TSTP Solution File: SWW178+1 by Princess---230619
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- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWW178+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n032.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 : Fri Sep 1 00:49:20 EDT 2023
% Result : Theorem 150.53s 20.71s
% Output : Proof 280.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : SWW178+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.09 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.09/0.27 % Computer : n032.cluster.edu
% 0.09/0.27 % Model : x86_64 x86_64
% 0.09/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.27 % Memory : 8042.1875MB
% 0.09/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.27 % CPULimit : 300
% 0.09/0.27 % WCLimit : 300
% 0.09/0.27 % DateTime : Sun Aug 27 18:29:30 EDT 2023
% 0.09/0.27 % CPUTime :
% 0.12/0.56 ________ _____
% 0.12/0.56 ___ __ \_________(_)________________________________
% 0.12/0.56 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.12/0.56 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.12/0.56 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.12/0.56
% 0.12/0.56 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.12/0.56 (2023-06-19)
% 0.12/0.56
% 0.12/0.56 (c) Philipp Rümmer, 2009-2023
% 0.12/0.56 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.12/0.56 Amanda Stjerna.
% 0.12/0.56 Free software under BSD-3-Clause.
% 0.12/0.56
% 0.12/0.56 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.12/0.56
% 0.12/0.56 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.12/0.57 Running up to 7 provers in parallel.
% 0.12/0.58 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.12/0.58 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.12/0.58 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.12/0.58 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.12/0.58 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.12/0.58 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.12/0.58 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 18.14/3.17 Prover 1: Preprocessing ...
% 18.58/3.20 Prover 6: Preprocessing ...
% 18.58/3.20 Prover 2: Preprocessing ...
% 18.58/3.21 Prover 3: Preprocessing ...
% 18.58/3.21 Prover 5: Preprocessing ...
% 18.58/3.21 Prover 0: Preprocessing ...
% 18.58/3.21 Prover 4: Preprocessing ...
% 50.62/7.44 Prover 1: Warning: ignoring some quantifiers
% 51.19/7.52 Prover 3: Warning: ignoring some quantifiers
% 52.58/7.71 Prover 3: Constructing countermodel ...
% 52.58/7.73 Prover 1: Constructing countermodel ...
% 52.97/7.78 Prover 6: Proving ...
% 60.70/8.81 Prover 4: Warning: ignoring some quantifiers
% 61.35/8.87 Prover 5: Proving ...
% 63.69/9.17 Prover 4: Constructing countermodel ...
% 67.69/9.75 Prover 0: Proving ...
% 72.09/10.31 Prover 2: Proving ...
% 85.71/12.14 Prover 2: stopped
% 85.71/12.15 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 92.49/12.99 Prover 7: Preprocessing ...
% 99.58/13.92 Prover 5: stopped
% 99.58/13.94 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 105.67/14.80 Prover 7: Warning: ignoring some quantifiers
% 105.67/14.81 Prover 8: Preprocessing ...
% 107.51/14.99 Prover 7: Constructing countermodel ...
% 114.24/15.94 Prover 1: stopped
% 114.24/15.96 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 117.62/16.34 Prover 8: Warning: ignoring some quantifiers
% 119.08/16.62 Prover 9: Preprocessing ...
% 119.08/16.62 Prover 8: Constructing countermodel ...
% 128.89/17.83 Prover 6: stopped
% 128.89/17.85 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 136.28/18.79 Prover 10: Preprocessing ...
% 141.53/19.52 Prover 9: Warning: ignoring some quantifiers
% 143.02/19.68 Prover 9: Constructing countermodel ...
% 144.24/19.97 Prover 10: Warning: ignoring some quantifiers
% 145.79/20.07 Prover 10: Constructing countermodel ...
% 150.53/20.71 Prover 9: proved (4743ms)
% 150.53/20.71
% 150.53/20.71 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 150.53/20.71
% 150.53/20.71 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 150.53/20.72 Prover 3: stopped
% 150.53/20.74 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 150.53/20.74 Prover 0: stopped
% 150.53/20.74 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 160.63/22.06 Prover 13: Preprocessing ...
% 161.99/22.24 Prover 16: Preprocessing ...
% 162.26/22.26 Prover 11: Preprocessing ...
% 172.30/23.61 Prover 16: Warning: ignoring some quantifiers
% 172.93/23.70 Prover 16: Constructing countermodel ...
% 175.99/24.26 Prover 13: Warning: ignoring some quantifiers
% 178.95/24.55 Prover 11: Warning: ignoring some quantifiers
% 179.68/24.58 Prover 13: Constructing countermodel ...
% 180.06/24.78 Prover 11: Constructing countermodel ...
% 181.43/24.90 Prover 16: stopped
% 181.43/24.90 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 186.90/25.64 Prover 19: Preprocessing ...
% 196.99/26.99 Prover 19: Warning: ignoring some quantifiers
% 196.99/27.09 Prover 19: Constructing countermodel ...
% 207.99/28.38 Prover 19: stopped
% 211.39/28.86 Prover 13: stopped
% 226.87/31.61 Prover 7: stopped
% 277.23/40.75 Prover 10: Found proof (size 1018)
% 277.23/40.75 Prover 10: proved (22902ms)
% 277.23/40.75 Prover 8: stopped
% 277.23/40.76 Prover 11: stopped
% 277.23/40.76 Prover 4: stopped
% 277.23/40.76
% 277.23/40.76 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 277.23/40.76
% 278.60/41.56 % SZS output start Proof for theBenchmark
% 278.73/41.58 Assumptions after simplification:
% 278.73/41.58 ---------------------------------
% 278.73/41.58
% 278.73/41.58 (arity_Complex__Ocomplex__Groups_Ogroup__add)
% 278.73/41.59 $i(tc_Complex_Ocomplex) & class_Groups_Ogroup__add(tc_Complex_Ocomplex)
% 278.73/41.59
% 278.73/41.59 (arity_Complex__Ocomplex__RealVector_Oreal__normed__vector)
% 278.73/41.59 $i(tc_Complex_Ocomplex) &
% 278.73/41.59 class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
% 278.73/41.59
% 278.73/41.59 (arity_Complex__Ocomplex__Rings_Ocomm__semiring__1)
% 278.73/41.59 $i(tc_Complex_Ocomplex) & class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)
% 278.73/41.59
% 278.73/41.59 (arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add)
% 278.73/41.59 $i(tc_RealDef_Oreal) &
% 278.73/41.59 class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal)
% 278.73/41.59
% 278.73/41.59 (arity_RealDef__Oreal__Rings_Olinordered__semidom)
% 278.73/41.59 $i(tc_RealDef_Oreal) & class_Rings_Olinordered__semidom(tc_RealDef_Oreal)
% 278.73/41.59
% 278.73/41.59 (conj_0)
% 278.85/41.61 $i(v_z) & $i(v_w) & $i(tc_Complex_Ocomplex) & $i(tc_RealDef_Oreal) & ? [v0:
% 278.85/41.61 $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 278.85/41.61 (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v_w, v_z) = v1 &
% 278.85/41.61 c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v3) = v4 &
% 278.85/41.61 c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v1) = v2 &
% 278.85/41.61 c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_z) = v3 &
% 278.85/41.61 c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w) = v0 & $i(v4) &
% 278.85/41.61 $i(v3) & $i(v2) & $i(v1) & $i(v0) & ~
% 278.85/41.61 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v4))
% 278.85/41.61
% 278.85/41.61 (fact_BseqD)
% 278.85/41.61 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 278.85/41.61 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 278.85/41.61 ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ c_SEQ_OBseq(v2, v1) | ~
% 278.85/41.61 class_RealVector_Oreal__normed__vector(v2) | ? [v3: $i] : ($i(v3) &
% 278.85/41.61 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) & ! [v4: $i] :
% 278.85/41.61 ! [v5: $i] : ! [v6: $i] : ( ~ (c_RealVector_Onorm__class_Onorm(v2, v5)
% 278.85/41.61 = v6) | ~ (hAPP(v1, v4) = v5) | ~ $i(v4) |
% 278.85/41.61 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v3)))))
% 278.85/41.61
% 278.85/41.61 (fact_BseqI)
% 278.85/41.62 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 278.85/41.62 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ? [v1: $i] :
% 278.85/41.62 ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 278.85/41.62 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ~
% 278.85/41.62 class_RealVector_Oreal__normed__vector(v3) | c_SEQ_OBseq(v3, v1) | ? [v4:
% 278.85/41.62 $i] : ? [v5: $i] : ? [v6: $i] : (c_RealVector_Onorm__class_Onorm(v3,
% 278.85/41.62 v5) = v6 & hAPP(v1, v4) = v5 & $i(v6) & $i(v5) & $i(v4) & ~
% 278.85/41.62 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v2))))
% 278.85/41.62
% 278.85/41.62 (fact_Bseq__def)
% 278.85/41.62 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 278.85/41.62 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ? [v1: $i] :
% 278.85/41.62 ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 278.85/41.62 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | ~
% 278.85/41.62 class_RealVector_Oreal__normed__vector(v2) | c_SEQ_OBseq(v2, v1) | ? [v4:
% 278.85/41.62 $i] : ? [v5: $i] : ? [v6: $i] : (c_RealVector_Onorm__class_Onorm(v2,
% 278.85/41.62 v5) = v6 & hAPP(v1, v4) = v5 & $i(v6) & $i(v5) & $i(v4) & ~
% 278.85/41.62 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v3))) & ! [v1:
% 278.85/41.62 $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ c_SEQ_OBseq(v2, v1) | ~
% 278.85/41.62 class_RealVector_Oreal__normed__vector(v2) | ? [v3: $i] : ($i(v3) &
% 278.85/41.62 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) & ! [v4: $i] :
% 278.85/41.62 ! [v5: $i] : ! [v6: $i] : ( ~ (c_RealVector_Onorm__class_Onorm(v2, v5)
% 278.85/41.62 = v6) | ~ (hAPP(v1, v4) = v5) | ~ $i(v4) |
% 278.85/41.62 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v3)))))
% 278.85/41.62
% 278.85/41.62 (fact_Bseq__iff2)
% 278.85/41.62 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 278.85/41.62 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ? [v1: $i] :
% 278.85/41.62 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 278.85/41.62 (c_Groups_Ouminus__class_Ouminus(v2, v4) = v5) | ~ $i(v4) | ~ $i(v3) |
% 278.85/41.62 ~ $i(v2) | ~ $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 278.85/41.62 v0, v3) | ~ class_RealVector_Oreal__normed__vector(v2) |
% 278.85/41.62 c_SEQ_OBseq(v2, v1) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9:
% 278.85/41.62 $i] : (c_Groups_Oplus__class_Oplus(v2, v7, v5) = v8 &
% 278.85/41.62 c_RealVector_Onorm__class_Onorm(v2, v8) = v9 & hAPP(v1, v6) = v7 &
% 278.85/41.62 $i(v9) & $i(v8) & $i(v7) & $i(v6) & ~
% 278.85/41.62 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v9, v3))) & ! [v1:
% 278.85/41.62 $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ c_SEQ_OBseq(v2, v1) | ~
% 278.85/41.62 class_RealVector_Oreal__normed__vector(v2) | ? [v3: $i] : ? [v4: $i] :
% 278.85/41.62 ? [v5: $i] : (c_Groups_Ouminus__class_Ouminus(v2, v4) = v5 & $i(v5) &
% 278.85/41.62 $i(v4) & $i(v3) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0,
% 278.85/41.63 v3) & ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~
% 278.85/41.63 (c_Groups_Oplus__class_Oplus(v2, v7, v5) = v8) | ~
% 278.85/41.63 (c_RealVector_Onorm__class_Onorm(v2, v8) = v9) | ~ (hAPP(v1, v6) =
% 278.85/41.63 v7) | ~ $i(v6) |
% 278.85/41.63 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v9, v3)))))
% 278.85/41.63
% 278.85/41.63 (fact_Bseq__iff3)
% 278.95/41.63 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 278.95/41.63 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 278.95/41.63 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 278.95/41.63 (c_Groups_Ouminus__class_Ouminus(v2, v5) = v6) | ~ (hAPP(v1, v4) = v5) |
% 278.95/41.63 ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 278.95/41.63 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | ~
% 278.95/41.63 class_RealVector_Oreal__normed__vector(v2) | c_SEQ_OBseq(v2, v1) | ? [v7:
% 278.95/41.63 $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] :
% 278.95/41.63 (c_Groups_Oplus__class_Oplus(v2, v8, v6) = v9 &
% 278.95/41.63 c_RealVector_Onorm__class_Onorm(v2, v9) = v10 & hAPP(v1, v7) = v8 &
% 278.95/41.63 $i(v10) & $i(v9) & $i(v8) & $i(v7) & ~
% 278.95/41.63 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v10, v3))) & ! [v1:
% 278.95/41.63 $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ c_SEQ_OBseq(v2, v1) | ~
% 278.95/41.63 class_RealVector_Oreal__normed__vector(v2) | ? [v3: $i] : ? [v4: $i] :
% 278.95/41.63 ? [v5: $i] : ? [v6: $i] : (c_Groups_Ouminus__class_Ouminus(v2, v5) = v6 &
% 278.95/41.63 hAPP(v1, v4) = v5 & $i(v6) & $i(v5) & $i(v4) & $i(v3) &
% 278.95/41.63 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) & ! [v7: $i] :
% 278.95/41.63 ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ( ~
% 278.95/41.63 (c_Groups_Oplus__class_Oplus(v2, v8, v6) = v9) | ~
% 278.95/41.63 (c_RealVector_Onorm__class_Onorm(v2, v9) = v10) | ~ (hAPP(v1, v7) =
% 278.95/41.63 v8) | ~ $i(v7) |
% 278.95/41.63 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v10, v3)))))
% 278.95/41.63
% 278.95/41.63 (fact_Complex__eq__0)
% 278.95/41.63 $i(tc_Complex_Ocomplex) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 278.95/41.63 (c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v0 &
% 278.95/41.63 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0) & !
% 278.95/41.63 [v2: $i] : ! [v3: $i] : (v3 = v1 | ~ (c_Complex_Ocomplex_OComplex(v3, v2)
% 278.95/41.63 = v0) | ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v2 = v1 |
% 278.95/41.63 ~ (c_Complex_Ocomplex_OComplex(v3, v2) = v0) | ~ $i(v3) | ~ $i(v2)) & !
% 278.95/41.64 [v2: $i] : (v2 = v0 | ~ (c_Complex_Ocomplex_OComplex(v1, v1) = v2)))
% 278.95/41.64
% 278.95/41.64 (fact_Complex__eq__1)
% 278.95/41.64 $i(tc_Complex_Ocomplex) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 278.95/41.64 ? [v2: $i] : (c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = v0 &
% 278.95/41.64 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 278.95/41.64 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v2 & $i(v2) & $i(v1) &
% 278.95/41.64 $i(v0) & ! [v3: $i] : ! [v4: $i] : (v4 = v1 | ~
% 278.95/41.64 (c_Complex_Ocomplex_OComplex(v4, v3) = v0) | ~ $i(v4) | ~ $i(v3)) & !
% 278.95/41.64 [v3: $i] : ! [v4: $i] : (v3 = v2 | ~ (c_Complex_Ocomplex_OComplex(v4, v3)
% 278.95/41.64 = v0) | ~ $i(v4) | ~ $i(v3)) & ! [v3: $i] : (v3 = v0 | ~
% 278.95/41.64 (c_Complex_Ocomplex_OComplex(v1, v2) = v3)))
% 278.95/41.64
% 278.95/41.64 (fact_Complex__eq__i)
% 278.95/41.64 $i(c_Complex_Oii) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 278.95/41.64 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 278.95/41.64 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 278.95/41.64 [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ (c_Complex_Ocomplex_OComplex(v3, v2)
% 278.95/41.64 = c_Complex_Oii) | ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] :
% 278.95/41.64 (v2 = v1 | ~ (c_Complex_Ocomplex_OComplex(v3, v2) = c_Complex_Oii) | ~
% 278.95/41.64 $i(v3) | ~ $i(v2)) & ! [v2: $i] : (v2 = c_Complex_Oii | ~
% 278.95/41.64 (c_Complex_Ocomplex_OComplex(v0, v1) = v2)))
% 278.95/41.64
% 278.95/41.64 (fact_Im_Ononneg__bounded)
% 278.95/41.64 $i(tc_Complex_Ocomplex) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 278.95/41.64 ? [v2: $i] : (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 278.95/41.64 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v2) & $i(v1) &
% 278.95/41.64 $i(v0) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) & !
% 278.95/41.64 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 278.95/41.64 (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v3) = v4) | ~
% 278.95/41.64 (hAPP(v5, v2) = v6) | ~ (hAPP(v1, v4) = v5) | ~ $i(v3) | ? [v7: $i] :
% 278.95/41.64 ? [v8: $i] : (c_Complex_OIm(v3) = v7 &
% 278.95/41.64 c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal, v7) = v8 & $i(v8) &
% 278.95/41.64 $i(v7) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v8, v6))))
% 278.95/41.64
% 278.95/41.64 (fact_Im_Opos__bounded)
% 278.95/41.65 $i(tc_Complex_Ocomplex) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 278.95/41.65 ? [v2: $i] : (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 278.95/41.65 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v2) & $i(v1) &
% 278.95/41.65 $i(v0) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) & ! [v3:
% 278.95/41.65 $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 278.95/41.65 (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v3) = v4) | ~
% 278.95/41.65 (hAPP(v5, v2) = v6) | ~ (hAPP(v1, v4) = v5) | ~ $i(v3) | ? [v7: $i] :
% 278.95/41.65 ? [v8: $i] : (c_Complex_OIm(v3) = v7 &
% 278.95/41.65 c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal, v7) = v8 & $i(v8) &
% 278.95/41.65 $i(v7) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v8, v6))))
% 278.95/41.65
% 278.95/41.65 (fact_Im_Ozero)
% 278.95/41.65 $i(tc_Complex_Ocomplex) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 278.95/41.65 (c_Complex_OIm(v0) = v1 & c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) =
% 278.95/41.65 v0 & c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0))
% 278.95/41.65
% 278.95/41.65 (fact_LIMSEQ__inverse__realpow__zero__lemma)
% 278.95/41.65 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 278.95/41.65 $i] : ? [v3: $i] : (c_Power_Opower__class_Opower(tc_RealDef_Oreal) = v3 &
% 278.95/41.65 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v2 &
% 278.95/41.65 c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 278.95/41.65 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v3) & $i(v2) &
% 278.95/41.65 $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : !
% 278.95/41.65 [v8: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v5, v2) = v6)
% 278.95/41.65 | ~ (hAPP(v7, v4) = v8) | ~ (hAPP(v3, v6) = v7) | ~ $i(v5) | ~ $i(v4)
% 278.95/41.65 | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v5) | ? [v9:
% 278.95/41.65 $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] :
% 278.95/41.65 (c_RealDef_Oreal(tc_Nat_Onat, v4) = v9 &
% 278.95/41.65 c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v11, v2) = v12 & hAPP(v10,
% 278.95/41.65 v5) = v11 & hAPP(v1, v9) = v10 & $i(v12) & $i(v11) & $i(v10) & $i(v9)
% 278.95/41.65 & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v12, v8))))
% 278.95/41.65
% 278.95/41.65 (fact_Re_Ononneg__bounded)
% 278.95/41.65 $i(tc_Complex_Ocomplex) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 278.95/41.65 ? [v2: $i] : (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 278.95/41.65 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v2) & $i(v1) &
% 278.95/41.65 $i(v0) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) & !
% 278.95/41.65 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 278.95/41.65 (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v3) = v4) | ~
% 278.95/41.65 (hAPP(v5, v2) = v6) | ~ (hAPP(v1, v4) = v5) | ~ $i(v3) | ? [v7: $i] :
% 278.95/41.65 ? [v8: $i] : (c_Complex_ORe(v3) = v7 &
% 278.95/41.65 c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal, v7) = v8 & $i(v8) &
% 278.95/41.65 $i(v7) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v8, v6))))
% 278.95/41.65
% 278.95/41.65 (fact_Re_Opos__bounded)
% 278.95/41.66 $i(tc_Complex_Ocomplex) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 278.95/41.66 ? [v2: $i] : (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 278.95/41.66 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v2) & $i(v1) &
% 278.95/41.66 $i(v0) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) & ! [v3:
% 278.95/41.66 $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 278.95/41.66 (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v3) = v4) | ~
% 278.95/41.66 (hAPP(v5, v2) = v6) | ~ (hAPP(v1, v4) = v5) | ~ $i(v3) | ? [v7: $i] :
% 278.95/41.66 ? [v8: $i] : (c_Complex_ORe(v3) = v7 &
% 278.95/41.66 c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal, v7) = v8 & $i(v8) &
% 278.95/41.66 $i(v7) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v8, v6))))
% 278.95/41.66
% 278.95/41.66 (fact_Re_Ozero)
% 278.95/41.66 $i(tc_Complex_Ocomplex) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 278.95/41.66 (c_Complex_ORe(v0) = v1 & c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) =
% 278.95/41.66 v0 & c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0))
% 278.95/41.66
% 278.95/41.66 (fact__096cmod_A_Iw_A_L_Az_A_L_A_N_Az_J_A_N_Acmod_A_Iw_A_L_Az_J_A_060_061_Acmod_A_I_N_Az_J_096)
% 278.95/41.66 $i(v_z) & $i(v_w) & $i(tc_Complex_Ocomplex) & $i(tc_RealDef_Oreal) & ? [v0:
% 278.95/41.66 $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] :
% 278.95/41.66 ? [v6: $i] : (c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_z) = v1 &
% 278.95/41.66 c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v0, v1) = v2 &
% 278.95/41.66 c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v_w, v_z) = v0 &
% 278.95/41.66 c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v3, v4) = v5 &
% 278.95/41.66 c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v2) = v3 &
% 278.95/41.66 c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v1) = v6 &
% 278.95/41.66 c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v0) = v4 & $i(v6) &
% 278.95/41.66 $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) &
% 278.95/41.66 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, v6))
% 278.95/41.66
% 278.95/41.66 (fact_abs__add__one__gt__zero)
% 278.95/41.66 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 278.95/41.66 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 278.95/41.66 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 278.95/41.66 [v2: $i] : ! [v3: $i] : ( ~ (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,
% 278.95/41.66 v2) = v3) | ~ $i(v2) | ? [v4: $i] :
% 278.95/41.66 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1, v3) = v4 & $i(v4) &
% 278.95/41.66 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4))))
% 278.95/41.66
% 278.95/41.66 (fact_abs__add__one__not__less__self)
% 278.95/41.66 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 278.95/41.66 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : !
% 278.95/41.66 [v2: $i] : ( ~ (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v1) = v2) | ~
% 278.95/41.66 $i(v1) | ? [v3: $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2,
% 278.95/41.66 v0) = v3 & $i(v3) & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 278.95/41.66 v3, v1))))
% 278.95/41.66
% 278.95/41.66 (fact_abs__norm__cancel)
% 278.95/41.66 $i(tc_RealDef_Oreal) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 278.95/41.66 (c_RealVector_Onorm__class_Onorm(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 278.95/41.66 class_RealVector_Oreal__normed__vector(v1) |
% 278.95/41.66 (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v2) = v2 & $i(v2)))
% 278.95/41.66
% 278.95/41.66 (fact_abs__real__def)
% 278.95/41.66 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 278.95/41.66 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 278.95/41.66 ! [v2: $i] : (v2 = v1 | ~ (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v1)
% 278.95/41.66 = v2) | ~ $i(v1) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1,
% 278.95/41.66 v0)) & ! [v1: $i] : ! [v2: $i] : ( ~
% 278.95/41.66 (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v1) = v2) | ~ $i(v1) | ~
% 278.95/41.66 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v0) |
% 278.95/41.66 (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v1) = v2 & $i(v2))))
% 278.95/41.66
% 278.95/41.66 (fact_add__neg__neg)
% 278.95/41.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 278.95/41.67 (c_Groups_Oplus__class_Oplus(v2, v1, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 278.95/41.67 $i(v0) | ~ class_Groups_Oordered__comm__monoid__add(v2) | ? [v4: $i] :
% 278.95/41.67 (c_Groups_Ozero__class_Ozero(v2) = v4 & $i(v4) & ( ~
% 278.95/41.67 c_Orderings_Oord__class_Oless(v2, v1, v4) | ~
% 278.95/41.67 c_Orderings_Oord__class_Oless(v2, v0, v4) |
% 278.95/41.67 c_Orderings_Oord__class_Oless(v2, v3, v4))))
% 278.95/41.67
% 278.95/41.67 (fact_add__neg__nonpos)
% 278.95/41.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 278.95/41.67 (c_Groups_Oplus__class_Oplus(v2, v1, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 278.95/41.67 $i(v0) | ~ class_Groups_Oordered__comm__monoid__add(v2) | ? [v4: $i] :
% 278.95/41.67 (c_Groups_Ozero__class_Ozero(v2) = v4 & $i(v4) & ( ~
% 278.95/41.67 c_Orderings_Oord__class_Oless(v2, v1, v4) | ~
% 278.95/41.67 c_Orderings_Oord__class_Oless__eq(v2, v0, v4) |
% 278.95/41.67 c_Orderings_Oord__class_Oless(v2, v3, v4))))
% 278.95/41.67
% 278.95/41.67 (fact_add__nonneg__eq__0__iff)
% 278.95/41.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 278.95/41.67 (c_Groups_Oplus__class_Oplus(v2, v1, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 278.95/41.67 $i(v0) | ~ class_Groups_Oordered__comm__monoid__add(v2) | ? [v4: $i] :
% 278.95/41.67 (c_Groups_Ozero__class_Ozero(v2) = v4 & $i(v4) & ( ~
% 278.95/41.67 c_Orderings_Oord__class_Oless__eq(v2, v4, v1) | ~
% 278.95/41.67 c_Orderings_Oord__class_Oless__eq(v2, v4, v0) | (( ~ (v4 = v3) | (v3 =
% 278.95/41.67 v0 & v1 = v0)) & ( ~ (v4 = v0) | ~ (v1 = v0) | v3 = v0)))))
% 278.95/41.67
% 278.95/41.67 (fact_add__nonneg__nonneg)
% 278.95/41.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 278.95/41.67 (c_Groups_Oplus__class_Oplus(v2, v1, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 278.95/41.67 $i(v0) | ~ class_Groups_Oordered__comm__monoid__add(v2) | ? [v4: $i] :
% 278.95/41.67 (c_Groups_Ozero__class_Ozero(v2) = v4 & $i(v4) & ( ~
% 278.95/41.67 c_Orderings_Oord__class_Oless__eq(v2, v4, v1) | ~
% 278.95/41.67 c_Orderings_Oord__class_Oless__eq(v2, v4, v0) |
% 278.95/41.67 c_Orderings_Oord__class_Oless__eq(v2, v4, v3))))
% 278.95/41.67
% 278.95/41.67 (fact_add__nonneg__pos)
% 278.95/41.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 278.95/41.67 (c_Groups_Oplus__class_Oplus(v2, v1, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 278.95/41.67 $i(v0) | ~ class_Groups_Oordered__comm__monoid__add(v2) | ? [v4: $i] :
% 278.95/41.67 (c_Groups_Ozero__class_Ozero(v2) = v4 & $i(v4) & ( ~
% 278.95/41.67 c_Orderings_Oord__class_Oless(v2, v4, v0) | ~
% 278.95/41.67 c_Orderings_Oord__class_Oless__eq(v2, v4, v1) |
% 278.95/41.67 c_Orderings_Oord__class_Oless(v2, v4, v3))))
% 278.95/41.67
% 278.95/41.67 (fact_add__nonpos__neg)
% 278.95/41.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 278.95/41.67 (c_Groups_Oplus__class_Oplus(v2, v1, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 278.95/41.67 $i(v0) | ~ class_Groups_Oordered__comm__monoid__add(v2) | ? [v4: $i] :
% 278.95/41.67 (c_Groups_Ozero__class_Ozero(v2) = v4 & $i(v4) & ( ~
% 278.95/41.67 c_Orderings_Oord__class_Oless(v2, v0, v4) | ~
% 278.95/41.67 c_Orderings_Oord__class_Oless__eq(v2, v1, v4) |
% 278.95/41.67 c_Orderings_Oord__class_Oless(v2, v3, v4))))
% 278.95/41.67
% 278.95/41.67 (fact_add__nonpos__nonpos)
% 278.95/41.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 278.95/41.67 (c_Groups_Oplus__class_Oplus(v2, v1, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 278.95/41.67 $i(v0) | ~ class_Groups_Oordered__comm__monoid__add(v2) | ? [v4: $i] :
% 278.95/41.67 (c_Groups_Ozero__class_Ozero(v2) = v4 & $i(v4) & ( ~
% 278.95/41.67 c_Orderings_Oord__class_Oless__eq(v2, v1, v4) | ~
% 278.95/41.67 c_Orderings_Oord__class_Oless__eq(v2, v0, v4) |
% 278.95/41.67 c_Orderings_Oord__class_Oless__eq(v2, v3, v4))))
% 278.95/41.67
% 278.95/41.67 (fact_add__pos__nonneg)
% 278.95/41.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 278.95/41.67 (c_Groups_Oplus__class_Oplus(v2, v1, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 278.95/41.67 $i(v0) | ~ class_Groups_Oordered__comm__monoid__add(v2) | ? [v4: $i] :
% 278.95/41.67 (c_Groups_Ozero__class_Ozero(v2) = v4 & $i(v4) & ( ~
% 278.95/41.67 c_Orderings_Oord__class_Oless(v2, v4, v1) | ~
% 278.95/41.67 c_Orderings_Oord__class_Oless__eq(v2, v4, v0) |
% 278.95/41.67 c_Orderings_Oord__class_Oless(v2, v4, v3))))
% 278.95/41.67
% 278.95/41.67 (fact_add__pos__pos)
% 278.95/41.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 278.95/41.68 (c_Groups_Oplus__class_Oplus(v2, v1, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 278.95/41.68 $i(v0) | ~ class_Groups_Oordered__comm__monoid__add(v2) | ? [v4: $i] :
% 278.95/41.68 (c_Groups_Ozero__class_Ozero(v2) = v4 & $i(v4) & ( ~
% 278.95/41.68 c_Orderings_Oord__class_Oless(v2, v4, v1) | ~
% 278.95/41.68 c_Orderings_Oord__class_Oless(v2, v4, v0) |
% 278.95/41.68 c_Orderings_Oord__class_Oless(v2, v4, v3))))
% 278.95/41.68
% 278.95/41.68 (fact_bounded__bilinear_Ononneg__bounded)
% 278.95/41.68 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 278.95/41.68 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 278.95/41.68 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 278.95/41.68 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ $i(v5) | ~ $i(v4)
% 278.95/41.68 | ~ $i(v3) | ~ $i(v2) | ~ c_RealVector_Obounded__bilinear(v3, v4, v5,
% 278.95/41.68 v2) | ~ class_RealVector_Oreal__normed__vector(v5) | ~
% 278.95/41.68 class_RealVector_Oreal__normed__vector(v4) | ~
% 278.95/41.68 class_RealVector_Oreal__normed__vector(v3) | ? [v6: $i] : ($i(v6) &
% 278.95/41.68 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v6) & ! [v7:
% 278.95/41.68 $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : !
% 278.95/41.68 [v12: $i] : ! [v13: $i] : ! [v14: $i] : ( ~
% 278.95/41.68 (c_RealVector_Onorm__class_Onorm(v4, v8) = v11) | ~
% 278.95/41.68 (c_RealVector_Onorm__class_Onorm(v3, v7) = v9) | ~ (hAPP(v13, v6) =
% 278.95/41.68 v14) | ~ (hAPP(v10, v11) = v12) | ~ (hAPP(v1, v12) = v13) | ~
% 278.95/41.68 (hAPP(v1, v9) = v10) | ~ $i(v8) | ~ $i(v7) | ? [v15: $i] : ? [v16:
% 278.95/41.68 $i] : ? [v17: $i] : (c_RealVector_Onorm__class_Onorm(v5, v16) = v17
% 278.95/41.68 & hAPP(v15, v8) = v16 & hAPP(v2, v7) = v15 & $i(v17) & $i(v16) &
% 278.95/41.68 $i(v15) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v17,
% 278.95/41.68 v14))))))
% 278.95/41.68
% 278.95/41.68 (fact_bounded__bilinear_Opos__bounded)
% 278.95/41.68 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 278.95/41.68 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 278.95/41.68 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 278.95/41.68 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ $i(v5) | ~ $i(v4)
% 278.95/41.68 | ~ $i(v3) | ~ $i(v2) | ~ c_RealVector_Obounded__bilinear(v3, v4, v5,
% 278.95/41.68 v2) | ~ class_RealVector_Oreal__normed__vector(v5) | ~
% 278.95/41.68 class_RealVector_Oreal__normed__vector(v4) | ~
% 278.95/41.68 class_RealVector_Oreal__normed__vector(v3) | ? [v6: $i] : ($i(v6) &
% 278.95/41.68 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v6) & ! [v7: $i] :
% 278.95/41.68 ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ! [v12: $i] :
% 278.95/41.68 ! [v13: $i] : ! [v14: $i] : ( ~ (c_RealVector_Onorm__class_Onorm(v4,
% 278.95/41.68 v8) = v11) | ~ (c_RealVector_Onorm__class_Onorm(v3, v7) = v9) |
% 278.95/41.68 ~ (hAPP(v13, v6) = v14) | ~ (hAPP(v10, v11) = v12) | ~ (hAPP(v1,
% 278.95/41.68 v12) = v13) | ~ (hAPP(v1, v9) = v10) | ~ $i(v8) | ~ $i(v7) | ?
% 278.95/41.68 [v15: $i] : ? [v16: $i] : ? [v17: $i] :
% 278.95/41.68 (c_RealVector_Onorm__class_Onorm(v5, v16) = v17 & hAPP(v15, v8) = v16
% 278.95/41.68 & hAPP(v2, v7) = v15 & $i(v17) & $i(v16) & $i(v15) &
% 278.95/41.68 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v17, v14))))))
% 278.95/41.68
% 278.95/41.68 (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J)
% 278.95/41.68 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 278.95/41.68 (c_Groups_Oplus__class_Oplus(v2, v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 278.95/41.68 $i(v0) | ~ class_Rings_Ocomm__semiring__1(v2) |
% 278.95/41.68 (c_Groups_Oplus__class_Oplus(v2, v1, v0) = v3 & $i(v3)))
% 278.95/41.68
% 278.95/41.68 (fact_complex__Im__i)
% 278.95/41.68 $i(c_Complex_Oii) & $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 278.95/41.68 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 278.95/41.68 c_Complex_OIm(c_Complex_Oii) = v0 & $i(v0))
% 278.95/41.68
% 278.95/41.68 (fact_complex__Im__one)
% 278.95/41.68 $i(tc_Complex_Ocomplex) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 278.95/41.68 (c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = v0 & c_Complex_OIm(v0) = v1
% 278.95/41.68 & c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0))
% 278.95/41.68
% 278.95/41.68 (fact_complex__Re__i)
% 278.95/41.68 $i(c_Complex_Oii) & $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 278.95/41.68 (c_Complex_ORe(c_Complex_Oii) = v0 &
% 278.95/41.68 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0))
% 278.95/41.68
% 278.95/41.68 (fact_complex__Re__one)
% 278.95/41.68 $i(tc_Complex_Ocomplex) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 278.95/41.68 (c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = v0 &
% 278.95/41.68 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & c_Complex_ORe(v0) = v1 &
% 278.95/41.68 $i(v1) & $i(v0))
% 278.95/41.68
% 278.95/41.68 (fact_complex__diff__def)
% 278.95/41.69 $i(tc_Complex_Ocomplex) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 278.95/41.69 $i] : ( ~ (c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v0) = v2) |
% 278.95/41.69 ~ (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v1, v2) = v3) | ~
% 278.95/41.69 $i(v1) | ~ $i(v0) | (c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v1,
% 278.95/41.69 v0) = v3 & $i(v3)))
% 278.95/41.69
% 278.95/41.69 (fact_complex__one__def)
% 278.95/41.69 $i(tc_Complex_Ocomplex) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 278.95/41.69 ? [v2: $i] : (c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = v0 &
% 278.95/41.69 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 278.95/41.69 c_Complex_Ocomplex_OComplex(v1, v2) = v0 &
% 278.95/41.69 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v2 & $i(v2) & $i(v1) &
% 278.95/41.69 $i(v0))
% 278.95/41.69
% 278.95/41.69 (fact_complex__zero__def)
% 278.95/41.69 $i(tc_Complex_Ocomplex) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 278.95/41.69 (c_Complex_Ocomplex_OComplex(v1, v1) = v0 &
% 278.95/41.69 c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v0 &
% 278.95/41.69 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0))
% 278.95/41.69
% 278.95/41.69 (fact_dist__eq__0__iff)
% 278.95/41.69 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 278.95/41.69 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 278.95/41.69 ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~
% 278.95/41.69 (c_RealVector_Odist__class_Odist(v2, v1, v1) = v3) | ~ $i(v2) | ~ $i(v1)
% 278.95/41.69 | ~ class_RealVector_Ometric__space(v2)) & ! [v1: $i] : ! [v2: $i] : !
% 278.95/41.69 [v3: $i] : (v2 = v1 | ~ (c_RealVector_Odist__class_Odist(v3, v2, v1) = v0)
% 278.95/41.69 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 278.95/41.69 class_RealVector_Ometric__space(v3)))
% 278.95/41.69
% 278.95/41.69 (fact_dist__le__zero__iff)
% 278.95/41.69 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 278.95/41.69 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 278.95/41.69 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v1 | ~
% 278.95/41.69 (c_RealVector_Odist__class_Odist(v3, v2, v1) = v4) | ~ $i(v3) | ~ $i(v2)
% 278.95/41.69 | ~ $i(v1) | ~ class_RealVector_Ometric__space(v3) | ~
% 278.95/41.69 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v0)) & ! [v1: $i]
% 278.95/41.69 : ! [v2: $i] : ! [v3: $i] : ( ~ (c_RealVector_Odist__class_Odist(v2, v1,
% 278.95/41.69 v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 278.95/41.69 class_RealVector_Ometric__space(v2) |
% 278.95/41.69 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v0)))
% 278.95/41.69
% 278.95/41.69 (fact_dist__not__less__zero)
% 278.95/41.69 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 278.95/41.69 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 278.95/41.69 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 278.95/41.69 (c_RealVector_Odist__class_Odist(v3, v2, v1) = v4) | ~ $i(v3) | ~ $i(v2)
% 278.95/41.69 | ~ $i(v1) | ~ class_RealVector_Ometric__space(v3) | ~
% 278.95/41.69 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v4, v0)))
% 278.95/41.69
% 278.95/41.69 (fact_dist__self)
% 278.95/41.69 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 278.95/41.69 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 278.95/41.69 ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~
% 278.95/41.69 (c_RealVector_Odist__class_Odist(v2, v1, v1) = v3) | ~ $i(v2) | ~ $i(v1)
% 278.95/41.69 | ~ class_RealVector_Ometric__space(v2)))
% 278.95/41.69
% 278.95/41.69 (fact_i__def)
% 278.95/41.69 $i(c_Complex_Oii) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 278.95/41.69 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 278.95/41.69 c_Complex_Ocomplex_OComplex(v0, v1) = c_Complex_Oii &
% 278.95/41.69 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0))
% 278.95/41.69
% 278.95/41.69 (fact_le__mult__natfloor)
% 278.95/41.69 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 278.95/41.69 $i] : (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 278.95/41.69 c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v2 &
% 278.95/41.69 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v2) & $i(v1) &
% 278.95/41.69 $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 278.95/41.69 : ! [v8: $i] : ( ~ (c_RComplete_Onatfloor(v4) = v5) | ~
% 278.95/41.69 (c_RComplete_Onatfloor(v3) = v7) | ~ (hAPP(v6, v7) = v8) | ~ (hAPP(v1,
% 278.95/41.69 v5) = v6) | ~ $i(v4) | ~ $i(v3) | ~
% 278.95/41.69 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v4) | ~
% 278.95/41.69 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) | ? [v9: $i]
% 278.95/41.69 : ? [v10: $i] : ? [v11: $i] : (c_RComplete_Onatfloor(v10) = v11 &
% 278.95/41.69 hAPP(v9, v3) = v10 & hAPP(v2, v4) = v9 & $i(v11) & $i(v10) & $i(v9) &
% 278.95/41.69 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v8, v11))))
% 278.95/41.69
% 278.95/41.69 (fact_le__natfloor__eq)
% 278.95/41.70 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 278.95/41.70 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 278.95/41.70 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat,
% 278.95/41.70 v1) = v4) | ~ (c_RComplete_Onatfloor(v2) = v3) | ~ $i(v2) | ~
% 278.95/41.70 $i(v1) | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v3) | ~
% 278.95/41.70 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) |
% 278.95/41.70 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v2)) & ! [v1: $i]
% 278.95/41.70 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 278.95/41.70 (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~ (c_RComplete_Onatfloor(v2) =
% 278.95/41.70 v3) | ~ $i(v2) | ~ $i(v1) | ~
% 278.95/41.70 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v2) | ~
% 278.95/41.70 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) |
% 278.95/41.70 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v3)))
% 278.95/41.70
% 278.95/41.70 (fact_le__natfloor__eq__one)
% 278.95/41.70 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 278.95/41.70 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 &
% 278.95/41.70 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0) & ! [v2:
% 278.95/41.70 $i] : ! [v3: $i] : ( ~ (c_RComplete_Onatfloor(v2) = v3) | ~ $i(v2) | ~
% 278.95/41.70 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, v3) |
% 278.95/41.70 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v2)) & ! [v2: $i]
% 278.95/41.70 : ! [v3: $i] : ( ~ (c_RComplete_Onatfloor(v2) = v3) | ~ $i(v2) | ~
% 278.95/41.70 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v2) |
% 278.95/41.70 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, v3)))
% 278.95/41.70
% 278.95/41.70 (fact_lemmaCauchy)
% 278.95/41.70 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 278.95/41.70 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : !
% 278.95/41.70 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 278.95/41.70 (c_RealVector_Onorm__class_Onorm(v4, v5) = v6) | ~ (hAPP(v1, v2) = v5) |
% 278.95/41.70 ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ class_Orderings_Oord(v3)
% 278.95/41.70 | ~ class_RealVector_Oreal__normed__vector(v4) | ? [v7: $i] : ? [v8:
% 278.95/41.70 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ($i(v8) &
% 278.95/41.70 ((c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v0, v6) = v7 & $i(v7) &
% 278.95/41.70 ! [v12: $i] : ! [v13: $i] : ! [v14: $i] : ( ~
% 278.95/41.70 (c_RealVector_Onorm__class_Onorm(v4, v13) = v14) | ~ (hAPP(v1,
% 278.95/41.70 v12) = v13) | ~ $i(v12) | ~
% 278.95/41.70 c_Orderings_Oord__class_Oless__eq(v3, v2, v12) |
% 278.95/41.70 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v14, v7))) |
% 278.95/41.70 (c_Groups_Ominus__class_Ominus(v4, v5, v9) = v10 &
% 278.95/41.70 c_RealVector_Onorm__class_Onorm(v4, v10) = v11 & hAPP(v1, v8) = v9 &
% 278.95/41.70 $i(v11) & $i(v10) & $i(v9) & c_Orderings_Oord__class_Oless__eq(v3,
% 278.95/41.70 v2, v8) & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v11,
% 278.95/41.70 v0))))))
% 278.95/41.70
% 278.95/41.70 (fact_lemma__NBseq__def2)
% 278.95/41.70 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 278.95/41.70 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ? [v1: $i] :
% 278.95/41.70 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_Nat_OSuc(v3) = v4) | ~
% 278.95/41.70 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 278.95/41.70 class_RealVector_Oreal__normed__vector(v2) | ? [v5: $i] : ? [v6: $i] :
% 278.95/41.70 ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ($i(v7) & $i(v5) &
% 278.95/41.70 ((c_RealDef_Oreal(tc_Nat_Onat, v4) = v6 &
% 278.95/41.70 c_RealVector_Onorm__class_Onorm(v2, v8) = v9 & hAPP(v1, v7) = v8 &
% 278.95/41.70 $i(v9) & $i(v8) & $i(v6) & ~
% 278.95/41.70 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v9, v6)) |
% 278.95/41.70 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v5) & ! [v10:
% 278.95/41.70 $i] : ! [v11: $i] : ! [v12: $i] : ( ~
% 278.95/41.70 (c_RealVector_Onorm__class_Onorm(v2, v11) = v12) | ~ (hAPP(v1,
% 278.95/41.70 v10) = v11) | ~ $i(v10) |
% 278.95/41.70 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v12, v5))))))
% 278.95/41.70 & ? [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~
% 278.95/41.70 $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | ~
% 278.95/41.70 class_RealVector_Oreal__normed__vector(v2) | ? [v4: $i] : ? [v5: $i] :
% 278.95/41.70 ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ($i(v7) & $i(v4) &
% 278.95/41.70 ((c_Nat_OSuc(v4) = v5 & c_RealDef_Oreal(tc_Nat_Onat, v5) = v6 & $i(v6) &
% 278.95/41.70 $i(v5) & ! [v10: $i] : ! [v11: $i] : ! [v12: $i] : ( ~
% 278.95/41.70 (c_RealVector_Onorm__class_Onorm(v2, v11) = v12) | ~ (hAPP(v1,
% 278.95/41.70 v10) = v11) | ~ $i(v10) |
% 278.95/41.70 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v12, v6))) |
% 278.95/41.70 (c_RealVector_Onorm__class_Onorm(v2, v8) = v9 & hAPP(v1, v7) = v8 &
% 278.95/41.70 $i(v9) & $i(v8) & ~
% 278.95/41.70 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v9, v3))))))
% 278.95/41.70
% 278.95/41.70 (fact_lemma__interval)
% 278.95/41.71 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 278.95/41.71 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 278.95/41.71 ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 278.95/41.71 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v2) | ~
% 278.95/41.71 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v1) | ? [v4: $i] :
% 278.95/41.71 ($i(v4) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) & !
% 278.95/41.71 [v5: $i] : ! [v6: $i] : ( ~
% 278.95/41.71 (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v2, v5) = v6) | ~
% 278.95/41.71 $i(v5) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, v1) |
% 278.95/41.71 ? [v7: $i] : (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v6) = v7 &
% 278.95/41.71 $i(v7) & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v7,
% 278.95/41.71 v4))) & ! [v5: $i] : ! [v6: $i] : ( ~
% 278.95/41.71 (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v2, v5) = v6) | ~
% 278.95/41.71 $i(v5) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v5) |
% 278.95/41.71 ? [v7: $i] : (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v6) = v7 &
% 278.95/41.71 $i(v7) & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v7,
% 278.95/41.71 v4))))))
% 278.95/41.71
% 278.95/41.71 (fact_lemma__interval__lt)
% 278.95/41.71 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 278.95/41.71 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 278.95/41.71 ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 278.95/41.71 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v2) | ~
% 278.95/41.71 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v1) | ? [v4: $i] :
% 278.95/41.71 ($i(v4) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) & !
% 278.95/41.71 [v5: $i] : ! [v6: $i] : ( ~
% 278.95/41.71 (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v2, v5) = v6) | ~
% 278.95/41.71 $i(v5) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v5, v1) | ?
% 278.95/41.71 [v7: $i] : (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v6) = v7 &
% 278.95/41.71 $i(v7) & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v7,
% 278.95/41.71 v4))) & ! [v5: $i] : ! [v6: $i] : ( ~
% 278.95/41.71 (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v2, v5) = v6) | ~
% 278.95/41.71 $i(v5) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v5) | ?
% 278.95/41.71 [v7: $i] : (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v6) = v7 &
% 278.95/41.71 $i(v7) & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v7,
% 278.95/41.71 v4))))))
% 278.95/41.71
% 278.95/41.71 (fact_less__natfloor)
% 278.95/41.71 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 278.95/41.71 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 278.95/41.71 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat,
% 278.95/41.71 v1) = v3) | ~ (c_RComplete_Onatfloor(v2) = v4) | ~ $i(v2) | ~
% 278.95/41.71 $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v3) | ~
% 278.95/41.71 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) |
% 278.95/41.71 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v1)))
% 278.95/41.71
% 278.95/41.71 (fact_ln__add__one__self__le__self)
% 278.95/41.71 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 278.95/41.71 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 278.95/41.71 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 278.95/41.71 [v2: $i] : ! [v3: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,
% 278.95/41.71 v1, v2) = v3) | ~ $i(v2) | ~
% 278.95/41.71 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) | ? [v4: $i]
% 278.95/41.71 : (c_Transcendental_Oln(v3) = v4 & $i(v4) &
% 278.95/41.71 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v2))))
% 278.95/41.71
% 278.95/41.71 (fact_ln__eq__zero__iff)
% 278.95/41.71 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 278.95/41.71 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 278.95/41.71 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 278.95/41.71 [v2: $i] : (v2 = v1 | ~ (c_Transcendental_Oln(v2) = v0) | ~ $i(v2) | ~
% 278.95/41.71 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2)) & ! [v2: $i] :
% 278.95/41.71 (v2 = v0 | ~ (c_Transcendental_Oln(v1) = v2) | ~
% 278.95/41.71 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v1)))
% 278.95/41.71
% 278.95/41.71 (fact_ln__ge__zero)
% 278.95/41.71 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 278.95/41.71 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 278.95/41.71 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0) & !
% 278.95/41.71 [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2) = v3) | ~ $i(v2) |
% 278.95/41.71 ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) |
% 278.95/41.71 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v3)))
% 278.95/41.71
% 278.95/41.71 (fact_ln__ge__zero__iff)
% 278.95/41.71 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 278.95/41.71 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 278.95/41.71 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 278.95/41.71 [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2) = v3) | ~ $i(v2) |
% 278.95/41.71 ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ~
% 278.95/41.71 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v2) |
% 278.95/41.71 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3)) & ! [v2: $i]
% 278.95/41.71 : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2) = v3) | ~ $i(v2) | ~
% 278.95/41.71 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ~
% 278.95/41.71 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) |
% 278.95/41.71 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v2)))
% 278.95/41.71
% 278.95/41.71 (fact_ln__ge__zero__imp__ge__one)
% 278.95/41.72 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 278.95/41.72 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 278.95/41.72 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 278.95/41.72 [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2) = v3) | ~ $i(v2) |
% 278.95/41.72 ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ~
% 278.95/41.72 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) |
% 278.95/41.72 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v2)))
% 278.95/41.72
% 278.95/41.72 (fact_ln__gt__zero)
% 278.95/41.72 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 278.95/41.72 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 278.95/41.72 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0) & !
% 278.95/41.72 [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2) = v3) | ~ $i(v2) |
% 278.95/41.72 ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) |
% 278.95/41.72 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v3)))
% 278.95/41.72
% 278.95/41.72 (fact_ln__gt__zero__iff)
% 279.36/41.72 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 279.36/41.72 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 279.36/41.72 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 279.36/41.72 [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2) = v3) | ~ $i(v2) |
% 279.36/41.72 ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v2) | ~
% 279.36/41.72 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) |
% 279.36/41.72 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3)) & ! [v2: $i] :
% 279.36/41.72 ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2) = v3) | ~ $i(v2) | ~
% 279.36/41.72 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | ~
% 279.36/41.72 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) |
% 279.36/41.72 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v2)))
% 279.36/41.72
% 279.36/41.72 (fact_ln__gt__zero__imp__gt__one)
% 279.36/41.72 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 279.36/41.72 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 279.36/41.72 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 279.36/41.72 [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2) = v3) | ~ $i(v2) |
% 279.36/41.72 ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | ~
% 279.36/41.72 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) |
% 279.36/41.72 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v2)))
% 279.36/41.72
% 279.36/41.72 (fact_ln__inj__iff)
% 279.36/41.72 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 279.36/41.72 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 279.36/41.72 ! [v2: $i] : ! [v3: $i] : (v2 = v1 | ~ (c_Transcendental_Oln(v2) = v3) |
% 279.36/41.72 ~ (c_Transcendental_Oln(v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 279.36/41.72 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ~
% 279.36/41.72 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v1)))
% 279.36/41.72
% 279.36/41.72 (fact_ln__le__cancel__iff)
% 279.36/41.72 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 279.36/41.72 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 279.36/41.72 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_Transcendental_Oln(v2) = v3)
% 279.36/41.72 | ~ (c_Transcendental_Oln(v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~
% 279.36/41.72 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ~
% 279.36/41.72 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v1) | ~
% 279.36/41.72 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v4) |
% 279.36/41.72 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v1)) & ! [v1: $i]
% 279.36/41.72 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_Transcendental_Oln(v2) =
% 279.36/41.72 v3) | ~ (c_Transcendental_Oln(v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~
% 279.36/41.72 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ~
% 279.36/41.72 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v1) | ~
% 279.36/41.72 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v1) |
% 279.36/41.72 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v4)))
% 279.36/41.72
% 279.36/41.72 (fact_ln__less__cancel__iff)
% 279.36/41.73 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 279.36/41.73 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 279.36/41.73 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_Transcendental_Oln(v2) = v3)
% 279.36/41.73 | ~ (c_Transcendental_Oln(v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~
% 279.36/41.73 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v4) | ~
% 279.36/41.73 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ~
% 279.36/41.73 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v1) |
% 279.36/41.73 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v1)) & ! [v1: $i] :
% 279.36/41.73 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_Transcendental_Oln(v2) = v3)
% 279.36/41.73 | ~ (c_Transcendental_Oln(v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~
% 279.36/41.73 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v1) | ~
% 279.36/41.73 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ~
% 279.36/41.73 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v1) |
% 279.36/41.73 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v4)))
% 279.36/41.73
% 279.36/41.73 (fact_ln__less__self)
% 279.36/41.73 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 279.36/41.73 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 279.36/41.73 ! [v2: $i] : ( ~ (c_Transcendental_Oln(v1) = v2) | ~ $i(v1) | ~
% 279.36/41.73 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v1) |
% 279.36/41.73 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v1)))
% 279.36/41.73
% 279.36/41.73 (fact_ln__less__zero)
% 279.36/41.73 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 279.36/41.73 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 279.36/41.73 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 279.36/41.73 [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2) = v3) | ~ $i(v2) |
% 279.36/41.73 ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v1) | ~
% 279.36/41.73 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) |
% 279.36/41.73 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v0)))
% 279.36/41.73
% 279.36/41.73 (fact_ln__less__zero__iff)
% 279.36/41.73 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 279.36/41.73 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 279.36/41.73 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 279.36/41.73 [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2) = v3) | ~ $i(v2) |
% 279.36/41.73 ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v0) | ~
% 279.36/41.73 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) |
% 279.36/41.73 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v1)) & ! [v2: $i] :
% 279.36/41.73 ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2) = v3) | ~ $i(v2) | ~
% 279.36/41.73 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v1) | ~
% 279.36/41.73 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) |
% 279.36/41.73 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v0)))
% 279.36/41.73
% 279.36/41.73 (fact_ln__mult)
% 279.36/41.73 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 279.36/41.73 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 279.36/41.73 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 279.36/41.73 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 279.36/41.73 (c_Transcendental_Oln(v3) = v4) | ~ (c_Transcendental_Oln(v2) = v5) | ~
% 279.36/41.73 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v4, v5) = v6) | ~ $i(v3) |
% 279.36/41.73 ~ $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) |
% 279.36/41.73 ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ? [v7: $i] :
% 279.36/41.73 ? [v8: $i] : (c_Transcendental_Oln(v8) = v6 & hAPP(v7, v2) = v8 & hAPP(v1,
% 279.36/41.73 v3) = v7 & $i(v8) & $i(v7) & $i(v6))))
% 279.36/41.73
% 279.36/41.73 (fact_ln__one)
% 279.36/41.73 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : (c_Transcendental_Oln(v0) =
% 279.36/41.73 v1 & c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 279.36/41.73 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0))
% 279.36/41.73
% 279.36/41.73 (fact_ln__realpow)
% 279.36/41.73 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 279.36/41.73 $i] : (c_Power_Opower__class_Opower(tc_RealDef_Oreal) = v1 &
% 279.36/41.73 c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v2 &
% 279.36/41.73 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v2) & $i(v1) &
% 279.36/41.73 $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 279.36/41.73 : ! [v8: $i] : ( ~ (c_Transcendental_Oln(v4) = v7) | ~
% 279.36/41.73 (c_RealDef_Oreal(tc_Nat_Onat, v3) = v5) | ~ (hAPP(v6, v7) = v8) | ~
% 279.36/41.73 (hAPP(v2, v5) = v6) | ~ $i(v4) | ~ $i(v3) | ~
% 279.36/41.73 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) | ? [v9: $i] : ?
% 279.36/41.73 [v10: $i] : (c_Transcendental_Oln(v10) = v8 & hAPP(v9, v3) = v10 &
% 279.36/41.73 hAPP(v1, v4) = v9 & $i(v10) & $i(v9) & $i(v8))))
% 279.36/41.73
% 279.36/41.73 (fact_minus__add__cancel)
% 279.36/41.73 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 279.36/41.73 $i] : (v5 = v0 | ~ (c_Groups_Ouminus__class_Ouminus(v2, v1) = v3) | ~
% 279.36/41.73 (c_Groups_Oplus__class_Oplus(v2, v3, v4) = v5) | ~
% 279.36/41.73 (c_Groups_Oplus__class_Oplus(v2, v1, v0) = v4) | ~ $i(v2) | ~ $i(v1) | ~
% 279.36/41.73 $i(v0) | ~ class_Groups_Ogroup__add(v2))
% 279.36/41.73
% 279.36/41.73 (fact_mult_Ononneg__bounded)
% 279.36/41.74 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 279.36/41.74 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 279.36/41.74 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 279.36/41.74 [v2: $i] : ! [v3: $i] : ( ~ (c_Groups_Otimes__class_Otimes(v2) = v3) | ~
% 279.36/41.74 $i(v2) | ~ class_RealVector_Oreal__normed__algebra(v2) | ? [v4: $i] :
% 279.36/41.74 ($i(v4) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v4) & !
% 279.36/41.74 [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : !
% 279.36/41.74 [v10: $i] : ! [v11: $i] : ! [v12: $i] : ( ~
% 279.36/41.74 (c_RealVector_Onorm__class_Onorm(v2, v6) = v9) | ~
% 279.36/41.74 (c_RealVector_Onorm__class_Onorm(v2, v5) = v7) | ~ (hAPP(v11, v4) =
% 279.36/41.74 v12) | ~ (hAPP(v8, v9) = v10) | ~ (hAPP(v1, v10) = v11) | ~
% 279.36/41.74 (hAPP(v1, v7) = v8) | ~ $i(v6) | ~ $i(v5) | ? [v13: $i] : ? [v14:
% 279.36/41.74 $i] : ? [v15: $i] : (c_RealVector_Onorm__class_Onorm(v2, v14) = v15
% 279.36/41.74 & hAPP(v13, v6) = v14 & hAPP(v3, v5) = v13 & $i(v15) & $i(v14) &
% 279.36/41.74 $i(v13) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v15,
% 279.36/41.74 v12))))))
% 279.36/41.74
% 279.36/41.74 (fact_mult_Opos__bounded)
% 279.36/41.74 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 279.36/41.74 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 279.36/41.74 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 279.36/41.74 [v2: $i] : ! [v3: $i] : ( ~ (c_Groups_Otimes__class_Otimes(v2) = v3) | ~
% 279.36/41.74 $i(v2) | ~ class_RealVector_Oreal__normed__algebra(v2) | ? [v4: $i] :
% 279.36/41.74 ($i(v4) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) & !
% 279.36/41.74 [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : !
% 279.36/41.74 [v10: $i] : ! [v11: $i] : ! [v12: $i] : ( ~
% 279.36/41.74 (c_RealVector_Onorm__class_Onorm(v2, v6) = v9) | ~
% 279.36/41.74 (c_RealVector_Onorm__class_Onorm(v2, v5) = v7) | ~ (hAPP(v11, v4) =
% 279.36/41.74 v12) | ~ (hAPP(v8, v9) = v10) | ~ (hAPP(v1, v10) = v11) | ~
% 279.36/41.74 (hAPP(v1, v7) = v8) | ~ $i(v6) | ~ $i(v5) | ? [v13: $i] : ? [v14:
% 279.36/41.74 $i] : ? [v15: $i] : (c_RealVector_Onorm__class_Onorm(v2, v14) = v15
% 279.36/41.74 & hAPP(v13, v6) = v14 & hAPP(v3, v5) = v13 & $i(v15) & $i(v14) &
% 279.36/41.74 $i(v13) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v15,
% 279.36/41.74 v12))))))
% 279.36/41.74
% 279.36/41.74 (fact_mult__left_Ononneg__bounded)
% 279.36/41.74 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 279.36/41.74 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 279.36/41.74 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & ?
% 279.36/41.74 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 279.36/41.74 (c_Groups_Otimes__class_Otimes(v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 279.36/41.74 class_RealVector_Oreal__normed__algebra(v3) | ? [v5: $i] : ($i(v5) &
% 279.36/41.74 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v5) & ! [v6:
% 279.36/41.74 $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~
% 279.36/41.74 (c_RealVector_Onorm__class_Onorm(v3, v6) = v7) | ~ (hAPP(v8, v5) =
% 279.36/41.74 v9) | ~ (hAPP(v1, v7) = v8) | ~ $i(v6) | ? [v10: $i] : ? [v11:
% 279.36/41.74 $i] : ? [v12: $i] : (c_RealVector_Onorm__class_Onorm(v3, v11) = v12
% 279.36/41.74 & hAPP(v10, v2) = v11 & hAPP(v4, v6) = v10 & $i(v12) & $i(v11) &
% 279.36/41.74 $i(v10) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v12,
% 279.36/41.74 v9))))))
% 279.36/41.74
% 279.36/41.74 (fact_mult__left_Opos__bounded)
% 279.36/41.74 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 279.36/41.74 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 279.36/41.74 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & ?
% 279.36/41.74 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 279.36/41.74 (c_Groups_Otimes__class_Otimes(v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 279.36/41.74 class_RealVector_Oreal__normed__algebra(v3) | ? [v5: $i] : ($i(v5) &
% 279.36/41.74 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v5) & ! [v6: $i] :
% 279.36/41.74 ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~
% 279.36/41.74 (c_RealVector_Onorm__class_Onorm(v3, v6) = v7) | ~ (hAPP(v8, v5) =
% 279.36/41.74 v9) | ~ (hAPP(v1, v7) = v8) | ~ $i(v6) | ? [v10: $i] : ? [v11:
% 279.36/41.74 $i] : ? [v12: $i] : (c_RealVector_Onorm__class_Onorm(v3, v11) = v12
% 279.36/41.74 & hAPP(v10, v2) = v11 & hAPP(v4, v6) = v10 & $i(v12) & $i(v11) &
% 279.36/41.74 $i(v10) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v12,
% 279.36/41.74 v9))))))
% 279.36/41.74
% 279.36/41.74 (fact_mult__right_Ononneg__bounded)
% 279.36/41.74 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 279.36/41.74 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 279.36/41.74 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 279.36/41.74 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 279.36/41.74 (c_Groups_Otimes__class_Otimes(v3) = v4) | ~ (hAPP(v4, v2) = v5) | ~
% 279.36/41.74 $i(v3) | ~ $i(v2) | ~ class_RealVector_Oreal__normed__algebra(v3) | ?
% 279.36/41.74 [v6: $i] : ($i(v6) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 279.36/41.74 v0, v6) & ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ( ~
% 279.36/41.74 (c_RealVector_Onorm__class_Onorm(v3, v7) = v8) | ~ (hAPP(v9, v6) =
% 279.36/41.74 v10) | ~ (hAPP(v1, v8) = v9) | ~ $i(v7) | ? [v11: $i] : ? [v12:
% 279.36/41.74 $i] : (c_RealVector_Onorm__class_Onorm(v3, v11) = v12 & hAPP(v5, v7)
% 279.36/41.74 = v11 & $i(v12) & $i(v11) &
% 279.36/41.74 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v12, v10))))))
% 279.36/41.74
% 279.36/41.74 (fact_mult__right_Opos__bounded)
% 279.36/41.74 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 279.36/41.74 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 279.36/41.74 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 279.36/41.74 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 279.36/41.74 (c_Groups_Otimes__class_Otimes(v3) = v4) | ~ (hAPP(v4, v2) = v5) | ~
% 279.36/41.74 $i(v3) | ~ $i(v2) | ~ class_RealVector_Oreal__normed__algebra(v3) | ?
% 279.36/41.74 [v6: $i] : ($i(v6) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0,
% 279.36/41.74 v6) & ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ( ~
% 279.36/41.74 (c_RealVector_Onorm__class_Onorm(v3, v7) = v8) | ~ (hAPP(v9, v6) =
% 279.36/41.74 v10) | ~ (hAPP(v1, v8) = v9) | ~ $i(v7) | ? [v11: $i] : ? [v12:
% 279.36/41.74 $i] : (c_RealVector_Onorm__class_Onorm(v3, v11) = v12 & hAPP(v5, v7)
% 279.36/41.74 = v11 & $i(v12) & $i(v11) &
% 279.36/41.74 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v12, v10))))))
% 279.36/41.74
% 279.36/41.74 (fact_nat__le__real__less)
% 279.36/41.75 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 279.36/41.75 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : !
% 279.36/41.75 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v2)
% 279.36/41.75 = v3) | ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~ $i(v2) | ~
% 279.36/41.75 $i(v1) | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1) | ?
% 279.36/41.75 [v5: $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v4, v0) = v5 &
% 279.36/41.75 $i(v5) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v5))) & !
% 279.36/41.75 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 279.36/41.75 (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~ (c_RealDef_Oreal(tc_Nat_Onat,
% 279.36/41.75 v1) = v4) | ~ $i(v2) | ~ $i(v1) |
% 279.36/41.75 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1) | ? [v5: $i] :
% 279.36/41.75 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v4, v0) = v5 & $i(v5) & ~
% 279.36/41.75 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v5))))
% 279.36/41.75
% 279.36/41.75 (fact_nat__less__real__le)
% 279.36/41.75 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 279.36/41.75 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : !
% 279.36/41.75 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v2)
% 279.36/41.75 = v3) | ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~ $i(v2) | ~
% 279.36/41.75 $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) | ? [v5:
% 279.36/41.75 $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v0) = v5 &
% 279.36/41.75 $i(v5) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, v4))) &
% 279.36/41.75 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 279.36/41.75 (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~ (c_RealDef_Oreal(tc_Nat_Onat,
% 279.36/41.75 v1) = v4) | ~ $i(v2) | ~ $i(v1) |
% 279.36/41.75 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) | ? [v5: $i] :
% 279.36/41.75 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v0) = v5 & $i(v5) & ~
% 279.36/41.75 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, v4))))
% 279.36/41.75
% 279.36/41.75 (fact_natceiling__add)
% 279.36/41.75 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 279.36/41.75 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 279.36/41.75 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat,
% 279.36/41.75 v1) = v3) | ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v3)
% 279.36/41.75 = v4) | ~ $i(v2) | ~ $i(v1) | ~
% 279.36/41.75 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) | ? [v5: $i]
% 279.36/41.75 : ? [v6: $i] : (c_RComplete_Onatceiling(v4) = v5 &
% 279.36/41.75 c_RComplete_Onatceiling(v2) = v6 &
% 279.36/41.75 c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v6, v1) = v5 & $i(v6) &
% 279.36/41.75 $i(v5))))
% 279.36/41.75
% 279.36/41.75 (fact_natceiling__add__one)
% 279.36/41.75 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 279.36/41.75 $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 &
% 279.36/41.75 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 279.36/41.75 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v2) & $i(v1) &
% 279.36/41.75 $i(v0) & ! [v3: $i] : ! [v4: $i] : ( ~
% 279.36/41.75 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v1) = v4) | ~ $i(v3) |
% 279.36/41.75 ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) | ? [v5:
% 279.36/41.75 $i] : ? [v6: $i] : (c_RComplete_Onatceiling(v4) = v5 &
% 279.36/41.75 c_RComplete_Onatceiling(v3) = v6 &
% 279.36/41.75 c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v6, v2) = v5 & $i(v6) &
% 279.36/41.75 $i(v5))))
% 279.36/41.75
% 279.36/41.75 (fact_natceiling__eq)
% 279.36/41.75 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 279.36/41.75 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 &
% 279.36/41.75 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & ! [v2:
% 279.36/41.75 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v4 | ~
% 279.36/41.75 (c_RComplete_Onatceiling(v2) = v4) | ~
% 279.36/41.75 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v1) = v5) | ~ $i(v3) | ~
% 279.36/41.75 $i(v2) | ? [v6: $i] : ? [v7: $i] : (c_RealDef_Oreal(tc_Nat_Onat, v3) =
% 279.36/41.75 v6 & $i(v6) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v6,
% 279.36/41.75 v2) | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v6, v0) = v7 &
% 279.36/41.75 $i(v7) & ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2,
% 279.36/41.75 v7))))))
% 279.36/41.75
% 279.36/41.75 (fact_natceiling__le__eq)
% 279.36/41.75 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 279.36/41.75 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 279.36/41.75 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_RComplete_Onatceiling(v2) =
% 279.36/41.75 v3) | ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~ $i(v2) | ~ $i(v1)
% 279.36/41.75 | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v1) | ~
% 279.36/41.75 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) |
% 279.36/41.75 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v4)) & ! [v1: $i]
% 279.36/41.75 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_RComplete_Onatceiling(v2)
% 279.36/41.75 = v3) | ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~ $i(v2) | ~
% 279.36/41.75 $i(v1) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v4) |
% 279.36/41.75 ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) |
% 279.36/41.75 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v1)))
% 279.36/41.75
% 279.36/41.75 (fact_natceiling__le__eq__one)
% 279.36/41.75 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 279.36/41.75 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 &
% 279.36/41.75 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0) & ! [v2:
% 279.36/41.75 $i] : ! [v3: $i] : ( ~ (c_RComplete_Onatceiling(v2) = v3) | ~ $i(v2) |
% 279.36/41.75 ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v0) |
% 279.36/41.75 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v1)) & ! [v2: $i]
% 279.36/41.75 : ! [v3: $i] : ( ~ (c_RComplete_Onatceiling(v2) = v3) | ~ $i(v2) | ~
% 279.36/41.75 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v1) |
% 279.36/41.75 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v0)))
% 279.36/41.75
% 279.36/41.75 (fact_natceiling__neg)
% 279.36/41.75 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 279.36/41.75 (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 &
% 279.36/41.75 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 279.36/41.75 [v2: $i] : ! [v3: $i] : (v3 = v1 | ~ (c_RComplete_Onatceiling(v2) = v3) |
% 279.36/41.75 ~ $i(v2) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2,
% 279.36/41.75 v0)))
% 279.36/41.75
% 279.36/41.75 (fact_natceiling__one)
% 279.36/41.75 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 279.36/41.75 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 &
% 279.36/41.75 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 279.36/41.75 c_RComplete_Onatceiling(v0) = v1 & $i(v1) & $i(v0))
% 279.36/41.75
% 279.36/41.75 (fact_natceiling__zero)
% 279.36/41.75 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 279.36/41.75 (c_RComplete_Onatceiling(v0) = v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) =
% 279.36/41.75 v1 & c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0))
% 279.36/41.75
% 279.36/41.75 (fact_natfloor__add)
% 279.36/41.76 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 279.36/41.76 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 279.36/41.76 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat,
% 279.36/41.76 v1) = v3) | ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v3)
% 279.36/41.76 = v4) | ~ $i(v2) | ~ $i(v1) | ~
% 279.36/41.76 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) | ? [v5: $i]
% 279.36/41.76 : ? [v6: $i] : (c_RComplete_Onatfloor(v4) = v5 &
% 279.36/41.76 c_RComplete_Onatfloor(v2) = v6 &
% 279.36/41.76 c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v6, v1) = v5 & $i(v6) &
% 279.36/41.76 $i(v5))))
% 279.36/41.76
% 279.36/41.76 (fact_natfloor__add__one)
% 279.36/41.76 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 279.36/41.76 $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 &
% 279.36/41.76 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 279.36/41.76 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v2) & $i(v1) &
% 279.36/41.76 $i(v0) & ! [v3: $i] : ! [v4: $i] : ( ~
% 279.36/41.76 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v1) = v4) | ~ $i(v3) |
% 279.36/41.76 ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) | ? [v5:
% 279.36/41.76 $i] : ? [v6: $i] : (c_RComplete_Onatfloor(v4) = v5 &
% 279.36/41.76 c_RComplete_Onatfloor(v3) = v6 &
% 279.36/41.76 c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v6, v2) = v5 & $i(v6) &
% 279.36/41.76 $i(v5))))
% 279.36/41.76
% 279.36/41.76 (fact_natfloor__eq)
% 279.36/41.76 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 279.36/41.76 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : !
% 279.36/41.76 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v2 | ~
% 279.36/41.76 (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~ (c_RComplete_Onatfloor(v1) =
% 279.36/41.76 v4) | ~ $i(v2) | ~ $i(v1) | ~
% 279.36/41.76 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v1) | ? [v5: $i]
% 279.36/41.76 : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v0) = v5 & $i(v5) &
% 279.36/41.76 ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v5))))
% 279.36/41.76
% 279.36/41.76 (fact_natfloor__neg)
% 279.36/41.76 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 279.36/41.76 (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 &
% 279.36/41.76 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 279.36/41.76 [v2: $i] : ! [v3: $i] : (v3 = v1 | ~ (c_RComplete_Onatfloor(v2) = v3) | ~
% 279.36/41.76 $i(v2) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v0)))
% 279.36/41.76
% 279.36/41.76 (fact_natfloor__one)
% 279.36/41.76 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 279.36/41.76 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 &
% 279.36/41.76 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & c_RComplete_Onatfloor(v0)
% 279.36/41.76 = v1 & $i(v1) & $i(v0))
% 279.36/41.76
% 279.36/41.76 (fact_natfloor__zero)
% 279.36/41.76 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 279.36/41.76 (c_RComplete_Onatfloor(v0) = v1 & c_Groups_Ozero__class_Ozero(tc_Nat_Onat) =
% 279.36/41.76 v1 & c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0))
% 279.36/41.76
% 279.36/41.76 (fact_norm__eq__zero)
% 279.36/41.76 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 279.36/41.76 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 279.36/41.76 ! [v2: $i] : ! [v3: $i] : ( ~ (c_RealVector_Onorm__class_Onorm(v2, v1) =
% 279.36/41.76 v3) | ~ $i(v2) | ~ $i(v1) | ~
% 279.36/41.76 class_RealVector_Oreal__normed__vector(v2) | ? [v4: $i] : (( ~ (v3 = v0)
% 279.36/41.76 | (v4 = v1 & c_Groups_Ozero__class_Ozero(v2) = v1)) & (v3 = v0 | ( ~
% 279.36/41.76 (v4 = v1) & c_Groups_Ozero__class_Ozero(v2) = v4 & $i(v4))))))
% 279.36/41.76
% 279.36/41.76 (fact_norm__ge__zero)
% 279.36/41.76 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 279.36/41.76 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 279.36/41.76 ! [v2: $i] : ! [v3: $i] : ( ~ (c_RealVector_Onorm__class_Onorm(v2, v1) =
% 279.36/41.76 v3) | ~ $i(v2) | ~ $i(v1) | ~
% 279.36/41.76 class_RealVector_Oreal__normed__vector(v2) |
% 279.36/41.76 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3)))
% 279.36/41.76
% 279.36/41.76 (fact_norm__le__zero__iff)
% 279.36/41.76 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 279.36/41.76 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 279.36/41.76 ! [v2: $i] : ! [v3: $i] : ( ~ (c_RealVector_Onorm__class_Onorm(v2, v1) =
% 279.36/41.76 v3) | ~ $i(v2) | ~ $i(v1) | ~
% 279.36/41.76 class_RealVector_Oreal__normed__vector(v2) | ? [v4: $i] : (( ~
% 279.36/41.76 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v0) | (v4 = v1
% 279.36/41.76 & c_Groups_Ozero__class_Ozero(v2) = v1)) &
% 279.36/41.76 (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v0) | ( ~ (v4 =
% 279.36/41.76 v1) & c_Groups_Ozero__class_Ozero(v2) = v4 & $i(v4))))))
% 279.36/41.76
% 279.36/41.76 (fact_norm__minus__cancel)
% 279.36/41.76 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 279.36/41.76 (c_Groups_Ouminus__class_Ouminus(v1, v0) = v2) | ~
% 279.36/41.76 (c_RealVector_Onorm__class_Onorm(v1, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ~
% 279.36/41.76 class_RealVector_Oreal__normed__vector(v1) |
% 279.36/41.76 (c_RealVector_Onorm__class_Onorm(v1, v0) = v3 & $i(v3)))
% 279.36/41.76
% 279.36/41.76 (fact_norm__not__less__zero)
% 279.36/41.76 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 279.36/41.76 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 279.36/41.76 ! [v2: $i] : ! [v3: $i] : ( ~ (c_RealVector_Onorm__class_Onorm(v2, v1) =
% 279.36/41.76 v3) | ~ $i(v2) | ~ $i(v1) | ~
% 279.36/41.76 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v0) | ~
% 279.36/41.76 class_RealVector_Oreal__normed__vector(v2)))
% 279.36/41.76
% 279.36/41.76 (fact_norm__one)
% 279.36/41.76 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 279.36/41.76 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : !
% 279.36/41.76 [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ (c_Groups_Oone__class_Oone(v1) = v2)
% 279.36/41.76 | ~ (c_RealVector_Onorm__class_Onorm(v1, v2) = v3) | ~ $i(v1) | ~
% 279.36/41.76 class_RealVector_Oreal__normed__algebra__1(v1)))
% 279.36/41.76
% 279.36/41.76 (fact_norm__ratiotest__lemma)
% 279.36/41.76 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 279.36/41.76 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 279.36/41.76 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 279.36/41.76 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 279.36/41.76 $i] : ! [v8: $i] : ! [v9: $i] : ( ~ (c_RealVector_Onorm__class_Onorm(v5,
% 279.36/41.76 v3) = v6) | ~ (c_RealVector_Onorm__class_Onorm(v5, v2) = v8) | ~
% 279.36/41.76 (hAPP(v7, v8) = v9) | ~ (hAPP(v1, v4) = v7) | ~ $i(v5) | ~ $i(v4) | ~
% 279.36/41.76 $i(v3) | ~ $i(v2) | ~ class_RealVector_Oreal__normed__vector(v5) | ~
% 279.36/41.76 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v9) | ~
% 279.36/41.77 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v0) |
% 279.36/41.77 c_Groups_Ozero__class_Ozero(v5) = v3))
% 279.36/41.77
% 279.36/41.77 (fact_norm__triangle__ineq4)
% 279.36/41.77 $i(tc_RealDef_Oreal) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 279.36/41.77 ! [v4: $i] : ! [v5: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,
% 279.36/41.77 v3, v4) = v5) | ~ (c_RealVector_Onorm__class_Onorm(v2, v1) = v3) | ~
% 279.36/41.77 (c_RealVector_Onorm__class_Onorm(v2, v0) = v4) | ~ $i(v2) | ~ $i(v1) | ~
% 279.36/41.77 $i(v0) | ~ class_RealVector_Oreal__normed__vector(v2) | ? [v6: $i] : ?
% 279.36/41.77 [v7: $i] : (c_Groups_Ominus__class_Ominus(v2, v1, v0) = v6 &
% 279.36/41.77 c_RealVector_Onorm__class_Onorm(v2, v6) = v7 & $i(v7) & $i(v6) &
% 279.36/41.77 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v7, v5)))
% 279.36/41.77
% 279.36/41.77 (fact_norm__zero)
% 279.36/41.77 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 279.36/41.77 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 279.36/41.77 ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ (c_Groups_Ozero__class_Ozero(v1) =
% 279.36/41.77 v2) | ~ (c_RealVector_Onorm__class_Onorm(v1, v2) = v3) | ~ $i(v1) | ~
% 279.36/41.77 class_RealVector_Oreal__normed__vector(v1)))
% 279.36/41.77
% 279.36/41.77 (fact_not__one__le__zero)
% 279.36/41.77 ! [v0: $i] : ! [v1: $i] : ( ~ (c_Groups_Oone__class_Oone(v0) = v1) | ~
% 279.36/41.77 $i(v0) | ~ class_Rings_Olinordered__semidom(v0) | ? [v2: $i] :
% 279.36/41.77 (c_Groups_Ozero__class_Ozero(v0) = v2 & $i(v2) & ~
% 279.36/41.77 c_Orderings_Oord__class_Oless__eq(v0, v1, v2)))
% 279.36/41.77
% 279.36/41.77 (fact_not__one__less__zero)
% 279.36/41.77 ! [v0: $i] : ! [v1: $i] : ( ~ (c_Groups_Oone__class_Oone(v0) = v1) | ~
% 279.36/41.77 $i(v0) | ~ class_Rings_Olinordered__semidom(v0) | ? [v2: $i] :
% 279.36/41.77 (c_Groups_Ozero__class_Ozero(v0) = v2 & $i(v2) & ~
% 279.36/41.77 c_Orderings_Oord__class_Oless(v0, v1, v2)))
% 279.36/41.77
% 279.36/41.77 (fact_not__real__of__nat__less__zero)
% 279.36/41.77 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 279.36/41.77 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 279.36/41.77 ! [v2: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) | ~ $i(v1) | ~
% 279.36/41.77 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v0)))
% 279.36/41.77
% 279.36/41.77 (fact_not__real__square__gt__zero)
% 279.36/41.77 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 279.36/41.77 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 279.36/41.77 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 279.36/41.77 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v0 | ~ (hAPP(v3, v2) = v4) |
% 279.36/41.77 ~ (hAPP(v1, v2) = v3) | ~ $i(v2) |
% 279.36/41.77 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4)) & ! [v2: $i] :
% 279.36/41.77 ! [v3: $i] : ( ~ (hAPP(v2, v0) = v3) | ~ (hAPP(v1, v0) = v2) | ~
% 279.36/41.77 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3)))
% 279.36/41.77
% 279.36/41.77 (fact_rabs__ratiotest__lemma)
% 279.36/41.77 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 279.36/41.77 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 279.36/41.77 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 279.36/41.77 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 279.36/41.77 $i] : ! [v8: $i] : (v3 = v0 | ~
% 279.36/41.77 (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v3) = v5) | ~
% 279.36/41.77 (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v2) = v7) | ~ (hAPP(v6, v7)
% 279.36/41.77 = v8) | ~ (hAPP(v1, v4) = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 279.36/41.77 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, v8) | ~
% 279.36/41.77 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v0)))
% 279.36/41.77
% 279.36/41.77 (fact_rcis__zero__mod)
% 279.36/41.77 $i(tc_Complex_Ocomplex) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 279.36/41.77 (c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v1 &
% 279.36/41.77 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 279.36/41.77 [v2: $i] : ! [v3: $i] : (v3 = v1 | ~ (c_Complex_Orcis(v0, v2) = v3) | ~
% 279.36/41.77 $i(v2)))
% 279.36/41.77
% 279.36/41.77 (fact_real__0__le__add__iff)
% 279.36/41.77 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 279.36/41.77 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 279.36/41.77 ! [v2: $i] : ! [v3: $i] : ( ~
% 279.36/41.77 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v1) = v3) | ~ $i(v2) |
% 279.36/41.77 ~ $i(v1) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3)
% 279.36/41.77 | ? [v4: $i] : (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v2) =
% 279.36/41.77 v4 & $i(v4) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4,
% 279.36/41.77 v1))) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 279.36/41.77 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v1) = v3) | ~ $i(v2) |
% 279.36/41.77 ~ $i(v1) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) |
% 279.36/41.77 ? [v4: $i] : (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v2) = v4 &
% 279.36/41.77 $i(v4) & ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4,
% 279.36/41.77 v1))))
% 279.36/41.77
% 279.36/41.77 (fact_real__0__less__add__iff)
% 279.36/41.77 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 279.36/41.77 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 279.36/41.77 ! [v2: $i] : ! [v3: $i] : ( ~
% 279.36/41.77 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v1) = v3) | ~ $i(v2) |
% 279.36/41.77 ~ $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) |
% 279.36/41.77 ? [v4: $i] : (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v2) = v4 &
% 279.36/41.77 $i(v4) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v4, v1))) & !
% 279.36/41.77 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 279.36/41.77 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v1) = v3) | ~ $i(v2) |
% 279.36/41.77 ~ $i(v1) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | ?
% 279.36/41.77 [v4: $i] : (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v2) = v4 &
% 279.36/41.77 $i(v4) & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v4, v1))))
% 279.36/41.77
% 279.36/41.77 (fact_real__abs__def)
% 279.36/41.77 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 279.36/41.77 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 279.36/41.77 ! [v2: $i] : (v2 = v1 | ~ (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v1)
% 279.36/41.77 = v2) | ~ $i(v1) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1,
% 279.36/41.77 v0)) & ! [v1: $i] : ! [v2: $i] : ( ~
% 279.36/41.77 (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v1) = v2) | ~ $i(v1) | ~
% 279.36/41.77 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v0) |
% 279.36/41.77 (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v1) = v2 & $i(v2))))
% 279.36/41.77
% 279.36/41.77 (fact_real__add__eq__0__iff)
% 279.36/41.77 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 279.36/41.77 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 279.36/41.77 ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~
% 279.36/41.77 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v1) = v3) | ~ $i(v2) |
% 279.36/41.77 ~ $i(v1) | ? [v4: $i] : ( ~ (v4 = v1) &
% 279.36/41.77 c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v2) = v4 & $i(v4))) &
% 279.36/41.77 ! [v1: $i] : ! [v2: $i] : ( ~
% 279.36/41.77 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v1) = v0) | ~ $i(v2) |
% 279.36/41.77 ~ $i(v1) | c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v2) = v1))
% 279.36/41.77
% 279.36/41.77 (fact_real__add__le__0__iff)
% 279.36/41.78 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 279.36/41.78 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 279.36/41.78 ! [v2: $i] : ! [v3: $i] : ( ~
% 279.36/41.78 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v1) = v3) | ~ $i(v2) |
% 279.36/41.78 ~ $i(v1) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v0)
% 279.36/41.78 | ? [v4: $i] : (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v2) =
% 279.36/41.78 v4 & $i(v4) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1,
% 279.36/41.78 v4))) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 279.36/41.78 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v1) = v3) | ~ $i(v2) |
% 279.36/41.78 ~ $i(v1) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v0) |
% 279.36/41.78 ? [v4: $i] : (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v2) = v4 &
% 279.36/41.78 $i(v4) & ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1,
% 279.36/41.78 v4))))
% 279.36/41.78
% 279.36/41.78 (fact_real__add__less__0__iff)
% 279.36/41.78 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 279.36/41.78 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 279.36/41.78 ! [v2: $i] : ! [v3: $i] : ( ~
% 279.36/41.78 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v1) = v3) | ~ $i(v2) |
% 279.36/41.78 ~ $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v0) |
% 279.36/41.78 ? [v4: $i] : (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v2) = v4 &
% 279.36/41.78 $i(v4) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v4))) & !
% 279.36/41.78 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 279.36/41.78 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v1) = v3) | ~ $i(v2) |
% 279.36/41.78 ~ $i(v1) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v0) | ?
% 279.36/41.78 [v4: $i] : (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v2) = v4 &
% 279.36/41.78 $i(v4) & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v4))))
% 279.36/41.78
% 279.36/41.78 (fact_real__add__minus__iff)
% 279.36/41.78 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 279.36/41.78 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 279.36/41.78 ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~
% 279.36/41.78 (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v1) = v2) | ~
% 279.36/41.78 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1, v2) = v3) | ~ $i(v1))
% 279.36/41.78 & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v1 | ~
% 279.36/41.78 (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v1) = v3) | ~
% 279.36/41.78 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v3) = v0) | ~ $i(v2) |
% 279.36/41.78 ~ $i(v1)))
% 279.36/41.78
% 279.36/41.78 (fact_real__le__eq__diff)
% 279.36/41.78 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 279.36/41.78 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 279.36/41.78 ! [v2: $i] : ! [v3: $i] : ( ~
% 279.36/41.78 (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v2, v1) = v3) | ~ $i(v2)
% 279.36/41.78 | ~ $i(v1) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3,
% 279.36/41.78 v0) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v1)) & !
% 279.36/41.78 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 279.36/41.78 (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v2, v1) = v3) | ~ $i(v2)
% 279.36/41.78 | ~ $i(v1) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2,
% 279.36/41.78 v1) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v0)))
% 279.36/41.78
% 279.36/41.78 (fact_real__mult__1)
% 279.36/41.78 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 279.36/41.78 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 279.36/41.78 c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v0 & hAPP(v0, v1) = v2 &
% 279.36/41.78 $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : (v4 = v3 | ~
% 279.36/41.78 (hAPP(v2, v3) = v4) | ~ $i(v3)))
% 279.36/41.78
% 279.36/41.78 (fact_real__mult__le__cancel__iff1)
% 279.36/41.78 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 279.36/41.78 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 279.36/41.78 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 279.36/41.78 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 279.36/41.78 $i] : ! [v8: $i] : ( ~ (hAPP(v7, v4) = v8) | ~ (hAPP(v5, v4) = v6) | ~
% 279.36/41.78 (hAPP(v1, v3) = v5) | ~ (hAPP(v1, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~
% 279.36/41.78 $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) | ~
% 279.36/41.78 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v8) |
% 279.36/41.78 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v2)) & ! [v2: $i]
% 279.36/41.78 : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : !
% 279.36/41.78 [v8: $i] : ( ~ (hAPP(v7, v4) = v8) | ~ (hAPP(v5, v4) = v6) | ~ (hAPP(v1,
% 279.36/41.78 v3) = v5) | ~ (hAPP(v1, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2)
% 279.36/41.78 | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) | ~
% 279.36/41.78 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v2) |
% 279.36/41.78 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v8)))
% 279.36/41.78
% 279.36/41.78 (fact_real__mult__le__cancel__iff2)
% 279.36/41.78 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 279.36/41.78 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 279.36/41.78 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 279.36/41.78 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 279.36/41.78 $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v1, v4)
% 279.36/41.78 = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 279.36/41.78 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) | ~
% 279.36/41.78 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v7) |
% 279.36/41.78 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v2)) & ! [v2: $i]
% 279.36/41.78 : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~
% 279.36/41.78 (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v1, v4) = v5) | ~
% 279.36/41.78 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 279.36/41.78 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) | ~
% 279.36/41.78 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v2) |
% 279.36/41.78 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v7)))
% 279.36/41.78
% 279.36/41.78 (fact_real__mult__left__cancel)
% 279.36/41.78 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 279.36/41.78 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 279.36/41.78 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 279.36/41.78 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v4 = v0
% 279.36/41.78 | v3 = v2 | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v6) | ~ (hAPP(v1,
% 279.36/41.78 v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2)))
% 279.36/41.78
% 279.36/41.78 (fact_real__mult__less__iff1)
% 279.36/41.78 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 279.36/41.78 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 279.36/41.78 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 279.36/41.78 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 279.36/41.78 $i] : ! [v8: $i] : ( ~ (hAPP(v7, v4) = v8) | ~ (hAPP(v5, v4) = v6) | ~
% 279.36/41.78 (hAPP(v1, v3) = v5) | ~ (hAPP(v1, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~
% 279.36/41.78 $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v6, v8) | ~
% 279.36/41.78 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) |
% 279.36/41.78 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v2)) & ! [v2: $i] :
% 279.36/41.78 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8:
% 279.36/41.78 $i] : ( ~ (hAPP(v7, v4) = v8) | ~ (hAPP(v5, v4) = v6) | ~ (hAPP(v1, v3)
% 279.36/41.78 = v5) | ~ (hAPP(v1, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 279.36/41.78 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v2) | ~
% 279.36/41.78 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) |
% 279.36/41.78 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v6, v8)))
% 279.36/41.78
% 279.36/41.78 (fact_real__mult__less__mono2)
% 279.36/41.79 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 279.36/41.79 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 279.36/41.79 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 279.36/41.79 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 279.36/41.79 $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v1, v4)
% 279.36/41.79 = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 279.36/41.79 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v2) | ~
% 279.36/41.79 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) |
% 279.36/41.79 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v6, v7)))
% 279.36/41.79
% 279.36/41.79 (fact_real__mult__order)
% 279.69/41.79 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 279.69/41.79 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 279.69/41.79 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 279.69/41.79 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, v2) = v5)
% 279.69/41.79 | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 279.69/41.79 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | ~
% 279.69/41.79 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) |
% 279.69/41.79 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v5)))
% 279.69/41.79
% 279.69/41.79 (fact_real__mult__right__cancel)
% 279.69/41.79 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 279.69/41.79 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 279.69/41.79 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 279.69/41.79 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 279.69/41.79 $i] : (v4 = v0 | v3 = v2 | ~ (hAPP(v7, v4) = v6) | ~ (hAPP(v5, v4) = v6)
% 279.69/41.79 | ~ (hAPP(v1, v3) = v5) | ~ (hAPP(v1, v2) = v7) | ~ $i(v4) | ~ $i(v3)
% 279.69/41.79 | ~ $i(v2)))
% 279.69/41.79
% 279.69/41.79 (fact_real__natfloor__add__one__gt)
% 279.69/41.79 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 279.69/41.79 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : !
% 279.69/41.79 [v2: $i] : ( ~ (c_RComplete_Onatfloor(v1) = v2) | ~ $i(v1) | ? [v3: $i] :
% 279.69/41.79 ? [v4: $i] : (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3 &
% 279.69/41.79 c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v0) = v4 & $i(v4) &
% 279.69/41.79 $i(v3) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v4))))
% 279.69/41.79
% 279.69/41.79 (fact_real__natfloor__gt__diff__one)
% 279.69/41.79 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 279.69/41.79 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : !
% 279.69/41.79 [v2: $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v1, v0) =
% 279.69/41.79 v2) | ~ $i(v1) | ? [v3: $i] : ? [v4: $i] :
% 279.69/41.79 (c_RealDef_Oreal(tc_Nat_Onat, v3) = v4 & c_RComplete_Onatfloor(v1) = v3 &
% 279.69/41.79 $i(v4) & $i(v3) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2,
% 279.69/41.79 v4))))
% 279.69/41.79
% 279.69/41.79 (fact_real__natfloor__le)
% 279.69/41.79 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 279.69/41.79 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 279.69/41.79 ! [v2: $i] : ( ~ (c_RComplete_Onatfloor(v1) = v2) | ~ $i(v1) | ~
% 279.69/41.79 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v1) | ? [v3: $i]
% 279.69/41.79 : (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3 & $i(v3) &
% 279.69/41.79 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v1))))
% 279.69/41.79
% 279.69/41.79 (fact_real__of__nat__1)
% 279.69/41.79 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 279.69/41.79 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 &
% 279.69/41.79 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 279.69/41.79 c_RealDef_Oreal(tc_Nat_Onat, v0) = v1 & $i(v1) & $i(v0))
% 279.69/41.79
% 279.69/41.79 (fact_real__of__nat__ge__zero)
% 279.69/41.79 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 279.69/41.79 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 279.69/41.79 ! [v2: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) | ~ $i(v1) |
% 279.69/41.79 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2)))
% 279.69/41.79
% 279.69/41.79 (fact_real__of__nat__gt__zero__cancel__iff)
% 279.69/41.79 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 279.69/41.79 (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 &
% 279.69/41.79 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 279.69/41.79 [v2: $i] : ! [v3: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~
% 279.69/41.79 $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2) |
% 279.69/41.79 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3)) & ! [v2: $i] :
% 279.69/41.79 ! [v3: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~ $i(v2) | ~
% 279.69/41.79 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) |
% 279.69/41.79 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2)))
% 279.69/41.79
% 279.69/41.79 (fact_real__of__nat__le__zero__cancel__iff)
% 279.69/41.79 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 279.69/41.79 (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 &
% 279.69/41.79 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 279.69/41.79 [v2: $i] : ! [v3: $i] : (v2 = v1 | ~ (c_RealDef_Oreal(tc_Nat_Onat, v2) =
% 279.69/41.79 v3) | ~ $i(v2) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 279.69/41.79 v3, v0)) & ! [v2: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) |
% 279.69/41.79 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v0)))
% 279.69/41.79
% 279.69/41.79 (fact_real__of__nat__zero)
% 279.69/41.79 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 279.69/41.79 (c_RealDef_Oreal(tc_Nat_Onat, v0) = v1 &
% 279.69/41.79 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 &
% 279.69/41.79 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0))
% 279.69/41.79
% 279.69/41.79 (fact_real__of__nat__zero__iff)
% 279.69/41.79 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 279.69/41.79 (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 &
% 279.69/41.79 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 279.69/41.79 [v2: $i] : (v2 = v1 | ~ (c_RealDef_Oreal(tc_Nat_Onat, v2) = v0) | ~
% 279.69/41.79 $i(v2)) & ! [v2: $i] : (v2 = v0 | ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) =
% 279.69/41.79 v2)))
% 279.69/41.79
% 279.69/41.79 (fact_real__two__squares__add__zero__iff)
% 279.69/41.79 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 279.69/41.79 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v0 &
% 279.69/41.79 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0) & !
% 279.69/41.79 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 279.69/41.79 $i] : (v3 = v1 | ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v5, v7)
% 279.69/41.79 = v1) | ~ (hAPP(v6, v2) = v7) | ~ (hAPP(v4, v3) = v5) | ~ (hAPP(v0,
% 279.69/41.79 v3) = v4) | ~ (hAPP(v0, v2) = v6) | ~ $i(v3) | ~ $i(v2)) & ! [v2:
% 279.69/41.79 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 279.69/41.79 : (v2 = v1 | ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v5, v7) = v1)
% 279.69/41.79 | ~ (hAPP(v6, v2) = v7) | ~ (hAPP(v4, v3) = v5) | ~ (hAPP(v0, v3) = v4)
% 279.69/41.79 | ~ (hAPP(v0, v2) = v6) | ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3:
% 279.69/41.79 $i] : ! [v4: $i] : (v4 = v1 | ~
% 279.69/41.79 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v3) = v4) | ~
% 279.69/41.79 (hAPP(v2, v1) = v3) | ~ (hAPP(v0, v1) = v2)))
% 279.69/41.79
% 279.69/41.79 (fact_real__vector_Oscale__one)
% 279.69/41.80 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 279.69/41.80 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : !
% 279.69/41.80 [v2: $i] : ! [v3: $i] : (v3 = v1 | ~
% 279.69/41.80 (c_RealVector_OscaleR__class_OscaleR(v2, v0, v1) = v3) | ~ $i(v2) | ~
% 279.69/41.80 $i(v1) | ~ class_RealVector_Oreal__vector(v2)))
% 279.69/41.80
% 279.69/41.80 (fact_real__zero__not__eq__one)
% 279.69/41.80 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) &
% 279.69/41.80 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 279.69/41.80 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0))
% 279.69/41.80
% 279.69/41.80 (fact_realpow__pos__nth)
% 279.69/41.80 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 279.69/41.80 $i] : (c_Power_Opower__class_Opower(tc_RealDef_Oreal) = v2 &
% 279.69/41.80 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 &
% 279.69/41.80 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v2) & $i(v1) &
% 279.69/41.80 $i(v0) & ! [v3: $i] : ! [v4: $i] : ( ~ $i(v4) | ~ $i(v3) | ~
% 279.69/41.80 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) | ~
% 279.69/41.80 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v3) | ? [v5: $i] : ?
% 279.69/41.80 [v6: $i] : (hAPP(v6, v4) = v3 & hAPP(v2, v5) = v6 & $i(v6) & $i(v5) &
% 279.69/41.80 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v5))))
% 279.69/41.80
% 279.69/41.80 (fact_realpow__pos__nth__unique)
% 279.69/41.80 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 279.69/41.80 $i] : (c_Power_Opower__class_Opower(tc_RealDef_Oreal) = v2 &
% 279.69/41.80 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 &
% 279.69/41.80 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v2) & $i(v1) &
% 279.69/41.80 $i(v0) & ! [v3: $i] : ! [v4: $i] : ( ~ $i(v4) | ~ $i(v3) | ~
% 279.69/41.80 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) | ~
% 279.69/41.80 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v3) | ? [v5: $i] : ?
% 279.69/41.80 [v6: $i] : (hAPP(v6, v4) = v3 & hAPP(v2, v5) = v6 & $i(v6) & $i(v5) &
% 279.69/41.80 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v5) & ! [v7: $i] :
% 279.69/41.80 ! [v8: $i] : (v7 = v5 | ~ (hAPP(v8, v4) = v3) | ~ (hAPP(v2, v7) = v8)
% 279.69/41.80 | ~ $i(v7) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1,
% 279.69/41.80 v7)))))
% 279.69/41.80
% 279.69/41.80 (fact_reals__Archimedean6)
% 279.69/41.80 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 279.69/41.80 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 &
% 279.69/41.80 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 279.69/41.80 [v2: $i] : ( ~ $i(v2) | ~
% 279.69/41.80 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) | ? [v3: $i]
% 279.69/41.80 : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : (c_RealDef_Oreal(tc_Nat_Onat,
% 279.69/41.80 v4) = v5 & c_RealDef_Oreal(tc_Nat_Onat, v3) = v6 &
% 279.69/41.80 c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v3, v1) = v4 & $i(v6) &
% 279.69/41.80 $i(v5) & $i(v4) & $i(v3) &
% 279.69/41.80 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v6) &
% 279.69/41.80 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, v2))))
% 279.69/41.80
% 279.69/41.80 (fact_scaleR_Ononneg__bounded)
% 279.69/41.80 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 279.69/41.80 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 279.69/41.80 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 279.69/41.80 [v2: $i] : ( ~ $i(v2) | ~ class_RealVector_Oreal__normed__vector(v2) | ?
% 279.69/41.80 [v3: $i] : ($i(v3) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 279.69/41.80 v0, v3) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : !
% 279.69/41.80 [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~
% 279.69/41.80 (c_RealVector_Onorm__class_Onorm(v2, v5) = v8) | ~
% 279.69/41.80 (c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal, v4) = v6) | ~
% 279.69/41.80 (hAPP(v10, v3) = v11) | ~ (hAPP(v7, v8) = v9) | ~ (hAPP(v1, v9) =
% 279.69/41.80 v10) | ~ (hAPP(v1, v6) = v7) | ~ $i(v5) | ~ $i(v4) | ? [v12: $i]
% 279.69/41.80 : ? [v13: $i] : (c_RealVector_OscaleR__class_OscaleR(v2, v4, v5) =
% 279.69/41.80 v12 & c_RealVector_Onorm__class_Onorm(v2, v12) = v13 & $i(v13) &
% 279.69/41.80 $i(v12) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v13,
% 279.69/41.80 v11))))))
% 279.69/41.80
% 279.69/41.80 (fact_scaleR_Opos__bounded)
% 279.69/41.80 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 279.69/41.80 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 279.69/41.80 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 279.69/41.80 [v2: $i] : ( ~ $i(v2) | ~ class_RealVector_Oreal__normed__vector(v2) | ?
% 279.69/41.80 [v3: $i] : ($i(v3) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0,
% 279.69/41.80 v3) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8:
% 279.69/41.80 $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~
% 279.69/41.80 (c_RealVector_Onorm__class_Onorm(v2, v5) = v8) | ~
% 279.69/41.80 (c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal, v4) = v6) | ~
% 279.69/41.80 (hAPP(v10, v3) = v11) | ~ (hAPP(v7, v8) = v9) | ~ (hAPP(v1, v9) =
% 279.69/41.80 v10) | ~ (hAPP(v1, v6) = v7) | ~ $i(v5) | ~ $i(v4) | ? [v12: $i]
% 279.69/41.80 : ? [v13: $i] : (c_RealVector_OscaleR__class_OscaleR(v2, v4, v5) =
% 279.69/41.80 v12 & c_RealVector_Onorm__class_Onorm(v2, v12) = v13 & $i(v13) &
% 279.69/41.80 $i(v12) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v13,
% 279.69/41.80 v11))))))
% 279.69/41.80
% 279.69/41.80 (fact_scaleR_Ozero__left)
% 279.69/41.80 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 279.69/41.80 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 279.69/41.80 ! [v2: $i] : ! [v3: $i] : ( ~ (c_RealVector_OscaleR__class_OscaleR(v2, v0,
% 279.69/41.80 v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 279.69/41.80 class_RealVector_Oreal__normed__vector(v2) |
% 279.69/41.80 (c_Groups_Ozero__class_Ozero(v2) = v3 & $i(v3))))
% 279.69/41.80
% 279.69/41.80 (fact_scaleR__cancel__left)
% 279.69/41.80 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 279.69/41.80 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 279.69/41.80 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v4 | ~
% 279.69/41.80 (c_RealVector_OscaleR__class_OscaleR(v3, v0, v2) = v4) | ~
% 279.69/41.80 (c_RealVector_OscaleR__class_OscaleR(v3, v0, v1) = v5) | ~ $i(v3) | ~
% 279.69/41.80 $i(v2) | ~ $i(v1) | ~ class_RealVector_Oreal__vector(v3)) & ! [v1: $i]
% 279.69/41.80 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v3 = v0 | v2 = v1
% 279.69/41.80 | ~ (c_RealVector_OscaleR__class_OscaleR(v4, v3, v2) = v5) | ~
% 279.69/41.80 (c_RealVector_OscaleR__class_OscaleR(v4, v3, v1) = v5) | ~ $i(v4) | ~
% 279.69/41.80 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ class_RealVector_Oreal__vector(v4)))
% 279.69/41.80
% 279.69/41.80 (fact_scaleR__eq__0__iff)
% 279.69/41.80 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 279.69/41.80 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 279.69/41.80 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 279.69/41.80 (c_RealVector_OscaleR__class_OscaleR(v3, v2, v1) = v4) | ~ $i(v3) | ~
% 279.69/41.80 $i(v2) | ~ $i(v1) | ~ class_RealVector_Oreal__vector(v3) | ? [v5: $i] :
% 279.69/41.80 (c_Groups_Ozero__class_Ozero(v3) = v5 & $i(v5) & ( ~ (v5 = v4) | v4 = v1 |
% 279.69/41.80 v2 = v0) & (v5 = v4 | ( ~ (v5 = v1) & ~ (v2 = v0))))))
% 279.69/41.80
% 279.69/41.80 (fact_scaleR__left_Ononneg__bounded)
% 279.69/41.80 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 279.69/41.80 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 279.69/41.80 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & ?
% 279.69/41.80 [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~
% 279.69/41.80 class_RealVector_Oreal__normed__vector(v3) | ? [v4: $i] : ($i(v4) &
% 279.69/41.80 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v4) & ! [v5:
% 279.69/41.80 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~
% 279.69/41.80 (c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal, v5) = v6) | ~
% 279.69/41.80 (hAPP(v7, v4) = v8) | ~ (hAPP(v1, v6) = v7) | ~ $i(v5) | ? [v9: $i]
% 279.69/41.80 : ? [v10: $i] : (c_RealVector_OscaleR__class_OscaleR(v3, v5, v2) = v9
% 279.69/41.80 & c_RealVector_Onorm__class_Onorm(v3, v9) = v10 & $i(v10) & $i(v9) &
% 279.69/41.80 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v10, v8))))))
% 279.69/41.80
% 279.69/41.80 (fact_scaleR__left_Opos__bounded)
% 279.69/41.81 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 279.69/41.81 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 279.69/41.81 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & ?
% 279.69/41.81 [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~
% 279.69/41.81 class_RealVector_Oreal__normed__vector(v3) | ? [v4: $i] : ($i(v4) &
% 279.69/41.81 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) & ! [v5: $i] :
% 279.69/41.81 ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~
% 279.69/41.81 (c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal, v5) = v6) | ~
% 279.69/41.81 (hAPP(v7, v4) = v8) | ~ (hAPP(v1, v6) = v7) | ~ $i(v5) | ? [v9: $i]
% 279.69/41.81 : ? [v10: $i] : (c_RealVector_OscaleR__class_OscaleR(v3, v5, v2) = v9
% 279.69/41.81 & c_RealVector_Onorm__class_Onorm(v3, v9) = v10 & $i(v10) & $i(v9) &
% 279.69/41.81 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v10, v8))))))
% 279.69/41.81
% 279.69/41.81 (fact_scaleR__left_Ozero)
% 279.69/41.81 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 279.69/41.81 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 279.69/41.81 ! [v2: $i] : ! [v3: $i] : ( ~ (c_RealVector_OscaleR__class_OscaleR(v2, v0,
% 279.69/41.81 v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 279.69/41.81 class_RealVector_Oreal__vector(v2) | (c_Groups_Ozero__class_Ozero(v2) = v3
% 279.69/41.81 & $i(v3))))
% 279.69/41.81
% 279.69/41.81 (fact_scaleR__left__imp__eq)
% 279.69/41.81 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 279.69/41.81 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 279.69/41.81 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v3 = v0 | v2 = v1 |
% 279.69/41.81 ~ (c_RealVector_OscaleR__class_OscaleR(v4, v3, v2) = v5) | ~
% 279.69/41.81 (c_RealVector_OscaleR__class_OscaleR(v4, v3, v1) = v5) | ~ $i(v4) | ~
% 279.69/41.81 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ class_RealVector_Oreal__vector(v4)))
% 279.69/41.81
% 279.69/41.81 (fact_scaleR__right_Ononneg__bounded)
% 279.69/41.81 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 279.69/41.81 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 279.69/41.81 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & ?
% 279.69/41.81 [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~
% 279.69/41.81 class_RealVector_Oreal__normed__vector(v3) | ? [v4: $i] : ($i(v4) &
% 279.69/41.81 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v4) & ! [v5:
% 279.69/41.81 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~
% 279.69/41.81 (c_RealVector_Onorm__class_Onorm(v3, v5) = v6) | ~ (hAPP(v7, v4) =
% 279.69/41.81 v8) | ~ (hAPP(v1, v6) = v7) | ~ $i(v5) | ? [v9: $i] : ? [v10:
% 279.69/41.81 $i] : (c_RealVector_OscaleR__class_OscaleR(v3, v2, v5) = v9 &
% 279.69/41.81 c_RealVector_Onorm__class_Onorm(v3, v9) = v10 & $i(v10) & $i(v9) &
% 279.69/41.81 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v10, v8))))))
% 279.69/41.81
% 279.69/41.81 (fact_scaleR__right_Opos__bounded)
% 279.69/41.81 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 279.69/41.81 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 279.69/41.81 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & ?
% 279.69/41.81 [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~
% 279.69/41.81 class_RealVector_Oreal__normed__vector(v3) | ? [v4: $i] : ($i(v4) &
% 279.69/41.81 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) & ! [v5: $i] :
% 279.69/41.81 ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~
% 279.69/41.81 (c_RealVector_Onorm__class_Onorm(v3, v5) = v6) | ~ (hAPP(v7, v4) =
% 279.69/41.81 v8) | ~ (hAPP(v1, v6) = v7) | ~ $i(v5) | ? [v9: $i] : ? [v10:
% 279.69/41.81 $i] : (c_RealVector_OscaleR__class_OscaleR(v3, v2, v5) = v9 &
% 279.69/41.81 c_RealVector_Onorm__class_Onorm(v3, v9) = v10 & $i(v10) & $i(v9) &
% 279.69/41.81 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v10, v8))))))
% 279.69/41.81
% 279.69/41.81 (fact_zero__le__dist)
% 279.69/41.81 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 279.69/41.81 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 279.69/41.81 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 279.69/41.81 (c_RealVector_Odist__class_Odist(v3, v2, v1) = v4) | ~ $i(v3) | ~ $i(v2)
% 279.69/41.81 | ~ $i(v1) | ~ class_RealVector_Ometric__space(v3) |
% 279.69/41.81 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v4)))
% 279.69/41.81
% 279.69/41.81 (fact_zero__le__one)
% 279.69/41.81 ! [v0: $i] : ! [v1: $i] : ( ~ (c_Groups_Oone__class_Oone(v0) = v1) | ~
% 279.69/41.81 $i(v0) | ~ class_Rings_Olinordered__semidom(v0) | ? [v2: $i] :
% 279.69/41.81 (c_Groups_Ozero__class_Ozero(v0) = v2 & $i(v2) &
% 279.69/41.81 c_Orderings_Oord__class_Oless__eq(v0, v2, v1)))
% 279.69/41.81
% 279.69/41.81 (fact_zero__less__dist__iff)
% 279.69/41.81 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 279.69/41.81 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 279.69/41.81 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v1 | ~
% 279.69/41.81 (c_RealVector_Odist__class_Odist(v3, v2, v1) = v4) | ~ $i(v3) | ~ $i(v2)
% 279.69/41.81 | ~ $i(v1) | ~ class_RealVector_Ometric__space(v3) |
% 279.69/41.81 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4)) & ! [v1: $i] :
% 279.69/41.81 ! [v2: $i] : ! [v3: $i] : ( ~ (c_RealVector_Odist__class_Odist(v2, v1, v1)
% 279.69/41.81 = v3) | ~ $i(v2) | ~ $i(v1) | ~ class_RealVector_Ometric__space(v2) |
% 279.69/41.81 ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3)))
% 279.69/41.81
% 279.69/41.81 (fact_zero__less__norm__iff)
% 279.69/41.81 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 279.69/41.81 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 279.69/41.81 ! [v2: $i] : ! [v3: $i] : ( ~ (c_RealVector_Onorm__class_Onorm(v2, v1) =
% 279.69/41.81 v3) | ~ $i(v2) | ~ $i(v1) | ~
% 279.69/41.81 class_RealVector_Oreal__normed__vector(v2) | ? [v4: $i] : (( ~
% 279.69/41.81 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | ( ~ (v4 =
% 279.69/41.81 v1) & c_Groups_Ozero__class_Ozero(v2) = v4 & $i(v4))) &
% 279.69/41.81 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | (v4 = v1 &
% 279.69/41.81 c_Groups_Ozero__class_Ozero(v2) = v1)))))
% 279.69/41.81
% 279.69/41.81 (fact_zero__less__one)
% 279.69/41.81 ! [v0: $i] : ! [v1: $i] : ( ~ (c_Groups_Oone__class_Oone(v0) = v1) | ~
% 279.69/41.81 $i(v0) | ~ class_Rings_Olinordered__semidom(v0) | ? [v2: $i] :
% 279.69/41.81 (c_Groups_Ozero__class_Ozero(v0) = v2 & $i(v2) &
% 279.69/41.81 c_Orderings_Oord__class_Oless(v0, v2, v1)))
% 279.69/41.81
% 279.69/41.81 (function-axioms)
% 279.69/41.82 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 279.69/41.82 | ~ (c_Power_Opower_Opower(v4, v3, v2) = v1) | ~
% 279.69/41.82 (c_Power_Opower_Opower(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 279.69/41.82 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 279.69/41.82 (c_Complex_Ocomplex_Ocomplex__case(v4, v3, v2) = v1) | ~
% 279.69/41.82 (c_Complex_Ocomplex_Ocomplex__case(v4, v3, v2) = v0)) & ! [v0: $i] : !
% 279.69/41.82 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 279.69/41.82 (c_Complex_Ocomplex_Ocomplex__rec(v4, v3, v2) = v1) | ~
% 279.69/41.82 (c_Complex_Ocomplex_Ocomplex__rec(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 279.69/41.82 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 279.69/41.82 (c_RealVector_Odist__class_Odist(v4, v3, v2) = v1) | ~
% 279.69/41.82 (c_RealVector_Odist__class_Odist(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 279.69/41.82 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 279.69/41.82 (c_RealVector_OscaleR__class_OscaleR(v4, v3, v2) = v1) | ~
% 279.69/41.82 (c_RealVector_OscaleR__class_OscaleR(v4, v3, v2) = v0)) & ! [v0: $i] : !
% 279.69/41.82 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 279.69/41.82 (c_Groups_Oplus__class_Oplus(v4, v3, v2) = v1) | ~
% 279.69/41.82 (c_Groups_Oplus__class_Oplus(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 279.69/41.82 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 279.69/41.82 (c_Groups_Ominus__class_Ominus(v4, v3, v2) = v1) | ~
% 279.69/41.82 (c_Groups_Ominus__class_Ominus(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 279.69/41.82 $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (c_Nat__Transfer_Otsub(v3,
% 279.69/41.82 v2) = v1) | ~ (c_Nat__Transfer_Otsub(v3, v2) = v0)) & ! [v0: $i] : !
% 279.69/41.82 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (c_RealDef_Oreal(v3, v2)
% 279.69/41.82 = v1) | ~ (c_RealDef_Oreal(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 279.69/41.82 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (c_Nat_Osize__class_Osize(v3, v2) =
% 279.69/41.82 v1) | ~ (c_Nat_Osize__class_Osize(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 279.69/41.82 $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 279.69/41.82 (c_Complex_Ocomplex_OComplex(v3, v2) = v1) | ~
% 279.69/41.82 (c_Complex_Ocomplex_OComplex(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 279.69/41.82 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (c_Complex_Orcis(v3, v2) = v1) | ~
% 279.69/41.82 (c_Complex_Orcis(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 279.69/41.82 ! [v3: $i] : (v1 = v0 | ~ (c_Groups_Oabs__class_Oabs(v3, v2) = v1) | ~
% 279.69/41.82 (c_Groups_Oabs__class_Oabs(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 279.69/41.82 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tc_fun(v3, v2) = v1) | ~ (tc_fun(v3,
% 279.69/41.82 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 279.69/41.82 = v0 | ~ (c_Groups_Ouminus__class_Ouminus(v3, v2) = v1) | ~
% 279.69/41.82 (c_Groups_Ouminus__class_Ouminus(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 279.69/41.82 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 279.69/41.82 (c_RealVector_Onorm__class_Onorm(v3, v2) = v1) | ~
% 279.69/41.82 (c_RealVector_Onorm__class_Onorm(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 279.69/41.82 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP(v3, v2) = v1) | ~ (hAPP(v3,
% 279.69/41.82 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 279.69/41.82 (c_Nat_OSuc(v2) = v1) | ~ (c_Nat_OSuc(v2) = v0)) & ! [v0: $i] : ! [v1:
% 279.69/41.82 $i] : ! [v2: $i] : (v1 = v0 | ~ (c_Transcendental_Oln(v2) = v1) | ~
% 279.69/41.82 (c_Transcendental_Oln(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 279.69/41.82 (v1 = v0 | ~ (c_Power_Opower__class_Opower(v2) = v1) | ~
% 279.69/41.82 (c_Power_Opower__class_Opower(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 279.69/41.82 [v2: $i] : (v1 = v0 | ~ (c_Groups_Oone__class_Oone(v2) = v1) | ~
% 279.69/41.82 (c_Groups_Oone__class_Oone(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 279.69/41.82 $i] : (v1 = v0 | ~ (c_RComplete_Onatceiling(v2) = v1) | ~
% 279.69/41.82 (c_RComplete_Onatceiling(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 279.69/41.82 $i] : (v1 = v0 | ~ (c_Complex_Oexpi(v2) = v1) | ~ (c_Complex_Oexpi(v2) =
% 279.69/41.82 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 279.69/41.82 (c_RComplete_Onatfloor(v2) = v1) | ~ (c_RComplete_Onatfloor(v2) = v0)) & !
% 279.69/41.82 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 279.69/41.82 (c_Groups_Otimes__class_Otimes(v2) = v1) | ~
% 279.69/41.82 (c_Groups_Otimes__class_Otimes(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 279.69/41.82 [v2: $i] : (v1 = v0 | ~ (c_Complex_Ocomplex_Ocomplex__size(v2) = v1) | ~
% 279.69/41.82 (c_Complex_Ocomplex_Ocomplex__size(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 279.69/41.82 ! [v2: $i] : (v1 = v0 | ~ (c_Complex_ORe(v2) = v1) | ~ (c_Complex_ORe(v2) =
% 279.69/41.82 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 279.69/41.82 (c_Complex_OIm(v2) = v1) | ~ (c_Complex_OIm(v2) = v0)) & ! [v0: $i] : !
% 279.69/41.82 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (c_Groups_Ozero__class_Ozero(v2) = v1)
% 279.69/41.82 | ~ (c_Groups_Ozero__class_Ozero(v2) = v0))
% 279.69/41.82
% 279.69/41.82 Further assumptions not needed in the proof:
% 279.69/41.82 --------------------------------------------
% 279.69/41.82 arity_Complex__Ocomplex__Groups_Oab__group__add,
% 279.69/41.82 arity_Complex__Ocomplex__Groups_Oab__semigroup__add,
% 279.69/41.82 arity_Complex__Ocomplex__Groups_Oab__semigroup__mult,
% 279.69/41.82 arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add,
% 279.69/41.82 arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add,
% 279.69/41.82 arity_Complex__Ocomplex__Groups_Ocomm__monoid__add,
% 279.69/41.82 arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult,
% 279.69/41.82 arity_Complex__Ocomplex__Groups_Ominus,
% 279.69/41.82 arity_Complex__Ocomplex__Groups_Omonoid__add,
% 279.69/41.82 arity_Complex__Ocomplex__Groups_Omonoid__mult,
% 279.69/41.82 arity_Complex__Ocomplex__Groups_Oone, arity_Complex__Ocomplex__Groups_Ouminus,
% 279.69/41.82 arity_Complex__Ocomplex__Groups_Ozero, arity_Complex__Ocomplex__Power_Opower,
% 279.69/41.82 arity_Complex__Ocomplex__RealVector_Odist__norm,
% 279.69/41.82 arity_Complex__Ocomplex__RealVector_Ometric__space,
% 279.69/41.82 arity_Complex__Ocomplex__RealVector_Oreal__algebra,
% 279.69/41.82 arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra,
% 279.69/41.82 arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1,
% 279.69/41.82 arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra,
% 279.69/41.82 arity_Complex__Ocomplex__RealVector_Oreal__vector,
% 279.69/41.82 arity_Complex__Ocomplex__Rings_Ocomm__ring__1,
% 279.69/41.82 arity_Complex__Ocomplex__Rings_Ocomm__semiring,
% 279.69/41.82 arity_Complex__Ocomplex__Rings_Oidom,
% 279.69/41.82 arity_Complex__Ocomplex__Rings_Omult__zero,
% 279.69/41.82 arity_Complex__Ocomplex__Rings_Ono__zero__divisors,
% 279.69/41.82 arity_Complex__Ocomplex__Rings_Oring, arity_Complex__Ocomplex__Rings_Oring__1,
% 279.69/41.82 arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors,
% 279.69/41.82 arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors,
% 279.69/41.82 arity_Complex__Ocomplex__Rings_Osemiring,
% 279.69/41.82 arity_Complex__Ocomplex__Rings_Osemiring__0,
% 279.69/41.82 arity_Complex__Ocomplex__Rings_Ozero__neq__one,
% 279.69/41.82 arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
% 279.69/41.82 arity_HOL__Obool__Groups_Ominus, arity_HOL__Obool__Groups_Ouminus,
% 279.69/41.82 arity_HOL__Obool__Lattices_Oboolean__algebra, arity_HOL__Obool__Orderings_Oord,
% 279.69/41.82 arity_HOL__Obool__Orderings_Oorder, arity_HOL__Obool__Orderings_Opreorder,
% 279.69/41.82 arity_Int__Oint__Groups_Oab__group__add,
% 279.69/41.82 arity_Int__Oint__Groups_Oab__semigroup__add,
% 279.69/41.82 arity_Int__Oint__Groups_Oab__semigroup__mult, arity_Int__Oint__Groups_Oabs__if,
% 279.69/41.82 arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,
% 279.69/41.82 arity_Int__Oint__Groups_Ocancel__semigroup__add,
% 279.69/41.82 arity_Int__Oint__Groups_Ocomm__monoid__add,
% 279.69/41.82 arity_Int__Oint__Groups_Ocomm__monoid__mult,
% 279.69/41.82 arity_Int__Oint__Groups_Ogroup__add,
% 279.69/41.82 arity_Int__Oint__Groups_Olinordered__ab__group__add,
% 279.69/41.82 arity_Int__Oint__Groups_Ominus, arity_Int__Oint__Groups_Omonoid__add,
% 279.69/41.82 arity_Int__Oint__Groups_Omonoid__mult, arity_Int__Oint__Groups_Oone,
% 279.69/41.82 arity_Int__Oint__Groups_Oordered__ab__group__add,
% 279.69/41.82 arity_Int__Oint__Groups_Oordered__ab__group__add__abs,
% 279.69/41.82 arity_Int__Oint__Groups_Oordered__ab__semigroup__add,
% 279.69/41.82 arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,
% 279.69/41.82 arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,
% 279.69/41.82 arity_Int__Oint__Groups_Oordered__comm__monoid__add,
% 279.69/41.82 arity_Int__Oint__Groups_Ouminus, arity_Int__Oint__Groups_Ozero,
% 279.69/41.82 arity_Int__Oint__Orderings_Olinorder, arity_Int__Oint__Orderings_Oord,
% 279.69/41.82 arity_Int__Oint__Orderings_Oorder, arity_Int__Oint__Orderings_Opreorder,
% 279.69/41.82 arity_Int__Oint__Power_Opower, arity_Int__Oint__Rings_Ocomm__ring__1,
% 279.69/41.82 arity_Int__Oint__Rings_Ocomm__semiring,
% 279.69/41.82 arity_Int__Oint__Rings_Ocomm__semiring__1, arity_Int__Oint__Rings_Oidom,
% 279.69/41.82 arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,
% 279.69/41.82 arity_Int__Oint__Rings_Olinordered__idom,
% 279.69/41.82 arity_Int__Oint__Rings_Olinordered__ring,
% 279.69/41.82 arity_Int__Oint__Rings_Olinordered__ring__strict,
% 279.69/41.82 arity_Int__Oint__Rings_Olinordered__semidom,
% 279.69/41.82 arity_Int__Oint__Rings_Olinordered__semiring,
% 279.69/41.82 arity_Int__Oint__Rings_Olinordered__semiring__1,
% 279.69/41.82 arity_Int__Oint__Rings_Olinordered__semiring__1__strict,
% 279.69/41.82 arity_Int__Oint__Rings_Olinordered__semiring__strict,
% 279.69/41.82 arity_Int__Oint__Rings_Omult__zero, arity_Int__Oint__Rings_Ono__zero__divisors,
% 279.69/41.82 arity_Int__Oint__Rings_Oordered__cancel__semiring,
% 279.69/41.82 arity_Int__Oint__Rings_Oordered__comm__semiring,
% 279.69/41.82 arity_Int__Oint__Rings_Oordered__ring,
% 279.69/41.82 arity_Int__Oint__Rings_Oordered__ring__abs,
% 279.69/41.82 arity_Int__Oint__Rings_Oordered__semiring, arity_Int__Oint__Rings_Oring,
% 279.69/41.82 arity_Int__Oint__Rings_Oring__1,
% 279.69/41.82 arity_Int__Oint__Rings_Oring__1__no__zero__divisors,
% 279.69/41.82 arity_Int__Oint__Rings_Oring__no__zero__divisors,
% 279.69/41.82 arity_Int__Oint__Rings_Osemiring, arity_Int__Oint__Rings_Osemiring__0,
% 279.69/41.82 arity_Int__Oint__Rings_Ozero__neq__one,
% 279.69/41.82 arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
% 279.69/41.82 arity_Nat__Onat__Groups_Oab__semigroup__add,
% 279.69/41.82 arity_Nat__Onat__Groups_Oab__semigroup__mult,
% 279.69/41.82 arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,
% 279.69/41.82 arity_Nat__Onat__Groups_Ocancel__semigroup__add,
% 279.69/41.82 arity_Nat__Onat__Groups_Ocomm__monoid__add,
% 279.69/41.82 arity_Nat__Onat__Groups_Ocomm__monoid__mult, arity_Nat__Onat__Groups_Ominus,
% 279.69/41.82 arity_Nat__Onat__Groups_Omonoid__add, arity_Nat__Onat__Groups_Omonoid__mult,
% 279.69/41.82 arity_Nat__Onat__Groups_Oone,
% 279.69/41.82 arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,
% 279.69/41.82 arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,
% 279.69/41.82 arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,
% 279.69/41.82 arity_Nat__Onat__Groups_Oordered__comm__monoid__add,
% 279.69/41.82 arity_Nat__Onat__Groups_Ozero, arity_Nat__Onat__Orderings_Olinorder,
% 279.69/41.82 arity_Nat__Onat__Orderings_Oord, arity_Nat__Onat__Orderings_Oorder,
% 279.69/41.82 arity_Nat__Onat__Orderings_Opreorder, arity_Nat__Onat__Power_Opower,
% 279.69/41.82 arity_Nat__Onat__Rings_Ocomm__semiring,
% 279.69/41.82 arity_Nat__Onat__Rings_Ocomm__semiring__1,
% 279.69/41.82 arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,
% 279.69/41.82 arity_Nat__Onat__Rings_Olinordered__semidom,
% 279.69/41.82 arity_Nat__Onat__Rings_Olinordered__semiring,
% 279.69/41.82 arity_Nat__Onat__Rings_Olinordered__semiring__strict,
% 279.69/41.82 arity_Nat__Onat__Rings_Omult__zero, arity_Nat__Onat__Rings_Ono__zero__divisors,
% 279.69/41.82 arity_Nat__Onat__Rings_Oordered__cancel__semiring,
% 279.69/41.82 arity_Nat__Onat__Rings_Oordered__comm__semiring,
% 279.69/41.82 arity_Nat__Onat__Rings_Oordered__semiring, arity_Nat__Onat__Rings_Osemiring,
% 279.69/41.82 arity_Nat__Onat__Rings_Osemiring__0, arity_Nat__Onat__Rings_Ozero__neq__one,
% 279.69/41.82 arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
% 279.69/41.82 arity_RealDef__Oreal__Groups_Oab__group__add,
% 279.69/41.82 arity_RealDef__Oreal__Groups_Oab__semigroup__add,
% 279.69/41.82 arity_RealDef__Oreal__Groups_Oab__semigroup__mult,
% 279.69/41.82 arity_RealDef__Oreal__Groups_Oabs__if,
% 279.69/41.82 arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add,
% 279.69/41.82 arity_RealDef__Oreal__Groups_Ocancel__semigroup__add,
% 279.69/41.82 arity_RealDef__Oreal__Groups_Ocomm__monoid__add,
% 279.69/41.82 arity_RealDef__Oreal__Groups_Ocomm__monoid__mult,
% 279.69/41.82 arity_RealDef__Oreal__Groups_Ogroup__add,
% 279.69/41.82 arity_RealDef__Oreal__Groups_Olinordered__ab__group__add,
% 279.69/41.82 arity_RealDef__Oreal__Groups_Ominus, arity_RealDef__Oreal__Groups_Omonoid__add,
% 279.69/41.82 arity_RealDef__Oreal__Groups_Omonoid__mult, arity_RealDef__Oreal__Groups_Oone,
% 279.69/41.82 arity_RealDef__Oreal__Groups_Oordered__ab__group__add,
% 279.69/41.82 arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs,
% 279.69/41.82 arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add,
% 279.69/41.82 arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le,
% 279.69/41.82 arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add,
% 279.69/41.82 arity_RealDef__Oreal__Groups_Ouminus, arity_RealDef__Oreal__Groups_Ozero,
% 279.69/41.82 arity_RealDef__Oreal__Orderings_Olinorder, arity_RealDef__Oreal__Orderings_Oord,
% 279.69/41.82 arity_RealDef__Oreal__Orderings_Oorder,
% 279.69/41.82 arity_RealDef__Oreal__Orderings_Opreorder, arity_RealDef__Oreal__Power_Opower,
% 279.69/41.82 arity_RealDef__Oreal__RealVector_Odist__norm,
% 279.69/41.82 arity_RealDef__Oreal__RealVector_Ometric__space,
% 279.69/41.82 arity_RealDef__Oreal__RealVector_Oreal__algebra,
% 279.69/41.82 arity_RealDef__Oreal__RealVector_Oreal__normed__algebra,
% 279.69/41.82 arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1,
% 279.69/41.82 arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra,
% 279.69/41.82 arity_RealDef__Oreal__RealVector_Oreal__normed__vector,
% 279.69/41.82 arity_RealDef__Oreal__RealVector_Oreal__vector,
% 279.69/41.82 arity_RealDef__Oreal__Rings_Ocomm__ring__1,
% 279.69/41.82 arity_RealDef__Oreal__Rings_Ocomm__semiring,
% 279.69/41.82 arity_RealDef__Oreal__Rings_Ocomm__semiring__1,
% 279.69/41.82 arity_RealDef__Oreal__Rings_Oidom,
% 279.69/41.82 arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict,
% 279.69/41.82 arity_RealDef__Oreal__Rings_Olinordered__idom,
% 279.69/41.82 arity_RealDef__Oreal__Rings_Olinordered__ring,
% 279.69/41.82 arity_RealDef__Oreal__Rings_Olinordered__ring__strict,
% 279.69/41.82 arity_RealDef__Oreal__Rings_Olinordered__semiring,
% 279.69/41.82 arity_RealDef__Oreal__Rings_Olinordered__semiring__1,
% 279.69/41.82 arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict,
% 279.69/41.82 arity_RealDef__Oreal__Rings_Olinordered__semiring__strict,
% 279.69/41.82 arity_RealDef__Oreal__Rings_Omult__zero,
% 279.69/41.82 arity_RealDef__Oreal__Rings_Ono__zero__divisors,
% 279.69/41.82 arity_RealDef__Oreal__Rings_Oordered__cancel__semiring,
% 279.69/41.82 arity_RealDef__Oreal__Rings_Oordered__comm__semiring,
% 279.69/41.82 arity_RealDef__Oreal__Rings_Oordered__ring,
% 279.69/41.82 arity_RealDef__Oreal__Rings_Oordered__ring__abs,
% 279.69/41.82 arity_RealDef__Oreal__Rings_Oordered__semiring,
% 279.69/41.82 arity_RealDef__Oreal__Rings_Oring, arity_RealDef__Oreal__Rings_Oring__1,
% 279.69/41.82 arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors,
% 279.69/41.82 arity_RealDef__Oreal__Rings_Oring__no__zero__divisors,
% 279.69/41.82 arity_RealDef__Oreal__Rings_Osemiring, arity_RealDef__Oreal__Rings_Osemiring__0,
% 279.69/41.82 arity_RealDef__Oreal__Rings_Ozero__neq__one,
% 279.69/41.82 arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
% 279.69/41.82 arity_fun__Groups_Ominus, arity_fun__Groups_Ouminus,
% 279.69/41.82 arity_fun__Lattices_Oboolean__algebra, arity_fun__Orderings_Oord,
% 279.69/41.82 arity_fun__Orderings_Oorder, arity_fun__Orderings_Opreorder, fact_BseqI2_H,
% 279.69/41.82 fact_Complex__mult__i, fact_DeMoivre2, fact_Deriv_Oadd__diff__add, fact_Im,
% 279.69/41.82 fact_Im_Oadd, fact_Im_Obounded, fact_Im_Odiff, fact_Im_Ominus, fact_Im_OscaleR,
% 279.69/41.82 fact_Limits_Ominus__diff__minus, fact_Nat_Oadd__0__right,
% 279.69/41.82 fact_Nat_Odiff__diff__eq,
% 279.69/41.82 fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,
% 279.69/41.82 fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,
% 279.69/41.82 fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,
% 279.69/41.82 fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,
% 279.69/41.82 fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,
% 279.69/41.82 fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,
% 279.69/41.82 fact_One__nat__def, fact_Re, fact_Re_Oadd, fact_Re_Obounded, fact_Re_Odiff,
% 279.69/41.82 fact_Re_Ominus, fact_Re_OscaleR, fact_Suc__diff__diff, fact_Suc__diff__le,
% 279.69/41.82 fact_Suc__eq__plus1, fact_Suc__eq__plus1__left, fact_Suc__inject, fact_Suc__leD,
% 279.69/41.82 fact_Suc__leI, fact_Suc__le__eq, fact_Suc__le__lessD, fact_Suc__le__mono,
% 279.69/41.82 fact_Suc__lessD, fact_Suc__lessI, fact_Suc__less__SucD, fact_Suc__less__eq,
% 279.69/41.82 fact_Suc__mono, fact_Suc__mult__cancel1, fact_Suc__mult__le__cancel1,
% 279.69/41.82 fact_Suc__mult__less__cancel1, fact_Suc__n__not__le__n, fact_Suc__n__not__n,
% 279.69/41.82 fact_Suc__neq__Zero, fact_Suc__not__Zero, fact_Suc__pred, fact_Zero__neq__Suc,
% 279.69/41.82 fact_Zero__not__Suc, fact_ab__diff__minus, fact_ab__left__minus,
% 279.69/41.82 fact_ab__semigroup__add__class_Oadd__ac_I1_J,
% 279.69/41.82 fact_ab__semigroup__mult__class_Omult__ac_I1_J, fact_abs__Im__le__cmod,
% 279.69/41.82 fact_abs__Re__le__cmod, fact_abs__add__abs, fact_abs__diff__less__iff,
% 279.69/41.82 fact_abs__diff__triangle__ineq, fact_abs__eq__0, fact_abs__eq__mult,
% 279.69/41.82 fact_abs__ge__minus__self, fact_abs__ge__self, fact_abs__ge__zero,
% 279.69/41.82 fact_abs__idempotent, fact_abs__if, fact_abs__leI, fact_abs__le__D1,
% 279.69/41.82 fact_abs__le__D2, fact_abs__le__iff, fact_abs__le__interval__iff,
% 279.69/41.82 fact_abs__le__zero__iff, fact_abs__less__iff, fact_abs__minus__add__cancel,
% 279.69/41.82 fact_abs__minus__cancel, fact_abs__minus__commute, fact_abs__minus__le__zero,
% 279.69/41.82 fact_abs__mult, fact_abs__mult__less, fact_abs__mult__pos, fact_abs__mult__self,
% 279.69/41.82 fact_abs__not__less__zero, fact_abs__of__neg, fact_abs__of__nonneg,
% 279.69/41.82 fact_abs__of__nonpos, fact_abs__of__pos, fact_abs__one, fact_abs__power__minus,
% 279.69/41.82 fact_abs__real__of__nat__cancel, fact_abs__sum__triangle__ineq,
% 279.69/41.82 fact_abs__triangle__ineq, fact_abs__triangle__ineq2,
% 279.69/41.82 fact_abs__triangle__ineq2__sym, fact_abs__triangle__ineq3,
% 279.69/41.82 fact_abs__triangle__ineq4, fact_abs__zero, fact_abs__zmult__eq__1,
% 279.69/41.82 fact_add1__zle__eq, fact_add_Ocomm__neutral, fact_add__0, fact_add__0__iff,
% 279.69/41.82 fact_add__0__left, fact_add__0__right, fact_add__Suc, fact_add__Suc__right,
% 279.69/41.82 fact_add__Suc__shift, fact_add__diff__assoc, fact_add__diff__assoc2,
% 279.69/41.82 fact_add__diff__cancel, fact_add__diff__inverse, fact_add__eq__0__iff,
% 279.69/41.82 fact_add__eq__self__zero, fact_add__gr__0, fact_add__imp__eq,
% 279.69/41.82 fact_add__increasing, fact_add__increasing2, fact_add__is__0, fact_add__is__1,
% 279.69/41.82 fact_add__leD1, fact_add__leD2, fact_add__leE, fact_add__le__cancel__left,
% 279.69/41.82 fact_add__le__cancel__right, fact_add__le__imp__le__left,
% 279.69/41.82 fact_add__le__imp__le__right, fact_add__le__less__mono, fact_add__le__mono,
% 279.69/41.82 fact_add__le__mono1, fact_add__left__cancel, fact_add__left__imp__eq,
% 279.69/41.82 fact_add__left__mono, fact_add__lessD1, fact_add__less__cancel__left,
% 279.69/41.82 fact_add__less__cancel__right, fact_add__less__imp__less__left,
% 279.69/41.82 fact_add__less__imp__less__right, fact_add__less__le__mono,
% 279.69/41.82 fact_add__less__mono, fact_add__less__mono1, fact_add__minus__cancel,
% 279.69/41.82 fact_add__mono, fact_add__mult__distrib, fact_add__mult__distrib2,
% 279.69/41.82 fact_add__right__cancel, fact_add__right__imp__eq, fact_add__right__mono,
% 279.69/41.82 fact_add__scale__eq__noteq, fact_add__strict__increasing,
% 279.69/41.82 fact_add__strict__increasing2, fact_add__strict__left__mono,
% 279.69/41.82 fact_add__strict__mono, fact_add__strict__right__mono,
% 279.69/41.82 fact_bounded__bilinear_Oadd__left, fact_bounded__bilinear_Oadd__right,
% 279.69/41.82 fact_bounded__bilinear_Obounded, fact_bounded__bilinear_Odiff__left,
% 279.69/41.82 fact_bounded__bilinear_Odiff__right, fact_bounded__bilinear_Ominus__left,
% 279.69/41.82 fact_bounded__bilinear_Ominus__right, fact_bounded__bilinear_Oprod__diff__prod,
% 279.69/41.82 fact_bounded__bilinear_OscaleR__left, fact_bounded__bilinear_OscaleR__right,
% 279.69/41.82 fact_bounded__bilinear_Ozero__left, fact_bounded__bilinear_Ozero__right,
% 279.69/41.82 fact_combine__common__factor, fact_comm__mult__left__mono,
% 279.69/41.82 fact_comm__mult__strict__left__mono,
% 279.69/41.82 fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,
% 279.69/41.82 fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,
% 279.69/41.82 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,
% 279.69/41.82 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,
% 279.69/41.82 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,
% 279.69/41.82 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,
% 279.69/41.82 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,
% 279.69/41.82 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,
% 279.69/41.82 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,
% 279.69/41.82 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,
% 279.69/41.82 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,
% 279.69/41.82 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,
% 279.69/41.82 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,
% 279.69/41.82 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,
% 279.69/41.82 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,
% 279.69/41.82 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,
% 279.69/41.82 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,
% 279.69/41.82 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,
% 279.69/41.82 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,
% 279.69/41.82 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,
% 279.69/41.82 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,
% 279.69/41.82 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,
% 279.69/41.82 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,
% 279.69/41.82 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,
% 279.69/41.82 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,
% 279.69/41.82 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,
% 279.69/41.82 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,
% 279.69/41.82 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,
% 279.69/41.82 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,
% 279.69/41.82 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,
% 279.69/41.82 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,
% 279.69/41.82 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,
% 279.69/41.82 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,
% 279.69/41.82 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,
% 279.69/41.82 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,
% 279.69/41.82 fact_comm__semiring__class_Odistrib, fact_compl__eq__compl__iff,
% 279.69/41.82 fact_compl__le__compl__iff, fact_compl__mono, fact_complex_Oinject,
% 279.69/41.82 fact_complex_Orecs, fact_complex_Osimps_I2_J, fact_complex_Osize_I1_J,
% 279.69/41.82 fact_complex_Osize_I2_J, fact_complex__Im__mult, fact_complex__Im__scaleR,
% 279.69/41.82 fact_complex__Re__le__cmod, fact_complex__Re__mult, fact_complex__Re__scaleR,
% 279.69/41.82 fact_complex__add, fact_complex__add__def, fact_complex__diff,
% 279.69/41.82 fact_complex__equality, fact_complex__i__mult__minus, fact_complex__i__not__one,
% 279.69/41.82 fact_complex__i__not__zero, fact_complex__minus, fact_complex__minus__def,
% 279.69/41.82 fact_complex__mod__minus__le__complex__mod, fact_complex__mod__rcis,
% 279.69/41.82 fact_complex__mod__triangle__ineq2, fact_complex__mult, fact_complex__mult__def,
% 279.69/41.82 fact_complex__scaleR, fact_complex__scaleR__def, fact_complex__surj,
% 279.69/41.82 fact_convex__bound__le, fact_convex__bound__lt, fact_crossproduct__eq,
% 279.69/41.82 fact_crossproduct__noteq, fact_decr__lemma, fact_decr__mult__lemma,
% 279.69/41.82 fact_decseq__def, fact_diff__0, fact_diff__0__eq__0, fact_diff__0__right,
% 279.69/41.82 fact_diff__Suc__1, fact_diff__Suc__Suc, fact_diff__Suc__diff__eq1,
% 279.69/41.82 fact_diff__Suc__diff__eq2, fact_diff__Suc__eq__diff__pred, fact_diff__Suc__less,
% 279.69/41.82 fact_diff__add__0, fact_diff__add__assoc, fact_diff__add__assoc2,
% 279.69/41.82 fact_diff__add__cancel, fact_diff__add__inverse, fact_diff__add__inverse2,
% 279.69/41.82 fact_diff__cancel, fact_diff__cancel2, fact_diff__commute, fact_diff__def,
% 279.69/41.82 fact_diff__diff__cancel, fact_diff__diff__left, fact_diff__diff__right,
% 279.69/41.82 fact_diff__eq__diff__eq, fact_diff__eq__diff__less,
% 279.69/41.82 fact_diff__eq__diff__less__eq, fact_diff__int__def,
% 279.69/41.82 fact_diff__int__def__symmetric, fact_diff__is__0__eq, fact_diff__is__0__eq_H,
% 279.69/41.82 fact_diff__le__mono, fact_diff__le__mono2, fact_diff__le__self, fact_diff__less,
% 279.69/41.82 fact_diff__less__Suc, fact_diff__less__mono, fact_diff__less__mono2,
% 279.69/41.82 fact_diff__minus__eq__add, fact_diff__mult__distrib, fact_diff__mult__distrib2,
% 279.69/41.82 fact_diff__self, fact_diff__self__eq__0, fact_diffs0__imp__equal,
% 279.69/41.82 fact_dist__commute, fact_dist__complex__def, fact_dist__norm,
% 279.69/41.82 fact_dist__real__def, fact_dist__triangle, fact_dist__triangle2,
% 279.69/41.82 fact_dist__triangle3, fact_divisors__zero,
% 279.69/41.82 fact_double__add__le__zero__iff__single__add__le__zero,
% 279.69/41.82 fact_double__add__less__zero__iff__single__add__less__zero, fact_double__compl,
% 279.69/41.82 fact_double__eq__0__iff, fact_double__zero__sym, fact_eq__add__iff1,
% 279.69/41.82 fact_eq__add__iff2, fact_eq__diff__iff, fact_eq__iff__diff__eq__0,
% 279.69/41.82 fact_eq__imp__le, fact_eq__neg__iff__add__eq__0, fact_equal__neg__zero,
% 279.69/41.82 fact_equation__minus__iff, fact_even__less__0__iff, fact_ex__least__nat__less,
% 279.69/41.82 fact_expand__complex__eq, fact_expi__add, fact_expi__zero, fact_ext,
% 279.69/41.82 fact_field__power__not__zero, fact_ge__natfloor__plus__one__imp__gt, fact_gr0I,
% 279.69/41.82 fact_gr0__conv__Suc, fact_gr__implies__not0, fact_i__mult__Complex,
% 279.69/41.82 fact_i__mult__eq2, fact_incr__lemma, fact_incr__mult__lemma, fact_incseq__def,
% 279.69/41.82 fact_int__0__less__1, fact_int__0__neq__1, fact_int__one__le__iff__zero__less,
% 279.69/41.82 fact_int__val__lemma, fact_le0, fact_leD, fact_leI, fact_le__0__eq,
% 279.69/41.82 fact_le__SucE, fact_le__SucI, fact_le__Suc__eq, fact_le__Suc__ex__iff,
% 279.69/41.82 fact_le__add1, fact_le__add2, fact_le__add__diff, fact_le__add__diff__inverse,
% 279.69/41.82 fact_le__add__diff__inverse2, fact_le__add__iff1, fact_le__add__iff2,
% 279.69/41.82 fact_le__antisym, fact_le__cube, fact_le__diff__conv, fact_le__diff__conv2,
% 279.69/41.82 fact_le__diff__iff, fact_le__eq__less__or__eq, fact_le__funD, fact_le__funE,
% 279.69/41.82 fact_le__funI, fact_le__fun__def, fact_le__iff__add, fact_le__iff__diff__le__0,
% 279.69/41.82 fact_le__imp__0__less, fact_le__imp__diff__is__add, fact_le__imp__less__Suc,
% 279.69/41.82 fact_le__imp__neg__le, fact_le__less__Suc__eq, fact_le__minus__iff,
% 279.69/41.82 fact_le__minus__self__iff, fact_le__natfloor, fact_le__neq__implies__less,
% 279.69/41.82 fact_le__refl, fact_le__square, fact_le__trans, fact_left__add__mult__distrib,
% 279.69/41.82 fact_left__minus, fact_lessI, fact_less__1__mult, fact_less__Suc0,
% 279.69/41.82 fact_less__SucE, fact_less__SucI, fact_less__Suc__eq,
% 279.69/41.82 fact_less__Suc__eq__0__disj, fact_less__Suc__eq__le, fact_less__add__Suc1,
% 279.69/41.82 fact_less__add__Suc2, fact_less__add__eq__less, fact_less__add__iff1,
% 279.69/41.82 fact_less__add__iff2, fact_less__add__one, fact_less__antisym,
% 279.69/41.82 fact_less__bin__lemma, fact_less__diff__conv, fact_less__diff__iff,
% 279.69/41.82 fact_less__eq__Suc__le, fact_less__eq__nat_Osimps_I1_J,
% 279.69/41.82 fact_less__eq__real__def, fact_less__fun__def, fact_less__iff__Suc__add,
% 279.69/41.82 fact_less__iff__diff__less__0, fact_less__imp__diff__less,
% 279.69/41.82 fact_less__imp__le__nat, fact_less__imp__neq, fact_less__irrefl__nat,
% 279.69/41.82 fact_less__le__not__le, fact_less__minus__iff, fact_less__minus__self__iff,
% 279.69/41.82 fact_less__nat__zero__code, fact_less__not__refl, fact_less__not__refl2,
% 279.69/41.82 fact_less__not__refl3, fact_less__or__eq__imp__le, fact_less__trans__Suc,
% 279.69/41.82 fact_less__zeroE, fact_linorder__antisym__conv1, fact_linorder__antisym__conv2,
% 279.69/41.82 fact_linorder__antisym__conv3, fact_linorder__cases, fact_linorder__le__cases,
% 279.69/41.82 fact_linorder__le__less__linear, fact_linorder__less__linear,
% 279.69/41.82 fact_linorder__linear, fact_linorder__neqE,
% 279.69/41.82 fact_linorder__neqE__linordered__idom, fact_linorder__neqE__nat,
% 279.69/41.82 fact_linorder__neq__iff, fact_linorder__not__le, fact_linorder__not__less,
% 279.69/41.82 fact_minus__add, fact_minus__add__distrib, fact_minus__apply,
% 279.69/41.82 fact_minus__diff__eq, fact_minus__equation__iff, fact_minus__le__iff,
% 279.69/41.82 fact_minus__le__self__iff, fact_minus__less__iff, fact_minus__minus,
% 279.69/41.82 fact_minus__mult__commute, fact_minus__mult__left, fact_minus__mult__minus,
% 279.69/41.82 fact_minus__mult__right, fact_minus__nat_Odiff__0, fact_minus__real__def,
% 279.69/41.82 fact_minus__unique, fact_minus__zero, fact_mult_Oadd__left,
% 279.69/41.82 fact_mult_Oadd__right, fact_mult_Obounded, fact_mult_Ocomm__neutral,
% 279.69/41.82 fact_mult_Odiff__left, fact_mult_Odiff__right, fact_mult_Ominus__left,
% 279.69/41.82 fact_mult_Ominus__right, fact_mult_Oprod__diff__prod, fact_mult_OscaleR__left,
% 279.69/41.82 fact_mult_OscaleR__right, fact_mult_Ozero__left, fact_mult_Ozero__right,
% 279.69/41.82 fact_mult__0, fact_mult__0__right, fact_mult__1, fact_mult__1__left,
% 279.69/41.82 fact_mult__1__right, fact_mult__Suc, fact_mult__Suc__right, fact_mult__cancel1,
% 279.69/41.82 fact_mult__cancel2, fact_mult__diff__mult, fact_mult__eq__0__iff,
% 279.69/41.82 fact_mult__eq__1__iff, fact_mult__eq__if, fact_mult__eq__self__implies__10,
% 279.69/41.82 fact_mult__idem, fact_mult__is__0, fact_mult__le__0__iff,
% 279.69/41.82 fact_mult__le__cancel1, fact_mult__le__cancel2,
% 279.69/41.82 fact_mult__le__cancel__left__neg, fact_mult__le__cancel__left__pos,
% 279.69/41.82 fact_mult__le__less__imp__less, fact_mult__le__mono, fact_mult__le__mono1,
% 279.69/41.82 fact_mult__le__mono2, fact_mult__left_Oadd, fact_mult__left_Obounded,
% 279.69/41.82 fact_mult__left_Odiff, fact_mult__left_Ominus, fact_mult__left_OscaleR,
% 279.69/41.82 fact_mult__left_Ozero, fact_mult__left__idem, fact_mult__left__le__imp__le,
% 279.69/41.82 fact_mult__left__le__one__le, fact_mult__left__less__imp__less,
% 279.69/41.82 fact_mult__left__mono, fact_mult__left__mono__neg, fact_mult__less__cancel1,
% 279.69/41.82 fact_mult__less__cancel2, fact_mult__less__cancel__left__disj,
% 279.69/41.82 fact_mult__less__cancel__left__neg, fact_mult__less__cancel__left__pos,
% 279.69/41.82 fact_mult__less__cancel__right__disj, fact_mult__less__imp__less__left,
% 279.69/41.82 fact_mult__less__imp__less__right, fact_mult__less__le__imp__less,
% 279.69/41.82 fact_mult__less__mono1, fact_mult__less__mono2, fact_mult__mono,
% 279.69/41.82 fact_mult__mono_H, fact_mult__neg__neg, fact_mult__neg__pos,
% 279.69/41.82 fact_mult__nonneg__nonneg, fact_mult__nonneg__nonpos,
% 279.69/41.82 fact_mult__nonneg__nonpos2, fact_mult__nonpos__nonneg,
% 279.69/41.82 fact_mult__nonpos__nonpos, fact_mult__pos__neg, fact_mult__pos__neg2,
% 279.69/41.82 fact_mult__pos__pos, fact_mult__right_Oadd, fact_mult__right_Obounded,
% 279.69/41.82 fact_mult__right_Odiff, fact_mult__right_Ominus, fact_mult__right_OscaleR,
% 279.69/41.82 fact_mult__right_Ozero, fact_mult__right__le__imp__le,
% 279.69/41.82 fact_mult__right__le__one__le, fact_mult__right__less__imp__less,
% 279.69/41.82 fact_mult__right__mono, fact_mult__right__mono__neg, fact_mult__scaleR__left,
% 279.69/41.82 fact_mult__scaleR__right, fact_mult__strict__left__mono,
% 279.69/41.82 fact_mult__strict__left__mono__neg, fact_mult__strict__mono,
% 279.69/41.82 fact_mult__strict__mono_H, fact_mult__strict__right__mono,
% 279.69/41.82 fact_mult__strict__right__mono__neg, fact_mult__zero__left,
% 279.69/41.82 fact_mult__zero__right, fact_n__not__Suc__n, fact_nat0__intermed__int__val,
% 279.69/41.82 fact_nat_Oinject, fact_nat_Osimps_I2_J, fact_nat_Osimps_I3_J,
% 279.69/41.82 fact_nat__0__less__mult__iff, fact_nat__1__eq__mult__iff, fact_nat__add__assoc,
% 279.69/41.82 fact_nat__add__commute, fact_nat__add__left__cancel,
% 279.69/41.82 fact_nat__add__left__cancel__le, fact_nat__add__left__cancel__less,
% 279.69/41.82 fact_nat__add__left__commute, fact_nat__add__right__cancel,
% 279.69/41.82 fact_nat__diff__add__eq1, fact_nat__diff__add__eq2, fact_nat__diff__split,
% 279.69/41.82 fact_nat__diff__split__asm, fact_nat__eq__add__iff1, fact_nat__eq__add__iff2,
% 279.69/41.82 fact_nat__le__add__iff1, fact_nat__le__add__iff2, fact_nat__le__linear,
% 279.69/41.82 fact_nat__less__add__iff1, fact_nat__less__add__iff2, fact_nat__less__cases,
% 279.69/41.82 fact_nat__less__le, fact_nat__lt__two__imp__zero__or__one, fact_nat__mult__1,
% 279.69/41.82 fact_nat__mult__1__right, fact_nat__mult__assoc, fact_nat__mult__commute,
% 279.69/41.82 fact_nat__mult__eq__1__iff, fact_nat__mult__eq__cancel1,
% 279.69/41.82 fact_nat__mult__eq__cancel__disj, fact_nat__mult__le__cancel1,
% 279.69/41.82 fact_nat__mult__less__cancel1, fact_nat__neq__iff,
% 279.69/41.82 fact_nat__power__eq__Suc__0__iff, fact_nat__power__less__imp__less,
% 279.69/41.82 fact_nat__zero__less__power__iff, fact_natceiling__le, fact_natceiling__mono,
% 279.69/41.82 fact_natceiling__real__of__nat, fact_natceiling__subtract, fact_natfloor__mono,
% 279.69/41.82 fact_natfloor__power, fact_natfloor__real__of__nat, fact_natfloor__subtract,
% 279.69/41.82 fact_neg__0__equal__iff__equal, fact_neg__0__le__iff__le,
% 279.69/41.82 fact_neg__0__less__iff__less, fact_neg__equal__0__iff__equal,
% 279.69/41.82 fact_neg__equal__iff__equal, fact_neg__equal__zero, fact_neg__le__0__iff__le,
% 279.69/41.82 fact_neg__le__iff__le, fact_neg__less__0__iff__less, fact_neg__less__iff__less,
% 279.69/41.82 fact_neg__less__nonneg, fact_neq0__conv, fact_no__zero__divisors,
% 279.69/41.82 fact_norm__add__less, fact_norm__conv__dist, fact_norm__diff__ineq,
% 279.69/41.82 fact_norm__diff__triangle__ineq, fact_norm__minus__commute, fact_norm__mult,
% 279.69/41.82 fact_norm__mult__ineq, fact_norm__mult__less, fact_norm__power,
% 279.69/41.82 fact_norm__power__ineq, fact_norm__scaleR, fact_norm__triangle__ineq,
% 279.69/41.82 fact_norm__triangle__ineq2, fact_norm__triangle__ineq3, fact_not__add__less1,
% 279.69/41.82 fact_not__add__less2, fact_not__leE, fact_not__less0, fact_not__less__eq,
% 279.69/41.82 fact_not__less__eq__eq, fact_not__less__iff__gr__or__eq,
% 279.69/41.82 fact_not__less__less__Suc__eq, fact_not__square__less__zero,
% 279.69/41.82 fact_not__sum__squares__lt__zero, fact_odd__less__0, fact_odd__nonzero,
% 279.69/41.82 fact_one__is__add, fact_one__le__mult__iff, fact_one__le__power,
% 279.69/41.82 fact_one__less__power, fact_one__neq__zero, fact_one__reorient,
% 279.69/41.82 fact_ord__eq__le__trans, fact_ord__eq__less__trans, fact_ord__le__eq__trans,
% 279.69/41.82 fact_ord__less__eq__trans, fact_order__antisym, fact_order__antisym__conv,
% 279.69/41.82 fact_order__eq__iff, fact_order__eq__refl, fact_order__le__imp__less__or__eq,
% 279.69/41.82 fact_order__le__less, fact_order__le__less__trans, fact_order__le__neq__trans,
% 279.69/41.82 fact_order__less__asym, fact_order__less__asym_H, fact_order__less__imp__le,
% 279.69/41.82 fact_order__less__imp__not__eq, fact_order__less__imp__not__eq2,
% 279.69/41.82 fact_order__less__imp__not__less, fact_order__less__irrefl,
% 279.69/41.82 fact_order__less__le, fact_order__less__le__trans, fact_order__less__not__sym,
% 279.69/41.82 fact_order__less__trans, fact_order__neq__le__trans, fact_order__refl,
% 279.69/41.82 fact_order__trans, fact_plus__nat_Oadd__0, fact_pos__add__strict,
% 279.69/41.82 fact_pos__zmult__eq__1__iff, fact_power_Opower_Opower__0,
% 279.69/41.82 fact_power_Opower_Opower__Suc, fact_power__0, fact_power__0__Suc,
% 279.69/41.82 fact_power__0__left, fact_power__Suc, fact_power__Suc2, fact_power__Suc__0,
% 279.69/41.82 fact_power__Suc__less, fact_power__abs, fact_power__add, fact_power__commutes,
% 279.69/41.82 fact_power__decreasing, fact_power__eq__0__iff, fact_power__eq__if,
% 279.69/41.82 fact_power__eq__imp__eq__base, fact_power__gt1, fact_power__gt1__lemma,
% 279.69/41.82 fact_power__increasing, fact_power__increasing__iff, fact_power__inject__base,
% 279.69/41.82 fact_power__inject__exp, fact_power__le__imp__le__base,
% 279.69/41.82 fact_power__le__imp__le__exp, fact_power__less__imp__less__base,
% 279.69/41.82 fact_power__less__imp__less__exp, fact_power__less__power__Suc,
% 279.69/41.82 fact_power__minus, fact_power__mono, fact_power__mult,
% 279.69/41.82 fact_power__mult__distrib, fact_power__one, fact_power__one__right,
% 279.69/41.82 fact_power__power__power, fact_power__real__of__nat,
% 279.69/41.82 fact_power__strict__decreasing, fact_power__strict__increasing,
% 279.69/41.82 fact_power__strict__increasing__iff, fact_power__strict__mono,
% 279.69/41.82 fact_q__neg__lemma, fact_q__pos__lemma, fact_rcis__mult,
% 279.69/41.82 fact_real__add__left__mono, fact_real__add__mult__distrib, fact_real__diff__def,
% 279.69/41.82 fact_real__le__antisym, fact_real__le__linear, fact_real__le__refl,
% 279.69/41.82 fact_real__le__trans, fact_real__less__def, fact_real__minus__mult__self__le,
% 279.69/41.82 fact_real__mult__assoc, fact_real__mult__commute, fact_real__natceiling__ge,
% 279.69/41.82 fact_real__norm__def, fact_real__of__nat__add, fact_real__of__nat__diff,
% 279.69/41.82 fact_real__of__nat__inject, fact_real__of__nat__le__iff,
% 279.69/41.82 fact_real__of__nat__less__iff, fact_real__of__nat__mult,
% 279.69/41.82 fact_real__of__nat__power, fact_real__scaleR__def,
% 279.69/41.82 fact_real__squared__diff__one__factored,
% 279.69/41.82 fact_real__vector_Oscale__left__distrib, fact_real__vector_Oscale__scale,
% 279.69/41.82 fact_realpow__minus__mult, fact_realpow__num__eq__if, fact_right__minus,
% 279.69/41.82 fact_right__minus__eq, fact_scaleR_Oadd__left, fact_scaleR_Oadd__right,
% 279.69/41.82 fact_scaleR_Obounded, fact_scaleR_Odiff__left, fact_scaleR_Odiff__right,
% 279.69/41.82 fact_scaleR_Ominus__left, fact_scaleR_Ominus__right,
% 279.69/41.82 fact_scaleR_Oprod__diff__prod, fact_scaleR_OscaleR__left,
% 279.69/41.82 fact_scaleR_OscaleR__right, fact_scaleR_Ozero__right,
% 279.69/41.82 fact_scaleR__cancel__right, fact_scaleR__left_Oadd, fact_scaleR__left_Obounded,
% 279.69/41.82 fact_scaleR__left_Odiff, fact_scaleR__left_Ominus, fact_scaleR__left_OscaleR,
% 279.69/41.82 fact_scaleR__left__commute, fact_scaleR__left__diff__distrib,
% 279.69/41.82 fact_scaleR__minus__left, fact_scaleR__minus__right, fact_scaleR__right_Oadd,
% 279.69/41.82 fact_scaleR__right_Obounded, fact_scaleR__right_Odiff,
% 279.69/41.82 fact_scaleR__right_OscaleR, fact_scaleR__right_Ozero,
% 279.69/41.82 fact_scaleR__right__imp__eq, fact_self__quotient__aux1,
% 279.69/41.82 fact_self__quotient__aux2, fact_split__mult__neg__le, fact_split__mult__pos__le,
% 279.69/41.82 fact_square__eq__1__iff, fact_square__eq__iff, fact_sum__squares__eq__zero__iff,
% 279.69/41.82 fact_sum__squares__ge__zero, fact_sum__squares__gt__zero__iff,
% 279.69/41.82 fact_sum__squares__le__zero__iff, fact_termination__basic__simps_I1_J,
% 279.69/41.82 fact_termination__basic__simps_I2_J, fact_termination__basic__simps_I3_J,
% 279.69/41.82 fact_termination__basic__simps_I4_J, fact_termination__basic__simps_I5_J,
% 279.69/41.82 fact_times_Oidem, fact_trans__le__add1, fact_trans__le__add2,
% 279.69/41.82 fact_trans__less__add1, fact_trans__less__add2, fact_tsub__def, fact_tsub__eq,
% 279.69/41.82 fact_uminus__apply, fact_unique__quotient__lemma,
% 279.69/41.82 fact_unique__quotient__lemma__neg, fact_xt1_I10_J, fact_xt1_I11_J,
% 279.69/41.82 fact_xt1_I12_J, fact_xt1_I1_J, fact_xt1_I2_J, fact_xt1_I3_J, fact_xt1_I4_J,
% 279.69/41.82 fact_xt1_I5_J, fact_xt1_I6_J, fact_xt1_I7_J, fact_xt1_I8_J, fact_xt1_I9_J,
% 279.69/41.82 fact_zabs__def, fact_zabs__less__one__iff, fact_zadd__0, fact_zadd__0__right,
% 279.69/41.82 fact_zadd__assoc, fact_zadd__commute, fact_zadd__left__commute,
% 279.69/41.82 fact_zadd__left__mono, fact_zadd__strict__right__mono, fact_zadd__zless__mono,
% 279.69/41.82 fact_zadd__zminus__inverse2, fact_zadd__zmult__distrib,
% 279.69/41.82 fact_zadd__zmult__distrib2, fact_zdiff__zmult__distrib,
% 279.69/41.82 fact_zdiff__zmult__distrib2, fact_zdiv__mono2__lemma,
% 279.69/41.82 fact_zdiv__mono2__neg__lemma,
% 279.69/41.82 fact_zero__le__double__add__iff__zero__le__single__add,
% 279.69/41.82 fact_zero__le__mult__iff, fact_zero__le__natceiling, fact_zero__le__natfloor,
% 279.69/41.82 fact_zero__le__power, fact_zero__le__power__abs, fact_zero__le__square,
% 279.69/41.82 fact_zero__le__zpower__abs, fact_zero__less__Suc, fact_zero__less__abs__iff,
% 279.69/41.82 fact_zero__less__diff,
% 279.69/41.82 fact_zero__less__double__add__iff__zero__less__single__add,
% 279.69/41.82 fact_zero__less__mult__pos, fact_zero__less__mult__pos2, fact_zero__less__power,
% 279.69/41.82 fact_zero__less__power__nat__eq, fact_zero__less__two,
% 279.69/41.82 fact_zero__less__zpower__abs__iff, fact_zero__neq__one, fact_zero__reorient,
% 279.69/41.82 fact_zle__add1__eq__le, fact_zle__antisym, fact_zle__diff1__eq,
% 279.69/41.82 fact_zle__linear, fact_zle__refl, fact_zle__trans, fact_zless__add1__eq,
% 279.69/41.82 fact_zless__imp__add1__zle, fact_zless__le, fact_zless__linear, fact_zminus__0,
% 279.69/41.82 fact_zminus__zadd__distrib, fact_zminus__zminus, fact_zmult__1,
% 279.69/41.82 fact_zmult__1__right, fact_zmult__assoc, fact_zmult__commute,
% 279.69/41.82 fact_zmult__zless__mono2, fact_zmult__zminus, fact_zpower__zadd__distrib,
% 279.69/41.82 fact_zpower__zpower
% 279.69/41.82
% 279.69/41.82 Those formulas are unsatisfiable:
% 279.69/41.82 ---------------------------------
% 279.69/41.82
% 279.69/41.82 Begin of proof
% 279.69/41.83 |
% 279.69/41.83 | ALPHA: (fact__096cmod_A_Iw_A_L_Az_A_L_A_N_Az_J_A_N_Acmod_A_Iw_A_L_Az_J_A_060_061_Acmod_A_I_N_Az_J_096)
% 279.69/41.83 | implies:
% 279.69/41.83 | (1) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 279.69/41.83 | ? [v5: $i] : ? [v6: $i] :
% 279.69/41.83 | (c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_z) = v1 &
% 279.69/41.83 | c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v0, v1) = v2 &
% 279.69/41.83 | c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v_w, v_z) = v0 &
% 279.69/41.83 | c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v3, v4) = v5 &
% 279.69/41.83 | c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v2) = v3 &
% 279.69/41.83 | c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v1) = v6 &
% 279.69/41.83 | c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v0) = v4 &
% 279.69/41.83 | $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) &
% 279.69/41.83 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, v6))
% 279.69/41.83 |
% 279.69/41.83 | ALPHA: (fact_norm__triangle__ineq4) implies:
% 279.69/41.83 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 279.69/41.83 | ! [v5: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v4)
% 279.69/41.83 | = v5) | ~ (c_RealVector_Onorm__class_Onorm(v2, v1) = v3) | ~
% 279.69/41.83 | (c_RealVector_Onorm__class_Onorm(v2, v0) = v4) | ~ $i(v2) | ~
% 279.69/41.83 | $i(v1) | ~ $i(v0) | ~ class_RealVector_Oreal__normed__vector(v2) |
% 279.69/41.83 | ? [v6: $i] : ? [v7: $i] : (c_Groups_Ominus__class_Ominus(v2, v1, v0)
% 279.69/41.83 | = v6 & c_RealVector_Onorm__class_Onorm(v2, v6) = v7 & $i(v7) &
% 279.69/41.83 | $i(v6) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v7,
% 279.69/41.83 | v5)))
% 279.69/41.83 |
% 279.69/41.83 | ALPHA: (fact_abs__norm__cancel) implies:
% 279.69/41.83 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 279.69/41.83 | (c_RealVector_Onorm__class_Onorm(v1, v0) = v2) | ~ $i(v1) | ~
% 279.69/41.83 | $i(v0) | ~ class_RealVector_Oreal__normed__vector(v1) |
% 279.69/41.83 | (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v2) = v2 & $i(v2)))
% 279.69/41.83 |
% 279.69/41.83 | ALPHA: (fact_complex__diff__def) implies:
% 279.69/41.83 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 279.69/41.83 | (c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v0) = v2) | ~
% 279.69/41.83 | (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v1, v2) = v3) | ~
% 279.69/41.83 | $i(v1) | ~ $i(v0) |
% 279.69/41.83 | (c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v1, v0) = v3 &
% 279.69/41.83 | $i(v3)))
% 279.69/41.83 |
% 279.69/41.83 | ALPHA: (fact_rcis__zero__mod) implies:
% 279.69/41.83 | (5) ? [v0: $i] : ? [v1: $i] :
% 279.69/41.83 | (c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v1 &
% 279.69/41.83 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 279.69/41.83 | & ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~ (c_Complex_Orcis(v0, v2)
% 279.69/41.83 | = v3) | ~ $i(v2)))
% 279.69/41.83 |
% 279.69/41.83 | ALPHA: (fact_Re_Ozero) implies:
% 279.69/41.83 | (6) ? [v0: $i] : ? [v1: $i] : (c_Complex_ORe(v0) = v1 &
% 279.69/41.83 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v0 &
% 279.69/41.83 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0))
% 279.69/41.83 |
% 279.69/41.83 | ALPHA: (fact_Im_Ozero) implies:
% 279.69/41.83 | (7) ? [v0: $i] : ? [v1: $i] : (c_Complex_OIm(v0) = v1 &
% 279.69/41.83 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v0 &
% 279.69/41.83 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0))
% 279.69/41.83 |
% 279.69/41.83 | ALPHA: (fact_scaleR__left__imp__eq) implies:
% 279.69/41.83 | (8) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 279.69/41.83 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 279.69/41.83 | [v5: $i] : (v3 = v0 | v2 = v1 | ~
% 279.69/41.83 | (c_RealVector_OscaleR__class_OscaleR(v4, v3, v2) = v5) | ~
% 279.69/41.83 | (c_RealVector_OscaleR__class_OscaleR(v4, v3, v1) = v5) | ~ $i(v4)
% 279.69/41.83 | | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 279.69/41.83 | class_RealVector_Oreal__vector(v4)))
% 279.69/41.83 |
% 279.69/41.83 | ALPHA: (fact_scaleR__cancel__left) implies:
% 279.69/41.84 | (9) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 279.69/41.84 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 279.69/41.84 | [v5: $i] : (v5 = v4 | ~ (c_RealVector_OscaleR__class_OscaleR(v3, v0,
% 279.69/41.84 | v2) = v4) | ~ (c_RealVector_OscaleR__class_OscaleR(v3, v0, v1)
% 279.69/41.84 | = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 279.69/41.84 | class_RealVector_Oreal__vector(v3)) & ! [v1: $i] : ! [v2: $i] :
% 279.69/41.84 | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v3 = v0 | v2 = v1 | ~
% 279.69/41.84 | (c_RealVector_OscaleR__class_OscaleR(v4, v3, v2) = v5) | ~
% 279.69/41.84 | (c_RealVector_OscaleR__class_OscaleR(v4, v3, v1) = v5) | ~ $i(v4)
% 279.69/41.84 | | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 279.69/41.84 | class_RealVector_Oreal__vector(v4)))
% 279.69/41.84 |
% 279.69/41.84 | ALPHA: (fact_scaleR__eq__0__iff) implies:
% 279.69/41.84 | (10) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 279.69/41.84 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 279.69/41.84 | (c_RealVector_OscaleR__class_OscaleR(v3, v2, v1) = v4) | ~ $i(v3)
% 279.69/41.84 | | ~ $i(v2) | ~ $i(v1) | ~ class_RealVector_Oreal__vector(v3) |
% 279.69/41.84 | ? [v5: $i] : (c_Groups_Ozero__class_Ozero(v3) = v5 & $i(v5) & ( ~
% 279.69/41.84 | (v5 = v4) | v4 = v1 | v2 = v0) & (v5 = v4 | ( ~ (v5 = v1) & ~
% 279.69/41.84 | (v2 = v0))))))
% 279.69/41.84 |
% 279.69/41.84 | ALPHA: (fact_dist__eq__0__iff) implies:
% 279.69/41.84 | (11) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 279.69/41.84 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~
% 279.69/41.84 | (c_RealVector_Odist__class_Odist(v2, v1, v1) = v3) | ~ $i(v2) |
% 279.69/41.84 | ~ $i(v1) | ~ class_RealVector_Ometric__space(v2)) & ! [v1: $i] :
% 279.69/41.84 | ! [v2: $i] : ! [v3: $i] : (v2 = v1 | ~
% 279.69/41.84 | (c_RealVector_Odist__class_Odist(v3, v2, v1) = v0) | ~ $i(v3) |
% 279.69/41.84 | ~ $i(v2) | ~ $i(v1) | ~ class_RealVector_Ometric__space(v3)))
% 279.69/41.84 |
% 279.69/41.84 | ALPHA: (fact_dist__self) implies:
% 279.69/41.84 | (12) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 279.69/41.84 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~
% 279.69/41.84 | (c_RealVector_Odist__class_Odist(v2, v1, v1) = v3) | ~ $i(v2) |
% 279.69/41.84 | ~ $i(v1) | ~ class_RealVector_Ometric__space(v2)))
% 279.69/41.84 |
% 279.69/41.84 | ALPHA: (fact_zero__less__dist__iff) implies:
% 279.69/41.84 | (13) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 279.69/41.84 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2
% 279.69/41.84 | = v1 | ~ (c_RealVector_Odist__class_Odist(v3, v2, v1) = v4) | ~
% 279.69/41.84 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 279.69/41.84 | class_RealVector_Ometric__space(v3) |
% 279.69/41.84 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4)) & ! [v1:
% 279.69/41.84 | $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 279.69/41.84 | (c_RealVector_Odist__class_Odist(v2, v1, v1) = v3) | ~ $i(v2) |
% 279.69/41.84 | ~ $i(v1) | ~ class_RealVector_Ometric__space(v2) | ~
% 279.69/41.84 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3)))
% 279.69/41.84 |
% 279.69/41.84 | ALPHA: (fact_zero__less__norm__iff) implies:
% 279.69/41.84 | (14) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 279.69/41.84 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 279.69/41.84 | (c_RealVector_Onorm__class_Onorm(v2, v1) = v3) | ~ $i(v2) | ~
% 279.69/41.84 | $i(v1) | ~ class_RealVector_Oreal__normed__vector(v2) | ? [v4:
% 279.69/41.84 | $i] : (( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0,
% 279.69/41.84 | v3) | ( ~ (v4 = v1) & c_Groups_Ozero__class_Ozero(v2) = v4 &
% 279.69/41.84 | $i(v4))) & (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 279.69/41.84 | v0, v3) | (v4 = v1 & c_Groups_Ozero__class_Ozero(v2) =
% 279.69/41.84 | v1)))))
% 279.69/41.84 |
% 279.69/41.84 | ALPHA: (fact_scaleR__left_Ozero) implies:
% 279.69/41.84 | (15) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 279.69/41.84 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 279.69/41.84 | (c_RealVector_OscaleR__class_OscaleR(v2, v0, v1) = v3) | ~ $i(v2)
% 279.69/41.84 | | ~ $i(v1) | ~ class_RealVector_Oreal__vector(v2) |
% 279.69/41.84 | (c_Groups_Ozero__class_Ozero(v2) = v3 & $i(v3))))
% 279.69/41.84 |
% 279.69/41.84 | ALPHA: (fact_scaleR_Ozero__left) implies:
% 279.69/41.84 | (16) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 279.69/41.84 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 279.69/41.84 | (c_RealVector_OscaleR__class_OscaleR(v2, v0, v1) = v3) | ~ $i(v2)
% 279.69/41.84 | | ~ $i(v1) | ~ class_RealVector_Oreal__normed__vector(v2) |
% 279.69/41.84 | (c_Groups_Ozero__class_Ozero(v2) = v3 & $i(v3))))
% 279.69/41.84 |
% 279.69/41.84 | ALPHA: (fact_dist__not__less__zero) implies:
% 279.69/41.84 | (17) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 279.69/41.84 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 279.69/41.84 | (c_RealVector_Odist__class_Odist(v3, v2, v1) = v4) | ~ $i(v3) |
% 279.69/41.84 | ~ $i(v2) | ~ $i(v1) | ~ class_RealVector_Ometric__space(v3) | ~
% 279.69/41.84 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v4, v0)))
% 279.69/41.84 |
% 279.69/41.84 | ALPHA: (fact_norm__not__less__zero) implies:
% 279.69/41.84 | (18) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 279.69/41.84 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 279.69/41.84 | (c_RealVector_Onorm__class_Onorm(v2, v1) = v3) | ~ $i(v2) | ~
% 279.69/41.84 | $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3,
% 279.69/41.84 | v0) | ~ class_RealVector_Oreal__normed__vector(v2)))
% 279.69/41.84 |
% 279.69/41.84 | ALPHA: (fact_zero__le__dist) implies:
% 279.69/41.84 | (19) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 279.69/41.84 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 279.69/41.84 | (c_RealVector_Odist__class_Odist(v3, v2, v1) = v4) | ~ $i(v3) |
% 279.69/41.84 | ~ $i(v2) | ~ $i(v1) | ~ class_RealVector_Ometric__space(v3) |
% 279.69/41.84 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v4)))
% 279.69/41.84 |
% 279.69/41.84 | ALPHA: (fact_dist__le__zero__iff) implies:
% 279.69/41.84 | (20) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 279.69/41.84 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2
% 279.69/41.84 | = v1 | ~ (c_RealVector_Odist__class_Odist(v3, v2, v1) = v4) | ~
% 279.69/41.84 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 279.69/41.84 | class_RealVector_Ometric__space(v3) | ~
% 279.69/41.84 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v0)) & !
% 279.69/41.84 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 279.69/41.84 | (c_RealVector_Odist__class_Odist(v2, v1, v1) = v3) | ~ $i(v2) |
% 279.69/41.84 | ~ $i(v1) | ~ class_RealVector_Ometric__space(v2) |
% 279.69/41.84 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v0)))
% 279.69/41.84 |
% 279.69/41.84 | ALPHA: (fact_real__add__less__0__iff) implies:
% 279.69/41.84 | (21) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 279.69/41.84 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 279.69/41.84 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v1) = v3) | ~
% 279.69/41.84 | $i(v2) | ~ $i(v1) | ~
% 279.69/41.84 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v0) | ? [v4:
% 279.69/41.84 | $i] : (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v2) =
% 279.69/41.84 | v4 & $i(v4) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 279.69/41.84 | v1, v4))) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 279.69/41.84 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v1) = v3) | ~
% 279.69/41.84 | $i(v2) | ~ $i(v1) |
% 279.69/41.84 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v0) | ? [v4:
% 279.69/41.84 | $i] : (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v2) =
% 279.69/41.84 | v4 & $i(v4) & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 279.69/41.84 | v1, v4))))
% 279.69/41.84 |
% 279.69/41.84 | ALPHA: (fact_real__0__less__add__iff) implies:
% 279.69/41.84 | (22) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 279.69/41.84 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 279.69/41.85 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v1) = v3) | ~
% 279.69/41.85 | $i(v2) | ~ $i(v1) | ~
% 279.69/41.85 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | ? [v4:
% 279.69/41.85 | $i] : (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v2) =
% 279.69/41.85 | v4 & $i(v4) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 279.69/41.85 | v4, v1))) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 279.69/41.85 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v1) = v3) | ~
% 279.69/41.85 | $i(v2) | ~ $i(v1) |
% 279.69/41.85 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | ? [v4:
% 279.69/41.85 | $i] : (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v2) =
% 279.69/41.85 | v4 & $i(v4) & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 279.69/41.85 | v4, v1))))
% 279.69/41.85 |
% 279.69/41.85 | ALPHA: (fact_norm__zero) implies:
% 279.69/41.85 | (23) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 279.69/41.85 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~
% 279.69/41.85 | (c_Groups_Ozero__class_Ozero(v1) = v2) | ~
% 279.69/41.85 | (c_RealVector_Onorm__class_Onorm(v1, v2) = v3) | ~ $i(v1) | ~
% 279.69/41.85 | class_RealVector_Oreal__normed__vector(v1)))
% 279.69/41.85 |
% 279.69/41.85 | ALPHA: (fact_norm__eq__zero) implies:
% 279.69/41.85 | (24) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 279.69/41.85 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 279.69/41.85 | (c_RealVector_Onorm__class_Onorm(v2, v1) = v3) | ~ $i(v2) | ~
% 279.69/41.85 | $i(v1) | ~ class_RealVector_Oreal__normed__vector(v2) | ? [v4:
% 279.69/41.85 | $i] : (( ~ (v3 = v0) | (v4 = v1 &
% 279.69/41.85 | c_Groups_Ozero__class_Ozero(v2) = v1)) & (v3 = v0 | ( ~ (v4
% 279.69/41.85 | = v1) & c_Groups_Ozero__class_Ozero(v2) = v4 & $i(v4))))))
% 279.69/41.85 |
% 279.69/41.85 | ALPHA: (fact_real__abs__def) implies:
% 279.69/41.85 | (25) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 279.69/41.85 | $i(v0) & ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~
% 279.69/41.85 | (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v1) = v2) | ~ $i(v1)
% 279.69/41.85 | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v0)) & !
% 279.69/41.85 | [v1: $i] : ! [v2: $i] : ( ~
% 279.69/41.85 | (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v1) = v2) | ~ $i(v1)
% 279.69/41.85 | | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v0) |
% 279.69/41.85 | (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v1) = v2 &
% 279.69/41.85 | $i(v2))))
% 279.69/41.85 |
% 279.69/41.85 | ALPHA: (fact_norm__le__zero__iff) implies:
% 279.69/41.85 | (26) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 279.69/41.85 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 279.69/41.85 | (c_RealVector_Onorm__class_Onorm(v2, v1) = v3) | ~ $i(v2) | ~
% 279.69/41.85 | $i(v1) | ~ class_RealVector_Oreal__normed__vector(v2) | ? [v4:
% 279.69/41.85 | $i] : (( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 279.69/41.85 | v3, v0) | (v4 = v1 & c_Groups_Ozero__class_Ozero(v2) = v1))
% 279.69/41.85 | & (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v0) |
% 279.69/41.85 | ( ~ (v4 = v1) & c_Groups_Ozero__class_Ozero(v2) = v4 &
% 279.69/41.85 | $i(v4))))))
% 279.69/41.85 |
% 279.69/41.85 | ALPHA: (fact_real__add__eq__0__iff) implies:
% 279.69/41.85 | (27) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 279.69/41.85 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~
% 279.69/41.85 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v1) = v3) | ~
% 279.69/41.85 | $i(v2) | ~ $i(v1) | ? [v4: $i] : ( ~ (v4 = v1) &
% 279.69/41.85 | c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v2) = v4 &
% 279.69/41.85 | $i(v4))) & ! [v1: $i] : ! [v2: $i] : ( ~
% 279.69/41.85 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v1) = v0) | ~
% 279.69/41.85 | $i(v2) | ~ $i(v1) |
% 279.69/41.85 | c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v2) = v1))
% 279.69/41.85 |
% 279.69/41.85 | ALPHA: (fact_real__add__minus__iff) implies:
% 279.69/41.85 | (28) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 279.69/41.85 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~
% 279.69/41.85 | (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v1) = v2) | ~
% 279.69/41.85 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1, v2) = v3) | ~
% 279.69/41.85 | $i(v1)) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v1 | ~
% 279.69/41.85 | (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v1) = v3) | ~
% 279.69/41.85 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v3) = v0) | ~
% 279.69/41.85 | $i(v2) | ~ $i(v1)))
% 279.69/41.85 |
% 279.69/41.85 | ALPHA: (fact_norm__ge__zero) implies:
% 279.69/41.85 | (29) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 279.69/41.85 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 279.69/41.85 | (c_RealVector_Onorm__class_Onorm(v2, v1) = v3) | ~ $i(v2) | ~
% 279.69/41.85 | $i(v1) | ~ class_RealVector_Oreal__normed__vector(v2) |
% 279.69/41.85 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3)))
% 279.69/41.85 |
% 279.69/41.85 | ALPHA: (fact_real__add__le__0__iff) implies:
% 279.69/41.85 | (30) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 279.69/41.85 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 279.69/41.85 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v1) = v3) | ~
% 279.69/41.85 | $i(v2) | ~ $i(v1) | ~
% 279.69/41.85 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v0) | ?
% 279.69/41.85 | [v4: $i] : (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v2)
% 279.69/41.85 | = v4 & $i(v4) &
% 279.69/41.85 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v4))) &
% 279.69/41.85 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 279.69/41.85 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v1) = v3) | ~
% 279.69/41.85 | $i(v2) | ~ $i(v1) |
% 279.69/41.85 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v0) | ?
% 279.69/41.85 | [v4: $i] : (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v2)
% 279.69/41.85 | = v4 & $i(v4) & ~
% 279.69/41.85 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v4))))
% 279.69/41.85 |
% 279.69/41.85 | ALPHA: (fact_real__0__le__add__iff) implies:
% 279.69/41.85 | (31) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 279.69/41.85 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 279.69/41.85 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v1) = v3) | ~
% 279.69/41.85 | $i(v2) | ~ $i(v1) | ~
% 279.69/41.85 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) | ?
% 279.69/41.85 | [v4: $i] : (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v2)
% 279.69/41.85 | = v4 & $i(v4) &
% 279.69/41.85 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v1))) &
% 279.69/41.85 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 279.69/41.85 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v1) = v3) | ~
% 279.69/41.85 | $i(v2) | ~ $i(v1) |
% 279.69/41.85 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) | ?
% 279.69/41.85 | [v4: $i] : (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v2)
% 279.69/41.85 | = v4 & $i(v4) & ~
% 279.69/41.85 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v1))))
% 279.69/41.85 |
% 279.69/41.85 | ALPHA: (fact_real__le__eq__diff) implies:
% 279.69/41.85 | (32) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 279.69/41.85 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 279.69/41.85 | (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v2, v1) = v3) |
% 279.69/41.85 | ~ $i(v2) | ~ $i(v1) | ~
% 279.69/41.85 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v0) |
% 279.69/41.85 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v1)) & !
% 279.69/41.85 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 279.69/41.85 | (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v2, v1) = v3) |
% 279.69/41.85 | ~ $i(v2) | ~ $i(v1) | ~
% 279.69/41.85 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v1) |
% 279.69/41.85 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v0)))
% 279.69/41.85 |
% 279.69/41.85 | ALPHA: (fact_lemma__interval) implies:
% 279.69/41.85 | (33) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 279.69/41.85 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~
% 279.69/41.85 | $i(v2) | ~ $i(v1) | ~
% 279.69/41.85 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v2) | ~
% 279.69/41.85 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v1) | ? [v4:
% 279.69/41.85 | $i] : ($i(v4) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 279.69/41.85 | v0, v4) & ! [v5: $i] : ! [v6: $i] : ( ~
% 279.69/41.85 | (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v2, v5) = v6)
% 279.69/41.85 | | ~ $i(v5) |
% 279.69/41.85 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, v1) |
% 279.69/41.85 | ? [v7: $i] : (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v6)
% 279.69/41.85 | = v7 & $i(v7) & ~
% 279.69/41.85 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v7, v4))) &
% 279.69/41.85 | ! [v5: $i] : ! [v6: $i] : ( ~
% 279.69/41.85 | (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v2, v5) = v6)
% 279.69/41.85 | | ~ $i(v5) |
% 279.69/41.85 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v5) |
% 279.69/41.85 | ? [v7: $i] : (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v6)
% 279.69/41.85 | = v7 & $i(v7) & ~
% 279.69/41.85 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v7, v4))))))
% 279.69/41.85 |
% 279.69/41.85 | ALPHA: (fact_Complex__eq__0) implies:
% 279.69/41.86 | (34) ? [v0: $i] : ? [v1: $i] :
% 279.69/41.86 | (c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v0 &
% 279.69/41.86 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0)
% 279.69/41.86 | & ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~
% 279.69/41.86 | (c_Complex_Ocomplex_OComplex(v3, v2) = v0) | ~ $i(v3) | ~
% 279.69/41.86 | $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v2 = v1 | ~
% 279.69/41.86 | (c_Complex_Ocomplex_OComplex(v3, v2) = v0) | ~ $i(v3) | ~
% 279.69/41.86 | $i(v2)) & ! [v2: $i] : (v2 = v0 | ~
% 279.69/41.86 | (c_Complex_Ocomplex_OComplex(v1, v1) = v2)))
% 279.69/41.86 |
% 279.69/41.86 | ALPHA: (fact_complex__zero__def) implies:
% 279.69/41.86 | (35) ? [v0: $i] : ? [v1: $i] : (c_Complex_Ocomplex_OComplex(v1, v1) = v0
% 279.69/41.86 | & c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v0 &
% 279.69/41.86 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v1) &
% 279.69/41.86 | $i(v0))
% 279.69/41.86 |
% 279.69/41.86 | ALPHA: (fact_lemma__interval__lt) implies:
% 279.69/41.86 | (36) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 279.69/41.86 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~
% 279.69/41.86 | $i(v2) | ~ $i(v1) | ~
% 279.69/41.86 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v2) | ~
% 279.69/41.86 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v1) | ? [v4:
% 279.69/41.86 | $i] : ($i(v4) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 279.69/41.86 | v0, v4) & ! [v5: $i] : ! [v6: $i] : ( ~
% 279.69/41.86 | (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v2, v5) = v6)
% 279.69/41.86 | | ~ $i(v5) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 279.69/41.86 | v5, v1) | ? [v7: $i] :
% 279.69/41.86 | (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v6) = v7 & $i(v7)
% 279.69/41.86 | & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v7,
% 279.69/41.86 | v4))) & ! [v5: $i] : ! [v6: $i] : ( ~
% 279.69/41.86 | (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v2, v5) = v6)
% 279.69/41.86 | | ~ $i(v5) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 279.69/41.86 | v3, v5) | ? [v7: $i] :
% 279.69/41.86 | (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v6) = v7 & $i(v7)
% 279.69/41.86 | & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v7,
% 279.69/41.86 | v4))))))
% 279.69/41.86 |
% 279.69/41.86 | ALPHA: (fact_real__mult__right__cancel) implies:
% 279.69/41.86 | (37) ? [v0: $i] : ? [v1: $i] :
% 279.69/41.86 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 279.69/41.86 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 279.69/41.86 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 279.69/41.86 | $i] : ! [v7: $i] : (v4 = v0 | v3 = v2 | ~ (hAPP(v7, v4) = v6) |
% 279.69/41.86 | ~ (hAPP(v5, v4) = v6) | ~ (hAPP(v1, v3) = v5) | ~ (hAPP(v1, v2)
% 279.69/41.86 | = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2)))
% 279.69/41.86 |
% 279.69/41.86 | ALPHA: (fact_real__mult__left__cancel) implies:
% 279.69/41.86 | (38) ? [v0: $i] : ? [v1: $i] :
% 279.69/41.86 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 279.69/41.86 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 279.69/41.86 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 279.69/41.86 | $i] : (v4 = v0 | v3 = v2 | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5,
% 279.69/41.86 | v2) = v6) | ~ (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) |
% 279.69/41.86 | ~ $i(v2)))
% 279.69/41.86 |
% 279.69/41.86 | ALPHA: (fact_real__mult__less__mono2) implies:
% 279.69/41.86 | (39) ? [v0: $i] : ? [v1: $i] :
% 279.69/41.86 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 279.69/41.86 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 279.69/41.86 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 279.69/41.86 | $i] : ! [v7: $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) =
% 279.69/41.86 | v7) | ~ (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2)
% 279.69/41.86 | | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v2) | ~
% 279.69/41.86 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) |
% 279.69/41.86 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v6, v7)))
% 279.69/41.86 |
% 279.69/41.86 | ALPHA: (fact_real__mult__order) implies:
% 279.69/41.86 | (40) ? [v0: $i] : ? [v1: $i] :
% 279.69/41.86 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 279.69/41.86 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 279.69/41.86 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 279.69/41.86 | (hAPP(v4, v2) = v5) | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~
% 279.69/41.86 | $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0,
% 279.69/41.86 | v3) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2)
% 279.69/41.86 | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v5)))
% 279.69/41.86 |
% 279.69/41.86 | ALPHA: (fact_real__mult__less__iff1) implies:
% 279.69/41.86 | (41) ? [v0: $i] : ? [v1: $i] :
% 279.69/41.86 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 279.69/41.86 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 279.69/41.86 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 279.69/41.86 | $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (hAPP(v7, v4) = v8) | ~
% 279.69/41.86 | (hAPP(v5, v4) = v6) | ~ (hAPP(v1, v3) = v5) | ~ (hAPP(v1, v2) =
% 279.69/41.86 | v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 279.69/41.86 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v6, v8) | ~
% 279.69/41.86 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) |
% 279.69/41.86 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v2)) & ! [v2:
% 279.69/41.86 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 279.69/41.86 | [v7: $i] : ! [v8: $i] : ( ~ (hAPP(v7, v4) = v8) | ~ (hAPP(v5, v4)
% 279.69/41.86 | = v6) | ~ (hAPP(v1, v3) = v5) | ~ (hAPP(v1, v2) = v7) | ~
% 279.69/41.86 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 279.69/41.86 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v2) | ~
% 279.69/41.86 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) |
% 279.69/41.86 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v6, v8)))
% 279.69/41.86 |
% 279.69/41.86 | ALPHA: (fact_real__two__squares__add__zero__iff) implies:
% 279.69/41.86 | (42) ? [v0: $i] : ? [v1: $i] :
% 279.69/41.86 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v0 &
% 279.69/41.86 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0)
% 279.69/41.86 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 279.69/41.86 | $i] : ! [v7: $i] : (v3 = v1 | ~
% 279.69/41.86 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v5, v7) = v1) | ~
% 279.69/41.86 | (hAPP(v6, v2) = v7) | ~ (hAPP(v4, v3) = v5) | ~ (hAPP(v0, v3) =
% 279.69/41.86 | v4) | ~ (hAPP(v0, v2) = v6) | ~ $i(v3) | ~ $i(v2)) & ! [v2:
% 279.69/41.86 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 279.69/41.86 | [v7: $i] : (v2 = v1 | ~
% 279.69/41.86 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v5, v7) = v1) | ~
% 279.69/41.86 | (hAPP(v6, v2) = v7) | ~ (hAPP(v4, v3) = v5) | ~ (hAPP(v0, v3) =
% 279.69/41.86 | v4) | ~ (hAPP(v0, v2) = v6) | ~ $i(v3) | ~ $i(v2)) & ! [v2:
% 279.69/41.86 | $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v1 | ~
% 279.69/41.86 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v3) = v4) | ~
% 279.69/41.86 | (hAPP(v2, v1) = v3) | ~ (hAPP(v0, v1) = v2)))
% 279.69/41.86 |
% 279.69/41.86 | ALPHA: (fact_real__mult__le__cancel__iff1) implies:
% 279.69/41.86 | (43) ? [v0: $i] : ? [v1: $i] :
% 279.69/41.86 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 279.69/41.86 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 279.69/41.86 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 279.69/41.86 | $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (hAPP(v7, v4) = v8) | ~
% 279.69/41.86 | (hAPP(v5, v4) = v6) | ~ (hAPP(v1, v3) = v5) | ~ (hAPP(v1, v2) =
% 279.69/41.86 | v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 279.69/41.86 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) | ~
% 279.69/41.86 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v8) |
% 279.69/41.86 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v2)) & !
% 279.69/41.86 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] :
% 279.69/41.86 | ! [v7: $i] : ! [v8: $i] : ( ~ (hAPP(v7, v4) = v8) | ~ (hAPP(v5,
% 279.69/41.86 | v4) = v6) | ~ (hAPP(v1, v3) = v5) | ~ (hAPP(v1, v2) = v7) |
% 279.69/41.86 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 279.69/41.86 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) | ~
% 279.69/41.86 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v2) |
% 279.69/41.86 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v8)))
% 279.69/41.86 |
% 279.69/41.86 | ALPHA: (fact_real__mult__le__cancel__iff2) implies:
% 280.01/41.87 | (44) ? [v0: $i] : ? [v1: $i] :
% 280.01/41.87 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 280.01/41.87 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 280.01/41.87 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 280.01/41.87 | $i] : ! [v7: $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) =
% 280.01/41.87 | v7) | ~ (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2)
% 280.01/41.87 | | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) | ~
% 280.01/41.87 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v7) |
% 280.01/41.87 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v2)) & !
% 280.01/41.87 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] :
% 280.01/41.87 | ! [v7: $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~
% 280.01/41.87 | (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 280.01/41.87 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) | ~
% 280.01/41.87 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v2) |
% 280.01/41.87 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v7)))
% 280.01/41.87 |
% 280.01/41.87 | ALPHA: (fact_norm__ratiotest__lemma) implies:
% 280.01/41.87 | (45) ? [v0: $i] : ? [v1: $i] :
% 280.01/41.87 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 280.01/41.87 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 280.01/41.87 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 280.01/41.87 | $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~
% 280.01/41.87 | (c_RealVector_Onorm__class_Onorm(v5, v3) = v6) | ~
% 280.01/41.87 | (c_RealVector_Onorm__class_Onorm(v5, v2) = v8) | ~ (hAPP(v7, v8)
% 280.01/41.87 | = v9) | ~ (hAPP(v1, v4) = v7) | ~ $i(v5) | ~ $i(v4) | ~
% 280.01/41.87 | $i(v3) | ~ $i(v2) | ~ class_RealVector_Oreal__normed__vector(v5)
% 280.01/41.87 | | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v9) |
% 280.01/41.87 | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v0) |
% 280.01/41.87 | c_Groups_Ozero__class_Ozero(v5) = v3))
% 280.01/41.87 |
% 280.01/41.87 | ALPHA: (fact_rabs__ratiotest__lemma) implies:
% 280.01/41.87 | (46) ? [v0: $i] : ? [v1: $i] :
% 280.01/41.87 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 280.01/41.87 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 280.01/41.87 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 280.01/41.87 | $i] : ! [v7: $i] : ! [v8: $i] : (v3 = v0 | ~
% 280.01/41.87 | (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v3) = v5) | ~
% 280.01/41.87 | (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v2) = v7) | ~
% 280.01/41.87 | (hAPP(v6, v7) = v8) | ~ (hAPP(v1, v4) = v6) | ~ $i(v4) | ~
% 280.01/41.87 | $i(v3) | ~ $i(v2) | ~
% 280.01/41.87 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, v8) | ~
% 280.01/41.87 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v0)))
% 280.01/41.87 |
% 280.01/41.87 | ALPHA: (fact_not__real__square__gt__zero) implies:
% 280.01/41.87 | (47) ? [v0: $i] : ? [v1: $i] :
% 280.01/41.87 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 280.01/41.87 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 280.01/41.87 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v0 | ~ (hAPP(v3,
% 280.01/41.87 | v2) = v4) | ~ (hAPP(v1, v2) = v3) | ~ $i(v2) |
% 280.01/41.87 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4)) & ! [v2:
% 280.01/41.87 | $i] : ! [v3: $i] : ( ~ (hAPP(v2, v0) = v3) | ~ (hAPP(v1, v0) =
% 280.01/41.87 | v2) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0,
% 280.01/41.87 | v3)))
% 280.01/41.87 |
% 280.01/41.87 | ALPHA: (fact_Im_Opos__bounded) implies:
% 280.01/41.87 | (48) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 280.01/41.87 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 280.01/41.87 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v2) & $i(v1)
% 280.01/41.87 | & $i(v0) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) &
% 280.01/41.87 | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 280.01/41.87 | (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v3) = v4) |
% 280.01/41.87 | ~ (hAPP(v5, v2) = v6) | ~ (hAPP(v1, v4) = v5) | ~ $i(v3) | ?
% 280.01/41.87 | [v7: $i] : ? [v8: $i] : (c_Complex_OIm(v3) = v7 &
% 280.01/41.87 | c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal, v7) = v8 &
% 280.01/41.87 | $i(v8) & $i(v7) &
% 280.01/41.87 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v8, v6))))
% 280.01/41.87 |
% 280.01/41.87 | ALPHA: (fact_Re_Opos__bounded) implies:
% 280.01/41.87 | (49) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 280.01/41.87 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 280.01/41.87 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v2) & $i(v1)
% 280.01/41.87 | & $i(v0) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) &
% 280.01/41.87 | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 280.01/41.87 | (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v3) = v4) |
% 280.01/41.87 | ~ (hAPP(v5, v2) = v6) | ~ (hAPP(v1, v4) = v5) | ~ $i(v3) | ?
% 280.01/41.87 | [v7: $i] : ? [v8: $i] : (c_Complex_ORe(v3) = v7 &
% 280.01/41.87 | c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal, v7) = v8 &
% 280.01/41.87 | $i(v8) & $i(v7) &
% 280.01/41.87 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v8, v6))))
% 280.01/41.87 |
% 280.01/41.87 | ALPHA: (fact_scaleR__left_Opos__bounded) implies:
% 280.01/41.87 | (50) ? [v0: $i] : ? [v1: $i] :
% 280.01/41.87 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 280.01/41.87 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 280.01/41.87 | & ? [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~
% 280.01/41.87 | class_RealVector_Oreal__normed__vector(v3) | ? [v4: $i] : ($i(v4)
% 280.01/41.87 | & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) & !
% 280.01/41.87 | [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~
% 280.01/41.87 | (c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal, v5) = v6) |
% 280.01/41.87 | ~ (hAPP(v7, v4) = v8) | ~ (hAPP(v1, v6) = v7) | ~ $i(v5) |
% 280.01/41.87 | ? [v9: $i] : ? [v10: $i] :
% 280.01/41.87 | (c_RealVector_OscaleR__class_OscaleR(v3, v5, v2) = v9 &
% 280.01/41.87 | c_RealVector_Onorm__class_Onorm(v3, v9) = v10 & $i(v10) &
% 280.01/41.87 | $i(v9) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 280.01/41.87 | v10, v8))))))
% 280.01/41.87 |
% 280.01/41.87 | ALPHA: (fact_scaleR_Opos__bounded) implies:
% 280.01/41.87 | (51) ? [v0: $i] : ? [v1: $i] :
% 280.01/41.87 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 280.01/41.87 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 280.01/41.87 | & ! [v2: $i] : ( ~ $i(v2) | ~
% 280.01/41.87 | class_RealVector_Oreal__normed__vector(v2) | ? [v3: $i] : ($i(v3)
% 280.01/41.87 | & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) & !
% 280.01/41.87 | [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i]
% 280.01/41.87 | : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~
% 280.01/41.87 | (c_RealVector_Onorm__class_Onorm(v2, v5) = v8) | ~
% 280.01/41.87 | (c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal, v4) = v6) |
% 280.01/41.87 | ~ (hAPP(v10, v3) = v11) | ~ (hAPP(v7, v8) = v9) | ~
% 280.01/41.87 | (hAPP(v1, v9) = v10) | ~ (hAPP(v1, v6) = v7) | ~ $i(v5) | ~
% 280.01/41.87 | $i(v4) | ? [v12: $i] : ? [v13: $i] :
% 280.01/41.87 | (c_RealVector_OscaleR__class_OscaleR(v2, v4, v5) = v12 &
% 280.01/41.87 | c_RealVector_Onorm__class_Onorm(v2, v12) = v13 & $i(v13) &
% 280.01/41.87 | $i(v12) &
% 280.01/41.87 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v13,
% 280.01/41.87 | v11))))))
% 280.01/41.87 |
% 280.01/41.87 | ALPHA: (fact_Im_Ononneg__bounded) implies:
% 280.01/41.87 | (52) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 280.01/41.87 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 280.01/41.87 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v2) & $i(v1)
% 280.01/41.87 | & $i(v0) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0,
% 280.01/41.87 | v2) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 280.01/41.87 | (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v3) = v4) |
% 280.01/41.87 | ~ (hAPP(v5, v2) = v6) | ~ (hAPP(v1, v4) = v5) | ~ $i(v3) | ?
% 280.01/41.87 | [v7: $i] : ? [v8: $i] : (c_Complex_OIm(v3) = v7 &
% 280.01/41.87 | c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal, v7) = v8 &
% 280.01/41.87 | $i(v8) & $i(v7) &
% 280.01/41.87 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v8, v6))))
% 280.01/41.87 |
% 280.01/41.87 | ALPHA: (fact_Re_Ononneg__bounded) implies:
% 280.01/41.87 | (53) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 280.01/41.87 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 280.01/41.87 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v2) & $i(v1)
% 280.01/41.87 | & $i(v0) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0,
% 280.01/41.87 | v2) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 280.01/41.87 | (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v3) = v4) |
% 280.01/41.87 | ~ (hAPP(v5, v2) = v6) | ~ (hAPP(v1, v4) = v5) | ~ $i(v3) | ?
% 280.01/41.87 | [v7: $i] : ? [v8: $i] : (c_Complex_ORe(v3) = v7 &
% 280.01/41.87 | c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal, v7) = v8 &
% 280.01/41.87 | $i(v8) & $i(v7) &
% 280.01/41.87 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v8, v6))))
% 280.01/41.87 |
% 280.01/41.87 | ALPHA: (fact_scaleR_Ononneg__bounded) implies:
% 280.01/41.87 | (54) ? [v0: $i] : ? [v1: $i] :
% 280.01/41.87 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 280.01/41.87 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 280.01/41.87 | & ! [v2: $i] : ( ~ $i(v2) | ~
% 280.01/41.87 | class_RealVector_Oreal__normed__vector(v2) | ? [v3: $i] : ($i(v3)
% 280.01/41.87 | & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) &
% 280.01/41.87 | ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8:
% 280.01/41.87 | $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~
% 280.01/41.87 | (c_RealVector_Onorm__class_Onorm(v2, v5) = v8) | ~
% 280.01/41.87 | (c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal, v4) = v6) |
% 280.01/41.87 | ~ (hAPP(v10, v3) = v11) | ~ (hAPP(v7, v8) = v9) | ~
% 280.01/41.87 | (hAPP(v1, v9) = v10) | ~ (hAPP(v1, v6) = v7) | ~ $i(v5) | ~
% 280.01/41.87 | $i(v4) | ? [v12: $i] : ? [v13: $i] :
% 280.01/41.87 | (c_RealVector_OscaleR__class_OscaleR(v2, v4, v5) = v12 &
% 280.01/41.87 | c_RealVector_Onorm__class_Onorm(v2, v12) = v13 & $i(v13) &
% 280.01/41.87 | $i(v12) &
% 280.01/41.87 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v13,
% 280.01/41.87 | v11))))))
% 280.01/41.87 |
% 280.01/41.87 | ALPHA: (fact_scaleR__left_Ononneg__bounded) implies:
% 280.01/41.87 | (55) ? [v0: $i] : ? [v1: $i] :
% 280.01/41.87 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 280.01/41.87 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 280.01/41.87 | & ? [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~
% 280.01/41.87 | class_RealVector_Oreal__normed__vector(v3) | ? [v4: $i] : ($i(v4)
% 280.01/41.87 | & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v4) &
% 280.01/41.87 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~
% 280.01/41.87 | (c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal, v5) = v6) |
% 280.01/41.87 | ~ (hAPP(v7, v4) = v8) | ~ (hAPP(v1, v6) = v7) | ~ $i(v5) |
% 280.01/41.87 | ? [v9: $i] : ? [v10: $i] :
% 280.01/41.87 | (c_RealVector_OscaleR__class_OscaleR(v3, v5, v2) = v9 &
% 280.01/41.87 | c_RealVector_Onorm__class_Onorm(v3, v9) = v10 & $i(v10) &
% 280.01/41.87 | $i(v9) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 280.01/41.87 | v10, v8))))))
% 280.01/41.87 |
% 280.01/41.87 | ALPHA: (fact_bounded__bilinear_Opos__bounded) implies:
% 280.01/41.87 | (56) ? [v0: $i] : ? [v1: $i] :
% 280.01/41.87 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 280.01/41.87 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 280.01/41.87 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ $i(v5)
% 280.01/41.87 | | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 280.01/41.87 | c_RealVector_Obounded__bilinear(v3, v4, v5, v2) | ~
% 280.01/41.87 | class_RealVector_Oreal__normed__vector(v5) | ~
% 280.01/41.87 | class_RealVector_Oreal__normed__vector(v4) | ~
% 280.01/41.87 | class_RealVector_Oreal__normed__vector(v3) | ? [v6: $i] : ($i(v6)
% 280.01/41.87 | & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v6) & !
% 280.01/41.87 | [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11:
% 280.01/41.87 | $i] : ! [v12: $i] : ! [v13: $i] : ! [v14: $i] : ( ~
% 280.01/41.87 | (c_RealVector_Onorm__class_Onorm(v4, v8) = v11) | ~
% 280.01/41.87 | (c_RealVector_Onorm__class_Onorm(v3, v7) = v9) | ~ (hAPP(v13,
% 280.01/41.87 | v6) = v14) | ~ (hAPP(v10, v11) = v12) | ~ (hAPP(v1, v12)
% 280.01/41.87 | = v13) | ~ (hAPP(v1, v9) = v10) | ~ $i(v8) | ~ $i(v7) |
% 280.01/41.87 | ? [v15: $i] : ? [v16: $i] : ? [v17: $i] :
% 280.01/41.87 | (c_RealVector_Onorm__class_Onorm(v5, v16) = v17 & hAPP(v15,
% 280.01/41.87 | v8) = v16 & hAPP(v2, v7) = v15 & $i(v17) & $i(v16) &
% 280.01/41.87 | $i(v15) &
% 280.01/41.87 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v17,
% 280.01/41.87 | v14))))))
% 280.01/41.87 |
% 280.01/41.87 | ALPHA: (fact_scaleR__right_Opos__bounded) implies:
% 280.01/41.87 | (57) ? [v0: $i] : ? [v1: $i] :
% 280.01/41.87 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 280.01/41.87 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 280.01/41.87 | & ? [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~
% 280.01/41.87 | class_RealVector_Oreal__normed__vector(v3) | ? [v4: $i] : ($i(v4)
% 280.01/41.87 | & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) & !
% 280.01/41.87 | [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~
% 280.01/41.87 | (c_RealVector_Onorm__class_Onorm(v3, v5) = v6) | ~ (hAPP(v7,
% 280.01/41.87 | v4) = v8) | ~ (hAPP(v1, v6) = v7) | ~ $i(v5) | ? [v9:
% 280.01/41.87 | $i] : ? [v10: $i] :
% 280.01/41.87 | (c_RealVector_OscaleR__class_OscaleR(v3, v2, v5) = v9 &
% 280.01/41.87 | c_RealVector_Onorm__class_Onorm(v3, v9) = v10 & $i(v10) &
% 280.01/41.87 | $i(v9) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 280.01/41.87 | v10, v8))))))
% 280.01/41.87 |
% 280.01/41.87 | ALPHA: (fact_mult_Opos__bounded) implies:
% 280.01/41.87 | (58) ? [v0: $i] : ? [v1: $i] :
% 280.01/41.87 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 280.01/41.87 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 280.01/41.87 | & ! [v2: $i] : ! [v3: $i] : ( ~ (c_Groups_Otimes__class_Otimes(v2)
% 280.01/41.87 | = v3) | ~ $i(v2) | ~
% 280.01/41.87 | class_RealVector_Oreal__normed__algebra(v2) | ? [v4: $i] :
% 280.01/41.87 | ($i(v4) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4)
% 280.01/41.87 | & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : !
% 280.01/41.87 | [v9: $i] : ! [v10: $i] : ! [v11: $i] : ! [v12: $i] : ( ~
% 280.01/41.87 | (c_RealVector_Onorm__class_Onorm(v2, v6) = v9) | ~
% 280.01/41.87 | (c_RealVector_Onorm__class_Onorm(v2, v5) = v7) | ~ (hAPP(v11,
% 280.01/41.87 | v4) = v12) | ~ (hAPP(v8, v9) = v10) | ~ (hAPP(v1, v10) =
% 280.01/41.87 | v11) | ~ (hAPP(v1, v7) = v8) | ~ $i(v6) | ~ $i(v5) | ?
% 280.01/41.87 | [v13: $i] : ? [v14: $i] : ? [v15: $i] :
% 280.01/41.87 | (c_RealVector_Onorm__class_Onorm(v2, v14) = v15 & hAPP(v13,
% 280.01/41.87 | v6) = v14 & hAPP(v3, v5) = v13 & $i(v15) & $i(v14) &
% 280.01/41.87 | $i(v13) &
% 280.01/41.87 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v15,
% 280.01/41.87 | v12))))))
% 280.01/41.87 |
% 280.01/41.87 | ALPHA: (fact_mult__left_Opos__bounded) implies:
% 280.01/41.87 | (59) ? [v0: $i] : ? [v1: $i] :
% 280.01/41.87 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 280.01/41.87 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 280.01/41.87 | & ? [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 280.01/41.87 | (c_Groups_Otimes__class_Otimes(v3) = v4) | ~ $i(v3) | ~ $i(v2) |
% 280.01/41.87 | ~ class_RealVector_Oreal__normed__algebra(v3) | ? [v5: $i] :
% 280.01/41.87 | ($i(v5) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v5)
% 280.01/41.87 | & ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~
% 280.01/41.87 | (c_RealVector_Onorm__class_Onorm(v3, v6) = v7) | ~ (hAPP(v8,
% 280.01/41.87 | v5) = v9) | ~ (hAPP(v1, v7) = v8) | ~ $i(v6) | ? [v10:
% 280.01/41.87 | $i] : ? [v11: $i] : ? [v12: $i] :
% 280.01/41.87 | (c_RealVector_Onorm__class_Onorm(v3, v11) = v12 & hAPP(v10,
% 280.01/41.87 | v2) = v11 & hAPP(v4, v6) = v10 & $i(v12) & $i(v11) &
% 280.01/41.87 | $i(v10) &
% 280.01/41.87 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v12,
% 280.01/41.87 | v9))))))
% 280.01/41.88 |
% 280.01/41.88 | ALPHA: (fact_mult__right_Opos__bounded) implies:
% 280.01/41.88 | (60) ? [v0: $i] : ? [v1: $i] :
% 280.01/41.88 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 280.01/41.88 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 280.01/41.88 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 280.01/41.88 | (c_Groups_Otimes__class_Otimes(v3) = v4) | ~ (hAPP(v4, v2) = v5)
% 280.01/41.88 | | ~ $i(v3) | ~ $i(v2) | ~
% 280.01/41.88 | class_RealVector_Oreal__normed__algebra(v3) | ? [v6: $i] :
% 280.01/41.88 | ($i(v6) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v6)
% 280.01/41.88 | & ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ( ~
% 280.01/41.88 | (c_RealVector_Onorm__class_Onorm(v3, v7) = v8) | ~ (hAPP(v9,
% 280.01/41.88 | v6) = v10) | ~ (hAPP(v1, v8) = v9) | ~ $i(v7) | ? [v11:
% 280.01/41.88 | $i] : ? [v12: $i] : (c_RealVector_Onorm__class_Onorm(v3,
% 280.01/41.88 | v11) = v12 & hAPP(v5, v7) = v11 & $i(v12) & $i(v11) &
% 280.01/41.88 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v12,
% 280.01/41.88 | v10))))))
% 280.01/41.88 |
% 280.01/41.88 | ALPHA: (fact_bounded__bilinear_Ononneg__bounded) implies:
% 280.06/41.88 | (61) ? [v0: $i] : ? [v1: $i] :
% 280.06/41.88 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 280.06/41.88 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 280.06/41.88 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ $i(v5)
% 280.06/41.88 | | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 280.06/41.88 | c_RealVector_Obounded__bilinear(v3, v4, v5, v2) | ~
% 280.06/41.88 | class_RealVector_Oreal__normed__vector(v5) | ~
% 280.06/41.88 | class_RealVector_Oreal__normed__vector(v4) | ~
% 280.06/41.88 | class_RealVector_Oreal__normed__vector(v3) | ? [v6: $i] : ($i(v6)
% 280.06/41.88 | & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v6) &
% 280.06/41.88 | ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11:
% 280.06/41.88 | $i] : ! [v12: $i] : ! [v13: $i] : ! [v14: $i] : ( ~
% 280.06/41.88 | (c_RealVector_Onorm__class_Onorm(v4, v8) = v11) | ~
% 280.06/41.88 | (c_RealVector_Onorm__class_Onorm(v3, v7) = v9) | ~ (hAPP(v13,
% 280.06/41.88 | v6) = v14) | ~ (hAPP(v10, v11) = v12) | ~ (hAPP(v1, v12)
% 280.06/41.88 | = v13) | ~ (hAPP(v1, v9) = v10) | ~ $i(v8) | ~ $i(v7) |
% 280.06/41.88 | ? [v15: $i] : ? [v16: $i] : ? [v17: $i] :
% 280.06/41.88 | (c_RealVector_Onorm__class_Onorm(v5, v16) = v17 & hAPP(v15,
% 280.06/41.88 | v8) = v16 & hAPP(v2, v7) = v15 & $i(v17) & $i(v16) &
% 280.06/41.88 | $i(v15) &
% 280.06/41.88 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v17,
% 280.06/41.88 | v14))))))
% 280.06/41.88 |
% 280.06/41.88 | ALPHA: (fact_scaleR__right_Ononneg__bounded) implies:
% 280.06/41.88 | (62) ? [v0: $i] : ? [v1: $i] :
% 280.06/41.88 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 280.06/41.88 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 280.06/41.88 | & ? [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~
% 280.06/41.88 | class_RealVector_Oreal__normed__vector(v3) | ? [v4: $i] : ($i(v4)
% 280.06/41.88 | & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v4) &
% 280.06/41.88 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~
% 280.06/41.88 | (c_RealVector_Onorm__class_Onorm(v3, v5) = v6) | ~ (hAPP(v7,
% 280.06/41.88 | v4) = v8) | ~ (hAPP(v1, v6) = v7) | ~ $i(v5) | ? [v9:
% 280.06/41.88 | $i] : ? [v10: $i] :
% 280.06/41.88 | (c_RealVector_OscaleR__class_OscaleR(v3, v2, v5) = v9 &
% 280.06/41.88 | c_RealVector_Onorm__class_Onorm(v3, v9) = v10 & $i(v10) &
% 280.06/41.88 | $i(v9) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 280.06/41.88 | v10, v8))))))
% 280.06/41.88 |
% 280.06/41.88 | ALPHA: (fact_mult_Ononneg__bounded) implies:
% 280.06/41.88 | (63) ? [v0: $i] : ? [v1: $i] :
% 280.06/41.88 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 280.06/41.88 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 280.06/41.88 | & ! [v2: $i] : ! [v3: $i] : ( ~ (c_Groups_Otimes__class_Otimes(v2)
% 280.06/41.88 | = v3) | ~ $i(v2) | ~
% 280.06/41.88 | class_RealVector_Oreal__normed__algebra(v2) | ? [v4: $i] :
% 280.06/41.88 | ($i(v4) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0,
% 280.06/41.88 | v4) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] :
% 280.06/41.88 | ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ! [v12: $i] : ( ~
% 280.06/41.88 | (c_RealVector_Onorm__class_Onorm(v2, v6) = v9) | ~
% 280.06/41.88 | (c_RealVector_Onorm__class_Onorm(v2, v5) = v7) | ~ (hAPP(v11,
% 280.06/41.88 | v4) = v12) | ~ (hAPP(v8, v9) = v10) | ~ (hAPP(v1, v10) =
% 280.06/41.88 | v11) | ~ (hAPP(v1, v7) = v8) | ~ $i(v6) | ~ $i(v5) | ?
% 280.06/41.88 | [v13: $i] : ? [v14: $i] : ? [v15: $i] :
% 280.06/41.88 | (c_RealVector_Onorm__class_Onorm(v2, v14) = v15 & hAPP(v13,
% 280.06/41.88 | v6) = v14 & hAPP(v3, v5) = v13 & $i(v15) & $i(v14) &
% 280.06/41.88 | $i(v13) &
% 280.06/41.88 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v15,
% 280.06/41.88 | v12))))))
% 280.06/41.88 |
% 280.06/41.88 | ALPHA: (fact_mult__right_Ononneg__bounded) implies:
% 280.06/41.88 | (64) ? [v0: $i] : ? [v1: $i] :
% 280.06/41.88 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 280.06/41.88 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 280.06/41.88 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 280.06/41.88 | (c_Groups_Otimes__class_Otimes(v3) = v4) | ~ (hAPP(v4, v2) = v5)
% 280.06/41.88 | | ~ $i(v3) | ~ $i(v2) | ~
% 280.06/41.88 | class_RealVector_Oreal__normed__algebra(v3) | ? [v6: $i] :
% 280.06/41.88 | ($i(v6) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0,
% 280.06/41.88 | v6) & ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] :
% 280.06/41.88 | ( ~ (c_RealVector_Onorm__class_Onorm(v3, v7) = v8) | ~
% 280.06/41.88 | (hAPP(v9, v6) = v10) | ~ (hAPP(v1, v8) = v9) | ~ $i(v7) | ?
% 280.06/41.88 | [v11: $i] : ? [v12: $i] :
% 280.06/41.88 | (c_RealVector_Onorm__class_Onorm(v3, v11) = v12 & hAPP(v5, v7)
% 280.06/41.88 | = v11 & $i(v12) & $i(v11) &
% 280.06/41.88 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v12,
% 280.06/41.88 | v10))))))
% 280.06/41.88 |
% 280.06/41.88 | ALPHA: (fact_mult__left_Ononneg__bounded) implies:
% 280.06/41.88 | (65) ? [v0: $i] : ? [v1: $i] :
% 280.06/41.88 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 280.06/41.88 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 280.06/41.88 | & ? [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 280.06/41.88 | (c_Groups_Otimes__class_Otimes(v3) = v4) | ~ $i(v3) | ~ $i(v2) |
% 280.06/41.88 | ~ class_RealVector_Oreal__normed__algebra(v3) | ? [v5: $i] :
% 280.06/41.88 | ($i(v5) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0,
% 280.06/41.88 | v5) & ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] :
% 280.06/41.88 | ( ~ (c_RealVector_Onorm__class_Onorm(v3, v6) = v7) | ~
% 280.06/41.88 | (hAPP(v8, v5) = v9) | ~ (hAPP(v1, v7) = v8) | ~ $i(v6) | ?
% 280.06/41.88 | [v10: $i] : ? [v11: $i] : ? [v12: $i] :
% 280.06/41.88 | (c_RealVector_Onorm__class_Onorm(v3, v11) = v12 & hAPP(v10,
% 280.06/41.88 | v2) = v11 & hAPP(v4, v6) = v10 & $i(v12) & $i(v11) &
% 280.06/41.88 | $i(v10) &
% 280.06/41.88 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v12,
% 280.06/41.88 | v9))))))
% 280.06/41.88 |
% 280.06/41.88 | ALPHA: (fact_le__mult__natfloor) implies:
% 280.06/41.88 | (66) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 280.06/41.88 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 280.06/41.88 | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v2 &
% 280.06/41.88 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v2) & $i(v1)
% 280.06/41.88 | & $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] :
% 280.06/41.88 | ! [v7: $i] : ! [v8: $i] : ( ~ (c_RComplete_Onatfloor(v4) = v5) | ~
% 280.06/41.88 | (c_RComplete_Onatfloor(v3) = v7) | ~ (hAPP(v6, v7) = v8) | ~
% 280.06/41.88 | (hAPP(v1, v5) = v6) | ~ $i(v4) | ~ $i(v3) | ~
% 280.06/41.88 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v4) | ~
% 280.06/41.88 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) | ?
% 280.06/41.88 | [v9: $i] : ? [v10: $i] : ? [v11: $i] :
% 280.06/41.88 | (c_RComplete_Onatfloor(v10) = v11 & hAPP(v9, v3) = v10 & hAPP(v2,
% 280.06/41.88 | v4) = v9 & $i(v11) & $i(v10) & $i(v9) &
% 280.06/41.88 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v8, v11))))
% 280.06/41.88 |
% 280.06/41.88 | ALPHA: (fact_natfloor__zero) implies:
% 280.06/41.88 | (67) ? [v0: $i] : ? [v1: $i] : (c_RComplete_Onatfloor(v0) = v1 &
% 280.06/41.88 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 &
% 280.06/41.88 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) &
% 280.06/41.88 | $i(v0))
% 280.06/41.88 |
% 280.06/41.88 | ALPHA: (fact_natfloor__neg) implies:
% 280.06/41.88 | (68) ? [v0: $i] : ? [v1: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 280.06/41.88 | = v1 & c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) &
% 280.06/41.88 | $i(v0) & ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~
% 280.06/41.88 | (c_RComplete_Onatfloor(v2) = v3) | ~ $i(v2) | ~
% 280.06/41.88 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v0)))
% 280.06/41.88 |
% 280.06/41.88 | ALPHA: (fact_natfloor__add) implies:
% 280.06/41.88 | (69) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 280.06/41.88 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 280.06/41.88 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v3) | ~
% 280.06/41.88 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v3) = v4) | ~
% 280.06/41.88 | $i(v2) | ~ $i(v1) | ~
% 280.06/41.88 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) | ?
% 280.06/41.88 | [v5: $i] : ? [v6: $i] : (c_RComplete_Onatfloor(v4) = v5 &
% 280.06/41.88 | c_RComplete_Onatfloor(v2) = v6 &
% 280.06/41.88 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v6, v1) = v5 & $i(v6) &
% 280.06/41.88 | $i(v5))))
% 280.06/41.88 |
% 280.06/41.88 | ALPHA: (fact_less__natfloor) implies:
% 280.06/41.88 | (70) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 280.06/41.88 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 280.06/41.88 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v3) | ~
% 280.06/41.88 | (c_RComplete_Onatfloor(v2) = v4) | ~ $i(v2) | ~ $i(v1) | ~
% 280.06/41.88 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v3) | ~
% 280.06/41.88 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) |
% 280.06/41.88 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v1)))
% 280.06/41.88 |
% 280.06/41.88 | ALPHA: (fact_real__of__nat__ge__zero) implies:
% 280.06/41.88 | (71) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 280.06/41.88 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~
% 280.06/41.88 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) | ~ $i(v1) |
% 280.06/41.88 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2)))
% 280.06/41.88 |
% 280.06/41.88 | ALPHA: (fact_not__real__of__nat__less__zero) implies:
% 280.06/41.88 | (72) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 280.06/41.88 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~
% 280.06/41.88 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) | ~ $i(v1) | ~
% 280.06/41.88 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v0)))
% 280.06/41.88 |
% 280.06/41.88 | ALPHA: (fact_real__of__nat__zero__iff) implies:
% 280.06/41.88 | (73) ? [v0: $i] : ? [v1: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 280.06/41.88 | = v1 & c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) &
% 280.06/41.88 | $i(v0) & ! [v2: $i] : (v2 = v1 | ~ (c_RealDef_Oreal(tc_Nat_Onat,
% 280.06/41.88 | v2) = v0) | ~ $i(v2)) & ! [v2: $i] : (v2 = v0 | ~
% 280.06/41.88 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2)))
% 280.06/41.88 |
% 280.06/41.88 | ALPHA: (fact_real__of__nat__zero) implies:
% 280.06/41.88 | (74) ? [v0: $i] : ? [v1: $i] : (c_RealDef_Oreal(tc_Nat_Onat, v0) = v1 &
% 280.06/41.88 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 &
% 280.06/41.88 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v1) &
% 280.06/41.88 | $i(v0))
% 280.06/41.88 |
% 280.06/41.88 | ALPHA: (fact_real__of__nat__le__zero__cancel__iff) implies:
% 280.06/41.88 | (75) ? [v0: $i] : ? [v1: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 280.06/41.88 | = v1 & c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) &
% 280.06/41.88 | $i(v0) & ! [v2: $i] : ! [v3: $i] : (v2 = v1 | ~
% 280.06/41.88 | (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~ $i(v2) | ~
% 280.06/41.88 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v0)) & !
% 280.06/41.88 | [v2: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) |
% 280.06/41.88 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v0)))
% 280.06/41.88 |
% 280.06/41.88 | ALPHA: (fact_real__natfloor__le) implies:
% 280.06/41.88 | (76) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 280.06/41.88 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ (c_RComplete_Onatfloor(v1)
% 280.06/41.88 | = v2) | ~ $i(v1) | ~
% 280.06/41.88 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v1) | ?
% 280.06/41.88 | [v3: $i] : (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3 & $i(v3) &
% 280.06/41.88 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v1))))
% 280.06/41.88 |
% 280.06/41.88 | ALPHA: (fact_real__of__nat__gt__zero__cancel__iff) implies:
% 280.06/41.88 | (77) ? [v0: $i] : ? [v1: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 280.06/41.88 | = v1 & c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) &
% 280.06/41.88 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~
% 280.06/41.88 | (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~ $i(v2) | ~
% 280.06/41.88 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2) |
% 280.06/41.88 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3)) & ! [v2:
% 280.06/41.88 | $i] : ! [v3: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) |
% 280.06/41.88 | ~ $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0,
% 280.06/41.88 | v3) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2)))
% 280.06/41.88 |
% 280.06/41.88 | ALPHA: (fact_le__natfloor__eq) implies:
% 280.06/41.88 | (78) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 280.06/41.88 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 280.06/41.88 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~
% 280.06/41.88 | (c_RComplete_Onatfloor(v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 280.06/41.88 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v3) | ~
% 280.06/41.88 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) |
% 280.06/41.88 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v2)) & !
% 280.06/41.88 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 280.06/41.88 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~
% 280.06/41.88 | (c_RComplete_Onatfloor(v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 280.06/41.88 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v2) | ~
% 280.06/41.88 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) |
% 280.06/41.88 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v3)))
% 280.06/41.88 |
% 280.06/41.88 | ALPHA: (fact_natceiling__add) implies:
% 280.06/41.88 | (79) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 280.06/41.88 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 280.06/41.88 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v3) | ~
% 280.06/41.88 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v3) = v4) | ~
% 280.06/41.88 | $i(v2) | ~ $i(v1) | ~
% 280.06/41.88 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) | ?
% 280.06/41.88 | [v5: $i] : ? [v6: $i] : (c_RComplete_Onatceiling(v4) = v5 &
% 280.06/41.88 | c_RComplete_Onatceiling(v2) = v6 &
% 280.06/41.88 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v6, v1) = v5 & $i(v6) &
% 280.06/41.88 | $i(v5))))
% 280.06/41.88 |
% 280.06/41.88 | ALPHA: (fact_natfloor__eq) implies:
% 280.06/41.88 | (80) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 280.06/41.88 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4
% 280.06/41.88 | = v2 | ~ (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~
% 280.06/41.88 | (c_RComplete_Onatfloor(v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~
% 280.06/41.88 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v1) | ?
% 280.06/41.88 | [v5: $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v0)
% 280.06/41.88 | = v5 & $i(v5) & ~
% 280.06/41.88 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v5))))
% 280.06/41.88 |
% 280.06/41.88 | ALPHA: (fact_real__mult__1) implies:
% 280.06/41.88 | (81) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 280.06/41.88 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 280.06/41.88 | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v0 & hAPP(v0, v1)
% 280.06/41.88 | = v2 & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : (v4 =
% 280.06/41.88 | v3 | ~ (hAPP(v2, v3) = v4) | ~ $i(v3)))
% 280.06/41.88 |
% 280.06/41.88 | ALPHA: (fact_norm__one) implies:
% 280.06/41.88 | (82) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 280.06/41.88 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~
% 280.06/41.88 | (c_Groups_Oone__class_Oone(v1) = v2) | ~
% 280.06/41.88 | (c_RealVector_Onorm__class_Onorm(v1, v2) = v3) | ~ $i(v1) | ~
% 280.06/41.88 | class_RealVector_Oreal__normed__algebra__1(v1)))
% 280.06/41.88 |
% 280.06/41.88 | ALPHA: (fact_real__vector_Oscale__one) implies:
% 280.06/41.88 | (83) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 280.06/41.88 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~
% 280.06/41.88 | (c_RealVector_OscaleR__class_OscaleR(v2, v0, v1) = v3) | ~ $i(v2)
% 280.06/41.88 | | ~ $i(v1) | ~ class_RealVector_Oreal__vector(v2)))
% 280.06/41.88 |
% 280.06/41.89 | ALPHA: (fact_real__zero__not__eq__one) implies:
% 280.06/41.89 | (84) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) &
% 280.06/41.89 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 280.06/41.89 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) &
% 280.06/41.89 | $i(v0))
% 280.06/41.89 |
% 280.06/41.89 | ALPHA: (fact_natceiling__zero) implies:
% 280.06/41.89 | (85) ? [v0: $i] : ? [v1: $i] : (c_RComplete_Onatceiling(v0) = v1 &
% 280.06/41.89 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 &
% 280.06/41.89 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) &
% 280.06/41.89 | $i(v0))
% 280.06/41.89 |
% 280.06/41.89 | ALPHA: (fact_abs__add__one__not__less__self) implies:
% 280.06/41.89 | (86) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 280.06/41.89 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~
% 280.06/41.89 | (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v1) = v2) | ~ $i(v1)
% 280.06/41.89 | | ? [v3: $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2,
% 280.06/41.89 | v0) = v3 & $i(v3) & ~
% 280.06/41.89 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v1))))
% 280.06/41.89 |
% 280.06/41.89 | ALPHA: (fact_natceiling__neg) implies:
% 280.06/41.89 | (87) ? [v0: $i] : ? [v1: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 280.06/41.89 | = v1 & c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) &
% 280.06/41.89 | $i(v0) & ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~
% 280.06/41.89 | (c_RComplete_Onatceiling(v2) = v3) | ~ $i(v2) | ~
% 280.06/41.89 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v0)))
% 280.06/41.89 |
% 280.06/41.89 | ALPHA: (fact_nat__less__real__le) implies:
% 280.06/41.89 | (88) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 280.06/41.89 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 280.06/41.89 | (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~
% 280.06/41.89 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~ $i(v2) | ~ $i(v1) |
% 280.06/41.89 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) | ? [v5: $i]
% 280.06/41.89 | : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v0) = v5 &
% 280.06/41.89 | $i(v5) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5,
% 280.06/41.89 | v4))) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 280.06/41.89 | : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~
% 280.06/41.89 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~ $i(v2) | ~ $i(v1) |
% 280.06/41.89 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) | ? [v5: $i] :
% 280.06/41.89 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v0) = v5 &
% 280.06/41.89 | $i(v5) & ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 280.06/41.89 | v5, v4))))
% 280.06/41.89 |
% 280.06/41.89 | ALPHA: (fact_nat__le__real__less) implies:
% 280.06/41.89 | (89) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 280.06/41.89 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 280.06/41.89 | (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~
% 280.06/41.89 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~ $i(v2) | ~ $i(v1) |
% 280.06/41.89 | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1) | ? [v5:
% 280.06/41.89 | $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v4, v0) =
% 280.06/41.89 | v5 & $i(v5) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 280.06/41.89 | v3, v5))) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 280.06/41.89 | $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~
% 280.06/41.89 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~ $i(v2) | ~ $i(v1) |
% 280.06/41.89 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1) | ? [v5:
% 280.06/41.89 | $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v4, v0) =
% 280.06/41.89 | v5 & $i(v5) & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 280.06/41.89 | v3, v5))))
% 280.06/41.89 |
% 280.06/41.89 | ALPHA: (fact_abs__add__one__gt__zero) implies:
% 280.06/41.89 | (90) ? [v0: $i] : ? [v1: $i] :
% 280.06/41.89 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 280.06/41.89 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 280.06/41.89 | & ! [v2: $i] : ! [v3: $i] : ( ~
% 280.06/41.89 | (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v2) = v3) | ~ $i(v2)
% 280.06/41.89 | | ? [v4: $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1,
% 280.06/41.89 | v3) = v4 & $i(v4) &
% 280.06/41.89 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4))))
% 280.06/41.89 |
% 280.06/41.89 | ALPHA: (fact_real__natfloor__add__one__gt) implies:
% 280.06/41.89 | (91) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 280.06/41.89 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ (c_RComplete_Onatfloor(v1)
% 280.06/41.89 | = v2) | ~ $i(v1) | ? [v3: $i] : ? [v4: $i] :
% 280.06/41.89 | (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3 &
% 280.06/41.89 | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v0) = v4 &
% 280.06/41.89 | $i(v4) & $i(v3) &
% 280.06/41.89 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v4))))
% 280.06/41.89 |
% 280.06/41.89 | ALPHA: (fact_real__natfloor__gt__diff__one) implies:
% 280.06/41.89 | (92) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 280.06/41.89 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~
% 280.06/41.89 | (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v1, v0) = v2) |
% 280.06/41.89 | ~ $i(v1) | ? [v3: $i] : ? [v4: $i] :
% 280.06/41.89 | (c_RealDef_Oreal(tc_Nat_Onat, v3) = v4 & c_RComplete_Onatfloor(v1)
% 280.06/41.89 | = v3 & $i(v4) & $i(v3) &
% 280.06/41.89 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v4))))
% 280.06/41.89 |
% 280.06/41.89 | ALPHA: (fact_natceiling__le__eq) implies:
% 280.06/41.89 | (93) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 280.06/41.89 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 280.06/41.89 | (c_RComplete_Onatceiling(v2) = v3) | ~
% 280.06/41.89 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~ $i(v2) | ~ $i(v1) |
% 280.06/41.89 | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v1) | ~
% 280.06/41.89 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) |
% 280.06/41.89 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v4)) & !
% 280.06/41.89 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 280.06/41.89 | (c_RComplete_Onatceiling(v2) = v3) | ~
% 280.06/41.89 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~ $i(v2) | ~ $i(v1) |
% 280.06/41.89 | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v4) | ~
% 280.06/41.89 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) |
% 280.06/41.89 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v1)))
% 280.06/41.89 |
% 280.06/41.89 | ALPHA: (fact_natceiling__eq) implies:
% 280.06/41.89 | (94) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) =
% 280.06/41.89 | v1 & c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v1) &
% 280.06/41.89 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5
% 280.06/41.89 | = v4 | ~ (c_RComplete_Onatceiling(v2) = v4) | ~
% 280.06/41.89 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v1) = v5) | ~
% 280.06/41.89 | $i(v3) | ~ $i(v2) | ? [v6: $i] : ? [v7: $i] :
% 280.06/41.89 | (c_RealDef_Oreal(tc_Nat_Onat, v3) = v6 & $i(v6) & ( ~
% 280.06/41.89 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v6, v2) |
% 280.06/41.89 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v6, v0) = v7 &
% 280.06/41.89 | $i(v7) & ~
% 280.06/41.89 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2,
% 280.06/41.89 | v7))))))
% 280.06/41.89 |
% 280.06/41.89 | ALPHA: (fact_natceiling__add__one) implies:
% 280.06/41.89 | (95) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 280.06/41.89 | (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 &
% 280.06/41.89 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 280.06/41.89 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v2) & $i(v1)
% 280.06/41.89 | & $i(v0) & ! [v3: $i] : ! [v4: $i] : ( ~
% 280.06/41.89 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v1) = v4) | ~
% 280.06/41.89 | $i(v3) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 280.06/41.89 | v0, v3) | ? [v5: $i] : ? [v6: $i] :
% 280.06/41.89 | (c_RComplete_Onatceiling(v4) = v5 & c_RComplete_Onatceiling(v3) =
% 280.06/41.89 | v6 & c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v6, v2) = v5 &
% 280.06/41.89 | $i(v6) & $i(v5))))
% 280.06/41.89 |
% 280.06/41.89 | ALPHA: (fact_natfloor__add__one) implies:
% 280.06/41.89 | (96) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 280.06/41.89 | (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 &
% 280.06/41.89 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 280.06/41.89 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v2) & $i(v1)
% 280.06/41.89 | & $i(v0) & ! [v3: $i] : ! [v4: $i] : ( ~
% 280.06/41.89 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v1) = v4) | ~
% 280.06/41.89 | $i(v3) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 280.06/41.89 | v0, v3) | ? [v5: $i] : ? [v6: $i] : (c_RComplete_Onatfloor(v4)
% 280.06/41.89 | = v5 & c_RComplete_Onatfloor(v3) = v6 &
% 280.06/41.89 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v6, v2) = v5 & $i(v6) &
% 280.06/41.89 | $i(v5))))
% 280.06/41.89 |
% 280.06/41.89 | ALPHA: (fact_complex__Im__one) implies:
% 280.06/41.89 | (97) ? [v0: $i] : ? [v1: $i] :
% 280.06/41.89 | (c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = v0 &
% 280.06/41.89 | c_Complex_OIm(v0) = v1 &
% 280.06/41.89 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v1) &
% 280.06/41.89 | $i(v0))
% 280.06/41.89 |
% 280.06/41.89 | ALPHA: (fact_complex__Re__one) implies:
% 280.06/41.89 | (98) ? [v0: $i] : ? [v1: $i] :
% 280.06/41.89 | (c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = v0 &
% 280.06/41.89 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & c_Complex_ORe(v0)
% 280.06/41.89 | = v1 & $i(v1) & $i(v0))
% 280.06/41.89 |
% 280.06/41.89 | ALPHA: (fact_real__of__nat__1) implies:
% 280.06/41.89 | (99) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) =
% 280.06/41.89 | v0 & c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 280.06/41.89 | c_RealDef_Oreal(tc_Nat_Onat, v0) = v1 & $i(v1) & $i(v0))
% 280.06/41.89 |
% 280.06/41.89 | ALPHA: (fact_natfloor__one) implies:
% 280.06/41.89 | (100) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) =
% 280.06/41.89 | v1 & c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 280.06/41.89 | c_RComplete_Onatfloor(v0) = v1 & $i(v1) & $i(v0))
% 280.06/41.89 |
% 280.06/41.89 | ALPHA: (fact_natceiling__one) implies:
% 280.06/41.89 | (101) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) =
% 280.06/41.89 | v1 & c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 280.06/41.89 | c_RComplete_Onatceiling(v0) = v1 & $i(v1) & $i(v0))
% 280.06/41.89 |
% 280.06/41.89 | ALPHA: (fact_Complex__eq__1) implies:
% 280.06/41.89 | (102) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 280.06/41.89 | (c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = v0 &
% 280.06/41.89 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 280.06/41.89 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v2 & $i(v2) &
% 280.06/41.89 | $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : (v4 = v1 | ~
% 280.06/41.89 | (c_Complex_Ocomplex_OComplex(v4, v3) = v0) | ~ $i(v4) | ~
% 280.06/41.89 | $i(v3)) & ! [v3: $i] : ! [v4: $i] : (v3 = v2 | ~
% 280.06/41.89 | (c_Complex_Ocomplex_OComplex(v4, v3) = v0) | ~ $i(v4) | ~
% 280.06/41.89 | $i(v3)) & ! [v3: $i] : (v3 = v0 | ~
% 280.06/41.89 | (c_Complex_Ocomplex_OComplex(v1, v2) = v3)))
% 280.06/41.89 |
% 280.06/41.89 | ALPHA: (fact_complex__one__def) implies:
% 280.06/41.89 | (103) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 280.06/41.89 | (c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = v0 &
% 280.06/41.89 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 280.06/41.89 | c_Complex_Ocomplex_OComplex(v1, v2) = v0 &
% 280.06/41.89 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v2 & $i(v2) &
% 280.06/41.89 | $i(v1) & $i(v0))
% 280.06/41.89 |
% 280.06/41.89 | ALPHA: (fact_le__natfloor__eq__one) implies:
% 280.06/41.89 | (104) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) =
% 280.06/41.89 | v0 & c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & $i(v1) &
% 280.06/41.89 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (c_RComplete_Onatfloor(v2)
% 280.06/41.89 | = v3) | ~ $i(v2) | ~
% 280.06/41.89 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, v3) |
% 280.06/41.89 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v2)) & !
% 280.06/41.89 | [v2: $i] : ! [v3: $i] : ( ~ (c_RComplete_Onatfloor(v2) = v3) | ~
% 280.06/41.89 | $i(v2) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 280.06/41.89 | v1, v2) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0,
% 280.06/41.89 | v3)))
% 280.06/41.89 |
% 280.06/41.89 | ALPHA: (fact_natceiling__le__eq__one) implies:
% 280.06/41.89 | (105) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) =
% 280.06/41.89 | v0 & c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & $i(v1) &
% 280.06/41.89 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~
% 280.06/41.89 | (c_RComplete_Onatceiling(v2) = v3) | ~ $i(v2) | ~
% 280.06/41.89 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v0) |
% 280.06/41.89 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v1)) & !
% 280.06/41.89 | [v2: $i] : ! [v3: $i] : ( ~ (c_RComplete_Onatceiling(v2) = v3) |
% 280.06/41.89 | ~ $i(v2) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 280.06/41.89 | v2, v1) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3,
% 280.06/41.89 | v0)))
% 280.06/41.89 |
% 280.06/41.89 | ALPHA: (fact_reals__Archimedean6) implies:
% 280.06/41.89 | (106) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) =
% 280.06/41.89 | v1 & c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) &
% 280.06/41.89 | $i(v0) & ! [v2: $i] : ( ~ $i(v2) | ~
% 280.06/41.89 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) | ?
% 280.06/41.89 | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] :
% 280.06/41.89 | (c_RealDef_Oreal(tc_Nat_Onat, v4) = v5 &
% 280.06/41.89 | c_RealDef_Oreal(tc_Nat_Onat, v3) = v6 &
% 280.06/41.89 | c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v3, v1) = v4 &
% 280.06/41.89 | $i(v6) & $i(v5) & $i(v4) & $i(v3) &
% 280.06/41.89 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v6) &
% 280.06/41.89 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, v2))))
% 280.06/41.89 |
% 280.06/41.89 | ALPHA: (fact_lemmaCauchy) implies:
% 280.06/41.89 | (107) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 280.06/41.89 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 280.06/41.89 | [v5: $i] : ! [v6: $i] : ( ~ (c_RealVector_Onorm__class_Onorm(v4,
% 280.06/41.89 | v5) = v6) | ~ (hAPP(v1, v2) = v5) | ~ $i(v4) | ~ $i(v3) |
% 280.06/41.89 | ~ $i(v2) | ~ $i(v1) | ~ class_Orderings_Oord(v3) | ~
% 280.06/41.89 | class_RealVector_Oreal__normed__vector(v4) | ? [v7: $i] : ?
% 280.06/41.89 | [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ($i(v8) &
% 280.06/41.89 | ((c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v0, v6) = v7 &
% 280.06/41.89 | $i(v7) & ! [v12: $i] : ! [v13: $i] : ! [v14: $i] : ( ~
% 280.06/41.89 | (c_RealVector_Onorm__class_Onorm(v4, v13) = v14) | ~
% 280.06/41.89 | (hAPP(v1, v12) = v13) | ~ $i(v12) | ~
% 280.06/41.89 | c_Orderings_Oord__class_Oless__eq(v3, v2, v12) |
% 280.06/41.89 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v14,
% 280.06/41.89 | v7))) | (c_Groups_Ominus__class_Ominus(v4, v5, v9) =
% 280.06/41.89 | v10 & c_RealVector_Onorm__class_Onorm(v4, v10) = v11 &
% 280.06/41.89 | hAPP(v1, v8) = v9 & $i(v11) & $i(v10) & $i(v9) &
% 280.06/41.89 | c_Orderings_Oord__class_Oless__eq(v3, v2, v8) & ~
% 280.06/41.89 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v11,
% 280.06/41.89 | v0))))))
% 280.06/41.89 |
% 280.06/41.89 | ALPHA: (fact_complex__Re__i) implies:
% 280.06/41.89 | (108) ? [v0: $i] : (c_Complex_ORe(c_Complex_Oii) = v0 &
% 280.06/41.89 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v0))
% 280.06/41.89 |
% 280.06/41.89 | ALPHA: (fact_complex__Im__i) implies:
% 280.06/41.89 | (109) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 280.06/41.89 | c_Complex_OIm(c_Complex_Oii) = v0 & $i(v0))
% 280.06/41.89 |
% 280.06/41.89 | ALPHA: (fact_i__def) implies:
% 280.06/41.89 | (110) ? [v0: $i] : ? [v1: $i] :
% 280.06/41.89 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 280.06/41.89 | c_Complex_Ocomplex_OComplex(v0, v1) = c_Complex_Oii &
% 280.06/41.89 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) &
% 280.06/41.89 | $i(v0))
% 280.06/41.89 |
% 280.06/41.89 | ALPHA: (fact_Complex__eq__i) implies:
% 280.06/41.89 | (111) ? [v0: $i] : ? [v1: $i] :
% 280.06/41.89 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 280.06/41.89 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) &
% 280.06/41.89 | $i(v0) & ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~
% 280.06/41.89 | (c_Complex_Ocomplex_OComplex(v3, v2) = c_Complex_Oii) | ~ $i(v3)
% 280.06/41.89 | | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v2 = v1 | ~
% 280.06/41.89 | (c_Complex_Ocomplex_OComplex(v3, v2) = c_Complex_Oii) | ~ $i(v3)
% 280.06/41.89 | | ~ $i(v2)) & ! [v2: $i] : (v2 = c_Complex_Oii | ~
% 280.06/41.89 | (c_Complex_Ocomplex_OComplex(v0, v1) = v2)))
% 280.06/41.89 |
% 280.06/41.89 | ALPHA: (fact_LIMSEQ__inverse__realpow__zero__lemma) implies:
% 280.06/41.90 | (112) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 280.06/41.90 | (c_Power_Opower__class_Opower(tc_RealDef_Oreal) = v3 &
% 280.06/41.90 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v2 &
% 280.06/41.90 | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 280.06/41.90 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v3) &
% 280.06/41.90 | $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i]
% 280.06/41.90 | : ! [v7: $i] : ! [v8: $i] : ( ~
% 280.06/41.90 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v5, v2) = v6) | ~
% 280.06/41.90 | (hAPP(v7, v4) = v8) | ~ (hAPP(v3, v6) = v7) | ~ $i(v5) | ~
% 280.06/41.90 | $i(v4) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 280.06/41.90 | v0, v5) | ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12:
% 280.06/41.90 | $i] : (c_RealDef_Oreal(tc_Nat_Onat, v4) = v9 &
% 280.06/41.90 | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v11, v2) = v12 &
% 280.06/41.90 | hAPP(v10, v5) = v11 & hAPP(v1, v9) = v10 & $i(v12) & $i(v11) &
% 280.06/41.90 | $i(v10) & $i(v9) &
% 280.06/41.90 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v12, v8))))
% 280.06/41.90 |
% 280.06/41.90 | ALPHA: (fact_realpow__pos__nth__unique) implies:
% 280.06/41.90 | (113) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 280.06/41.90 | (c_Power_Opower__class_Opower(tc_RealDef_Oreal) = v2 &
% 280.06/41.90 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 &
% 280.06/41.90 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v2) &
% 280.06/41.90 | $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ( ~ $i(v4) | ~
% 280.06/41.90 | $i(v3) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) |
% 280.06/41.90 | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v3) | ?
% 280.06/41.90 | [v5: $i] : ? [v6: $i] : (hAPP(v6, v4) = v3 & hAPP(v2, v5) = v6 &
% 280.06/41.90 | $i(v6) & $i(v5) &
% 280.06/41.90 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v5) & !
% 280.06/41.90 | [v7: $i] : ! [v8: $i] : (v7 = v5 | ~ (hAPP(v8, v4) = v3) | ~
% 280.06/41.90 | (hAPP(v2, v7) = v8) | ~ $i(v7) | ~
% 280.06/41.90 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v7)))))
% 280.06/41.90 |
% 280.06/41.90 | ALPHA: (fact_realpow__pos__nth) implies:
% 280.06/41.90 | (114) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 280.06/41.90 | (c_Power_Opower__class_Opower(tc_RealDef_Oreal) = v2 &
% 280.06/41.90 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 &
% 280.06/41.90 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v2) &
% 280.06/41.90 | $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ( ~ $i(v4) | ~
% 280.06/41.90 | $i(v3) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4) |
% 280.06/41.90 | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v3) | ?
% 280.06/41.90 | [v5: $i] : ? [v6: $i] : (hAPP(v6, v4) = v3 & hAPP(v2, v5) = v6 &
% 280.06/41.90 | $i(v6) & $i(v5) &
% 280.06/41.90 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v5))))
% 280.06/41.90 |
% 280.06/41.90 | ALPHA: (fact_ln__realpow) implies:
% 280.06/41.90 | (115) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 280.06/41.90 | (c_Power_Opower__class_Opower(tc_RealDef_Oreal) = v1 &
% 280.06/41.90 | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v2 &
% 280.06/41.90 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v2) &
% 280.06/41.90 | $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 280.06/41.90 | $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (c_Transcendental_Oln(v4) =
% 280.06/41.90 | v7) | ~ (c_RealDef_Oreal(tc_Nat_Onat, v3) = v5) | ~ (hAPP(v6,
% 280.06/41.90 | v7) = v8) | ~ (hAPP(v2, v5) = v6) | ~ $i(v4) | ~ $i(v3) |
% 280.06/41.90 | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) | ?
% 280.06/41.90 | [v9: $i] : ? [v10: $i] : (c_Transcendental_Oln(v10) = v8 &
% 280.06/41.90 | hAPP(v9, v3) = v10 & hAPP(v1, v4) = v9 & $i(v10) & $i(v9) &
% 280.06/41.90 | $i(v8))))
% 280.06/41.90 |
% 280.06/41.90 | ALPHA: (fact_ln__one) implies:
% 280.06/41.90 | (116) ? [v0: $i] : ? [v1: $i] : (c_Transcendental_Oln(v0) = v1 &
% 280.06/41.90 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 280.06/41.90 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v1) &
% 280.06/41.90 | $i(v0))
% 280.06/41.90 |
% 280.06/41.90 | ALPHA: (fact_ln__less__self) implies:
% 280.06/41.90 | (117) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 280.06/41.90 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ (c_Transcendental_Oln(v1)
% 280.06/41.90 | = v2) | ~ $i(v1) | ~
% 280.06/41.90 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v1) |
% 280.06/41.90 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v1)))
% 280.06/41.90 |
% 280.06/41.90 | ALPHA: (fact_ln__inj__iff) implies:
% 280.06/41.90 | (118) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 280.06/41.90 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v1 | ~
% 280.06/41.90 | (c_Transcendental_Oln(v2) = v3) | ~ (c_Transcendental_Oln(v1) =
% 280.06/41.90 | v3) | ~ $i(v2) | ~ $i(v1) | ~
% 280.06/41.90 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ~
% 280.06/41.90 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v1)))
% 280.06/41.90 |
% 280.06/41.90 | ALPHA: (fact_ln__less__cancel__iff) implies:
% 280.06/41.90 | (119) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 280.06/41.90 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 280.06/41.90 | ~ (c_Transcendental_Oln(v2) = v3) | ~ (c_Transcendental_Oln(v1)
% 280.06/41.90 | = v4) | ~ $i(v2) | ~ $i(v1) | ~
% 280.06/41.90 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v4) | ~
% 280.06/41.90 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ~
% 280.06/41.90 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v1) |
% 280.06/41.90 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v1)) & !
% 280.06/41.90 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 280.06/41.90 | (c_Transcendental_Oln(v2) = v3) | ~ (c_Transcendental_Oln(v1) =
% 280.06/41.90 | v4) | ~ $i(v2) | ~ $i(v1) | ~
% 280.06/41.90 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v1) | ~
% 280.06/41.90 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ~
% 280.06/41.90 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v1) |
% 280.06/41.90 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v4)))
% 280.06/41.90 |
% 280.06/41.90 | ALPHA: (fact_ln__le__cancel__iff) implies:
% 280.06/41.90 | (120) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 280.06/41.90 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 280.06/41.90 | ~ (c_Transcendental_Oln(v2) = v3) | ~ (c_Transcendental_Oln(v1)
% 280.06/41.90 | = v4) | ~ $i(v2) | ~ $i(v1) | ~
% 280.06/41.90 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ~
% 280.06/41.90 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v1) | ~
% 280.06/41.90 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v4) |
% 280.06/41.90 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v1)) & !
% 280.06/41.90 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 280.06/41.90 | (c_Transcendental_Oln(v2) = v3) | ~ (c_Transcendental_Oln(v1) =
% 280.06/41.90 | v4) | ~ $i(v2) | ~ $i(v1) | ~
% 280.06/41.90 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ~
% 280.06/41.90 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v1) | ~
% 280.06/41.90 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v1) |
% 280.06/41.90 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v4)))
% 280.06/41.90 |
% 280.06/41.90 | ALPHA: (fact_ln__ge__zero) implies:
% 280.06/41.90 | (121) ? [v0: $i] : ? [v1: $i] :
% 280.06/41.90 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 280.06/41.90 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v1) &
% 280.06/41.90 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2)
% 280.06/41.90 | = v3) | ~ $i(v2) | ~
% 280.06/41.90 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) |
% 280.06/41.90 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v3)))
% 280.06/41.90 |
% 280.06/41.90 | ALPHA: (fact_ln__gt__zero) implies:
% 280.06/41.90 | (122) ? [v0: $i] : ? [v1: $i] :
% 280.06/41.90 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 280.06/41.90 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v1) &
% 280.06/41.90 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2)
% 280.06/41.90 | = v3) | ~ $i(v2) | ~
% 280.06/41.90 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) |
% 280.06/41.90 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v3)))
% 280.06/41.90 |
% 280.06/41.90 | ALPHA: (fact_ln__gt__zero__iff) implies:
% 280.06/41.90 | (123) ? [v0: $i] : ? [v1: $i] :
% 280.06/41.90 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 280.06/41.90 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) &
% 280.06/41.90 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2)
% 280.06/41.90 | = v3) | ~ $i(v2) | ~
% 280.06/41.90 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v2) | ~
% 280.06/41.90 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) |
% 280.06/41.90 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3)) & !
% 280.06/41.90 | [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2) = v3) | ~
% 280.06/41.90 | $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0,
% 280.06/41.90 | v3) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0,
% 280.06/41.90 | v2) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v2)))
% 280.06/41.90 |
% 280.06/41.90 | ALPHA: (fact_ln__eq__zero__iff) implies:
% 280.06/41.90 | (124) ? [v0: $i] : ? [v1: $i] :
% 280.06/41.90 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 280.06/41.90 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) &
% 280.06/41.90 | $i(v0) & ! [v2: $i] : (v2 = v1 | ~ (c_Transcendental_Oln(v2) =
% 280.06/41.90 | v0) | ~ $i(v2) | ~
% 280.06/41.90 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2)) & !
% 280.06/41.90 | [v2: $i] : (v2 = v0 | ~ (c_Transcendental_Oln(v1) = v2) | ~
% 280.06/41.90 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v1)))
% 280.06/41.90 |
% 280.06/41.90 | ALPHA: (fact_ln__less__zero__iff) implies:
% 280.06/41.90 | (125) ? [v0: $i] : ? [v1: $i] :
% 280.06/41.90 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 280.06/41.90 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) &
% 280.06/41.90 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2)
% 280.06/41.90 | = v3) | ~ $i(v2) | ~
% 280.06/41.90 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v0) | ~
% 280.06/41.90 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) |
% 280.06/41.90 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v1)) & !
% 280.06/41.90 | [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2) = v3) | ~
% 280.06/41.90 | $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2,
% 280.06/41.90 | v1) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0,
% 280.06/41.90 | v2) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v0)))
% 280.06/41.90 |
% 280.06/41.90 | ALPHA: (fact_ln__less__zero) implies:
% 280.06/41.90 | (126) ? [v0: $i] : ? [v1: $i] :
% 280.06/41.90 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 280.06/41.90 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) &
% 280.06/41.90 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2)
% 280.06/41.90 | = v3) | ~ $i(v2) | ~
% 280.06/41.90 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v1) | ~
% 280.06/41.90 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) |
% 280.06/41.90 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v0)))
% 280.06/41.90 |
% 280.06/41.90 | ALPHA: (fact_ln__gt__zero__imp__gt__one) implies:
% 280.06/41.90 | (127) ? [v0: $i] : ? [v1: $i] :
% 280.06/41.90 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 280.06/41.90 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) &
% 280.06/41.90 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2)
% 280.06/41.90 | = v3) | ~ $i(v2) | ~
% 280.06/41.90 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | ~
% 280.06/41.90 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) |
% 280.06/41.90 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v2)))
% 280.06/41.90 |
% 280.06/41.90 | ALPHA: (fact_ln__ge__zero__imp__ge__one) implies:
% 280.06/41.90 | (128) ? [v0: $i] : ? [v1: $i] :
% 280.06/41.90 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 280.06/41.90 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) &
% 280.06/41.90 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2)
% 280.06/41.90 | = v3) | ~ $i(v2) | ~
% 280.06/41.90 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ~
% 280.06/41.90 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) |
% 280.06/41.90 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v2)))
% 280.06/41.90 |
% 280.06/41.90 | ALPHA: (fact_ln__ge__zero__iff) implies:
% 280.06/41.90 | (129) ? [v0: $i] : ? [v1: $i] :
% 280.06/41.90 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 280.06/41.90 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) &
% 280.06/41.90 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2)
% 280.06/41.90 | = v3) | ~ $i(v2) | ~
% 280.06/41.90 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ~
% 280.06/41.90 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v2) |
% 280.06/41.90 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3)) & !
% 280.06/41.90 | [v2: $i] : ! [v3: $i] : ( ~ (c_Transcendental_Oln(v2) = v3) | ~
% 280.06/41.90 | $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0,
% 280.06/41.90 | v2) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 280.06/41.90 | v0, v3) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 280.06/41.90 | v1, v2)))
% 280.06/41.90 |
% 280.06/41.90 | ALPHA: (fact_ln__mult) implies:
% 280.06/41.90 | (130) ? [v0: $i] : ? [v1: $i] :
% 280.06/41.90 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 280.06/41.90 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) &
% 280.06/41.90 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : !
% 280.06/41.90 | [v6: $i] : ( ~ (c_Transcendental_Oln(v3) = v4) | ~
% 280.06/41.90 | (c_Transcendental_Oln(v2) = v5) | ~
% 280.06/41.90 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v4, v5) = v6) | ~
% 280.06/41.90 | $i(v3) | ~ $i(v2) | ~
% 280.06/41.90 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | ~
% 280.06/41.90 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ? [v7:
% 280.06/41.90 | $i] : ? [v8: $i] : (c_Transcendental_Oln(v8) = v6 & hAPP(v7,
% 280.06/41.90 | v2) = v8 & hAPP(v1, v3) = v7 & $i(v8) & $i(v7) & $i(v6))))
% 280.06/41.90 |
% 280.06/41.90 | ALPHA: (fact_ln__add__one__self__le__self) implies:
% 280.06/41.90 | (131) ? [v0: $i] : ? [v1: $i] :
% 280.06/41.90 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 280.06/41.90 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) &
% 280.06/41.90 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~
% 280.06/41.90 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1, v2) = v3) | ~
% 280.06/41.90 | $i(v2) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 280.06/41.90 | v0, v2) | ? [v4: $i] : (c_Transcendental_Oln(v3) = v4 & $i(v4)
% 280.06/41.90 | & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4,
% 280.06/41.90 | v2))))
% 280.06/41.90 |
% 280.06/41.90 | ALPHA: (fact_Bseq__def) implies:
% 280.06/41.90 | (132) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 280.06/41.90 | $i(v0) & ? [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~
% 280.06/41.90 | $i(v2) | ~ $i(v1) | ~
% 280.06/41.90 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | ~
% 280.06/41.90 | class_RealVector_Oreal__normed__vector(v2) | c_SEQ_OBseq(v2, v1)
% 280.06/41.90 | | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] :
% 280.06/41.90 | (c_RealVector_Onorm__class_Onorm(v2, v5) = v6 & hAPP(v1, v4) = v5
% 280.06/41.90 | & $i(v6) & $i(v5) & $i(v4) & ~
% 280.06/41.90 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v3))) &
% 280.06/41.90 | ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 280.06/41.90 | c_SEQ_OBseq(v2, v1) | ~
% 280.06/41.90 | class_RealVector_Oreal__normed__vector(v2) | ? [v3: $i] :
% 280.06/41.90 | ($i(v3) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3)
% 280.06/41.90 | & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 280.06/41.90 | (c_RealVector_Onorm__class_Onorm(v2, v5) = v6) | ~ (hAPP(v1,
% 280.06/41.90 | v4) = v5) | ~ $i(v4) |
% 280.06/41.90 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6,
% 280.06/41.90 | v3)))))
% 280.06/41.90 |
% 280.06/41.90 | ALPHA: (fact_Bseq__iff3) implies:
% 280.06/41.90 | (133) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 280.06/41.90 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 280.06/41.90 | [v5: $i] : ! [v6: $i] : ( ~ (c_Groups_Ouminus__class_Ouminus(v2,
% 280.06/41.90 | v5) = v6) | ~ (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) |
% 280.06/41.90 | ~ $i(v2) | ~ $i(v1) | ~
% 280.06/41.90 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | ~
% 280.06/41.90 | class_RealVector_Oreal__normed__vector(v2) | c_SEQ_OBseq(v2, v1)
% 280.06/41.90 | | ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] :
% 280.06/41.90 | (c_Groups_Oplus__class_Oplus(v2, v8, v6) = v9 &
% 280.06/41.90 | c_RealVector_Onorm__class_Onorm(v2, v9) = v10 & hAPP(v1, v7) =
% 280.06/41.90 | v8 & $i(v10) & $i(v9) & $i(v8) & $i(v7) & ~
% 280.06/41.90 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v10, v3)))
% 280.06/41.90 | & ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 280.06/41.90 | c_SEQ_OBseq(v2, v1) | ~
% 280.06/41.90 | class_RealVector_Oreal__normed__vector(v2) | ? [v3: $i] : ?
% 280.06/41.90 | [v4: $i] : ? [v5: $i] : ? [v6: $i] :
% 280.06/41.90 | (c_Groups_Ouminus__class_Ouminus(v2, v5) = v6 & hAPP(v1, v4) = v5
% 280.06/41.90 | & $i(v6) & $i(v5) & $i(v4) & $i(v3) &
% 280.06/41.90 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) & !
% 280.06/41.90 | [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ( ~
% 280.06/41.90 | (c_Groups_Oplus__class_Oplus(v2, v8, v6) = v9) | ~
% 280.06/41.90 | (c_RealVector_Onorm__class_Onorm(v2, v9) = v10) | ~
% 280.06/41.90 | (hAPP(v1, v7) = v8) | ~ $i(v7) |
% 280.06/41.90 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v10,
% 280.06/41.90 | v3)))))
% 280.06/41.90 |
% 280.06/41.90 | ALPHA: (fact_Bseq__iff2) implies:
% 280.06/41.90 | (134) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 280.06/41.90 | $i(v0) & ? [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 280.06/41.90 | [v5: $i] : ( ~ (c_Groups_Ouminus__class_Ouminus(v2, v4) = v5) | ~
% 280.06/41.90 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 280.06/41.90 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | ~
% 280.06/41.90 | class_RealVector_Oreal__normed__vector(v2) | c_SEQ_OBseq(v2, v1)
% 280.06/41.90 | | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 280.06/41.90 | (c_Groups_Oplus__class_Oplus(v2, v7, v5) = v8 &
% 280.06/41.90 | c_RealVector_Onorm__class_Onorm(v2, v8) = v9 & hAPP(v1, v6) =
% 280.06/41.90 | v7 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & ~
% 280.06/41.90 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v9, v3))) &
% 280.06/41.90 | ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 280.06/41.90 | c_SEQ_OBseq(v2, v1) | ~
% 280.06/41.90 | class_RealVector_Oreal__normed__vector(v2) | ? [v3: $i] : ?
% 280.06/41.90 | [v4: $i] : ? [v5: $i] : (c_Groups_Ouminus__class_Ouminus(v2, v4)
% 280.06/41.90 | = v5 & $i(v5) & $i(v4) & $i(v3) &
% 280.06/41.90 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) & !
% 280.06/41.90 | [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~
% 280.06/41.90 | (c_Groups_Oplus__class_Oplus(v2, v7, v5) = v8) | ~
% 280.06/41.90 | (c_RealVector_Onorm__class_Onorm(v2, v8) = v9) | ~ (hAPP(v1,
% 280.06/41.90 | v6) = v7) | ~ $i(v6) |
% 280.06/41.90 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v9,
% 280.06/41.90 | v3)))))
% 280.06/41.90 |
% 280.06/41.90 | ALPHA: (fact_BseqD) implies:
% 280.06/41.90 | (135) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 280.06/41.90 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 280.06/41.90 | c_SEQ_OBseq(v2, v1) | ~
% 280.06/41.90 | class_RealVector_Oreal__normed__vector(v2) | ? [v3: $i] :
% 280.06/41.90 | ($i(v3) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3)
% 280.06/41.90 | & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 280.06/41.90 | (c_RealVector_Onorm__class_Onorm(v2, v5) = v6) | ~ (hAPP(v1,
% 280.06/41.90 | v4) = v5) | ~ $i(v4) |
% 280.06/41.90 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6,
% 280.06/41.90 | v3)))))
% 280.06/41.90 |
% 280.06/41.90 | ALPHA: (fact_BseqI) implies:
% 280.06/41.91 | (136) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 280.06/41.91 | $i(v0) & ? [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~
% 280.06/41.91 | $i(v2) | ~ $i(v1) | ~
% 280.06/41.91 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ~
% 280.06/41.91 | class_RealVector_Oreal__normed__vector(v3) | c_SEQ_OBseq(v3, v1)
% 280.06/41.91 | | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] :
% 280.06/41.91 | (c_RealVector_Onorm__class_Onorm(v3, v5) = v6 & hAPP(v1, v4) = v5
% 280.06/41.91 | & $i(v6) & $i(v5) & $i(v4) & ~
% 280.06/41.91 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v2))))
% 280.06/41.91 |
% 280.06/41.91 | ALPHA: (fact_lemma__NBseq__def2) implies:
% 280.06/41.91 | (137) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 280.06/41.91 | $i(v0) & ? [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 280.06/41.91 | ~ (c_Nat_OSuc(v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 280.06/41.91 | class_RealVector_Oreal__normed__vector(v2) | ? [v5: $i] : ?
% 280.06/41.91 | [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ($i(v7) &
% 280.06/41.91 | $i(v5) & ((c_RealDef_Oreal(tc_Nat_Onat, v4) = v6 &
% 280.06/41.91 | c_RealVector_Onorm__class_Onorm(v2, v8) = v9 & hAPP(v1, v7)
% 280.06/41.91 | = v8 & $i(v9) & $i(v8) & $i(v6) & ~
% 280.06/41.91 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v9, v6)) |
% 280.06/41.91 | (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v5) & !
% 280.06/41.91 | [v10: $i] : ! [v11: $i] : ! [v12: $i] : ( ~
% 280.06/41.91 | (c_RealVector_Onorm__class_Onorm(v2, v11) = v12) | ~
% 280.06/41.91 | (hAPP(v1, v10) = v11) | ~ $i(v10) |
% 280.06/41.91 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v12,
% 280.06/41.91 | v5)))))) & ? [v1: $i] : ! [v2: $i] : ! [v3: $i] : (
% 280.06/41.91 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 280.06/41.91 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | ~
% 280.06/41.91 | class_RealVector_Oreal__normed__vector(v2) | ? [v4: $i] : ?
% 280.06/41.91 | [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i]
% 280.06/41.91 | : ($i(v7) & $i(v4) & ((c_Nat_OSuc(v4) = v5 &
% 280.06/41.91 | c_RealDef_Oreal(tc_Nat_Onat, v5) = v6 & $i(v6) & $i(v5) &
% 280.06/41.91 | ! [v10: $i] : ! [v11: $i] : ! [v12: $i] : ( ~
% 280.06/41.91 | (c_RealVector_Onorm__class_Onorm(v2, v11) = v12) | ~
% 280.06/41.91 | (hAPP(v1, v10) = v11) | ~ $i(v10) |
% 280.06/41.91 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v12,
% 280.06/41.91 | v6))) | (c_RealVector_Onorm__class_Onorm(v2, v8) = v9 &
% 280.06/41.91 | hAPP(v1, v7) = v8 & $i(v9) & $i(v8) & ~
% 280.06/41.91 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v9,
% 280.06/41.91 | v3))))))
% 280.06/41.91 |
% 280.06/41.91 | ALPHA: (arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add) implies:
% 280.06/41.91 | (138) class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal)
% 280.06/41.91 |
% 280.06/41.91 | ALPHA: (arity_RealDef__Oreal__Rings_Olinordered__semidom) implies:
% 280.06/41.91 | (139) class_Rings_Olinordered__semidom(tc_RealDef_Oreal)
% 280.06/41.91 |
% 280.06/41.91 | ALPHA: (arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) implies:
% 280.06/41.91 | (140) class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
% 280.06/41.91 |
% 280.06/41.91 | ALPHA: (arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) implies:
% 280.06/41.91 | (141) class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)
% 280.06/41.91 |
% 280.06/41.91 | ALPHA: (arity_Complex__Ocomplex__Groups_Ogroup__add) implies:
% 280.06/41.91 | (142) class_Groups_Ogroup__add(tc_Complex_Ocomplex)
% 280.06/41.91 |
% 280.06/41.91 | ALPHA: (conj_0) implies:
% 280.06/41.91 | (143) $i(tc_RealDef_Oreal)
% 280.06/41.91 | (144) $i(tc_Complex_Ocomplex)
% 280.06/41.91 | (145) $i(v_w)
% 280.06/41.91 | (146) $i(v_z)
% 280.06/41.91 | (147) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 280.06/41.91 | (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v_w, v_z) = v1 &
% 280.06/41.91 | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v3) = v4 &
% 280.06/41.91 | c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v1) = v2 &
% 280.06/41.91 | c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_z) = v3 &
% 280.06/41.91 | c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w) = v0 &
% 280.06/41.91 | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ~
% 280.06/41.91 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v4))
% 280.06/41.91 |
% 280.06/41.91 | ALPHA: (function-axioms) implies:
% 280.06/41.91 | (148) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 280.06/41.91 | (c_Groups_Ozero__class_Ozero(v2) = v1) | ~
% 280.06/41.91 | (c_Groups_Ozero__class_Ozero(v2) = v0))
% 280.06/41.91 | (149) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 280.06/41.91 | (c_Groups_Oone__class_Oone(v2) = v1) | ~
% 280.06/41.91 | (c_Groups_Oone__class_Oone(v2) = v0))
% 280.06/41.91 | (150) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 280.06/41.91 | (c_RealVector_Onorm__class_Onorm(v3, v2) = v1) | ~
% 280.06/41.91 | (c_RealVector_Onorm__class_Onorm(v3, v2) = v0))
% 280.06/41.91 | (151) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 280.06/41.91 | (v1 = v0 | ~ (c_Groups_Ominus__class_Ominus(v4, v3, v2) = v1) | ~
% 280.06/41.91 | (c_Groups_Ominus__class_Ominus(v4, v3, v2) = v0))
% 280.06/41.91 | (152) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 280.06/41.91 | (v1 = v0 | ~ (c_Groups_Oplus__class_Oplus(v4, v3, v2) = v1) | ~
% 280.06/41.91 | (c_Groups_Oplus__class_Oplus(v4, v3, v2) = v0))
% 280.06/41.91 |
% 280.06/41.91 | DELTA: instantiating (108) with fresh symbol all_631_0 gives:
% 280.06/41.91 | (153) c_Complex_ORe(c_Complex_Oii) = all_631_0 &
% 280.06/41.91 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_631_0 &
% 280.06/41.91 | $i(all_631_0)
% 280.06/41.91 |
% 280.06/41.91 | ALPHA: (153) implies:
% 280.06/41.91 | (154) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_631_0
% 280.06/41.91 |
% 280.06/41.91 | DELTA: instantiating (109) with fresh symbol all_633_0 gives:
% 280.06/41.91 | (155) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_633_0 &
% 280.06/41.91 | c_Complex_OIm(c_Complex_Oii) = all_633_0 & $i(all_633_0)
% 280.06/41.91 |
% 280.06/41.91 | ALPHA: (155) implies:
% 280.06/41.91 | (156) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_633_0
% 280.06/41.91 |
% 280.06/41.91 | DELTA: instantiating (35) with fresh symbols all_682_0, all_682_1 gives:
% 280.06/41.91 | (157) c_Complex_Ocomplex_OComplex(all_682_0, all_682_0) = all_682_1 &
% 280.06/41.91 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_682_1 &
% 280.06/41.91 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_682_0 &
% 280.06/41.91 | $i(all_682_0) & $i(all_682_1)
% 280.06/41.91 |
% 280.06/41.91 | ALPHA: (157) implies:
% 280.06/41.91 | (158) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_682_0
% 280.06/41.91 |
% 280.06/41.91 | DELTA: instantiating (7) with fresh symbols all_684_0, all_684_1 gives:
% 280.06/41.91 | (159) c_Complex_OIm(all_684_1) = all_684_0 &
% 280.06/41.91 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_684_1 &
% 280.06/41.91 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_684_0 &
% 280.06/41.91 | $i(all_684_0) & $i(all_684_1)
% 280.06/41.91 |
% 280.06/41.91 | ALPHA: (159) implies:
% 280.06/41.91 | (160) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_684_0
% 280.06/41.91 |
% 280.06/41.91 | DELTA: instantiating (6) with fresh symbols all_691_0, all_691_1 gives:
% 280.06/41.91 | (161) c_Complex_ORe(all_691_1) = all_691_0 &
% 280.06/41.91 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_691_1 &
% 280.06/41.91 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_691_0 &
% 280.06/41.91 | $i(all_691_0) & $i(all_691_1)
% 280.06/41.91 |
% 280.06/41.91 | ALPHA: (161) implies:
% 280.06/41.91 | (162) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_691_0
% 280.06/41.91 |
% 280.06/41.91 | DELTA: instantiating (74) with fresh symbols all_696_0, all_696_1 gives:
% 280.06/41.91 | (163) c_RealDef_Oreal(tc_Nat_Onat, all_696_1) = all_696_0 &
% 280.06/41.91 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_696_1 &
% 280.06/41.91 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_696_0 &
% 280.06/41.91 | $i(all_696_0) & $i(all_696_1)
% 280.06/41.91 |
% 280.06/41.91 | ALPHA: (163) implies:
% 280.06/41.91 | (164) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_696_0
% 280.06/41.91 |
% 280.06/41.91 | DELTA: instantiating (72) with fresh symbol all_704_0 gives:
% 280.06/41.91 | (165) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_704_0 &
% 280.06/41.91 | $i(all_704_0) & ! [v0: $i] : ! [v1: $i] : ( ~
% 280.06/41.91 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v1) | ~ $i(v0) | ~
% 280.06/41.91 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, all_704_0))
% 280.06/41.91 |
% 280.06/41.91 | ALPHA: (165) implies:
% 280.06/41.91 | (166) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_704_0
% 280.06/41.91 |
% 280.06/41.91 | DELTA: instantiating (116) with fresh symbols all_724_0, all_724_1 gives:
% 280.06/41.91 | (167) c_Transcendental_Oln(all_724_1) = all_724_0 &
% 280.06/41.91 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_724_1 &
% 280.06/41.91 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_724_0 &
% 280.06/41.91 | $i(all_724_0) & $i(all_724_1)
% 280.06/41.91 |
% 280.06/41.91 | ALPHA: (167) implies:
% 280.06/41.91 | (168) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_724_0
% 280.06/41.91 | (169) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_724_1
% 280.06/41.91 |
% 280.06/41.91 | DELTA: instantiating (85) with fresh symbols all_735_0, all_735_1 gives:
% 280.06/41.91 | (170) c_RComplete_Onatceiling(all_735_1) = all_735_0 &
% 280.06/41.91 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_735_0 &
% 280.06/41.91 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_735_1 &
% 280.06/41.91 | $i(all_735_0) & $i(all_735_1)
% 280.06/41.91 |
% 280.06/41.91 | ALPHA: (170) implies:
% 280.06/41.91 | (171) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_735_1
% 280.06/41.91 |
% 280.06/41.91 | DELTA: instantiating (110) with fresh symbols all_740_0, all_740_1 gives:
% 280.06/41.91 | (172) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_740_0 &
% 280.06/41.91 | c_Complex_Ocomplex_OComplex(all_740_1, all_740_0) = c_Complex_Oii &
% 280.06/41.91 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_740_1 &
% 280.06/41.91 | $i(all_740_0) & $i(all_740_1)
% 280.06/41.91 |
% 280.06/41.91 | ALPHA: (172) implies:
% 280.06/41.91 | (173) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_740_1
% 280.06/41.91 | (174) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_740_0
% 280.06/41.91 |
% 280.06/41.91 | DELTA: instantiating (71) with fresh symbol all_742_0 gives:
% 280.06/41.91 | (175) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_742_0 &
% 280.06/41.91 | $i(all_742_0) & ! [v0: $i] : ! [v1: $i] : ( ~
% 280.06/41.91 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v1) | ~ $i(v0) |
% 280.06/41.91 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_742_0, v1))
% 280.06/41.91 |
% 280.06/41.91 | ALPHA: (175) implies:
% 280.06/41.91 | (176) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_742_0
% 280.06/41.91 |
% 280.06/41.91 | DELTA: instantiating (99) with fresh symbols all_749_0, all_749_1 gives:
% 280.06/41.91 | (177) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_749_1 &
% 280.06/41.91 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_749_0 &
% 280.06/41.91 | c_RealDef_Oreal(tc_Nat_Onat, all_749_1) = all_749_0 & $i(all_749_0) &
% 280.06/41.91 | $i(all_749_1)
% 280.06/41.91 |
% 280.06/41.91 | ALPHA: (177) implies:
% 280.06/41.91 | (178) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_749_0
% 280.06/41.91 |
% 280.06/41.91 | DELTA: instantiating (101) with fresh symbols all_751_0, all_751_1 gives:
% 280.06/41.91 | (179) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_751_0 &
% 280.06/41.91 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_751_1 &
% 280.06/41.91 | c_RComplete_Onatceiling(all_751_1) = all_751_0 & $i(all_751_0) &
% 280.06/41.91 | $i(all_751_1)
% 280.06/41.91 |
% 280.06/41.91 | ALPHA: (179) implies:
% 280.06/41.91 | (180) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_751_1
% 280.06/41.91 |
% 280.06/41.91 | DELTA: instantiating (84) with fresh symbols all_753_0, all_753_1 gives:
% 280.06/41.91 | (181) ~ (all_753_0 = all_753_1) &
% 280.06/41.91 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_753_0 &
% 280.06/41.91 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_753_1 &
% 280.06/41.91 | $i(all_753_0) & $i(all_753_1)
% 280.06/41.91 |
% 280.06/41.91 | ALPHA: (181) implies:
% 280.06/41.91 | (182) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_753_1
% 280.06/41.91 | (183) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_753_0
% 280.06/41.91 |
% 280.06/41.91 | DELTA: instantiating (100) with fresh symbols all_755_0, all_755_1 gives:
% 280.06/41.91 | (184) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_755_0 &
% 280.06/41.91 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_755_1 &
% 280.06/41.91 | c_RComplete_Onatfloor(all_755_1) = all_755_0 & $i(all_755_0) &
% 280.06/41.91 | $i(all_755_1)
% 280.06/41.91 |
% 280.06/41.91 | ALPHA: (184) implies:
% 280.06/41.91 | (185) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_755_1
% 280.06/41.91 |
% 280.06/41.91 | DELTA: instantiating (98) with fresh symbols all_757_0, all_757_1 gives:
% 280.06/41.91 | (186) c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = all_757_1 &
% 280.06/41.91 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_757_0 &
% 280.06/41.91 | c_Complex_ORe(all_757_1) = all_757_0 & $i(all_757_0) & $i(all_757_1)
% 280.06/41.91 |
% 280.06/41.91 | ALPHA: (186) implies:
% 280.06/41.91 | (187) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_757_0
% 280.06/41.91 |
% 280.06/41.91 | DELTA: instantiating (67) with fresh symbols all_759_0, all_759_1 gives:
% 280.06/41.91 | (188) c_RComplete_Onatfloor(all_759_1) = all_759_0 &
% 280.06/41.91 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_759_0 &
% 280.06/41.91 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_759_1 &
% 280.06/41.91 | $i(all_759_0) & $i(all_759_1)
% 280.06/41.91 |
% 280.06/41.91 | ALPHA: (188) implies:
% 280.06/41.91 | (189) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_759_1
% 280.06/41.91 |
% 280.06/41.91 | DELTA: instantiating (97) with fresh symbols all_767_0, all_767_1 gives:
% 280.06/41.92 | (190) c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = all_767_1 &
% 280.06/41.92 | c_Complex_OIm(all_767_1) = all_767_0 &
% 280.06/41.92 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_767_0 &
% 280.06/41.92 | $i(all_767_0) & $i(all_767_1)
% 280.06/41.92 |
% 280.06/41.92 | ALPHA: (190) implies:
% 280.06/41.92 | (191) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_767_0
% 280.06/41.92 |
% 280.06/41.92 | DELTA: instantiating (117) with fresh symbol all_779_0 gives:
% 280.06/41.92 | (192) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_779_0 &
% 280.06/41.92 | $i(all_779_0) & ! [v0: $i] : ! [v1: $i] : ( ~
% 280.06/41.92 | (c_Transcendental_Oln(v0) = v1) | ~ $i(v0) | ~
% 280.06/41.92 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_779_0, v0) |
% 280.06/41.92 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v0))
% 280.06/41.92 |
% 280.06/41.92 | ALPHA: (192) implies:
% 280.06/41.92 | (193) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_779_0
% 280.06/41.92 |
% 280.06/41.92 | DELTA: instantiating (86) with fresh symbol all_820_0 gives:
% 280.06/41.92 | (194) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_820_0 &
% 280.06/41.92 | $i(all_820_0) & ! [v0: $i] : ! [v1: $i] : ( ~
% 280.06/41.92 | (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v0) = v1) | ~ $i(v0)
% 280.06/41.92 | | ? [v2: $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1,
% 280.06/41.92 | all_820_0) = v2 & $i(v2) & ~
% 280.06/41.92 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v0)))
% 280.06/41.92 |
% 280.06/41.92 | ALPHA: (194) implies:
% 280.06/41.92 | (195) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_820_0
% 280.06/41.92 |
% 280.06/41.92 | DELTA: instantiating (82) with fresh symbol all_826_0 gives:
% 280.06/41.92 | (196) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_826_0 &
% 280.06/41.92 | $i(all_826_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 =
% 280.06/41.92 | all_826_0 | ~ (c_Groups_Oone__class_Oone(v0) = v1) | ~
% 280.06/41.92 | (c_RealVector_Onorm__class_Onorm(v0, v1) = v2) | ~ $i(v0) | ~
% 280.06/41.92 | class_RealVector_Oreal__normed__algebra__1(v0))
% 280.06/41.92 |
% 280.06/41.92 | ALPHA: (196) implies:
% 280.06/41.92 | (197) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_826_0
% 280.06/41.92 |
% 280.06/41.92 | DELTA: instantiating (83) with fresh symbol all_838_0 gives:
% 280.06/41.92 | (198) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_838_0 &
% 280.06/41.92 | $i(all_838_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 |
% 280.06/41.92 | ~ (c_RealVector_OscaleR__class_OscaleR(v1, all_838_0, v0) = v2) |
% 280.06/41.92 | ~ $i(v1) | ~ $i(v0) | ~ class_RealVector_Oreal__vector(v1))
% 280.06/41.92 |
% 280.06/41.92 | ALPHA: (198) implies:
% 280.06/41.92 | (199) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_838_0
% 280.06/41.92 |
% 280.06/41.92 | DELTA: instantiating (18) with fresh symbol all_843_0 gives:
% 280.06/41.92 | (200) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_843_0 &
% 280.06/41.92 | $i(all_843_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 280.06/41.92 | (c_RealVector_Onorm__class_Onorm(v1, v0) = v2) | ~ $i(v1) | ~
% 280.06/41.92 | $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2,
% 280.06/41.92 | all_843_0) | ~ class_RealVector_Oreal__normed__vector(v1))
% 280.06/41.92 |
% 280.06/41.92 | ALPHA: (200) implies:
% 280.06/41.92 | (201) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_843_0
% 280.06/41.92 |
% 280.06/41.92 | DELTA: instantiating (5) with fresh symbols all_853_0, all_853_1 gives:
% 280.06/41.92 | (202) c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_853_0 &
% 280.06/41.92 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_853_1 &
% 280.06/41.92 | $i(all_853_0) & $i(all_853_1) & ! [v0: $i] : ! [v1: int] : (v1 =
% 280.06/41.92 | all_853_0 | ~ (c_Complex_Orcis(all_853_1, v0) = v1) | ~ $i(v0))
% 280.06/41.92 |
% 280.06/41.92 | ALPHA: (202) implies:
% 280.06/41.92 | (203) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_853_1
% 280.06/41.92 |
% 280.06/41.92 | DELTA: instantiating (12) with fresh symbol all_856_0 gives:
% 280.06/41.92 | (204) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_856_0 &
% 280.06/41.92 | $i(all_856_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 =
% 280.06/41.92 | all_856_0 | ~ (c_RealVector_Odist__class_Odist(v1, v0, v0) = v2) |
% 280.06/41.92 | ~ $i(v1) | ~ $i(v0) | ~ class_RealVector_Ometric__space(v1))
% 280.06/41.92 |
% 280.06/41.92 | ALPHA: (204) implies:
% 280.06/41.92 | (205) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_856_0
% 280.06/41.92 |
% 280.06/41.92 | DELTA: instantiating (103) with fresh symbols all_861_0, all_861_1, all_861_2
% 280.06/41.92 | gives:
% 280.06/41.92 | (206) c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = all_861_2 &
% 280.06/41.92 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_861_1 &
% 280.06/41.92 | c_Complex_Ocomplex_OComplex(all_861_1, all_861_0) = all_861_2 &
% 280.06/41.92 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_861_0 &
% 280.06/41.92 | $i(all_861_0) & $i(all_861_1) & $i(all_861_2)
% 280.06/41.92 |
% 280.06/41.92 | ALPHA: (206) implies:
% 280.06/41.92 | (207) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_861_0
% 280.06/41.92 | (208) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_861_1
% 280.06/41.92 |
% 280.06/41.92 | DELTA: instantiating (23) with fresh symbol all_868_0 gives:
% 280.06/41.92 | (209) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_868_0 &
% 280.06/41.92 | $i(all_868_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 =
% 280.06/41.92 | all_868_0 | ~ (c_Groups_Ozero__class_Ozero(v0) = v1) | ~
% 280.06/41.92 | (c_RealVector_Onorm__class_Onorm(v0, v1) = v2) | ~ $i(v0) | ~
% 280.06/41.92 | class_RealVector_Oreal__normed__vector(v0))
% 280.06/41.92 |
% 280.06/41.92 | ALPHA: (209) implies:
% 280.06/41.92 | (210) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_868_0
% 280.06/41.92 |
% 280.06/41.92 | DELTA: instantiating (29) with fresh symbol all_874_0 gives:
% 280.06/41.92 | (211) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_874_0 &
% 280.06/41.92 | $i(all_874_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 280.06/41.92 | (c_RealVector_Onorm__class_Onorm(v1, v0) = v2) | ~ $i(v1) | ~
% 280.06/41.92 | $i(v0) | ~ class_RealVector_Oreal__normed__vector(v1) |
% 280.06/41.92 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_874_0, v2))
% 280.06/41.92 |
% 280.06/41.92 | ALPHA: (211) implies:
% 280.06/41.92 | (212) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_874_0
% 280.06/41.92 | (213) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 280.06/41.92 | (c_RealVector_Onorm__class_Onorm(v1, v0) = v2) | ~ $i(v1) | ~
% 280.06/41.92 | $i(v0) | ~ class_RealVector_Oreal__normed__vector(v1) |
% 280.06/41.92 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_874_0, v2))
% 280.06/41.92 |
% 280.06/41.92 | DELTA: instantiating (68) with fresh symbols all_882_0, all_882_1 gives:
% 280.06/41.92 | (214) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_882_0 &
% 280.06/41.92 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_882_1 &
% 280.06/41.92 | $i(all_882_0) & $i(all_882_1) & ! [v0: $i] : ! [v1: int] : (v1 =
% 280.06/41.92 | all_882_0 | ~ (c_RComplete_Onatfloor(v0) = v1) | ~ $i(v0) | ~
% 280.06/41.92 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, all_882_1))
% 280.06/41.92 |
% 280.06/41.92 | ALPHA: (214) implies:
% 280.06/41.92 | (215) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_882_1
% 280.06/41.92 |
% 280.06/41.92 | DELTA: instantiating (17) with fresh symbol all_885_0 gives:
% 280.06/41.92 | (216) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_885_0 &
% 280.06/41.92 | $i(all_885_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 280.06/41.92 | : ( ~ (c_RealVector_Odist__class_Odist(v2, v1, v0) = v3) | ~ $i(v2)
% 280.06/41.92 | | ~ $i(v1) | ~ $i(v0) | ~ class_RealVector_Ometric__space(v2) |
% 280.06/41.92 | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, all_885_0))
% 280.06/41.92 |
% 280.06/41.92 | ALPHA: (216) implies:
% 280.06/41.92 | (217) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_885_0
% 280.06/41.92 |
% 280.06/41.92 | DELTA: instantiating (15) with fresh symbol all_888_0 gives:
% 280.06/41.92 | (218) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_888_0 &
% 280.06/41.92 | $i(all_888_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 280.06/41.92 | (c_RealVector_OscaleR__class_OscaleR(v1, all_888_0, v0) = v2) | ~
% 280.06/41.92 | $i(v1) | ~ $i(v0) | ~ class_RealVector_Oreal__vector(v1) |
% 280.06/41.92 | (c_Groups_Ozero__class_Ozero(v1) = v2 & $i(v2)))
% 280.06/41.92 |
% 280.06/41.92 | ALPHA: (218) implies:
% 280.06/41.92 | (219) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_888_0
% 280.06/41.92 |
% 280.06/41.92 | DELTA: instantiating (16) with fresh symbol all_894_0 gives:
% 280.06/41.92 | (220) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_894_0 &
% 280.06/41.92 | $i(all_894_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 280.06/41.92 | (c_RealVector_OscaleR__class_OscaleR(v1, all_894_0, v0) = v2) | ~
% 280.06/41.92 | $i(v1) | ~ $i(v0) | ~ class_RealVector_Oreal__normed__vector(v1)
% 280.06/41.92 | | (c_Groups_Ozero__class_Ozero(v1) = v2 & $i(v2)))
% 280.06/41.92 |
% 280.06/41.92 | ALPHA: (220) implies:
% 280.06/41.92 | (221) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_894_0
% 280.06/41.92 |
% 280.06/41.92 | DELTA: instantiating (19) with fresh symbol all_897_0 gives:
% 280.06/41.92 | (222) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_897_0 &
% 280.06/41.92 | $i(all_897_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 280.06/41.92 | : ( ~ (c_RealVector_Odist__class_Odist(v2, v1, v0) = v3) | ~ $i(v2)
% 280.06/41.92 | | ~ $i(v1) | ~ $i(v0) | ~ class_RealVector_Ometric__space(v2) |
% 280.06/41.92 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_897_0, v3))
% 280.06/41.92 |
% 280.06/41.92 | ALPHA: (222) implies:
% 280.06/41.92 | (223) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_897_0
% 280.06/41.92 |
% 280.06/41.92 | DELTA: instantiating (121) with fresh symbols all_906_0, all_906_1 gives:
% 280.06/41.92 | (224) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_906_1 &
% 280.06/41.92 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_906_0 &
% 280.06/41.92 | $i(all_906_0) & $i(all_906_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 280.06/41.92 | (c_Transcendental_Oln(v0) = v1) | ~ $i(v0) | ~
% 280.06/41.92 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_906_1, v0)
% 280.06/41.92 | | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_906_0,
% 280.06/41.92 | v1))
% 280.06/41.92 |
% 280.06/41.92 | ALPHA: (224) implies:
% 280.06/41.92 | (225) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_906_0
% 280.06/41.92 | (226) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_906_1
% 280.06/41.92 |
% 280.06/41.92 | DELTA: instantiating (87) with fresh symbols all_912_0, all_912_1 gives:
% 280.06/41.92 | (227) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_912_0 &
% 280.06/41.92 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_912_1 &
% 280.06/41.92 | $i(all_912_0) & $i(all_912_1) & ! [v0: $i] : ! [v1: int] : (v1 =
% 280.06/41.92 | all_912_0 | ~ (c_RComplete_Onatceiling(v0) = v1) | ~ $i(v0) | ~
% 280.06/41.92 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, all_912_1))
% 280.06/41.92 |
% 280.06/41.92 | ALPHA: (227) implies:
% 280.06/41.92 | (228) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_912_1
% 280.06/41.92 |
% 280.06/41.92 | DELTA: instantiating (76) with fresh symbol all_927_0 gives:
% 280.06/41.92 | (229) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_927_0 &
% 280.06/41.92 | $i(all_927_0) & ! [v0: $i] : ! [v1: $i] : ( ~
% 280.06/41.92 | (c_RComplete_Onatfloor(v0) = v1) | ~ $i(v0) | ~
% 280.06/41.92 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_927_0, v0)
% 280.06/41.92 | | ? [v2: $i] : (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2 & $i(v2) &
% 280.06/41.92 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v0)))
% 280.06/41.92 |
% 280.06/41.92 | ALPHA: (229) implies:
% 280.06/41.92 | (230) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_927_0
% 280.06/41.92 |
% 280.06/41.92 | DELTA: instantiating (122) with fresh symbols all_933_0, all_933_1 gives:
% 280.06/41.92 | (231) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_933_1 &
% 280.06/41.92 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_933_0 &
% 280.06/41.92 | $i(all_933_0) & $i(all_933_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 280.06/41.92 | (c_Transcendental_Oln(v0) = v1) | ~ $i(v0) | ~
% 280.06/41.92 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_933_1, v0) |
% 280.06/41.92 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_933_0, v1))
% 280.06/41.92 |
% 280.06/41.92 | ALPHA: (231) implies:
% 280.06/41.92 | (232) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_933_0
% 280.06/41.92 | (233) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_933_1
% 280.06/41.92 |
% 280.06/41.92 | DELTA: instantiating (118) with fresh symbol all_948_0 gives:
% 280.06/41.92 | (234) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_948_0 &
% 280.06/41.92 | $i(all_948_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 280.06/41.92 | ~ (c_Transcendental_Oln(v1) = v2) | ~ (c_Transcendental_Oln(v0) =
% 280.06/41.92 | v2) | ~ $i(v1) | ~ $i(v0) | ~
% 280.06/41.92 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_948_0, v1) | ~
% 280.06/41.92 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_948_0, v0))
% 280.06/41.92 |
% 280.06/41.92 | ALPHA: (234) implies:
% 280.06/41.92 | (235) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_948_0
% 280.06/41.92 |
% 280.06/41.92 | DELTA: instantiating (81) with fresh symbols all_954_0, all_954_1, all_954_2
% 280.06/41.92 | gives:
% 280.06/41.92 | (236) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_954_1 &
% 280.06/41.92 | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_954_2 &
% 280.06/41.92 | hAPP(all_954_2, all_954_1) = all_954_0 & $i(all_954_0) &
% 280.06/41.92 | $i(all_954_1) & $i(all_954_2) & ! [v0: $i] : ! [v1: $i] : (v1 = v0
% 280.06/41.92 | | ~ (hAPP(all_954_0, v0) = v1) | ~ $i(v0))
% 280.06/41.92 |
% 280.06/41.92 | ALPHA: (236) implies:
% 280.06/41.92 | (237) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_954_1
% 280.06/41.92 |
% 280.06/41.92 | DELTA: instantiating (73) with fresh symbols all_958_0, all_958_1 gives:
% 280.06/41.93 | (238) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_958_0 &
% 280.06/41.93 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_958_1 &
% 280.06/41.93 | $i(all_958_0) & $i(all_958_1) & ! [v0: any] : (v0 = all_958_0 | ~
% 280.06/41.93 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = all_958_1) | ~ $i(v0)) & !
% 280.06/41.93 | [v0: int] : (v0 = all_958_1 | ~ (c_RealDef_Oreal(tc_Nat_Onat,
% 280.06/41.93 | all_958_0) = v0))
% 280.06/41.93 |
% 280.06/41.93 | ALPHA: (238) implies:
% 280.06/41.93 | (239) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_958_1
% 280.06/41.93 |
% 280.06/41.93 | DELTA: instantiating (92) with fresh symbol all_961_0 gives:
% 280.06/41.93 | (240) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_961_0 &
% 280.06/41.93 | $i(all_961_0) & ! [v0: $i] : ! [v1: $i] : ( ~
% 280.06/41.93 | (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v0, all_961_0) =
% 280.06/41.93 | v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] :
% 280.06/41.93 | (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3 & c_RComplete_Onatfloor(v0)
% 280.06/41.93 | = v2 & $i(v3) & $i(v2) &
% 280.06/41.93 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v3)))
% 280.06/41.93 |
% 280.06/41.93 | ALPHA: (240) implies:
% 280.06/41.93 | (241) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_961_0
% 280.06/41.93 |
% 280.06/41.93 | DELTA: instantiating (90) with fresh symbols all_964_0, all_964_1 gives:
% 280.06/41.93 | (242) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_964_0 &
% 280.06/41.93 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_964_1 &
% 280.06/41.93 | $i(all_964_0) & $i(all_964_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 280.06/41.93 | (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v0) = v1) | ~ $i(v0)
% 280.06/41.93 | | ? [v2: $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,
% 280.06/41.93 | all_964_0, v1) = v2 & $i(v2) &
% 280.06/41.93 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_964_1, v2)))
% 280.06/41.93 |
% 280.06/41.93 | ALPHA: (242) implies:
% 280.06/41.93 | (243) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_964_1
% 280.06/41.93 | (244) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_964_0
% 280.06/41.93 |
% 280.06/41.93 | DELTA: instantiating (126) with fresh symbols all_967_0, all_967_1 gives:
% 280.06/41.93 | (245) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_967_0 &
% 280.06/41.93 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_967_1 &
% 280.06/41.93 | $i(all_967_0) & $i(all_967_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 280.06/41.93 | (c_Transcendental_Oln(v0) = v1) | ~ $i(v0) | ~
% 280.06/41.93 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, all_967_0) | ~
% 280.06/41.93 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_967_1, v0) |
% 280.06/41.93 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, all_967_1))
% 280.06/41.93 |
% 280.06/41.93 | ALPHA: (245) implies:
% 280.06/41.93 | (246) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_967_1
% 280.06/41.93 | (247) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_967_0
% 280.06/41.93 |
% 280.06/41.93 | DELTA: instantiating (128) with fresh symbols all_970_0, all_970_1 gives:
% 280.06/41.93 | (248) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_970_0 &
% 280.06/41.93 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_970_1 &
% 280.06/41.93 | $i(all_970_0) & $i(all_970_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 280.06/41.93 | (c_Transcendental_Oln(v0) = v1) | ~ $i(v0) | ~
% 280.06/41.93 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_970_1, v0) | ~
% 280.06/41.93 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_970_1, v1)
% 280.06/41.93 | | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_970_0,
% 280.06/41.93 | v0))
% 280.06/41.93 |
% 280.06/41.93 | ALPHA: (248) implies:
% 280.06/41.93 | (249) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_970_1
% 280.06/41.93 | (250) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_970_0
% 280.06/41.93 |
% 280.06/41.93 | DELTA: instantiating (127) with fresh symbols all_973_0, all_973_1 gives:
% 280.06/41.93 | (251) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_973_0 &
% 280.06/41.93 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_973_1 &
% 280.06/41.93 | $i(all_973_0) & $i(all_973_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 280.06/41.93 | (c_Transcendental_Oln(v0) = v1) | ~ $i(v0) | ~
% 280.06/41.93 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_973_1, v1) | ~
% 280.06/41.93 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_973_1, v0) |
% 280.06/41.93 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_973_0, v0))
% 280.06/41.93 |
% 280.06/41.93 | ALPHA: (251) implies:
% 280.06/41.93 | (252) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_973_1
% 280.06/41.93 | (253) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_973_0
% 280.06/41.93 |
% 280.06/41.93 | DELTA: instantiating (91) with fresh symbol all_978_0 gives:
% 280.06/41.93 | (254) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_978_0 &
% 280.06/41.93 | $i(all_978_0) & ! [v0: $i] : ! [v1: $i] : ( ~
% 280.06/41.93 | (c_RComplete_Onatfloor(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ?
% 280.06/41.93 | [v3: $i] : (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2 &
% 280.06/41.93 | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, all_978_0) = v3
% 280.06/41.93 | & $i(v3) & $i(v2) &
% 280.06/41.93 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3)))
% 280.06/41.93 |
% 280.06/41.93 | ALPHA: (254) implies:
% 280.06/41.93 | (255) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_978_0
% 280.06/41.93 |
% 280.06/41.93 | DELTA: instantiating (70) with fresh symbol all_984_0 gives:
% 280.06/41.93 | (256) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_984_0 &
% 280.06/41.93 | $i(all_984_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 280.06/41.93 | : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v0) = v2) | ~
% 280.06/41.93 | (c_RComplete_Onatfloor(v1) = v3) | ~ $i(v1) | ~ $i(v0) | ~
% 280.06/41.93 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v2) | ~
% 280.06/41.93 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_984_0, v1)
% 280.06/41.93 | | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v3, v0))
% 280.06/41.93 |
% 280.06/41.93 | ALPHA: (256) implies:
% 280.06/41.93 | (257) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_984_0
% 280.06/41.93 |
% 280.06/41.93 | DELTA: instantiating (131) with fresh symbols all_999_0, all_999_1 gives:
% 280.06/41.93 | (258) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_999_0 &
% 280.06/41.93 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_999_1 &
% 280.06/41.93 | $i(all_999_0) & $i(all_999_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 280.06/41.93 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_999_0, v0) = v1)
% 280.06/41.93 | | ~ $i(v0) | ~
% 280.06/41.93 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_999_1, v0)
% 280.06/41.93 | | ? [v2: $i] : (c_Transcendental_Oln(v1) = v2 & $i(v2) &
% 280.06/41.93 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v0)))
% 280.06/41.93 |
% 280.06/41.93 | ALPHA: (258) implies:
% 280.06/41.93 | (259) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_999_1
% 280.06/41.93 | (260) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_999_0
% 280.06/41.93 |
% 280.06/41.93 | DELTA: instantiating (75) with fresh symbols all_1005_0, all_1005_1 gives:
% 280.06/41.93 | (261) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1005_0 &
% 280.06/41.93 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1005_1 &
% 280.06/41.93 | $i(all_1005_0) & $i(all_1005_1) & ! [v0: any] : ! [v1: $i] : (v0 =
% 280.06/41.93 | all_1005_0 | ~ (c_RealDef_Oreal(tc_Nat_Onat, v0) = v1) | ~ $i(v0)
% 280.06/41.93 | | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1,
% 280.06/41.93 | all_1005_1)) & ! [v0: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat,
% 280.06/41.93 | all_1005_0) = v0) |
% 280.06/41.93 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0,
% 280.06/41.93 | all_1005_1))
% 280.06/41.93 |
% 280.06/41.93 | ALPHA: (261) implies:
% 280.06/41.93 | (262) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1005_1
% 280.06/41.93 |
% 280.06/41.93 | DELTA: instantiating (25) with fresh symbol all_1044_0 gives:
% 280.06/41.93 | (263) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1044_0 &
% 280.06/41.93 | $i(all_1044_0) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~
% 280.06/41.93 | (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v0) = v1) | ~ $i(v0)
% 280.06/41.93 | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, all_1044_0))
% 280.06/41.93 | & ! [v0: $i] : ! [v1: $i] : ( ~
% 280.06/41.93 | (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v0) = v1) | ~ $i(v0)
% 280.06/41.93 | | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0,
% 280.06/41.93 | all_1044_0) | (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,
% 280.06/41.93 | v0) = v1 & $i(v1)))
% 280.06/41.93 |
% 280.06/41.93 | ALPHA: (263) implies:
% 280.06/41.93 | (264) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1044_0
% 280.06/41.93 |
% 280.06/41.93 | DELTA: instantiating (25) with fresh symbol all_1047_0 gives:
% 280.06/41.93 | (265) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1047_0 &
% 280.06/41.93 | $i(all_1047_0) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~
% 280.06/41.93 | (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v0) = v1) | ~ $i(v0)
% 280.06/41.93 | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, all_1047_0))
% 280.06/41.93 | & ! [v0: $i] : ! [v1: $i] : ( ~
% 280.06/41.93 | (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v0) = v1) | ~ $i(v0)
% 280.06/41.93 | | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0,
% 280.06/41.93 | all_1047_0) | (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,
% 280.06/41.93 | v0) = v1 & $i(v1)))
% 280.06/41.93 |
% 280.06/41.93 | ALPHA: (265) implies:
% 280.06/41.93 | (266) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1047_0
% 280.06/41.93 |
% 280.06/41.93 | DELTA: instantiating (80) with fresh symbol all_1050_0 gives:
% 280.06/41.93 | (267) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1050_0 &
% 280.06/41.93 | $i(all_1050_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 280.06/41.93 | $i] : (v3 = v1 | ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) | ~
% 280.06/41.93 | (c_RComplete_Onatfloor(v0) = v3) | ~ $i(v1) | ~ $i(v0) | ~
% 280.06/41.93 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v0) | ?
% 280.06/41.93 | [v4: $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2,
% 280.06/41.93 | all_1050_0) = v4 & $i(v4) & ~
% 280.06/41.93 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4)))
% 280.06/41.93 |
% 280.06/41.93 | ALPHA: (267) implies:
% 280.06/41.93 | (268) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1050_0
% 280.06/41.93 |
% 280.06/41.93 | DELTA: instantiating (124) with fresh symbols all_1056_0, all_1056_1 gives:
% 280.06/41.93 | (269) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1056_0 &
% 280.06/41.93 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1056_1 &
% 280.06/41.93 | $i(all_1056_0) & $i(all_1056_1) & ! [v0: any] : (v0 = all_1056_0 |
% 280.06/41.93 | ~ (c_Transcendental_Oln(v0) = all_1056_1) | ~ $i(v0) | ~
% 280.06/41.93 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1056_1, v0)) &
% 280.06/41.93 | ! [v0: int] : (v0 = all_1056_1 | ~ (c_Transcendental_Oln(all_1056_0)
% 280.06/41.93 | = v0) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 280.06/41.93 | all_1056_1, all_1056_0))
% 280.06/41.93 |
% 280.06/41.93 | ALPHA: (269) implies:
% 280.06/41.93 | (270) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1056_1
% 280.06/41.93 | (271) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1056_0
% 280.06/41.93 |
% 280.06/41.93 | DELTA: instantiating (28) with fresh symbol all_1059_0 gives:
% 280.06/41.93 | (272) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1059_0 &
% 280.06/41.93 | $i(all_1059_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 =
% 280.06/41.93 | all_1059_0 | ~ (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,
% 280.06/41.93 | v0) = v1) | ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,
% 280.06/41.93 | v0, v1) = v2) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : !
% 280.06/41.93 | [v2: $i] : (v1 = v0 | ~
% 280.06/41.93 | (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v0) = v2) | ~
% 280.06/41.93 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1, v2) =
% 280.06/41.93 | all_1059_0) | ~ $i(v1) | ~ $i(v0))
% 280.06/41.93 |
% 280.06/41.93 | ALPHA: (272) implies:
% 280.06/41.93 | (273) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1059_0
% 280.06/41.93 |
% 280.06/41.93 | DELTA: instantiating (40) with fresh symbols all_1062_0, all_1062_1 gives:
% 280.06/41.93 | (274) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1062_0 &
% 280.06/41.93 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1062_1 &
% 280.06/41.93 | $i(all_1062_0) & $i(all_1062_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 280.06/41.93 | $i] : ! [v3: $i] : ( ~ (hAPP(v2, v0) = v3) | ~ (hAPP(all_1062_0,
% 280.06/41.93 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 280.06/41.93 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1062_1, v1) |
% 280.06/41.93 | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1062_1, v0) |
% 280.06/41.93 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1062_1, v3))
% 280.06/41.93 |
% 280.06/41.93 | ALPHA: (274) implies:
% 280.06/41.93 | (275) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1062_1
% 280.06/41.93 |
% 280.06/41.93 | DELTA: instantiating (147) with fresh symbols all_1068_0, all_1068_1,
% 280.06/41.93 | all_1068_2, all_1068_3, all_1068_4 gives:
% 280.06/41.93 | (276) c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v_w, v_z) =
% 280.06/41.93 | all_1068_3 & c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,
% 280.06/41.93 | all_1068_2, all_1068_1) = all_1068_0 &
% 280.06/41.93 | c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, all_1068_3) =
% 280.06/41.93 | all_1068_2 & c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,
% 280.06/41.93 | v_z) = all_1068_1 &
% 280.06/41.93 | c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w) =
% 280.06/41.93 | all_1068_4 & $i(all_1068_0) & $i(all_1068_1) & $i(all_1068_2) &
% 280.06/41.93 | $i(all_1068_3) & $i(all_1068_4) & ~
% 280.06/41.93 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1068_4,
% 280.06/41.93 | all_1068_0)
% 280.06/41.93 |
% 280.06/41.93 | ALPHA: (276) implies:
% 280.06/41.93 | (277) ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1068_4,
% 280.06/41.93 | all_1068_0)
% 280.06/41.93 | (278) c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w) =
% 280.06/41.93 | all_1068_4
% 280.06/41.93 | (279) c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_z) =
% 280.06/41.93 | all_1068_1
% 280.06/41.93 | (280) c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, all_1068_3) =
% 280.06/41.93 | all_1068_2
% 280.06/41.93 | (281) c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_1068_2, all_1068_1)
% 280.06/41.93 | = all_1068_0
% 280.06/41.93 | (282) c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v_w, v_z) =
% 280.06/41.93 | all_1068_3
% 280.06/41.93 |
% 280.06/41.93 | DELTA: instantiating (8) with fresh symbol all_1073_0 gives:
% 280.06/41.93 | (283) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1073_0 &
% 280.06/41.93 | $i(all_1073_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ! [v3:
% 280.06/41.93 | $i] : ! [v4: $i] : (v2 = all_1073_0 | v1 = v0 | ~
% 280.06/41.93 | (c_RealVector_OscaleR__class_OscaleR(v3, v2, v1) = v4) | ~
% 280.06/41.93 | (c_RealVector_OscaleR__class_OscaleR(v3, v2, v0) = v4) | ~ $i(v3)
% 280.06/41.93 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 280.06/41.93 | class_RealVector_Oreal__vector(v3))
% 280.06/41.93 |
% 280.06/41.93 | ALPHA: (283) implies:
% 280.06/41.93 | (284) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1073_0
% 280.06/41.93 |
% 280.06/41.93 | DELTA: instantiating (135) with fresh symbol all_1091_0 gives:
% 280.06/41.93 | (285) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1091_0 &
% 280.06/41.93 | $i(all_1091_0) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) |
% 280.06/41.93 | ~ c_SEQ_OBseq(v1, v0) | ~
% 280.06/41.93 | class_RealVector_Oreal__normed__vector(v1) | ? [v2: $i] : ($i(v2)
% 280.06/41.93 | & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1091_0, v2)
% 280.06/41.93 | & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 280.06/41.93 | (c_RealVector_Onorm__class_Onorm(v1, v4) = v5) | ~ (hAPP(v0,
% 280.06/41.93 | v3) = v4) | ~ $i(v3) |
% 280.06/41.93 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, v2))))
% 280.06/41.93 |
% 280.06/41.94 | ALPHA: (285) implies:
% 280.06/41.94 | (286) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1091_0
% 280.06/41.94 |
% 280.06/41.94 | DELTA: instantiating (105) with fresh symbols all_1105_0, all_1105_1 gives:
% 280.06/41.94 | (287) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1105_1 &
% 280.06/41.94 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1105_0 &
% 280.06/41.94 | $i(all_1105_0) & $i(all_1105_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 280.06/41.94 | (c_RComplete_Onatceiling(v0) = v1) | ~ $i(v0) | ~
% 280.06/41.94 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, all_1105_1) |
% 280.06/41.94 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0,
% 280.06/41.94 | all_1105_0)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 280.06/41.94 | (c_RComplete_Onatceiling(v0) = v1) | ~ $i(v0) | ~
% 280.06/41.94 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, all_1105_0)
% 280.06/41.94 | | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, all_1105_1))
% 280.06/41.94 |
% 280.06/41.94 | ALPHA: (287) implies:
% 280.06/41.94 | (288) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1105_0
% 280.06/41.94 |
% 280.06/41.94 | DELTA: instantiating (77) with fresh symbols all_1114_0, all_1114_1 gives:
% 280.06/41.94 | (289) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1114_0 &
% 280.06/41.94 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1114_1 &
% 280.06/41.94 | $i(all_1114_0) & $i(all_1114_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 280.06/41.94 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v1) | ~ $i(v0) | ~
% 280.06/41.94 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1114_0, v0) |
% 280.06/41.94 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1114_1, v1)) &
% 280.06/41.94 | ! [v0: $i] : ! [v1: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v0) =
% 280.06/41.94 | v1) | ~ $i(v0) | ~
% 280.06/41.94 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1114_1, v1) |
% 280.06/41.94 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1114_0, v0))
% 280.06/41.94 |
% 280.06/41.94 | ALPHA: (289) implies:
% 280.06/41.94 | (290) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1114_1
% 280.06/41.94 |
% 280.06/41.94 | DELTA: instantiating (47) with fresh symbols all_1117_0, all_1117_1 gives:
% 280.06/41.94 | (291) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1117_0 &
% 280.06/41.94 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1117_1 &
% 280.06/41.94 | $i(all_1117_0) & $i(all_1117_1) & ! [v0: any] : ! [v1: $i] : !
% 280.06/41.94 | [v2: $i] : (v0 = all_1117_1 | ~ (hAPP(v1, v0) = v2) | ~
% 280.06/41.94 | (hAPP(all_1117_0, v0) = v1) | ~ $i(v0) |
% 280.06/41.94 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1117_1, v2)) &
% 280.06/41.94 | ! [v0: $i] : ! [v1: $i] : ( ~ (hAPP(v0, all_1117_1) = v1) | ~
% 280.06/41.94 | (hAPP(all_1117_0, all_1117_1) = v0) | ~
% 280.06/41.94 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1117_1, v1))
% 280.06/41.94 |
% 280.06/41.94 | ALPHA: (291) implies:
% 280.06/41.94 | (292) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1117_1
% 280.06/41.94 |
% 280.06/41.94 | DELTA: instantiating (69) with fresh symbol all_1120_0 gives:
% 280.06/41.94 | (293) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1120_0 &
% 280.06/41.94 | $i(all_1120_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 280.06/41.94 | $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v0) = v2) | ~
% 280.06/41.94 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1, v2) = v3) | ~
% 280.06/41.94 | $i(v1) | ~ $i(v0) | ~
% 280.06/41.94 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1120_0, v1)
% 280.06/41.94 | | ? [v4: $i] : ? [v5: $i] : (c_RComplete_Onatfloor(v3) = v4 &
% 280.06/41.94 | c_RComplete_Onatfloor(v1) = v5 &
% 280.06/41.94 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v5, v0) = v4 & $i(v5) &
% 280.06/41.94 | $i(v4)))
% 280.06/41.94 |
% 280.06/41.94 | ALPHA: (293) implies:
% 280.06/41.94 | (294) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1120_0
% 280.06/41.94 |
% 280.06/41.94 | DELTA: instantiating (32) with fresh symbol all_1135_0 gives:
% 280.06/41.94 | (295) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1135_0 &
% 280.06/41.94 | $i(all_1135_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 280.06/41.94 | (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v1, v0) = v2) | ~
% 280.06/41.94 | $i(v1) | ~ $i(v0) | ~
% 280.06/41.94 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, all_1135_0)
% 280.06/41.94 | | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v0)) & !
% 280.06/41.94 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 280.06/41.94 | (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v1, v0) = v2) | ~
% 280.06/41.94 | $i(v1) | ~ $i(v0) | ~
% 280.06/41.94 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v0) |
% 280.06/41.94 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2,
% 280.06/41.94 | all_1135_0))
% 280.06/41.94 |
% 280.06/41.94 | ALPHA: (295) implies:
% 280.06/41.94 | (296) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1135_0
% 280.06/41.94 |
% 280.06/41.94 | DELTA: instantiating (104) with fresh symbols all_1150_0, all_1150_1 gives:
% 280.06/41.94 | (297) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1150_1 &
% 280.06/41.94 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1150_0 &
% 280.06/41.94 | $i(all_1150_0) & $i(all_1150_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 280.06/41.94 | (c_RComplete_Onatfloor(v0) = v1) | ~ $i(v0) | ~
% 280.06/41.94 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_1150_1, v1) |
% 280.06/41.94 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1150_0,
% 280.06/41.94 | v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ (c_RComplete_Onatfloor(v0)
% 280.06/41.94 | = v1) | ~ $i(v0) | ~
% 280.06/41.94 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1150_0, v0)
% 280.06/41.94 | | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_1150_1, v1))
% 280.06/41.94 |
% 280.06/41.94 | ALPHA: (297) implies:
% 280.06/41.94 | (298) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1150_0
% 280.06/41.94 |
% 280.06/41.94 | DELTA: instantiating (79) with fresh symbol all_1155_0 gives:
% 280.06/41.94 | (299) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1155_0 &
% 280.06/41.94 | $i(all_1155_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 280.06/41.94 | $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v0) = v2) | ~
% 280.06/41.94 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1, v2) = v3) | ~
% 280.06/41.94 | $i(v1) | ~ $i(v0) | ~
% 280.06/41.94 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1155_0, v1)
% 280.06/41.94 | | ? [v4: $i] : ? [v5: $i] : (c_RComplete_Onatceiling(v3) = v4 &
% 280.06/41.94 | c_RComplete_Onatceiling(v1) = v5 &
% 280.06/41.94 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v5, v0) = v4 & $i(v5) &
% 280.06/41.94 | $i(v4)))
% 280.06/41.94 |
% 280.06/41.94 | ALPHA: (299) implies:
% 280.06/41.94 | (300) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1155_0
% 280.06/41.94 |
% 280.06/41.94 | DELTA: instantiating (38) with fresh symbols all_1158_0, all_1158_1 gives:
% 280.06/41.94 | (301) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1158_0 &
% 280.06/41.94 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1158_1 &
% 280.06/41.94 | $i(all_1158_0) & $i(all_1158_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 280.06/41.94 | any] : ! [v3: $i] : ! [v4: $i] : (v2 = all_1158_1 | v1 = v0 | ~
% 280.06/41.94 | (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v4) | ~ (hAPP(all_1158_0,
% 280.06/41.94 | v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0))
% 280.06/41.94 |
% 280.06/41.94 | ALPHA: (301) implies:
% 280.06/41.94 | (302) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1158_1
% 280.06/41.94 |
% 280.06/41.94 | DELTA: instantiating (27) with fresh symbol all_1166_0 gives:
% 280.06/41.94 | (303) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1166_0 &
% 280.06/41.94 | $i(all_1166_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 =
% 280.06/41.94 | all_1166_0 | ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1,
% 280.06/41.94 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ( ~ (v3 = v0)
% 280.06/41.94 | & c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v1) = v3 &
% 280.06/41.94 | $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 280.06/41.94 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1, v0) =
% 280.06/41.94 | all_1166_0) | ~ $i(v1) | ~ $i(v0) |
% 280.06/41.94 | c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v1) = v0)
% 280.06/41.94 |
% 280.06/41.94 | ALPHA: (303) implies:
% 280.06/41.94 | (304) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1166_0
% 280.06/41.94 |
% 280.06/41.94 | DELTA: instantiating (11) with fresh symbol all_1182_0 gives:
% 280.06/41.94 | (305) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1182_0 &
% 280.06/41.94 | $i(all_1182_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 =
% 280.06/41.94 | all_1182_0 | ~ (c_RealVector_Odist__class_Odist(v1, v0, v0) = v2)
% 280.06/41.94 | | ~ $i(v1) | ~ $i(v0) | ~ class_RealVector_Ometric__space(v1)) &
% 280.06/41.94 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 280.06/41.94 | (c_RealVector_Odist__class_Odist(v2, v1, v0) = all_1182_0) | ~
% 280.06/41.94 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 280.06/41.94 | class_RealVector_Ometric__space(v2))
% 280.06/41.94 |
% 280.06/41.94 | ALPHA: (305) implies:
% 280.06/41.94 | (306) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1182_0
% 280.06/41.94 |
% 280.06/41.94 | DELTA: instantiating (26) with fresh symbol all_1185_0 gives:
% 280.06/41.94 | (307) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1185_0 &
% 280.06/41.94 | $i(all_1185_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 280.06/41.94 | (c_RealVector_Onorm__class_Onorm(v1, v0) = v2) | ~ $i(v1) | ~
% 280.06/41.94 | $i(v0) | ~ class_RealVector_Oreal__normed__vector(v1) | ? [v3:
% 280.06/41.94 | $i] : (( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 280.06/41.94 | v2, all_1185_0) | (v3 = v0 & c_Groups_Ozero__class_Ozero(v1)
% 280.06/41.94 | = v0)) & (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 280.06/41.94 | v2, all_1185_0) | ( ~ (v3 = v0) &
% 280.06/41.94 | c_Groups_Ozero__class_Ozero(v1) = v3 & $i(v3)))))
% 280.06/41.94 |
% 280.06/41.94 | ALPHA: (307) implies:
% 280.06/41.94 | (308) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1185_0
% 280.06/41.94 |
% 280.06/41.94 | DELTA: instantiating (24) with fresh symbol all_1200_0 gives:
% 280.06/41.94 | (309) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1200_0 &
% 280.06/41.94 | $i(all_1200_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 280.06/41.94 | (c_RealVector_Onorm__class_Onorm(v1, v0) = v2) | ~ $i(v1) | ~
% 280.06/41.94 | $i(v0) | ~ class_RealVector_Oreal__normed__vector(v1) | ? [v3:
% 280.06/41.94 | $i] : (( ~ (v2 = all_1200_0) | (v3 = v0 &
% 280.06/41.94 | c_Groups_Ozero__class_Ozero(v1) = v0)) & (v2 = all_1200_0 | (
% 280.06/41.94 | ~ (v3 = v0) & c_Groups_Ozero__class_Ozero(v1) = v3 &
% 280.06/41.94 | $i(v3)))))
% 280.06/41.94 |
% 280.06/41.94 | ALPHA: (309) implies:
% 280.06/41.94 | (310) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1200_0
% 280.06/41.94 |
% 280.06/41.94 | DELTA: instantiating (37) with fresh symbols all_1206_0, all_1206_1 gives:
% 280.06/41.94 | (311) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1206_0 &
% 280.06/41.94 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1206_1 &
% 280.06/41.94 | $i(all_1206_0) & $i(all_1206_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 280.06/41.94 | any] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v2 = all_1206_1 |
% 280.06/41.94 | v1 = v0 | ~ (hAPP(v5, v2) = v4) | ~ (hAPP(v3, v2) = v4) | ~
% 280.06/41.94 | (hAPP(all_1206_0, v1) = v3) | ~ (hAPP(all_1206_0, v0) = v5) | ~
% 280.06/41.94 | $i(v2) | ~ $i(v1) | ~ $i(v0))
% 280.06/41.94 |
% 280.06/41.94 | ALPHA: (311) implies:
% 280.06/41.94 | (312) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1206_1
% 280.06/41.94 |
% 280.06/41.94 | DELTA: instantiating (14) with fresh symbol all_1209_0 gives:
% 280.06/41.94 | (313) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1209_0 &
% 280.06/41.94 | $i(all_1209_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 280.06/41.94 | (c_RealVector_Onorm__class_Onorm(v1, v0) = v2) | ~ $i(v1) | ~
% 280.06/41.94 | $i(v0) | ~ class_RealVector_Oreal__normed__vector(v1) | ? [v3:
% 280.06/41.94 | $i] : (( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 280.06/41.94 | all_1209_0, v2) | ( ~ (v3 = v0) &
% 280.06/41.94 | c_Groups_Ozero__class_Ozero(v1) = v3 & $i(v3))) &
% 280.06/41.94 | (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1209_0, v2)
% 280.06/41.94 | | (v3 = v0 & c_Groups_Ozero__class_Ozero(v1) = v0))))
% 280.06/41.94 |
% 280.06/41.94 | ALPHA: (313) implies:
% 280.06/41.94 | (314) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1209_0
% 280.06/41.94 |
% 280.06/41.94 | DELTA: instantiating (39) with fresh symbols all_1218_0, all_1218_1 gives:
% 280.06/41.94 | (315) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1218_0 &
% 280.06/41.94 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1218_1 &
% 280.06/41.94 | $i(all_1218_0) & $i(all_1218_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 280.06/41.94 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v3, v1) =
% 280.06/41.94 | v4) | ~ (hAPP(v3, v0) = v5) | ~ (hAPP(all_1218_0, v2) = v3) |
% 280.06/41.94 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 280.06/41.94 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v0) | ~
% 280.06/41.94 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1218_1, v2) |
% 280.06/41.94 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v4, v5))
% 280.06/41.94 |
% 280.06/41.94 | ALPHA: (315) implies:
% 280.06/41.94 | (316) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1218_1
% 280.06/41.94 |
% 280.06/41.94 | DELTA: instantiating (129) with fresh symbols all_1239_0, all_1239_1 gives:
% 280.06/41.94 | (317) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1239_0 &
% 280.06/41.94 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1239_1 &
% 280.06/41.94 | $i(all_1239_0) & $i(all_1239_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 280.06/41.94 | (c_Transcendental_Oln(v0) = v1) | ~ $i(v0) | ~
% 280.06/41.94 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1239_1, v0) |
% 280.06/41.94 | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1239_0,
% 280.06/41.94 | v0) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 280.06/41.94 | all_1239_1, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 280.06/41.94 | (c_Transcendental_Oln(v0) = v1) | ~ $i(v0) | ~
% 280.06/41.94 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1239_1, v0) |
% 280.06/41.94 | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1239_1,
% 280.06/41.94 | v1) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 280.06/41.94 | all_1239_0, v0))
% 280.06/41.94 |
% 280.06/41.94 | ALPHA: (317) implies:
% 280.06/41.94 | (318) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1239_1
% 280.06/41.94 | (319) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1239_0
% 280.06/41.94 |
% 280.06/41.94 | DELTA: instantiating (96) with fresh symbols all_1248_0, all_1248_1,
% 280.06/41.94 | all_1248_2 gives:
% 280.06/41.94 | (320) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1248_0 &
% 280.06/41.94 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1248_1 &
% 280.06/41.94 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1248_2 &
% 280.06/41.94 | $i(all_1248_0) & $i(all_1248_1) & $i(all_1248_2) & ! [v0: $i] : !
% 280.06/41.94 | [v1: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v0,
% 280.06/41.94 | all_1248_1) = v1) | ~ $i(v0) | ~
% 280.06/41.94 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1248_2, v0)
% 280.06/41.94 | | ? [v2: $i] : ? [v3: $i] : (c_RComplete_Onatfloor(v1) = v2 &
% 280.06/41.94 | c_RComplete_Onatfloor(v0) = v3 &
% 280.06/41.94 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, all_1248_0) = v2 &
% 280.06/41.94 | $i(v3) & $i(v2)))
% 280.06/41.94 |
% 280.06/41.94 | ALPHA: (320) implies:
% 280.06/41.94 | (321) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1248_2
% 280.06/41.94 | (322) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1248_1
% 280.06/41.94 |
% 280.06/41.94 | DELTA: instantiating (95) with fresh symbols all_1251_0, all_1251_1,
% 280.06/41.94 | all_1251_2 gives:
% 280.06/41.94 | (323) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1251_0 &
% 280.06/41.94 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1251_1 &
% 280.06/41.94 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1251_2 &
% 280.06/41.94 | $i(all_1251_0) & $i(all_1251_1) & $i(all_1251_2) & ! [v0: $i] : !
% 280.06/41.94 | [v1: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v0,
% 280.06/41.94 | all_1251_1) = v1) | ~ $i(v0) | ~
% 280.06/41.94 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1251_2, v0)
% 280.06/41.94 | | ? [v2: $i] : ? [v3: $i] : (c_RComplete_Onatceiling(v1) = v2 &
% 280.06/41.94 | c_RComplete_Onatceiling(v0) = v3 &
% 280.06/41.94 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, all_1251_0) = v2 &
% 280.06/41.94 | $i(v3) & $i(v2)))
% 280.06/41.94 |
% 280.06/41.94 | ALPHA: (323) implies:
% 280.06/41.94 | (324) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1251_2
% 280.06/41.95 | (325) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1251_1
% 280.06/41.95 |
% 280.06/41.95 | DELTA: instantiating (34) with fresh symbols all_1254_0, all_1254_1 gives:
% 280.06/41.95 | (326) c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1254_1 &
% 280.06/41.95 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1254_0 &
% 280.06/41.95 | $i(all_1254_0) & $i(all_1254_1) & ! [v0: $i] : ! [v1: any] : (v1 =
% 280.06/41.95 | all_1254_0 | ~ (c_Complex_Ocomplex_OComplex(v1, v0) = all_1254_1)
% 280.06/41.95 | | ~ $i(v1) | ~ $i(v0)) & ! [v0: any] : ! [v1: $i] : (v0 =
% 280.06/41.95 | all_1254_0 | ~ (c_Complex_Ocomplex_OComplex(v1, v0) = all_1254_1)
% 280.06/41.95 | | ~ $i(v1) | ~ $i(v0)) & ! [v0: int] : (v0 = all_1254_1 | ~
% 280.06/41.95 | (c_Complex_Ocomplex_OComplex(all_1254_0, all_1254_0) = v0))
% 280.06/41.95 |
% 280.06/41.95 | ALPHA: (326) implies:
% 280.06/41.95 | (327) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1254_0
% 280.06/41.95 |
% 280.06/41.95 | DELTA: instantiating (111) with fresh symbols all_1257_0, all_1257_1 gives:
% 280.06/41.95 | (328) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1257_0 &
% 280.06/41.95 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1257_1 &
% 280.06/41.95 | $i(all_1257_0) & $i(all_1257_1) & ! [v0: $i] : ! [v1: any] : (v1 =
% 280.06/41.95 | all_1257_1 | ~ (c_Complex_Ocomplex_OComplex(v1, v0) =
% 280.06/41.95 | c_Complex_Oii) | ~ $i(v1) | ~ $i(v0)) & ! [v0: any] : ! [v1:
% 280.06/41.95 | $i] : (v0 = all_1257_0 | ~ (c_Complex_Ocomplex_OComplex(v1, v0) =
% 280.06/41.95 | c_Complex_Oii) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : (v0 =
% 280.06/41.95 | c_Complex_Oii | ~ (c_Complex_Ocomplex_OComplex(all_1257_1,
% 280.06/41.95 | all_1257_0) = v0))
% 280.06/41.95 |
% 280.06/41.95 | ALPHA: (328) implies:
% 280.06/41.95 | (329) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1257_1
% 280.06/41.95 | (330) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1257_0
% 280.06/41.95 |
% 280.06/41.95 | DELTA: instantiating (123) with fresh symbols all_1260_0, all_1260_1 gives:
% 280.06/41.95 | (331) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1260_0 &
% 280.06/41.95 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1260_1 &
% 280.06/41.95 | $i(all_1260_0) & $i(all_1260_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 280.06/41.95 | (c_Transcendental_Oln(v0) = v1) | ~ $i(v0) | ~
% 280.06/41.95 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1260_0, v0) |
% 280.06/41.95 | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1260_1, v0) |
% 280.06/41.95 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1260_1, v1)) &
% 280.06/41.95 | ! [v0: $i] : ! [v1: $i] : ( ~ (c_Transcendental_Oln(v0) = v1) | ~
% 280.06/41.95 | $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 280.06/41.95 | all_1260_1, v1) | ~
% 280.06/41.95 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1260_1, v0) |
% 280.06/41.95 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1260_0, v0))
% 280.06/41.95 |
% 280.06/41.95 | ALPHA: (331) implies:
% 280.06/41.95 | (332) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1260_1
% 280.06/41.95 | (333) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1260_0
% 280.06/41.95 |
% 280.06/41.95 | DELTA: instantiating (125) with fresh symbols all_1263_0, all_1263_1 gives:
% 280.06/41.95 | (334) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1263_0 &
% 280.06/41.95 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1263_1 &
% 280.06/41.95 | $i(all_1263_0) & $i(all_1263_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 280.06/41.95 | (c_Transcendental_Oln(v0) = v1) | ~ $i(v0) | ~
% 280.06/41.95 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, all_1263_1) |
% 280.06/41.95 | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1263_1, v0) |
% 280.06/41.95 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, all_1263_0)) &
% 280.06/41.95 | ! [v0: $i] : ! [v1: $i] : ( ~ (c_Transcendental_Oln(v0) = v1) | ~
% 280.06/41.95 | $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0,
% 280.06/41.95 | all_1263_0) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 280.06/41.95 | all_1263_1, v0) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 280.06/41.95 | v1, all_1263_1))
% 280.06/41.95 |
% 280.06/41.95 | ALPHA: (334) implies:
% 280.06/41.95 | (335) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1263_1
% 280.06/41.95 | (336) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1263_0
% 280.06/41.95 |
% 280.06/41.95 | DELTA: instantiating (136) with fresh symbol all_1266_0 gives:
% 280.06/41.95 | (337) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1266_0 &
% 280.06/41.95 | $i(all_1266_0) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2)
% 280.06/41.95 | | ~ $i(v1) | ~ $i(v0) | ~
% 280.06/41.95 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1266_0, v1) |
% 280.06/41.95 | ~ class_RealVector_Oreal__normed__vector(v2) | c_SEQ_OBseq(v2, v0)
% 280.06/41.95 | | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] :
% 280.06/41.95 | (c_RealVector_Onorm__class_Onorm(v2, v4) = v5 & hAPP(v0, v3) = v4 &
% 280.06/41.95 | $i(v5) & $i(v4) & $i(v3) & ~
% 280.06/41.95 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, v1)))
% 280.06/41.95 |
% 280.06/41.95 | ALPHA: (337) implies:
% 280.06/41.95 | (338) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1266_0
% 280.06/41.95 |
% 280.06/41.95 | DELTA: instantiating (20) with fresh symbol all_1268_0 gives:
% 280.06/41.95 | (339) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1268_0 &
% 280.06/41.95 | $i(all_1268_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 280.06/41.95 | $i] : (v1 = v0 | ~ (c_RealVector_Odist__class_Odist(v2, v1, v0) =
% 280.06/41.95 | v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 280.06/41.95 | class_RealVector_Ometric__space(v2) | ~
% 280.06/41.95 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3,
% 280.06/41.95 | all_1268_0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 280.06/41.95 | (c_RealVector_Odist__class_Odist(v1, v0, v0) = v2) | ~ $i(v1) | ~
% 280.06/41.95 | $i(v0) | ~ class_RealVector_Ometric__space(v1) |
% 280.06/41.95 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2,
% 280.06/41.95 | all_1268_0))
% 280.06/41.95 |
% 280.06/41.95 | ALPHA: (339) implies:
% 280.06/41.95 | (340) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1268_0
% 280.06/41.95 |
% 280.06/41.95 | DELTA: instantiating (46) with fresh symbols all_1274_0, all_1274_1 gives:
% 280.06/41.95 | (341) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1274_0 &
% 280.06/41.95 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1274_1 &
% 280.06/41.95 | $i(all_1274_0) & $i(all_1274_1) & ! [v0: $i] : ! [v1: any] : !
% 280.06/41.95 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] :
% 280.06/41.95 | (v1 = all_1274_1 | ~ (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,
% 280.06/41.95 | v1) = v3) | ~ (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v0)
% 280.06/41.95 | = v5) | ~ (hAPP(v4, v5) = v6) | ~ (hAPP(all_1274_0, v2) = v4) |
% 280.06/41.95 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 280.06/41.95 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v6) | ~
% 280.06/41.95 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2,
% 280.06/41.95 | all_1274_1))
% 280.06/41.95 |
% 280.06/41.95 | ALPHA: (341) implies:
% 280.06/41.95 | (342) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1274_1
% 280.06/41.95 |
% 280.06/41.95 | DELTA: instantiating (13) with fresh symbol all_1277_0 gives:
% 280.06/41.95 | (343) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1277_0 &
% 280.06/41.95 | $i(all_1277_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 280.06/41.95 | $i] : (v1 = v0 | ~ (c_RealVector_Odist__class_Odist(v2, v1, v0) =
% 280.06/41.95 | v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 280.06/41.95 | class_RealVector_Ometric__space(v2) |
% 280.06/41.95 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1277_0, v3)) &
% 280.06/41.95 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 280.06/41.95 | (c_RealVector_Odist__class_Odist(v1, v0, v0) = v2) | ~ $i(v1) | ~
% 280.06/41.95 | $i(v0) | ~ class_RealVector_Ometric__space(v1) | ~
% 280.06/41.95 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1277_0, v2))
% 280.06/41.95 |
% 280.06/41.95 | ALPHA: (343) implies:
% 280.06/41.95 | (344) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1277_0
% 280.06/41.95 |
% 280.06/41.95 | DELTA: instantiating (106) with fresh symbols all_1280_0, all_1280_1 gives:
% 280.06/41.95 | (345) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1280_0 &
% 280.06/41.95 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1280_1 &
% 280.06/41.95 | $i(all_1280_0) & $i(all_1280_1) & ! [v0: $i] : ( ~ $i(v0) | ~
% 280.06/41.95 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1280_1, v0)
% 280.06/41.95 | | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 280.06/41.95 | (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3 &
% 280.06/41.95 | c_RealDef_Oreal(tc_Nat_Onat, v1) = v4 &
% 280.06/41.95 | c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, all_1280_0) = v2 &
% 280.06/41.95 | $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 280.06/41.95 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) &
% 280.06/41.95 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v0)))
% 280.06/41.95 |
% 280.06/41.95 | ALPHA: (345) implies:
% 280.06/41.95 | (346) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1280_1
% 280.06/41.95 |
% 280.06/41.95 | DELTA: instantiating (48) with fresh symbols all_1283_0, all_1283_1,
% 280.06/41.95 | all_1283_2 gives:
% 280.06/41.95 | (347) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1283_1 &
% 280.06/41.95 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1283_2 &
% 280.06/41.95 | $i(all_1283_0) & $i(all_1283_1) & $i(all_1283_2) &
% 280.06/41.95 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1283_2,
% 280.06/41.95 | all_1283_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 280.06/41.95 | : ( ~ (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v0) = v1)
% 280.06/41.95 | | ~ (hAPP(v2, all_1283_0) = v3) | ~ (hAPP(all_1283_1, v1) = v2) |
% 280.06/41.95 | ~ $i(v0) | ? [v4: $i] : ? [v5: $i] : (c_Complex_OIm(v0) = v4 &
% 280.06/41.95 | c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal, v4) = v5 &
% 280.06/41.95 | $i(v5) & $i(v4) &
% 280.06/41.95 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, v3)))
% 280.06/41.95 |
% 280.06/41.95 | ALPHA: (347) implies:
% 280.06/41.95 | (348) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1283_2
% 280.06/41.95 |
% 280.06/41.95 | DELTA: instantiating (94) with fresh symbols all_1286_0, all_1286_1 gives:
% 280.06/41.95 | (349) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1286_0 &
% 280.06/41.95 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1286_1 &
% 280.06/41.95 | $i(all_1286_0) & $i(all_1286_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 280.06/41.95 | $i] : ! [v3: $i] : (v3 = v2 | ~ (c_RComplete_Onatceiling(v0) =
% 280.06/41.95 | v2) | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1,
% 280.06/41.95 | all_1286_0) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ?
% 280.06/41.95 | [v5: $i] : (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4 & $i(v4) & ( ~
% 280.06/41.95 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v4, v0) |
% 280.06/41.95 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v4, all_1286_1)
% 280.06/41.95 | = v5 & $i(v5) & ~
% 280.06/41.95 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0,
% 280.06/41.95 | v5)))))
% 280.06/41.95 |
% 280.06/41.95 | ALPHA: (349) implies:
% 280.06/41.95 | (350) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1286_1
% 280.06/41.95 |
% 280.06/41.95 | DELTA: instantiating (52) with fresh symbols all_1299_0, all_1299_1,
% 280.06/41.95 | all_1299_2 gives:
% 280.06/41.95 | (351) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1299_1 &
% 280.06/41.95 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1299_2 &
% 280.06/41.95 | $i(all_1299_0) & $i(all_1299_1) & $i(all_1299_2) &
% 280.06/41.95 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1299_2,
% 280.06/41.95 | all_1299_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 280.06/41.95 | : ( ~ (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v0) = v1)
% 280.06/41.95 | | ~ (hAPP(v2, all_1299_0) = v3) | ~ (hAPP(all_1299_1, v1) = v2) |
% 280.06/41.95 | ~ $i(v0) | ? [v4: $i] : ? [v5: $i] : (c_Complex_OIm(v0) = v4 &
% 280.06/41.95 | c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal, v4) = v5 &
% 280.06/41.95 | $i(v5) & $i(v4) &
% 280.06/41.95 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, v3)))
% 280.06/41.95 |
% 280.06/41.95 | ALPHA: (351) implies:
% 280.06/41.95 | (352) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1299_2
% 280.06/41.95 |
% 280.06/41.95 | DELTA: instantiating (1) with fresh symbols all_1308_0, all_1308_1,
% 280.06/41.95 | all_1308_2, all_1308_3, all_1308_4, all_1308_5, all_1308_6 gives:
% 280.06/41.95 | (353) c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_z) =
% 280.06/41.95 | all_1308_5 & c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,
% 280.06/41.95 | all_1308_6, all_1308_5) = all_1308_4 &
% 280.06/41.95 | c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v_w, v_z) =
% 280.06/41.95 | all_1308_6 & c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,
% 280.06/41.95 | all_1308_3, all_1308_2) = all_1308_1 &
% 280.06/41.95 | c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, all_1308_4) =
% 280.06/41.95 | all_1308_3 & c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,
% 280.06/41.95 | all_1308_5) = all_1308_0 &
% 280.06/41.95 | c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, all_1308_6) =
% 280.06/41.95 | all_1308_2 & $i(all_1308_0) & $i(all_1308_1) & $i(all_1308_2) &
% 280.06/41.95 | $i(all_1308_3) & $i(all_1308_4) & $i(all_1308_5) & $i(all_1308_6) &
% 280.06/41.95 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1308_1,
% 280.06/41.95 | all_1308_0)
% 280.06/41.95 |
% 280.06/41.95 | ALPHA: (353) implies:
% 280.06/41.95 | (354) $i(all_1308_6)
% 280.06/41.95 | (355) $i(all_1308_5)
% 280.06/41.95 | (356) c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, all_1308_6) =
% 280.06/41.95 | all_1308_2
% 280.06/41.95 | (357) c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, all_1308_5) =
% 280.06/41.95 | all_1308_0
% 280.06/41.95 | (358) c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, all_1308_4) =
% 280.06/41.95 | all_1308_3
% 280.06/41.95 | (359) c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v_w, v_z) =
% 280.06/41.95 | all_1308_6
% 280.06/41.95 | (360) c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, all_1308_6,
% 280.06/41.95 | all_1308_5) = all_1308_4
% 280.06/41.95 | (361) c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_z) =
% 280.06/41.95 | all_1308_5
% 280.06/41.95 |
% 280.06/41.95 | DELTA: instantiating (49) with fresh symbols all_1316_0, all_1316_1,
% 280.06/41.95 | all_1316_2 gives:
% 280.06/41.95 | (362) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1316_1 &
% 280.06/41.95 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1316_2 &
% 280.06/41.95 | $i(all_1316_0) & $i(all_1316_1) & $i(all_1316_2) &
% 280.06/41.95 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1316_2,
% 280.06/41.95 | all_1316_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 280.06/41.95 | : ( ~ (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v0) = v1)
% 280.06/41.95 | | ~ (hAPP(v2, all_1316_0) = v3) | ~ (hAPP(all_1316_1, v1) = v2) |
% 280.06/41.95 | ~ $i(v0) | ? [v4: $i] : ? [v5: $i] : (c_Complex_ORe(v0) = v4 &
% 280.06/41.95 | c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal, v4) = v5 &
% 280.06/41.95 | $i(v5) & $i(v4) &
% 280.06/41.95 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, v3)))
% 280.06/41.95 |
% 280.06/41.95 | ALPHA: (362) implies:
% 280.06/41.95 | (363) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1316_2
% 280.06/41.95 |
% 280.06/41.95 | DELTA: instantiating (53) with fresh symbols all_1319_0, all_1319_1,
% 280.06/41.95 | all_1319_2 gives:
% 280.06/41.95 | (364) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1319_1 &
% 280.06/41.95 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1319_2 &
% 280.06/41.95 | $i(all_1319_0) & $i(all_1319_1) & $i(all_1319_2) &
% 280.06/41.95 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1319_2,
% 280.06/41.95 | all_1319_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 280.06/41.95 | : ( ~ (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v0) = v1)
% 280.06/41.95 | | ~ (hAPP(v2, all_1319_0) = v3) | ~ (hAPP(all_1319_1, v1) = v2) |
% 280.06/41.95 | ~ $i(v0) | ? [v4: $i] : ? [v5: $i] : (c_Complex_ORe(v0) = v4 &
% 280.06/41.95 | c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal, v4) = v5 &
% 280.06/41.95 | $i(v5) & $i(v4) &
% 280.06/41.95 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, v3)))
% 280.06/41.95 |
% 280.06/41.95 | ALPHA: (364) implies:
% 280.06/41.95 | (365) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1319_2
% 280.06/41.95 |
% 280.06/41.95 | DELTA: instantiating (10) with fresh symbol all_1322_0 gives:
% 280.06/41.95 | (366) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1322_0 &
% 280.06/41.95 | $i(all_1322_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 280.06/41.95 | $i] : ( ~ (c_RealVector_OscaleR__class_OscaleR(v2, v1, v0) = v3) |
% 280.06/41.95 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 280.06/41.95 | class_RealVector_Oreal__vector(v2) | ? [v4: $i] :
% 280.06/41.95 | (c_Groups_Ozero__class_Ozero(v2) = v4 & $i(v4) & ( ~ (v4 = v3) | v3
% 280.06/41.95 | = v0 | v1 = all_1322_0) & (v4 = v3 | ( ~ (v4 = v0) & ~ (v1 =
% 280.06/41.95 | all_1322_0)))))
% 280.06/41.95 |
% 280.06/41.95 | ALPHA: (366) implies:
% 280.06/41.95 | (367) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1322_0
% 280.06/41.95 |
% 280.06/41.95 | DELTA: instantiating (114) with fresh symbols all_1325_0, all_1325_1,
% 280.06/41.95 | all_1325_2 gives:
% 280.06/41.96 | (368) c_Power_Opower__class_Opower(tc_RealDef_Oreal) = all_1325_0 &
% 280.06/41.96 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1325_2 &
% 280.06/41.96 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1325_1 &
% 280.06/41.96 | $i(all_1325_0) & $i(all_1325_1) & $i(all_1325_2) & ! [v0: $i] : !
% 280.06/41.96 | [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 280.06/41.96 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1325_2, v1) | ~
% 280.06/41.96 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1325_1, v0) |
% 280.06/41.96 | ? [v2: $i] : ? [v3: $i] : (hAPP(v3, v1) = v0 & hAPP(all_1325_0,
% 280.06/41.96 | v2) = v3 & $i(v3) & $i(v2) &
% 280.06/41.96 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1325_1, v2)))
% 280.06/41.96 |
% 280.06/41.96 | ALPHA: (368) implies:
% 280.06/41.96 | (369) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1325_1
% 280.06/41.96 |
% 280.06/41.96 | DELTA: instantiating (21) with fresh symbol all_1335_0 gives:
% 280.06/41.96 | (370) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1335_0 &
% 280.06/41.96 | $i(all_1335_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 280.06/41.96 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1, v0) = v2) | ~
% 280.06/41.96 | $i(v1) | ~ $i(v0) | ~
% 280.06/41.96 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, all_1335_0) |
% 280.06/41.96 | ? [v3: $i] : (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v1)
% 280.06/41.96 | = v3 & $i(v3) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 280.06/41.96 | v0, v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 280.06/41.96 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1, v0) = v2) | ~
% 280.06/41.96 | $i(v1) | ~ $i(v0) |
% 280.06/41.96 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, all_1335_0) |
% 280.06/41.96 | ? [v3: $i] : (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v1)
% 280.06/41.96 | = v3 & $i(v3) & ~
% 280.06/41.96 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3)))
% 280.06/41.96 |
% 280.06/41.96 | ALPHA: (370) implies:
% 280.06/41.96 | (371) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1335_0
% 280.06/41.96 |
% 280.06/41.96 | DELTA: instantiating (93) with fresh symbol all_1338_0 gives:
% 280.06/41.96 | (372) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1338_0 &
% 280.06/41.96 | $i(all_1338_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 280.06/41.96 | $i] : ( ~ (c_RComplete_Onatceiling(v1) = v2) | ~
% 280.06/41.96 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v3) | ~ $i(v1) | ~ $i(v0) |
% 280.06/41.96 | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v0) | ~
% 280.06/41.96 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1338_0, v1)
% 280.06/41.96 | | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v3)) & !
% 280.06/41.96 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 280.06/41.96 | (c_RComplete_Onatceiling(v1) = v2) | ~
% 280.06/41.96 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v3) | ~ $i(v1) | ~ $i(v0) |
% 280.06/41.96 | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v3) | ~
% 280.06/41.96 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1338_0, v1)
% 280.06/41.96 | | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v0))
% 280.06/41.96 |
% 280.06/41.96 | ALPHA: (372) implies:
% 280.06/41.96 | (373) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1338_0
% 280.06/41.96 |
% 280.06/41.96 | DELTA: instantiating (31) with fresh symbol all_1341_0 gives:
% 280.06/41.96 | (374) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1341_0 &
% 280.06/41.96 | $i(all_1341_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 280.06/41.96 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1, v0) = v2) | ~
% 280.06/41.96 | $i(v1) | ~ $i(v0) | ~
% 280.06/41.96 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1341_0, v2)
% 280.06/41.96 | | ? [v3: $i] : (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,
% 280.06/41.96 | v1) = v3 & $i(v3) &
% 280.06/41.96 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v0))) &
% 280.06/41.96 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 280.06/41.96 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1, v0) = v2) | ~
% 280.06/41.96 | $i(v1) | ~ $i(v0) |
% 280.06/41.96 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1341_0, v2)
% 280.06/41.96 | | ? [v3: $i] : (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,
% 280.06/41.96 | v1) = v3 & $i(v3) & ~
% 280.06/41.96 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v0)))
% 280.06/41.96 |
% 280.06/41.96 | ALPHA: (374) implies:
% 280.06/41.96 | (375) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1341_0
% 280.06/41.96 |
% 280.06/41.96 | DELTA: instantiating (78) with fresh symbol all_1344_0 gives:
% 280.06/41.96 | (376) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1344_0 &
% 280.06/41.96 | $i(all_1344_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 280.06/41.96 | $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v0) = v3) | ~
% 280.06/41.96 | (c_RComplete_Onatfloor(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 280.06/41.96 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, v2) | ~
% 280.06/41.96 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1344_0, v1)
% 280.06/41.96 | | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v1)) & !
% 280.06/41.96 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 280.06/41.96 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v3) | ~
% 280.06/41.96 | (c_RComplete_Onatfloor(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 280.06/41.96 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v1) | ~
% 280.06/41.96 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1344_0, v1)
% 280.06/41.96 | | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, v2))
% 280.06/41.96 |
% 280.06/41.96 | ALPHA: (376) implies:
% 280.06/41.96 | (377) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1344_0
% 280.06/41.96 |
% 280.06/41.96 | DELTA: instantiating (30) with fresh symbol all_1353_0 gives:
% 280.06/41.96 | (378) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1353_0 &
% 280.06/41.96 | $i(all_1353_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 280.06/41.96 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1, v0) = v2) | ~
% 280.06/41.96 | $i(v1) | ~ $i(v0) | ~
% 280.06/41.96 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, all_1353_0)
% 280.06/41.96 | | ? [v3: $i] : (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,
% 280.06/41.96 | v1) = v3 & $i(v3) &
% 280.06/41.96 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3))) &
% 280.06/41.96 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 280.06/41.96 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1, v0) = v2) | ~
% 280.06/41.96 | $i(v1) | ~ $i(v0) |
% 280.06/41.96 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, all_1353_0)
% 280.06/41.96 | | ? [v3: $i] : (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,
% 280.06/41.96 | v1) = v3 & $i(v3) & ~
% 280.06/41.96 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3)))
% 280.06/41.96 |
% 280.06/41.96 | ALPHA: (378) implies:
% 280.06/41.96 | (379) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1353_0
% 280.06/41.96 |
% 280.06/41.96 | DELTA: instantiating (102) with fresh symbols all_1356_0, all_1356_1,
% 280.06/41.96 | all_1356_2 gives:
% 280.06/41.96 | (380) c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = all_1356_2 &
% 280.06/41.96 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1356_1 &
% 280.06/41.96 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1356_0 &
% 280.06/41.96 | $i(all_1356_0) & $i(all_1356_1) & $i(all_1356_2) & ! [v0: $i] : !
% 280.06/41.96 | [v1: any] : (v1 = all_1356_1 | ~ (c_Complex_Ocomplex_OComplex(v1,
% 280.06/41.96 | v0) = all_1356_2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: any] : !
% 280.06/41.96 | [v1: $i] : (v0 = all_1356_0 | ~ (c_Complex_Ocomplex_OComplex(v1, v0)
% 280.06/41.96 | = all_1356_2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: int] : (v0 =
% 280.06/41.96 | all_1356_2 | ~ (c_Complex_Ocomplex_OComplex(all_1356_1,
% 280.06/41.96 | all_1356_0) = v0))
% 280.06/41.96 |
% 280.06/41.96 | ALPHA: (380) implies:
% 280.06/41.96 | (381) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1356_0
% 280.06/41.96 | (382) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1356_1
% 280.06/41.96 |
% 280.06/41.96 | DELTA: instantiating (45) with fresh symbols all_1365_0, all_1365_1 gives:
% 280.06/41.96 | (383) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1365_0 &
% 280.06/41.96 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1365_1 &
% 280.06/41.96 | $i(all_1365_0) & $i(all_1365_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 280.06/41.96 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 280.06/41.96 | [v7: $i] : ( ~ (c_RealVector_Onorm__class_Onorm(v3, v1) = v4) | ~
% 280.06/41.96 | (c_RealVector_Onorm__class_Onorm(v3, v0) = v6) | ~ (hAPP(v5, v6) =
% 280.06/41.96 | v7) | ~ (hAPP(all_1365_0, v2) = v5) | ~ $i(v3) | ~ $i(v2) | ~
% 280.06/41.96 | $i(v1) | ~ $i(v0) | ~ class_RealVector_Oreal__normed__vector(v3)
% 280.06/41.96 | | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v7) |
% 280.06/41.96 | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2,
% 280.06/41.96 | all_1365_1) | c_Groups_Ozero__class_Ozero(v3) = v1)
% 280.06/41.96 |
% 280.06/41.96 | ALPHA: (383) implies:
% 280.06/41.96 | (384) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1365_1
% 280.06/41.96 |
% 280.06/41.96 | DELTA: instantiating (22) with fresh symbol all_1377_0 gives:
% 280.06/41.96 | (385) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1377_0 &
% 280.06/41.96 | $i(all_1377_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 280.06/41.96 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1, v0) = v2) | ~
% 280.06/41.96 | $i(v1) | ~ $i(v0) | ~
% 280.06/41.96 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1377_0, v2) |
% 280.06/41.96 | ? [v3: $i] : (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v1)
% 280.06/41.96 | = v3 & $i(v3) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 280.06/41.96 | v3, v0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 280.06/41.96 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1, v0) = v2) | ~
% 280.06/41.96 | $i(v1) | ~ $i(v0) |
% 280.06/41.96 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1377_0, v2) |
% 280.06/41.96 | ? [v3: $i] : (c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, v1)
% 280.06/41.96 | = v3 & $i(v3) & ~
% 280.06/41.96 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v0)))
% 280.06/41.96 |
% 280.06/41.96 | ALPHA: (385) implies:
% 280.06/41.96 | (386) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1377_0
% 280.06/41.96 |
% 280.06/41.96 | DELTA: instantiating (130) with fresh symbols all_1386_0, all_1386_1 gives:
% 280.06/41.96 | (387) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1386_0 &
% 280.06/41.96 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1386_1 &
% 280.06/41.96 | $i(all_1386_0) & $i(all_1386_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 280.06/41.96 | $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_Transcendental_Oln(v1) =
% 280.06/41.96 | v2) | ~ (c_Transcendental_Oln(v0) = v3) | ~
% 280.06/41.96 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v3) = v4) | ~
% 280.06/41.96 | $i(v1) | ~ $i(v0) | ~
% 280.06/41.96 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1386_1, v1) |
% 280.06/41.96 | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1386_1, v0) |
% 280.06/41.96 | ? [v5: $i] : ? [v6: $i] : (c_Transcendental_Oln(v6) = v4 &
% 280.06/41.96 | hAPP(v5, v0) = v6 & hAPP(all_1386_0, v1) = v5 & $i(v6) & $i(v5) &
% 280.06/41.96 | $i(v4)))
% 280.06/41.96 |
% 280.06/41.96 | ALPHA: (387) implies:
% 280.06/41.96 | (388) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1386_1
% 280.06/41.96 |
% 280.06/41.96 | DELTA: instantiating (50) with fresh symbols all_1410_0, all_1410_1 gives:
% 280.06/41.96 | (389) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1410_0 &
% 280.06/41.96 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1410_1 &
% 280.06/41.96 | $i(all_1410_0) & $i(all_1410_1) & ? [v0: $i] : ! [v1: $i] : ( ~
% 280.06/41.96 | $i(v1) | ~ $i(v0) | ~ class_RealVector_Oreal__normed__vector(v1)
% 280.06/41.96 | | ? [v2: $i] : ($i(v2) &
% 280.06/41.96 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1410_1, v2) &
% 280.06/41.96 | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 280.06/41.96 | (c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal, v3) = v4) |
% 280.06/41.96 | ~ (hAPP(v5, v2) = v6) | ~ (hAPP(all_1410_0, v4) = v5) | ~
% 280.06/41.96 | $i(v3) | ? [v7: $i] : ? [v8: $i] :
% 280.06/41.96 | (c_RealVector_OscaleR__class_OscaleR(v1, v3, v0) = v7 &
% 280.06/41.96 | c_RealVector_Onorm__class_Onorm(v1, v7) = v8 & $i(v8) &
% 280.06/41.96 | $i(v7) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 280.06/41.96 | v8, v6)))))
% 280.06/41.96 |
% 280.06/41.96 | ALPHA: (389) implies:
% 280.06/41.96 | (390) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1410_1
% 280.06/41.96 |
% 280.06/41.96 | DELTA: instantiating (89) with fresh symbol all_1412_0 gives:
% 280.06/41.96 | (391) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1412_0 &
% 280.06/41.96 | $i(all_1412_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 280.06/41.96 | $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) | ~
% 280.06/41.96 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v3) | ~ $i(v1) | ~ $i(v0) |
% 280.06/41.96 | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0) | ? [v4:
% 280.06/41.96 | $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3,
% 280.06/41.96 | all_1412_0) = v4 & $i(v4) &
% 280.06/41.96 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v4))) & !
% 280.06/41.96 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 280.06/41.96 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) | ~
% 280.06/41.96 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v3) | ~ $i(v1) | ~ $i(v0) |
% 280.06/41.96 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0) | ? [v4:
% 280.06/41.96 | $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3,
% 280.06/41.96 | all_1412_0) = v4 & $i(v4) & ~
% 280.06/41.96 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v4)))
% 280.06/41.96 |
% 280.06/41.96 | ALPHA: (391) implies:
% 280.06/41.96 | (392) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1412_0
% 280.06/41.96 |
% 280.06/41.96 | DELTA: instantiating (57) with fresh symbols all_1415_0, all_1415_1 gives:
% 280.06/41.96 | (393) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1415_0 &
% 280.06/41.96 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1415_1 &
% 280.06/41.96 | $i(all_1415_0) & $i(all_1415_1) & ? [v0: $i] : ! [v1: $i] : ( ~
% 280.06/41.96 | $i(v1) | ~ $i(v0) | ~ class_RealVector_Oreal__normed__vector(v1)
% 280.06/41.96 | | ? [v2: $i] : ($i(v2) &
% 280.06/41.96 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1415_1, v2) &
% 280.06/41.96 | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 280.06/41.96 | (c_RealVector_Onorm__class_Onorm(v1, v3) = v4) | ~ (hAPP(v5,
% 280.06/41.96 | v2) = v6) | ~ (hAPP(all_1415_0, v4) = v5) | ~ $i(v3) | ?
% 280.06/41.96 | [v7: $i] : ? [v8: $i] :
% 280.06/41.96 | (c_RealVector_OscaleR__class_OscaleR(v1, v0, v3) = v7 &
% 280.06/41.96 | c_RealVector_Onorm__class_Onorm(v1, v7) = v8 & $i(v8) &
% 280.06/41.96 | $i(v7) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 280.06/41.96 | v8, v6)))))
% 280.06/41.96 |
% 280.06/41.96 | ALPHA: (393) implies:
% 280.06/41.96 | (394) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1415_1
% 280.06/41.96 |
% 280.06/41.96 | DELTA: instantiating (9) with fresh symbol all_1423_0 gives:
% 280.06/41.96 | (395) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1423_0 &
% 280.06/41.96 | $i(all_1423_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 280.06/41.96 | $i] : ! [v4: $i] : (v4 = v3 | ~
% 280.06/41.96 | (c_RealVector_OscaleR__class_OscaleR(v2, all_1423_0, v1) = v3) | ~
% 280.06/41.96 | (c_RealVector_OscaleR__class_OscaleR(v2, all_1423_0, v0) = v4) | ~
% 280.06/41.96 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 280.06/41.96 | class_RealVector_Oreal__vector(v2)) & ! [v0: $i] : ! [v1: $i] :
% 280.06/41.96 | ! [v2: any] : ! [v3: $i] : ! [v4: $i] : (v2 = all_1423_0 | v1 = v0
% 280.06/41.96 | | ~ (c_RealVector_OscaleR__class_OscaleR(v3, v2, v1) = v4) | ~
% 280.06/41.96 | (c_RealVector_OscaleR__class_OscaleR(v3, v2, v0) = v4) | ~ $i(v3)
% 280.06/41.96 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 280.06/41.96 | class_RealVector_Oreal__vector(v3))
% 280.06/41.96 |
% 280.06/41.96 | ALPHA: (395) implies:
% 280.06/41.96 | (396) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1423_0
% 280.06/41.96 |
% 280.06/41.96 | DELTA: instantiating (120) with fresh symbol all_1429_0 gives:
% 280.06/41.96 | (397) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1429_0 &
% 280.06/41.96 | $i(all_1429_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 280.06/41.96 | $i] : ( ~ (c_Transcendental_Oln(v1) = v2) | ~
% 280.06/41.96 | (c_Transcendental_Oln(v0) = v3) | ~ $i(v1) | ~ $i(v0) | ~
% 280.06/41.96 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1429_0, v1) |
% 280.06/41.96 | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1429_0, v0) |
% 280.06/41.96 | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v3) |
% 280.06/41.96 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v0)) & !
% 280.06/41.96 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 280.06/41.96 | (c_Transcendental_Oln(v1) = v2) | ~ (c_Transcendental_Oln(v0) =
% 280.06/41.96 | v3) | ~ $i(v1) | ~ $i(v0) | ~
% 280.06/41.96 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1429_0, v1) |
% 280.06/41.96 | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1429_0, v0) |
% 280.06/41.96 | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v0) |
% 280.06/41.96 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v3))
% 280.06/41.96 |
% 280.06/41.96 | ALPHA: (397) implies:
% 280.06/41.96 | (398) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1429_0
% 280.06/41.96 |
% 280.06/41.96 | DELTA: instantiating (88) with fresh symbol all_1432_0 gives:
% 280.06/41.96 | (399) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1432_0 &
% 280.06/41.96 | $i(all_1432_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 280.06/41.96 | $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) | ~
% 280.06/41.96 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v3) | ~ $i(v1) | ~ $i(v0) |
% 280.06/41.96 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0) | ? [v4: $i]
% 280.06/41.96 | : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, all_1432_0) =
% 280.06/41.96 | v4 & $i(v4) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 280.06/41.96 | v4, v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 280.06/41.96 | $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) | ~
% 280.06/41.96 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v3) | ~ $i(v1) | ~ $i(v0) |
% 280.06/41.96 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0) | ? [v4: $i] :
% 280.06/41.96 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, all_1432_0) = v4
% 280.06/41.96 | & $i(v4) & ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 280.06/41.96 | v4, v3)))
% 280.06/41.96 |
% 280.06/41.96 | ALPHA: (399) implies:
% 280.06/41.96 | (400) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1432_0
% 280.06/41.96 |
% 280.06/41.96 | DELTA: instantiating (55) with fresh symbols all_1441_0, all_1441_1 gives:
% 280.06/41.96 | (401) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1441_0 &
% 280.06/41.96 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1441_1 &
% 280.06/41.96 | $i(all_1441_0) & $i(all_1441_1) & ? [v0: $i] : ! [v1: $i] : ( ~
% 280.06/41.96 | $i(v1) | ~ $i(v0) | ~ class_RealVector_Oreal__normed__vector(v1)
% 280.06/41.96 | | ? [v2: $i] : ($i(v2) &
% 280.06/41.96 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1441_1,
% 280.06/41.96 | v2) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (
% 280.06/41.96 | ~ (c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal, v3) = v4)
% 280.06/41.96 | | ~ (hAPP(v5, v2) = v6) | ~ (hAPP(all_1441_0, v4) = v5) | ~
% 280.06/41.96 | $i(v3) | ? [v7: $i] : ? [v8: $i] :
% 280.06/41.96 | (c_RealVector_OscaleR__class_OscaleR(v1, v3, v0) = v7 &
% 280.06/41.96 | c_RealVector_Onorm__class_Onorm(v1, v7) = v8 & $i(v8) &
% 280.06/41.96 | $i(v7) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 280.06/41.96 | v8, v6)))))
% 280.06/41.96 |
% 280.06/41.96 | ALPHA: (401) implies:
% 280.06/41.96 | (402) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1441_1
% 280.06/41.96 |
% 280.06/41.96 | DELTA: instantiating (62) with fresh symbols all_1443_0, all_1443_1 gives:
% 280.06/41.97 | (403) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1443_0 &
% 280.06/41.97 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1443_1 &
% 280.06/41.97 | $i(all_1443_0) & $i(all_1443_1) & ? [v0: $i] : ! [v1: $i] : ( ~
% 280.06/41.97 | $i(v1) | ~ $i(v0) | ~ class_RealVector_Oreal__normed__vector(v1)
% 280.06/41.97 | | ? [v2: $i] : ($i(v2) &
% 280.06/41.97 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1443_1,
% 280.06/41.97 | v2) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (
% 280.06/41.97 | ~ (c_RealVector_Onorm__class_Onorm(v1, v3) = v4) | ~ (hAPP(v5,
% 280.06/41.97 | v2) = v6) | ~ (hAPP(all_1443_0, v4) = v5) | ~ $i(v3) | ?
% 280.06/41.97 | [v7: $i] : ? [v8: $i] :
% 280.06/41.97 | (c_RealVector_OscaleR__class_OscaleR(v1, v0, v3) = v7 &
% 280.06/41.97 | c_RealVector_Onorm__class_Onorm(v1, v7) = v8 & $i(v8) &
% 280.06/41.97 | $i(v7) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 280.06/41.97 | v8, v6)))))
% 280.06/41.97 |
% 280.06/41.97 | ALPHA: (403) implies:
% 280.06/41.97 | (404) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1443_1
% 280.06/41.97 |
% 280.06/41.97 | DELTA: instantiating (119) with fresh symbol all_1450_0 gives:
% 280.06/41.97 | (405) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1450_0 &
% 280.06/41.97 | $i(all_1450_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 280.06/41.97 | $i] : ( ~ (c_Transcendental_Oln(v1) = v2) | ~
% 280.06/41.97 | (c_Transcendental_Oln(v0) = v3) | ~ $i(v1) | ~ $i(v0) | ~
% 280.06/41.97 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v3) | ~
% 280.06/41.97 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1450_0, v1) |
% 280.06/41.97 | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1450_0, v0) |
% 280.06/41.97 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v0)) & ! [v0:
% 280.06/41.97 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 280.06/41.97 | (c_Transcendental_Oln(v1) = v2) | ~ (c_Transcendental_Oln(v0) =
% 280.06/41.97 | v3) | ~ $i(v1) | ~ $i(v0) | ~
% 280.06/41.97 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v0) | ~
% 280.06/41.97 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1450_0, v1) |
% 280.06/41.97 | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1450_0, v0) |
% 280.06/41.97 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v3))
% 280.06/41.97 |
% 280.06/41.97 | ALPHA: (405) implies:
% 280.06/41.97 | (406) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1450_0
% 280.06/41.97 |
% 280.06/41.97 | DELTA: instantiating (115) with fresh symbols all_1480_0, all_1480_1,
% 280.06/41.97 | all_1480_2 gives:
% 280.06/41.97 | (407) c_Power_Opower__class_Opower(tc_RealDef_Oreal) = all_1480_1 &
% 280.06/41.97 | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1480_0 &
% 280.06/41.97 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1480_2 &
% 280.06/41.97 | $i(all_1480_0) & $i(all_1480_1) & $i(all_1480_2) & ! [v0: $i] : !
% 280.06/41.97 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (
% 280.06/41.97 | ~ (c_Transcendental_Oln(v1) = v4) | ~
% 280.06/41.97 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v2) | ~ (hAPP(v3, v4) = v5) |
% 280.06/41.97 | ~ (hAPP(all_1480_0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ~
% 280.06/41.97 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1480_2, v1) |
% 280.06/41.97 | ? [v6: $i] : ? [v7: $i] : (c_Transcendental_Oln(v7) = v5 &
% 280.06/41.97 | hAPP(v6, v0) = v7 & hAPP(all_1480_1, v1) = v6 & $i(v7) & $i(v6) &
% 280.06/41.97 | $i(v5)))
% 280.06/41.97 |
% 280.06/41.97 | ALPHA: (407) implies:
% 280.06/41.97 | (408) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1480_2
% 280.06/41.97 |
% 280.06/41.97 | DELTA: instantiating (64) with fresh symbols all_1486_0, all_1486_1 gives:
% 280.06/41.97 | (409) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1486_0 &
% 280.06/41.97 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1486_1 &
% 280.06/41.97 | $i(all_1486_0) & $i(all_1486_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 280.06/41.97 | $i] : ! [v3: $i] : ( ~ (c_Groups_Otimes__class_Otimes(v1) = v2) |
% 280.06/41.97 | ~ (hAPP(v2, v0) = v3) | ~ $i(v1) | ~ $i(v0) | ~
% 280.06/41.97 | class_RealVector_Oreal__normed__algebra(v1) | ? [v4: $i] : ($i(v4)
% 280.06/41.97 | & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1486_1,
% 280.06/41.97 | v4) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : (
% 280.06/41.97 | ~ (c_RealVector_Onorm__class_Onorm(v1, v5) = v6) | ~ (hAPP(v7,
% 280.06/41.97 | v4) = v8) | ~ (hAPP(all_1486_0, v6) = v7) | ~ $i(v5) | ?
% 280.06/41.97 | [v9: $i] : ? [v10: $i] : (c_RealVector_Onorm__class_Onorm(v1,
% 280.06/41.97 | v9) = v10 & hAPP(v3, v5) = v9 & $i(v10) & $i(v9) &
% 280.06/41.97 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v10,
% 280.06/41.97 | v8)))))
% 280.06/41.97 |
% 280.06/41.97 | ALPHA: (409) implies:
% 280.06/41.97 | (410) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1486_1
% 280.06/41.97 |
% 280.06/41.97 | DELTA: instantiating (113) with fresh symbols all_1489_0, all_1489_1,
% 280.06/41.97 | all_1489_2 gives:
% 280.06/41.97 | (411) c_Power_Opower__class_Opower(tc_RealDef_Oreal) = all_1489_0 &
% 280.06/41.97 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1489_2 &
% 280.06/41.97 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1489_1 &
% 280.06/41.97 | $i(all_1489_0) & $i(all_1489_1) & $i(all_1489_2) & ! [v0: $i] : !
% 280.06/41.97 | [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 280.06/41.97 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1489_2, v1) | ~
% 280.06/41.97 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1489_1, v0) |
% 280.06/41.97 | ? [v2: $i] : ? [v3: $i] : (hAPP(v3, v1) = v0 & hAPP(all_1489_0,
% 280.06/41.97 | v2) = v3 & $i(v3) & $i(v2) &
% 280.06/41.97 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1489_1, v2) &
% 280.06/41.97 | ! [v4: $i] : ! [v5: $i] : (v4 = v2 | ~ (hAPP(v5, v1) = v0) |
% 280.06/41.97 | ~ (hAPP(all_1489_0, v4) = v5) | ~ $i(v4) | ~
% 280.06/41.97 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1489_1,
% 280.06/41.97 | v4))))
% 280.06/41.97 |
% 280.06/41.97 | ALPHA: (411) implies:
% 280.06/41.97 | (412) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1489_1
% 280.06/41.97 |
% 280.06/41.97 | DELTA: instantiating (60) with fresh symbols all_1492_0, all_1492_1 gives:
% 280.06/41.97 | (413) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1492_0 &
% 280.06/41.97 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1492_1 &
% 280.06/41.97 | $i(all_1492_0) & $i(all_1492_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 280.06/41.97 | $i] : ! [v3: $i] : ( ~ (c_Groups_Otimes__class_Otimes(v1) = v2) |
% 280.06/41.97 | ~ (hAPP(v2, v0) = v3) | ~ $i(v1) | ~ $i(v0) | ~
% 280.06/41.97 | class_RealVector_Oreal__normed__algebra(v1) | ? [v4: $i] : ($i(v4)
% 280.06/41.97 | & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1492_1, v4)
% 280.06/41.97 | & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~
% 280.06/41.97 | (c_RealVector_Onorm__class_Onorm(v1, v5) = v6) | ~ (hAPP(v7,
% 280.06/41.97 | v4) = v8) | ~ (hAPP(all_1492_0, v6) = v7) | ~ $i(v5) | ?
% 280.06/41.97 | [v9: $i] : ? [v10: $i] : (c_RealVector_Onorm__class_Onorm(v1,
% 280.06/41.97 | v9) = v10 & hAPP(v3, v5) = v9 & $i(v10) & $i(v9) &
% 280.06/41.97 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v10,
% 280.06/41.97 | v8)))))
% 280.06/41.97 |
% 280.06/41.97 | ALPHA: (413) implies:
% 280.06/41.97 | (414) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1492_1
% 280.06/41.97 |
% 280.06/41.97 | DELTA: instantiating (51) with fresh symbols all_1522_0, all_1522_1 gives:
% 280.06/41.97 | (415) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1522_0 &
% 280.06/41.97 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1522_1 &
% 280.06/41.97 | $i(all_1522_0) & $i(all_1522_1) & ! [v0: $i] : ( ~ $i(v0) | ~
% 280.06/41.97 | class_RealVector_Oreal__normed__vector(v0) | ? [v1: $i] : ($i(v1)
% 280.06/41.97 | & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1522_1, v1)
% 280.06/41.97 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 280.06/41.97 | $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~
% 280.06/41.97 | (c_RealVector_Onorm__class_Onorm(v0, v3) = v6) | ~
% 280.06/41.97 | (c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal, v2) = v4) |
% 280.06/41.97 | ~ (hAPP(v8, v1) = v9) | ~ (hAPP(v5, v6) = v7) | ~
% 280.06/41.97 | (hAPP(all_1522_0, v7) = v8) | ~ (hAPP(all_1522_0, v4) = v5) |
% 280.06/41.97 | ~ $i(v3) | ~ $i(v2) | ? [v10: $i] : ? [v11: $i] :
% 280.06/41.97 | (c_RealVector_OscaleR__class_OscaleR(v0, v2, v3) = v10 &
% 280.06/41.97 | c_RealVector_Onorm__class_Onorm(v0, v10) = v11 & $i(v11) &
% 280.06/41.97 | $i(v10) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 280.06/41.97 | v11, v9)))))
% 280.06/41.97 |
% 280.06/41.97 | ALPHA: (415) implies:
% 280.06/41.97 | (416) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1522_1
% 280.06/41.97 |
% 280.06/41.97 | DELTA: instantiating (66) with fresh symbols all_1528_0, all_1528_1,
% 280.06/41.97 | all_1528_2 gives:
% 280.06/41.97 | (417) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1528_1 &
% 280.06/41.97 | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1528_0 &
% 280.06/41.97 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1528_2 &
% 280.06/41.97 | $i(all_1528_0) & $i(all_1528_1) & $i(all_1528_2) & ! [v0: $i] : !
% 280.06/41.97 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (
% 280.06/41.97 | ~ (c_RComplete_Onatfloor(v1) = v2) | ~ (c_RComplete_Onatfloor(v0)
% 280.06/41.97 | = v4) | ~ (hAPP(v3, v4) = v5) | ~ (hAPP(all_1528_1, v2) = v3) |
% 280.06/41.97 | ~ $i(v1) | ~ $i(v0) | ~
% 280.06/41.97 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1528_2, v1)
% 280.06/41.97 | | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 280.06/41.97 | all_1528_2, v0) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] :
% 280.06/41.97 | (c_RComplete_Onatfloor(v7) = v8 & hAPP(v6, v0) = v7 &
% 280.06/41.97 | hAPP(all_1528_0, v1) = v6 & $i(v8) & $i(v7) & $i(v6) &
% 280.06/41.97 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v5, v8)))
% 280.06/41.97 |
% 280.06/41.97 | ALPHA: (417) implies:
% 280.06/41.97 | (418) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1528_2
% 280.06/41.97 |
% 280.06/41.97 | DELTA: instantiating (36) with fresh symbol all_1531_0 gives:
% 280.06/41.97 | (419) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1531_0 &
% 280.06/41.97 | $i(all_1531_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2)
% 280.06/41.97 | | ~ $i(v1) | ~ $i(v0) | ~
% 280.06/41.97 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v1) | ~
% 280.06/41.97 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v0) | ? [v3:
% 280.06/41.97 | $i] : ($i(v3) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 280.06/41.97 | all_1531_0, v3) & ! [v4: $i] : ! [v5: $i] : ( ~
% 280.06/41.97 | (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v1, v4) = v5)
% 280.06/41.97 | | ~ $i(v4) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 280.06/41.97 | v4, v0) | ? [v6: $i] :
% 280.06/41.97 | (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v5) = v6 & $i(v6)
% 280.06/41.97 | & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v6,
% 280.06/41.97 | v3))) & ! [v4: $i] : ! [v5: $i] : ( ~
% 280.06/41.97 | (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v1, v4) = v5)
% 280.06/41.97 | | ~ $i(v4) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 280.06/41.97 | v2, v4) | ? [v6: $i] :
% 280.06/41.97 | (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v5) = v6 & $i(v6)
% 280.06/41.97 | & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v6,
% 280.06/41.97 | v3)))))
% 280.06/41.97 |
% 280.06/41.97 | ALPHA: (419) implies:
% 280.06/41.97 | (420) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1531_0
% 280.06/41.97 |
% 280.06/41.97 | DELTA: instantiating (54) with fresh symbols all_1537_0, all_1537_1 gives:
% 280.06/41.97 | (421) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1537_0 &
% 280.06/41.97 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1537_1 &
% 280.06/41.97 | $i(all_1537_0) & $i(all_1537_1) & ! [v0: $i] : ( ~ $i(v0) | ~
% 280.06/41.97 | class_RealVector_Oreal__normed__vector(v0) | ? [v1: $i] : ($i(v1)
% 280.06/41.97 | & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1537_1,
% 280.06/41.97 | v1) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] :
% 280.06/41.97 | ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~
% 280.06/41.97 | (c_RealVector_Onorm__class_Onorm(v0, v3) = v6) | ~
% 280.06/41.97 | (c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal, v2) = v4) |
% 280.06/41.97 | ~ (hAPP(v8, v1) = v9) | ~ (hAPP(v5, v6) = v7) | ~
% 280.06/41.97 | (hAPP(all_1537_0, v7) = v8) | ~ (hAPP(all_1537_0, v4) = v5) |
% 280.06/41.97 | ~ $i(v3) | ~ $i(v2) | ? [v10: $i] : ? [v11: $i] :
% 280.06/41.97 | (c_RealVector_OscaleR__class_OscaleR(v0, v2, v3) = v10 &
% 280.06/41.97 | c_RealVector_Onorm__class_Onorm(v0, v10) = v11 & $i(v11) &
% 280.06/41.97 | $i(v10) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 280.06/41.97 | v11, v9)))))
% 280.06/41.97 |
% 280.06/41.97 | ALPHA: (421) implies:
% 280.06/41.97 | (422) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1537_1
% 280.06/41.97 |
% 280.06/41.97 | DELTA: instantiating (59) with fresh symbols all_1555_0, all_1555_1 gives:
% 280.06/41.97 | (423) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1555_0 &
% 280.06/41.97 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1555_1 &
% 280.06/41.97 | $i(all_1555_0) & $i(all_1555_1) & ? [v0: $i] : ! [v1: $i] : ! [v2:
% 280.06/41.97 | $i] : ( ~ (c_Groups_Otimes__class_Otimes(v1) = v2) | ~ $i(v1) | ~
% 280.06/41.97 | $i(v0) | ~ class_RealVector_Oreal__normed__algebra(v1) | ? [v3:
% 280.06/41.97 | $i] : ($i(v3) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 280.06/41.97 | all_1555_1, v3) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 280.06/41.97 | [v7: $i] : ( ~ (c_RealVector_Onorm__class_Onorm(v1, v4) = v5) |
% 280.06/41.97 | ~ (hAPP(v6, v3) = v7) | ~ (hAPP(all_1555_0, v5) = v6) | ~
% 280.06/41.97 | $i(v4) | ? [v8: $i] : ? [v9: $i] : ? [v10: $i] :
% 280.06/41.97 | (c_RealVector_Onorm__class_Onorm(v1, v9) = v10 & hAPP(v8, v0) =
% 280.06/41.97 | v9 & hAPP(v2, v4) = v8 & $i(v10) & $i(v9) & $i(v8) &
% 280.06/41.97 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v10,
% 280.06/41.97 | v7)))))
% 280.06/41.97 |
% 280.06/41.97 | ALPHA: (423) implies:
% 280.06/41.97 | (424) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1555_1
% 280.06/41.97 |
% 280.06/41.97 | DELTA: instantiating (33) with fresh symbol all_1557_0 gives:
% 280.06/41.97 | (425) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1557_0 &
% 280.06/41.97 | $i(all_1557_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2)
% 280.06/41.97 | | ~ $i(v1) | ~ $i(v0) | ~
% 280.06/41.97 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v1) | ~
% 280.06/41.97 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v0) | ? [v3:
% 280.06/41.97 | $i] : ($i(v3) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 280.06/41.97 | all_1557_0, v3) & ! [v4: $i] : ! [v5: $i] : ( ~
% 280.06/41.97 | (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v1, v4) = v5)
% 280.06/41.97 | | ~ $i(v4) |
% 280.06/41.97 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v0) |
% 280.06/41.97 | ? [v6: $i] : (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v5) =
% 280.06/41.97 | v6 & $i(v6) & ~
% 280.06/41.97 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v6, v3))) &
% 280.06/41.97 | ! [v4: $i] : ! [v5: $i] : ( ~
% 280.06/41.97 | (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v1, v4) = v5)
% 280.06/41.97 | | ~ $i(v4) |
% 280.06/41.97 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v4) |
% 280.06/41.97 | ? [v6: $i] : (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v5) =
% 280.06/41.97 | v6 & $i(v6) & ~
% 280.06/41.97 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v6, v3)))))
% 280.06/41.97 |
% 280.06/41.97 | ALPHA: (425) implies:
% 280.06/41.97 | (426) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1557_0
% 280.06/41.97 |
% 280.06/41.97 | DELTA: instantiating (65) with fresh symbols all_1563_0, all_1563_1 gives:
% 280.06/41.97 | (427) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1563_0 &
% 280.06/41.97 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1563_1 &
% 280.06/41.97 | $i(all_1563_0) & $i(all_1563_1) & ? [v0: $i] : ! [v1: $i] : ! [v2:
% 280.06/41.97 | $i] : ( ~ (c_Groups_Otimes__class_Otimes(v1) = v2) | ~ $i(v1) | ~
% 280.06/41.97 | $i(v0) | ~ class_RealVector_Oreal__normed__algebra(v1) | ? [v3:
% 280.06/41.97 | $i] : ($i(v3) &
% 280.06/41.97 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1563_1,
% 280.06/41.97 | v3) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (
% 280.06/41.97 | ~ (c_RealVector_Onorm__class_Onorm(v1, v4) = v5) | ~ (hAPP(v6,
% 280.06/41.97 | v3) = v7) | ~ (hAPP(all_1563_0, v5) = v6) | ~ $i(v4) | ?
% 280.06/41.97 | [v8: $i] : ? [v9: $i] : ? [v10: $i] :
% 280.06/41.97 | (c_RealVector_Onorm__class_Onorm(v1, v9) = v10 & hAPP(v8, v0) =
% 280.06/41.97 | v9 & hAPP(v2, v4) = v8 & $i(v10) & $i(v9) & $i(v8) &
% 280.06/41.97 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v10,
% 280.06/41.97 | v7)))))
% 280.06/41.97 |
% 280.06/41.97 | ALPHA: (427) implies:
% 280.06/41.97 | (428) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1563_1
% 280.06/41.97 |
% 280.06/41.97 | DELTA: instantiating (44) with fresh symbols all_1565_0, all_1565_1 gives:
% 280.06/41.97 | (429) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1565_0 &
% 280.06/41.97 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1565_1 &
% 280.06/41.97 | $i(all_1565_0) & $i(all_1565_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 280.06/41.97 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v3, v1) =
% 280.06/41.97 | v4) | ~ (hAPP(v3, v0) = v5) | ~ (hAPP(all_1565_0, v2) = v3) |
% 280.06/41.97 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 280.06/41.97 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1565_1, v2) |
% 280.06/41.97 | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v5) |
% 280.06/41.97 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v0)) & !
% 280.06/41.97 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 280.06/41.97 | [v5: $i] : ( ~ (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v5) | ~
% 280.06/41.97 | (hAPP(all_1565_0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 280.06/41.97 | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1565_1, v2) |
% 280.06/41.97 | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v0) |
% 280.06/41.97 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v5))
% 280.06/41.97 |
% 280.06/41.97 | ALPHA: (429) implies:
% 280.06/41.97 | (430) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1565_1
% 280.06/41.97 |
% 280.06/41.97 | DELTA: instantiating (112) with fresh symbols all_1589_0, all_1589_1,
% 280.06/41.97 | all_1589_2, all_1589_3 gives:
% 280.06/41.97 | (431) c_Power_Opower__class_Opower(tc_RealDef_Oreal) = all_1589_0 &
% 280.06/41.97 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1589_1 &
% 280.06/41.97 | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1589_2 &
% 280.06/41.97 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1589_3 &
% 280.06/41.97 | $i(all_1589_0) & $i(all_1589_1) & $i(all_1589_2) & $i(all_1589_3) &
% 280.06/41.97 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 280.06/41.97 | ( ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1, all_1589_1) =
% 280.06/41.97 | v2) | ~ (hAPP(v3, v0) = v4) | ~ (hAPP(all_1589_0, v2) = v3) |
% 280.06/41.97 | ~ $i(v1) | ~ $i(v0) | ~
% 280.06/41.97 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1589_3, v1)
% 280.06/41.97 | | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] :
% 280.06/41.97 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v5 &
% 280.06/41.97 | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v7, all_1589_1) =
% 280.06/41.97 | v8 & hAPP(v6, v1) = v7 & hAPP(all_1589_2, v5) = v6 & $i(v8) &
% 280.06/41.97 | $i(v7) & $i(v6) & $i(v5) &
% 280.06/41.97 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v8, v4)))
% 280.06/41.97 |
% 280.06/41.97 | ALPHA: (431) implies:
% 280.06/41.97 | (432) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1589_3
% 280.06/41.97 | (433) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1589_1
% 280.06/41.97 |
% 280.06/41.97 | DELTA: instantiating (63) with fresh symbols all_1601_0, all_1601_1 gives:
% 280.06/41.98 | (434) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1601_0 &
% 280.06/41.98 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1601_1 &
% 280.06/41.98 | $i(all_1601_0) & $i(all_1601_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 280.06/41.98 | (c_Groups_Otimes__class_Otimes(v0) = v1) | ~ $i(v0) | ~
% 280.06/41.98 | class_RealVector_Oreal__normed__algebra(v0) | ? [v2: $i] : ($i(v2)
% 280.06/41.98 | & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1601_1,
% 280.06/41.98 | v2) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] :
% 280.06/41.98 | ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ( ~
% 280.06/41.98 | (c_RealVector_Onorm__class_Onorm(v0, v4) = v7) | ~
% 280.06/41.98 | (c_RealVector_Onorm__class_Onorm(v0, v3) = v5) | ~ (hAPP(v9,
% 280.06/41.98 | v2) = v10) | ~ (hAPP(v6, v7) = v8) | ~ (hAPP(all_1601_0,
% 280.06/41.98 | v8) = v9) | ~ (hAPP(all_1601_0, v5) = v6) | ~ $i(v4) | ~
% 280.06/41.98 | $i(v3) | ? [v11: $i] : ? [v12: $i] : ? [v13: $i] :
% 280.06/41.98 | (c_RealVector_Onorm__class_Onorm(v0, v12) = v13 & hAPP(v11, v4)
% 280.06/41.98 | = v12 & hAPP(v1, v3) = v11 & $i(v13) & $i(v12) & $i(v11) &
% 280.06/41.98 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v13,
% 280.06/41.98 | v10)))))
% 280.06/41.98 |
% 280.06/41.98 | ALPHA: (434) implies:
% 280.06/41.98 | (435) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1601_1
% 280.06/41.98 |
% 280.06/41.98 | DELTA: instantiating (132) with fresh symbol all_1607_0 gives:
% 280.06/41.98 | (436) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1607_0 &
% 280.06/41.98 | $i(all_1607_0) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2)
% 280.06/41.98 | | ~ $i(v1) | ~ $i(v0) | ~
% 280.06/41.98 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1607_0, v2) |
% 280.06/41.98 | ~ class_RealVector_Oreal__normed__vector(v1) | c_SEQ_OBseq(v1, v0)
% 280.06/41.98 | | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] :
% 280.06/41.98 | (c_RealVector_Onorm__class_Onorm(v1, v4) = v5 & hAPP(v0, v3) = v4 &
% 280.06/41.98 | $i(v5) & $i(v4) & $i(v3) & ~
% 280.06/41.98 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, v2))) &
% 280.06/41.98 | ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 280.06/41.98 | c_SEQ_OBseq(v1, v0) | ~ class_RealVector_Oreal__normed__vector(v1)
% 280.06/41.98 | | ? [v2: $i] : ($i(v2) &
% 280.06/41.98 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1607_0, v2) &
% 280.06/41.98 | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 280.06/41.98 | (c_RealVector_Onorm__class_Onorm(v1, v4) = v5) | ~ (hAPP(v0,
% 280.06/41.98 | v3) = v4) | ~ $i(v3) |
% 280.06/41.98 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, v2))))
% 280.06/41.98 |
% 280.06/41.98 | ALPHA: (436) implies:
% 280.06/41.98 | (437) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1607_0
% 280.06/41.98 |
% 280.06/41.98 | DELTA: instantiating (42) with fresh symbols all_1610_0, all_1610_1 gives:
% 280.06/41.98 | (438) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1610_1 &
% 280.06/41.98 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1610_0 &
% 280.06/41.98 | $i(all_1610_0) & $i(all_1610_1) & ! [v0: $i] : ! [v1: any] : !
% 280.06/41.98 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = all_1610_0
% 280.06/41.98 | | ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v5) =
% 280.06/41.98 | all_1610_0) | ~ (hAPP(v4, v0) = v5) | ~ (hAPP(v2, v1) = v3) |
% 280.06/41.98 | ~ (hAPP(all_1610_1, v1) = v2) | ~ (hAPP(all_1610_1, v0) = v4) | ~
% 280.06/41.98 | $i(v1) | ~ $i(v0)) & ! [v0: any] : ! [v1: $i] : ! [v2: $i] : !
% 280.06/41.98 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v0 = all_1610_0 | ~
% 280.06/41.98 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v5) =
% 280.06/41.98 | all_1610_0) | ~ (hAPP(v4, v0) = v5) | ~ (hAPP(v2, v1) = v3) |
% 280.06/41.98 | ~ (hAPP(all_1610_1, v1) = v2) | ~ (hAPP(all_1610_1, v0) = v4) | ~
% 280.06/41.98 | $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] :
% 280.06/41.98 | (v2 = all_1610_0 | ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,
% 280.06/41.98 | v1, v1) = v2) | ~ (hAPP(v0, all_1610_0) = v1) | ~
% 280.06/41.98 | (hAPP(all_1610_1, all_1610_0) = v0))
% 280.06/41.98 |
% 280.06/41.98 | ALPHA: (438) implies:
% 280.06/41.98 | (439) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1610_0
% 280.06/41.98 |
% 280.06/41.98 | DELTA: instantiating (41) with fresh symbols all_1613_0, all_1613_1 gives:
% 280.06/41.98 | (440) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1613_0 &
% 280.06/41.98 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1613_1 &
% 280.06/41.98 | $i(all_1613_0) & $i(all_1613_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 280.06/41.98 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 280.06/41.98 | (hAPP(v5, v2) = v6) | ~ (hAPP(v3, v2) = v4) | ~ (hAPP(all_1613_0,
% 280.06/41.98 | v1) = v3) | ~ (hAPP(all_1613_0, v0) = v5) | ~ $i(v2) | ~
% 280.06/41.98 | $i(v1) | ~ $i(v0) | ~
% 280.06/41.98 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v4, v6) | ~
% 280.06/41.98 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1613_1, v2) |
% 280.06/41.98 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v0)) & ! [v0:
% 280.06/41.98 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 280.06/41.98 | [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5, v2) = v6) | ~ (hAPP(v3, v2) =
% 280.06/41.98 | v4) | ~ (hAPP(all_1613_0, v1) = v3) | ~ (hAPP(all_1613_0, v0) =
% 280.06/41.98 | v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 280.06/41.98 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v0) | ~
% 280.06/41.98 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1613_1, v2) |
% 280.06/41.98 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v4, v6))
% 280.06/41.98 |
% 280.06/41.98 | ALPHA: (440) implies:
% 280.06/41.98 | (441) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1613_1
% 280.06/41.98 |
% 280.06/41.98 | DELTA: instantiating (43) with fresh symbols all_1616_0, all_1616_1 gives:
% 280.06/41.98 | (442) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1616_0 &
% 280.06/41.98 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1616_1 &
% 280.06/41.98 | $i(all_1616_0) & $i(all_1616_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 280.06/41.98 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 280.06/41.98 | (hAPP(v5, v2) = v6) | ~ (hAPP(v3, v2) = v4) | ~ (hAPP(all_1616_0,
% 280.06/41.98 | v1) = v3) | ~ (hAPP(all_1616_0, v0) = v5) | ~ $i(v2) | ~
% 280.06/41.98 | $i(v1) | ~ $i(v0) | ~
% 280.06/41.98 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1616_1, v2) |
% 280.06/41.98 | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v6) |
% 280.06/41.98 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v0)) & !
% 280.06/41.98 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 280.06/41.98 | [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5, v2) = v6) | ~ (hAPP(v3, v2) =
% 280.06/41.98 | v4) | ~ (hAPP(all_1616_0, v1) = v3) | ~ (hAPP(all_1616_0, v0) =
% 280.06/41.98 | v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 280.06/41.98 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1616_1, v2) |
% 280.06/41.98 | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v0) |
% 280.06/41.98 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v6))
% 280.06/41.98 |
% 280.06/41.98 | ALPHA: (442) implies:
% 280.06/41.98 | (443) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1616_1
% 280.06/41.98 |
% 280.06/41.98 | DELTA: instantiating (58) with fresh symbols all_1619_0, all_1619_1 gives:
% 280.06/41.98 | (444) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1619_0 &
% 280.06/41.98 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1619_1 &
% 280.06/41.98 | $i(all_1619_0) & $i(all_1619_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 280.06/41.98 | (c_Groups_Otimes__class_Otimes(v0) = v1) | ~ $i(v0) | ~
% 280.06/41.98 | class_RealVector_Oreal__normed__algebra(v0) | ? [v2: $i] : ($i(v2)
% 280.06/41.98 | & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1619_1, v2)
% 280.06/41.98 | & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 280.06/41.98 | $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ( ~
% 280.06/41.98 | (c_RealVector_Onorm__class_Onorm(v0, v4) = v7) | ~
% 280.06/41.98 | (c_RealVector_Onorm__class_Onorm(v0, v3) = v5) | ~ (hAPP(v9,
% 280.06/41.98 | v2) = v10) | ~ (hAPP(v6, v7) = v8) | ~ (hAPP(all_1619_0,
% 280.06/41.98 | v8) = v9) | ~ (hAPP(all_1619_0, v5) = v6) | ~ $i(v4) | ~
% 280.06/41.98 | $i(v3) | ? [v11: $i] : ? [v12: $i] : ? [v13: $i] :
% 280.06/41.98 | (c_RealVector_Onorm__class_Onorm(v0, v12) = v13 & hAPP(v11, v4)
% 280.06/41.98 | = v12 & hAPP(v1, v3) = v11 & $i(v13) & $i(v12) & $i(v11) &
% 280.06/41.98 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v13,
% 280.06/41.98 | v10)))))
% 280.06/41.98 |
% 280.06/41.98 | ALPHA: (444) implies:
% 280.06/41.98 | (445) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1619_1
% 280.06/41.98 |
% 280.06/41.98 | DELTA: instantiating (107) with fresh symbol all_1637_0 gives:
% 280.06/41.98 | (446) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1637_0 &
% 280.06/41.98 | $i(all_1637_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 280.06/41.98 | $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 280.06/41.98 | (c_RealVector_Onorm__class_Onorm(v3, v4) = v5) | ~ (hAPP(v0, v1) =
% 280.06/41.98 | v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 280.06/41.98 | class_Orderings_Oord(v2) | ~
% 280.06/41.98 | class_RealVector_Oreal__normed__vector(v3) | ? [v6: $i] : ? [v7:
% 280.06/41.98 | $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ($i(v7) &
% 280.06/41.98 | ((c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_1637_0, v5) =
% 280.06/41.98 | v6 & $i(v6) & ! [v11: $i] : ! [v12: $i] : ! [v13: $i] : (
% 280.06/41.98 | ~ (c_RealVector_Onorm__class_Onorm(v3, v12) = v13) | ~
% 280.06/41.98 | (hAPP(v0, v11) = v12) | ~ $i(v11) | ~
% 280.06/41.98 | c_Orderings_Oord__class_Oless__eq(v2, v1, v11) |
% 280.06/41.98 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v13, v6)))
% 280.06/41.98 | | (c_Groups_Ominus__class_Ominus(v3, v4, v8) = v9 &
% 280.06/41.98 | c_RealVector_Onorm__class_Onorm(v3, v9) = v10 & hAPP(v0, v7)
% 280.06/41.98 | = v8 & $i(v10) & $i(v9) & $i(v8) &
% 280.06/41.98 | c_Orderings_Oord__class_Oless__eq(v2, v1, v7) & ~
% 280.06/41.98 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v10,
% 280.06/41.98 | all_1637_0)))))
% 280.06/41.98 |
% 280.06/41.98 | ALPHA: (446) implies:
% 280.06/41.98 | (447) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1637_0
% 280.06/41.98 |
% 280.06/41.98 | DELTA: instantiating (61) with fresh symbols all_1652_0, all_1652_1 gives:
% 280.06/41.98 | (448) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1652_0 &
% 280.06/41.98 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1652_1 &
% 280.06/41.98 | $i(all_1652_0) & $i(all_1652_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 280.06/41.98 | $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 280.06/41.98 | | ~ c_RealVector_Obounded__bilinear(v1, v2, v3, v0) | ~
% 280.06/41.98 | class_RealVector_Oreal__normed__vector(v3) | ~
% 280.06/41.98 | class_RealVector_Oreal__normed__vector(v2) | ~
% 280.06/41.98 | class_RealVector_Oreal__normed__vector(v1) | ? [v4: $i] : ($i(v4)
% 280.06/41.98 | & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1652_1,
% 280.06/41.98 | v4) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] :
% 280.06/41.98 | ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ! [v12: $i] : ( ~
% 280.06/41.98 | (c_RealVector_Onorm__class_Onorm(v2, v6) = v9) | ~
% 280.06/41.98 | (c_RealVector_Onorm__class_Onorm(v1, v5) = v7) | ~ (hAPP(v11,
% 280.06/41.98 | v4) = v12) | ~ (hAPP(v8, v9) = v10) | ~ (hAPP(all_1652_0,
% 280.06/41.98 | v10) = v11) | ~ (hAPP(all_1652_0, v7) = v8) | ~ $i(v6) |
% 280.06/41.98 | ~ $i(v5) | ? [v13: $i] : ? [v14: $i] : ? [v15: $i] :
% 280.06/41.98 | (c_RealVector_Onorm__class_Onorm(v3, v14) = v15 & hAPP(v13, v6)
% 280.06/41.98 | = v14 & hAPP(v0, v5) = v13 & $i(v15) & $i(v14) & $i(v13) &
% 280.06/41.98 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v15,
% 280.06/41.98 | v12)))))
% 280.06/41.98 |
% 280.06/41.98 | ALPHA: (448) implies:
% 280.06/41.98 | (449) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1652_1
% 280.06/41.98 |
% 280.06/41.98 | DELTA: instantiating (56) with fresh symbols all_1655_0, all_1655_1 gives:
% 280.06/41.98 | (450) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1655_0 &
% 280.06/41.98 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1655_1 &
% 280.06/41.98 | $i(all_1655_0) & $i(all_1655_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 280.06/41.98 | $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 280.06/41.98 | | ~ c_RealVector_Obounded__bilinear(v1, v2, v3, v0) | ~
% 280.06/41.98 | class_RealVector_Oreal__normed__vector(v3) | ~
% 280.06/41.98 | class_RealVector_Oreal__normed__vector(v2) | ~
% 280.06/41.98 | class_RealVector_Oreal__normed__vector(v1) | ? [v4: $i] : ($i(v4)
% 280.06/41.98 | & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1655_1, v4)
% 280.06/41.98 | & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9:
% 280.06/41.98 | $i] : ! [v10: $i] : ! [v11: $i] : ! [v12: $i] : ( ~
% 280.06/41.98 | (c_RealVector_Onorm__class_Onorm(v2, v6) = v9) | ~
% 280.06/41.98 | (c_RealVector_Onorm__class_Onorm(v1, v5) = v7) | ~ (hAPP(v11,
% 280.06/41.98 | v4) = v12) | ~ (hAPP(v8, v9) = v10) | ~ (hAPP(all_1655_0,
% 280.06/41.98 | v10) = v11) | ~ (hAPP(all_1655_0, v7) = v8) | ~ $i(v6) |
% 280.06/41.98 | ~ $i(v5) | ? [v13: $i] : ? [v14: $i] : ? [v15: $i] :
% 280.06/41.98 | (c_RealVector_Onorm__class_Onorm(v3, v14) = v15 & hAPP(v13, v6)
% 280.06/41.98 | = v14 & hAPP(v0, v5) = v13 & $i(v15) & $i(v14) & $i(v13) &
% 280.06/41.98 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v15,
% 280.06/41.98 | v12)))))
% 280.06/41.98 |
% 280.06/41.98 | ALPHA: (450) implies:
% 280.06/41.98 | (451) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1655_1
% 280.06/41.98 |
% 280.06/41.98 | DELTA: instantiating (134) with fresh symbol all_1691_0 gives:
% 280.06/41.98 | (452) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1691_0 &
% 280.06/41.98 | $i(all_1691_0) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 280.06/41.98 | $i] : ! [v4: $i] : ( ~ (c_Groups_Ouminus__class_Ouminus(v1, v3) =
% 280.06/41.98 | v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 280.06/41.98 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1691_0, v2) |
% 280.06/41.98 | ~ class_RealVector_Oreal__normed__vector(v1) | c_SEQ_OBseq(v1, v0)
% 280.06/41.98 | | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] :
% 280.06/41.98 | (c_Groups_Oplus__class_Oplus(v1, v6, v4) = v7 &
% 280.06/41.98 | c_RealVector_Onorm__class_Onorm(v1, v7) = v8 & hAPP(v0, v5) = v6
% 280.06/41.98 | & $i(v8) & $i(v7) & $i(v6) & $i(v5) & ~
% 280.06/41.98 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v8, v2))) &
% 280.06/41.98 | ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 280.06/41.98 | c_SEQ_OBseq(v1, v0) | ~ class_RealVector_Oreal__normed__vector(v1)
% 280.06/41.98 | | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 280.06/41.98 | (c_Groups_Ouminus__class_Ouminus(v1, v3) = v4 & $i(v4) & $i(v3) &
% 280.06/41.98 | $i(v2) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 280.06/41.98 | all_1691_0, v2) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : !
% 280.06/41.98 | [v8: $i] : ( ~ (c_Groups_Oplus__class_Oplus(v1, v6, v4) = v7) |
% 280.06/41.98 | ~ (c_RealVector_Onorm__class_Onorm(v1, v7) = v8) | ~ (hAPP(v0,
% 280.06/41.98 | v5) = v6) | ~ $i(v5) |
% 280.06/41.98 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v8, v2))))
% 280.06/41.98 |
% 280.06/41.98 | ALPHA: (452) implies:
% 280.06/41.98 | (453) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1691_0
% 280.06/41.98 |
% 280.06/41.98 | DELTA: instantiating (133) with fresh symbol all_1697_0 gives:
% 280.06/41.98 | (454) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1697_0 &
% 280.06/41.98 | $i(all_1697_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 280.06/41.98 | $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 280.06/41.98 | (c_Groups_Ouminus__class_Ouminus(v1, v4) = v5) | ~ (hAPP(v0, v3) =
% 280.06/41.98 | v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 280.06/41.98 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1697_0, v2) |
% 280.06/41.98 | ~ class_RealVector_Oreal__normed__vector(v1) | c_SEQ_OBseq(v1, v0)
% 280.06/41.98 | | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 280.06/41.98 | (c_Groups_Oplus__class_Oplus(v1, v7, v5) = v8 &
% 280.06/41.98 | c_RealVector_Onorm__class_Onorm(v1, v8) = v9 & hAPP(v0, v6) = v7
% 280.06/41.98 | & $i(v9) & $i(v8) & $i(v7) & $i(v6) & ~
% 280.06/41.98 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v9, v2))) &
% 280.06/41.98 | ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 280.06/41.98 | c_SEQ_OBseq(v1, v0) | ~ class_RealVector_Oreal__normed__vector(v1)
% 280.06/41.98 | | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] :
% 280.06/41.98 | (c_Groups_Ouminus__class_Ouminus(v1, v4) = v5 & hAPP(v0, v3) = v4 &
% 280.06/41.98 | $i(v5) & $i(v4) & $i(v3) & $i(v2) &
% 280.06/41.98 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1697_0, v2) &
% 280.06/41.98 | ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~
% 280.06/41.98 | (c_Groups_Oplus__class_Oplus(v1, v7, v5) = v8) | ~
% 280.06/41.98 | (c_RealVector_Onorm__class_Onorm(v1, v8) = v9) | ~ (hAPP(v0,
% 280.06/41.98 | v6) = v7) | ~ $i(v6) |
% 280.06/41.98 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v9, v2))))
% 280.06/41.98 |
% 280.06/41.98 | ALPHA: (454) implies:
% 280.06/41.98 | (455) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1697_0
% 280.06/41.98 |
% 280.06/41.98 | DELTA: instantiating (137) with fresh symbol all_1700_0 gives:
% 280.06/41.98 | (456) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1700_0 &
% 280.06/41.98 | $i(all_1700_0) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 280.06/41.98 | $i] : ( ~ (c_Nat_OSuc(v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 280.06/41.98 | | ~ class_RealVector_Oreal__normed__vector(v1) | ? [v4: $i] : ?
% 280.06/41.98 | [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ($i(v6) &
% 280.06/41.98 | $i(v4) & ((c_RealDef_Oreal(tc_Nat_Onat, v3) = v5 &
% 280.06/41.98 | c_RealVector_Onorm__class_Onorm(v1, v7) = v8 & hAPP(v0, v6) =
% 280.06/41.98 | v7 & $i(v8) & $i(v7) & $i(v5) & ~
% 280.06/41.98 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v8, v5)) |
% 280.06/41.98 | (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1700_0,
% 280.06/41.98 | v4) & ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~
% 280.06/41.98 | (c_RealVector_Onorm__class_Onorm(v1, v10) = v11) | ~
% 280.06/41.98 | (hAPP(v0, v9) = v10) | ~ $i(v9) |
% 280.06/41.98 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v11,
% 280.06/41.98 | v4)))))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 280.06/41.98 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 280.06/41.98 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1700_0, v2) |
% 280.06/41.98 | ~ class_RealVector_Oreal__normed__vector(v1) | ? [v3: $i] : ?
% 280.06/41.98 | [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] :
% 280.06/41.98 | ($i(v6) & $i(v3) & ((c_Nat_OSuc(v3) = v4 &
% 280.06/41.98 | c_RealDef_Oreal(tc_Nat_Onat, v4) = v5 & $i(v5) & $i(v4) & !
% 280.06/41.98 | [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~
% 280.06/41.98 | (c_RealVector_Onorm__class_Onorm(v1, v10) = v11) | ~
% 280.06/41.98 | (hAPP(v0, v9) = v10) | ~ $i(v9) |
% 280.06/41.98 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v11, v5)))
% 280.06/41.98 | | (c_RealVector_Onorm__class_Onorm(v1, v7) = v8 & hAPP(v0, v6)
% 280.06/41.98 | = v7 & $i(v8) & $i(v7) & ~
% 280.06/41.98 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v8,
% 280.06/41.98 | v2)))))
% 280.06/41.98 |
% 280.06/41.98 | ALPHA: (456) implies:
% 280.06/41.98 | (457) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1700_0
% 280.06/41.98 |
% 280.06/41.99 | GROUND_INST: instantiating (152) with all_1068_3, all_1308_6, v_z, v_w,
% 280.06/41.99 | tc_Complex_Ocomplex, simplifying with (282), (359) gives:
% 280.06/41.99 | (458) all_1308_6 = all_1068_3
% 280.06/41.99 |
% 280.06/41.99 | GROUND_INST: instantiating (148) with all_682_0, all_684_0, tc_RealDef_Oreal,
% 280.06/41.99 | simplifying with (158), (160) gives:
% 280.06/41.99 | (459) all_684_0 = all_682_0
% 280.06/41.99 |
% 280.06/41.99 | GROUND_INST: instantiating (148) with all_684_0, all_691_0, tc_RealDef_Oreal,
% 280.06/41.99 | simplifying with (160), (162) gives:
% 280.06/41.99 | (460) all_691_0 = all_684_0
% 280.06/41.99 |
% 280.06/41.99 | GROUND_INST: instantiating (148) with all_691_0, all_696_0, tc_RealDef_Oreal,
% 280.06/41.99 | simplifying with (162), (164) gives:
% 280.06/41.99 | (461) all_696_0 = all_691_0
% 280.06/41.99 |
% 280.06/41.99 | GROUND_INST: instantiating (148) with all_696_0, all_704_0, tc_RealDef_Oreal,
% 280.06/41.99 | simplifying with (164), (166) gives:
% 280.06/41.99 | (462) all_704_0 = all_696_0
% 280.06/41.99 |
% 280.06/41.99 | GROUND_INST: instantiating (148) with all_735_1, all_740_1, tc_RealDef_Oreal,
% 280.06/41.99 | simplifying with (171), (173) gives:
% 280.06/41.99 | (463) all_740_1 = all_735_1
% 280.06/41.99 |
% 280.06/41.99 | GROUND_INST: instantiating (148) with all_740_1, all_742_0, tc_RealDef_Oreal,
% 280.06/41.99 | simplifying with (173), (176) gives:
% 280.06/41.99 | (464) all_742_0 = all_740_1
% 280.06/41.99 |
% 280.06/41.99 | GROUND_INST: instantiating (148) with all_742_0, all_753_1, tc_RealDef_Oreal,
% 280.06/41.99 | simplifying with (176), (182) gives:
% 280.06/41.99 | (465) all_753_1 = all_742_0
% 280.06/41.99 |
% 280.06/41.99 | GROUND_INST: instantiating (148) with all_753_1, all_759_1, tc_RealDef_Oreal,
% 280.06/41.99 | simplifying with (182), (189) gives:
% 280.06/41.99 | (466) all_759_1 = all_753_1
% 280.06/41.99 |
% 280.06/41.99 | GROUND_INST: instantiating (148) with all_759_1, all_767_0, tc_RealDef_Oreal,
% 280.06/41.99 | simplifying with (189), (191) gives:
% 280.06/41.99 | (467) all_767_0 = all_759_1
% 280.06/41.99 |
% 280.06/41.99 | GROUND_INST: instantiating (148) with all_767_0, all_779_0, tc_RealDef_Oreal,
% 280.06/41.99 | simplifying with (191), (193) gives:
% 280.06/41.99 | (468) all_779_0 = all_767_0
% 280.06/41.99 |
% 280.06/41.99 | GROUND_INST: instantiating (148) with all_779_0, all_843_0, tc_RealDef_Oreal,
% 280.06/41.99 | simplifying with (193), (201) gives:
% 280.06/41.99 | (469) all_843_0 = all_779_0
% 280.06/41.99 |
% 280.06/41.99 | GROUND_INST: instantiating (148) with all_843_0, all_853_1, tc_RealDef_Oreal,
% 280.06/41.99 | simplifying with (201), (203) gives:
% 280.06/41.99 | (470) all_853_1 = all_843_0
% 280.06/41.99 |
% 280.06/41.99 | GROUND_INST: instantiating (148) with all_735_1, all_856_0, tc_RealDef_Oreal,
% 280.06/41.99 | simplifying with (171), (205) gives:
% 280.06/41.99 | (471) all_856_0 = all_735_1
% 280.06/41.99 |
% 280.06/41.99 | GROUND_INST: instantiating (148) with all_724_0, all_856_0, tc_RealDef_Oreal,
% 280.06/41.99 | simplifying with (168), (205) gives:
% 280.06/41.99 | (472) all_856_0 = all_724_0
% 280.06/41.99 |
% 280.06/41.99 | GROUND_INST: instantiating (148) with all_704_0, all_856_0, tc_RealDef_Oreal,
% 280.06/41.99 | simplifying with (166), (205) gives:
% 280.06/41.99 | (473) all_856_0 = all_704_0
% 280.06/41.99 |
% 280.06/41.99 | GROUND_INST: instantiating (148) with all_853_1, all_868_0, tc_RealDef_Oreal,
% 280.06/41.99 | simplifying with (203), (210) gives:
% 280.06/41.99 | (474) all_868_0 = all_853_1
% 280.06/41.99 |
% 280.06/41.99 | GROUND_INST: instantiating (148) with all_868_0, all_874_0, tc_RealDef_Oreal,
% 280.06/41.99 | simplifying with (210), (212) gives:
% 280.06/41.99 | (475) all_874_0 = all_868_0
% 280.06/41.99 |
% 280.06/41.99 | GROUND_INST: instantiating (148) with all_868_0, all_882_1, tc_RealDef_Oreal,
% 280.06/41.99 | simplifying with (210), (215) gives:
% 280.06/41.99 | (476) all_882_1 = all_868_0
% 280.06/41.99 |
% 280.06/41.99 | GROUND_INST: instantiating (148) with all_874_0, all_885_0, tc_RealDef_Oreal,
% 280.06/41.99 | simplifying with (212), (217) gives:
% 280.06/41.99 | (477) all_885_0 = all_874_0
% 280.06/41.99 |
% 280.06/41.99 | GROUND_INST: instantiating (148) with all_885_0, all_888_0, tc_RealDef_Oreal,
% 280.06/41.99 | simplifying with (217), (219) gives:
% 280.06/41.99 | (478) all_888_0 = all_885_0
% 280.06/41.99 |
% 280.06/41.99 | GROUND_INST: instantiating (148) with all_882_1, all_894_0, tc_RealDef_Oreal,
% 280.06/41.99 | simplifying with (215), (221) gives:
% 280.06/41.99 | (479) all_894_0 = all_882_1
% 280.06/41.99 |
% 280.06/41.99 | GROUND_INST: instantiating (148) with all_888_0, all_897_0, tc_RealDef_Oreal,
% 280.06/41.99 | simplifying with (219), (223) gives:
% 280.06/41.99 | (480) all_897_0 = all_888_0
% 280.06/41.99 |
% 280.06/41.99 | GROUND_INST: instantiating (148) with all_912_1, all_927_0, tc_RealDef_Oreal,
% 280.06/41.99 | simplifying with (228), (230) gives:
% 280.06/41.99 | (481) all_927_0 = all_912_1
% 280.06/41.99 |
% 280.06/41.99 | GROUND_INST: instantiating (148) with all_912_1, all_948_0, tc_RealDef_Oreal,
% 280.06/41.99 | simplifying with (228), (235) gives:
% 280.06/41.99 | (482) all_948_0 = all_912_1
% 280.06/41.99 |
% 280.06/41.99 | GROUND_INST: instantiating (148) with all_897_0, all_948_0, tc_RealDef_Oreal,
% 280.06/41.99 | simplifying with (223), (235) gives:
% 280.06/41.99 | (483) all_948_0 = all_897_0
% 280.06/41.99 |
% 280.06/41.99 | GROUND_INST: instantiating (148) with all_933_0, all_958_1, tc_RealDef_Oreal,
% 280.06/41.99 | simplifying with (232), (239) gives:
% 280.06/41.99 | (484) all_958_1 = all_933_0
% 280.06/41.99 |
% 280.06/41.99 | GROUND_INST: instantiating (148) with all_927_0, all_958_1, tc_RealDef_Oreal,
% 280.06/41.99 | simplifying with (230), (239) gives:
% 280.06/41.99 | (485) all_958_1 = all_927_0
% 280.06/41.99 |
% 280.06/41.99 | GROUND_INST: instantiating (148) with all_967_1, all_970_1, tc_RealDef_Oreal,
% 280.06/41.99 | simplifying with (246), (249) gives:
% 280.06/41.99 | (486) all_970_1 = all_967_1
% 280.06/41.99 |
% 280.06/41.99 | GROUND_INST: instantiating (148) with all_970_1, all_973_1, tc_RealDef_Oreal,
% 280.06/41.99 | simplifying with (249), (252) gives:
% 280.06/41.99 | (487) all_973_1 = all_970_1
% 280.06/41.99 |
% 280.06/41.99 | GROUND_INST: instantiating (148) with all_894_0, all_984_0, tc_RealDef_Oreal,
% 280.06/41.99 | simplifying with (221), (257) gives:
% 280.06/41.99 | (488) all_984_0 = all_894_0
% 280.06/41.99 |
% 280.06/41.99 | GROUND_INST: instantiating (148) with all_861_0, all_984_0, tc_RealDef_Oreal,
% 280.06/41.99 | simplifying with (207), (257) gives:
% 280.06/41.99 | (489) all_984_0 = all_861_0
% 280.06/41.99 |
% 280.06/41.99 | GROUND_INST: instantiating (148) with all_973_1, all_999_1, tc_RealDef_Oreal,
% 280.06/41.99 | simplifying with (252), (259) gives:
% 280.06/41.99 | (490) all_999_1 = all_973_1
% 280.06/41.99 |
% 280.06/41.99 | GROUND_INST: instantiating (148) with all_1044_0, all_1047_0,
% 280.06/41.99 | tc_RealDef_Oreal, simplifying with (264), (266) gives:
% 280.06/41.99 | (491) all_1047_0 = all_1044_0
% 280.06/41.99 |
% 280.06/41.99 | GROUND_INST: instantiating (148) with all_1047_0, all_1059_0,
% 280.06/41.99 | tc_RealDef_Oreal, simplifying with (266), (273) gives:
% 280.06/41.99 | (492) all_1059_0 = all_1047_0
% 280.06/41.99 |
% 280.06/41.99 | GROUND_INST: instantiating (148) with all_1059_0, all_1062_1,
% 280.06/41.99 | tc_RealDef_Oreal, simplifying with (273), (275) gives:
% 280.06/41.99 | (493) all_1062_1 = all_1059_0
% 280.06/41.99 |
% 280.06/41.99 | GROUND_INST: instantiating (148) with all_1062_1, all_1073_0,
% 280.06/41.99 | tc_RealDef_Oreal, simplifying with (275), (284) gives:
% 280.06/41.99 | (494) all_1073_0 = all_1062_1
% 280.06/41.99 |
% 280.06/41.99 | GROUND_INST: instantiating (148) with all_1073_0, all_1091_0,
% 280.06/41.99 | tc_RealDef_Oreal, simplifying with (284), (286) gives:
% 280.06/41.99 | (495) all_1091_0 = all_1073_0
% 280.06/41.99 |
% 280.06/41.99 | GROUND_INST: instantiating (148) with all_948_0, all_1114_1, tc_RealDef_Oreal,
% 280.06/41.99 | simplifying with (235), (290) gives:
% 280.06/41.99 | (496) all_1114_1 = all_948_0
% 280.06/41.99 |
% 280.06/41.99 | GROUND_INST: instantiating (148) with all_1091_0, all_1117_1,
% 280.06/41.99 | tc_RealDef_Oreal, simplifying with (286), (292) gives:
% 280.06/41.99 | (497) all_1117_1 = all_1091_0
% 280.06/41.99 |
% 280.06/41.99 | GROUND_INST: instantiating (148) with all_1117_1, all_1120_0,
% 280.06/41.99 | tc_RealDef_Oreal, simplifying with (292), (294) gives:
% 280.06/41.99 | (498) all_1120_0 = all_1117_1
% 280.06/41.99 |
% 280.06/41.99 | GROUND_INST: instantiating (148) with all_1120_0, all_1135_0,
% 280.06/41.99 | tc_RealDef_Oreal, simplifying with (294), (296) gives:
% 280.06/41.99 | (499) all_1135_0 = all_1120_0
% 280.06/41.99 |
% 280.06/41.99 | GROUND_INST: instantiating (148) with all_1135_0, all_1155_0,
% 280.06/41.99 | tc_RealDef_Oreal, simplifying with (296), (300) gives:
% 280.06/41.99 | (500) all_1155_0 = all_1135_0
% 280.06/41.99 |
% 280.06/41.99 | GROUND_INST: instantiating (148) with all_1155_0, all_1158_1,
% 280.06/41.99 | tc_RealDef_Oreal, simplifying with (300), (302) gives:
% 280.06/41.99 | (501) all_1158_1 = all_1155_0
% 280.06/41.99 |
% 280.06/41.99 | GROUND_INST: instantiating (148) with all_1158_1, all_1166_0,
% 280.06/41.99 | tc_RealDef_Oreal, simplifying with (302), (304) gives:
% 280.06/41.99 | (502) all_1166_0 = all_1158_1
% 280.06/41.99 |
% 280.06/41.99 | GROUND_INST: instantiating (148) with all_1166_0, all_1182_0,
% 280.06/41.99 | tc_RealDef_Oreal, simplifying with (304), (306) gives:
% 280.06/41.99 | (503) all_1182_0 = all_1166_0
% 280.06/41.99 |
% 280.06/41.99 | GROUND_INST: instantiating (148) with all_1182_0, all_1185_0,
% 280.06/41.99 | tc_RealDef_Oreal, simplifying with (306), (308) gives:
% 280.06/41.99 | (504) all_1185_0 = all_1182_0
% 280.06/41.99 |
% 280.06/41.99 | GROUND_INST: instantiating (148) with all_1185_0, all_1200_0,
% 280.06/41.99 | tc_RealDef_Oreal, simplifying with (308), (310) gives:
% 280.06/41.99 | (505) all_1200_0 = all_1185_0
% 280.06/41.99 |
% 280.06/41.99 | GROUND_INST: instantiating (148) with all_1200_0, all_1206_1,
% 280.06/41.99 | tc_RealDef_Oreal, simplifying with (310), (312) gives:
% 280.06/41.99 | (506) all_1206_1 = all_1200_0
% 280.06/41.99 |
% 280.06/41.99 | GROUND_INST: instantiating (148) with all_967_1, all_1209_0, tc_RealDef_Oreal,
% 280.06/41.99 | simplifying with (246), (314) gives:
% 280.06/41.99 | (507) all_1209_0 = all_967_1
% 280.06/41.99 |
% 280.06/41.99 | GROUND_INST: instantiating (148) with all_958_1, all_1209_0, tc_RealDef_Oreal,
% 280.06/41.99 | simplifying with (239), (314) gives:
% 280.06/41.99 | (508) all_1209_0 = all_958_1
% 280.06/41.99 |
% 280.06/41.99 | GROUND_INST: instantiating (148) with all_1206_1, all_1218_1,
% 280.06/41.99 | tc_RealDef_Oreal, simplifying with (312), (316) gives:
% 280.06/41.99 | (509) all_1218_1 = all_1206_1
% 280.06/41.99 |
% 280.06/41.99 | GROUND_INST: instantiating (148) with all_1218_1, all_1239_1,
% 280.06/41.99 | tc_RealDef_Oreal, simplifying with (316), (318) gives:
% 280.06/41.99 | (510) all_1239_1 = all_1218_1
% 280.06/41.99 |
% 280.06/41.99 | GROUND_INST: instantiating (148) with all_1239_1, all_1248_2,
% 280.06/41.99 | tc_RealDef_Oreal, simplifying with (318), (321) gives:
% 280.06/41.99 | (511) all_1248_2 = all_1239_1
% 280.06/41.99 |
% 280.06/41.99 | GROUND_INST: instantiating (148) with all_1254_0, all_1257_1,
% 280.06/41.99 | tc_RealDef_Oreal, simplifying with (327), (329) gives:
% 280.06/41.99 | (512) all_1257_1 = all_1254_0
% 280.06/41.99 |
% 280.06/41.99 | GROUND_INST: instantiating (148) with all_1257_1, all_1260_1,
% 280.06/41.99 | tc_RealDef_Oreal, simplifying with (329), (332) gives:
% 280.06/41.99 | (513) all_1260_1 = all_1257_1
% 280.06/41.99 |
% 280.06/41.99 | GROUND_INST: instantiating (148) with all_1260_1, all_1263_1,
% 280.06/41.99 | tc_RealDef_Oreal, simplifying with (332), (335) gives:
% 280.06/41.99 | (514) all_1263_1 = all_1260_1
% 280.06/41.99 |
% 280.06/41.99 | GROUND_INST: instantiating (148) with all_1263_1, all_1266_0,
% 280.06/41.99 | tc_RealDef_Oreal, simplifying with (335), (338) gives:
% 280.06/41.99 | (515) all_1266_0 = all_1263_1
% 280.06/41.99 |
% 280.06/41.99 | GROUND_INST: instantiating (148) with all_1266_0, all_1268_0,
% 280.06/41.99 | tc_RealDef_Oreal, simplifying with (338), (340) gives:
% 280.06/42.00 | (516) all_1268_0 = all_1266_0
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (148) with all_1114_1, all_1274_1,
% 280.06/42.00 | tc_RealDef_Oreal, simplifying with (290), (342) gives:
% 280.06/42.00 | (517) all_1274_1 = all_1114_1
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (148) with all_906_0, all_1274_1, tc_RealDef_Oreal,
% 280.06/42.00 | simplifying with (225), (342) gives:
% 280.06/42.00 | (518) all_1274_1 = all_906_0
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (148) with all_1268_0, all_1277_0,
% 280.06/42.00 | tc_RealDef_Oreal, simplifying with (340), (344) gives:
% 280.06/42.00 | (519) all_1277_0 = all_1268_0
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (148) with all_1056_1, all_1280_1,
% 280.06/42.00 | tc_RealDef_Oreal, simplifying with (270), (346) gives:
% 280.06/42.00 | (520) all_1280_1 = all_1056_1
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (148) with all_1044_0, all_1280_1,
% 280.06/42.00 | tc_RealDef_Oreal, simplifying with (264), (346) gives:
% 280.06/42.00 | (521) all_1280_1 = all_1044_0
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (148) with all_1005_1, all_1280_1,
% 280.06/42.00 | tc_RealDef_Oreal, simplifying with (262), (346) gives:
% 280.06/42.00 | (522) all_1280_1 = all_1005_1
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (148) with all_999_1, all_1280_1, tc_RealDef_Oreal,
% 280.06/42.00 | simplifying with (259), (346) gives:
% 280.06/42.00 | (523) all_1280_1 = all_999_1
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (148) with all_1277_0, all_1283_2,
% 280.06/42.00 | tc_RealDef_Oreal, simplifying with (344), (348) gives:
% 280.06/42.00 | (524) all_1283_2 = all_1277_0
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (148) with all_1209_0, all_1299_2,
% 280.06/42.00 | tc_RealDef_Oreal, simplifying with (314), (352) gives:
% 280.06/42.00 | (525) all_1299_2 = all_1209_0
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (148) with all_964_1, all_1299_2, tc_RealDef_Oreal,
% 280.06/42.00 | simplifying with (243), (352) gives:
% 280.06/42.00 | (526) all_1299_2 = all_964_1
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (148) with all_1283_2, all_1316_2,
% 280.06/42.00 | tc_RealDef_Oreal, simplifying with (348), (363) gives:
% 280.06/42.00 | (527) all_1316_2 = all_1283_2
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (148) with all_1316_2, all_1319_2,
% 280.06/42.00 | tc_RealDef_Oreal, simplifying with (363), (365) gives:
% 280.06/42.00 | (528) all_1319_2 = all_1316_2
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (148) with all_1319_2, all_1322_0,
% 280.06/42.00 | tc_RealDef_Oreal, simplifying with (365), (367) gives:
% 280.06/42.00 | (529) all_1322_0 = all_1319_2
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (148) with all_1322_0, all_1325_1,
% 280.06/42.00 | tc_RealDef_Oreal, simplifying with (367), (369) gives:
% 280.06/42.00 | (530) all_1325_1 = all_1322_0
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (148) with all_1325_1, all_1335_0,
% 280.06/42.00 | tc_RealDef_Oreal, simplifying with (369), (371) gives:
% 280.06/42.00 | (531) all_1335_0 = all_1325_1
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (148) with all_1335_0, all_1338_0,
% 280.06/42.00 | tc_RealDef_Oreal, simplifying with (371), (373) gives:
% 280.06/42.00 | (532) all_1338_0 = all_1335_0
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (148) with all_1338_0, all_1341_0,
% 280.06/42.00 | tc_RealDef_Oreal, simplifying with (373), (375) gives:
% 280.06/42.00 | (533) all_1341_0 = all_1338_0
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (148) with all_1341_0, all_1344_0,
% 280.06/42.00 | tc_RealDef_Oreal, simplifying with (375), (377) gives:
% 280.06/42.00 | (534) all_1344_0 = all_1341_0
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (148) with all_1344_0, all_1353_0,
% 280.06/42.00 | tc_RealDef_Oreal, simplifying with (377), (379) gives:
% 280.06/42.00 | (535) all_1353_0 = all_1344_0
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (148) with all_1353_0, all_1356_0,
% 280.06/42.00 | tc_RealDef_Oreal, simplifying with (379), (381) gives:
% 280.06/42.00 | (536) all_1356_0 = all_1353_0
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (148) with all_1356_0, all_1365_1,
% 280.06/42.00 | tc_RealDef_Oreal, simplifying with (381), (384) gives:
% 280.06/42.00 | (537) all_1365_1 = all_1356_0
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (148) with all_1365_1, all_1377_0,
% 280.06/42.00 | tc_RealDef_Oreal, simplifying with (384), (386) gives:
% 280.06/42.00 | (538) all_1377_0 = all_1365_1
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (148) with all_1377_0, all_1386_1,
% 280.06/42.00 | tc_RealDef_Oreal, simplifying with (386), (388) gives:
% 280.06/42.00 | (539) all_1386_1 = all_1377_0
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (148) with all_1386_1, all_1410_1,
% 280.06/42.00 | tc_RealDef_Oreal, simplifying with (388), (390) gives:
% 280.06/42.00 | (540) all_1410_1 = all_1386_1
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (148) with all_1410_1, all_1415_1,
% 280.06/42.00 | tc_RealDef_Oreal, simplifying with (390), (394) gives:
% 280.06/42.00 | (541) all_1415_1 = all_1410_1
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (148) with all_1415_1, all_1423_0,
% 280.06/42.00 | tc_RealDef_Oreal, simplifying with (394), (396) gives:
% 280.06/42.00 | (542) all_1423_0 = all_1415_1
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (148) with all_1423_0, all_1429_0,
% 280.06/42.00 | tc_RealDef_Oreal, simplifying with (396), (398) gives:
% 280.06/42.00 | (543) all_1429_0 = all_1423_0
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (148) with all_1429_0, all_1441_1,
% 280.06/42.00 | tc_RealDef_Oreal, simplifying with (398), (402) gives:
% 280.06/42.00 | (544) all_1441_1 = all_1429_0
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (148) with all_1441_1, all_1443_1,
% 280.06/42.00 | tc_RealDef_Oreal, simplifying with (402), (404) gives:
% 280.06/42.00 | (545) all_1443_1 = all_1441_1
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (148) with all_1443_1, all_1450_0,
% 280.06/42.00 | tc_RealDef_Oreal, simplifying with (404), (406) gives:
% 280.06/42.00 | (546) all_1450_0 = all_1443_1
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (148) with all_1450_0, all_1480_2,
% 280.06/42.00 | tc_RealDef_Oreal, simplifying with (406), (408) gives:
% 280.06/42.00 | (547) all_1480_2 = all_1450_0
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (148) with all_1480_2, all_1486_1,
% 280.06/42.00 | tc_RealDef_Oreal, simplifying with (408), (410) gives:
% 280.06/42.00 | (548) all_1486_1 = all_1480_2
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (148) with all_1486_1, all_1489_1,
% 280.06/42.00 | tc_RealDef_Oreal, simplifying with (410), (412) gives:
% 280.06/42.00 | (549) all_1489_1 = all_1486_1
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (148) with all_1489_1, all_1492_1,
% 280.06/42.00 | tc_RealDef_Oreal, simplifying with (412), (414) gives:
% 280.06/42.00 | (550) all_1492_1 = all_1489_1
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (148) with all_1492_1, all_1522_1,
% 280.06/42.00 | tc_RealDef_Oreal, simplifying with (414), (416) gives:
% 280.06/42.00 | (551) all_1522_1 = all_1492_1
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (148) with all_1522_1, all_1528_2,
% 280.06/42.00 | tc_RealDef_Oreal, simplifying with (416), (418) gives:
% 280.06/42.00 | (552) all_1528_2 = all_1522_1
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (148) with all_1528_2, all_1531_0,
% 280.06/42.00 | tc_RealDef_Oreal, simplifying with (418), (420) gives:
% 280.06/42.00 | (553) all_1531_0 = all_1528_2
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (148) with all_1531_0, all_1537_1,
% 280.06/42.00 | tc_RealDef_Oreal, simplifying with (420), (422) gives:
% 280.06/42.00 | (554) all_1537_1 = all_1531_0
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (148) with all_1537_1, all_1555_1,
% 280.06/42.00 | tc_RealDef_Oreal, simplifying with (422), (424) gives:
% 280.06/42.00 | (555) all_1555_1 = all_1537_1
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (148) with all_1555_1, all_1557_0,
% 280.06/42.00 | tc_RealDef_Oreal, simplifying with (424), (426) gives:
% 280.06/42.00 | (556) all_1557_0 = all_1555_1
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (148) with all_1557_0, all_1563_1,
% 280.06/42.00 | tc_RealDef_Oreal, simplifying with (426), (428) gives:
% 280.06/42.00 | (557) all_1563_1 = all_1557_0
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (148) with all_1563_1, all_1565_1,
% 280.06/42.00 | tc_RealDef_Oreal, simplifying with (428), (430) gives:
% 280.06/42.00 | (558) all_1565_1 = all_1563_1
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (148) with all_1565_1, all_1589_3,
% 280.06/42.00 | tc_RealDef_Oreal, simplifying with (430), (432) gives:
% 280.06/42.00 | (559) all_1589_3 = all_1565_1
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (148) with all_1589_3, all_1601_1,
% 280.06/42.00 | tc_RealDef_Oreal, simplifying with (432), (435) gives:
% 280.06/42.00 | (560) all_1601_1 = all_1589_3
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (148) with all_1601_1, all_1607_0,
% 280.06/42.00 | tc_RealDef_Oreal, simplifying with (435), (437) gives:
% 280.06/42.00 | (561) all_1607_0 = all_1601_1
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (148) with all_1607_0, all_1610_0,
% 280.06/42.00 | tc_RealDef_Oreal, simplifying with (437), (439) gives:
% 280.06/42.00 | (562) all_1610_0 = all_1607_0
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (148) with all_1610_0, all_1613_1,
% 280.06/42.00 | tc_RealDef_Oreal, simplifying with (439), (441) gives:
% 280.06/42.00 | (563) all_1613_1 = all_1610_0
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (148) with all_1613_1, all_1616_1,
% 280.06/42.00 | tc_RealDef_Oreal, simplifying with (441), (443) gives:
% 280.06/42.00 | (564) all_1616_1 = all_1613_1
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (148) with all_1616_1, all_1619_1,
% 280.06/42.00 | tc_RealDef_Oreal, simplifying with (443), (445) gives:
% 280.06/42.00 | (565) all_1619_1 = all_1616_1
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (148) with all_1619_1, all_1652_1,
% 280.06/42.00 | tc_RealDef_Oreal, simplifying with (445), (449) gives:
% 280.06/42.00 | (566) all_1652_1 = all_1619_1
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (148) with all_1652_1, all_1655_1,
% 280.06/42.00 | tc_RealDef_Oreal, simplifying with (449), (451) gives:
% 280.06/42.00 | (567) all_1655_1 = all_1652_1
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (148) with all_1655_1, all_1691_0,
% 280.06/42.00 | tc_RealDef_Oreal, simplifying with (451), (453) gives:
% 280.06/42.00 | (568) all_1691_0 = all_1655_1
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (148) with all_1254_0, all_1697_0,
% 280.06/42.00 | tc_RealDef_Oreal, simplifying with (327), (455) gives:
% 280.06/42.00 | (569) all_1697_0 = all_1254_0
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (148) with all_1251_2, all_1697_0,
% 280.06/42.00 | tc_RealDef_Oreal, simplifying with (324), (455) gives:
% 280.06/42.00 | (570) all_1697_0 = all_1251_2
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (148) with all_1248_2, all_1697_0,
% 280.06/42.00 | tc_RealDef_Oreal, simplifying with (321), (455) gives:
% 280.06/42.00 | (571) all_1697_0 = all_1248_2
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (148) with all_1691_0, all_1700_0,
% 280.06/42.00 | tc_RealDef_Oreal, simplifying with (453), (457) gives:
% 280.06/42.00 | (572) all_1700_0 = all_1691_0
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (148) with all_631_0, all_1700_0, tc_RealDef_Oreal,
% 280.06/42.00 | simplifying with (154), (457) gives:
% 280.06/42.00 | (573) all_1700_0 = all_631_0
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (149) with all_740_0, all_749_0, tc_RealDef_Oreal,
% 280.06/42.00 | simplifying with (174), (178) gives:
% 280.06/42.00 | (574) all_749_0 = all_740_0
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (149) with all_740_0, all_753_0, tc_RealDef_Oreal,
% 280.06/42.00 | simplifying with (174), (183) gives:
% 280.06/42.00 | (575) all_753_0 = all_740_0
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (149) with all_724_1, all_753_0, tc_RealDef_Oreal,
% 280.06/42.00 | simplifying with (169), (183) gives:
% 280.06/42.00 | (576) all_753_0 = all_724_1
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (149) with all_755_1, all_757_0, tc_RealDef_Oreal,
% 280.06/42.00 | simplifying with (185), (187) gives:
% 280.06/42.00 | (577) all_757_0 = all_755_1
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (149) with all_755_1, all_820_0, tc_RealDef_Oreal,
% 280.06/42.00 | simplifying with (185), (195) gives:
% 280.06/42.00 | (578) all_820_0 = all_755_1
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (149) with all_749_0, all_820_0, tc_RealDef_Oreal,
% 280.06/42.00 | simplifying with (178), (195) gives:
% 280.06/42.00 | (579) all_820_0 = all_749_0
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (149) with all_757_0, all_826_0, tc_RealDef_Oreal,
% 280.06/42.00 | simplifying with (187), (197) gives:
% 280.06/42.00 | (580) all_826_0 = all_757_0
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (149) with all_826_0, all_838_0, tc_RealDef_Oreal,
% 280.06/42.00 | simplifying with (197), (199) gives:
% 280.06/42.00 | (581) all_838_0 = all_826_0
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (149) with all_820_0, all_861_1, tc_RealDef_Oreal,
% 280.06/42.00 | simplifying with (195), (208) gives:
% 280.06/42.00 | (582) all_861_1 = all_820_0
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (149) with all_838_0, all_906_1, tc_RealDef_Oreal,
% 280.06/42.00 | simplifying with (199), (226) gives:
% 280.06/42.00 | (583) all_906_1 = all_838_0
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (149) with all_906_1, all_961_0, tc_RealDef_Oreal,
% 280.06/42.00 | simplifying with (226), (241) gives:
% 280.06/42.00 | (584) all_961_0 = all_906_1
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (149) with all_961_0, all_967_0, tc_RealDef_Oreal,
% 280.06/42.00 | simplifying with (241), (247) gives:
% 280.06/42.00 | (585) all_967_0 = all_961_0
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (149) with all_967_0, all_970_0, tc_RealDef_Oreal,
% 280.06/42.00 | simplifying with (247), (250) gives:
% 280.06/42.00 | (586) all_970_0 = all_967_0
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (149) with all_954_1, all_973_0, tc_RealDef_Oreal,
% 280.06/42.00 | simplifying with (237), (253) gives:
% 280.06/42.00 | (587) all_973_0 = all_954_1
% 280.06/42.00 |
% 280.06/42.00 | GROUND_INST: instantiating (149) with all_970_0, all_999_0, tc_RealDef_Oreal,
% 280.06/42.00 | simplifying with (250), (260) gives:
% 280.06/42.01 | (588) all_999_0 = all_970_0
% 280.06/42.01 |
% 280.06/42.01 | GROUND_INST: instantiating (149) with all_999_0, all_1050_0, tc_RealDef_Oreal,
% 280.06/42.01 | simplifying with (260), (268) gives:
% 280.06/42.01 | (589) all_1050_0 = all_999_0
% 280.06/42.01 |
% 280.06/42.01 | GROUND_INST: instantiating (149) with all_1056_0, all_1150_0,
% 280.06/42.01 | tc_RealDef_Oreal, simplifying with (271), (298) gives:
% 280.06/42.01 | (590) all_1150_0 = all_1056_0
% 280.06/42.01 |
% 280.06/42.01 | GROUND_INST: instantiating (149) with all_978_0, all_1150_0, tc_RealDef_Oreal,
% 280.06/42.01 | simplifying with (255), (298) gives:
% 280.06/42.01 | (591) all_1150_0 = all_978_0
% 280.06/42.01 |
% 280.06/42.01 | GROUND_INST: instantiating (149) with all_954_1, all_1150_0, tc_RealDef_Oreal,
% 280.06/42.01 | simplifying with (237), (298) gives:
% 280.06/42.01 | (592) all_1150_0 = all_954_1
% 280.06/42.01 |
% 280.06/42.01 | GROUND_INST: instantiating (149) with all_933_1, all_1150_0, tc_RealDef_Oreal,
% 280.06/42.01 | simplifying with (233), (298) gives:
% 280.06/42.01 | (593) all_1150_0 = all_933_1
% 280.06/42.01 |
% 280.06/42.01 | GROUND_INST: instantiating (149) with all_861_1, all_1150_0, tc_RealDef_Oreal,
% 280.06/42.01 | simplifying with (208), (298) gives:
% 280.06/42.01 | (594) all_1150_0 = all_861_1
% 280.06/42.01 |
% 280.06/42.01 | GROUND_INST: instantiating (149) with all_1150_0, all_1239_0,
% 280.06/42.01 | tc_RealDef_Oreal, simplifying with (298), (319) gives:
% 280.06/42.01 | (595) all_1239_0 = all_1150_0
% 280.06/42.01 |
% 280.06/42.01 | GROUND_INST: instantiating (149) with all_1050_0, all_1251_1,
% 280.06/42.01 | tc_RealDef_Oreal, simplifying with (268), (325) gives:
% 280.06/42.01 | (596) all_1251_1 = all_1050_0
% 280.06/42.01 |
% 280.06/42.01 | GROUND_INST: instantiating (149) with all_1251_1, all_1257_0,
% 280.06/42.01 | tc_RealDef_Oreal, simplifying with (325), (330) gives:
% 280.06/42.01 | (597) all_1257_0 = all_1251_1
% 280.06/42.01 |
% 280.06/42.01 | GROUND_INST: instantiating (149) with all_633_0, all_1257_0, tc_RealDef_Oreal,
% 280.06/42.01 | simplifying with (156), (330) gives:
% 280.06/42.01 | (598) all_1257_0 = all_633_0
% 280.06/42.01 |
% 280.06/42.01 | GROUND_INST: instantiating (149) with all_1056_0, all_1263_0,
% 280.06/42.01 | tc_RealDef_Oreal, simplifying with (271), (336) gives:
% 280.06/42.01 | (599) all_1263_0 = all_1056_0
% 280.06/42.01 |
% 280.06/42.01 | GROUND_INST: instantiating (149) with all_964_0, all_1263_0, tc_RealDef_Oreal,
% 280.06/42.01 | simplifying with (244), (336) gives:
% 280.06/42.01 | (600) all_1263_0 = all_964_0
% 280.06/42.01 |
% 280.06/42.01 | GROUND_INST: instantiating (149) with all_1248_1, all_1356_1,
% 280.06/42.01 | tc_RealDef_Oreal, simplifying with (322), (382) gives:
% 280.06/42.01 | (601) all_1356_1 = all_1248_1
% 280.06/42.01 |
% 280.06/42.01 | GROUND_INST: instantiating (149) with all_973_0, all_1356_1, tc_RealDef_Oreal,
% 280.06/42.01 | simplifying with (253), (382) gives:
% 280.06/42.01 | (602) all_1356_1 = all_973_0
% 280.06/42.01 |
% 280.06/42.01 | GROUND_INST: instantiating (149) with all_751_1, all_1356_1, tc_RealDef_Oreal,
% 280.06/42.01 | simplifying with (180), (382) gives:
% 280.06/42.01 | (603) all_1356_1 = all_751_1
% 280.06/42.01 |
% 280.06/42.01 | GROUND_INST: instantiating (149) with all_1286_1, all_1412_0,
% 280.06/42.01 | tc_RealDef_Oreal, simplifying with (350), (392) gives:
% 280.06/42.01 | (604) all_1412_0 = all_1286_1
% 280.06/42.01 |
% 280.06/42.01 | GROUND_INST: instantiating (149) with all_1239_0, all_1412_0,
% 280.06/42.01 | tc_RealDef_Oreal, simplifying with (319), (392) gives:
% 280.06/42.01 | (605) all_1412_0 = all_1239_0
% 280.06/42.01 |
% 280.06/42.01 | GROUND_INST: instantiating (149) with all_1105_0, all_1412_0,
% 280.06/42.01 | tc_RealDef_Oreal, simplifying with (288), (392) gives:
% 280.06/42.01 | (606) all_1412_0 = all_1105_0
% 280.06/42.01 |
% 280.06/42.01 | GROUND_INST: instantiating (149) with all_1263_0, all_1432_0,
% 280.06/42.01 | tc_RealDef_Oreal, simplifying with (336), (400) gives:
% 280.06/42.01 | (607) all_1432_0 = all_1263_0
% 280.06/42.01 |
% 280.06/42.01 | GROUND_INST: instantiating (149) with all_1432_0, all_1589_1,
% 280.06/42.01 | tc_RealDef_Oreal, simplifying with (400), (433) gives:
% 280.06/42.01 | (608) all_1589_1 = all_1432_0
% 280.06/42.01 |
% 280.06/42.01 | GROUND_INST: instantiating (149) with all_1589_1, all_1637_0,
% 280.06/42.01 | tc_RealDef_Oreal, simplifying with (433), (447) gives:
% 280.06/42.01 | (609) all_1637_0 = all_1589_1
% 280.06/42.01 |
% 280.06/42.01 | GROUND_INST: instantiating (149) with all_1260_0, all_1637_0,
% 280.06/42.01 | tc_RealDef_Oreal, simplifying with (333), (447) gives:
% 280.06/42.01 | (610) all_1637_0 = all_1260_0
% 280.06/42.01 |
% 280.06/42.01 | COMBINE_EQS: (572), (573) imply:
% 280.06/42.01 | (611) all_1691_0 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | SIMP: (611) implies:
% 280.06/42.01 | (612) all_1691_0 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | COMBINE_EQS: (569), (570) imply:
% 280.06/42.01 | (613) all_1254_0 = all_1251_2
% 280.06/42.01 |
% 280.06/42.01 | SIMP: (613) implies:
% 280.06/42.01 | (614) all_1254_0 = all_1251_2
% 280.06/42.01 |
% 280.06/42.01 | COMBINE_EQS: (570), (571) imply:
% 280.06/42.01 | (615) all_1251_2 = all_1248_2
% 280.06/42.01 |
% 280.06/42.01 | COMBINE_EQS: (568), (612) imply:
% 280.06/42.01 | (616) all_1655_1 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | SIMP: (616) implies:
% 280.06/42.01 | (617) all_1655_1 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | COMBINE_EQS: (567), (617) imply:
% 280.06/42.01 | (618) all_1652_1 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | SIMP: (618) implies:
% 280.06/42.01 | (619) all_1652_1 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | COMBINE_EQS: (566), (619) imply:
% 280.06/42.01 | (620) all_1619_1 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | SIMP: (620) implies:
% 280.06/42.01 | (621) all_1619_1 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | COMBINE_EQS: (609), (610) imply:
% 280.06/42.01 | (622) all_1589_1 = all_1260_0
% 280.06/42.01 |
% 280.06/42.01 | SIMP: (622) implies:
% 280.06/42.01 | (623) all_1589_1 = all_1260_0
% 280.06/42.01 |
% 280.06/42.01 | COMBINE_EQS: (565), (621) imply:
% 280.06/42.01 | (624) all_1616_1 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | SIMP: (624) implies:
% 280.06/42.01 | (625) all_1616_1 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | COMBINE_EQS: (564), (625) imply:
% 280.06/42.01 | (626) all_1613_1 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | SIMP: (626) implies:
% 280.06/42.01 | (627) all_1613_1 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | COMBINE_EQS: (563), (627) imply:
% 280.06/42.01 | (628) all_1610_0 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | SIMP: (628) implies:
% 280.06/42.01 | (629) all_1610_0 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | COMBINE_EQS: (562), (629) imply:
% 280.06/42.01 | (630) all_1607_0 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | SIMP: (630) implies:
% 280.06/42.01 | (631) all_1607_0 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | COMBINE_EQS: (561), (631) imply:
% 280.06/42.01 | (632) all_1601_1 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | SIMP: (632) implies:
% 280.06/42.01 | (633) all_1601_1 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | COMBINE_EQS: (560), (633) imply:
% 280.06/42.01 | (634) all_1589_3 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | SIMP: (634) implies:
% 280.06/42.01 | (635) all_1589_3 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | COMBINE_EQS: (608), (623) imply:
% 280.06/42.01 | (636) all_1432_0 = all_1260_0
% 280.06/42.01 |
% 280.06/42.01 | SIMP: (636) implies:
% 280.06/42.01 | (637) all_1432_0 = all_1260_0
% 280.06/42.01 |
% 280.06/42.01 | COMBINE_EQS: (559), (635) imply:
% 280.06/42.01 | (638) all_1565_1 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | SIMP: (638) implies:
% 280.06/42.01 | (639) all_1565_1 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | COMBINE_EQS: (558), (639) imply:
% 280.06/42.01 | (640) all_1563_1 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | SIMP: (640) implies:
% 280.06/42.01 | (641) all_1563_1 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | COMBINE_EQS: (557), (641) imply:
% 280.06/42.01 | (642) all_1557_0 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | SIMP: (642) implies:
% 280.06/42.01 | (643) all_1557_0 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | COMBINE_EQS: (556), (643) imply:
% 280.06/42.01 | (644) all_1555_1 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | SIMP: (644) implies:
% 280.06/42.01 | (645) all_1555_1 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | COMBINE_EQS: (555), (645) imply:
% 280.06/42.01 | (646) all_1537_1 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | SIMP: (646) implies:
% 280.06/42.01 | (647) all_1537_1 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | COMBINE_EQS: (554), (647) imply:
% 280.06/42.01 | (648) all_1531_0 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | SIMP: (648) implies:
% 280.06/42.01 | (649) all_1531_0 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | COMBINE_EQS: (553), (649) imply:
% 280.06/42.01 | (650) all_1528_2 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | SIMP: (650) implies:
% 280.06/42.01 | (651) all_1528_2 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | COMBINE_EQS: (552), (651) imply:
% 280.06/42.01 | (652) all_1522_1 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | SIMP: (652) implies:
% 280.06/42.01 | (653) all_1522_1 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | COMBINE_EQS: (551), (653) imply:
% 280.06/42.01 | (654) all_1492_1 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | SIMP: (654) implies:
% 280.06/42.01 | (655) all_1492_1 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | COMBINE_EQS: (550), (655) imply:
% 280.06/42.01 | (656) all_1489_1 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | SIMP: (656) implies:
% 280.06/42.01 | (657) all_1489_1 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | COMBINE_EQS: (549), (657) imply:
% 280.06/42.01 | (658) all_1486_1 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | SIMP: (658) implies:
% 280.06/42.01 | (659) all_1486_1 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | COMBINE_EQS: (548), (659) imply:
% 280.06/42.01 | (660) all_1480_2 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | SIMP: (660) implies:
% 280.06/42.01 | (661) all_1480_2 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | COMBINE_EQS: (547), (661) imply:
% 280.06/42.01 | (662) all_1450_0 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | SIMP: (662) implies:
% 280.06/42.01 | (663) all_1450_0 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | COMBINE_EQS: (546), (663) imply:
% 280.06/42.01 | (664) all_1443_1 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | SIMP: (664) implies:
% 280.06/42.01 | (665) all_1443_1 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | COMBINE_EQS: (545), (665) imply:
% 280.06/42.01 | (666) all_1441_1 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | SIMP: (666) implies:
% 280.06/42.01 | (667) all_1441_1 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | COMBINE_EQS: (544), (667) imply:
% 280.06/42.01 | (668) all_1429_0 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | SIMP: (668) implies:
% 280.06/42.01 | (669) all_1429_0 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | COMBINE_EQS: (607), (637) imply:
% 280.06/42.01 | (670) all_1263_0 = all_1260_0
% 280.06/42.01 |
% 280.06/42.01 | SIMP: (670) implies:
% 280.06/42.01 | (671) all_1263_0 = all_1260_0
% 280.06/42.01 |
% 280.06/42.01 | COMBINE_EQS: (543), (669) imply:
% 280.06/42.01 | (672) all_1423_0 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | SIMP: (672) implies:
% 280.06/42.01 | (673) all_1423_0 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | COMBINE_EQS: (542), (673) imply:
% 280.06/42.01 | (674) all_1415_1 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | SIMP: (674) implies:
% 280.06/42.01 | (675) all_1415_1 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | COMBINE_EQS: (541), (675) imply:
% 280.06/42.01 | (676) all_1410_1 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | SIMP: (676) implies:
% 280.06/42.01 | (677) all_1410_1 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | COMBINE_EQS: (604), (605) imply:
% 280.06/42.01 | (678) all_1286_1 = all_1239_0
% 280.06/42.01 |
% 280.06/42.01 | COMBINE_EQS: (604), (606) imply:
% 280.06/42.01 | (679) all_1286_1 = all_1105_0
% 280.06/42.01 |
% 280.06/42.01 | COMBINE_EQS: (540), (677) imply:
% 280.06/42.01 | (680) all_1386_1 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | SIMP: (680) implies:
% 280.06/42.01 | (681) all_1386_1 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | COMBINE_EQS: (539), (681) imply:
% 280.06/42.01 | (682) all_1377_0 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | SIMP: (682) implies:
% 280.06/42.01 | (683) all_1377_0 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | COMBINE_EQS: (538), (683) imply:
% 280.06/42.01 | (684) all_1365_1 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | SIMP: (684) implies:
% 280.06/42.01 | (685) all_1365_1 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | COMBINE_EQS: (537), (685) imply:
% 280.06/42.01 | (686) all_1356_0 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | SIMP: (686) implies:
% 280.06/42.01 | (687) all_1356_0 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | COMBINE_EQS: (536), (687) imply:
% 280.06/42.01 | (688) all_1353_0 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | SIMP: (688) implies:
% 280.06/42.01 | (689) all_1353_0 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | COMBINE_EQS: (601), (602) imply:
% 280.06/42.01 | (690) all_1248_1 = all_973_0
% 280.06/42.01 |
% 280.06/42.01 | COMBINE_EQS: (601), (603) imply:
% 280.06/42.01 | (691) all_1248_1 = all_751_1
% 280.06/42.01 |
% 280.06/42.01 | COMBINE_EQS: (535), (689) imply:
% 280.06/42.01 | (692) all_1344_0 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | SIMP: (692) implies:
% 280.06/42.01 | (693) all_1344_0 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | COMBINE_EQS: (534), (693) imply:
% 280.06/42.01 | (694) all_1341_0 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | SIMP: (694) implies:
% 280.06/42.01 | (695) all_1341_0 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | COMBINE_EQS: (533), (695) imply:
% 280.06/42.01 | (696) all_1338_0 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | SIMP: (696) implies:
% 280.06/42.01 | (697) all_1338_0 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | COMBINE_EQS: (532), (697) imply:
% 280.06/42.01 | (698) all_1335_0 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | SIMP: (698) implies:
% 280.06/42.01 | (699) all_1335_0 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | COMBINE_EQS: (531), (699) imply:
% 280.06/42.01 | (700) all_1325_1 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | SIMP: (700) implies:
% 280.06/42.01 | (701) all_1325_1 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | COMBINE_EQS: (530), (701) imply:
% 280.06/42.01 | (702) all_1322_0 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | SIMP: (702) implies:
% 280.06/42.01 | (703) all_1322_0 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | COMBINE_EQS: (529), (703) imply:
% 280.06/42.01 | (704) all_1319_2 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | SIMP: (704) implies:
% 280.06/42.01 | (705) all_1319_2 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | COMBINE_EQS: (528), (705) imply:
% 280.06/42.01 | (706) all_1316_2 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | SIMP: (706) implies:
% 280.06/42.01 | (707) all_1316_2 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | COMBINE_EQS: (527), (707) imply:
% 280.06/42.01 | (708) all_1283_2 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | SIMP: (708) implies:
% 280.06/42.01 | (709) all_1283_2 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | COMBINE_EQS: (525), (526) imply:
% 280.06/42.01 | (710) all_1209_0 = all_964_1
% 280.06/42.01 |
% 280.06/42.01 | SIMP: (710) implies:
% 280.06/42.01 | (711) all_1209_0 = all_964_1
% 280.06/42.01 |
% 280.06/42.01 | COMBINE_EQS: (678), (679) imply:
% 280.06/42.01 | (712) all_1239_0 = all_1105_0
% 280.06/42.01 |
% 280.06/42.01 | SIMP: (712) implies:
% 280.06/42.01 | (713) all_1239_0 = all_1105_0
% 280.06/42.01 |
% 280.06/42.01 | COMBINE_EQS: (524), (709) imply:
% 280.06/42.01 | (714) all_1277_0 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | SIMP: (714) implies:
% 280.06/42.01 | (715) all_1277_0 = all_631_0
% 280.06/42.01 |
% 280.06/42.01 | COMBINE_EQS: (520), (523) imply:
% 280.06/42.01 | (716) all_1056_1 = all_999_1
% 280.06/42.01 |
% 280.06/42.02 | COMBINE_EQS: (520), (521) imply:
% 280.06/42.02 | (717) all_1056_1 = all_1044_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (520), (522) imply:
% 280.06/42.02 | (718) all_1056_1 = all_1005_1
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (519), (715) imply:
% 280.06/42.02 | (719) all_1268_0 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (719) implies:
% 280.06/42.02 | (720) all_1268_0 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (517), (518) imply:
% 280.06/42.02 | (721) all_1114_1 = all_906_0
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (721) implies:
% 280.06/42.02 | (722) all_1114_1 = all_906_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (516), (720) imply:
% 280.06/42.02 | (723) all_1266_0 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (723) implies:
% 280.06/42.02 | (724) all_1266_0 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (515), (724) imply:
% 280.06/42.02 | (725) all_1263_1 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (725) implies:
% 280.06/42.02 | (726) all_1263_1 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (599), (671) imply:
% 280.06/42.02 | (727) all_1260_0 = all_1056_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (600), (671) imply:
% 280.06/42.02 | (728) all_1260_0 = all_964_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (514), (726) imply:
% 280.06/42.02 | (729) all_1260_1 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (729) implies:
% 280.06/42.02 | (730) all_1260_1 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (727), (728) imply:
% 280.06/42.02 | (731) all_1056_0 = all_964_0
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (731) implies:
% 280.06/42.02 | (732) all_1056_0 = all_964_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (513), (730) imply:
% 280.06/42.02 | (733) all_1257_1 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (733) implies:
% 280.06/42.02 | (734) all_1257_1 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (597), (598) imply:
% 280.06/42.02 | (735) all_1251_1 = all_633_0
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (735) implies:
% 280.06/42.02 | (736) all_1251_1 = all_633_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (512), (734) imply:
% 280.06/42.02 | (737) all_1254_0 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (737) implies:
% 280.06/42.02 | (738) all_1254_0 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (614), (738) imply:
% 280.06/42.02 | (739) all_1251_2 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (739) implies:
% 280.06/42.02 | (740) all_1251_2 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (596), (736) imply:
% 280.06/42.02 | (741) all_1050_0 = all_633_0
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (741) implies:
% 280.06/42.02 | (742) all_1050_0 = all_633_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (615), (740) imply:
% 280.06/42.02 | (743) all_1248_2 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (743) implies:
% 280.06/42.02 | (744) all_1248_2 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (690), (691) imply:
% 280.06/42.02 | (745) all_973_0 = all_751_1
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (745) implies:
% 280.06/42.02 | (746) all_973_0 = all_751_1
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (511), (744) imply:
% 280.06/42.02 | (747) all_1239_1 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (747) implies:
% 280.06/42.02 | (748) all_1239_1 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (595), (713) imply:
% 280.06/42.02 | (749) all_1150_0 = all_1105_0
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (749) implies:
% 280.06/42.02 | (750) all_1150_0 = all_1105_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (510), (748) imply:
% 280.06/42.02 | (751) all_1218_1 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (751) implies:
% 280.06/42.02 | (752) all_1218_1 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (509), (752) imply:
% 280.06/42.02 | (753) all_1206_1 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (753) implies:
% 280.06/42.02 | (754) all_1206_1 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (507), (711) imply:
% 280.06/42.02 | (755) all_967_1 = all_964_1
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (755) implies:
% 280.06/42.02 | (756) all_967_1 = all_964_1
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (508), (711) imply:
% 280.06/42.02 | (757) all_964_1 = all_958_1
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (506), (754) imply:
% 280.06/42.02 | (758) all_1200_0 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (758) implies:
% 280.06/42.02 | (759) all_1200_0 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (505), (759) imply:
% 280.06/42.02 | (760) all_1185_0 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (760) implies:
% 280.06/42.02 | (761) all_1185_0 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (504), (761) imply:
% 280.06/42.02 | (762) all_1182_0 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (762) implies:
% 280.06/42.02 | (763) all_1182_0 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (503), (763) imply:
% 280.06/42.02 | (764) all_1166_0 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (764) implies:
% 280.06/42.02 | (765) all_1166_0 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (502), (765) imply:
% 280.06/42.02 | (766) all_1158_1 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (766) implies:
% 280.06/42.02 | (767) all_1158_1 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (501), (767) imply:
% 280.06/42.02 | (768) all_1155_0 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (768) implies:
% 280.06/42.02 | (769) all_1155_0 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (500), (769) imply:
% 280.06/42.02 | (770) all_1135_0 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (770) implies:
% 280.06/42.02 | (771) all_1135_0 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (590), (750) imply:
% 280.06/42.02 | (772) all_1105_0 = all_1056_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (591), (750) imply:
% 280.06/42.02 | (773) all_1105_0 = all_978_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (594), (750) imply:
% 280.06/42.02 | (774) all_1105_0 = all_861_1
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (593), (750) imply:
% 280.06/42.02 | (775) all_1105_0 = all_933_1
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (592), (750) imply:
% 280.06/42.02 | (776) all_1105_0 = all_954_1
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (499), (771) imply:
% 280.06/42.02 | (777) all_1120_0 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (777) implies:
% 280.06/42.02 | (778) all_1120_0 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (498), (778) imply:
% 280.06/42.02 | (779) all_1117_1 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (779) implies:
% 280.06/42.02 | (780) all_1117_1 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (497), (780) imply:
% 280.06/42.02 | (781) all_1091_0 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (781) implies:
% 280.06/42.02 | (782) all_1091_0 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (496), (722) imply:
% 280.06/42.02 | (783) all_948_0 = all_906_0
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (783) implies:
% 280.06/42.02 | (784) all_948_0 = all_906_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (772), (773) imply:
% 280.06/42.02 | (785) all_1056_0 = all_978_0
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (785) implies:
% 280.06/42.02 | (786) all_1056_0 = all_978_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (773), (776) imply:
% 280.06/42.02 | (787) all_978_0 = all_954_1
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (773), (775) imply:
% 280.06/42.02 | (788) all_978_0 = all_933_1
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (773), (774) imply:
% 280.06/42.02 | (789) all_978_0 = all_861_1
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (495), (782) imply:
% 280.06/42.02 | (790) all_1073_0 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (790) implies:
% 280.06/42.02 | (791) all_1073_0 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (494), (791) imply:
% 280.06/42.02 | (792) all_1062_1 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (792) implies:
% 280.06/42.02 | (793) all_1062_1 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (493), (793) imply:
% 280.06/42.02 | (794) all_1059_0 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (794) implies:
% 280.06/42.02 | (795) all_1059_0 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (492), (795) imply:
% 280.06/42.02 | (796) all_1047_0 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (796) implies:
% 280.06/42.02 | (797) all_1047_0 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (732), (786) imply:
% 280.06/42.02 | (798) all_978_0 = all_964_0
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (798) implies:
% 280.06/42.02 | (799) all_978_0 = all_964_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (716), (718) imply:
% 280.06/42.02 | (800) all_1005_1 = all_999_1
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (717), (718) imply:
% 280.06/42.02 | (801) all_1044_0 = all_1005_1
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (801) implies:
% 280.06/42.02 | (802) all_1044_0 = all_1005_1
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (589), (742) imply:
% 280.06/42.02 | (803) all_999_0 = all_633_0
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (803) implies:
% 280.06/42.02 | (804) all_999_0 = all_633_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (491), (797) imply:
% 280.06/42.02 | (805) all_1044_0 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (805) implies:
% 280.06/42.02 | (806) all_1044_0 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (802), (806) imply:
% 280.06/42.02 | (807) all_1005_1 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (807) implies:
% 280.06/42.02 | (808) all_1005_1 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (800), (808) imply:
% 280.06/42.02 | (809) all_999_1 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (809) implies:
% 280.06/42.02 | (810) all_999_1 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (588), (804) imply:
% 280.06/42.02 | (811) all_970_0 = all_633_0
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (811) implies:
% 280.06/42.02 | (812) all_970_0 = all_633_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (490), (810) imply:
% 280.06/42.02 | (813) all_973_1 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (813) implies:
% 280.06/42.02 | (814) all_973_1 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (488), (489) imply:
% 280.06/42.02 | (815) all_894_0 = all_861_0
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (815) implies:
% 280.06/42.02 | (816) all_894_0 = all_861_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (787), (799) imply:
% 280.06/42.02 | (817) all_964_0 = all_954_1
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (788), (799) imply:
% 280.06/42.02 | (818) all_964_0 = all_933_1
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (789), (799) imply:
% 280.06/42.02 | (819) all_964_0 = all_861_1
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (587), (746) imply:
% 280.06/42.02 | (820) all_954_1 = all_751_1
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (820) implies:
% 280.06/42.02 | (821) all_954_1 = all_751_1
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (487), (814) imply:
% 280.06/42.02 | (822) all_970_1 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (822) implies:
% 280.06/42.02 | (823) all_970_1 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (586), (812) imply:
% 280.06/42.02 | (824) all_967_0 = all_633_0
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (824) implies:
% 280.06/42.02 | (825) all_967_0 = all_633_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (486), (823) imply:
% 280.06/42.02 | (826) all_967_1 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (826) implies:
% 280.06/42.02 | (827) all_967_1 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (585), (825) imply:
% 280.06/42.02 | (828) all_961_0 = all_633_0
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (828) implies:
% 280.06/42.02 | (829) all_961_0 = all_633_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (756), (827) imply:
% 280.06/42.02 | (830) all_964_1 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (830) implies:
% 280.06/42.02 | (831) all_964_1 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (817), (818) imply:
% 280.06/42.02 | (832) all_954_1 = all_933_1
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (832) implies:
% 280.06/42.02 | (833) all_954_1 = all_933_1
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (818), (819) imply:
% 280.06/42.02 | (834) all_933_1 = all_861_1
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (757), (831) imply:
% 280.06/42.02 | (835) all_958_1 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (835) implies:
% 280.06/42.02 | (836) all_958_1 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (584), (829) imply:
% 280.06/42.02 | (837) all_906_1 = all_633_0
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (837) implies:
% 280.06/42.02 | (838) all_906_1 = all_633_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (484), (485) imply:
% 280.06/42.02 | (839) all_933_0 = all_927_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (484), (836) imply:
% 280.06/42.02 | (840) all_933_0 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (821), (833) imply:
% 280.06/42.02 | (841) all_933_1 = all_751_1
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (841) implies:
% 280.06/42.02 | (842) all_933_1 = all_751_1
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (483), (784) imply:
% 280.06/42.02 | (843) all_906_0 = all_897_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (482), (784) imply:
% 280.06/42.02 | (844) all_912_1 = all_906_0
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (844) implies:
% 280.06/42.02 | (845) all_912_1 = all_906_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (839), (840) imply:
% 280.06/42.02 | (846) all_927_0 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (846) implies:
% 280.06/42.02 | (847) all_927_0 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (834), (842) imply:
% 280.06/42.02 | (848) all_861_1 = all_751_1
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (848) implies:
% 280.06/42.02 | (849) all_861_1 = all_751_1
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (481), (847) imply:
% 280.06/42.02 | (850) all_912_1 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (850) implies:
% 280.06/42.02 | (851) all_912_1 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (845), (851) imply:
% 280.06/42.02 | (852) all_906_0 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (852) implies:
% 280.06/42.02 | (853) all_906_0 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (843), (853) imply:
% 280.06/42.02 | (854) all_897_0 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (854) implies:
% 280.06/42.02 | (855) all_897_0 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (583), (838) imply:
% 280.06/42.02 | (856) all_838_0 = all_633_0
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (856) implies:
% 280.06/42.02 | (857) all_838_0 = all_633_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (480), (855) imply:
% 280.06/42.02 | (858) all_888_0 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (858) implies:
% 280.06/42.02 | (859) all_888_0 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (479), (816) imply:
% 280.06/42.02 | (860) all_882_1 = all_861_0
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (860) implies:
% 280.06/42.02 | (861) all_882_1 = all_861_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (478), (859) imply:
% 280.06/42.02 | (862) all_885_0 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (862) implies:
% 280.06/42.02 | (863) all_885_0 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (477), (863) imply:
% 280.06/42.02 | (864) all_874_0 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (864) implies:
% 280.06/42.02 | (865) all_874_0 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (476), (861) imply:
% 280.06/42.02 | (866) all_868_0 = all_861_0
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (866) implies:
% 280.06/42.02 | (867) all_868_0 = all_861_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (475), (865) imply:
% 280.06/42.02 | (868) all_868_0 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (868) implies:
% 280.06/42.02 | (869) all_868_0 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (474), (867) imply:
% 280.06/42.02 | (870) all_861_0 = all_853_1
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (867), (869) imply:
% 280.06/42.02 | (871) all_861_0 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (870), (871) imply:
% 280.06/42.02 | (872) all_853_1 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (872) implies:
% 280.06/42.02 | (873) all_853_1 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (582), (849) imply:
% 280.06/42.02 | (874) all_820_0 = all_751_1
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (874) implies:
% 280.06/42.02 | (875) all_820_0 = all_751_1
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (472), (473) imply:
% 280.06/42.02 | (876) all_724_0 = all_704_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (471), (472) imply:
% 280.06/42.02 | (877) all_735_1 = all_724_0
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (877) implies:
% 280.06/42.02 | (878) all_735_1 = all_724_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (470), (873) imply:
% 280.06/42.02 | (879) all_843_0 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (879) implies:
% 280.06/42.02 | (880) all_843_0 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (469), (880) imply:
% 280.06/42.02 | (881) all_779_0 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (881) implies:
% 280.06/42.02 | (882) all_779_0 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (581), (857) imply:
% 280.06/42.02 | (883) all_826_0 = all_633_0
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (883) implies:
% 280.06/42.02 | (884) all_826_0 = all_633_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (580), (884) imply:
% 280.06/42.02 | (885) all_757_0 = all_633_0
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (885) implies:
% 280.06/42.02 | (886) all_757_0 = all_633_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (579), (875) imply:
% 280.06/42.02 | (887) all_751_1 = all_749_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (578), (875) imply:
% 280.06/42.02 | (888) all_755_1 = all_751_1
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (888) implies:
% 280.06/42.02 | (889) all_755_1 = all_751_1
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (468), (882) imply:
% 280.06/42.02 | (890) all_767_0 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (890) implies:
% 280.06/42.02 | (891) all_767_0 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (467), (891) imply:
% 280.06/42.02 | (892) all_759_1 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (892) implies:
% 280.06/42.02 | (893) all_759_1 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | COMBINE_EQS: (466), (893) imply:
% 280.06/42.02 | (894) all_753_1 = all_631_0
% 280.06/42.02 |
% 280.06/42.02 | SIMP: (894) implies:
% 280.06/42.02 | (895) all_753_1 = all_631_0
% 280.06/42.02 |
% 280.06/42.03 | COMBINE_EQS: (577), (886) imply:
% 280.06/42.03 | (896) all_755_1 = all_633_0
% 280.06/42.03 |
% 280.06/42.03 | SIMP: (896) implies:
% 280.06/42.03 | (897) all_755_1 = all_633_0
% 280.06/42.03 |
% 280.06/42.03 | COMBINE_EQS: (889), (897) imply:
% 280.06/42.03 | (898) all_751_1 = all_633_0
% 280.06/42.03 |
% 280.06/42.03 | SIMP: (898) implies:
% 280.06/42.03 | (899) all_751_1 = all_633_0
% 280.06/42.03 |
% 280.06/42.03 | COMBINE_EQS: (575), (576) imply:
% 280.06/42.03 | (900) all_740_0 = all_724_1
% 280.06/42.03 |
% 280.06/42.03 | SIMP: (900) implies:
% 280.06/42.03 | (901) all_740_0 = all_724_1
% 280.06/42.03 |
% 280.06/42.03 | COMBINE_EQS: (465), (895) imply:
% 280.06/42.03 | (902) all_742_0 = all_631_0
% 280.06/42.03 |
% 280.06/42.03 | SIMP: (902) implies:
% 280.06/42.03 | (903) all_742_0 = all_631_0
% 280.06/42.03 |
% 280.06/42.03 | COMBINE_EQS: (887), (899) imply:
% 280.06/42.03 | (904) all_749_0 = all_633_0
% 280.06/42.03 |
% 280.06/42.03 | SIMP: (904) implies:
% 280.06/42.03 | (905) all_749_0 = all_633_0
% 280.06/42.03 |
% 280.06/42.03 | COMBINE_EQS: (574), (905) imply:
% 280.06/42.03 | (906) all_740_0 = all_633_0
% 280.06/42.03 |
% 280.06/42.03 | SIMP: (906) implies:
% 280.06/42.03 | (907) all_740_0 = all_633_0
% 280.06/42.03 |
% 280.06/42.03 | COMBINE_EQS: (464), (903) imply:
% 280.06/42.03 | (908) all_740_1 = all_631_0
% 280.06/42.03 |
% 280.06/42.03 | SIMP: (908) implies:
% 280.06/42.03 | (909) all_740_1 = all_631_0
% 280.06/42.03 |
% 280.06/42.03 | COMBINE_EQS: (901), (907) imply:
% 280.06/42.03 | (910) all_724_1 = all_633_0
% 280.06/42.03 |
% 280.06/42.03 | SIMP: (910) implies:
% 280.06/42.03 | (911) all_724_1 = all_633_0
% 280.06/42.03 |
% 280.06/42.03 | COMBINE_EQS: (463), (909) imply:
% 280.06/42.03 | (912) all_735_1 = all_631_0
% 280.06/42.03 |
% 280.06/42.03 | SIMP: (912) implies:
% 280.06/42.03 | (913) all_735_1 = all_631_0
% 280.06/42.03 |
% 280.06/42.03 | COMBINE_EQS: (878), (913) imply:
% 280.06/42.03 | (914) all_724_0 = all_631_0
% 280.06/42.03 |
% 280.50/42.03 | SIMP: (914) implies:
% 280.50/42.03 | (915) all_724_0 = all_631_0
% 280.50/42.03 |
% 280.50/42.03 | COMBINE_EQS: (876), (915) imply:
% 280.50/42.03 | (916) all_704_0 = all_631_0
% 280.50/42.03 |
% 280.50/42.03 | SIMP: (916) implies:
% 280.50/42.03 | (917) all_704_0 = all_631_0
% 280.50/42.03 |
% 280.50/42.03 | COMBINE_EQS: (462), (917) imply:
% 280.50/42.03 | (918) all_696_0 = all_631_0
% 280.50/42.03 |
% 280.50/42.03 | SIMP: (918) implies:
% 280.50/42.03 | (919) all_696_0 = all_631_0
% 280.50/42.03 |
% 280.50/42.03 | COMBINE_EQS: (461), (919) imply:
% 280.50/42.03 | (920) all_691_0 = all_631_0
% 280.50/42.03 |
% 280.50/42.03 | SIMP: (920) implies:
% 280.50/42.03 | (921) all_691_0 = all_631_0
% 280.50/42.03 |
% 280.50/42.03 | COMBINE_EQS: (460), (921) imply:
% 280.50/42.03 | (922) all_684_0 = all_631_0
% 280.50/42.03 |
% 280.50/42.03 | SIMP: (922) implies:
% 280.50/42.03 | (923) all_684_0 = all_631_0
% 280.50/42.03 |
% 280.50/42.03 | COMBINE_EQS: (459), (923) imply:
% 280.50/42.03 | (924) all_682_0 = all_631_0
% 280.50/42.03 |
% 280.50/42.03 | SIMP: (924) implies:
% 280.50/42.03 | (925) all_682_0 = all_631_0
% 280.50/42.03 |
% 280.50/42.03 | REDUCE: (360), (458) imply:
% 280.50/42.03 | (926) c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, all_1068_3,
% 280.50/42.03 | all_1308_5) = all_1308_4
% 280.50/42.03 |
% 280.50/42.03 | REDUCE: (356), (458) imply:
% 280.50/42.03 | (927) c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, all_1068_3) =
% 280.50/42.03 | all_1308_2
% 280.50/42.03 |
% 280.50/42.03 | REDUCE: (354), (458) imply:
% 280.50/42.03 | (928) $i(all_1068_3)
% 280.50/42.03 |
% 280.50/42.03 | GROUND_INST: instantiating (150) with all_1068_2, all_1308_2, all_1068_3,
% 280.50/42.03 | tc_Complex_Ocomplex, simplifying with (280), (927) gives:
% 280.50/42.03 | (929) all_1308_2 = all_1068_2
% 280.50/42.03 |
% 280.50/42.03 | GROUND_INST: instantiating (3) with v_z, tc_Complex_Ocomplex, all_1068_1,
% 280.50/42.03 | simplifying with (140), (144), (146), (279) gives:
% 280.50/42.03 | (930) c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, all_1068_1) = all_1068_1
% 280.50/42.03 | & $i(all_1068_1)
% 280.50/42.03 |
% 280.50/42.03 | ALPHA: (930) implies:
% 280.50/42.03 | (931) $i(all_1068_1)
% 280.50/42.03 |
% 280.50/42.03 | GROUND_INST: instantiating (213) with all_1068_3, tc_Complex_Ocomplex,
% 280.50/42.03 | all_1068_2, simplifying with (140), (144), (280), (928) gives:
% 280.50/42.03 | (932) c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_874_0,
% 280.50/42.03 | all_1068_2)
% 280.50/42.03 |
% 280.50/42.03 | GROUND_INST: instantiating (3) with all_1068_3, tc_Complex_Ocomplex,
% 280.50/42.03 | all_1068_2, simplifying with (140), (144), (280), (928) gives:
% 280.50/42.03 | (933) c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, all_1068_2) = all_1068_2
% 280.50/42.03 | & $i(all_1068_2)
% 280.50/42.03 |
% 280.50/42.03 | ALPHA: (933) implies:
% 280.50/42.03 | (934) $i(all_1068_2)
% 280.50/42.03 |
% 280.50/42.03 | GROUND_INST: instantiating (213) with all_1308_5, tc_Complex_Ocomplex,
% 280.50/42.03 | all_1308_0, simplifying with (140), (144), (355), (357) gives:
% 280.50/42.03 | (935) c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_874_0,
% 280.50/42.03 | all_1308_0)
% 280.50/42.03 |
% 280.50/42.03 | GROUND_INST: instantiating (fact_add__pos__pos) with all_1068_1, all_1068_2,
% 280.50/42.03 | tc_RealDef_Oreal, all_1068_0, simplifying with (138), (143),
% 280.50/42.03 | (281), (931), (934) gives:
% 280.50/42.03 | (936) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 280.50/42.03 | $i(v0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0,
% 280.50/42.03 | all_1068_1) | ~
% 280.50/42.03 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, all_1068_2) |
% 280.50/42.03 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, all_1068_0)))
% 280.50/42.03 |
% 280.50/42.03 | GROUND_INST: instantiating (fact_add__pos__nonneg) with all_1068_1,
% 280.50/42.03 | all_1068_2, tc_RealDef_Oreal, all_1068_0, simplifying with (138),
% 280.50/42.03 | (143), (281), (931), (934) gives:
% 280.50/42.03 | (937) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 280.50/42.03 | $i(v0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0,
% 280.50/42.03 | all_1068_2) | ~
% 280.50/42.03 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0,
% 280.50/42.03 | all_1068_1) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 280.50/42.03 | v0, all_1068_0)))
% 280.50/42.03 |
% 280.50/42.03 | GROUND_INST: instantiating (fact_add__nonneg__pos) with all_1068_1,
% 280.50/42.03 | all_1068_2, tc_RealDef_Oreal, all_1068_0, simplifying with (138),
% 280.50/42.03 | (143), (281), (931), (934) gives:
% 280.50/42.03 | (938) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 280.50/42.03 | $i(v0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0,
% 280.50/42.03 | all_1068_1) | ~
% 280.50/42.03 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0,
% 280.50/42.03 | all_1068_2) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 280.50/42.03 | v0, all_1068_0)))
% 280.50/42.03 |
% 280.50/42.03 | GROUND_INST: instantiating (fact_add__neg__neg) with all_1068_1, all_1068_2,
% 280.50/42.03 | tc_RealDef_Oreal, all_1068_0, simplifying with (138), (143),
% 280.50/42.03 | (281), (931), (934) gives:
% 280.50/42.03 | (939) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 280.50/42.03 | $i(v0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 280.50/42.03 | all_1068_1, v0) | ~
% 280.50/42.03 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1068_2, v0) |
% 280.50/42.03 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1068_0, v0)))
% 280.50/42.03 |
% 280.50/42.03 | GROUND_INST: instantiating (fact_add__neg__nonpos) with all_1068_1,
% 280.50/42.03 | all_1068_2, tc_RealDef_Oreal, all_1068_0, simplifying with (138),
% 280.50/42.03 | (143), (281), (931), (934) gives:
% 280.50/42.03 | (940) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 280.50/42.03 | $i(v0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 280.50/42.03 | all_1068_2, v0) | ~
% 280.50/42.03 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1068_1,
% 280.50/42.03 | v0) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 280.50/42.03 | all_1068_0, v0)))
% 280.50/42.03 |
% 280.50/42.03 | GROUND_INST: instantiating (fact_add__nonpos__neg) with all_1068_1,
% 280.50/42.03 | all_1068_2, tc_RealDef_Oreal, all_1068_0, simplifying with (138),
% 280.50/42.03 | (143), (281), (931), (934) gives:
% 280.50/42.03 | (941) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 280.50/42.03 | $i(v0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 280.50/42.03 | all_1068_1, v0) | ~
% 280.50/42.03 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1068_2,
% 280.50/42.03 | v0) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 280.50/42.03 | all_1068_0, v0)))
% 280.50/42.03 |
% 280.50/42.03 | GROUND_INST: instantiating (fact_add__nonneg__nonneg) with all_1068_1,
% 280.50/42.03 | all_1068_2, tc_RealDef_Oreal, all_1068_0, simplifying with (138),
% 280.50/42.03 | (143), (281), (931), (934) gives:
% 280.50/42.03 | (942) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 280.50/42.03 | $i(v0) & ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 280.50/42.03 | v0, all_1068_1) | ~
% 280.50/42.03 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0,
% 280.50/42.03 | all_1068_2) |
% 280.50/42.03 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0,
% 280.50/42.03 | all_1068_0)))
% 280.50/42.03 |
% 280.50/42.03 | GROUND_INST: instantiating (fact_add__nonneg__eq__0__iff) with all_1068_1,
% 280.50/42.03 | all_1068_2, tc_RealDef_Oreal, all_1068_0, simplifying with (138),
% 280.50/42.03 | (143), (281), (931), (934) gives:
% 280.50/42.03 | (943) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 280.50/42.03 | $i(v0) & ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 280.50/42.03 | v0, all_1068_1) | ~
% 280.50/42.03 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0,
% 280.50/42.03 | all_1068_2) | (( ~ (v0 = all_1068_0) | (all_1068_0 = all_1068_2
% 280.50/42.03 | & all_1068_1 = all_1068_2)) & ( ~ (v0 = all_1068_2) | ~
% 280.50/42.03 | (all_1068_1 = all_1068_2) | all_1068_0 = all_1068_2))))
% 280.50/42.03 |
% 280.50/42.03 | GROUND_INST: instantiating (fact_add__nonpos__nonpos) with all_1068_1,
% 280.50/42.03 | all_1068_2, tc_RealDef_Oreal, all_1068_0, simplifying with (138),
% 280.50/42.03 | (143), (281), (931), (934) gives:
% 280.50/42.03 | (944) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 280.50/42.03 | $i(v0) & ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 280.50/42.03 | all_1068_1, v0) | ~
% 280.50/42.03 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1068_2,
% 280.50/42.03 | v0) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 280.50/42.03 | all_1068_0, v0)))
% 280.50/42.03 |
% 280.50/42.03 | GROUND_INST: instantiating (2) with v_z, all_1068_3, tc_Complex_Ocomplex,
% 280.50/42.03 | all_1068_2, all_1068_1, all_1068_0, simplifying with (140),
% 280.50/42.03 | (144), (146), (279), (280), (281), (928) gives:
% 280.50/42.03 | (945) ? [v0: $i] : ? [v1: $i] :
% 280.50/42.03 | (c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, all_1068_3, v_z)
% 280.50/42.03 | = v0 & c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v0) =
% 280.50/42.03 | v1 & $i(v1) & $i(v0) &
% 280.50/42.03 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1,
% 280.50/42.03 | all_1068_0))
% 280.50/42.03 |
% 280.50/42.03 | GROUND_INST: instantiating
% 280.50/42.03 | (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J)
% 280.50/42.03 | with v_w, v_z, tc_Complex_Ocomplex, all_1068_3, simplifying with
% 280.50/42.03 | (141), (144), (145), (146), (282) gives:
% 280.50/42.03 | (946) c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v_z, v_w) =
% 280.50/42.03 | all_1068_3 & $i(all_1068_3)
% 280.50/42.03 |
% 280.50/42.03 | ALPHA: (946) implies:
% 280.50/42.03 | (947) c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v_z, v_w) =
% 280.50/42.03 | all_1068_3
% 280.50/42.03 |
% 280.50/42.03 | GROUND_INST: instantiating
% 280.50/42.03 | (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J)
% 280.50/42.03 | with all_1068_3, all_1308_5, tc_Complex_Ocomplex, all_1308_4,
% 280.50/42.03 | simplifying with (141), (144), (355), (926), (928) gives:
% 280.50/42.03 | (948) c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, all_1308_5,
% 280.50/42.03 | all_1068_3) = all_1308_4 & $i(all_1308_4)
% 280.50/42.03 |
% 280.50/42.03 | ALPHA: (948) implies:
% 280.50/42.03 | (949) c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, all_1308_5,
% 280.50/42.03 | all_1068_3) = all_1308_4
% 280.50/42.03 |
% 280.50/42.03 | GROUND_INST: instantiating (fact_norm__minus__cancel) with v_z,
% 280.50/42.03 | tc_Complex_Ocomplex, all_1308_5, all_1308_0, simplifying with
% 280.50/42.03 | (140), (144), (146), (357), (361) gives:
% 280.50/42.03 | (950) c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_z) =
% 280.50/42.03 | all_1308_0 & $i(all_1308_0)
% 280.50/42.03 |
% 280.50/42.03 | ALPHA: (950) implies:
% 280.50/42.03 | (951) c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_z) =
% 280.50/42.03 | all_1308_0
% 280.50/42.03 |
% 280.50/42.03 | GROUND_INST: instantiating (4) with v_z, all_1068_3, all_1308_5, all_1308_4,
% 280.50/42.03 | simplifying with (146), (361), (926), (928) gives:
% 280.50/42.03 | (952) c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, all_1068_3, v_z) =
% 280.50/42.03 | all_1308_4 & $i(all_1308_4)
% 280.50/42.03 |
% 280.50/42.03 | ALPHA: (952) implies:
% 280.50/42.03 | (953) c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, all_1068_3, v_z) =
% 280.50/42.03 | all_1308_4
% 280.50/42.03 |
% 280.50/42.03 | GROUND_INST: instantiating (fact_zero__less__one) with tc_RealDef_Oreal,
% 280.50/42.03 | all_633_0, simplifying with (139), (143), (156) gives:
% 280.50/42.03 | (954) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 280.50/42.03 | $i(v0) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0,
% 280.50/42.03 | all_633_0))
% 280.50/42.03 |
% 280.50/42.03 | GROUND_INST: instantiating (fact_zero__le__one) with tc_RealDef_Oreal,
% 280.50/42.03 | all_633_0, simplifying with (139), (143), (156) gives:
% 280.50/42.03 | (955) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 280.50/42.03 | $i(v0) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0,
% 280.50/42.03 | all_633_0))
% 280.50/42.03 |
% 280.50/42.03 | GROUND_INST: instantiating (fact_not__one__less__zero) with tc_RealDef_Oreal,
% 280.50/42.03 | all_633_0, simplifying with (139), (143), (156) gives:
% 280.50/42.03 | (956) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 280.50/42.03 | $i(v0) & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 280.50/42.03 | all_633_0, v0))
% 280.50/42.03 |
% 280.50/42.03 | GROUND_INST: instantiating (fact_not__one__le__zero) with tc_RealDef_Oreal,
% 280.50/42.03 | all_633_0, simplifying with (139), (143), (156) gives:
% 280.50/42.03 | (957) ? [v0: $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 280.50/42.03 | $i(v0) & ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 280.50/42.03 | all_633_0, v0))
% 280.50/42.03 |
% 280.50/42.03 | DELTA: instantiating (957) with fresh symbol all_1778_0 gives:
% 280.50/42.03 | (958) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1778_0 &
% 280.50/42.03 | $i(all_1778_0) & ~
% 280.50/42.03 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_633_0,
% 280.50/42.03 | all_1778_0)
% 280.50/42.03 |
% 280.50/42.03 | ALPHA: (958) implies:
% 280.50/42.03 | (959) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1778_0
% 280.50/42.03 |
% 280.50/42.03 | DELTA: instantiating (956) with fresh symbol all_1780_0 gives:
% 280.50/42.03 | (960) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1780_0 &
% 280.50/42.03 | $i(all_1780_0) & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 280.50/42.03 | all_633_0, all_1780_0)
% 280.50/42.03 |
% 280.50/42.03 | ALPHA: (960) implies:
% 280.50/42.03 | (961) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1780_0
% 280.50/42.03 |
% 280.50/42.03 | DELTA: instantiating (955) with fresh symbol all_1782_0 gives:
% 280.50/42.03 | (962) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1782_0 &
% 280.50/42.03 | $i(all_1782_0) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 280.50/42.03 | all_1782_0, all_633_0)
% 280.50/42.03 |
% 280.50/42.03 | ALPHA: (962) implies:
% 280.50/42.03 | (963) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1782_0
% 280.50/42.03 |
% 280.50/42.03 | DELTA: instantiating (954) with fresh symbol all_1784_0 gives:
% 280.50/42.03 | (964) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1784_0 &
% 280.50/42.03 | $i(all_1784_0) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 280.50/42.03 | all_1784_0, all_633_0)
% 280.50/42.03 |
% 280.50/42.03 | ALPHA: (964) implies:
% 280.50/42.03 | (965) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1784_0
% 280.50/42.03 |
% 280.50/42.03 | DELTA: instantiating (942) with fresh symbol all_1828_0 gives:
% 280.50/42.03 | (966) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1828_0 &
% 280.50/42.03 | $i(all_1828_0) & ( ~
% 280.50/42.03 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1828_0,
% 280.50/42.03 | all_1068_1) | ~
% 280.50/42.03 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1828_0,
% 280.50/42.03 | all_1068_2) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 280.50/42.03 | all_1828_0, all_1068_0))
% 280.50/42.03 |
% 280.50/42.03 | ALPHA: (966) implies:
% 280.50/42.03 | (967) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1828_0
% 280.50/42.03 | (968) ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1828_0,
% 280.50/42.03 | all_1068_1) | ~
% 280.50/42.03 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1828_0,
% 280.50/42.03 | all_1068_2) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 280.50/42.03 | all_1828_0, all_1068_0)
% 280.50/42.03 |
% 280.50/42.03 | DELTA: instantiating (939) with fresh symbol all_1830_0 gives:
% 280.50/42.03 | (969) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1830_0 &
% 280.50/42.03 | $i(all_1830_0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 280.50/42.03 | all_1068_1, all_1830_0) | ~
% 280.50/42.03 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1068_2,
% 280.50/42.03 | all_1830_0) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 280.50/42.03 | all_1068_0, all_1830_0))
% 280.50/42.03 |
% 280.50/42.03 | ALPHA: (969) implies:
% 280.50/42.03 | (970) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1830_0
% 280.50/42.03 |
% 280.50/42.03 | DELTA: instantiating (937) with fresh symbol all_1832_0 gives:
% 280.50/42.03 | (971) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1832_0 &
% 280.50/42.03 | $i(all_1832_0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 280.50/42.03 | all_1832_0, all_1068_2) | ~
% 280.50/42.03 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1832_0,
% 280.50/42.03 | all_1068_1) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 280.50/42.03 | all_1832_0, all_1068_0))
% 280.50/42.03 |
% 280.50/42.03 | ALPHA: (971) implies:
% 280.50/42.03 | (972) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1832_0
% 280.50/42.03 |
% 280.50/42.03 | DELTA: instantiating (936) with fresh symbol all_1834_0 gives:
% 280.50/42.03 | (973) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1834_0 &
% 280.50/42.03 | $i(all_1834_0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 280.50/42.03 | all_1834_0, all_1068_1) | ~
% 280.50/42.03 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1834_0,
% 280.50/42.03 | all_1068_2) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 280.50/42.03 | all_1834_0, all_1068_0))
% 280.50/42.03 |
% 280.50/42.03 | ALPHA: (973) implies:
% 280.50/42.03 | (974) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1834_0
% 280.50/42.03 |
% 280.50/42.03 | DELTA: instantiating (938) with fresh symbol all_1840_0 gives:
% 280.50/42.03 | (975) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1840_0 &
% 280.50/42.03 | $i(all_1840_0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 280.50/42.03 | all_1840_0, all_1068_1) | ~
% 280.50/42.03 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1840_0,
% 280.50/42.03 | all_1068_2) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 280.50/42.03 | all_1840_0, all_1068_0))
% 280.50/42.03 |
% 280.50/42.03 | ALPHA: (975) implies:
% 280.50/42.03 | (976) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1840_0
% 280.50/42.03 |
% 280.50/42.03 | DELTA: instantiating (941) with fresh symbol all_1842_0 gives:
% 280.50/42.03 | (977) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1842_0 &
% 280.50/42.03 | $i(all_1842_0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 280.50/42.03 | all_1068_1, all_1842_0) | ~
% 280.50/42.03 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1068_2,
% 280.50/42.03 | all_1842_0) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 280.50/42.03 | all_1068_0, all_1842_0))
% 280.50/42.03 |
% 280.50/42.03 | ALPHA: (977) implies:
% 280.50/42.03 | (978) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1842_0
% 280.50/42.03 |
% 280.50/42.03 | DELTA: instantiating (940) with fresh symbol all_1844_0 gives:
% 280.50/42.04 | (979) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1844_0 &
% 280.50/42.04 | $i(all_1844_0) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 280.50/42.04 | all_1068_2, all_1844_0) | ~
% 280.50/42.04 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1068_1,
% 280.50/42.04 | all_1844_0) | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 280.50/42.04 | all_1068_0, all_1844_0))
% 280.50/42.04 |
% 280.50/42.04 | ALPHA: (979) implies:
% 280.50/42.04 | (980) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1844_0
% 280.50/42.04 |
% 280.50/42.04 | DELTA: instantiating (945) with fresh symbols all_1846_0, all_1846_1 gives:
% 280.50/42.04 | (981) c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, all_1068_3, v_z) =
% 280.50/42.04 | all_1846_1 & c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,
% 280.50/42.04 | all_1846_1) = all_1846_0 & $i(all_1846_0) & $i(all_1846_1) &
% 280.50/42.04 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1846_0,
% 280.50/42.04 | all_1068_0)
% 280.50/42.04 |
% 280.50/42.04 | ALPHA: (981) implies:
% 280.50/42.04 | (982) c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1846_0,
% 280.50/42.04 | all_1068_0)
% 280.50/42.04 | (983) c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, all_1846_1) =
% 280.50/42.04 | all_1846_0
% 280.50/42.04 | (984) c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, all_1068_3, v_z) =
% 280.50/42.04 | all_1846_1
% 280.50/42.04 |
% 280.50/42.04 | DELTA: instantiating (944) with fresh symbol all_1864_0 gives:
% 280.50/42.04 | (985) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1864_0 &
% 280.50/42.04 | $i(all_1864_0) & ( ~
% 280.50/42.04 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1068_1,
% 280.50/42.04 | all_1864_0) | ~
% 280.50/42.04 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1068_2,
% 280.50/42.04 | all_1864_0) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 280.50/42.04 | all_1068_0, all_1864_0))
% 280.50/42.04 |
% 280.50/42.04 | ALPHA: (985) implies:
% 280.50/42.04 | (986) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1864_0
% 280.50/42.04 |
% 280.50/42.04 | DELTA: instantiating (943) with fresh symbol all_1915_0 gives:
% 280.50/42.04 | (987) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1915_0 &
% 280.50/42.04 | $i(all_1915_0) & ( ~
% 280.50/42.04 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1915_0,
% 280.50/42.04 | all_1068_1) | ~
% 280.50/42.04 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1915_0,
% 280.50/42.04 | all_1068_2) | (( ~ (all_1915_0 = all_1068_0) | (all_1068_0 =
% 280.50/42.04 | all_1068_2 & all_1068_1 = all_1068_2)) & ( ~ (all_1915_0 =
% 280.50/42.04 | all_1068_2) | ~ (all_1068_1 = all_1068_2) | all_1068_0 =
% 280.50/42.04 | all_1068_2)))
% 280.50/42.04 |
% 280.50/42.04 | ALPHA: (987) implies:
% 280.50/42.04 | (988) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1915_0
% 280.50/42.04 |
% 280.50/42.04 | REDUCE: (865), (935) imply:
% 280.50/42.04 | (989) c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_631_0,
% 280.50/42.04 | all_1308_0)
% 280.50/42.04 |
% 280.50/42.04 | REDUCE: (865), (932) imply:
% 280.50/42.04 | (990) c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_631_0,
% 280.50/42.04 | all_1068_2)
% 280.50/42.04 |
% 280.50/42.04 | GROUND_INST: instantiating (150) with all_1068_1, all_1308_0, v_z,
% 280.50/42.04 | tc_Complex_Ocomplex, simplifying with (279), (951) gives:
% 280.50/42.04 | (991) all_1308_0 = all_1068_1
% 280.50/42.04 |
% 280.50/42.04 | GROUND_INST: instantiating (151) with all_1308_4, all_1846_1, v_z, all_1068_3,
% 280.50/42.04 | tc_Complex_Ocomplex, simplifying with (953), (984) gives:
% 280.50/42.04 | (992) all_1846_1 = all_1308_4
% 280.50/42.04 |
% 280.50/42.04 | GROUND_INST: instantiating (148) with all_631_0, all_1828_0, tc_RealDef_Oreal,
% 280.50/42.04 | simplifying with (154), (967) gives:
% 280.50/42.04 | (993) all_1828_0 = all_631_0
% 280.50/42.04 |
% 280.50/42.04 | GROUND_INST: instantiating (148) with all_1782_0, all_1828_0,
% 280.50/42.04 | tc_RealDef_Oreal, simplifying with (963), (967) gives:
% 280.50/42.04 | (994) all_1828_0 = all_1782_0
% 280.50/42.04 |
% 280.50/42.04 | GROUND_INST: instantiating (148) with all_1780_0, all_1828_0,
% 280.50/42.04 | tc_RealDef_Oreal, simplifying with (961), (967) gives:
% 280.50/42.04 | (995) all_1828_0 = all_1780_0
% 280.50/42.04 |
% 280.50/42.04 | GROUND_INST: instantiating (148) with all_1834_0, all_1840_0,
% 280.50/42.04 | tc_RealDef_Oreal, simplifying with (974), (976) gives:
% 280.50/42.04 | (996) all_1840_0 = all_1834_0
% 280.50/42.04 |
% 280.50/42.04 | GROUND_INST: instantiating (148) with all_1834_0, all_1842_0,
% 280.50/42.04 | tc_RealDef_Oreal, simplifying with (974), (978) gives:
% 280.50/42.04 | (997) all_1842_0 = all_1834_0
% 280.50/42.04 |
% 280.50/42.04 | GROUND_INST: instantiating (148) with all_1832_0, all_1842_0,
% 280.50/42.04 | tc_RealDef_Oreal, simplifying with (972), (978) gives:
% 280.50/42.04 | (998) all_1842_0 = all_1832_0
% 280.50/42.04 |
% 280.50/42.04 | GROUND_INST: instantiating (148) with all_1830_0, all_1842_0,
% 280.50/42.04 | tc_RealDef_Oreal, simplifying with (970), (978) gives:
% 280.50/42.04 | (999) all_1842_0 = all_1830_0
% 280.50/42.04 |
% 280.50/42.04 | GROUND_INST: instantiating (148) with all_1840_0, all_1844_0,
% 280.50/42.04 | tc_RealDef_Oreal, simplifying with (976), (980) gives:
% 280.50/42.04 | (1000) all_1844_0 = all_1840_0
% 280.50/42.04 |
% 280.50/42.04 | GROUND_INST: instantiating (148) with all_1830_0, all_1864_0,
% 280.50/42.04 | tc_RealDef_Oreal, simplifying with (970), (986) gives:
% 280.50/42.04 | (1001) all_1864_0 = all_1830_0
% 280.50/42.04 |
% 280.50/42.04 | GROUND_INST: instantiating (148) with all_1828_0, all_1864_0,
% 280.50/42.04 | tc_RealDef_Oreal, simplifying with (967), (986) gives:
% 280.50/42.04 | (1002) all_1864_0 = all_1828_0
% 280.50/42.04 |
% 280.50/42.04 | GROUND_INST: instantiating (148) with all_1784_0, all_1864_0,
% 280.50/42.04 | tc_RealDef_Oreal, simplifying with (965), (986) gives:
% 280.50/42.04 | (1003) all_1864_0 = all_1784_0
% 280.50/42.04 |
% 280.50/42.04 | GROUND_INST: instantiating (148) with all_1844_0, all_1915_0,
% 280.50/42.04 | tc_RealDef_Oreal, simplifying with (980), (988) gives:
% 280.50/42.04 | (1004) all_1915_0 = all_1844_0
% 280.50/42.04 |
% 280.50/42.04 | GROUND_INST: instantiating (148) with all_1778_0, all_1915_0,
% 280.50/42.04 | tc_RealDef_Oreal, simplifying with (959), (988) gives:
% 280.50/42.04 | (1005) all_1915_0 = all_1778_0
% 280.50/42.04 |
% 280.50/42.04 | COMBINE_EQS: (1004), (1005) imply:
% 280.50/42.04 | (1006) all_1844_0 = all_1778_0
% 280.50/42.04 |
% 280.50/42.04 | SIMP: (1006) implies:
% 280.50/42.04 | (1007) all_1844_0 = all_1778_0
% 280.50/42.04 |
% 280.50/42.04 | COMBINE_EQS: (1002), (1003) imply:
% 280.50/42.04 | (1008) all_1828_0 = all_1784_0
% 280.50/42.04 |
% 280.50/42.04 | SIMP: (1008) implies:
% 280.50/42.04 | (1009) all_1828_0 = all_1784_0
% 280.50/42.04 |
% 280.50/42.04 | COMBINE_EQS: (1001), (1003) imply:
% 280.50/42.04 | (1010) all_1830_0 = all_1784_0
% 280.50/42.04 |
% 280.50/42.04 | SIMP: (1010) implies:
% 280.50/42.04 | (1011) all_1830_0 = all_1784_0
% 280.50/42.04 |
% 280.50/42.04 | COMBINE_EQS: (1000), (1007) imply:
% 280.50/42.04 | (1012) all_1840_0 = all_1778_0
% 280.50/42.04 |
% 280.50/42.04 | SIMP: (1012) implies:
% 280.50/42.04 | (1013) all_1840_0 = all_1778_0
% 280.50/42.04 |
% 280.50/42.04 | COMBINE_EQS: (997), (998) imply:
% 280.50/42.04 | (1014) all_1834_0 = all_1832_0
% 280.50/42.04 |
% 280.50/42.04 | SIMP: (1014) implies:
% 280.50/42.04 | (1015) all_1834_0 = all_1832_0
% 280.50/42.04 |
% 280.50/42.04 | COMBINE_EQS: (998), (999) imply:
% 280.50/42.04 | (1016) all_1832_0 = all_1830_0
% 280.50/42.04 |
% 280.50/42.04 | COMBINE_EQS: (996), (1013) imply:
% 280.50/42.04 | (1017) all_1834_0 = all_1778_0
% 280.50/42.04 |
% 280.50/42.04 | SIMP: (1017) implies:
% 280.50/42.04 | (1018) all_1834_0 = all_1778_0
% 280.50/42.04 |
% 280.50/42.04 | COMBINE_EQS: (1015), (1018) imply:
% 280.50/42.04 | (1019) all_1832_0 = all_1778_0
% 280.50/42.04 |
% 280.50/42.04 | SIMP: (1019) implies:
% 280.50/42.04 | (1020) all_1832_0 = all_1778_0
% 280.50/42.04 |
% 280.50/42.04 | COMBINE_EQS: (1016), (1020) imply:
% 280.50/42.04 | (1021) all_1830_0 = all_1778_0
% 280.50/42.04 |
% 280.50/42.04 | SIMP: (1021) implies:
% 280.50/42.04 | (1022) all_1830_0 = all_1778_0
% 280.50/42.04 |
% 280.50/42.04 | COMBINE_EQS: (1011), (1022) imply:
% 280.50/42.04 | (1023) all_1784_0 = all_1778_0
% 280.50/42.04 |
% 280.50/42.04 | SIMP: (1023) implies:
% 280.50/42.04 | (1024) all_1784_0 = all_1778_0
% 280.50/42.04 |
% 280.50/42.04 | COMBINE_EQS: (993), (994) imply:
% 280.50/42.04 | (1025) all_1782_0 = all_631_0
% 280.50/42.04 |
% 280.50/42.04 | COMBINE_EQS: (994), (995) imply:
% 280.50/42.04 | (1026) all_1782_0 = all_1780_0
% 280.50/42.04 |
% 280.50/42.04 | COMBINE_EQS: (994), (1009) imply:
% 280.50/42.04 | (1027) all_1784_0 = all_1782_0
% 280.50/42.04 |
% 280.50/42.04 | SIMP: (1027) implies:
% 280.50/42.04 | (1028) all_1784_0 = all_1782_0
% 280.50/42.04 |
% 280.50/42.04 | COMBINE_EQS: (1024), (1028) imply:
% 280.50/42.04 | (1029) all_1782_0 = all_1778_0
% 280.50/42.04 |
% 280.50/42.04 | SIMP: (1029) implies:
% 280.50/42.04 | (1030) all_1782_0 = all_1778_0
% 280.50/42.04 |
% 280.50/42.04 | COMBINE_EQS: (1025), (1026) imply:
% 280.50/42.04 | (1031) all_1780_0 = all_631_0
% 280.50/42.04 |
% 280.50/42.04 | COMBINE_EQS: (1026), (1030) imply:
% 280.50/42.04 | (1032) all_1780_0 = all_1778_0
% 280.50/42.04 |
% 280.50/42.04 | COMBINE_EQS: (1031), (1032) imply:
% 280.50/42.04 | (1033) all_1778_0 = all_631_0
% 280.50/42.04 |
% 280.50/42.04 | REDUCE: (983), (992) imply:
% 280.50/42.04 | (1034) c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, all_1308_4) =
% 280.50/42.04 | all_1846_0
% 280.50/42.04 |
% 280.50/42.04 | REDUCE: (989), (991) imply:
% 280.50/42.04 | (1035) c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_631_0,
% 280.50/42.04 | all_1068_1)
% 280.50/42.04 |
% 280.50/42.04 | BETA: splitting (968) gives:
% 280.50/42.04 |
% 280.50/42.04 | Case 1:
% 280.50/42.04 | |
% 280.50/42.04 | | (1036) ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1828_0,
% 280.50/42.04 | | all_1068_1)
% 280.50/42.04 | |
% 280.50/42.04 | | REDUCE: (993), (1036) imply:
% 280.50/42.04 | | (1037) ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_631_0,
% 280.50/42.04 | | all_1068_1)
% 280.50/42.04 | |
% 280.50/42.04 | | PRED_UNIFY: (1035), (1037) imply:
% 280.50/42.04 | | (1038) $false
% 280.50/42.04 | |
% 280.50/42.04 | | CLOSE: (1038) is inconsistent.
% 280.50/42.04 | |
% 280.50/42.04 | Case 2:
% 280.50/42.04 | |
% 280.50/42.04 | | (1039) ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1828_0,
% 280.50/42.04 | | all_1068_2) |
% 280.50/42.04 | | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1828_0,
% 280.50/42.04 | | all_1068_0)
% 280.50/42.04 | |
% 280.50/42.04 | | BETA: splitting (1039) gives:
% 280.50/42.04 | |
% 280.50/42.04 | | Case 1:
% 280.50/42.04 | | |
% 280.50/42.04 | | | (1040) ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 280.50/42.04 | | | all_1828_0, all_1068_2)
% 280.50/42.04 | | |
% 280.50/42.04 | | | REDUCE: (993), (1040) imply:
% 280.50/42.04 | | | (1041) ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 280.50/42.04 | | | all_631_0, all_1068_2)
% 280.50/42.04 | | |
% 280.50/42.04 | | | PRED_UNIFY: (990), (1041) imply:
% 280.50/42.04 | | | (1042) $false
% 280.50/42.04 | | |
% 280.50/42.04 | | | CLOSE: (1042) is inconsistent.
% 280.50/42.04 | | |
% 280.50/42.04 | | Case 2:
% 280.50/42.04 | | |
% 280.50/42.04 | | |
% 280.50/42.04 | | | GROUND_INST: instantiating (150) with all_1308_3, all_1846_0, all_1308_4,
% 280.50/42.04 | | | tc_Complex_Ocomplex, simplifying with (358), (1034) gives:
% 280.50/42.04 | | | (1043) all_1846_0 = all_1308_3
% 280.50/42.04 | | |
% 280.50/42.04 | | | REDUCE: (982), (1043) imply:
% 280.50/42.04 | | | (1044) c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1308_3,
% 280.50/42.04 | | | all_1068_0)
% 280.50/42.04 | | |
% 280.50/42.04 | | | GROUND_INST: instantiating (fact_minus__add__cancel) with v_w, v_z,
% 280.50/42.04 | | | tc_Complex_Ocomplex, all_1308_5, all_1068_3, all_1308_4,
% 280.50/42.04 | | | simplifying with (142), (144), (145), (146), (361), (947),
% 280.50/42.04 | | | (949) gives:
% 280.50/42.04 | | | (1045) all_1308_4 = v_w
% 280.50/42.04 | | |
% 280.50/42.04 | | | REDUCE: (358), (1045) imply:
% 280.50/42.04 | | | (1046) c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w) =
% 280.50/42.04 | | | all_1308_3
% 280.50/42.04 | | |
% 280.50/42.04 | | | GROUND_INST: instantiating (150) with all_1068_4, all_1308_3, v_w,
% 280.50/42.04 | | | tc_Complex_Ocomplex, simplifying with (278), (1046) gives:
% 280.50/42.04 | | | (1047) all_1308_3 = all_1068_4
% 280.50/42.04 | | |
% 280.50/42.04 | | | REDUCE: (1044), (1047) imply:
% 280.50/42.04 | | | (1048) c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1068_4,
% 280.50/42.04 | | | all_1068_0)
% 280.50/42.04 | | |
% 280.50/42.04 | | | PRED_UNIFY: (277), (1048) imply:
% 280.50/42.04 | | | (1049) $false
% 280.50/42.04 | | |
% 280.50/42.04 | | | CLOSE: (1049) is inconsistent.
% 280.50/42.04 | | |
% 280.50/42.04 | | End of split
% 280.50/42.04 | |
% 280.50/42.04 | End of split
% 280.50/42.04 |
% 280.50/42.04 End of proof
% 280.50/42.04 % SZS output end Proof for theBenchmark
% 280.50/42.04
% 280.50/42.04 41486ms
%------------------------------------------------------------------------------