% 24.53/6.41 (((cartprodmempair) =>
% 24.53/6.41 (((setunionE2) =>
% 24.53/6.41 ((
% 24.53/6.41 (setunionsingleton1) =>
% 24.53/6.41 ((
% 24.53/6.41 (setunionsingleton2) =>
% 24.53/6.41 ((
% 24.53/6.41 (setunionsingleton) =>
% 24.53/6.41 ((
% 24.53/6.41 (singletonprop) =>
% 24.53/6.41 ((
% 24.53/6.41 (ex1E1) =>
% 24.53/6.41 ((
% 24.53/6.41 (ex1I) =>
% 24.53/6.41 ((
% 24.53/6.41 (ex1I2) =>
% 24.53/6.41 ((
% 24.53/6.41 (singletonsuniq) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjL1) =>
% 24.53/6.41 ((
% 24.53/6.41 (kfstsingleton) =>
% 24.53/6.41 ((
% 24.53/6.41 (theprop) =>
% 24.53/6.41 ((
% 24.53/6.41 (kfstpairEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodfstin) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjL2) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjL) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR11) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR12) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR1) =>
% 24.53/6.41 ((
% 24.53/6.41 (upairequniteq) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR2) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR) =>
% 24.53/6.41 ((
% 24.53/6.41 (ksndsingleton) =>
% 24.53/6.41 ((
% 24.53/6.41 (ksndpairEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (kpairsurjEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodsndin) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodpairmemEL) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodpairmemER) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodmempaircEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodfstpairEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodsndpairEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodpairsurjEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (dpsetconstrI) =>
% 24.53/6.41 ((
% 24.53/6.41 (!!) @ (
% 24.53/6.41 (('#B') @ (
% 24.53/6.41 !!) @
% 24.53/6.41 (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 !!))) @
% 24.53/6.41 (
% 24.53/6.41 (
% 24.53/6.41 ('#S') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 '#S') @
% 24.53/6.41 (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 '#C'))) @
% 24.53/6.41 (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ subset)))) @
% 24.53/6.41 dpsetconstr)))))) @
% 24.53/6.41 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1264])).
% 24.53/6.41 thf(zip_derived_cl1280, plain,
% 24.53/6.41 (~ (((setminusERneg) =>
% 24.53/6.41 (((setminusELneg) =>
% 24.53/6.41 (((setminusILneg) =>
% 24.53/6.41 (((setminusIRneg) =>
% 24.53/6.41 (((setminusLsub) =>
% 24.53/6.41 (((setminusSubset1) =>
% 24.53/6.41 (((symdiffE) =>
% 24.53/6.41 (((symdiffI1) =>
% 24.53/6.41 (((symdiffI2) =>
% 24.53/6.41 (((symdiffIneg1) =>
% 24.53/6.41 (((symdiffIneg2) =>
% 24.53/6.41 (((secondinupair) =>
% 24.53/6.41 (((setukpairIL) =>
% 24.53/6.41 (((setukpairIR) =>
% 24.53/6.41 (((kpairiskpair) =>
% 24.53/6.41 (((kpairp) =>
% 24.53/6.41 (((singletonsubset) =>
% 24.53/6.41 (((singletoninpowerset) =>
% 24.53/6.41 (((singletoninpowunion) =>
% 24.53/6.41 (((upairset2E) =>
% 24.53/6.41 (((upairsubunion) =>
% 24.53/6.41 (((upairinpowunion) =>
% 24.53/6.41 (((ubforcartprodlem1) =>
% 24.53/6.41 (((ubforcartprodlem2) =>
% 24.53/6.41 (((ubforcartprodlem3) =>
% 24.53/6.41 (((cartprodpairin) =>
% 24.53/6.41 (((cartprodmempair1) =>
% 24.53/6.41 (((cartprodmempair) =>
% 24.53/6.41 (((setunionE2) =>
% 24.53/6.41 (((setunionsingleton1) =>
% 24.53/6.41 ((
% 24.53/6.41 (setunionsingleton2) =>
% 24.53/6.41 ((
% 24.53/6.41 (setunionsingleton) =>
% 24.53/6.41 ((
% 24.53/6.41 (singletonprop) =>
% 24.53/6.41 ((
% 24.53/6.41 (ex1E1) =>
% 24.53/6.41 ((
% 24.53/6.41 (ex1I) =>
% 24.53/6.41 ((
% 24.53/6.41 (ex1I2) =>
% 24.53/6.41 ((
% 24.53/6.41 (singletonsuniq) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjL1) =>
% 24.53/6.41 ((
% 24.53/6.41 (kfstsingleton) =>
% 24.53/6.41 ((
% 24.53/6.41 (theprop) =>
% 24.53/6.41 ((
% 24.53/6.41 (kfstpairEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodfstin) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjL2) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjL) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR11) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR12) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR1) =>
% 24.53/6.41 ((
% 24.53/6.41 (upairequniteq) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR2) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR) =>
% 24.53/6.41 ((
% 24.53/6.41 (ksndsingleton) =>
% 24.53/6.41 ((
% 24.53/6.41 (ksndpairEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (kpairsurjEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodsndin) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodpairmemEL) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodpairmemER) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodmempaircEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodfstpairEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodsndpairEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodpairsurjEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (dpsetconstrI) =>
% 24.53/6.41 ((
% 24.53/6.41 (!!) @ (
% 24.53/6.41 (('#B') @ (
% 24.53/6.41 !!) @
% 24.53/6.41 (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 !!))) @
% 24.53/6.41 (
% 24.53/6.41 (
% 24.53/6.41 ('#S') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 '#S') @
% 24.53/6.41 (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 '#C'))) @
% 24.53/6.41 (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ subset)))) @
% 24.53/6.41 dpsetconstr)))))) @
% 24.53/6.41 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1272])).
% 24.53/6.41 thf(zip_derived_cl1288, plain,
% 24.53/6.41 (~ (((setminusELneg) =>
% 24.53/6.41 (((setminusILneg) =>
% 24.53/6.41 (((setminusIRneg) =>
% 24.53/6.41 (((setminusLsub) =>
% 24.53/6.41 (((setminusSubset1) =>
% 24.53/6.41 (((symdiffE) =>
% 24.53/6.41 (((symdiffI1) =>
% 24.53/6.41 (((symdiffI2) =>
% 24.53/6.41 (((symdiffIneg1) =>
% 24.53/6.41 (((symdiffIneg2) =>
% 24.53/6.41 (((secondinupair) =>
% 24.53/6.41 (((setukpairIL) =>
% 24.53/6.41 (((setukpairIR) =>
% 24.53/6.41 (((kpairiskpair) =>
% 24.53/6.41 (((kpairp) =>
% 24.53/6.41 (((singletonsubset) =>
% 24.53/6.41 (((singletoninpowerset) =>
% 24.53/6.41 (((singletoninpowunion) =>
% 24.53/6.41 (((upairset2E) =>
% 24.53/6.41 (((upairsubunion) =>
% 24.53/6.41 (((upairinpowunion) =>
% 24.53/6.41 (((ubforcartprodlem1) =>
% 24.53/6.41 (((ubforcartprodlem2) =>
% 24.53/6.41 (((ubforcartprodlem3) =>
% 24.53/6.41 (((cartprodpairin) =>
% 24.53/6.41 (((cartprodmempair1) =>
% 24.53/6.41 (((cartprodmempair) =>
% 24.53/6.41 (((setunionE2) =>
% 24.53/6.41 (((setunionsingleton1) =>
% 24.53/6.41 (((setunionsingleton2) =>
% 24.53/6.41 ((
% 24.53/6.41 (setunionsingleton) =>
% 24.53/6.41 ((
% 24.53/6.41 (singletonprop) =>
% 24.53/6.41 ((
% 24.53/6.41 (ex1E1) =>
% 24.53/6.41 ((
% 24.53/6.41 (ex1I) =>
% 24.53/6.41 ((
% 24.53/6.41 (ex1I2) =>
% 24.53/6.41 ((
% 24.53/6.41 (singletonsuniq) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjL1) =>
% 24.53/6.41 ((
% 24.53/6.41 (kfstsingleton) =>
% 24.53/6.41 ((
% 24.53/6.41 (theprop) =>
% 24.53/6.41 ((
% 24.53/6.41 (kfstpairEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodfstin) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjL2) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjL) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR11) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR12) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR1) =>
% 24.53/6.41 ((
% 24.53/6.41 (upairequniteq) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR2) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR) =>
% 24.53/6.41 ((
% 24.53/6.41 (ksndsingleton) =>
% 24.53/6.41 ((
% 24.53/6.41 (ksndpairEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (kpairsurjEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodsndin) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodpairmemEL) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodpairmemER) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodmempaircEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodfstpairEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodsndpairEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodpairsurjEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (dpsetconstrI) =>
% 24.53/6.41 ((
% 24.53/6.41 (!!) @ (
% 24.53/6.41 (('#B') @ (
% 24.53/6.41 !!) @
% 24.53/6.41 (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 !!))) @
% 24.53/6.41 (
% 24.53/6.41 (
% 24.53/6.41 ('#S') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 '#S') @
% 24.53/6.41 (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 '#C'))) @
% 24.53/6.41 (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ subset)))) @
% 24.53/6.41 dpsetconstr)))))) @
% 24.53/6.41 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1280])).
% 24.53/6.41 thf(zip_derived_cl1296, plain,
% 24.53/6.41 (~ (((setminusILneg) =>
% 24.53/6.41 (((setminusIRneg) =>
% 24.53/6.41 (((setminusLsub) =>
% 24.53/6.41 (((setminusSubset1) =>
% 24.53/6.41 (((symdiffE) =>
% 24.53/6.41 (((symdiffI1) =>
% 24.53/6.41 (((symdiffI2) =>
% 24.53/6.41 (((symdiffIneg1) =>
% 24.53/6.41 (((symdiffIneg2) =>
% 24.53/6.41 (((secondinupair) =>
% 24.53/6.41 (((setukpairIL) =>
% 24.53/6.41 (((setukpairIR) =>
% 24.53/6.41 (((kpairiskpair) =>
% 24.53/6.41 (((kpairp) =>
% 24.53/6.41 (((singletonsubset) =>
% 24.53/6.41 (((singletoninpowerset) =>
% 24.53/6.41 (((singletoninpowunion) =>
% 24.53/6.41 (((upairset2E) =>
% 24.53/6.41 (((upairsubunion) =>
% 24.53/6.41 (((upairinpowunion) =>
% 24.53/6.41 (((ubforcartprodlem1) =>
% 24.53/6.41 (((ubforcartprodlem2) =>
% 24.53/6.41 (((ubforcartprodlem3) =>
% 24.53/6.41 (((cartprodpairin) =>
% 24.53/6.41 (((cartprodmempair1) =>
% 24.53/6.41 (((cartprodmempair) =>
% 24.53/6.41 (((setunionE2) =>
% 24.53/6.41 (((setunionsingleton1) =>
% 24.53/6.41 (((setunionsingleton2) =>
% 24.53/6.41 (((setunionsingleton) =>
% 24.53/6.41 ((
% 24.53/6.41 (singletonprop) =>
% 24.53/6.41 ((
% 24.53/6.41 (ex1E1) =>
% 24.53/6.41 ((
% 24.53/6.41 (ex1I) =>
% 24.53/6.41 ((
% 24.53/6.41 (ex1I2) =>
% 24.53/6.41 ((
% 24.53/6.41 (singletonsuniq) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjL1) =>
% 24.53/6.41 ((
% 24.53/6.41 (kfstsingleton) =>
% 24.53/6.41 ((
% 24.53/6.41 (theprop) =>
% 24.53/6.41 ((
% 24.53/6.41 (kfstpairEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodfstin) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjL2) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjL) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR11) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR12) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR1) =>
% 24.53/6.41 ((
% 24.53/6.41 (upairequniteq) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR2) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR) =>
% 24.53/6.41 ((
% 24.53/6.41 (ksndsingleton) =>
% 24.53/6.41 ((
% 24.53/6.41 (ksndpairEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (kpairsurjEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodsndin) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodpairmemEL) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodpairmemER) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodmempaircEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodfstpairEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodsndpairEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodpairsurjEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (dpsetconstrI) =>
% 24.53/6.41 ((
% 24.53/6.41 (!!) @ (
% 24.53/6.41 (('#B') @ (
% 24.53/6.41 !!) @
% 24.53/6.41 (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 !!))) @
% 24.53/6.41 (
% 24.53/6.41 (
% 24.53/6.41 ('#S') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 '#S') @
% 24.53/6.41 (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 '#C'))) @
% 24.53/6.41 (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ subset)))) @
% 24.53/6.41 dpsetconstr)))))) @
% 24.53/6.41 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1288])).
% 24.53/6.41 thf(zip_derived_cl1305, plain,
% 24.53/6.41 (~ (((setminusIRneg) =>
% 24.53/6.41 (((setminusLsub) =>
% 24.53/6.41 (((setminusSubset1) =>
% 24.53/6.41 (((symdiffE) =>
% 24.53/6.41 (((symdiffI1) =>
% 24.53/6.41 (((symdiffI2) =>
% 24.53/6.41 (((symdiffIneg1) =>
% 24.53/6.41 (((symdiffIneg2) =>
% 24.53/6.41 (((secondinupair) =>
% 24.53/6.41 (((setukpairIL) =>
% 24.53/6.41 (((setukpairIR) =>
% 24.53/6.41 (((kpairiskpair) =>
% 24.53/6.41 (((kpairp) =>
% 24.53/6.41 (((singletonsubset) =>
% 24.53/6.41 (((singletoninpowerset) =>
% 24.53/6.41 (((singletoninpowunion) =>
% 24.53/6.41 (((upairset2E) =>
% 24.53/6.41 (((upairsubunion) =>
% 24.53/6.41 (((upairinpowunion) =>
% 24.53/6.41 (((ubforcartprodlem1) =>
% 24.53/6.41 (((ubforcartprodlem2) =>
% 24.53/6.41 (((ubforcartprodlem3) =>
% 24.53/6.41 (((cartprodpairin) =>
% 24.53/6.41 (((cartprodmempair1) =>
% 24.53/6.41 (((cartprodmempair) =>
% 24.53/6.41 (((setunionE2) =>
% 24.53/6.41 (((setunionsingleton1) =>
% 24.53/6.41 (((setunionsingleton2) =>
% 24.53/6.41 (((setunionsingleton) =>
% 24.53/6.41 (((singletonprop) =>
% 24.53/6.41 ((
% 24.53/6.41 (ex1E1) =>
% 24.53/6.41 ((
% 24.53/6.41 (ex1I) =>
% 24.53/6.41 ((
% 24.53/6.41 (ex1I2) =>
% 24.53/6.41 ((
% 24.53/6.41 (singletonsuniq) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjL1) =>
% 24.53/6.41 ((
% 24.53/6.41 (kfstsingleton) =>
% 24.53/6.41 ((
% 24.53/6.41 (theprop) =>
% 24.53/6.41 ((
% 24.53/6.41 (kfstpairEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodfstin) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjL2) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjL) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR11) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR12) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR1) =>
% 24.53/6.41 ((
% 24.53/6.41 (upairequniteq) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR2) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR) =>
% 24.53/6.41 ((
% 24.53/6.41 (ksndsingleton) =>
% 24.53/6.41 ((
% 24.53/6.41 (ksndpairEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (kpairsurjEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodsndin) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodpairmemEL) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodpairmemER) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodmempaircEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodfstpairEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodsndpairEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodpairsurjEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (dpsetconstrI) =>
% 24.53/6.41 ((
% 24.53/6.41 (!!) @ (
% 24.53/6.41 (('#B') @ (
% 24.53/6.41 !!) @
% 24.53/6.41 (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 !!))) @
% 24.53/6.41 (
% 24.53/6.41 (
% 24.53/6.41 ('#S') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 '#S') @
% 24.53/6.41 (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 '#C'))) @
% 24.53/6.41 (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ subset)))) @
% 24.53/6.41 dpsetconstr)))))) @
% 24.53/6.41 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1296])).
% 24.53/6.41 thf(zip_derived_cl1313, plain,
% 24.53/6.41 (~ (((setminusLsub) =>
% 24.53/6.41 (((setminusSubset1) =>
% 24.53/6.41 (((symdiffE) =>
% 24.53/6.41 (((symdiffI1) =>
% 24.53/6.41 (((symdiffI2) =>
% 24.53/6.41 (((symdiffIneg1) =>
% 24.53/6.41 (((symdiffIneg2) =>
% 24.53/6.41 (((secondinupair) =>
% 24.53/6.41 (((setukpairIL) =>
% 24.53/6.41 (((setukpairIR) =>
% 24.53/6.41 (((kpairiskpair) =>
% 24.53/6.41 (((kpairp) =>
% 24.53/6.41 (((singletonsubset) =>
% 24.53/6.41 (((singletoninpowerset) =>
% 24.53/6.41 (((singletoninpowunion) =>
% 24.53/6.41 (((upairset2E) =>
% 24.53/6.41 (((upairsubunion) =>
% 24.53/6.41 (((upairinpowunion) =>
% 24.53/6.41 (((ubforcartprodlem1) =>
% 24.53/6.41 (((ubforcartprodlem2) =>
% 24.53/6.41 (((ubforcartprodlem3) =>
% 24.53/6.41 (((cartprodpairin) =>
% 24.53/6.41 (((cartprodmempair1) =>
% 24.53/6.41 (((cartprodmempair) =>
% 24.53/6.41 (((setunionE2) =>
% 24.53/6.41 (((setunionsingleton1) =>
% 24.53/6.41 (((setunionsingleton2) =>
% 24.53/6.41 (((setunionsingleton) =>
% 24.53/6.41 (((singletonprop) =>
% 24.53/6.41 (((ex1E1) =>
% 24.53/6.41 ((
% 24.53/6.41 (ex1I) =>
% 24.53/6.41 ((
% 24.53/6.41 (ex1I2) =>
% 24.53/6.41 ((
% 24.53/6.41 (singletonsuniq) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjL1) =>
% 24.53/6.41 ((
% 24.53/6.41 (kfstsingleton) =>
% 24.53/6.41 ((
% 24.53/6.41 (theprop) =>
% 24.53/6.41 ((
% 24.53/6.41 (kfstpairEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodfstin) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjL2) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjL) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR11) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR12) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR1) =>
% 24.53/6.41 ((
% 24.53/6.41 (upairequniteq) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR2) =>
% 24.53/6.41 ((
% 24.53/6.41 (setukpairinjR) =>
% 24.53/6.41 ((
% 24.53/6.41 (ksndsingleton) =>
% 24.53/6.41 ((
% 24.53/6.41 (ksndpairEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (kpairsurjEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodsndin) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodpairmemEL) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodpairmemER) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodmempaircEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodfstpairEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodsndpairEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (cartprodpairsurjEq) =>
% 24.53/6.41 ((
% 24.53/6.41 (dpsetconstrI) =>
% 24.53/6.41 ((
% 24.53/6.41 (!!) @ (
% 24.53/6.41 (('#B') @ (
% 24.53/6.41 !!) @
% 24.53/6.41 (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.41 !!))) @
% 24.53/6.41 (
% 24.53/6.41 (
% 24.53/6.41 ('#S') @ (
% 24.53/6.41 (
% 24.53/6.41 ('#B') @ (
% 24.53/6.42 '#S') @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 '#C'))) @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ subset)))) @
% 24.53/6.42 dpsetconstr)))))) @
% 24.53/6.42 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1305])).
% 24.53/6.42 thf(zip_derived_cl1321, plain,
% 24.53/6.42 (~ (((setminusSubset1) =>
% 24.53/6.42 (((symdiffE) =>
% 24.53/6.42 (((symdiffI1) =>
% 24.53/6.42 (((symdiffI2) =>
% 24.53/6.42 (((symdiffIneg1) =>
% 24.53/6.42 (((symdiffIneg2) =>
% 24.53/6.42 (((secondinupair) =>
% 24.53/6.42 (((setukpairIL) =>
% 24.53/6.42 (((setukpairIR) =>
% 24.53/6.42 (((kpairiskpair) =>
% 24.53/6.42 (((kpairp) =>
% 24.53/6.42 (((singletonsubset) =>
% 24.53/6.42 (((singletoninpowerset) =>
% 24.53/6.42 (((singletoninpowunion) =>
% 24.53/6.42 (((upairset2E) =>
% 24.53/6.42 (((upairsubunion) =>
% 24.53/6.42 (((upairinpowunion) =>
% 24.53/6.42 (((ubforcartprodlem1) =>
% 24.53/6.42 (((ubforcartprodlem2) =>
% 24.53/6.42 (((ubforcartprodlem3) =>
% 24.53/6.42 (((cartprodpairin) =>
% 24.53/6.42 (((cartprodmempair1) =>
% 24.53/6.42 (((cartprodmempair) =>
% 24.53/6.42 (((setunionE2) =>
% 24.53/6.42 (((setunionsingleton1) =>
% 24.53/6.42 (((setunionsingleton2) =>
% 24.53/6.42 (((setunionsingleton) =>
% 24.53/6.42 (((singletonprop) =>
% 24.53/6.42 (((ex1E1) =>
% 24.53/6.42 (((ex1I) =>
% 24.53/6.42 ((
% 24.53/6.42 (ex1I2) =>
% 24.53/6.42 ((
% 24.53/6.42 (singletonsuniq) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjL1) =>
% 24.53/6.42 ((
% 24.53/6.42 (kfstsingleton) =>
% 24.53/6.42 ((
% 24.53/6.42 (theprop) =>
% 24.53/6.42 ((
% 24.53/6.42 (kfstpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodfstin) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjL2) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjL) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjR11) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjR12) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjR1) =>
% 24.53/6.42 ((
% 24.53/6.42 (upairequniteq) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjR2) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjR) =>
% 24.53/6.42 ((
% 24.53/6.42 (ksndsingleton) =>
% 24.53/6.42 ((
% 24.53/6.42 (ksndpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (kpairsurjEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodsndin) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodpairmemEL) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodpairmemER) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodmempaircEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodfstpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodsndpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodpairsurjEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (dpsetconstrI) =>
% 24.53/6.42 ((
% 24.53/6.42 (!!) @ (
% 24.53/6.42 (('#B') @ (
% 24.53/6.42 !!) @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 !!))) @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#S') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 '#S') @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 '#C'))) @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ subset)))) @
% 24.53/6.42 dpsetconstr)))))) @
% 24.53/6.42 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1313])).
% 24.53/6.42 thf(zip_derived_cl1329, plain,
% 24.53/6.42 (~ (((symdiffE) =>
% 24.53/6.42 (((symdiffI1) =>
% 24.53/6.42 (((symdiffI2) =>
% 24.53/6.42 (((symdiffIneg1) =>
% 24.53/6.42 (((symdiffIneg2) =>
% 24.53/6.42 (((secondinupair) =>
% 24.53/6.42 (((setukpairIL) =>
% 24.53/6.42 (((setukpairIR) =>
% 24.53/6.42 (((kpairiskpair) =>
% 24.53/6.42 (((kpairp) =>
% 24.53/6.42 (((singletonsubset) =>
% 24.53/6.42 (((singletoninpowerset) =>
% 24.53/6.42 (((singletoninpowunion) =>
% 24.53/6.42 (((upairset2E) =>
% 24.53/6.42 (((upairsubunion) =>
% 24.53/6.42 (((upairinpowunion) =>
% 24.53/6.42 (((ubforcartprodlem1) =>
% 24.53/6.42 (((ubforcartprodlem2) =>
% 24.53/6.42 (((ubforcartprodlem3) =>
% 24.53/6.42 (((cartprodpairin) =>
% 24.53/6.42 (((cartprodmempair1) =>
% 24.53/6.42 (((cartprodmempair) =>
% 24.53/6.42 (((setunionE2) =>
% 24.53/6.42 (((setunionsingleton1) =>
% 24.53/6.42 (((setunionsingleton2) =>
% 24.53/6.42 (((setunionsingleton) =>
% 24.53/6.42 (((singletonprop) =>
% 24.53/6.42 (((ex1E1) =>
% 24.53/6.42 (((ex1I) =>
% 24.53/6.42 (((ex1I2) =>
% 24.53/6.42 ((
% 24.53/6.42 (singletonsuniq) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjL1) =>
% 24.53/6.42 ((
% 24.53/6.42 (kfstsingleton) =>
% 24.53/6.42 ((
% 24.53/6.42 (theprop) =>
% 24.53/6.42 ((
% 24.53/6.42 (kfstpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodfstin) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjL2) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjL) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjR11) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjR12) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjR1) =>
% 24.53/6.42 ((
% 24.53/6.42 (upairequniteq) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjR2) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjR) =>
% 24.53/6.42 ((
% 24.53/6.42 (ksndsingleton) =>
% 24.53/6.42 ((
% 24.53/6.42 (ksndpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (kpairsurjEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodsndin) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodpairmemEL) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodpairmemER) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodmempaircEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodfstpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodsndpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodpairsurjEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (dpsetconstrI) =>
% 24.53/6.42 ((
% 24.53/6.42 (!!) @ (
% 24.53/6.42 (('#B') @ (
% 24.53/6.42 !!) @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 !!))) @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#S') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 '#S') @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 '#C'))) @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ subset)))) @
% 24.53/6.42 dpsetconstr)))))) @
% 24.53/6.42 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1321])).
% 24.53/6.42 thf(zip_derived_cl1338, plain,
% 24.53/6.42 (~ (((symdiffI1) =>
% 24.53/6.42 (((symdiffI2) =>
% 24.53/6.42 (((symdiffIneg1) =>
% 24.53/6.42 (((symdiffIneg2) =>
% 24.53/6.42 (((secondinupair) =>
% 24.53/6.42 (((setukpairIL) =>
% 24.53/6.42 (((setukpairIR) =>
% 24.53/6.42 (((kpairiskpair) =>
% 24.53/6.42 (((kpairp) =>
% 24.53/6.42 (((singletonsubset) =>
% 24.53/6.42 (((singletoninpowerset) =>
% 24.53/6.42 (((singletoninpowunion) =>
% 24.53/6.42 (((upairset2E) =>
% 24.53/6.42 (((upairsubunion) =>
% 24.53/6.42 (((upairinpowunion) =>
% 24.53/6.42 (((ubforcartprodlem1) =>
% 24.53/6.42 (((ubforcartprodlem2) =>
% 24.53/6.42 (((ubforcartprodlem3) =>
% 24.53/6.42 (((cartprodpairin) =>
% 24.53/6.42 (((cartprodmempair1) =>
% 24.53/6.42 (((cartprodmempair) =>
% 24.53/6.42 (((setunionE2) =>
% 24.53/6.42 (((setunionsingleton1) =>
% 24.53/6.42 (((setunionsingleton2) =>
% 24.53/6.42 (((setunionsingleton) =>
% 24.53/6.42 (((singletonprop) =>
% 24.53/6.42 (((ex1E1) =>
% 24.53/6.42 (((ex1I) =>
% 24.53/6.42 (((ex1I2) =>
% 24.53/6.42 (((singletonsuniq) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjL1) =>
% 24.53/6.42 ((
% 24.53/6.42 (kfstsingleton) =>
% 24.53/6.42 ((
% 24.53/6.42 (theprop) =>
% 24.53/6.42 ((
% 24.53/6.42 (kfstpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodfstin) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjL2) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjL) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjR11) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjR12) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjR1) =>
% 24.53/6.42 ((
% 24.53/6.42 (upairequniteq) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjR2) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjR) =>
% 24.53/6.42 ((
% 24.53/6.42 (ksndsingleton) =>
% 24.53/6.42 ((
% 24.53/6.42 (ksndpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (kpairsurjEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodsndin) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodpairmemEL) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodpairmemER) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodmempaircEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodfstpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodsndpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodpairsurjEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (dpsetconstrI) =>
% 24.53/6.42 ((
% 24.53/6.42 (!!) @ (
% 24.53/6.42 (('#B') @ (
% 24.53/6.42 !!) @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 !!))) @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#S') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 '#S') @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 '#C'))) @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ subset)))) @
% 24.53/6.42 dpsetconstr)))))) @
% 24.53/6.42 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1329])).
% 24.53/6.42 thf(zip_derived_cl1347, plain,
% 24.53/6.42 (~ (((symdiffI2) =>
% 24.53/6.42 (((symdiffIneg1) =>
% 24.53/6.42 (((symdiffIneg2) =>
% 24.53/6.42 (((secondinupair) =>
% 24.53/6.42 (((setukpairIL) =>
% 24.53/6.42 (((setukpairIR) =>
% 24.53/6.42 (((kpairiskpair) =>
% 24.53/6.42 (((kpairp) =>
% 24.53/6.42 (((singletonsubset) =>
% 24.53/6.42 (((singletoninpowerset) =>
% 24.53/6.42 (((singletoninpowunion) =>
% 24.53/6.42 (((upairset2E) =>
% 24.53/6.42 (((upairsubunion) =>
% 24.53/6.42 (((upairinpowunion) =>
% 24.53/6.42 (((ubforcartprodlem1) =>
% 24.53/6.42 (((ubforcartprodlem2) =>
% 24.53/6.42 (((ubforcartprodlem3) =>
% 24.53/6.42 (((cartprodpairin) =>
% 24.53/6.42 (((cartprodmempair1) =>
% 24.53/6.42 (((cartprodmempair) =>
% 24.53/6.42 (((setunionE2) =>
% 24.53/6.42 (((setunionsingleton1) =>
% 24.53/6.42 (((setunionsingleton2) =>
% 24.53/6.42 (((setunionsingleton) =>
% 24.53/6.42 (((singletonprop) =>
% 24.53/6.42 (((ex1E1) =>
% 24.53/6.42 (((ex1I) =>
% 24.53/6.42 (((ex1I2) =>
% 24.53/6.42 (((singletonsuniq) =>
% 24.53/6.42 (((setukpairinjL1) =>
% 24.53/6.42 ((
% 24.53/6.42 (kfstsingleton) =>
% 24.53/6.42 ((
% 24.53/6.42 (theprop) =>
% 24.53/6.42 ((
% 24.53/6.42 (kfstpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodfstin) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjL2) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjL) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjR11) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjR12) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjR1) =>
% 24.53/6.42 ((
% 24.53/6.42 (upairequniteq) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjR2) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjR) =>
% 24.53/6.42 ((
% 24.53/6.42 (ksndsingleton) =>
% 24.53/6.42 ((
% 24.53/6.42 (ksndpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (kpairsurjEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodsndin) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodpairmemEL) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodpairmemER) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodmempaircEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodfstpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodsndpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodpairsurjEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (dpsetconstrI) =>
% 24.53/6.42 ((
% 24.53/6.42 (!!) @ (
% 24.53/6.42 (('#B') @ (
% 24.53/6.42 !!) @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 !!))) @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#S') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 '#S') @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 '#C'))) @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ subset)))) @
% 24.53/6.42 dpsetconstr)))))) @
% 24.53/6.42 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1338])).
% 24.53/6.42 thf(zip_derived_cl1354, plain,
% 24.53/6.42 (~ (((symdiffIneg1) =>
% 24.53/6.42 (((symdiffIneg2) =>
% 24.53/6.42 (((secondinupair) =>
% 24.53/6.42 (((setukpairIL) =>
% 24.53/6.42 (((setukpairIR) =>
% 24.53/6.42 (((kpairiskpair) =>
% 24.53/6.42 (((kpairp) =>
% 24.53/6.42 (((singletonsubset) =>
% 24.53/6.42 (((singletoninpowerset) =>
% 24.53/6.42 (((singletoninpowunion) =>
% 24.53/6.42 (((upairset2E) =>
% 24.53/6.42 (((upairsubunion) =>
% 24.53/6.42 (((upairinpowunion) =>
% 24.53/6.42 (((ubforcartprodlem1) =>
% 24.53/6.42 (((ubforcartprodlem2) =>
% 24.53/6.42 (((ubforcartprodlem3) =>
% 24.53/6.42 (((cartprodpairin) =>
% 24.53/6.42 (((cartprodmempair1) =>
% 24.53/6.42 (((cartprodmempair) =>
% 24.53/6.42 (((setunionE2) =>
% 24.53/6.42 (((setunionsingleton1) =>
% 24.53/6.42 (((setunionsingleton2) =>
% 24.53/6.42 (((setunionsingleton) =>
% 24.53/6.42 (((singletonprop) =>
% 24.53/6.42 (((ex1E1) =>
% 24.53/6.42 (((ex1I) =>
% 24.53/6.42 (((ex1I2) =>
% 24.53/6.42 (((singletonsuniq) =>
% 24.53/6.42 (((setukpairinjL1) =>
% 24.53/6.42 (((kfstsingleton) =>
% 24.53/6.42 ((
% 24.53/6.42 (theprop) =>
% 24.53/6.42 ((
% 24.53/6.42 (kfstpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodfstin) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjL2) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjL) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjR11) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjR12) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjR1) =>
% 24.53/6.42 ((
% 24.53/6.42 (upairequniteq) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjR2) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjR) =>
% 24.53/6.42 ((
% 24.53/6.42 (ksndsingleton) =>
% 24.53/6.42 ((
% 24.53/6.42 (ksndpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (kpairsurjEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodsndin) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodpairmemEL) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodpairmemER) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodmempaircEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodfstpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodsndpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodpairsurjEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (dpsetconstrI) =>
% 24.53/6.42 ((
% 24.53/6.42 (!!) @ (
% 24.53/6.42 (('#B') @ (
% 24.53/6.42 !!) @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 !!))) @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#S') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 '#S') @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 '#C'))) @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ subset)))) @
% 24.53/6.42 dpsetconstr)))))) @
% 24.53/6.42 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1347])).
% 24.53/6.42 thf(zip_derived_cl1361, plain,
% 24.53/6.42 (~ (((symdiffIneg2) =>
% 24.53/6.42 (((secondinupair) =>
% 24.53/6.42 (((setukpairIL) =>
% 24.53/6.42 (((setukpairIR) =>
% 24.53/6.42 (((kpairiskpair) =>
% 24.53/6.42 (((kpairp) =>
% 24.53/6.42 (((singletonsubset) =>
% 24.53/6.42 (((singletoninpowerset) =>
% 24.53/6.42 (((singletoninpowunion) =>
% 24.53/6.42 (((upairset2E) =>
% 24.53/6.42 (((upairsubunion) =>
% 24.53/6.42 (((upairinpowunion) =>
% 24.53/6.42 (((ubforcartprodlem1) =>
% 24.53/6.42 (((ubforcartprodlem2) =>
% 24.53/6.42 (((ubforcartprodlem3) =>
% 24.53/6.42 (((cartprodpairin) =>
% 24.53/6.42 (((cartprodmempair1) =>
% 24.53/6.42 (((cartprodmempair) =>
% 24.53/6.42 (((setunionE2) =>
% 24.53/6.42 (((setunionsingleton1) =>
% 24.53/6.42 (((setunionsingleton2) =>
% 24.53/6.42 (((setunionsingleton) =>
% 24.53/6.42 (((singletonprop) =>
% 24.53/6.42 (((ex1E1) =>
% 24.53/6.42 (((ex1I) =>
% 24.53/6.42 (((ex1I2) =>
% 24.53/6.42 (((singletonsuniq) =>
% 24.53/6.42 (((setukpairinjL1) =>
% 24.53/6.42 (((kfstsingleton) =>
% 24.53/6.42 (((theprop) =>
% 24.53/6.42 ((
% 24.53/6.42 (kfstpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodfstin) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjL2) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjL) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjR11) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjR12) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjR1) =>
% 24.53/6.42 ((
% 24.53/6.42 (upairequniteq) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjR2) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjR) =>
% 24.53/6.42 ((
% 24.53/6.42 (ksndsingleton) =>
% 24.53/6.42 ((
% 24.53/6.42 (ksndpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (kpairsurjEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodsndin) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodpairmemEL) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodpairmemER) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodmempaircEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodfstpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodsndpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodpairsurjEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (dpsetconstrI) =>
% 24.53/6.42 ((
% 24.53/6.42 (!!) @ (
% 24.53/6.42 (('#B') @ (
% 24.53/6.42 !!) @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 !!))) @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#S') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 '#S') @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 '#C'))) @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ subset)))) @
% 24.53/6.42 dpsetconstr)))))) @
% 24.53/6.42 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1354])).
% 24.53/6.42 thf(zip_derived_cl1369, plain,
% 24.53/6.42 (~ (((secondinupair) =>
% 24.53/6.42 (((setukpairIL) =>
% 24.53/6.42 (((setukpairIR) =>
% 24.53/6.42 (((kpairiskpair) =>
% 24.53/6.42 (((kpairp) =>
% 24.53/6.42 (((singletonsubset) =>
% 24.53/6.42 (((singletoninpowerset) =>
% 24.53/6.42 (((singletoninpowunion) =>
% 24.53/6.42 (((upairset2E) =>
% 24.53/6.42 (((upairsubunion) =>
% 24.53/6.42 (((upairinpowunion) =>
% 24.53/6.42 (((ubforcartprodlem1) =>
% 24.53/6.42 (((ubforcartprodlem2) =>
% 24.53/6.42 (((ubforcartprodlem3) =>
% 24.53/6.42 (((cartprodpairin) =>
% 24.53/6.42 (((cartprodmempair1) =>
% 24.53/6.42 (((cartprodmempair) =>
% 24.53/6.42 (((setunionE2) =>
% 24.53/6.42 (((setunionsingleton1) =>
% 24.53/6.42 (((setunionsingleton2) =>
% 24.53/6.42 (((setunionsingleton) =>
% 24.53/6.42 (((singletonprop) =>
% 24.53/6.42 (((ex1E1) =>
% 24.53/6.42 (((ex1I) =>
% 24.53/6.42 (((ex1I2) =>
% 24.53/6.42 (((singletonsuniq) =>
% 24.53/6.42 (((setukpairinjL1) =>
% 24.53/6.42 (((kfstsingleton) =>
% 24.53/6.42 (((theprop) =>
% 24.53/6.42 (((kfstpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodfstin) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjL2) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjL) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjR11) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjR12) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjR1) =>
% 24.53/6.42 ((
% 24.53/6.42 (upairequniteq) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjR2) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjR) =>
% 24.53/6.42 ((
% 24.53/6.42 (ksndsingleton) =>
% 24.53/6.42 ((
% 24.53/6.42 (ksndpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (kpairsurjEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodsndin) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodpairmemEL) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodpairmemER) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodmempaircEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodfstpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodsndpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodpairsurjEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (dpsetconstrI) =>
% 24.53/6.42 ((
% 24.53/6.42 (!!) @ (
% 24.53/6.42 (('#B') @ (
% 24.53/6.42 !!) @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 !!))) @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#S') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 '#S') @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 '#C'))) @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ subset)))) @
% 24.53/6.42 dpsetconstr)))))) @
% 24.53/6.42 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1361])).
% 24.53/6.42 thf(zip_derived_cl1377, plain,
% 24.53/6.42 (~ (((setukpairIL) =>
% 24.53/6.42 (((setukpairIR) =>
% 24.53/6.42 (((kpairiskpair) =>
% 24.53/6.42 (((kpairp) =>
% 24.53/6.42 (((singletonsubset) =>
% 24.53/6.42 (((singletoninpowerset) =>
% 24.53/6.42 (((singletoninpowunion) =>
% 24.53/6.42 (((upairset2E) =>
% 24.53/6.42 (((upairsubunion) =>
% 24.53/6.42 (((upairinpowunion) =>
% 24.53/6.42 (((ubforcartprodlem1) =>
% 24.53/6.42 (((ubforcartprodlem2) =>
% 24.53/6.42 (((ubforcartprodlem3) =>
% 24.53/6.42 (((cartprodpairin) =>
% 24.53/6.42 (((cartprodmempair1) =>
% 24.53/6.42 (((cartprodmempair) =>
% 24.53/6.42 (((setunionE2) =>
% 24.53/6.42 (((setunionsingleton1) =>
% 24.53/6.42 (((setunionsingleton2) =>
% 24.53/6.42 (((setunionsingleton) =>
% 24.53/6.42 (((singletonprop) =>
% 24.53/6.42 (((ex1E1) =>
% 24.53/6.42 (((ex1I) =>
% 24.53/6.42 (((ex1I2) =>
% 24.53/6.42 (((singletonsuniq) =>
% 24.53/6.42 (((setukpairinjL1) =>
% 24.53/6.42 (((kfstsingleton) =>
% 24.53/6.42 (((theprop) =>
% 24.53/6.42 (((kfstpairEq) =>
% 24.53/6.42 (((cartprodfstin) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjL2) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjL) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjR11) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjR12) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjR1) =>
% 24.53/6.42 ((
% 24.53/6.42 (upairequniteq) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjR2) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjR) =>
% 24.53/6.42 ((
% 24.53/6.42 (ksndsingleton) =>
% 24.53/6.42 ((
% 24.53/6.42 (ksndpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (kpairsurjEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodsndin) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodpairmemEL) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodpairmemER) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodmempaircEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodfstpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodsndpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodpairsurjEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (dpsetconstrI) =>
% 24.53/6.42 ((
% 24.53/6.42 (!!) @ (
% 24.53/6.42 (('#B') @ (
% 24.53/6.42 !!) @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 !!))) @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#S') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 '#S') @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 '#C'))) @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ subset)))) @
% 24.53/6.42 dpsetconstr)))))) @
% 24.53/6.42 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1369])).
% 24.53/6.42 thf(zip_derived_cl1386, plain,
% 24.53/6.42 (~ (((setukpairIR) =>
% 24.53/6.42 (((kpairiskpair) =>
% 24.53/6.42 (((kpairp) =>
% 24.53/6.42 (((singletonsubset) =>
% 24.53/6.42 (((singletoninpowerset) =>
% 24.53/6.42 (((singletoninpowunion) =>
% 24.53/6.42 (((upairset2E) =>
% 24.53/6.42 (((upairsubunion) =>
% 24.53/6.42 (((upairinpowunion) =>
% 24.53/6.42 (((ubforcartprodlem1) =>
% 24.53/6.42 (((ubforcartprodlem2) =>
% 24.53/6.42 (((ubforcartprodlem3) =>
% 24.53/6.42 (((cartprodpairin) =>
% 24.53/6.42 (((cartprodmempair1) =>
% 24.53/6.42 (((cartprodmempair) =>
% 24.53/6.42 (((setunionE2) =>
% 24.53/6.42 (((setunionsingleton1) =>
% 24.53/6.42 (((setunionsingleton2) =>
% 24.53/6.42 (((setunionsingleton) =>
% 24.53/6.42 (((singletonprop) =>
% 24.53/6.42 (((ex1E1) =>
% 24.53/6.42 (((ex1I) =>
% 24.53/6.42 (((ex1I2) =>
% 24.53/6.42 (((singletonsuniq) =>
% 24.53/6.42 (((setukpairinjL1) =>
% 24.53/6.42 (((kfstsingleton) =>
% 24.53/6.42 (((theprop) =>
% 24.53/6.42 (((kfstpairEq) =>
% 24.53/6.42 (((cartprodfstin) =>
% 24.53/6.42 (((setukpairinjL2) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjL) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjR11) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjR12) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjR1) =>
% 24.53/6.42 ((
% 24.53/6.42 (upairequniteq) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjR2) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjR) =>
% 24.53/6.42 ((
% 24.53/6.42 (ksndsingleton) =>
% 24.53/6.42 ((
% 24.53/6.42 (ksndpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (kpairsurjEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodsndin) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodpairmemEL) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodpairmemER) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodmempaircEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodfstpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodsndpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodpairsurjEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (dpsetconstrI) =>
% 24.53/6.42 ((
% 24.53/6.42 (!!) @ (
% 24.53/6.42 (('#B') @ (
% 24.53/6.42 !!) @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 !!))) @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#S') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 '#S') @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 '#C'))) @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ subset)))) @
% 24.53/6.42 dpsetconstr)))))) @
% 24.53/6.42 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1377])).
% 24.53/6.42 thf(zip_derived_cl1396, plain,
% 24.53/6.42 (~ (((kpairiskpair) =>
% 24.53/6.42 (((kpairp) =>
% 24.53/6.42 (((singletonsubset) =>
% 24.53/6.42 (((singletoninpowerset) =>
% 24.53/6.42 (((singletoninpowunion) =>
% 24.53/6.42 (((upairset2E) =>
% 24.53/6.42 (((upairsubunion) =>
% 24.53/6.42 (((upairinpowunion) =>
% 24.53/6.42 (((ubforcartprodlem1) =>
% 24.53/6.42 (((ubforcartprodlem2) =>
% 24.53/6.42 (((ubforcartprodlem3) =>
% 24.53/6.42 (((cartprodpairin) =>
% 24.53/6.42 (((cartprodmempair1) =>
% 24.53/6.42 (((cartprodmempair) =>
% 24.53/6.42 (((setunionE2) =>
% 24.53/6.42 (((setunionsingleton1) =>
% 24.53/6.42 (((setunionsingleton2) =>
% 24.53/6.42 (((setunionsingleton) =>
% 24.53/6.42 (((singletonprop) =>
% 24.53/6.42 (((ex1E1) =>
% 24.53/6.42 (((ex1I) =>
% 24.53/6.42 (((ex1I2) =>
% 24.53/6.42 (((singletonsuniq) =>
% 24.53/6.42 (((setukpairinjL1) =>
% 24.53/6.42 (((kfstsingleton) =>
% 24.53/6.42 (((theprop) =>
% 24.53/6.42 (((kfstpairEq) =>
% 24.53/6.42 (((cartprodfstin) =>
% 24.53/6.42 (((setukpairinjL2) =>
% 24.53/6.42 (((setukpairinjL) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjR11) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjR12) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjR1) =>
% 24.53/6.42 ((
% 24.53/6.42 (upairequniteq) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjR2) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjR) =>
% 24.53/6.42 ((
% 24.53/6.42 (ksndsingleton) =>
% 24.53/6.42 ((
% 24.53/6.42 (ksndpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (kpairsurjEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodsndin) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodpairmemEL) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodpairmemER) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodmempaircEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodfstpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodsndpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodpairsurjEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (dpsetconstrI) =>
% 24.53/6.42 ((
% 24.53/6.42 (!!) @ (
% 24.53/6.42 (('#B') @ (
% 24.53/6.42 !!) @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 !!))) @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#S') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 '#S') @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 '#C'))) @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ subset)))) @
% 24.53/6.42 dpsetconstr)))))) @
% 24.53/6.42 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1386])).
% 24.53/6.42 thf(zip_derived_cl1407, plain,
% 24.53/6.42 (~ (((kpairp) =>
% 24.53/6.42 (((singletonsubset) =>
% 24.53/6.42 (((singletoninpowerset) =>
% 24.53/6.42 (((singletoninpowunion) =>
% 24.53/6.42 (((upairset2E) =>
% 24.53/6.42 (((upairsubunion) =>
% 24.53/6.42 (((upairinpowunion) =>
% 24.53/6.42 (((ubforcartprodlem1) =>
% 24.53/6.42 (((ubforcartprodlem2) =>
% 24.53/6.42 (((ubforcartprodlem3) =>
% 24.53/6.42 (((cartprodpairin) =>
% 24.53/6.42 (((cartprodmempair1) =>
% 24.53/6.42 (((cartprodmempair) =>
% 24.53/6.42 (((setunionE2) =>
% 24.53/6.42 (((setunionsingleton1) =>
% 24.53/6.42 (((setunionsingleton2) =>
% 24.53/6.42 (((setunionsingleton) =>
% 24.53/6.42 (((singletonprop) =>
% 24.53/6.42 (((ex1E1) =>
% 24.53/6.42 (((ex1I) =>
% 24.53/6.42 (((ex1I2) =>
% 24.53/6.42 (((singletonsuniq) =>
% 24.53/6.42 (((setukpairinjL1) =>
% 24.53/6.42 (((kfstsingleton) =>
% 24.53/6.42 (((theprop) =>
% 24.53/6.42 (((kfstpairEq) =>
% 24.53/6.42 (((cartprodfstin) =>
% 24.53/6.42 (((setukpairinjL2) =>
% 24.53/6.42 (((setukpairinjL) =>
% 24.53/6.42 (((setukpairinjR11) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjR12) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjR1) =>
% 24.53/6.42 ((
% 24.53/6.42 (upairequniteq) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjR2) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjR) =>
% 24.53/6.42 ((
% 24.53/6.42 (ksndsingleton) =>
% 24.53/6.42 ((
% 24.53/6.42 (ksndpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (kpairsurjEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodsndin) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodpairmemEL) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodpairmemER) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodmempaircEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodfstpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodsndpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodpairsurjEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (dpsetconstrI) =>
% 24.53/6.42 ((
% 24.53/6.42 (!!) @ (
% 24.53/6.42 (('#B') @ (
% 24.53/6.42 !!) @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 !!))) @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#S') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 '#S') @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 '#C'))) @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ subset)))) @
% 24.53/6.42 dpsetconstr)))))) @
% 24.53/6.42 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1396])).
% 24.53/6.42 thf(zip_derived_cl1420, plain,
% 24.53/6.42 (~ (((singletonsubset) =>
% 24.53/6.42 (((singletoninpowerset) =>
% 24.53/6.42 (((singletoninpowunion) =>
% 24.53/6.42 (((upairset2E) =>
% 24.53/6.42 (((upairsubunion) =>
% 24.53/6.42 (((upairinpowunion) =>
% 24.53/6.42 (((ubforcartprodlem1) =>
% 24.53/6.42 (((ubforcartprodlem2) =>
% 24.53/6.42 (((ubforcartprodlem3) =>
% 24.53/6.42 (((cartprodpairin) =>
% 24.53/6.42 (((cartprodmempair1) =>
% 24.53/6.42 (((cartprodmempair) =>
% 24.53/6.42 (((setunionE2) =>
% 24.53/6.42 (((setunionsingleton1) =>
% 24.53/6.42 (((setunionsingleton2) =>
% 24.53/6.42 (((setunionsingleton) =>
% 24.53/6.42 (((singletonprop) =>
% 24.53/6.42 (((ex1E1) =>
% 24.53/6.42 (((ex1I) =>
% 24.53/6.42 (((ex1I2) =>
% 24.53/6.42 (((singletonsuniq) =>
% 24.53/6.42 (((setukpairinjL1) =>
% 24.53/6.42 (((kfstsingleton) =>
% 24.53/6.42 (((theprop) =>
% 24.53/6.42 (((kfstpairEq) =>
% 24.53/6.42 (((cartprodfstin) =>
% 24.53/6.42 (((setukpairinjL2) =>
% 24.53/6.42 (((setukpairinjL) =>
% 24.53/6.42 (((setukpairinjR11) =>
% 24.53/6.42 (((setukpairinjR12) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjR1) =>
% 24.53/6.42 ((
% 24.53/6.42 (upairequniteq) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjR2) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjR) =>
% 24.53/6.42 ((
% 24.53/6.42 (ksndsingleton) =>
% 24.53/6.42 ((
% 24.53/6.42 (ksndpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (kpairsurjEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodsndin) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodpairmemEL) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodpairmemER) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodmempaircEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodfstpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodsndpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodpairsurjEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (dpsetconstrI) =>
% 24.53/6.42 ((
% 24.53/6.42 (!!) @ (
% 24.53/6.42 (('#B') @ (
% 24.53/6.42 !!) @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 !!))) @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#S') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 '#S') @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 '#C'))) @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ subset)))) @
% 24.53/6.42 dpsetconstr)))))) @
% 24.53/6.42 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1407])).
% 24.53/6.42 thf(zip_derived_cl1433, plain,
% 24.53/6.42 (~ (((singletoninpowerset) =>
% 24.53/6.42 (((singletoninpowunion) =>
% 24.53/6.42 (((upairset2E) =>
% 24.53/6.42 (((upairsubunion) =>
% 24.53/6.42 (((upairinpowunion) =>
% 24.53/6.42 (((ubforcartprodlem1) =>
% 24.53/6.42 (((ubforcartprodlem2) =>
% 24.53/6.42 (((ubforcartprodlem3) =>
% 24.53/6.42 (((cartprodpairin) =>
% 24.53/6.42 (((cartprodmempair1) =>
% 24.53/6.42 (((cartprodmempair) =>
% 24.53/6.42 (((setunionE2) =>
% 24.53/6.42 (((setunionsingleton1) =>
% 24.53/6.42 (((setunionsingleton2) =>
% 24.53/6.42 (((setunionsingleton) =>
% 24.53/6.42 (((singletonprop) =>
% 24.53/6.42 (((ex1E1) =>
% 24.53/6.42 (((ex1I) =>
% 24.53/6.42 (((ex1I2) =>
% 24.53/6.42 (((singletonsuniq) =>
% 24.53/6.42 (((setukpairinjL1) =>
% 24.53/6.42 (((kfstsingleton) =>
% 24.53/6.42 (((theprop) =>
% 24.53/6.42 (((kfstpairEq) =>
% 24.53/6.42 (((cartprodfstin) =>
% 24.53/6.42 (((setukpairinjL2) =>
% 24.53/6.42 (((setukpairinjL) =>
% 24.53/6.42 (((setukpairinjR11) =>
% 24.53/6.42 (((setukpairinjR12) =>
% 24.53/6.42 (((setukpairinjR1) =>
% 24.53/6.42 ((
% 24.53/6.42 (upairequniteq) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjR2) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjR) =>
% 24.53/6.42 ((
% 24.53/6.42 (ksndsingleton) =>
% 24.53/6.42 ((
% 24.53/6.42 (ksndpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (kpairsurjEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodsndin) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodpairmemEL) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodpairmemER) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodmempaircEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodfstpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodsndpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodpairsurjEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (dpsetconstrI) =>
% 24.53/6.42 ((
% 24.53/6.42 (!!) @ (
% 24.53/6.42 (('#B') @ (
% 24.53/6.42 !!) @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 !!))) @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#S') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 '#S') @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 '#C'))) @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ subset)))) @
% 24.53/6.42 dpsetconstr)))))) @
% 24.53/6.42 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1420])).
% 24.53/6.42 thf(zip_derived_cl1444, plain,
% 24.53/6.42 (~ (((singletoninpowunion) =>
% 24.53/6.42 (((upairset2E) =>
% 24.53/6.42 (((upairsubunion) =>
% 24.53/6.42 (((upairinpowunion) =>
% 24.53/6.42 (((ubforcartprodlem1) =>
% 24.53/6.42 (((ubforcartprodlem2) =>
% 24.53/6.42 (((ubforcartprodlem3) =>
% 24.53/6.42 (((cartprodpairin) =>
% 24.53/6.42 (((cartprodmempair1) =>
% 24.53/6.42 (((cartprodmempair) =>
% 24.53/6.42 (((setunionE2) =>
% 24.53/6.42 (((setunionsingleton1) =>
% 24.53/6.42 (((setunionsingleton2) =>
% 24.53/6.42 (((setunionsingleton) =>
% 24.53/6.42 (((singletonprop) =>
% 24.53/6.42 (((ex1E1) =>
% 24.53/6.42 (((ex1I) =>
% 24.53/6.42 (((ex1I2) =>
% 24.53/6.42 (((singletonsuniq) =>
% 24.53/6.42 (((setukpairinjL1) =>
% 24.53/6.42 (((kfstsingleton) =>
% 24.53/6.42 (((theprop) =>
% 24.53/6.42 (((kfstpairEq) =>
% 24.53/6.42 (((cartprodfstin) =>
% 24.53/6.42 (((setukpairinjL2) =>
% 24.53/6.42 (((setukpairinjL) =>
% 24.53/6.42 (((setukpairinjR11) =>
% 24.53/6.42 (((setukpairinjR12) =>
% 24.53/6.42 (((setukpairinjR1) =>
% 24.53/6.42 (((upairequniteq) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjR2) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjR) =>
% 24.53/6.42 ((
% 24.53/6.42 (ksndsingleton) =>
% 24.53/6.42 ((
% 24.53/6.42 (ksndpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (kpairsurjEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodsndin) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodpairmemEL) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodpairmemER) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodmempaircEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodfstpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodsndpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodpairsurjEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (dpsetconstrI) =>
% 24.53/6.42 ((
% 24.53/6.42 (!!) @ (
% 24.53/6.42 (('#B') @ (
% 24.53/6.42 !!) @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 !!))) @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#S') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 '#S') @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 '#C'))) @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ subset)))) @
% 24.53/6.42 dpsetconstr)))))) @
% 24.53/6.42 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1433])).
% 24.53/6.42 thf(zip_derived_cl1452, plain,
% 24.53/6.42 (~ (((upairset2E) =>
% 24.53/6.42 (((upairsubunion) =>
% 24.53/6.42 (((upairinpowunion) =>
% 24.53/6.42 (((ubforcartprodlem1) =>
% 24.53/6.42 (((ubforcartprodlem2) =>
% 24.53/6.42 (((ubforcartprodlem3) =>
% 24.53/6.42 (((cartprodpairin) =>
% 24.53/6.42 (((cartprodmempair1) =>
% 24.53/6.42 (((cartprodmempair) =>
% 24.53/6.42 (((setunionE2) =>
% 24.53/6.42 (((setunionsingleton1) =>
% 24.53/6.42 (((setunionsingleton2) =>
% 24.53/6.42 (((setunionsingleton) =>
% 24.53/6.42 (((singletonprop) =>
% 24.53/6.42 (((ex1E1) =>
% 24.53/6.42 (((ex1I) =>
% 24.53/6.42 (((ex1I2) =>
% 24.53/6.42 (((singletonsuniq) =>
% 24.53/6.42 (((setukpairinjL1) =>
% 24.53/6.42 (((kfstsingleton) =>
% 24.53/6.42 (((theprop) =>
% 24.53/6.42 (((kfstpairEq) =>
% 24.53/6.42 (((cartprodfstin) =>
% 24.53/6.42 (((setukpairinjL2) =>
% 24.53/6.42 (((setukpairinjL) =>
% 24.53/6.42 (((setukpairinjR11) =>
% 24.53/6.42 (((setukpairinjR12) =>
% 24.53/6.42 (((setukpairinjR1) =>
% 24.53/6.42 (((upairequniteq) =>
% 24.53/6.42 (((setukpairinjR2) =>
% 24.53/6.42 ((
% 24.53/6.42 (setukpairinjR) =>
% 24.53/6.42 ((
% 24.53/6.42 (ksndsingleton) =>
% 24.53/6.42 ((
% 24.53/6.42 (ksndpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (kpairsurjEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodsndin) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodpairmemEL) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodpairmemER) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodmempaircEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodfstpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodsndpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodpairsurjEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (dpsetconstrI) =>
% 24.53/6.42 ((
% 24.53/6.42 (!!) @ (
% 24.53/6.42 (('#B') @ (
% 24.53/6.42 !!) @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 !!))) @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#S') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 '#S') @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 '#C'))) @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ subset)))) @
% 24.53/6.42 dpsetconstr)))))) @
% 24.53/6.42 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1444])).
% 24.53/6.42 thf(zip_derived_cl1459, plain,
% 24.53/6.42 (~ (((upairsubunion) =>
% 24.53/6.42 (((upairinpowunion) =>
% 24.53/6.42 (((ubforcartprodlem1) =>
% 24.53/6.42 (((ubforcartprodlem2) =>
% 24.53/6.42 (((ubforcartprodlem3) =>
% 24.53/6.42 (((cartprodpairin) =>
% 24.53/6.42 (((cartprodmempair1) =>
% 24.53/6.42 (((cartprodmempair) =>
% 24.53/6.42 (((setunionE2) =>
% 24.53/6.42 (((setunionsingleton1) =>
% 24.53/6.42 (((setunionsingleton2) =>
% 24.53/6.42 (((setunionsingleton) =>
% 24.53/6.42 (((singletonprop) =>
% 24.53/6.42 (((ex1E1) =>
% 24.53/6.42 (((ex1I) =>
% 24.53/6.42 (((ex1I2) =>
% 24.53/6.42 (((singletonsuniq) =>
% 24.53/6.42 (((setukpairinjL1) =>
% 24.53/6.42 (((kfstsingleton) =>
% 24.53/6.42 (((theprop) =>
% 24.53/6.42 (((kfstpairEq) =>
% 24.53/6.42 (((cartprodfstin) =>
% 24.53/6.42 (((setukpairinjL2) =>
% 24.53/6.42 (((setukpairinjL) =>
% 24.53/6.42 (((setukpairinjR11) =>
% 24.53/6.42 (((setukpairinjR12) =>
% 24.53/6.42 (((setukpairinjR1) =>
% 24.53/6.42 (((upairequniteq) =>
% 24.53/6.42 (((setukpairinjR2) =>
% 24.53/6.42 (((setukpairinjR) =>
% 24.53/6.42 ((
% 24.53/6.42 (ksndsingleton) =>
% 24.53/6.42 ((
% 24.53/6.42 (ksndpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (kpairsurjEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodsndin) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodpairmemEL) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodpairmemER) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodmempaircEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodfstpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodsndpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodpairsurjEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (dpsetconstrI) =>
% 24.53/6.42 ((
% 24.53/6.42 (!!) @ (
% 24.53/6.42 (('#B') @ (
% 24.53/6.42 !!) @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 !!))) @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#S') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 '#S') @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 '#C'))) @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ subset)))) @
% 24.53/6.42 dpsetconstr)))))) @
% 24.53/6.42 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1452])).
% 24.53/6.42 thf(zip_derived_cl1466, plain,
% 24.53/6.42 (~ (((upairinpowunion) =>
% 24.53/6.42 (((ubforcartprodlem1) =>
% 24.53/6.42 (((ubforcartprodlem2) =>
% 24.53/6.42 (((ubforcartprodlem3) =>
% 24.53/6.42 (((cartprodpairin) =>
% 24.53/6.42 (((cartprodmempair1) =>
% 24.53/6.42 (((cartprodmempair) =>
% 24.53/6.42 (((setunionE2) =>
% 24.53/6.42 (((setunionsingleton1) =>
% 24.53/6.42 (((setunionsingleton2) =>
% 24.53/6.42 (((setunionsingleton) =>
% 24.53/6.42 (((singletonprop) =>
% 24.53/6.42 (((ex1E1) =>
% 24.53/6.42 (((ex1I) =>
% 24.53/6.42 (((ex1I2) =>
% 24.53/6.42 (((singletonsuniq) =>
% 24.53/6.42 (((setukpairinjL1) =>
% 24.53/6.42 (((kfstsingleton) =>
% 24.53/6.42 (((theprop) =>
% 24.53/6.42 (((kfstpairEq) =>
% 24.53/6.42 (((cartprodfstin) =>
% 24.53/6.42 (((setukpairinjL2) =>
% 24.53/6.42 (((setukpairinjL) =>
% 24.53/6.42 (((setukpairinjR11) =>
% 24.53/6.42 (((setukpairinjR12) =>
% 24.53/6.42 (((setukpairinjR1) =>
% 24.53/6.42 (((upairequniteq) =>
% 24.53/6.42 (((setukpairinjR2) =>
% 24.53/6.42 (((setukpairinjR) =>
% 24.53/6.42 (((ksndsingleton) =>
% 24.53/6.42 ((
% 24.53/6.42 (ksndpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (kpairsurjEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodsndin) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodpairmemEL) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodpairmemER) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodmempaircEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodfstpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodsndpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodpairsurjEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (dpsetconstrI) =>
% 24.53/6.42 ((
% 24.53/6.42 (!!) @ (
% 24.53/6.42 (('#B') @ (
% 24.53/6.42 !!) @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 !!))) @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#S') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 '#S') @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 '#C'))) @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ subset)))) @
% 24.53/6.42 dpsetconstr)))))) @
% 24.53/6.42 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1459])).
% 24.53/6.42 thf(zip_derived_cl1473, plain,
% 24.53/6.42 (~ (((ubforcartprodlem1) =>
% 24.53/6.42 (((ubforcartprodlem2) =>
% 24.53/6.42 (((ubforcartprodlem3) =>
% 24.53/6.42 (((cartprodpairin) =>
% 24.53/6.42 (((cartprodmempair1) =>
% 24.53/6.42 (((cartprodmempair) =>
% 24.53/6.42 (((setunionE2) =>
% 24.53/6.42 (((setunionsingleton1) =>
% 24.53/6.42 (((setunionsingleton2) =>
% 24.53/6.42 (((setunionsingleton) =>
% 24.53/6.42 (((singletonprop) =>
% 24.53/6.42 (((ex1E1) =>
% 24.53/6.42 (((ex1I) =>
% 24.53/6.42 (((ex1I2) =>
% 24.53/6.42 (((singletonsuniq) =>
% 24.53/6.42 (((setukpairinjL1) =>
% 24.53/6.42 (((kfstsingleton) =>
% 24.53/6.42 (((theprop) =>
% 24.53/6.42 (((kfstpairEq) =>
% 24.53/6.42 (((cartprodfstin) =>
% 24.53/6.42 (((setukpairinjL2) =>
% 24.53/6.42 (((setukpairinjL) =>
% 24.53/6.42 (((setukpairinjR11) =>
% 24.53/6.42 (((setukpairinjR12) =>
% 24.53/6.42 (((setukpairinjR1) =>
% 24.53/6.42 (((upairequniteq) =>
% 24.53/6.42 (((setukpairinjR2) =>
% 24.53/6.42 (((setukpairinjR) =>
% 24.53/6.42 (((ksndsingleton) =>
% 24.53/6.42 (((ksndpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (kpairsurjEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodsndin) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodpairmemEL) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodpairmemER) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodmempaircEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodfstpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodsndpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodpairsurjEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (dpsetconstrI) =>
% 24.53/6.42 ((
% 24.53/6.42 (!!) @ (
% 24.53/6.42 (('#B') @ (
% 24.53/6.42 !!) @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 !!))) @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#S') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 '#S') @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 '#C'))) @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ subset)))) @
% 24.53/6.42 dpsetconstr)))))) @
% 24.53/6.42 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1466])).
% 24.53/6.42 thf(zip_derived_cl1480, plain,
% 24.53/6.42 (~ (((ubforcartprodlem2) =>
% 24.53/6.42 (((ubforcartprodlem3) =>
% 24.53/6.42 (((cartprodpairin) =>
% 24.53/6.42 (((cartprodmempair1) =>
% 24.53/6.42 (((cartprodmempair) =>
% 24.53/6.42 (((setunionE2) =>
% 24.53/6.42 (((setunionsingleton1) =>
% 24.53/6.42 (((setunionsingleton2) =>
% 24.53/6.42 (((setunionsingleton) =>
% 24.53/6.42 (((singletonprop) =>
% 24.53/6.42 (((ex1E1) =>
% 24.53/6.42 (((ex1I) =>
% 24.53/6.42 (((ex1I2) =>
% 24.53/6.42 (((singletonsuniq) =>
% 24.53/6.42 (((setukpairinjL1) =>
% 24.53/6.42 (((kfstsingleton) =>
% 24.53/6.42 (((theprop) =>
% 24.53/6.42 (((kfstpairEq) =>
% 24.53/6.42 (((cartprodfstin) =>
% 24.53/6.42 (((setukpairinjL2) =>
% 24.53/6.42 (((setukpairinjL) =>
% 24.53/6.42 (((setukpairinjR11) =>
% 24.53/6.42 (((setukpairinjR12) =>
% 24.53/6.42 (((setukpairinjR1) =>
% 24.53/6.42 (((upairequniteq) =>
% 24.53/6.42 (((setukpairinjR2) =>
% 24.53/6.42 (((setukpairinjR) =>
% 24.53/6.42 (((ksndsingleton) =>
% 24.53/6.42 (((ksndpairEq) =>
% 24.53/6.42 (((kpairsurjEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodsndin) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodpairmemEL) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodpairmemER) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodmempaircEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodfstpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodsndpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodpairsurjEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (dpsetconstrI) =>
% 24.53/6.42 ((
% 24.53/6.42 (!!) @ (
% 24.53/6.42 (('#B') @ (
% 24.53/6.42 !!) @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 !!))) @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#S') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 '#S') @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 '#C'))) @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ subset)))) @
% 24.53/6.42 dpsetconstr)))))) @
% 24.53/6.42 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1473])).
% 24.53/6.42 thf(zip_derived_cl1488, plain,
% 24.53/6.42 (~ (((ubforcartprodlem3) =>
% 24.53/6.42 (((cartprodpairin) =>
% 24.53/6.42 (((cartprodmempair1) =>
% 24.53/6.42 (((cartprodmempair) =>
% 24.53/6.42 (((setunionE2) =>
% 24.53/6.42 (((setunionsingleton1) =>
% 24.53/6.42 (((setunionsingleton2) =>
% 24.53/6.42 (((setunionsingleton) =>
% 24.53/6.42 (((singletonprop) =>
% 24.53/6.42 (((ex1E1) =>
% 24.53/6.42 (((ex1I) =>
% 24.53/6.42 (((ex1I2) =>
% 24.53/6.42 (((singletonsuniq) =>
% 24.53/6.42 (((setukpairinjL1) =>
% 24.53/6.42 (((kfstsingleton) =>
% 24.53/6.42 (((theprop) =>
% 24.53/6.42 (((kfstpairEq) =>
% 24.53/6.42 (((cartprodfstin) =>
% 24.53/6.42 (((setukpairinjL2) =>
% 24.53/6.42 (((setukpairinjL) =>
% 24.53/6.42 (((setukpairinjR11) =>
% 24.53/6.42 (((setukpairinjR12) =>
% 24.53/6.42 (((setukpairinjR1) =>
% 24.53/6.42 (((upairequniteq) =>
% 24.53/6.42 (((setukpairinjR2) =>
% 24.53/6.42 (((setukpairinjR) =>
% 24.53/6.42 (((ksndsingleton) =>
% 24.53/6.42 (((ksndpairEq) =>
% 24.53/6.42 (((kpairsurjEq) =>
% 24.53/6.42 (((cartprodsndin) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodpairmemEL) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodpairmemER) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodmempaircEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodfstpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodsndpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodpairsurjEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (dpsetconstrI) =>
% 24.53/6.42 ((
% 24.53/6.42 (!!) @ (
% 24.53/6.42 (('#B') @ (
% 24.53/6.42 !!) @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 !!))) @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#S') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 '#S') @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 '#C'))) @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ subset)))) @
% 24.53/6.42 dpsetconstr)))))) @
% 24.53/6.42 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1480])).
% 24.53/6.42 thf(zip_derived_cl1496, plain,
% 24.53/6.42 (~ (((cartprodpairin) =>
% 24.53/6.42 (((cartprodmempair1) =>
% 24.53/6.42 (((cartprodmempair) =>
% 24.53/6.42 (((setunionE2) =>
% 24.53/6.42 (((setunionsingleton1) =>
% 24.53/6.42 (((setunionsingleton2) =>
% 24.53/6.42 (((setunionsingleton) =>
% 24.53/6.42 (((singletonprop) =>
% 24.53/6.42 (((ex1E1) =>
% 24.53/6.42 (((ex1I) =>
% 24.53/6.42 (((ex1I2) =>
% 24.53/6.42 (((singletonsuniq) =>
% 24.53/6.42 (((setukpairinjL1) =>
% 24.53/6.42 (((kfstsingleton) =>
% 24.53/6.42 (((theprop) =>
% 24.53/6.42 (((kfstpairEq) =>
% 24.53/6.42 (((cartprodfstin) =>
% 24.53/6.42 (((setukpairinjL2) =>
% 24.53/6.42 (((setukpairinjL) =>
% 24.53/6.42 (((setukpairinjR11) =>
% 24.53/6.42 (((setukpairinjR12) =>
% 24.53/6.42 (((setukpairinjR1) =>
% 24.53/6.42 (((upairequniteq) =>
% 24.53/6.42 (((setukpairinjR2) =>
% 24.53/6.42 (((setukpairinjR) =>
% 24.53/6.42 (((ksndsingleton) =>
% 24.53/6.42 (((ksndpairEq) =>
% 24.53/6.42 (((kpairsurjEq) =>
% 24.53/6.42 (((cartprodsndin) =>
% 24.53/6.42 (((cartprodpairmemEL) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodpairmemER) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodmempaircEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodfstpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodsndpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodpairsurjEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (dpsetconstrI) =>
% 24.53/6.42 ((
% 24.53/6.42 (!!) @ (
% 24.53/6.42 (('#B') @ (
% 24.53/6.42 !!) @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 !!))) @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#S') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 '#S') @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 '#C'))) @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ subset)))) @
% 24.53/6.42 dpsetconstr)))))) @
% 24.53/6.42 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1488])).
% 24.53/6.42 thf(zip_derived_cl1505, plain,
% 24.53/6.42 (~ (((cartprodmempair1) =>
% 24.53/6.42 (((cartprodmempair) =>
% 24.53/6.42 (((setunionE2) =>
% 24.53/6.42 (((setunionsingleton1) =>
% 24.53/6.42 (((setunionsingleton2) =>
% 24.53/6.42 (((setunionsingleton) =>
% 24.53/6.42 (((singletonprop) =>
% 24.53/6.42 (((ex1E1) =>
% 24.53/6.42 (((ex1I) =>
% 24.53/6.42 (((ex1I2) =>
% 24.53/6.42 (((singletonsuniq) =>
% 24.53/6.42 (((setukpairinjL1) =>
% 24.53/6.42 (((kfstsingleton) =>
% 24.53/6.42 (((theprop) =>
% 24.53/6.42 (((kfstpairEq) =>
% 24.53/6.42 (((cartprodfstin) =>
% 24.53/6.42 (((setukpairinjL2) =>
% 24.53/6.42 (((setukpairinjL) =>
% 24.53/6.42 (((setukpairinjR11) =>
% 24.53/6.42 (((setukpairinjR12) =>
% 24.53/6.42 (((setukpairinjR1) =>
% 24.53/6.42 (((upairequniteq) =>
% 24.53/6.42 (((setukpairinjR2) =>
% 24.53/6.42 (((setukpairinjR) =>
% 24.53/6.42 (((ksndsingleton) =>
% 24.53/6.42 (((ksndpairEq) =>
% 24.53/6.42 (((kpairsurjEq) =>
% 24.53/6.42 (((cartprodsndin) =>
% 24.53/6.42 (((cartprodpairmemEL) =>
% 24.53/6.42 (((cartprodpairmemER) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodmempaircEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodfstpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodsndpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodpairsurjEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (dpsetconstrI) =>
% 24.53/6.42 ((
% 24.53/6.42 (!!) @ (
% 24.53/6.42 (('#B') @ (
% 24.53/6.42 !!) @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 !!))) @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#S') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 '#S') @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 '#C'))) @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ subset)))) @
% 24.53/6.42 dpsetconstr)))))) @
% 24.53/6.42 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1496])).
% 24.53/6.42 thf(zip_derived_cl1515, plain,
% 24.53/6.42 (~ (((cartprodmempair) =>
% 24.53/6.42 (((setunionE2) =>
% 24.53/6.42 (((setunionsingleton1) =>
% 24.53/6.42 (((setunionsingleton2) =>
% 24.53/6.42 (((setunionsingleton) =>
% 24.53/6.42 (((singletonprop) =>
% 24.53/6.42 (((ex1E1) =>
% 24.53/6.42 (((ex1I) =>
% 24.53/6.42 (((ex1I2) =>
% 24.53/6.42 (((singletonsuniq) =>
% 24.53/6.42 (((setukpairinjL1) =>
% 24.53/6.42 (((kfstsingleton) =>
% 24.53/6.42 (((theprop) =>
% 24.53/6.42 (((kfstpairEq) =>
% 24.53/6.42 (((cartprodfstin) =>
% 24.53/6.42 (((setukpairinjL2) =>
% 24.53/6.42 (((setukpairinjL) =>
% 24.53/6.42 (((setukpairinjR11) =>
% 24.53/6.42 (((setukpairinjR12) =>
% 24.53/6.42 (((setukpairinjR1) =>
% 24.53/6.42 (((upairequniteq) =>
% 24.53/6.42 (((setukpairinjR2) =>
% 24.53/6.42 (((setukpairinjR) =>
% 24.53/6.42 (((ksndsingleton) =>
% 24.53/6.42 (((ksndpairEq) =>
% 24.53/6.42 (((kpairsurjEq) =>
% 24.53/6.42 (((cartprodsndin) =>
% 24.53/6.42 (((cartprodpairmemEL) =>
% 24.53/6.42 (((cartprodpairmemER) =>
% 24.53/6.42 (((cartprodmempaircEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodfstpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodsndpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodpairsurjEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (dpsetconstrI) =>
% 24.53/6.42 ((
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% 24.53/6.42 (('#B') @ (
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% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
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% 24.53/6.42 (
% 24.53/6.42 (
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% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 '#S') @
% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
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% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
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% 24.53/6.42 dpsetconstr)))))) @
% 24.53/6.42 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1505])).
% 24.53/6.42 thf(zip_derived_cl1525, plain,
% 24.53/6.42 (~ (((setunionE2) =>
% 24.53/6.42 (((setunionsingleton1) =>
% 24.53/6.42 (((setunionsingleton2) =>
% 24.53/6.42 (((setunionsingleton) =>
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% 24.53/6.42 (((kfstsingleton) =>
% 24.53/6.42 (((theprop) =>
% 24.53/6.42 (((kfstpairEq) =>
% 24.53/6.42 (((cartprodfstin) =>
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% 24.53/6.42 (((setukpairinjL) =>
% 24.53/6.42 (((setukpairinjR11) =>
% 24.53/6.42 (((setukpairinjR12) =>
% 24.53/6.42 (((setukpairinjR1) =>
% 24.53/6.42 (((upairequniteq) =>
% 24.53/6.42 (((setukpairinjR2) =>
% 24.53/6.42 (((setukpairinjR) =>
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% 24.53/6.42 (((kpairsurjEq) =>
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% 24.53/6.42 (((cartprodpairmemEL) =>
% 24.53/6.42 (((cartprodpairmemER) =>
% 24.53/6.42 (((cartprodmempaircEq) =>
% 24.53/6.42 (((cartprodfstpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodsndpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodpairsurjEq) =>
% 24.53/6.42 ((
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% 24.53/6.42 ((
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% 24.53/6.42 (
% 24.53/6.42 (
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% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
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% 24.53/6.42 (
% 24.53/6.42 (
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% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
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% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
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% 24.53/6.42 (
% 24.53/6.42 (
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% 24.53/6.42 ('#B') @ (
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% 24.53/6.42 dpsetconstr)))))) @
% 24.53/6.42 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1515])).
% 24.53/6.42 thf(zip_derived_cl1535, plain,
% 24.53/6.42 (~ (((setunionsingleton1) =>
% 24.53/6.42 (((setunionsingleton2) =>
% 24.53/6.42 (((setunionsingleton) =>
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% 24.53/6.42 (((setukpairinjR12) =>
% 24.53/6.42 (((setukpairinjR1) =>
% 24.53/6.42 (((upairequniteq) =>
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% 24.53/6.42 (((setukpairinjR) =>
% 24.53/6.42 (((ksndsingleton) =>
% 24.53/6.42 (((ksndpairEq) =>
% 24.53/6.42 (((kpairsurjEq) =>
% 24.53/6.42 (((cartprodsndin) =>
% 24.53/6.42 (((cartprodpairmemEL) =>
% 24.53/6.42 (((cartprodpairmemER) =>
% 24.53/6.42 (((cartprodmempaircEq) =>
% 24.53/6.42 (((cartprodfstpairEq) =>
% 24.53/6.42 (((cartprodsndpairEq) =>
% 24.53/6.42 ((
% 24.53/6.42 (cartprodpairsurjEq) =>
% 24.53/6.42 ((
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% 24.53/6.42 ((
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% 24.53/6.42 (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
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% 24.53/6.42 (
% 24.53/6.42 (
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% 24.53/6.42 ('#B') @ (
% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
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% 24.53/6.42 (
% 24.53/6.42 ('#B') @ (
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% 24.53/6.42 ('#B') @ (
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% 24.53/6.42 dpsetconstr)))))) @
% 24.53/6.42 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1525])).
% 24.53/6.42 thf(zip_derived_cl1545, plain,
% 24.53/6.42 (~ (((setunionsingleton2) =>
% 24.53/6.42 (((setunionsingleton) =>
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% 24.53/6.42 (((kfstsingleton) =>
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% 24.53/6.42 (((kfstpairEq) =>
% 24.53/6.42 (((cartprodfstin) =>
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% 24.53/6.42 (((setukpairinjR12) =>
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% 24.53/6.42 (((setukpairinjR2) =>
% 24.53/6.42 (((setukpairinjR) =>
% 24.53/6.42 (((ksndsingleton) =>
% 24.53/6.42 (((ksndpairEq) =>
% 24.53/6.42 (((kpairsurjEq) =>
% 24.53/6.42 (((cartprodsndin) =>
% 24.53/6.43 (((cartprodpairmemEL) =>
% 24.53/6.43 (((cartprodpairmemER) =>
% 24.53/6.43 (((cartprodmempaircEq) =>
% 24.53/6.43 (((cartprodfstpairEq) =>
% 24.53/6.43 (((cartprodsndpairEq) =>
% 24.53/6.43 (((cartprodpairsurjEq) =>
% 24.53/6.43 ((
% 24.53/6.43 (dpsetconstrI) =>
% 24.53/6.43 ((
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% 24.53/6.43 (
% 24.53/6.43 (
% 24.53/6.43 ('#B') @ (
% 24.53/6.43 (
% 24.53/6.43 ('#B') @ (
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% 24.53/6.43 (
% 24.53/6.43 (
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% 24.53/6.43 (
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% 24.53/6.43 (
% 24.53/6.43 ('#B') @ (
% 24.53/6.43 (
% 24.53/6.43 ('#B') @ (
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% 24.53/6.43 (
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% 24.53/6.43 dpsetconstr)))))) @
% 24.53/6.43 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.43 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1535])).
% 24.53/6.43 thf(zip_derived_cl1555, plain,
% 24.53/6.43 (~ (((setunionsingleton) =>
% 24.53/6.43 (((singletonprop) =>
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% 24.53/6.43 (((ex1I) =>
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% 24.53/6.43 (((kfstsingleton) =>
% 24.53/6.43 (((theprop) =>
% 24.53/6.43 (((kfstpairEq) =>
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% 24.53/6.43 (((setukpairinjR12) =>
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% 24.53/6.43 (((upairequniteq) =>
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% 24.53/6.43 (((ksndsingleton) =>
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% 24.53/6.43 (((kpairsurjEq) =>
% 24.53/6.43 (((cartprodsndin) =>
% 24.53/6.43 (((cartprodpairmemEL) =>
% 24.53/6.43 (((cartprodpairmemER) =>
% 24.53/6.43 (((cartprodmempaircEq) =>
% 24.53/6.43 (((cartprodfstpairEq) =>
% 24.53/6.43 (((cartprodsndpairEq) =>
% 24.53/6.43 (((cartprodpairsurjEq) =>
% 24.53/6.43 (((dpsetconstrI) =>
% 24.53/6.43 ((
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% 24.53/6.43 ('#B') @ (
% 24.53/6.43 (
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% 24.53/6.43 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1545])).
% 24.53/6.43 thf(zip_derived_cl1565, plain,
% 24.53/6.43 (~ (((singletonprop) =>
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% 24.53/6.43 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1555])).
% 24.53/6.43 thf(zip_derived_cl1574, plain,
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% 24.53/6.43 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1565])).
% 24.53/6.43 thf(zip_derived_cl1582, plain,
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% 24.53/6.43 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.43 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1574])).
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% 24.53/6.43 (((setukpairinjR12) =>
% 24.53/6.43 (((setukpairinjR1) =>
% 24.53/6.43 (((upairequniteq) =>
% 24.53/6.43 (((setukpairinjR2) =>
% 24.53/6.43 (((setukpairinjR) =>
% 24.53/6.43 (((ksndsingleton) =>
% 24.53/6.43 (((ksndpairEq) =>
% 24.53/6.43 (((kpairsurjEq) =>
% 24.53/6.43 (((cartprodsndin) =>
% 24.53/6.43 (((cartprodpairmemEL) =>
% 24.53/6.43 (((cartprodpairmemER) =>
% 24.53/6.43 (((cartprodmempaircEq) =>
% 24.53/6.43 (((cartprodfstpairEq) =>
% 24.53/6.43 (((cartprodsndpairEq) =>
% 24.53/6.43 (((cartprodpairsurjEq) =>
% 24.53/6.43 (((dpsetconstrI) =>
% 24.53/6.43 (((!!) @ (
% 24.53/6.43 (('#B') @ (
% 24.53/6.43 !!) @
% 24.53/6.43 ((('#B') @ (
% 24.53/6.43 (('#B') @ (
% 24.53/6.43 !!))) @
% 24.53/6.43 ((('#S') @ (
% 24.53/6.43 (('#B') @ (
% 24.53/6.43 '#S') @
% 24.53/6.43 ((
% 24.53/6.43 ('#B') @ (
% 24.53/6.43 (
% 24.53/6.43 ('#B') @ (
% 24.53/6.43 '#C'))) @
% 24.53/6.43 (
% 24.53/6.43 (
% 24.53/6.43 ('#B') @ (
% 24.53/6.43 (
% 24.53/6.43 ('#B') @ (
% 24.53/6.43 (
% 24.53/6.43 ('#B') @ subset)))) @
% 24.53/6.43 dpsetconstr)))))) @
% 24.53/6.43 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.43 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1582])).
% 24.53/6.43 thf(zip_derived_cl1599, plain,
% 24.53/6.43 (~ (((singletonsuniq) =>
% 24.53/6.43 (((setukpairinjL1) =>
% 24.53/6.43 (((kfstsingleton) =>
% 24.53/6.43 (((theprop) =>
% 24.53/6.43 (((kfstpairEq) =>
% 24.53/6.43 (((cartprodfstin) =>
% 24.53/6.43 (((setukpairinjL2) =>
% 24.53/6.43 (((setukpairinjL) =>
% 24.53/6.43 (((setukpairinjR11) =>
% 24.53/6.43 (((setukpairinjR12) =>
% 24.53/6.43 (((setukpairinjR1) =>
% 24.53/6.43 (((upairequniteq) =>
% 24.53/6.43 (((setukpairinjR2) =>
% 24.53/6.43 (((setukpairinjR) =>
% 24.53/6.43 (((ksndsingleton) =>
% 24.53/6.43 (((ksndpairEq) =>
% 24.53/6.43 (((kpairsurjEq) =>
% 24.53/6.43 (((cartprodsndin) =>
% 24.53/6.43 (((cartprodpairmemEL) =>
% 24.53/6.43 (((cartprodpairmemER) =>
% 24.53/6.43 (((cartprodmempaircEq) =>
% 24.53/6.43 (((cartprodfstpairEq) =>
% 24.53/6.43 (((cartprodsndpairEq) =>
% 24.53/6.43 (((cartprodpairsurjEq) =>
% 24.53/6.43 (((dpsetconstrI) =>
% 24.53/6.43 (((!!) @ ((('#B') @ (
% 24.53/6.43 !!) @
% 24.53/6.43 (
% 24.53/6.43 (
% 24.53/6.43 ('#B') @ (
% 24.53/6.43 (
% 24.53/6.43 ('#B') @ (
% 24.53/6.43 !!))) @
% 24.53/6.43 (
% 24.53/6.43 (
% 24.53/6.43 ('#S') @ (
% 24.53/6.43 (
% 24.53/6.43 ('#B') @ (
% 24.53/6.43 '#S') @
% 24.53/6.43 (
% 24.53/6.43 (
% 24.53/6.43 ('#B') @ (
% 24.53/6.43 (
% 24.53/6.43 ('#B') @ (
% 24.53/6.43 '#C'))) @
% 24.53/6.43 (
% 24.53/6.43 (
% 24.53/6.43 ('#B') @ (
% 24.53/6.43 (
% 24.53/6.43 ('#B') @ (
% 24.53/6.43 (
% 24.53/6.43 ('#B') @ subset)))) @
% 24.53/6.43 dpsetconstr)))))) @
% 24.53/6.43 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.43 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1591])).
% 24.53/6.43 thf(zip_derived_cl1607, plain,
% 24.53/6.43 (~ (((setukpairinjL1) =>
% 24.53/6.43 (((kfstsingleton) =>
% 24.53/6.43 (((theprop) =>
% 24.53/6.43 (((kfstpairEq) =>
% 24.53/6.43 (((cartprodfstin) =>
% 24.53/6.43 (((setukpairinjL2) =>
% 24.53/6.43 (((setukpairinjL) =>
% 24.53/6.43 (((setukpairinjR11) =>
% 24.53/6.43 (((setukpairinjR12) =>
% 24.53/6.43 (((setukpairinjR1) =>
% 24.53/6.43 (((upairequniteq) =>
% 24.53/6.43 (((setukpairinjR2) =>
% 24.53/6.43 (((setukpairinjR) =>
% 24.53/6.43 (((ksndsingleton) =>
% 24.53/6.43 (((ksndpairEq) =>
% 24.53/6.43 (((kpairsurjEq) =>
% 24.53/6.43 (((cartprodsndin) =>
% 24.53/6.43 (((cartprodpairmemEL) =>
% 24.53/6.43 (((cartprodpairmemER) =>
% 24.53/6.43 (((cartprodmempaircEq) =>
% 24.53/6.43 (((cartprodfstpairEq) =>
% 24.53/6.43 (((cartprodsndpairEq) =>
% 24.53/6.43 (((cartprodpairsurjEq) =>
% 24.53/6.43 (((dpsetconstrI) =>
% 24.53/6.43 (((!!) @ ((('#B') @ (
% 24.53/6.43 !!) @
% 24.53/6.43 ((('#B') @ (
% 24.53/6.43 (
% 24.53/6.43 ('#B') @ (
% 24.53/6.43 !!))) @
% 24.53/6.43 (
% 24.53/6.43 (
% 24.53/6.43 ('#S') @ (
% 24.53/6.43 (
% 24.53/6.43 ('#B') @ (
% 24.53/6.43 '#S') @
% 24.53/6.43 (
% 24.53/6.43 (
% 24.53/6.43 ('#B') @ (
% 24.53/6.43 (
% 24.53/6.43 ('#B') @ (
% 24.53/6.43 '#C'))) @
% 24.53/6.43 (
% 24.53/6.43 (
% 24.53/6.43 ('#B') @ (
% 24.53/6.43 (
% 24.53/6.43 ('#B') @ (
% 24.53/6.43 (
% 24.53/6.43 ('#B') @ subset)))) @
% 24.53/6.43 dpsetconstr)))))) @
% 24.53/6.43 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.43 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1599])).
% 24.53/6.43 thf(zip_derived_cl1616, plain,
% 24.53/6.43 (~ (((kfstsingleton) =>
% 24.53/6.43 (((theprop) =>
% 24.53/6.43 (((kfstpairEq) =>
% 24.53/6.43 (((cartprodfstin) =>
% 24.53/6.43 (((setukpairinjL2) =>
% 24.53/6.43 (((setukpairinjL) =>
% 24.53/6.43 (((setukpairinjR11) =>
% 24.53/6.43 (((setukpairinjR12) =>
% 24.53/6.43 (((setukpairinjR1) =>
% 24.53/6.43 (((upairequniteq) =>
% 24.53/6.43 (((setukpairinjR2) =>
% 24.53/6.43 (((setukpairinjR) =>
% 24.53/6.43 (((ksndsingleton) =>
% 24.53/6.43 (((ksndpairEq) =>
% 24.53/6.43 (((kpairsurjEq) =>
% 24.53/6.43 (((cartprodsndin) =>
% 24.53/6.43 (((cartprodpairmemEL) =>
% 24.53/6.43 (((cartprodpairmemER) =>
% 24.53/6.43 (((cartprodmempaircEq) =>
% 24.53/6.43 (((cartprodfstpairEq) =>
% 24.53/6.43 (((cartprodsndpairEq) =>
% 24.53/6.43 (((cartprodpairsurjEq) =>
% 24.53/6.43 (((dpsetconstrI) =>
% 24.53/6.43 (((!!) @ ((('#B') @ (
% 24.53/6.43 !!) @
% 24.53/6.43 ((('#B') @ (
% 24.53/6.43 (('#B') @ (
% 24.53/6.43 !!))) @
% 24.53/6.43 ((('#S') @ (
% 24.53/6.43 (
% 24.53/6.43 ('#B') @ (
% 24.53/6.43 '#S') @
% 24.53/6.43 (
% 24.53/6.43 (
% 24.53/6.43 ('#B') @ (
% 24.53/6.43 (
% 24.53/6.43 ('#B') @ (
% 24.53/6.43 '#C'))) @
% 24.53/6.43 (
% 24.53/6.43 (
% 24.53/6.43 ('#B') @ (
% 24.53/6.43 (
% 24.53/6.43 ('#B') @ (
% 24.53/6.43 (
% 24.53/6.43 ('#B') @ subset)))) @
% 24.53/6.43 dpsetconstr)))))) @
% 24.53/6.43 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.43 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1607])).
% 24.53/6.43 thf(zip_derived_cl1627, plain,
% 24.53/6.43 (~ (((theprop) =>
% 24.53/6.43 (((kfstpairEq) =>
% 24.53/6.43 (((cartprodfstin) =>
% 24.53/6.43 (((setukpairinjL2) =>
% 24.53/6.43 (((setukpairinjL) =>
% 24.53/6.43 (((setukpairinjR11) =>
% 24.53/6.43 (((setukpairinjR12) =>
% 24.53/6.43 (((setukpairinjR1) =>
% 24.53/6.43 (((upairequniteq) =>
% 24.53/6.43 (((setukpairinjR2) =>
% 24.53/6.43 (((setukpairinjR) =>
% 24.53/6.43 (((ksndsingleton) =>
% 24.53/6.43 (((ksndpairEq) =>
% 24.53/6.43 (((kpairsurjEq) =>
% 24.53/6.43 (((cartprodsndin) =>
% 24.53/6.43 (((cartprodpairmemEL) =>
% 24.53/6.43 (((cartprodpairmemER) =>
% 24.53/6.43 (((cartprodmempaircEq) =>
% 24.53/6.43 (((cartprodfstpairEq) =>
% 24.53/6.43 (((cartprodsndpairEq) =>
% 24.53/6.43 (((cartprodpairsurjEq) =>
% 24.53/6.43 (((dpsetconstrI) =>
% 24.53/6.43 (((!!) @ ((('#B') @ (
% 24.53/6.43 !!) @
% 24.53/6.43 ((('#B') @ (
% 24.53/6.43 (('#B') @ (
% 24.53/6.43 !!))) @
% 24.53/6.43 ((('#S') @ (
% 24.53/6.43 (('#B') @ (
% 24.53/6.43 '#S') @
% 24.53/6.43 ((
% 24.53/6.43 ('#B') @ (
% 24.53/6.43 (
% 24.53/6.43 ('#B') @ (
% 24.53/6.43 '#C'))) @
% 24.53/6.43 (
% 24.53/6.43 (
% 24.53/6.43 ('#B') @ (
% 24.53/6.43 (
% 24.53/6.43 ('#B') @ (
% 24.53/6.43 (
% 24.53/6.43 ('#B') @ subset)))) @
% 24.53/6.43 dpsetconstr)))))) @
% 24.53/6.43 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.43 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1616])).
% 24.53/6.43 thf(zip_derived_cl1640, plain,
% 24.53/6.43 (~ (((kfstpairEq) =>
% 24.53/6.43 (((cartprodfstin) =>
% 24.53/6.43 (((setukpairinjL2) =>
% 24.53/6.43 (((setukpairinjL) =>
% 24.53/6.43 (((setukpairinjR11) =>
% 24.53/6.43 (((setukpairinjR12) =>
% 24.53/6.43 (((setukpairinjR1) =>
% 24.53/6.43 (((upairequniteq) =>
% 24.53/6.43 (((setukpairinjR2) =>
% 24.53/6.43 (((setukpairinjR) =>
% 24.53/6.43 (((ksndsingleton) =>
% 24.53/6.43 (((ksndpairEq) =>
% 24.53/6.43 (((kpairsurjEq) =>
% 24.53/6.43 (((cartprodsndin) =>
% 24.53/6.43 (((cartprodpairmemEL) =>
% 24.53/6.43 (((cartprodpairmemER) =>
% 24.53/6.43 (((cartprodmempaircEq) =>
% 24.53/6.43 (((cartprodfstpairEq) =>
% 24.53/6.43 (((cartprodsndpairEq) =>
% 24.53/6.43 (((cartprodpairsurjEq) =>
% 24.53/6.43 (((dpsetconstrI) =>
% 24.53/6.43 (((!!) @ ((('#B') @ (
% 24.53/6.43 !!) @
% 24.53/6.43 ((('#B') @ (
% 24.53/6.43 (('#B') @ (!!))) @
% 24.53/6.43 ((('#S') @ (
% 24.53/6.43 (('#B') @ (
% 24.53/6.43 '#S') @
% 24.53/6.43 ((('#B') @ (
% 24.53/6.43 (('#B') @ (
% 24.53/6.43 '#C'))) @
% 24.53/6.43 ((
% 24.53/6.43 ('#B') @ (
% 24.53/6.43 (
% 24.53/6.43 ('#B') @ (
% 24.53/6.43 (
% 24.53/6.43 ('#B') @ subset)))) @
% 24.53/6.43 dpsetconstr)))))) @
% 24.53/6.43 cartprod))))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.43 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1627])).
% 24.53/6.43 thf(zip_derived_cl1653, plain,
% 24.53/6.43 (~ (((cartprodfstin) =>
% 24.53/6.43 (((setukpairinjL2) =>
% 24.53/6.43 (((setukpairinjL) =>
% 24.53/6.43 (((setukpairinjR11) =>
% 24.53/6.43 (((setukpairinjR12) =>
% 24.53/6.43 (((setukpairinjR1) =>
% 24.53/6.43 (((upairequniteq) =>
% 24.53/6.43 (((setukpairinjR2) =>
% 24.53/6.43 (((setukpairinjR) =>
% 24.53/6.43 (((ksndsingleton) =>
% 24.53/6.43 (((ksndpairEq) =>
% 24.53/6.43 (((kpairsurjEq) =>
% 24.53/6.43 (((cartprodsndin) =>
% 24.53/6.43 (((cartprodpairmemEL) =>
% 24.53/6.43 (((cartprodpairmemER) =>
% 24.53/6.43 (((cartprodmempaircEq) =>
% 24.53/6.43 (((cartprodfstpairEq) =>
% 24.53/6.43 (((cartprodsndpairEq) =>
% 24.53/6.43 (((cartprodpairsurjEq) =>
% 24.53/6.43 (((dpsetconstrI) =>
% 24.53/6.43 (((!!) @ ((('#B') @ (!!) @
% 24.53/6.43 ((('#B') @ (
% 24.53/6.43 (('#B') @ (!!))) @
% 24.53/6.43 ((('#S') @ (
% 24.53/6.43 (('#B') @ (
% 24.53/6.43 '#S') @
% 24.53/6.43 ((('#B') @ (
% 24.53/6.43 (('#B') @ (
% 24.53/6.43 '#C'))) @
% 24.53/6.43 ((('#B') @ (
% 24.53/6.43 (('#B') @ (
% 24.53/6.43 (
% 24.53/6.43 ('#B') @ subset)))) @
% 24.53/6.43 dpsetconstr)))))) @
% 24.53/6.43 cartprod))))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.43 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1640])).
% 24.53/6.43 thf(zip_derived_cl1671, plain,
% 24.53/6.43 (~ (((setukpairinjL2) =>
% 24.53/6.43 (((setukpairinjL) =>
% 24.53/6.43 (((setukpairinjR11) =>
% 24.53/6.43 (((setukpairinjR12) =>
% 24.53/6.43 (((setukpairinjR1) =>
% 24.53/6.43 (((upairequniteq) =>
% 24.53/6.43 (((setukpairinjR2) =>
% 24.53/6.43 (((setukpairinjR) =>
% 24.53/6.43 (((ksndsingleton) =>
% 24.53/6.43 (((ksndpairEq) =>
% 24.53/6.43 (((kpairsurjEq) =>
% 24.53/6.43 (((cartprodsndin) =>
% 24.53/6.43 (((cartprodpairmemEL) =>
% 24.53/6.43 (((cartprodpairmemER) =>
% 24.53/6.43 (((cartprodmempaircEq) =>
% 24.53/6.43 (((cartprodfstpairEq) =>
% 24.53/6.43 (((cartprodsndpairEq) =>
% 24.53/6.43 (((cartprodpairsurjEq) =>
% 24.53/6.43 (((dpsetconstrI) =>
% 24.53/6.43 (((!!) @ ((('#B') @ (!!) @
% 24.53/6.43 ((('#B') @ ((
% 24.53/6.43 ('#B') @ (
% 24.53/6.43 !!))) @
% 24.53/6.43 ((('#S') @ (
% 24.53/6.43 (('#B') @ (
% 24.53/6.43 '#S') @
% 24.53/6.43 ((('#B') @ (
% 24.53/6.43 (('#B') @ (
% 24.53/6.43 '#C'))) @
% 24.53/6.43 ((('#B') @ (
% 24.53/6.43 (('#B') @ (
% 24.53/6.43 (('#B') @ subset)))) @
% 24.53/6.43 dpsetconstr)))))) @
% 24.53/6.43 cartprod))))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.43 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1653])).
% 24.53/6.43 thf(zip_derived_cl1690, plain,
% 24.53/6.43 (~ (((setukpairinjL) =>
% 24.53/6.43 (((setukpairinjR11) =>
% 24.53/6.43 (((setukpairinjR12) =>
% 24.53/6.43 (((setukpairinjR1) =>
% 24.53/6.43 (((upairequniteq) =>
% 24.53/6.43 (((setukpairinjR2) =>
% 24.53/6.43 (((setukpairinjR) =>
% 24.53/6.43 (((ksndsingleton) =>
% 24.53/6.43 (((ksndpairEq) =>
% 24.53/6.43 (((kpairsurjEq) =>
% 24.53/6.43 (((cartprodsndin) =>
% 24.53/6.43 (((cartprodpairmemEL) =>
% 24.53/6.43 (((cartprodpairmemER) =>
% 24.53/6.43 (((cartprodmempaircEq) =>
% 24.53/6.43 (((cartprodfstpairEq) =>
% 24.53/6.43 (((cartprodsndpairEq) =>
% 24.53/6.43 (((cartprodpairsurjEq) =>
% 24.53/6.43 (((dpsetconstrI) =>
% 24.53/6.43 (((!!) @ ((('#B') @ (!!) @
% 24.53/6.43 ((('#B') @ ((('#B') @ (
% 24.53/6.43 !!))) @
% 24.53/6.43 ((('#S') @ ((
% 24.53/6.43 ('#B') @ (
% 24.53/6.43 '#S') @
% 24.53/6.43 (
% 24.53/6.43 (
% 24.53/6.43 ('#B') @ (
% 24.53/6.43 (
% 24.53/6.43 ('#B') @ (
% 24.53/6.43 '#C'))) @
% 24.53/6.43 (
% 24.53/6.43 (
% 24.53/6.43 ('#B') @ (
% 24.53/6.43 (
% 24.53/6.43 ('#B') @ (
% 24.53/6.43 (
% 24.53/6.43 ('#B') @ subset)))) @
% 24.53/6.43 dpsetconstr)))))) @
% 24.53/6.43 cartprod))))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.43 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1671])).
% 24.53/6.43 thf(zip_derived_cl1714, plain,
% 24.53/6.43 (~ (((setukpairinjR11) =>
% 24.53/6.43 (((setukpairinjR12) =>
% 24.53/6.43 (((setukpairinjR1) =>
% 24.53/6.43 (((upairequniteq) =>
% 24.53/6.43 (((setukpairinjR2) =>
% 24.53/6.43 (((setukpairinjR) =>
% 24.53/6.43 (((ksndsingleton) =>
% 24.53/6.43 (((ksndpairEq) =>
% 24.53/6.43 (((kpairsurjEq) =>
% 24.53/6.43 (((cartprodsndin) =>
% 24.53/6.43 (((cartprodpairmemEL) =>
% 24.53/6.43 (((cartprodpairmemER) =>
% 24.53/6.43 (((cartprodmempaircEq) =>
% 24.53/6.43 (((cartprodfstpairEq) =>
% 24.53/6.43 (((cartprodsndpairEq) =>
% 24.53/6.43 (((cartprodpairsurjEq) =>
% 24.53/6.43 (((dpsetconstrI) =>
% 24.53/6.43 (((!!) @ ((('#B') @ (!!) @
% 24.53/6.43 ((('#B') @ ((('#B') @ (
% 24.53/6.43 !!))) @
% 24.53/6.43 ((('#S') @ ((('#B') @ (
% 24.53/6.43 '#S') @
% 24.53/6.43 ((
% 24.53/6.43 ('#B') @ (
% 24.53/6.43 (
% 24.53/6.43 ('#B') @ (
% 24.53/6.43 '#C'))) @
% 24.53/6.43 (
% 24.53/6.43 (
% 24.53/6.43 ('#B') @ (
% 24.53/6.43 (
% 24.53/6.43 ('#B') @ (
% 24.53/6.43 (
% 24.53/6.43 ('#B') @ subset)))) @
% 24.53/6.43 dpsetconstr)))))) @
% 24.53/6.43 cartprod))))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.43 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1690])).
% 24.53/6.43 thf(zip_derived_cl1740, plain,
% 24.53/6.43 (~ (((setukpairinjR12) =>
% 24.53/6.43 (((setukpairinjR1) =>
% 24.53/6.43 (((upairequniteq) =>
% 24.53/6.43 (((setukpairinjR2) =>
% 24.53/6.43 (((setukpairinjR) =>
% 24.53/6.43 (((ksndsingleton) =>
% 24.53/6.43 (((ksndpairEq) =>
% 24.53/6.43 (((kpairsurjEq) =>
% 24.53/6.43 (((cartprodsndin) =>
% 24.53/6.43 (((cartprodpairmemEL) =>
% 24.53/6.43 (((cartprodpairmemER) =>
% 24.53/6.43 (((cartprodmempaircEq) =>
% 24.53/6.43 (((cartprodfstpairEq) =>
% 24.53/6.43 (((cartprodsndpairEq) =>
% 24.53/6.43 (((cartprodpairsurjEq) =>
% 24.53/6.43 (((dpsetconstrI) =>
% 24.53/6.43 (((!!) @ ((('#B') @ (!!) @
% 24.53/6.43 ((('#B') @ ((('#B') @ (!!))) @
% 24.53/6.43 ((('#S') @ ((('#B') @ (
% 24.53/6.43 '#S') @
% 24.53/6.43 ((('#B') @ (
% 24.53/6.43 (('#B') @ (
% 24.53/6.43 '#C'))) @
% 24.53/6.43 ((
% 24.53/6.43 ('#B') @ (
% 24.53/6.43 (
% 24.53/6.43 ('#B') @ (
% 24.53/6.43 (
% 24.53/6.43 ('#B') @ subset)))) @
% 24.53/6.43 dpsetconstr)))))) @
% 24.53/6.43 cartprod))))))))))))))))))))))))))))))))))))))))),
% 24.53/6.43 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1714])).
% 24.53/6.43 thf(zip_derived_cl1767, plain,
% 24.53/6.43 (~ (((setukpairinjR1) =>
% 24.53/6.43 (((upairequniteq) =>
% 24.53/6.43 (((setukpairinjR2) =>
% 24.53/6.43 (((setukpairinjR) =>
% 24.53/6.43 (((ksndsingleton) =>
% 24.53/6.43 (((ksndpairEq) =>
% 24.53/6.43 (((kpairsurjEq) =>
% 24.53/6.43 (((cartprodsndin) =>
% 24.53/6.43 (((cartprodpairmemEL) =>
% 24.53/6.43 (((cartprodpairmemER) =>
% 24.53/6.43 (((cartprodmempaircEq) =>
% 24.53/6.43 (((cartprodfstpairEq) =>
% 24.53/6.43 (((cartprodsndpairEq) =>
% 24.53/6.43 (((cartprodpairsurjEq) =>
% 24.53/6.43 (((dpsetconstrI) =>
% 24.53/6.43 (((!!) @ ((('#B') @ (!!) @
% 24.53/6.43 ((('#B') @ ((('#B') @ (!!))) @
% 24.53/6.43 ((('#S') @ ((('#B') @ (
% 24.53/6.43 '#S') @
% 24.53/6.43 ((('#B') @ (
% 24.53/6.43 (('#B') @ (
% 24.53/6.43 '#C'))) @
% 24.53/6.43 ((('#B') @ (
% 24.53/6.43 (('#B') @ (
% 24.53/6.43 (
% 24.53/6.43 ('#B') @ subset)))) @
% 24.53/6.43 dpsetconstr)))))) @
% 24.53/6.43 cartprod))))))))))))))))))))))))))))))))))))))),
% 24.53/6.43 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1740])).
% 24.53/6.43 thf(zip_derived_cl1798, plain,
% 24.53/6.43 (~ (((upairequniteq) =>
% 24.53/6.43 (((setukpairinjR2) =>
% 24.53/6.43 (((setukpairinjR) =>
% 24.53/6.43 (((ksndsingleton) =>
% 24.53/6.43 (((ksndpairEq) =>
% 24.53/6.43 (((kpairsurjEq) =>
% 24.53/6.43 (((cartprodsndin) =>
% 24.53/6.43 (((cartprodpairmemEL) =>
% 24.53/6.43 (((cartprodpairmemER) =>
% 24.53/6.43 (((cartprodmempaircEq) =>
% 24.53/6.43 (((cartprodfstpairEq) =>
% 24.53/6.43 (((cartprodsndpairEq) =>
% 24.53/6.43 (((cartprodpairsurjEq) =>
% 24.53/6.43 (((dpsetconstrI) =>
% 24.53/6.43 (((!!) @ ((('#B') @ (!!) @
% 24.53/6.43 ((('#B') @ ((('#B') @ (!!))) @
% 24.53/6.43 ((('#S') @ ((('#B') @ (
% 24.53/6.43 '#S') @
% 24.53/6.43 ((('#B') @ (
% 24.53/6.43 (('#B') @ (
% 24.53/6.43 '#C'))) @
% 24.53/6.43 ((('#B') @ (
% 24.53/6.43 (('#B') @ (
% 24.53/6.43 (('#B') @ subset)))) @
% 24.53/6.43 dpsetconstr)))))) @
% 24.53/6.43 cartprod))))))))))))))))))))))))))))))))))))),
% 24.53/6.43 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1767])).
% 24.53/6.43 thf(zip_derived_cl1826, plain,
% 24.53/6.43 (~ (((setukpairinjR2) =>
% 24.53/6.43 (((setukpairinjR) =>
% 24.53/6.43 (((ksndsingleton) =>
% 24.53/6.43 (((ksndpairEq) =>
% 24.53/6.43 (((kpairsurjEq) =>
% 24.53/6.43 (((cartprodsndin) =>
% 24.53/6.43 (((cartprodpairmemEL) =>
% 24.53/6.43 (((cartprodpairmemER) =>
% 24.53/6.43 (((cartprodmempaircEq) =>
% 24.53/6.43 (((cartprodfstpairEq) =>
% 24.53/6.43 (((cartprodsndpairEq) =>
% 24.53/6.43 (((cartprodpairsurjEq) =>
% 24.53/6.43 (((dpsetconstrI) =>
% 24.53/6.43 (((!!) @ ((('#B') @ (!!) @
% 24.53/6.43 ((('#B') @ ((('#B') @ (!!))) @
% 24.53/6.43 ((('#S') @ ((('#B') @ (
% 24.53/6.43 '#S') @
% 24.53/6.43 ((('#B') @ (
% 24.53/6.43 (('#B') @ ('#C'))) @
% 24.53/6.43 ((('#B') @ (
% 24.53/6.43 (('#B') @ (
% 24.53/6.43 (('#B') @ subset)))) @
% 24.53/6.43 dpsetconstr)))))) @
% 24.53/6.43 cartprod))))))))))))))))))))))))))))))))))),
% 24.53/6.43 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1798])).
% 24.53/6.43 thf(zip_derived_cl1850, plain,
% 24.53/6.43 (~ (((setukpairinjR) =>
% 24.53/6.43 (((ksndsingleton) =>
% 24.53/6.43 (((ksndpairEq) =>
% 24.53/6.43 (((kpairsurjEq) =>
% 24.53/6.43 (((cartprodsndin) =>
% 24.53/6.43 (((cartprodpairmemEL) =>
% 24.53/6.43 (((cartprodpairmemER) =>
% 24.53/6.43 (((cartprodmempaircEq) =>
% 24.53/6.43 (((cartprodfstpairEq) =>
% 24.53/6.43 (((cartprodsndpairEq) =>
% 24.53/6.43 (((cartprodpairsurjEq) =>
% 24.53/6.43 (((dpsetconstrI) =>
% 24.53/6.43 (((!!) @ ((('#B') @ (!!) @
% 24.53/6.43 ((('#B') @ ((('#B') @ (!!))) @
% 24.53/6.43 ((('#S') @ ((('#B') @ ('#S') @
% 24.53/6.43 ((('#B') @ (
% 24.53/6.43 (('#B') @ ('#C'))) @
% 24.53/6.43 ((('#B') @ (
% 24.53/6.43 (('#B') @ (
% 24.53/6.43 (('#B') @ subset)))) @
% 24.53/6.43 dpsetconstr)))))) @
% 24.53/6.43 cartprod))))))))))))))))))))))))))))))))),
% 24.53/6.43 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1826])).
% 24.53/6.43 thf(zip_derived_cl1869, plain,
% 24.53/6.43 (~ (((ksndsingleton) =>
% 24.53/6.43 (((ksndpairEq) =>
% 24.53/6.43 (((kpairsurjEq) =>
% 24.53/6.43 (((cartprodsndin) =>
% 24.53/6.43 (((cartprodpairmemEL) =>
% 24.53/6.43 (((cartprodpairmemER) =>
% 24.53/6.43 (((cartprodmempaircEq) =>
% 24.53/6.43 (((cartprodfstpairEq) =>
% 24.53/6.43 (((cartprodsndpairEq) =>
% 24.53/6.43 (((cartprodpairsurjEq) =>
% 24.53/6.43 (((dpsetconstrI) =>
% 24.53/6.43 (((!!) @ ((('#B') @ (!!) @
% 24.53/6.43 ((('#B') @ ((('#B') @ (!!))) @
% 24.53/6.43 ((('#S') @ ((('#B') @ ('#S') @
% 24.53/6.43 ((('#B') @ ((('#B') @ (
% 24.53/6.43 '#C'))) @
% 24.53/6.43 ((('#B') @ (
% 24.53/6.43 (('#B') @ (
% 24.53/6.43 (('#B') @ subset)))) @
% 24.53/6.43 dpsetconstr)))))) @
% 24.53/6.43 cartprod))))))))))))))))))))))))))))))),
% 24.53/6.43 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1850])).
% 24.53/6.43 thf(zip_derived_cl1886, plain,
% 24.53/6.43 (~ (((ksndpairEq) =>
% 24.53/6.43 (((kpairsurjEq) =>
% 24.53/6.43 (((cartprodsndin) =>
% 24.53/6.43 (((cartprodpairmemEL) =>
% 24.53/6.43 (((cartprodpairmemER) =>
% 24.53/6.43 (((cartprodmempaircEq) =>
% 24.53/6.43 (((cartprodfstpairEq) =>
% 24.53/6.43 (((cartprodsndpairEq) =>
% 24.53/6.43 (((cartprodpairsurjEq) =>
% 24.53/6.43 (((dpsetconstrI) =>
% 24.53/6.43 (((!!) @ ((('#B') @ (!!) @
% 24.53/6.43 ((('#B') @ ((('#B') @ (!!))) @
% 24.53/6.43 ((('#S') @ ((('#B') @ ('#S') @
% 24.53/6.43 ((('#B') @ ((('#B') @ (
% 24.53/6.43 '#C'))) @
% 24.53/6.43 ((('#B') @ ((('#B') @ (
% 24.53/6.43 (
% 24.53/6.43 ('#B') @ subset)))) @
% 24.53/6.43 dpsetconstr)))))) @
% 24.53/6.43 cartprod))))))))))))))))))))))))))))),
% 24.53/6.43 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1869])).
% 24.53/6.43 thf(zip_derived_cl1898, plain,
% 24.53/6.43 (~ (((kpairsurjEq) =>
% 24.53/6.43 (((cartprodsndin) =>
% 24.53/6.43 (((cartprodpairmemEL) =>
% 24.53/6.43 (((cartprodpairmemER) =>
% 24.53/6.43 (((cartprodmempaircEq) =>
% 24.53/6.43 (((cartprodfstpairEq) =>
% 24.53/6.43 (((cartprodsndpairEq) =>
% 24.53/6.43 (((cartprodpairsurjEq) =>
% 24.53/6.43 (((dpsetconstrI) =>
% 24.53/6.43 (((!!) @ ((('#B') @ (!!) @
% 24.53/6.43 ((('#B') @ ((('#B') @ (!!))) @
% 24.53/6.43 ((('#S') @ ((('#B') @ ('#S') @
% 24.53/6.43 ((('#B') @ ((('#B') @ (
% 24.53/6.43 '#C'))) @
% 24.53/6.43 ((('#B') @ ((('#B') @ (
% 24.53/6.43 (('#B') @ subset)))) @
% 24.53/6.43 dpsetconstr)))))) @
% 24.53/6.43 cartprod))))))))))))))))))))))))))),
% 24.53/6.43 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1886])).
% 24.53/6.43 thf(zip_derived_cl1907, plain,
% 24.53/6.43 (~ (((cartprodsndin) =>
% 24.53/6.43 (((cartprodpairmemEL) =>
% 24.53/6.43 (((cartprodpairmemER) =>
% 24.53/6.43 (((cartprodmempaircEq) =>
% 24.53/6.43 (((cartprodfstpairEq) =>
% 24.53/6.43 (((cartprodsndpairEq) =>
% 24.53/6.43 (((cartprodpairsurjEq) =>
% 24.53/6.43 (((dpsetconstrI) =>
% 24.53/6.43 (((!!) @ ((('#B') @ (!!) @
% 24.53/6.43 ((('#B') @ ((('#B') @ (!!))) @
% 24.53/6.43 ((('#S') @ ((('#B') @ ('#S') @
% 24.53/6.43 ((('#B') @ ((('#B') @ ('#C'))) @
% 24.53/6.43 ((('#B') @ ((('#B') @ (
% 24.53/6.43 (('#B') @ subset)))) @
% 24.53/6.43 dpsetconstr)))))) @
% 24.53/6.43 cartprod))))))))))))))))))))))))),
% 24.53/6.43 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1898])).
% 24.53/6.43 thf(zip_derived_cl1918, plain,
% 24.53/6.43 (~ (((cartprodpairmemEL) =>
% 24.53/6.43 (((cartprodpairmemER) =>
% 24.53/6.43 (((cartprodmempaircEq) =>
% 24.53/6.43 (((cartprodfstpairEq) =>
% 24.53/6.43 (((cartprodsndpairEq) =>
% 24.53/6.43 (((cartprodpairsurjEq) =>
% 24.53/6.43 (((dpsetconstrI) =>
% 24.53/6.43 (((!!) @ ((('#B') @ (!!) @
% 24.53/6.43 ((('#B') @ ((('#B') @ (!!))) @
% 24.53/6.43 ((('#S') @ ((('#B') @ ('#S') @
% 24.53/6.43 ((('#B') @ ((('#B') @ ('#C'))) @
% 24.53/6.43 ((('#B') @ ((('#B') @ (
% 24.53/6.43 (('#B') @ subset)))) @
% 24.53/6.43 dpsetconstr)))))) @
% 24.53/6.43 cartprod))))))))))))))))))))))),
% 24.53/6.43 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1907])).
% 24.53/6.43 thf(zip_derived_cl1928, plain,
% 24.53/6.43 (~ (((cartprodpairmemER) =>
% 24.53/6.43 (((cartprodmempaircEq) =>
% 24.53/6.43 (((cartprodfstpairEq) =>
% 24.53/6.43 (((cartprodsndpairEq) =>
% 24.53/6.43 (((cartprodpairsurjEq) =>
% 24.53/6.43 (((dpsetconstrI) =>
% 24.53/6.43 (((!!) @ ((('#B') @ (!!) @
% 24.53/6.43 ((('#B') @ ((('#B') @ (!!))) @
% 24.53/6.43 ((('#S') @ ((('#B') @ ('#S') @
% 24.53/6.43 ((('#B') @ ((('#B') @ ('#C'))) @
% 24.53/6.43 ((('#B') @ ((('#B') @ (
% 24.53/6.43 (('#B') @ subset)))) @
% 24.53/6.43 dpsetconstr)))))) @
% 24.53/6.43 cartprod))))))))))))))))))))),
% 24.53/6.43 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1918])).
% 24.53/6.43 thf(zip_derived_cl1939, plain,
% 24.53/6.43 (~ (((cartprodmempaircEq) =>
% 24.53/6.43 (((cartprodfstpairEq) =>
% 24.53/6.43 (((cartprodsndpairEq) =>
% 24.53/6.43 (((cartprodpairsurjEq) =>
% 24.53/6.43 (((dpsetconstrI) =>
% 24.53/6.43 (((!!) @ ((('#B') @ (!!) @
% 24.53/6.43 ((('#B') @ ((('#B') @ (!!))) @
% 24.53/6.43 ((('#S') @ ((('#B') @ ('#S') @
% 24.53/6.43 ((('#B') @ ((('#B') @ ('#C'))) @
% 24.53/6.43 ((('#B') @ ((('#B') @ ((
% 24.53/6.43 ('#B') @ subset)))) @
% 24.53/6.43 dpsetconstr)))))) @
% 24.53/6.43 cartprod))))))))))))))))))),
% 24.53/6.43 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1928])).
% 24.53/6.43 thf(zip_derived_cl1949, plain,
% 24.53/6.43 (~ (((cartprodfstpairEq) =>
% 24.53/6.43 (((cartprodsndpairEq) =>
% 24.53/6.43 (((cartprodpairsurjEq) =>
% 24.53/6.43 (((dpsetconstrI) =>
% 24.53/6.43 (((!!) @ ((('#B') @ (!!) @
% 24.53/6.43 ((('#B') @ ((('#B') @ (!!))) @
% 24.53/6.43 ((('#S') @ ((('#B') @ ('#S') @
% 24.53/6.43 ((('#B') @ ((('#B') @ ('#C'))) @
% 24.53/6.43 ((('#B') @ ((('#B') @ ((('#B') @ subset)))) @
% 24.53/6.43 dpsetconstr)))))) @
% 24.53/6.43 cartprod))))))))))))))))),
% 24.53/6.43 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1939])).
% 24.53/6.43 thf(zip_derived_cl1957, plain,
% 24.53/6.43 (~ (((cartprodsndpairEq) =>
% 24.53/6.43 (((cartprodpairsurjEq) =>
% 24.53/6.43 (((dpsetconstrI) =>
% 24.53/6.43 (((!!) @ ((('#B') @ (!!) @
% 24.53/6.43 ((('#B') @ ((('#B') @ (!!))) @
% 24.53/6.43 ((('#S') @ ((('#B') @ ('#S') @
% 24.53/6.43 ((('#B') @ ((('#B') @ ('#C'))) @
% 24.53/6.43 ((('#B') @ ((('#B') @ ((('#B') @ subset)))) @
% 24.53/6.43 dpsetconstr)))))) @
% 24.53/6.43 cartprod))))))))))))))),
% 24.53/6.43 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1949])).
% 24.53/6.43 thf(zip_derived_cl1965, plain,
% 24.53/6.43 (~ (((cartprodpairsurjEq) =>
% 24.53/6.43 (((dpsetconstrI) =>
% 24.53/6.43 (((!!) @ ((('#B') @ (!!) @
% 24.53/6.43 ((('#B') @ ((('#B') @ (!!))) @
% 24.53/6.43 ((('#S') @ ((('#B') @ ('#S') @
% 24.53/6.43 ((('#B') @ ((('#B') @ ('#C'))) @
% 24.53/6.43 ((('#B') @ ((('#B') @ ((('#B') @ subset)))) @
% 24.53/6.43 dpsetconstr)))))) @
% 24.53/6.43 cartprod))))))))))))),
% 24.53/6.43 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1957])).
% 24.53/6.43 thf(zip_derived_cl1973, plain,
% 24.53/6.43 (~ (((dpsetconstrI) =>
% 24.53/6.43 (((!!) @ ((('#B') @ (!!) @
% 24.53/6.43 ((('#B') @ ((('#B') @ (!!))) @
% 24.53/6.43 ((('#S') @ ((('#B') @ ('#S') @
% 24.53/6.43 ((('#B') @ ((('#B') @ ('#C'))) @
% 24.53/6.43 ((('#B') @ ((('#B') @ ((('#B') @ subset)))) @
% 24.53/6.43 dpsetconstr)))))) @
% 24.53/6.43 cartprod))))))))))),
% 24.53/6.43 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1965])).
% 24.53/6.43 thf(zip_derived_cl1982, plain,
% 24.53/6.43 (~ (((!!) @ ((('#B') @ (!!) @
% 24.53/6.43 ((('#B') @ ((('#B') @ (!!))) @
% 24.53/6.43 ((('#S') @ ((('#B') @ ('#S') @
% 24.53/6.43 ((('#B') @ ((('#B') @ ('#C'))) @
% 24.53/6.43 ((('#B') @ ((('#B') @ ((('#B') @ subset)))) @
% 24.53/6.43 dpsetconstr)))))) @
% 24.53/6.43 cartprod))))))))),
% 24.53/6.43 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1973])).
% 24.53/6.43 thf(zip_derived_cl1990, plain,
% 24.53/6.43 (~ (((!!) @ ((('#B') @ (!!) @
% 24.53/6.43 ((('#S') @ ((('#B') @ ('#C') @
% 24.53/6.43 ((('#B') @ ((('#B') @ subset)) @
% 24.53/6.43 (dpsetconstr @ '#sk36'))))) @
% 24.53/6.43 (cartprod @ '#sk36')))))))),
% 24.53/6.43 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1982])).
% 24.53/6.43 thf(zip_derived_cl1997, plain,
% 24.53/6.43 (~ (((!!) @ ((('#C') @ ((('#B') @ subset @
% 24.53/6.43 (dpsetconstr @ '#sk36' @ '#sk37'))) @
% 24.53/6.43 (cartprod @ '#sk36' @ '#sk37')))))),
% 24.53/6.43 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1990])).
% 24.53/6.43 thf(zip_derived_cl2003, plain,
% 24.53/6.43 (~ (subset @ (dpsetconstr @ '#sk36' @ '#sk37' @ '#sk38') @
% 24.53/6.43 (cartprod @ '#sk36' @ '#sk37'))),
% 24.53/6.43 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1997])).
% 24.53/6.43 thf(dpsetconstr, axiom,(( dpsetconstr @ (X0)@ (X1)@ (X2)) =
% 24.53/6.43 ((dsetconstr @ (cartprod @ X0 @ X1) @
% 24.53/6.43 (^[Y0 : $i]:
% 24.53/6.43 (((??) @ (^[Y1 : $i]:
% 24.53/6.43 (((in @ Y1 @ X0) &
% 24.53/6.43 (((??) @ (^[Y2 : $i]:
% 24.53/6.43 (((in @ Y2 @ X1) & (X2 @ Y1 @ Y2) &
% 24.53/6.43 (((Y0) = (kpair @ Y1 @ Y2)))))))))))))))))).
% 24.53/6.43 thf('4', plain,
% 24.53/6.43 (![X2:( $i > $i > $o ),X1:$i,X0:$i]:
% 24.53/6.43 ( ( dpsetconstr @ X0 @ X1 @ X2 ) =
% 24.53/6.43 ( dsetconstr @
% 24.53/6.43 ( cartprod @ X0 @ X1 ) @
% 24.53/6.43 ( ^[V_1:$i]:
% 24.53/6.43 ( ?[X6:$i]:
% 24.53/6.43 ( ( in @ X6 @ X0 ) &
% 24.53/6.43 ( ?[X8:$i]:
% 24.53/6.43 ( ( in @ X8 @ X1 ) & ( X2 @ X6 @ X8 ) &
% 24.53/6.43 ( ( V_1 ) = ( kpair @ X6 @ X8 ) ) ) ) ) ) ) ) )),
% 24.53/6.43 define([status(thm)])).
% 24.53/6.43 thf(zip_derived_cl2008, plain,
% 24.53/6.43 (~ (subset @
% 24.53/6.43 (dsetconstr @ (cartprod @ '#sk36' @ '#sk37') @
% 24.53/6.43 ((('#B') @ (??) @
% 24.53/6.43 ((('#B') @ ((('#S') @ ((('#B') @ (&) @ ((('#C') @ in @ '#sk36')))))) @
% 24.53/6.43 ((('#B') @ ((('#B') @ (??))) @
% 24.53/6.43 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @
% 24.53/6.43 ((('#B') @ ((('#S') @ ((('#B') @ (
% 24.53/6.43 &) @
% 24.53/6.43 ((('#C') @ in @
% 24.53/6.43 '#sk37')))))) @
% 24.53/6.43 '#sk38')))))) @
% 24.53/6.43 ((('#C') @ ((('#B') @ ('#B') @ ((('#B') @ ('#B') @ (=))))) @
% 24.53/6.43 kpair))))))))))) @
% 24.53/6.43 (cartprod @ '#sk36' @ '#sk37'))),
% 24.53/6.43 inference('rw', [status(thm)], [zip_derived_cl2003, '4'])).
% 24.53/6.43 thf(zip_derived_cl1095, plain, ( (sepSubset)),
% 24.53/6.43 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1090])).
% 24.53/6.43 thf(sepSubset, axiom, (sepSubset) =>
% 24.53/6.43 ((((!!) @ (^[Y0 : $i]:
% 24.53/6.43 (((!!) @ (^[Y1 : $i > $o]:
% 24.53/6.43 (subset @
% 24.53/6.43 (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))) @ Y0)))))))
% 24.53/6.43 = ($true))).
% 24.53/6.43 thf('5', plain,
% 24.53/6.43 (( sepSubset ) <=>
% 24.53/6.43 ( ![X5:$i,X7:( $i > $o )]:
% 24.53/6.43 ( subset @ ( dsetconstr @ X5 @ ( ^[V_1:$i]: ( X7 @ V_1 ) ) ) @ X5 ) )),
% 24.53/6.43 inference('rw.lit', [status(esa)], [sepSubset])).
% 24.53/6.43 thf(zip_derived_cl1100, plain,
% 24.53/6.43 ( (((!!) @ (^[Y0 : $i]:
% 24.53/6.43 (((!!) @ (^[Y1 : $i > $o]:
% 24.53/6.43 (subset @
% 24.53/6.43 (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))) @
% 24.53/6.43 Y0)))))))),
% 24.53/6.43 inference('rw_clause', [status(thm)], [zip_derived_cl1095, '5'])).
% 24.53/6.43 thf(zip_derived_cl1105, plain,
% 24.53/6.43 ( (((!!) @ ((('#B') @ (!!) @
% 24.53/6.43 ((('#S') @ ((('#B') @ ('#C') @
% 24.53/6.43 ((('#B') @ ((('#B') @ subset)) @ dsetconstr)))) @
% 24.53/6.43 ('#I')))))))),
% 24.53/6.43 inference('comb-normalize', [status(thm)], [zip_derived_cl1100])).
% 24.53/6.43 thf(zip_derived_cl1106, plain,
% 24.53/6.43 (![X2 : $i]:
% 24.53/6.43 (((!!) @ ((('#C') @ ((('#B') @ subset @ (dsetconstr @ X2))) @ X2))))),
% 24.53/6.43 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1105])).
% 24.53/6.43 thf(zip_derived_cl1110, plain,
% 24.53/6.43 (![X2 : $i, X4 : $i > $o]: (subset @ (dsetconstr @ X2 @ X4) @ X2)),
% 24.53/6.43 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1106])).
% 24.53/6.43 thf(zip_derived_cl2028, plain, ($false),
% 24.53/6.43 inference('demod', [status(thm)],
% 24.53/6.43 [zip_derived_cl2008, zip_derived_cl1110])).
% 24.53/6.43
% 24.53/6.43 % SZS output end Refutation
% 24.53/6.43
% 24.53/6.43
% 24.53/6.43 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s
% 24.53/6.43 % Terminating...
% 25.32/6.62 % Runner terminated.
% 25.32/6.64 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------