TSTP Solution File: ITP396_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ITP001_1 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n026.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 04:12:00 EDT 2023
% Result : Theorem 51.92s 7.71s
% Output : Proof 102.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP001_1 : TPTP v8.1.2. Released v8.1.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Aug 27 11:45:34 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.61 ________ _____
% 0.20/0.61 ___ __ \_________(_)________________________________
% 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61
% 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61 (2023-06-19)
% 0.20/0.61
% 0.20/0.61 (c) Philipp Rümmer, 2009-2023
% 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61 Amanda Stjerna.
% 0.20/0.61 Free software under BSD-3-Clause.
% 0.20/0.61
% 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61
% 0.20/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.62 Running up to 7 provers in parallel.
% 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 14.83/2.73 Prover 1: Preprocessing ...
% 15.39/2.88 Prover 4: Preprocessing ...
% 15.39/2.89 Prover 6: Preprocessing ...
% 15.39/2.90 Prover 0: Preprocessing ...
% 15.39/2.91 Prover 2: Preprocessing ...
% 15.39/2.92 Prover 5: Preprocessing ...
% 16.86/2.98 Prover 3: Preprocessing ...
% 37.16/5.82 Prover 1: Warning: ignoring some quantifiers
% 39.60/6.03 Prover 6: Proving ...
% 39.60/6.03 Prover 3: Warning: ignoring some quantifiers
% 40.26/6.10 Prover 3: Constructing countermodel ...
% 40.26/6.10 Prover 1: Constructing countermodel ...
% 47.46/7.13 Prover 4: Warning: ignoring some quantifiers
% 49.63/7.39 Prover 5: Proving ...
% 50.45/7.53 Prover 4: Constructing countermodel ...
% 51.92/7.66 Prover 2: Proving ...
% 51.92/7.69 Prover 3: proved (7062ms)
% 51.92/7.69
% 51.92/7.71 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 51.92/7.71
% 51.92/7.71 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 51.92/7.72 Prover 6: stopped
% 51.92/7.72 Prover 5: stopped
% 51.92/7.78 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 51.92/7.78 Prover 2: stopped
% 51.92/7.79 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 51.92/7.79 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 58.07/8.65 Prover 0: Proving ...
% 58.07/8.65 Prover 0: stopped
% 59.01/8.66 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 62.02/9.09 Prover 7: Preprocessing ...
% 62.80/9.23 Prover 8: Preprocessing ...
% 62.80/9.31 Prover 10: Preprocessing ...
% 62.80/9.35 Prover 11: Preprocessing ...
% 65.39/9.53 Prover 13: Preprocessing ...
% 72.96/10.48 Prover 10: Warning: ignoring some quantifiers
% 73.88/10.62 Prover 10: Constructing countermodel ...
% 75.15/10.83 Prover 8: Warning: ignoring some quantifiers
% 75.15/10.84 Prover 7: Warning: ignoring some quantifiers
% 76.79/10.97 Prover 13: Warning: ignoring some quantifiers
% 77.16/11.03 Prover 7: Constructing countermodel ...
% 77.55/11.05 Prover 8: Constructing countermodel ...
% 78.45/11.18 Prover 13: Constructing countermodel ...
% 82.51/11.76 Prover 11: Warning: ignoring some quantifiers
% 84.88/12.04 Prover 11: Constructing countermodel ...
% 93.70/13.16 Prover 13: stopped
% 93.70/13.18 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 99.09/13.91 Prover 16: Preprocessing ...
% 99.98/14.00 Prover 1: Found proof (size 475)
% 99.98/14.00 Prover 1: proved (13370ms)
% 99.98/14.00 Prover 11: stopped
% 99.98/14.00 Prover 7: stopped
% 99.98/14.01 Prover 10: stopped
% 99.98/14.01 Prover 4: stopped
% 99.98/14.01 Prover 8: stopped
% 100.60/14.16 Prover 16: stopped
% 100.60/14.16
% 100.60/14.16 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 100.60/14.16
% 100.60/14.23 % SZS output start Proof for theBenchmark
% 100.60/14.26 Assumptions after simplification:
% 100.60/14.26 ---------------------------------
% 100.60/14.26
% 100.60/14.26 (axiom106)
% 100.60/14.28 ! [v0: C_ell2_c_ell2_cblinfun$] : ! [v1:
% 100.60/14.28 B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v2:
% 100.60/14.28 B_ell2_b_ell2_cblinfun_set$] : ! [v3:
% 100.60/14.28 C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$] : ! [v4:
% 100.60/14.28 B_ell2_b_ell2_cblinfun$] : ! [v5: C_ell2_c_ell2_cblinfun$] : (v5 = v0 | ~
% 100.60/14.28 (fun_app$c(v1, v4) = v5) | ~ (inv_into$(v2, v1) = v3) | ~ (fun_app$d(v3,
% 100.60/14.28 v0) = v4) | ~ B_ell2_b_ell2_cblinfun_set$(v2) | ~
% 100.60/14.28 B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$(v1) | ~
% 100.60/14.28 C_ell2_c_ell2_cblinfun$(v0) | ? [v6: C_ell2_c_ell2_cblinfun_set_bool_fun$]
% 100.60/14.28 : ? [v7: C_ell2_c_ell2_cblinfun_set$] : ? [v8: int] : ( ~ (v8 = 0) &
% 100.60/14.28 image$(v1, v2) = v7 & member$(v0) = v6 & fun_app$a(v6, v7) = v8 &
% 100.60/14.28 C_ell2_c_ell2_cblinfun_set$(v7) &
% 100.60/14.28 C_ell2_c_ell2_cblinfun_set_bool_fun$(v6)))
% 100.60/14.28
% 100.60/14.28 (axiom204)
% 100.60/14.28 A_ell2_a_ell2_cblinfun_set$(top$b) &
% 100.60/14.28 B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$(g$) &
% 100.60/14.28 A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$(f$) & ? [v0:
% 100.60/14.28 C_ell2_c_ell2_cblinfun_set$] : (image$a(f$, top$b) = v0 &
% 100.60/14.28 C_ell2_c_ell2_cblinfun_set$(v0) & ! [v1: B_ell2_b_ell2_cblinfun$] : ! [v2:
% 100.60/14.28 C_ell2_c_ell2_cblinfun$] : ( ~ (fun_app$c(g$, v1) = v2) | ~
% 100.60/14.28 B_ell2_b_ell2_cblinfun$(v1) | ? [v3:
% 100.60/14.28 C_ell2_c_ell2_cblinfun_set_bool_fun$] : (member$(v2) = v3 &
% 100.60/14.28 fun_app$a(v3, v0) = 0 & C_ell2_c_ell2_cblinfun_set_bool_fun$(v3))))
% 100.60/14.28
% 100.60/14.28 (axiom207)
% 100.60/14.29 A_ell2_a_ell2_cblinfun_set$(top$b) & ! [v0:
% 100.60/14.29 A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v1:
% 100.60/14.29 C_ell2_c_ell2_cblinfun$] : ! [v2: C_ell2_c_ell2_cblinfun_set_bool_fun$] :
% 100.60/14.29 ! [v3: C_ell2_c_ell2_cblinfun_set$] : ! [v4: any] : ( ~ (image$a(v0, top$b) =
% 100.60/14.29 v3) | ~ (member$(v1) = v2) | ~ (fun_app$a(v2, v3) = v4) | ~
% 100.60/14.29 C_ell2_c_ell2_cblinfun$(v1) | ~
% 100.60/14.29 A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$(v0) | ? [v5: int] : ( ~
% 100.60/14.29 (v5 = 0) & inj_on$a(v0, top$b) = v5) | (( ~ (v4 = 0) | ? [v5:
% 100.60/14.29 A_ell2_a_ell2_cblinfun$] : (fun_app$e(v0, v5) = v1 &
% 100.60/14.29 A_ell2_a_ell2_cblinfun$(v5) & ! [v6: A_ell2_a_ell2_cblinfun$] : (v6 =
% 100.60/14.29 v5 | ~ (fun_app$e(v0, v6) = v1) | ~ A_ell2_a_ell2_cblinfun$(v6))))
% 100.60/14.29 & (v4 = 0 | ! [v5: A_ell2_a_ell2_cblinfun$] : ( ~ (fun_app$e(v0, v5) =
% 100.60/14.29 v1) | ~ A_ell2_a_ell2_cblinfun$(v5) | ? [v6:
% 100.60/14.29 A_ell2_a_ell2_cblinfun$] : ( ~ (v6 = v5) & fun_app$e(v0, v6) = v1 &
% 100.60/14.29 A_ell2_a_ell2_cblinfun$(v6))))))
% 100.60/14.29
% 100.60/14.29 (axiom21)
% 100.60/14.29 clinear$(f$) = 0 & A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$(f$)
% 100.60/14.29
% 100.60/14.29 (axiom219)
% 100.60/14.29 A_ell2_a_ell2_cblinfun_set$(top$b) & ! [v0:
% 100.60/14.29 A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v1:
% 100.60/14.29 A_ell2_a_ell2_cblinfun$] : ! [v2: A_ell2_a_ell2_cblinfun_set$] : ! [v3:
% 100.60/14.29 C_ell2_c_ell2_cblinfun$] : ! [v4: C_ell2_c_ell2_cblinfun_set_bool_fun$] :
% 100.60/14.29 ! [v5: C_ell2_c_ell2_cblinfun_set$] : ! [v6: any] : ( ~ (image$a(v0, v2) =
% 100.60/14.29 v5) | ~ (fun_app$e(v0, v1) = v3) | ~ (member$(v3) = v4) | ~
% 100.60/14.29 (fun_app$a(v4, v5) = v6) | ~ A_ell2_a_ell2_cblinfun_set$(v2) | ~
% 100.60/14.29 A_ell2_a_ell2_cblinfun$(v1) | ~
% 100.60/14.29 A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$(v0) | ? [v7: any] : ?
% 100.60/14.29 [v8: any] : (inj_on$a(v0, top$b) = v7 & member$c(v1, v2) = v8 & ( ~ (v7 = 0)
% 100.60/14.29 | (( ~ (v8 = 0) | v6 = 0) & ( ~ (v6 = 0) | v8 = 0)))))
% 100.60/14.29
% 100.60/14.29 (axiom22)
% 100.60/14.29 clinear$a(g$) = 0 & B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$(g$)
% 100.60/14.29
% 100.60/14.29 (axiom230)
% 100.60/14.29 ! [v0: A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v1:
% 100.60/14.29 A_ell2_a_ell2_cblinfun$] : ! [v2: A_ell2_a_ell2_cblinfun$] : ! [v3:
% 100.60/14.29 C_ell2_c_ell2_cblinfun$] : ! [v4:
% 100.60/14.29 C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v5:
% 100.60/14.29 C_ell2_c_ell2_cblinfun$] : ! [v6: C_ell2_c_ell2_cblinfun$] : ( ~
% 100.60/14.29 (cblinfun_compose$a(v3) = v4) | ~ (fun_app$g(v4, v5) = v6) | ~
% 100.60/14.29 (fun_app$e(v0, v2) = v5) | ~ (fun_app$e(v0, v1) = v3) | ~
% 100.60/14.29 A_ell2_a_ell2_cblinfun$(v2) | ~ A_ell2_a_ell2_cblinfun$(v1) | ~
% 100.60/14.29 A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$(v0) | ? [v7: any] : ?
% 100.60/14.29 [v8: A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$] : ? [v9:
% 100.60/14.29 A_ell2_a_ell2_cblinfun$] : ? [v10: C_ell2_c_ell2_cblinfun$] :
% 100.60/14.29 (cblinfun_compose$(v1) = v8 & fun_app$f(v8, v2) = v9 & register$a(v0) = v7 &
% 100.60/14.29 fun_app$e(v0, v9) = v10 &
% 100.60/14.29 A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$(v8) &
% 100.60/14.29 C_ell2_c_ell2_cblinfun$(v10) & A_ell2_a_ell2_cblinfun$(v9) & ( ~ (v7 = 0)
% 100.60/14.29 | v10 = v6)))
% 100.60/14.29
% 100.60/14.29 (axiom232)
% 100.60/14.30 ! [v0: B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v1:
% 100.60/14.30 B_ell2_b_ell2_cblinfun$] : ! [v2: B_ell2_b_ell2_cblinfun$] : ! [v3:
% 100.60/14.30 C_ell2_c_ell2_cblinfun$] : ! [v4:
% 100.60/14.30 C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v5:
% 100.60/14.30 C_ell2_c_ell2_cblinfun$] : ! [v6: C_ell2_c_ell2_cblinfun$] : ( ~
% 100.60/14.30 (cblinfun_compose$a(v3) = v4) | ~ (fun_app$g(v4, v5) = v6) | ~
% 100.60/14.30 (fun_app$c(v0, v2) = v5) | ~ (fun_app$c(v0, v1) = v3) | ~
% 100.60/14.30 B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$(v0) | ~
% 100.60/14.30 B_ell2_b_ell2_cblinfun$(v2) | ~ B_ell2_b_ell2_cblinfun$(v1) | ? [v7: any]
% 100.60/14.30 : ? [v8: B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$] : ? [v9:
% 100.60/14.30 B_ell2_b_ell2_cblinfun$] : ? [v10: C_ell2_c_ell2_cblinfun$] :
% 100.60/14.30 (cblinfun_compose$b(v1) = v8 & fun_app$j(v8, v2) = v9 & fun_app$c(v0, v9) =
% 100.60/14.30 v10 & register$(v0) = v7 &
% 100.60/14.30 B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$(v8) &
% 100.60/14.30 C_ell2_c_ell2_cblinfun$(v10) & B_ell2_b_ell2_cblinfun$(v9) & ( ~ (v7 = 0)
% 100.60/14.30 | v10 = v6)))
% 100.60/14.30
% 100.60/14.30 (axiom236)
% 100.60/14.30 inj_on$a(f$, top$b) = 0 & A_ell2_a_ell2_cblinfun_set$(top$b) &
% 100.60/14.30 A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$(f$)
% 100.60/14.30
% 100.60/14.30 (axiom3)
% 100.60/14.30 B_ell2_b_ell2_cblinfun_set$(top$) &
% 100.60/14.30 B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$(g$) &
% 100.60/14.30 A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$(j$) &
% 100.60/14.30 A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$(f$) & ? [v0:
% 100.60/14.30 C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$] : (inv_into$(top$, g$) =
% 100.60/14.30 v0 & C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$(v0) & ! [v1:
% 100.60/14.30 A_ell2_a_ell2_cblinfun$] : ! [v2: B_ell2_b_ell2_cblinfun$] : ( ~
% 100.60/14.30 (fun_app$h(j$, v1) = v2) | ~ A_ell2_a_ell2_cblinfun$(v1) | ? [v3:
% 100.60/14.30 C_ell2_c_ell2_cblinfun$] : (fun_app$e(f$, v1) = v3 & fun_app$d(v0, v3) =
% 100.60/14.30 v2 & C_ell2_c_ell2_cblinfun$(v3) & B_ell2_b_ell2_cblinfun$(v2))))
% 100.60/14.30
% 100.60/14.30 (axiom4)
% 100.60/14.30 register$(g$) = 0 & B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$(g$)
% 100.60/14.30
% 100.60/14.30 (axiom41)
% 100.60/14.30 A_ell2_a_ell2_cblinfun_set$(top$b) & B_ell2_b_ell2_cblinfun_set$(top$) &
% 100.60/14.30 B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$(g$) &
% 100.60/14.30 A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$(f$) & ? [v0:
% 100.60/14.30 C_ell2_c_ell2_cblinfun_set$] : (image$a(f$, top$b) = v0 & image$(g$, top$) =
% 100.60/14.30 v0 & C_ell2_c_ell2_cblinfun_set$(v0))
% 100.60/14.30
% 100.60/14.30 (axiom5)
% 100.60/14.30 register$a(f$) = 0 & A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$(f$)
% 100.60/14.30
% 100.60/14.30 (axiom508)
% 100.60/14.30 cspan$b(top$) = top$ & B_ell2_b_ell2_cblinfun_set$(top$)
% 100.60/14.30
% 100.60/14.30 (axiom509)
% 100.60/14.30 cspan$a(top$b) = top$b & A_ell2_a_ell2_cblinfun_set$(top$b)
% 100.60/14.30
% 100.60/14.30 (axiom514)
% 100.60/14.30 csubspace$b(top$) = 0 & B_ell2_b_ell2_cblinfun_set$(top$)
% 100.60/14.30
% 100.60/14.30 (axiom515)
% 100.60/14.30 csubspace$a(top$b) = 0 & A_ell2_a_ell2_cblinfun_set$(top$b)
% 100.60/14.30
% 100.60/14.30 (axiom523)
% 100.60/14.30 ! [v0: A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v1:
% 100.60/14.30 A_ell2_a_ell2_cblinfun_set$] : ! [v2: A_ell2_a_ell2_cblinfun_set$] : !
% 100.60/14.30 [v3: C_ell2_c_ell2_cblinfun_set$] : ( ~ (cspan$a(v1) = v2) | ~ (image$a(v0,
% 100.60/14.30 v2) = v3) | ~ A_ell2_a_ell2_cblinfun_set$(v1) | ~
% 100.60/14.30 A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$(v0) | ? [v4: any] : ?
% 100.60/14.30 [v5: C_ell2_c_ell2_cblinfun_set$] : ? [v6: C_ell2_c_ell2_cblinfun_set$] :
% 100.60/14.30 (cspan$(v5) = v6 & image$a(v0, v1) = v5 & clinear$(v0) = v4 &
% 100.60/14.30 C_ell2_c_ell2_cblinfun_set$(v6) & C_ell2_c_ell2_cblinfun_set$(v5) & ( ~
% 100.60/14.30 (v4 = 0) | v6 = v3)))
% 100.60/14.30
% 100.60/14.30 (axiom524)
% 100.60/14.30 ! [v0: B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v1:
% 100.60/14.30 B_ell2_b_ell2_cblinfun_set$] : ! [v2: B_ell2_b_ell2_cblinfun_set$] : !
% 100.60/14.30 [v3: C_ell2_c_ell2_cblinfun_set$] : ( ~ (cspan$b(v1) = v2) | ~ (image$(v0,
% 100.60/14.30 v2) = v3) | ~ B_ell2_b_ell2_cblinfun_set$(v1) | ~
% 100.60/14.30 B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$(v0) | ? [v4: any] : ?
% 100.60/14.30 [v5: C_ell2_c_ell2_cblinfun_set$] : ? [v6: C_ell2_c_ell2_cblinfun_set$] :
% 100.60/14.30 (cspan$(v5) = v6 & clinear$a(v0) = v4 & image$(v0, v1) = v5 &
% 100.60/14.30 C_ell2_c_ell2_cblinfun_set$(v6) & C_ell2_c_ell2_cblinfun_set$(v5) & ( ~
% 100.60/14.30 (v4 = 0) | v6 = v3)))
% 100.60/14.30
% 100.60/14.30 (axiom525)
% 100.60/14.30 C_ell2_c_ell2_cblinfun_set_bool_fun$(csubspace$) & ! [v0:
% 100.60/14.30 A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v1:
% 100.60/14.30 A_ell2_a_ell2_cblinfun_set$] : ( ~ (csubspace$a(v1) = 0) | ~ (clinear$(v0)
% 100.60/14.30 = 0) | ~ A_ell2_a_ell2_cblinfun_set$(v1) | ~
% 100.60/14.30 A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$(v0) | ? [v2:
% 100.60/14.30 C_ell2_c_ell2_cblinfun_set$] : (image$a(v0, v1) = v2 &
% 100.60/14.30 fun_app$a(csubspace$, v2) = 0 & C_ell2_c_ell2_cblinfun_set$(v2)))
% 100.60/14.30
% 100.60/14.30 (axiom526)
% 100.60/14.30 C_ell2_c_ell2_cblinfun_set_bool_fun$(csubspace$) & ! [v0:
% 100.60/14.30 B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v1:
% 100.60/14.30 B_ell2_b_ell2_cblinfun_set$] : ( ~ (csubspace$b(v1) = 0) | ~ (clinear$a(v0)
% 100.60/14.30 = 0) | ~ B_ell2_b_ell2_cblinfun_set$(v1) | ~
% 100.60/14.30 B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$(v0) | ? [v2:
% 100.60/14.30 C_ell2_c_ell2_cblinfun_set$] : (image$(v0, v1) = v2 &
% 100.60/14.30 fun_app$a(csubspace$, v2) = 0 & C_ell2_c_ell2_cblinfun_set$(v2)))
% 100.60/14.30
% 100.60/14.30 (axiom543)
% 100.60/14.31 C_ell2_c_ell2_cblinfun_set$(top$a) & ! [v0:
% 100.60/14.31 A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v1:
% 100.60/14.31 A_ell2_a_ell2_cblinfun_set$] : ( ~ (csubspace$a(v1) = 0) | ~ (clinear$(v0)
% 100.60/14.31 = 0) | ~ A_ell2_a_ell2_cblinfun_set$(v1) | ~
% 100.60/14.31 A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$(v0) | ? [v2:
% 100.60/14.31 C_ell2_c_ell2_cblinfun_set$] : (image$a(v0, v1) = v2 &
% 100.60/14.31 C_ell2_c_ell2_cblinfun_set$(v2) & ? [v3:
% 100.60/14.31 C_ell2_c_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$] : ? [v4:
% 100.60/14.31 A_ell2_a_ell2_cblinfun_set$] : (clinear$b(v3) = 0 & less_eq$b(v4, v1) =
% 100.60/14.31 0 & image$s(v3, top$a) = v4 &
% 100.60/14.31 C_ell2_c_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$(v3) &
% 100.60/14.31 A_ell2_a_ell2_cblinfun_set$(v4) & ! [v5: C_ell2_c_ell2_cblinfun$] : !
% 100.60/14.31 [v6: C_ell2_c_ell2_cblinfun_set_bool_fun$] : ( ~ (member$(v5) = v6) | ~
% 100.60/14.31 (fun_app$a(v6, v2) = 0) | ~ C_ell2_c_ell2_cblinfun$(v5) | ? [v7:
% 100.60/14.31 A_ell2_a_ell2_cblinfun$] : (fun_app$i(v3, v5) = v7 & fun_app$e(v0,
% 100.60/14.31 v7) = v5 & A_ell2_a_ell2_cblinfun$(v7))))))
% 100.60/14.31
% 100.60/14.31 (axiom544)
% 100.60/14.31 C_ell2_c_ell2_cblinfun_set$(top$a) & ! [v0:
% 100.60/14.31 B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v1:
% 100.60/14.31 B_ell2_b_ell2_cblinfun_set$] : ( ~ (csubspace$b(v1) = 0) | ~ (clinear$a(v0)
% 100.60/14.31 = 0) | ~ B_ell2_b_ell2_cblinfun_set$(v1) | ~
% 100.60/14.31 B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$(v0) | ? [v2:
% 100.60/14.31 C_ell2_c_ell2_cblinfun_set$] : (image$(v0, v1) = v2 &
% 100.60/14.31 C_ell2_c_ell2_cblinfun_set$(v2) & ? [v3:
% 100.60/14.31 C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$] : ? [v4:
% 100.60/14.31 B_ell2_b_ell2_cblinfun_set$] : (clinear$c(v3) = 0 & less_eq$a(v4, v1) =
% 100.60/14.31 0 & image$r(v3, top$a) = v4 & B_ell2_b_ell2_cblinfun_set$(v4) &
% 100.60/14.31 C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$(v3) & ! [v5:
% 100.60/14.31 C_ell2_c_ell2_cblinfun$] : ! [v6:
% 100.60/14.31 C_ell2_c_ell2_cblinfun_set_bool_fun$] : ( ~ (member$(v5) = v6) | ~
% 100.60/14.31 (fun_app$a(v6, v2) = 0) | ~ C_ell2_c_ell2_cblinfun$(v5) | ? [v7:
% 100.60/14.31 B_ell2_b_ell2_cblinfun$] : (fun_app$c(v0, v7) = v5 & fun_app$d(v3,
% 100.60/14.31 v5) = v7 & B_ell2_b_ell2_cblinfun$(v7))))))
% 100.60/14.31
% 100.60/14.31 (axiom549)
% 100.60/14.31 C_ell2_c_ell2_cblinfun_set_bool_fun$(cdependent$) & ! [v0:
% 100.60/14.31 A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v1:
% 100.60/14.31 A_ell2_a_ell2_cblinfun_set$] : ! [v2: A_ell2_a_ell2_cblinfun_set$] : !
% 100.60/14.31 [v3: any] : ( ~ (cspan$a(v1) = v2) | ~ (inj_on$a(v0, v2) = v3) | ~
% 100.60/14.31 A_ell2_a_ell2_cblinfun_set$(v1) | ~
% 100.60/14.31 A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$(v0) | ? [v4: any] : ?
% 100.60/14.31 [v5: C_ell2_c_ell2_cblinfun_set$] : ? [v6: any] : ? [v7: any] :
% 100.60/14.31 (inj_on$a(v0, v1) = v7 & image$a(v0, v1) = v5 & clinear$(v0) = v4 &
% 100.60/14.31 fun_app$a(cdependent$, v5) = v6 & C_ell2_c_ell2_cblinfun_set$(v5) & ( ~
% 100.60/14.31 (v4 = 0) | v6 = 0 | (( ~ (v7 = 0) | v3 = 0) & ( ~ (v3 = 0) | v7 = 0)))))
% 100.60/14.31
% 100.60/14.31 (axiom550)
% 100.60/14.31 C_ell2_c_ell2_cblinfun_set_bool_fun$(cdependent$) & ! [v0:
% 100.60/14.31 B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v1:
% 100.60/14.31 B_ell2_b_ell2_cblinfun_set$] : ! [v2: B_ell2_b_ell2_cblinfun_set$] : !
% 100.60/14.31 [v3: any] : ( ~ (cspan$b(v1) = v2) | ~ (inj_on$(v0, v2) = v3) | ~
% 100.60/14.31 B_ell2_b_ell2_cblinfun_set$(v1) | ~
% 100.60/14.31 B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$(v0) | ? [v4: any] : ?
% 100.60/14.31 [v5: C_ell2_c_ell2_cblinfun_set$] : ? [v6: any] : ? [v7: any] :
% 100.60/14.31 (clinear$a(v0) = v4 & inj_on$(v0, v1) = v7 & image$(v0, v1) = v5 &
% 100.60/14.31 fun_app$a(cdependent$, v5) = v6 & C_ell2_c_ell2_cblinfun_set$(v5) & ( ~
% 100.60/14.31 (v4 = 0) | v6 = 0 | (( ~ (v7 = 0) | v3 = 0) & ( ~ (v3 = 0) | v7 = 0)))))
% 100.60/14.31
% 100.60/14.31 (axiom553)
% 100.60/14.31 C_ell2_c_ell2_cblinfun_set_bool_fun$(cdependent$) & ! [v0:
% 100.60/14.31 A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v1:
% 100.60/14.31 A_ell2_a_ell2_cblinfun_set$] : ! [v2: A_ell2_a_ell2_cblinfun_set$] : ( ~
% 100.60/14.31 (cspan$a(v1) = v2) | ~ (inj_on$a(v0, v2) = 0) | ~
% 100.60/14.31 A_ell2_a_ell2_cblinfun_set$(v1) | ~
% 100.60/14.31 A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$(v0) | ? [v3: any] : ?
% 100.60/14.31 [v4: any] : ? [v5: C_ell2_c_ell2_cblinfun_set$] : ? [v6: any] :
% 100.60/14.31 (cdependent$a(v1) = v4 & image$a(v0, v1) = v5 & clinear$(v0) = v3 &
% 100.60/14.31 fun_app$a(cdependent$, v5) = v6 & C_ell2_c_ell2_cblinfun_set$(v5) & ( ~
% 100.60/14.31 (v6 = 0) | ~ (v3 = 0) | v4 = 0)))
% 100.60/14.31
% 100.60/14.31 (axiom554)
% 100.60/14.32 C_ell2_c_ell2_cblinfun_set_bool_fun$(cdependent$) & ! [v0:
% 100.60/14.32 B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v1:
% 100.60/14.32 B_ell2_b_ell2_cblinfun_set$] : ! [v2: B_ell2_b_ell2_cblinfun_set$] : ( ~
% 100.60/14.32 (cspan$b(v1) = v2) | ~ (inj_on$(v0, v2) = 0) | ~
% 100.60/14.32 B_ell2_b_ell2_cblinfun_set$(v1) | ~
% 100.60/14.32 B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$(v0) | ? [v3: any] : ?
% 100.60/14.32 [v4: any] : ? [v5: C_ell2_c_ell2_cblinfun_set$] : ? [v6: any] :
% 100.60/14.32 (cdependent$b(v1) = v4 & clinear$a(v0) = v3 & image$(v0, v1) = v5 &
% 100.60/14.32 fun_app$a(cdependent$, v5) = v6 & C_ell2_c_ell2_cblinfun_set$(v5) & ( ~
% 100.60/14.32 (v6 = 0) | ~ (v3 = 0) | v4 = 0)))
% 100.60/14.32
% 100.60/14.32 (axiom561)
% 100.60/14.32 C_ell2_c_ell2_cblinfun_set_bool_fun$(cdependent$) & ! [v0:
% 100.60/14.32 A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v1:
% 100.60/14.32 A_ell2_a_ell2_cblinfun_set$] : ! [v2: A_ell2_a_ell2_cblinfun_set$] : ( ~
% 100.60/14.32 (cspan$a(v1) = v2) | ~ (inj_on$a(v0, v2) = 0) | ~
% 100.60/14.32 A_ell2_a_ell2_cblinfun_set$(v1) | ~
% 100.60/14.32 A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$(v0) | ? [v3: any] : ?
% 100.60/14.32 [v4: C_ell2_c_ell2_cblinfun_set$] : ? [v5: any] : ? [v6: any] :
% 100.60/14.32 (cdependent$a(v1) = v6 & image$a(v0, v1) = v4 & clinear$(v0) = v3 &
% 100.60/14.32 fun_app$a(cdependent$, v4) = v5 & C_ell2_c_ell2_cblinfun_set$(v4) & ( ~
% 100.60/14.32 (v5 = 0) | ~ (v3 = 0) | v6 = 0)))
% 100.60/14.32
% 100.60/14.32 (axiom562)
% 100.60/14.32 C_ell2_c_ell2_cblinfun_set_bool_fun$(cdependent$) & ! [v0:
% 100.60/14.32 B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v1:
% 100.60/14.32 B_ell2_b_ell2_cblinfun_set$] : ! [v2: B_ell2_b_ell2_cblinfun_set$] : ( ~
% 100.60/14.32 (cspan$b(v1) = v2) | ~ (inj_on$(v0, v2) = 0) | ~
% 100.60/14.32 B_ell2_b_ell2_cblinfun_set$(v1) | ~
% 100.60/14.32 B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$(v0) | ? [v3: any] : ?
% 100.60/14.32 [v4: C_ell2_c_ell2_cblinfun_set$] : ? [v5: any] : ? [v6: any] :
% 100.60/14.32 (cdependent$b(v1) = v6 & clinear$a(v0) = v3 & image$(v0, v1) = v4 &
% 100.60/14.32 fun_app$a(cdependent$, v4) = v5 & C_ell2_c_ell2_cblinfun_set$(v4) & ( ~
% 100.60/14.32 (v5 = 0) | ~ (v3 = 0) | v6 = 0)))
% 100.60/14.32
% 100.60/14.32 (axiom567)
% 100.60/14.32 ! [v0: B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v1:
% 100.60/14.32 B_ell2_b_ell2_cblinfun_set$] : ( ~ (inj_on$(v0, v1) = 0) | ~
% 100.60/14.32 B_ell2_b_ell2_cblinfun_set$(v1) | ~
% 100.60/14.32 B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$(v0) | ? [v2:
% 100.60/14.32 C_ell2_c_ell2_cblinfun_set$] : ? [v3: Nat$] : ? [v4: int] : ? [v5:
% 100.60/14.32 Nat$] : (card$(v2) = v3 & card$a(v1) = v5 & of_nat$(v5) = v4 & of_nat$(v3)
% 100.60/14.32 = v4 & image$(v0, v1) = v2 & C_ell2_c_ell2_cblinfun_set$(v2) & Nat$(v5) &
% 100.60/14.32 Nat$(v3)))
% 100.60/14.32
% 100.60/14.32 (axiom568)
% 100.60/14.32 ! [v0: A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v1:
% 100.60/14.32 A_ell2_a_ell2_cblinfun_set$] : ( ~ (inj_on$a(v0, v1) = 0) | ~
% 100.60/14.32 A_ell2_a_ell2_cblinfun_set$(v1) | ~
% 100.60/14.32 A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$(v0) | ? [v2:
% 100.60/14.32 C_ell2_c_ell2_cblinfun_set$] : ? [v3: Nat$] : ? [v4: int] : ? [v5:
% 100.60/14.32 Nat$] : (card$b(v1) = v5 & card$(v2) = v3 & of_nat$(v5) = v4 & of_nat$(v3)
% 100.60/14.32 = v4 & image$a(v0, v1) = v2 & C_ell2_c_ell2_cblinfun_set$(v2) & Nat$(v5) &
% 100.60/14.32 Nat$(v3)))
% 100.60/14.32
% 100.60/14.32 (axiom576)
% 100.60/14.32 Unit_ell2_set$(top$j) & Unit_set$(top$d) & ? [v0: Nat$] : ? [v1: int] : ?
% 100.60/14.32 [v2: Nat$] : (cdim$c(top$j) = v0 & card$c(top$d) = v2 & of_nat$(v2) = v1 &
% 100.60/14.32 of_nat$(v0) = v1 & Nat$(v2) & Nat$(v0))
% 100.60/14.32
% 100.60/14.32 (axiom577)
% 100.60/14.32 ! [v0: Nat$] : ! [v1: Unit_set$] : ! [v2: Nat$] : ! [v3: int] : ( ~
% 100.60/14.32 (card$c(v1) = v2) | ~ (of_nat$(v0) = v3) | ~ Nat$(v0) | ~ Unit_set$(v1) |
% 100.60/14.32 ? [v4: Unit_set$] : ? [v5: Nat$] : (card$c(v4) = v5 & of_nat$(v5) = v3 &
% 100.60/14.32 less_eq$d(v4, v1) = 0 & Nat$(v5) & Unit_set$(v4)) | ? [v4: int] :
% 100.60/14.32 ($lesseq(1, $difference(v3, v4)) & of_nat$(v2) = v4))
% 100.60/14.32
% 100.60/14.32 (axiom580)
% 101.30/14.32 Nat_set$(top$c) & Nat_nat_sum_set$(top$k) & ? [v0: any] : ? [v1: any] :
% 101.30/14.32 (finite$c(top$k) = v0 & finite$d(top$c) = v1 & ((v1 = 0 & v0 = 0) | ( ~ (v1 =
% 101.30/14.32 0) & ~ (v0 = 0))))
% 101.30/14.32
% 101.30/14.32 (axiom581)
% 101.30/14.32 Nat_set$(top$c) & Nat_unit_sum_set$(top$l) & Unit_set$(top$d) & ? [v0: any] :
% 101.30/14.32 ? [v1: any] : ? [v2: any] : (finite$e(top$l) = v0 & finite$f(top$d) = v2 &
% 101.30/14.32 finite$d(top$c) = v1 & ((v2 = 0 & v1 = 0 & v0 = 0) | ( ~ (v0 = 0) & ( ~ (v2
% 101.30/14.33 = 0) | ~ (v1 = 0)))))
% 101.30/14.33
% 101.30/14.33 (axiom582)
% 101.30/14.33 Nat_set$(top$c) & Unit_nat_sum_set$(top$m) & Unit_set$(top$d) & ? [v0: any] :
% 101.30/14.33 ? [v1: any] : ? [v2: any] : (finite$g(top$m) = v0 & finite$f(top$d) = v1 &
% 101.30/14.33 finite$d(top$c) = v2 & ((v2 = 0 & v1 = 0 & v0 = 0) | ( ~ (v0 = 0) & ( ~ (v2
% 101.30/14.33 = 0) | ~ (v1 = 0)))))
% 101.30/14.33
% 101.30/14.33 (axiom584)
% 101.30/14.33 Nat_set$(top$c) & B_ell2_b_ell2_cblinfun_nat_sum_set$(top$o) &
% 101.30/14.33 B_ell2_b_ell2_cblinfun_set$(top$) & ? [v0: any] : ? [v1: any] : ? [v2: any]
% 101.30/14.33 : (finite$i(top$o) = v0 & finite$d(top$c) = v2 & finite$b(top$) = v1 & ((v2 =
% 101.30/14.33 0 & v1 = 0 & v0 = 0) | ( ~ (v0 = 0) & ( ~ (v2 = 0) | ~ (v1 = 0)))))
% 101.30/14.33
% 101.30/14.33 (axiom585)
% 101.30/14.33 B_ell2_b_ell2_cblinfun_set$(top$) &
% 101.30/14.33 B_ell2_b_ell2_cblinfun_unit_sum_set$(top$p) & Unit_set$(top$d) & ? [v0: any]
% 101.30/14.33 : ? [v1: any] : ? [v2: any] : (finite$j(top$p) = v0 & finite$f(top$d) = v2 &
% 101.30/14.33 finite$b(top$) = v1 & ((v2 = 0 & v1 = 0 & v0 = 0) | ( ~ (v0 = 0) & ( ~ (v2 =
% 101.30/14.33 0) | ~ (v1 = 0)))))
% 101.30/14.33
% 101.30/14.33 (axiom586)
% 101.30/14.33 Nat_set$(top$c) & A_ell2_a_ell2_cblinfun_set$(top$b) &
% 101.30/14.33 A_ell2_a_ell2_cblinfun_nat_sum_set$(top$q) & ? [v0: any] : ? [v1: any] : ?
% 101.30/14.33 [v2: any] : (finite$k(top$q) = v0 & finite$d(top$c) = v2 & finite$(top$b) = v1
% 101.30/14.33 & ((v2 = 0 & v1 = 0 & v0 = 0) | ( ~ (v0 = 0) & ( ~ (v2 = 0) | ~ (v1 =
% 101.30/14.33 0)))))
% 101.30/14.33
% 101.30/14.33 (axiom588)
% 101.30/14.33 Nat_set$(top$c) & B_ell2_b_ell2_cblinfun_set$(top$) &
% 101.30/14.33 Nat_b_ell2_b_ell2_cblinfun_sum_set$(top$s) & ? [v0: any] : ? [v1: any] : ?
% 101.30/14.33 [v2: any] : (finite$m(top$s) = v0 & finite$d(top$c) = v1 & finite$b(top$) = v2
% 101.30/14.33 & ((v2 = 0 & v1 = 0 & v0 = 0) | ( ~ (v0 = 0) & ( ~ (v2 = 0) | ~ (v1 =
% 101.30/14.33 0)))))
% 101.30/14.33
% 101.30/14.33 (axiom589)
% 101.30/14.33 Nat_set$(top$c) & A_ell2_a_ell2_cblinfun_set$(top$b) &
% 101.30/14.33 Nat_a_ell2_a_ell2_cblinfun_sum_set$(top$t) & ? [v0: any] : ? [v1: any] : ?
% 101.30/14.33 [v2: any] : (finite$n(top$t) = v0 & finite$d(top$c) = v1 & finite$(top$b) = v2
% 101.30/14.33 & ((v2 = 0 & v1 = 0 & v0 = 0) | ( ~ (v0 = 0) & ( ~ (v2 = 0) | ~ (v1 =
% 101.30/14.33 0)))))
% 101.30/14.33
% 101.30/14.33 (axiom590)
% 101.30/14.33 C_ell2_c_ell2_cblinfun_set_bool_fun$(finite$a) & ! [v0:
% 101.30/14.33 B_ell2_b_ell2_cblinfun_set$] : ! [v1:
% 101.30/14.33 B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v2:
% 101.30/14.33 C_ell2_c_ell2_cblinfun_set$] : ( ~ (image$(v1, v0) = v2) | ~
% 101.30/14.33 B_ell2_b_ell2_cblinfun_set$(v0) | ~
% 101.30/14.33 B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$(v1) | ? [v3: any] : ?
% 101.30/14.33 [v4: any] : (finite$b(v0) = v3 & fun_app$a(finite$a, v2) = v4 & ( ~ (v3 = 0)
% 101.30/14.33 | v4 = 0)))
% 101.30/14.33
% 101.30/14.33 (axiom591)
% 101.30/14.33 C_ell2_c_ell2_cblinfun_set_bool_fun$(finite$a) & ! [v0:
% 101.30/14.33 A_ell2_a_ell2_cblinfun_set$] : ! [v1:
% 101.30/14.33 A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v2:
% 101.30/14.33 C_ell2_c_ell2_cblinfun_set$] : ( ~ (image$a(v1, v0) = v2) | ~
% 101.30/14.33 A_ell2_a_ell2_cblinfun_set$(v0) | ~
% 101.30/14.33 A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$(v1) | ? [v3: any] : ?
% 101.30/14.33 [v4: any] : (finite$(v0) = v3 & fun_app$a(finite$a, v2) = v4 & ( ~ (v3 = 0)
% 101.30/14.33 | v4 = 0)))
% 101.30/14.33
% 101.30/14.33 (axiom593)
% 101.30/14.34 C_ell2_c_ell2_cblinfun_set_bool_fun$(finite$a) & ! [v0:
% 101.30/14.34 B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v1:
% 101.30/14.34 B_ell2_b_ell2_cblinfun_set$] : ( ~ (inj_on$(v0, v1) = 0) | ~
% 101.30/14.34 B_ell2_b_ell2_cblinfun_set$(v1) | ~
% 101.30/14.34 B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$(v0) | ? [v2:
% 101.30/14.34 C_ell2_c_ell2_cblinfun_set$] : ? [v3: any] : ? [v4: any] : (finite$b(v1)
% 101.30/14.34 = v4 & image$(v0, v1) = v2 & fun_app$a(finite$a, v2) = v3 &
% 101.30/14.34 C_ell2_c_ell2_cblinfun_set$(v2) & ( ~ (v4 = 0) | v3 = 0) & ( ~ (v3 = 0) |
% 101.30/14.34 v4 = 0)))
% 101.30/14.34
% 101.30/14.34 (axiom594)
% 101.30/14.34 C_ell2_c_ell2_cblinfun_set_bool_fun$(finite$a) & ! [v0:
% 101.30/14.34 A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v1:
% 101.30/14.34 A_ell2_a_ell2_cblinfun_set$] : ( ~ (inj_on$a(v0, v1) = 0) | ~
% 101.30/14.34 A_ell2_a_ell2_cblinfun_set$(v1) | ~
% 101.30/14.34 A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$(v0) | ? [v2:
% 101.30/14.34 C_ell2_c_ell2_cblinfun_set$] : ? [v3: any] : ? [v4: any] : (finite$(v1)
% 101.30/14.34 = v4 & image$a(v0, v1) = v2 & fun_app$a(finite$a, v2) = v3 &
% 101.30/14.34 C_ell2_c_ell2_cblinfun_set$(v2) & ( ~ (v4 = 0) | v3 = 0) & ( ~ (v3 = 0) |
% 101.30/14.34 v4 = 0)))
% 101.30/14.34
% 101.30/14.34 (axiom596)
% 101.30/14.34 Nat_set$(top$c) & ? [v0: any] : (finite$d(top$c) = v0 & ! [v1: Nat_set$] :
% 101.30/14.34 ! [v2: Nat_set$] : ( ~ (uminus$c(v1) = v2) | ~ Nat_set$(v1) | ? [v3: any]
% 101.30/14.34 : ? [v4: any] : (finite$d(v2) = v4 & finite$d(v1) = v3 & ( ~ (v3 = 0) |
% 101.30/14.34 (( ~ (v4 = 0) | v0 = 0) & ( ~ (v0 = 0) | v4 = 0))))))
% 101.30/14.34
% 101.30/14.34 (axiom598)
% 101.30/14.34 Nat_set$(top$c) & ? [v0: int] : ( ~ (v0 = 0) & finite$d(top$c) = v0)
% 101.30/14.34
% 101.30/14.34 (axiom6)
% 101.30/14.34 B_ell2_b_ell2_cblinfun_set$(top$) &
% 101.30/14.34 B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$(g$) &
% 101.30/14.34 A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$(j$) &
% 101.30/14.34 A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$(f$) & ? [v0:
% 101.30/14.34 C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$] : (inv_into$(top$, g$) =
% 101.30/14.34 v0 & C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$(v0) & ! [v1:
% 101.30/14.34 A_ell2_a_ell2_cblinfun$] : ! [v2: B_ell2_b_ell2_cblinfun$] : ( ~
% 101.30/14.34 (fun_app$h(j$, v1) = v2) | ~ A_ell2_a_ell2_cblinfun$(v1) | ? [v3:
% 101.30/14.34 C_ell2_c_ell2_cblinfun$] : (fun_app$e(f$, v1) = v3 & fun_app$d(v0, v3) =
% 101.30/14.34 v2 & C_ell2_c_ell2_cblinfun$(v3) & B_ell2_b_ell2_cblinfun$(v2))))
% 101.30/14.34
% 101.30/14.34 (axiom623)
% 101.30/14.34 Unit_set$(top$d) & ? [v0: Nat$] : (card$c(top$d) = v0 & of_nat$(v0) = 1 &
% 101.30/14.34 Nat$(v0))
% 101.30/14.34
% 101.30/14.34 (axiom637)
% 101.30/14.34 ! [v0: Nat$] : ! [v1: int] : ( ~ (of_nat$(v0) = v1) | ~ Nat$(v0) | nat$(v1)
% 101.30/14.34 = v0)
% 101.30/14.34
% 101.30/14.34 (axiom7)
% 101.30/14.34 B_ell2_b_ell2_cblinfun_set$(top$) &
% 101.30/14.34 B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$(g$) &
% 101.30/14.34 A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$(f$) & ? [v0:
% 101.30/14.34 C_ell2_c_ell2_cblinfun_set$] : (image$(g$, top$) = v0 &
% 101.30/14.34 C_ell2_c_ell2_cblinfun_set$(v0) & ! [v1: A_ell2_a_ell2_cblinfun$] : ! [v2:
% 101.30/14.34 C_ell2_c_ell2_cblinfun$] : ( ~ (fun_app$e(f$, v1) = v2) | ~
% 101.30/14.34 A_ell2_a_ell2_cblinfun$(v1) | ? [v3:
% 101.30/14.34 C_ell2_c_ell2_cblinfun_set_bool_fun$] : (member$(v2) = v3 &
% 101.30/14.34 fun_app$a(v3, v0) = 0 & C_ell2_c_ell2_cblinfun_set_bool_fun$(v3))))
% 101.30/14.34
% 101.30/14.34 (axiom8)
% 101.30/14.34 inj_on$(g$, top$) = 0 & B_ell2_b_ell2_cblinfun_set$(top$) &
% 101.30/14.34 B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$(g$)
% 101.30/14.34
% 101.30/14.34 (conjecture2)
% 101.30/14.34 B_ell2_b_ell2_cblinfun_set$(top$) &
% 101.30/14.34 B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$(g$) &
% 101.30/14.34 A_ell2_a_ell2_cblinfun$(a$) & A_ell2_a_ell2_cblinfun$(b$) &
% 101.30/14.34 A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$(f$) & ? [v0:
% 101.30/14.34 C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$] : ? [v1:
% 101.30/14.34 A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$] : ? [v2:
% 101.30/14.34 A_ell2_a_ell2_cblinfun$] : ? [v3: C_ell2_c_ell2_cblinfun$] : ? [v4:
% 101.30/14.34 B_ell2_b_ell2_cblinfun$] : ? [v5: C_ell2_c_ell2_cblinfun$] : ? [v6:
% 101.30/14.34 C_ell2_c_ell2_cblinfun$] : ? [v7: B_ell2_b_ell2_cblinfun$] : ? [v8:
% 101.30/14.34 C_ell2_c_ell2_cblinfun$] : ? [v9:
% 101.30/14.34 C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ? [v10:
% 101.30/14.34 C_ell2_c_ell2_cblinfun$] : ? [v11: B_ell2_b_ell2_cblinfun$] : ? [v12:
% 101.30/14.34 C_ell2_c_ell2_cblinfun$] : ? [v13: C_ell2_c_ell2_cblinfun$] : ( ~ (v13 =
% 101.30/14.34 v5) & cblinfun_compose$a(v8) = v9 & fun_app$g(v9, v12) = v13 &
% 101.30/14.34 cblinfun_compose$(a$) = v1 & fun_app$f(v1, b$) = v2 & fun_app$c(g$, v11) =
% 101.30/14.34 v12 & fun_app$c(g$, v7) = v8 & fun_app$c(g$, v4) = v5 & inv_into$(top$, g$)
% 101.30/14.34 = v0 & fun_app$e(f$, v2) = v3 & fun_app$e(f$, a$) = v6 & fun_app$e(f$, b$) =
% 101.30/14.34 v10 & fun_app$d(v0, v10) = v11 & fun_app$d(v0, v6) = v7 & fun_app$d(v0, v3)
% 101.30/14.34 = v4 & C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$(v9) &
% 101.30/14.34 A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$(v1) &
% 101.30/14.34 C_ell2_c_ell2_cblinfun$(v13) & C_ell2_c_ell2_cblinfun$(v12) &
% 101.30/14.34 C_ell2_c_ell2_cblinfun$(v10) & C_ell2_c_ell2_cblinfun$(v8) &
% 101.30/14.34 C_ell2_c_ell2_cblinfun$(v6) & C_ell2_c_ell2_cblinfun$(v5) &
% 101.30/14.34 C_ell2_c_ell2_cblinfun$(v3) & B_ell2_b_ell2_cblinfun$(v11) &
% 101.30/14.34 B_ell2_b_ell2_cblinfun$(v7) & B_ell2_b_ell2_cblinfun$(v4) &
% 101.30/14.34 C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$(v0) &
% 101.30/14.34 A_ell2_a_ell2_cblinfun$(v2))
% 101.30/14.34
% 101.30/14.35 (function-axioms)
% 101.30/14.38 ! [v0: Unit$] : ! [v1: Unit$] : ! [v2: C_ell2_c_ell2_cblinfun$] : ! [v3:
% 101.30/14.38 Unit_c_ell2_c_ell2_cblinfun_fun$] : ! [v4: Unit_set$] : (v1 = v0 | ~
% 101.30/14.38 (inv_into$q(v4, v3, v2) = v1) | ~ (inv_into$q(v4, v3, v2) = v0)) & ! [v0:
% 101.30/14.38 Nat_bool_fun$] : ! [v1: Nat_bool_fun$] : ! [v2: Nat$] : ! [v3:
% 101.30/14.38 Nat_nat_bool_fun_fun$] : (v1 = v0 | ~ (fun_app$ag(v3, v2) = v1) | ~
% 101.30/14.38 (fun_app$ag(v3, v2) = v0)) & ! [v0:
% 101.30/14.38 A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v1:
% 101.30/14.38 A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v2:
% 101.30/14.38 A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v3:
% 101.30/14.38 A_ell2_a_ell2_cblinfun_set$] : (v1 = v0 | ~ (cconstruct$a(v3, v2) = v1) |
% 101.30/14.38 ~ (cconstruct$a(v3, v2) = v0)) & ! [v0:
% 101.30/14.38 B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v1:
% 101.30/14.38 B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v2:
% 101.30/14.38 B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v3:
% 101.30/14.38 B_ell2_b_ell2_cblinfun_set$] : (v1 = v0 | ~ (cconstruct$(v3, v2) = v1) | ~
% 101.30/14.38 (cconstruct$(v3, v2) = v0)) & ! [v0: B_ell2_b_ell2_cblinfun_set$] : ! [v1:
% 101.30/14.38 B_ell2_b_ell2_cblinfun_set$] : ! [v2: A_ell2_a_ell2_cblinfun_set$] : !
% 101.30/14.38 [v3: A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$] : (v1 = v0 | ~
% 101.30/14.38 (image$w(v3, v2) = v1) | ~ (image$w(v3, v2) = v0)) & ! [v0:
% 101.30/14.38 A_ell2_a_ell2_cblinfun_set$] : ! [v1: A_ell2_a_ell2_cblinfun_set$] : !
% 101.30/14.38 [v2: B_ell2_b_ell2_cblinfun_set$] : ! [v3:
% 101.30/14.38 B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$] : (v1 = v0 | ~
% 101.30/14.38 (image$v(v3, v2) = v1) | ~ (image$v(v3, v2) = v0)) & ! [v0:
% 101.30/14.38 A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v1:
% 101.30/14.38 A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v2:
% 101.30/14.38 C_ell2_c_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$] : ! [v3:
% 101.30/14.38 C_ell2_c_ell2_cblinfun_set$] : (v1 = v0 | ~ (the_inv_into$g(v3, v2) = v1) |
% 101.30/14.38 ~ (the_inv_into$g(v3, v2) = v0)) & ! [v0:
% 101.30/14.38 B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v1:
% 101.30/14.38 B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v2:
% 101.30/14.38 C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$] : ! [v3:
% 101.30/14.38 C_ell2_c_ell2_cblinfun_set$] : (v1 = v0 | ~ (the_inv_into$f(v3, v2) = v1) |
% 101.30/14.38 ~ (the_inv_into$f(v3, v2) = v0)) & ! [v0: Nat_nat_fun$] : ! [v1:
% 101.30/14.38 Nat_nat_fun$] : ! [v2: Nat_nat_fun$] : ! [v3: Nat_set$] : (v1 = v0 | ~
% 101.30/14.38 (the_inv_into$e(v3, v2) = v1) | ~ (the_inv_into$e(v3, v2) = v0)) & ! [v0:
% 101.30/14.38 Nat_c_ell2_c_ell2_cblinfun_fun$] : ! [v1: Nat_c_ell2_c_ell2_cblinfun_fun$]
% 101.30/14.38 : ! [v2: C_ell2_c_ell2_cblinfun_nat_fun$] : ! [v3:
% 101.30/14.38 C_ell2_c_ell2_cblinfun_set$] : (v1 = v0 | ~ (the_inv_into$d(v3, v2) = v1) |
% 101.30/14.38 ~ (the_inv_into$d(v3, v2) = v0)) & ! [v0: C_ell2_c_ell2_cblinfun_nat_fun$]
% 101.30/14.38 : ! [v1: C_ell2_c_ell2_cblinfun_nat_fun$] : ! [v2:
% 101.30/14.38 Nat_c_ell2_c_ell2_cblinfun_fun$] : ! [v3: Nat_set$] : (v1 = v0 | ~
% 101.30/14.38 (the_inv_into$c(v3, v2) = v1) | ~ (the_inv_into$c(v3, v2) = v0)) & ! [v0:
% 101.30/14.38 C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v1:
% 101.30/14.38 C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v2:
% 101.30/14.38 C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v3:
% 101.30/14.38 C_ell2_c_ell2_cblinfun_set$] : (v1 = v0 | ~ (the_inv_into$b(v3, v2) = v1) |
% 101.30/14.38 ~ (the_inv_into$b(v3, v2) = v0)) & ! [v0:
% 101.30/14.38 C_ell2_c_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$] : ! [v1:
% 101.30/14.38 C_ell2_c_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$] : ! [v2:
% 101.30/14.38 A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v3:
% 101.30/14.38 A_ell2_a_ell2_cblinfun_set$] : (v1 = v0 | ~ (the_inv_into$a(v3, v2) = v1) |
% 101.30/14.38 ~ (the_inv_into$a(v3, v2) = v0)) & ! [v0:
% 101.30/14.38 C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$] : ! [v1:
% 101.30/14.38 C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$] : ! [v2:
% 101.30/14.38 B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v3:
% 101.30/14.38 B_ell2_b_ell2_cblinfun_set$] : (v1 = v0 | ~ (the_inv_into$(v3, v2) = v1) |
% 101.30/14.38 ~ (the_inv_into$(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 101.30/14.38 MultipleValueBool] : ! [v2: Unit_set$] : ! [v3: Unit_set$] : (v1 = v0 | ~
% 101.30/14.38 (less_eq$d(v3, v2) = v1) | ~ (less_eq$d(v3, v2) = v0)) & ! [v0:
% 101.30/14.38 Int_bool_fun$] : ! [v1: Int_bool_fun$] : ! [v2: int] : ! [v3:
% 101.30/14.38 Int_int_bool_fun_fun$] : (v1 = v0 | ~ (fun_app$af(v3, v2) = v1) | ~
% 101.30/14.38 (fun_app$af(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 101.30/14.38 MultipleValueBool] : ! [v2: int] : ! [v3: Int_bool_fun$] : (v1 = v0 | ~
% 101.30/14.38 (fun_app$ae(v3, v2) = v1) | ~ (fun_app$ae(v3, v2) = v0)) & ! [v0: int] :
% 101.30/14.38 ! [v1: int] : ! [v2: int] : ! [v3: Int_int_fun$] : (v1 = v0 | ~
% 101.30/14.38 (fun_app$ad(v3, v2) = v1) | ~ (fun_app$ad(v3, v2) = v0)) & ! [v0:
% 101.30/14.38 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: Nat_set$] : !
% 101.30/14.38 [v3: Nat_set$] : (v1 = v0 | ~ (less_eq$c(v3, v2) = v1) | ~ (less_eq$c(v3,
% 101.30/14.38 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 101.30/14.38 ! [v2: A_ell2_a_ell2_cblinfun_set$] : ! [v3: A_ell2_a_ell2_cblinfun_set$] :
% 101.30/14.38 (v1 = v0 | ~ (less_eq$b(v3, v2) = v1) | ~ (less_eq$b(v3, v2) = v0)) & !
% 101.30/14.38 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 101.30/14.38 B_ell2_b_ell2_cblinfun_set$] : ! [v3: B_ell2_b_ell2_cblinfun_set$] : (v1 =
% 101.30/14.38 v0 | ~ (less_eq$a(v3, v2) = v1) | ~ (less_eq$a(v3, v2) = v0)) & ! [v0:
% 101.30/14.38 A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$] : ! [v1:
% 101.30/14.38 A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$] : ! [v2:
% 101.30/14.38 A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$] : ! [v3:
% 101.30/14.38 A_ell2_a_ell2_cblinfun_set$] : (v1 = v0 | ~ (inv_into$s(v3, v2) = v1) | ~
% 101.30/14.38 (inv_into$s(v3, v2) = v0)) & ! [v0:
% 101.30/14.38 B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$] : ! [v1:
% 101.30/14.38 B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$] : ! [v2:
% 101.30/14.38 B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$] : ! [v3:
% 101.30/14.38 B_ell2_b_ell2_cblinfun_set$] : (v1 = v0 | ~ (inv_into$r(v3, v2) = v1) | ~
% 101.30/14.38 (inv_into$r(v3, v2) = v0)) & ! [v0: A_ell2_a_ell2_cblinfun_set$] : ! [v1:
% 101.30/14.38 A_ell2_a_ell2_cblinfun_set$] : ! [v2: A_ell2_a_ell2_cblinfun_set$] : !
% 101.30/14.38 [v3: A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$] : (v1 = v0 | ~
% 101.30/14.38 (image$u(v3, v2) = v1) | ~ (image$u(v3, v2) = v0)) & ! [v0:
% 101.30/14.38 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 101.30/14.38 A_ell2_a_ell2_cblinfun_set$] : ! [v3:
% 101.30/14.38 A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$] : (v1 = v0 | ~
% 101.30/14.38 (inj_on$u(v3, v2) = v1) | ~ (inj_on$u(v3, v2) = v0)) & ! [v0:
% 101.30/14.38 B_ell2_b_ell2_cblinfun_set$] : ! [v1: B_ell2_b_ell2_cblinfun_set$] : !
% 101.30/14.38 [v2: B_ell2_b_ell2_cblinfun_set$] : ! [v3:
% 101.30/14.38 B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$] : (v1 = v0 | ~
% 101.30/14.38 (image$t(v3, v2) = v1) | ~ (image$t(v3, v2) = v0)) & ! [v0:
% 101.30/14.38 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 101.30/14.38 B_ell2_b_ell2_cblinfun_set$] : ! [v3:
% 101.30/14.38 B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$] : (v1 = v0 | ~
% 101.30/14.38 (inj_on$t(v3, v2) = v1) | ~ (inj_on$t(v3, v2) = v0)) & ! [v0: Unit$] : !
% 101.30/14.38 [v1: Unit$] : ! [v2: A_ell2_a_ell2_cblinfun$] : ! [v3:
% 101.30/14.38 A_ell2_a_ell2_cblinfun_unit_fun$] : (v1 = v0 | ~ (fun_app$ac(v3, v2) = v1)
% 101.30/14.38 | ~ (fun_app$ac(v3, v2) = v0)) & ! [v0: A_ell2_a_ell2_cblinfun$] : ! [v1:
% 101.30/14.38 A_ell2_a_ell2_cblinfun$] : ! [v2: Unit$] : ! [v3:
% 101.30/14.38 Unit_a_ell2_a_ell2_cblinfun_fun$] : (v1 = v0 | ~ (fun_app$ab(v3, v2) = v1)
% 101.30/14.38 | ~ (fun_app$ab(v3, v2) = v0)) & ! [v0: Unit$] : ! [v1: Unit$] : ! [v2:
% 101.30/14.38 B_ell2_b_ell2_cblinfun$] : ! [v3: B_ell2_b_ell2_cblinfun_unit_fun$] : (v1 =
% 101.30/14.38 v0 | ~ (fun_app$aa(v3, v2) = v1) | ~ (fun_app$aa(v3, v2) = v0)) & ! [v0:
% 101.30/14.38 B_ell2_b_ell2_cblinfun$] : ! [v1: B_ell2_b_ell2_cblinfun$] : ! [v2: Unit$]
% 101.30/14.38 : ! [v3: Unit_b_ell2_b_ell2_cblinfun_fun$] : (v1 = v0 | ~ (fun_app$z(v3, v2)
% 101.30/14.38 = v1) | ~ (fun_app$z(v3, v2) = v0)) & ! [v0: Unit$] : ! [v1: Unit$] :
% 101.30/14.38 ! [v2: Unit$] : ! [v3: Unit_unit_fun$] : (v1 = v0 | ~ (fun_app$y(v3, v2) =
% 101.30/14.38 v1) | ~ (fun_app$y(v3, v2) = v0)) & ! [v0: Unit$] : ! [v1: Unit$] : !
% 101.30/14.38 [v2: Nat$] : ! [v3: Nat_unit_fun$] : (v1 = v0 | ~ (fun_app$x(v3, v2) = v1) |
% 101.30/14.38 ~ (fun_app$x(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 101.30/14.38 MultipleValueBool] : ! [v2: Unit_set$] : ! [v3:
% 101.30/14.38 Unit_c_ell2_c_ell2_cblinfun_fun$] : (v1 = v0 | ~ (inj_on$q(v3, v2) = v1) |
% 101.30/14.38 ~ (inj_on$q(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 101.30/14.38 MultipleValueBool] : ! [v2: Unit$] : ! [v3: Unit_bool_fun$] : (v1 = v0 |
% 101.30/14.38 ~ (fun_app$w(v3, v2) = v1) | ~ (fun_app$w(v3, v2) = v0)) & ! [v0:
% 101.30/14.38 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: Nat_set$] : !
% 101.30/14.38 [v3: Nat_c_ell2_c_ell2_cblinfun_fun$] : (v1 = v0 | ~ (inj_on$p(v3, v2) = v1)
% 101.30/14.38 | ~ (inj_on$p(v3, v2) = v0)) & ! [v0: A_ell2_a_ell2_cblinfun$] : ! [v1:
% 101.30/14.38 A_ell2_a_ell2_cblinfun$] : ! [v2: Nat$] : ! [v3:
% 101.30/14.38 Nat_a_ell2_a_ell2_cblinfun_fun$] : (v1 = v0 | ~ (fun_app$v(v3, v2) = v1) |
% 101.30/14.38 ~ (fun_app$v(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 101.30/14.38 MultipleValueBool] : ! [v2: A_ell2_a_ell2_cblinfun$] : ! [v3:
% 101.30/14.38 A_ell2_a_ell2_cblinfun_bool_fun$] : (v1 = v0 | ~ (fun_app$u(v3, v2) = v1) |
% 101.30/14.38 ~ (fun_app$u(v3, v2) = v0)) & ! [v0: B_ell2_b_ell2_cblinfun$] : ! [v1:
% 101.30/14.38 B_ell2_b_ell2_cblinfun$] : ! [v2: Nat$] : ! [v3:
% 101.30/14.38 Nat_b_ell2_b_ell2_cblinfun_fun$] : (v1 = v0 | ~ (fun_app$t(v3, v2) = v1) |
% 101.30/14.38 ~ (fun_app$t(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 101.30/14.38 MultipleValueBool] : ! [v2: B_ell2_b_ell2_cblinfun$] : ! [v3:
% 101.30/14.38 B_ell2_b_ell2_cblinfun_bool_fun$] : (v1 = v0 | ~ (fun_app$s(v3, v2) = v1) |
% 101.30/14.38 ~ (fun_app$s(v3, v2) = v0)) & ! [v0:
% 101.30/14.38 A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v1:
% 101.30/14.38 A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v2:
% 101.30/14.38 C_ell2_c_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$] : ! [v3:
% 101.30/14.38 C_ell2_c_ell2_cblinfun_set$] : (v1 = v0 | ~ (inv_into$p(v3, v2) = v1) | ~
% 101.30/14.38 (inv_into$p(v3, v2) = v0)) & ! [v0: A_ell2_a_ell2_cblinfun_set$] : ! [v1:
% 101.30/14.38 A_ell2_a_ell2_cblinfun_set$] : ! [v2: C_ell2_c_ell2_cblinfun_set$] : !
% 101.30/14.38 [v3: C_ell2_c_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$] : (v1 = v0 | ~
% 101.30/14.38 (image$s(v3, v2) = v1) | ~ (image$s(v3, v2) = v0)) & ! [v0:
% 101.30/14.38 B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v1:
% 101.30/14.38 B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v2:
% 101.30/14.38 C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$] : ! [v3:
% 101.30/14.38 C_ell2_c_ell2_cblinfun_set$] : (v1 = v0 | ~ (inv_into$o(v3, v2) = v1) | ~
% 101.30/14.38 (inv_into$o(v3, v2) = v0)) & ! [v0: B_ell2_b_ell2_cblinfun_set$] : ! [v1:
% 101.30/14.38 B_ell2_b_ell2_cblinfun_set$] : ! [v2: C_ell2_c_ell2_cblinfun_set$] : !
% 101.30/14.38 [v3: C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$] : (v1 = v0 | ~
% 101.30/14.38 (image$r(v3, v2) = v1) | ~ (image$r(v3, v2) = v0)) & ! [v0:
% 101.30/14.38 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 101.30/14.38 A_ell2_a_ell2_cblinfun_set$] : ! [v3: A_ell2_a_ell2_cblinfun_unit_fun$] :
% 101.30/14.38 (v1 = v0 | ~ (inj_on$m(v3, v2) = v1) | ~ (inj_on$m(v3, v2) = v0)) & ! [v0:
% 101.30/14.38 A_ell2_a_ell2_cblinfun_set$] : ! [v1: A_ell2_a_ell2_cblinfun_set$] : !
% 101.30/14.38 [v2: Unit_set$] : ! [v3: Unit_a_ell2_a_ell2_cblinfun_fun$] : (v1 = v0 | ~
% 101.30/14.38 (image$q(v3, v2) = v1) | ~ (image$q(v3, v2) = v0)) & ! [v0:
% 101.30/14.38 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 101.30/14.38 B_ell2_b_ell2_cblinfun_set$] : ! [v3: B_ell2_b_ell2_cblinfun_unit_fun$] :
% 101.30/14.38 (v1 = v0 | ~ (inj_on$l(v3, v2) = v1) | ~ (inj_on$l(v3, v2) = v0)) & ! [v0:
% 101.30/14.38 B_ell2_b_ell2_cblinfun_set$] : ! [v1: B_ell2_b_ell2_cblinfun_set$] : !
% 101.30/14.38 [v2: Unit_set$] : ! [v3: Unit_b_ell2_b_ell2_cblinfun_fun$] : (v1 = v0 | ~
% 101.30/14.38 (image$p(v3, v2) = v1) | ~ (image$p(v3, v2) = v0)) & ! [v0:
% 101.30/14.38 A_ell2_a_ell2_cblinfun_nat_fun$] : ! [v1: A_ell2_a_ell2_cblinfun_nat_fun$]
% 101.30/14.38 : ! [v2: Nat_a_ell2_a_ell2_cblinfun_fun$] : ! [v3: Nat_set$] : (v1 = v0 | ~
% 101.30/14.38 (inv_into$n(v3, v2) = v1) | ~ (inv_into$n(v3, v2) = v0)) & ! [v0:
% 101.30/14.38 A_ell2_a_ell2_cblinfun_set$] : ! [v1: A_ell2_a_ell2_cblinfun_set$] : !
% 101.30/14.38 [v2: Nat_set$] : ! [v3: Nat_a_ell2_a_ell2_cblinfun_fun$] : (v1 = v0 | ~
% 101.30/14.38 (image$o(v3, v2) = v1) | ~ (image$o(v3, v2) = v0)) & ! [v0:
% 101.30/14.38 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 101.30/14.38 A_ell2_a_ell2_cblinfun_set$] : ! [v3: A_ell2_a_ell2_cblinfun_nat_fun$] :
% 101.30/14.38 (v1 = v0 | ~ (inj_on$k(v3, v2) = v1) | ~ (inj_on$k(v3, v2) = v0)) & ! [v0:
% 101.30/14.38 B_ell2_b_ell2_cblinfun_nat_fun$] : ! [v1: B_ell2_b_ell2_cblinfun_nat_fun$]
% 101.30/14.38 : ! [v2: Nat_b_ell2_b_ell2_cblinfun_fun$] : ! [v3: Nat_set$] : (v1 = v0 | ~
% 101.30/14.38 (inv_into$m(v3, v2) = v1) | ~ (inv_into$m(v3, v2) = v0)) & ! [v0:
% 101.30/14.38 B_ell2_b_ell2_cblinfun_set$] : ! [v1: B_ell2_b_ell2_cblinfun_set$] : !
% 101.30/14.38 [v2: Nat_set$] : ! [v3: Nat_b_ell2_b_ell2_cblinfun_fun$] : (v1 = v0 | ~
% 101.30/14.38 (image$n(v3, v2) = v1) | ~ (image$n(v3, v2) = v0)) & ! [v0:
% 101.30/14.38 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 101.30/14.38 B_ell2_b_ell2_cblinfun_set$] : ! [v3: B_ell2_b_ell2_cblinfun_nat_fun$] :
% 101.30/14.38 (v1 = v0 | ~ (inj_on$j(v3, v2) = v1) | ~ (inj_on$j(v3, v2) = v0)) & ! [v0:
% 101.30/14.38 Unit_a_ell2_a_ell2_cblinfun_fun$] : ! [v1:
% 101.30/14.38 Unit_a_ell2_a_ell2_cblinfun_fun$] : ! [v2:
% 101.30/14.38 A_ell2_a_ell2_cblinfun_unit_fun$] : ! [v3: A_ell2_a_ell2_cblinfun_set$] :
% 101.30/14.38 (v1 = v0 | ~ (inv_into$l(v3, v2) = v1) | ~ (inv_into$l(v3, v2) = v0)) & !
% 101.30/14.38 [v0: Unit_set$] : ! [v1: Unit_set$] : ! [v2: A_ell2_a_ell2_cblinfun_set$] :
% 101.30/14.38 ! [v3: A_ell2_a_ell2_cblinfun_unit_fun$] : (v1 = v0 | ~ (image$m(v3, v2) =
% 101.30/14.38 v1) | ~ (image$m(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 101.30/14.38 MultipleValueBool] : ! [v2: Unit_set$] : ! [v3:
% 101.30/14.38 Unit_a_ell2_a_ell2_cblinfun_fun$] : (v1 = v0 | ~ (inj_on$i(v3, v2) = v1) |
% 101.30/14.38 ~ (inj_on$i(v3, v2) = v0)) & ! [v0: Nat_a_ell2_a_ell2_cblinfun_fun$] : !
% 101.30/14.38 [v1: Nat_a_ell2_a_ell2_cblinfun_fun$] : ! [v2:
% 101.30/14.38 A_ell2_a_ell2_cblinfun_nat_fun$] : ! [v3: A_ell2_a_ell2_cblinfun_set$] :
% 101.30/14.38 (v1 = v0 | ~ (inv_into$k(v3, v2) = v1) | ~ (inv_into$k(v3, v2) = v0)) & !
% 101.30/14.38 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: Nat_set$] : !
% 101.30/14.38 [v3: Nat_a_ell2_a_ell2_cblinfun_fun$] : (v1 = v0 | ~ (inj_on$h(v3, v2) = v1)
% 101.30/14.38 | ~ (inj_on$h(v3, v2) = v0)) & ! [v0: Unit_b_ell2_b_ell2_cblinfun_fun$] :
% 101.30/14.38 ! [v1: Unit_b_ell2_b_ell2_cblinfun_fun$] : ! [v2:
% 101.30/14.38 B_ell2_b_ell2_cblinfun_unit_fun$] : ! [v3: B_ell2_b_ell2_cblinfun_set$] :
% 101.30/14.38 (v1 = v0 | ~ (inv_into$j(v3, v2) = v1) | ~ (inv_into$j(v3, v2) = v0)) & !
% 101.30/14.38 [v0: Unit_set$] : ! [v1: Unit_set$] : ! [v2: B_ell2_b_ell2_cblinfun_set$] :
% 101.30/14.38 ! [v3: B_ell2_b_ell2_cblinfun_unit_fun$] : (v1 = v0 | ~ (image$l(v3, v2) =
% 101.30/14.38 v1) | ~ (image$l(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 101.30/14.38 MultipleValueBool] : ! [v2: Unit_set$] : ! [v3:
% 101.30/14.38 Unit_b_ell2_b_ell2_cblinfun_fun$] : (v1 = v0 | ~ (inj_on$g(v3, v2) = v1) |
% 101.30/14.38 ~ (inj_on$g(v3, v2) = v0)) & ! [v0: Nat_b_ell2_b_ell2_cblinfun_fun$] : !
% 101.30/14.38 [v1: Nat_b_ell2_b_ell2_cblinfun_fun$] : ! [v2:
% 101.30/14.38 B_ell2_b_ell2_cblinfun_nat_fun$] : ! [v3: B_ell2_b_ell2_cblinfun_set$] :
% 101.30/14.38 (v1 = v0 | ~ (inv_into$i(v3, v2) = v1) | ~ (inv_into$i(v3, v2) = v0)) & !
% 101.30/14.38 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: Nat_set$] : !
% 101.30/14.38 [v3: Nat_b_ell2_b_ell2_cblinfun_fun$] : (v1 = v0 | ~ (inj_on$f(v3, v2) = v1)
% 101.30/14.38 | ~ (inj_on$f(v3, v2) = v0)) & ! [v0: Unit_set$] : ! [v1: Unit_set$] : !
% 101.30/14.38 [v2: Unit_set$] : ! [v3: Unit_unit_fun$] : (v1 = v0 | ~ (image$k(v3, v2) =
% 101.30/14.38 v1) | ~ (image$k(v3, v2) = v0)) & ! [v0: Unit_unit_fun$] : ! [v1:
% 101.30/14.38 Unit_unit_fun$] : ! [v2: Unit_unit_fun$] : ! [v3: Unit_set$] : (v1 = v0 |
% 101.30/14.38 ~ (inv_into$h(v3, v2) = v1) | ~ (inv_into$h(v3, v2) = v0)) & ! [v0:
% 101.30/14.38 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: Unit_set$] : !
% 101.30/14.38 [v3: Unit_unit_fun$] : (v1 = v0 | ~ (inj_on$e(v3, v2) = v1) | ~
% 101.30/14.38 (inj_on$e(v3, v2) = v0)) & ! [v0: Nat_unit_fun$] : ! [v1: Nat_unit_fun$] :
% 101.30/14.38 ! [v2: Unit_nat_fun$] : ! [v3: Unit_set$] : (v1 = v0 | ~ (inv_into$g(v3,
% 101.30/14.38 v2) = v1) | ~ (inv_into$g(v3, v2) = v0)) & ! [v0: MultipleValueBool] :
% 101.30/14.38 ! [v1: MultipleValueBool] : ! [v2: Nat_set$] : ! [v3: Nat_unit_fun$] : (v1
% 101.30/14.38 = v0 | ~ (inj_on$d(v3, v2) = v1) | ~ (inj_on$d(v3, v2) = v0)) & ! [v0:
% 101.30/14.38 Unit_nat_fun$] : ! [v1: Unit_nat_fun$] : ! [v2: Nat_unit_fun$] : ! [v3:
% 101.30/14.38 Nat_set$] : (v1 = v0 | ~ (inv_into$f(v3, v2) = v1) | ~ (inv_into$f(v3, v2)
% 101.30/14.38 = v0)) & ! [v0: Unit_set$] : ! [v1: Unit_set$] : ! [v2: Nat_set$] : !
% 101.30/14.38 [v3: Nat_unit_fun$] : (v1 = v0 | ~ (image$j(v3, v2) = v1) | ~ (image$j(v3,
% 101.30/14.38 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 101.30/14.38 ! [v2: Unit_set$] : ! [v3: Unit_nat_fun$] : (v1 = v0 | ~ (inj_on$c(v3, v2) =
% 101.30/14.38 v1) | ~ (inj_on$c(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 101.30/14.38 MultipleValueBool] : ! [v2: Nat_set$] : ! [v3: Nat_nat_fun$] : (v1 = v0 |
% 101.30/14.38 ~ (inj_on$b(v3, v2) = v1) | ~ (inj_on$b(v3, v2) = v0)) & ! [v0:
% 101.30/14.38 Nat_nat_fun$] : ! [v1: Nat_nat_fun$] : ! [v2: Nat_nat_fun$] : ! [v3:
% 101.30/14.38 Nat_set$] : (v1 = v0 | ~ (inv_into$e(v3, v2) = v1) | ~ (inv_into$e(v3, v2)
% 101.30/14.38 = v0)) & ! [v0: Nat_c_ell2_c_ell2_cblinfun_fun$] : ! [v1:
% 101.30/14.38 Nat_c_ell2_c_ell2_cblinfun_fun$] : ! [v2: C_ell2_c_ell2_cblinfun_nat_fun$]
% 101.30/14.38 : ! [v3: C_ell2_c_ell2_cblinfun_set$] : (v1 = v0 | ~ (inv_into$d(v3, v2) =
% 101.30/14.38 v1) | ~ (inv_into$d(v3, v2) = v0)) & ! [v0:
% 101.30/14.38 C_ell2_c_ell2_cblinfun_nat_fun$] : ! [v1: C_ell2_c_ell2_cblinfun_nat_fun$]
% 101.30/14.38 : ! [v2: Nat_c_ell2_c_ell2_cblinfun_fun$] : ! [v3: Nat_set$] : (v1 = v0 | ~
% 101.30/14.38 (inv_into$c(v3, v2) = v1) | ~ (inv_into$c(v3, v2) = v0)) & ! [v0:
% 101.30/14.38 C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v1:
% 101.30/14.38 C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v2:
% 101.30/14.38 C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v3:
% 101.30/14.38 C_ell2_c_ell2_cblinfun_set$] : (v1 = v0 | ~ (inv_into$b(v3, v2) = v1) | ~
% 101.30/14.38 (inv_into$b(v3, v2) = v0)) & ! [v0: Nat$] : ! [v1: Nat$] : ! [v2: Unit$]
% 101.30/14.38 : ! [v3: Unit_nat_fun$] : (v1 = v0 | ~ (fun_app$r(v3, v2) = v1) | ~
% 101.30/14.38 (fun_app$r(v3, v2) = v0)) & ! [v0: Nat_set$] : ! [v1: Nat_set$] : ! [v2:
% 101.30/14.38 Unit_set$] : ! [v3: Unit_nat_fun$] : (v1 = v0 | ~ (image$i(v3, v2) = v1) |
% 101.30/14.38 ~ (image$i(v3, v2) = v0)) & ! [v0: C_ell2_c_ell2_cblinfun$] : ! [v1:
% 101.30/14.38 C_ell2_c_ell2_cblinfun$] : ! [v2: Unit$] : ! [v3:
% 101.30/14.38 Unit_c_ell2_c_ell2_cblinfun_fun$] : (v1 = v0 | ~ (fun_app$q(v3, v2) = v1) |
% 101.30/14.38 ~ (fun_app$q(v3, v2) = v0)) & ! [v0: C_ell2_c_ell2_cblinfun_set$] : !
% 101.30/14.38 [v1: C_ell2_c_ell2_cblinfun_set$] : ! [v2: Unit_set$] : ! [v3:
% 101.30/14.38 Unit_c_ell2_c_ell2_cblinfun_fun$] : (v1 = v0 | ~ (image$h(v3, v2) = v1) |
% 101.30/14.38 ~ (image$h(v3, v2) = v0)) & ! [v0: Nat$] : ! [v1: Nat$] : ! [v2:
% 101.30/14.38 A_ell2_a_ell2_cblinfun$] : ! [v3: A_ell2_a_ell2_cblinfun_nat_fun$] : (v1 =
% 101.30/14.38 v0 | ~ (fun_app$p(v3, v2) = v1) | ~ (fun_app$p(v3, v2) = v0)) & ! [v0:
% 101.30/14.38 Nat_set$] : ! [v1: Nat_set$] : ! [v2: A_ell2_a_ell2_cblinfun_set$] : !
% 101.30/14.38 [v3: A_ell2_a_ell2_cblinfun_nat_fun$] : (v1 = v0 | ~ (image$g(v3, v2) = v1) |
% 101.30/14.38 ~ (image$g(v3, v2) = v0)) & ! [v0: Nat$] : ! [v1: Nat$] : ! [v2:
% 101.30/14.38 B_ell2_b_ell2_cblinfun$] : ! [v3: B_ell2_b_ell2_cblinfun_nat_fun$] : (v1 =
% 101.30/14.38 v0 | ~ (fun_app$o(v3, v2) = v1) | ~ (fun_app$o(v3, v2) = v0)) & ! [v0:
% 101.30/14.38 Nat_set$] : ! [v1: Nat_set$] : ! [v2: B_ell2_b_ell2_cblinfun_set$] : !
% 101.30/14.38 [v3: B_ell2_b_ell2_cblinfun_nat_fun$] : (v1 = v0 | ~ (image$f(v3, v2) = v1) |
% 101.30/14.38 ~ (image$f(v3, v2) = v0)) & ! [v0: A_ell2_a_ell2_cblinfun$] : ! [v1:
% 101.30/14.38 A_ell2_a_ell2_cblinfun$] : ! [v2: B_ell2_b_ell2_cblinfun$] : ! [v3:
% 101.30/14.38 B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$] : (v1 = v0 | ~
% 101.30/14.38 (fun_app$n(v3, v2) = v1) | ~ (fun_app$n(v3, v2) = v0)) & ! [v0:
% 101.30/14.38 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 101.30/14.38 A_ell2_a_ell2_cblinfun_set$] : ! [v3:
% 101.30/14.38 A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : (v1 = v0 | ~
% 101.30/14.38 (inj_on$a(v3, v2) = v1) | ~ (inj_on$a(v3, v2) = v0)) & ! [v0: Nat$] : !
% 101.30/14.38 [v1: Nat$] : ! [v2: Nat$] : ! [v3: Nat_nat_fun$] : (v1 = v0 | ~
% 101.30/14.38 (fun_app$m(v3, v2) = v1) | ~ (fun_app$m(v3, v2) = v0)) & ! [v0: Nat_set$]
% 101.30/14.38 : ! [v1: Nat_set$] : ! [v2: Nat_set$] : ! [v3: Nat_nat_fun$] : (v1 = v0 |
% 101.30/14.38 ~ (image$e(v3, v2) = v1) | ~ (image$e(v3, v2) = v0)) & ! [v0:
% 101.30/14.38 C_ell2_c_ell2_cblinfun$] : ! [v1: C_ell2_c_ell2_cblinfun$] : ! [v2: Nat$]
% 101.30/14.38 : ! [v3: Nat_c_ell2_c_ell2_cblinfun_fun$] : (v1 = v0 | ~ (fun_app$l(v3, v2)
% 101.30/14.38 = v1) | ~ (fun_app$l(v3, v2) = v0)) & ! [v0:
% 101.30/14.38 C_ell2_c_ell2_cblinfun_set$] : ! [v1: C_ell2_c_ell2_cblinfun_set$] : !
% 101.30/14.38 [v2: Nat_set$] : ! [v3: Nat_c_ell2_c_ell2_cblinfun_fun$] : (v1 = v0 | ~
% 101.30/14.38 (image$d(v3, v2) = v1) | ~ (image$d(v3, v2) = v0)) & ! [v0: Nat_set$] : !
% 101.30/14.38 [v1: Nat_set$] : ! [v2: C_ell2_c_ell2_cblinfun_set$] : ! [v3:
% 101.30/14.38 C_ell2_c_ell2_cblinfun_nat_fun$] : (v1 = v0 | ~ (image$c(v3, v2) = v1) | ~
% 101.30/14.38 (image$c(v3, v2) = v0)) & ! [v0: Nat$] : ! [v1: Nat$] : ! [v2:
% 101.30/14.38 C_ell2_c_ell2_cblinfun$] : ! [v3: C_ell2_c_ell2_cblinfun_nat_fun$] : (v1 =
% 101.30/14.38 v0 | ~ (fun_app$k(v3, v2) = v1) | ~ (fun_app$k(v3, v2) = v0)) & ! [v0:
% 101.30/14.38 C_ell2_c_ell2_cblinfun_set$] : ! [v1: C_ell2_c_ell2_cblinfun_set$] : !
% 101.30/14.38 [v2: C_ell2_c_ell2_cblinfun_set$] : ! [v3:
% 101.30/14.38 C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : (v1 = v0 | ~
% 101.30/14.38 (image$b(v3, v2) = v1) | ~ (image$b(v3, v2) = v0)) & ! [v0:
% 101.30/14.38 C_ell2_c_ell2_cblinfun_set$] : ! [v1: C_ell2_c_ell2_cblinfun_set$] : !
% 101.30/14.38 [v2: A_ell2_a_ell2_cblinfun_set$] : ! [v3:
% 101.30/14.38 A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : (v1 = v0 | ~
% 101.30/14.38 (image$a(v3, v2) = v1) | ~ (image$a(v3, v2) = v0)) & ! [v0:
% 101.30/14.38 B_ell2_b_ell2_cblinfun$] : ! [v1: B_ell2_b_ell2_cblinfun$] : ! [v2:
% 101.30/14.38 B_ell2_b_ell2_cblinfun$] : ! [v3:
% 101.30/14.38 B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$] : (v1 = v0 | ~
% 101.30/14.38 (fun_app$j(v3, v2) = v1) | ~ (fun_app$j(v3, v2) = v0)) & ! [v0:
% 101.30/14.38 C_ell2_c_ell2_cblinfun$] : ! [v1: C_ell2_c_ell2_cblinfun$] : ! [v2:
% 101.30/14.38 C_ell2_c_ell2_cblinfun$] : ! [v3:
% 101.30/14.38 C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : (v1 = v0 | ~
% 101.30/14.38 (fun_app$g(v3, v2) = v1) | ~ (fun_app$g(v3, v2) = v0)) & ! [v0:
% 101.30/14.38 A_ell2_a_ell2_cblinfun$] : ! [v1: A_ell2_a_ell2_cblinfun$] : ! [v2:
% 101.30/14.38 A_ell2_a_ell2_cblinfun$] : ! [v3:
% 101.30/14.38 A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$] : (v1 = v0 | ~
% 101.30/14.38 (fun_app$f(v3, v2) = v1) | ~ (fun_app$f(v3, v2) = v0)) & ! [v0:
% 101.30/14.38 C_ell2_c_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$] : ! [v1:
% 101.30/14.38 C_ell2_c_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$] : ! [v2:
% 101.30/14.38 A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v3:
% 101.30/14.39 A_ell2_a_ell2_cblinfun_set$] : (v1 = v0 | ~ (inv_into$a(v3, v2) = v1) | ~
% 101.30/14.39 (inv_into$a(v3, v2) = v0)) & ! [v0: A_ell2_a_ell2_cblinfun$] : ! [v1:
% 101.30/14.39 A_ell2_a_ell2_cblinfun$] : ! [v2: C_ell2_c_ell2_cblinfun$] : ! [v3:
% 101.30/14.39 C_ell2_c_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$] : (v1 = v0 | ~
% 101.30/14.39 (fun_app$i(v3, v2) = v1) | ~ (fun_app$i(v3, v2) = v0)) & ! [v0:
% 101.30/14.39 C_ell2_c_ell2_cblinfun$] : ! [v1: C_ell2_c_ell2_cblinfun$] : ! [v2:
% 101.30/14.39 B_ell2_b_ell2_cblinfun$] : ! [v3:
% 101.30/14.39 B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : (v1 = v0 | ~
% 101.30/14.39 (fun_app$c(v3, v2) = v1) | ~ (fun_app$c(v3, v2) = v0)) & ! [v0:
% 101.30/14.39 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: Unit_set$] : !
% 101.30/14.39 [v3: Unit$] : (v1 = v0 | ~ (member$d(v3, v2) = v1) | ~ (member$d(v3, v2) =
% 101.30/14.39 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 101.30/14.39 A_ell2_a_ell2_cblinfun_set$] : ! [v3: A_ell2_a_ell2_cblinfun$] : (v1 = v0 |
% 101.30/14.39 ~ (member$c(v3, v2) = v1) | ~ (member$c(v3, v2) = v0)) & ! [v0:
% 101.30/14.39 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 101.30/14.39 B_ell2_b_ell2_cblinfun_set$] : ! [v3: B_ell2_b_ell2_cblinfun$] : (v1 = v0 |
% 101.30/14.39 ~ (member$b(v3, v2) = v1) | ~ (member$b(v3, v2) = v0)) & ! [v0:
% 101.30/14.39 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 101.30/14.39 B_ell2_b_ell2_cblinfun_set$] : ! [v3:
% 101.30/14.39 B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : (v1 = v0 | ~
% 101.30/14.39 (inj_on$(v3, v2) = v1) | ~ (inj_on$(v3, v2) = v0)) & ! [v0:
% 101.30/14.39 C_ell2_c_ell2_cblinfun_set$] : ! [v1: C_ell2_c_ell2_cblinfun_set$] : !
% 101.30/14.39 [v2: B_ell2_b_ell2_cblinfun_set$] : ! [v3:
% 101.30/14.39 B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : (v1 = v0 | ~
% 101.30/14.39 (image$(v3, v2) = v1) | ~ (image$(v3, v2) = v0)) & ! [v0:
% 101.30/14.39 C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$] : ! [v1:
% 101.30/14.39 C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$] : ! [v2:
% 101.30/14.39 B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v3:
% 101.30/14.39 B_ell2_b_ell2_cblinfun_set$] : (v1 = v0 | ~ (inv_into$(v3, v2) = v1) | ~
% 101.30/14.39 (inv_into$(v3, v2) = v0)) & ! [v0: B_ell2_b_ell2_cblinfun$] : ! [v1:
% 101.30/14.39 B_ell2_b_ell2_cblinfun$] : ! [v2: A_ell2_a_ell2_cblinfun$] : ! [v3:
% 101.30/14.39 A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$] : (v1 = v0 | ~
% 101.30/14.39 (fun_app$h(v3, v2) = v1) | ~ (fun_app$h(v3, v2) = v0)) & ! [v0:
% 101.30/14.39 C_ell2_c_ell2_cblinfun$] : ! [v1: C_ell2_c_ell2_cblinfun$] : ! [v2:
% 101.30/14.39 A_ell2_a_ell2_cblinfun$] : ! [v3:
% 101.30/14.39 A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : (v1 = v0 | ~
% 101.30/14.39 (fun_app$e(v3, v2) = v1) | ~ (fun_app$e(v3, v2) = v0)) & ! [v0:
% 101.30/14.39 B_ell2_b_ell2_cblinfun$] : ! [v1: B_ell2_b_ell2_cblinfun$] : ! [v2:
% 101.30/14.39 C_ell2_c_ell2_cblinfun$] : ! [v3:
% 101.30/14.39 C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$] : (v1 = v0 | ~
% 101.30/14.39 (fun_app$d(v3, v2) = v1) | ~ (fun_app$d(v3, v2) = v0)) & ! [v0:
% 101.30/14.39 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: Nat$] : ! [v3:
% 101.30/14.39 Nat_bool_fun$] : (v1 = v0 | ~ (fun_app$b(v3, v2) = v1) | ~ (fun_app$b(v3,
% 101.30/14.39 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 101.30/14.39 ! [v2: Nat_set$] : ! [v3: Nat$] : (v1 = v0 | ~ (member$a(v3, v2) = v1) | ~
% 101.30/14.39 (member$a(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 101.30/14.39 MultipleValueBool] : ! [v2: C_ell2_c_ell2_cblinfun$] : ! [v3:
% 101.30/14.39 C_ell2_c_ell2_cblinfun_bool_fun$] : (v1 = v0 | ~ (fun_app$(v3, v2) = v1) |
% 101.30/14.39 ~ (fun_app$(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 101.30/14.39 MultipleValueBool] : ! [v2: C_ell2_c_ell2_cblinfun_set$] : ! [v3:
% 101.30/14.39 C_ell2_c_ell2_cblinfun_set_bool_fun$] : (v1 = v0 | ~ (fun_app$a(v3, v2) =
% 101.30/14.39 v1) | ~ (fun_app$a(v3, v2) = v0)) & ! [v0: Nat$] : ! [v1: Nat$] : !
% 101.30/14.39 [v2: int] : (v1 = v0 | ~ (nat$(v2) = v1) | ~ (nat$(v2) = v0)) & ! [v0:
% 101.30/14.39 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 101.30/14.39 Nat_a_ell2_a_ell2_cblinfun_sum_set$] : (v1 = v0 | ~ (finite$n(v2) = v1) |
% 101.30/14.39 ~ (finite$n(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 101.30/14.39 MultipleValueBool] : ! [v2: Nat_b_ell2_b_ell2_cblinfun_sum_set$] : (v1 = v0
% 101.30/14.39 | ~ (finite$m(v2) = v1) | ~ (finite$m(v2) = v0)) & ! [v0:
% 101.30/14.39 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 101.30/14.39 A_ell2_a_ell2_cblinfun_unit_sum_set$] : (v1 = v0 | ~ (finite$l(v2) = v1) |
% 101.30/14.39 ~ (finite$l(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 101.30/14.39 MultipleValueBool] : ! [v2: A_ell2_a_ell2_cblinfun_nat_sum_set$] : (v1 = v0
% 101.30/14.39 | ~ (finite$k(v2) = v1) | ~ (finite$k(v2) = v0)) & ! [v0:
% 101.30/14.39 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 101.30/14.39 B_ell2_b_ell2_cblinfun_unit_sum_set$] : (v1 = v0 | ~ (finite$j(v2) = v1) |
% 101.30/14.39 ~ (finite$j(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 101.30/14.39 MultipleValueBool] : ! [v2: B_ell2_b_ell2_cblinfun_nat_sum_set$] : (v1 = v0
% 101.30/14.39 | ~ (finite$i(v2) = v1) | ~ (finite$i(v2) = v0)) & ! [v0:
% 101.30/14.39 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 101.30/14.39 Unit_unit_sum_set$] : (v1 = v0 | ~ (finite$h(v2) = v1) | ~ (finite$h(v2) =
% 101.30/14.39 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 101.30/14.39 Unit_nat_sum_set$] : (v1 = v0 | ~ (finite$g(v2) = v1) | ~ (finite$g(v2) =
% 101.30/14.39 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 101.30/14.39 Nat_unit_sum_set$] : (v1 = v0 | ~ (finite$e(v2) = v1) | ~ (finite$e(v2) =
% 101.30/14.39 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 101.30/14.39 Unit_set$] : (v1 = v0 | ~ (finite$f(v2) = v1) | ~ (finite$f(v2) = v0)) &
% 101.30/14.39 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 101.30/14.39 Nat_nat_sum_set$] : (v1 = v0 | ~ (finite$c(v2) = v1) | ~ (finite$c(v2) =
% 101.30/14.39 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 101.30/14.39 Nat_set$] : (v1 = v0 | ~ (finite$d(v2) = v1) | ~ (finite$d(v2) = v0)) & !
% 101.30/14.39 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 101.30/14.39 B_ell2_b_ell2_cblinfun_set$] : (v1 = v0 | ~ (finite$b(v2) = v1) | ~
% 101.30/14.39 (finite$b(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 101.30/14.39 MultipleValueBool] : ! [v2: A_ell2_a_ell2_cblinfun_set$] : (v1 = v0 | ~
% 101.30/14.39 (finite$(v2) = v1) | ~ (finite$(v2) = v0)) & ! [v0: Nat$] : ! [v1: Nat$]
% 101.30/14.39 : ! [v2: Unit_ell2_set$] : (v1 = v0 | ~ (cdim$c(v2) = v1) | ~ (cdim$c(v2) =
% 101.30/14.39 v0)) & ! [v0: Nat$] : ! [v1: Nat$] : ! [v2: Unit_set$] : (v1 = v0 | ~
% 101.30/14.39 (card$c(v2) = v1) | ~ (card$c(v2) = v0)) & ! [v0: Nat$] : ! [v1: Nat$] :
% 101.30/14.39 ! [v2: A_ell2_a_ell2_cblinfun_set$] : (v1 = v0 | ~ (card$b(v2) = v1) | ~
% 101.30/14.39 (card$b(v2) = v0)) & ! [v0: Nat$] : ! [v1: Nat$] : ! [v2:
% 101.30/14.39 C_ell2_c_ell2_cblinfun_set$] : (v1 = v0 | ~ (card$(v2) = v1) | ~
% 101.30/14.39 (card$(v2) = v0)) & ! [v0: Nat$] : ! [v1: Nat$] : ! [v2:
% 101.30/14.39 B_ell2_b_ell2_cblinfun_set$] : (v1 = v0 | ~ (card$a(v2) = v1) | ~
% 101.30/14.39 (card$a(v2) = v0)) & ! [v0: A_ell2_a_ell2_cblinfun_set$] : ! [v1:
% 101.30/14.39 A_ell2_a_ell2_cblinfun_set$] : ! [v2: A_ell2_a_ell2_cblinfun_set$] : (v1 =
% 101.30/14.39 v0 | ~ (cextend_basis$a(v2) = v1) | ~ (cextend_basis$a(v2) = v0)) & !
% 101.30/14.39 [v0: B_ell2_b_ell2_cblinfun_set$] : ! [v1: B_ell2_b_ell2_cblinfun_set$] : !
% 101.30/14.39 [v2: B_ell2_b_ell2_cblinfun_set$] : (v1 = v0 | ~ (cextend_basis$(v2) = v1) |
% 101.30/14.39 ~ (cextend_basis$(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 101.30/14.39 MultipleValueBool] : ! [v2: B_ell2_b_ell2_cblinfun_set$] : (v1 = v0 | ~
% 101.30/14.39 (cdependent$b(v2) = v1) | ~ (cdependent$b(v2) = v0)) & ! [v0:
% 101.30/14.39 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 101.30/14.39 A_ell2_a_ell2_cblinfun_set$] : (v1 = v0 | ~ (cdependent$a(v2) = v1) | ~
% 101.30/14.39 (cdependent$a(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 101.30/14.39 MultipleValueBool] : ! [v2:
% 101.30/14.39 A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$] : (v1 = v0 | ~
% 101.30/14.39 (clinear$g(v2) = v1) | ~ (clinear$g(v2) = v0)) & ! [v0: MultipleValueBool]
% 101.30/14.39 : ! [v1: MultipleValueBool] : ! [v2:
% 101.30/14.39 A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$] : (v1 = v0 | ~
% 101.30/14.39 (clinear$f(v2) = v1) | ~ (clinear$f(v2) = v0)) & ! [v0: MultipleValueBool]
% 101.30/14.39 : ! [v1: MultipleValueBool] : ! [v2:
% 101.30/14.39 B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$] : (v1 = v0 | ~
% 101.30/14.39 (clinear$e(v2) = v1) | ~ (clinear$e(v2) = v0)) & ! [v0: MultipleValueBool]
% 101.30/14.39 : ! [v1: MultipleValueBool] : ! [v2:
% 101.30/14.39 B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$] : (v1 = v0 | ~
% 101.30/14.39 (clinear$d(v2) = v1) | ~ (clinear$d(v2) = v0)) & ! [v0: Nat$] : ! [v1:
% 101.30/14.39 Nat$] : ! [v2: B_ell2_b_ell2_cblinfun_set$] : (v1 = v0 | ~ (cdim$b(v2) =
% 101.30/14.39 v1) | ~ (cdim$b(v2) = v0)) & ! [v0: Nat$] : ! [v1: Nat$] : ! [v2:
% 101.30/14.39 C_ell2_c_ell2_cblinfun_set$] : (v1 = v0 | ~ (cdim$a(v2) = v1) | ~
% 101.30/14.39 (cdim$a(v2) = v0)) & ! [v0: Nat$] : ! [v1: Nat$] : ! [v2:
% 101.30/14.39 A_ell2_a_ell2_cblinfun_set$] : (v1 = v0 | ~ (cdim$(v2) = v1) | ~
% 101.30/14.39 (cdim$(v2) = v0)) & ! [v0: int] : ! [v1: int] : ! [v2: Nat$] : (v1 = v0 |
% 101.30/14.39 ~ (of_nat$(v2) = v1) | ~ (of_nat$(v2) = v0)) & ! [v0:
% 101.30/14.39 B_ell2_b_ell2_cblinfun_set$] : ! [v1: B_ell2_b_ell2_cblinfun_set$] : !
% 101.30/14.39 [v2: B_ell2_b_ell2_cblinfun_set$] : (v1 = v0 | ~ (cspan$b(v2) = v1) | ~
% 101.30/14.39 (cspan$b(v2) = v0)) & ! [v0: A_ell2_a_ell2_cblinfun_set$] : ! [v1:
% 101.30/14.39 A_ell2_a_ell2_cblinfun_set$] : ! [v2: A_ell2_a_ell2_cblinfun_set$] : (v1 =
% 101.30/14.39 v0 | ~ (cspan$a(v2) = v1) | ~ (cspan$a(v2) = v0)) & ! [v0:
% 101.30/14.39 C_ell2_c_ell2_cblinfun_set$] : ! [v1: C_ell2_c_ell2_cblinfun_set$] : !
% 101.30/14.39 [v2: C_ell2_c_ell2_cblinfun_set$] : (v1 = v0 | ~ (cspan$(v2) = v1) | ~
% 101.30/14.39 (cspan$(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool]
% 101.30/14.39 : ! [v2: B_ell2_b_ell2_cblinfun_set$] : (v1 = v0 | ~ (csubspace$b(v2) = v1)
% 101.30/14.39 | ~ (csubspace$b(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 101.30/14.39 MultipleValueBool] : ! [v2: A_ell2_a_ell2_cblinfun_set$] : (v1 = v0 | ~
% 101.30/14.39 (csubspace$a(v2) = v1) | ~ (csubspace$a(v2) = v0)) & ! [v0:
% 101.30/14.39 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 101.30/14.39 C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$] : (v1 = v0 | ~
% 101.30/14.39 (clinear$c(v2) = v1) | ~ (clinear$c(v2) = v0)) & ! [v0: MultipleValueBool]
% 101.30/14.39 : ! [v1: MultipleValueBool] : ! [v2:
% 101.30/14.39 C_ell2_c_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$] : (v1 = v0 | ~
% 101.30/14.39 (clinear$b(v2) = v1) | ~ (clinear$b(v2) = v0)) & ! [v0: Unit_set$] : !
% 101.30/14.39 [v1: Unit_set$] : ! [v2: Unit_set$] : (v1 = v0 | ~ (uminus$d(v2) = v1) | ~
% 101.30/14.39 (uminus$d(v2) = v0)) & ! [v0: Nat_set$] : ! [v1: Nat_set$] : ! [v2:
% 101.30/14.39 Nat_set$] : (v1 = v0 | ~ (uminus$c(v2) = v1) | ~ (uminus$c(v2) = v0)) & !
% 101.30/14.39 [v0: A_ell2_a_ell2_cblinfun_set$] : ! [v1: A_ell2_a_ell2_cblinfun_set$] : !
% 101.30/14.39 [v2: A_ell2_a_ell2_cblinfun_set$] : (v1 = v0 | ~ (uminus$b(v2) = v1) | ~
% 101.30/14.39 (uminus$b(v2) = v0)) & ! [v0: B_ell2_b_ell2_cblinfun_set$] : ! [v1:
% 101.30/14.39 B_ell2_b_ell2_cblinfun_set$] : ! [v2: B_ell2_b_ell2_cblinfun_set$] : (v1 =
% 101.30/14.39 v0 | ~ (uminus$(v2) = v1) | ~ (uminus$(v2) = v0)) & ! [v0:
% 101.30/14.39 C_ell2_c_ell2_cblinfun_set$] : ! [v1: C_ell2_c_ell2_cblinfun_set$] : !
% 101.30/14.39 [v2: C_ell2_c_ell2_cblinfun_set$] : (v1 = v0 | ~ (uminus$a(v2) = v1) | ~
% 101.30/14.39 (uminus$a(v2) = v0)) & ! [v0: C_ell2_c_ell2_cblinfun_set_bool_fun$] : !
% 101.30/14.39 [v1: C_ell2_c_ell2_cblinfun_set_bool_fun$] : ! [v2:
% 101.30/14.39 C_ell2_c_ell2_cblinfun_set$] : (v1 = v0 | ~ (less_eq$(v2) = v1) | ~
% 101.30/14.39 (less_eq$(v2) = v0)) & ! [v0:
% 101.30/14.39 B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v1:
% 101.30/14.39 B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v2:
% 101.30/14.39 B_ell2_c_ell2_cblinfun$] : (v1 = v0 | ~ (sandwich$a(v2) = v1) | ~
% 101.30/14.39 (sandwich$a(v2) = v0)) & ! [v0:
% 101.30/14.39 A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v1:
% 101.30/14.39 A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v2:
% 101.30/14.39 A_ell2_c_ell2_cblinfun$] : (v1 = v0 | ~ (sandwich$(v2) = v1) | ~
% 101.30/14.39 (sandwich$(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 101.30/14.39 MultipleValueBool] : ! [v2: Unit_unit_fun$] : (v1 = v0 | ~
% 101.30/14.39 (bijection$c(v2) = v1) | ~ (bijection$c(v2) = v0)) & ! [v0:
% 101.30/14.39 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: Nat_nat_fun$] :
% 101.30/14.39 (v1 = v0 | ~ (bijection$b(v2) = v1) | ~ (bijection$b(v2) = v0)) & ! [v0:
% 101.30/14.39 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 101.30/14.39 A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$] : (v1 = v0 | ~
% 101.30/14.39 (bijection$a(v2) = v1) | ~ (bijection$a(v2) = v0)) & ! [v0:
% 101.30/14.39 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 101.30/14.39 B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$] : (v1 = v0 | ~
% 101.30/14.39 (bijection$(v2) = v1) | ~ (bijection$(v2) = v0)) & ! [v0:
% 101.30/14.39 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 101.30/14.39 B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$] : (v1 = v0 | ~
% 101.30/14.39 (register$h(v2) = v1) | ~ (register$h(v2) = v0)) & ! [v0:
% 101.30/14.39 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 101.30/14.39 C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$] : (v1 = v0 | ~
% 101.30/14.39 (register$g(v2) = v1) | ~ (register$g(v2) = v0)) & ! [v0:
% 101.30/14.39 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 101.30/14.39 A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$] : (v1 = v0 | ~
% 101.30/14.39 (register$f(v2) = v1) | ~ (register$f(v2) = v0)) & ! [v0:
% 101.30/14.39 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 101.30/14.39 C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : (v1 = v0 | ~
% 101.30/14.39 (register$e(v2) = v1) | ~ (register$e(v2) = v0)) & ! [v0:
% 101.30/14.39 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 101.30/14.39 B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$] : (v1 = v0 | ~
% 101.30/14.39 (register$d(v2) = v1) | ~ (register$d(v2) = v0)) & ! [v0:
% 101.30/14.39 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 101.30/14.39 C_ell2_c_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$] : (v1 = v0 | ~
% 101.30/14.39 (register$c(v2) = v1) | ~ (register$c(v2) = v0)) & ! [v0:
% 101.30/14.39 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 101.30/14.39 A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$] : (v1 = v0 | ~
% 101.30/14.39 (register$b(v2) = v1) | ~ (register$b(v2) = v0)) & ! [v0:
% 101.30/14.39 C_ell2_c_ell2_cblinfun_set_bool_fun$] : ! [v1:
% 101.30/14.39 C_ell2_c_ell2_cblinfun_set_bool_fun$] : ! [v2:
% 101.30/14.39 C_ell2_c_ell2_cblinfun_nat_fun$] : (v1 = v0 | ~ (inj_on$s(v2) = v1) | ~
% 101.30/14.39 (inj_on$s(v2) = v0)) & ! [v0: C_ell2_c_ell2_cblinfun_set_bool_fun$] : !
% 101.30/14.39 [v1: C_ell2_c_ell2_cblinfun_set_bool_fun$] : ! [v2:
% 101.30/14.39 C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : (v1 = v0 | ~
% 101.30/14.39 (inj_on$r(v2) = v1) | ~ (inj_on$r(v2) = v0)) & ! [v0:
% 101.30/14.39 C_ell2_c_ell2_cblinfun_set$] : ! [v1: C_ell2_c_ell2_cblinfun_set$] : !
% 101.30/14.39 [v2: C_ell2_c_ell2_cblinfun_bool_fun$] : (v1 = v0 | ~ (collect$d(v2) = v1) |
% 101.30/14.39 ~ (collect$d(v2) = v0)) & ! [v0: C_ell2_c_ell2_cblinfun_set_bool_fun$] : !
% 101.30/14.39 [v1: C_ell2_c_ell2_cblinfun_set_bool_fun$] : ! [v2:
% 101.30/14.39 C_ell2_c_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$] : (v1 = v0 | ~
% 101.30/14.39 (inj_on$o(v2) = v1) | ~ (inj_on$o(v2) = v0)) & ! [v0:
% 101.30/14.39 C_ell2_c_ell2_cblinfun_set_bool_fun$] : ! [v1:
% 101.30/14.39 C_ell2_c_ell2_cblinfun_set_bool_fun$] : ! [v2:
% 101.30/14.39 C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$] : (v1 = v0 | ~
% 101.30/14.39 (inj_on$n(v2) = v1) | ~ (inj_on$n(v2) = v0)) & ! [v0: Unit_set$] : ! [v1:
% 101.30/14.39 Unit_set$] : ! [v2: Unit_bool_fun$] : (v1 = v0 | ~ (collect$c(v2) = v1) |
% 101.30/14.39 ~ (collect$c(v2) = v0)) & ! [v0: Nat_set$] : ! [v1: Nat_set$] : ! [v2:
% 101.30/14.39 Nat_bool_fun$] : (v1 = v0 | ~ (collect$b(v2) = v1) | ~ (collect$b(v2) =
% 101.30/14.39 v0)) & ! [v0: A_ell2_a_ell2_cblinfun_set$] : ! [v1:
% 101.30/14.39 A_ell2_a_ell2_cblinfun_set$] : ! [v2: A_ell2_a_ell2_cblinfun_bool_fun$] :
% 101.30/14.39 (v1 = v0 | ~ (collect$a(v2) = v1) | ~ (collect$a(v2) = v0)) & ! [v0:
% 101.30/14.39 B_ell2_b_ell2_cblinfun_set$] : ! [v1: B_ell2_b_ell2_cblinfun_set$] : !
% 101.30/14.39 [v2: B_ell2_b_ell2_cblinfun_bool_fun$] : (v1 = v0 | ~ (collect$(v2) = v1) |
% 101.30/14.39 ~ (collect$(v2) = v0)) & ! [v0:
% 101.30/14.39 B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$] : ! [v1:
% 101.30/14.39 B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$] : ! [v2:
% 101.30/14.39 B_ell2_b_ell2_cblinfun$] : (v1 = v0 | ~ (cblinfun_compose$b(v2) = v1) | ~
% 101.30/14.39 (cblinfun_compose$b(v2) = v0)) & ! [v0:
% 101.30/14.39 C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v1:
% 101.30/14.39 C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v2:
% 101.30/14.39 C_ell2_c_ell2_cblinfun$] : (v1 = v0 | ~ (cblinfun_compose$a(v2) = v1) | ~
% 101.30/14.39 (cblinfun_compose$a(v2) = v0)) & ! [v0:
% 101.30/14.39 A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$] : ! [v1:
% 101.30/14.39 A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$] : ! [v2:
% 101.30/14.39 A_ell2_a_ell2_cblinfun$] : (v1 = v0 | ~ (cblinfun_compose$(v2) = v1) | ~
% 101.30/14.39 (cblinfun_compose$(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 101.30/14.39 MultipleValueBool] : ! [v2:
% 101.30/14.39 B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : (v1 = v0 | ~
% 101.30/14.39 (clinear$a(v2) = v1) | ~ (clinear$a(v2) = v0)) & ! [v0: MultipleValueBool]
% 101.30/14.39 : ! [v1: MultipleValueBool] : ! [v2:
% 101.30/14.39 A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : (v1 = v0 | ~
% 101.30/14.39 (clinear$(v2) = v1) | ~ (clinear$(v2) = v0)) & ! [v0: MultipleValueBool] :
% 101.30/14.39 ! [v1: MultipleValueBool] : ! [v2:
% 101.30/14.39 A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : (v1 = v0 | ~
% 101.30/14.39 (register$a(v2) = v1) | ~ (register$a(v2) = v0)) & ! [v0:
% 101.30/14.39 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 101.30/14.39 B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : (v1 = v0 | ~
% 101.30/14.39 (register$(v2) = v1) | ~ (register$(v2) = v0)) & ! [v0: Nat_bool_fun$] :
% 101.30/14.39 ! [v1: Nat_bool_fun$] : ! [v2: Nat_set$] : (v1 = v0 | ~ (uua$(v2) = v1) | ~
% 101.30/14.39 (uua$(v2) = v0)) & ! [v0: C_ell2_c_ell2_cblinfun_bool_fun$] : ! [v1:
% 101.30/14.39 C_ell2_c_ell2_cblinfun_bool_fun$] : ! [v2: C_ell2_c_ell2_cblinfun_set$] :
% 101.30/14.39 (v1 = v0 | ~ (uu$(v2) = v1) | ~ (uu$(v2) = v0)) & ! [v0:
% 101.30/14.39 C_ell2_c_ell2_cblinfun_set_bool_fun$] : ! [v1:
% 101.30/14.39 C_ell2_c_ell2_cblinfun_set_bool_fun$] : ! [v2: C_ell2_c_ell2_cblinfun$] :
% 101.30/14.39 (v1 = v0 | ~ (member$(v2) = v1) | ~ (member$(v2) = v0))
% 101.30/14.39
% 101.30/14.39 Further assumptions not needed in the proof:
% 101.30/14.39 --------------------------------------------
% 101.30/14.39 axiom0, axiom1, axiom10, axiom100, axiom101, axiom102, axiom103, axiom104,
% 101.30/14.39 axiom105, axiom107, axiom108, axiom109, axiom11, axiom110, axiom111, axiom112,
% 101.30/14.39 axiom113, axiom114, axiom115, axiom116, axiom117, axiom118, axiom119, axiom12,
% 101.30/14.39 axiom120, axiom121, axiom122, axiom123, axiom124, axiom125, axiom126, axiom127,
% 101.30/14.39 axiom128, axiom129, axiom13, axiom130, axiom131, axiom132, axiom133, axiom134,
% 101.30/14.39 axiom135, axiom136, axiom137, axiom138, axiom139, axiom14, axiom140, axiom141,
% 101.30/14.39 axiom142, axiom143, axiom144, axiom145, axiom146, axiom147, axiom148, axiom149,
% 101.30/14.39 axiom15, axiom150, axiom151, axiom152, axiom153, axiom154, axiom155, axiom156,
% 101.30/14.39 axiom157, axiom158, axiom159, axiom16, axiom160, axiom161, axiom162, axiom163,
% 101.30/14.39 axiom164, axiom165, axiom166, axiom167, axiom168, axiom169, axiom17, axiom170,
% 101.30/14.39 axiom171, axiom172, axiom173, axiom174, axiom175, axiom176, axiom177, axiom178,
% 101.30/14.39 axiom179, axiom18, axiom180, axiom181, axiom182, axiom183, axiom184, axiom185,
% 101.30/14.39 axiom186, axiom187, axiom188, axiom189, axiom19, axiom190, axiom191, axiom192,
% 101.30/14.39 axiom193, axiom194, axiom195, axiom196, axiom197, axiom198, axiom199, axiom20,
% 101.30/14.39 axiom200, axiom201, axiom202, axiom203, axiom205, axiom206, axiom208, axiom209,
% 101.30/14.39 axiom210, axiom211, axiom212, axiom213, axiom214, axiom215, axiom216, axiom217,
% 101.30/14.39 axiom218, axiom220, axiom221, axiom222, axiom223, axiom224, axiom225, axiom226,
% 101.30/14.39 axiom227, axiom228, axiom229, axiom23, axiom231, axiom233, axiom234, axiom235,
% 101.30/14.39 axiom237, axiom238, axiom239, axiom24, axiom240, axiom241, axiom242, axiom243,
% 101.30/14.39 axiom244, axiom245, axiom246, axiom247, axiom248, axiom249, axiom25, axiom250,
% 101.30/14.39 axiom251, axiom252, axiom253, axiom254, axiom255, axiom256, axiom257, axiom258,
% 101.30/14.39 axiom259, axiom26, axiom260, axiom261, axiom262, axiom263, axiom264, axiom265,
% 101.30/14.39 axiom266, axiom267, axiom268, axiom269, axiom27, axiom270, axiom271, axiom272,
% 101.30/14.39 axiom273, axiom274, axiom275, axiom276, axiom277, axiom278, axiom279, axiom28,
% 101.30/14.39 axiom280, axiom281, axiom282, axiom283, axiom284, axiom285, axiom286, axiom287,
% 101.30/14.39 axiom288, axiom289, axiom29, axiom290, axiom291, axiom292, axiom293, axiom294,
% 101.30/14.39 axiom295, axiom296, axiom297, axiom298, axiom299, axiom30, axiom300, axiom301,
% 101.30/14.39 axiom302, axiom303, axiom304, axiom305, axiom306, axiom307, axiom308, axiom309,
% 101.30/14.39 axiom31, axiom310, axiom311, axiom312, axiom313, axiom314, axiom315, axiom316,
% 101.30/14.39 axiom317, axiom318, axiom319, axiom32, axiom320, axiom321, axiom322, axiom323,
% 101.30/14.39 axiom324, axiom325, axiom326, axiom327, axiom328, axiom329, axiom33, axiom330,
% 101.30/14.39 axiom331, axiom332, axiom333, axiom334, axiom335, axiom336, axiom337, axiom338,
% 101.30/14.39 axiom339, axiom34, axiom340, axiom341, axiom342, axiom343, axiom344, axiom345,
% 101.30/14.39 axiom346, axiom347, axiom348, axiom349, axiom35, axiom350, axiom351, axiom352,
% 101.30/14.39 axiom353, axiom354, axiom355, axiom356, axiom357, axiom358, axiom359, axiom36,
% 101.30/14.39 axiom360, axiom361, axiom362, axiom363, axiom364, axiom365, axiom366, axiom367,
% 101.30/14.39 axiom368, axiom369, axiom37, axiom370, axiom371, axiom372, axiom373, axiom374,
% 101.30/14.39 axiom375, axiom376, axiom377, axiom378, axiom379, axiom38, axiom380, axiom381,
% 101.30/14.39 axiom382, axiom383, axiom384, axiom385, axiom386, axiom387, axiom388, axiom389,
% 101.30/14.39 axiom39, axiom390, axiom391, axiom392, axiom393, axiom394, axiom395, axiom396,
% 101.30/14.39 axiom397, axiom398, axiom399, axiom40, axiom400, axiom401, axiom402, axiom403,
% 101.30/14.39 axiom404, axiom405, axiom406, axiom407, axiom408, axiom409, axiom410, axiom411,
% 101.30/14.39 axiom412, axiom413, axiom414, axiom415, axiom416, axiom417, axiom418, axiom419,
% 101.30/14.39 axiom42, axiom420, axiom421, axiom422, axiom423, axiom424, axiom425, axiom426,
% 101.30/14.39 axiom427, axiom428, axiom429, axiom43, axiom430, axiom431, axiom432, axiom433,
% 101.30/14.39 axiom434, axiom435, axiom436, axiom437, axiom438, axiom439, axiom44, axiom440,
% 101.30/14.39 axiom441, axiom442, axiom443, axiom444, axiom445, axiom446, axiom447, axiom448,
% 101.30/14.39 axiom449, axiom45, axiom450, axiom451, axiom452, axiom453, axiom454, axiom455,
% 101.30/14.39 axiom456, axiom457, axiom458, axiom459, axiom46, axiom460, axiom461, axiom462,
% 101.30/14.39 axiom463, axiom464, axiom465, axiom466, axiom467, axiom468, axiom469, axiom47,
% 101.30/14.39 axiom470, axiom471, axiom472, axiom473, axiom474, axiom475, axiom476, axiom477,
% 101.30/14.39 axiom478, axiom479, axiom48, axiom480, axiom481, axiom482, axiom483, axiom484,
% 101.30/14.39 axiom485, axiom486, axiom487, axiom488, axiom489, axiom49, axiom490, axiom491,
% 101.30/14.39 axiom492, axiom493, axiom494, axiom495, axiom496, axiom497, axiom498, axiom499,
% 101.30/14.39 axiom50, axiom500, axiom501, axiom502, axiom503, axiom504, axiom505, axiom506,
% 101.30/14.39 axiom507, axiom51, axiom510, axiom511, axiom512, axiom513, axiom516, axiom517,
% 101.30/14.39 axiom518, axiom519, axiom52, axiom520, axiom521, axiom522, axiom527, axiom528,
% 101.30/14.39 axiom529, axiom53, axiom530, axiom531, axiom532, axiom533, axiom534, axiom535,
% 101.30/14.39 axiom536, axiom537, axiom538, axiom539, axiom54, axiom540, axiom541, axiom542,
% 101.30/14.39 axiom545, axiom546, axiom547, axiom548, axiom55, axiom551, axiom552, axiom555,
% 101.30/14.39 axiom556, axiom557, axiom558, axiom559, axiom56, axiom560, axiom563, axiom564,
% 101.30/14.39 axiom565, axiom566, axiom569, axiom57, axiom570, axiom571, axiom572, axiom573,
% 101.30/14.39 axiom574, axiom575, axiom578, axiom579, axiom58, axiom583, axiom587, axiom59,
% 101.30/14.39 axiom592, axiom595, axiom597, axiom599, axiom60, axiom600, axiom601, axiom602,
% 101.30/14.39 axiom603, axiom604, axiom605, axiom606, axiom607, axiom608, axiom609, axiom61,
% 101.30/14.39 axiom610, axiom611, axiom612, axiom613, axiom614, axiom615, axiom616, axiom617,
% 101.30/14.39 axiom618, axiom619, axiom62, axiom620, axiom621, axiom622, axiom624, axiom625,
% 101.30/14.39 axiom626, axiom627, axiom628, axiom629, axiom63, axiom630, axiom631, axiom632,
% 101.30/14.39 axiom633, axiom634, axiom635, axiom636, axiom638, axiom64, axiom65, axiom66,
% 101.30/14.39 axiom67, axiom68, axiom69, axiom70, axiom71, axiom72, axiom73, axiom74, axiom75,
% 101.30/14.39 axiom76, axiom77, axiom78, axiom79, axiom80, axiom81, axiom82, axiom83, axiom84,
% 101.30/14.39 axiom85, axiom86, axiom87, axiom88, axiom89, axiom9, axiom90, axiom91, axiom92,
% 101.30/14.39 axiom93, axiom94, axiom95, axiom96, axiom97, axiom98, axiom99
% 101.30/14.39
% 101.30/14.39 Those formulas are unsatisfiable:
% 101.30/14.39 ---------------------------------
% 101.30/14.39
% 101.30/14.39 Begin of proof
% 101.30/14.39 |
% 101.30/14.39 | ALPHA: (axiom4) implies:
% 101.30/14.39 | (1) register$(g$) = 0
% 101.30/14.39 |
% 101.30/14.39 | ALPHA: (axiom5) implies:
% 101.30/14.39 | (2) register$a(f$) = 0
% 101.30/14.39 |
% 101.30/14.39 | ALPHA: (axiom6) implies:
% 101.30/14.39 | (3) ? [v0: C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$] :
% 101.30/14.39 | (inv_into$(top$, g$) = v0 &
% 101.30/14.39 | C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$(v0) & ! [v1:
% 101.30/14.39 | A_ell2_a_ell2_cblinfun$] : ! [v2: B_ell2_b_ell2_cblinfun$] : ( ~
% 101.30/14.39 | (fun_app$h(j$, v1) = v2) | ~ A_ell2_a_ell2_cblinfun$(v1) | ? [v3:
% 101.30/14.39 | C_ell2_c_ell2_cblinfun$] : (fun_app$e(f$, v1) = v3 &
% 101.30/14.39 | fun_app$d(v0, v3) = v2 & C_ell2_c_ell2_cblinfun$(v3) &
% 101.30/14.39 | B_ell2_b_ell2_cblinfun$(v2))))
% 101.30/14.39 |
% 101.30/14.39 | ALPHA: (axiom7) implies:
% 101.30/14.39 | (4) ? [v0: C_ell2_c_ell2_cblinfun_set$] : (image$(g$, top$) = v0 &
% 101.30/14.39 | C_ell2_c_ell2_cblinfun_set$(v0) & ! [v1: A_ell2_a_ell2_cblinfun$] :
% 101.30/14.39 | ! [v2: C_ell2_c_ell2_cblinfun$] : ( ~ (fun_app$e(f$, v1) = v2) | ~
% 101.30/14.39 | A_ell2_a_ell2_cblinfun$(v1) | ? [v3:
% 101.30/14.39 | C_ell2_c_ell2_cblinfun_set_bool_fun$] : (member$(v2) = v3 &
% 101.30/14.39 | fun_app$a(v3, v0) = 0 &
% 101.30/14.39 | C_ell2_c_ell2_cblinfun_set_bool_fun$(v3))))
% 101.30/14.39 |
% 101.30/14.39 | ALPHA: (axiom8) implies:
% 101.30/14.39 | (5) inj_on$(g$, top$) = 0
% 101.30/14.40 |
% 101.30/14.40 | ALPHA: (axiom21) implies:
% 101.30/14.40 | (6) clinear$(f$) = 0
% 101.30/14.40 |
% 101.30/14.40 | ALPHA: (axiom22) implies:
% 101.30/14.40 | (7) clinear$a(g$) = 0
% 101.30/14.40 |
% 101.30/14.40 | ALPHA: (axiom41) implies:
% 101.30/14.40 | (8) ? [v0: C_ell2_c_ell2_cblinfun_set$] : (image$a(f$, top$b) = v0 &
% 101.30/14.40 | image$(g$, top$) = v0 & C_ell2_c_ell2_cblinfun_set$(v0))
% 101.30/14.40 |
% 101.30/14.40 | ALPHA: (axiom204) implies:
% 101.30/14.40 | (9) ? [v0: C_ell2_c_ell2_cblinfun_set$] : (image$a(f$, top$b) = v0 &
% 101.30/14.40 | C_ell2_c_ell2_cblinfun_set$(v0) & ! [v1: B_ell2_b_ell2_cblinfun$] :
% 101.30/14.40 | ! [v2: C_ell2_c_ell2_cblinfun$] : ( ~ (fun_app$c(g$, v1) = v2) | ~
% 101.30/14.40 | B_ell2_b_ell2_cblinfun$(v1) | ? [v3:
% 101.30/14.40 | C_ell2_c_ell2_cblinfun_set_bool_fun$] : (member$(v2) = v3 &
% 101.30/14.40 | fun_app$a(v3, v0) = 0 &
% 101.30/14.40 | C_ell2_c_ell2_cblinfun_set_bool_fun$(v3))))
% 101.30/14.40 |
% 101.30/14.40 | ALPHA: (axiom207) implies:
% 101.30/14.40 | (10) ! [v0: A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v1:
% 101.30/14.40 | C_ell2_c_ell2_cblinfun$] : ! [v2:
% 101.30/14.40 | C_ell2_c_ell2_cblinfun_set_bool_fun$] : ! [v3:
% 101.30/14.40 | C_ell2_c_ell2_cblinfun_set$] : ! [v4: any] : ( ~ (image$a(v0,
% 101.30/14.40 | top$b) = v3) | ~ (member$(v1) = v2) | ~ (fun_app$a(v2, v3) =
% 101.30/14.40 | v4) | ~ C_ell2_c_ell2_cblinfun$(v1) | ~
% 101.30/14.40 | A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$(v0) | ? [v5:
% 101.30/14.40 | int] : ( ~ (v5 = 0) & inj_on$a(v0, top$b) = v5) | (( ~ (v4 = 0) |
% 101.30/14.40 | ? [v5: A_ell2_a_ell2_cblinfun$] : (fun_app$e(v0, v5) = v1 &
% 101.30/14.40 | A_ell2_a_ell2_cblinfun$(v5) & ! [v6: A_ell2_a_ell2_cblinfun$]
% 101.30/14.40 | : (v6 = v5 | ~ (fun_app$e(v0, v6) = v1) | ~
% 101.30/14.40 | A_ell2_a_ell2_cblinfun$(v6)))) & (v4 = 0 | ! [v5:
% 101.30/14.40 | A_ell2_a_ell2_cblinfun$] : ( ~ (fun_app$e(v0, v5) = v1) | ~
% 101.30/14.40 | A_ell2_a_ell2_cblinfun$(v5) | ? [v6: A_ell2_a_ell2_cblinfun$]
% 101.30/14.40 | : ( ~ (v6 = v5) & fun_app$e(v0, v6) = v1 &
% 101.30/14.40 | A_ell2_a_ell2_cblinfun$(v6))))))
% 101.30/14.40 |
% 101.30/14.40 | ALPHA: (axiom219) implies:
% 101.30/14.40 | (11) ! [v0: A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v1:
% 101.30/14.40 | A_ell2_a_ell2_cblinfun$] : ! [v2: A_ell2_a_ell2_cblinfun_set$] : !
% 101.30/14.40 | [v3: C_ell2_c_ell2_cblinfun$] : ! [v4:
% 101.30/14.40 | C_ell2_c_ell2_cblinfun_set_bool_fun$] : ! [v5:
% 101.30/14.40 | C_ell2_c_ell2_cblinfun_set$] : ! [v6: any] : ( ~ (image$a(v0, v2) =
% 101.30/14.40 | v5) | ~ (fun_app$e(v0, v1) = v3) | ~ (member$(v3) = v4) | ~
% 101.30/14.40 | (fun_app$a(v4, v5) = v6) | ~ A_ell2_a_ell2_cblinfun_set$(v2) | ~
% 101.30/14.40 | A_ell2_a_ell2_cblinfun$(v1) | ~
% 101.30/14.40 | A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$(v0) | ? [v7:
% 101.30/14.40 | any] : ? [v8: any] : (inj_on$a(v0, top$b) = v7 & member$c(v1, v2)
% 101.30/14.40 | = v8 & ( ~ (v7 = 0) | (( ~ (v8 = 0) | v6 = 0) & ( ~ (v6 = 0) | v8
% 101.30/14.40 | = 0)))))
% 101.30/14.40 |
% 101.30/14.40 | ALPHA: (axiom236) implies:
% 101.30/14.40 | (12) inj_on$a(f$, top$b) = 0
% 101.30/14.40 |
% 101.30/14.40 | ALPHA: (axiom508) implies:
% 101.30/14.40 | (13) cspan$b(top$) = top$
% 101.30/14.40 |
% 101.30/14.40 | ALPHA: (axiom509) implies:
% 101.30/14.40 | (14) cspan$a(top$b) = top$b
% 101.30/14.40 |
% 101.30/14.40 | ALPHA: (axiom514) implies:
% 101.30/14.40 | (15) csubspace$b(top$) = 0
% 101.30/14.40 |
% 101.30/14.40 | ALPHA: (axiom515) implies:
% 101.30/14.40 | (16) csubspace$a(top$b) = 0
% 101.30/14.40 |
% 101.30/14.40 | ALPHA: (axiom525) implies:
% 101.30/14.40 | (17) ! [v0: A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v1:
% 101.30/14.40 | A_ell2_a_ell2_cblinfun_set$] : ( ~ (csubspace$a(v1) = 0) | ~
% 101.30/14.40 | (clinear$(v0) = 0) | ~ A_ell2_a_ell2_cblinfun_set$(v1) | ~
% 101.30/14.40 | A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$(v0) | ? [v2:
% 101.30/14.40 | C_ell2_c_ell2_cblinfun_set$] : (image$a(v0, v1) = v2 &
% 101.30/14.40 | fun_app$a(csubspace$, v2) = 0 & C_ell2_c_ell2_cblinfun_set$(v2)))
% 101.30/14.40 |
% 101.30/14.40 | ALPHA: (axiom526) implies:
% 101.30/14.40 | (18) ! [v0: B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v1:
% 101.30/14.40 | B_ell2_b_ell2_cblinfun_set$] : ( ~ (csubspace$b(v1) = 0) | ~
% 101.30/14.40 | (clinear$a(v0) = 0) | ~ B_ell2_b_ell2_cblinfun_set$(v1) | ~
% 101.30/14.40 | B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$(v0) | ? [v2:
% 101.30/14.40 | C_ell2_c_ell2_cblinfun_set$] : (image$(v0, v1) = v2 &
% 101.30/14.40 | fun_app$a(csubspace$, v2) = 0 & C_ell2_c_ell2_cblinfun_set$(v2)))
% 101.30/14.40 |
% 101.30/14.40 | ALPHA: (axiom543) implies:
% 101.30/14.40 | (19) ! [v0: A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v1:
% 101.30/14.40 | A_ell2_a_ell2_cblinfun_set$] : ( ~ (csubspace$a(v1) = 0) | ~
% 101.30/14.40 | (clinear$(v0) = 0) | ~ A_ell2_a_ell2_cblinfun_set$(v1) | ~
% 101.30/14.40 | A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$(v0) | ? [v2:
% 101.30/14.40 | C_ell2_c_ell2_cblinfun_set$] : (image$a(v0, v1) = v2 &
% 101.30/14.40 | C_ell2_c_ell2_cblinfun_set$(v2) & ? [v3:
% 101.30/14.40 | C_ell2_c_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$] : ? [v4:
% 101.30/14.40 | A_ell2_a_ell2_cblinfun_set$] : (clinear$b(v3) = 0 &
% 101.30/14.40 | less_eq$b(v4, v1) = 0 & image$s(v3, top$a) = v4 &
% 101.30/14.40 | C_ell2_c_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$(v3) &
% 101.30/14.40 | A_ell2_a_ell2_cblinfun_set$(v4) & ! [v5:
% 101.30/14.40 | C_ell2_c_ell2_cblinfun$] : ! [v6:
% 101.30/14.40 | C_ell2_c_ell2_cblinfun_set_bool_fun$] : ( ~ (member$(v5) = v6)
% 101.30/14.40 | | ~ (fun_app$a(v6, v2) = 0) | ~ C_ell2_c_ell2_cblinfun$(v5)
% 101.30/14.40 | | ? [v7: A_ell2_a_ell2_cblinfun$] : (fun_app$i(v3, v5) = v7 &
% 101.30/14.40 | fun_app$e(v0, v7) = v5 & A_ell2_a_ell2_cblinfun$(v7))))))
% 101.30/14.40 |
% 101.30/14.40 | ALPHA: (axiom544) implies:
% 101.30/14.40 | (20) ! [v0: B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v1:
% 101.30/14.40 | B_ell2_b_ell2_cblinfun_set$] : ( ~ (csubspace$b(v1) = 0) | ~
% 101.30/14.40 | (clinear$a(v0) = 0) | ~ B_ell2_b_ell2_cblinfun_set$(v1) | ~
% 101.30/14.40 | B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$(v0) | ? [v2:
% 101.30/14.40 | C_ell2_c_ell2_cblinfun_set$] : (image$(v0, v1) = v2 &
% 101.30/14.40 | C_ell2_c_ell2_cblinfun_set$(v2) & ? [v3:
% 101.30/14.40 | C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$] : ? [v4:
% 101.30/14.40 | B_ell2_b_ell2_cblinfun_set$] : (clinear$c(v3) = 0 &
% 101.30/14.40 | less_eq$a(v4, v1) = 0 & image$r(v3, top$a) = v4 &
% 101.30/14.40 | B_ell2_b_ell2_cblinfun_set$(v4) &
% 101.30/14.40 | C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$(v3) & ! [v5:
% 101.30/14.40 | C_ell2_c_ell2_cblinfun$] : ! [v6:
% 101.30/14.40 | C_ell2_c_ell2_cblinfun_set_bool_fun$] : ( ~ (member$(v5) = v6)
% 101.30/14.40 | | ~ (fun_app$a(v6, v2) = 0) | ~ C_ell2_c_ell2_cblinfun$(v5)
% 101.30/14.40 | | ? [v7: B_ell2_b_ell2_cblinfun$] : (fun_app$c(v0, v7) = v5 &
% 101.30/14.40 | fun_app$d(v3, v5) = v7 & B_ell2_b_ell2_cblinfun$(v7))))))
% 101.30/14.40 |
% 101.30/14.40 | ALPHA: (axiom549) implies:
% 101.30/14.40 | (21) ! [v0: A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v1:
% 101.30/14.40 | A_ell2_a_ell2_cblinfun_set$] : ! [v2: A_ell2_a_ell2_cblinfun_set$]
% 101.30/14.40 | : ! [v3: any] : ( ~ (cspan$a(v1) = v2) | ~ (inj_on$a(v0, v2) = v3) |
% 101.30/14.40 | ~ A_ell2_a_ell2_cblinfun_set$(v1) | ~
% 101.30/14.40 | A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$(v0) | ? [v4:
% 101.30/14.40 | any] : ? [v5: C_ell2_c_ell2_cblinfun_set$] : ? [v6: any] : ?
% 101.30/14.40 | [v7: any] : (inj_on$a(v0, v1) = v7 & image$a(v0, v1) = v5 &
% 101.30/14.40 | clinear$(v0) = v4 & fun_app$a(cdependent$, v5) = v6 &
% 101.30/14.40 | C_ell2_c_ell2_cblinfun_set$(v5) & ( ~ (v4 = 0) | v6 = 0 | (( ~ (v7
% 101.30/14.40 | = 0) | v3 = 0) & ( ~ (v3 = 0) | v7 = 0)))))
% 101.30/14.40 |
% 101.30/14.40 | ALPHA: (axiom550) implies:
% 101.30/14.41 | (22) ! [v0: B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v1:
% 101.30/14.41 | B_ell2_b_ell2_cblinfun_set$] : ! [v2: B_ell2_b_ell2_cblinfun_set$]
% 101.30/14.41 | : ! [v3: any] : ( ~ (cspan$b(v1) = v2) | ~ (inj_on$(v0, v2) = v3) |
% 101.30/14.41 | ~ B_ell2_b_ell2_cblinfun_set$(v1) | ~
% 101.30/14.41 | B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$(v0) | ? [v4:
% 101.30/14.41 | any] : ? [v5: C_ell2_c_ell2_cblinfun_set$] : ? [v6: any] : ?
% 101.30/14.41 | [v7: any] : (clinear$a(v0) = v4 & inj_on$(v0, v1) = v7 & image$(v0,
% 101.30/14.41 | v1) = v5 & fun_app$a(cdependent$, v5) = v6 &
% 101.30/14.41 | C_ell2_c_ell2_cblinfun_set$(v5) & ( ~ (v4 = 0) | v6 = 0 | (( ~ (v7
% 101.30/14.41 | = 0) | v3 = 0) & ( ~ (v3 = 0) | v7 = 0)))))
% 101.30/14.41 |
% 101.30/14.41 | ALPHA: (axiom553) implies:
% 101.88/14.41 | (23) ! [v0: A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v1:
% 101.88/14.41 | A_ell2_a_ell2_cblinfun_set$] : ! [v2: A_ell2_a_ell2_cblinfun_set$]
% 101.88/14.41 | : ( ~ (cspan$a(v1) = v2) | ~ (inj_on$a(v0, v2) = 0) | ~
% 101.88/14.41 | A_ell2_a_ell2_cblinfun_set$(v1) | ~
% 101.88/14.41 | A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$(v0) | ? [v3:
% 101.88/14.41 | any] : ? [v4: any] : ? [v5: C_ell2_c_ell2_cblinfun_set$] : ?
% 101.88/14.41 | [v6: any] : (cdependent$a(v1) = v4 & image$a(v0, v1) = v5 &
% 101.88/14.41 | clinear$(v0) = v3 & fun_app$a(cdependent$, v5) = v6 &
% 101.88/14.41 | C_ell2_c_ell2_cblinfun_set$(v5) & ( ~ (v6 = 0) | ~ (v3 = 0) | v4
% 101.88/14.41 | = 0)))
% 101.88/14.41 |
% 101.88/14.41 | ALPHA: (axiom554) implies:
% 101.88/14.41 | (24) ! [v0: B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v1:
% 101.88/14.41 | B_ell2_b_ell2_cblinfun_set$] : ! [v2: B_ell2_b_ell2_cblinfun_set$]
% 101.88/14.41 | : ( ~ (cspan$b(v1) = v2) | ~ (inj_on$(v0, v2) = 0) | ~
% 101.88/14.41 | B_ell2_b_ell2_cblinfun_set$(v1) | ~
% 101.88/14.41 | B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$(v0) | ? [v3:
% 101.88/14.41 | any] : ? [v4: any] : ? [v5: C_ell2_c_ell2_cblinfun_set$] : ?
% 101.88/14.41 | [v6: any] : (cdependent$b(v1) = v4 & clinear$a(v0) = v3 & image$(v0,
% 101.88/14.41 | v1) = v5 & fun_app$a(cdependent$, v5) = v6 &
% 101.88/14.41 | C_ell2_c_ell2_cblinfun_set$(v5) & ( ~ (v6 = 0) | ~ (v3 = 0) | v4
% 101.88/14.41 | = 0)))
% 101.88/14.41 |
% 101.88/14.41 | ALPHA: (axiom561) implies:
% 101.88/14.41 | (25) ! [v0: A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v1:
% 101.88/14.41 | A_ell2_a_ell2_cblinfun_set$] : ! [v2: A_ell2_a_ell2_cblinfun_set$]
% 101.88/14.41 | : ( ~ (cspan$a(v1) = v2) | ~ (inj_on$a(v0, v2) = 0) | ~
% 101.88/14.41 | A_ell2_a_ell2_cblinfun_set$(v1) | ~
% 101.88/14.41 | A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$(v0) | ? [v3:
% 101.88/14.41 | any] : ? [v4: C_ell2_c_ell2_cblinfun_set$] : ? [v5: any] : ?
% 101.88/14.41 | [v6: any] : (cdependent$a(v1) = v6 & image$a(v0, v1) = v4 &
% 101.88/14.41 | clinear$(v0) = v3 & fun_app$a(cdependent$, v4) = v5 &
% 101.88/14.41 | C_ell2_c_ell2_cblinfun_set$(v4) & ( ~ (v5 = 0) | ~ (v3 = 0) | v6
% 101.88/14.41 | = 0)))
% 101.88/14.41 |
% 101.88/14.41 | ALPHA: (axiom562) implies:
% 101.88/14.41 | (26) ! [v0: B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v1:
% 101.88/14.41 | B_ell2_b_ell2_cblinfun_set$] : ! [v2: B_ell2_b_ell2_cblinfun_set$]
% 101.88/14.41 | : ( ~ (cspan$b(v1) = v2) | ~ (inj_on$(v0, v2) = 0) | ~
% 101.88/14.41 | B_ell2_b_ell2_cblinfun_set$(v1) | ~
% 101.88/14.41 | B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$(v0) | ? [v3:
% 101.88/14.41 | any] : ? [v4: C_ell2_c_ell2_cblinfun_set$] : ? [v5: any] : ?
% 101.88/14.41 | [v6: any] : (cdependent$b(v1) = v6 & clinear$a(v0) = v3 & image$(v0,
% 101.88/14.41 | v1) = v4 & fun_app$a(cdependent$, v4) = v5 &
% 101.88/14.41 | C_ell2_c_ell2_cblinfun_set$(v4) & ( ~ (v5 = 0) | ~ (v3 = 0) | v6
% 101.88/14.41 | = 0)))
% 101.88/14.41 |
% 101.88/14.41 | ALPHA: (axiom576) implies:
% 101.88/14.41 | (27) ? [v0: Nat$] : ? [v1: int] : ? [v2: Nat$] : (cdim$c(top$j) = v0 &
% 101.88/14.41 | card$c(top$d) = v2 & of_nat$(v2) = v1 & of_nat$(v0) = v1 & Nat$(v2)
% 101.88/14.41 | & Nat$(v0))
% 101.88/14.41 |
% 101.88/14.41 | ALPHA: (axiom580) implies:
% 101.88/14.41 | (28) ? [v0: any] : ? [v1: any] : (finite$c(top$k) = v0 & finite$d(top$c)
% 101.88/14.41 | = v1 & ((v1 = 0 & v0 = 0) | ( ~ (v1 = 0) & ~ (v0 = 0))))
% 101.88/14.41 |
% 101.88/14.41 | ALPHA: (axiom581) implies:
% 101.88/14.41 | (29) ? [v0: any] : ? [v1: any] : ? [v2: any] : (finite$e(top$l) = v0 &
% 101.88/14.41 | finite$f(top$d) = v2 & finite$d(top$c) = v1 & ((v2 = 0 & v1 = 0 & v0
% 101.88/14.41 | = 0) | ( ~ (v0 = 0) & ( ~ (v2 = 0) | ~ (v1 = 0)))))
% 101.88/14.41 |
% 101.88/14.41 | ALPHA: (axiom582) implies:
% 101.88/14.41 | (30) ? [v0: any] : ? [v1: any] : ? [v2: any] : (finite$g(top$m) = v0 &
% 101.88/14.41 | finite$f(top$d) = v1 & finite$d(top$c) = v2 & ((v2 = 0 & v1 = 0 & v0
% 101.88/14.41 | = 0) | ( ~ (v0 = 0) & ( ~ (v2 = 0) | ~ (v1 = 0)))))
% 101.88/14.41 |
% 101.88/14.41 | ALPHA: (axiom584) implies:
% 101.88/14.41 | (31) ? [v0: any] : ? [v1: any] : ? [v2: any] : (finite$i(top$o) = v0 &
% 101.88/14.41 | finite$d(top$c) = v2 & finite$b(top$) = v1 & ((v2 = 0 & v1 = 0 & v0
% 101.88/14.41 | = 0) | ( ~ (v0 = 0) & ( ~ (v2 = 0) | ~ (v1 = 0)))))
% 101.88/14.41 |
% 101.88/14.41 | ALPHA: (axiom585) implies:
% 101.88/14.41 | (32) ? [v0: any] : ? [v1: any] : ? [v2: any] : (finite$j(top$p) = v0 &
% 101.88/14.41 | finite$f(top$d) = v2 & finite$b(top$) = v1 & ((v2 = 0 & v1 = 0 & v0
% 101.88/14.41 | = 0) | ( ~ (v0 = 0) & ( ~ (v2 = 0) | ~ (v1 = 0)))))
% 101.88/14.41 |
% 101.88/14.41 | ALPHA: (axiom586) implies:
% 101.88/14.41 | (33) ? [v0: any] : ? [v1: any] : ? [v2: any] : (finite$k(top$q) = v0 &
% 101.88/14.41 | finite$d(top$c) = v2 & finite$(top$b) = v1 & ((v2 = 0 & v1 = 0 & v0
% 101.88/14.41 | = 0) | ( ~ (v0 = 0) & ( ~ (v2 = 0) | ~ (v1 = 0)))))
% 101.88/14.41 |
% 101.88/14.41 | ALPHA: (axiom588) implies:
% 101.88/14.41 | (34) ? [v0: any] : ? [v1: any] : ? [v2: any] : (finite$m(top$s) = v0 &
% 101.88/14.41 | finite$d(top$c) = v1 & finite$b(top$) = v2 & ((v2 = 0 & v1 = 0 & v0
% 101.88/14.41 | = 0) | ( ~ (v0 = 0) & ( ~ (v2 = 0) | ~ (v1 = 0)))))
% 101.88/14.41 |
% 101.88/14.41 | ALPHA: (axiom589) implies:
% 101.88/14.42 | (35) A_ell2_a_ell2_cblinfun_set$(top$b)
% 101.88/14.42 | (36) ? [v0: any] : ? [v1: any] : ? [v2: any] : (finite$n(top$t) = v0 &
% 101.88/14.42 | finite$d(top$c) = v1 & finite$(top$b) = v2 & ((v2 = 0 & v1 = 0 & v0
% 101.88/14.42 | = 0) | ( ~ (v0 = 0) & ( ~ (v2 = 0) | ~ (v1 = 0)))))
% 101.88/14.42 |
% 101.88/14.42 | ALPHA: (axiom590) implies:
% 101.88/14.42 | (37) ! [v0: B_ell2_b_ell2_cblinfun_set$] : ! [v1:
% 101.88/14.42 | B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v2:
% 101.88/14.42 | C_ell2_c_ell2_cblinfun_set$] : ( ~ (image$(v1, v0) = v2) | ~
% 101.88/14.42 | B_ell2_b_ell2_cblinfun_set$(v0) | ~
% 101.88/14.42 | B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$(v1) | ? [v3:
% 101.88/14.42 | any] : ? [v4: any] : (finite$b(v0) = v3 & fun_app$a(finite$a, v2)
% 101.88/14.42 | = v4 & ( ~ (v3 = 0) | v4 = 0)))
% 101.88/14.42 |
% 101.88/14.42 | ALPHA: (axiom591) implies:
% 101.88/14.42 | (38) ! [v0: A_ell2_a_ell2_cblinfun_set$] : ! [v1:
% 101.88/14.42 | A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v2:
% 101.88/14.42 | C_ell2_c_ell2_cblinfun_set$] : ( ~ (image$a(v1, v0) = v2) | ~
% 101.88/14.42 | A_ell2_a_ell2_cblinfun_set$(v0) | ~
% 101.88/14.42 | A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$(v1) | ? [v3:
% 101.88/14.42 | any] : ? [v4: any] : (finite$(v0) = v3 & fun_app$a(finite$a, v2)
% 101.88/14.42 | = v4 & ( ~ (v3 = 0) | v4 = 0)))
% 101.88/14.42 |
% 101.88/14.42 | ALPHA: (axiom593) implies:
% 101.88/14.42 | (39) ! [v0: B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v1:
% 101.88/14.42 | B_ell2_b_ell2_cblinfun_set$] : ( ~ (inj_on$(v0, v1) = 0) | ~
% 101.88/14.42 | B_ell2_b_ell2_cblinfun_set$(v1) | ~
% 101.88/14.42 | B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$(v0) | ? [v2:
% 101.88/14.42 | C_ell2_c_ell2_cblinfun_set$] : ? [v3: any] : ? [v4: any] :
% 101.88/14.42 | (finite$b(v1) = v4 & image$(v0, v1) = v2 & fun_app$a(finite$a, v2) =
% 101.88/14.42 | v3 & C_ell2_c_ell2_cblinfun_set$(v2) & ( ~ (v4 = 0) | v3 = 0) & (
% 101.88/14.42 | ~ (v3 = 0) | v4 = 0)))
% 101.88/14.42 |
% 101.88/14.42 | ALPHA: (axiom594) implies:
% 101.88/14.42 | (40) ! [v0: A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v1:
% 101.88/14.42 | A_ell2_a_ell2_cblinfun_set$] : ( ~ (inj_on$a(v0, v1) = 0) | ~
% 101.88/14.42 | A_ell2_a_ell2_cblinfun_set$(v1) | ~
% 101.88/14.42 | A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$(v0) | ? [v2:
% 101.88/14.42 | C_ell2_c_ell2_cblinfun_set$] : ? [v3: any] : ? [v4: any] :
% 101.88/14.42 | (finite$(v1) = v4 & image$a(v0, v1) = v2 & fun_app$a(finite$a, v2) =
% 101.88/14.42 | v3 & C_ell2_c_ell2_cblinfun_set$(v2) & ( ~ (v4 = 0) | v3 = 0) & (
% 101.88/14.42 | ~ (v3 = 0) | v4 = 0)))
% 101.88/14.42 |
% 101.88/14.42 | ALPHA: (axiom596) implies:
% 101.88/14.42 | (41) ? [v0: any] : (finite$d(top$c) = v0 & ! [v1: Nat_set$] : ! [v2:
% 101.88/14.42 | Nat_set$] : ( ~ (uminus$c(v1) = v2) | ~ Nat_set$(v1) | ? [v3:
% 101.88/14.42 | any] : ? [v4: any] : (finite$d(v2) = v4 & finite$d(v1) = v3 & (
% 101.88/14.42 | ~ (v3 = 0) | (( ~ (v4 = 0) | v0 = 0) & ( ~ (v0 = 0) | v4 =
% 101.88/14.42 | 0))))))
% 101.88/14.42 |
% 101.88/14.42 | ALPHA: (axiom598) implies:
% 101.88/14.42 | (42) ? [v0: int] : ( ~ (v0 = 0) & finite$d(top$c) = v0)
% 101.88/14.42 |
% 101.88/14.42 | ALPHA: (axiom623) implies:
% 101.88/14.42 | (43) Unit_set$(top$d)
% 101.88/14.42 | (44) ? [v0: Nat$] : (card$c(top$d) = v0 & of_nat$(v0) = 1 & Nat$(v0))
% 101.88/14.42 |
% 101.88/14.42 | ALPHA: (conjecture2) implies:
% 101.88/14.42 | (45) A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$(f$)
% 101.88/14.42 | (46) A_ell2_a_ell2_cblinfun$(b$)
% 101.88/14.42 | (47) A_ell2_a_ell2_cblinfun$(a$)
% 101.88/14.42 | (48) B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$(g$)
% 101.88/14.42 | (49) B_ell2_b_ell2_cblinfun_set$(top$)
% 101.88/14.42 | (50) ? [v0: C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$] : ? [v1:
% 101.88/14.42 | A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$] : ? [v2:
% 101.88/14.42 | A_ell2_a_ell2_cblinfun$] : ? [v3: C_ell2_c_ell2_cblinfun$] : ?
% 101.88/14.42 | [v4: B_ell2_b_ell2_cblinfun$] : ? [v5: C_ell2_c_ell2_cblinfun$] : ?
% 101.88/14.42 | [v6: C_ell2_c_ell2_cblinfun$] : ? [v7: B_ell2_b_ell2_cblinfun$] : ?
% 101.88/14.42 | [v8: C_ell2_c_ell2_cblinfun$] : ? [v9:
% 101.88/14.42 | C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ? [v10:
% 101.88/14.42 | C_ell2_c_ell2_cblinfun$] : ? [v11: B_ell2_b_ell2_cblinfun$] : ?
% 101.88/14.42 | [v12: C_ell2_c_ell2_cblinfun$] : ? [v13: C_ell2_c_ell2_cblinfun$] : (
% 101.88/14.42 | ~ (v13 = v5) & cblinfun_compose$a(v8) = v9 & fun_app$g(v9, v12) =
% 101.88/14.42 | v13 & cblinfun_compose$(a$) = v1 & fun_app$f(v1, b$) = v2 &
% 101.88/14.42 | fun_app$c(g$, v11) = v12 & fun_app$c(g$, v7) = v8 & fun_app$c(g$,
% 101.88/14.42 | v4) = v5 & inv_into$(top$, g$) = v0 & fun_app$e(f$, v2) = v3 &
% 101.88/14.42 | fun_app$e(f$, a$) = v6 & fun_app$e(f$, b$) = v10 & fun_app$d(v0,
% 101.88/14.42 | v10) = v11 & fun_app$d(v0, v6) = v7 & fun_app$d(v0, v3) = v4 &
% 101.88/14.42 | C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$(v9) &
% 101.88/14.42 | A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$(v1) &
% 101.88/14.42 | C_ell2_c_ell2_cblinfun$(v13) & C_ell2_c_ell2_cblinfun$(v12) &
% 101.88/14.42 | C_ell2_c_ell2_cblinfun$(v10) & C_ell2_c_ell2_cblinfun$(v8) &
% 101.88/14.42 | C_ell2_c_ell2_cblinfun$(v6) & C_ell2_c_ell2_cblinfun$(v5) &
% 101.88/14.42 | C_ell2_c_ell2_cblinfun$(v3) & B_ell2_b_ell2_cblinfun$(v11) &
% 101.88/14.42 | B_ell2_b_ell2_cblinfun$(v7) & B_ell2_b_ell2_cblinfun$(v4) &
% 101.88/14.42 | C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$(v0) &
% 101.88/14.42 | A_ell2_a_ell2_cblinfun$(v2))
% 101.88/14.42 |
% 101.88/14.42 | ALPHA: (function-axioms) implies:
% 101.88/14.43 | (51) ! [v0: C_ell2_c_ell2_cblinfun_set_bool_fun$] : ! [v1:
% 101.88/14.43 | C_ell2_c_ell2_cblinfun_set_bool_fun$] : ! [v2:
% 101.88/14.43 | C_ell2_c_ell2_cblinfun$] : (v1 = v0 | ~ (member$(v2) = v1) | ~
% 101.88/14.43 | (member$(v2) = v0))
% 101.88/14.43 | (52) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 101.88/14.43 | B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : (v1 = v0 | ~
% 101.88/14.43 | (register$(v2) = v1) | ~ (register$(v2) = v0))
% 101.88/14.43 | (53) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 101.88/14.43 | A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : (v1 = v0 | ~
% 101.88/14.43 | (register$a(v2) = v1) | ~ (register$a(v2) = v0))
% 101.88/14.43 | (54) ! [v0: A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$] : ! [v1:
% 101.88/14.43 | A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$] : ! [v2:
% 101.88/14.43 | A_ell2_a_ell2_cblinfun$] : (v1 = v0 | ~ (cblinfun_compose$(v2) =
% 101.88/14.43 | v1) | ~ (cblinfun_compose$(v2) = v0))
% 101.88/14.43 | (55) ! [v0: int] : ! [v1: int] : ! [v2: Nat$] : (v1 = v0 | ~
% 101.88/14.43 | (of_nat$(v2) = v1) | ~ (of_nat$(v2) = v0))
% 101.88/14.43 | (56) ! [v0: Nat$] : ! [v1: Nat$] : ! [v2: Unit_set$] : (v1 = v0 | ~
% 101.88/14.43 | (card$c(v2) = v1) | ~ (card$c(v2) = v0))
% 101.88/14.43 | (57) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 101.88/14.43 | B_ell2_b_ell2_cblinfun_set$] : (v1 = v0 | ~ (finite$b(v2) = v1) |
% 101.88/14.43 | ~ (finite$b(v2) = v0))
% 101.88/14.43 | (58) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 101.88/14.43 | Nat_set$] : (v1 = v0 | ~ (finite$d(v2) = v1) | ~ (finite$d(v2) =
% 101.88/14.43 | v0))
% 101.88/14.43 | (59) ! [v0: Nat$] : ! [v1: Nat$] : ! [v2: int] : (v1 = v0 | ~ (nat$(v2)
% 101.88/14.43 | = v1) | ~ (nat$(v2) = v0))
% 101.88/14.43 | (60) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 101.88/14.43 | C_ell2_c_ell2_cblinfun_set$] : ! [v3:
% 101.88/14.43 | C_ell2_c_ell2_cblinfun_set_bool_fun$] : (v1 = v0 | ~ (fun_app$a(v3,
% 101.88/14.43 | v2) = v1) | ~ (fun_app$a(v3, v2) = v0))
% 101.88/14.43 | (61) ! [v0: C_ell2_c_ell2_cblinfun$] : ! [v1: C_ell2_c_ell2_cblinfun$] :
% 101.88/14.43 | ! [v2: A_ell2_a_ell2_cblinfun$] : ! [v3:
% 101.88/14.43 | A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : (v1 = v0 | ~
% 101.88/14.43 | (fun_app$e(v3, v2) = v1) | ~ (fun_app$e(v3, v2) = v0))
% 101.88/14.43 | (62) ! [v0: C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$] : ! [v1:
% 101.88/14.43 | C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$] : ! [v2:
% 101.88/14.43 | B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : ! [v3:
% 101.88/14.43 | B_ell2_b_ell2_cblinfun_set$] : (v1 = v0 | ~ (inv_into$(v3, v2) =
% 101.88/14.43 | v1) | ~ (inv_into$(v3, v2) = v0))
% 101.88/14.43 | (63) ! [v0: C_ell2_c_ell2_cblinfun_set$] : ! [v1:
% 101.88/14.43 | C_ell2_c_ell2_cblinfun_set$] : ! [v2: B_ell2_b_ell2_cblinfun_set$]
% 101.88/14.43 | : ! [v3: B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : (v1 =
% 101.88/14.43 | v0 | ~ (image$(v3, v2) = v1) | ~ (image$(v3, v2) = v0))
% 101.88/14.43 | (64) ! [v0: A_ell2_a_ell2_cblinfun$] : ! [v1: A_ell2_a_ell2_cblinfun$] :
% 101.88/14.43 | ! [v2: A_ell2_a_ell2_cblinfun$] : ! [v3:
% 101.88/14.43 | A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$] : (v1 = v0 | ~
% 101.88/14.43 | (fun_app$f(v3, v2) = v1) | ~ (fun_app$f(v3, v2) = v0))
% 101.88/14.43 | (65) ! [v0: C_ell2_c_ell2_cblinfun_set$] : ! [v1:
% 101.88/14.43 | C_ell2_c_ell2_cblinfun_set$] : ! [v2: A_ell2_a_ell2_cblinfun_set$]
% 101.88/14.43 | : ! [v3: A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : (v1 =
% 101.88/14.43 | v0 | ~ (image$a(v3, v2) = v1) | ~ (image$a(v3, v2) = v0))
% 101.88/14.43 | (66) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 101.88/14.43 | A_ell2_a_ell2_cblinfun_set$] : ! [v3:
% 101.88/14.43 | A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$] : (v1 = v0 | ~
% 101.88/14.43 | (inj_on$a(v3, v2) = v1) | ~ (inj_on$a(v3, v2) = v0))
% 101.88/14.43 |
% 101.88/14.43 | DELTA: instantiating (42) with fresh symbol all_592_0 gives:
% 101.88/14.43 | (67) ~ (all_592_0 = 0) & finite$d(top$c) = all_592_0
% 101.88/14.43 |
% 101.88/14.43 | ALPHA: (67) implies:
% 101.88/14.43 | (68) ~ (all_592_0 = 0)
% 101.88/14.43 | (69) finite$d(top$c) = all_592_0
% 101.88/14.43 |
% 101.88/14.43 | DELTA: instantiating (44) with fresh symbol all_602_0 gives:
% 101.88/14.43 | (70) card$c(top$d) = all_602_0 & of_nat$(all_602_0) = 1 & Nat$(all_602_0)
% 101.88/14.43 |
% 101.88/14.43 | ALPHA: (70) implies:
% 101.88/14.43 | (71) of_nat$(all_602_0) = 1
% 101.88/14.43 | (72) card$c(top$d) = all_602_0
% 101.88/14.43 |
% 101.88/14.43 | DELTA: instantiating (8) with fresh symbol all_604_0 gives:
% 101.88/14.43 | (73) image$a(f$, top$b) = all_604_0 & image$(g$, top$) = all_604_0 &
% 101.88/14.43 | C_ell2_c_ell2_cblinfun_set$(all_604_0)
% 101.88/14.43 |
% 101.88/14.43 | ALPHA: (73) implies:
% 101.88/14.43 | (74) image$(g$, top$) = all_604_0
% 101.88/14.43 | (75) image$a(f$, top$b) = all_604_0
% 101.88/14.43 |
% 101.88/14.43 | DELTA: instantiating (28) with fresh symbols all_652_0, all_652_1 gives:
% 101.88/14.43 | (76) finite$c(top$k) = all_652_1 & finite$d(top$c) = all_652_0 &
% 101.88/14.43 | ((all_652_0 = 0 & all_652_1 = 0) | ( ~ (all_652_0 = 0) & ~ (all_652_1
% 101.88/14.43 | = 0)))
% 101.88/14.43 |
% 101.88/14.43 | ALPHA: (76) implies:
% 101.88/14.43 | (77) finite$d(top$c) = all_652_0
% 101.88/14.43 |
% 101.88/14.43 | DELTA: instantiating (27) with fresh symbols all_654_0, all_654_1, all_654_2
% 101.88/14.43 | gives:
% 101.88/14.43 | (78) cdim$c(top$j) = all_654_2 & card$c(top$d) = all_654_0 &
% 101.88/14.43 | of_nat$(all_654_0) = all_654_1 & of_nat$(all_654_2) = all_654_1 &
% 101.88/14.43 | Nat$(all_654_0) & Nat$(all_654_2)
% 101.88/14.43 |
% 101.88/14.43 | ALPHA: (78) implies:
% 101.88/14.43 | (79) Nat$(all_654_2)
% 101.88/14.43 | (80) Nat$(all_654_0)
% 101.88/14.43 | (81) of_nat$(all_654_2) = all_654_1
% 101.88/14.43 | (82) of_nat$(all_654_0) = all_654_1
% 101.88/14.43 | (83) card$c(top$d) = all_654_0
% 101.88/14.43 |
% 101.88/14.43 | DELTA: instantiating (9) with fresh symbol all_659_0 gives:
% 101.88/14.43 | (84) image$a(f$, top$b) = all_659_0 &
% 101.88/14.43 | C_ell2_c_ell2_cblinfun_set$(all_659_0) & ! [v0:
% 101.88/14.43 | B_ell2_b_ell2_cblinfun$] : ! [v1: C_ell2_c_ell2_cblinfun$] : ( ~
% 101.88/14.43 | (fun_app$c(g$, v0) = v1) | ~ B_ell2_b_ell2_cblinfun$(v0) | ? [v2:
% 101.88/14.43 | C_ell2_c_ell2_cblinfun_set_bool_fun$] : (member$(v1) = v2 &
% 101.88/14.43 | fun_app$a(v2, all_659_0) = 0 &
% 101.88/14.43 | C_ell2_c_ell2_cblinfun_set_bool_fun$(v2)))
% 101.88/14.43 |
% 101.88/14.43 | ALPHA: (84) implies:
% 101.88/14.43 | (85) image$a(f$, top$b) = all_659_0
% 101.88/14.44 | (86) ! [v0: B_ell2_b_ell2_cblinfun$] : ! [v1: C_ell2_c_ell2_cblinfun$] :
% 101.88/14.44 | ( ~ (fun_app$c(g$, v0) = v1) | ~ B_ell2_b_ell2_cblinfun$(v0) | ?
% 101.88/14.44 | [v2: C_ell2_c_ell2_cblinfun_set_bool_fun$] : (member$(v1) = v2 &
% 101.88/14.44 | fun_app$a(v2, all_659_0) = 0 &
% 101.88/14.44 | C_ell2_c_ell2_cblinfun_set_bool_fun$(v2)))
% 101.88/14.44 |
% 101.88/14.44 | DELTA: instantiating (4) with fresh symbol all_662_0 gives:
% 101.88/14.44 | (87) image$(g$, top$) = all_662_0 & C_ell2_c_ell2_cblinfun_set$(all_662_0)
% 101.88/14.44 | & ! [v0: A_ell2_a_ell2_cblinfun$] : ! [v1: C_ell2_c_ell2_cblinfun$]
% 101.88/14.44 | : ( ~ (fun_app$e(f$, v0) = v1) | ~ A_ell2_a_ell2_cblinfun$(v0) | ?
% 101.88/14.44 | [v2: C_ell2_c_ell2_cblinfun_set_bool_fun$] : (member$(v1) = v2 &
% 101.88/14.44 | fun_app$a(v2, all_662_0) = 0 &
% 101.88/14.44 | C_ell2_c_ell2_cblinfun_set_bool_fun$(v2)))
% 101.88/14.44 |
% 101.88/14.44 | ALPHA: (87) implies:
% 101.88/14.44 | (88) image$(g$, top$) = all_662_0
% 101.88/14.44 | (89) ! [v0: A_ell2_a_ell2_cblinfun$] : ! [v1: C_ell2_c_ell2_cblinfun$] :
% 101.88/14.44 | ( ~ (fun_app$e(f$, v0) = v1) | ~ A_ell2_a_ell2_cblinfun$(v0) | ?
% 101.88/14.44 | [v2: C_ell2_c_ell2_cblinfun_set_bool_fun$] : (member$(v1) = v2 &
% 101.88/14.44 | fun_app$a(v2, all_662_0) = 0 &
% 101.88/14.44 | C_ell2_c_ell2_cblinfun_set_bool_fun$(v2)))
% 101.88/14.44 |
% 101.88/14.44 | DELTA: instantiating (3) with fresh symbol all_668_0 gives:
% 101.88/14.44 | (90) inv_into$(top$, g$) = all_668_0 &
% 101.88/14.44 | C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$(all_668_0) & !
% 101.88/14.44 | [v0: A_ell2_a_ell2_cblinfun$] : ! [v1: B_ell2_b_ell2_cblinfun$] : ( ~
% 101.88/14.44 | (fun_app$h(j$, v0) = v1) | ~ A_ell2_a_ell2_cblinfun$(v0) | ? [v2:
% 101.88/14.44 | C_ell2_c_ell2_cblinfun$] : (fun_app$e(f$, v0) = v2 &
% 101.88/14.44 | fun_app$d(all_668_0, v2) = v1 & C_ell2_c_ell2_cblinfun$(v2) &
% 101.88/14.44 | B_ell2_b_ell2_cblinfun$(v1)))
% 101.88/14.44 |
% 101.88/14.44 | ALPHA: (90) implies:
% 101.88/14.44 | (91) inv_into$(top$, g$) = all_668_0
% 101.88/14.44 |
% 101.88/14.44 | DELTA: instantiating (3) with fresh symbol all_671_0 gives:
% 101.88/14.44 | (92) inv_into$(top$, g$) = all_671_0 &
% 101.88/14.44 | C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$(all_671_0) & !
% 101.88/14.44 | [v0: A_ell2_a_ell2_cblinfun$] : ! [v1: B_ell2_b_ell2_cblinfun$] : ( ~
% 101.88/14.44 | (fun_app$h(j$, v0) = v1) | ~ A_ell2_a_ell2_cblinfun$(v0) | ? [v2:
% 101.88/14.44 | C_ell2_c_ell2_cblinfun$] : (fun_app$e(f$, v0) = v2 &
% 101.88/14.44 | fun_app$d(all_671_0, v2) = v1 & C_ell2_c_ell2_cblinfun$(v2) &
% 101.88/14.44 | B_ell2_b_ell2_cblinfun$(v1)))
% 101.88/14.44 |
% 101.88/14.44 | ALPHA: (92) implies:
% 101.88/14.44 | (93) inv_into$(top$, g$) = all_671_0
% 101.88/14.44 |
% 101.88/14.44 | DELTA: instantiating (29) with fresh symbols all_677_0, all_677_1, all_677_2
% 101.88/14.44 | gives:
% 102.03/14.44 | (94) finite$e(top$l) = all_677_2 & finite$f(top$d) = all_677_0 &
% 102.03/14.44 | finite$d(top$c) = all_677_1 & ((all_677_0 = 0 & all_677_1 = 0 &
% 102.03/14.44 | all_677_2 = 0) | ( ~ (all_677_2 = 0) & ( ~ (all_677_0 = 0) | ~
% 102.03/14.44 | (all_677_1 = 0))))
% 102.03/14.44 |
% 102.03/14.44 | ALPHA: (94) implies:
% 102.03/14.44 | (95) finite$d(top$c) = all_677_1
% 102.03/14.44 |
% 102.03/14.44 | DELTA: instantiating (36) with fresh symbols all_681_0, all_681_1, all_681_2
% 102.03/14.44 | gives:
% 102.03/14.44 | (96) finite$n(top$t) = all_681_2 & finite$d(top$c) = all_681_1 &
% 102.03/14.44 | finite$(top$b) = all_681_0 & ((all_681_0 = 0 & all_681_1 = 0 &
% 102.03/14.44 | all_681_2 = 0) | ( ~ (all_681_2 = 0) & ( ~ (all_681_0 = 0) | ~
% 102.03/14.44 | (all_681_1 = 0))))
% 102.03/14.44 |
% 102.03/14.44 | ALPHA: (96) implies:
% 102.03/14.44 | (97) finite$d(top$c) = all_681_1
% 102.03/14.44 |
% 102.03/14.44 | DELTA: instantiating (30) with fresh symbols all_683_0, all_683_1, all_683_2
% 102.03/14.44 | gives:
% 102.03/14.44 | (98) finite$g(top$m) = all_683_2 & finite$f(top$d) = all_683_1 &
% 102.03/14.44 | finite$d(top$c) = all_683_0 & ((all_683_0 = 0 & all_683_1 = 0 &
% 102.03/14.44 | all_683_2 = 0) | ( ~ (all_683_2 = 0) & ( ~ (all_683_0 = 0) | ~
% 102.03/14.44 | (all_683_1 = 0))))
% 102.03/14.44 |
% 102.03/14.44 | ALPHA: (98) implies:
% 102.03/14.44 | (99) finite$d(top$c) = all_683_0
% 102.03/14.44 |
% 102.03/14.44 | DELTA: instantiating (31) with fresh symbols all_685_0, all_685_1, all_685_2
% 102.03/14.44 | gives:
% 102.03/14.44 | (100) finite$i(top$o) = all_685_2 & finite$d(top$c) = all_685_0 &
% 102.03/14.44 | finite$b(top$) = all_685_1 & ((all_685_0 = 0 & all_685_1 = 0 &
% 102.03/14.44 | all_685_2 = 0) | ( ~ (all_685_2 = 0) & ( ~ (all_685_0 = 0) | ~
% 102.03/14.44 | (all_685_1 = 0))))
% 102.03/14.44 |
% 102.03/14.44 | ALPHA: (100) implies:
% 102.03/14.44 | (101) finite$b(top$) = all_685_1
% 102.03/14.44 | (102) finite$d(top$c) = all_685_0
% 102.03/14.44 |
% 102.03/14.44 | DELTA: instantiating (33) with fresh symbols all_687_0, all_687_1, all_687_2
% 102.03/14.44 | gives:
% 102.03/14.44 | (103) finite$k(top$q) = all_687_2 & finite$d(top$c) = all_687_0 &
% 102.03/14.44 | finite$(top$b) = all_687_1 & ((all_687_0 = 0 & all_687_1 = 0 &
% 102.03/14.44 | all_687_2 = 0) | ( ~ (all_687_2 = 0) & ( ~ (all_687_0 = 0) | ~
% 102.03/14.44 | (all_687_1 = 0))))
% 102.03/14.44 |
% 102.03/14.44 | ALPHA: (103) implies:
% 102.03/14.44 | (104) finite$d(top$c) = all_687_0
% 102.03/14.44 | (105) (all_687_0 = 0 & all_687_1 = 0 & all_687_2 = 0) | ( ~ (all_687_2 = 0)
% 102.03/14.44 | & ( ~ (all_687_0 = 0) | ~ (all_687_1 = 0)))
% 102.03/14.44 |
% 102.03/14.44 | DELTA: instantiating (32) with fresh symbols all_689_0, all_689_1, all_689_2
% 102.03/14.44 | gives:
% 102.03/14.44 | (106) finite$j(top$p) = all_689_2 & finite$f(top$d) = all_689_0 &
% 102.03/14.44 | finite$b(top$) = all_689_1 & ((all_689_0 = 0 & all_689_1 = 0 &
% 102.03/14.44 | all_689_2 = 0) | ( ~ (all_689_2 = 0) & ( ~ (all_689_0 = 0) | ~
% 102.03/14.44 | (all_689_1 = 0))))
% 102.03/14.44 |
% 102.03/14.44 | ALPHA: (106) implies:
% 102.03/14.44 | (107) finite$b(top$) = all_689_1
% 102.03/14.44 | (108) (all_689_0 = 0 & all_689_1 = 0 & all_689_2 = 0) | ( ~ (all_689_2 = 0)
% 102.03/14.44 | & ( ~ (all_689_0 = 0) | ~ (all_689_1 = 0)))
% 102.03/14.44 |
% 102.03/14.44 | DELTA: instantiating (34) with fresh symbols all_691_0, all_691_1, all_691_2
% 102.03/14.44 | gives:
% 102.03/14.44 | (109) finite$m(top$s) = all_691_2 & finite$d(top$c) = all_691_1 &
% 102.03/14.44 | finite$b(top$) = all_691_0 & ((all_691_0 = 0 & all_691_1 = 0 &
% 102.03/14.44 | all_691_2 = 0) | ( ~ (all_691_2 = 0) & ( ~ (all_691_0 = 0) | ~
% 102.03/14.44 | (all_691_1 = 0))))
% 102.03/14.44 |
% 102.03/14.44 | ALPHA: (109) implies:
% 102.03/14.44 | (110) finite$b(top$) = all_691_0
% 102.03/14.44 | (111) finite$d(top$c) = all_691_1
% 102.03/14.44 |
% 102.03/14.44 | DELTA: instantiating (41) with fresh symbol all_711_0 gives:
% 102.03/14.44 | (112) finite$d(top$c) = all_711_0 & ! [v0: Nat_set$] : ! [v1: Nat_set$] :
% 102.03/14.44 | ( ~ (uminus$c(v0) = v1) | ~ Nat_set$(v0) | ? [v2: any] : ? [v3:
% 102.03/14.44 | any] : (finite$d(v1) = v3 & finite$d(v0) = v2 & ( ~ (v2 = 0) | ((
% 102.03/14.44 | ~ (v3 = 0) | all_711_0 = 0) & ( ~ (all_711_0 = 0) | v3 =
% 102.03/14.44 | 0)))))
% 102.03/14.44 |
% 102.03/14.44 | ALPHA: (112) implies:
% 102.03/14.44 | (113) finite$d(top$c) = all_711_0
% 102.03/14.44 |
% 102.03/14.44 | DELTA: instantiating (50) with fresh symbols all_809_0, all_809_1, all_809_2,
% 102.03/14.44 | all_809_3, all_809_4, all_809_5, all_809_6, all_809_7, all_809_8,
% 102.03/14.44 | all_809_9, all_809_10, all_809_11, all_809_12, all_809_13 gives:
% 102.03/14.45 | (114) ~ (all_809_0 = all_809_8) & cblinfun_compose$a(all_809_5) =
% 102.03/14.45 | all_809_4 & fun_app$g(all_809_4, all_809_1) = all_809_0 &
% 102.03/14.45 | cblinfun_compose$(a$) = all_809_12 & fun_app$f(all_809_12, b$) =
% 102.03/14.45 | all_809_11 & fun_app$c(g$, all_809_2) = all_809_1 & fun_app$c(g$,
% 102.03/14.45 | all_809_6) = all_809_5 & fun_app$c(g$, all_809_9) = all_809_8 &
% 102.03/14.45 | inv_into$(top$, g$) = all_809_13 & fun_app$e(f$, all_809_11) =
% 102.03/14.45 | all_809_10 & fun_app$e(f$, a$) = all_809_7 & fun_app$e(f$, b$) =
% 102.03/14.45 | all_809_3 & fun_app$d(all_809_13, all_809_3) = all_809_2 &
% 102.03/14.45 | fun_app$d(all_809_13, all_809_7) = all_809_6 & fun_app$d(all_809_13,
% 102.03/14.45 | all_809_10) = all_809_9 &
% 102.03/14.45 | C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$(all_809_4) &
% 102.03/14.45 | A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$(all_809_12) &
% 102.03/14.45 | C_ell2_c_ell2_cblinfun$(all_809_0) &
% 102.03/14.45 | C_ell2_c_ell2_cblinfun$(all_809_1) &
% 102.03/14.45 | C_ell2_c_ell2_cblinfun$(all_809_3) &
% 102.03/14.45 | C_ell2_c_ell2_cblinfun$(all_809_5) &
% 102.03/14.45 | C_ell2_c_ell2_cblinfun$(all_809_7) &
% 102.03/14.45 | C_ell2_c_ell2_cblinfun$(all_809_8) &
% 102.03/14.45 | C_ell2_c_ell2_cblinfun$(all_809_10) &
% 102.03/14.45 | B_ell2_b_ell2_cblinfun$(all_809_2) &
% 102.03/14.45 | B_ell2_b_ell2_cblinfun$(all_809_6) &
% 102.03/14.45 | B_ell2_b_ell2_cblinfun$(all_809_9) &
% 102.03/14.45 | C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$(all_809_13) &
% 102.03/14.45 | A_ell2_a_ell2_cblinfun$(all_809_11)
% 102.03/14.45 |
% 102.03/14.45 | ALPHA: (114) implies:
% 102.03/14.45 | (115) ~ (all_809_0 = all_809_8)
% 102.03/14.45 | (116) A_ell2_a_ell2_cblinfun$(all_809_11)
% 102.03/14.45 | (117) B_ell2_b_ell2_cblinfun$(all_809_9)
% 102.03/14.45 | (118) B_ell2_b_ell2_cblinfun$(all_809_6)
% 102.03/14.45 | (119) B_ell2_b_ell2_cblinfun$(all_809_2)
% 102.03/14.45 | (120) C_ell2_c_ell2_cblinfun$(all_809_10)
% 102.03/14.45 | (121) C_ell2_c_ell2_cblinfun$(all_809_8)
% 102.03/14.45 | (122) C_ell2_c_ell2_cblinfun$(all_809_7)
% 102.03/14.45 | (123) C_ell2_c_ell2_cblinfun$(all_809_3)
% 102.03/14.45 | (124) fun_app$d(all_809_13, all_809_10) = all_809_9
% 102.03/14.45 | (125) fun_app$d(all_809_13, all_809_7) = all_809_6
% 102.03/14.45 | (126) fun_app$d(all_809_13, all_809_3) = all_809_2
% 102.03/14.45 | (127) fun_app$e(f$, b$) = all_809_3
% 102.03/14.45 | (128) fun_app$e(f$, a$) = all_809_7
% 102.03/14.45 | (129) fun_app$e(f$, all_809_11) = all_809_10
% 102.03/14.45 | (130) inv_into$(top$, g$) = all_809_13
% 102.03/14.45 | (131) fun_app$c(g$, all_809_9) = all_809_8
% 102.03/14.45 | (132) fun_app$c(g$, all_809_6) = all_809_5
% 102.03/14.45 | (133) fun_app$c(g$, all_809_2) = all_809_1
% 102.03/14.45 | (134) fun_app$f(all_809_12, b$) = all_809_11
% 102.03/14.45 | (135) cblinfun_compose$(a$) = all_809_12
% 102.03/14.45 | (136) fun_app$g(all_809_4, all_809_1) = all_809_0
% 102.03/14.45 | (137) cblinfun_compose$a(all_809_5) = all_809_4
% 102.03/14.45 |
% 102.03/14.45 | GROUND_INST: instantiating (62) with all_671_0, all_809_13, g$, top$,
% 102.03/14.45 | simplifying with (93), (130) gives:
% 102.03/14.45 | (138) all_809_13 = all_671_0
% 102.03/14.45 |
% 102.03/14.45 | GROUND_INST: instantiating (62) with all_668_0, all_809_13, g$, top$,
% 102.03/14.45 | simplifying with (91), (130) gives:
% 102.03/14.45 | (139) all_809_13 = all_668_0
% 102.03/14.45 |
% 102.03/14.45 | GROUND_INST: instantiating (63) with all_604_0, all_662_0, top$, g$,
% 102.03/14.45 | simplifying with (74), (88) gives:
% 102.03/14.45 | (140) all_662_0 = all_604_0
% 102.03/14.45 |
% 102.03/14.45 | GROUND_INST: instantiating (65) with all_604_0, all_659_0, top$b, f$,
% 102.03/14.45 | simplifying with (75), (85) gives:
% 102.03/14.45 | (141) all_659_0 = all_604_0
% 102.03/14.45 |
% 102.03/14.45 | GROUND_INST: instantiating (56) with all_602_0, all_654_0, top$d, simplifying
% 102.03/14.45 | with (72), (83) gives:
% 102.03/14.45 | (142) all_654_0 = all_602_0
% 102.03/14.45 |
% 102.03/14.45 | GROUND_INST: instantiating (57) with all_689_1, all_691_0, top$, simplifying
% 102.03/14.45 | with (107), (110) gives:
% 102.03/14.45 | (143) all_691_0 = all_689_1
% 102.03/14.45 |
% 102.03/14.45 | GROUND_INST: instantiating (57) with all_685_1, all_691_0, top$, simplifying
% 102.03/14.45 | with (101), (110) gives:
% 102.03/14.45 | (144) all_691_0 = all_685_1
% 102.03/14.45 |
% 102.03/14.45 | GROUND_INST: instantiating (58) with all_681_1, all_683_0, top$c, simplifying
% 102.03/14.45 | with (97), (99) gives:
% 102.03/14.45 | (145) all_683_0 = all_681_1
% 102.03/14.45 |
% 102.03/14.45 | GROUND_INST: instantiating (58) with all_592_0, all_683_0, top$c, simplifying
% 102.03/14.45 | with (69), (99) gives:
% 102.03/14.45 | (146) all_683_0 = all_592_0
% 102.03/14.45 |
% 102.03/14.45 | GROUND_INST: instantiating (58) with all_681_1, all_687_0, top$c, simplifying
% 102.03/14.45 | with (97), (104) gives:
% 102.03/14.45 | (147) all_687_0 = all_681_1
% 102.03/14.45 |
% 102.03/14.45 | GROUND_INST: instantiating (58) with all_652_0, all_687_0, top$c, simplifying
% 102.03/14.45 | with (77), (104) gives:
% 102.03/14.45 | (148) all_687_0 = all_652_0
% 102.03/14.45 |
% 102.03/14.45 | GROUND_INST: instantiating (58) with all_681_1, all_691_1, top$c, simplifying
% 102.03/14.45 | with (97), (111) gives:
% 102.03/14.45 | (149) all_691_1 = all_681_1
% 102.03/14.45 |
% 102.03/14.45 | GROUND_INST: instantiating (58) with all_677_1, all_691_1, top$c, simplifying
% 102.03/14.45 | with (95), (111) gives:
% 102.03/14.45 | (150) all_691_1 = all_677_1
% 102.03/14.45 |
% 102.03/14.45 | GROUND_INST: instantiating (58) with all_687_0, all_711_0, top$c, simplifying
% 102.03/14.45 | with (104), (113) gives:
% 102.03/14.45 | (151) all_711_0 = all_687_0
% 102.03/14.45 |
% 102.03/14.45 | GROUND_INST: instantiating (58) with all_685_0, all_711_0, top$c, simplifying
% 102.03/14.45 | with (102), (113) gives:
% 102.03/14.45 | (152) all_711_0 = all_685_0
% 102.03/14.45 |
% 102.03/14.45 | COMBINE_EQS: (138), (139) imply:
% 102.03/14.45 | (153) all_671_0 = all_668_0
% 102.03/14.45 |
% 102.03/14.45 | COMBINE_EQS: (151), (152) imply:
% 102.03/14.45 | (154) all_687_0 = all_685_0
% 102.03/14.45 |
% 102.03/14.45 | SIMP: (154) implies:
% 102.03/14.45 | (155) all_687_0 = all_685_0
% 102.03/14.45 |
% 102.03/14.45 | COMBINE_EQS: (143), (144) imply:
% 102.03/14.45 | (156) all_689_1 = all_685_1
% 102.03/14.45 |
% 102.03/14.45 | SIMP: (156) implies:
% 102.03/14.45 | (157) all_689_1 = all_685_1
% 102.03/14.45 |
% 102.03/14.45 | COMBINE_EQS: (149), (150) imply:
% 102.03/14.45 | (158) all_681_1 = all_677_1
% 102.03/14.45 |
% 102.03/14.45 | SIMP: (158) implies:
% 102.03/14.45 | (159) all_681_1 = all_677_1
% 102.03/14.45 |
% 102.03/14.45 | COMBINE_EQS: (147), (155) imply:
% 102.03/14.45 | (160) all_685_0 = all_681_1
% 102.03/14.45 |
% 102.03/14.45 | COMBINE_EQS: (148), (155) imply:
% 102.03/14.45 | (161) all_685_0 = all_652_0
% 102.03/14.45 |
% 102.03/14.45 | COMBINE_EQS: (160), (161) imply:
% 102.03/14.45 | (162) all_681_1 = all_652_0
% 102.03/14.45 |
% 102.03/14.45 | SIMP: (162) implies:
% 102.03/14.45 | (163) all_681_1 = all_652_0
% 102.03/14.45 |
% 102.03/14.45 | COMBINE_EQS: (145), (146) imply:
% 102.03/14.45 | (164) all_681_1 = all_592_0
% 102.03/14.45 |
% 102.03/14.45 | SIMP: (164) implies:
% 102.03/14.45 | (165) all_681_1 = all_592_0
% 102.03/14.45 |
% 102.03/14.45 | COMBINE_EQS: (159), (163) imply:
% 102.03/14.45 | (166) all_677_1 = all_652_0
% 102.03/14.45 |
% 102.03/14.45 | COMBINE_EQS: (159), (165) imply:
% 102.03/14.45 | (167) all_677_1 = all_592_0
% 102.03/14.45 |
% 102.03/14.45 | COMBINE_EQS: (166), (167) imply:
% 102.03/14.45 | (168) all_652_0 = all_592_0
% 102.03/14.45 |
% 102.03/14.45 | SIMP: (168) implies:
% 102.03/14.45 | (169) all_652_0 = all_592_0
% 102.03/14.46 |
% 102.03/14.46 | COMBINE_EQS: (161), (169) imply:
% 102.03/14.46 | (170) all_685_0 = all_592_0
% 102.03/14.46 |
% 102.03/14.46 | COMBINE_EQS: (155), (170) imply:
% 102.03/14.46 | (171) all_687_0 = all_592_0
% 102.03/14.46 |
% 102.03/14.46 | REDUCE: (82), (142) imply:
% 102.03/14.46 | (172) of_nat$(all_602_0) = all_654_1
% 102.03/14.46 |
% 102.03/14.46 | REDUCE: (126), (139) imply:
% 102.03/14.46 | (173) fun_app$d(all_668_0, all_809_3) = all_809_2
% 102.03/14.46 |
% 102.03/14.46 | REDUCE: (125), (139) imply:
% 102.03/14.46 | (174) fun_app$d(all_668_0, all_809_7) = all_809_6
% 102.03/14.46 |
% 102.03/14.46 | REDUCE: (124), (139) imply:
% 102.03/14.46 | (175) fun_app$d(all_668_0, all_809_10) = all_809_9
% 102.03/14.46 |
% 102.03/14.46 | REDUCE: (80), (142) imply:
% 102.03/14.46 | (176) Nat$(all_602_0)
% 102.03/14.46 |
% 102.03/14.46 | BETA: splitting (105) gives:
% 102.03/14.46 |
% 102.03/14.46 | Case 1:
% 102.03/14.46 | |
% 102.03/14.46 | | (177) all_687_0 = 0 & all_687_1 = 0 & all_687_2 = 0
% 102.03/14.46 | |
% 102.03/14.46 | | ALPHA: (177) implies:
% 102.03/14.46 | | (178) all_687_0 = 0
% 102.03/14.46 | |
% 102.03/14.46 | | COMBINE_EQS: (171), (178) imply:
% 102.03/14.46 | | (179) all_592_0 = 0
% 102.03/14.46 | |
% 102.03/14.46 | | REDUCE: (68), (179) imply:
% 102.03/14.46 | | (180) $false
% 102.03/14.46 | |
% 102.03/14.46 | | CLOSE: (180) is inconsistent.
% 102.03/14.46 | |
% 102.03/14.46 | Case 2:
% 102.03/14.46 | |
% 102.03/14.46 | |
% 102.03/14.46 | | GROUND_INST: instantiating (55) with 1, all_654_1, all_602_0, simplifying
% 102.03/14.46 | | with (71), (172) gives:
% 102.03/14.46 | | (181) all_654_1 = 1
% 102.03/14.46 | |
% 102.03/14.46 | | REDUCE: (81), (181) imply:
% 102.03/14.46 | | (182) of_nat$(all_654_2) = 1
% 102.03/14.46 | |
% 102.03/14.46 | | GROUND_INST: instantiating (89) with b$, all_809_3, simplifying with (46),
% 102.03/14.46 | | (127) gives:
% 102.03/14.46 | | (183) ? [v0: C_ell2_c_ell2_cblinfun_set_bool_fun$] : (member$(all_809_3)
% 102.03/14.46 | | = v0 & fun_app$a(v0, all_662_0) = 0 &
% 102.03/14.46 | | C_ell2_c_ell2_cblinfun_set_bool_fun$(v0))
% 102.03/14.46 | |
% 102.03/14.46 | | GROUND_INST: instantiating (89) with a$, all_809_7, simplifying with (47),
% 102.03/14.46 | | (128) gives:
% 102.03/14.46 | | (184) ? [v0: C_ell2_c_ell2_cblinfun_set_bool_fun$] : (member$(all_809_7)
% 102.03/14.46 | | = v0 & fun_app$a(v0, all_662_0) = 0 &
% 102.03/14.46 | | C_ell2_c_ell2_cblinfun_set_bool_fun$(v0))
% 102.03/14.46 | |
% 102.03/14.46 | | GROUND_INST: instantiating (89) with all_809_11, all_809_10, simplifying
% 102.03/14.46 | | with (116), (129) gives:
% 102.03/14.46 | | (185) ? [v0: C_ell2_c_ell2_cblinfun_set_bool_fun$] :
% 102.03/14.46 | | (member$(all_809_10) = v0 & fun_app$a(v0, all_662_0) = 0 &
% 102.03/14.46 | | C_ell2_c_ell2_cblinfun_set_bool_fun$(v0))
% 102.03/14.46 | |
% 102.03/14.46 | | GROUND_INST: instantiating (37) with top$, g$, all_604_0, simplifying with
% 102.03/14.46 | | (48), (49), (74) gives:
% 102.03/14.46 | | (186) ? [v0: any] : ? [v1: any] : (finite$b(top$) = v0 &
% 102.03/14.46 | | fun_app$a(finite$a, all_604_0) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 102.03/14.46 | |
% 102.03/14.46 | | GROUND_INST: instantiating (axiom567) with g$, top$, simplifying with (5),
% 102.03/14.46 | | (48), (49) gives:
% 102.03/14.46 | | (187) ? [v0: C_ell2_c_ell2_cblinfun_set$] : ? [v1: Nat$] : ? [v2: int]
% 102.03/14.46 | | : ? [v3: Nat$] : (card$(v0) = v1 & card$a(top$) = v3 & of_nat$(v3)
% 102.03/14.46 | | = v2 & of_nat$(v1) = v2 & image$(g$, top$) = v0 &
% 102.03/14.46 | | C_ell2_c_ell2_cblinfun_set$(v0) & Nat$(v3) & Nat$(v1))
% 102.03/14.46 | |
% 102.03/14.46 | | GROUND_INST: instantiating (39) with g$, top$, simplifying with (5), (48),
% 102.03/14.46 | | (49) gives:
% 102.03/14.46 | | (188) ? [v0: C_ell2_c_ell2_cblinfun_set$] : ? [v1: any] : ? [v2: any]
% 102.03/14.46 | | : (finite$b(top$) = v2 & image$(g$, top$) = v0 &
% 102.03/14.46 | | fun_app$a(finite$a, v0) = v1 & C_ell2_c_ell2_cblinfun_set$(v0) &
% 102.03/14.46 | | ( ~ (v2 = 0) | v1 = 0) & ( ~ (v1 = 0) | v2 = 0))
% 102.03/14.46 | |
% 102.03/14.46 | | GROUND_INST: instantiating (axiom106) with all_809_10, g$, top$, all_668_0,
% 102.03/14.46 | | all_809_9, all_809_8, simplifying with (48), (49), (91), (120),
% 102.03/14.46 | | (131), (175) gives:
% 102.03/14.46 | | (189) all_809_8 = all_809_10 | ? [v0:
% 102.03/14.46 | | C_ell2_c_ell2_cblinfun_set_bool_fun$] : ? [v1:
% 102.03/14.46 | | C_ell2_c_ell2_cblinfun_set$] : ? [v2: int] : ( ~ (v2 = 0) &
% 102.03/14.46 | | image$(g$, top$) = v1 & member$(all_809_10) = v0 & fun_app$a(v0,
% 102.03/14.46 | | v1) = v2 & C_ell2_c_ell2_cblinfun_set$(v1) &
% 102.03/14.46 | | C_ell2_c_ell2_cblinfun_set_bool_fun$(v0))
% 102.03/14.46 | |
% 102.03/14.46 | | GROUND_INST: instantiating (86) with all_809_9, all_809_8, simplifying with
% 102.03/14.46 | | (117), (131) gives:
% 102.03/14.46 | | (190) ? [v0: C_ell2_c_ell2_cblinfun_set_bool_fun$] : (member$(all_809_8)
% 102.03/14.46 | | = v0 & fun_app$a(v0, all_659_0) = 0 &
% 102.03/14.46 | | C_ell2_c_ell2_cblinfun_set_bool_fun$(v0))
% 102.03/14.46 | |
% 102.03/14.46 | | GROUND_INST: instantiating (axiom106) with all_809_7, g$, top$, all_668_0,
% 102.03/14.46 | | all_809_6, all_809_5, simplifying with (48), (49), (91), (122),
% 102.03/14.46 | | (132), (174) gives:
% 102.03/14.46 | | (191) all_809_5 = all_809_7 | ? [v0:
% 102.03/14.46 | | C_ell2_c_ell2_cblinfun_set_bool_fun$] : ? [v1:
% 102.03/14.46 | | C_ell2_c_ell2_cblinfun_set$] : ? [v2: int] : ( ~ (v2 = 0) &
% 102.03/14.46 | | image$(g$, top$) = v1 & member$(all_809_7) = v0 & fun_app$a(v0,
% 102.03/14.46 | | v1) = v2 & C_ell2_c_ell2_cblinfun_set$(v1) &
% 102.03/14.46 | | C_ell2_c_ell2_cblinfun_set_bool_fun$(v0))
% 102.03/14.46 | |
% 102.03/14.46 | | GROUND_INST: instantiating (86) with all_809_6, all_809_5, simplifying with
% 102.03/14.46 | | (118), (132) gives:
% 102.03/14.46 | | (192) ? [v0: C_ell2_c_ell2_cblinfun_set_bool_fun$] : (member$(all_809_5)
% 102.03/14.46 | | = v0 & fun_app$a(v0, all_659_0) = 0 &
% 102.03/14.46 | | C_ell2_c_ell2_cblinfun_set_bool_fun$(v0))
% 102.03/14.47 | |
% 102.03/14.47 | | GROUND_INST: instantiating (axiom106) with all_809_3, g$, top$, all_668_0,
% 102.03/14.47 | | all_809_2, all_809_1, simplifying with (48), (49), (91), (123),
% 102.03/14.47 | | (133), (173) gives:
% 102.03/14.47 | | (193) all_809_1 = all_809_3 | ? [v0:
% 102.03/14.47 | | C_ell2_c_ell2_cblinfun_set_bool_fun$] : ? [v1:
% 102.03/14.47 | | C_ell2_c_ell2_cblinfun_set$] : ? [v2: int] : ( ~ (v2 = 0) &
% 102.03/14.47 | | image$(g$, top$) = v1 & member$(all_809_3) = v0 & fun_app$a(v0,
% 102.03/14.47 | | v1) = v2 & C_ell2_c_ell2_cblinfun_set$(v1) &
% 102.03/14.47 | | C_ell2_c_ell2_cblinfun_set_bool_fun$(v0))
% 102.03/14.47 | |
% 102.03/14.47 | | GROUND_INST: instantiating (86) with all_809_2, all_809_1, simplifying with
% 102.03/14.47 | | (119), (133) gives:
% 102.03/14.47 | | (194) ? [v0: C_ell2_c_ell2_cblinfun_set_bool_fun$] : (member$(all_809_1)
% 102.03/14.47 | | = v0 & fun_app$a(v0, all_659_0) = 0 &
% 102.03/14.47 | | C_ell2_c_ell2_cblinfun_set_bool_fun$(v0))
% 102.03/14.47 | |
% 102.03/14.47 | | GROUND_INST: instantiating (axiom232) with g$, all_809_6, all_809_2,
% 102.03/14.47 | | all_809_5, all_809_4, all_809_1, all_809_0, simplifying with
% 102.03/14.47 | | (48), (118), (119), (132), (133), (136), (137) gives:
% 102.03/14.47 | | (195) ? [v0: any] : ? [v1:
% 102.03/14.47 | | B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$] : ? [v2:
% 102.03/14.47 | | B_ell2_b_ell2_cblinfun$] : ? [v3: C_ell2_c_ell2_cblinfun$] :
% 102.03/14.47 | | (cblinfun_compose$b(all_809_6) = v1 & fun_app$j(v1, all_809_2) = v2
% 102.03/14.47 | | & fun_app$c(g$, v2) = v3 & register$(g$) = v0 &
% 102.03/14.47 | | B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$(v1) &
% 102.03/14.47 | | C_ell2_c_ell2_cblinfun$(v3) & B_ell2_b_ell2_cblinfun$(v2) & ( ~
% 102.03/14.47 | | (v0 = 0) | v3 = all_809_0))
% 102.03/14.47 | |
% 102.03/14.47 | | GROUND_INST: instantiating (38) with top$b, f$, all_604_0, simplifying with
% 102.03/14.47 | | (35), (45), (75) gives:
% 102.03/14.47 | | (196) ? [v0: any] : ? [v1: any] : (finite$(top$b) = v0 &
% 102.03/14.47 | | fun_app$a(finite$a, all_604_0) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 102.03/14.47 | |
% 102.03/14.47 | | GROUND_INST: instantiating (axiom568) with f$, top$b, simplifying with (12),
% 102.03/14.47 | | (35), (45) gives:
% 102.03/14.47 | | (197) ? [v0: C_ell2_c_ell2_cblinfun_set$] : ? [v1: Nat$] : ? [v2: int]
% 102.03/14.47 | | : ? [v3: Nat$] : (card$b(top$b) = v3 & card$(v0) = v1 &
% 102.03/14.47 | | of_nat$(v3) = v2 & of_nat$(v1) = v2 & image$a(f$, top$b) = v0 &
% 102.03/14.47 | | C_ell2_c_ell2_cblinfun_set$(v0) & Nat$(v3) & Nat$(v1))
% 102.03/14.47 | |
% 102.03/14.47 | | GROUND_INST: instantiating (40) with f$, top$b, simplifying with (12), (35),
% 102.03/14.47 | | (45) gives:
% 102.03/14.47 | | (198) ? [v0: C_ell2_c_ell2_cblinfun_set$] : ? [v1: any] : ? [v2: any]
% 102.03/14.47 | | : (finite$(top$b) = v2 & image$a(f$, top$b) = v0 &
% 102.03/14.47 | | fun_app$a(finite$a, v0) = v1 & C_ell2_c_ell2_cblinfun_set$(v0) &
% 102.03/14.47 | | ( ~ (v2 = 0) | v1 = 0) & ( ~ (v1 = 0) | v2 = 0))
% 102.03/14.47 | |
% 102.03/14.47 | | GROUND_INST: instantiating (17) with f$, top$b, simplifying with (6), (16),
% 102.03/14.47 | | (35), (45) gives:
% 102.03/14.47 | | (199) ? [v0: C_ell2_c_ell2_cblinfun_set$] : (image$a(f$, top$b) = v0 &
% 102.03/14.47 | | fun_app$a(csubspace$, v0) = 0 & C_ell2_c_ell2_cblinfun_set$(v0))
% 102.03/14.47 | |
% 102.03/14.47 | | GROUND_INST: instantiating (19) with f$, top$b, simplifying with (6), (16),
% 102.03/14.47 | | (35), (45) gives:
% 102.03/14.47 | | (200) ? [v0: C_ell2_c_ell2_cblinfun_set$] : (image$a(f$, top$b) = v0 &
% 102.03/14.47 | | C_ell2_c_ell2_cblinfun_set$(v0) & ? [v1:
% 102.03/14.47 | | C_ell2_c_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$] : ? [v2:
% 102.03/14.47 | | A_ell2_a_ell2_cblinfun_set$] : (clinear$b(v1) = 0 &
% 102.03/14.47 | | less_eq$b(v2, top$b) = 0 & image$s(v1, top$a) = v2 &
% 102.03/14.47 | | C_ell2_c_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$(v1) &
% 102.03/14.47 | | A_ell2_a_ell2_cblinfun_set$(v2) & ! [v3:
% 102.03/14.47 | | C_ell2_c_ell2_cblinfun$] : ! [v4:
% 102.03/14.47 | | C_ell2_c_ell2_cblinfun_set_bool_fun$] : ( ~ (member$(v3) =
% 102.03/14.47 | | v4) | ~ (fun_app$a(v4, v0) = 0) | ~
% 102.03/14.47 | | C_ell2_c_ell2_cblinfun$(v3) | ? [v5:
% 102.03/14.47 | | A_ell2_a_ell2_cblinfun$] : (fun_app$i(v1, v3) = v5 &
% 102.03/14.47 | | fun_app$e(f$, v5) = v3 & A_ell2_a_ell2_cblinfun$(v5)))))
% 102.03/14.47 | |
% 102.03/14.47 | | GROUND_INST: instantiating (18) with g$, top$, simplifying with (7), (15),
% 102.03/14.47 | | (48), (49) gives:
% 102.03/14.47 | | (201) ? [v0: C_ell2_c_ell2_cblinfun_set$] : (image$(g$, top$) = v0 &
% 102.03/14.47 | | fun_app$a(csubspace$, v0) = 0 & C_ell2_c_ell2_cblinfun_set$(v0))
% 102.03/14.47 | |
% 102.03/14.47 | | GROUND_INST: instantiating (20) with g$, top$, simplifying with (7), (15),
% 102.03/14.47 | | (48), (49) gives:
% 102.03/14.47 | | (202) ? [v0: C_ell2_c_ell2_cblinfun_set$] : (image$(g$, top$) = v0 &
% 102.03/14.47 | | C_ell2_c_ell2_cblinfun_set$(v0) & ? [v1:
% 102.03/14.47 | | C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$] : ? [v2:
% 102.03/14.47 | | B_ell2_b_ell2_cblinfun_set$] : (clinear$c(v1) = 0 &
% 102.03/14.47 | | less_eq$a(v2, top$) = 0 & image$r(v1, top$a) = v2 &
% 102.03/14.47 | | B_ell2_b_ell2_cblinfun_set$(v2) &
% 102.03/14.47 | | C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$(v1) & !
% 102.03/14.47 | | [v3: C_ell2_c_ell2_cblinfun$] : ! [v4:
% 102.03/14.47 | | C_ell2_c_ell2_cblinfun_set_bool_fun$] : ( ~ (member$(v3) =
% 102.03/14.47 | | v4) | ~ (fun_app$a(v4, v0) = 0) | ~
% 102.03/14.47 | | C_ell2_c_ell2_cblinfun$(v3) | ? [v5:
% 102.03/14.47 | | B_ell2_b_ell2_cblinfun$] : (fun_app$c(g$, v5) = v3 &
% 102.03/14.47 | | fun_app$d(v1, v3) = v5 & B_ell2_b_ell2_cblinfun$(v5)))))
% 102.03/14.47 | |
% 102.03/14.47 | | GROUND_INST: instantiating (25) with f$, top$b, top$b, simplifying with
% 102.03/14.47 | | (12), (14), (35), (45) gives:
% 102.03/14.47 | | (203) ? [v0: any] : ? [v1: C_ell2_c_ell2_cblinfun_set$] : ? [v2: any]
% 102.03/14.47 | | : ? [v3: any] : (cdependent$a(top$b) = v3 & image$a(f$, top$b) =
% 102.03/14.47 | | v1 & clinear$(f$) = v0 & fun_app$a(cdependent$, v1) = v2 &
% 102.03/14.47 | | C_ell2_c_ell2_cblinfun_set$(v1) & ( ~ (v2 = 0) | ~ (v0 = 0) | v3
% 102.03/14.47 | | = 0))
% 102.03/14.47 | |
% 102.03/14.47 | | GROUND_INST: instantiating (23) with f$, top$b, top$b, simplifying with
% 102.03/14.47 | | (12), (14), (35), (45) gives:
% 102.03/14.47 | | (204) ? [v0: any] : ? [v1: any] : ? [v2: C_ell2_c_ell2_cblinfun_set$]
% 102.03/14.47 | | : ? [v3: any] : (cdependent$a(top$b) = v1 & image$a(f$, top$b) =
% 102.03/14.47 | | v2 & clinear$(f$) = v0 & fun_app$a(cdependent$, v2) = v3 &
% 102.03/14.47 | | C_ell2_c_ell2_cblinfun_set$(v2) & ( ~ (v3 = 0) | ~ (v0 = 0) | v1
% 102.03/14.47 | | = 0))
% 102.03/14.47 | |
% 102.03/14.47 | | GROUND_INST: instantiating (21) with f$, top$b, top$b, 0, simplifying with
% 102.03/14.47 | | (12), (14), (35), (45) gives:
% 102.03/14.47 | | (205) ? [v0: any] : ? [v1: C_ell2_c_ell2_cblinfun_set$] : ? [v2: any]
% 102.03/14.47 | | : ? [v3: any] : (inj_on$a(f$, top$b) = v3 & image$a(f$, top$b) =
% 102.03/14.47 | | v1 & clinear$(f$) = v0 & fun_app$a(cdependent$, v1) = v2 &
% 102.03/14.47 | | C_ell2_c_ell2_cblinfun_set$(v1) & ( ~ (v0 = 0) | v3 = 0 | v2 =
% 102.03/14.47 | | 0))
% 102.03/14.47 | |
% 102.03/14.47 | | GROUND_INST: instantiating (axiom523) with f$, top$b, top$b, all_604_0,
% 102.03/14.47 | | simplifying with (14), (35), (45), (75) gives:
% 102.03/14.48 | | (206) ? [v0: any] : ? [v1: C_ell2_c_ell2_cblinfun_set$] : ? [v2:
% 102.03/14.48 | | C_ell2_c_ell2_cblinfun_set$] : (cspan$(v1) = v2 & image$a(f$,
% 102.03/14.48 | | top$b) = v1 & clinear$(f$) = v0 &
% 102.03/14.48 | | C_ell2_c_ell2_cblinfun_set$(v2) & C_ell2_c_ell2_cblinfun_set$(v1)
% 102.03/14.48 | | & ( ~ (v0 = 0) | v2 = all_604_0))
% 102.03/14.48 | |
% 102.03/14.48 | | GROUND_INST: instantiating (26) with g$, top$, top$, simplifying with (5),
% 102.03/14.48 | | (13), (48), (49) gives:
% 102.03/14.48 | | (207) ? [v0: any] : ? [v1: C_ell2_c_ell2_cblinfun_set$] : ? [v2: any]
% 102.03/14.48 | | : ? [v3: any] : (cdependent$b(top$) = v3 & clinear$a(g$) = v0 &
% 102.03/14.48 | | image$(g$, top$) = v1 & fun_app$a(cdependent$, v1) = v2 &
% 102.03/14.48 | | C_ell2_c_ell2_cblinfun_set$(v1) & ( ~ (v2 = 0) | ~ (v0 = 0) | v3
% 102.03/14.48 | | = 0))
% 102.03/14.48 | |
% 102.03/14.48 | | GROUND_INST: instantiating (24) with g$, top$, top$, simplifying with (5),
% 102.03/14.48 | | (13), (48), (49) gives:
% 102.03/14.48 | | (208) ? [v0: any] : ? [v1: any] : ? [v2: C_ell2_c_ell2_cblinfun_set$]
% 102.03/14.48 | | : ? [v3: any] : (cdependent$b(top$) = v1 & clinear$a(g$) = v0 &
% 102.03/14.48 | | image$(g$, top$) = v2 & fun_app$a(cdependent$, v2) = v3 &
% 102.03/14.48 | | C_ell2_c_ell2_cblinfun_set$(v2) & ( ~ (v3 = 0) | ~ (v0 = 0) | v1
% 102.03/14.48 | | = 0))
% 102.03/14.48 | |
% 102.03/14.48 | | GROUND_INST: instantiating (22) with g$, top$, top$, 0, simplifying with
% 102.03/14.48 | | (5), (13), (48), (49) gives:
% 102.03/14.48 | | (209) ? [v0: any] : ? [v1: C_ell2_c_ell2_cblinfun_set$] : ? [v2: any]
% 102.03/14.48 | | : ? [v3: any] : (clinear$a(g$) = v0 & inj_on$(g$, top$) = v3 &
% 102.03/14.48 | | image$(g$, top$) = v1 & fun_app$a(cdependent$, v1) = v2 &
% 102.03/14.48 | | C_ell2_c_ell2_cblinfun_set$(v1) & ( ~ (v0 = 0) | v3 = 0 | v2 =
% 102.03/14.48 | | 0))
% 102.03/14.48 | |
% 102.03/14.48 | | GROUND_INST: instantiating (axiom524) with g$, top$, top$, all_604_0,
% 102.03/14.48 | | simplifying with (13), (48), (49), (74) gives:
% 102.03/14.48 | | (210) ? [v0: any] : ? [v1: C_ell2_c_ell2_cblinfun_set$] : ? [v2:
% 102.03/14.48 | | C_ell2_c_ell2_cblinfun_set$] : (cspan$(v1) = v2 & clinear$a(g$) =
% 102.03/14.48 | | v0 & image$(g$, top$) = v1 & C_ell2_c_ell2_cblinfun_set$(v2) &
% 102.03/14.48 | | C_ell2_c_ell2_cblinfun_set$(v1) & ( ~ (v0 = 0) | v2 = all_604_0))
% 102.03/14.48 | |
% 102.03/14.48 | | GROUND_INST: instantiating (axiom637) with all_602_0, 1, simplifying with
% 102.03/14.48 | | (71), (176) gives:
% 102.03/14.48 | | (211) nat$(1) = all_602_0
% 102.03/14.48 | |
% 102.03/14.48 | | GROUND_INST: instantiating (axiom637) with all_654_2, 1, simplifying with
% 102.03/14.48 | | (79), (182) gives:
% 102.03/14.48 | | (212) nat$(1) = all_654_2
% 102.03/14.48 | |
% 102.03/14.48 | | GROUND_INST: instantiating (axiom577) with all_602_0, top$d, all_602_0, 1,
% 102.03/14.48 | | simplifying with (43), (71), (72), (176) gives:
% 102.03/14.48 | | (213) ? [v0: Unit_set$] : ? [v1: Nat$] : (card$c(v0) = v1 & of_nat$(v1)
% 102.03/14.48 | | = 1 & less_eq$d(v0, top$d) = 0 & Nat$(v1) & Unit_set$(v0)) | ?
% 102.03/14.48 | | [v0: int] : ($lesseq(v0, 0)of_nat$(all_602_0) = v0)
% 102.03/14.48 | |
% 102.03/14.48 | | DELTA: instantiating (201) with fresh symbol all_861_0 gives:
% 102.03/14.48 | | (214) image$(g$, top$) = all_861_0 & fun_app$a(csubspace$, all_861_0) = 0
% 102.03/14.48 | | & C_ell2_c_ell2_cblinfun_set$(all_861_0)
% 102.03/14.48 | |
% 102.03/14.48 | | ALPHA: (214) implies:
% 102.03/14.48 | | (215) image$(g$, top$) = all_861_0
% 102.03/14.48 | |
% 102.03/14.48 | | DELTA: instantiating (199) with fresh symbol all_863_0 gives:
% 102.03/14.48 | | (216) image$a(f$, top$b) = all_863_0 & fun_app$a(csubspace$, all_863_0) =
% 102.03/14.48 | | 0 & C_ell2_c_ell2_cblinfun_set$(all_863_0)
% 102.03/14.48 | |
% 102.03/14.48 | | ALPHA: (216) implies:
% 102.03/14.48 | | (217) image$a(f$, top$b) = all_863_0
% 102.03/14.48 | |
% 102.03/14.48 | | DELTA: instantiating (194) with fresh symbol all_865_0 gives:
% 102.03/14.48 | | (218) member$(all_809_1) = all_865_0 & fun_app$a(all_865_0, all_659_0) =
% 102.03/14.48 | | 0 & C_ell2_c_ell2_cblinfun_set_bool_fun$(all_865_0)
% 102.03/14.48 | |
% 102.03/14.48 | | ALPHA: (218) implies:
% 102.03/14.48 | | (219) member$(all_809_1) = all_865_0
% 102.03/14.48 | |
% 102.03/14.48 | | DELTA: instantiating (185) with fresh symbol all_867_0 gives:
% 102.03/14.48 | | (220) member$(all_809_10) = all_867_0 & fun_app$a(all_867_0, all_662_0) =
% 102.03/14.48 | | 0 & C_ell2_c_ell2_cblinfun_set_bool_fun$(all_867_0)
% 102.03/14.48 | |
% 102.03/14.48 | | ALPHA: (220) implies:
% 102.03/14.48 | | (221) fun_app$a(all_867_0, all_662_0) = 0
% 102.03/14.48 | | (222) member$(all_809_10) = all_867_0
% 102.03/14.48 | |
% 102.03/14.48 | | DELTA: instantiating (184) with fresh symbol all_869_0 gives:
% 102.03/14.48 | | (223) member$(all_809_7) = all_869_0 & fun_app$a(all_869_0, all_662_0) =
% 102.03/14.48 | | 0 & C_ell2_c_ell2_cblinfun_set_bool_fun$(all_869_0)
% 102.03/14.48 | |
% 102.03/14.48 | | ALPHA: (223) implies:
% 102.03/14.48 | | (224) fun_app$a(all_869_0, all_662_0) = 0
% 102.03/14.48 | | (225) member$(all_809_7) = all_869_0
% 102.03/14.48 | |
% 102.03/14.48 | | DELTA: instantiating (183) with fresh symbol all_871_0 gives:
% 102.03/14.48 | | (226) member$(all_809_3) = all_871_0 & fun_app$a(all_871_0, all_662_0) =
% 102.03/14.48 | | 0 & C_ell2_c_ell2_cblinfun_set_bool_fun$(all_871_0)
% 102.03/14.48 | |
% 102.03/14.48 | | ALPHA: (226) implies:
% 102.03/14.48 | | (227) fun_app$a(all_871_0, all_662_0) = 0
% 102.03/14.48 | | (228) member$(all_809_3) = all_871_0
% 102.03/14.48 | |
% 102.03/14.48 | | DELTA: instantiating (192) with fresh symbol all_873_0 gives:
% 102.03/14.48 | | (229) member$(all_809_5) = all_873_0 & fun_app$a(all_873_0, all_659_0) =
% 102.03/14.48 | | 0 & C_ell2_c_ell2_cblinfun_set_bool_fun$(all_873_0)
% 102.03/14.48 | |
% 102.03/14.48 | | ALPHA: (229) implies:
% 102.03/14.48 | | (230) fun_app$a(all_873_0, all_659_0) = 0
% 102.03/14.48 | | (231) member$(all_809_5) = all_873_0
% 102.03/14.48 | |
% 102.03/14.48 | | DELTA: instantiating (190) with fresh symbol all_875_0 gives:
% 102.03/14.48 | | (232) member$(all_809_8) = all_875_0 & fun_app$a(all_875_0, all_659_0) =
% 102.03/14.48 | | 0 & C_ell2_c_ell2_cblinfun_set_bool_fun$(all_875_0)
% 102.03/14.48 | |
% 102.03/14.48 | | ALPHA: (232) implies:
% 102.03/14.48 | | (233) fun_app$a(all_875_0, all_659_0) = 0
% 102.03/14.48 | | (234) member$(all_809_8) = all_875_0
% 102.03/14.48 | |
% 102.03/14.48 | | DELTA: instantiating (196) with fresh symbols all_879_0, all_879_1 gives:
% 102.03/14.48 | | (235) finite$(top$b) = all_879_1 & fun_app$a(finite$a, all_604_0) =
% 102.03/14.48 | | all_879_0 & ( ~ (all_879_1 = 0) | all_879_0 = 0)
% 102.03/14.48 | |
% 102.03/14.48 | | ALPHA: (235) implies:
% 102.03/14.48 | | (236) fun_app$a(finite$a, all_604_0) = all_879_0
% 102.03/14.48 | |
% 102.03/14.48 | | DELTA: instantiating (186) with fresh symbols all_881_0, all_881_1 gives:
% 102.03/14.48 | | (237) finite$b(top$) = all_881_1 & fun_app$a(finite$a, all_604_0) =
% 102.03/14.48 | | all_881_0 & ( ~ (all_881_1 = 0) | all_881_0 = 0)
% 102.03/14.48 | |
% 102.03/14.48 | | ALPHA: (237) implies:
% 102.03/14.48 | | (238) fun_app$a(finite$a, all_604_0) = all_881_0
% 102.03/14.48 | | (239) finite$b(top$) = all_881_1
% 102.03/14.48 | |
% 102.03/14.48 | | DELTA: instantiating (210) with fresh symbols all_885_0, all_885_1,
% 102.03/14.48 | | all_885_2 gives:
% 102.03/14.48 | | (240) cspan$(all_885_1) = all_885_0 & clinear$a(g$) = all_885_2 &
% 102.03/14.48 | | image$(g$, top$) = all_885_1 &
% 102.03/14.48 | | C_ell2_c_ell2_cblinfun_set$(all_885_0) &
% 102.03/14.48 | | C_ell2_c_ell2_cblinfun_set$(all_885_1) & ( ~ (all_885_2 = 0) |
% 102.03/14.48 | | all_885_0 = all_604_0)
% 102.03/14.48 | |
% 102.03/14.48 | | ALPHA: (240) implies:
% 102.03/14.48 | | (241) image$(g$, top$) = all_885_1
% 102.03/14.48 | |
% 102.03/14.48 | | DELTA: instantiating (206) with fresh symbols all_887_0, all_887_1,
% 102.03/14.48 | | all_887_2 gives:
% 102.03/14.48 | | (242) cspan$(all_887_1) = all_887_0 & image$a(f$, top$b) = all_887_1 &
% 102.03/14.48 | | clinear$(f$) = all_887_2 & C_ell2_c_ell2_cblinfun_set$(all_887_0) &
% 102.03/14.48 | | C_ell2_c_ell2_cblinfun_set$(all_887_1) & ( ~ (all_887_2 = 0) |
% 102.03/14.48 | | all_887_0 = all_604_0)
% 102.03/14.48 | |
% 102.03/14.48 | | ALPHA: (242) implies:
% 102.03/14.48 | | (243) image$a(f$, top$b) = all_887_1
% 102.03/14.48 | |
% 102.03/14.48 | | DELTA: instantiating (209) with fresh symbols all_889_0, all_889_1,
% 102.03/14.48 | | all_889_2, all_889_3 gives:
% 102.03/14.48 | | (244) clinear$a(g$) = all_889_3 & inj_on$(g$, top$) = all_889_0 &
% 102.03/14.48 | | image$(g$, top$) = all_889_2 & fun_app$a(cdependent$, all_889_2) =
% 102.03/14.48 | | all_889_1 & C_ell2_c_ell2_cblinfun_set$(all_889_2) & ( ~ (all_889_3
% 102.03/14.48 | | = 0) | all_889_0 = 0 | all_889_1 = 0)
% 102.03/14.48 | |
% 102.03/14.48 | | ALPHA: (244) implies:
% 102.03/14.48 | | (245) image$(g$, top$) = all_889_2
% 102.03/14.48 | |
% 102.03/14.48 | | DELTA: instantiating (208) with fresh symbols all_891_0, all_891_1,
% 102.03/14.48 | | all_891_2, all_891_3 gives:
% 102.03/14.48 | | (246) cdependent$b(top$) = all_891_2 & clinear$a(g$) = all_891_3 &
% 102.03/14.48 | | image$(g$, top$) = all_891_1 & fun_app$a(cdependent$, all_891_1) =
% 102.03/14.48 | | all_891_0 & C_ell2_c_ell2_cblinfun_set$(all_891_1) & ( ~ (all_891_0
% 102.03/14.48 | | = 0) | ~ (all_891_3 = 0) | all_891_2 = 0)
% 102.03/14.48 | |
% 102.03/14.48 | | ALPHA: (246) implies:
% 102.03/14.48 | | (247) image$(g$, top$) = all_891_1
% 102.03/14.48 | |
% 102.03/14.48 | | DELTA: instantiating (207) with fresh symbols all_893_0, all_893_1,
% 102.03/14.48 | | all_893_2, all_893_3 gives:
% 102.03/14.49 | | (248) cdependent$b(top$) = all_893_0 & clinear$a(g$) = all_893_3 &
% 102.03/14.49 | | image$(g$, top$) = all_893_2 & fun_app$a(cdependent$, all_893_2) =
% 102.03/14.49 | | all_893_1 & C_ell2_c_ell2_cblinfun_set$(all_893_2) & ( ~ (all_893_1
% 102.03/14.49 | | = 0) | ~ (all_893_3 = 0) | all_893_0 = 0)
% 102.03/14.49 | |
% 102.03/14.49 | | ALPHA: (248) implies:
% 102.03/14.49 | | (249) image$(g$, top$) = all_893_2
% 102.03/14.49 | |
% 102.03/14.49 | | DELTA: instantiating (198) with fresh symbols all_895_0, all_895_1,
% 102.03/14.49 | | all_895_2 gives:
% 102.03/14.49 | | (250) finite$(top$b) = all_895_0 & image$a(f$, top$b) = all_895_2 &
% 102.03/14.49 | | fun_app$a(finite$a, all_895_2) = all_895_1 &
% 102.03/14.49 | | C_ell2_c_ell2_cblinfun_set$(all_895_2) & ( ~ (all_895_0 = 0) |
% 102.03/14.49 | | all_895_1 = 0) & ( ~ (all_895_1 = 0) | all_895_0 = 0)
% 102.03/14.49 | |
% 102.03/14.49 | | ALPHA: (250) implies:
% 102.03/14.49 | | (251) fun_app$a(finite$a, all_895_2) = all_895_1
% 102.03/14.49 | | (252) image$a(f$, top$b) = all_895_2
% 102.03/14.49 | | (253) ~ (all_895_1 = 0) | all_895_0 = 0
% 102.03/14.49 | |
% 102.03/14.49 | | DELTA: instantiating (197) with fresh symbols all_897_0, all_897_1,
% 102.03/14.49 | | all_897_2, all_897_3 gives:
% 102.03/14.49 | | (254) card$b(top$b) = all_897_0 & card$(all_897_3) = all_897_2 &
% 102.03/14.49 | | of_nat$(all_897_0) = all_897_1 & of_nat$(all_897_2) = all_897_1 &
% 102.03/14.49 | | image$a(f$, top$b) = all_897_3 &
% 102.03/14.49 | | C_ell2_c_ell2_cblinfun_set$(all_897_3) & Nat$(all_897_0) &
% 102.03/14.49 | | Nat$(all_897_2)
% 102.03/14.49 | |
% 102.03/14.49 | | ALPHA: (254) implies:
% 102.03/14.49 | | (255) image$a(f$, top$b) = all_897_3
% 102.03/14.49 | |
% 102.03/14.49 | | DELTA: instantiating (188) with fresh symbols all_899_0, all_899_1,
% 102.03/14.49 | | all_899_2 gives:
% 102.03/14.49 | | (256) finite$b(top$) = all_899_0 & image$(g$, top$) = all_899_2 &
% 102.03/14.49 | | fun_app$a(finite$a, all_899_2) = all_899_1 &
% 102.03/14.49 | | C_ell2_c_ell2_cblinfun_set$(all_899_2) & ( ~ (all_899_0 = 0) |
% 102.03/14.49 | | all_899_1 = 0) & ( ~ (all_899_1 = 0) | all_899_0 = 0)
% 102.03/14.49 | |
% 102.03/14.49 | | ALPHA: (256) implies:
% 102.03/14.49 | | (257) fun_app$a(finite$a, all_899_2) = all_899_1
% 102.03/14.49 | | (258) image$(g$, top$) = all_899_2
% 102.03/14.49 | | (259) finite$b(top$) = all_899_0
% 102.03/14.49 | | (260) ~ (all_899_1 = 0) | all_899_0 = 0
% 102.03/14.49 | |
% 102.03/14.49 | | DELTA: instantiating (204) with fresh symbols all_901_0, all_901_1,
% 102.03/14.49 | | all_901_2, all_901_3 gives:
% 102.03/14.49 | | (261) cdependent$a(top$b) = all_901_2 & image$a(f$, top$b) = all_901_1 &
% 102.03/14.49 | | clinear$(f$) = all_901_3 & fun_app$a(cdependent$, all_901_1) =
% 102.03/14.49 | | all_901_0 & C_ell2_c_ell2_cblinfun_set$(all_901_1) & ( ~ (all_901_0
% 102.03/14.49 | | = 0) | ~ (all_901_3 = 0) | all_901_2 = 0)
% 102.03/14.49 | |
% 102.03/14.49 | | ALPHA: (261) implies:
% 102.03/14.49 | | (262) image$a(f$, top$b) = all_901_1
% 102.03/14.49 | |
% 102.03/14.49 | | DELTA: instantiating (203) with fresh symbols all_903_0, all_903_1,
% 102.03/14.49 | | all_903_2, all_903_3 gives:
% 102.03/14.49 | | (263) cdependent$a(top$b) = all_903_0 & image$a(f$, top$b) = all_903_2 &
% 102.03/14.49 | | clinear$(f$) = all_903_3 & fun_app$a(cdependent$, all_903_2) =
% 102.03/14.49 | | all_903_1 & C_ell2_c_ell2_cblinfun_set$(all_903_2) & ( ~ (all_903_1
% 102.03/14.49 | | = 0) | ~ (all_903_3 = 0) | all_903_0 = 0)
% 102.03/14.49 | |
% 102.03/14.49 | | ALPHA: (263) implies:
% 102.03/14.49 | | (264) image$a(f$, top$b) = all_903_2
% 102.03/14.49 | |
% 102.03/14.49 | | DELTA: instantiating (187) with fresh symbols all_905_0, all_905_1,
% 102.03/14.49 | | all_905_2, all_905_3 gives:
% 102.03/14.49 | | (265) card$(all_905_3) = all_905_2 & card$a(top$) = all_905_0 &
% 102.03/14.49 | | of_nat$(all_905_0) = all_905_1 & of_nat$(all_905_2) = all_905_1 &
% 102.03/14.49 | | image$(g$, top$) = all_905_3 &
% 102.03/14.49 | | C_ell2_c_ell2_cblinfun_set$(all_905_3) & Nat$(all_905_0) &
% 102.03/14.49 | | Nat$(all_905_2)
% 102.03/14.49 | |
% 102.03/14.49 | | ALPHA: (265) implies:
% 102.03/14.49 | | (266) image$(g$, top$) = all_905_3
% 102.03/14.49 | |
% 102.03/14.49 | | DELTA: instantiating (205) with fresh symbols all_907_0, all_907_1,
% 102.03/14.49 | | all_907_2, all_907_3 gives:
% 102.03/14.49 | | (267) inj_on$a(f$, top$b) = all_907_0 & image$a(f$, top$b) = all_907_2 &
% 102.03/14.49 | | clinear$(f$) = all_907_3 & fun_app$a(cdependent$, all_907_2) =
% 102.03/14.49 | | all_907_1 & C_ell2_c_ell2_cblinfun_set$(all_907_2) & ( ~ (all_907_3
% 102.03/14.49 | | = 0) | all_907_0 = 0 | all_907_1 = 0)
% 102.03/14.49 | |
% 102.03/14.49 | | ALPHA: (267) implies:
% 102.03/14.49 | | (268) image$a(f$, top$b) = all_907_2
% 102.03/14.49 | | (269) inj_on$a(f$, top$b) = all_907_0
% 102.03/14.49 | |
% 102.03/14.49 | | DELTA: instantiating (195) with fresh symbols all_909_0, all_909_1,
% 102.03/14.49 | | all_909_2, all_909_3 gives:
% 102.03/14.49 | | (270) cblinfun_compose$b(all_809_6) = all_909_2 & fun_app$j(all_909_2,
% 102.03/14.49 | | all_809_2) = all_909_1 & fun_app$c(g$, all_909_1) = all_909_0 &
% 102.03/14.49 | | register$(g$) = all_909_3 &
% 102.03/14.49 | | B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$(all_909_2) &
% 102.03/14.49 | | C_ell2_c_ell2_cblinfun$(all_909_0) &
% 102.03/14.49 | | B_ell2_b_ell2_cblinfun$(all_909_1) & ( ~ (all_909_3 = 0) |
% 102.03/14.49 | | all_909_0 = all_809_0)
% 102.03/14.49 | |
% 102.03/14.49 | | ALPHA: (270) implies:
% 102.03/14.49 | | (271) register$(g$) = all_909_3
% 102.03/14.49 | | (272) ~ (all_909_3 = 0) | all_909_0 = all_809_0
% 102.03/14.49 | |
% 102.03/14.49 | | DELTA: instantiating (202) with fresh symbol all_921_0 gives:
% 102.03/14.49 | | (273) image$(g$, top$) = all_921_0 &
% 102.03/14.49 | | C_ell2_c_ell2_cblinfun_set$(all_921_0) & ? [v0:
% 102.03/14.49 | | C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$] : ? [v1:
% 102.03/14.49 | | B_ell2_b_ell2_cblinfun_set$] : (clinear$c(v0) = 0 & less_eq$a(v1,
% 102.03/14.49 | | top$) = 0 & image$r(v0, top$a) = v1 &
% 102.03/14.49 | | B_ell2_b_ell2_cblinfun_set$(v1) &
% 102.03/14.49 | | C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$(v0) & ! [v2:
% 102.03/14.49 | | C_ell2_c_ell2_cblinfun$] : ! [v3:
% 102.03/14.49 | | C_ell2_c_ell2_cblinfun_set_bool_fun$] : ( ~ (member$(v2) = v3)
% 102.03/14.49 | | | ~ (fun_app$a(v3, all_921_0) = 0) | ~
% 102.03/14.49 | | C_ell2_c_ell2_cblinfun$(v2) | ? [v4: B_ell2_b_ell2_cblinfun$]
% 102.03/14.49 | | : (fun_app$c(g$, v4) = v2 & fun_app$d(v0, v2) = v4 &
% 102.03/14.49 | | B_ell2_b_ell2_cblinfun$(v4))))
% 102.03/14.49 | |
% 102.03/14.49 | | ALPHA: (273) implies:
% 102.03/14.49 | | (274) image$(g$, top$) = all_921_0
% 102.03/14.49 | |
% 102.03/14.49 | | DELTA: instantiating (200) with fresh symbol all_923_0 gives:
% 102.03/14.49 | | (275) image$a(f$, top$b) = all_923_0 &
% 102.03/14.49 | | C_ell2_c_ell2_cblinfun_set$(all_923_0) & ? [v0:
% 102.03/14.49 | | C_ell2_c_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$] : ? [v1:
% 102.03/14.49 | | A_ell2_a_ell2_cblinfun_set$] : (clinear$b(v0) = 0 & less_eq$b(v1,
% 102.03/14.49 | | top$b) = 0 & image$s(v0, top$a) = v1 &
% 102.03/14.49 | | C_ell2_c_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$(v0) &
% 102.03/14.49 | | A_ell2_a_ell2_cblinfun_set$(v1) & ! [v2:
% 102.03/14.49 | | C_ell2_c_ell2_cblinfun$] : ! [v3:
% 102.03/14.49 | | C_ell2_c_ell2_cblinfun_set_bool_fun$] : ( ~ (member$(v2) = v3)
% 102.03/14.49 | | | ~ (fun_app$a(v3, all_923_0) = 0) | ~
% 102.03/14.49 | | C_ell2_c_ell2_cblinfun$(v2) | ? [v4: A_ell2_a_ell2_cblinfun$]
% 102.03/14.49 | | : (fun_app$i(v0, v2) = v4 & fun_app$e(f$, v4) = v2 &
% 102.03/14.49 | | A_ell2_a_ell2_cblinfun$(v4))))
% 102.03/14.49 | |
% 102.03/14.49 | | ALPHA: (275) implies:
% 102.03/14.49 | | (276) image$a(f$, top$b) = all_923_0
% 102.03/14.49 | |
% 102.03/14.49 | | REDUCE: (141), (233) imply:
% 102.03/14.49 | | (277) fun_app$a(all_875_0, all_604_0) = 0
% 102.03/14.49 | |
% 102.03/14.49 | | REDUCE: (141), (230) imply:
% 102.03/14.49 | | (278) fun_app$a(all_873_0, all_604_0) = 0
% 102.03/14.49 | |
% 102.03/14.49 | | REDUCE: (140), (227) imply:
% 102.03/14.49 | | (279) fun_app$a(all_871_0, all_604_0) = 0
% 102.03/14.49 | |
% 102.03/14.49 | | REDUCE: (140), (224) imply:
% 102.03/14.49 | | (280) fun_app$a(all_869_0, all_604_0) = 0
% 102.03/14.49 | |
% 102.03/14.49 | | REDUCE: (140), (221) imply:
% 102.03/14.49 | | (281) fun_app$a(all_867_0, all_604_0) = 0
% 102.03/14.49 | |
% 102.03/14.49 | | BETA: splitting (213) gives:
% 102.03/14.49 | |
% 102.03/14.49 | | Case 1:
% 102.03/14.49 | | |
% 102.03/14.49 | | | (282) ? [v0: Unit_set$] : ? [v1: Nat$] : (card$c(v0) = v1 &
% 102.03/14.49 | | | of_nat$(v1) = 1 & less_eq$d(v0, top$d) = 0 & Nat$(v1) &
% 102.03/14.49 | | | Unit_set$(v0))
% 102.03/14.49 | | |
% 102.03/14.49 | | | DELTA: instantiating (282) with fresh symbols all_941_0, all_941_1 gives:
% 102.03/14.49 | | | (283) card$c(all_941_1) = all_941_0 & of_nat$(all_941_0) = 1 &
% 102.03/14.49 | | | less_eq$d(all_941_1, top$d) = 0 & Nat$(all_941_0) &
% 102.03/14.49 | | | Unit_set$(all_941_1)
% 102.03/14.49 | | |
% 102.03/14.49 | | | ALPHA: (283) implies:
% 102.03/14.49 | | | (284) Unit_set$(all_941_1)
% 102.03/14.49 | | | (285) Nat$(all_941_0)
% 102.03/14.49 | | | (286) of_nat$(all_941_0) = 1
% 102.03/14.49 | | | (287) card$c(all_941_1) = all_941_0
% 102.03/14.49 | | |
% 102.03/14.49 | | | GROUND_INST: instantiating (60) with all_879_0, all_881_0, all_604_0,
% 102.03/14.49 | | | finite$a, simplifying with (236), (238) gives:
% 102.03/14.49 | | | (288) all_881_0 = all_879_0
% 102.03/14.49 | | |
% 102.03/14.49 | | | GROUND_INST: instantiating (52) with 0, all_909_3, g$, simplifying with
% 102.03/14.49 | | | (1), (271) gives:
% 102.03/14.50 | | | (289) all_909_3 = 0
% 102.03/14.50 | | |
% 102.03/14.50 | | | GROUND_INST: instantiating (63) with all_604_0, all_891_1, top$, g$,
% 102.03/14.50 | | | simplifying with (74), (247) gives:
% 102.03/14.50 | | | (290) all_891_1 = all_604_0
% 102.03/14.50 | | |
% 102.03/14.50 | | | GROUND_INST: instantiating (63) with all_891_1, all_893_2, top$, g$,
% 102.03/14.50 | | | simplifying with (247), (249) gives:
% 102.03/14.50 | | | (291) all_893_2 = all_891_1
% 102.03/14.50 | | |
% 102.03/14.50 | | | GROUND_INST: instantiating (63) with all_885_1, all_893_2, top$, g$,
% 102.03/14.50 | | | simplifying with (241), (249) gives:
% 102.03/14.50 | | | (292) all_893_2 = all_885_1
% 102.03/14.50 | | |
% 102.03/14.50 | | | GROUND_INST: instantiating (63) with all_891_1, all_899_2, top$, g$,
% 102.03/14.50 | | | simplifying with (247), (258) gives:
% 102.03/14.50 | | | (293) all_899_2 = all_891_1
% 102.03/14.50 | | |
% 102.03/14.50 | | | GROUND_INST: instantiating (63) with all_889_2, all_899_2, top$, g$,
% 102.03/14.50 | | | simplifying with (245), (258) gives:
% 102.03/14.50 | | | (294) all_899_2 = all_889_2
% 102.03/14.50 | | |
% 102.03/14.50 | | | GROUND_INST: instantiating (63) with all_899_2, all_905_3, top$, g$,
% 102.03/14.50 | | | simplifying with (258), (266) gives:
% 102.03/14.50 | | | (295) all_905_3 = all_899_2
% 102.03/14.50 | | |
% 102.03/14.50 | | | GROUND_INST: instantiating (63) with all_905_3, all_921_0, top$, g$,
% 102.03/14.50 | | | simplifying with (266), (274) gives:
% 102.03/14.50 | | | (296) all_921_0 = all_905_3
% 102.03/14.50 | | |
% 102.03/14.50 | | | GROUND_INST: instantiating (63) with all_861_0, all_921_0, top$, g$,
% 102.03/14.50 | | | simplifying with (215), (274) gives:
% 102.03/14.50 | | | (297) all_921_0 = all_861_0
% 102.03/14.50 | | |
% 102.03/14.50 | | | GROUND_INST: instantiating (65) with all_887_1, all_895_2, top$b, f$,
% 102.03/14.50 | | | simplifying with (243), (252) gives:
% 102.03/14.50 | | | (298) all_895_2 = all_887_1
% 102.03/14.50 | | |
% 102.03/14.50 | | | GROUND_INST: instantiating (65) with all_895_2, all_897_3, top$b, f$,
% 102.03/14.50 | | | simplifying with (252), (255) gives:
% 102.03/14.50 | | | (299) all_897_3 = all_895_2
% 102.03/14.50 | | |
% 102.03/14.50 | | | GROUND_INST: instantiating (65) with all_897_3, all_901_1, top$b, f$,
% 102.03/14.50 | | | simplifying with (255), (262) gives:
% 102.03/14.50 | | | (300) all_901_1 = all_897_3
% 102.03/14.50 | | |
% 102.03/14.50 | | | GROUND_INST: instantiating (65) with all_604_0, all_903_2, top$b, f$,
% 102.03/14.50 | | | simplifying with (75), (264) gives:
% 102.03/14.50 | | | (301) all_903_2 = all_604_0
% 102.03/14.50 | | |
% 102.03/14.50 | | | GROUND_INST: instantiating (65) with all_887_1, all_903_2, top$b, f$,
% 102.03/14.50 | | | simplifying with (243), (264) gives:
% 102.03/14.50 | | | (302) all_903_2 = all_887_1
% 102.03/14.50 | | |
% 102.03/14.50 | | | GROUND_INST: instantiating (65) with all_901_1, all_907_2, top$b, f$,
% 102.03/14.50 | | | simplifying with (262), (268) gives:
% 102.03/14.50 | | | (303) all_907_2 = all_901_1
% 102.03/14.50 | | |
% 102.03/14.50 | | | GROUND_INST: instantiating (65) with all_907_2, all_923_0, top$b, f$,
% 102.03/14.50 | | | simplifying with (268), (276) gives:
% 102.03/14.50 | | | (304) all_923_0 = all_907_2
% 102.03/14.50 | | |
% 102.03/14.50 | | | GROUND_INST: instantiating (65) with all_863_0, all_923_0, top$b, f$,
% 102.03/14.50 | | | simplifying with (217), (276) gives:
% 102.03/14.50 | | | (305) all_923_0 = all_863_0
% 102.03/14.50 | | |
% 102.03/14.50 | | | GROUND_INST: instantiating (66) with 0, all_907_0, top$b, f$, simplifying
% 102.03/14.50 | | | with (12), (269) gives:
% 102.03/14.50 | | | (306) all_907_0 = 0
% 102.03/14.50 | | |
% 102.03/14.50 | | | GROUND_INST: instantiating (57) with all_685_1, all_899_0, top$,
% 102.03/14.50 | | | simplifying with (101), (259) gives:
% 102.03/14.50 | | | (307) all_899_0 = all_685_1
% 102.03/14.50 | | |
% 102.03/14.50 | | | GROUND_INST: instantiating (57) with all_881_1, all_899_0, top$,
% 102.03/14.50 | | | simplifying with (239), (259) gives:
% 102.03/14.50 | | | (308) all_899_0 = all_881_1
% 102.03/14.50 | | |
% 102.03/14.50 | | | GROUND_INST: instantiating (59) with all_602_0, all_654_2, 1, simplifying
% 102.03/14.50 | | | with (211), (212) gives:
% 102.03/14.50 | | | (309) all_654_2 = all_602_0
% 102.03/14.50 | | |
% 102.03/14.50 | | | COMBINE_EQS: (304), (305) imply:
% 102.03/14.50 | | | (310) all_907_2 = all_863_0
% 102.03/14.50 | | |
% 102.03/14.50 | | | SIMP: (310) implies:
% 102.03/14.50 | | | (311) all_907_2 = all_863_0
% 102.03/14.50 | | |
% 102.03/14.50 | | | COMBINE_EQS: (296), (297) imply:
% 102.03/14.50 | | | (312) all_905_3 = all_861_0
% 102.03/14.50 | | |
% 102.03/14.50 | | | SIMP: (312) implies:
% 102.03/14.50 | | | (313) all_905_3 = all_861_0
% 102.03/14.50 | | |
% 102.03/14.50 | | | COMBINE_EQS: (303), (311) imply:
% 102.03/14.50 | | | (314) all_901_1 = all_863_0
% 102.03/14.50 | | |
% 102.03/14.50 | | | SIMP: (314) implies:
% 102.03/14.50 | | | (315) all_901_1 = all_863_0
% 102.03/14.50 | | |
% 102.03/14.50 | | | COMBINE_EQS: (295), (313) imply:
% 102.03/14.50 | | | (316) all_899_2 = all_861_0
% 102.03/14.50 | | |
% 102.03/14.50 | | | SIMP: (316) implies:
% 102.03/14.50 | | | (317) all_899_2 = all_861_0
% 102.03/14.50 | | |
% 102.03/14.50 | | | COMBINE_EQS: (301), (302) imply:
% 102.03/14.50 | | | (318) all_887_1 = all_604_0
% 102.03/14.50 | | |
% 102.03/14.50 | | | SIMP: (318) implies:
% 102.03/14.50 | | | (319) all_887_1 = all_604_0
% 102.03/14.50 | | |
% 102.03/14.50 | | | COMBINE_EQS: (300), (315) imply:
% 102.03/14.50 | | | (320) all_897_3 = all_863_0
% 102.03/14.50 | | |
% 102.03/14.50 | | | SIMP: (320) implies:
% 102.03/14.50 | | | (321) all_897_3 = all_863_0
% 102.03/14.50 | | |
% 102.03/14.50 | | | COMBINE_EQS: (307), (308) imply:
% 102.03/14.50 | | | (322) all_881_1 = all_685_1
% 102.03/14.50 | | |
% 102.03/14.50 | | | COMBINE_EQS: (293), (294) imply:
% 102.03/14.50 | | | (323) all_891_1 = all_889_2
% 102.03/14.50 | | |
% 102.03/14.50 | | | SIMP: (323) implies:
% 102.03/14.50 | | | (324) all_891_1 = all_889_2
% 102.03/14.50 | | |
% 102.03/14.50 | | | COMBINE_EQS: (294), (317) imply:
% 102.03/14.50 | | | (325) all_889_2 = all_861_0
% 102.03/14.50 | | |
% 102.03/14.50 | | | COMBINE_EQS: (299), (321) imply:
% 102.03/14.50 | | | (326) all_895_2 = all_863_0
% 102.03/14.50 | | |
% 102.03/14.50 | | | SIMP: (326) implies:
% 102.03/14.50 | | | (327) all_895_2 = all_863_0
% 102.03/14.50 | | |
% 102.03/14.50 | | | COMBINE_EQS: (298), (327) imply:
% 102.03/14.50 | | | (328) all_887_1 = all_863_0
% 102.03/14.50 | | |
% 102.03/14.50 | | | SIMP: (328) implies:
% 102.03/14.50 | | | (329) all_887_1 = all_863_0
% 102.03/14.50 | | |
% 102.03/14.50 | | | COMBINE_EQS: (291), (292) imply:
% 102.03/14.50 | | | (330) all_891_1 = all_885_1
% 102.03/14.50 | | |
% 102.03/14.50 | | | SIMP: (330) implies:
% 102.03/14.50 | | | (331) all_891_1 = all_885_1
% 102.03/14.50 | | |
% 102.03/14.50 | | | COMBINE_EQS: (290), (331) imply:
% 102.03/14.50 | | | (332) all_885_1 = all_604_0
% 102.03/14.50 | | |
% 102.03/14.50 | | | COMBINE_EQS: (324), (331) imply:
% 102.03/14.50 | | | (333) all_889_2 = all_885_1
% 102.03/14.50 | | |
% 102.03/14.50 | | | SIMP: (333) implies:
% 102.03/14.50 | | | (334) all_889_2 = all_885_1
% 102.03/14.50 | | |
% 102.03/14.50 | | | COMBINE_EQS: (325), (334) imply:
% 102.03/14.50 | | | (335) all_885_1 = all_861_0
% 102.03/14.50 | | |
% 102.03/14.50 | | | SIMP: (335) implies:
% 102.03/14.50 | | | (336) all_885_1 = all_861_0
% 102.03/14.50 | | |
% 102.03/14.50 | | | COMBINE_EQS: (319), (329) imply:
% 102.03/14.50 | | | (337) all_863_0 = all_604_0
% 102.03/14.50 | | |
% 102.03/14.50 | | | COMBINE_EQS: (332), (336) imply:
% 102.03/14.50 | | | (338) all_861_0 = all_604_0
% 102.03/14.50 | | |
% 102.03/14.50 | | | SIMP: (338) implies:
% 102.03/14.50 | | | (339) all_861_0 = all_604_0
% 102.03/14.50 | | |
% 102.03/14.50 | | | COMBINE_EQS: (325), (339) imply:
% 102.03/14.50 | | | (340) all_889_2 = all_604_0
% 102.03/14.50 | | |
% 102.03/14.50 | | | COMBINE_EQS: (327), (337) imply:
% 102.03/14.50 | | | (341) all_895_2 = all_604_0
% 102.03/14.50 | | |
% 102.03/14.50 | | | COMBINE_EQS: (294), (340) imply:
% 102.03/14.50 | | | (342) all_899_2 = all_604_0
% 102.03/14.50 | | |
% 102.03/14.50 | | | REDUCE: (257), (342) imply:
% 102.03/14.50 | | | (343) fun_app$a(finite$a, all_604_0) = all_899_1
% 102.03/14.50 | | |
% 102.03/14.50 | | | REDUCE: (251), (341) imply:
% 102.03/14.50 | | | (344) fun_app$a(finite$a, all_604_0) = all_895_1
% 102.03/14.50 | | |
% 102.03/14.50 | | | BETA: splitting (189) gives:
% 102.03/14.50 | | |
% 102.03/14.50 | | | Case 1:
% 102.03/14.50 | | | |
% 102.03/14.50 | | | | (345) all_809_8 = all_809_10
% 102.03/14.50 | | | |
% 102.03/14.50 | | | | REDUCE: (115), (345) imply:
% 102.03/14.50 | | | | (346) ~ (all_809_0 = all_809_10)
% 102.03/14.50 | | | |
% 102.03/14.50 | | | | REDUCE: (234), (345) imply:
% 102.03/14.50 | | | | (347) member$(all_809_10) = all_875_0
% 102.03/14.50 | | | |
% 102.03/14.50 | | | | BETA: splitting (193) gives:
% 102.03/14.50 | | | |
% 102.03/14.50 | | | | Case 1:
% 102.03/14.50 | | | | |
% 102.03/14.50 | | | | | (348) all_809_1 = all_809_3
% 102.03/14.50 | | | | |
% 102.03/14.50 | | | | | REDUCE: (136), (348) imply:
% 102.03/14.50 | | | | | (349) fun_app$g(all_809_4, all_809_3) = all_809_0
% 102.03/14.50 | | | | |
% 102.03/14.50 | | | | | REDUCE: (219), (348) imply:
% 102.03/14.50 | | | | | (350) member$(all_809_3) = all_865_0
% 102.03/14.50 | | | | |
% 102.03/14.50 | | | | | BETA: splitting (191) gives:
% 102.03/14.50 | | | | |
% 102.03/14.50 | | | | | Case 1:
% 102.03/14.50 | | | | | |
% 102.03/14.50 | | | | | | (351) all_809_5 = all_809_7
% 102.03/14.50 | | | | | |
% 102.03/14.50 | | | | | | REDUCE: (137), (351) imply:
% 102.03/14.50 | | | | | | (352) cblinfun_compose$a(all_809_7) = all_809_4
% 102.03/14.50 | | | | | |
% 102.03/14.50 | | | | | | REDUCE: (231), (351) imply:
% 102.03/14.50 | | | | | | (353) member$(all_809_7) = all_873_0
% 102.03/14.50 | | | | | |
% 102.03/14.50 | | | | | | BETA: splitting (272) gives:
% 102.03/14.50 | | | | | |
% 102.03/14.50 | | | | | | Case 1:
% 102.03/14.50 | | | | | | |
% 102.03/14.50 | | | | | | | (354) ~ (all_909_3 = 0)
% 102.03/14.50 | | | | | | |
% 102.03/14.50 | | | | | | | REDUCE: (289), (354) imply:
% 102.03/14.50 | | | | | | | (355) $false
% 102.03/14.50 | | | | | | |
% 102.03/14.50 | | | | | | | CLOSE: (355) is inconsistent.
% 102.03/14.50 | | | | | | |
% 102.03/14.50 | | | | | | Case 2:
% 102.03/14.50 | | | | | | |
% 102.03/14.50 | | | | | | |
% 102.03/14.50 | | | | | | | GROUND_INST: instantiating (60) with all_879_0, all_899_1,
% 102.03/14.50 | | | | | | | all_604_0, finite$a, simplifying with (236), (343)
% 102.03/14.50 | | | | | | | gives:
% 102.03/14.50 | | | | | | | (356) all_899_1 = all_879_0
% 102.03/14.50 | | | | | | |
% 102.03/14.50 | | | | | | | GROUND_INST: instantiating (60) with all_895_1, all_899_1,
% 102.03/14.50 | | | | | | | all_604_0, finite$a, simplifying with (343), (344)
% 102.03/14.50 | | | | | | | gives:
% 102.03/14.50 | | | | | | | (357) all_899_1 = all_895_1
% 102.03/14.50 | | | | | | |
% 102.03/14.50 | | | | | | | GROUND_INST: instantiating (51) with all_867_0, all_875_0,
% 102.03/14.50 | | | | | | | all_809_10, simplifying with (222), (347) gives:
% 102.03/14.50 | | | | | | | (358) all_875_0 = all_867_0
% 102.03/14.50 | | | | | | |
% 102.03/14.51 | | | | | | | GROUND_INST: instantiating (51) with all_869_0, all_873_0,
% 102.03/14.51 | | | | | | | all_809_7, simplifying with (225), (353) gives:
% 102.03/14.51 | | | | | | | (359) all_873_0 = all_869_0
% 102.03/14.51 | | | | | | |
% 102.03/14.51 | | | | | | | GROUND_INST: instantiating (51) with all_871_0, all_865_0,
% 102.03/14.51 | | | | | | | all_809_3, simplifying with (228), (350) gives:
% 102.03/14.51 | | | | | | | (360) all_871_0 = all_865_0
% 102.03/14.51 | | | | | | |
% 102.03/14.51 | | | | | | | COMBINE_EQS: (356), (357) imply:
% 102.03/14.51 | | | | | | | (361) all_895_1 = all_879_0
% 102.03/14.51 | | | | | | |
% 102.03/14.51 | | | | | | | SIMP: (361) implies:
% 102.03/14.51 | | | | | | | (362) all_895_1 = all_879_0
% 102.03/14.51 | | | | | | |
% 102.03/14.51 | | | | | | | REDUCE: (279), (360) imply:
% 102.03/14.51 | | | | | | | (363) fun_app$a(all_865_0, all_604_0) = 0
% 102.03/14.51 | | | | | | |
% 102.03/14.51 | | | | | | | BETA: splitting (108) gives:
% 102.03/14.51 | | | | | | |
% 102.03/14.51 | | | | | | | Case 1:
% 102.03/14.51 | | | | | | | |
% 102.03/14.51 | | | | | | | | (364) all_689_0 = 0 & all_689_1 = 0 & all_689_2 = 0
% 102.03/14.51 | | | | | | | |
% 102.03/14.51 | | | | | | | | ALPHA: (364) implies:
% 102.03/14.51 | | | | | | | | (365) all_689_0 = 0
% 102.03/14.51 | | | | | | | |
% 102.03/14.51 | | | | | | | | BETA: splitting (253) gives:
% 102.03/14.51 | | | | | | | |
% 102.03/14.51 | | | | | | | | Case 1:
% 102.03/14.51 | | | | | | | | |
% 102.03/14.51 | | | | | | | | |
% 102.03/14.51 | | | | | | | | | GROUND_INST: instantiating (axiom230) with f$, a$, b$,
% 102.03/14.51 | | | | | | | | | all_809_7, all_809_4, all_809_3, all_809_0,
% 102.03/14.51 | | | | | | | | | simplifying with (45), (46), (47), (127), (128),
% 102.03/14.51 | | | | | | | | | (349), (352) gives:
% 102.03/14.51 | | | | | | | | | (366) ? [v0: any] : ? [v1:
% 102.03/14.51 | | | | | | | | | A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$]
% 102.03/14.51 | | | | | | | | | : ? [v2: A_ell2_a_ell2_cblinfun$] : ? [v3:
% 102.03/14.51 | | | | | | | | | C_ell2_c_ell2_cblinfun$] : (cblinfun_compose$(a$) =
% 102.03/14.51 | | | | | | | | | v1 & fun_app$f(v1, b$) = v2 & register$a(f$) = v0 &
% 102.03/14.51 | | | | | | | | | fun_app$e(f$, v2) = v3 &
% 102.03/14.51 | | | | | | | | | A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$(v1)
% 102.03/14.51 | | | | | | | | | & C_ell2_c_ell2_cblinfun$(v3) &
% 102.03/14.51 | | | | | | | | | A_ell2_a_ell2_cblinfun$(v2) & ( ~ (v0 = 0) | v3 =
% 102.03/14.51 | | | | | | | | | all_809_0))
% 102.03/14.51 | | | | | | | | |
% 102.03/14.51 | | | | | | | | | DELTA: instantiating (366) with fresh symbols all_1149_0,
% 102.03/14.51 | | | | | | | | | all_1149_1, all_1149_2, all_1149_3 gives:
% 102.03/14.51 | | | | | | | | | (367) cblinfun_compose$(a$) = all_1149_2 &
% 102.03/14.51 | | | | | | | | | fun_app$f(all_1149_2, b$) = all_1149_1 &
% 102.03/14.51 | | | | | | | | | register$a(f$) = all_1149_3 & fun_app$e(f$,
% 102.03/14.51 | | | | | | | | | all_1149_1) = all_1149_0 &
% 102.03/14.51 | | | | | | | | | A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$(all_1149_2)
% 102.03/14.51 | | | | | | | | | & C_ell2_c_ell2_cblinfun$(all_1149_0) &
% 102.03/14.51 | | | | | | | | | A_ell2_a_ell2_cblinfun$(all_1149_1) & ( ~ (all_1149_3
% 102.03/14.51 | | | | | | | | | = 0) | all_1149_0 = all_809_0)
% 102.03/14.51 | | | | | | | | |
% 102.03/14.51 | | | | | | | | | ALPHA: (367) implies:
% 102.03/14.51 | | | | | | | | | (368) fun_app$e(f$, all_1149_1) = all_1149_0
% 102.03/14.51 | | | | | | | | | (369) register$a(f$) = all_1149_3
% 102.03/14.51 | | | | | | | | | (370) fun_app$f(all_1149_2, b$) = all_1149_1
% 102.03/14.51 | | | | | | | | | (371) cblinfun_compose$(a$) = all_1149_2
% 102.03/14.51 | | | | | | | | | (372) ~ (all_1149_3 = 0) | all_1149_0 = all_809_0
% 102.03/14.51 | | | | | | | | |
% 102.03/14.51 | | | | | | | | | BETA: splitting (213) gives:
% 102.03/14.51 | | | | | | | | |
% 102.03/14.51 | | | | | | | | | Case 1:
% 102.03/14.51 | | | | | | | | | |
% 102.03/14.51 | | | | | | | | | |
% 102.03/14.51 | | | | | | | | | | GROUND_INST: instantiating (53) with 0, all_1149_3, f$,
% 102.03/14.51 | | | | | | | | | | simplifying with (2), (369) gives:
% 102.03/14.51 | | | | | | | | | | (373) all_1149_3 = 0
% 102.03/14.51 | | | | | | | | | |
% 102.03/14.51 | | | | | | | | | | GROUND_INST: instantiating (54) with all_809_12, all_1149_2,
% 102.03/14.51 | | | | | | | | | | a$, simplifying with (135), (371) gives:
% 102.03/14.51 | | | | | | | | | | (374) all_1149_2 = all_809_12
% 102.03/14.51 | | | | | | | | | |
% 102.03/14.51 | | | | | | | | | | REDUCE: (370), (374) imply:
% 102.03/14.51 | | | | | | | | | | (375) fun_app$f(all_809_12, b$) = all_1149_1
% 102.03/14.51 | | | | | | | | | |
% 102.03/14.51 | | | | | | | | | | BETA: splitting (372) gives:
% 102.03/14.51 | | | | | | | | | |
% 102.03/14.51 | | | | | | | | | | Case 1:
% 102.03/14.51 | | | | | | | | | | |
% 102.03/14.51 | | | | | | | | | | | (376) ~ (all_1149_3 = 0)
% 102.03/14.51 | | | | | | | | | | |
% 102.03/14.51 | | | | | | | | | | | REDUCE: (373), (376) imply:
% 102.03/14.51 | | | | | | | | | | | (377) $false
% 102.03/14.51 | | | | | | | | | | |
% 102.03/14.51 | | | | | | | | | | | CLOSE: (377) is inconsistent.
% 102.03/14.51 | | | | | | | | | | |
% 102.03/14.51 | | | | | | | | | | Case 2:
% 102.03/14.51 | | | | | | | | | | |
% 102.03/14.51 | | | | | | | | | | | (378) all_1149_0 = all_809_0
% 102.03/14.51 | | | | | | | | | | |
% 102.03/14.51 | | | | | | | | | | | REDUCE: (368), (378) imply:
% 102.03/14.51 | | | | | | | | | | | (379) fun_app$e(f$, all_1149_1) = all_809_0
% 102.03/14.51 | | | | | | | | | | |
% 102.03/14.51 | | | | | | | | | | | GROUND_INST: instantiating (64) with all_809_11, all_1149_1,
% 102.03/14.51 | | | | | | | | | | | b$, all_809_12, simplifying with (134), (375)
% 102.03/14.51 | | | | | | | | | | | gives:
% 102.03/14.51 | | | | | | | | | | | (380) all_1149_1 = all_809_11
% 102.03/14.51 | | | | | | | | | | |
% 102.03/14.51 | | | | | | | | | | | REDUCE: (379), (380) imply:
% 102.03/14.51 | | | | | | | | | | | (381) fun_app$e(f$, all_809_11) = all_809_0
% 102.03/14.51 | | | | | | | | | | |
% 102.03/14.51 | | | | | | | | | | | GROUND_INST: instantiating (61) with all_809_10, all_809_0,
% 102.03/14.51 | | | | | | | | | | | all_809_11, f$, simplifying with (129), (381)
% 102.03/14.51 | | | | | | | | | | | gives:
% 102.03/14.51 | | | | | | | | | | | (382) all_809_0 = all_809_10
% 102.03/14.51 | | | | | | | | | | |
% 102.03/14.51 | | | | | | | | | | | REDUCE: (346), (382) imply:
% 102.03/14.51 | | | | | | | | | | | (383) $false
% 102.03/14.51 | | | | | | | | | | |
% 102.03/14.51 | | | | | | | | | | | CLOSE: (383) is inconsistent.
% 102.03/14.51 | | | | | | | | | | |
% 102.03/14.51 | | | | | | | | | | End of split
% 102.03/14.51 | | | | | | | | | |
% 102.03/14.51 | | | | | | | | | Case 2:
% 102.03/14.51 | | | | | | | | | |
% 102.03/14.51 | | | | | | | | | | (384) ? [v0: int] : ($lesseq(v0, 0)of_nat$(all_602_0) =
% 102.03/14.51 | | | | | | | | | | v0)
% 102.03/14.51 | | | | | | | | | |
% 102.03/14.51 | | | | | | | | | | DELTA: instantiating (384) with fresh symbol all_941_0
% 102.03/14.51 | | | | | | | | | | gives:
% 102.03/14.51 | | | | | | | | | | (385) $lesseq(all_941_0, 0)of_nat$(all_602_0) = all_941_0
% 102.03/14.51 | | | | | | | | | |
% 102.03/14.51 | | | | | | | | | | REF_CLOSE: (55), (71), (385) are inconsistent by sub-proof
% 102.03/14.51 | | | | | | | | | | #1.
% 102.03/14.51 | | | | | | | | | |
% 102.03/14.51 | | | | | | | | | End of split
% 102.03/14.51 | | | | | | | | |
% 102.03/14.51 | | | | | | | | Case 2:
% 102.03/14.51 | | | | | | | | |
% 102.03/14.51 | | | | | | | | | (386) all_895_1 = 0
% 102.03/14.51 | | | | | | | | |
% 102.03/14.51 | | | | | | | | | COMBINE_EQS: (362), (386) imply:
% 102.03/14.51 | | | | | | | | | (387) all_879_0 = 0
% 102.03/14.51 | | | | | | | | |
% 102.03/14.51 | | | | | | | | | COMBINE_EQS: (356), (387) imply:
% 102.03/14.51 | | | | | | | | | (388) all_899_1 = 0
% 102.03/14.51 | | | | | | | | |
% 102.03/14.51 | | | | | | | | | BETA: splitting (260) gives:
% 102.03/14.51 | | | | | | | | |
% 102.03/14.51 | | | | | | | | | Case 1:
% 102.03/14.51 | | | | | | | | | |
% 102.03/14.51 | | | | | | | | | | (389) ~ (all_899_1 = 0)
% 102.03/14.51 | | | | | | | | | |
% 102.03/14.51 | | | | | | | | | | REDUCE: (388), (389) imply:
% 102.03/14.51 | | | | | | | | | | (390) $false
% 102.03/14.51 | | | | | | | | | |
% 102.03/14.51 | | | | | | | | | | CLOSE: (390) is inconsistent.
% 102.03/14.51 | | | | | | | | | |
% 102.03/14.51 | | | | | | | | | Case 2:
% 102.03/14.51 | | | | | | | | | |
% 102.03/14.51 | | | | | | | | | | (391) all_899_0 = 0
% 102.03/14.51 | | | | | | | | | |
% 102.03/14.51 | | | | | | | | | | COMBINE_EQS: (307), (391) imply:
% 102.03/14.51 | | | | | | | | | | (392) all_685_1 = 0
% 102.03/14.51 | | | | | | | | | |
% 102.03/14.51 | | | | | | | | | | SIMP: (392) implies:
% 102.03/14.51 | | | | | | | | | | (393) all_685_1 = 0
% 102.03/14.51 | | | | | | | | | |
% 102.03/14.51 | | | | | | | | | | COMBINE_EQS: (157), (393) imply:
% 102.03/14.51 | | | | | | | | | | (394) all_689_1 = 0
% 102.03/14.51 | | | | | | | | | |
% 102.03/14.51 | | | | | | | | | | BETA: splitting (108) gives:
% 102.03/14.51 | | | | | | | | | |
% 102.03/14.51 | | | | | | | | | | Case 1:
% 102.03/14.51 | | | | | | | | | | |
% 102.03/14.51 | | | | | | | | | | |
% 102.03/14.51 | | | | | | | | | | | GROUND_INST: instantiating (11) with f$, all_809_11, top$b,
% 102.03/14.51 | | | | | | | | | | | all_809_10, all_867_0, all_604_0, 0, simplifying
% 102.03/14.51 | | | | | | | | | | | with (35), (45), (75), (116), (129), (222), (281)
% 102.03/14.51 | | | | | | | | | | | gives:
% 102.03/14.51 | | | | | | | | | | | (395) ? [v0: any] : ? [v1: any] : (inj_on$a(f$, top$b)
% 102.03/14.51 | | | | | | | | | | | = v0 & member$c(all_809_11, top$b) = v1 & ( ~
% 102.03/14.51 | | | | | | | | | | | (v0 = 0) | v1 = 0))
% 102.03/14.51 | | | | | | | | | | |
% 102.03/14.51 | | | | | | | | | | | GROUND_INST: instantiating (10) with f$, all_809_10, all_867_0,
% 102.03/14.51 | | | | | | | | | | | all_604_0, 0, simplifying with (45), (75), (120),
% 102.03/14.51 | | | | | | | | | | | (222), (281) gives:
% 102.03/14.51 | | | | | | | | | | | (396) ? [v0: int] : ( ~ (v0 = 0) & inj_on$a(f$, top$b)
% 102.03/14.51 | | | | | | | | | | | = v0) | ? [v0: A_ell2_a_ell2_cblinfun$] :
% 102.03/14.51 | | | | | | | | | | | (fun_app$e(f$, v0) = all_809_10 &
% 102.03/14.51 | | | | | | | | | | | A_ell2_a_ell2_cblinfun$(v0) & ! [v1:
% 102.03/14.51 | | | | | | | | | | | A_ell2_a_ell2_cblinfun$] : (v1 = v0 | ~
% 102.03/14.51 | | | | | | | | | | | (fun_app$e(f$, v1) = all_809_10) | ~
% 102.03/14.51 | | | | | | | | | | | A_ell2_a_ell2_cblinfun$(v1)))
% 102.03/14.51 | | | | | | | | | | |
% 102.03/14.51 | | | | | | | | | | | GROUND_INST: instantiating (11) with f$, a$, top$b, all_809_7,
% 102.03/14.51 | | | | | | | | | | | all_869_0, all_604_0, 0, simplifying with (35),
% 102.03/14.51 | | | | | | | | | | | (45), (47), (75), (128), (225), (280) gives:
% 102.03/14.51 | | | | | | | | | | | (397) ? [v0: any] : ? [v1: any] : (inj_on$a(f$, top$b)
% 102.03/14.51 | | | | | | | | | | | = v0 & member$c(a$, top$b) = v1 & ( ~ (v0 = 0) |
% 102.03/14.51 | | | | | | | | | | | v1 = 0))
% 102.03/14.51 | | | | | | | | | | |
% 102.03/14.51 | | | | | | | | | | | GROUND_INST: instantiating (11) with f$, b$, top$b, all_809_3,
% 102.03/14.51 | | | | | | | | | | | all_865_0, all_604_0, 0, simplifying with (35),
% 102.03/14.51 | | | | | | | | | | | (45), (46), (75), (127), (350), (363) gives:
% 102.03/14.51 | | | | | | | | | | | (398) ? [v0: any] : ? [v1: any] : (inj_on$a(f$, top$b)
% 102.03/14.51 | | | | | | | | | | | = v0 & member$c(b$, top$b) = v1 & ( ~ (v0 = 0) |
% 102.03/14.51 | | | | | | | | | | | v1 = 0))
% 102.03/14.51 | | | | | | | | | | |
% 102.03/14.51 | | | | | | | | | | | GROUND_INST: instantiating (axiom230) with f$, a$, b$,
% 102.03/14.51 | | | | | | | | | | | all_809_7, all_809_4, all_809_3, all_809_0,
% 102.03/14.51 | | | | | | | | | | | simplifying with (45), (46), (47), (127), (128),
% 102.03/14.51 | | | | | | | | | | | (349), (352) gives:
% 102.03/14.51 | | | | | | | | | | | (399) ? [v0: any] : ? [v1:
% 102.03/14.51 | | | | | | | | | | | A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$]
% 102.03/14.51 | | | | | | | | | | | : ? [v2: A_ell2_a_ell2_cblinfun$] : ? [v3:
% 102.03/14.51 | | | | | | | | | | | C_ell2_c_ell2_cblinfun$] :
% 102.03/14.51 | | | | | | | | | | | (cblinfun_compose$(a$) = v1 & fun_app$f(v1, b$) =
% 102.03/14.51 | | | | | | | | | | | v2 & register$a(f$) = v0 & fun_app$e(f$, v2) =
% 102.03/14.51 | | | | | | | | | | | v3 &
% 102.03/14.51 | | | | | | | | | | | A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$(v1)
% 102.03/14.51 | | | | | | | | | | | & C_ell2_c_ell2_cblinfun$(v3) &
% 102.03/14.51 | | | | | | | | | | | A_ell2_a_ell2_cblinfun$(v2) & ( ~ (v0 = 0) | v3
% 102.03/14.51 | | | | | | | | | | | = all_809_0))
% 102.03/14.51 | | | | | | | | | | |
% 102.03/14.51 | | | | | | | | | | | GROUND_INST: instantiating (axiom577) with all_941_0,
% 102.03/14.51 | | | | | | | | | | | all_941_1, all_941_0, 1, simplifying with (284),
% 102.03/14.51 | | | | | | | | | | | (285), (286), (287) gives:
% 102.03/14.51 | | | | | | | | | | | (400) ? [v0: Unit_set$] : ? [v1: Nat$] : (card$c(v0) =
% 102.03/14.51 | | | | | | | | | | | v1 & of_nat$(v1) = 1 & less_eq$d(v0, all_941_1)
% 102.03/14.51 | | | | | | | | | | | = 0 & Nat$(v1) & Unit_set$(v0)) | ? [v0: int] :
% 102.03/14.51 | | | | | | | | | | | ($lesseq(v0, 0)of_nat$(all_941_0) = v0)
% 102.03/14.51 | | | | | | | | | | |
% 102.03/14.51 | | | | | | | | | | | DELTA: instantiating (397) with fresh symbols all_1100_0,
% 102.03/14.51 | | | | | | | | | | | all_1100_1 gives:
% 102.03/14.52 | | | | | | | | | | | (401) inj_on$a(f$, top$b) = all_1100_1 & member$c(a$,
% 102.03/14.52 | | | | | | | | | | | top$b) = all_1100_0 & ( ~ (all_1100_1 = 0) |
% 102.03/14.52 | | | | | | | | | | | all_1100_0 = 0)
% 102.03/14.52 | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | | ALPHA: (401) implies:
% 102.03/14.52 | | | | | | | | | | | (402) inj_on$a(f$, top$b) = all_1100_1
% 102.03/14.52 | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | | DELTA: instantiating (398) with fresh symbols all_1102_0,
% 102.03/14.52 | | | | | | | | | | | all_1102_1 gives:
% 102.03/14.52 | | | | | | | | | | | (403) inj_on$a(f$, top$b) = all_1102_1 & member$c(b$,
% 102.03/14.52 | | | | | | | | | | | top$b) = all_1102_0 & ( ~ (all_1102_1 = 0) |
% 102.03/14.52 | | | | | | | | | | | all_1102_0 = 0)
% 102.03/14.52 | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | | ALPHA: (403) implies:
% 102.03/14.52 | | | | | | | | | | | (404) inj_on$a(f$, top$b) = all_1102_1
% 102.03/14.52 | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | | DELTA: instantiating (395) with fresh symbols all_1114_0,
% 102.03/14.52 | | | | | | | | | | | all_1114_1 gives:
% 102.03/14.52 | | | | | | | | | | | (405) inj_on$a(f$, top$b) = all_1114_1 &
% 102.03/14.52 | | | | | | | | | | | member$c(all_809_11, top$b) = all_1114_0 & ( ~
% 102.03/14.52 | | | | | | | | | | | (all_1114_1 = 0) | all_1114_0 = 0)
% 102.03/14.52 | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | | ALPHA: (405) implies:
% 102.03/14.52 | | | | | | | | | | | (406) inj_on$a(f$, top$b) = all_1114_1
% 102.03/14.52 | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | | DELTA: instantiating (399) with fresh symbols all_1145_0,
% 102.03/14.52 | | | | | | | | | | | all_1145_1, all_1145_2, all_1145_3 gives:
% 102.03/14.52 | | | | | | | | | | | (407) cblinfun_compose$(a$) = all_1145_2 &
% 102.03/14.52 | | | | | | | | | | | fun_app$f(all_1145_2, b$) = all_1145_1 &
% 102.03/14.52 | | | | | | | | | | | register$a(f$) = all_1145_3 & fun_app$e(f$,
% 102.03/14.52 | | | | | | | | | | | all_1145_1) = all_1145_0 &
% 102.03/14.52 | | | | | | | | | | | A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$(all_1145_2)
% 102.03/14.52 | | | | | | | | | | | & C_ell2_c_ell2_cblinfun$(all_1145_0) &
% 102.03/14.52 | | | | | | | | | | | A_ell2_a_ell2_cblinfun$(all_1145_1) & ( ~
% 102.03/14.52 | | | | | | | | | | | (all_1145_3 = 0) | all_1145_0 = all_809_0)
% 102.03/14.52 | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | | ALPHA: (407) implies:
% 102.03/14.52 | | | | | | | | | | | (408) fun_app$e(f$, all_1145_1) = all_1145_0
% 102.03/14.52 | | | | | | | | | | | (409) register$a(f$) = all_1145_3
% 102.03/14.52 | | | | | | | | | | | (410) fun_app$f(all_1145_2, b$) = all_1145_1
% 102.03/14.52 | | | | | | | | | | | (411) cblinfun_compose$(a$) = all_1145_2
% 102.03/14.52 | | | | | | | | | | | (412) ~ (all_1145_3 = 0) | all_1145_0 = all_809_0
% 102.03/14.52 | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | | BETA: splitting (400) gives:
% 102.03/14.52 | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | | Case 1:
% 102.03/14.52 | | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | | | GROUND_INST: instantiating (53) with 0, all_1145_3, f$,
% 102.03/14.52 | | | | | | | | | | | | simplifying with (2), (409) gives:
% 102.03/14.52 | | | | | | | | | | | | (413) all_1145_3 = 0
% 102.03/14.52 | | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | | | GROUND_INST: instantiating (54) with all_809_12, all_1145_2,
% 102.03/14.52 | | | | | | | | | | | | a$, simplifying with (135), (411) gives:
% 102.03/14.52 | | | | | | | | | | | | (414) all_1145_2 = all_809_12
% 102.03/14.52 | | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | | | GROUND_INST: instantiating (66) with 0, all_1102_1, top$b, f$,
% 102.03/14.52 | | | | | | | | | | | | simplifying with (12), (404) gives:
% 102.03/14.52 | | | | | | | | | | | | (415) all_1102_1 = 0
% 102.03/14.52 | | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | | | GROUND_INST: instantiating (66) with all_1102_1, all_1114_1,
% 102.03/14.52 | | | | | | | | | | | | top$b, f$, simplifying with (404), (406) gives:
% 102.03/14.52 | | | | | | | | | | | | (416) all_1114_1 = all_1102_1
% 102.03/14.52 | | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | | | GROUND_INST: instantiating (66) with all_1100_1, all_1114_1,
% 102.03/14.52 | | | | | | | | | | | | top$b, f$, simplifying with (402), (406) gives:
% 102.03/14.52 | | | | | | | | | | | | (417) all_1114_1 = all_1100_1
% 102.03/14.52 | | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | | | COMBINE_EQS: (416), (417) imply:
% 102.03/14.52 | | | | | | | | | | | | (418) all_1102_1 = all_1100_1
% 102.03/14.52 | | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | | | SIMP: (418) implies:
% 102.03/14.52 | | | | | | | | | | | | (419) all_1102_1 = all_1100_1
% 102.03/14.52 | | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | | | COMBINE_EQS: (415), (419) imply:
% 102.03/14.52 | | | | | | | | | | | | (420) all_1100_1 = 0
% 102.03/14.52 | | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | | | SIMP: (420) implies:
% 102.03/14.52 | | | | | | | | | | | | (421) all_1100_1 = 0
% 102.03/14.52 | | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | | | REDUCE: (410), (414) imply:
% 102.03/14.52 | | | | | | | | | | | | (422) fun_app$f(all_809_12, b$) = all_1145_1
% 102.03/14.52 | | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | | | BETA: splitting (412) gives:
% 102.03/14.52 | | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | | | Case 1:
% 102.03/14.52 | | | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | | | | (423) ~ (all_1145_3 = 0)
% 102.03/14.52 | | | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | | | | REDUCE: (413), (423) imply:
% 102.03/14.52 | | | | | | | | | | | | | (424) $false
% 102.03/14.52 | | | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | | | | CLOSE: (424) is inconsistent.
% 102.03/14.52 | | | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | | | Case 2:
% 102.03/14.52 | | | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | | | | (425) all_1145_0 = all_809_0
% 102.03/14.52 | | | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | | | | REDUCE: (408), (425) imply:
% 102.03/14.52 | | | | | | | | | | | | | (426) fun_app$e(f$, all_1145_1) = all_809_0
% 102.03/14.52 | | | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | | | | BETA: splitting (396) gives:
% 102.03/14.52 | | | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | | | | Case 1:
% 102.03/14.52 | | | | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | | | | | (427) ? [v0: int] : ( ~ (v0 = 0) & inj_on$a(f$, top$b)
% 102.03/14.52 | | | | | | | | | | | | | | = v0)
% 102.03/14.52 | | | | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | | | | | DELTA: instantiating (427) with fresh symbol all_1000_0
% 102.03/14.52 | | | | | | | | | | | | | | gives:
% 102.03/14.52 | | | | | | | | | | | | | | (428) ~ (all_1000_0 = 0) & inj_on$a(f$, top$b) =
% 102.03/14.52 | | | | | | | | | | | | | | all_1000_0
% 102.03/14.52 | | | | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | | | | | ALPHA: (428) implies:
% 102.03/14.52 | | | | | | | | | | | | | | (429) ~ (all_1000_0 = 0)
% 102.03/14.52 | | | | | | | | | | | | | | (430) inj_on$a(f$, top$b) = all_1000_0
% 102.03/14.52 | | | | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | | | | | GROUND_INST: instantiating (66) with 0, all_1000_0, top$b, f$,
% 102.03/14.52 | | | | | | | | | | | | | | simplifying with (12), (430) gives:
% 102.03/14.52 | | | | | | | | | | | | | | (431) all_1000_0 = 0
% 102.03/14.52 | | | | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | | | | | REDUCE: (429), (431) imply:
% 102.03/14.52 | | | | | | | | | | | | | | (432) $false
% 102.03/14.52 | | | | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | | | | | CLOSE: (432) is inconsistent.
% 102.03/14.52 | | | | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | | | | Case 2:
% 102.03/14.52 | | | | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | | | | | (433) ? [v0: A_ell2_a_ell2_cblinfun$] : (fun_app$e(f$,
% 102.03/14.52 | | | | | | | | | | | | | | v0) = all_809_10 & A_ell2_a_ell2_cblinfun$(v0)
% 102.03/14.52 | | | | | | | | | | | | | | & ! [v1: A_ell2_a_ell2_cblinfun$] : (v1 = v0 |
% 102.03/14.52 | | | | | | | | | | | | | | ~ (fun_app$e(f$, v1) = all_809_10) | ~
% 102.03/14.52 | | | | | | | | | | | | | | A_ell2_a_ell2_cblinfun$(v1)))
% 102.03/14.52 | | | | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | | | | | DELTA: instantiating (433) with fresh symbol all_1256_0
% 102.03/14.52 | | | | | | | | | | | | | | gives:
% 102.03/14.52 | | | | | | | | | | | | | | (434) fun_app$e(f$, all_1256_0) = all_809_10 &
% 102.03/14.52 | | | | | | | | | | | | | | A_ell2_a_ell2_cblinfun$(all_1256_0) & ! [v0: any]
% 102.03/14.52 | | | | | | | | | | | | | | : (v0 = all_1256_0 | ~ (fun_app$e(f$, v0) =
% 102.03/14.52 | | | | | | | | | | | | | | all_809_10) | ~ A_ell2_a_ell2_cblinfun$(v0))
% 102.03/14.52 | | | | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | | | | | ALPHA: (434) implies:
% 102.03/14.52 | | | | | | | | | | | | | | (435) fun_app$e(f$, all_1256_0) = all_809_10
% 102.03/14.52 | | | | | | | | | | | | | | (436) ! [v0: any] : (v0 = all_1256_0 | ~
% 102.03/14.52 | | | | | | | | | | | | | | (fun_app$e(f$, v0) = all_809_10) | ~
% 102.03/14.52 | | | | | | | | | | | | | | A_ell2_a_ell2_cblinfun$(v0))
% 102.03/14.52 | | | | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | | | | | GROUND_INST: instantiating (436) with all_809_11, simplifying
% 102.03/14.52 | | | | | | | | | | | | | | with (116), (129) gives:
% 102.03/14.52 | | | | | | | | | | | | | | (437) all_1256_0 = all_809_11
% 102.03/14.52 | | | | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | | | | | GROUND_INST: instantiating (64) with all_809_11, all_1145_1,
% 102.03/14.52 | | | | | | | | | | | | | | b$, all_809_12, simplifying with (134), (422)
% 102.03/14.52 | | | | | | | | | | | | | | gives:
% 102.03/14.52 | | | | | | | | | | | | | | (438) all_1145_1 = all_809_11
% 102.03/14.52 | | | | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | | | | | REDUCE: (426), (438) imply:
% 102.03/14.52 | | | | | | | | | | | | | | (439) fun_app$e(f$, all_809_11) = all_809_0
% 102.03/14.52 | | | | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | | | | | GROUND_INST: instantiating (61) with all_809_10, all_809_0,
% 102.03/14.52 | | | | | | | | | | | | | | all_809_11, f$, simplifying with (129), (439)
% 102.03/14.52 | | | | | | | | | | | | | | gives:
% 102.03/14.52 | | | | | | | | | | | | | | (440) all_809_0 = all_809_10
% 102.03/14.52 | | | | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | | | | | REDUCE: (346), (440) imply:
% 102.03/14.52 | | | | | | | | | | | | | | (441) $false
% 102.03/14.52 | | | | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | | | | | CLOSE: (441) is inconsistent.
% 102.03/14.52 | | | | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | | | | End of split
% 102.03/14.52 | | | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | | | End of split
% 102.03/14.52 | | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | | Case 2:
% 102.03/14.52 | | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | | | (442) ? [v0: int] : ($lesseq(v0, 0)of_nat$(all_941_0) =
% 102.03/14.52 | | | | | | | | | | | | v0)
% 102.03/14.52 | | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | | | DELTA: instantiating (442) with fresh symbol all_1184_0
% 102.03/14.52 | | | | | | | | | | | | gives:
% 102.03/14.52 | | | | | | | | | | | | (443) $lesseq(all_1184_0, 0)of_nat$(all_941_0) =
% 102.03/14.52 | | | | | | | | | | | | all_1184_0
% 102.03/14.52 | | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | | | ALPHA: (443) implies:
% 102.03/14.52 | | | | | | | | | | | | (444) $lesseq(all_1184_0, 0)
% 102.03/14.52 | | | | | | | | | | | | (445) of_nat$(all_941_0) = all_1184_0
% 102.03/14.52 | | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | | | GROUND_INST: instantiating (55) with 1, all_1184_0, all_941_0,
% 102.03/14.52 | | | | | | | | | | | | simplifying with (286), (445) gives:
% 102.03/14.52 | | | | | | | | | | | | (446) all_1184_0 = 1
% 102.03/14.52 | | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | | | REDUCE: (444), (446) imply:
% 102.03/14.52 | | | | | | | | | | | | (447) $false
% 102.03/14.52 | | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | | | CLOSE: (447) is inconsistent.
% 102.03/14.52 | | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | | End of split
% 102.03/14.52 | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | Case 2:
% 102.03/14.52 | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | | (448) ~ (all_689_2 = 0) & ( ~ (all_689_0 = 0) | ~
% 102.03/14.52 | | | | | | | | | | | (all_689_1 = 0))
% 102.03/14.52 | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | | ALPHA: (448) implies:
% 102.03/14.52 | | | | | | | | | | | (449) ~ (all_689_0 = 0) | ~ (all_689_1 = 0)
% 102.03/14.52 | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | | BETA: splitting (449) gives:
% 102.03/14.52 | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | | Case 1:
% 102.03/14.52 | | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | | | (450) ~ (all_689_0 = 0)
% 102.03/14.52 | | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | | | REDUCE: (365), (450) imply:
% 102.03/14.52 | | | | | | | | | | | | (451) $false
% 102.03/14.52 | | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | | | CLOSE: (451) is inconsistent.
% 102.03/14.52 | | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | | Case 2:
% 102.03/14.52 | | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | | | (452) ~ (all_689_1 = 0)
% 102.03/14.52 | | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | | | REDUCE: (394), (452) imply:
% 102.03/14.52 | | | | | | | | | | | | (453) $false
% 102.03/14.52 | | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | | | CLOSE: (453) is inconsistent.
% 102.03/14.52 | | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | | End of split
% 102.03/14.52 | | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | | End of split
% 102.03/14.52 | | | | | | | | | |
% 102.03/14.52 | | | | | | | | | End of split
% 102.03/14.52 | | | | | | | | |
% 102.03/14.52 | | | | | | | | End of split
% 102.03/14.52 | | | | | | | |
% 102.03/14.52 | | | | | | | Case 2:
% 102.03/14.52 | | | | | | | |
% 102.03/14.52 | | | | | | | |
% 102.03/14.52 | | | | | | | | GROUND_INST: instantiating (axiom230) with f$, a$, b$,
% 102.03/14.52 | | | | | | | | all_809_7, all_809_4, all_809_3, all_809_0,
% 102.03/14.52 | | | | | | | | simplifying with (45), (46), (47), (127), (128),
% 102.03/14.52 | | | | | | | | (349), (352) gives:
% 102.03/14.53 | | | | | | | | (454) ? [v0: any] : ? [v1:
% 102.03/14.53 | | | | | | | | A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$] :
% 102.03/14.53 | | | | | | | | ? [v2: A_ell2_a_ell2_cblinfun$] : ? [v3:
% 102.03/14.53 | | | | | | | | C_ell2_c_ell2_cblinfun$] : (cblinfun_compose$(a$) =
% 102.03/14.53 | | | | | | | | v1 & fun_app$f(v1, b$) = v2 & register$a(f$) = v0 &
% 102.03/14.53 | | | | | | | | fun_app$e(f$, v2) = v3 &
% 102.03/14.53 | | | | | | | | A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$(v1)
% 102.03/14.53 | | | | | | | | & C_ell2_c_ell2_cblinfun$(v3) &
% 102.03/14.53 | | | | | | | | A_ell2_a_ell2_cblinfun$(v2) & ( ~ (v0 = 0) | v3 =
% 102.03/14.53 | | | | | | | | all_809_0))
% 102.03/14.53 | | | | | | | |
% 102.03/14.53 | | | | | | | | DELTA: instantiating (454) with fresh symbols all_1135_0,
% 102.03/14.53 | | | | | | | | all_1135_1, all_1135_2, all_1135_3 gives:
% 102.03/14.53 | | | | | | | | (455) cblinfun_compose$(a$) = all_1135_2 &
% 102.03/14.53 | | | | | | | | fun_app$f(all_1135_2, b$) = all_1135_1 & register$a(f$)
% 102.03/14.53 | | | | | | | | = all_1135_3 & fun_app$e(f$, all_1135_1) = all_1135_0 &
% 102.03/14.53 | | | | | | | | A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$(all_1135_2)
% 102.03/14.53 | | | | | | | | & C_ell2_c_ell2_cblinfun$(all_1135_0) &
% 102.03/14.53 | | | | | | | | A_ell2_a_ell2_cblinfun$(all_1135_1) & ( ~ (all_1135_3 =
% 102.03/14.53 | | | | | | | | 0) | all_1135_0 = all_809_0)
% 102.03/14.53 | | | | | | | |
% 102.03/14.53 | | | | | | | | ALPHA: (455) implies:
% 102.03/14.53 | | | | | | | | (456) fun_app$e(f$, all_1135_1) = all_1135_0
% 102.03/14.53 | | | | | | | | (457) register$a(f$) = all_1135_3
% 102.03/14.53 | | | | | | | | (458) fun_app$f(all_1135_2, b$) = all_1135_1
% 102.03/14.53 | | | | | | | | (459) cblinfun_compose$(a$) = all_1135_2
% 102.03/14.53 | | | | | | | | (460) ~ (all_1135_3 = 0) | all_1135_0 = all_809_0
% 102.03/14.53 | | | | | | | |
% 102.03/14.53 | | | | | | | | BETA: splitting (213) gives:
% 102.03/14.53 | | | | | | | |
% 102.03/14.53 | | | | | | | | Case 1:
% 102.03/14.53 | | | | | | | | |
% 102.03/14.53 | | | | | | | | |
% 102.03/14.53 | | | | | | | | | GROUND_INST: instantiating (53) with 0, all_1135_3, f$,
% 102.03/14.53 | | | | | | | | | simplifying with (2), (457) gives:
% 102.03/14.53 | | | | | | | | | (461) all_1135_3 = 0
% 102.03/14.53 | | | | | | | | |
% 102.03/14.53 | | | | | | | | | GROUND_INST: instantiating (54) with all_809_12, all_1135_2,
% 102.03/14.53 | | | | | | | | | a$, simplifying with (135), (459) gives:
% 102.03/14.53 | | | | | | | | | (462) all_1135_2 = all_809_12
% 102.03/14.53 | | | | | | | | |
% 102.03/14.53 | | | | | | | | | REDUCE: (458), (462) imply:
% 102.03/14.53 | | | | | | | | | (463) fun_app$f(all_809_12, b$) = all_1135_1
% 102.03/14.53 | | | | | | | | |
% 102.03/14.53 | | | | | | | | | BETA: splitting (460) gives:
% 102.03/14.53 | | | | | | | | |
% 102.03/14.53 | | | | | | | | | Case 1:
% 102.03/14.53 | | | | | | | | | |
% 102.03/14.53 | | | | | | | | | | (464) ~ (all_1135_3 = 0)
% 102.03/14.53 | | | | | | | | | |
% 102.03/14.53 | | | | | | | | | | REDUCE: (461), (464) imply:
% 102.03/14.53 | | | | | | | | | | (465) $false
% 102.03/14.53 | | | | | | | | | |
% 102.03/14.53 | | | | | | | | | | CLOSE: (465) is inconsistent.
% 102.03/14.53 | | | | | | | | | |
% 102.03/14.53 | | | | | | | | | Case 2:
% 102.03/14.53 | | | | | | | | | |
% 102.03/14.53 | | | | | | | | | | (466) all_1135_0 = all_809_0
% 102.03/14.53 | | | | | | | | | |
% 102.03/14.53 | | | | | | | | | | REDUCE: (456), (466) imply:
% 102.03/14.53 | | | | | | | | | | (467) fun_app$e(f$, all_1135_1) = all_809_0
% 102.03/14.53 | | | | | | | | | |
% 102.03/14.53 | | | | | | | | | | GROUND_INST: instantiating (64) with all_809_11, all_1135_1,
% 102.03/14.53 | | | | | | | | | | b$, all_809_12, simplifying with (134), (463)
% 102.03/14.53 | | | | | | | | | | gives:
% 102.03/14.53 | | | | | | | | | | (468) all_1135_1 = all_809_11
% 102.03/14.53 | | | | | | | | | |
% 102.03/14.53 | | | | | | | | | | REDUCE: (467), (468) imply:
% 102.03/14.53 | | | | | | | | | | (469) fun_app$e(f$, all_809_11) = all_809_0
% 102.03/14.53 | | | | | | | | | |
% 102.03/14.53 | | | | | | | | | | GROUND_INST: instantiating (61) with all_809_10, all_809_0,
% 102.03/14.53 | | | | | | | | | | all_809_11, f$, simplifying with (129), (469)
% 102.03/14.53 | | | | | | | | | | gives:
% 102.03/14.53 | | | | | | | | | | (470) all_809_0 = all_809_10
% 102.03/14.53 | | | | | | | | | |
% 102.03/14.53 | | | | | | | | | | REDUCE: (346), (470) imply:
% 102.03/14.53 | | | | | | | | | | (471) $false
% 102.03/14.53 | | | | | | | | | |
% 102.03/14.53 | | | | | | | | | | CLOSE: (471) is inconsistent.
% 102.03/14.53 | | | | | | | | | |
% 102.03/14.53 | | | | | | | | | End of split
% 102.03/14.53 | | | | | | | | |
% 102.03/14.53 | | | | | | | | Case 2:
% 102.03/14.53 | | | | | | | | |
% 102.03/14.53 | | | | | | | | | (472) ? [v0: int] : ($lesseq(v0, 0)of_nat$(all_602_0) =
% 102.03/14.53 | | | | | | | | | v0)
% 102.03/14.53 | | | | | | | | |
% 102.03/14.53 | | | | | | | | | DELTA: instantiating (472) with fresh symbol all_941_0 gives:
% 102.03/14.53 | | | | | | | | | (473) $lesseq(all_941_0, 0)of_nat$(all_602_0) = all_941_0
% 102.03/14.53 | | | | | | | | |
% 102.03/14.53 | | | | | | | | | REF_CLOSE: (55), (71), (473) are inconsistent by sub-proof #1.
% 102.03/14.53 | | | | | | | | |
% 102.03/14.53 | | | | | | | | End of split
% 102.03/14.53 | | | | | | | |
% 102.03/14.53 | | | | | | | End of split
% 102.03/14.53 | | | | | | |
% 102.03/14.53 | | | | | | End of split
% 102.03/14.53 | | | | | |
% 102.03/14.53 | | | | | Case 2:
% 102.03/14.53 | | | | | |
% 102.42/14.53 | | | | | | (474) ? [v0: C_ell2_c_ell2_cblinfun_set_bool_fun$] : ? [v1:
% 102.42/14.53 | | | | | | C_ell2_c_ell2_cblinfun_set$] : ? [v2: int] : ( ~ (v2 =
% 102.42/14.53 | | | | | | 0) & image$(g$, top$) = v1 & member$(all_809_7) = v0 &
% 102.42/14.53 | | | | | | fun_app$a(v0, v1) = v2 & C_ell2_c_ell2_cblinfun_set$(v1)
% 102.42/14.53 | | | | | | & C_ell2_c_ell2_cblinfun_set_bool_fun$(v0))
% 102.42/14.53 | | | | | |
% 102.42/14.53 | | | | | | DELTA: instantiating (474) with fresh symbols all_985_0, all_985_1,
% 102.42/14.53 | | | | | | all_985_2 gives:
% 102.42/14.53 | | | | | | (475) ~ (all_985_0 = 0) & image$(g$, top$) = all_985_1 &
% 102.42/14.53 | | | | | | member$(all_809_7) = all_985_2 & fun_app$a(all_985_2,
% 102.42/14.53 | | | | | | all_985_1) = all_985_0 &
% 102.42/14.53 | | | | | | C_ell2_c_ell2_cblinfun_set$(all_985_1) &
% 102.42/14.53 | | | | | | C_ell2_c_ell2_cblinfun_set_bool_fun$(all_985_2)
% 102.42/14.53 | | | | | |
% 102.42/14.53 | | | | | | ALPHA: (475) implies:
% 102.42/14.53 | | | | | | (476) ~ (all_985_0 = 0)
% 102.42/14.53 | | | | | | (477) fun_app$a(all_985_2, all_985_1) = all_985_0
% 102.42/14.53 | | | | | | (478) member$(all_809_7) = all_985_2
% 102.42/14.53 | | | | | | (479) image$(g$, top$) = all_985_1
% 102.42/14.53 | | | | | |
% 102.42/14.53 | | | | | | GROUND_INST: instantiating (51) with all_869_0, all_985_2,
% 102.42/14.53 | | | | | | all_809_7, simplifying with (225), (478) gives:
% 102.42/14.53 | | | | | | (480) all_985_2 = all_869_0
% 102.42/14.53 | | | | | |
% 102.42/14.53 | | | | | | GROUND_INST: instantiating (63) with all_604_0, all_985_1, top$, g$,
% 102.42/14.53 | | | | | | simplifying with (74), (479) gives:
% 102.42/14.53 | | | | | | (481) all_985_1 = all_604_0
% 102.42/14.53 | | | | | |
% 102.42/14.53 | | | | | | REDUCE: (477), (480), (481) imply:
% 102.42/14.53 | | | | | | (482) fun_app$a(all_869_0, all_604_0) = all_985_0
% 102.42/14.53 | | | | | |
% 102.42/14.53 | | | | | | GROUND_INST: instantiating (60) with 0, all_985_0, all_604_0,
% 102.42/14.53 | | | | | | all_869_0, simplifying with (280), (482) gives:
% 102.42/14.53 | | | | | | (483) all_985_0 = 0
% 102.42/14.53 | | | | | |
% 102.42/14.53 | | | | | | REDUCE: (476), (483) imply:
% 102.42/14.53 | | | | | | (484) $false
% 102.42/14.53 | | | | | |
% 102.42/14.53 | | | | | | CLOSE: (484) is inconsistent.
% 102.42/14.53 | | | | | |
% 102.42/14.53 | | | | | End of split
% 102.42/14.53 | | | | |
% 102.42/14.53 | | | | Case 2:
% 102.42/14.53 | | | | |
% 102.42/14.53 | | | | | (485) ? [v0: C_ell2_c_ell2_cblinfun_set_bool_fun$] : ? [v1:
% 102.42/14.53 | | | | | C_ell2_c_ell2_cblinfun_set$] : ? [v2: int] : ( ~ (v2 = 0)
% 102.42/14.53 | | | | | & image$(g$, top$) = v1 & member$(all_809_3) = v0 &
% 102.42/14.53 | | | | | fun_app$a(v0, v1) = v2 & C_ell2_c_ell2_cblinfun_set$(v1) &
% 102.42/14.53 | | | | | C_ell2_c_ell2_cblinfun_set_bool_fun$(v0))
% 102.42/14.53 | | | | |
% 102.42/14.53 | | | | | DELTA: instantiating (485) with fresh symbols all_981_0, all_981_1,
% 102.42/14.53 | | | | | all_981_2 gives:
% 102.42/14.53 | | | | | (486) ~ (all_981_0 = 0) & image$(g$, top$) = all_981_1 &
% 102.42/14.53 | | | | | member$(all_809_3) = all_981_2 & fun_app$a(all_981_2,
% 102.42/14.53 | | | | | all_981_1) = all_981_0 &
% 102.42/14.53 | | | | | C_ell2_c_ell2_cblinfun_set$(all_981_1) &
% 102.42/14.53 | | | | | C_ell2_c_ell2_cblinfun_set_bool_fun$(all_981_2)
% 102.42/14.53 | | | | |
% 102.42/14.53 | | | | | ALPHA: (486) implies:
% 102.42/14.53 | | | | | (487) ~ (all_981_0 = 0)
% 102.42/14.53 | | | | | (488) fun_app$a(all_981_2, all_981_1) = all_981_0
% 102.42/14.53 | | | | | (489) member$(all_809_3) = all_981_2
% 102.42/14.53 | | | | | (490) image$(g$, top$) = all_981_1
% 102.42/14.53 | | | | |
% 102.42/14.53 | | | | | GROUND_INST: instantiating (51) with all_871_0, all_981_2, all_809_3,
% 102.42/14.53 | | | | | simplifying with (228), (489) gives:
% 102.42/14.53 | | | | | (491) all_981_2 = all_871_0
% 102.42/14.53 | | | | |
% 102.42/14.53 | | | | | GROUND_INST: instantiating (63) with all_604_0, all_981_1, top$, g$,
% 102.42/14.53 | | | | | simplifying with (74), (490) gives:
% 102.42/14.53 | | | | | (492) all_981_1 = all_604_0
% 102.42/14.53 | | | | |
% 102.42/14.53 | | | | | REDUCE: (488), (491), (492) imply:
% 102.42/14.53 | | | | | (493) fun_app$a(all_871_0, all_604_0) = all_981_0
% 102.42/14.53 | | | | |
% 102.42/14.53 | | | | | GROUND_INST: instantiating (60) with 0, all_981_0, all_604_0,
% 102.42/14.53 | | | | | all_871_0, simplifying with (279), (493) gives:
% 102.42/14.53 | | | | | (494) all_981_0 = 0
% 102.42/14.53 | | | | |
% 102.42/14.53 | | | | | REDUCE: (487), (494) imply:
% 102.42/14.53 | | | | | (495) $false
% 102.42/14.53 | | | | |
% 102.42/14.53 | | | | | CLOSE: (495) is inconsistent.
% 102.42/14.53 | | | | |
% 102.42/14.53 | | | | End of split
% 102.42/14.53 | | | |
% 102.42/14.53 | | | Case 2:
% 102.42/14.53 | | | |
% 102.42/14.53 | | | | (496) ? [v0: C_ell2_c_ell2_cblinfun_set_bool_fun$] : ? [v1:
% 102.42/14.53 | | | | C_ell2_c_ell2_cblinfun_set$] : ? [v2: int] : ( ~ (v2 = 0) &
% 102.42/14.53 | | | | image$(g$, top$) = v1 & member$(all_809_10) = v0 &
% 102.42/14.53 | | | | fun_app$a(v0, v1) = v2 & C_ell2_c_ell2_cblinfun_set$(v1) &
% 102.42/14.53 | | | | C_ell2_c_ell2_cblinfun_set_bool_fun$(v0))
% 102.42/14.53 | | | |
% 102.42/14.53 | | | | DELTA: instantiating (496) with fresh symbols all_966_0, all_966_1,
% 102.42/14.53 | | | | all_966_2 gives:
% 102.42/14.54 | | | | (497) ~ (all_966_0 = 0) & image$(g$, top$) = all_966_1 &
% 102.42/14.54 | | | | member$(all_809_10) = all_966_2 & fun_app$a(all_966_2,
% 102.42/14.54 | | | | all_966_1) = all_966_0 &
% 102.42/14.54 | | | | C_ell2_c_ell2_cblinfun_set$(all_966_1) &
% 102.42/14.54 | | | | C_ell2_c_ell2_cblinfun_set_bool_fun$(all_966_2)
% 102.42/14.54 | | | |
% 102.42/14.54 | | | | ALPHA: (497) implies:
% 102.42/14.54 | | | | (498) ~ (all_966_0 = 0)
% 102.42/14.54 | | | | (499) fun_app$a(all_966_2, all_966_1) = all_966_0
% 102.42/14.54 | | | | (500) member$(all_809_10) = all_966_2
% 102.42/14.54 | | | | (501) image$(g$, top$) = all_966_1
% 102.42/14.54 | | | |
% 102.42/14.54 | | | | GROUND_INST: instantiating (51) with all_867_0, all_966_2, all_809_10,
% 102.42/14.54 | | | | simplifying with (222), (500) gives:
% 102.42/14.54 | | | | (502) all_966_2 = all_867_0
% 102.42/14.54 | | | |
% 102.42/14.54 | | | | GROUND_INST: instantiating (63) with all_604_0, all_966_1, top$, g$,
% 102.42/14.54 | | | | simplifying with (74), (501) gives:
% 102.42/14.54 | | | | (503) all_966_1 = all_604_0
% 102.42/14.54 | | | |
% 102.42/14.54 | | | | REDUCE: (499), (502), (503) imply:
% 102.42/14.54 | | | | (504) fun_app$a(all_867_0, all_604_0) = all_966_0
% 102.42/14.54 | | | |
% 102.42/14.54 | | | | GROUND_INST: instantiating (60) with 0, all_966_0, all_604_0, all_867_0,
% 102.42/14.54 | | | | simplifying with (281), (504) gives:
% 102.42/14.54 | | | | (505) all_966_0 = 0
% 102.42/14.54 | | | |
% 102.42/14.54 | | | | REDUCE: (498), (505) imply:
% 102.42/14.54 | | | | (506) $false
% 102.42/14.54 | | | |
% 102.42/14.54 | | | | CLOSE: (506) is inconsistent.
% 102.42/14.54 | | | |
% 102.42/14.54 | | | End of split
% 102.42/14.54 | | |
% 102.42/14.54 | | Case 2:
% 102.42/14.54 | | |
% 102.42/14.54 | | | (507) ? [v0: int] : ($lesseq(v0, 0)of_nat$(all_602_0) = v0)
% 102.42/14.54 | | |
% 102.42/14.54 | | | DELTA: instantiating (507) with fresh symbol all_941_0 gives:
% 102.42/14.54 | | | (508) $lesseq(all_941_0, 0)of_nat$(all_602_0) = all_941_0
% 102.42/14.54 | | |
% 102.42/14.54 | | | REF_CLOSE: (55), (71), (508) are inconsistent by sub-proof #1.
% 102.42/14.54 | | |
% 102.42/14.54 | | End of split
% 102.42/14.54 | |
% 102.42/14.54 | End of split
% 102.42/14.54 |
% 102.42/14.54 End of proof
% 102.42/14.54
% 102.42/14.54 Sub-proof #1 shows that the following formulas are inconsistent:
% 102.42/14.54 ----------------------------------------------------------------
% 102.42/14.54 (1) $lesseq(all_941_0, 0)of_nat$(all_602_0) = all_941_0
% 102.42/14.54 (2) ! [v0: int] : ! [v1: int] : ! [v2: Nat$] : (v1 = v0 | ~ (of_nat$(v2)
% 102.42/14.54 = v1) | ~ (of_nat$(v2) = v0))
% 102.42/14.54 (3) of_nat$(all_602_0) = 1
% 102.42/14.54
% 102.42/14.54 Begin of proof
% 102.42/14.54 |
% 102.42/14.54 | ALPHA: (1) implies:
% 102.42/14.54 | (4) $lesseq(all_941_0, 0)
% 102.42/14.54 | (5) of_nat$(all_602_0) = all_941_0
% 102.42/14.54 |
% 102.42/14.54 | GROUND_INST: instantiating (2) with 1, all_941_0, all_602_0, simplifying with
% 102.42/14.54 | (3), (5) gives:
% 102.42/14.54 | (6) all_941_0 = 1
% 102.42/14.54 |
% 102.42/14.54 | REDUCE: (4), (6) imply:
% 102.42/14.54 | (7) $false
% 102.42/14.54 |
% 102.42/14.54 | CLOSE: (7) is inconsistent.
% 102.42/14.54 |
% 102.42/14.54 End of proof
% 102.42/14.54 % SZS output end Proof for theBenchmark
% 102.42/14.54
% 102.42/14.54 13931ms
%------------------------------------------------------------------------------