%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU585^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.8WbxdpG53r true
% Computer : n007.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 Aug 31 19:14:09 EDT 2023
% Result : Theorem 120.37s 16.01s
% Output : Refutation 120.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU585^1 : TPTP v8.1.2. Released v3.7.0.
% 0.07/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.8WbxdpG53r true
% 0.14/0.34 % Computer : n007.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Aug 24 00:04:39 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % Running portfolio for 300 s
% 0.14/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.35 % Number of cores: 8
% 0.19/0.35 % Python version: Python 3.6.8
% 0.20/0.35 % Running in HO mode
% 0.20/0.68 % Total configuration time : 828
% 0.20/0.68 % Estimated wc time : 1656
% 0.20/0.68 % Estimated cpu time (8 cpus) : 207.0
% 0.20/0.71 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.20/0.74 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.20/0.75 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.20/0.75 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 1.39/0.77 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 1.39/0.77 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 1.39/0.77 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 1.39/0.78 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.45/0.84 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s
% 120.37/16.01 % Solved by lams/30_b.l.sh.
% 120.37/16.01 % done 503 iterations in 15.057s
% 120.37/16.01 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 120.37/16.01 % SZS output start Refutation
% 120.37/16.01 thf(setadjoinAx_type, type, setadjoinAx: $o).
% 120.37/16.01 thf(notdexE_type, type, notdexE: $o).
% 120.37/16.01 thf(setunionAx_type, type, setunionAx: $o).
% 120.37/16.01 thf(upairset2IR_type, type, upairset2IR: $o).
% 120.37/16.01 thf(powersetE_type, type, powersetE: $o).
% 120.37/16.01 thf(omegaSAx_type, type, omegaSAx: $o).
% 120.37/16.01 thf(exuI1_type, type, exuI1: $o).
% 120.37/16.01 thf(exuI2_type, type, exuI2: $o).
% 120.37/16.01 thf(notequalI2_type, type, notequalI2: $o).
% 120.37/16.01 thf(powerset__Cong_type, type, powerset__Cong: $o).
% 120.37/16.01 thf(wellorderingAx_type, type, wellorderingAx: $o).
% 120.37/16.01 thf(setadjoinSub2_type, type, setadjoinSub2: $o).
% 120.37/16.01 thf(setoftrueEq_type, type, setoftrueEq: $o).
% 120.37/16.01 thf(emptyset__Cong_type, type, emptyset__Cong: $o).
% 120.37/16.01 thf(sepInPowerset_type, type, sepInPowerset: $o).
% 120.37/16.01 thf(setext_type, type, setext: $o).
% 120.37/16.01 thf(emptyinPowerset_type, type, emptyinPowerset: $o).
% 120.37/16.01 thf(descr__Cong_type, type, descr__Cong: $o).
% 120.37/16.01 thf(in_type, type, in: $i > $i > $o).
% 120.37/16.01 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o).
% 120.37/16.01 thf(binunion_type, type, binunion: $i > $i > $i).
% 120.37/16.01 thf(setadjoinIR_type, type, setadjoinIR: $o).
% 120.37/16.01 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o).
% 120.37/16.01 thf(subsetE_type, type, subsetE: $o).
% 120.37/16.01 thf(prop2set2propI_type, type, prop2set2propI: $o).
% 120.37/16.01 thf(dsetconstrEL_type, type, dsetconstrEL: $o).
% 120.37/16.01 thf(setbeta_type, type, setbeta: $o).
% 120.37/16.01 thf(eqinunit_type, type, eqinunit: $o).
% 120.37/16.01 thf(upairsetIL_type, type, upairsetIL: $o).
% 120.37/16.01 thf(powersetI1_type, type, powersetI1: $o).
% 120.37/16.01 thf(powersetAx_type, type, powersetAx: $o).
% 120.37/16.01 thf(powersetI_type, type, powersetI: $o).
% 120.37/16.01 thf(upairsetIR_type, type, upairsetIR: $o).
% 120.37/16.01 thf(inCongP_type, type, inCongP: $o).
% 120.37/16.01 thf(setadjoinSub_type, type, setadjoinSub: $o).
% 120.37/16.01 thf(exuE3e_type, type, exuE3e: $o).
% 120.37/16.01 thf(emptysetE_type, type, emptysetE: $o).
% 120.37/16.01 thf('#form251_type', type, '#form251': $i > $i > $o > $o).
% 120.37/16.01 thf(setunionI_type, type, setunionI: $o).
% 120.37/16.01 thf(setunion__Cong_type, type, setunion__Cong: $o).
% 120.37/16.01 thf(prop2setI_type, type, prop2setI: $o).
% 120.37/16.01 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o).
% 120.37/16.01 thf(exuE2_type, type, exuE2: $o).
% 120.37/16.01 thf(emptyset_type, type, emptyset: $i).
% 120.37/16.01 thf(powersetsubset_type, type, powersetsubset: $o).
% 120.37/16.01 thf(subPowSU_type, type, subPowSU: $o).
% 120.37/16.01 thf(notequalI1_type, type, notequalI1: $o).
% 120.37/16.01 thf(notinemptyset_type, type, notinemptyset: $o).
% 120.37/16.01 thf(nonemptyI1_type, type, nonemptyI1: $o).
% 120.37/16.01 thf(subsetTrans_type, type, subsetTrans: $o).
% 120.37/16.01 thf('#sk256_type', type, '#sk256': $i > $i > $o > $i).
% 120.37/16.01 thf(subsetE2_type, type, subsetE2: $o).
% 120.37/16.01 thf(singletonsswitch_type, type, singletonsswitch: $o).
% 120.37/16.01 thf(setextsub_type, type, setextsub: $o).
% 120.37/16.01 thf('#sk783_type', type, '#sk783': $i).
% 120.37/16.01 thf(emptysetsubset_type, type, emptysetsubset: $o).
% 120.37/16.01 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o).
% 120.37/16.01 thf(setunionE_type, type, setunionE: $o).
% 120.37/16.01 thf(emptyinunitempty_type, type, emptyinunitempty: $o).
% 120.37/16.01 thf(setadjoinE_type, type, setadjoinE: $o).
% 120.37/16.01 thf(setadjoinIL_type, type, setadjoinIL: $o).
% 120.37/16.01 thf(exuE1_type, type, exuE1: $o).
% 120.37/16.01 thf(notinsingleton_type, type, notinsingleton: $o).
% 120.37/16.01 thf(eqimpsubset2_type, type, eqimpsubset2: $o).
% 120.37/16.01 thf(exuEu_type, type, exuEu: $o).
% 120.37/16.01 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o).
% 120.37/16.01 thf(upairsetE_type, type, upairsetE: $o).
% 120.37/16.01 thf(omega0Ax_type, type, omega0Ax: $o).
% 120.37/16.01 thf(notsubsetI_type, type, notsubsetI: $o).
% 120.37/16.01 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o).
% 120.37/16.01 thf(setextAx_type, type, setextAx: $o).
% 120.37/16.01 thf(powersetE1_type, type, powersetE1: $o).
% 120.37/16.01 thf(noeltsimpempty_type, type, noeltsimpempty: $o).
% 120.37/16.01 thf(setunion_type, type, setunion: $i > $i).
% 120.37/16.01 thf(subsetI1_type, type, subsetI1: $o).
% 120.37/16.01 thf(descrp_type, type, descrp: $o).
% 120.37/16.01 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o).
% 120.37/16.01 thf(foundationAx_type, type, foundationAx: $o).
% 120.37/16.01 thf(emptysetAx_type, type, emptysetAx: $o).
% 120.37/16.01 thf(emptyI_type, type, emptyI: $o).
% 120.37/16.01 thf(setadjoinOr_type, type, setadjoinOr: $o).
% 120.37/16.01 thf(emptyE1_type, type, emptyE1: $o).
% 120.37/16.01 thf(emptyInPowerset_type, type, emptyInPowerset: $o).
% 120.37/16.01 thf(vacuousDall_type, type, vacuousDall: $o).
% 120.37/16.01 thf(dsetconstrER_type, type, dsetconstrER: $o).
% 120.37/16.01 thf('#sk781_type', type, '#sk781': $i).
% 120.37/16.01 thf('#sk784_type', type, '#sk784': $o).
% 120.37/16.01 thf(subsetI2_type, type, subsetI2: $o).
% 120.37/16.01 thf(binunionIR_type, type, binunionIR: $o).
% 120.37/16.01 thf(omega__Cong_type, type, omega__Cong: $o).
% 120.37/16.01 thf(subsetRefl_type, type, subsetRefl: $o).
% 120.37/16.01 thf('#sk782_type', type, '#sk782': $i).
% 120.37/16.01 thf(uniqinunit_type, type, uniqinunit: $o).
% 120.37/16.01 thf(prop2setE_type, type, prop2setE: $o).
% 120.37/16.01 thf(omega_type, type, omega: $i).
% 120.37/16.01 thf(nonemptyI_type, type, nonemptyI: $o).
% 120.37/16.01 thf(exuE3u_type, type, exuE3u: $o).
% 120.37/16.01 thf(sepSubset_type, type, sepSubset: $o).
% 120.37/16.01 thf(eqimpsubset1_type, type, eqimpsubset1: $o).
% 120.37/16.01 thf(exuI3_type, type, exuI3: $o).
% 120.37/16.01 thf(notdallE_type, type, notdallE: $o).
% 120.37/16.01 thf(dsetconstrI_type, type, dsetconstrI: $o).
% 120.37/16.01 thf(setadjoin_type, type, setadjoin: $i > $i > $i).
% 120.37/16.01 thf(exu__Cong_type, type, exu__Cong: $o).
% 120.37/16.01 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o).
% 120.37/16.01 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o).
% 120.37/16.01 thf(replAx_type, type, replAx: $o).
% 120.37/16.01 thf(nonemptyE1_type, type, nonemptyE1: $o).
% 120.37/16.01 thf(omegaIndAx_type, type, omegaIndAx: $o).
% 120.37/16.01 thf(inPowerset_type, type, inPowerset: $o).
% 120.37/16.01 thf(binunionIL_type, type, binunionIL: $o).
% 120.37/16.01 thf(in__Cong_type, type, in__Cong: $o).
% 120.37/16.01 thf(subset2powerset_type, type, subset2powerset: $o).
% 120.37/16.01 thf(binunionEcases, conjecture,
% 120.37/16.01 (( setextAx ) =>
% 120.37/16.01 ( ( emptysetAx ) =>
% 120.37/16.01 ( ( setadjoinAx ) =>
% 120.37/16.01 ( ( powersetAx ) =>
% 120.37/16.01 ( ( setunionAx ) =>
% 120.37/16.01 ( ( omega0Ax ) =>
% 120.37/16.01 ( ( omegaSAx ) =>
% 120.37/16.01 ( ( omegaIndAx ) =>
% 120.37/16.01 ( ( replAx ) =>
% 120.37/16.01 ( ( foundationAx ) =>
% 120.37/16.01 ( ( wellorderingAx ) =>
% 120.37/16.01 ( ( descrp ) =>
% 120.37/16.01 ( ( dsetconstrI ) =>
% 120.37/16.01 ( ( dsetconstrEL ) =>
% 120.37/16.01 ( ( dsetconstrER ) =>
% 120.37/16.01 ( ( exuE1 ) =>
% 120.37/16.01 ( ( prop2setE ) =>
% 120.37/16.01 ( ( emptysetE ) =>
% 120.37/16.01 ( ( emptysetimpfalse ) =>
% 120.37/16.01 ( ( notinemptyset ) =>
% 120.37/16.01 ( ( exuE3e ) =>
% 120.37/16.01 ( ( setext ) =>
% 120.37/16.01 ( ( emptyI ) =>
% 120.37/16.01 ( ( noeltsimpempty ) =>
% 120.37/16.01 ( ( setbeta ) =>
% 120.37/16.01 ( ( nonemptyE1 ) =>
% 120.37/16.01 ( ( nonemptyI ) =>
% 120.37/16.01 ( ( nonemptyI1 ) =>
% 120.37/16.01 ( ( setadjoinIL ) =>
% 120.37/16.01 ( ( emptyinunitempty ) =>
% 120.37/16.01 ( ( setadjoinIR ) =>
% 120.37/16.01 ( ( setadjoinE ) =>
% 120.37/16.01 ( (
% 120.37/16.01 setadjoinOr ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 setoftrueEq ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 powersetI ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 emptyinPowerset ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 emptyInPowerset ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 powersetE ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 setunionI ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 setunionE ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 subPowSU ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 exuE2 ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 nonemptyImpWitness ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 uniqinunit ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 notinsingleton ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 eqinunit ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 singletonsswitch ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 upairsetE ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 upairsetIL ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 upairsetIR ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 emptyE1 ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 vacuousDall ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 quantDeMorgan1 ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 quantDeMorgan2 ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 quantDeMorgan3 ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 quantDeMorgan4 ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 prop2setI ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 prop2set2propI ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 notdexE ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 notdallE ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 exuI1 ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 exuI3 ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 exuI2 ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 inCongP ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 in__Cong ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 exuE3u ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 exu__Cong ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 emptyset__Cong ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 setadjoin__Cong ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 powerset__Cong ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 setunion__Cong ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 omega__Cong ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 exuEu ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 descr__Cong ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 dsetconstr__Cong ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 subsetI1 ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 eqimpsubset2 ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 eqimpsubset1 ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 subsetI2 ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 emptysetsubset ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 subsetE ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 subsetE2 ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 notsubsetI ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 notequalI1 ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 notequalI2 ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 subsetRefl ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 subsetTrans ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 setadjoinSub ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 setadjoinSub2 ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 subset2powerset ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 setextsub ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 subsetemptysetimpeq ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 powersetI1 ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 powersetE1 ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 inPowerset ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 powersetsubset ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 sepInPowerset ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 sepSubset ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 binunionIL ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 upairset2IR ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 binunionIR ) =>
% 120.37/16.01 (
% 120.37/16.01 ![
% 120.37/16.01 A:$i,B:$i,
% 120.37/16.01 Xx:$i,
% 120.37/16.01 Xphi:$o]:
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 in @
% 120.37/16.01 Xx @
% 120.37/16.01 (
% 120.37/16.01 binunion @
% 120.37/16.01 A @ B ) ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 in @
% 120.37/16.01 Xx @ A ) =>
% 120.37/16.01 (
% 120.37/16.01 Xphi ) ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 in @
% 120.37/16.01 Xx @ B ) =>
% 120.37/16.01 (
% 120.37/16.01 Xphi ) ) =>
% 120.37/16.01 (
% 120.37/16.01 Xphi ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 120.37/16.01 thf(zf_stmt_0, negated_conjecture,
% 120.37/16.01 (~( ( setextAx ) =>
% 120.37/16.01 ( ( emptysetAx ) =>
% 120.37/16.01 ( ( setadjoinAx ) =>
% 120.37/16.01 ( ( powersetAx ) =>
% 120.37/16.01 ( ( setunionAx ) =>
% 120.37/16.01 ( ( omega0Ax ) =>
% 120.37/16.01 ( ( omegaSAx ) =>
% 120.37/16.01 ( ( omegaIndAx ) =>
% 120.37/16.01 ( ( replAx ) =>
% 120.37/16.01 ( ( foundationAx ) =>
% 120.37/16.01 ( ( wellorderingAx ) =>
% 120.37/16.01 ( ( descrp ) =>
% 120.37/16.01 ( ( dsetconstrI ) =>
% 120.37/16.01 ( ( dsetconstrEL ) =>
% 120.37/16.01 ( ( dsetconstrER ) =>
% 120.37/16.01 ( ( exuE1 ) =>
% 120.37/16.01 ( ( prop2setE ) =>
% 120.37/16.01 ( ( emptysetE ) =>
% 120.37/16.01 ( ( emptysetimpfalse ) =>
% 120.37/16.01 ( ( notinemptyset ) =>
% 120.37/16.01 ( ( exuE3e ) =>
% 120.37/16.01 ( ( setext ) =>
% 120.37/16.01 ( ( emptyI ) =>
% 120.37/16.01 ( ( noeltsimpempty ) =>
% 120.37/16.01 ( ( setbeta ) =>
% 120.37/16.01 ( ( nonemptyE1 ) =>
% 120.37/16.01 ( ( nonemptyI ) =>
% 120.37/16.01 ( ( nonemptyI1 ) =>
% 120.37/16.01 ( ( setadjoinIL ) =>
% 120.37/16.01 ( ( emptyinunitempty ) =>
% 120.37/16.01 ( ( setadjoinIR ) =>
% 120.37/16.01 ( (
% 120.37/16.01 setadjoinE ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 setadjoinOr ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 setoftrueEq ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 powersetI ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 emptyinPowerset ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 emptyInPowerset ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 powersetE ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 setunionI ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 setunionE ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 subPowSU ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 exuE2 ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 nonemptyImpWitness ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 uniqinunit ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 notinsingleton ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 eqinunit ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 singletonsswitch ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 upairsetE ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 upairsetIL ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 upairsetIR ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 emptyE1 ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 vacuousDall ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 quantDeMorgan1 ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 quantDeMorgan2 ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 quantDeMorgan3 ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 quantDeMorgan4 ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 prop2setI ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 prop2set2propI ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 notdexE ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 notdallE ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 exuI1 ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 exuI3 ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 exuI2 ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 inCongP ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 in__Cong ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 exuE3u ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 exu__Cong ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 emptyset__Cong ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 setadjoin__Cong ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 powerset__Cong ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 setunion__Cong ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 omega__Cong ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 exuEu ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 descr__Cong ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 dsetconstr__Cong ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 subsetI1 ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 eqimpsubset2 ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 eqimpsubset1 ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 subsetI2 ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 emptysetsubset ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 subsetE ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 subsetE2 ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 notsubsetI ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 notequalI1 ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 notequalI2 ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 subsetRefl ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 subsetTrans ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 setadjoinSub ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 setadjoinSub2 ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 subset2powerset ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 setextsub ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 subsetemptysetimpeq ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 powersetI1 ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 powersetE1 ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 inPowerset ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 powersetsubset ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 sepInPowerset ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 sepSubset ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 binunionIL ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 upairset2IR ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 binunionIR ) =>
% 120.37/16.01 (
% 120.37/16.01 ![
% 120.37/16.01 A:$i,
% 120.37/16.01 B:$i,
% 120.37/16.01 Xx:$i,
% 120.37/16.01 Xphi:$o]:
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 in @
% 120.37/16.01 Xx @
% 120.37/16.01 (
% 120.37/16.01 binunion
% 120.37/16.01 @
% 120.37/16.01 A @ B ) ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 in @
% 120.37/16.01 Xx @ A ) =>
% 120.37/16.01 (
% 120.37/16.01 Xphi ) ) =>
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 (
% 120.37/16.01 in @
% 120.37/16.01 Xx @ B ) =>
% 120.37/16.01 (
% 120.37/16.01 Xphi ) ) =>
% 120.37/16.01 (
% 120.37/16.01 Xphi ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 120.37/16.01 inference('cnf.neg', [status(esa)], [binunionEcases])).
% 120.37/16.01 thf(zip_derived_cl0, plain,
% 120.37/16.01 (~ (((setextAx) =>
% 120.37/16.01 (((emptysetAx) =>
% 120.37/16.01 (((setadjoinAx) =>
% 120.37/16.01 (((powersetAx) =>
% 120.37/16.01 (((setunionAx) =>
% 120.37/16.01 (((omega0Ax) =>
% 120.37/16.01 (((omegaSAx) =>
% 120.37/16.01 (((omegaIndAx) =>
% 120.37/16.01 (((replAx) =>
% 120.37/16.01 (((foundationAx) =>
% 120.37/16.01 (((wellorderingAx) =>
% 120.37/16.01 (((descrp) =>
% 120.37/16.01 (((dsetconstrI) =>
% 120.37/16.01 (((dsetconstrEL) =>
% 120.37/16.01 (((dsetconstrER) =>
% 120.37/16.01 (((exuE1) =>
% 120.37/16.01 (((prop2setE) =>
% 120.37/16.01 (((emptysetE) =>
% 120.37/16.01 (((emptysetimpfalse) =>
% 120.37/16.01 (((notinemptyset) =>
% 120.37/16.01 (((exuE3e) =>
% 120.37/16.01 (((setext) =>
% 120.37/16.01 (((emptyI) =>
% 120.37/16.01 (((noeltsimpempty) =>
% 120.37/16.01 (((setbeta) =>
% 120.37/16.01 (((nonemptyE1) =>
% 120.37/16.01 (((nonemptyI) =>
% 120.37/16.01 (((nonemptyI1) =>
% 120.37/16.01 (((setadjoinIL) =>
% 120.37/16.01 (((emptyinunitempty) =>
% 120.37/16.01 ((
% 120.37/16.01 (setadjoinIR) =>
% 120.37/16.01 ((
% 120.37/16.01 (setadjoinE) =>
% 120.37/16.01 ((
% 120.37/16.01 (setadjoinOr) =>
% 120.37/16.01 ((
% 120.37/16.01 (setoftrueEq) =>
% 120.37/16.01 ((
% 120.37/16.01 (powersetI) =>
% 120.37/16.01 ((
% 120.37/16.01 (emptyinPowerset) =>
% 120.37/16.01 ((
% 120.37/16.01 (emptyInPowerset) =>
% 120.37/16.01 ((
% 120.37/16.01 (powersetE) =>
% 120.37/16.01 ((
% 120.37/16.01 (setunionI) =>
% 120.37/16.01 ((
% 120.37/16.01 (setunionE) =>
% 120.37/16.01 ((
% 120.37/16.01 (subPowSU) =>
% 120.37/16.01 ((
% 120.37/16.01 (exuE2) =>
% 120.37/16.01 ((
% 120.37/16.01 (nonemptyImpWitness) =>
% 120.37/16.01 ((
% 120.37/16.01 (uniqinunit) =>
% 120.37/16.01 ((
% 120.37/16.01 (notinsingleton) =>
% 120.37/16.01 ((
% 120.37/16.01 (eqinunit) =>
% 120.37/16.01 ((
% 120.37/16.01 (singletonsswitch) =>
% 120.37/16.01 ((
% 120.37/16.01 (upairsetE) =>
% 120.37/16.01 ((
% 120.37/16.01 (upairsetIL) =>
% 120.37/16.01 ((
% 120.37/16.01 (upairsetIR) =>
% 120.37/16.01 ((
% 120.37/16.01 (emptyE1) =>
% 120.37/16.01 ((
% 120.37/16.01 (vacuousDall) =>
% 120.37/16.01 ((
% 120.37/16.01 (quantDeMorgan1) =>
% 120.37/16.01 ((
% 120.37/16.01 (quantDeMorgan2) =>
% 120.37/16.01 ((
% 120.37/16.01 (quantDeMorgan3) =>
% 120.37/16.01 ((
% 120.37/16.01 (quantDeMorgan4) =>
% 120.37/16.01 ((
% 120.37/16.01 (prop2setI) =>
% 120.37/16.01 ((
% 120.37/16.01 (prop2set2propI) =>
% 120.37/16.01 ((
% 120.37/16.01 (notdexE) =>
% 120.37/16.01 ((
% 120.37/16.01 (notdallE) =>
% 120.37/16.01 ((
% 120.37/16.01 (exuI1) =>
% 120.37/16.01 ((
% 120.37/16.01 (exuI3) =>
% 120.37/16.01 ((
% 120.37/16.01 (exuI2) =>
% 120.37/16.01 ((
% 120.37/16.01 (inCongP) =>
% 120.37/16.01 ((
% 120.37/16.01 (in__Cong) =>
% 120.37/16.01 ((
% 120.37/16.01 (exuE3u) =>
% 120.37/16.01 ((
% 120.37/16.01 (exu__Cong) =>
% 120.37/16.01 ((
% 120.37/16.01 (emptyset__Cong) =>
% 120.37/16.01 ((
% 120.37/16.01 (setadjoin__Cong) =>
% 120.37/16.01 ((
% 120.37/16.01 (powerset__Cong) =>
% 120.37/16.01 ((
% 120.37/16.01 (setunion__Cong) =>
% 120.37/16.01 ((
% 120.37/16.01 (omega__Cong) =>
% 120.37/16.01 ((
% 120.37/16.01 (exuEu) =>
% 120.37/16.01 ((
% 120.37/16.01 (descr__Cong) =>
% 120.37/16.01 ((
% 120.37/16.01 (dsetconstr__Cong) =>
% 120.37/16.01 ((
% 120.37/16.01 (subsetI1) =>
% 120.37/16.01 ((
% 120.37/16.01 (eqimpsubset2) =>
% 120.37/16.01 ((
% 120.37/16.01 (eqimpsubset1) =>
% 120.37/16.01 ((
% 120.37/16.01 (subsetI2) =>
% 120.37/16.01 ((
% 120.37/16.01 (emptysetsubset) =>
% 120.37/16.01 ((
% 120.37/16.01 (subsetE) =>
% 120.37/16.01 ((
% 120.37/16.01 (subsetE2) =>
% 120.37/16.01 ((
% 120.37/16.01 (notsubsetI) =>
% 120.37/16.01 ((
% 120.37/16.01 (notequalI1) =>
% 120.37/16.01 ((
% 120.37/16.01 (notequalI2) =>
% 120.37/16.01 ((
% 120.37/16.01 (subsetRefl) =>
% 120.37/16.01 ((
% 120.37/16.01 (subsetTrans) =>
% 120.37/16.01 ((
% 120.37/16.01 (setadjoinSub) =>
% 120.37/16.01 ((
% 120.37/16.01 (setadjoinSub2) =>
% 120.37/16.01 ((
% 120.37/16.01 (subset2powerset) =>
% 120.37/16.01 ((
% 120.37/16.01 (setextsub) =>
% 120.37/16.01 ((
% 120.37/16.01 (subsetemptysetimpeq) =>
% 120.37/16.01 ((
% 120.37/16.01 (powersetI1) =>
% 120.37/16.01 ((
% 120.37/16.01 (powersetE1) =>
% 120.37/16.01 ((
% 120.37/16.01 (inPowerset) =>
% 120.37/16.01 ((
% 120.37/16.01 (powersetsubset) =>
% 120.37/16.01 ((
% 120.37/16.01 (sepInPowerset) =>
% 120.37/16.01 ((
% 120.37/16.01 (sepSubset) =>
% 120.37/16.01 ((
% 120.37/16.01 (binunionIL) =>
% 120.37/16.01 ((
% 120.37/16.01 (upairset2IR) =>
% 120.37/16.01 ((
% 120.37/16.01 (binunionIR) =>
% 120.37/16.01 ((
% 120.37/16.01 (!!) @ (
% 120.37/16.01 ^[Y0 : $i]:
% 120.37/16.01 ((
% 120.37/16.01 (!!) @ (
% 120.37/16.01 ^[Y1 : $i]:
% 120.37/16.01 ((
% 120.37/16.01 (!!) @ (
% 120.37/16.01 ^[Y2 : $i]:
% 120.37/16.01 ((
% 120.37/16.01 (!!) @ (
% 120.37/16.01 ^[Y3 : $o]:
% 120.37/16.01 ((
% 120.37/16.01 (in @
% 120.37/16.01 Y2 @
% 120.37/16.01 (
% 120.37/16.01 binunion @
% 120.37/16.01 Y0 @ Y1)) =>
% 120.37/16.02 ((
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 Y0) =>
% 120.37/16.02 (Y3))) =>
% 120.37/16.02 ((
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 Y1) =>
% 120.37/16.02 (Y3))) =>
% 120.37/16.02 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.02 inference('cnf', [status(esa)], [zf_stmt_0])).
% 120.37/16.02 thf(omega0Ax, axiom,(( omega0Ax ) = ((in @ emptyset @ omega)))).
% 120.37/16.02 thf('0', plain, (( omega0Ax ) = ( in @ emptyset @ omega )),
% 120.37/16.02 define([status(thm)])).
% 120.37/16.02 thf(emptyinunitempty, axiom,(( emptyinunitempty ) =
% 120.37/16.02 ((in @ emptyset @ (setadjoin @ emptyset @ emptyset))))).
% 120.37/16.02 thf('1', plain,
% 120.37/16.02 (( emptyinunitempty ) =
% 120.37/16.02 ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )),
% 120.37/16.02 define([status(thm)])).
% 120.37/16.02 thf(emptyset__Cong, axiom,(( emptyset__Cong ) =
% 120.37/16.02 ((((emptyset) = (emptyset)))))).
% 120.37/16.02 thf('2', plain, (( emptyset__Cong ) = ( ( emptyset ) = ( emptyset ) )),
% 120.37/16.02 define([status(thm)])).
% 120.37/16.02 thf(omega__Cong, axiom,(( omega__Cong ) = ((((omega) = (omega)))))).
% 120.37/16.02 thf('3', plain, (( omega__Cong ) = ( ( omega ) = ( omega ) )),
% 120.37/16.02 define([status(thm)])).
% 120.37/16.02 thf(zip_derived_cl1, plain,
% 120.37/16.02 (~ (((setextAx) =>
% 120.37/16.02 (((emptysetAx) =>
% 120.37/16.02 (((setadjoinAx) =>
% 120.37/16.02 (((powersetAx) =>
% 120.37/16.02 (((setunionAx) =>
% 120.37/16.02 (((in @ emptyset @ omega) =>
% 120.37/16.02 (((omegaSAx) =>
% 120.37/16.02 (((omegaIndAx) =>
% 120.37/16.02 (((replAx) =>
% 120.37/16.02 (((foundationAx) =>
% 120.37/16.02 (((wellorderingAx) =>
% 120.37/16.02 (((descrp) =>
% 120.37/16.02 (((dsetconstrI) =>
% 120.37/16.02 (((dsetconstrEL) =>
% 120.37/16.02 (((dsetconstrER) =>
% 120.37/16.02 (((exuE1) =>
% 120.37/16.02 (((prop2setE) =>
% 120.37/16.02 (((emptysetE) =>
% 120.37/16.02 (((emptysetimpfalse) =>
% 120.37/16.02 (((notinemptyset) =>
% 120.37/16.02 (((exuE3e) =>
% 120.37/16.02 (((setext) =>
% 120.37/16.02 (((emptyI) =>
% 120.37/16.02 (((noeltsimpempty) =>
% 120.37/16.02 (((setbeta) =>
% 120.37/16.02 (((nonemptyE1) =>
% 120.37/16.02 (((nonemptyI) =>
% 120.37/16.02 (((nonemptyI1) =>
% 120.37/16.02 (((setadjoinIL) =>
% 120.37/16.02 (((in @
% 120.37/16.02 emptyset @
% 120.37/16.02 (setadjoin @
% 120.37/16.02 emptyset @
% 120.37/16.02 emptyset)) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinIR) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinE) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinOr) =>
% 120.37/16.02 ((
% 120.37/16.02 (setoftrueEq) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetI) =>
% 120.37/16.02 ((
% 120.37/16.02 (emptyinPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (emptyInPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetE) =>
% 120.37/16.02 ((
% 120.37/16.02 (setunionI) =>
% 120.37/16.02 ((
% 120.37/16.02 (setunionE) =>
% 120.37/16.02 ((
% 120.37/16.02 (subPowSU) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuE2) =>
% 120.37/16.02 ((
% 120.37/16.02 (nonemptyImpWitness) =>
% 120.37/16.02 ((
% 120.37/16.02 (uniqinunit) =>
% 120.37/16.02 ((
% 120.37/16.02 (notinsingleton) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqinunit) =>
% 120.37/16.02 ((
% 120.37/16.02 (singletonsswitch) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairsetE) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairsetIL) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairsetIR) =>
% 120.37/16.02 ((
% 120.37/16.02 (emptyE1) =>
% 120.37/16.02 ((
% 120.37/16.02 (vacuousDall) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan1) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan2) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan3) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan4) =>
% 120.37/16.02 ((
% 120.37/16.02 (prop2setI) =>
% 120.37/16.02 ((
% 120.37/16.02 (prop2set2propI) =>
% 120.37/16.02 ((
% 120.37/16.02 (notdexE) =>
% 120.37/16.02 ((
% 120.37/16.02 (notdallE) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI3) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (inCongP) =>
% 120.37/16.02 ((
% 120.37/16.02 (in__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuE3u) =>
% 120.37/16.02 ((
% 120.37/16.02 (exu__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 ((
% 120.37/16.02 (emptyset) =
% 120.37/16.02 (emptyset))) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoin__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (powerset__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (setunion__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 ((
% 120.37/16.02 (omega) =
% 120.37/16.02 (omega))) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuEu) =>
% 120.37/16.02 ((
% 120.37/16.02 (descr__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (dsetconstr__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqimpsubset2) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqimpsubset1) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (emptysetsubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetE) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetE2) =>
% 120.37/16.02 ((
% 120.37/16.02 (notsubsetI) =>
% 120.37/16.02 ((
% 120.37/16.02 (notequalI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (notequalI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetRefl) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetTrans) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinSub) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinSub2) =>
% 120.37/16.02 ((
% 120.37/16.02 (subset2powerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (setextsub) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetemptysetimpeq) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetE1) =>
% 120.37/16.02 ((
% 120.37/16.02 (inPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetsubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (sepInPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (sepSubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (binunionIL) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairset2IR) =>
% 120.37/16.02 ((
% 120.37/16.02 (binunionIR) =>
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y0 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y1 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y2 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y3 : $o]:
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 (
% 120.37/16.02 binunion @
% 120.37/16.02 Y0 @ Y1)) =>
% 120.37/16.02 ((
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 Y0) =>
% 120.37/16.02 (Y3))) =>
% 120.37/16.02 ((
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 Y1) =>
% 120.37/16.02 (Y3))) =>
% 120.37/16.02 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.02 inference('rw', [status(thm)], [zip_derived_cl0, '0', '1', '2', '3'])).
% 120.37/16.02 thf(zip_derived_cl2, plain,
% 120.37/16.02 (~ (((setextAx) =>
% 120.37/16.02 (((emptysetAx) =>
% 120.37/16.02 (((setadjoinAx) =>
% 120.37/16.02 (((powersetAx) =>
% 120.37/16.02 (((setunionAx) =>
% 120.37/16.02 (((in @ emptyset @ omega) =>
% 120.37/16.02 (((omegaSAx) =>
% 120.37/16.02 (((omegaIndAx) =>
% 120.37/16.02 (((replAx) =>
% 120.37/16.02 (((foundationAx) =>
% 120.37/16.02 (((wellorderingAx) =>
% 120.37/16.02 (((descrp) =>
% 120.37/16.02 (((dsetconstrI) =>
% 120.37/16.02 (((dsetconstrEL) =>
% 120.37/16.02 (((dsetconstrER) =>
% 120.37/16.02 (((exuE1) =>
% 120.37/16.02 (((prop2setE) =>
% 120.37/16.02 (((emptysetE) =>
% 120.37/16.02 (((emptysetimpfalse) =>
% 120.37/16.02 (((notinemptyset) =>
% 120.37/16.02 (((exuE3e) =>
% 120.37/16.02 (((setext) =>
% 120.37/16.02 (((emptyI) =>
% 120.37/16.02 (((noeltsimpempty) =>
% 120.37/16.02 (((setbeta) =>
% 120.37/16.02 (((nonemptyE1) =>
% 120.37/16.02 (((nonemptyI) =>
% 120.37/16.02 (((nonemptyI1) =>
% 120.37/16.02 (((setadjoinIL) =>
% 120.37/16.02 (((in @
% 120.37/16.02 emptyset @
% 120.37/16.02 (setadjoin @
% 120.37/16.02 emptyset @
% 120.37/16.02 emptyset)) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinIR) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinE) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinOr) =>
% 120.37/16.02 ((
% 120.37/16.02 (setoftrueEq) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetI) =>
% 120.37/16.02 ((
% 120.37/16.02 (emptyinPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (emptyInPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetE) =>
% 120.37/16.02 ((
% 120.37/16.02 (setunionI) =>
% 120.37/16.02 ((
% 120.37/16.02 (setunionE) =>
% 120.37/16.02 ((
% 120.37/16.02 (subPowSU) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuE2) =>
% 120.37/16.02 ((
% 120.37/16.02 (nonemptyImpWitness) =>
% 120.37/16.02 ((
% 120.37/16.02 (uniqinunit) =>
% 120.37/16.02 ((
% 120.37/16.02 (notinsingleton) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqinunit) =>
% 120.37/16.02 ((
% 120.37/16.02 (singletonsswitch) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairsetE) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairsetIL) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairsetIR) =>
% 120.37/16.02 ((
% 120.37/16.02 (emptyE1) =>
% 120.37/16.02 ((
% 120.37/16.02 (vacuousDall) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan1) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan2) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan3) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan4) =>
% 120.37/16.02 ((
% 120.37/16.02 (prop2setI) =>
% 120.37/16.02 ((
% 120.37/16.02 (prop2set2propI) =>
% 120.37/16.02 ((
% 120.37/16.02 (notdexE) =>
% 120.37/16.02 ((
% 120.37/16.02 (notdallE) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI3) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (inCongP) =>
% 120.37/16.02 ((
% 120.37/16.02 (in__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuE3u) =>
% 120.37/16.02 ((
% 120.37/16.02 (exu__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoin__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (powerset__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (setunion__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuEu) =>
% 120.37/16.02 ((
% 120.37/16.02 (descr__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (dsetconstr__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqimpsubset2) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqimpsubset1) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (emptysetsubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetE) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetE2) =>
% 120.37/16.02 ((
% 120.37/16.02 (notsubsetI) =>
% 120.37/16.02 ((
% 120.37/16.02 (notequalI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (notequalI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetRefl) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetTrans) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinSub) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinSub2) =>
% 120.37/16.02 ((
% 120.37/16.02 (subset2powerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (setextsub) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetemptysetimpeq) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetE1) =>
% 120.37/16.02 ((
% 120.37/16.02 (inPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetsubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (sepInPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (sepSubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (binunionIL) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairset2IR) =>
% 120.37/16.02 ((
% 120.37/16.02 (binunionIR) =>
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y0 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y1 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y2 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y3 : $o]:
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 (
% 120.37/16.02 binunion @
% 120.37/16.02 Y0 @ Y1)) =>
% 120.37/16.02 ((
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 Y0) =>
% 120.37/16.02 (Y3))) =>
% 120.37/16.02 ((
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 Y1) =>
% 120.37/16.02 (Y3))) =>
% 120.37/16.02 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.02 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl1])).
% 120.37/16.02 thf(zip_derived_cl4, plain,
% 120.37/16.02 (~ (((emptysetAx) =>
% 120.37/16.02 (((setadjoinAx) =>
% 120.37/16.02 (((powersetAx) =>
% 120.37/16.02 (((setunionAx) =>
% 120.37/16.02 (((in @ emptyset @ omega) =>
% 120.37/16.02 (((omegaSAx) =>
% 120.37/16.02 (((omegaIndAx) =>
% 120.37/16.02 (((replAx) =>
% 120.37/16.02 (((foundationAx) =>
% 120.37/16.02 (((wellorderingAx) =>
% 120.37/16.02 (((descrp) =>
% 120.37/16.02 (((dsetconstrI) =>
% 120.37/16.02 (((dsetconstrEL) =>
% 120.37/16.02 (((dsetconstrER) =>
% 120.37/16.02 (((exuE1) =>
% 120.37/16.02 (((prop2setE) =>
% 120.37/16.02 (((emptysetE) =>
% 120.37/16.02 (((emptysetimpfalse) =>
% 120.37/16.02 (((notinemptyset) =>
% 120.37/16.02 (((exuE3e) =>
% 120.37/16.02 (((setext) =>
% 120.37/16.02 (((emptyI) =>
% 120.37/16.02 (((noeltsimpempty) =>
% 120.37/16.02 (((setbeta) =>
% 120.37/16.02 (((nonemptyE1) =>
% 120.37/16.02 (((nonemptyI) =>
% 120.37/16.02 (((nonemptyI1) =>
% 120.37/16.02 (((setadjoinIL) =>
% 120.37/16.02 (((in @
% 120.37/16.02 emptyset @
% 120.37/16.02 (setadjoin @
% 120.37/16.02 emptyset @
% 120.37/16.02 emptyset)) =>
% 120.37/16.02 (((setadjoinIR) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinE) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinOr) =>
% 120.37/16.02 ((
% 120.37/16.02 (setoftrueEq) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetI) =>
% 120.37/16.02 ((
% 120.37/16.02 (emptyinPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (emptyInPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetE) =>
% 120.37/16.02 ((
% 120.37/16.02 (setunionI) =>
% 120.37/16.02 ((
% 120.37/16.02 (setunionE) =>
% 120.37/16.02 ((
% 120.37/16.02 (subPowSU) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuE2) =>
% 120.37/16.02 ((
% 120.37/16.02 (nonemptyImpWitness) =>
% 120.37/16.02 ((
% 120.37/16.02 (uniqinunit) =>
% 120.37/16.02 ((
% 120.37/16.02 (notinsingleton) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqinunit) =>
% 120.37/16.02 ((
% 120.37/16.02 (singletonsswitch) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairsetE) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairsetIL) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairsetIR) =>
% 120.37/16.02 ((
% 120.37/16.02 (emptyE1) =>
% 120.37/16.02 ((
% 120.37/16.02 (vacuousDall) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan1) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan2) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan3) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan4) =>
% 120.37/16.02 ((
% 120.37/16.02 (prop2setI) =>
% 120.37/16.02 ((
% 120.37/16.02 (prop2set2propI) =>
% 120.37/16.02 ((
% 120.37/16.02 (notdexE) =>
% 120.37/16.02 ((
% 120.37/16.02 (notdallE) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI3) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (inCongP) =>
% 120.37/16.02 ((
% 120.37/16.02 (in__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuE3u) =>
% 120.37/16.02 ((
% 120.37/16.02 (exu__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoin__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (powerset__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (setunion__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuEu) =>
% 120.37/16.02 ((
% 120.37/16.02 (descr__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (dsetconstr__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqimpsubset2) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqimpsubset1) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (emptysetsubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetE) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetE2) =>
% 120.37/16.02 ((
% 120.37/16.02 (notsubsetI) =>
% 120.37/16.02 ((
% 120.37/16.02 (notequalI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (notequalI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetRefl) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetTrans) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinSub) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinSub2) =>
% 120.37/16.02 ((
% 120.37/16.02 (subset2powerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (setextsub) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetemptysetimpeq) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetE1) =>
% 120.37/16.02 ((
% 120.37/16.02 (inPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetsubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (sepInPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (sepSubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (binunionIL) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairset2IR) =>
% 120.37/16.02 ((
% 120.37/16.02 (binunionIR) =>
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y0 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y1 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y2 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y3 : $o]:
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 (
% 120.37/16.02 binunion @
% 120.37/16.02 Y0 @ Y1)) =>
% 120.37/16.02 ((
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 Y0) =>
% 120.37/16.02 (Y3))) =>
% 120.37/16.02 ((
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 Y1) =>
% 120.37/16.02 (Y3))) =>
% 120.37/16.02 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2])).
% 120.37/16.02 thf(zip_derived_cl7, plain,
% 120.37/16.02 (~ (((setadjoinAx) =>
% 120.37/16.02 (((powersetAx) =>
% 120.37/16.02 (((setunionAx) =>
% 120.37/16.02 (((in @ emptyset @ omega) =>
% 120.37/16.02 (((omegaSAx) =>
% 120.37/16.02 (((omegaIndAx) =>
% 120.37/16.02 (((replAx) =>
% 120.37/16.02 (((foundationAx) =>
% 120.37/16.02 (((wellorderingAx) =>
% 120.37/16.02 (((descrp) =>
% 120.37/16.02 (((dsetconstrI) =>
% 120.37/16.02 (((dsetconstrEL) =>
% 120.37/16.02 (((dsetconstrER) =>
% 120.37/16.02 (((exuE1) =>
% 120.37/16.02 (((prop2setE) =>
% 120.37/16.02 (((emptysetE) =>
% 120.37/16.02 (((emptysetimpfalse) =>
% 120.37/16.02 (((notinemptyset) =>
% 120.37/16.02 (((exuE3e) =>
% 120.37/16.02 (((setext) =>
% 120.37/16.02 (((emptyI) =>
% 120.37/16.02 (((noeltsimpempty) =>
% 120.37/16.02 (((setbeta) =>
% 120.37/16.02 (((nonemptyE1) =>
% 120.37/16.02 (((nonemptyI) =>
% 120.37/16.02 (((nonemptyI1) =>
% 120.37/16.02 (((setadjoinIL) =>
% 120.37/16.02 (((in @
% 120.37/16.02 emptyset @
% 120.37/16.02 (setadjoin @
% 120.37/16.02 emptyset @
% 120.37/16.02 emptyset)) =>
% 120.37/16.02 (((setadjoinIR) =>
% 120.37/16.02 (((setadjoinE) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinOr) =>
% 120.37/16.02 ((
% 120.37/16.02 (setoftrueEq) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetI) =>
% 120.37/16.02 ((
% 120.37/16.02 (emptyinPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (emptyInPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetE) =>
% 120.37/16.02 ((
% 120.37/16.02 (setunionI) =>
% 120.37/16.02 ((
% 120.37/16.02 (setunionE) =>
% 120.37/16.02 ((
% 120.37/16.02 (subPowSU) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuE2) =>
% 120.37/16.02 ((
% 120.37/16.02 (nonemptyImpWitness) =>
% 120.37/16.02 ((
% 120.37/16.02 (uniqinunit) =>
% 120.37/16.02 ((
% 120.37/16.02 (notinsingleton) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqinunit) =>
% 120.37/16.02 ((
% 120.37/16.02 (singletonsswitch) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairsetE) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairsetIL) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairsetIR) =>
% 120.37/16.02 ((
% 120.37/16.02 (emptyE1) =>
% 120.37/16.02 ((
% 120.37/16.02 (vacuousDall) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan1) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan2) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan3) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan4) =>
% 120.37/16.02 ((
% 120.37/16.02 (prop2setI) =>
% 120.37/16.02 ((
% 120.37/16.02 (prop2set2propI) =>
% 120.37/16.02 ((
% 120.37/16.02 (notdexE) =>
% 120.37/16.02 ((
% 120.37/16.02 (notdallE) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI3) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (inCongP) =>
% 120.37/16.02 ((
% 120.37/16.02 (in__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuE3u) =>
% 120.37/16.02 ((
% 120.37/16.02 (exu__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoin__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (powerset__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (setunion__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuEu) =>
% 120.37/16.02 ((
% 120.37/16.02 (descr__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (dsetconstr__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqimpsubset2) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqimpsubset1) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (emptysetsubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetE) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetE2) =>
% 120.37/16.02 ((
% 120.37/16.02 (notsubsetI) =>
% 120.37/16.02 ((
% 120.37/16.02 (notequalI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (notequalI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetRefl) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetTrans) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinSub) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinSub2) =>
% 120.37/16.02 ((
% 120.37/16.02 (subset2powerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (setextsub) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetemptysetimpeq) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetE1) =>
% 120.37/16.02 ((
% 120.37/16.02 (inPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetsubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (sepInPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (sepSubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (binunionIL) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairset2IR) =>
% 120.37/16.02 ((
% 120.37/16.02 (binunionIR) =>
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y0 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y1 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y2 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y3 : $o]:
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 (
% 120.37/16.02 binunion @
% 120.37/16.02 Y0 @ Y1)) =>
% 120.37/16.02 ((
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 Y0) =>
% 120.37/16.02 (Y3))) =>
% 120.37/16.02 ((
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 Y1) =>
% 120.37/16.02 (Y3))) =>
% 120.37/16.02 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl4])).
% 120.37/16.02 thf(zip_derived_cl11, plain,
% 120.37/16.02 (~ (((powersetAx) =>
% 120.37/16.02 (((setunionAx) =>
% 120.37/16.02 (((in @ emptyset @ omega) =>
% 120.37/16.02 (((omegaSAx) =>
% 120.37/16.02 (((omegaIndAx) =>
% 120.37/16.02 (((replAx) =>
% 120.37/16.02 (((foundationAx) =>
% 120.37/16.02 (((wellorderingAx) =>
% 120.37/16.02 (((descrp) =>
% 120.37/16.02 (((dsetconstrI) =>
% 120.37/16.02 (((dsetconstrEL) =>
% 120.37/16.02 (((dsetconstrER) =>
% 120.37/16.02 (((exuE1) =>
% 120.37/16.02 (((prop2setE) =>
% 120.37/16.02 (((emptysetE) =>
% 120.37/16.02 (((emptysetimpfalse) =>
% 120.37/16.02 (((notinemptyset) =>
% 120.37/16.02 (((exuE3e) =>
% 120.37/16.02 (((setext) =>
% 120.37/16.02 (((emptyI) =>
% 120.37/16.02 (((noeltsimpempty) =>
% 120.37/16.02 (((setbeta) =>
% 120.37/16.02 (((nonemptyE1) =>
% 120.37/16.02 (((nonemptyI) =>
% 120.37/16.02 (((nonemptyI1) =>
% 120.37/16.02 (((setadjoinIL) =>
% 120.37/16.02 (((in @
% 120.37/16.02 emptyset @
% 120.37/16.02 (setadjoin @
% 120.37/16.02 emptyset @
% 120.37/16.02 emptyset)) =>
% 120.37/16.02 (((setadjoinIR) =>
% 120.37/16.02 (((setadjoinE) =>
% 120.37/16.02 (((setadjoinOr) =>
% 120.37/16.02 ((
% 120.37/16.02 (setoftrueEq) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetI) =>
% 120.37/16.02 ((
% 120.37/16.02 (emptyinPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (emptyInPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetE) =>
% 120.37/16.02 ((
% 120.37/16.02 (setunionI) =>
% 120.37/16.02 ((
% 120.37/16.02 (setunionE) =>
% 120.37/16.02 ((
% 120.37/16.02 (subPowSU) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuE2) =>
% 120.37/16.02 ((
% 120.37/16.02 (nonemptyImpWitness) =>
% 120.37/16.02 ((
% 120.37/16.02 (uniqinunit) =>
% 120.37/16.02 ((
% 120.37/16.02 (notinsingleton) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqinunit) =>
% 120.37/16.02 ((
% 120.37/16.02 (singletonsswitch) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairsetE) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairsetIL) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairsetIR) =>
% 120.37/16.02 ((
% 120.37/16.02 (emptyE1) =>
% 120.37/16.02 ((
% 120.37/16.02 (vacuousDall) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan1) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan2) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan3) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan4) =>
% 120.37/16.02 ((
% 120.37/16.02 (prop2setI) =>
% 120.37/16.02 ((
% 120.37/16.02 (prop2set2propI) =>
% 120.37/16.02 ((
% 120.37/16.02 (notdexE) =>
% 120.37/16.02 ((
% 120.37/16.02 (notdallE) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI3) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (inCongP) =>
% 120.37/16.02 ((
% 120.37/16.02 (in__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuE3u) =>
% 120.37/16.02 ((
% 120.37/16.02 (exu__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoin__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (powerset__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (setunion__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuEu) =>
% 120.37/16.02 ((
% 120.37/16.02 (descr__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (dsetconstr__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqimpsubset2) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqimpsubset1) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (emptysetsubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetE) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetE2) =>
% 120.37/16.02 ((
% 120.37/16.02 (notsubsetI) =>
% 120.37/16.02 ((
% 120.37/16.02 (notequalI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (notequalI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetRefl) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetTrans) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinSub) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinSub2) =>
% 120.37/16.02 ((
% 120.37/16.02 (subset2powerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (setextsub) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetemptysetimpeq) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetE1) =>
% 120.37/16.02 ((
% 120.37/16.02 (inPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetsubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (sepInPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (sepSubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (binunionIL) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairset2IR) =>
% 120.37/16.02 ((
% 120.37/16.02 (binunionIR) =>
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y0 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y1 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y2 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y3 : $o]:
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 (
% 120.37/16.02 binunion @
% 120.37/16.02 Y0 @ Y1)) =>
% 120.37/16.02 ((
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 Y0) =>
% 120.37/16.02 (Y3))) =>
% 120.37/16.02 ((
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 Y1) =>
% 120.37/16.02 (Y3))) =>
% 120.37/16.02 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl7])).
% 120.37/16.02 thf(zip_derived_cl16, plain,
% 120.37/16.02 (~ (((setunionAx) =>
% 120.37/16.02 (((in @ emptyset @ omega) =>
% 120.37/16.02 (((omegaSAx) =>
% 120.37/16.02 (((omegaIndAx) =>
% 120.37/16.02 (((replAx) =>
% 120.37/16.02 (((foundationAx) =>
% 120.37/16.02 (((wellorderingAx) =>
% 120.37/16.02 (((descrp) =>
% 120.37/16.02 (((dsetconstrI) =>
% 120.37/16.02 (((dsetconstrEL) =>
% 120.37/16.02 (((dsetconstrER) =>
% 120.37/16.02 (((exuE1) =>
% 120.37/16.02 (((prop2setE) =>
% 120.37/16.02 (((emptysetE) =>
% 120.37/16.02 (((emptysetimpfalse) =>
% 120.37/16.02 (((notinemptyset) =>
% 120.37/16.02 (((exuE3e) =>
% 120.37/16.02 (((setext) =>
% 120.37/16.02 (((emptyI) =>
% 120.37/16.02 (((noeltsimpempty) =>
% 120.37/16.02 (((setbeta) =>
% 120.37/16.02 (((nonemptyE1) =>
% 120.37/16.02 (((nonemptyI) =>
% 120.37/16.02 (((nonemptyI1) =>
% 120.37/16.02 (((setadjoinIL) =>
% 120.37/16.02 (((in @ emptyset @
% 120.37/16.02 (setadjoin @
% 120.37/16.02 emptyset @
% 120.37/16.02 emptyset)) =>
% 120.37/16.02 (((setadjoinIR) =>
% 120.37/16.02 (((setadjoinE) =>
% 120.37/16.02 (((setadjoinOr) =>
% 120.37/16.02 (((setoftrueEq) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetI) =>
% 120.37/16.02 ((
% 120.37/16.02 (emptyinPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (emptyInPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetE) =>
% 120.37/16.02 ((
% 120.37/16.02 (setunionI) =>
% 120.37/16.02 ((
% 120.37/16.02 (setunionE) =>
% 120.37/16.02 ((
% 120.37/16.02 (subPowSU) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuE2) =>
% 120.37/16.02 ((
% 120.37/16.02 (nonemptyImpWitness) =>
% 120.37/16.02 ((
% 120.37/16.02 (uniqinunit) =>
% 120.37/16.02 ((
% 120.37/16.02 (notinsingleton) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqinunit) =>
% 120.37/16.02 ((
% 120.37/16.02 (singletonsswitch) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairsetE) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairsetIL) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairsetIR) =>
% 120.37/16.02 ((
% 120.37/16.02 (emptyE1) =>
% 120.37/16.02 ((
% 120.37/16.02 (vacuousDall) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan1) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan2) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan3) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan4) =>
% 120.37/16.02 ((
% 120.37/16.02 (prop2setI) =>
% 120.37/16.02 ((
% 120.37/16.02 (prop2set2propI) =>
% 120.37/16.02 ((
% 120.37/16.02 (notdexE) =>
% 120.37/16.02 ((
% 120.37/16.02 (notdallE) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI3) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (inCongP) =>
% 120.37/16.02 ((
% 120.37/16.02 (in__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuE3u) =>
% 120.37/16.02 ((
% 120.37/16.02 (exu__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoin__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (powerset__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (setunion__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuEu) =>
% 120.37/16.02 ((
% 120.37/16.02 (descr__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (dsetconstr__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqimpsubset2) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqimpsubset1) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (emptysetsubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetE) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetE2) =>
% 120.37/16.02 ((
% 120.37/16.02 (notsubsetI) =>
% 120.37/16.02 ((
% 120.37/16.02 (notequalI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (notequalI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetRefl) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetTrans) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinSub) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinSub2) =>
% 120.37/16.02 ((
% 120.37/16.02 (subset2powerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (setextsub) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetemptysetimpeq) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetE1) =>
% 120.37/16.02 ((
% 120.37/16.02 (inPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetsubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (sepInPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (sepSubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (binunionIL) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairset2IR) =>
% 120.37/16.02 ((
% 120.37/16.02 (binunionIR) =>
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y0 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y1 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y2 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y3 : $o]:
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 (
% 120.37/16.02 binunion @
% 120.37/16.02 Y0 @ Y1)) =>
% 120.37/16.02 ((
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 Y0) =>
% 120.37/16.02 (Y3))) =>
% 120.37/16.02 ((
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 Y1) =>
% 120.37/16.02 (Y3))) =>
% 120.37/16.02 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl11])).
% 120.37/16.02 thf(zip_derived_cl21, plain,
% 120.37/16.02 (~ (((in @ emptyset @ omega) =>
% 120.37/16.02 (((omegaSAx) =>
% 120.37/16.02 (((omegaIndAx) =>
% 120.37/16.02 (((replAx) =>
% 120.37/16.02 (((foundationAx) =>
% 120.37/16.02 (((wellorderingAx) =>
% 120.37/16.02 (((descrp) =>
% 120.37/16.02 (((dsetconstrI) =>
% 120.37/16.02 (((dsetconstrEL) =>
% 120.37/16.02 (((dsetconstrER) =>
% 120.37/16.02 (((exuE1) =>
% 120.37/16.02 (((prop2setE) =>
% 120.37/16.02 (((emptysetE) =>
% 120.37/16.02 (((emptysetimpfalse) =>
% 120.37/16.02 (((notinemptyset) =>
% 120.37/16.02 (((exuE3e) =>
% 120.37/16.02 (((setext) =>
% 120.37/16.02 (((emptyI) =>
% 120.37/16.02 (((noeltsimpempty) =>
% 120.37/16.02 (((setbeta) =>
% 120.37/16.02 (((nonemptyE1) =>
% 120.37/16.02 (((nonemptyI) =>
% 120.37/16.02 (((nonemptyI1) =>
% 120.37/16.02 (((setadjoinIL) =>
% 120.37/16.02 (((in @ emptyset @
% 120.37/16.02 (setadjoin @
% 120.37/16.02 emptyset @ emptyset)) =>
% 120.37/16.02 (((setadjoinIR) =>
% 120.37/16.02 (((setadjoinE) =>
% 120.37/16.02 (((setadjoinOr) =>
% 120.37/16.02 (((setoftrueEq) =>
% 120.37/16.02 (((powersetI) =>
% 120.37/16.02 ((
% 120.37/16.02 (emptyinPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (emptyInPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetE) =>
% 120.37/16.02 ((
% 120.37/16.02 (setunionI) =>
% 120.37/16.02 ((
% 120.37/16.02 (setunionE) =>
% 120.37/16.02 ((
% 120.37/16.02 (subPowSU) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuE2) =>
% 120.37/16.02 ((
% 120.37/16.02 (nonemptyImpWitness) =>
% 120.37/16.02 ((
% 120.37/16.02 (uniqinunit) =>
% 120.37/16.02 ((
% 120.37/16.02 (notinsingleton) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqinunit) =>
% 120.37/16.02 ((
% 120.37/16.02 (singletonsswitch) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairsetE) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairsetIL) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairsetIR) =>
% 120.37/16.02 ((
% 120.37/16.02 (emptyE1) =>
% 120.37/16.02 ((
% 120.37/16.02 (vacuousDall) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan1) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan2) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan3) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan4) =>
% 120.37/16.02 ((
% 120.37/16.02 (prop2setI) =>
% 120.37/16.02 ((
% 120.37/16.02 (prop2set2propI) =>
% 120.37/16.02 ((
% 120.37/16.02 (notdexE) =>
% 120.37/16.02 ((
% 120.37/16.02 (notdallE) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI3) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (inCongP) =>
% 120.37/16.02 ((
% 120.37/16.02 (in__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuE3u) =>
% 120.37/16.02 ((
% 120.37/16.02 (exu__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoin__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (powerset__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (setunion__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuEu) =>
% 120.37/16.02 ((
% 120.37/16.02 (descr__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (dsetconstr__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqimpsubset2) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqimpsubset1) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (emptysetsubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetE) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetE2) =>
% 120.37/16.02 ((
% 120.37/16.02 (notsubsetI) =>
% 120.37/16.02 ((
% 120.37/16.02 (notequalI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (notequalI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetRefl) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetTrans) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinSub) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinSub2) =>
% 120.37/16.02 ((
% 120.37/16.02 (subset2powerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (setextsub) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetemptysetimpeq) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetE1) =>
% 120.37/16.02 ((
% 120.37/16.02 (inPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetsubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (sepInPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (sepSubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (binunionIL) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairset2IR) =>
% 120.37/16.02 ((
% 120.37/16.02 (binunionIR) =>
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y0 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y1 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y2 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y3 : $o]:
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 (
% 120.37/16.02 binunion @
% 120.37/16.02 Y0 @ Y1)) =>
% 120.37/16.02 ((
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 Y0) =>
% 120.37/16.02 (Y3))) =>
% 120.37/16.02 ((
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 Y1) =>
% 120.37/16.02 (Y3))) =>
% 120.37/16.02 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl16])).
% 120.37/16.02 thf(zip_derived_cl28, plain,
% 120.37/16.02 (~ (((omegaSAx) =>
% 120.37/16.02 (((omegaIndAx) =>
% 120.37/16.02 (((replAx) =>
% 120.37/16.02 (((foundationAx) =>
% 120.37/16.02 (((wellorderingAx) =>
% 120.37/16.02 (((descrp) =>
% 120.37/16.02 (((dsetconstrI) =>
% 120.37/16.02 (((dsetconstrEL) =>
% 120.37/16.02 (((dsetconstrER) =>
% 120.37/16.02 (((exuE1) =>
% 120.37/16.02 (((prop2setE) =>
% 120.37/16.02 (((emptysetE) =>
% 120.37/16.02 (((emptysetimpfalse) =>
% 120.37/16.02 (((notinemptyset) =>
% 120.37/16.02 (((exuE3e) =>
% 120.37/16.02 (((setext) =>
% 120.37/16.02 (((emptyI) =>
% 120.37/16.02 (((noeltsimpempty) =>
% 120.37/16.02 (((setbeta) =>
% 120.37/16.02 (((nonemptyE1) =>
% 120.37/16.02 (((nonemptyI) =>
% 120.37/16.02 (((nonemptyI1) =>
% 120.37/16.02 (((setadjoinIL) =>
% 120.37/16.02 (((in @ emptyset @
% 120.37/16.02 (setadjoin @
% 120.37/16.02 emptyset @ emptyset)) =>
% 120.37/16.02 (((setadjoinIR) =>
% 120.37/16.02 (((setadjoinE) =>
% 120.37/16.02 (((setadjoinOr) =>
% 120.37/16.02 (((setoftrueEq) =>
% 120.37/16.02 (((powersetI) =>
% 120.37/16.02 (((emptyinPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (emptyInPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetE) =>
% 120.37/16.02 ((
% 120.37/16.02 (setunionI) =>
% 120.37/16.02 ((
% 120.37/16.02 (setunionE) =>
% 120.37/16.02 ((
% 120.37/16.02 (subPowSU) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuE2) =>
% 120.37/16.02 ((
% 120.37/16.02 (nonemptyImpWitness) =>
% 120.37/16.02 ((
% 120.37/16.02 (uniqinunit) =>
% 120.37/16.02 ((
% 120.37/16.02 (notinsingleton) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqinunit) =>
% 120.37/16.02 ((
% 120.37/16.02 (singletonsswitch) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairsetE) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairsetIL) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairsetIR) =>
% 120.37/16.02 ((
% 120.37/16.02 (emptyE1) =>
% 120.37/16.02 ((
% 120.37/16.02 (vacuousDall) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan1) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan2) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan3) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan4) =>
% 120.37/16.02 ((
% 120.37/16.02 (prop2setI) =>
% 120.37/16.02 ((
% 120.37/16.02 (prop2set2propI) =>
% 120.37/16.02 ((
% 120.37/16.02 (notdexE) =>
% 120.37/16.02 ((
% 120.37/16.02 (notdallE) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI3) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (inCongP) =>
% 120.37/16.02 ((
% 120.37/16.02 (in__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuE3u) =>
% 120.37/16.02 ((
% 120.37/16.02 (exu__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoin__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (powerset__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (setunion__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuEu) =>
% 120.37/16.02 ((
% 120.37/16.02 (descr__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (dsetconstr__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqimpsubset2) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqimpsubset1) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (emptysetsubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetE) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetE2) =>
% 120.37/16.02 ((
% 120.37/16.02 (notsubsetI) =>
% 120.37/16.02 ((
% 120.37/16.02 (notequalI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (notequalI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetRefl) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetTrans) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinSub) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinSub2) =>
% 120.37/16.02 ((
% 120.37/16.02 (subset2powerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (setextsub) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetemptysetimpeq) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetE1) =>
% 120.37/16.02 ((
% 120.37/16.02 (inPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetsubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (sepInPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (sepSubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (binunionIL) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairset2IR) =>
% 120.37/16.02 ((
% 120.37/16.02 (binunionIR) =>
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y0 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y1 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y2 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y3 : $o]:
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 (
% 120.37/16.02 binunion @
% 120.37/16.02 Y0 @ Y1)) =>
% 120.37/16.02 ((
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 Y0) =>
% 120.37/16.02 (Y3))) =>
% 120.37/16.02 ((
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 Y1) =>
% 120.37/16.02 (Y3))) =>
% 120.37/16.02 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl21])).
% 120.37/16.02 thf(zip_derived_cl34, plain,
% 120.37/16.02 (~ (((omegaIndAx) =>
% 120.37/16.02 (((replAx) =>
% 120.37/16.02 (((foundationAx) =>
% 120.37/16.02 (((wellorderingAx) =>
% 120.37/16.02 (((descrp) =>
% 120.37/16.02 (((dsetconstrI) =>
% 120.37/16.02 (((dsetconstrEL) =>
% 120.37/16.02 (((dsetconstrER) =>
% 120.37/16.02 (((exuE1) =>
% 120.37/16.02 (((prop2setE) =>
% 120.37/16.02 (((emptysetE) =>
% 120.37/16.02 (((emptysetimpfalse) =>
% 120.37/16.02 (((notinemptyset) =>
% 120.37/16.02 (((exuE3e) =>
% 120.37/16.02 (((setext) =>
% 120.37/16.02 (((emptyI) =>
% 120.37/16.02 (((noeltsimpempty) =>
% 120.37/16.02 (((setbeta) =>
% 120.37/16.02 (((nonemptyE1) =>
% 120.37/16.02 (((nonemptyI) =>
% 120.37/16.02 (((nonemptyI1) =>
% 120.37/16.02 (((setadjoinIL) =>
% 120.37/16.02 (((in @ emptyset @
% 120.37/16.02 (setadjoin @ emptyset @
% 120.37/16.02 emptyset)) =>
% 120.37/16.02 (((setadjoinIR) =>
% 120.37/16.02 (((setadjoinE) =>
% 120.37/16.02 (((setadjoinOr) =>
% 120.37/16.02 (((setoftrueEq) =>
% 120.37/16.02 (((powersetI) =>
% 120.37/16.02 (((emptyinPowerset) =>
% 120.37/16.02 (((emptyInPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetE) =>
% 120.37/16.02 ((
% 120.37/16.02 (setunionI) =>
% 120.37/16.02 ((
% 120.37/16.02 (setunionE) =>
% 120.37/16.02 ((
% 120.37/16.02 (subPowSU) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuE2) =>
% 120.37/16.02 ((
% 120.37/16.02 (nonemptyImpWitness) =>
% 120.37/16.02 ((
% 120.37/16.02 (uniqinunit) =>
% 120.37/16.02 ((
% 120.37/16.02 (notinsingleton) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqinunit) =>
% 120.37/16.02 ((
% 120.37/16.02 (singletonsswitch) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairsetE) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairsetIL) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairsetIR) =>
% 120.37/16.02 ((
% 120.37/16.02 (emptyE1) =>
% 120.37/16.02 ((
% 120.37/16.02 (vacuousDall) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan1) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan2) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan3) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan4) =>
% 120.37/16.02 ((
% 120.37/16.02 (prop2setI) =>
% 120.37/16.02 ((
% 120.37/16.02 (prop2set2propI) =>
% 120.37/16.02 ((
% 120.37/16.02 (notdexE) =>
% 120.37/16.02 ((
% 120.37/16.02 (notdallE) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI3) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (inCongP) =>
% 120.37/16.02 ((
% 120.37/16.02 (in__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuE3u) =>
% 120.37/16.02 ((
% 120.37/16.02 (exu__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoin__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (powerset__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (setunion__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuEu) =>
% 120.37/16.02 ((
% 120.37/16.02 (descr__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (dsetconstr__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqimpsubset2) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqimpsubset1) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (emptysetsubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetE) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetE2) =>
% 120.37/16.02 ((
% 120.37/16.02 (notsubsetI) =>
% 120.37/16.02 ((
% 120.37/16.02 (notequalI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (notequalI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetRefl) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetTrans) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinSub) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinSub2) =>
% 120.37/16.02 ((
% 120.37/16.02 (subset2powerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (setextsub) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetemptysetimpeq) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetE1) =>
% 120.37/16.02 ((
% 120.37/16.02 (inPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetsubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (sepInPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (sepSubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (binunionIL) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairset2IR) =>
% 120.37/16.02 ((
% 120.37/16.02 (binunionIR) =>
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y0 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y1 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y2 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y3 : $o]:
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 (
% 120.37/16.02 binunion @
% 120.37/16.02 Y0 @ Y1)) =>
% 120.37/16.02 ((
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 Y0) =>
% 120.37/16.02 (Y3))) =>
% 120.37/16.02 ((
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 Y1) =>
% 120.37/16.02 (Y3))) =>
% 120.37/16.02 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl28])).
% 120.37/16.02 thf(zip_derived_cl40, plain,
% 120.37/16.02 (~ (((replAx) =>
% 120.37/16.02 (((foundationAx) =>
% 120.37/16.02 (((wellorderingAx) =>
% 120.37/16.02 (((descrp) =>
% 120.37/16.02 (((dsetconstrI) =>
% 120.37/16.02 (((dsetconstrEL) =>
% 120.37/16.02 (((dsetconstrER) =>
% 120.37/16.02 (((exuE1) =>
% 120.37/16.02 (((prop2setE) =>
% 120.37/16.02 (((emptysetE) =>
% 120.37/16.02 (((emptysetimpfalse) =>
% 120.37/16.02 (((notinemptyset) =>
% 120.37/16.02 (((exuE3e) =>
% 120.37/16.02 (((setext) =>
% 120.37/16.02 (((emptyI) =>
% 120.37/16.02 (((noeltsimpempty) =>
% 120.37/16.02 (((setbeta) =>
% 120.37/16.02 (((nonemptyE1) =>
% 120.37/16.02 (((nonemptyI) =>
% 120.37/16.02 (((nonemptyI1) =>
% 120.37/16.02 (((setadjoinIL) =>
% 120.37/16.02 (((in @ emptyset @
% 120.37/16.02 (setadjoin @ emptyset @
% 120.37/16.02 emptyset)) =>
% 120.37/16.02 (((setadjoinIR) =>
% 120.37/16.02 (((setadjoinE) =>
% 120.37/16.02 (((setadjoinOr) =>
% 120.37/16.02 (((setoftrueEq) =>
% 120.37/16.02 (((powersetI) =>
% 120.37/16.02 (((emptyinPowerset) =>
% 120.37/16.02 (((emptyInPowerset) =>
% 120.37/16.02 (((powersetE) =>
% 120.37/16.02 ((
% 120.37/16.02 (setunionI) =>
% 120.37/16.02 ((
% 120.37/16.02 (setunionE) =>
% 120.37/16.02 ((
% 120.37/16.02 (subPowSU) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuE2) =>
% 120.37/16.02 ((
% 120.37/16.02 (nonemptyImpWitness) =>
% 120.37/16.02 ((
% 120.37/16.02 (uniqinunit) =>
% 120.37/16.02 ((
% 120.37/16.02 (notinsingleton) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqinunit) =>
% 120.37/16.02 ((
% 120.37/16.02 (singletonsswitch) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairsetE) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairsetIL) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairsetIR) =>
% 120.37/16.02 ((
% 120.37/16.02 (emptyE1) =>
% 120.37/16.02 ((
% 120.37/16.02 (vacuousDall) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan1) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan2) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan3) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan4) =>
% 120.37/16.02 ((
% 120.37/16.02 (prop2setI) =>
% 120.37/16.02 ((
% 120.37/16.02 (prop2set2propI) =>
% 120.37/16.02 ((
% 120.37/16.02 (notdexE) =>
% 120.37/16.02 ((
% 120.37/16.02 (notdallE) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI3) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (inCongP) =>
% 120.37/16.02 ((
% 120.37/16.02 (in__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuE3u) =>
% 120.37/16.02 ((
% 120.37/16.02 (exu__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoin__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (powerset__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (setunion__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuEu) =>
% 120.37/16.02 ((
% 120.37/16.02 (descr__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (dsetconstr__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqimpsubset2) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqimpsubset1) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (emptysetsubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetE) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetE2) =>
% 120.37/16.02 ((
% 120.37/16.02 (notsubsetI) =>
% 120.37/16.02 ((
% 120.37/16.02 (notequalI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (notequalI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetRefl) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetTrans) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinSub) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinSub2) =>
% 120.37/16.02 ((
% 120.37/16.02 (subset2powerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (setextsub) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetemptysetimpeq) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetE1) =>
% 120.37/16.02 ((
% 120.37/16.02 (inPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetsubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (sepInPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (sepSubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (binunionIL) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairset2IR) =>
% 120.37/16.02 ((
% 120.37/16.02 (binunionIR) =>
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y0 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y1 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y2 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y3 : $o]:
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 (
% 120.37/16.02 binunion @
% 120.37/16.02 Y0 @ Y1)) =>
% 120.37/16.02 ((
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 Y0) =>
% 120.37/16.02 (Y3))) =>
% 120.37/16.02 ((
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 Y1) =>
% 120.37/16.02 (Y3))) =>
% 120.37/16.02 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl34])).
% 120.37/16.02 thf(zip_derived_cl45, plain,
% 120.37/16.02 (~ (((foundationAx) =>
% 120.37/16.02 (((wellorderingAx) =>
% 120.37/16.02 (((descrp) =>
% 120.37/16.02 (((dsetconstrI) =>
% 120.37/16.02 (((dsetconstrEL) =>
% 120.37/16.02 (((dsetconstrER) =>
% 120.37/16.02 (((exuE1) =>
% 120.37/16.02 (((prop2setE) =>
% 120.37/16.02 (((emptysetE) =>
% 120.37/16.02 (((emptysetimpfalse) =>
% 120.37/16.02 (((notinemptyset) =>
% 120.37/16.02 (((exuE3e) =>
% 120.37/16.02 (((setext) =>
% 120.37/16.02 (((emptyI) =>
% 120.37/16.02 (((noeltsimpempty) =>
% 120.37/16.02 (((setbeta) =>
% 120.37/16.02 (((nonemptyE1) =>
% 120.37/16.02 (((nonemptyI) =>
% 120.37/16.02 (((nonemptyI1) =>
% 120.37/16.02 (((setadjoinIL) =>
% 120.37/16.02 (((in @ emptyset @
% 120.37/16.02 (setadjoin @ emptyset @
% 120.37/16.02 emptyset)) =>
% 120.37/16.02 (((setadjoinIR) =>
% 120.37/16.02 (((setadjoinE) =>
% 120.37/16.02 (((setadjoinOr) =>
% 120.37/16.02 (((setoftrueEq) =>
% 120.37/16.02 (((powersetI) =>
% 120.37/16.02 (((emptyinPowerset) =>
% 120.37/16.02 (((emptyInPowerset) =>
% 120.37/16.02 (((powersetE) =>
% 120.37/16.02 (((setunionI) =>
% 120.37/16.02 ((
% 120.37/16.02 (setunionE) =>
% 120.37/16.02 ((
% 120.37/16.02 (subPowSU) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuE2) =>
% 120.37/16.02 ((
% 120.37/16.02 (nonemptyImpWitness) =>
% 120.37/16.02 ((
% 120.37/16.02 (uniqinunit) =>
% 120.37/16.02 ((
% 120.37/16.02 (notinsingleton) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqinunit) =>
% 120.37/16.02 ((
% 120.37/16.02 (singletonsswitch) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairsetE) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairsetIL) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairsetIR) =>
% 120.37/16.02 ((
% 120.37/16.02 (emptyE1) =>
% 120.37/16.02 ((
% 120.37/16.02 (vacuousDall) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan1) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan2) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan3) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan4) =>
% 120.37/16.02 ((
% 120.37/16.02 (prop2setI) =>
% 120.37/16.02 ((
% 120.37/16.02 (prop2set2propI) =>
% 120.37/16.02 ((
% 120.37/16.02 (notdexE) =>
% 120.37/16.02 ((
% 120.37/16.02 (notdallE) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI3) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (inCongP) =>
% 120.37/16.02 ((
% 120.37/16.02 (in__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuE3u) =>
% 120.37/16.02 ((
% 120.37/16.02 (exu__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoin__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (powerset__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (setunion__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuEu) =>
% 120.37/16.02 ((
% 120.37/16.02 (descr__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (dsetconstr__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqimpsubset2) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqimpsubset1) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (emptysetsubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetE) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetE2) =>
% 120.37/16.02 ((
% 120.37/16.02 (notsubsetI) =>
% 120.37/16.02 ((
% 120.37/16.02 (notequalI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (notequalI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetRefl) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetTrans) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinSub) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinSub2) =>
% 120.37/16.02 ((
% 120.37/16.02 (subset2powerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (setextsub) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetemptysetimpeq) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetE1) =>
% 120.37/16.02 ((
% 120.37/16.02 (inPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetsubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (sepInPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (sepSubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (binunionIL) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairset2IR) =>
% 120.37/16.02 ((
% 120.37/16.02 (binunionIR) =>
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y0 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y1 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y2 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y3 : $o]:
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 (
% 120.37/16.02 binunion @
% 120.37/16.02 Y0 @ Y1)) =>
% 120.37/16.02 ((
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 Y0) =>
% 120.37/16.02 (Y3))) =>
% 120.37/16.02 ((
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 Y1) =>
% 120.37/16.02 (Y3))) =>
% 120.37/16.02 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl40])).
% 120.37/16.02 thf(zip_derived_cl50, plain,
% 120.37/16.02 (~ (((wellorderingAx) =>
% 120.37/16.02 (((descrp) =>
% 120.37/16.02 (((dsetconstrI) =>
% 120.37/16.02 (((dsetconstrEL) =>
% 120.37/16.02 (((dsetconstrER) =>
% 120.37/16.02 (((exuE1) =>
% 120.37/16.02 (((prop2setE) =>
% 120.37/16.02 (((emptysetE) =>
% 120.37/16.02 (((emptysetimpfalse) =>
% 120.37/16.02 (((notinemptyset) =>
% 120.37/16.02 (((exuE3e) =>
% 120.37/16.02 (((setext) =>
% 120.37/16.02 (((emptyI) =>
% 120.37/16.02 (((noeltsimpempty) =>
% 120.37/16.02 (((setbeta) =>
% 120.37/16.02 (((nonemptyE1) =>
% 120.37/16.02 (((nonemptyI) =>
% 120.37/16.02 (((nonemptyI1) =>
% 120.37/16.02 (((setadjoinIL) =>
% 120.37/16.02 (((in @ emptyset @
% 120.37/16.02 (setadjoin @ emptyset @
% 120.37/16.02 emptyset)) =>
% 120.37/16.02 (((setadjoinIR) =>
% 120.37/16.02 (((setadjoinE) =>
% 120.37/16.02 (((setadjoinOr) =>
% 120.37/16.02 (((setoftrueEq) =>
% 120.37/16.02 (((powersetI) =>
% 120.37/16.02 (((emptyinPowerset) =>
% 120.37/16.02 (((emptyInPowerset) =>
% 120.37/16.02 (((powersetE) =>
% 120.37/16.02 (((setunionI) =>
% 120.37/16.02 (((setunionE) =>
% 120.37/16.02 ((
% 120.37/16.02 (subPowSU) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuE2) =>
% 120.37/16.02 ((
% 120.37/16.02 (nonemptyImpWitness) =>
% 120.37/16.02 ((
% 120.37/16.02 (uniqinunit) =>
% 120.37/16.02 ((
% 120.37/16.02 (notinsingleton) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqinunit) =>
% 120.37/16.02 ((
% 120.37/16.02 (singletonsswitch) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairsetE) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairsetIL) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairsetIR) =>
% 120.37/16.02 ((
% 120.37/16.02 (emptyE1) =>
% 120.37/16.02 ((
% 120.37/16.02 (vacuousDall) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan1) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan2) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan3) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan4) =>
% 120.37/16.02 ((
% 120.37/16.02 (prop2setI) =>
% 120.37/16.02 ((
% 120.37/16.02 (prop2set2propI) =>
% 120.37/16.02 ((
% 120.37/16.02 (notdexE) =>
% 120.37/16.02 ((
% 120.37/16.02 (notdallE) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI3) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (inCongP) =>
% 120.37/16.02 ((
% 120.37/16.02 (in__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuE3u) =>
% 120.37/16.02 ((
% 120.37/16.02 (exu__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoin__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (powerset__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (setunion__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuEu) =>
% 120.37/16.02 ((
% 120.37/16.02 (descr__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (dsetconstr__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqimpsubset2) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqimpsubset1) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (emptysetsubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetE) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetE2) =>
% 120.37/16.02 ((
% 120.37/16.02 (notsubsetI) =>
% 120.37/16.02 ((
% 120.37/16.02 (notequalI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (notequalI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetRefl) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetTrans) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinSub) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinSub2) =>
% 120.37/16.02 ((
% 120.37/16.02 (subset2powerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (setextsub) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetemptysetimpeq) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetE1) =>
% 120.37/16.02 ((
% 120.37/16.02 (inPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetsubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (sepInPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (sepSubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (binunionIL) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairset2IR) =>
% 120.37/16.02 ((
% 120.37/16.02 (binunionIR) =>
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y0 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y1 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y2 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y3 : $o]:
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 (
% 120.37/16.02 binunion @
% 120.37/16.02 Y0 @ Y1)) =>
% 120.37/16.02 ((
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 Y0) =>
% 120.37/16.02 (Y3))) =>
% 120.37/16.02 ((
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 Y1) =>
% 120.37/16.02 (Y3))) =>
% 120.37/16.02 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl45])).
% 120.37/16.02 thf(zip_derived_cl56, plain,
% 120.37/16.02 (~ (((descrp) =>
% 120.37/16.02 (((dsetconstrI) =>
% 120.37/16.02 (((dsetconstrEL) =>
% 120.37/16.02 (((dsetconstrER) =>
% 120.37/16.02 (((exuE1) =>
% 120.37/16.02 (((prop2setE) =>
% 120.37/16.02 (((emptysetE) =>
% 120.37/16.02 (((emptysetimpfalse) =>
% 120.37/16.02 (((notinemptyset) =>
% 120.37/16.02 (((exuE3e) =>
% 120.37/16.02 (((setext) =>
% 120.37/16.02 (((emptyI) =>
% 120.37/16.02 (((noeltsimpempty) =>
% 120.37/16.02 (((setbeta) =>
% 120.37/16.02 (((nonemptyE1) =>
% 120.37/16.02 (((nonemptyI) =>
% 120.37/16.02 (((nonemptyI1) =>
% 120.37/16.02 (((setadjoinIL) =>
% 120.37/16.02 (((in @ emptyset @
% 120.37/16.02 (setadjoin @ emptyset @ emptyset)) =>
% 120.37/16.02 (((setadjoinIR) =>
% 120.37/16.02 (((setadjoinE) =>
% 120.37/16.02 (((setadjoinOr) =>
% 120.37/16.02 (((setoftrueEq) =>
% 120.37/16.02 (((powersetI) =>
% 120.37/16.02 (((emptyinPowerset) =>
% 120.37/16.02 (((emptyInPowerset) =>
% 120.37/16.02 (((powersetE) =>
% 120.37/16.02 (((setunionI) =>
% 120.37/16.02 (((setunionE) =>
% 120.37/16.02 (((subPowSU) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuE2) =>
% 120.37/16.02 ((
% 120.37/16.02 (nonemptyImpWitness) =>
% 120.37/16.02 ((
% 120.37/16.02 (uniqinunit) =>
% 120.37/16.02 ((
% 120.37/16.02 (notinsingleton) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqinunit) =>
% 120.37/16.02 ((
% 120.37/16.02 (singletonsswitch) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairsetE) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairsetIL) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairsetIR) =>
% 120.37/16.02 ((
% 120.37/16.02 (emptyE1) =>
% 120.37/16.02 ((
% 120.37/16.02 (vacuousDall) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan1) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan2) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan3) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan4) =>
% 120.37/16.02 ((
% 120.37/16.02 (prop2setI) =>
% 120.37/16.02 ((
% 120.37/16.02 (prop2set2propI) =>
% 120.37/16.02 ((
% 120.37/16.02 (notdexE) =>
% 120.37/16.02 ((
% 120.37/16.02 (notdallE) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI3) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (inCongP) =>
% 120.37/16.02 ((
% 120.37/16.02 (in__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuE3u) =>
% 120.37/16.02 ((
% 120.37/16.02 (exu__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoin__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (powerset__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (setunion__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuEu) =>
% 120.37/16.02 ((
% 120.37/16.02 (descr__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (dsetconstr__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqimpsubset2) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqimpsubset1) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (emptysetsubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetE) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetE2) =>
% 120.37/16.02 ((
% 120.37/16.02 (notsubsetI) =>
% 120.37/16.02 ((
% 120.37/16.02 (notequalI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (notequalI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetRefl) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetTrans) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinSub) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinSub2) =>
% 120.37/16.02 ((
% 120.37/16.02 (subset2powerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (setextsub) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetemptysetimpeq) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetE1) =>
% 120.37/16.02 ((
% 120.37/16.02 (inPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetsubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (sepInPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (sepSubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (binunionIL) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairset2IR) =>
% 120.37/16.02 ((
% 120.37/16.02 (binunionIR) =>
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y0 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y1 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y2 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y3 : $o]:
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 (
% 120.37/16.02 binunion @
% 120.37/16.02 Y0 @ Y1)) =>
% 120.37/16.02 ((
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 Y0) =>
% 120.37/16.02 (Y3))) =>
% 120.37/16.02 ((
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 Y1) =>
% 120.37/16.02 (Y3))) =>
% 120.37/16.02 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl50])).
% 120.37/16.02 thf(zip_derived_cl62, plain,
% 120.37/16.02 (~ (((dsetconstrI) =>
% 120.37/16.02 (((dsetconstrEL) =>
% 120.37/16.02 (((dsetconstrER) =>
% 120.37/16.02 (((exuE1) =>
% 120.37/16.02 (((prop2setE) =>
% 120.37/16.02 (((emptysetE) =>
% 120.37/16.02 (((emptysetimpfalse) =>
% 120.37/16.02 (((notinemptyset) =>
% 120.37/16.02 (((exuE3e) =>
% 120.37/16.02 (((setext) =>
% 120.37/16.02 (((emptyI) =>
% 120.37/16.02 (((noeltsimpempty) =>
% 120.37/16.02 (((setbeta) =>
% 120.37/16.02 (((nonemptyE1) =>
% 120.37/16.02 (((nonemptyI) =>
% 120.37/16.02 (((nonemptyI1) =>
% 120.37/16.02 (((setadjoinIL) =>
% 120.37/16.02 (((in @ emptyset @
% 120.37/16.02 (setadjoin @ emptyset @ emptyset)) =>
% 120.37/16.02 (((setadjoinIR) =>
% 120.37/16.02 (((setadjoinE) =>
% 120.37/16.02 (((setadjoinOr) =>
% 120.37/16.02 (((setoftrueEq) =>
% 120.37/16.02 (((powersetI) =>
% 120.37/16.02 (((emptyinPowerset) =>
% 120.37/16.02 (((emptyInPowerset) =>
% 120.37/16.02 (((powersetE) =>
% 120.37/16.02 (((setunionI) =>
% 120.37/16.02 (((setunionE) =>
% 120.37/16.02 (((subPowSU) =>
% 120.37/16.02 (((exuE2) =>
% 120.37/16.02 ((
% 120.37/16.02 (nonemptyImpWitness) =>
% 120.37/16.02 ((
% 120.37/16.02 (uniqinunit) =>
% 120.37/16.02 ((
% 120.37/16.02 (notinsingleton) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqinunit) =>
% 120.37/16.02 ((
% 120.37/16.02 (singletonsswitch) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairsetE) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairsetIL) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairsetIR) =>
% 120.37/16.02 ((
% 120.37/16.02 (emptyE1) =>
% 120.37/16.02 ((
% 120.37/16.02 (vacuousDall) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan1) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan2) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan3) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan4) =>
% 120.37/16.02 ((
% 120.37/16.02 (prop2setI) =>
% 120.37/16.02 ((
% 120.37/16.02 (prop2set2propI) =>
% 120.37/16.02 ((
% 120.37/16.02 (notdexE) =>
% 120.37/16.02 ((
% 120.37/16.02 (notdallE) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI3) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (inCongP) =>
% 120.37/16.02 ((
% 120.37/16.02 (in__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuE3u) =>
% 120.37/16.02 ((
% 120.37/16.02 (exu__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoin__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (powerset__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (setunion__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuEu) =>
% 120.37/16.02 ((
% 120.37/16.02 (descr__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (dsetconstr__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqimpsubset2) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqimpsubset1) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (emptysetsubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetE) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetE2) =>
% 120.37/16.02 ((
% 120.37/16.02 (notsubsetI) =>
% 120.37/16.02 ((
% 120.37/16.02 (notequalI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (notequalI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetRefl) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetTrans) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinSub) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinSub2) =>
% 120.37/16.02 ((
% 120.37/16.02 (subset2powerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (setextsub) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetemptysetimpeq) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetE1) =>
% 120.37/16.02 ((
% 120.37/16.02 (inPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetsubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (sepInPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (sepSubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (binunionIL) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairset2IR) =>
% 120.37/16.02 ((
% 120.37/16.02 (binunionIR) =>
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y0 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y1 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y2 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y3 : $o]:
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 (
% 120.37/16.02 binunion @
% 120.37/16.02 Y0 @ Y1)) =>
% 120.37/16.02 ((
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 Y0) =>
% 120.37/16.02 (Y3))) =>
% 120.37/16.02 ((
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 Y1) =>
% 120.37/16.02 (Y3))) =>
% 120.37/16.02 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl56])).
% 120.37/16.02 thf(zip_derived_cl69, plain,
% 120.37/16.02 (~ (((dsetconstrEL) =>
% 120.37/16.02 (((dsetconstrER) =>
% 120.37/16.02 (((exuE1) =>
% 120.37/16.02 (((prop2setE) =>
% 120.37/16.02 (((emptysetE) =>
% 120.37/16.02 (((emptysetimpfalse) =>
% 120.37/16.02 (((notinemptyset) =>
% 120.37/16.02 (((exuE3e) =>
% 120.37/16.02 (((setext) =>
% 120.37/16.02 (((emptyI) =>
% 120.37/16.02 (((noeltsimpempty) =>
% 120.37/16.02 (((setbeta) =>
% 120.37/16.02 (((nonemptyE1) =>
% 120.37/16.02 (((nonemptyI) =>
% 120.37/16.02 (((nonemptyI1) =>
% 120.37/16.02 (((setadjoinIL) =>
% 120.37/16.02 (((in @ emptyset @
% 120.37/16.02 (setadjoin @ emptyset @ emptyset)) =>
% 120.37/16.02 (((setadjoinIR) =>
% 120.37/16.02 (((setadjoinE) =>
% 120.37/16.02 (((setadjoinOr) =>
% 120.37/16.02 (((setoftrueEq) =>
% 120.37/16.02 (((powersetI) =>
% 120.37/16.02 (((emptyinPowerset) =>
% 120.37/16.02 (((emptyInPowerset) =>
% 120.37/16.02 (((powersetE) =>
% 120.37/16.02 (((setunionI) =>
% 120.37/16.02 (((setunionE) =>
% 120.37/16.02 (((subPowSU) =>
% 120.37/16.02 (((exuE2) =>
% 120.37/16.02 (((nonemptyImpWitness) =>
% 120.37/16.02 ((
% 120.37/16.02 (uniqinunit) =>
% 120.37/16.02 ((
% 120.37/16.02 (notinsingleton) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqinunit) =>
% 120.37/16.02 ((
% 120.37/16.02 (singletonsswitch) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairsetE) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairsetIL) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairsetIR) =>
% 120.37/16.02 ((
% 120.37/16.02 (emptyE1) =>
% 120.37/16.02 ((
% 120.37/16.02 (vacuousDall) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan1) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan2) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan3) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan4) =>
% 120.37/16.02 ((
% 120.37/16.02 (prop2setI) =>
% 120.37/16.02 ((
% 120.37/16.02 (prop2set2propI) =>
% 120.37/16.02 ((
% 120.37/16.02 (notdexE) =>
% 120.37/16.02 ((
% 120.37/16.02 (notdallE) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI3) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (inCongP) =>
% 120.37/16.02 ((
% 120.37/16.02 (in__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuE3u) =>
% 120.37/16.02 ((
% 120.37/16.02 (exu__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoin__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (powerset__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (setunion__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuEu) =>
% 120.37/16.02 ((
% 120.37/16.02 (descr__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (dsetconstr__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqimpsubset2) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqimpsubset1) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (emptysetsubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetE) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetE2) =>
% 120.37/16.02 ((
% 120.37/16.02 (notsubsetI) =>
% 120.37/16.02 ((
% 120.37/16.02 (notequalI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (notequalI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetRefl) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetTrans) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinSub) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinSub2) =>
% 120.37/16.02 ((
% 120.37/16.02 (subset2powerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (setextsub) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetemptysetimpeq) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetE1) =>
% 120.37/16.02 ((
% 120.37/16.02 (inPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetsubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (sepInPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (sepSubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (binunionIL) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairset2IR) =>
% 120.37/16.02 ((
% 120.37/16.02 (binunionIR) =>
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y0 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y1 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y2 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y3 : $o]:
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 (
% 120.37/16.02 binunion @
% 120.37/16.02 Y0 @ Y1)) =>
% 120.37/16.02 ((
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 Y0) =>
% 120.37/16.02 (Y3))) =>
% 120.37/16.02 ((
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 Y1) =>
% 120.37/16.02 (Y3))) =>
% 120.37/16.02 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl62])).
% 120.37/16.02 thf(zip_derived_cl79, plain,
% 120.37/16.02 (~ (((dsetconstrER) =>
% 120.37/16.02 (((exuE1) =>
% 120.37/16.02 (((prop2setE) =>
% 120.37/16.02 (((emptysetE) =>
% 120.37/16.02 (((emptysetimpfalse) =>
% 120.37/16.02 (((notinemptyset) =>
% 120.37/16.02 (((exuE3e) =>
% 120.37/16.02 (((setext) =>
% 120.37/16.02 (((emptyI) =>
% 120.37/16.02 (((noeltsimpempty) =>
% 120.37/16.02 (((setbeta) =>
% 120.37/16.02 (((nonemptyE1) =>
% 120.37/16.02 (((nonemptyI) =>
% 120.37/16.02 (((nonemptyI1) =>
% 120.37/16.02 (((setadjoinIL) =>
% 120.37/16.02 (((in @ emptyset @
% 120.37/16.02 (setadjoin @ emptyset @ emptyset)) =>
% 120.37/16.02 (((setadjoinIR) =>
% 120.37/16.02 (((setadjoinE) =>
% 120.37/16.02 (((setadjoinOr) =>
% 120.37/16.02 (((setoftrueEq) =>
% 120.37/16.02 (((powersetI) =>
% 120.37/16.02 (((emptyinPowerset) =>
% 120.37/16.02 (((emptyInPowerset) =>
% 120.37/16.02 (((powersetE) =>
% 120.37/16.02 (((setunionI) =>
% 120.37/16.02 (((setunionE) =>
% 120.37/16.02 (((subPowSU) =>
% 120.37/16.02 (((exuE2) =>
% 120.37/16.02 (((nonemptyImpWitness) =>
% 120.37/16.02 (((uniqinunit) =>
% 120.37/16.02 ((
% 120.37/16.02 (notinsingleton) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqinunit) =>
% 120.37/16.02 ((
% 120.37/16.02 (singletonsswitch) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairsetE) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairsetIL) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairsetIR) =>
% 120.37/16.02 ((
% 120.37/16.02 (emptyE1) =>
% 120.37/16.02 ((
% 120.37/16.02 (vacuousDall) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan1) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan2) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan3) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan4) =>
% 120.37/16.02 ((
% 120.37/16.02 (prop2setI) =>
% 120.37/16.02 ((
% 120.37/16.02 (prop2set2propI) =>
% 120.37/16.02 ((
% 120.37/16.02 (notdexE) =>
% 120.37/16.02 ((
% 120.37/16.02 (notdallE) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI3) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (inCongP) =>
% 120.37/16.02 ((
% 120.37/16.02 (in__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuE3u) =>
% 120.37/16.02 ((
% 120.37/16.02 (exu__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoin__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (powerset__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (setunion__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuEu) =>
% 120.37/16.02 ((
% 120.37/16.02 (descr__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (dsetconstr__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqimpsubset2) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqimpsubset1) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (emptysetsubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetE) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetE2) =>
% 120.37/16.02 ((
% 120.37/16.02 (notsubsetI) =>
% 120.37/16.02 ((
% 120.37/16.02 (notequalI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (notequalI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetRefl) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetTrans) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinSub) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinSub2) =>
% 120.37/16.02 ((
% 120.37/16.02 (subset2powerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (setextsub) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetemptysetimpeq) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetE1) =>
% 120.37/16.02 ((
% 120.37/16.02 (inPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetsubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (sepInPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (sepSubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (binunionIL) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairset2IR) =>
% 120.37/16.02 ((
% 120.37/16.02 (binunionIR) =>
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y0 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y1 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y2 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y3 : $o]:
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 (
% 120.37/16.02 binunion @
% 120.37/16.02 Y0 @ Y1)) =>
% 120.37/16.02 ((
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 Y0) =>
% 120.37/16.02 (Y3))) =>
% 120.37/16.02 ((
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 Y1) =>
% 120.37/16.02 (Y3))) =>
% 120.37/16.02 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl69])).
% 120.37/16.02 thf(zip_derived_cl95, plain,
% 120.37/16.02 (~ (((exuE1) =>
% 120.37/16.02 (((prop2setE) =>
% 120.37/16.02 (((emptysetE) =>
% 120.37/16.02 (((emptysetimpfalse) =>
% 120.37/16.02 (((notinemptyset) =>
% 120.37/16.02 (((exuE3e) =>
% 120.37/16.02 (((setext) =>
% 120.37/16.02 (((emptyI) =>
% 120.37/16.02 (((noeltsimpempty) =>
% 120.37/16.02 (((setbeta) =>
% 120.37/16.02 (((nonemptyE1) =>
% 120.37/16.02 (((nonemptyI) =>
% 120.37/16.02 (((nonemptyI1) =>
% 120.37/16.02 (((setadjoinIL) =>
% 120.37/16.02 (((in @ emptyset @
% 120.37/16.02 (setadjoin @ emptyset @ emptyset)) =>
% 120.37/16.02 (((setadjoinIR) =>
% 120.37/16.02 (((setadjoinE) =>
% 120.37/16.02 (((setadjoinOr) =>
% 120.37/16.02 (((setoftrueEq) =>
% 120.37/16.02 (((powersetI) =>
% 120.37/16.02 (((emptyinPowerset) =>
% 120.37/16.02 (((emptyInPowerset) =>
% 120.37/16.02 (((powersetE) =>
% 120.37/16.02 (((setunionI) =>
% 120.37/16.02 (((setunionE) =>
% 120.37/16.02 (((subPowSU) =>
% 120.37/16.02 (((exuE2) =>
% 120.37/16.02 (((nonemptyImpWitness) =>
% 120.37/16.02 (((uniqinunit) =>
% 120.37/16.02 (((notinsingleton) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqinunit) =>
% 120.37/16.02 ((
% 120.37/16.02 (singletonsswitch) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairsetE) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairsetIL) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairsetIR) =>
% 120.37/16.02 ((
% 120.37/16.02 (emptyE1) =>
% 120.37/16.02 ((
% 120.37/16.02 (vacuousDall) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan1) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan2) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan3) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan4) =>
% 120.37/16.02 ((
% 120.37/16.02 (prop2setI) =>
% 120.37/16.02 ((
% 120.37/16.02 (prop2set2propI) =>
% 120.37/16.02 ((
% 120.37/16.02 (notdexE) =>
% 120.37/16.02 ((
% 120.37/16.02 (notdallE) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI3) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (inCongP) =>
% 120.37/16.02 ((
% 120.37/16.02 (in__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuE3u) =>
% 120.37/16.02 ((
% 120.37/16.02 (exu__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoin__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (powerset__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (setunion__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuEu) =>
% 120.37/16.02 ((
% 120.37/16.02 (descr__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (dsetconstr__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqimpsubset2) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqimpsubset1) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (emptysetsubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetE) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetE2) =>
% 120.37/16.02 ((
% 120.37/16.02 (notsubsetI) =>
% 120.37/16.02 ((
% 120.37/16.02 (notequalI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (notequalI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetRefl) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetTrans) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinSub) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinSub2) =>
% 120.37/16.02 ((
% 120.37/16.02 (subset2powerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (setextsub) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetemptysetimpeq) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetE1) =>
% 120.37/16.02 ((
% 120.37/16.02 (inPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetsubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (sepInPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (sepSubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (binunionIL) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairset2IR) =>
% 120.37/16.02 ((
% 120.37/16.02 (binunionIR) =>
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y0 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y1 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y2 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y3 : $o]:
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 (
% 120.37/16.02 binunion @
% 120.37/16.02 Y0 @ Y1)) =>
% 120.37/16.02 ((
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 Y0) =>
% 120.37/16.02 (Y3))) =>
% 120.37/16.02 ((
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 Y1) =>
% 120.37/16.02 (Y3))) =>
% 120.37/16.02 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl79])).
% 120.37/16.02 thf(zip_derived_cl115, plain,
% 120.37/16.02 (~ (((prop2setE) =>
% 120.37/16.02 (((emptysetE) =>
% 120.37/16.02 (((emptysetimpfalse) =>
% 120.37/16.02 (((notinemptyset) =>
% 120.37/16.02 (((exuE3e) =>
% 120.37/16.02 (((setext) =>
% 120.37/16.02 (((emptyI) =>
% 120.37/16.02 (((noeltsimpempty) =>
% 120.37/16.02 (((setbeta) =>
% 120.37/16.02 (((nonemptyE1) =>
% 120.37/16.02 (((nonemptyI) =>
% 120.37/16.02 (((nonemptyI1) =>
% 120.37/16.02 (((setadjoinIL) =>
% 120.37/16.02 (((in @ emptyset @
% 120.37/16.02 (setadjoin @ emptyset @ emptyset)) =>
% 120.37/16.02 (((setadjoinIR) =>
% 120.37/16.02 (((setadjoinE) =>
% 120.37/16.02 (((setadjoinOr) =>
% 120.37/16.02 (((setoftrueEq) =>
% 120.37/16.02 (((powersetI) =>
% 120.37/16.02 (((emptyinPowerset) =>
% 120.37/16.02 (((emptyInPowerset) =>
% 120.37/16.02 (((powersetE) =>
% 120.37/16.02 (((setunionI) =>
% 120.37/16.02 (((setunionE) =>
% 120.37/16.02 (((subPowSU) =>
% 120.37/16.02 (((exuE2) =>
% 120.37/16.02 (((nonemptyImpWitness) =>
% 120.37/16.02 (((uniqinunit) =>
% 120.37/16.02 (((notinsingleton) =>
% 120.37/16.02 (((eqinunit) =>
% 120.37/16.02 ((
% 120.37/16.02 (singletonsswitch) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairsetE) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairsetIL) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairsetIR) =>
% 120.37/16.02 ((
% 120.37/16.02 (emptyE1) =>
% 120.37/16.02 ((
% 120.37/16.02 (vacuousDall) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan1) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan2) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan3) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan4) =>
% 120.37/16.02 ((
% 120.37/16.02 (prop2setI) =>
% 120.37/16.02 ((
% 120.37/16.02 (prop2set2propI) =>
% 120.37/16.02 ((
% 120.37/16.02 (notdexE) =>
% 120.37/16.02 ((
% 120.37/16.02 (notdallE) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI3) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (inCongP) =>
% 120.37/16.02 ((
% 120.37/16.02 (in__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuE3u) =>
% 120.37/16.02 ((
% 120.37/16.02 (exu__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoin__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (powerset__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (setunion__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuEu) =>
% 120.37/16.02 ((
% 120.37/16.02 (descr__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (dsetconstr__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqimpsubset2) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqimpsubset1) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (emptysetsubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetE) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetE2) =>
% 120.37/16.02 ((
% 120.37/16.02 (notsubsetI) =>
% 120.37/16.02 ((
% 120.37/16.02 (notequalI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (notequalI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetRefl) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetTrans) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinSub) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinSub2) =>
% 120.37/16.02 ((
% 120.37/16.02 (subset2powerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (setextsub) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetemptysetimpeq) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetE1) =>
% 120.37/16.02 ((
% 120.37/16.02 (inPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetsubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (sepInPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (sepSubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (binunionIL) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairset2IR) =>
% 120.37/16.02 ((
% 120.37/16.02 (binunionIR) =>
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y0 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y1 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y2 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y3 : $o]:
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 (
% 120.37/16.02 binunion @
% 120.37/16.02 Y0 @ Y1)) =>
% 120.37/16.02 ((
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 Y0) =>
% 120.37/16.02 (Y3))) =>
% 120.37/16.02 ((
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 Y1) =>
% 120.37/16.02 (Y3))) =>
% 120.37/16.02 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl95])).
% 120.37/16.02 thf(zip_derived_cl133, plain,
% 120.37/16.02 (~ (((emptysetE) =>
% 120.37/16.02 (((emptysetimpfalse) =>
% 120.37/16.02 (((notinemptyset) =>
% 120.37/16.02 (((exuE3e) =>
% 120.37/16.02 (((setext) =>
% 120.37/16.02 (((emptyI) =>
% 120.37/16.02 (((noeltsimpempty) =>
% 120.37/16.02 (((setbeta) =>
% 120.37/16.02 (((nonemptyE1) =>
% 120.37/16.02 (((nonemptyI) =>
% 120.37/16.02 (((nonemptyI1) =>
% 120.37/16.02 (((setadjoinIL) =>
% 120.37/16.02 (((in @ emptyset @
% 120.37/16.02 (setadjoin @ emptyset @ emptyset)) =>
% 120.37/16.02 (((setadjoinIR) =>
% 120.37/16.02 (((setadjoinE) =>
% 120.37/16.02 (((setadjoinOr) =>
% 120.37/16.02 (((setoftrueEq) =>
% 120.37/16.02 (((powersetI) =>
% 120.37/16.02 (((emptyinPowerset) =>
% 120.37/16.02 (((emptyInPowerset) =>
% 120.37/16.02 (((powersetE) =>
% 120.37/16.02 (((setunionI) =>
% 120.37/16.02 (((setunionE) =>
% 120.37/16.02 (((subPowSU) =>
% 120.37/16.02 (((exuE2) =>
% 120.37/16.02 (((nonemptyImpWitness) =>
% 120.37/16.02 (((uniqinunit) =>
% 120.37/16.02 (((notinsingleton) =>
% 120.37/16.02 (((eqinunit) =>
% 120.37/16.02 (((singletonsswitch) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairsetE) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairsetIL) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairsetIR) =>
% 120.37/16.02 ((
% 120.37/16.02 (emptyE1) =>
% 120.37/16.02 ((
% 120.37/16.02 (vacuousDall) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan1) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan2) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan3) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan4) =>
% 120.37/16.02 ((
% 120.37/16.02 (prop2setI) =>
% 120.37/16.02 ((
% 120.37/16.02 (prop2set2propI) =>
% 120.37/16.02 ((
% 120.37/16.02 (notdexE) =>
% 120.37/16.02 ((
% 120.37/16.02 (notdallE) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI3) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (inCongP) =>
% 120.37/16.02 ((
% 120.37/16.02 (in__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuE3u) =>
% 120.37/16.02 ((
% 120.37/16.02 (exu__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoin__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (powerset__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (setunion__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuEu) =>
% 120.37/16.02 ((
% 120.37/16.02 (descr__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (dsetconstr__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqimpsubset2) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqimpsubset1) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (emptysetsubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetE) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetE2) =>
% 120.37/16.02 ((
% 120.37/16.02 (notsubsetI) =>
% 120.37/16.02 ((
% 120.37/16.02 (notequalI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (notequalI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetRefl) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetTrans) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinSub) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinSub2) =>
% 120.37/16.02 ((
% 120.37/16.02 (subset2powerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (setextsub) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetemptysetimpeq) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetE1) =>
% 120.37/16.02 ((
% 120.37/16.02 (inPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetsubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (sepInPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (sepSubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (binunionIL) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairset2IR) =>
% 120.37/16.02 ((
% 120.37/16.02 (binunionIR) =>
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y0 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y1 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y2 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y3 : $o]:
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 (
% 120.37/16.02 binunion @
% 120.37/16.02 Y0 @ Y1)) =>
% 120.37/16.02 ((
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 Y0) =>
% 120.37/16.02 (Y3))) =>
% 120.37/16.02 ((
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 Y1) =>
% 120.37/16.02 (Y3))) =>
% 120.37/16.02 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl115])).
% 120.37/16.02 thf(zip_derived_cl149, plain,
% 120.37/16.02 (~ (((emptysetimpfalse) =>
% 120.37/16.02 (((notinemptyset) =>
% 120.37/16.02 (((exuE3e) =>
% 120.37/16.02 (((setext) =>
% 120.37/16.02 (((emptyI) =>
% 120.37/16.02 (((noeltsimpempty) =>
% 120.37/16.02 (((setbeta) =>
% 120.37/16.02 (((nonemptyE1) =>
% 120.37/16.02 (((nonemptyI) =>
% 120.37/16.02 (((nonemptyI1) =>
% 120.37/16.02 (((setadjoinIL) =>
% 120.37/16.02 (((in @ emptyset @
% 120.37/16.02 (setadjoin @ emptyset @ emptyset)) =>
% 120.37/16.02 (((setadjoinIR) =>
% 120.37/16.02 (((setadjoinE) =>
% 120.37/16.02 (((setadjoinOr) =>
% 120.37/16.02 (((setoftrueEq) =>
% 120.37/16.02 (((powersetI) =>
% 120.37/16.02 (((emptyinPowerset) =>
% 120.37/16.02 (((emptyInPowerset) =>
% 120.37/16.02 (((powersetE) =>
% 120.37/16.02 (((setunionI) =>
% 120.37/16.02 (((setunionE) =>
% 120.37/16.02 (((subPowSU) =>
% 120.37/16.02 (((exuE2) =>
% 120.37/16.02 (((nonemptyImpWitness) =>
% 120.37/16.02 (((uniqinunit) =>
% 120.37/16.02 (((notinsingleton) =>
% 120.37/16.02 (((eqinunit) =>
% 120.37/16.02 (((singletonsswitch) =>
% 120.37/16.02 (((upairsetE) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairsetIL) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairsetIR) =>
% 120.37/16.02 ((
% 120.37/16.02 (emptyE1) =>
% 120.37/16.02 ((
% 120.37/16.02 (vacuousDall) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan1) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan2) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan3) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan4) =>
% 120.37/16.02 ((
% 120.37/16.02 (prop2setI) =>
% 120.37/16.02 ((
% 120.37/16.02 (prop2set2propI) =>
% 120.37/16.02 ((
% 120.37/16.02 (notdexE) =>
% 120.37/16.02 ((
% 120.37/16.02 (notdallE) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI3) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (inCongP) =>
% 120.37/16.02 ((
% 120.37/16.02 (in__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuE3u) =>
% 120.37/16.02 ((
% 120.37/16.02 (exu__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoin__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (powerset__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (setunion__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuEu) =>
% 120.37/16.02 ((
% 120.37/16.02 (descr__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (dsetconstr__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqimpsubset2) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqimpsubset1) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (emptysetsubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetE) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetE2) =>
% 120.37/16.02 ((
% 120.37/16.02 (notsubsetI) =>
% 120.37/16.02 ((
% 120.37/16.02 (notequalI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (notequalI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetRefl) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetTrans) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinSub) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinSub2) =>
% 120.37/16.02 ((
% 120.37/16.02 (subset2powerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (setextsub) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetemptysetimpeq) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetE1) =>
% 120.37/16.02 ((
% 120.37/16.02 (inPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetsubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (sepInPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (sepSubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (binunionIL) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairset2IR) =>
% 120.37/16.02 ((
% 120.37/16.02 (binunionIR) =>
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y0 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y1 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y2 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y3 : $o]:
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 (
% 120.37/16.02 binunion @
% 120.37/16.02 Y0 @ Y1)) =>
% 120.37/16.02 ((
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 Y0) =>
% 120.37/16.02 (Y3))) =>
% 120.37/16.02 ((
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 Y1) =>
% 120.37/16.02 (Y3))) =>
% 120.37/16.02 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl133])).
% 120.37/16.02 thf(zip_derived_cl164, plain,
% 120.37/16.02 (~ (((notinemptyset) =>
% 120.37/16.02 (((exuE3e) =>
% 120.37/16.02 (((setext) =>
% 120.37/16.02 (((emptyI) =>
% 120.37/16.02 (((noeltsimpempty) =>
% 120.37/16.02 (((setbeta) =>
% 120.37/16.02 (((nonemptyE1) =>
% 120.37/16.02 (((nonemptyI) =>
% 120.37/16.02 (((nonemptyI1) =>
% 120.37/16.02 (((setadjoinIL) =>
% 120.37/16.02 (((in @ emptyset @
% 120.37/16.02 (setadjoin @ emptyset @ emptyset)) =>
% 120.37/16.02 (((setadjoinIR) =>
% 120.37/16.02 (((setadjoinE) =>
% 120.37/16.02 (((setadjoinOr) =>
% 120.37/16.02 (((setoftrueEq) =>
% 120.37/16.02 (((powersetI) =>
% 120.37/16.02 (((emptyinPowerset) =>
% 120.37/16.02 (((emptyInPowerset) =>
% 120.37/16.02 (((powersetE) =>
% 120.37/16.02 (((setunionI) =>
% 120.37/16.02 (((setunionE) =>
% 120.37/16.02 (((subPowSU) =>
% 120.37/16.02 (((exuE2) =>
% 120.37/16.02 (((nonemptyImpWitness) =>
% 120.37/16.02 (((uniqinunit) =>
% 120.37/16.02 (((notinsingleton) =>
% 120.37/16.02 (((eqinunit) =>
% 120.37/16.02 (((singletonsswitch) =>
% 120.37/16.02 (((upairsetE) =>
% 120.37/16.02 (((upairsetIL) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairsetIR) =>
% 120.37/16.02 ((
% 120.37/16.02 (emptyE1) =>
% 120.37/16.02 ((
% 120.37/16.02 (vacuousDall) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan1) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan2) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan3) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan4) =>
% 120.37/16.02 ((
% 120.37/16.02 (prop2setI) =>
% 120.37/16.02 ((
% 120.37/16.02 (prop2set2propI) =>
% 120.37/16.02 ((
% 120.37/16.02 (notdexE) =>
% 120.37/16.02 ((
% 120.37/16.02 (notdallE) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI3) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (inCongP) =>
% 120.37/16.02 ((
% 120.37/16.02 (in__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuE3u) =>
% 120.37/16.02 ((
% 120.37/16.02 (exu__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoin__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (powerset__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (setunion__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuEu) =>
% 120.37/16.02 ((
% 120.37/16.02 (descr__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (dsetconstr__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqimpsubset2) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqimpsubset1) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (emptysetsubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetE) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetE2) =>
% 120.37/16.02 ((
% 120.37/16.02 (notsubsetI) =>
% 120.37/16.02 ((
% 120.37/16.02 (notequalI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (notequalI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetRefl) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetTrans) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinSub) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinSub2) =>
% 120.37/16.02 ((
% 120.37/16.02 (subset2powerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (setextsub) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetemptysetimpeq) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetE1) =>
% 120.37/16.02 ((
% 120.37/16.02 (inPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetsubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (sepInPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (sepSubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (binunionIL) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairset2IR) =>
% 120.37/16.02 ((
% 120.37/16.02 (binunionIR) =>
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y0 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y1 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y2 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y3 : $o]:
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 (
% 120.37/16.02 binunion @
% 120.37/16.02 Y0 @ Y1)) =>
% 120.37/16.02 ((
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 Y0) =>
% 120.37/16.02 (Y3))) =>
% 120.37/16.02 ((
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 Y1) =>
% 120.37/16.02 (Y3))) =>
% 120.37/16.02 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl149])).
% 120.37/16.02 thf(zip_derived_cl177, plain,
% 120.37/16.02 (~ (((exuE3e) =>
% 120.37/16.02 (((setext) =>
% 120.37/16.02 (((emptyI) =>
% 120.37/16.02 (((noeltsimpempty) =>
% 120.37/16.02 (((setbeta) =>
% 120.37/16.02 (((nonemptyE1) =>
% 120.37/16.02 (((nonemptyI) =>
% 120.37/16.02 (((nonemptyI1) =>
% 120.37/16.02 (((setadjoinIL) =>
% 120.37/16.02 (((in @ emptyset @
% 120.37/16.02 (setadjoin @ emptyset @ emptyset)) =>
% 120.37/16.02 (((setadjoinIR) =>
% 120.37/16.02 (((setadjoinE) =>
% 120.37/16.02 (((setadjoinOr) =>
% 120.37/16.02 (((setoftrueEq) =>
% 120.37/16.02 (((powersetI) =>
% 120.37/16.02 (((emptyinPowerset) =>
% 120.37/16.02 (((emptyInPowerset) =>
% 120.37/16.02 (((powersetE) =>
% 120.37/16.02 (((setunionI) =>
% 120.37/16.02 (((setunionE) =>
% 120.37/16.02 (((subPowSU) =>
% 120.37/16.02 (((exuE2) =>
% 120.37/16.02 (((nonemptyImpWitness) =>
% 120.37/16.02 (((uniqinunit) =>
% 120.37/16.02 (((notinsingleton) =>
% 120.37/16.02 (((eqinunit) =>
% 120.37/16.02 (((singletonsswitch) =>
% 120.37/16.02 (((upairsetE) =>
% 120.37/16.02 (((upairsetIL) =>
% 120.37/16.02 (((upairsetIR) =>
% 120.37/16.02 ((
% 120.37/16.02 (emptyE1) =>
% 120.37/16.02 ((
% 120.37/16.02 (vacuousDall) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan1) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan2) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan3) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan4) =>
% 120.37/16.02 ((
% 120.37/16.02 (prop2setI) =>
% 120.37/16.02 ((
% 120.37/16.02 (prop2set2propI) =>
% 120.37/16.02 ((
% 120.37/16.02 (notdexE) =>
% 120.37/16.02 ((
% 120.37/16.02 (notdallE) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI3) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (inCongP) =>
% 120.37/16.02 ((
% 120.37/16.02 (in__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuE3u) =>
% 120.37/16.02 ((
% 120.37/16.02 (exu__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoin__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (powerset__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (setunion__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuEu) =>
% 120.37/16.02 ((
% 120.37/16.02 (descr__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (dsetconstr__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqimpsubset2) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqimpsubset1) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (emptysetsubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetE) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetE2) =>
% 120.37/16.02 ((
% 120.37/16.02 (notsubsetI) =>
% 120.37/16.02 ((
% 120.37/16.02 (notequalI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (notequalI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetRefl) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetTrans) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinSub) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinSub2) =>
% 120.37/16.02 ((
% 120.37/16.02 (subset2powerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (setextsub) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetemptysetimpeq) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetE1) =>
% 120.37/16.02 ((
% 120.37/16.02 (inPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetsubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (sepInPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (sepSubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (binunionIL) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairset2IR) =>
% 120.37/16.02 ((
% 120.37/16.02 (binunionIR) =>
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y0 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y1 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y2 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y3 : $o]:
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 (
% 120.37/16.02 binunion @
% 120.37/16.02 Y0 @ Y1)) =>
% 120.37/16.02 ((
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 Y0) =>
% 120.37/16.02 (Y3))) =>
% 120.37/16.02 ((
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 Y1) =>
% 120.37/16.02 (Y3))) =>
% 120.37/16.02 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl164])).
% 120.37/16.02 thf(zip_derived_cl191, plain,
% 120.37/16.02 (~ (((setext) =>
% 120.37/16.02 (((emptyI) =>
% 120.37/16.02 (((noeltsimpempty) =>
% 120.37/16.02 (((setbeta) =>
% 120.37/16.02 (((nonemptyE1) =>
% 120.37/16.02 (((nonemptyI) =>
% 120.37/16.02 (((nonemptyI1) =>
% 120.37/16.02 (((setadjoinIL) =>
% 120.37/16.02 (((in @ emptyset @
% 120.37/16.02 (setadjoin @ emptyset @ emptyset)) =>
% 120.37/16.02 (((setadjoinIR) =>
% 120.37/16.02 (((setadjoinE) =>
% 120.37/16.02 (((setadjoinOr) =>
% 120.37/16.02 (((setoftrueEq) =>
% 120.37/16.02 (((powersetI) =>
% 120.37/16.02 (((emptyinPowerset) =>
% 120.37/16.02 (((emptyInPowerset) =>
% 120.37/16.02 (((powersetE) =>
% 120.37/16.02 (((setunionI) =>
% 120.37/16.02 (((setunionE) =>
% 120.37/16.02 (((subPowSU) =>
% 120.37/16.02 (((exuE2) =>
% 120.37/16.02 (((nonemptyImpWitness) =>
% 120.37/16.02 (((uniqinunit) =>
% 120.37/16.02 (((notinsingleton) =>
% 120.37/16.02 (((eqinunit) =>
% 120.37/16.02 (((singletonsswitch) =>
% 120.37/16.02 (((upairsetE) =>
% 120.37/16.02 (((upairsetIL) =>
% 120.37/16.02 (((upairsetIR) =>
% 120.37/16.02 (((emptyE1) =>
% 120.37/16.02 ((
% 120.37/16.02 (vacuousDall) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan1) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan2) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan3) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan4) =>
% 120.37/16.02 ((
% 120.37/16.02 (prop2setI) =>
% 120.37/16.02 ((
% 120.37/16.02 (prop2set2propI) =>
% 120.37/16.02 ((
% 120.37/16.02 (notdexE) =>
% 120.37/16.02 ((
% 120.37/16.02 (notdallE) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI3) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (inCongP) =>
% 120.37/16.02 ((
% 120.37/16.02 (in__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuE3u) =>
% 120.37/16.02 ((
% 120.37/16.02 (exu__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoin__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (powerset__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (setunion__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuEu) =>
% 120.37/16.02 ((
% 120.37/16.02 (descr__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (dsetconstr__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqimpsubset2) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqimpsubset1) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (emptysetsubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetE) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetE2) =>
% 120.37/16.02 ((
% 120.37/16.02 (notsubsetI) =>
% 120.37/16.02 ((
% 120.37/16.02 (notequalI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (notequalI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetRefl) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetTrans) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinSub) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinSub2) =>
% 120.37/16.02 ((
% 120.37/16.02 (subset2powerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (setextsub) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetemptysetimpeq) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetE1) =>
% 120.37/16.02 ((
% 120.37/16.02 (inPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetsubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (sepInPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (sepSubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (binunionIL) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairset2IR) =>
% 120.37/16.02 ((
% 120.37/16.02 (binunionIR) =>
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y0 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y1 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y2 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y3 : $o]:
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 (
% 120.37/16.02 binunion @
% 120.37/16.02 Y0 @ Y1)) =>
% 120.37/16.02 ((
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 Y0) =>
% 120.37/16.02 (Y3))) =>
% 120.37/16.02 ((
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 Y1) =>
% 120.37/16.02 (Y3))) =>
% 120.37/16.02 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl177])).
% 120.37/16.02 thf(zip_derived_cl205, plain,
% 120.37/16.02 (~ (((emptyI) =>
% 120.37/16.02 (((noeltsimpempty) =>
% 120.37/16.02 (((setbeta) =>
% 120.37/16.02 (((nonemptyE1) =>
% 120.37/16.02 (((nonemptyI) =>
% 120.37/16.02 (((nonemptyI1) =>
% 120.37/16.02 (((setadjoinIL) =>
% 120.37/16.02 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 120.37/16.02 (((setadjoinIR) =>
% 120.37/16.02 (((setadjoinE) =>
% 120.37/16.02 (((setadjoinOr) =>
% 120.37/16.02 (((setoftrueEq) =>
% 120.37/16.02 (((powersetI) =>
% 120.37/16.02 (((emptyinPowerset) =>
% 120.37/16.02 (((emptyInPowerset) =>
% 120.37/16.02 (((powersetE) =>
% 120.37/16.02 (((setunionI) =>
% 120.37/16.02 (((setunionE) =>
% 120.37/16.02 (((subPowSU) =>
% 120.37/16.02 (((exuE2) =>
% 120.37/16.02 (((nonemptyImpWitness) =>
% 120.37/16.02 (((uniqinunit) =>
% 120.37/16.02 (((notinsingleton) =>
% 120.37/16.02 (((eqinunit) =>
% 120.37/16.02 (((singletonsswitch) =>
% 120.37/16.02 (((upairsetE) =>
% 120.37/16.02 (((upairsetIL) =>
% 120.37/16.02 (((upairsetIR) =>
% 120.37/16.02 (((emptyE1) =>
% 120.37/16.02 (((vacuousDall) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan1) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan2) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan3) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan4) =>
% 120.37/16.02 ((
% 120.37/16.02 (prop2setI) =>
% 120.37/16.02 ((
% 120.37/16.02 (prop2set2propI) =>
% 120.37/16.02 ((
% 120.37/16.02 (notdexE) =>
% 120.37/16.02 ((
% 120.37/16.02 (notdallE) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI3) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (inCongP) =>
% 120.37/16.02 ((
% 120.37/16.02 (in__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuE3u) =>
% 120.37/16.02 ((
% 120.37/16.02 (exu__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoin__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (powerset__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (setunion__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuEu) =>
% 120.37/16.02 ((
% 120.37/16.02 (descr__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (dsetconstr__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqimpsubset2) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqimpsubset1) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (emptysetsubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetE) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetE2) =>
% 120.37/16.02 ((
% 120.37/16.02 (notsubsetI) =>
% 120.37/16.02 ((
% 120.37/16.02 (notequalI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (notequalI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetRefl) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetTrans) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinSub) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinSub2) =>
% 120.37/16.02 ((
% 120.37/16.02 (subset2powerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (setextsub) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetemptysetimpeq) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetE1) =>
% 120.37/16.02 ((
% 120.37/16.02 (inPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetsubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (sepInPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (sepSubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (binunionIL) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairset2IR) =>
% 120.37/16.02 ((
% 120.37/16.02 (binunionIR) =>
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y0 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y1 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y2 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y3 : $o]:
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 (
% 120.37/16.02 binunion @
% 120.37/16.02 Y0 @ Y1)) =>
% 120.37/16.02 ((
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 Y0) =>
% 120.37/16.02 (Y3))) =>
% 120.37/16.02 ((
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 Y1) =>
% 120.37/16.02 (Y3))) =>
% 120.37/16.02 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl191])).
% 120.37/16.02 thf(zip_derived_cl219, plain,
% 120.37/16.02 (~ (((noeltsimpempty) =>
% 120.37/16.02 (((setbeta) =>
% 120.37/16.02 (((nonemptyE1) =>
% 120.37/16.02 (((nonemptyI) =>
% 120.37/16.02 (((nonemptyI1) =>
% 120.37/16.02 (((setadjoinIL) =>
% 120.37/16.02 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 120.37/16.02 (((setadjoinIR) =>
% 120.37/16.02 (((setadjoinE) =>
% 120.37/16.02 (((setadjoinOr) =>
% 120.37/16.02 (((setoftrueEq) =>
% 120.37/16.02 (((powersetI) =>
% 120.37/16.02 (((emptyinPowerset) =>
% 120.37/16.02 (((emptyInPowerset) =>
% 120.37/16.02 (((powersetE) =>
% 120.37/16.02 (((setunionI) =>
% 120.37/16.02 (((setunionE) =>
% 120.37/16.02 (((subPowSU) =>
% 120.37/16.02 (((exuE2) =>
% 120.37/16.02 (((nonemptyImpWitness) =>
% 120.37/16.02 (((uniqinunit) =>
% 120.37/16.02 (((notinsingleton) =>
% 120.37/16.02 (((eqinunit) =>
% 120.37/16.02 (((singletonsswitch) =>
% 120.37/16.02 (((upairsetE) =>
% 120.37/16.02 (((upairsetIL) =>
% 120.37/16.02 (((upairsetIR) =>
% 120.37/16.02 (((emptyE1) =>
% 120.37/16.02 (((vacuousDall) =>
% 120.37/16.02 (((quantDeMorgan1) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan2) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan3) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan4) =>
% 120.37/16.02 ((
% 120.37/16.02 (prop2setI) =>
% 120.37/16.02 ((
% 120.37/16.02 (prop2set2propI) =>
% 120.37/16.02 ((
% 120.37/16.02 (notdexE) =>
% 120.37/16.02 ((
% 120.37/16.02 (notdallE) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI3) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (inCongP) =>
% 120.37/16.02 ((
% 120.37/16.02 (in__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuE3u) =>
% 120.37/16.02 ((
% 120.37/16.02 (exu__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoin__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (powerset__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (setunion__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuEu) =>
% 120.37/16.02 ((
% 120.37/16.02 (descr__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (dsetconstr__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqimpsubset2) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqimpsubset1) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (emptysetsubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetE) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetE2) =>
% 120.37/16.02 ((
% 120.37/16.02 (notsubsetI) =>
% 120.37/16.02 ((
% 120.37/16.02 (notequalI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (notequalI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetRefl) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetTrans) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinSub) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinSub2) =>
% 120.37/16.02 ((
% 120.37/16.02 (subset2powerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (setextsub) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetemptysetimpeq) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetE1) =>
% 120.37/16.02 ((
% 120.37/16.02 (inPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetsubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (sepInPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (sepSubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (binunionIL) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairset2IR) =>
% 120.37/16.02 ((
% 120.37/16.02 (binunionIR) =>
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y0 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y1 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y2 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y3 : $o]:
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 (
% 120.37/16.02 binunion @
% 120.37/16.02 Y0 @ Y1)) =>
% 120.37/16.02 ((
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 Y0) =>
% 120.37/16.02 (Y3))) =>
% 120.37/16.02 ((
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 Y1) =>
% 120.37/16.02 (Y3))) =>
% 120.37/16.02 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl205])).
% 120.37/16.02 thf(zip_derived_cl231, plain,
% 120.37/16.02 (~ (((setbeta) =>
% 120.37/16.02 (((nonemptyE1) =>
% 120.37/16.02 (((nonemptyI) =>
% 120.37/16.02 (((nonemptyI1) =>
% 120.37/16.02 (((setadjoinIL) =>
% 120.37/16.02 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 120.37/16.02 (((setadjoinIR) =>
% 120.37/16.02 (((setadjoinE) =>
% 120.37/16.02 (((setadjoinOr) =>
% 120.37/16.02 (((setoftrueEq) =>
% 120.37/16.02 (((powersetI) =>
% 120.37/16.02 (((emptyinPowerset) =>
% 120.37/16.02 (((emptyInPowerset) =>
% 120.37/16.02 (((powersetE) =>
% 120.37/16.02 (((setunionI) =>
% 120.37/16.02 (((setunionE) =>
% 120.37/16.02 (((subPowSU) =>
% 120.37/16.02 (((exuE2) =>
% 120.37/16.02 (((nonemptyImpWitness) =>
% 120.37/16.02 (((uniqinunit) =>
% 120.37/16.02 (((notinsingleton) =>
% 120.37/16.02 (((eqinunit) =>
% 120.37/16.02 (((singletonsswitch) =>
% 120.37/16.02 (((upairsetE) =>
% 120.37/16.02 (((upairsetIL) =>
% 120.37/16.02 (((upairsetIR) =>
% 120.37/16.02 (((emptyE1) =>
% 120.37/16.02 (((vacuousDall) =>
% 120.37/16.02 (((quantDeMorgan1) =>
% 120.37/16.02 (((quantDeMorgan2) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan3) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan4) =>
% 120.37/16.02 ((
% 120.37/16.02 (prop2setI) =>
% 120.37/16.02 ((
% 120.37/16.02 (prop2set2propI) =>
% 120.37/16.02 ((
% 120.37/16.02 (notdexE) =>
% 120.37/16.02 ((
% 120.37/16.02 (notdallE) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI3) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (inCongP) =>
% 120.37/16.02 ((
% 120.37/16.02 (in__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuE3u) =>
% 120.37/16.02 ((
% 120.37/16.02 (exu__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoin__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (powerset__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (setunion__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuEu) =>
% 120.37/16.02 ((
% 120.37/16.02 (descr__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (dsetconstr__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqimpsubset2) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqimpsubset1) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (emptysetsubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetE) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetE2) =>
% 120.37/16.02 ((
% 120.37/16.02 (notsubsetI) =>
% 120.37/16.02 ((
% 120.37/16.02 (notequalI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (notequalI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetRefl) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetTrans) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinSub) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinSub2) =>
% 120.37/16.02 ((
% 120.37/16.02 (subset2powerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (setextsub) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetemptysetimpeq) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetE1) =>
% 120.37/16.02 ((
% 120.37/16.02 (inPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetsubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (sepInPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (sepSubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (binunionIL) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairset2IR) =>
% 120.37/16.02 ((
% 120.37/16.02 (binunionIR) =>
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y0 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y1 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y2 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y3 : $o]:
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 (
% 120.37/16.02 binunion @
% 120.37/16.02 Y0 @ Y1)) =>
% 120.37/16.02 ((
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 Y0) =>
% 120.37/16.02 (Y3))) =>
% 120.37/16.02 ((
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 Y1) =>
% 120.37/16.02 (Y3))) =>
% 120.37/16.02 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl219])).
% 120.37/16.02 thf(zip_derived_cl244, plain,
% 120.37/16.02 (~ (((nonemptyE1) =>
% 120.37/16.02 (((nonemptyI) =>
% 120.37/16.02 (((nonemptyI1) =>
% 120.37/16.02 (((setadjoinIL) =>
% 120.37/16.02 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 120.37/16.02 (((setadjoinIR) =>
% 120.37/16.02 (((setadjoinE) =>
% 120.37/16.02 (((setadjoinOr) =>
% 120.37/16.02 (((setoftrueEq) =>
% 120.37/16.02 (((powersetI) =>
% 120.37/16.02 (((emptyinPowerset) =>
% 120.37/16.02 (((emptyInPowerset) =>
% 120.37/16.02 (((powersetE) =>
% 120.37/16.02 (((setunionI) =>
% 120.37/16.02 (((setunionE) =>
% 120.37/16.02 (((subPowSU) =>
% 120.37/16.02 (((exuE2) =>
% 120.37/16.02 (((nonemptyImpWitness) =>
% 120.37/16.02 (((uniqinunit) =>
% 120.37/16.02 (((notinsingleton) =>
% 120.37/16.02 (((eqinunit) =>
% 120.37/16.02 (((singletonsswitch) =>
% 120.37/16.02 (((upairsetE) =>
% 120.37/16.02 (((upairsetIL) =>
% 120.37/16.02 (((upairsetIR) =>
% 120.37/16.02 (((emptyE1) =>
% 120.37/16.02 (((vacuousDall) =>
% 120.37/16.02 (((quantDeMorgan1) =>
% 120.37/16.02 (((quantDeMorgan2) =>
% 120.37/16.02 (((quantDeMorgan3) =>
% 120.37/16.02 ((
% 120.37/16.02 (quantDeMorgan4) =>
% 120.37/16.02 ((
% 120.37/16.02 (prop2setI) =>
% 120.37/16.02 ((
% 120.37/16.02 (prop2set2propI) =>
% 120.37/16.02 ((
% 120.37/16.02 (notdexE) =>
% 120.37/16.02 ((
% 120.37/16.02 (notdallE) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI3) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (inCongP) =>
% 120.37/16.02 ((
% 120.37/16.02 (in__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuE3u) =>
% 120.37/16.02 ((
% 120.37/16.02 (exu__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoin__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (powerset__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (setunion__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuEu) =>
% 120.37/16.02 ((
% 120.37/16.02 (descr__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (dsetconstr__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqimpsubset2) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqimpsubset1) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (emptysetsubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetE) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetE2) =>
% 120.37/16.02 ((
% 120.37/16.02 (notsubsetI) =>
% 120.37/16.02 ((
% 120.37/16.02 (notequalI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (notequalI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetRefl) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetTrans) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinSub) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinSub2) =>
% 120.37/16.02 ((
% 120.37/16.02 (subset2powerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (setextsub) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetemptysetimpeq) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetE1) =>
% 120.37/16.02 ((
% 120.37/16.02 (inPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetsubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (sepInPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (sepSubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (binunionIL) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairset2IR) =>
% 120.37/16.02 ((
% 120.37/16.02 (binunionIR) =>
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y0 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y1 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y2 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y3 : $o]:
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 (
% 120.37/16.02 binunion @
% 120.37/16.02 Y0 @ Y1)) =>
% 120.37/16.02 ((
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 Y0) =>
% 120.37/16.02 (Y3))) =>
% 120.37/16.02 ((
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 Y1) =>
% 120.37/16.02 (Y3))) =>
% 120.37/16.02 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl231])).
% 120.37/16.02 thf(zip_derived_cl258, plain,
% 120.37/16.02 (~ (((nonemptyI) =>
% 120.37/16.02 (((nonemptyI1) =>
% 120.37/16.02 (((setadjoinIL) =>
% 120.37/16.02 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 120.37/16.02 (((setadjoinIR) =>
% 120.37/16.02 (((setadjoinE) =>
% 120.37/16.02 (((setadjoinOr) =>
% 120.37/16.02 (((setoftrueEq) =>
% 120.37/16.02 (((powersetI) =>
% 120.37/16.02 (((emptyinPowerset) =>
% 120.37/16.02 (((emptyInPowerset) =>
% 120.37/16.02 (((powersetE) =>
% 120.37/16.02 (((setunionI) =>
% 120.37/16.02 (((setunionE) =>
% 120.37/16.02 (((subPowSU) =>
% 120.37/16.02 (((exuE2) =>
% 120.37/16.02 (((nonemptyImpWitness) =>
% 120.37/16.02 (((uniqinunit) =>
% 120.37/16.02 (((notinsingleton) =>
% 120.37/16.02 (((eqinunit) =>
% 120.37/16.02 (((singletonsswitch) =>
% 120.37/16.02 (((upairsetE) =>
% 120.37/16.02 (((upairsetIL) =>
% 120.37/16.02 (((upairsetIR) =>
% 120.37/16.02 (((emptyE1) =>
% 120.37/16.02 (((vacuousDall) =>
% 120.37/16.02 (((quantDeMorgan1) =>
% 120.37/16.02 (((quantDeMorgan2) =>
% 120.37/16.02 (((quantDeMorgan3) =>
% 120.37/16.02 (((quantDeMorgan4) =>
% 120.37/16.02 ((
% 120.37/16.02 (prop2setI) =>
% 120.37/16.02 ((
% 120.37/16.02 (prop2set2propI) =>
% 120.37/16.02 ((
% 120.37/16.02 (notdexE) =>
% 120.37/16.02 ((
% 120.37/16.02 (notdallE) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI3) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (inCongP) =>
% 120.37/16.02 ((
% 120.37/16.02 (in__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuE3u) =>
% 120.37/16.02 ((
% 120.37/16.02 (exu__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoin__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (powerset__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (setunion__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuEu) =>
% 120.37/16.02 ((
% 120.37/16.02 (descr__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (dsetconstr__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqimpsubset2) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqimpsubset1) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (emptysetsubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetE) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetE2) =>
% 120.37/16.02 ((
% 120.37/16.02 (notsubsetI) =>
% 120.37/16.02 ((
% 120.37/16.02 (notequalI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (notequalI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetRefl) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetTrans) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinSub) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinSub2) =>
% 120.37/16.02 ((
% 120.37/16.02 (subset2powerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (setextsub) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetemptysetimpeq) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetE1) =>
% 120.37/16.02 ((
% 120.37/16.02 (inPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetsubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (sepInPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (sepSubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (binunionIL) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairset2IR) =>
% 120.37/16.02 ((
% 120.37/16.02 (binunionIR) =>
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y0 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y1 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y2 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y3 : $o]:
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 (
% 120.37/16.02 binunion @
% 120.37/16.02 Y0 @ Y1)) =>
% 120.37/16.02 ((
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 Y0) =>
% 120.37/16.02 (Y3))) =>
% 120.37/16.02 ((
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 Y1) =>
% 120.37/16.02 (Y3))) =>
% 120.37/16.02 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl244])).
% 120.37/16.02 thf(zip_derived_cl274, plain,
% 120.37/16.02 (~ (((nonemptyI1) =>
% 120.37/16.02 (((setadjoinIL) =>
% 120.37/16.02 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 120.37/16.02 (((setadjoinIR) =>
% 120.37/16.02 (((setadjoinE) =>
% 120.37/16.02 (((setadjoinOr) =>
% 120.37/16.02 (((setoftrueEq) =>
% 120.37/16.02 (((powersetI) =>
% 120.37/16.02 (((emptyinPowerset) =>
% 120.37/16.02 (((emptyInPowerset) =>
% 120.37/16.02 (((powersetE) =>
% 120.37/16.02 (((setunionI) =>
% 120.37/16.02 (((setunionE) =>
% 120.37/16.02 (((subPowSU) =>
% 120.37/16.02 (((exuE2) =>
% 120.37/16.02 (((nonemptyImpWitness) =>
% 120.37/16.02 (((uniqinunit) =>
% 120.37/16.02 (((notinsingleton) =>
% 120.37/16.02 (((eqinunit) =>
% 120.37/16.02 (((singletonsswitch) =>
% 120.37/16.02 (((upairsetE) =>
% 120.37/16.02 (((upairsetIL) =>
% 120.37/16.02 (((upairsetIR) =>
% 120.37/16.02 (((emptyE1) =>
% 120.37/16.02 (((vacuousDall) =>
% 120.37/16.02 (((quantDeMorgan1) =>
% 120.37/16.02 (((quantDeMorgan2) =>
% 120.37/16.02 (((quantDeMorgan3) =>
% 120.37/16.02 (((quantDeMorgan4) =>
% 120.37/16.02 (((prop2setI) =>
% 120.37/16.02 ((
% 120.37/16.02 (prop2set2propI) =>
% 120.37/16.02 ((
% 120.37/16.02 (notdexE) =>
% 120.37/16.02 ((
% 120.37/16.02 (notdallE) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI3) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (inCongP) =>
% 120.37/16.02 ((
% 120.37/16.02 (in__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuE3u) =>
% 120.37/16.02 ((
% 120.37/16.02 (exu__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoin__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (powerset__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (setunion__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuEu) =>
% 120.37/16.02 ((
% 120.37/16.02 (descr__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (dsetconstr__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqimpsubset2) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqimpsubset1) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (emptysetsubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetE) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetE2) =>
% 120.37/16.02 ((
% 120.37/16.02 (notsubsetI) =>
% 120.37/16.02 ((
% 120.37/16.02 (notequalI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (notequalI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetRefl) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetTrans) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinSub) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinSub2) =>
% 120.37/16.02 ((
% 120.37/16.02 (subset2powerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (setextsub) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetemptysetimpeq) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetE1) =>
% 120.37/16.02 ((
% 120.37/16.02 (inPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetsubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (sepInPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (sepSubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (binunionIL) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairset2IR) =>
% 120.37/16.02 ((
% 120.37/16.02 (binunionIR) =>
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y0 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y1 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y2 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y3 : $o]:
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 (
% 120.37/16.02 binunion @
% 120.37/16.02 Y0 @ Y1)) =>
% 120.37/16.02 ((
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 Y0) =>
% 120.37/16.02 (Y3))) =>
% 120.37/16.02 ((
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 Y1) =>
% 120.37/16.02 (Y3))) =>
% 120.37/16.02 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl258])).
% 120.37/16.02 thf(zip_derived_cl285, plain,
% 120.37/16.02 (~ (((setadjoinIL) =>
% 120.37/16.02 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 120.37/16.02 (((setadjoinIR) =>
% 120.37/16.02 (((setadjoinE) =>
% 120.37/16.02 (((setadjoinOr) =>
% 120.37/16.02 (((setoftrueEq) =>
% 120.37/16.02 (((powersetI) =>
% 120.37/16.02 (((emptyinPowerset) =>
% 120.37/16.02 (((emptyInPowerset) =>
% 120.37/16.02 (((powersetE) =>
% 120.37/16.02 (((setunionI) =>
% 120.37/16.02 (((setunionE) =>
% 120.37/16.02 (((subPowSU) =>
% 120.37/16.02 (((exuE2) =>
% 120.37/16.02 (((nonemptyImpWitness) =>
% 120.37/16.02 (((uniqinunit) =>
% 120.37/16.02 (((notinsingleton) =>
% 120.37/16.02 (((eqinunit) =>
% 120.37/16.02 (((singletonsswitch) =>
% 120.37/16.02 (((upairsetE) =>
% 120.37/16.02 (((upairsetIL) =>
% 120.37/16.02 (((upairsetIR) =>
% 120.37/16.02 (((emptyE1) =>
% 120.37/16.02 (((vacuousDall) =>
% 120.37/16.02 (((quantDeMorgan1) =>
% 120.37/16.02 (((quantDeMorgan2) =>
% 120.37/16.02 (((quantDeMorgan3) =>
% 120.37/16.02 (((quantDeMorgan4) =>
% 120.37/16.02 (((prop2setI) =>
% 120.37/16.02 (((prop2set2propI) =>
% 120.37/16.02 ((
% 120.37/16.02 (notdexE) =>
% 120.37/16.02 ((
% 120.37/16.02 (notdallE) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI3) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (inCongP) =>
% 120.37/16.02 ((
% 120.37/16.02 (in__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuE3u) =>
% 120.37/16.02 ((
% 120.37/16.02 (exu__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoin__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (powerset__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (setunion__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuEu) =>
% 120.37/16.02 ((
% 120.37/16.02 (descr__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (dsetconstr__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqimpsubset2) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqimpsubset1) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (emptysetsubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetE) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetE2) =>
% 120.37/16.02 ((
% 120.37/16.02 (notsubsetI) =>
% 120.37/16.02 ((
% 120.37/16.02 (notequalI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (notequalI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetRefl) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetTrans) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinSub) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinSub2) =>
% 120.37/16.02 ((
% 120.37/16.02 (subset2powerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (setextsub) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetemptysetimpeq) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetE1) =>
% 120.37/16.02 ((
% 120.37/16.02 (inPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetsubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (sepInPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (sepSubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (binunionIL) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairset2IR) =>
% 120.37/16.02 ((
% 120.37/16.02 (binunionIR) =>
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y0 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y1 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y2 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y3 : $o]:
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 (
% 120.37/16.02 binunion @
% 120.37/16.02 Y0 @ Y1)) =>
% 120.37/16.02 ((
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 Y0) =>
% 120.37/16.02 (Y3))) =>
% 120.37/16.02 ((
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 Y1) =>
% 120.37/16.02 (Y3))) =>
% 120.37/16.02 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl274])).
% 120.37/16.02 thf(zip_derived_cl297, plain,
% 120.37/16.02 (~ (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 120.37/16.02 (((setadjoinIR) =>
% 120.37/16.02 (((setadjoinE) =>
% 120.37/16.02 (((setadjoinOr) =>
% 120.37/16.02 (((setoftrueEq) =>
% 120.37/16.02 (((powersetI) =>
% 120.37/16.02 (((emptyinPowerset) =>
% 120.37/16.02 (((emptyInPowerset) =>
% 120.37/16.02 (((powersetE) =>
% 120.37/16.02 (((setunionI) =>
% 120.37/16.02 (((setunionE) =>
% 120.37/16.02 (((subPowSU) =>
% 120.37/16.02 (((exuE2) =>
% 120.37/16.02 (((nonemptyImpWitness) =>
% 120.37/16.02 (((uniqinunit) =>
% 120.37/16.02 (((notinsingleton) =>
% 120.37/16.02 (((eqinunit) =>
% 120.37/16.02 (((singletonsswitch) =>
% 120.37/16.02 (((upairsetE) =>
% 120.37/16.02 (((upairsetIL) =>
% 120.37/16.02 (((upairsetIR) =>
% 120.37/16.02 (((emptyE1) =>
% 120.37/16.02 (((vacuousDall) =>
% 120.37/16.02 (((quantDeMorgan1) =>
% 120.37/16.02 (((quantDeMorgan2) =>
% 120.37/16.02 (((quantDeMorgan3) =>
% 120.37/16.02 (((quantDeMorgan4) =>
% 120.37/16.02 (((prop2setI) =>
% 120.37/16.02 (((prop2set2propI) =>
% 120.37/16.02 (((notdexE) =>
% 120.37/16.02 ((
% 120.37/16.02 (notdallE) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI3) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (inCongP) =>
% 120.37/16.02 ((
% 120.37/16.02 (in__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuE3u) =>
% 120.37/16.02 ((
% 120.37/16.02 (exu__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoin__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (powerset__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (setunion__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuEu) =>
% 120.37/16.02 ((
% 120.37/16.02 (descr__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (dsetconstr__Cong) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqimpsubset2) =>
% 120.37/16.02 ((
% 120.37/16.02 (eqimpsubset1) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (emptysetsubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetE) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetE2) =>
% 120.37/16.02 ((
% 120.37/16.02 (notsubsetI) =>
% 120.37/16.02 ((
% 120.37/16.02 (notequalI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (notequalI2) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetRefl) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetTrans) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinSub) =>
% 120.37/16.02 ((
% 120.37/16.02 (setadjoinSub2) =>
% 120.37/16.02 ((
% 120.37/16.02 (subset2powerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (setextsub) =>
% 120.37/16.02 ((
% 120.37/16.02 (subsetemptysetimpeq) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetI1) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetE1) =>
% 120.37/16.02 ((
% 120.37/16.02 (inPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (powersetsubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (sepInPowerset) =>
% 120.37/16.02 ((
% 120.37/16.02 (sepSubset) =>
% 120.37/16.02 ((
% 120.37/16.02 (binunionIL) =>
% 120.37/16.02 ((
% 120.37/16.02 (upairset2IR) =>
% 120.37/16.02 ((
% 120.37/16.02 (binunionIR) =>
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y0 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y1 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y2 : $i]:
% 120.37/16.02 ((
% 120.37/16.02 (!!) @ (
% 120.37/16.02 ^[Y3 : $o]:
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 (
% 120.37/16.02 binunion @
% 120.37/16.02 Y0 @ Y1)) =>
% 120.37/16.02 ((
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 Y0) =>
% 120.37/16.02 (Y3))) =>
% 120.37/16.02 ((
% 120.37/16.02 ((
% 120.37/16.02 (in @
% 120.37/16.02 Y2 @
% 120.37/16.02 Y1) =>
% 120.37/16.02 (Y3))) =>
% 120.37/16.02 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl285])).
% 120.37/16.02 thf(zip_derived_cl305, plain,
% 120.37/16.02 (~ (((setadjoinIR) =>
% 120.37/16.02 (((setadjoinE) =>
% 120.37/16.02 (((setadjoinOr) =>
% 120.37/16.02 (((setoftrueEq) =>
% 120.37/16.02 (((powersetI) =>
% 120.37/16.02 (((emptyinPowerset) =>
% 120.37/16.02 (((emptyInPowerset) =>
% 120.37/16.02 (((powersetE) =>
% 120.37/16.02 (((setunionI) =>
% 120.37/16.02 (((setunionE) =>
% 120.37/16.02 (((subPowSU) =>
% 120.37/16.02 (((exuE2) =>
% 120.37/16.02 (((nonemptyImpWitness) =>
% 120.37/16.02 (((uniqinunit) =>
% 120.37/16.02 (((notinsingleton) =>
% 120.37/16.02 (((eqinunit) =>
% 120.37/16.02 (((singletonsswitch) =>
% 120.37/16.02 (((upairsetE) =>
% 120.37/16.02 (((upairsetIL) =>
% 120.37/16.02 (((upairsetIR) =>
% 120.37/16.02 (((emptyE1) =>
% 120.37/16.02 (((vacuousDall) =>
% 120.37/16.02 (((quantDeMorgan1) =>
% 120.37/16.02 (((quantDeMorgan2) =>
% 120.37/16.02 (((quantDeMorgan3) =>
% 120.37/16.02 (((quantDeMorgan4) =>
% 120.37/16.02 (((prop2setI) =>
% 120.37/16.02 (((prop2set2propI) =>
% 120.37/16.02 (((notdexE) =>
% 120.37/16.02 (((notdallE) =>
% 120.37/16.02 ((
% 120.37/16.02 (exuI1) =>
% 120.37/16.02 ((
% 120.37/16.03 (exuI3) =>
% 120.37/16.03 ((
% 120.37/16.03 (exuI2) =>
% 120.37/16.03 ((
% 120.37/16.03 (inCongP) =>
% 120.37/16.03 ((
% 120.37/16.03 (in__Cong) =>
% 120.37/16.03 ((
% 120.37/16.03 (exuE3u) =>
% 120.37/16.03 ((
% 120.37/16.03 (exu__Cong) =>
% 120.37/16.03 ((
% 120.37/16.03 (setadjoin__Cong) =>
% 120.37/16.03 ((
% 120.37/16.03 (powerset__Cong) =>
% 120.37/16.03 ((
% 120.37/16.03 (setunion__Cong) =>
% 120.37/16.03 ((
% 120.37/16.03 (exuEu) =>
% 120.37/16.03 ((
% 120.37/16.03 (descr__Cong) =>
% 120.37/16.03 ((
% 120.37/16.03 (dsetconstr__Cong) =>
% 120.37/16.03 ((
% 120.37/16.03 (subsetI1) =>
% 120.37/16.03 ((
% 120.37/16.03 (eqimpsubset2) =>
% 120.37/16.03 ((
% 120.37/16.03 (eqimpsubset1) =>
% 120.37/16.03 ((
% 120.37/16.03 (subsetI2) =>
% 120.37/16.03 ((
% 120.37/16.03 (emptysetsubset) =>
% 120.37/16.03 ((
% 120.37/16.03 (subsetE) =>
% 120.37/16.03 ((
% 120.37/16.03 (subsetE2) =>
% 120.37/16.03 ((
% 120.37/16.03 (notsubsetI) =>
% 120.37/16.03 ((
% 120.37/16.03 (notequalI1) =>
% 120.37/16.03 ((
% 120.37/16.03 (notequalI2) =>
% 120.37/16.03 ((
% 120.37/16.03 (subsetRefl) =>
% 120.37/16.03 ((
% 120.37/16.03 (subsetTrans) =>
% 120.37/16.03 ((
% 120.37/16.03 (setadjoinSub) =>
% 120.37/16.03 ((
% 120.37/16.03 (setadjoinSub2) =>
% 120.37/16.03 ((
% 120.37/16.03 (subset2powerset) =>
% 120.37/16.03 ((
% 120.37/16.03 (setextsub) =>
% 120.37/16.03 ((
% 120.37/16.03 (subsetemptysetimpeq) =>
% 120.37/16.03 ((
% 120.37/16.03 (powersetI1) =>
% 120.37/16.03 ((
% 120.37/16.03 (powersetE1) =>
% 120.37/16.03 ((
% 120.37/16.03 (inPowerset) =>
% 120.37/16.03 ((
% 120.37/16.03 (powersetsubset) =>
% 120.37/16.03 ((
% 120.37/16.03 (sepInPowerset) =>
% 120.37/16.03 ((
% 120.37/16.03 (sepSubset) =>
% 120.37/16.03 ((
% 120.37/16.03 (binunionIL) =>
% 120.37/16.03 ((
% 120.37/16.03 (upairset2IR) =>
% 120.37/16.03 ((
% 120.37/16.03 (binunionIR) =>
% 120.37/16.03 ((
% 120.37/16.03 (!!) @ (
% 120.37/16.03 ^[Y0 : $i]:
% 120.37/16.03 ((
% 120.37/16.03 (!!) @ (
% 120.37/16.03 ^[Y1 : $i]:
% 120.37/16.03 ((
% 120.37/16.03 (!!) @ (
% 120.37/16.03 ^[Y2 : $i]:
% 120.37/16.03 ((
% 120.37/16.03 (!!) @ (
% 120.37/16.03 ^[Y3 : $o]:
% 120.37/16.03 ((
% 120.37/16.03 (in @
% 120.37/16.03 Y2 @
% 120.37/16.03 (
% 120.37/16.03 binunion @
% 120.37/16.03 Y0 @ Y1)) =>
% 120.37/16.03 ((
% 120.37/16.03 ((
% 120.37/16.03 (in @
% 120.37/16.03 Y2 @
% 120.37/16.03 Y0) =>
% 120.37/16.03 (Y3))) =>
% 120.37/16.03 ((
% 120.37/16.03 ((
% 120.37/16.03 (in @
% 120.37/16.03 Y2 @
% 120.37/16.03 Y1) =>
% 120.37/16.03 (Y3))) =>
% 120.37/16.03 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl297])).
% 120.37/16.03 thf(zip_derived_cl312, plain,
% 120.37/16.03 (~ (((setadjoinE) =>
% 120.37/16.03 (((setadjoinOr) =>
% 120.37/16.03 (((setoftrueEq) =>
% 120.37/16.03 (((powersetI) =>
% 120.37/16.03 (((emptyinPowerset) =>
% 120.37/16.03 (((emptyInPowerset) =>
% 120.37/16.03 (((powersetE) =>
% 120.37/16.03 (((setunionI) =>
% 120.37/16.03 (((setunionE) =>
% 120.37/16.03 (((subPowSU) =>
% 120.37/16.03 (((exuE2) =>
% 120.37/16.03 (((nonemptyImpWitness) =>
% 120.37/16.03 (((uniqinunit) =>
% 120.37/16.03 (((notinsingleton) =>
% 120.37/16.03 (((eqinunit) =>
% 120.37/16.03 (((singletonsswitch) =>
% 120.37/16.03 (((upairsetE) =>
% 120.37/16.03 (((upairsetIL) =>
% 120.37/16.03 (((upairsetIR) =>
% 120.37/16.03 (((emptyE1) =>
% 120.37/16.03 (((vacuousDall) =>
% 120.37/16.03 (((quantDeMorgan1) =>
% 120.37/16.03 (((quantDeMorgan2) =>
% 120.37/16.03 (((quantDeMorgan3) =>
% 120.37/16.03 (((quantDeMorgan4) =>
% 120.37/16.03 (((prop2setI) =>
% 120.37/16.03 (((prop2set2propI) =>
% 120.37/16.03 (((notdexE) =>
% 120.37/16.03 (((notdallE) =>
% 120.37/16.03 (((exuI1) =>
% 120.37/16.03 ((
% 120.37/16.03 (exuI3) =>
% 120.37/16.03 ((
% 120.37/16.03 (exuI2) =>
% 120.37/16.03 ((
% 120.37/16.03 (inCongP) =>
% 120.37/16.03 ((
% 120.37/16.03 (in__Cong) =>
% 120.37/16.03 ((
% 120.37/16.03 (exuE3u) =>
% 120.37/16.03 ((
% 120.37/16.03 (exu__Cong) =>
% 120.37/16.03 ((
% 120.37/16.03 (setadjoin__Cong) =>
% 120.37/16.03 ((
% 120.37/16.03 (powerset__Cong) =>
% 120.37/16.03 ((
% 120.37/16.03 (setunion__Cong) =>
% 120.37/16.03 ((
% 120.37/16.03 (exuEu) =>
% 120.37/16.03 ((
% 120.37/16.03 (descr__Cong) =>
% 120.37/16.03 ((
% 120.37/16.03 (dsetconstr__Cong) =>
% 120.37/16.03 ((
% 120.37/16.03 (subsetI1) =>
% 120.37/16.03 ((
% 120.37/16.03 (eqimpsubset2) =>
% 120.37/16.03 ((
% 120.37/16.03 (eqimpsubset1) =>
% 120.37/16.03 ((
% 120.37/16.03 (subsetI2) =>
% 120.37/16.03 ((
% 120.37/16.03 (emptysetsubset) =>
% 120.37/16.03 ((
% 120.37/16.03 (subsetE) =>
% 120.37/16.03 ((
% 120.37/16.03 (subsetE2) =>
% 120.37/16.03 ((
% 120.37/16.03 (notsubsetI) =>
% 120.37/16.03 ((
% 120.37/16.03 (notequalI1) =>
% 120.37/16.03 ((
% 120.37/16.03 (notequalI2) =>
% 120.37/16.03 ((
% 120.37/16.03 (subsetRefl) =>
% 120.37/16.03 ((
% 120.37/16.03 (subsetTrans) =>
% 120.37/16.03 ((
% 120.37/16.03 (setadjoinSub) =>
% 120.37/16.03 ((
% 120.37/16.03 (setadjoinSub2) =>
% 120.37/16.03 ((
% 120.37/16.03 (subset2powerset) =>
% 120.37/16.03 ((
% 120.37/16.03 (setextsub) =>
% 120.37/16.03 ((
% 120.37/16.03 (subsetemptysetimpeq) =>
% 120.37/16.03 ((
% 120.37/16.03 (powersetI1) =>
% 120.37/16.03 ((
% 120.37/16.03 (powersetE1) =>
% 120.37/16.03 ((
% 120.37/16.03 (inPowerset) =>
% 120.37/16.03 ((
% 120.37/16.03 (powersetsubset) =>
% 120.37/16.03 ((
% 120.37/16.03 (sepInPowerset) =>
% 120.37/16.03 ((
% 120.37/16.03 (sepSubset) =>
% 120.37/16.03 ((
% 120.37/16.03 (binunionIL) =>
% 120.37/16.03 ((
% 120.37/16.03 (upairset2IR) =>
% 120.37/16.03 ((
% 120.37/16.03 (binunionIR) =>
% 120.37/16.03 ((
% 120.37/16.03 (!!) @ (
% 120.37/16.03 ^[Y0 : $i]:
% 120.37/16.03 ((
% 120.37/16.03 (!!) @ (
% 120.37/16.03 ^[Y1 : $i]:
% 120.37/16.03 ((
% 120.37/16.03 (!!) @ (
% 120.37/16.03 ^[Y2 : $i]:
% 120.37/16.03 ((
% 120.37/16.03 (!!) @ (
% 120.37/16.03 ^[Y3 : $o]:
% 120.37/16.03 ((
% 120.37/16.03 (in @
% 120.37/16.03 Y2 @
% 120.37/16.03 (
% 120.37/16.03 binunion @
% 120.37/16.03 Y0 @ Y1)) =>
% 120.37/16.03 ((
% 120.37/16.03 ((
% 120.37/16.03 (in @
% 120.37/16.03 Y2 @
% 120.37/16.03 Y0) =>
% 120.37/16.03 (Y3))) =>
% 120.37/16.03 ((
% 120.37/16.03 ((
% 120.37/16.03 (in @
% 120.37/16.03 Y2 @
% 120.37/16.03 Y1) =>
% 120.37/16.03 (Y3))) =>
% 120.37/16.03 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl305])).
% 120.37/16.03 thf(zip_derived_cl318, plain,
% 120.37/16.03 (~ (((setadjoinOr) =>
% 120.37/16.03 (((setoftrueEq) =>
% 120.37/16.03 (((powersetI) =>
% 120.37/16.03 (((emptyinPowerset) =>
% 120.37/16.03 (((emptyInPowerset) =>
% 120.37/16.03 (((powersetE) =>
% 120.37/16.03 (((setunionI) =>
% 120.37/16.03 (((setunionE) =>
% 120.37/16.03 (((subPowSU) =>
% 120.37/16.03 (((exuE2) =>
% 120.37/16.03 (((nonemptyImpWitness) =>
% 120.37/16.03 (((uniqinunit) =>
% 120.37/16.03 (((notinsingleton) =>
% 120.37/16.03 (((eqinunit) =>
% 120.37/16.03 (((singletonsswitch) =>
% 120.37/16.03 (((upairsetE) =>
% 120.37/16.03 (((upairsetIL) =>
% 120.37/16.03 (((upairsetIR) =>
% 120.37/16.03 (((emptyE1) =>
% 120.37/16.03 (((vacuousDall) =>
% 120.37/16.03 (((quantDeMorgan1) =>
% 120.37/16.03 (((quantDeMorgan2) =>
% 120.37/16.03 (((quantDeMorgan3) =>
% 120.37/16.03 (((quantDeMorgan4) =>
% 120.37/16.03 (((prop2setI) =>
% 120.37/16.03 (((prop2set2propI) =>
% 120.37/16.03 (((notdexE) =>
% 120.37/16.03 (((notdallE) =>
% 120.37/16.03 (((exuI1) =>
% 120.37/16.03 (((exuI3) =>
% 120.37/16.03 ((
% 120.37/16.03 (exuI2) =>
% 120.37/16.03 ((
% 120.37/16.03 (inCongP) =>
% 120.37/16.03 ((
% 120.37/16.03 (in__Cong) =>
% 120.37/16.03 ((
% 120.37/16.03 (exuE3u) =>
% 120.37/16.03 ((
% 120.37/16.03 (exu__Cong) =>
% 120.37/16.03 ((
% 120.37/16.03 (setadjoin__Cong) =>
% 120.37/16.03 ((
% 120.37/16.03 (powerset__Cong) =>
% 120.37/16.03 ((
% 120.37/16.03 (setunion__Cong) =>
% 120.37/16.03 ((
% 120.37/16.03 (exuEu) =>
% 120.37/16.03 ((
% 120.37/16.03 (descr__Cong) =>
% 120.37/16.03 ((
% 120.37/16.03 (dsetconstr__Cong) =>
% 120.37/16.03 ((
% 120.37/16.03 (subsetI1) =>
% 120.37/16.03 ((
% 120.37/16.03 (eqimpsubset2) =>
% 120.37/16.03 ((
% 120.37/16.03 (eqimpsubset1) =>
% 120.37/16.03 ((
% 120.37/16.03 (subsetI2) =>
% 120.37/16.03 ((
% 120.37/16.03 (emptysetsubset) =>
% 120.37/16.03 ((
% 120.37/16.03 (subsetE) =>
% 120.37/16.03 ((
% 120.37/16.03 (subsetE2) =>
% 120.37/16.03 ((
% 120.37/16.03 (notsubsetI) =>
% 120.37/16.03 ((
% 120.37/16.03 (notequalI1) =>
% 120.37/16.03 ((
% 120.37/16.03 (notequalI2) =>
% 120.37/16.03 ((
% 120.37/16.03 (subsetRefl) =>
% 120.37/16.03 ((
% 120.37/16.03 (subsetTrans) =>
% 120.37/16.03 ((
% 120.37/16.03 (setadjoinSub) =>
% 120.37/16.03 ((
% 120.37/16.03 (setadjoinSub2) =>
% 120.37/16.03 ((
% 120.37/16.03 (subset2powerset) =>
% 120.37/16.03 ((
% 120.37/16.03 (setextsub) =>
% 120.37/16.03 ((
% 120.37/16.03 (subsetemptysetimpeq) =>
% 120.37/16.03 ((
% 120.37/16.03 (powersetI1) =>
% 120.37/16.03 ((
% 120.37/16.03 (powersetE1) =>
% 120.37/16.03 ((
% 120.37/16.03 (inPowerset) =>
% 120.37/16.03 ((
% 120.37/16.03 (powersetsubset) =>
% 120.37/16.03 ((
% 120.37/16.03 (sepInPowerset) =>
% 120.37/16.03 ((
% 120.37/16.03 (sepSubset) =>
% 120.37/16.03 ((
% 120.37/16.03 (binunionIL) =>
% 120.37/16.03 ((
% 120.37/16.03 (upairset2IR) =>
% 120.37/16.03 ((
% 120.37/16.03 (binunionIR) =>
% 120.37/16.03 ((
% 120.37/16.03 (!!) @ (
% 120.37/16.03 ^[Y0 : $i]:
% 120.37/16.03 ((
% 120.37/16.03 (!!) @ (
% 120.37/16.03 ^[Y1 : $i]:
% 120.37/16.03 ((
% 120.37/16.03 (!!) @ (
% 120.37/16.03 ^[Y2 : $i]:
% 120.37/16.03 ((
% 120.37/16.03 (!!) @ (
% 120.37/16.03 ^[Y3 : $o]:
% 120.37/16.03 ((
% 120.37/16.03 (in @
% 120.37/16.03 Y2 @
% 120.37/16.03 (
% 120.37/16.03 binunion @
% 120.37/16.03 Y0 @ Y1)) =>
% 120.37/16.03 ((
% 120.37/16.03 ((
% 120.37/16.03 (in @
% 120.37/16.03 Y2 @
% 120.37/16.03 Y0) =>
% 120.37/16.03 (Y3))) =>
% 120.37/16.03 ((
% 120.37/16.03 ((
% 120.37/16.03 (in @
% 120.37/16.03 Y2 @
% 120.37/16.03 Y1) =>
% 120.37/16.03 (Y3))) =>
% 120.37/16.03 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl312])).
% 120.37/16.03 thf(zip_derived_cl325, plain,
% 120.37/16.03 (~ (((setoftrueEq) =>
% 120.37/16.03 (((powersetI) =>
% 120.37/16.03 (((emptyinPowerset) =>
% 120.37/16.03 (((emptyInPowerset) =>
% 120.37/16.03 (((powersetE) =>
% 120.37/16.03 (((setunionI) =>
% 120.37/16.03 (((setunionE) =>
% 120.37/16.03 (((subPowSU) =>
% 120.37/16.03 (((exuE2) =>
% 120.37/16.03 (((nonemptyImpWitness) =>
% 120.37/16.03 (((uniqinunit) =>
% 120.37/16.03 (((notinsingleton) =>
% 120.37/16.03 (((eqinunit) =>
% 120.37/16.03 (((singletonsswitch) =>
% 120.37/16.03 (((upairsetE) =>
% 120.37/16.03 (((upairsetIL) =>
% 120.37/16.03 (((upairsetIR) =>
% 120.37/16.03 (((emptyE1) =>
% 120.37/16.03 (((vacuousDall) =>
% 120.37/16.03 (((quantDeMorgan1) =>
% 120.37/16.03 (((quantDeMorgan2) =>
% 120.37/16.03 (((quantDeMorgan3) =>
% 120.37/16.03 (((quantDeMorgan4) =>
% 120.37/16.03 (((prop2setI) =>
% 120.37/16.03 (((prop2set2propI) =>
% 120.37/16.03 (((notdexE) =>
% 120.37/16.03 (((notdallE) =>
% 120.37/16.03 (((exuI1) =>
% 120.37/16.03 (((exuI3) =>
% 120.37/16.03 (((exuI2) =>
% 120.37/16.03 ((
% 120.37/16.03 (inCongP) =>
% 120.37/16.03 ((
% 120.37/16.03 (in__Cong) =>
% 120.37/16.03 ((
% 120.37/16.03 (exuE3u) =>
% 120.37/16.03 ((
% 120.37/16.03 (exu__Cong) =>
% 120.37/16.03 ((
% 120.37/16.03 (setadjoin__Cong) =>
% 120.37/16.03 ((
% 120.37/16.03 (powerset__Cong) =>
% 120.37/16.03 ((
% 120.37/16.03 (setunion__Cong) =>
% 120.37/16.03 ((
% 120.37/16.03 (exuEu) =>
% 120.37/16.03 ((
% 120.37/16.03 (descr__Cong) =>
% 120.37/16.03 ((
% 120.37/16.03 (dsetconstr__Cong) =>
% 120.37/16.03 ((
% 120.37/16.03 (subsetI1) =>
% 120.37/16.03 ((
% 120.37/16.03 (eqimpsubset2) =>
% 120.37/16.03 ((
% 120.37/16.03 (eqimpsubset1) =>
% 120.37/16.03 ((
% 120.37/16.03 (subsetI2) =>
% 120.37/16.03 ((
% 120.37/16.03 (emptysetsubset) =>
% 120.37/16.03 ((
% 120.37/16.03 (subsetE) =>
% 120.37/16.03 ((
% 120.37/16.03 (subsetE2) =>
% 120.37/16.03 ((
% 120.37/16.03 (notsubsetI) =>
% 120.37/16.03 ((
% 120.37/16.03 (notequalI1) =>
% 120.37/16.03 ((
% 120.37/16.03 (notequalI2) =>
% 120.37/16.03 ((
% 120.37/16.03 (subsetRefl) =>
% 120.37/16.03 ((
% 120.37/16.03 (subsetTrans) =>
% 120.37/16.03 ((
% 120.37/16.03 (setadjoinSub) =>
% 120.37/16.03 ((
% 120.37/16.03 (setadjoinSub2) =>
% 120.37/16.03 ((
% 120.37/16.03 (subset2powerset) =>
% 120.37/16.03 ((
% 120.37/16.03 (setextsub) =>
% 120.37/16.03 ((
% 120.37/16.03 (subsetemptysetimpeq) =>
% 120.37/16.03 ((
% 120.37/16.03 (powersetI1) =>
% 120.37/16.03 ((
% 120.37/16.03 (powersetE1) =>
% 120.37/16.03 ((
% 120.37/16.03 (inPowerset) =>
% 120.37/16.03 ((
% 120.37/16.03 (powersetsubset) =>
% 120.37/16.03 ((
% 120.37/16.03 (sepInPowerset) =>
% 120.37/16.03 ((
% 120.37/16.03 (sepSubset) =>
% 120.37/16.03 ((
% 120.37/16.03 (binunionIL) =>
% 120.37/16.03 ((
% 120.37/16.03 (upairset2IR) =>
% 120.37/16.03 ((
% 120.37/16.03 (binunionIR) =>
% 120.37/16.03 ((
% 120.37/16.03 (!!) @ (
% 120.37/16.03 ^[Y0 : $i]:
% 120.37/16.03 ((
% 120.37/16.03 (!!) @ (
% 120.37/16.03 ^[Y1 : $i]:
% 120.37/16.03 ((
% 120.37/16.03 (!!) @ (
% 120.37/16.03 ^[Y2 : $i]:
% 120.37/16.03 ((
% 120.37/16.03 (!!) @ (
% 120.37/16.03 ^[Y3 : $o]:
% 120.37/16.03 ((
% 120.37/16.03 (in @
% 120.37/16.03 Y2 @
% 120.37/16.03 (
% 120.37/16.03 binunion @
% 120.37/16.03 Y0 @ Y1)) =>
% 120.37/16.03 ((
% 120.37/16.03 ((
% 120.37/16.03 (in @
% 120.37/16.03 Y2 @
% 120.37/16.03 Y0) =>
% 120.37/16.03 (Y3))) =>
% 120.37/16.03 ((
% 120.37/16.03 ((
% 120.37/16.03 (in @
% 120.37/16.03 Y2 @
% 120.37/16.03 Y1) =>
% 120.37/16.03 (Y3))) =>
% 120.37/16.03 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl318])).
% 120.37/16.03 thf(zip_derived_cl331, plain,
% 120.37/16.03 (~ (((powersetI) =>
% 120.37/16.03 (((emptyinPowerset) =>
% 120.37/16.03 (((emptyInPowerset) =>
% 120.37/16.03 (((powersetE) =>
% 120.37/16.03 (((setunionI) =>
% 120.37/16.03 (((setunionE) =>
% 120.37/16.03 (((subPowSU) =>
% 120.37/16.03 (((exuE2) =>
% 120.37/16.03 (((nonemptyImpWitness) =>
% 120.37/16.03 (((uniqinunit) =>
% 120.37/16.03 (((notinsingleton) =>
% 120.37/16.03 (((eqinunit) =>
% 120.37/16.03 (((singletonsswitch) =>
% 120.37/16.03 (((upairsetE) =>
% 120.37/16.03 (((upairsetIL) =>
% 120.37/16.03 (((upairsetIR) =>
% 120.37/16.03 (((emptyE1) =>
% 120.37/16.03 (((vacuousDall) =>
% 120.37/16.03 (((quantDeMorgan1) =>
% 120.37/16.03 (((quantDeMorgan2) =>
% 120.37/16.03 (((quantDeMorgan3) =>
% 120.37/16.03 (((quantDeMorgan4) =>
% 120.37/16.03 (((prop2setI) =>
% 120.37/16.03 (((prop2set2propI) =>
% 120.37/16.03 (((notdexE) =>
% 120.37/16.03 (((notdallE) =>
% 120.37/16.03 (((exuI1) =>
% 120.37/16.03 (((exuI3) =>
% 120.37/16.03 (((exuI2) =>
% 120.37/16.03 (((inCongP) =>
% 120.37/16.03 ((
% 120.37/16.03 (in__Cong) =>
% 120.37/16.03 ((
% 120.37/16.03 (exuE3u) =>
% 120.37/16.03 ((
% 120.37/16.03 (exu__Cong) =>
% 120.37/16.03 ((
% 120.37/16.03 (setadjoin__Cong) =>
% 120.37/16.03 ((
% 120.37/16.03 (powerset__Cong) =>
% 120.37/16.03 ((
% 120.37/16.03 (setunion__Cong) =>
% 120.37/16.03 ((
% 120.37/16.03 (exuEu) =>
% 120.37/16.03 ((
% 120.37/16.03 (descr__Cong) =>
% 120.37/16.03 ((
% 120.37/16.03 (dsetconstr__Cong) =>
% 120.37/16.03 ((
% 120.37/16.03 (subsetI1) =>
% 120.37/16.03 ((
% 120.37/16.03 (eqimpsubset2) =>
% 120.37/16.03 ((
% 120.37/16.03 (eqimpsubset1) =>
% 120.37/16.03 ((
% 120.37/16.03 (subsetI2) =>
% 120.37/16.03 ((
% 120.37/16.03 (emptysetsubset) =>
% 120.37/16.03 ((
% 120.37/16.03 (subsetE) =>
% 120.37/16.03 ((
% 120.37/16.03 (subsetE2) =>
% 120.37/16.03 ((
% 120.37/16.03 (notsubsetI) =>
% 120.37/16.03 ((
% 120.37/16.03 (notequalI1) =>
% 120.37/16.03 ((
% 120.37/16.03 (notequalI2) =>
% 120.37/16.03 ((
% 120.37/16.03 (subsetRefl) =>
% 120.37/16.03 ((
% 120.37/16.03 (subsetTrans) =>
% 120.37/16.03 ((
% 120.37/16.03 (setadjoinSub) =>
% 120.37/16.03 ((
% 120.37/16.03 (setadjoinSub2) =>
% 120.37/16.03 ((
% 120.37/16.03 (subset2powerset) =>
% 120.37/16.03 ((
% 120.37/16.03 (setextsub) =>
% 120.37/16.03 ((
% 120.37/16.03 (subsetemptysetimpeq) =>
% 120.37/16.03 ((
% 120.37/16.03 (powersetI1) =>
% 120.37/16.03 ((
% 120.37/16.03 (powersetE1) =>
% 120.37/16.03 ((
% 120.37/16.03 (inPowerset) =>
% 120.37/16.03 ((
% 120.37/16.03 (powersetsubset) =>
% 120.37/16.03 ((
% 120.37/16.03 (sepInPowerset) =>
% 120.37/16.03 ((
% 120.37/16.03 (sepSubset) =>
% 120.37/16.03 ((
% 120.37/16.03 (binunionIL) =>
% 120.37/16.03 ((
% 120.37/16.03 (upairset2IR) =>
% 120.37/16.03 ((
% 120.37/16.03 (binunionIR) =>
% 120.37/16.03 ((
% 120.37/16.03 (!!) @ (
% 120.37/16.03 ^[Y0 : $i]:
% 120.37/16.03 ((
% 120.37/16.03 (!!) @ (
% 120.37/16.03 ^[Y1 : $i]:
% 120.37/16.03 ((
% 120.37/16.03 (!!) @ (
% 120.37/16.03 ^[Y2 : $i]:
% 120.37/16.03 ((
% 120.37/16.03 (!!) @ (
% 120.37/16.03 ^[Y3 : $o]:
% 120.37/16.03 ((
% 120.37/16.03 (in @
% 120.37/16.03 Y2 @
% 120.37/16.03 (
% 120.37/16.03 binunion @
% 120.37/16.03 Y0 @ Y1)) =>
% 120.37/16.03 ((
% 120.37/16.03 ((
% 120.37/16.03 (in @
% 120.37/16.03 Y2 @
% 120.37/16.03 Y0) =>
% 120.37/16.03 (Y3))) =>
% 120.37/16.03 ((
% 120.37/16.03 ((
% 120.37/16.03 (in @
% 120.37/16.03 Y2 @
% 120.37/16.03 Y1) =>
% 120.37/16.03 (Y3))) =>
% 120.37/16.03 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.03 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl325])).
% 120.37/16.03 thf(zip_derived_cl337, plain,
% 120.37/16.03 (~ (((emptyinPowerset) =>
% 120.37/16.03 (((emptyInPowerset) =>
% 120.37/16.03 (((powersetE) =>
% 120.37/16.03 (((setunionI) =>
% 120.37/16.03 (((setunionE) =>
% 120.37/16.03 (((subPowSU) =>
% 120.37/16.03 (((exuE2) =>
% 120.37/16.03 (((nonemptyImpWitness) =>
% 120.37/16.03 (((uniqinunit) =>
% 120.37/16.03 (((notinsingleton) =>
% 120.37/16.03 (((eqinunit) =>
% 120.37/16.03 (((singletonsswitch) =>
% 120.37/16.03 (((upairsetE) =>
% 120.37/16.03 (((upairsetIL) =>
% 120.37/16.03 (((upairsetIR) =>
% 120.37/16.03 (((emptyE1) =>
% 120.37/16.03 (((vacuousDall) =>
% 120.37/16.03 (((quantDeMorgan1) =>
% 120.37/16.03 (((quantDeMorgan2) =>
% 120.37/16.03 (((quantDeMorgan3) =>
% 120.37/16.03 (((quantDeMorgan4) =>
% 120.37/16.03 (((prop2setI) =>
% 120.37/16.03 (((prop2set2propI) =>
% 120.37/16.03 (((notdexE) =>
% 120.37/16.03 (((notdallE) =>
% 120.37/16.03 (((exuI1) =>
% 120.37/16.03 (((exuI3) =>
% 120.37/16.03 (((exuI2) =>
% 120.37/16.03 (((inCongP) =>
% 120.37/16.03 (((in__Cong) =>
% 120.37/16.03 ((
% 120.37/16.03 (exuE3u) =>
% 120.37/16.03 ((
% 120.37/16.03 (exu__Cong) =>
% 120.37/16.03 ((
% 120.37/16.03 (setadjoin__Cong) =>
% 120.37/16.03 ((
% 120.37/16.03 (powerset__Cong) =>
% 120.37/16.03 ((
% 120.37/16.03 (setunion__Cong) =>
% 120.37/16.03 ((
% 120.37/16.03 (exuEu) =>
% 120.37/16.03 ((
% 120.37/16.03 (descr__Cong) =>
% 120.37/16.03 ((
% 120.37/16.03 (dsetconstr__Cong) =>
% 120.37/16.03 ((
% 120.37/16.03 (subsetI1) =>
% 120.37/16.03 ((
% 120.37/16.03 (eqimpsubset2) =>
% 120.37/16.03 ((
% 120.37/16.03 (eqimpsubset1) =>
% 120.37/16.03 ((
% 120.37/16.03 (subsetI2) =>
% 120.37/16.03 ((
% 120.37/16.03 (emptysetsubset) =>
% 120.37/16.03 ((
% 120.37/16.03 (subsetE) =>
% 120.37/16.03 ((
% 120.37/16.03 (subsetE2) =>
% 120.37/16.03 ((
% 120.37/16.03 (notsubsetI) =>
% 120.37/16.03 ((
% 120.37/16.03 (notequalI1) =>
% 120.37/16.03 ((
% 120.37/16.03 (notequalI2) =>
% 120.37/16.03 ((
% 120.37/16.03 (subsetRefl) =>
% 120.37/16.03 ((
% 120.37/16.03 (subsetTrans) =>
% 120.37/16.03 ((
% 120.37/16.03 (setadjoinSub) =>
% 120.37/16.03 ((
% 120.37/16.03 (setadjoinSub2) =>
% 120.37/16.03 ((
% 120.37/16.03 (subset2powerset) =>
% 120.37/16.03 ((
% 120.37/16.03 (setextsub) =>
% 120.37/16.03 ((
% 120.37/16.03 (subsetemptysetimpeq) =>
% 120.37/16.03 ((
% 120.37/16.03 (powersetI1) =>
% 120.37/16.03 ((
% 120.37/16.03 (powersetE1) =>
% 120.37/16.03 ((
% 120.37/16.03 (inPowerset) =>
% 120.37/16.03 ((
% 120.37/16.03 (powersetsubset) =>
% 120.37/16.03 ((
% 120.37/16.03 (sepInPowerset) =>
% 120.37/16.03 ((
% 120.37/16.03 (sepSubset) =>
% 120.37/16.03 ((
% 120.37/16.03 (binunionIL) =>
% 120.37/16.03 ((
% 120.37/16.03 (upairset2IR) =>
% 120.37/16.03 ((
% 120.37/16.03 (binunionIR) =>
% 120.37/16.03 ((
% 120.37/16.03 (!!) @ (
% 120.37/16.03 ^[Y0 : $i]:
% 120.37/16.03 ((
% 120.37/16.03 (!!) @ (
% 120.37/16.03 ^[Y1 : $i]:
% 120.37/16.03 ((
% 120.37/16.03 (!!) @ (
% 120.37/16.03 ^[Y2 : $i]:
% 120.37/16.03 ((
% 120.37/16.03 (!!) @ (
% 120.37/16.04 ^[Y3 : $o]:
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 (
% 120.37/16.04 binunion @
% 120.37/16.04 Y0 @ Y1)) =>
% 120.37/16.04 ((
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 Y0) =>
% 120.37/16.04 (Y3))) =>
% 120.37/16.04 ((
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 Y1) =>
% 120.37/16.04 (Y3))) =>
% 120.37/16.04 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl331])).
% 120.37/16.04 thf(zip_derived_cl343, plain,
% 120.37/16.04 (~ (((emptyInPowerset) =>
% 120.37/16.04 (((powersetE) =>
% 120.37/16.04 (((setunionI) =>
% 120.37/16.04 (((setunionE) =>
% 120.37/16.04 (((subPowSU) =>
% 120.37/16.04 (((exuE2) =>
% 120.37/16.04 (((nonemptyImpWitness) =>
% 120.37/16.04 (((uniqinunit) =>
% 120.37/16.04 (((notinsingleton) =>
% 120.37/16.04 (((eqinunit) =>
% 120.37/16.04 (((singletonsswitch) =>
% 120.37/16.04 (((upairsetE) =>
% 120.37/16.04 (((upairsetIL) =>
% 120.37/16.04 (((upairsetIR) =>
% 120.37/16.04 (((emptyE1) =>
% 120.37/16.04 (((vacuousDall) =>
% 120.37/16.04 (((quantDeMorgan1) =>
% 120.37/16.04 (((quantDeMorgan2) =>
% 120.37/16.04 (((quantDeMorgan3) =>
% 120.37/16.04 (((quantDeMorgan4) =>
% 120.37/16.04 (((prop2setI) =>
% 120.37/16.04 (((prop2set2propI) =>
% 120.37/16.04 (((notdexE) =>
% 120.37/16.04 (((notdallE) =>
% 120.37/16.04 (((exuI1) =>
% 120.37/16.04 (((exuI3) =>
% 120.37/16.04 (((exuI2) =>
% 120.37/16.04 (((inCongP) =>
% 120.37/16.04 (((in__Cong) =>
% 120.37/16.04 (((exuE3u) =>
% 120.37/16.04 ((
% 120.37/16.04 (exu__Cong) =>
% 120.37/16.04 ((
% 120.37/16.04 (setadjoin__Cong) =>
% 120.37/16.04 ((
% 120.37/16.04 (powerset__Cong) =>
% 120.37/16.04 ((
% 120.37/16.04 (setunion__Cong) =>
% 120.37/16.04 ((
% 120.37/16.04 (exuEu) =>
% 120.37/16.04 ((
% 120.37/16.04 (descr__Cong) =>
% 120.37/16.04 ((
% 120.37/16.04 (dsetconstr__Cong) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetI1) =>
% 120.37/16.04 ((
% 120.37/16.04 (eqimpsubset2) =>
% 120.37/16.04 ((
% 120.37/16.04 (eqimpsubset1) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetI2) =>
% 120.37/16.04 ((
% 120.37/16.04 (emptysetsubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetE) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetE2) =>
% 120.37/16.04 ((
% 120.37/16.04 (notsubsetI) =>
% 120.37/16.04 ((
% 120.37/16.04 (notequalI1) =>
% 120.37/16.04 ((
% 120.37/16.04 (notequalI2) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetRefl) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetTrans) =>
% 120.37/16.04 ((
% 120.37/16.04 (setadjoinSub) =>
% 120.37/16.04 ((
% 120.37/16.04 (setadjoinSub2) =>
% 120.37/16.04 ((
% 120.37/16.04 (subset2powerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (setextsub) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetemptysetimpeq) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetI1) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetE1) =>
% 120.37/16.04 ((
% 120.37/16.04 (inPowerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetsubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (sepInPowerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (sepSubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (binunionIL) =>
% 120.37/16.04 ((
% 120.37/16.04 (upairset2IR) =>
% 120.37/16.04 ((
% 120.37/16.04 (binunionIR) =>
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y0 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y1 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y2 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y3 : $o]:
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 (
% 120.37/16.04 binunion @
% 120.37/16.04 Y0 @ Y1)) =>
% 120.37/16.04 ((
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 Y0) =>
% 120.37/16.04 (Y3))) =>
% 120.37/16.04 ((
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 Y1) =>
% 120.37/16.04 (Y3))) =>
% 120.37/16.04 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl337])).
% 120.37/16.04 thf(zip_derived_cl350, plain,
% 120.37/16.04 (~ (((powersetE) =>
% 120.37/16.04 (((setunionI) =>
% 120.37/16.04 (((setunionE) =>
% 120.37/16.04 (((subPowSU) =>
% 120.37/16.04 (((exuE2) =>
% 120.37/16.04 (((nonemptyImpWitness) =>
% 120.37/16.04 (((uniqinunit) =>
% 120.37/16.04 (((notinsingleton) =>
% 120.37/16.04 (((eqinunit) =>
% 120.37/16.04 (((singletonsswitch) =>
% 120.37/16.04 (((upairsetE) =>
% 120.37/16.04 (((upairsetIL) =>
% 120.37/16.04 (((upairsetIR) =>
% 120.37/16.04 (((emptyE1) =>
% 120.37/16.04 (((vacuousDall) =>
% 120.37/16.04 (((quantDeMorgan1) =>
% 120.37/16.04 (((quantDeMorgan2) =>
% 120.37/16.04 (((quantDeMorgan3) =>
% 120.37/16.04 (((quantDeMorgan4) =>
% 120.37/16.04 (((prop2setI) =>
% 120.37/16.04 (((prop2set2propI) =>
% 120.37/16.04 (((notdexE) =>
% 120.37/16.04 (((notdallE) =>
% 120.37/16.04 (((exuI1) =>
% 120.37/16.04 (((exuI3) =>
% 120.37/16.04 (((exuI2) =>
% 120.37/16.04 (((inCongP) =>
% 120.37/16.04 (((in__Cong) =>
% 120.37/16.04 (((exuE3u) =>
% 120.37/16.04 (((exu__Cong) =>
% 120.37/16.04 ((
% 120.37/16.04 (setadjoin__Cong) =>
% 120.37/16.04 ((
% 120.37/16.04 (powerset__Cong) =>
% 120.37/16.04 ((
% 120.37/16.04 (setunion__Cong) =>
% 120.37/16.04 ((
% 120.37/16.04 (exuEu) =>
% 120.37/16.04 ((
% 120.37/16.04 (descr__Cong) =>
% 120.37/16.04 ((
% 120.37/16.04 (dsetconstr__Cong) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetI1) =>
% 120.37/16.04 ((
% 120.37/16.04 (eqimpsubset2) =>
% 120.37/16.04 ((
% 120.37/16.04 (eqimpsubset1) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetI2) =>
% 120.37/16.04 ((
% 120.37/16.04 (emptysetsubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetE) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetE2) =>
% 120.37/16.04 ((
% 120.37/16.04 (notsubsetI) =>
% 120.37/16.04 ((
% 120.37/16.04 (notequalI1) =>
% 120.37/16.04 ((
% 120.37/16.04 (notequalI2) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetRefl) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetTrans) =>
% 120.37/16.04 ((
% 120.37/16.04 (setadjoinSub) =>
% 120.37/16.04 ((
% 120.37/16.04 (setadjoinSub2) =>
% 120.37/16.04 ((
% 120.37/16.04 (subset2powerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (setextsub) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetemptysetimpeq) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetI1) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetE1) =>
% 120.37/16.04 ((
% 120.37/16.04 (inPowerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetsubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (sepInPowerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (sepSubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (binunionIL) =>
% 120.37/16.04 ((
% 120.37/16.04 (upairset2IR) =>
% 120.37/16.04 ((
% 120.37/16.04 (binunionIR) =>
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y0 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y1 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y2 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y3 : $o]:
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 (
% 120.37/16.04 binunion @
% 120.37/16.04 Y0 @ Y1)) =>
% 120.37/16.04 ((
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 Y0) =>
% 120.37/16.04 (Y3))) =>
% 120.37/16.04 ((
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 Y1) =>
% 120.37/16.04 (Y3))) =>
% 120.37/16.04 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl343])).
% 120.37/16.04 thf(zip_derived_cl357, plain,
% 120.37/16.04 (~ (((setunionI) =>
% 120.37/16.04 (((setunionE) =>
% 120.37/16.04 (((subPowSU) =>
% 120.37/16.04 (((exuE2) =>
% 120.37/16.04 (((nonemptyImpWitness) =>
% 120.37/16.04 (((uniqinunit) =>
% 120.37/16.04 (((notinsingleton) =>
% 120.37/16.04 (((eqinunit) =>
% 120.37/16.04 (((singletonsswitch) =>
% 120.37/16.04 (((upairsetE) =>
% 120.37/16.04 (((upairsetIL) =>
% 120.37/16.04 (((upairsetIR) =>
% 120.37/16.04 (((emptyE1) =>
% 120.37/16.04 (((vacuousDall) =>
% 120.37/16.04 (((quantDeMorgan1) =>
% 120.37/16.04 (((quantDeMorgan2) =>
% 120.37/16.04 (((quantDeMorgan3) =>
% 120.37/16.04 (((quantDeMorgan4) =>
% 120.37/16.04 (((prop2setI) =>
% 120.37/16.04 (((prop2set2propI) =>
% 120.37/16.04 (((notdexE) =>
% 120.37/16.04 (((notdallE) =>
% 120.37/16.04 (((exuI1) =>
% 120.37/16.04 (((exuI3) =>
% 120.37/16.04 (((exuI2) =>
% 120.37/16.04 (((inCongP) =>
% 120.37/16.04 (((in__Cong) =>
% 120.37/16.04 (((exuE3u) =>
% 120.37/16.04 (((exu__Cong) =>
% 120.37/16.04 (((setadjoin__Cong) =>
% 120.37/16.04 ((
% 120.37/16.04 (powerset__Cong) =>
% 120.37/16.04 ((
% 120.37/16.04 (setunion__Cong) =>
% 120.37/16.04 ((
% 120.37/16.04 (exuEu) =>
% 120.37/16.04 ((
% 120.37/16.04 (descr__Cong) =>
% 120.37/16.04 ((
% 120.37/16.04 (dsetconstr__Cong) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetI1) =>
% 120.37/16.04 ((
% 120.37/16.04 (eqimpsubset2) =>
% 120.37/16.04 ((
% 120.37/16.04 (eqimpsubset1) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetI2) =>
% 120.37/16.04 ((
% 120.37/16.04 (emptysetsubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetE) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetE2) =>
% 120.37/16.04 ((
% 120.37/16.04 (notsubsetI) =>
% 120.37/16.04 ((
% 120.37/16.04 (notequalI1) =>
% 120.37/16.04 ((
% 120.37/16.04 (notequalI2) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetRefl) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetTrans) =>
% 120.37/16.04 ((
% 120.37/16.04 (setadjoinSub) =>
% 120.37/16.04 ((
% 120.37/16.04 (setadjoinSub2) =>
% 120.37/16.04 ((
% 120.37/16.04 (subset2powerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (setextsub) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetemptysetimpeq) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetI1) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetE1) =>
% 120.37/16.04 ((
% 120.37/16.04 (inPowerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetsubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (sepInPowerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (sepSubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (binunionIL) =>
% 120.37/16.04 ((
% 120.37/16.04 (upairset2IR) =>
% 120.37/16.04 ((
% 120.37/16.04 (binunionIR) =>
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y0 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y1 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y2 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y3 : $o]:
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 (
% 120.37/16.04 binunion @
% 120.37/16.04 Y0 @ Y1)) =>
% 120.37/16.04 ((
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 Y0) =>
% 120.37/16.04 (Y3))) =>
% 120.37/16.04 ((
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 Y1) =>
% 120.37/16.04 (Y3))) =>
% 120.37/16.04 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl350])).
% 120.37/16.04 thf(zip_derived_cl364, plain,
% 120.37/16.04 (~ (((setunionE) =>
% 120.37/16.04 (((subPowSU) =>
% 120.37/16.04 (((exuE2) =>
% 120.37/16.04 (((nonemptyImpWitness) =>
% 120.37/16.04 (((uniqinunit) =>
% 120.37/16.04 (((notinsingleton) =>
% 120.37/16.04 (((eqinunit) =>
% 120.37/16.04 (((singletonsswitch) =>
% 120.37/16.04 (((upairsetE) =>
% 120.37/16.04 (((upairsetIL) =>
% 120.37/16.04 (((upairsetIR) =>
% 120.37/16.04 (((emptyE1) =>
% 120.37/16.04 (((vacuousDall) =>
% 120.37/16.04 (((quantDeMorgan1) =>
% 120.37/16.04 (((quantDeMorgan2) =>
% 120.37/16.04 (((quantDeMorgan3) =>
% 120.37/16.04 (((quantDeMorgan4) =>
% 120.37/16.04 (((prop2setI) =>
% 120.37/16.04 (((prop2set2propI) =>
% 120.37/16.04 (((notdexE) =>
% 120.37/16.04 (((notdallE) =>
% 120.37/16.04 (((exuI1) =>
% 120.37/16.04 (((exuI3) =>
% 120.37/16.04 (((exuI2) =>
% 120.37/16.04 (((inCongP) =>
% 120.37/16.04 (((in__Cong) =>
% 120.37/16.04 (((exuE3u) =>
% 120.37/16.04 (((exu__Cong) =>
% 120.37/16.04 (((setadjoin__Cong) =>
% 120.37/16.04 (((powerset__Cong) =>
% 120.37/16.04 ((
% 120.37/16.04 (setunion__Cong) =>
% 120.37/16.04 ((
% 120.37/16.04 (exuEu) =>
% 120.37/16.04 ((
% 120.37/16.04 (descr__Cong) =>
% 120.37/16.04 ((
% 120.37/16.04 (dsetconstr__Cong) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetI1) =>
% 120.37/16.04 ((
% 120.37/16.04 (eqimpsubset2) =>
% 120.37/16.04 ((
% 120.37/16.04 (eqimpsubset1) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetI2) =>
% 120.37/16.04 ((
% 120.37/16.04 (emptysetsubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetE) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetE2) =>
% 120.37/16.04 ((
% 120.37/16.04 (notsubsetI) =>
% 120.37/16.04 ((
% 120.37/16.04 (notequalI1) =>
% 120.37/16.04 ((
% 120.37/16.04 (notequalI2) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetRefl) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetTrans) =>
% 120.37/16.04 ((
% 120.37/16.04 (setadjoinSub) =>
% 120.37/16.04 ((
% 120.37/16.04 (setadjoinSub2) =>
% 120.37/16.04 ((
% 120.37/16.04 (subset2powerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (setextsub) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetemptysetimpeq) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetI1) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetE1) =>
% 120.37/16.04 ((
% 120.37/16.04 (inPowerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetsubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (sepInPowerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (sepSubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (binunionIL) =>
% 120.37/16.04 ((
% 120.37/16.04 (upairset2IR) =>
% 120.37/16.04 ((
% 120.37/16.04 (binunionIR) =>
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y0 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y1 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y2 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y3 : $o]:
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 (
% 120.37/16.04 binunion @
% 120.37/16.04 Y0 @ Y1)) =>
% 120.37/16.04 ((
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 Y0) =>
% 120.37/16.04 (Y3))) =>
% 120.37/16.04 ((
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 Y1) =>
% 120.37/16.04 (Y3))) =>
% 120.37/16.04 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl357])).
% 120.37/16.04 thf(zip_derived_cl372, plain,
% 120.37/16.04 (~ (((subPowSU) =>
% 120.37/16.04 (((exuE2) =>
% 120.37/16.04 (((nonemptyImpWitness) =>
% 120.37/16.04 (((uniqinunit) =>
% 120.37/16.04 (((notinsingleton) =>
% 120.37/16.04 (((eqinunit) =>
% 120.37/16.04 (((singletonsswitch) =>
% 120.37/16.04 (((upairsetE) =>
% 120.37/16.04 (((upairsetIL) =>
% 120.37/16.04 (((upairsetIR) =>
% 120.37/16.04 (((emptyE1) =>
% 120.37/16.04 (((vacuousDall) =>
% 120.37/16.04 (((quantDeMorgan1) =>
% 120.37/16.04 (((quantDeMorgan2) =>
% 120.37/16.04 (((quantDeMorgan3) =>
% 120.37/16.04 (((quantDeMorgan4) =>
% 120.37/16.04 (((prop2setI) =>
% 120.37/16.04 (((prop2set2propI) =>
% 120.37/16.04 (((notdexE) =>
% 120.37/16.04 (((notdallE) =>
% 120.37/16.04 (((exuI1) =>
% 120.37/16.04 (((exuI3) =>
% 120.37/16.04 (((exuI2) =>
% 120.37/16.04 (((inCongP) =>
% 120.37/16.04 (((in__Cong) =>
% 120.37/16.04 (((exuE3u) =>
% 120.37/16.04 (((exu__Cong) =>
% 120.37/16.04 (((setadjoin__Cong) =>
% 120.37/16.04 (((powerset__Cong) =>
% 120.37/16.04 (((setunion__Cong) =>
% 120.37/16.04 ((
% 120.37/16.04 (exuEu) =>
% 120.37/16.04 ((
% 120.37/16.04 (descr__Cong) =>
% 120.37/16.04 ((
% 120.37/16.04 (dsetconstr__Cong) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetI1) =>
% 120.37/16.04 ((
% 120.37/16.04 (eqimpsubset2) =>
% 120.37/16.04 ((
% 120.37/16.04 (eqimpsubset1) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetI2) =>
% 120.37/16.04 ((
% 120.37/16.04 (emptysetsubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetE) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetE2) =>
% 120.37/16.04 ((
% 120.37/16.04 (notsubsetI) =>
% 120.37/16.04 ((
% 120.37/16.04 (notequalI1) =>
% 120.37/16.04 ((
% 120.37/16.04 (notequalI2) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetRefl) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetTrans) =>
% 120.37/16.04 ((
% 120.37/16.04 (setadjoinSub) =>
% 120.37/16.04 ((
% 120.37/16.04 (setadjoinSub2) =>
% 120.37/16.04 ((
% 120.37/16.04 (subset2powerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (setextsub) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetemptysetimpeq) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetI1) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetE1) =>
% 120.37/16.04 ((
% 120.37/16.04 (inPowerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetsubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (sepInPowerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (sepSubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (binunionIL) =>
% 120.37/16.04 ((
% 120.37/16.04 (upairset2IR) =>
% 120.37/16.04 ((
% 120.37/16.04 (binunionIR) =>
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y0 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y1 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y2 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y3 : $o]:
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 (
% 120.37/16.04 binunion @
% 120.37/16.04 Y0 @ Y1)) =>
% 120.37/16.04 ((
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 Y0) =>
% 120.37/16.04 (Y3))) =>
% 120.37/16.04 ((
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 Y1) =>
% 120.37/16.04 (Y3))) =>
% 120.37/16.04 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl364])).
% 120.37/16.04 thf(zip_derived_cl382, plain,
% 120.37/16.04 (~ (((exuE2) =>
% 120.37/16.04 (((nonemptyImpWitness) =>
% 120.37/16.04 (((uniqinunit) =>
% 120.37/16.04 (((notinsingleton) =>
% 120.37/16.04 (((eqinunit) =>
% 120.37/16.04 (((singletonsswitch) =>
% 120.37/16.04 (((upairsetE) =>
% 120.37/16.04 (((upairsetIL) =>
% 120.37/16.04 (((upairsetIR) =>
% 120.37/16.04 (((emptyE1) =>
% 120.37/16.04 (((vacuousDall) =>
% 120.37/16.04 (((quantDeMorgan1) =>
% 120.37/16.04 (((quantDeMorgan2) =>
% 120.37/16.04 (((quantDeMorgan3) =>
% 120.37/16.04 (((quantDeMorgan4) =>
% 120.37/16.04 (((prop2setI) =>
% 120.37/16.04 (((prop2set2propI) =>
% 120.37/16.04 (((notdexE) =>
% 120.37/16.04 (((notdallE) =>
% 120.37/16.04 (((exuI1) =>
% 120.37/16.04 (((exuI3) =>
% 120.37/16.04 (((exuI2) =>
% 120.37/16.04 (((inCongP) =>
% 120.37/16.04 (((in__Cong) =>
% 120.37/16.04 (((exuE3u) =>
% 120.37/16.04 (((exu__Cong) =>
% 120.37/16.04 (((setadjoin__Cong) =>
% 120.37/16.04 (((powerset__Cong) =>
% 120.37/16.04 (((setunion__Cong) =>
% 120.37/16.04 (((exuEu) =>
% 120.37/16.04 ((
% 120.37/16.04 (descr__Cong) =>
% 120.37/16.04 ((
% 120.37/16.04 (dsetconstr__Cong) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetI1) =>
% 120.37/16.04 ((
% 120.37/16.04 (eqimpsubset2) =>
% 120.37/16.04 ((
% 120.37/16.04 (eqimpsubset1) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetI2) =>
% 120.37/16.04 ((
% 120.37/16.04 (emptysetsubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetE) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetE2) =>
% 120.37/16.04 ((
% 120.37/16.04 (notsubsetI) =>
% 120.37/16.04 ((
% 120.37/16.04 (notequalI1) =>
% 120.37/16.04 ((
% 120.37/16.04 (notequalI2) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetRefl) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetTrans) =>
% 120.37/16.04 ((
% 120.37/16.04 (setadjoinSub) =>
% 120.37/16.04 ((
% 120.37/16.04 (setadjoinSub2) =>
% 120.37/16.04 ((
% 120.37/16.04 (subset2powerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (setextsub) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetemptysetimpeq) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetI1) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetE1) =>
% 120.37/16.04 ((
% 120.37/16.04 (inPowerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetsubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (sepInPowerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (sepSubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (binunionIL) =>
% 120.37/16.04 ((
% 120.37/16.04 (upairset2IR) =>
% 120.37/16.04 ((
% 120.37/16.04 (binunionIR) =>
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y0 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y1 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y2 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y3 : $o]:
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 (
% 120.37/16.04 binunion @
% 120.37/16.04 Y0 @ Y1)) =>
% 120.37/16.04 ((
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 Y0) =>
% 120.37/16.04 (Y3))) =>
% 120.37/16.04 ((
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 Y1) =>
% 120.37/16.04 (Y3))) =>
% 120.37/16.04 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl372])).
% 120.37/16.04 thf(zip_derived_cl390, plain,
% 120.37/16.04 (~ (((nonemptyImpWitness) =>
% 120.37/16.04 (((uniqinunit) =>
% 120.37/16.04 (((notinsingleton) =>
% 120.37/16.04 (((eqinunit) =>
% 120.37/16.04 (((singletonsswitch) =>
% 120.37/16.04 (((upairsetE) =>
% 120.37/16.04 (((upairsetIL) =>
% 120.37/16.04 (((upairsetIR) =>
% 120.37/16.04 (((emptyE1) =>
% 120.37/16.04 (((vacuousDall) =>
% 120.37/16.04 (((quantDeMorgan1) =>
% 120.37/16.04 (((quantDeMorgan2) =>
% 120.37/16.04 (((quantDeMorgan3) =>
% 120.37/16.04 (((quantDeMorgan4) =>
% 120.37/16.04 (((prop2setI) =>
% 120.37/16.04 (((prop2set2propI) =>
% 120.37/16.04 (((notdexE) =>
% 120.37/16.04 (((notdallE) =>
% 120.37/16.04 (((exuI1) =>
% 120.37/16.04 (((exuI3) =>
% 120.37/16.04 (((exuI2) =>
% 120.37/16.04 (((inCongP) =>
% 120.37/16.04 (((in__Cong) =>
% 120.37/16.04 (((exuE3u) =>
% 120.37/16.04 (((exu__Cong) =>
% 120.37/16.04 (((setadjoin__Cong) =>
% 120.37/16.04 (((powerset__Cong) =>
% 120.37/16.04 (((setunion__Cong) =>
% 120.37/16.04 (((exuEu) =>
% 120.37/16.04 (((descr__Cong) =>
% 120.37/16.04 ((
% 120.37/16.04 (dsetconstr__Cong) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetI1) =>
% 120.37/16.04 ((
% 120.37/16.04 (eqimpsubset2) =>
% 120.37/16.04 ((
% 120.37/16.04 (eqimpsubset1) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetI2) =>
% 120.37/16.04 ((
% 120.37/16.04 (emptysetsubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetE) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetE2) =>
% 120.37/16.04 ((
% 120.37/16.04 (notsubsetI) =>
% 120.37/16.04 ((
% 120.37/16.04 (notequalI1) =>
% 120.37/16.04 ((
% 120.37/16.04 (notequalI2) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetRefl) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetTrans) =>
% 120.37/16.04 ((
% 120.37/16.04 (setadjoinSub) =>
% 120.37/16.04 ((
% 120.37/16.04 (setadjoinSub2) =>
% 120.37/16.04 ((
% 120.37/16.04 (subset2powerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (setextsub) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetemptysetimpeq) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetI1) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetE1) =>
% 120.37/16.04 ((
% 120.37/16.04 (inPowerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetsubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (sepInPowerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (sepSubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (binunionIL) =>
% 120.37/16.04 ((
% 120.37/16.04 (upairset2IR) =>
% 120.37/16.04 ((
% 120.37/16.04 (binunionIR) =>
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y0 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y1 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y2 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y3 : $o]:
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 (
% 120.37/16.04 binunion @
% 120.37/16.04 Y0 @ Y1)) =>
% 120.37/16.04 ((
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 Y0) =>
% 120.37/16.04 (Y3))) =>
% 120.37/16.04 ((
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 Y1) =>
% 120.37/16.04 (Y3))) =>
% 120.37/16.04 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl382])).
% 120.37/16.04 thf(zip_derived_cl397, plain,
% 120.37/16.04 (~ (((uniqinunit) =>
% 120.37/16.04 (((notinsingleton) =>
% 120.37/16.04 (((eqinunit) =>
% 120.37/16.04 (((singletonsswitch) =>
% 120.37/16.04 (((upairsetE) =>
% 120.37/16.04 (((upairsetIL) =>
% 120.37/16.04 (((upairsetIR) =>
% 120.37/16.04 (((emptyE1) =>
% 120.37/16.04 (((vacuousDall) =>
% 120.37/16.04 (((quantDeMorgan1) =>
% 120.37/16.04 (((quantDeMorgan2) =>
% 120.37/16.04 (((quantDeMorgan3) =>
% 120.37/16.04 (((quantDeMorgan4) =>
% 120.37/16.04 (((prop2setI) =>
% 120.37/16.04 (((prop2set2propI) =>
% 120.37/16.04 (((notdexE) =>
% 120.37/16.04 (((notdallE) =>
% 120.37/16.04 (((exuI1) =>
% 120.37/16.04 (((exuI3) =>
% 120.37/16.04 (((exuI2) =>
% 120.37/16.04 (((inCongP) =>
% 120.37/16.04 (((in__Cong) =>
% 120.37/16.04 (((exuE3u) =>
% 120.37/16.04 (((exu__Cong) =>
% 120.37/16.04 (((setadjoin__Cong) =>
% 120.37/16.04 (((powerset__Cong) =>
% 120.37/16.04 (((setunion__Cong) =>
% 120.37/16.04 (((exuEu) =>
% 120.37/16.04 (((descr__Cong) =>
% 120.37/16.04 (((dsetconstr__Cong) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetI1) =>
% 120.37/16.04 ((
% 120.37/16.04 (eqimpsubset2) =>
% 120.37/16.04 ((
% 120.37/16.04 (eqimpsubset1) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetI2) =>
% 120.37/16.04 ((
% 120.37/16.04 (emptysetsubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetE) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetE2) =>
% 120.37/16.04 ((
% 120.37/16.04 (notsubsetI) =>
% 120.37/16.04 ((
% 120.37/16.04 (notequalI1) =>
% 120.37/16.04 ((
% 120.37/16.04 (notequalI2) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetRefl) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetTrans) =>
% 120.37/16.04 ((
% 120.37/16.04 (setadjoinSub) =>
% 120.37/16.04 ((
% 120.37/16.04 (setadjoinSub2) =>
% 120.37/16.04 ((
% 120.37/16.04 (subset2powerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (setextsub) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetemptysetimpeq) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetI1) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetE1) =>
% 120.37/16.04 ((
% 120.37/16.04 (inPowerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetsubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (sepInPowerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (sepSubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (binunionIL) =>
% 120.37/16.04 ((
% 120.37/16.04 (upairset2IR) =>
% 120.37/16.04 ((
% 120.37/16.04 (binunionIR) =>
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y0 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y1 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y2 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y3 : $o]:
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 (
% 120.37/16.04 binunion @
% 120.37/16.04 Y0 @ Y1)) =>
% 120.37/16.04 ((
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 Y0) =>
% 120.37/16.04 (Y3))) =>
% 120.37/16.04 ((
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 Y1) =>
% 120.37/16.04 (Y3))) =>
% 120.37/16.04 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl390])).
% 120.37/16.04 thf(zip_derived_cl406, plain,
% 120.37/16.04 (~ (((notinsingleton) =>
% 120.37/16.04 (((eqinunit) =>
% 120.37/16.04 (((singletonsswitch) =>
% 120.37/16.04 (((upairsetE) =>
% 120.37/16.04 (((upairsetIL) =>
% 120.37/16.04 (((upairsetIR) =>
% 120.37/16.04 (((emptyE1) =>
% 120.37/16.04 (((vacuousDall) =>
% 120.37/16.04 (((quantDeMorgan1) =>
% 120.37/16.04 (((quantDeMorgan2) =>
% 120.37/16.04 (((quantDeMorgan3) =>
% 120.37/16.04 (((quantDeMorgan4) =>
% 120.37/16.04 (((prop2setI) =>
% 120.37/16.04 (((prop2set2propI) =>
% 120.37/16.04 (((notdexE) =>
% 120.37/16.04 (((notdallE) =>
% 120.37/16.04 (((exuI1) =>
% 120.37/16.04 (((exuI3) =>
% 120.37/16.04 (((exuI2) =>
% 120.37/16.04 (((inCongP) =>
% 120.37/16.04 (((in__Cong) =>
% 120.37/16.04 (((exuE3u) =>
% 120.37/16.04 (((exu__Cong) =>
% 120.37/16.04 (((setadjoin__Cong) =>
% 120.37/16.04 (((powerset__Cong) =>
% 120.37/16.04 (((setunion__Cong) =>
% 120.37/16.04 (((exuEu) =>
% 120.37/16.04 (((descr__Cong) =>
% 120.37/16.04 (((dsetconstr__Cong) =>
% 120.37/16.04 (((subsetI1) =>
% 120.37/16.04 ((
% 120.37/16.04 (eqimpsubset2) =>
% 120.37/16.04 ((
% 120.37/16.04 (eqimpsubset1) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetI2) =>
% 120.37/16.04 ((
% 120.37/16.04 (emptysetsubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetE) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetE2) =>
% 120.37/16.04 ((
% 120.37/16.04 (notsubsetI) =>
% 120.37/16.04 ((
% 120.37/16.04 (notequalI1) =>
% 120.37/16.04 ((
% 120.37/16.04 (notequalI2) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetRefl) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetTrans) =>
% 120.37/16.04 ((
% 120.37/16.04 (setadjoinSub) =>
% 120.37/16.04 ((
% 120.37/16.04 (setadjoinSub2) =>
% 120.37/16.04 ((
% 120.37/16.04 (subset2powerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (setextsub) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetemptysetimpeq) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetI1) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetE1) =>
% 120.37/16.04 ((
% 120.37/16.04 (inPowerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetsubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (sepInPowerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (sepSubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (binunionIL) =>
% 120.37/16.04 ((
% 120.37/16.04 (upairset2IR) =>
% 120.37/16.04 ((
% 120.37/16.04 (binunionIR) =>
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y0 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y1 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y2 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y3 : $o]:
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 (
% 120.37/16.04 binunion @
% 120.37/16.04 Y0 @ Y1)) =>
% 120.37/16.04 ((
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 Y0) =>
% 120.37/16.04 (Y3))) =>
% 120.37/16.04 ((
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 Y1) =>
% 120.37/16.04 (Y3))) =>
% 120.37/16.04 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl397])).
% 120.37/16.04 thf(zip_derived_cl413, plain,
% 120.37/16.04 (~ (((eqinunit) =>
% 120.37/16.04 (((singletonsswitch) =>
% 120.37/16.04 (((upairsetE) =>
% 120.37/16.04 (((upairsetIL) =>
% 120.37/16.04 (((upairsetIR) =>
% 120.37/16.04 (((emptyE1) =>
% 120.37/16.04 (((vacuousDall) =>
% 120.37/16.04 (((quantDeMorgan1) =>
% 120.37/16.04 (((quantDeMorgan2) =>
% 120.37/16.04 (((quantDeMorgan3) =>
% 120.37/16.04 (((quantDeMorgan4) =>
% 120.37/16.04 (((prop2setI) =>
% 120.37/16.04 (((prop2set2propI) =>
% 120.37/16.04 (((notdexE) =>
% 120.37/16.04 (((notdallE) =>
% 120.37/16.04 (((exuI1) =>
% 120.37/16.04 (((exuI3) =>
% 120.37/16.04 (((exuI2) =>
% 120.37/16.04 (((inCongP) =>
% 120.37/16.04 (((in__Cong) =>
% 120.37/16.04 (((exuE3u) =>
% 120.37/16.04 (((exu__Cong) =>
% 120.37/16.04 (((setadjoin__Cong) =>
% 120.37/16.04 (((powerset__Cong) =>
% 120.37/16.04 (((setunion__Cong) =>
% 120.37/16.04 (((exuEu) =>
% 120.37/16.04 (((descr__Cong) =>
% 120.37/16.04 (((dsetconstr__Cong) =>
% 120.37/16.04 (((subsetI1) =>
% 120.37/16.04 (((eqimpsubset2) =>
% 120.37/16.04 ((
% 120.37/16.04 (eqimpsubset1) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetI2) =>
% 120.37/16.04 ((
% 120.37/16.04 (emptysetsubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetE) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetE2) =>
% 120.37/16.04 ((
% 120.37/16.04 (notsubsetI) =>
% 120.37/16.04 ((
% 120.37/16.04 (notequalI1) =>
% 120.37/16.04 ((
% 120.37/16.04 (notequalI2) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetRefl) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetTrans) =>
% 120.37/16.04 ((
% 120.37/16.04 (setadjoinSub) =>
% 120.37/16.04 ((
% 120.37/16.04 (setadjoinSub2) =>
% 120.37/16.04 ((
% 120.37/16.04 (subset2powerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (setextsub) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetemptysetimpeq) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetI1) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetE1) =>
% 120.37/16.04 ((
% 120.37/16.04 (inPowerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetsubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (sepInPowerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (sepSubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (binunionIL) =>
% 120.37/16.04 ((
% 120.37/16.04 (upairset2IR) =>
% 120.37/16.04 ((
% 120.37/16.04 (binunionIR) =>
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y0 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y1 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y2 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y3 : $o]:
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 (
% 120.37/16.04 binunion @
% 120.37/16.04 Y0 @ Y1)) =>
% 120.37/16.04 ((
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 Y0) =>
% 120.37/16.04 (Y3))) =>
% 120.37/16.04 ((
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 Y1) =>
% 120.37/16.04 (Y3))) =>
% 120.37/16.04 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl406])).
% 120.37/16.04 thf(zip_derived_cl420, plain,
% 120.37/16.04 (~ (((singletonsswitch) =>
% 120.37/16.04 (((upairsetE) =>
% 120.37/16.04 (((upairsetIL) =>
% 120.37/16.04 (((upairsetIR) =>
% 120.37/16.04 (((emptyE1) =>
% 120.37/16.04 (((vacuousDall) =>
% 120.37/16.04 (((quantDeMorgan1) =>
% 120.37/16.04 (((quantDeMorgan2) =>
% 120.37/16.04 (((quantDeMorgan3) =>
% 120.37/16.04 (((quantDeMorgan4) =>
% 120.37/16.04 (((prop2setI) =>
% 120.37/16.04 (((prop2set2propI) =>
% 120.37/16.04 (((notdexE) =>
% 120.37/16.04 (((notdallE) =>
% 120.37/16.04 (((exuI1) =>
% 120.37/16.04 (((exuI3) =>
% 120.37/16.04 (((exuI2) =>
% 120.37/16.04 (((inCongP) =>
% 120.37/16.04 (((in__Cong) =>
% 120.37/16.04 (((exuE3u) =>
% 120.37/16.04 (((exu__Cong) =>
% 120.37/16.04 (((setadjoin__Cong) =>
% 120.37/16.04 (((powerset__Cong) =>
% 120.37/16.04 (((setunion__Cong) =>
% 120.37/16.04 (((exuEu) =>
% 120.37/16.04 (((descr__Cong) =>
% 120.37/16.04 (((dsetconstr__Cong) =>
% 120.37/16.04 (((subsetI1) =>
% 120.37/16.04 (((eqimpsubset2) =>
% 120.37/16.04 (((eqimpsubset1) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetI2) =>
% 120.37/16.04 ((
% 120.37/16.04 (emptysetsubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetE) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetE2) =>
% 120.37/16.04 ((
% 120.37/16.04 (notsubsetI) =>
% 120.37/16.04 ((
% 120.37/16.04 (notequalI1) =>
% 120.37/16.04 ((
% 120.37/16.04 (notequalI2) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetRefl) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetTrans) =>
% 120.37/16.04 ((
% 120.37/16.04 (setadjoinSub) =>
% 120.37/16.04 ((
% 120.37/16.04 (setadjoinSub2) =>
% 120.37/16.04 ((
% 120.37/16.04 (subset2powerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (setextsub) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetemptysetimpeq) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetI1) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetE1) =>
% 120.37/16.04 ((
% 120.37/16.04 (inPowerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetsubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (sepInPowerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (sepSubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (binunionIL) =>
% 120.37/16.04 ((
% 120.37/16.04 (upairset2IR) =>
% 120.37/16.04 ((
% 120.37/16.04 (binunionIR) =>
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y0 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y1 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y2 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y3 : $o]:
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 (
% 120.37/16.04 binunion @
% 120.37/16.04 Y0 @ Y1)) =>
% 120.37/16.04 ((
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 Y0) =>
% 120.37/16.04 (Y3))) =>
% 120.37/16.04 ((
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 Y1) =>
% 120.37/16.04 (Y3))) =>
% 120.37/16.04 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl413])).
% 120.37/16.04 thf(zip_derived_cl428, plain,
% 120.37/16.04 (~ (((upairsetE) =>
% 120.37/16.04 (((upairsetIL) =>
% 120.37/16.04 (((upairsetIR) =>
% 120.37/16.04 (((emptyE1) =>
% 120.37/16.04 (((vacuousDall) =>
% 120.37/16.04 (((quantDeMorgan1) =>
% 120.37/16.04 (((quantDeMorgan2) =>
% 120.37/16.04 (((quantDeMorgan3) =>
% 120.37/16.04 (((quantDeMorgan4) =>
% 120.37/16.04 (((prop2setI) =>
% 120.37/16.04 (((prop2set2propI) =>
% 120.37/16.04 (((notdexE) =>
% 120.37/16.04 (((notdallE) =>
% 120.37/16.04 (((exuI1) =>
% 120.37/16.04 (((exuI3) =>
% 120.37/16.04 (((exuI2) =>
% 120.37/16.04 (((inCongP) =>
% 120.37/16.04 (((in__Cong) =>
% 120.37/16.04 (((exuE3u) =>
% 120.37/16.04 (((exu__Cong) =>
% 120.37/16.04 (((setadjoin__Cong) =>
% 120.37/16.04 (((powerset__Cong) =>
% 120.37/16.04 (((setunion__Cong) =>
% 120.37/16.04 (((exuEu) =>
% 120.37/16.04 (((descr__Cong) =>
% 120.37/16.04 (((dsetconstr__Cong) =>
% 120.37/16.04 (((subsetI1) =>
% 120.37/16.04 (((eqimpsubset2) =>
% 120.37/16.04 (((eqimpsubset1) =>
% 120.37/16.04 (((subsetI2) =>
% 120.37/16.04 ((
% 120.37/16.04 (emptysetsubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetE) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetE2) =>
% 120.37/16.04 ((
% 120.37/16.04 (notsubsetI) =>
% 120.37/16.04 ((
% 120.37/16.04 (notequalI1) =>
% 120.37/16.04 ((
% 120.37/16.04 (notequalI2) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetRefl) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetTrans) =>
% 120.37/16.04 ((
% 120.37/16.04 (setadjoinSub) =>
% 120.37/16.04 ((
% 120.37/16.04 (setadjoinSub2) =>
% 120.37/16.04 ((
% 120.37/16.04 (subset2powerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (setextsub) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetemptysetimpeq) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetI1) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetE1) =>
% 120.37/16.04 ((
% 120.37/16.04 (inPowerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetsubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (sepInPowerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (sepSubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (binunionIL) =>
% 120.37/16.04 ((
% 120.37/16.04 (upairset2IR) =>
% 120.37/16.04 ((
% 120.37/16.04 (binunionIR) =>
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y0 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y1 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y2 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y3 : $o]:
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 (
% 120.37/16.04 binunion @
% 120.37/16.04 Y0 @ Y1)) =>
% 120.37/16.04 ((
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 Y0) =>
% 120.37/16.04 (Y3))) =>
% 120.37/16.04 ((
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 Y1) =>
% 120.37/16.04 (Y3))) =>
% 120.37/16.04 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl420])).
% 120.37/16.04 thf(zip_derived_cl439, plain,
% 120.37/16.04 (~ (((upairsetIL) =>
% 120.37/16.04 (((upairsetIR) =>
% 120.37/16.04 (((emptyE1) =>
% 120.37/16.04 (((vacuousDall) =>
% 120.37/16.04 (((quantDeMorgan1) =>
% 120.37/16.04 (((quantDeMorgan2) =>
% 120.37/16.04 (((quantDeMorgan3) =>
% 120.37/16.04 (((quantDeMorgan4) =>
% 120.37/16.04 (((prop2setI) =>
% 120.37/16.04 (((prop2set2propI) =>
% 120.37/16.04 (((notdexE) =>
% 120.37/16.04 (((notdallE) =>
% 120.37/16.04 (((exuI1) =>
% 120.37/16.04 (((exuI3) =>
% 120.37/16.04 (((exuI2) =>
% 120.37/16.04 (((inCongP) =>
% 120.37/16.04 (((in__Cong) =>
% 120.37/16.04 (((exuE3u) =>
% 120.37/16.04 (((exu__Cong) =>
% 120.37/16.04 (((setadjoin__Cong) =>
% 120.37/16.04 (((powerset__Cong) =>
% 120.37/16.04 (((setunion__Cong) =>
% 120.37/16.04 (((exuEu) =>
% 120.37/16.04 (((descr__Cong) =>
% 120.37/16.04 (((dsetconstr__Cong) =>
% 120.37/16.04 (((subsetI1) =>
% 120.37/16.04 (((eqimpsubset2) =>
% 120.37/16.04 (((eqimpsubset1) =>
% 120.37/16.04 (((subsetI2) =>
% 120.37/16.04 (((emptysetsubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetE) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetE2) =>
% 120.37/16.04 ((
% 120.37/16.04 (notsubsetI) =>
% 120.37/16.04 ((
% 120.37/16.04 (notequalI1) =>
% 120.37/16.04 ((
% 120.37/16.04 (notequalI2) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetRefl) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetTrans) =>
% 120.37/16.04 ((
% 120.37/16.04 (setadjoinSub) =>
% 120.37/16.04 ((
% 120.37/16.04 (setadjoinSub2) =>
% 120.37/16.04 ((
% 120.37/16.04 (subset2powerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (setextsub) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetemptysetimpeq) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetI1) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetE1) =>
% 120.37/16.04 ((
% 120.37/16.04 (inPowerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetsubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (sepInPowerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (sepSubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (binunionIL) =>
% 120.37/16.04 ((
% 120.37/16.04 (upairset2IR) =>
% 120.37/16.04 ((
% 120.37/16.04 (binunionIR) =>
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y0 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y1 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y2 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y3 : $o]:
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 (
% 120.37/16.04 binunion @
% 120.37/16.04 Y0 @ Y1)) =>
% 120.37/16.04 ((
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 Y0) =>
% 120.37/16.04 (Y3))) =>
% 120.37/16.04 ((
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 Y1) =>
% 120.37/16.04 (Y3))) =>
% 120.37/16.04 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl428])).
% 120.37/16.04 thf(zip_derived_cl449, plain,
% 120.37/16.04 (~ (((upairsetIR) =>
% 120.37/16.04 (((emptyE1) =>
% 120.37/16.04 (((vacuousDall) =>
% 120.37/16.04 (((quantDeMorgan1) =>
% 120.37/16.04 (((quantDeMorgan2) =>
% 120.37/16.04 (((quantDeMorgan3) =>
% 120.37/16.04 (((quantDeMorgan4) =>
% 120.37/16.04 (((prop2setI) =>
% 120.37/16.04 (((prop2set2propI) =>
% 120.37/16.04 (((notdexE) =>
% 120.37/16.04 (((notdallE) =>
% 120.37/16.04 (((exuI1) =>
% 120.37/16.04 (((exuI3) =>
% 120.37/16.04 (((exuI2) =>
% 120.37/16.04 (((inCongP) =>
% 120.37/16.04 (((in__Cong) =>
% 120.37/16.04 (((exuE3u) =>
% 120.37/16.04 (((exu__Cong) =>
% 120.37/16.04 (((setadjoin__Cong) =>
% 120.37/16.04 (((powerset__Cong) =>
% 120.37/16.04 (((setunion__Cong) =>
% 120.37/16.04 (((exuEu) =>
% 120.37/16.04 (((descr__Cong) =>
% 120.37/16.04 (((dsetconstr__Cong) =>
% 120.37/16.04 (((subsetI1) =>
% 120.37/16.04 (((eqimpsubset2) =>
% 120.37/16.04 (((eqimpsubset1) =>
% 120.37/16.04 (((subsetI2) =>
% 120.37/16.04 (((emptysetsubset) =>
% 120.37/16.04 (((subsetE) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetE2) =>
% 120.37/16.04 ((
% 120.37/16.04 (notsubsetI) =>
% 120.37/16.04 ((
% 120.37/16.04 (notequalI1) =>
% 120.37/16.04 ((
% 120.37/16.04 (notequalI2) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetRefl) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetTrans) =>
% 120.37/16.04 ((
% 120.37/16.04 (setadjoinSub) =>
% 120.37/16.04 ((
% 120.37/16.04 (setadjoinSub2) =>
% 120.37/16.04 ((
% 120.37/16.04 (subset2powerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (setextsub) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetemptysetimpeq) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetI1) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetE1) =>
% 120.37/16.04 ((
% 120.37/16.04 (inPowerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetsubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (sepInPowerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (sepSubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (binunionIL) =>
% 120.37/16.04 ((
% 120.37/16.04 (upairset2IR) =>
% 120.37/16.04 ((
% 120.37/16.04 (binunionIR) =>
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y0 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y1 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y2 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y3 : $o]:
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 (
% 120.37/16.04 binunion @
% 120.37/16.04 Y0 @ Y1)) =>
% 120.37/16.04 ((
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 Y0) =>
% 120.37/16.04 (Y3))) =>
% 120.37/16.04 ((
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 Y1) =>
% 120.37/16.04 (Y3))) =>
% 120.37/16.04 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl439])).
% 120.37/16.04 thf(zip_derived_cl457, plain,
% 120.37/16.04 (~ (((emptyE1) =>
% 120.37/16.04 (((vacuousDall) =>
% 120.37/16.04 (((quantDeMorgan1) =>
% 120.37/16.04 (((quantDeMorgan2) =>
% 120.37/16.04 (((quantDeMorgan3) =>
% 120.37/16.04 (((quantDeMorgan4) =>
% 120.37/16.04 (((prop2setI) =>
% 120.37/16.04 (((prop2set2propI) =>
% 120.37/16.04 (((notdexE) =>
% 120.37/16.04 (((notdallE) =>
% 120.37/16.04 (((exuI1) =>
% 120.37/16.04 (((exuI3) =>
% 120.37/16.04 (((exuI2) =>
% 120.37/16.04 (((inCongP) =>
% 120.37/16.04 (((in__Cong) =>
% 120.37/16.04 (((exuE3u) =>
% 120.37/16.04 (((exu__Cong) =>
% 120.37/16.04 (((setadjoin__Cong) =>
% 120.37/16.04 (((powerset__Cong) =>
% 120.37/16.04 (((setunion__Cong) =>
% 120.37/16.04 (((exuEu) =>
% 120.37/16.04 (((descr__Cong) =>
% 120.37/16.04 (((dsetconstr__Cong) =>
% 120.37/16.04 (((subsetI1) =>
% 120.37/16.04 (((eqimpsubset2) =>
% 120.37/16.04 (((eqimpsubset1) =>
% 120.37/16.04 (((subsetI2) =>
% 120.37/16.04 (((emptysetsubset) =>
% 120.37/16.04 (((subsetE) =>
% 120.37/16.04 (((subsetE2) =>
% 120.37/16.04 ((
% 120.37/16.04 (notsubsetI) =>
% 120.37/16.04 ((
% 120.37/16.04 (notequalI1) =>
% 120.37/16.04 ((
% 120.37/16.04 (notequalI2) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetRefl) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetTrans) =>
% 120.37/16.04 ((
% 120.37/16.04 (setadjoinSub) =>
% 120.37/16.04 ((
% 120.37/16.04 (setadjoinSub2) =>
% 120.37/16.04 ((
% 120.37/16.04 (subset2powerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (setextsub) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetemptysetimpeq) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetI1) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetE1) =>
% 120.37/16.04 ((
% 120.37/16.04 (inPowerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetsubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (sepInPowerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (sepSubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (binunionIL) =>
% 120.37/16.04 ((
% 120.37/16.04 (upairset2IR) =>
% 120.37/16.04 ((
% 120.37/16.04 (binunionIR) =>
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y0 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y1 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y2 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y3 : $o]:
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 (
% 120.37/16.04 binunion @
% 120.37/16.04 Y0 @ Y1)) =>
% 120.37/16.04 ((
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 Y0) =>
% 120.37/16.04 (Y3))) =>
% 120.37/16.04 ((
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 Y1) =>
% 120.37/16.04 (Y3))) =>
% 120.37/16.04 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl449])).
% 120.37/16.04 thf(zip_derived_cl465, plain,
% 120.37/16.04 (~ (((vacuousDall) =>
% 120.37/16.04 (((quantDeMorgan1) =>
% 120.37/16.04 (((quantDeMorgan2) =>
% 120.37/16.04 (((quantDeMorgan3) =>
% 120.37/16.04 (((quantDeMorgan4) =>
% 120.37/16.04 (((prop2setI) =>
% 120.37/16.04 (((prop2set2propI) =>
% 120.37/16.04 (((notdexE) =>
% 120.37/16.04 (((notdallE) =>
% 120.37/16.04 (((exuI1) =>
% 120.37/16.04 (((exuI3) =>
% 120.37/16.04 (((exuI2) =>
% 120.37/16.04 (((inCongP) =>
% 120.37/16.04 (((in__Cong) =>
% 120.37/16.04 (((exuE3u) =>
% 120.37/16.04 (((exu__Cong) =>
% 120.37/16.04 (((setadjoin__Cong) =>
% 120.37/16.04 (((powerset__Cong) =>
% 120.37/16.04 (((setunion__Cong) =>
% 120.37/16.04 (((exuEu) =>
% 120.37/16.04 (((descr__Cong) =>
% 120.37/16.04 (((dsetconstr__Cong) =>
% 120.37/16.04 (((subsetI1) =>
% 120.37/16.04 (((eqimpsubset2) =>
% 120.37/16.04 (((eqimpsubset1) =>
% 120.37/16.04 (((subsetI2) =>
% 120.37/16.04 (((emptysetsubset) =>
% 120.37/16.04 (((subsetE) =>
% 120.37/16.04 (((subsetE2) =>
% 120.37/16.04 (((notsubsetI) =>
% 120.37/16.04 ((
% 120.37/16.04 (notequalI1) =>
% 120.37/16.04 ((
% 120.37/16.04 (notequalI2) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetRefl) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetTrans) =>
% 120.37/16.04 ((
% 120.37/16.04 (setadjoinSub) =>
% 120.37/16.04 ((
% 120.37/16.04 (setadjoinSub2) =>
% 120.37/16.04 ((
% 120.37/16.04 (subset2powerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (setextsub) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetemptysetimpeq) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetI1) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetE1) =>
% 120.37/16.04 ((
% 120.37/16.04 (inPowerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetsubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (sepInPowerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (sepSubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (binunionIL) =>
% 120.37/16.04 ((
% 120.37/16.04 (upairset2IR) =>
% 120.37/16.04 ((
% 120.37/16.04 (binunionIR) =>
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y0 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y1 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y2 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y3 : $o]:
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 (
% 120.37/16.04 binunion @
% 120.37/16.04 Y0 @ Y1)) =>
% 120.37/16.04 ((
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 Y0) =>
% 120.37/16.04 (Y3))) =>
% 120.37/16.04 ((
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 Y1) =>
% 120.37/16.04 (Y3))) =>
% 120.37/16.04 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl457])).
% 120.37/16.04 thf(zip_derived_cl471, plain,
% 120.37/16.04 (~ (((quantDeMorgan1) =>
% 120.37/16.04 (((quantDeMorgan2) =>
% 120.37/16.04 (((quantDeMorgan3) =>
% 120.37/16.04 (((quantDeMorgan4) =>
% 120.37/16.04 (((prop2setI) =>
% 120.37/16.04 (((prop2set2propI) =>
% 120.37/16.04 (((notdexE) =>
% 120.37/16.04 (((notdallE) =>
% 120.37/16.04 (((exuI1) =>
% 120.37/16.04 (((exuI3) =>
% 120.37/16.04 (((exuI2) =>
% 120.37/16.04 (((inCongP) =>
% 120.37/16.04 (((in__Cong) =>
% 120.37/16.04 (((exuE3u) =>
% 120.37/16.04 (((exu__Cong) =>
% 120.37/16.04 (((setadjoin__Cong) =>
% 120.37/16.04 (((powerset__Cong) =>
% 120.37/16.04 (((setunion__Cong) =>
% 120.37/16.04 (((exuEu) =>
% 120.37/16.04 (((descr__Cong) =>
% 120.37/16.04 (((dsetconstr__Cong) =>
% 120.37/16.04 (((subsetI1) =>
% 120.37/16.04 (((eqimpsubset2) =>
% 120.37/16.04 (((eqimpsubset1) =>
% 120.37/16.04 (((subsetI2) =>
% 120.37/16.04 (((emptysetsubset) =>
% 120.37/16.04 (((subsetE) =>
% 120.37/16.04 (((subsetE2) =>
% 120.37/16.04 (((notsubsetI) =>
% 120.37/16.04 (((notequalI1) =>
% 120.37/16.04 ((
% 120.37/16.04 (notequalI2) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetRefl) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetTrans) =>
% 120.37/16.04 ((
% 120.37/16.04 (setadjoinSub) =>
% 120.37/16.04 ((
% 120.37/16.04 (setadjoinSub2) =>
% 120.37/16.04 ((
% 120.37/16.04 (subset2powerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (setextsub) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetemptysetimpeq) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetI1) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetE1) =>
% 120.37/16.04 ((
% 120.37/16.04 (inPowerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetsubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (sepInPowerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (sepSubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (binunionIL) =>
% 120.37/16.04 ((
% 120.37/16.04 (upairset2IR) =>
% 120.37/16.04 ((
% 120.37/16.04 (binunionIR) =>
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y0 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y1 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y2 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y3 : $o]:
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 (
% 120.37/16.04 binunion @
% 120.37/16.04 Y0 @ Y1)) =>
% 120.37/16.04 ((
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 Y0) =>
% 120.37/16.04 (Y3))) =>
% 120.37/16.04 ((
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 Y1) =>
% 120.37/16.04 (Y3))) =>
% 120.37/16.04 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl465])).
% 120.37/16.04 thf(zip_derived_cl478, plain,
% 120.37/16.04 (~ (((quantDeMorgan2) =>
% 120.37/16.04 (((quantDeMorgan3) =>
% 120.37/16.04 (((quantDeMorgan4) =>
% 120.37/16.04 (((prop2setI) =>
% 120.37/16.04 (((prop2set2propI) =>
% 120.37/16.04 (((notdexE) =>
% 120.37/16.04 (((notdallE) =>
% 120.37/16.04 (((exuI1) =>
% 120.37/16.04 (((exuI3) =>
% 120.37/16.04 (((exuI2) =>
% 120.37/16.04 (((inCongP) =>
% 120.37/16.04 (((in__Cong) =>
% 120.37/16.04 (((exuE3u) =>
% 120.37/16.04 (((exu__Cong) =>
% 120.37/16.04 (((setadjoin__Cong) =>
% 120.37/16.04 (((powerset__Cong) =>
% 120.37/16.04 (((setunion__Cong) =>
% 120.37/16.04 (((exuEu) =>
% 120.37/16.04 (((descr__Cong) =>
% 120.37/16.04 (((dsetconstr__Cong) =>
% 120.37/16.04 (((subsetI1) =>
% 120.37/16.04 (((eqimpsubset2) =>
% 120.37/16.04 (((eqimpsubset1) =>
% 120.37/16.04 (((subsetI2) =>
% 120.37/16.04 (((emptysetsubset) =>
% 120.37/16.04 (((subsetE) =>
% 120.37/16.04 (((subsetE2) =>
% 120.37/16.04 (((notsubsetI) =>
% 120.37/16.04 (((notequalI1) =>
% 120.37/16.04 (((notequalI2) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetRefl) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetTrans) =>
% 120.37/16.04 ((
% 120.37/16.04 (setadjoinSub) =>
% 120.37/16.04 ((
% 120.37/16.04 (setadjoinSub2) =>
% 120.37/16.04 ((
% 120.37/16.04 (subset2powerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (setextsub) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetemptysetimpeq) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetI1) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetE1) =>
% 120.37/16.04 ((
% 120.37/16.04 (inPowerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetsubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (sepInPowerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (sepSubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (binunionIL) =>
% 120.37/16.04 ((
% 120.37/16.04 (upairset2IR) =>
% 120.37/16.04 ((
% 120.37/16.04 (binunionIR) =>
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y0 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y1 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y2 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y3 : $o]:
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 (
% 120.37/16.04 binunion @
% 120.37/16.04 Y0 @ Y1)) =>
% 120.37/16.04 ((
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 Y0) =>
% 120.37/16.04 (Y3))) =>
% 120.37/16.04 ((
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 Y1) =>
% 120.37/16.04 (Y3))) =>
% 120.37/16.04 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl471])).
% 120.37/16.04 thf(zip_derived_cl484, plain,
% 120.37/16.04 (~ (((quantDeMorgan3) =>
% 120.37/16.04 (((quantDeMorgan4) =>
% 120.37/16.04 (((prop2setI) =>
% 120.37/16.04 (((prop2set2propI) =>
% 120.37/16.04 (((notdexE) =>
% 120.37/16.04 (((notdallE) =>
% 120.37/16.04 (((exuI1) =>
% 120.37/16.04 (((exuI3) =>
% 120.37/16.04 (((exuI2) =>
% 120.37/16.04 (((inCongP) =>
% 120.37/16.04 (((in__Cong) =>
% 120.37/16.04 (((exuE3u) =>
% 120.37/16.04 (((exu__Cong) =>
% 120.37/16.04 (((setadjoin__Cong) =>
% 120.37/16.04 (((powerset__Cong) =>
% 120.37/16.04 (((setunion__Cong) =>
% 120.37/16.04 (((exuEu) =>
% 120.37/16.04 (((descr__Cong) =>
% 120.37/16.04 (((dsetconstr__Cong) =>
% 120.37/16.04 (((subsetI1) =>
% 120.37/16.04 (((eqimpsubset2) =>
% 120.37/16.04 (((eqimpsubset1) =>
% 120.37/16.04 (((subsetI2) =>
% 120.37/16.04 (((emptysetsubset) =>
% 120.37/16.04 (((subsetE) =>
% 120.37/16.04 (((subsetE2) =>
% 120.37/16.04 (((notsubsetI) =>
% 120.37/16.04 (((notequalI1) =>
% 120.37/16.04 (((notequalI2) =>
% 120.37/16.04 (((subsetRefl) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetTrans) =>
% 120.37/16.04 ((
% 120.37/16.04 (setadjoinSub) =>
% 120.37/16.04 ((
% 120.37/16.04 (setadjoinSub2) =>
% 120.37/16.04 ((
% 120.37/16.04 (subset2powerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (setextsub) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetemptysetimpeq) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetI1) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetE1) =>
% 120.37/16.04 ((
% 120.37/16.04 (inPowerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetsubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (sepInPowerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (sepSubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (binunionIL) =>
% 120.37/16.04 ((
% 120.37/16.04 (upairset2IR) =>
% 120.37/16.04 ((
% 120.37/16.04 (binunionIR) =>
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y0 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y1 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y2 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y3 : $o]:
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 (
% 120.37/16.04 binunion @
% 120.37/16.04 Y0 @ Y1)) =>
% 120.37/16.04 ((
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 Y0) =>
% 120.37/16.04 (Y3))) =>
% 120.37/16.04 ((
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 Y1) =>
% 120.37/16.04 (Y3))) =>
% 120.37/16.04 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl478])).
% 120.37/16.04 thf(zip_derived_cl491, plain,
% 120.37/16.04 (~ (((quantDeMorgan4) =>
% 120.37/16.04 (((prop2setI) =>
% 120.37/16.04 (((prop2set2propI) =>
% 120.37/16.04 (((notdexE) =>
% 120.37/16.04 (((notdallE) =>
% 120.37/16.04 (((exuI1) =>
% 120.37/16.04 (((exuI3) =>
% 120.37/16.04 (((exuI2) =>
% 120.37/16.04 (((inCongP) =>
% 120.37/16.04 (((in__Cong) =>
% 120.37/16.04 (((exuE3u) =>
% 120.37/16.04 (((exu__Cong) =>
% 120.37/16.04 (((setadjoin__Cong) =>
% 120.37/16.04 (((powerset__Cong) =>
% 120.37/16.04 (((setunion__Cong) =>
% 120.37/16.04 (((exuEu) =>
% 120.37/16.04 (((descr__Cong) =>
% 120.37/16.04 (((dsetconstr__Cong) =>
% 120.37/16.04 (((subsetI1) =>
% 120.37/16.04 (((eqimpsubset2) =>
% 120.37/16.04 (((eqimpsubset1) =>
% 120.37/16.04 (((subsetI2) =>
% 120.37/16.04 (((emptysetsubset) =>
% 120.37/16.04 (((subsetE) =>
% 120.37/16.04 (((subsetE2) =>
% 120.37/16.04 (((notsubsetI) =>
% 120.37/16.04 (((notequalI1) =>
% 120.37/16.04 (((notequalI2) =>
% 120.37/16.04 (((subsetRefl) =>
% 120.37/16.04 (((subsetTrans) =>
% 120.37/16.04 ((
% 120.37/16.04 (setadjoinSub) =>
% 120.37/16.04 ((
% 120.37/16.04 (setadjoinSub2) =>
% 120.37/16.04 ((
% 120.37/16.04 (subset2powerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (setextsub) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetemptysetimpeq) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetI1) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetE1) =>
% 120.37/16.04 ((
% 120.37/16.04 (inPowerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetsubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (sepInPowerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (sepSubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (binunionIL) =>
% 120.37/16.04 ((
% 120.37/16.04 (upairset2IR) =>
% 120.37/16.04 ((
% 120.37/16.04 (binunionIR) =>
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y0 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y1 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y2 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y3 : $o]:
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 (
% 120.37/16.04 binunion @
% 120.37/16.04 Y0 @ Y1)) =>
% 120.37/16.04 ((
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 Y0) =>
% 120.37/16.04 (Y3))) =>
% 120.37/16.04 ((
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 Y1) =>
% 120.37/16.04 (Y3))) =>
% 120.37/16.04 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl484])).
% 120.37/16.04 thf(zip_derived_cl501, plain,
% 120.37/16.04 (~ (((prop2setI) =>
% 120.37/16.04 (((prop2set2propI) =>
% 120.37/16.04 (((notdexE) =>
% 120.37/16.04 (((notdallE) =>
% 120.37/16.04 (((exuI1) =>
% 120.37/16.04 (((exuI3) =>
% 120.37/16.04 (((exuI2) =>
% 120.37/16.04 (((inCongP) =>
% 120.37/16.04 (((in__Cong) =>
% 120.37/16.04 (((exuE3u) =>
% 120.37/16.04 (((exu__Cong) =>
% 120.37/16.04 (((setadjoin__Cong) =>
% 120.37/16.04 (((powerset__Cong) =>
% 120.37/16.04 (((setunion__Cong) =>
% 120.37/16.04 (((exuEu) =>
% 120.37/16.04 (((descr__Cong) =>
% 120.37/16.04 (((dsetconstr__Cong) =>
% 120.37/16.04 (((subsetI1) =>
% 120.37/16.04 (((eqimpsubset2) =>
% 120.37/16.04 (((eqimpsubset1) =>
% 120.37/16.04 (((subsetI2) =>
% 120.37/16.04 (((emptysetsubset) =>
% 120.37/16.04 (((subsetE) =>
% 120.37/16.04 (((subsetE2) =>
% 120.37/16.04 (((notsubsetI) =>
% 120.37/16.04 (((notequalI1) =>
% 120.37/16.04 (((notequalI2) =>
% 120.37/16.04 (((subsetRefl) =>
% 120.37/16.04 (((subsetTrans) =>
% 120.37/16.04 (((setadjoinSub) =>
% 120.37/16.04 ((
% 120.37/16.04 (setadjoinSub2) =>
% 120.37/16.04 ((
% 120.37/16.04 (subset2powerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (setextsub) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetemptysetimpeq) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetI1) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetE1) =>
% 120.37/16.04 ((
% 120.37/16.04 (inPowerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetsubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (sepInPowerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (sepSubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (binunionIL) =>
% 120.37/16.04 ((
% 120.37/16.04 (upairset2IR) =>
% 120.37/16.04 ((
% 120.37/16.04 (binunionIR) =>
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y0 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y1 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y2 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y3 : $o]:
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 (
% 120.37/16.04 binunion @
% 120.37/16.04 Y0 @ Y1)) =>
% 120.37/16.04 ((
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 Y0) =>
% 120.37/16.04 (Y3))) =>
% 120.37/16.04 ((
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 Y1) =>
% 120.37/16.04 (Y3))) =>
% 120.37/16.04 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl491])).
% 120.37/16.04 thf(zip_derived_cl508, plain,
% 120.37/16.04 (~ (((prop2set2propI) =>
% 120.37/16.04 (((notdexE) =>
% 120.37/16.04 (((notdallE) =>
% 120.37/16.04 (((exuI1) =>
% 120.37/16.04 (((exuI3) =>
% 120.37/16.04 (((exuI2) =>
% 120.37/16.04 (((inCongP) =>
% 120.37/16.04 (((in__Cong) =>
% 120.37/16.04 (((exuE3u) =>
% 120.37/16.04 (((exu__Cong) =>
% 120.37/16.04 (((setadjoin__Cong) =>
% 120.37/16.04 (((powerset__Cong) =>
% 120.37/16.04 (((setunion__Cong) =>
% 120.37/16.04 (((exuEu) =>
% 120.37/16.04 (((descr__Cong) =>
% 120.37/16.04 (((dsetconstr__Cong) =>
% 120.37/16.04 (((subsetI1) =>
% 120.37/16.04 (((eqimpsubset2) =>
% 120.37/16.04 (((eqimpsubset1) =>
% 120.37/16.04 (((subsetI2) =>
% 120.37/16.04 (((emptysetsubset) =>
% 120.37/16.04 (((subsetE) =>
% 120.37/16.04 (((subsetE2) =>
% 120.37/16.04 (((notsubsetI) =>
% 120.37/16.04 (((notequalI1) =>
% 120.37/16.04 (((notequalI2) =>
% 120.37/16.04 (((subsetRefl) =>
% 120.37/16.04 (((subsetTrans) =>
% 120.37/16.04 (((setadjoinSub) =>
% 120.37/16.04 (((setadjoinSub2) =>
% 120.37/16.04 ((
% 120.37/16.04 (subset2powerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (setextsub) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetemptysetimpeq) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetI1) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetE1) =>
% 120.37/16.04 ((
% 120.37/16.04 (inPowerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetsubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (sepInPowerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (sepSubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (binunionIL) =>
% 120.37/16.04 ((
% 120.37/16.04 (upairset2IR) =>
% 120.37/16.04 ((
% 120.37/16.04 (binunionIR) =>
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y0 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y1 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y2 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y3 : $o]:
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 (
% 120.37/16.04 binunion @
% 120.37/16.04 Y0 @ Y1)) =>
% 120.37/16.04 ((
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 Y0) =>
% 120.37/16.04 (Y3))) =>
% 120.37/16.04 ((
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 Y1) =>
% 120.37/16.04 (Y3))) =>
% 120.37/16.04 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl501])).
% 120.37/16.04 thf(zip_derived_cl515, plain,
% 120.37/16.04 (~ (((notdexE) =>
% 120.37/16.04 (((notdallE) =>
% 120.37/16.04 (((exuI1) =>
% 120.37/16.04 (((exuI3) =>
% 120.37/16.04 (((exuI2) =>
% 120.37/16.04 (((inCongP) =>
% 120.37/16.04 (((in__Cong) =>
% 120.37/16.04 (((exuE3u) =>
% 120.37/16.04 (((exu__Cong) =>
% 120.37/16.04 (((setadjoin__Cong) =>
% 120.37/16.04 (((powerset__Cong) =>
% 120.37/16.04 (((setunion__Cong) =>
% 120.37/16.04 (((exuEu) =>
% 120.37/16.04 (((descr__Cong) =>
% 120.37/16.04 (((dsetconstr__Cong) =>
% 120.37/16.04 (((subsetI1) =>
% 120.37/16.04 (((eqimpsubset2) =>
% 120.37/16.04 (((eqimpsubset1) =>
% 120.37/16.04 (((subsetI2) =>
% 120.37/16.04 (((emptysetsubset) =>
% 120.37/16.04 (((subsetE) =>
% 120.37/16.04 (((subsetE2) =>
% 120.37/16.04 (((notsubsetI) =>
% 120.37/16.04 (((notequalI1) =>
% 120.37/16.04 (((notequalI2) =>
% 120.37/16.04 (((subsetRefl) =>
% 120.37/16.04 (((subsetTrans) =>
% 120.37/16.04 (((setadjoinSub) =>
% 120.37/16.04 (((setadjoinSub2) =>
% 120.37/16.04 (((subset2powerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (setextsub) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetemptysetimpeq) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetI1) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetE1) =>
% 120.37/16.04 ((
% 120.37/16.04 (inPowerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetsubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (sepInPowerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (sepSubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (binunionIL) =>
% 120.37/16.04 ((
% 120.37/16.04 (upairset2IR) =>
% 120.37/16.04 ((
% 120.37/16.04 (binunionIR) =>
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y0 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y1 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y2 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y3 : $o]:
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 (
% 120.37/16.04 binunion @
% 120.37/16.04 Y0 @ Y1)) =>
% 120.37/16.04 ((
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 Y0) =>
% 120.37/16.04 (Y3))) =>
% 120.37/16.04 ((
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 Y1) =>
% 120.37/16.04 (Y3))) =>
% 120.37/16.04 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl508])).
% 120.37/16.04 thf(zip_derived_cl523, plain,
% 120.37/16.04 (~ (((notdallE) =>
% 120.37/16.04 (((exuI1) =>
% 120.37/16.04 (((exuI3) =>
% 120.37/16.04 (((exuI2) =>
% 120.37/16.04 (((inCongP) =>
% 120.37/16.04 (((in__Cong) =>
% 120.37/16.04 (((exuE3u) =>
% 120.37/16.04 (((exu__Cong) =>
% 120.37/16.04 (((setadjoin__Cong) =>
% 120.37/16.04 (((powerset__Cong) =>
% 120.37/16.04 (((setunion__Cong) =>
% 120.37/16.04 (((exuEu) =>
% 120.37/16.04 (((descr__Cong) =>
% 120.37/16.04 (((dsetconstr__Cong) =>
% 120.37/16.04 (((subsetI1) =>
% 120.37/16.04 (((eqimpsubset2) =>
% 120.37/16.04 (((eqimpsubset1) =>
% 120.37/16.04 (((subsetI2) =>
% 120.37/16.04 (((emptysetsubset) =>
% 120.37/16.04 (((subsetE) =>
% 120.37/16.04 (((subsetE2) =>
% 120.37/16.04 (((notsubsetI) =>
% 120.37/16.04 (((notequalI1) =>
% 120.37/16.04 (((notequalI2) =>
% 120.37/16.04 (((subsetRefl) =>
% 120.37/16.04 (((subsetTrans) =>
% 120.37/16.04 (((setadjoinSub) =>
% 120.37/16.04 (((setadjoinSub2) =>
% 120.37/16.04 (((subset2powerset) =>
% 120.37/16.04 (((setextsub) =>
% 120.37/16.04 ((
% 120.37/16.04 (subsetemptysetimpeq) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetI1) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetE1) =>
% 120.37/16.04 ((
% 120.37/16.04 (inPowerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetsubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (sepInPowerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (sepSubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (binunionIL) =>
% 120.37/16.04 ((
% 120.37/16.04 (upairset2IR) =>
% 120.37/16.04 ((
% 120.37/16.04 (binunionIR) =>
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y0 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y1 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y2 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y3 : $o]:
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 (
% 120.37/16.04 binunion @
% 120.37/16.04 Y0 @ Y1)) =>
% 120.37/16.04 ((
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 Y0) =>
% 120.37/16.04 (Y3))) =>
% 120.37/16.04 ((
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 Y1) =>
% 120.37/16.04 (Y3))) =>
% 120.37/16.04 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl515])).
% 120.37/16.04 thf(zip_derived_cl535, plain,
% 120.37/16.04 (~ (((exuI1) =>
% 120.37/16.04 (((exuI3) =>
% 120.37/16.04 (((exuI2) =>
% 120.37/16.04 (((inCongP) =>
% 120.37/16.04 (((in__Cong) =>
% 120.37/16.04 (((exuE3u) =>
% 120.37/16.04 (((exu__Cong) =>
% 120.37/16.04 (((setadjoin__Cong) =>
% 120.37/16.04 (((powerset__Cong) =>
% 120.37/16.04 (((setunion__Cong) =>
% 120.37/16.04 (((exuEu) =>
% 120.37/16.04 (((descr__Cong) =>
% 120.37/16.04 (((dsetconstr__Cong) =>
% 120.37/16.04 (((subsetI1) =>
% 120.37/16.04 (((eqimpsubset2) =>
% 120.37/16.04 (((eqimpsubset1) =>
% 120.37/16.04 (((subsetI2) =>
% 120.37/16.04 (((emptysetsubset) =>
% 120.37/16.04 (((subsetE) =>
% 120.37/16.04 (((subsetE2) =>
% 120.37/16.04 (((notsubsetI) =>
% 120.37/16.04 (((notequalI1) =>
% 120.37/16.04 (((notequalI2) =>
% 120.37/16.04 (((subsetRefl) =>
% 120.37/16.04 (((subsetTrans) =>
% 120.37/16.04 (((setadjoinSub) =>
% 120.37/16.04 (((setadjoinSub2) =>
% 120.37/16.04 (((subset2powerset) =>
% 120.37/16.04 (((setextsub) =>
% 120.37/16.04 (((subsetemptysetimpeq) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetI1) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetE1) =>
% 120.37/16.04 ((
% 120.37/16.04 (inPowerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetsubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (sepInPowerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (sepSubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (binunionIL) =>
% 120.37/16.04 ((
% 120.37/16.04 (upairset2IR) =>
% 120.37/16.04 ((
% 120.37/16.04 (binunionIR) =>
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y0 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y1 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y2 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y3 : $o]:
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 (
% 120.37/16.04 binunion @
% 120.37/16.04 Y0 @ Y1)) =>
% 120.37/16.04 ((
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 Y0) =>
% 120.37/16.04 (Y3))) =>
% 120.37/16.04 ((
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 Y1) =>
% 120.37/16.04 (Y3))) =>
% 120.37/16.04 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl523])).
% 120.37/16.04 thf(zip_derived_cl550, plain,
% 120.37/16.04 (~ (((exuI3) =>
% 120.37/16.04 (((exuI2) =>
% 120.37/16.04 (((inCongP) =>
% 120.37/16.04 (((in__Cong) =>
% 120.37/16.04 (((exuE3u) =>
% 120.37/16.04 (((exu__Cong) =>
% 120.37/16.04 (((setadjoin__Cong) =>
% 120.37/16.04 (((powerset__Cong) =>
% 120.37/16.04 (((setunion__Cong) =>
% 120.37/16.04 (((exuEu) =>
% 120.37/16.04 (((descr__Cong) =>
% 120.37/16.04 (((dsetconstr__Cong) =>
% 120.37/16.04 (((subsetI1) =>
% 120.37/16.04 (((eqimpsubset2) =>
% 120.37/16.04 (((eqimpsubset1) =>
% 120.37/16.04 (((subsetI2) =>
% 120.37/16.04 (((emptysetsubset) =>
% 120.37/16.04 (((subsetE) =>
% 120.37/16.04 (((subsetE2) =>
% 120.37/16.04 (((notsubsetI) =>
% 120.37/16.04 (((notequalI1) =>
% 120.37/16.04 (((notequalI2) =>
% 120.37/16.04 (((subsetRefl) =>
% 120.37/16.04 (((subsetTrans) =>
% 120.37/16.04 (((setadjoinSub) =>
% 120.37/16.04 (((setadjoinSub2) =>
% 120.37/16.04 (((subset2powerset) =>
% 120.37/16.04 (((setextsub) =>
% 120.37/16.04 (((subsetemptysetimpeq) =>
% 120.37/16.04 (((powersetI1) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetE1) =>
% 120.37/16.04 ((
% 120.37/16.04 (inPowerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetsubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (sepInPowerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (sepSubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (binunionIL) =>
% 120.37/16.04 ((
% 120.37/16.04 (upairset2IR) =>
% 120.37/16.04 ((
% 120.37/16.04 (binunionIR) =>
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y0 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y1 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y2 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y3 : $o]:
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 (
% 120.37/16.04 binunion @
% 120.37/16.04 Y0 @ Y1)) =>
% 120.37/16.04 ((
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 Y0) =>
% 120.37/16.04 (Y3))) =>
% 120.37/16.04 ((
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 Y1) =>
% 120.37/16.04 (Y3))) =>
% 120.37/16.04 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl535])).
% 120.37/16.04 thf(zip_derived_cl560, plain,
% 120.37/16.04 (~ (((exuI2) =>
% 120.37/16.04 (((inCongP) =>
% 120.37/16.04 (((in__Cong) =>
% 120.37/16.04 (((exuE3u) =>
% 120.37/16.04 (((exu__Cong) =>
% 120.37/16.04 (((setadjoin__Cong) =>
% 120.37/16.04 (((powerset__Cong) =>
% 120.37/16.04 (((setunion__Cong) =>
% 120.37/16.04 (((exuEu) =>
% 120.37/16.04 (((descr__Cong) =>
% 120.37/16.04 (((dsetconstr__Cong) =>
% 120.37/16.04 (((subsetI1) =>
% 120.37/16.04 (((eqimpsubset2) =>
% 120.37/16.04 (((eqimpsubset1) =>
% 120.37/16.04 (((subsetI2) =>
% 120.37/16.04 (((emptysetsubset) =>
% 120.37/16.04 (((subsetE) =>
% 120.37/16.04 (((subsetE2) =>
% 120.37/16.04 (((notsubsetI) =>
% 120.37/16.04 (((notequalI1) =>
% 120.37/16.04 (((notequalI2) =>
% 120.37/16.04 (((subsetRefl) =>
% 120.37/16.04 (((subsetTrans) =>
% 120.37/16.04 (((setadjoinSub) =>
% 120.37/16.04 (((setadjoinSub2) =>
% 120.37/16.04 (((subset2powerset) =>
% 120.37/16.04 (((setextsub) =>
% 120.37/16.04 (((subsetemptysetimpeq) =>
% 120.37/16.04 (((powersetI1) =>
% 120.37/16.04 (((powersetE1) =>
% 120.37/16.04 ((
% 120.37/16.04 (inPowerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetsubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (sepInPowerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (sepSubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (binunionIL) =>
% 120.37/16.04 ((
% 120.37/16.04 (upairset2IR) =>
% 120.37/16.04 ((
% 120.37/16.04 (binunionIR) =>
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y0 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y1 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y2 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y3 : $o]:
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 (
% 120.37/16.04 binunion @
% 120.37/16.04 Y0 @ Y1)) =>
% 120.37/16.04 ((
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 Y0) =>
% 120.37/16.04 (Y3))) =>
% 120.37/16.04 ((
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 Y1) =>
% 120.37/16.04 (Y3))) =>
% 120.37/16.04 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl550])).
% 120.37/16.04 thf(zip_derived_cl568, plain,
% 120.37/16.04 (~ (((inCongP) =>
% 120.37/16.04 (((in__Cong) =>
% 120.37/16.04 (((exuE3u) =>
% 120.37/16.04 (((exu__Cong) =>
% 120.37/16.04 (((setadjoin__Cong) =>
% 120.37/16.04 (((powerset__Cong) =>
% 120.37/16.04 (((setunion__Cong) =>
% 120.37/16.04 (((exuEu) =>
% 120.37/16.04 (((descr__Cong) =>
% 120.37/16.04 (((dsetconstr__Cong) =>
% 120.37/16.04 (((subsetI1) =>
% 120.37/16.04 (((eqimpsubset2) =>
% 120.37/16.04 (((eqimpsubset1) =>
% 120.37/16.04 (((subsetI2) =>
% 120.37/16.04 (((emptysetsubset) =>
% 120.37/16.04 (((subsetE) =>
% 120.37/16.04 (((subsetE2) =>
% 120.37/16.04 (((notsubsetI) =>
% 120.37/16.04 (((notequalI1) =>
% 120.37/16.04 (((notequalI2) =>
% 120.37/16.04 (((subsetRefl) =>
% 120.37/16.04 (((subsetTrans) =>
% 120.37/16.04 (((setadjoinSub) =>
% 120.37/16.04 (((setadjoinSub2) =>
% 120.37/16.04 (((subset2powerset) =>
% 120.37/16.04 (((setextsub) =>
% 120.37/16.04 (((subsetemptysetimpeq) =>
% 120.37/16.04 (((powersetI1) =>
% 120.37/16.04 (((powersetE1) =>
% 120.37/16.04 (((inPowerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (powersetsubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (sepInPowerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (sepSubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (binunionIL) =>
% 120.37/16.04 ((
% 120.37/16.04 (upairset2IR) =>
% 120.37/16.04 ((
% 120.37/16.04 (binunionIR) =>
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y0 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y1 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y2 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y3 : $o]:
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 (
% 120.37/16.04 binunion @
% 120.37/16.04 Y0 @ Y1)) =>
% 120.37/16.04 ((
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 Y0) =>
% 120.37/16.04 (Y3))) =>
% 120.37/16.04 ((
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 Y1) =>
% 120.37/16.04 (Y3))) =>
% 120.37/16.04 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl560])).
% 120.37/16.04 thf(zip_derived_cl578, plain,
% 120.37/16.04 (~ (((in__Cong) =>
% 120.37/16.04 (((exuE3u) =>
% 120.37/16.04 (((exu__Cong) =>
% 120.37/16.04 (((setadjoin__Cong) =>
% 120.37/16.04 (((powerset__Cong) =>
% 120.37/16.04 (((setunion__Cong) =>
% 120.37/16.04 (((exuEu) =>
% 120.37/16.04 (((descr__Cong) =>
% 120.37/16.04 (((dsetconstr__Cong) =>
% 120.37/16.04 (((subsetI1) =>
% 120.37/16.04 (((eqimpsubset2) =>
% 120.37/16.04 (((eqimpsubset1) =>
% 120.37/16.04 (((subsetI2) =>
% 120.37/16.04 (((emptysetsubset) =>
% 120.37/16.04 (((subsetE) =>
% 120.37/16.04 (((subsetE2) =>
% 120.37/16.04 (((notsubsetI) =>
% 120.37/16.04 (((notequalI1) =>
% 120.37/16.04 (((notequalI2) =>
% 120.37/16.04 (((subsetRefl) =>
% 120.37/16.04 (((subsetTrans) =>
% 120.37/16.04 (((setadjoinSub) =>
% 120.37/16.04 (((setadjoinSub2) =>
% 120.37/16.04 (((subset2powerset) =>
% 120.37/16.04 (((setextsub) =>
% 120.37/16.04 (((subsetemptysetimpeq) =>
% 120.37/16.04 (((powersetI1) =>
% 120.37/16.04 (((powersetE1) =>
% 120.37/16.04 (((inPowerset) =>
% 120.37/16.04 (((powersetsubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (sepInPowerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (sepSubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (binunionIL) =>
% 120.37/16.04 ((
% 120.37/16.04 (upairset2IR) =>
% 120.37/16.04 ((
% 120.37/16.04 (binunionIR) =>
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y0 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y1 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y2 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y3 : $o]:
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 (
% 120.37/16.04 binunion @
% 120.37/16.04 Y0 @ Y1)) =>
% 120.37/16.04 ((
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 Y0) =>
% 120.37/16.04 (Y3))) =>
% 120.37/16.04 ((
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 Y1) =>
% 120.37/16.04 (Y3))) =>
% 120.37/16.04 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl568])).
% 120.37/16.04 thf(zip_derived_cl588, plain,
% 120.37/16.04 (~ (((exuE3u) =>
% 120.37/16.04 (((exu__Cong) =>
% 120.37/16.04 (((setadjoin__Cong) =>
% 120.37/16.04 (((powerset__Cong) =>
% 120.37/16.04 (((setunion__Cong) =>
% 120.37/16.04 (((exuEu) =>
% 120.37/16.04 (((descr__Cong) =>
% 120.37/16.04 (((dsetconstr__Cong) =>
% 120.37/16.04 (((subsetI1) =>
% 120.37/16.04 (((eqimpsubset2) =>
% 120.37/16.04 (((eqimpsubset1) =>
% 120.37/16.04 (((subsetI2) =>
% 120.37/16.04 (((emptysetsubset) =>
% 120.37/16.04 (((subsetE) =>
% 120.37/16.04 (((subsetE2) =>
% 120.37/16.04 (((notsubsetI) =>
% 120.37/16.04 (((notequalI1) =>
% 120.37/16.04 (((notequalI2) =>
% 120.37/16.04 (((subsetRefl) =>
% 120.37/16.04 (((subsetTrans) =>
% 120.37/16.04 (((setadjoinSub) =>
% 120.37/16.04 (((setadjoinSub2) =>
% 120.37/16.04 (((subset2powerset) =>
% 120.37/16.04 (((setextsub) =>
% 120.37/16.04 (((subsetemptysetimpeq) =>
% 120.37/16.04 (((powersetI1) =>
% 120.37/16.04 (((powersetE1) =>
% 120.37/16.04 (((inPowerset) =>
% 120.37/16.04 (((powersetsubset) =>
% 120.37/16.04 (((sepInPowerset) =>
% 120.37/16.04 ((
% 120.37/16.04 (sepSubset) =>
% 120.37/16.04 ((
% 120.37/16.04 (binunionIL) =>
% 120.37/16.04 ((
% 120.37/16.04 (upairset2IR) =>
% 120.37/16.04 ((
% 120.37/16.04 (binunionIR) =>
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y0 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y1 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y2 : $i]:
% 120.37/16.04 ((
% 120.37/16.04 (!!) @ (
% 120.37/16.04 ^[Y3 : $o]:
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 (
% 120.37/16.04 binunion @
% 120.37/16.04 Y0 @ Y1)) =>
% 120.37/16.04 ((
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 Y0) =>
% 120.37/16.04 (Y3))) =>
% 120.37/16.04 ((
% 120.37/16.04 ((
% 120.37/16.04 (in @
% 120.37/16.04 Y2 @
% 120.37/16.04 Y1) =>
% 120.37/16.04 (Y3))) =>
% 120.37/16.04 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.04 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl578])).
% 120.37/16.04 thf(zip_derived_cl598, plain,
% 120.37/16.04 (~ (((exu__Cong) =>
% 120.37/16.04 (((setadjoin__Cong) =>
% 120.37/16.04 (((powerset__Cong) =>
% 120.37/16.04 (((setunion__Cong) =>
% 120.37/16.04 (((exuEu) =>
% 120.37/16.04 (((descr__Cong) =>
% 120.37/16.04 (((dsetconstr__Cong) =>
% 120.37/16.04 (((subsetI1) =>
% 120.37/16.04 (((eqimpsubset2) =>
% 120.37/16.04 (((eqimpsubset1) =>
% 120.37/16.04 (((subsetI2) =>
% 120.37/16.04 (((emptysetsubset) =>
% 120.37/16.04 (((subsetE) =>
% 120.37/16.04 (((subsetE2) =>
% 120.37/16.04 (((notsubsetI) =>
% 120.37/16.04 (((notequalI1) =>
% 120.37/16.04 (((notequalI2) =>
% 120.37/16.04 (((subsetRefl) =>
% 120.37/16.05 (((subsetTrans) =>
% 120.37/16.05 (((setadjoinSub) =>
% 120.37/16.05 (((setadjoinSub2) =>
% 120.37/16.05 (((subset2powerset) =>
% 120.37/16.05 (((setextsub) =>
% 120.37/16.05 (((subsetemptysetimpeq) =>
% 120.37/16.05 (((powersetI1) =>
% 120.37/16.05 (((powersetE1) =>
% 120.37/16.05 (((inPowerset) =>
% 120.37/16.05 (((powersetsubset) =>
% 120.37/16.05 (((sepInPowerset) =>
% 120.37/16.05 (((sepSubset) =>
% 120.37/16.05 ((
% 120.37/16.05 (binunionIL) =>
% 120.37/16.05 ((
% 120.37/16.05 (upairset2IR) =>
% 120.37/16.05 ((
% 120.37/16.05 (binunionIR) =>
% 120.37/16.05 ((
% 120.37/16.05 (!!) @ (
% 120.37/16.05 ^[Y0 : $i]:
% 120.37/16.05 ((
% 120.37/16.05 (!!) @ (
% 120.37/16.05 ^[Y1 : $i]:
% 120.37/16.05 ((
% 120.37/16.05 (!!) @ (
% 120.37/16.05 ^[Y2 : $i]:
% 120.37/16.05 ((
% 120.37/16.05 (!!) @ (
% 120.37/16.05 ^[Y3 : $o]:
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 (
% 120.37/16.05 binunion @
% 120.37/16.05 Y0 @ Y1)) =>
% 120.37/16.05 ((
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 Y0) =>
% 120.37/16.05 (Y3))) =>
% 120.37/16.05 ((
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 Y1) =>
% 120.37/16.05 (Y3))) =>
% 120.37/16.05 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl588])).
% 120.37/16.05 thf(zip_derived_cl609, plain,
% 120.37/16.05 (~ (((setadjoin__Cong) =>
% 120.37/16.05 (((powerset__Cong) =>
% 120.37/16.05 (((setunion__Cong) =>
% 120.37/16.05 (((exuEu) =>
% 120.37/16.05 (((descr__Cong) =>
% 120.37/16.05 (((dsetconstr__Cong) =>
% 120.37/16.05 (((subsetI1) =>
% 120.37/16.05 (((eqimpsubset2) =>
% 120.37/16.05 (((eqimpsubset1) =>
% 120.37/16.05 (((subsetI2) =>
% 120.37/16.05 (((emptysetsubset) =>
% 120.37/16.05 (((subsetE) =>
% 120.37/16.05 (((subsetE2) =>
% 120.37/16.05 (((notsubsetI) =>
% 120.37/16.05 (((notequalI1) =>
% 120.37/16.05 (((notequalI2) =>
% 120.37/16.05 (((subsetRefl) =>
% 120.37/16.05 (((subsetTrans) =>
% 120.37/16.05 (((setadjoinSub) =>
% 120.37/16.05 (((setadjoinSub2) =>
% 120.37/16.05 (((subset2powerset) =>
% 120.37/16.05 (((setextsub) =>
% 120.37/16.05 (((subsetemptysetimpeq) =>
% 120.37/16.05 (((powersetI1) =>
% 120.37/16.05 (((powersetE1) =>
% 120.37/16.05 (((inPowerset) =>
% 120.37/16.05 (((powersetsubset) =>
% 120.37/16.05 (((sepInPowerset) =>
% 120.37/16.05 (((sepSubset) =>
% 120.37/16.05 (((binunionIL) =>
% 120.37/16.05 ((
% 120.37/16.05 (upairset2IR) =>
% 120.37/16.05 ((
% 120.37/16.05 (binunionIR) =>
% 120.37/16.05 ((
% 120.37/16.05 (!!) @ (
% 120.37/16.05 ^[Y0 : $i]:
% 120.37/16.05 ((
% 120.37/16.05 (!!) @ (
% 120.37/16.05 ^[Y1 : $i]:
% 120.37/16.05 ((
% 120.37/16.05 (!!) @ (
% 120.37/16.05 ^[Y2 : $i]:
% 120.37/16.05 ((
% 120.37/16.05 (!!) @ (
% 120.37/16.05 ^[Y3 : $o]:
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 (
% 120.37/16.05 binunion @
% 120.37/16.05 Y0 @ Y1)) =>
% 120.37/16.05 ((
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 Y0) =>
% 120.37/16.05 (Y3))) =>
% 120.37/16.05 ((
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 Y1) =>
% 120.37/16.05 (Y3))) =>
% 120.37/16.05 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl598])).
% 120.37/16.05 thf(zip_derived_cl623, plain,
% 120.37/16.05 (~ (((powerset__Cong) =>
% 120.37/16.05 (((setunion__Cong) =>
% 120.37/16.05 (((exuEu) =>
% 120.37/16.05 (((descr__Cong) =>
% 120.37/16.05 (((dsetconstr__Cong) =>
% 120.37/16.05 (((subsetI1) =>
% 120.37/16.05 (((eqimpsubset2) =>
% 120.37/16.05 (((eqimpsubset1) =>
% 120.37/16.05 (((subsetI2) =>
% 120.37/16.05 (((emptysetsubset) =>
% 120.37/16.05 (((subsetE) =>
% 120.37/16.05 (((subsetE2) =>
% 120.37/16.05 (((notsubsetI) =>
% 120.37/16.05 (((notequalI1) =>
% 120.37/16.05 (((notequalI2) =>
% 120.37/16.05 (((subsetRefl) =>
% 120.37/16.05 (((subsetTrans) =>
% 120.37/16.05 (((setadjoinSub) =>
% 120.37/16.05 (((setadjoinSub2) =>
% 120.37/16.05 (((subset2powerset) =>
% 120.37/16.05 (((setextsub) =>
% 120.37/16.05 (((subsetemptysetimpeq) =>
% 120.37/16.05 (((powersetI1) =>
% 120.37/16.05 (((powersetE1) =>
% 120.37/16.05 (((inPowerset) =>
% 120.37/16.05 (((powersetsubset) =>
% 120.37/16.05 (((sepInPowerset) =>
% 120.37/16.05 (((sepSubset) =>
% 120.37/16.05 (((binunionIL) =>
% 120.37/16.05 (((upairset2IR) =>
% 120.37/16.05 ((
% 120.37/16.05 (binunionIR) =>
% 120.37/16.05 ((
% 120.37/16.05 (!!) @ (
% 120.37/16.05 ^[Y0 : $i]:
% 120.37/16.05 ((
% 120.37/16.05 (!!) @ (
% 120.37/16.05 ^[Y1 : $i]:
% 120.37/16.05 ((
% 120.37/16.05 (!!) @ (
% 120.37/16.05 ^[Y2 : $i]:
% 120.37/16.05 ((
% 120.37/16.05 (!!) @ (
% 120.37/16.05 ^[Y3 : $o]:
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 (
% 120.37/16.05 binunion @
% 120.37/16.05 Y0 @ Y1)) =>
% 120.37/16.05 ((
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 Y0) =>
% 120.37/16.05 (Y3))) =>
% 120.37/16.05 ((
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 Y1) =>
% 120.37/16.05 (Y3))) =>
% 120.37/16.05 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl609])).
% 120.37/16.05 thf(zip_derived_cl637, plain,
% 120.37/16.05 (~ (((setunion__Cong) =>
% 120.37/16.05 (((exuEu) =>
% 120.37/16.05 (((descr__Cong) =>
% 120.37/16.05 (((dsetconstr__Cong) =>
% 120.37/16.05 (((subsetI1) =>
% 120.37/16.05 (((eqimpsubset2) =>
% 120.37/16.05 (((eqimpsubset1) =>
% 120.37/16.05 (((subsetI2) =>
% 120.37/16.05 (((emptysetsubset) =>
% 120.37/16.05 (((subsetE) =>
% 120.37/16.05 (((subsetE2) =>
% 120.37/16.05 (((notsubsetI) =>
% 120.37/16.05 (((notequalI1) =>
% 120.37/16.05 (((notequalI2) =>
% 120.37/16.05 (((subsetRefl) =>
% 120.37/16.05 (((subsetTrans) =>
% 120.37/16.05 (((setadjoinSub) =>
% 120.37/16.05 (((setadjoinSub2) =>
% 120.37/16.05 (((subset2powerset) =>
% 120.37/16.05 (((setextsub) =>
% 120.37/16.05 (((subsetemptysetimpeq) =>
% 120.37/16.05 (((powersetI1) =>
% 120.37/16.05 (((powersetE1) =>
% 120.37/16.05 (((inPowerset) =>
% 120.37/16.05 (((powersetsubset) =>
% 120.37/16.05 (((sepInPowerset) =>
% 120.37/16.05 (((sepSubset) =>
% 120.37/16.05 (((binunionIL) =>
% 120.37/16.05 (((upairset2IR) =>
% 120.37/16.05 (((binunionIR) =>
% 120.37/16.05 ((
% 120.37/16.05 (!!) @ (
% 120.37/16.05 ^[Y0 : $i]:
% 120.37/16.05 ((
% 120.37/16.05 (!!) @ (
% 120.37/16.05 ^[Y1 : $i]:
% 120.37/16.05 ((
% 120.37/16.05 (!!) @ (
% 120.37/16.05 ^[Y2 : $i]:
% 120.37/16.05 ((
% 120.37/16.05 (!!) @ (
% 120.37/16.05 ^[Y3 : $o]:
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 (
% 120.37/16.05 binunion @
% 120.37/16.05 Y0 @ Y1)) =>
% 120.37/16.05 ((
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 Y0) =>
% 120.37/16.05 (Y3))) =>
% 120.37/16.05 ((
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 Y1) =>
% 120.37/16.05 (Y3))) =>
% 120.37/16.05 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl623])).
% 120.37/16.05 thf(zip_derived_cl652, plain,
% 120.37/16.05 (~ (((exuEu) =>
% 120.37/16.05 (((descr__Cong) =>
% 120.37/16.05 (((dsetconstr__Cong) =>
% 120.37/16.05 (((subsetI1) =>
% 120.37/16.05 (((eqimpsubset2) =>
% 120.37/16.05 (((eqimpsubset1) =>
% 120.37/16.05 (((subsetI2) =>
% 120.37/16.05 (((emptysetsubset) =>
% 120.37/16.05 (((subsetE) =>
% 120.37/16.05 (((subsetE2) =>
% 120.37/16.05 (((notsubsetI) =>
% 120.37/16.05 (((notequalI1) =>
% 120.37/16.05 (((notequalI2) =>
% 120.37/16.05 (((subsetRefl) =>
% 120.37/16.05 (((subsetTrans) =>
% 120.37/16.05 (((setadjoinSub) =>
% 120.37/16.05 (((setadjoinSub2) =>
% 120.37/16.05 (((subset2powerset) =>
% 120.37/16.05 (((setextsub) =>
% 120.37/16.05 (((subsetemptysetimpeq) =>
% 120.37/16.05 (((powersetI1) =>
% 120.37/16.05 (((powersetE1) =>
% 120.37/16.05 (((inPowerset) =>
% 120.37/16.05 (((powersetsubset) =>
% 120.37/16.05 (((sepInPowerset) =>
% 120.37/16.05 (((sepSubset) =>
% 120.37/16.05 (((binunionIL) =>
% 120.37/16.05 (((upairset2IR) =>
% 120.37/16.05 (((binunionIR) =>
% 120.37/16.05 (((!!) @ (
% 120.37/16.05 ^[Y0 : $i]:
% 120.37/16.05 ((
% 120.37/16.05 (!!) @ (
% 120.37/16.05 ^[Y1 : $i]:
% 120.37/16.05 ((
% 120.37/16.05 (!!) @ (
% 120.37/16.05 ^[Y2 : $i]:
% 120.37/16.05 ((
% 120.37/16.05 (!!) @ (
% 120.37/16.05 ^[Y3 : $o]:
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 (
% 120.37/16.05 binunion @
% 120.37/16.05 Y0 @ Y1)) =>
% 120.37/16.05 ((
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 Y0) =>
% 120.37/16.05 (Y3))) =>
% 120.37/16.05 ((
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 Y1) =>
% 120.37/16.05 (Y3))) =>
% 120.37/16.05 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl637])).
% 120.37/16.05 thf(zip_derived_cl664, plain,
% 120.37/16.05 (~ (((descr__Cong) =>
% 120.37/16.05 (((dsetconstr__Cong) =>
% 120.37/16.05 (((subsetI1) =>
% 120.37/16.05 (((eqimpsubset2) =>
% 120.37/16.05 (((eqimpsubset1) =>
% 120.37/16.05 (((subsetI2) =>
% 120.37/16.05 (((emptysetsubset) =>
% 120.37/16.05 (((subsetE) =>
% 120.37/16.05 (((subsetE2) =>
% 120.37/16.05 (((notsubsetI) =>
% 120.37/16.05 (((notequalI1) =>
% 120.37/16.05 (((notequalI2) =>
% 120.37/16.05 (((subsetRefl) =>
% 120.37/16.05 (((subsetTrans) =>
% 120.37/16.05 (((setadjoinSub) =>
% 120.37/16.05 (((setadjoinSub2) =>
% 120.37/16.05 (((subset2powerset) =>
% 120.37/16.05 (((setextsub) =>
% 120.37/16.05 (((subsetemptysetimpeq) =>
% 120.37/16.05 (((powersetI1) =>
% 120.37/16.05 (((powersetE1) =>
% 120.37/16.05 (((inPowerset) =>
% 120.37/16.05 (((powersetsubset) =>
% 120.37/16.05 (((sepInPowerset) =>
% 120.37/16.05 (((sepSubset) =>
% 120.37/16.05 (((binunionIL) =>
% 120.37/16.05 (((upairset2IR) =>
% 120.37/16.05 (((binunionIR) =>
% 120.37/16.05 (((!!) @ (
% 120.37/16.05 ^[Y0 : $i]:
% 120.37/16.05 ((
% 120.37/16.05 (!!) @ (
% 120.37/16.05 ^[Y1 : $i]:
% 120.37/16.05 ((
% 120.37/16.05 (!!) @ (
% 120.37/16.05 ^[Y2 : $i]:
% 120.37/16.05 ((
% 120.37/16.05 (!!) @ (
% 120.37/16.05 ^[Y3 : $o]:
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 (
% 120.37/16.05 binunion @
% 120.37/16.05 Y0 @ Y1)) =>
% 120.37/16.05 ((
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 Y0) =>
% 120.37/16.05 (Y3))) =>
% 120.37/16.05 ((
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 Y1) =>
% 120.37/16.05 (Y3))) =>
% 120.37/16.05 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl652])).
% 120.37/16.05 thf(zip_derived_cl681, plain,
% 120.37/16.05 (~ (((dsetconstr__Cong) =>
% 120.37/16.05 (((subsetI1) =>
% 120.37/16.05 (((eqimpsubset2) =>
% 120.37/16.05 (((eqimpsubset1) =>
% 120.37/16.05 (((subsetI2) =>
% 120.37/16.05 (((emptysetsubset) =>
% 120.37/16.05 (((subsetE) =>
% 120.37/16.05 (((subsetE2) =>
% 120.37/16.05 (((notsubsetI) =>
% 120.37/16.05 (((notequalI1) =>
% 120.37/16.05 (((notequalI2) =>
% 120.37/16.05 (((subsetRefl) =>
% 120.37/16.05 (((subsetTrans) =>
% 120.37/16.05 (((setadjoinSub) =>
% 120.37/16.05 (((setadjoinSub2) =>
% 120.37/16.05 (((subset2powerset) =>
% 120.37/16.05 (((setextsub) =>
% 120.37/16.05 (((subsetemptysetimpeq) =>
% 120.37/16.05 (((powersetI1) =>
% 120.37/16.05 (((powersetE1) =>
% 120.37/16.05 (((inPowerset) =>
% 120.37/16.05 (((powersetsubset) =>
% 120.37/16.05 (((sepInPowerset) =>
% 120.37/16.05 (((sepSubset) =>
% 120.37/16.05 (((binunionIL) =>
% 120.37/16.05 (((upairset2IR) =>
% 120.37/16.05 (((binunionIR) =>
% 120.37/16.05 (((!!) @ (
% 120.37/16.05 ^[Y0 : $i]:
% 120.37/16.05 (((!!) @ (
% 120.37/16.05 ^[Y1 : $i]:
% 120.37/16.05 ((
% 120.37/16.05 (!!) @ (
% 120.37/16.05 ^[Y2 : $i]:
% 120.37/16.05 ((
% 120.37/16.05 (!!) @ (
% 120.37/16.05 ^[Y3 : $o]:
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 (
% 120.37/16.05 binunion @
% 120.37/16.05 Y0 @ Y1)) =>
% 120.37/16.05 ((
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 Y0) =>
% 120.37/16.05 (Y3))) =>
% 120.37/16.05 ((
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 Y1) =>
% 120.37/16.05 (Y3))) =>
% 120.37/16.05 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl664])).
% 120.37/16.05 thf(zip_derived_cl698, plain,
% 120.37/16.05 (~ (((subsetI1) =>
% 120.37/16.05 (((eqimpsubset2) =>
% 120.37/16.05 (((eqimpsubset1) =>
% 120.37/16.05 (((subsetI2) =>
% 120.37/16.05 (((emptysetsubset) =>
% 120.37/16.05 (((subsetE) =>
% 120.37/16.05 (((subsetE2) =>
% 120.37/16.05 (((notsubsetI) =>
% 120.37/16.05 (((notequalI1) =>
% 120.37/16.05 (((notequalI2) =>
% 120.37/16.05 (((subsetRefl) =>
% 120.37/16.05 (((subsetTrans) =>
% 120.37/16.05 (((setadjoinSub) =>
% 120.37/16.05 (((setadjoinSub2) =>
% 120.37/16.05 (((subset2powerset) =>
% 120.37/16.05 (((setextsub) =>
% 120.37/16.05 (((subsetemptysetimpeq) =>
% 120.37/16.05 (((powersetI1) =>
% 120.37/16.05 (((powersetE1) =>
% 120.37/16.05 (((inPowerset) =>
% 120.37/16.05 (((powersetsubset) =>
% 120.37/16.05 (((sepInPowerset) =>
% 120.37/16.05 (((sepSubset) =>
% 120.37/16.05 (((binunionIL) =>
% 120.37/16.05 (((upairset2IR) =>
% 120.37/16.05 (((binunionIR) =>
% 120.37/16.05 (((!!) @ (
% 120.37/16.05 ^[Y0 : $i]:
% 120.37/16.05 (((!!) @ (
% 120.37/16.05 ^[Y1 : $i]:
% 120.37/16.05 ((
% 120.37/16.05 (!!) @ (
% 120.37/16.05 ^[Y2 : $i]:
% 120.37/16.05 ((
% 120.37/16.05 (!!) @ (
% 120.37/16.05 ^[Y3 : $o]:
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 (
% 120.37/16.05 binunion @
% 120.37/16.05 Y0 @ Y1)) =>
% 120.37/16.05 ((
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 Y0) =>
% 120.37/16.05 (Y3))) =>
% 120.37/16.05 ((
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 Y1) =>
% 120.37/16.05 (Y3))) =>
% 120.37/16.05 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl681])).
% 120.37/16.05 thf(zip_derived_cl712, plain,
% 120.37/16.05 (~ (((eqimpsubset2) =>
% 120.37/16.05 (((eqimpsubset1) =>
% 120.37/16.05 (((subsetI2) =>
% 120.37/16.05 (((emptysetsubset) =>
% 120.37/16.05 (((subsetE) =>
% 120.37/16.05 (((subsetE2) =>
% 120.37/16.05 (((notsubsetI) =>
% 120.37/16.05 (((notequalI1) =>
% 120.37/16.05 (((notequalI2) =>
% 120.37/16.05 (((subsetRefl) =>
% 120.37/16.05 (((subsetTrans) =>
% 120.37/16.05 (((setadjoinSub) =>
% 120.37/16.05 (((setadjoinSub2) =>
% 120.37/16.05 (((subset2powerset) =>
% 120.37/16.05 (((setextsub) =>
% 120.37/16.05 (((subsetemptysetimpeq) =>
% 120.37/16.05 (((powersetI1) =>
% 120.37/16.05 (((powersetE1) =>
% 120.37/16.05 (((inPowerset) =>
% 120.37/16.05 (((powersetsubset) =>
% 120.37/16.05 (((sepInPowerset) =>
% 120.37/16.05 (((sepSubset) =>
% 120.37/16.05 (((binunionIL) =>
% 120.37/16.05 (((upairset2IR) =>
% 120.37/16.05 (((binunionIR) =>
% 120.37/16.05 (((!!) @ (^[Y0 : $i]:
% 120.37/16.05 ((
% 120.37/16.05 (!!) @ (
% 120.37/16.05 ^[Y1 : $i]:
% 120.37/16.05 ((
% 120.37/16.05 (!!) @ (
% 120.37/16.05 ^[Y2 : $i]:
% 120.37/16.05 ((
% 120.37/16.05 (!!) @ (
% 120.37/16.05 ^[Y3 : $o]:
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 (
% 120.37/16.05 binunion @
% 120.37/16.05 Y0 @ Y1)) =>
% 120.37/16.05 ((
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 Y0) =>
% 120.37/16.05 (Y3))) =>
% 120.37/16.05 ((
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 Y1) =>
% 120.37/16.05 (Y3))) =>
% 120.37/16.05 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl698])).
% 120.37/16.05 thf(zip_derived_cl725, plain,
% 120.37/16.05 (~ (((eqimpsubset1) =>
% 120.37/16.05 (((subsetI2) =>
% 120.37/16.05 (((emptysetsubset) =>
% 120.37/16.05 (((subsetE) =>
% 120.37/16.05 (((subsetE2) =>
% 120.37/16.05 (((notsubsetI) =>
% 120.37/16.05 (((notequalI1) =>
% 120.37/16.05 (((notequalI2) =>
% 120.37/16.05 (((subsetRefl) =>
% 120.37/16.05 (((subsetTrans) =>
% 120.37/16.05 (((setadjoinSub) =>
% 120.37/16.05 (((setadjoinSub2) =>
% 120.37/16.05 (((subset2powerset) =>
% 120.37/16.05 (((setextsub) =>
% 120.37/16.05 (((subsetemptysetimpeq) =>
% 120.37/16.05 (((powersetI1) =>
% 120.37/16.05 (((powersetE1) =>
% 120.37/16.05 (((inPowerset) =>
% 120.37/16.05 (((powersetsubset) =>
% 120.37/16.05 (((sepInPowerset) =>
% 120.37/16.05 (((sepSubset) =>
% 120.37/16.05 (((binunionIL) =>
% 120.37/16.05 (((upairset2IR) =>
% 120.37/16.05 (((binunionIR) =>
% 120.37/16.05 (((!!) @ (^[Y0 : $i]:
% 120.37/16.05 ((
% 120.37/16.05 (!!) @ (
% 120.37/16.05 ^[Y1 : $i]:
% 120.37/16.05 ((
% 120.37/16.05 (!!) @ (
% 120.37/16.05 ^[Y2 : $i]:
% 120.37/16.05 ((
% 120.37/16.05 (!!) @ (
% 120.37/16.05 ^[Y3 : $o]:
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 (
% 120.37/16.05 binunion @
% 120.37/16.05 Y0 @ Y1)) =>
% 120.37/16.05 ((
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 Y0) =>
% 120.37/16.05 (Y3))) =>
% 120.37/16.05 ((
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 Y1) =>
% 120.37/16.05 (Y3))) =>
% 120.37/16.05 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl712])).
% 120.37/16.05 thf(zip_derived_cl735, plain,
% 120.37/16.05 (~ (((subsetI2) =>
% 120.37/16.05 (((emptysetsubset) =>
% 120.37/16.05 (((subsetE) =>
% 120.37/16.05 (((subsetE2) =>
% 120.37/16.05 (((notsubsetI) =>
% 120.37/16.05 (((notequalI1) =>
% 120.37/16.05 (((notequalI2) =>
% 120.37/16.05 (((subsetRefl) =>
% 120.37/16.05 (((subsetTrans) =>
% 120.37/16.05 (((setadjoinSub) =>
% 120.37/16.05 (((setadjoinSub2) =>
% 120.37/16.05 (((subset2powerset) =>
% 120.37/16.05 (((setextsub) =>
% 120.37/16.05 (((subsetemptysetimpeq) =>
% 120.37/16.05 (((powersetI1) =>
% 120.37/16.05 (((powersetE1) =>
% 120.37/16.05 (((inPowerset) =>
% 120.37/16.05 (((powersetsubset) =>
% 120.37/16.05 (((sepInPowerset) =>
% 120.37/16.05 (((sepSubset) =>
% 120.37/16.05 (((binunionIL) =>
% 120.37/16.05 (((upairset2IR) =>
% 120.37/16.05 (((binunionIR) =>
% 120.37/16.05 (((!!) @ (^[Y0 : $i]:
% 120.37/16.05 (((!!) @ (
% 120.37/16.05 ^[Y1 : $i]:
% 120.37/16.05 ((
% 120.37/16.05 (!!) @ (
% 120.37/16.05 ^[Y2 : $i]:
% 120.37/16.05 ((
% 120.37/16.05 (!!) @ (
% 120.37/16.05 ^[Y3 : $o]:
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 (
% 120.37/16.05 binunion @
% 120.37/16.05 Y0 @ Y1)) =>
% 120.37/16.05 ((
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 Y0) =>
% 120.37/16.05 (Y3))) =>
% 120.37/16.05 ((
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 Y1) =>
% 120.37/16.05 (Y3))) =>
% 120.37/16.05 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl725])).
% 120.37/16.05 thf(zip_derived_cl746, plain,
% 120.37/16.05 (~ (((emptysetsubset) =>
% 120.37/16.05 (((subsetE) =>
% 120.37/16.05 (((subsetE2) =>
% 120.37/16.05 (((notsubsetI) =>
% 120.37/16.05 (((notequalI1) =>
% 120.37/16.05 (((notequalI2) =>
% 120.37/16.05 (((subsetRefl) =>
% 120.37/16.05 (((subsetTrans) =>
% 120.37/16.05 (((setadjoinSub) =>
% 120.37/16.05 (((setadjoinSub2) =>
% 120.37/16.05 (((subset2powerset) =>
% 120.37/16.05 (((setextsub) =>
% 120.37/16.05 (((subsetemptysetimpeq) =>
% 120.37/16.05 (((powersetI1) =>
% 120.37/16.05 (((powersetE1) =>
% 120.37/16.05 (((inPowerset) =>
% 120.37/16.05 (((powersetsubset) =>
% 120.37/16.05 (((sepInPowerset) =>
% 120.37/16.05 (((sepSubset) =>
% 120.37/16.05 (((binunionIL) =>
% 120.37/16.05 (((upairset2IR) =>
% 120.37/16.05 (((binunionIR) =>
% 120.37/16.05 (((!!) @ (^[Y0 : $i]:
% 120.37/16.05 (((!!) @ (
% 120.37/16.05 ^[Y1 : $i]:
% 120.37/16.05 ((
% 120.37/16.05 (!!) @ (
% 120.37/16.05 ^[Y2 : $i]:
% 120.37/16.05 ((
% 120.37/16.05 (!!) @ (
% 120.37/16.05 ^[Y3 : $o]:
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 (
% 120.37/16.05 binunion @
% 120.37/16.05 Y0 @ Y1)) =>
% 120.37/16.05 ((
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 Y0) =>
% 120.37/16.05 (Y3))) =>
% 120.37/16.05 ((
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 Y1) =>
% 120.37/16.05 (Y3))) =>
% 120.37/16.05 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl735])).
% 120.37/16.05 thf(zip_derived_cl758, plain,
% 120.37/16.05 (~ (((subsetE) =>
% 120.37/16.05 (((subsetE2) =>
% 120.37/16.05 (((notsubsetI) =>
% 120.37/16.05 (((notequalI1) =>
% 120.37/16.05 (((notequalI2) =>
% 120.37/16.05 (((subsetRefl) =>
% 120.37/16.05 (((subsetTrans) =>
% 120.37/16.05 (((setadjoinSub) =>
% 120.37/16.05 (((setadjoinSub2) =>
% 120.37/16.05 (((subset2powerset) =>
% 120.37/16.05 (((setextsub) =>
% 120.37/16.05 (((subsetemptysetimpeq) =>
% 120.37/16.05 (((powersetI1) =>
% 120.37/16.05 (((powersetE1) =>
% 120.37/16.05 (((inPowerset) =>
% 120.37/16.05 (((powersetsubset) =>
% 120.37/16.05 (((sepInPowerset) =>
% 120.37/16.05 (((sepSubset) =>
% 120.37/16.05 (((binunionIL) =>
% 120.37/16.05 (((upairset2IR) =>
% 120.37/16.05 (((binunionIR) =>
% 120.37/16.05 (((!!) @ (^[Y0 : $i]:
% 120.37/16.05 (((!!) @ (
% 120.37/16.05 ^[Y1 : $i]:
% 120.37/16.05 (((!!) @ (
% 120.37/16.05 ^[Y2 : $i]:
% 120.37/16.05 ((
% 120.37/16.05 (!!) @ (
% 120.37/16.05 ^[Y3 : $o]:
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 (
% 120.37/16.05 binunion @
% 120.37/16.05 Y0 @ Y1)) =>
% 120.37/16.05 ((
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 Y0) =>
% 120.37/16.05 (Y3))) =>
% 120.37/16.05 ((
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 Y1) =>
% 120.37/16.05 (Y3))) =>
% 120.37/16.05 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl746])).
% 120.37/16.05 thf(zip_derived_cl770, plain,
% 120.37/16.05 (~ (((subsetE2) =>
% 120.37/16.05 (((notsubsetI) =>
% 120.37/16.05 (((notequalI1) =>
% 120.37/16.05 (((notequalI2) =>
% 120.37/16.05 (((subsetRefl) =>
% 120.37/16.05 (((subsetTrans) =>
% 120.37/16.05 (((setadjoinSub) =>
% 120.37/16.05 (((setadjoinSub2) =>
% 120.37/16.05 (((subset2powerset) =>
% 120.37/16.05 (((setextsub) =>
% 120.37/16.05 (((subsetemptysetimpeq) =>
% 120.37/16.05 (((powersetI1) =>
% 120.37/16.05 (((powersetE1) =>
% 120.37/16.05 (((inPowerset) =>
% 120.37/16.05 (((powersetsubset) =>
% 120.37/16.05 (((sepInPowerset) =>
% 120.37/16.05 (((sepSubset) =>
% 120.37/16.05 (((binunionIL) =>
% 120.37/16.05 (((upairset2IR) =>
% 120.37/16.05 (((binunionIR) =>
% 120.37/16.05 (((!!) @ (^[Y0 : $i]:
% 120.37/16.05 (((!!) @ (
% 120.37/16.05 ^[Y1 : $i]:
% 120.37/16.05 (((!!) @ (
% 120.37/16.05 ^[Y2 : $i]:
% 120.37/16.05 ((
% 120.37/16.05 (!!) @ (
% 120.37/16.05 ^[Y3 : $o]:
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 (
% 120.37/16.05 binunion @
% 120.37/16.05 Y0 @ Y1)) =>
% 120.37/16.05 ((
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 Y0) =>
% 120.37/16.05 (Y3))) =>
% 120.37/16.05 ((
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 Y1) =>
% 120.37/16.05 (Y3))) =>
% 120.37/16.05 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl758])).
% 120.37/16.05 thf(zip_derived_cl783, plain,
% 120.37/16.05 (~ (((notsubsetI) =>
% 120.37/16.05 (((notequalI1) =>
% 120.37/16.05 (((notequalI2) =>
% 120.37/16.05 (((subsetRefl) =>
% 120.37/16.05 (((subsetTrans) =>
% 120.37/16.05 (((setadjoinSub) =>
% 120.37/16.05 (((setadjoinSub2) =>
% 120.37/16.05 (((subset2powerset) =>
% 120.37/16.05 (((setextsub) =>
% 120.37/16.05 (((subsetemptysetimpeq) =>
% 120.37/16.05 (((powersetI1) =>
% 120.37/16.05 (((powersetE1) =>
% 120.37/16.05 (((inPowerset) =>
% 120.37/16.05 (((powersetsubset) =>
% 120.37/16.05 (((sepInPowerset) =>
% 120.37/16.05 (((sepSubset) =>
% 120.37/16.05 (((binunionIL) =>
% 120.37/16.05 (((upairset2IR) =>
% 120.37/16.05 (((binunionIR) =>
% 120.37/16.05 (((!!) @ (^[Y0 : $i]:
% 120.37/16.05 (((!!) @ (^[Y1 : $i]:
% 120.37/16.05 ((
% 120.37/16.05 (!!) @ (
% 120.37/16.05 ^[Y2 : $i]:
% 120.37/16.05 ((
% 120.37/16.05 (!!) @ (
% 120.37/16.05 ^[Y3 : $o]:
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 (
% 120.37/16.05 binunion @
% 120.37/16.05 Y0 @ Y1)) =>
% 120.37/16.05 ((
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 Y0) =>
% 120.37/16.05 (Y3))) =>
% 120.37/16.05 ((
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 Y1) =>
% 120.37/16.05 (Y3))) =>
% 120.37/16.05 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl770])).
% 120.37/16.05 thf(zip_derived_cl795, plain,
% 120.37/16.05 (~ (((notequalI1) =>
% 120.37/16.05 (((notequalI2) =>
% 120.37/16.05 (((subsetRefl) =>
% 120.37/16.05 (((subsetTrans) =>
% 120.37/16.05 (((setadjoinSub) =>
% 120.37/16.05 (((setadjoinSub2) =>
% 120.37/16.05 (((subset2powerset) =>
% 120.37/16.05 (((setextsub) =>
% 120.37/16.05 (((subsetemptysetimpeq) =>
% 120.37/16.05 (((powersetI1) =>
% 120.37/16.05 (((powersetE1) =>
% 120.37/16.05 (((inPowerset) =>
% 120.37/16.05 (((powersetsubset) =>
% 120.37/16.05 (((sepInPowerset) =>
% 120.37/16.05 (((sepSubset) =>
% 120.37/16.05 (((binunionIL) =>
% 120.37/16.05 (((upairset2IR) =>
% 120.37/16.05 (((binunionIR) =>
% 120.37/16.05 (((!!) @ (^[Y0 : $i]:
% 120.37/16.05 (((!!) @ (^[Y1 : $i]:
% 120.37/16.05 ((
% 120.37/16.05 (!!) @ (
% 120.37/16.05 ^[Y2 : $i]:
% 120.37/16.05 ((
% 120.37/16.05 (!!) @ (
% 120.37/16.05 ^[Y3 : $o]:
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 (
% 120.37/16.05 binunion @
% 120.37/16.05 Y0 @ Y1)) =>
% 120.37/16.05 ((
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 Y0) =>
% 120.37/16.05 (Y3))) =>
% 120.37/16.05 ((
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 Y1) =>
% 120.37/16.05 (Y3))) =>
% 120.37/16.05 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl783])).
% 120.37/16.05 thf(zip_derived_cl805, plain,
% 120.37/16.05 (~ (((notequalI2) =>
% 120.37/16.05 (((subsetRefl) =>
% 120.37/16.05 (((subsetTrans) =>
% 120.37/16.05 (((setadjoinSub) =>
% 120.37/16.05 (((setadjoinSub2) =>
% 120.37/16.05 (((subset2powerset) =>
% 120.37/16.05 (((setextsub) =>
% 120.37/16.05 (((subsetemptysetimpeq) =>
% 120.37/16.05 (((powersetI1) =>
% 120.37/16.05 (((powersetE1) =>
% 120.37/16.05 (((inPowerset) =>
% 120.37/16.05 (((powersetsubset) =>
% 120.37/16.05 (((sepInPowerset) =>
% 120.37/16.05 (((sepSubset) =>
% 120.37/16.05 (((binunionIL) =>
% 120.37/16.05 (((upairset2IR) =>
% 120.37/16.05 (((binunionIR) =>
% 120.37/16.05 (((!!) @ (^[Y0 : $i]:
% 120.37/16.05 (((!!) @ (^[Y1 : $i]:
% 120.37/16.05 (((!!) @ (
% 120.37/16.05 ^[Y2 : $i]:
% 120.37/16.05 ((
% 120.37/16.05 (!!) @ (
% 120.37/16.05 ^[Y3 : $o]:
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 (
% 120.37/16.05 binunion @
% 120.37/16.05 Y0 @ Y1)) =>
% 120.37/16.05 ((
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 Y0) =>
% 120.37/16.05 (Y3))) =>
% 120.37/16.05 ((
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 Y1) =>
% 120.37/16.05 (Y3))) =>
% 120.37/16.05 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl795])).
% 120.37/16.05 thf(zip_derived_cl813, plain,
% 120.37/16.05 (~ (((subsetRefl) =>
% 120.37/16.05 (((subsetTrans) =>
% 120.37/16.05 (((setadjoinSub) =>
% 120.37/16.05 (((setadjoinSub2) =>
% 120.37/16.05 (((subset2powerset) =>
% 120.37/16.05 (((setextsub) =>
% 120.37/16.05 (((subsetemptysetimpeq) =>
% 120.37/16.05 (((powersetI1) =>
% 120.37/16.05 (((powersetE1) =>
% 120.37/16.05 (((inPowerset) =>
% 120.37/16.05 (((powersetsubset) =>
% 120.37/16.05 (((sepInPowerset) =>
% 120.37/16.05 (((sepSubset) =>
% 120.37/16.05 (((binunionIL) =>
% 120.37/16.05 (((upairset2IR) =>
% 120.37/16.05 (((binunionIR) =>
% 120.37/16.05 (((!!) @ (^[Y0 : $i]:
% 120.37/16.05 (((!!) @ (^[Y1 : $i]:
% 120.37/16.05 (((!!) @ (
% 120.37/16.05 ^[Y2 : $i]:
% 120.37/16.05 ((
% 120.37/16.05 (!!) @ (
% 120.37/16.05 ^[Y3 : $o]:
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 (
% 120.37/16.05 binunion @
% 120.37/16.05 Y0 @ Y1)) =>
% 120.37/16.05 ((
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 Y0) =>
% 120.37/16.05 (Y3))) =>
% 120.37/16.05 ((
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 Y1) =>
% 120.37/16.05 (Y3))) =>
% 120.37/16.05 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl805])).
% 120.37/16.05 thf(zip_derived_cl823, plain,
% 120.37/16.05 (~ (((subsetTrans) =>
% 120.37/16.05 (((setadjoinSub) =>
% 120.37/16.05 (((setadjoinSub2) =>
% 120.37/16.05 (((subset2powerset) =>
% 120.37/16.05 (((setextsub) =>
% 120.37/16.05 (((subsetemptysetimpeq) =>
% 120.37/16.05 (((powersetI1) =>
% 120.37/16.05 (((powersetE1) =>
% 120.37/16.05 (((inPowerset) =>
% 120.37/16.05 (((powersetsubset) =>
% 120.37/16.05 (((sepInPowerset) =>
% 120.37/16.05 (((sepSubset) =>
% 120.37/16.05 (((binunionIL) =>
% 120.37/16.05 (((upairset2IR) =>
% 120.37/16.05 (((binunionIR) =>
% 120.37/16.05 (((!!) @ (^[Y0 : $i]:
% 120.37/16.05 (((!!) @ (^[Y1 : $i]:
% 120.37/16.05 (((!!) @ (
% 120.37/16.05 ^[Y2 : $i]:
% 120.37/16.05 (((!!) @ (
% 120.37/16.05 ^[Y3 : $o]:
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 (
% 120.37/16.05 binunion @
% 120.37/16.05 Y0 @ Y1)) =>
% 120.37/16.05 ((
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 Y0) =>
% 120.37/16.05 (Y3))) =>
% 120.37/16.05 ((
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 Y1) =>
% 120.37/16.05 (Y3))) =>
% 120.37/16.05 (Y3)))))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl813])).
% 120.37/16.05 thf(zip_derived_cl833, plain,
% 120.37/16.05 (~ (((setadjoinSub) =>
% 120.37/16.05 (((setadjoinSub2) =>
% 120.37/16.05 (((subset2powerset) =>
% 120.37/16.05 (((setextsub) =>
% 120.37/16.05 (((subsetemptysetimpeq) =>
% 120.37/16.05 (((powersetI1) =>
% 120.37/16.05 (((powersetE1) =>
% 120.37/16.05 (((inPowerset) =>
% 120.37/16.05 (((powersetsubset) =>
% 120.37/16.05 (((sepInPowerset) =>
% 120.37/16.05 (((sepSubset) =>
% 120.37/16.05 (((binunionIL) =>
% 120.37/16.05 (((upairset2IR) =>
% 120.37/16.05 (((binunionIR) =>
% 120.37/16.05 (((!!) @ (^[Y0 : $i]:
% 120.37/16.05 (((!!) @ (^[Y1 : $i]:
% 120.37/16.05 (((!!) @ (
% 120.37/16.05 ^[Y2 : $i]:
% 120.37/16.05 (((!!) @ (
% 120.37/16.05 ^[Y3 : $o]:
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 (
% 120.37/16.05 binunion @
% 120.37/16.05 Y0 @ Y1)) =>
% 120.37/16.05 ((
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 Y0) =>
% 120.37/16.05 (Y3))) =>
% 120.37/16.05 ((
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 Y1) =>
% 120.37/16.05 (Y3))) =>
% 120.37/16.05 (Y3)))))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl823])).
% 120.37/16.05 thf(zip_derived_cl843, plain,
% 120.37/16.05 (~ (((setadjoinSub2) =>
% 120.37/16.05 (((subset2powerset) =>
% 120.37/16.05 (((setextsub) =>
% 120.37/16.05 (((subsetemptysetimpeq) =>
% 120.37/16.05 (((powersetI1) =>
% 120.37/16.05 (((powersetE1) =>
% 120.37/16.05 (((inPowerset) =>
% 120.37/16.05 (((powersetsubset) =>
% 120.37/16.05 (((sepInPowerset) =>
% 120.37/16.05 (((sepSubset) =>
% 120.37/16.05 (((binunionIL) =>
% 120.37/16.05 (((upairset2IR) =>
% 120.37/16.05 (((binunionIR) =>
% 120.37/16.05 (((!!) @ (^[Y0 : $i]:
% 120.37/16.05 (((!!) @ (^[Y1 : $i]:
% 120.37/16.05 (((!!) @ (^[Y2 : $i]:
% 120.37/16.05 ((
% 120.37/16.05 (!!) @ (
% 120.37/16.05 ^[Y3 : $o]:
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 (
% 120.37/16.05 binunion @
% 120.37/16.05 Y0 @ Y1)) =>
% 120.37/16.05 ((
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 Y0) =>
% 120.37/16.05 (Y3))) =>
% 120.37/16.05 ((
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 Y1) =>
% 120.37/16.05 (Y3))) =>
% 120.37/16.05 (Y3)))))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl833])).
% 120.37/16.05 thf(zip_derived_cl851, plain,
% 120.37/16.05 (~ (((subset2powerset) =>
% 120.37/16.05 (((setextsub) =>
% 120.37/16.05 (((subsetemptysetimpeq) =>
% 120.37/16.05 (((powersetI1) =>
% 120.37/16.05 (((powersetE1) =>
% 120.37/16.05 (((inPowerset) =>
% 120.37/16.05 (((powersetsubset) =>
% 120.37/16.05 (((sepInPowerset) =>
% 120.37/16.05 (((sepSubset) =>
% 120.37/16.05 (((binunionIL) =>
% 120.37/16.05 (((upairset2IR) =>
% 120.37/16.05 (((binunionIR) =>
% 120.37/16.05 (((!!) @ (^[Y0 : $i]:
% 120.37/16.05 (((!!) @ (^[Y1 : $i]:
% 120.37/16.05 (((!!) @ (^[Y2 : $i]:
% 120.37/16.05 ((
% 120.37/16.05 (!!) @ (
% 120.37/16.05 ^[Y3 : $o]:
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 (
% 120.37/16.05 binunion @
% 120.37/16.05 Y0 @ Y1)) =>
% 120.37/16.05 ((
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 Y0) =>
% 120.37/16.05 (Y3))) =>
% 120.37/16.05 ((
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 Y1) =>
% 120.37/16.05 (Y3))) =>
% 120.37/16.05 (Y3)))))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl843])).
% 120.37/16.05 thf(zip_derived_cl857, plain,
% 120.37/16.05 (~ (((setextsub) =>
% 120.37/16.05 (((subsetemptysetimpeq) =>
% 120.37/16.05 (((powersetI1) =>
% 120.37/16.05 (((powersetE1) =>
% 120.37/16.05 (((inPowerset) =>
% 120.37/16.05 (((powersetsubset) =>
% 120.37/16.05 (((sepInPowerset) =>
% 120.37/16.05 (((sepSubset) =>
% 120.37/16.05 (((binunionIL) =>
% 120.37/16.05 (((upairset2IR) =>
% 120.37/16.05 (((binunionIR) =>
% 120.37/16.05 (((!!) @ (^[Y0 : $i]:
% 120.37/16.05 (((!!) @ (^[Y1 : $i]:
% 120.37/16.05 (((!!) @ (^[Y2 : $i]:
% 120.37/16.05 (((!!) @ (
% 120.37/16.05 ^[Y3 : $o]:
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 (
% 120.37/16.05 binunion @
% 120.37/16.05 Y0 @ Y1)) =>
% 120.37/16.05 ((
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 Y0) =>
% 120.37/16.05 (Y3))) =>
% 120.37/16.05 ((
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 Y1) =>
% 120.37/16.05 (Y3))) =>
% 120.37/16.05 (Y3)))))))))))))))))))))))))))))))))))))))))),
% 120.37/16.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl851])).
% 120.37/16.05 thf(zip_derived_cl864, plain,
% 120.37/16.05 (~ (((subsetemptysetimpeq) =>
% 120.37/16.05 (((powersetI1) =>
% 120.37/16.05 (((powersetE1) =>
% 120.37/16.05 (((inPowerset) =>
% 120.37/16.05 (((powersetsubset) =>
% 120.37/16.05 (((sepInPowerset) =>
% 120.37/16.05 (((sepSubset) =>
% 120.37/16.05 (((binunionIL) =>
% 120.37/16.05 (((upairset2IR) =>
% 120.37/16.05 (((binunionIR) =>
% 120.37/16.05 (((!!) @ (^[Y0 : $i]:
% 120.37/16.05 (((!!) @ (^[Y1 : $i]:
% 120.37/16.05 (((!!) @ (^[Y2 : $i]:
% 120.37/16.05 (((!!) @ (
% 120.37/16.05 ^[Y3 : $o]:
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 (
% 120.37/16.05 binunion @
% 120.37/16.05 Y0 @ Y1)) =>
% 120.37/16.05 ((
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 Y0) =>
% 120.37/16.05 (Y3))) =>
% 120.37/16.05 ((
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 Y1) =>
% 120.37/16.05 (Y3))) =>
% 120.37/16.05 (Y3)))))))))))))))))))))))))))))))))))))))),
% 120.37/16.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl857])).
% 120.37/16.05 thf(zip_derived_cl872, plain,
% 120.37/16.05 (~ (((powersetI1) =>
% 120.37/16.05 (((powersetE1) =>
% 120.37/16.05 (((inPowerset) =>
% 120.37/16.05 (((powersetsubset) =>
% 120.37/16.05 (((sepInPowerset) =>
% 120.37/16.05 (((sepSubset) =>
% 120.37/16.05 (((binunionIL) =>
% 120.37/16.05 (((upairset2IR) =>
% 120.37/16.05 (((binunionIR) =>
% 120.37/16.05 (((!!) @ (^[Y0 : $i]:
% 120.37/16.05 (((!!) @ (^[Y1 : $i]:
% 120.37/16.05 (((!!) @ (^[Y2 : $i]:
% 120.37/16.05 (((!!) @ (
% 120.37/16.05 ^[Y3 : $o]:
% 120.37/16.05 (((in @
% 120.37/16.05 Y2 @
% 120.37/16.05 (binunion @
% 120.37/16.05 Y0 @ Y1)) =>
% 120.37/16.05 ((
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 Y0) =>
% 120.37/16.05 (Y3))) =>
% 120.37/16.05 ((
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 Y1) =>
% 120.37/16.05 (Y3))) =>
% 120.37/16.05 (Y3)))))))))))))))))))))))))))))))))))))),
% 120.37/16.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl864])).
% 120.37/16.05 thf(zip_derived_cl879, plain,
% 120.37/16.05 (~ (((powersetE1) =>
% 120.37/16.05 (((inPowerset) =>
% 120.37/16.05 (((powersetsubset) =>
% 120.37/16.05 (((sepInPowerset) =>
% 120.37/16.05 (((sepSubset) =>
% 120.37/16.05 (((binunionIL) =>
% 120.37/16.05 (((upairset2IR) =>
% 120.37/16.05 (((binunionIR) =>
% 120.37/16.05 (((!!) @ (^[Y0 : $i]:
% 120.37/16.05 (((!!) @ (^[Y1 : $i]:
% 120.37/16.05 (((!!) @ (^[Y2 : $i]:
% 120.37/16.05 (((!!) @ (
% 120.37/16.05 ^[Y3 : $o]:
% 120.37/16.05 (((in @ Y2 @
% 120.37/16.05 (binunion @
% 120.37/16.05 Y0 @ Y1)) =>
% 120.37/16.05 ((((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 Y0) =>
% 120.37/16.05 (Y3))) =>
% 120.37/16.05 ((
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 Y1) =>
% 120.37/16.05 (Y3))) =>
% 120.37/16.05 (Y3)))))))))))))))))))))))))))))))))))),
% 120.37/16.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl872])).
% 120.37/16.05 thf(zip_derived_cl886, plain,
% 120.37/16.05 (~ (((inPowerset) =>
% 120.37/16.05 (((powersetsubset) =>
% 120.37/16.05 (((sepInPowerset) =>
% 120.37/16.05 (((sepSubset) =>
% 120.37/16.05 (((binunionIL) =>
% 120.37/16.05 (((upairset2IR) =>
% 120.37/16.05 (((binunionIR) =>
% 120.37/16.05 (((!!) @ (^[Y0 : $i]:
% 120.37/16.05 (((!!) @ (^[Y1 : $i]:
% 120.37/16.05 (((!!) @ (^[Y2 : $i]:
% 120.37/16.05 (((!!) @ (^[Y3 : $o]:
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 (
% 120.37/16.05 binunion @
% 120.37/16.05 Y0 @ Y1)) =>
% 120.37/16.05 ((
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 Y0) =>
% 120.37/16.05 (Y3))) =>
% 120.37/16.05 ((
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 Y1) =>
% 120.37/16.05 (Y3))) =>
% 120.37/16.05 (Y3)))))))))))))))))))))))))))))))))),
% 120.37/16.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl879])).
% 120.37/16.05 thf(zip_derived_cl892, plain,
% 120.37/16.05 (~ (((powersetsubset) =>
% 120.37/16.05 (((sepInPowerset) =>
% 120.37/16.05 (((sepSubset) =>
% 120.37/16.05 (((binunionIL) =>
% 120.37/16.05 (((upairset2IR) =>
% 120.37/16.05 (((binunionIR) =>
% 120.37/16.05 (((!!) @ (^[Y0 : $i]:
% 120.37/16.05 (((!!) @ (^[Y1 : $i]:
% 120.37/16.05 (((!!) @ (^[Y2 : $i]:
% 120.37/16.05 (((!!) @ (^[Y3 : $o]:
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 (
% 120.37/16.05 binunion @
% 120.37/16.05 Y0 @ Y1)) =>
% 120.37/16.05 ((
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 Y0) =>
% 120.37/16.05 (Y3))) =>
% 120.37/16.05 ((
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 Y1) =>
% 120.37/16.05 (Y3))) =>
% 120.37/16.05 (Y3)))))))))))))))))))))))))))))))),
% 120.37/16.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl886])).
% 120.37/16.05 thf(zip_derived_cl899, plain,
% 120.37/16.05 (~ (((sepInPowerset) =>
% 120.37/16.05 (((sepSubset) =>
% 120.37/16.05 (((binunionIL) =>
% 120.37/16.05 (((upairset2IR) =>
% 120.37/16.05 (((binunionIR) =>
% 120.37/16.05 (((!!) @ (^[Y0 : $i]:
% 120.37/16.05 (((!!) @ (^[Y1 : $i]:
% 120.37/16.05 (((!!) @ (^[Y2 : $i]:
% 120.37/16.05 (((!!) @ (^[Y3 : $o]:
% 120.37/16.05 (((in @
% 120.37/16.05 Y2 @
% 120.37/16.05 (binunion @
% 120.37/16.05 Y0 @ Y1)) =>
% 120.37/16.05 ((
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 Y0) =>
% 120.37/16.05 (Y3))) =>
% 120.37/16.05 ((
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 Y1) =>
% 120.37/16.05 (Y3))) =>
% 120.37/16.05 (Y3)))))))))))))))))))))))))))))),
% 120.37/16.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl892])).
% 120.37/16.05 thf(zip_derived_cl906, plain,
% 120.37/16.05 (~ (((sepSubset) =>
% 120.37/16.05 (((binunionIL) =>
% 120.37/16.05 (((upairset2IR) =>
% 120.37/16.05 (((binunionIR) =>
% 120.37/16.05 (((!!) @ (^[Y0 : $i]:
% 120.37/16.05 (((!!) @ (^[Y1 : $i]:
% 120.37/16.05 (((!!) @ (^[Y2 : $i]:
% 120.37/16.05 (((!!) @ (^[Y3 : $o]:
% 120.37/16.05 (((in @ Y2 @
% 120.37/16.05 (binunion @
% 120.37/16.05 Y0 @ Y1)) =>
% 120.37/16.05 ((((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 Y0) =>
% 120.37/16.05 (Y3))) =>
% 120.37/16.05 ((
% 120.37/16.05 ((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 Y1) =>
% 120.37/16.05 (Y3))) =>
% 120.37/16.05 (Y3)))))))))))))))))))))))))))),
% 120.37/16.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl899])).
% 120.37/16.05 thf(zip_derived_cl911, plain,
% 120.37/16.05 (~ (((binunionIL) =>
% 120.37/16.05 (((upairset2IR) =>
% 120.37/16.05 (((binunionIR) =>
% 120.37/16.05 (((!!) @ (^[Y0 : $i]:
% 120.37/16.05 (((!!) @ (^[Y1 : $i]:
% 120.37/16.05 (((!!) @ (^[Y2 : $i]:
% 120.37/16.05 (((!!) @ (^[Y3 : $o]:
% 120.37/16.05 (((in @ Y2 @
% 120.37/16.05 (binunion @
% 120.37/16.05 Y0 @ Y1)) =>
% 120.37/16.05 (((((in @
% 120.37/16.05 Y2 @
% 120.37/16.05 Y0) =>
% 120.37/16.05 (Y3))) =>
% 120.37/16.05 ((((
% 120.37/16.05 (in @
% 120.37/16.05 Y2 @
% 120.37/16.05 Y1) =>
% 120.37/16.05 (Y3))) =>
% 120.37/16.05 (Y3)))))))))))))))))))))))))),
% 120.37/16.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl906])).
% 120.37/16.05 thf(zip_derived_cl917, plain,
% 120.37/16.05 (~ (((upairset2IR) =>
% 120.37/16.05 (((binunionIR) =>
% 120.37/16.05 (((!!) @ (^[Y0 : $i]:
% 120.37/16.05 (((!!) @ (^[Y1 : $i]:
% 120.37/16.05 (((!!) @ (^[Y2 : $i]:
% 120.37/16.05 (((!!) @ (^[Y3 : $o]:
% 120.37/16.05 (((in @ Y2 @
% 120.37/16.05 (binunion @
% 120.37/16.05 Y0 @ Y1)) =>
% 120.37/16.05 (((((in @ Y2 @
% 120.37/16.05 Y0) => (Y3))) =>
% 120.37/16.05 (((((in @
% 120.37/16.05 Y2 @
% 120.37/16.05 Y1) =>
% 120.37/16.05 (Y3))) =>
% 120.37/16.05 (Y3)))))))))))))))))))))))),
% 120.37/16.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl911])).
% 120.37/16.05 thf(zip_derived_cl924, plain,
% 120.37/16.05 (~ (((binunionIR) =>
% 120.37/16.05 (((!!) @ (^[Y0 : $i]:
% 120.37/16.05 (((!!) @ (^[Y1 : $i]:
% 120.37/16.05 (((!!) @ (^[Y2 : $i]:
% 120.37/16.05 (((!!) @ (^[Y3 : $o]:
% 120.37/16.05 (((in @ Y2 @
% 120.37/16.05 (binunion @ Y0 @
% 120.37/16.05 Y1)) =>
% 120.37/16.05 (((((in @ Y2 @
% 120.37/16.05 Y0) => (Y3))) =>
% 120.37/16.05 (((((in @ Y2 @
% 120.37/16.05 Y1) => (Y3))) =>
% 120.37/16.05 (Y3)))))))))))))))))))))),
% 120.37/16.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl917])).
% 120.37/16.05 thf(zip_derived_cl929, plain,
% 120.37/16.05 (~ (((!!) @ (^[Y0 : $i]:
% 120.37/16.05 (((!!) @ (^[Y1 : $i]:
% 120.37/16.05 (((!!) @ (^[Y2 : $i]:
% 120.37/16.05 (((!!) @ (^[Y3 : $o]:
% 120.37/16.05 (((in @ Y2 @
% 120.37/16.05 (binunion @ Y0 @ Y1)) =>
% 120.37/16.05 (((((in @ Y2 @
% 120.37/16.05 Y0) => (Y3))) =>
% 120.37/16.05 (((((in @ Y2 @
% 120.37/16.05 Y1) => (Y3))) =>
% 120.37/16.05 (Y3)))))))))))))))))))),
% 120.37/16.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl924])).
% 120.37/16.05 thf(zip_derived_cl933, plain,
% 120.37/16.05 (~ (((!!) @ (^[Y0 : $i]:
% 120.37/16.05 (((!!) @ (^[Y1 : $i]:
% 120.37/16.05 (((!!) @ (^[Y2 : $o]:
% 120.37/16.05 (((in @ Y1 @
% 120.37/16.05 (binunion @ '#sk781' @ Y0)) =>
% 120.37/16.05 (((((in @ Y1 @ '#sk781') => (Y2))) =>
% 120.37/16.05 (((((in @ Y1 @ Y0) => (Y2))) =>
% 120.37/16.05 (Y2))))))))))))))))),
% 120.37/16.05 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl929])).
% 120.37/16.05 thf(zip_derived_cl938, plain,
% 120.37/16.05 (~ (((!!) @ (^[Y0 : $i]:
% 120.37/16.05 (((!!) @ (^[Y1 : $o]:
% 120.37/16.05 (((in @ Y0 @
% 120.37/16.05 (binunion @ '#sk781' @ '#sk782')) =>
% 120.37/16.05 (((((in @ Y0 @ '#sk781') => (Y1))) =>
% 120.37/16.05 (((((in @ Y0 @ '#sk782') => (Y1))) => (Y1)))))))))))))),
% 120.37/16.05 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl933])).
% 120.37/16.05 thf(binunion, axiom,(( binunion @ (X0)@ (X1)) =
% 120.37/16.05 ((setunion @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)))))).
% 120.37/16.05 thf('4', plain,
% 120.37/16.05 (![X1:$i,X0:$i]:
% 120.37/16.05 ( ( binunion @ X0 @ X1 ) =
% 120.37/16.05 ( setunion @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) ) )),
% 120.37/16.05 define([status(thm)])).
% 120.37/16.05 thf(zip_derived_cl940, plain,
% 120.37/16.05 (~ (((!!) @ (^[Y0 : $i]:
% 120.37/16.05 (((!!) @ (^[Y1 : $o]:
% 120.37/16.05 (((in @ Y0 @
% 120.37/16.05 (setunion @
% 120.37/16.05 (setadjoin @ '#sk781' @
% 120.37/16.05 (setadjoin @ '#sk782' @ emptyset)))) =>
% 120.37/16.05 (((((in @ Y0 @ '#sk781') => (Y1))) =>
% 120.37/16.05 (((((in @ Y0 @ '#sk782') => (Y1))) => (Y1)))))))))))))),
% 120.37/16.05 inference('rw', [status(thm)], [zip_derived_cl938, '4'])).
% 120.37/16.05 thf(zip_derived_cl941, plain,
% 120.37/16.05 (~ (((!!) @ (^[Y0 : $o]:
% 120.37/16.05 (((in @ '#sk783' @
% 120.37/16.05 (setunion @
% 120.37/16.05 (setadjoin @ '#sk781' @
% 120.37/16.05 (setadjoin @ '#sk782' @ emptyset)))) =>
% 120.37/16.05 (((((in @ '#sk783' @ '#sk781') => (Y0))) =>
% 120.37/16.05 (((((in @ '#sk783' @ '#sk782') => (Y0))) => (Y0))))))))))),
% 120.37/16.05 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl940])).
% 120.37/16.05 thf(zip_derived_cl944, plain,
% 120.37/16.05 (~ (((in @ '#sk783' @
% 120.37/16.05 (setunion @
% 120.37/16.05 (setadjoin @ '#sk781' @ (setadjoin @ '#sk782' @ emptyset)))) =>
% 120.37/16.05 (((((in @ '#sk783' @ '#sk781') => ('#sk784'))) =>
% 120.37/16.05 (((((in @ '#sk783' @ '#sk782') => ('#sk784'))) => ('#sk784')))))))),
% 120.37/16.05 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl941])).
% 120.37/16.05 thf(zip_derived_cl945, plain,
% 120.37/16.05 ( (in @ '#sk783' @
% 120.37/16.05 (setunion @ (setadjoin @ '#sk781' @ (setadjoin @ '#sk782' @ emptyset))))),
% 120.37/16.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl944])).
% 120.37/16.05 thf(zip_derived_cl946, plain,
% 120.37/16.05 (~ (((((in @ '#sk783' @ '#sk781') => ('#sk784'))) =>
% 120.37/16.05 (((((in @ '#sk783' @ '#sk782') => ('#sk784'))) => ('#sk784')))))),
% 120.37/16.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl944])).
% 120.37/16.05 thf(zip_derived_cl948, plain,
% 120.37/16.05 (~ (((((in @ '#sk783' @ '#sk782') => ('#sk784'))) => ('#sk784')))),
% 120.37/16.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl946])).
% 120.37/16.05 thf(zip_derived_cl950, plain,
% 120.37/16.05 (![X4 : $i, X6 : $i, X8 : $o]:
% 120.37/16.05 ( ('#form251' @ X4 @ X6 @ X8)
% 120.37/16.05 | ~ (((((in @ X6 @ X4) => (X8))) => (X8))))),
% 120.37/16.05 define([status(thm)])).
% 120.37/16.05 thf(zip_derived_cl951, plain,
% 120.37/16.05 (![X4 : $i, X6 : $i, X8 : $o]:
% 120.37/16.05 ( (((in @ X6 @ X4) => (X8))) | ('#form251' @ X4 @ X6 @ X8))),
% 120.37/16.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl950])).
% 120.37/16.05 thf(zip_derived_cl954, plain,
% 120.37/16.05 (![X4 : $i, X6 : $i, X8 : $o]:
% 120.37/16.05 (~ (in @ X6 @ X4) | (X8) | ('#form251' @ X4 @ X6 @ X8))),
% 120.37/16.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl951])).
% 120.37/16.05 thf(zip_derived_cl952, plain,
% 120.37/16.05 (![X4 : $i, X6 : $i, X8 : $o]: (~ (X8) | ('#form251' @ X4 @ X6 @ X8))),
% 120.37/16.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl950])).
% 120.37/16.05 thf(zip_derived_cl959, plain,
% 120.37/16.05 (![X4 : $i, X6 : $i, X8 : $o]:
% 120.37/16.05 ( ('#form251' @ X4 @ X6 @ X8) | ~ (in @ X6 @ X4))),
% 120.37/16.05 inference('clc', [status(thm)], [zip_derived_cl954, zip_derived_cl952])).
% 120.37/16.05 thf(zip_derived_cl947, plain,
% 120.37/16.05 ( (((in @ '#sk783' @ '#sk781') => ('#sk784')))),
% 120.37/16.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl946])).
% 120.37/16.05 thf(zip_derived_cl949, plain, ((~ (in @ '#sk783' @ '#sk781') | ('#sk784'))),
% 120.37/16.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl947])).
% 120.37/16.05 thf(zip_derived_cl371, plain, ( (setunionE)),
% 120.37/16.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl364])).
% 120.37/16.05 thf(setunionE, axiom, (setunionE) =>
% 120.37/16.05 ((((!!) @ (^[Y0 : $i]:
% 120.37/16.05 (((!!) @ (^[Y1 : $i]:
% 120.37/16.05 (((in @ Y1 @ (setunion @ Y0)) =>
% 120.37/16.05 (((!!) @ (^[Y2 : $o]:
% 120.37/16.05 (((((!!) @ (^[Y3 : $i]:
% 120.37/16.05 (((in @ Y1 @ Y3) =>
% 120.37/16.05 (((in @ Y3 @ Y0) =>
% 120.37/16.05 (Y2)))))))) =>
% 120.37/16.05 (Y2))))))))))))))
% 120.37/16.05 = ($true))).
% 120.37/16.05 thf('5', plain,
% 120.37/16.05 (( setunionE ) <=>
% 120.37/16.05 ( ![X5:$i,X7:$i]:
% 120.37/16.05 ( ( in @ X7 @ ( setunion @ X5 ) ) =>
% 120.37/16.05 ( ![X9:$o]:
% 120.37/16.05 ( ( ![X11:$i]:
% 120.37/16.05 ( ( in @ X7 @ X11 ) => ( ( in @ X11 @ X5 ) => ( X9 ) ) ) ) =>
% 120.37/16.05 ( X9 ) ) ) ) )),
% 120.37/16.05 inference('rw.lit', [status(esa)], [setunionE])).
% 120.37/16.05 thf(zip_derived_cl380, plain,
% 120.37/16.05 ( (((!!) @ (^[Y0 : $i]:
% 120.37/16.05 (((!!) @ (^[Y1 : $i]:
% 120.37/16.05 (((in @ Y1 @ (setunion @ Y0)) =>
% 120.37/16.05 (((!!) @ (^[Y2 : $o]:
% 120.37/16.05 (((((!!) @ (^[Y3 : $i]:
% 120.37/16.05 (((in @ Y1 @ Y3) =>
% 120.37/16.05 (((in @ Y3 @
% 120.37/16.05 Y0) => (Y2)))))))) =>
% 120.37/16.05 (Y2))))))))))))))),
% 120.37/16.05 inference('rw_clause', [status(thm)], [zip_derived_cl371, '5'])).
% 120.37/16.05 thf(zip_derived_cl387, plain,
% 120.37/16.05 (![X2 : $i]:
% 120.37/16.05 (((!!) @ (^[Y0 : $i]:
% 120.37/16.05 (((in @ Y0 @ (setunion @ X2)) =>
% 120.37/16.05 (((!!) @ (^[Y1 : $o]:
% 120.37/16.05 (((((!!) @ (^[Y2 : $i]:
% 120.37/16.05 (((in @ Y0 @ Y2) =>
% 120.37/16.05 (((in @ Y2 @ X2) => (Y1)))))))) =>
% 120.37/16.05 (Y1)))))))))))),
% 120.37/16.05 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl380])).
% 120.37/16.05 thf(zip_derived_cl393, plain,
% 120.37/16.05 (![X2 : $i, X4 : $i]:
% 120.37/16.05 (((in @ X4 @ (setunion @ X2)) =>
% 120.37/16.05 (((!!) @ (^[Y0 : $o]:
% 120.37/16.05 (((((!!) @ (^[Y1 : $i]:
% 120.37/16.05 (((in @ X4 @ Y1) =>
% 120.37/16.05 (((in @ Y1 @ X2) => (Y0)))))))) =>
% 120.37/16.05 (Y0))))))))),
% 120.37/16.05 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl387])).
% 120.37/16.05 thf(zip_derived_cl400, plain,
% 120.37/16.05 (![X2 : $i, X4 : $i]:
% 120.37/16.05 (~ (in @ X4 @ (setunion @ X2))
% 120.37/16.05 | (((!!) @ (^[Y0 : $o]:
% 120.37/16.05 (((((!!) @ (^[Y1 : $i]:
% 120.37/16.05 (((in @ X4 @ Y1) =>
% 120.37/16.05 (((in @ Y1 @ X2) => (Y0)))))))) =>
% 120.37/16.05 (Y0)))))))),
% 120.37/16.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl393])).
% 120.37/16.05 thf(zip_derived_cl408, plain,
% 120.37/16.05 (![X2 : $i, X4 : $i, X6 : $o]:
% 120.37/16.05 ( (((((!!) @ (^[Y0 : $i]:
% 120.37/16.05 (((in @ X4 @ Y0) => (((in @ Y0 @ X2) => (X6)))))))) =>
% 120.37/16.05 (X6)))
% 120.37/16.05 | ~ (in @ X4 @ (setunion @ X2)))),
% 120.37/16.05 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl400])).
% 120.37/16.05 thf(zip_derived_cl414, plain,
% 120.37/16.05 (![X2 : $i, X4 : $i, X6 : $o]:
% 120.37/16.05 (~ (((!!) @ (^[Y0 : $i]:
% 120.37/16.05 (((in @ X4 @ Y0) => (((in @ Y0 @ X2) => (X6))))))))
% 120.37/16.05 | (X6)
% 120.37/16.05 | ~ (in @ X4 @ (setunion @ X2)))),
% 120.37/16.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl408])).
% 120.37/16.05 thf(zip_derived_cl421, plain,
% 120.37/16.05 (![X2 : $i, X4 : $i, X6 : $o]:
% 120.37/16.05 (~ (((in @ X4 @ ('#sk256' @ X2 @ X4 @ X6)) =>
% 120.37/16.05 (((in @ ('#sk256' @ X2 @ X4 @ X6) @ X2) => (X6)))))
% 120.37/16.05 | ~ (in @ X4 @ (setunion @ X2))
% 120.37/16.05 | (X6))),
% 120.37/16.05 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl414])).
% 120.37/16.05 thf(zip_derived_cl429, plain,
% 120.37/16.05 (![X2 : $i, X4 : $i, X6 : $o]:
% 120.37/16.05 ( (in @ X4 @ ('#sk256' @ X2 @ X4 @ X6))
% 120.37/16.05 | (X6)
% 120.37/16.05 | ~ (in @ X4 @ (setunion @ X2)))),
% 120.37/16.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl421])).
% 120.37/16.05 thf(zip_derived_cl952, plain,
% 120.37/16.05 (![X4 : $i, X6 : $i, X8 : $o]: (~ (X8) | ('#form251' @ X4 @ X6 @ X8))),
% 120.37/16.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl950])).
% 120.37/16.05 thf(zip_derived_cl948, plain,
% 120.37/16.05 (~ (((((in @ '#sk783' @ '#sk782') => ('#sk784'))) => ('#sk784')))),
% 120.37/16.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl946])).
% 120.37/16.05 thf(zip_derived_cl950, plain,
% 120.37/16.05 (![X4 : $i, X6 : $i, X8 : $o]:
% 120.37/16.05 ( ('#form251' @ X4 @ X6 @ X8)
% 120.37/16.05 | ~ (((((in @ X6 @ X4) => (X8))) => (X8))))),
% 120.37/16.05 define([status(thm)])).
% 120.37/16.05 thf(zip_derived_cl317, plain, ( (setadjoinE)),
% 120.37/16.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl312])).
% 120.37/16.05 thf(setadjoinE, axiom, (setadjoinE) =>
% 120.37/16.05 ((((!!) @ (^[Y0 : $i]:
% 120.37/16.05 (((!!) @ (^[Y1 : $i]:
% 120.37/16.05 (((!!) @ (^[Y2 : $i]:
% 120.37/16.05 (((in @ Y2 @ (setadjoin @ Y0 @ Y1)) =>
% 120.37/16.05 (((!!) @ (^[Y3 : $o]:
% 120.37/16.05 (((((((Y2) = (Y0))) =>
% 120.37/16.05 (Y3))) =>
% 120.37/16.05 (((((in @ Y2 @ Y1) =>
% 120.37/16.05 (Y3))) =>
% 120.37/16.05 (Y3)))))))))))))))))))
% 120.37/16.05 = ($true))).
% 120.37/16.05 thf('6', plain,
% 120.37/16.05 (( setadjoinE ) <=>
% 120.37/16.05 ( ![X5:$i,X7:$i,X9:$i]:
% 120.37/16.05 ( ( in @ X9 @ ( setadjoin @ X5 @ X7 ) ) =>
% 120.37/16.05 ( ![X11:$o]:
% 120.37/16.05 ( ( ( ( X9 ) = ( X5 ) ) => ( X11 ) ) =>
% 120.37/16.05 ( ( ( in @ X9 @ X7 ) => ( X11 ) ) => ( X11 ) ) ) ) ) )),
% 120.37/16.05 inference('rw.lit', [status(esa)], [setadjoinE])).
% 120.37/16.05 thf(zip_derived_cl323, plain,
% 120.37/16.05 ( (((!!) @ (^[Y0 : $i]:
% 120.37/16.05 (((!!) @ (^[Y1 : $i]:
% 120.37/16.05 (((!!) @ (^[Y2 : $i]:
% 120.37/16.05 (((in @ Y2 @
% 120.37/16.05 (setadjoin @ Y0 @ Y1)) =>
% 120.37/16.05 (((!!) @ (^[Y3 : $o]:
% 120.37/16.05 (((((((Y2) = (Y0))) =>
% 120.37/16.05 (Y3))) =>
% 120.37/16.05 (((((in @ Y2 @
% 120.37/16.05 Y1) => (Y3))) =>
% 120.37/16.05 (Y3)))))))))))))))))))),
% 120.37/16.05 inference('rw_clause', [status(thm)], [zip_derived_cl317, '6'])).
% 120.37/16.05 thf(zip_derived_cl328, plain,
% 120.37/16.05 (![X2 : $i]:
% 120.37/16.05 (((!!) @ (^[Y0 : $i]:
% 120.37/16.05 (((!!) @ (^[Y1 : $i]:
% 120.37/16.05 (((in @ Y1 @ (setadjoin @ X2 @ Y0)) =>
% 120.37/16.05 (((!!) @ (^[Y2 : $o]:
% 120.37/16.05 (((((((Y1) = (X2))) => (Y2))) =>
% 120.37/16.05 (((((in @ Y1 @ Y0) => (Y2))) =>
% 120.37/16.05 (Y2))))))))))))))))),
% 120.37/16.05 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl323])).
% 120.37/16.05 thf(zip_derived_cl333, plain,
% 120.37/16.05 (![X2 : $i, X4 : $i]:
% 120.37/16.05 (((!!) @ (^[Y0 : $i]:
% 120.37/16.05 (((in @ Y0 @ (setadjoin @ X2 @ X4)) =>
% 120.37/16.05 (((!!) @ (^[Y1 : $o]:
% 120.37/16.05 (((((((Y0) = (X2))) => (Y1))) =>
% 120.37/16.05 (((((in @ Y0 @ X4) => (Y1))) => (Y1)))))))))))))),
% 120.37/16.05 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl328])).
% 120.37/16.05 thf(zip_derived_cl338, plain,
% 120.37/16.05 (![X2 : $i, X4 : $i, X6 : $i]:
% 120.37/16.05 (((in @ X6 @ (setadjoin @ X2 @ X4)) =>
% 120.37/16.05 (((!!) @ (^[Y0 : $o]:
% 120.37/16.05 (((((((X6) = (X2))) => (Y0))) =>
% 120.37/16.05 (((((in @ X6 @ X4) => (Y0))) => (Y0))))))))))),
% 120.37/16.05 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl333])).
% 120.37/16.05 thf(zip_derived_cl344, plain,
% 120.37/16.05 (![X2 : $i, X4 : $i, X6 : $i]:
% 120.37/16.05 (~ (in @ X6 @ (setadjoin @ X2 @ X4))
% 120.37/16.05 | (((!!) @ (^[Y0 : $o]:
% 120.37/16.05 (((((((X6) = (X2))) => (Y0))) =>
% 120.37/16.05 (((((in @ X6 @ X4) => (Y0))) => (Y0)))))))))),
% 120.37/16.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl338])).
% 120.37/16.05 thf(zip_derived_cl351, plain,
% 120.37/16.05 (![X2 : $i, X4 : $i, X6 : $i, X8 : $o]:
% 120.37/16.05 ( (((((((X6) = (X2))) => (X8))) =>
% 120.37/16.05 (((((in @ X6 @ X4) => (X8))) => (X8)))))
% 120.37/16.05 | ~ (in @ X6 @ (setadjoin @ X2 @ X4)))),
% 120.37/16.05 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl344])).
% 120.37/16.05 thf(zip_derived_cl358, plain,
% 120.37/16.05 (![X2 : $i, X4 : $i, X6 : $i, X8 : $o]:
% 120.37/16.05 (~ (((((X6) = (X2))) => (X8)))
% 120.37/16.05 | (((((in @ X6 @ X4) => (X8))) => (X8)))
% 120.37/16.05 | ~ (in @ X6 @ (setadjoin @ X2 @ X4)))),
% 120.37/16.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl351])).
% 120.37/16.05 thf(zip_derived_cl365, plain,
% 120.37/16.05 (![X2 : $i, X4 : $i, X6 : $i, X8 : $o]:
% 120.37/16.05 ( (((X6) = (X2)))
% 120.37/16.05 | ~ (in @ X6 @ (setadjoin @ X2 @ X4))
% 120.37/16.05 | (((((in @ X6 @ X4) => (X8))) => (X8))))),
% 120.37/16.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl358])).
% 120.37/16.05 thf(zip_derived_cl373, plain,
% 120.37/16.05 (![X2 : $i, X4 : $i, X6 : $i, X8 : $o]:
% 120.37/16.05 (((X6) = (X2))
% 120.37/16.05 | ~ (in @ X6 @ (setadjoin @ X2 @ X4))
% 120.37/16.05 | (((((in @ X6 @ X4) => (X8))) => (X8))))),
% 120.37/16.05 inference('simplify nested equalities', [status(thm)],
% 120.37/16.05 [zip_derived_cl365])).
% 120.37/16.05 thf(zip_derived_cl374, plain,
% 120.37/16.05 (![X4 : $i, X6 : $i, X8 : $o]:
% 120.37/16.05 (~ ('#form251' @ X4 @ X6 @ X8)
% 120.37/16.05 | (((((in @ X6 @ X4) => (X8))) => (X8))))),
% 120.37/16.05 define([status(thm)])).
% 120.37/16.05 thf(zip_derived_cl953, plain,
% 120.37/16.05 (~ ('#form251' @ '#sk782' @ '#sk783' @ '#sk784')),
% 120.37/16.05 inference('renaming', [status(thm)],
% 120.37/16.05 [zip_derived_cl948, zip_derived_cl950, zip_derived_cl374])).
% 120.37/16.05 thf(zip_derived_cl430, plain,
% 120.37/16.05 (![X2 : $i, X4 : $i, X6 : $o]:
% 120.37/16.05 (~ (((in @ ('#sk256' @ X2 @ X4 @ X6) @ X2) => (X6)))
% 120.37/16.05 | (X6)
% 120.37/16.05 | ~ (in @ X4 @ (setunion @ X2)))),
% 120.37/16.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl421])).
% 120.37/16.05 thf(zip_derived_cl440, plain,
% 120.37/16.05 (![X2 : $i, X4 : $i, X6 : $o]:
% 120.37/16.05 ( (in @ ('#sk256' @ X2 @ X4 @ X6) @ X2)
% 120.37/16.05 | ~ (in @ X4 @ (setunion @ X2))
% 120.37/16.05 | (X6))),
% 120.37/16.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl430])).
% 120.37/16.05 thf(zip_derived_cl438, plain, ( (upairsetE)),
% 120.37/16.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl428])).
% 120.37/16.05 thf(upairsetE, axiom, (upairsetE) =>
% 120.37/16.05 ((((!!) @ (^[Y0 : $i]:
% 120.37/16.05 (((!!) @ (^[Y1 : $i]:
% 120.37/16.05 (((!!) @ (^[Y2 : $i]:
% 120.37/16.05 (((in @ Y2 @
% 120.37/16.05 (setadjoin @ Y0 @
% 120.37/16.05 (setadjoin @ Y1 @ emptyset))) =>
% 120.37/16.05 (((((Y2) = (Y1))) | (((Y2) = (Y0))))))))))))))))
% 120.37/16.05 = ($true))).
% 120.37/16.05 thf('7', plain,
% 120.37/16.05 (( upairsetE ) <=>
% 120.37/16.05 ( ![X5:$i,X7:$i,X9:$i]:
% 120.37/16.05 ( ( in @ X9 @ ( setadjoin @ X5 @ ( setadjoin @ X7 @ emptyset ) ) ) =>
% 120.37/16.05 ( ( ( X9 ) = ( X7 ) ) | ( ( X9 ) = ( X5 ) ) ) ) )),
% 120.37/16.05 inference('rw.lit', [status(esa)], [upairsetE])).
% 120.37/16.05 thf(zip_derived_cl447, plain,
% 120.37/16.05 ( (((!!) @ (^[Y0 : $i]:
% 120.37/16.05 (((!!) @ (^[Y1 : $i]:
% 120.37/16.05 (((!!) @ (^[Y2 : $i]:
% 120.37/16.05 (((in @ Y2 @
% 120.37/16.05 (setadjoin @ Y0 @
% 120.37/16.05 (setadjoin @ Y1 @ emptyset))) =>
% 120.37/16.05 (((((Y2) = (Y1))) |
% 120.37/16.05 (((Y2) = (Y0))))))))))))))))),
% 120.37/16.05 inference('rw_clause', [status(thm)], [zip_derived_cl438, '7'])).
% 120.37/16.05 thf(zip_derived_cl454, plain,
% 120.37/16.05 (![X2 : $i]:
% 120.37/16.05 (((!!) @ (^[Y0 : $i]:
% 120.37/16.05 (((!!) @ (^[Y1 : $i]:
% 120.37/16.05 (((in @ Y1 @
% 120.37/16.05 (setadjoin @ X2 @
% 120.37/16.05 (setadjoin @ Y0 @ emptyset))) =>
% 120.37/16.05 (((((Y1) = (Y0))) | (((Y1) = (X2)))))))))))))),
% 120.37/16.05 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl447])).
% 120.37/16.05 thf(zip_derived_cl461, plain,
% 120.37/16.05 (![X2 : $i, X4 : $i]:
% 120.37/16.05 (((!!) @ (^[Y0 : $i]:
% 120.37/16.05 (((in @ Y0 @
% 120.37/16.05 (setadjoin @ X2 @ (setadjoin @ X4 @ emptyset))) =>
% 120.37/16.05 (((((Y0) = (X4))) | (((Y0) = (X2))))))))))),
% 120.37/16.05 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl454])).
% 120.37/16.05 thf(zip_derived_cl466, plain,
% 120.37/16.05 (![X2 : $i, X4 : $i, X6 : $i]:
% 120.37/16.05 (((in @ X6 @ (setadjoin @ X2 @ (setadjoin @ X4 @ emptyset))) =>
% 120.37/16.05 (((((X6) = (X4))) | (((X6) = (X2)))))))),
% 120.37/16.05 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl461])).
% 120.37/16.05 thf(zip_derived_cl472, plain,
% 120.37/16.05 (![X2 : $i, X4 : $i, X6 : $i]:
% 120.37/16.05 (~ (in @ X6 @ (setadjoin @ X2 @ (setadjoin @ X4 @ emptyset)))
% 120.37/16.05 | (((((X6) = (X4))) | (((X6) = (X2))))))),
% 120.37/16.05 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl466])).
% 120.37/16.05 thf(zip_derived_cl479, plain,
% 120.37/16.05 (![X2 : $i, X4 : $i, X6 : $i]:
% 120.37/16.05 ( (((X6) = (X4)))
% 120.37/16.05 | (((X6) = (X2)))
% 120.37/16.05 | ~ (in @ X6 @ (setadjoin @ X2 @ (setadjoin @ X4 @ emptyset))))),
% 120.37/16.05 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl472])).
% 120.37/16.05 thf(zip_derived_cl485, plain,
% 120.37/16.05 (![X2 : $i, X4 : $i, X6 : $i]:
% 120.37/16.05 (((X6) = (X4))
% 120.37/16.05 | ((X6) = (X2))
% 120.37/16.05 | ~ (in @ X6 @ (setadjoin @ X2 @ (setadjoin @ X4 @ emptyset))))),
% 120.37/16.05 inference('simplify nested equalities', [status(thm)],
% 120.37/16.05 [zip_derived_cl479])).
% 120.37/16.05 thf(zip_derived_cl17206, plain, ($false),
% 120.37/16.05 inference('eprover', [status(thm)],
% 120.37/16.05 [zip_derived_cl945, zip_derived_cl959, zip_derived_cl949,
% 120.37/16.05 zip_derived_cl429, zip_derived_cl952, zip_derived_cl953,
% 120.37/16.05 zip_derived_cl440, zip_derived_cl485])).
% 120.37/16.05
% 120.37/16.05 % SZS output end Refutation
% 120.37/16.05
% 120.37/16.05
% 120.37/16.05 % Terminating...
% 121.35/16.26 % Runner terminated.
% 121.35/16.26 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------