TSTP Solution File: SWW217+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWW217+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 : n027.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 00:49:28 EDT 2023
% Result : Theorem 81.92s 11.70s
% Output : Proof 208.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW217+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.33 % Computer : n027.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sun Aug 27 21:50:06 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.60 ________ _____
% 0.19/0.60 ___ __ \_________(_)________________________________
% 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60
% 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60 (2023-06-19)
% 0.19/0.60
% 0.19/0.60 (c) Philipp Rümmer, 2009-2023
% 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60 Amanda Stjerna.
% 0.19/0.60 Free software under BSD-3-Clause.
% 0.19/0.60
% 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60
% 0.19/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.62 Running up to 7 provers in parallel.
% 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 18.53/3.33 Prover 1: Preprocessing ...
% 19.30/3.38 Prover 3: Preprocessing ...
% 19.30/3.38 Prover 0: Preprocessing ...
% 19.30/3.39 Prover 2: Preprocessing ...
% 19.30/3.39 Prover 5: Preprocessing ...
% 20.94/3.59 Prover 4: Preprocessing ...
% 22.79/3.82 Prover 6: Preprocessing ...
% 53.11/7.85 Prover 1: Warning: ignoring some quantifiers
% 53.63/8.10 Prover 3: Warning: ignoring some quantifiers
% 56.37/8.27 Prover 3: Constructing countermodel ...
% 57.05/8.34 Prover 1: Constructing countermodel ...
% 57.55/8.43 Prover 6: Proving ...
% 59.37/8.70 Prover 4: Warning: ignoring some quantifiers
% 63.23/9.18 Prover 4: Constructing countermodel ...
% 64.82/9.42 Prover 5: Proving ...
% 70.42/10.09 Prover 0: Proving ...
% 74.40/10.62 Prover 2: Proving ...
% 80.04/11.33 Prover 2: stopped
% 80.04/11.35 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 81.92/11.69 Prover 3: proved (11059ms)
% 81.92/11.70
% 81.92/11.70 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 81.92/11.70
% 81.92/11.70 Prover 6: stopped
% 81.92/11.71 Prover 5: stopped
% 82.46/11.71 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 82.46/11.71 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 82.46/11.71 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 83.23/11.76 Prover 0: stopped
% 83.23/11.76 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 90.57/12.72 Prover 7: Preprocessing ...
% 92.00/12.97 Prover 8: Preprocessing ...
% 94.86/13.31 Prover 10: Preprocessing ...
% 95.67/13.38 Prover 11: Preprocessing ...
% 95.67/13.40 Prover 13: Preprocessing ...
% 105.16/14.68 Prover 8: Warning: ignoring some quantifiers
% 106.71/14.86 Prover 8: Constructing countermodel ...
% 107.40/14.94 Prover 7: Warning: ignoring some quantifiers
% 107.40/14.95 Prover 10: Warning: ignoring some quantifiers
% 112.59/15.65 Prover 10: Constructing countermodel ...
% 112.99/15.69 Prover 7: Constructing countermodel ...
% 115.15/15.99 Prover 1: stopped
% 115.15/16.00 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 120.73/16.69 Prover 13: Warning: ignoring some quantifiers
% 121.57/16.78 Prover 16: Preprocessing ...
% 122.04/16.86 Prover 11: Warning: ignoring some quantifiers
% 122.79/16.96 Prover 13: Constructing countermodel ...
% 123.88/17.21 Prover 11: Constructing countermodel ...
% 134.12/18.46 Prover 16: Warning: ignoring some quantifiers
% 134.12/18.63 Prover 16: Constructing countermodel ...
% 150.73/20.83 Prover 16: stopped
% 151.51/20.87 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 158.16/21.65 Prover 19: Preprocessing ...
% 164.45/22.52 Prover 13: stopped
% 169.13/23.13 Prover 19: Warning: ignoring some quantifiers
% 169.53/23.24 Prover 19: Constructing countermodel ...
% 181.03/24.90 Prover 19: stopped
% 202.99/27.96 Prover 4: stopped
% 207.04/28.54 Prover 10: Found proof (size 283)
% 207.04/28.54 Prover 10: proved (16832ms)
% 207.04/28.54 Prover 11: stopped
% 207.04/28.54 Prover 7: stopped
% 207.04/28.55 Prover 8: stopped
% 207.04/28.55
% 207.04/28.55 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 207.04/28.55
% 207.43/28.63 % SZS output start Proof for theBenchmark
% 207.43/28.66 Assumptions after simplification:
% 207.43/28.66 ---------------------------------
% 207.43/28.66
% 207.43/28.66 (arity_RealDef__Oreal__Orderings_Oorder)
% 207.43/28.66 $i(tc_RealDef_Oreal) & class_Orderings_Oorder(tc_RealDef_Oreal)
% 207.43/28.66
% 207.43/28.66 (conj_0)
% 207.85/28.69 $i(v_cs____) & $i(tc_Complex_Ocomplex) & $i(v_e) & $i(tc_RealDef_Oreal) &
% 207.85/28.69 $i(v_w____) & $i(v_z) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i]
% 207.85/28.69 : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] :
% 207.85/28.69 (c_Polynomial_Opoly(tc_Complex_Ocomplex, v_cs____) = v4 &
% 207.85/28.69 c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v0 &
% 207.85/28.69 c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_w____, v_z) = v1 &
% 207.85/28.69 c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v5) = v6 &
% 207.85/28.69 c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v1) = v2 & hAPP(v4, v1)
% 207.85/28.69 = v5 & hAPP(v3, v6) = v7 & hAPP(v0, v2) = v3 & $i(v7) & $i(v6) & $i(v5) &
% 207.85/28.69 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ~
% 207.85/28.69 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v7, v_e))
% 207.85/28.69
% 207.85/28.69 (fact_DeMoivre2)
% 207.85/28.69 $i(tc_Nat_Onat) & $i(tc_Complex_Ocomplex) & $i(tc_RealDef_Oreal) & ? [v0: $i]
% 207.85/28.69 : ? [v1: $i] : ? [v2: $i] :
% 207.85/28.69 (c_Power_Opower__class_Opower(tc_Complex_Ocomplex) = v0 &
% 207.85/28.69 c_Power_Opower__class_Opower(tc_RealDef_Oreal) = v1 &
% 207.85/28.69 c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v2 & $i(v2) & $i(v1) &
% 207.85/28.69 $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 207.85/28.69 : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~
% 207.85/28.69 (c_Complex_Orcis(v7, v10) = v11) | ~ (c_RealDef_Oreal(tc_Nat_Onat, v3) =
% 207.85/28.69 v8) | ~ (hAPP(v9, v4) = v10) | ~ (hAPP(v6, v3) = v7) | ~ (hAPP(v2,
% 207.85/28.69 v8) = v9) | ~ (hAPP(v1, v5) = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3)
% 207.85/28.69 | ? [v12: $i] : ? [v13: $i] : (c_Complex_Orcis(v5, v4) = v12 & hAPP(v13,
% 207.85/28.69 v3) = v11 & hAPP(v0, v12) = v13 & $i(v13) & $i(v12) & $i(v11))))
% 207.85/28.69
% 207.85/28.69 (fact_LIMSEQ__inverse__realpow__zero__lemma)
% 207.85/28.69 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 207.85/28.69 $i] : ? [v3: $i] : (c_Power_Opower__class_Opower(tc_RealDef_Oreal) = v3 &
% 207.85/28.69 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v2 &
% 207.85/28.70 c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 207.85/28.70 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v3) & $i(v2) &
% 207.85/28.70 $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : !
% 207.85/28.70 [v8: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v5, v2) = v6)
% 207.85/28.70 | ~ (hAPP(v7, v4) = v8) | ~ (hAPP(v3, v6) = v7) | ~ $i(v5) | ~ $i(v4)
% 207.85/28.70 | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v5) | ? [v9:
% 207.85/28.70 $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] :
% 207.85/28.70 (c_RealDef_Oreal(tc_Nat_Onat, v4) = v9 &
% 207.85/28.70 c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v11, v2) = v12 & hAPP(v10,
% 207.85/28.70 v5) = v11 & hAPP(v1, v9) = v10 & $i(v12) & $i(v11) & $i(v10) & $i(v9)
% 207.85/28.70 & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v12, v8))))
% 207.85/28.70
% 207.85/28.70 (fact__096cmod_A_Iw_A_N_Az_J_A_K_Acmod_A_Ipoly_Acs_A_Iw_A_N_Az_J_J_A_060_061_Ad_A_K_Am_096)
% 207.85/28.70 $i(v_cs____) & $i(v_m____) & $i(v_da____) & $i(tc_Complex_Ocomplex) &
% 207.85/28.70 $i(tc_RealDef_Oreal) & $i(v_w____) & $i(v_z) & ? [v0: $i] : ? [v1: $i] : ?
% 207.85/28.70 [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i]
% 207.85/28.70 : ? [v8: $i] : ? [v9: $i] : (c_Polynomial_Opoly(tc_Complex_Ocomplex,
% 207.85/28.70 v_cs____) = v4 & c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v0 &
% 207.85/28.70 c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_w____, v_z) = v1 &
% 207.85/28.70 c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v5) = v6 &
% 207.85/28.70 c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v1) = v2 & hAPP(v8,
% 207.85/28.70 v_m____) = v9 & hAPP(v4, v1) = v5 & hAPP(v3, v6) = v7 & hAPP(v0, v2) = v3
% 207.85/28.70 & hAPP(v0, v_da____) = v8 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) &
% 207.85/28.70 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) &
% 207.85/28.70 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v7, v9))
% 207.85/28.70
% 207.85/28.70 (fact_d1_I1_J)
% 207.85/28.70 $i(tc_Complex_Ocomplex) & $i(tc_RealDef_Oreal) & $i(v_w____) & $i(v_z) & ?
% 207.85/28.70 [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 207.85/28.70 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v2 &
% 207.85/28.70 c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_w____, v_z) = v0 &
% 207.85/28.70 c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v0) = v1 & $i(v2) &
% 207.85/28.70 $i(v1) & $i(v0) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1,
% 207.85/28.70 v2))
% 207.85/28.70
% 207.85/28.70 (fact_divide_Ononneg__bounded)
% 207.94/28.70 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 207.94/28.70 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 207.94/28.70 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & ?
% 207.94/28.70 [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~
% 207.94/28.70 class_RealVector_Oreal__normed__field(v3) | ? [v4: $i] : ($i(v4) &
% 207.94/28.70 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v4) & ! [v5:
% 207.94/28.70 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~
% 207.94/28.70 (c_RealVector_Onorm__class_Onorm(v3, v5) = v6) | ~ (hAPP(v7, v4) =
% 207.94/28.70 v8) | ~ (hAPP(v1, v6) = v7) | ~ $i(v5) | ? [v9: $i] : ? [v10:
% 207.94/28.70 $i] : (c_Rings_Oinverse__class_Odivide(v3, v5, v2) = v9 &
% 207.94/28.70 c_RealVector_Onorm__class_Onorm(v3, v9) = v10 & $i(v10) & $i(v9) &
% 207.94/28.70 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v10, v8))))))
% 207.94/28.70
% 207.94/28.70 (fact_divide_Opos__bounded)
% 207.94/28.71 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 207.94/28.71 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 207.94/28.71 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & ?
% 207.94/28.71 [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~
% 207.94/28.71 class_RealVector_Oreal__normed__field(v3) | ? [v4: $i] : ($i(v4) &
% 207.94/28.71 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) & ! [v5: $i] :
% 207.94/28.71 ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~
% 207.94/28.71 (c_RealVector_Onorm__class_Onorm(v3, v5) = v6) | ~ (hAPP(v7, v4) =
% 207.94/28.71 v8) | ~ (hAPP(v1, v6) = v7) | ~ $i(v5) | ? [v9: $i] : ? [v10:
% 207.94/28.71 $i] : (c_Rings_Oinverse__class_Odivide(v3, v5, v2) = v9 &
% 207.94/28.71 c_RealVector_Onorm__class_Onorm(v3, v9) = v10 & $i(v10) & $i(v9) &
% 207.94/28.71 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v10, v8))))))
% 207.94/28.71
% 207.94/28.71 (fact_dme)
% 207.94/28.71 $i(v_m____) & $i(v_da____) & $i(v_e) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ?
% 207.94/28.71 [v1: $i] : ? [v2: $i] : (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v0
% 207.94/28.71 & hAPP(v1, v_m____) = v2 & hAPP(v0, v_da____) = v1 & $i(v2) & $i(v1) &
% 207.94/28.71 $i(v0) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v_e))
% 207.94/28.71
% 207.94/28.71 (fact_le__mult__natfloor)
% 207.94/28.71 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 207.94/28.71 $i] : (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 207.94/28.71 c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v2 &
% 207.94/28.71 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v2) & $i(v1) &
% 207.94/28.71 $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 207.94/28.71 : ! [v8: $i] : ( ~ (c_RComplete_Onatfloor(v4) = v5) | ~
% 207.94/28.71 (c_RComplete_Onatfloor(v3) = v7) | ~ (hAPP(v6, v7) = v8) | ~ (hAPP(v1,
% 207.94/28.71 v5) = v6) | ~ $i(v4) | ~ $i(v3) | ~
% 207.94/28.71 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v4) | ~
% 207.94/28.71 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) | ? [v9: $i]
% 207.94/28.71 : ? [v10: $i] : ? [v11: $i] : (c_RComplete_Onatfloor(v10) = v11 &
% 207.94/28.71 hAPP(v9, v3) = v10 & hAPP(v2, v4) = v9 & $i(v11) & $i(v10) & $i(v9) &
% 207.94/28.71 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v8, v11))))
% 207.94/28.71
% 207.94/28.71 (fact_lemma__MVT)
% 207.94/28.71 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 207.94/28.71 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 207.94/28.71 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 207.94/28.71 [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~
% 207.94/28.71 (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v6, v7) = v8) | ~
% 207.94/28.71 (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v5, v10) = v11) | ~
% 207.94/28.71 (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v5, v4) = v6) | ~
% 207.94/28.71 (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v1, v2) = v7) | ~
% 207.94/28.71 (hAPP(v9, v1) = v10) | ~ (hAPP(v3, v2) = v4) | ~ (hAPP(v3, v1) = v5) |
% 207.94/28.71 ~ (hAPP(v0, v8) = v9) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ? [v12: $i] :
% 207.94/28.71 (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v4, v12) = v11 & hAPP(v9,
% 207.94/28.71 v2) = v12 & $i(v12) & $i(v11))))
% 207.94/28.71
% 207.94/28.71 (fact_ln__mult)
% 207.94/28.71 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 207.94/28.71 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 207.94/28.71 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 207.94/28.71 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 207.94/28.71 (c_Transcendental_Oln(v3) = v4) | ~ (c_Transcendental_Oln(v2) = v5) | ~
% 207.94/28.71 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v4, v5) = v6) | ~ $i(v3) |
% 207.94/28.71 ~ $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) |
% 207.94/28.72 ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ? [v7: $i] :
% 207.94/28.72 ? [v8: $i] : (c_Transcendental_Oln(v8) = v6 & hAPP(v7, v2) = v8 & hAPP(v1,
% 207.94/28.72 v3) = v7 & $i(v8) & $i(v7) & $i(v6))))
% 207.94/28.72
% 207.94/28.72 (fact_ln__realpow)
% 207.94/28.72 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 207.94/28.72 $i] : (c_Power_Opower__class_Opower(tc_RealDef_Oreal) = v1 &
% 207.94/28.72 c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v2 &
% 207.94/28.72 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v2) & $i(v1) &
% 207.94/28.72 $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 207.94/28.72 : ! [v8: $i] : ( ~ (c_Transcendental_Oln(v4) = v7) | ~
% 207.94/28.72 (c_RealDef_Oreal(tc_Nat_Onat, v3) = v5) | ~ (hAPP(v6, v7) = v8) | ~
% 207.94/28.72 (hAPP(v2, v5) = v6) | ~ $i(v4) | ~ $i(v3) | ~
% 207.94/28.72 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) | ? [v9: $i] : ?
% 207.94/28.72 [v10: $i] : (c_Transcendental_Oln(v10) = v8 & hAPP(v9, v3) = v10 &
% 207.94/28.72 hAPP(v1, v4) = v9 & $i(v10) & $i(v9) & $i(v8))))
% 207.94/28.72
% 207.94/28.72 (fact_m_I2_J)
% 207.94/28.72 $i(v_cs____) & $i(v_m____) & $i(tc_Complex_Ocomplex) & $i(tc_RealDef_Oreal) &
% 207.94/28.72 ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 207.94/28.72 c_Polynomial_Opoly(tc_Complex_Ocomplex, v_cs____) = v1 & $i(v1) & $i(v0) &
% 207.94/28.72 ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v1, v2) = v3) | ~ $i(v2) | ? [v4: $i]
% 207.94/28.72 : ? [v5: $i] : ((c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v3)
% 207.94/28.72 = v5 & $i(v5) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 207.94/28.72 v5, v_m____)) |
% 207.94/28.72 (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v2) = v4 & $i(v4)
% 207.94/28.72 & ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v0)))))
% 207.94/28.72
% 207.94/28.72 (fact_mult_Ononneg__bounded)
% 208.03/28.72 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 208.03/28.72 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 208.03/28.72 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 208.03/28.72 [v2: $i] : ! [v3: $i] : ( ~ (c_Groups_Otimes__class_Otimes(v2) = v3) | ~
% 208.03/28.72 $i(v2) | ~ class_RealVector_Oreal__normed__algebra(v2) | ? [v4: $i] :
% 208.03/28.72 ($i(v4) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v4) & !
% 208.03/28.72 [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : !
% 208.03/28.72 [v10: $i] : ! [v11: $i] : ! [v12: $i] : ( ~
% 208.03/28.72 (c_RealVector_Onorm__class_Onorm(v2, v6) = v9) | ~
% 208.03/28.72 (c_RealVector_Onorm__class_Onorm(v2, v5) = v7) | ~ (hAPP(v11, v4) =
% 208.03/28.72 v12) | ~ (hAPP(v8, v9) = v10) | ~ (hAPP(v1, v10) = v11) | ~
% 208.03/28.72 (hAPP(v1, v7) = v8) | ~ $i(v6) | ~ $i(v5) | ? [v13: $i] : ? [v14:
% 208.03/28.72 $i] : ? [v15: $i] : (c_RealVector_Onorm__class_Onorm(v2, v14) = v15
% 208.03/28.72 & hAPP(v13, v6) = v14 & hAPP(v3, v5) = v13 & $i(v15) & $i(v14) &
% 208.03/28.72 $i(v13) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v15,
% 208.03/28.72 v12))))))
% 208.03/28.72
% 208.03/28.72 (fact_mult_Opos__bounded)
% 208.03/28.72 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 208.03/28.72 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 208.03/28.72 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 208.03/28.72 [v2: $i] : ! [v3: $i] : ( ~ (c_Groups_Otimes__class_Otimes(v2) = v3) | ~
% 208.03/28.72 $i(v2) | ~ class_RealVector_Oreal__normed__algebra(v2) | ? [v4: $i] :
% 208.03/28.72 ($i(v4) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) & !
% 208.03/28.72 [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : !
% 208.03/28.72 [v10: $i] : ! [v11: $i] : ! [v12: $i] : ( ~
% 208.03/28.72 (c_RealVector_Onorm__class_Onorm(v2, v6) = v9) | ~
% 208.03/28.72 (c_RealVector_Onorm__class_Onorm(v2, v5) = v7) | ~ (hAPP(v11, v4) =
% 208.03/28.72 v12) | ~ (hAPP(v8, v9) = v10) | ~ (hAPP(v1, v10) = v11) | ~
% 208.03/28.72 (hAPP(v1, v7) = v8) | ~ $i(v6) | ~ $i(v5) | ? [v13: $i] : ? [v14:
% 208.03/28.72 $i] : ? [v15: $i] : (c_RealVector_Onorm__class_Onorm(v2, v14) = v15
% 208.03/28.72 & hAPP(v13, v6) = v14 & hAPP(v3, v5) = v13 & $i(v15) & $i(v14) &
% 208.03/28.72 $i(v13) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v15,
% 208.03/28.72 v12))))))
% 208.03/28.72
% 208.03/28.72 (fact_mult__left_Ononneg__bounded)
% 208.03/28.73 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 208.03/28.73 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 208.03/28.73 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & ?
% 208.03/28.73 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 208.03/28.73 (c_Groups_Otimes__class_Otimes(v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 208.03/28.73 class_RealVector_Oreal__normed__algebra(v3) | ? [v5: $i] : ($i(v5) &
% 208.03/28.73 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v5) & ! [v6:
% 208.03/28.73 $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~
% 208.03/28.73 (c_RealVector_Onorm__class_Onorm(v3, v6) = v7) | ~ (hAPP(v8, v5) =
% 208.03/28.73 v9) | ~ (hAPP(v1, v7) = v8) | ~ $i(v6) | ? [v10: $i] : ? [v11:
% 208.03/28.73 $i] : ? [v12: $i] : (c_RealVector_Onorm__class_Onorm(v3, v11) = v12
% 208.03/28.73 & hAPP(v10, v2) = v11 & hAPP(v4, v6) = v10 & $i(v12) & $i(v11) &
% 208.03/28.73 $i(v10) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v12,
% 208.03/28.73 v9))))))
% 208.03/28.73
% 208.03/28.73 (fact_mult__left_Opos__bounded)
% 208.03/28.73 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 208.03/28.73 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 208.03/28.73 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & ?
% 208.03/28.73 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 208.03/28.73 (c_Groups_Otimes__class_Otimes(v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 208.03/28.73 class_RealVector_Oreal__normed__algebra(v3) | ? [v5: $i] : ($i(v5) &
% 208.03/28.73 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v5) & ! [v6: $i] :
% 208.03/28.73 ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~
% 208.03/28.73 (c_RealVector_Onorm__class_Onorm(v3, v6) = v7) | ~ (hAPP(v8, v5) =
% 208.03/28.73 v9) | ~ (hAPP(v1, v7) = v8) | ~ $i(v6) | ? [v10: $i] : ? [v11:
% 208.03/28.73 $i] : ? [v12: $i] : (c_RealVector_Onorm__class_Onorm(v3, v11) = v12
% 208.03/28.73 & hAPP(v10, v2) = v11 & hAPP(v4, v6) = v10 & $i(v12) & $i(v11) &
% 208.03/28.73 $i(v10) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v12,
% 208.03/28.73 v9))))))
% 208.03/28.73
% 208.03/28.73 (fact_mult__right_Ononneg__bounded)
% 208.03/28.73 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 208.03/28.73 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 208.03/28.73 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 208.03/28.73 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 208.03/28.73 (c_Groups_Otimes__class_Otimes(v3) = v4) | ~ (hAPP(v4, v2) = v5) | ~
% 208.03/28.73 $i(v3) | ~ $i(v2) | ~ class_RealVector_Oreal__normed__algebra(v3) | ?
% 208.03/28.73 [v6: $i] : ($i(v6) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 208.03/28.73 v0, v6) & ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ( ~
% 208.03/28.73 (c_RealVector_Onorm__class_Onorm(v3, v7) = v8) | ~ (hAPP(v9, v6) =
% 208.03/28.73 v10) | ~ (hAPP(v1, v8) = v9) | ~ $i(v7) | ? [v11: $i] : ? [v12:
% 208.03/28.73 $i] : (c_RealVector_Onorm__class_Onorm(v3, v11) = v12 & hAPP(v5, v7)
% 208.03/28.73 = v11 & $i(v12) & $i(v11) &
% 208.03/28.73 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v12, v10))))))
% 208.03/28.73
% 208.03/28.73 (fact_mult__right_Opos__bounded)
% 208.03/28.73 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 208.03/28.73 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 208.03/28.73 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 208.03/28.73 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 208.03/28.73 (c_Groups_Otimes__class_Otimes(v3) = v4) | ~ (hAPP(v4, v2) = v5) | ~
% 208.03/28.73 $i(v3) | ~ $i(v2) | ~ class_RealVector_Oreal__normed__algebra(v3) | ?
% 208.03/28.73 [v6: $i] : ($i(v6) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0,
% 208.03/28.73 v6) & ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ( ~
% 208.03/28.73 (c_RealVector_Onorm__class_Onorm(v3, v7) = v8) | ~ (hAPP(v9, v6) =
% 208.03/28.73 v10) | ~ (hAPP(v1, v8) = v9) | ~ $i(v7) | ? [v11: $i] : ? [v12:
% 208.03/28.73 $i] : (c_RealVector_Onorm__class_Onorm(v3, v11) = v12 & hAPP(v5, v7)
% 208.03/28.73 = v11 & $i(v12) & $i(v11) &
% 208.03/28.73 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v12, v10))))))
% 208.03/28.73
% 208.03/28.73 (fact_norm__mult)
% 208.03/28.73 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 208.03/28.73 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 208.03/28.74 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 208.03/28.74 [v7: $i] : ( ~ (c_RealVector_Onorm__class_Onorm(v3, v2) = v4) | ~
% 208.03/28.74 (c_RealVector_Onorm__class_Onorm(v3, v1) = v6) | ~ (hAPP(v5, v6) = v7) |
% 208.03/28.74 ~ (hAPP(v0, v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 208.03/28.74 class_RealVector_Oreal__normed__div__algebra(v3) | ? [v8: $i] : ? [v9:
% 208.03/28.74 $i] : ? [v10: $i] : (c_Groups_Otimes__class_Otimes(v3) = v8 &
% 208.03/28.74 c_RealVector_Onorm__class_Onorm(v3, v10) = v7 & hAPP(v9, v1) = v10 &
% 208.03/28.74 hAPP(v8, v2) = v9 & $i(v10) & $i(v9) & $i(v8) & $i(v7))))
% 208.03/28.74
% 208.03/28.74 (fact_norm__mult__ineq)
% 208.03/28.74 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 208.03/28.74 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 208.03/28.74 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 208.03/28.74 [v7: $i] : ( ~ (c_RealVector_Onorm__class_Onorm(v3, v2) = v4) | ~
% 208.03/28.74 (c_RealVector_Onorm__class_Onorm(v3, v1) = v6) | ~ (hAPP(v5, v6) = v7) |
% 208.03/28.74 ~ (hAPP(v0, v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 208.03/28.74 class_RealVector_Oreal__normed__algebra(v3) | ? [v8: $i] : ? [v9: $i] :
% 208.03/28.74 ? [v10: $i] : ? [v11: $i] : (c_Groups_Otimes__class_Otimes(v3) = v8 &
% 208.03/28.74 c_RealVector_Onorm__class_Onorm(v3, v10) = v11 & hAPP(v9, v1) = v10 &
% 208.03/28.74 hAPP(v8, v2) = v9 & $i(v11) & $i(v10) & $i(v9) & $i(v8) &
% 208.03/28.74 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v11, v7))))
% 208.03/28.74
% 208.03/28.74 (fact_norm__mult__less)
% 208.03/28.74 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 208.03/28.74 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 208.03/28.74 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 208.03/28.74 [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~
% 208.03/28.74 (c_Groups_Otimes__class_Otimes(v5) = v6) | ~
% 208.03/28.74 (c_RealVector_Onorm__class_Onorm(v5, v8) = v9) | ~ (hAPP(v10, v1) = v11)
% 208.03/28.74 | ~ (hAPP(v7, v2) = v8) | ~ (hAPP(v6, v4) = v7) | ~ (hAPP(v0, v3) =
% 208.03/28.74 v10) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 208.03/28.74 class_RealVector_Oreal__normed__algebra(v5) |
% 208.03/28.74 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v9, v11) | ? [v12: $i] :
% 208.03/28.74 ? [v13: $i] : ((c_RealVector_Onorm__class_Onorm(v5, v4) = v12 & $i(v12) &
% 208.03/28.74 ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v12, v3)) |
% 208.03/28.74 (c_RealVector_Onorm__class_Onorm(v5, v2) = v13 & $i(v13) & ~
% 208.03/28.74 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v13, v1)))))
% 208.03/28.74
% 208.03/28.74 (fact_norm__ratiotest__lemma)
% 208.03/28.74 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 208.03/28.74 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 208.03/28.74 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 208.03/28.74 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 208.03/28.74 $i] : ! [v8: $i] : ! [v9: $i] : ( ~ (c_RealVector_Onorm__class_Onorm(v5,
% 208.03/28.74 v3) = v6) | ~ (c_RealVector_Onorm__class_Onorm(v5, v2) = v8) | ~
% 208.03/28.74 (hAPP(v7, v8) = v9) | ~ (hAPP(v1, v4) = v7) | ~ $i(v5) | ~ $i(v4) | ~
% 208.03/28.74 $i(v3) | ~ $i(v2) | ~ class_RealVector_Oreal__normed__vector(v5) | ~
% 208.03/28.74 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v9) | ~
% 208.03/28.74 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v0) |
% 208.03/28.74 c_Groups_Ozero__class_Ozero(v5) = v3))
% 208.03/28.74
% 208.03/28.74 (fact_not__real__square__gt__zero)
% 208.03/28.74 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 208.03/28.74 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 208.03/28.74 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 208.03/28.74 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v0 | ~ (hAPP(v3, v2) = v4) |
% 208.03/28.74 ~ (hAPP(v1, v2) = v3) | ~ $i(v2) |
% 208.03/28.74 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4)) & ! [v2: $i] :
% 208.03/28.74 ! [v3: $i] : ( ~ (hAPP(v2, v0) = v3) | ~ (hAPP(v1, v0) = v2) | ~
% 208.03/28.74 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3)))
% 208.03/28.74
% 208.03/28.74 (fact_rcis__mult)
% 208.03/28.74 $i(tc_Complex_Ocomplex) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 208.03/28.74 (c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex) = v0 &
% 208.03/28.74 c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0) & !
% 208.03/28.74 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 208.03/28.74 $i] : ! [v8: $i] : ! [v9: $i] : ( ~ (c_Complex_Orcis(v7, v8) = v9) | ~
% 208.03/28.75 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v4, v2) = v8) | ~
% 208.03/28.75 (hAPP(v6, v3) = v7) | ~ (hAPP(v1, v5) = v6) | ~ $i(v5) | ~ $i(v4) | ~
% 208.03/28.75 $i(v3) | ~ $i(v2) | ? [v10: $i] : ? [v11: $i] : ? [v12: $i] :
% 208.03/28.75 (c_Complex_Orcis(v5, v4) = v10 & c_Complex_Orcis(v3, v2) = v12 & hAPP(v11,
% 208.03/28.75 v12) = v9 & hAPP(v0, v10) = v11 & $i(v12) & $i(v11) & $i(v10) &
% 208.03/28.75 $i(v9))))
% 208.03/28.75
% 208.03/28.75 (fact_real__add__mult__distrib)
% 208.03/28.75 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 208.03/28.75 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 208.03/28.75 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 208.03/28.75 [v7: $i] : ! [v8: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,
% 208.03/28.75 v5, v7) = v8) | ~ (hAPP(v6, v1) = v7) | ~ (hAPP(v4, v1) = v5) | ~
% 208.03/28.75 (hAPP(v0, v3) = v4) | ~ (hAPP(v0, v2) = v6) | ~ $i(v3) | ~ $i(v2) | ~
% 208.03/28.75 $i(v1) | ? [v9: $i] : ? [v10: $i] :
% 208.03/28.75 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v2) = v9 & hAPP(v10,
% 208.03/28.75 v1) = v8 & hAPP(v0, v9) = v10 & $i(v10) & $i(v9) & $i(v8))))
% 208.03/28.75
% 208.03/28.75 (fact_real__divide__square__eq)
% 208.03/28.75 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 208.03/28.75 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 208.03/28.75 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 208.03/28.75 (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v4, v5) = v6) | ~
% 208.03/28.75 (hAPP(v3, v2) = v5) | ~ (hAPP(v3, v1) = v4) | ~ (hAPP(v0, v2) = v3) | ~
% 208.03/28.75 $i(v2) | ~ $i(v1) | (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,
% 208.03/28.75 v1, v2) = v6 & $i(v6))))
% 208.03/28.75
% 208.03/28.75 (fact_real__mult__1)
% 208.03/28.75 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 208.03/28.75 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 208.03/28.75 c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v0 & hAPP(v0, v1) = v2 &
% 208.03/28.75 $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : (v4 = v3 | ~
% 208.03/28.75 (hAPP(v2, v3) = v4) | ~ $i(v3)))
% 208.03/28.75
% 208.03/28.75 (fact_real__mult__assoc)
% 208.03/28.75 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 208.03/28.75 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 208.03/28.75 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 208.03/28.75 [v7: $i] : ( ~ (hAPP(v6, v1) = v7) | ~ (hAPP(v4, v2) = v5) | ~ (hAPP(v0,
% 208.03/28.75 v5) = v6) | ~ (hAPP(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1)
% 208.03/28.75 | ? [v8: $i] : ? [v9: $i] : (hAPP(v8, v1) = v9 & hAPP(v4, v9) = v7 &
% 208.03/28.75 hAPP(v0, v2) = v8 & $i(v9) & $i(v8) & $i(v7))))
% 208.03/28.75
% 208.03/28.75 (fact_real__mult__commute)
% 208.03/28.75 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 208.03/28.75 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] :
% 208.03/28.75 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (hAPP(v3, v2) = v4) | ~
% 208.03/28.75 (hAPP(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ? [v5: $i] : (hAPP(v5, v1)
% 208.03/28.75 = v4 & hAPP(v0, v2) = v5 & $i(v5) & $i(v4))))
% 208.03/28.75
% 208.03/28.75 (fact_real__mult__le__cancel__iff1)
% 208.03/28.75 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 208.03/28.75 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 208.03/28.75 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 208.03/28.75 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 208.03/28.75 $i] : ! [v8: $i] : ( ~ (hAPP(v7, v4) = v8) | ~ (hAPP(v5, v4) = v6) | ~
% 208.03/28.75 (hAPP(v1, v3) = v5) | ~ (hAPP(v1, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~
% 208.03/28.75 $i(v2) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v8) |
% 208.03/28.75 ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) |
% 208.03/28.75 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v2)) & ! [v2: $i]
% 208.03/28.75 : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : !
% 208.03/28.75 [v8: $i] : ( ~ (hAPP(v7, v4) = v8) | ~ (hAPP(v5, v4) = v6) | ~ (hAPP(v1,
% 208.03/28.75 v3) = v5) | ~ (hAPP(v1, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2)
% 208.03/28.75 | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v2) | ~
% 208.03/28.75 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) |
% 208.03/28.75 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v8)))
% 208.03/28.75
% 208.03/28.75 (fact_real__mult__le__cancel__iff2)
% 208.03/28.76 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 208.03/28.76 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 208.03/28.76 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 208.03/28.76 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 208.03/28.76 $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v1, v4)
% 208.03/28.76 = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 208.03/28.76 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v7) | ~
% 208.03/28.76 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) |
% 208.03/28.76 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v2)) & ! [v2: $i]
% 208.03/28.76 : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~
% 208.03/28.76 (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v1, v4) = v5) | ~
% 208.03/28.76 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 208.03/28.76 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v2) | ~
% 208.03/28.76 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) |
% 208.03/28.76 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v7)))
% 208.03/28.76
% 208.03/28.76 (fact_real__mult__left__cancel)
% 208.03/28.76 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 208.03/28.76 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 208.03/28.76 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 208.03/28.76 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v4 = v0
% 208.03/28.76 | v3 = v2 | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v6) | ~ (hAPP(v1,
% 208.03/28.76 v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2)))
% 208.03/28.76
% 208.03/28.76 (fact_real__mult__less__iff1)
% 208.03/28.76 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 208.03/28.76 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 208.03/28.76 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 208.03/28.76 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 208.03/28.76 $i] : ! [v8: $i] : ( ~ (hAPP(v7, v4) = v8) | ~ (hAPP(v5, v4) = v6) | ~
% 208.03/28.76 (hAPP(v1, v3) = v5) | ~ (hAPP(v1, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~
% 208.03/28.76 $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v6, v8) | ~
% 208.03/28.76 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) |
% 208.03/28.76 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v2)) & ! [v2: $i] :
% 208.03/28.76 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8:
% 208.03/28.76 $i] : ( ~ (hAPP(v7, v4) = v8) | ~ (hAPP(v5, v4) = v6) | ~ (hAPP(v1, v3)
% 208.03/28.76 = v5) | ~ (hAPP(v1, v2) = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 208.03/28.76 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v2) | ~
% 208.03/28.76 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) |
% 208.03/28.76 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v6, v8)))
% 208.03/28.76
% 208.03/28.76 (fact_real__mult__less__mono2)
% 208.03/28.76 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 208.03/28.76 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 208.03/28.76 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 208.03/28.76 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 208.03/28.76 $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v1, v4)
% 208.03/28.76 = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 208.03/28.76 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v2) | ~
% 208.03/28.76 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) |
% 208.03/28.76 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v6, v7)))
% 208.03/28.76
% 208.03/28.76 (fact_real__mult__order)
% 208.03/28.76 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 208.03/28.76 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 208.03/28.76 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 208.03/28.76 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, v2) = v5)
% 208.03/28.76 | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 208.03/28.76 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | ~
% 208.03/28.76 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) |
% 208.03/28.76 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v5)))
% 208.03/28.76
% 208.03/28.76 (fact_real__mult__right__cancel)
% 208.03/28.76 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 208.03/28.76 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 208.03/28.76 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 208.03/28.76 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 208.03/28.76 $i] : (v4 = v0 | v3 = v2 | ~ (hAPP(v7, v4) = v6) | ~ (hAPP(v5, v4) = v6)
% 208.03/28.76 | ~ (hAPP(v1, v3) = v5) | ~ (hAPP(v1, v2) = v7) | ~ $i(v4) | ~ $i(v3)
% 208.03/28.76 | ~ $i(v2)))
% 208.03/28.76
% 208.03/28.76 (fact_real__of__nat__mult)
% 208.03/28.77 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 208.03/28.77 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 208.03/28.77 c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0) & !
% 208.03/28.77 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 208.03/28.77 $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v3) = v4) | ~
% 208.03/28.77 (c_RealDef_Oreal(tc_Nat_Onat, v2) = v6) | ~ (hAPP(v5, v6) = v7) | ~
% 208.03/28.77 (hAPP(v1, v4) = v5) | ~ $i(v3) | ~ $i(v2) | ? [v8: $i] : ? [v9: $i] :
% 208.03/28.77 (c_RealDef_Oreal(tc_Nat_Onat, v9) = v7 & hAPP(v8, v2) = v9 & hAPP(v0, v3)
% 208.03/28.77 = v8 & $i(v9) & $i(v8) & $i(v7))))
% 208.03/28.77
% 208.03/28.77 (fact_real__two__squares__add__zero__iff)
% 208.03/28.77 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 208.03/28.77 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v0 &
% 208.03/28.77 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0) & !
% 208.03/28.77 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 208.03/28.77 $i] : (v3 = v1 | ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v5, v7)
% 208.03/28.77 = v1) | ~ (hAPP(v6, v2) = v7) | ~ (hAPP(v4, v3) = v5) | ~ (hAPP(v0,
% 208.03/28.77 v3) = v4) | ~ (hAPP(v0, v2) = v6) | ~ $i(v3) | ~ $i(v2)) & ! [v2:
% 208.03/28.77 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 208.03/28.77 : (v2 = v1 | ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v5, v7) = v1)
% 208.03/28.77 | ~ (hAPP(v6, v2) = v7) | ~ (hAPP(v4, v3) = v5) | ~ (hAPP(v0, v3) = v4)
% 208.03/28.77 | ~ (hAPP(v0, v2) = v6) | ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3:
% 208.03/28.77 $i] : ! [v4: $i] : (v4 = v1 | ~
% 208.03/28.77 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v3) = v4) | ~
% 208.03/28.77 (hAPP(v2, v1) = v3) | ~ (hAPP(v0, v1) = v2)))
% 208.03/28.77
% 208.03/28.77 (fact_reals__Archimedean4)
% 208.03/28.77 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 208.03/28.77 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 208.03/28.77 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & !
% 208.03/28.77 [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~
% 208.03/28.77 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) | ~
% 208.03/28.77 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | ? [v4: $i] : ?
% 208.03/28.77 [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ?
% 208.03/28.77 [v10: $i] : ? [v11: $i] : (c_Nat_OSuc(v4) = v8 &
% 208.03/28.77 c_RealDef_Oreal(tc_Nat_Onat, v8) = v9 & c_RealDef_Oreal(tc_Nat_Onat, v4)
% 208.03/28.77 = v5 & hAPP(v10, v3) = v11 & hAPP(v6, v3) = v7 & hAPP(v1, v9) = v10 &
% 208.03/28.77 hAPP(v1, v5) = v6 & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) &
% 208.03/28.77 $i(v6) & $i(v5) & $i(v4) &
% 208.03/28.77 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v7, v2) &
% 208.03/28.77 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v11))))
% 208.03/28.77
% 208.03/28.77 (fact_th)
% 208.03/28.77 $i(v_da____) & $i(tc_Complex_Ocomplex) & $i(tc_RealDef_Oreal) & $i(v_w____) &
% 208.03/28.77 $i(v_z) & ? [v0: $i] : ? [v1: $i] :
% 208.03/28.77 (c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_w____, v_z) = v0 &
% 208.03/28.77 c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v0) = v1 & $i(v1) &
% 208.03/28.77 $i(v0) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v_da____))
% 208.03/28.77
% 208.03/28.77 (fact_xt1_I7_J)
% 208.03/28.77 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2)
% 208.03/28.77 | ~ $i(v1) | ~ $i(v0) | ~ class_Orderings_Oorder(v3) | ~
% 208.03/28.77 c_Orderings_Oord__class_Oless__eq(v3, v0, v2) | ~
% 208.03/28.77 c_Orderings_Oord__class_Oless(v3, v2, v1) |
% 208.03/28.77 c_Orderings_Oord__class_Oless(v3, v0, v1))
% 208.03/28.77
% 208.03/28.77 (function-axioms)
% 208.03/28.78 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 208.03/28.78 | ~ (c_Divides_Odiv__class_Omod(v4, v3, v2) = v1) | ~
% 208.03/28.78 (c_Divides_Odiv__class_Omod(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 208.03/28.78 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 208.03/28.78 (c_Power_Opower_Opower(v4, v3, v2) = v1) | ~ (c_Power_Opower_Opower(v4, v3,
% 208.03/28.78 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 208.03/28.78 [v4: $i] : (v1 = v0 | ~ (c_Divides_Odiv__class_Odiv(v4, v3, v2) = v1) | ~
% 208.03/28.78 (c_Divides_Odiv__class_Odiv(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 208.03/28.78 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 208.03/28.78 (c_Polynomial_Osynthetic__div(v4, v3, v2) = v1) | ~
% 208.03/28.78 (c_Polynomial_Osynthetic__div(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 208.03/28.78 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 208.03/28.78 (c_Polynomial_Opcompose(v4, v3, v2) = v1) | ~ (c_Polynomial_Opcompose(v4,
% 208.03/28.78 v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 208.03/28.78 ! [v4: $i] : (v1 = v0 | ~ (c_Polynomial_Oorder(v4, v3, v2) = v1) | ~
% 208.03/28.78 (c_Polynomial_Oorder(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 208.03/28.78 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 208.03/28.78 (c_Groups_Oplus__class_Oplus(v4, v3, v2) = v1) | ~
% 208.03/28.78 (c_Groups_Oplus__class_Oplus(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 208.03/28.78 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 208.03/28.78 (c_Rings_Oinverse__class_Odivide(v4, v3, v2) = v1) | ~
% 208.03/28.78 (c_Rings_Oinverse__class_Odivide(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 208.03/28.78 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 208.03/28.78 (c_Groups_Ominus__class_Ominus(v4, v3, v2) = v1) | ~
% 208.03/28.78 (c_Groups_Ominus__class_Ominus(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 208.03/28.78 $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (c_Nat__Transfer_Otsub(v3,
% 208.03/28.78 v2) = v1) | ~ (c_Nat__Transfer_Otsub(v3, v2) = v0)) & ! [v0: $i] : !
% 208.03/28.78 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (c_Complex_Orcis(v3, v2)
% 208.03/28.78 = v1) | ~ (c_Complex_Orcis(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 208.03/28.78 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (c_RealDef_Oreal(v3, v2) = v1) | ~
% 208.03/28.78 (c_RealDef_Oreal(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 208.03/28.78 ! [v3: $i] : (v1 = v0 | ~ (tc_fun(v3, v2) = v1) | ~ (tc_fun(v3, v2) = v0)) &
% 208.03/28.78 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 208.03/28.78 (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v3, v2) = v1) | ~
% 208.03/28.78 (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v3, v2) = v0)) & ! [v0:
% 208.03/28.78 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 208.03/28.78 (c_Polynomial_Odegree(v3, v2) = v1) | ~ (c_Polynomial_Odegree(v3, v2) =
% 208.03/28.78 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 208.03/28.78 ~ (c_Polynomial_Opoly(v3, v2) = v1) | ~ (c_Polynomial_Opoly(v3, v2) = v0))
% 208.03/28.78 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 208.03/28.78 (c_RealVector_Onorm__class_Onorm(v3, v2) = v1) | ~
% 208.03/28.78 (c_RealVector_Onorm__class_Onorm(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 208.03/28.78 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP(v3, v2) = v1) | ~ (hAPP(v3,
% 208.03/28.78 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 208.03/28.78 (c_Transcendental_Oln(v2) = v1) | ~ (c_Transcendental_Oln(v2) = v0)) & !
% 208.03/28.78 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (c_Nat_OSuc(v2) = v1) |
% 208.03/28.78 ~ (c_Nat_OSuc(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 208.03/28.78 v0 | ~ (c_Power_Opower__class_Opower(v2) = v1) | ~
% 208.03/28.78 (c_Power_Opower__class_Opower(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 208.03/28.78 [v2: $i] : (v1 = v0 | ~ (c_RComplete_Onatfloor(v2) = v1) | ~
% 208.03/28.78 (c_RComplete_Onatfloor(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 208.03/28.78 : (v1 = v0 | ~ (c_RComplete_Onatceiling(v2) = v1) | ~
% 208.03/28.78 (c_RComplete_Onatceiling(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 208.03/28.78 $i] : (v1 = v0 | ~ (c_Complex_Oexpi(v2) = v1) | ~ (c_Complex_Oexpi(v2) =
% 208.03/28.78 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 208.03/28.78 (c_Groups_Oone__class_Oone(v2) = v1) | ~ (c_Groups_Oone__class_Oone(v2) =
% 208.03/28.78 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 208.03/28.78 (tc_Polynomial_Opoly(v2) = v1) | ~ (tc_Polynomial_Opoly(v2) = v0)) & !
% 208.03/28.78 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 208.03/28.78 (c_Groups_Otimes__class_Otimes(v2) = v1) | ~
% 208.03/28.78 (c_Groups_Otimes__class_Otimes(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 208.03/28.78 [v2: $i] : (v1 = v0 | ~ (c_Groups_Ozero__class_Ozero(v2) = v1) | ~
% 208.03/28.78 (c_Groups_Ozero__class_Ozero(v2) = v0))
% 208.03/28.78
% 208.03/28.78 Further assumptions not needed in the proof:
% 208.03/28.78 --------------------------------------------
% 208.03/28.79 arity_Complex__Ocomplex__Fields_Ofield,
% 208.03/28.79 arity_Complex__Ocomplex__Fields_Ofield__inverse__zero,
% 208.03/28.79 arity_Complex__Ocomplex__Groups_Oab__group__add,
% 208.03/28.79 arity_Complex__Ocomplex__Groups_Oab__semigroup__add,
% 208.03/28.79 arity_Complex__Ocomplex__Groups_Oab__semigroup__mult,
% 208.03/28.79 arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add,
% 208.03/28.79 arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add,
% 208.03/28.79 arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add,
% 208.03/28.79 arity_Complex__Ocomplex__Groups_Ocomm__monoid__add,
% 208.03/28.79 arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult,
% 208.03/28.79 arity_Complex__Ocomplex__Groups_Ogroup__add,
% 208.03/28.79 arity_Complex__Ocomplex__Groups_Omonoid__add,
% 208.03/28.79 arity_Complex__Ocomplex__Groups_Omonoid__mult,
% 208.03/28.79 arity_Complex__Ocomplex__Groups_Oone, arity_Complex__Ocomplex__Groups_Ozero,
% 208.03/28.79 arity_Complex__Ocomplex__Int_Oring__char__0,
% 208.03/28.79 arity_Complex__Ocomplex__Power_Opower,
% 208.03/28.79 arity_Complex__Ocomplex__RealVector_Oreal__field,
% 208.03/28.79 arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra,
% 208.03/28.79 arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1,
% 208.03/28.79 arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra,
% 208.03/28.79 arity_Complex__Ocomplex__RealVector_Oreal__normed__field,
% 208.03/28.79 arity_Complex__Ocomplex__RealVector_Oreal__normed__vector,
% 208.03/28.79 arity_Complex__Ocomplex__Rings_Ocomm__ring,
% 208.03/28.79 arity_Complex__Ocomplex__Rings_Ocomm__ring__1,
% 208.03/28.79 arity_Complex__Ocomplex__Rings_Ocomm__semiring,
% 208.03/28.79 arity_Complex__Ocomplex__Rings_Ocomm__semiring__0,
% 208.03/28.79 arity_Complex__Ocomplex__Rings_Ocomm__semiring__1,
% 208.03/28.79 arity_Complex__Ocomplex__Rings_Odivision__ring,
% 208.03/28.79 arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero,
% 208.03/28.79 arity_Complex__Ocomplex__Rings_Oidom,
% 208.03/28.79 arity_Complex__Ocomplex__Rings_Omult__zero,
% 208.03/28.79 arity_Complex__Ocomplex__Rings_Ono__zero__divisors,
% 208.03/28.79 arity_Complex__Ocomplex__Rings_Oring, arity_Complex__Ocomplex__Rings_Oring__1,
% 208.03/28.79 arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors,
% 208.03/28.79 arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors,
% 208.03/28.79 arity_Complex__Ocomplex__Rings_Osemiring,
% 208.03/28.79 arity_Complex__Ocomplex__Rings_Osemiring__0,
% 208.03/28.79 arity_Complex__Ocomplex__Rings_Ozero__neq__one,
% 208.03/28.79 arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
% 208.03/28.79 arity_HOL__Obool__Orderings_Oord, arity_HOL__Obool__Orderings_Oorder,
% 208.03/28.79 arity_HOL__Obool__Orderings_Opreorder, arity_Int__Oint__Divides_Oring__div,
% 208.03/28.79 arity_Int__Oint__Divides_Osemiring__div,
% 208.03/28.79 arity_Int__Oint__Groups_Oab__group__add,
% 208.03/28.79 arity_Int__Oint__Groups_Oab__semigroup__add,
% 208.03/28.79 arity_Int__Oint__Groups_Oab__semigroup__mult,
% 208.03/28.79 arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,
% 208.03/28.79 arity_Int__Oint__Groups_Ocancel__comm__monoid__add,
% 208.03/28.79 arity_Int__Oint__Groups_Ocancel__semigroup__add,
% 208.03/28.79 arity_Int__Oint__Groups_Ocomm__monoid__add,
% 208.03/28.79 arity_Int__Oint__Groups_Ocomm__monoid__mult,
% 208.03/28.79 arity_Int__Oint__Groups_Ogroup__add,
% 208.03/28.79 arity_Int__Oint__Groups_Olinordered__ab__group__add,
% 208.03/28.79 arity_Int__Oint__Groups_Omonoid__add, arity_Int__Oint__Groups_Omonoid__mult,
% 208.03/28.79 arity_Int__Oint__Groups_Oone, arity_Int__Oint__Groups_Oordered__ab__group__add,
% 208.03/28.79 arity_Int__Oint__Groups_Oordered__ab__semigroup__add,
% 208.03/28.79 arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,
% 208.03/28.79 arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,
% 208.03/28.79 arity_Int__Oint__Groups_Oordered__comm__monoid__add,
% 208.03/28.79 arity_Int__Oint__Groups_Ozero, arity_Int__Oint__Int_Oring__char__0,
% 208.03/28.79 arity_Int__Oint__Orderings_Olinorder, arity_Int__Oint__Orderings_Oord,
% 208.03/28.79 arity_Int__Oint__Orderings_Oorder, arity_Int__Oint__Orderings_Opreorder,
% 208.03/28.79 arity_Int__Oint__Power_Opower, arity_Int__Oint__Rings_Ocomm__ring,
% 208.03/28.79 arity_Int__Oint__Rings_Ocomm__ring__1, arity_Int__Oint__Rings_Ocomm__semiring,
% 208.03/28.79 arity_Int__Oint__Rings_Ocomm__semiring__0,
% 208.03/28.79 arity_Int__Oint__Rings_Ocomm__semiring__1, arity_Int__Oint__Rings_Oidom,
% 208.03/28.79 arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,
% 208.03/28.79 arity_Int__Oint__Rings_Olinordered__idom,
% 208.03/28.79 arity_Int__Oint__Rings_Olinordered__ring,
% 208.03/28.79 arity_Int__Oint__Rings_Olinordered__ring__strict,
% 208.03/28.79 arity_Int__Oint__Rings_Olinordered__semidom,
% 208.03/28.79 arity_Int__Oint__Rings_Olinordered__semiring,
% 208.03/28.79 arity_Int__Oint__Rings_Olinordered__semiring__1,
% 208.03/28.79 arity_Int__Oint__Rings_Olinordered__semiring__1__strict,
% 208.03/28.79 arity_Int__Oint__Rings_Olinordered__semiring__strict,
% 208.03/28.79 arity_Int__Oint__Rings_Omult__zero, arity_Int__Oint__Rings_Ono__zero__divisors,
% 208.03/28.79 arity_Int__Oint__Rings_Oordered__cancel__semiring,
% 208.03/28.79 arity_Int__Oint__Rings_Oordered__comm__semiring,
% 208.03/28.79 arity_Int__Oint__Rings_Oordered__ring,
% 208.03/28.79 arity_Int__Oint__Rings_Oordered__semiring, arity_Int__Oint__Rings_Oring,
% 208.03/28.79 arity_Int__Oint__Rings_Oring__1,
% 208.03/28.79 arity_Int__Oint__Rings_Oring__1__no__zero__divisors,
% 208.03/28.79 arity_Int__Oint__Rings_Oring__no__zero__divisors,
% 208.03/28.79 arity_Int__Oint__Rings_Osemiring, arity_Int__Oint__Rings_Osemiring__0,
% 208.03/28.79 arity_Int__Oint__Rings_Ozero__neq__one,
% 208.03/28.79 arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
% 208.03/28.79 arity_Nat__Onat__Divides_Osemiring__div,
% 208.03/28.79 arity_Nat__Onat__Groups_Oab__semigroup__add,
% 208.03/28.79 arity_Nat__Onat__Groups_Oab__semigroup__mult,
% 208.03/28.79 arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,
% 208.03/28.79 arity_Nat__Onat__Groups_Ocancel__comm__monoid__add,
% 208.03/28.79 arity_Nat__Onat__Groups_Ocancel__semigroup__add,
% 208.03/28.79 arity_Nat__Onat__Groups_Ocomm__monoid__add,
% 208.03/28.79 arity_Nat__Onat__Groups_Ocomm__monoid__mult,
% 208.03/28.79 arity_Nat__Onat__Groups_Omonoid__add, arity_Nat__Onat__Groups_Omonoid__mult,
% 208.03/28.79 arity_Nat__Onat__Groups_Oone,
% 208.03/28.79 arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,
% 208.03/28.79 arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,
% 208.03/28.79 arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,
% 208.03/28.79 arity_Nat__Onat__Groups_Oordered__comm__monoid__add,
% 208.03/28.79 arity_Nat__Onat__Groups_Ozero, arity_Nat__Onat__Orderings_Olinorder,
% 208.03/28.79 arity_Nat__Onat__Orderings_Oord, arity_Nat__Onat__Orderings_Oorder,
% 208.03/28.79 arity_Nat__Onat__Orderings_Opreorder, arity_Nat__Onat__Power_Opower,
% 208.03/28.79 arity_Nat__Onat__Rings_Ocomm__semiring,
% 208.03/28.79 arity_Nat__Onat__Rings_Ocomm__semiring__0,
% 208.03/28.79 arity_Nat__Onat__Rings_Ocomm__semiring__1,
% 208.03/28.79 arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,
% 208.03/28.79 arity_Nat__Onat__Rings_Olinordered__semidom,
% 208.03/28.79 arity_Nat__Onat__Rings_Olinordered__semiring,
% 208.03/28.79 arity_Nat__Onat__Rings_Olinordered__semiring__strict,
% 208.03/28.79 arity_Nat__Onat__Rings_Omult__zero, arity_Nat__Onat__Rings_Ono__zero__divisors,
% 208.03/28.79 arity_Nat__Onat__Rings_Oordered__cancel__semiring,
% 208.03/28.79 arity_Nat__Onat__Rings_Oordered__comm__semiring,
% 208.03/28.79 arity_Nat__Onat__Rings_Oordered__semiring, arity_Nat__Onat__Rings_Osemiring,
% 208.03/28.79 arity_Nat__Onat__Rings_Osemiring__0, arity_Nat__Onat__Rings_Ozero__neq__one,
% 208.03/28.79 arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
% 208.03/28.79 arity_Polynomial__Opoly__Divides_Oring__div,
% 208.03/28.79 arity_Polynomial__Opoly__Divides_Osemiring__div,
% 208.03/28.79 arity_Polynomial__Opoly__Groups_Oab__group__add,
% 208.03/28.79 arity_Polynomial__Opoly__Groups_Oab__semigroup__add,
% 208.03/28.79 arity_Polynomial__Opoly__Groups_Oab__semigroup__mult,
% 208.03/28.79 arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add,
% 208.03/28.79 arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add,
% 208.03/28.79 arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add,
% 208.03/28.79 arity_Polynomial__Opoly__Groups_Ocomm__monoid__add,
% 208.03/28.79 arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult,
% 208.03/28.79 arity_Polynomial__Opoly__Groups_Ogroup__add,
% 208.03/28.79 arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add,
% 208.03/28.79 arity_Polynomial__Opoly__Groups_Omonoid__add,
% 208.03/28.79 arity_Polynomial__Opoly__Groups_Omonoid__mult,
% 208.03/28.79 arity_Polynomial__Opoly__Groups_Oone,
% 208.03/28.79 arity_Polynomial__Opoly__Groups_Oordered__ab__group__add,
% 208.03/28.79 arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add,
% 208.03/28.79 arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le,
% 208.03/28.79 arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add,
% 208.03/28.79 arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add,
% 208.03/28.79 arity_Polynomial__Opoly__Groups_Ozero,
% 208.03/28.79 arity_Polynomial__Opoly__Int_Oring__char__0,
% 208.03/28.79 arity_Polynomial__Opoly__Orderings_Olinorder,
% 208.03/28.79 arity_Polynomial__Opoly__Orderings_Oord,
% 208.03/28.79 arity_Polynomial__Opoly__Orderings_Oorder,
% 208.03/28.79 arity_Polynomial__Opoly__Orderings_Opreorder,
% 208.03/28.79 arity_Polynomial__Opoly__Power_Opower,
% 208.03/28.79 arity_Polynomial__Opoly__Rings_Ocomm__ring,
% 208.03/28.79 arity_Polynomial__Opoly__Rings_Ocomm__ring__1,
% 208.03/28.79 arity_Polynomial__Opoly__Rings_Ocomm__semiring,
% 208.03/28.79 arity_Polynomial__Opoly__Rings_Ocomm__semiring__0,
% 208.03/28.79 arity_Polynomial__Opoly__Rings_Ocomm__semiring__1,
% 208.03/28.79 arity_Polynomial__Opoly__Rings_Oidom,
% 208.03/28.79 arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict,
% 208.03/28.79 arity_Polynomial__Opoly__Rings_Olinordered__idom,
% 208.03/28.79 arity_Polynomial__Opoly__Rings_Olinordered__ring,
% 208.03/28.79 arity_Polynomial__Opoly__Rings_Olinordered__ring__strict,
% 208.03/28.79 arity_Polynomial__Opoly__Rings_Olinordered__semidom,
% 208.03/28.79 arity_Polynomial__Opoly__Rings_Olinordered__semiring,
% 208.03/28.79 arity_Polynomial__Opoly__Rings_Olinordered__semiring__1,
% 208.03/28.79 arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict,
% 208.03/28.79 arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict,
% 208.03/28.79 arity_Polynomial__Opoly__Rings_Omult__zero,
% 208.03/28.79 arity_Polynomial__Opoly__Rings_Ono__zero__divisors,
% 208.03/28.79 arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring,
% 208.03/28.79 arity_Polynomial__Opoly__Rings_Oordered__comm__semiring,
% 208.03/28.79 arity_Polynomial__Opoly__Rings_Oordered__ring,
% 208.03/28.79 arity_Polynomial__Opoly__Rings_Oordered__semiring,
% 208.03/28.79 arity_Polynomial__Opoly__Rings_Oring, arity_Polynomial__Opoly__Rings_Oring__1,
% 208.03/28.79 arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors,
% 208.03/28.79 arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors,
% 208.03/28.79 arity_Polynomial__Opoly__Rings_Osemiring,
% 208.03/28.79 arity_Polynomial__Opoly__Rings_Osemiring__0,
% 208.03/28.79 arity_Polynomial__Opoly__Rings_Ozero__neq__one,
% 208.03/28.79 arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
% 208.03/28.79 arity_RealDef__Oreal__Fields_Ofield,
% 208.03/28.79 arity_RealDef__Oreal__Fields_Ofield__inverse__zero,
% 208.03/28.79 arity_RealDef__Oreal__Fields_Olinordered__field,
% 208.03/28.79 arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero,
% 208.03/28.79 arity_RealDef__Oreal__Groups_Oab__group__add,
% 208.03/28.79 arity_RealDef__Oreal__Groups_Oab__semigroup__add,
% 208.03/28.79 arity_RealDef__Oreal__Groups_Oab__semigroup__mult,
% 208.03/28.79 arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add,
% 208.03/28.79 arity_RealDef__Oreal__Groups_Ocancel__comm__monoid__add,
% 208.03/28.79 arity_RealDef__Oreal__Groups_Ocancel__semigroup__add,
% 208.03/28.79 arity_RealDef__Oreal__Groups_Ocomm__monoid__add,
% 208.03/28.79 arity_RealDef__Oreal__Groups_Ocomm__monoid__mult,
% 208.03/28.79 arity_RealDef__Oreal__Groups_Ogroup__add,
% 208.03/28.79 arity_RealDef__Oreal__Groups_Olinordered__ab__group__add,
% 208.03/28.79 arity_RealDef__Oreal__Groups_Omonoid__add,
% 208.03/28.79 arity_RealDef__Oreal__Groups_Omonoid__mult, arity_RealDef__Oreal__Groups_Oone,
% 208.03/28.79 arity_RealDef__Oreal__Groups_Oordered__ab__group__add,
% 208.03/28.79 arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add,
% 208.03/28.79 arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le,
% 208.03/28.79 arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add,
% 208.03/28.79 arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add,
% 208.03/28.79 arity_RealDef__Oreal__Groups_Ozero, arity_RealDef__Oreal__Int_Oring__char__0,
% 208.03/28.79 arity_RealDef__Oreal__Orderings_Olinorder, arity_RealDef__Oreal__Orderings_Oord,
% 208.03/28.79 arity_RealDef__Oreal__Orderings_Opreorder, arity_RealDef__Oreal__Power_Opower,
% 208.03/28.79 arity_RealDef__Oreal__RealVector_Oreal__field,
% 208.03/28.79 arity_RealDef__Oreal__RealVector_Oreal__normed__algebra,
% 208.03/28.79 arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1,
% 208.03/28.79 arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra,
% 208.03/28.79 arity_RealDef__Oreal__RealVector_Oreal__normed__field,
% 208.03/28.79 arity_RealDef__Oreal__RealVector_Oreal__normed__vector,
% 208.03/28.79 arity_RealDef__Oreal__Rings_Ocomm__ring,
% 208.03/28.79 arity_RealDef__Oreal__Rings_Ocomm__ring__1,
% 208.03/28.79 arity_RealDef__Oreal__Rings_Ocomm__semiring,
% 208.03/28.79 arity_RealDef__Oreal__Rings_Ocomm__semiring__0,
% 208.03/28.79 arity_RealDef__Oreal__Rings_Ocomm__semiring__1,
% 208.03/28.79 arity_RealDef__Oreal__Rings_Odivision__ring,
% 208.03/28.79 arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero,
% 208.03/28.79 arity_RealDef__Oreal__Rings_Oidom,
% 208.03/28.79 arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict,
% 208.03/28.79 arity_RealDef__Oreal__Rings_Olinordered__idom,
% 208.03/28.79 arity_RealDef__Oreal__Rings_Olinordered__ring,
% 208.03/28.79 arity_RealDef__Oreal__Rings_Olinordered__ring__strict,
% 208.03/28.79 arity_RealDef__Oreal__Rings_Olinordered__semidom,
% 208.03/28.79 arity_RealDef__Oreal__Rings_Olinordered__semiring,
% 208.03/28.79 arity_RealDef__Oreal__Rings_Olinordered__semiring__1,
% 208.03/28.79 arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict,
% 208.03/28.79 arity_RealDef__Oreal__Rings_Olinordered__semiring__strict,
% 208.03/28.79 arity_RealDef__Oreal__Rings_Omult__zero,
% 208.03/28.79 arity_RealDef__Oreal__Rings_Ono__zero__divisors,
% 208.03/28.79 arity_RealDef__Oreal__Rings_Oordered__cancel__semiring,
% 208.03/28.79 arity_RealDef__Oreal__Rings_Oordered__comm__semiring,
% 208.03/28.79 arity_RealDef__Oreal__Rings_Oordered__ring,
% 208.03/28.79 arity_RealDef__Oreal__Rings_Oordered__semiring,
% 208.03/28.79 arity_RealDef__Oreal__Rings_Oring, arity_RealDef__Oreal__Rings_Oring__1,
% 208.03/28.79 arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors,
% 208.03/28.79 arity_RealDef__Oreal__Rings_Oring__no__zero__divisors,
% 208.03/28.79 arity_RealDef__Oreal__Rings_Osemiring, arity_RealDef__Oreal__Rings_Osemiring__0,
% 208.03/28.79 arity_RealDef__Oreal__Rings_Ozero__neq__one,
% 208.03/28.79 arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
% 208.03/28.79 arity_fun__Orderings_Oord, arity_fun__Orderings_Oorder,
% 208.03/28.79 arity_fun__Orderings_Opreorder, fact_DERIV__mult__lemma,
% 208.03/28.79 fact_DIVISION__BY__ZERO, fact_Deriv_Oadd__diff__add,
% 208.03/28.79 fact_Divides_Otransfer__nat__int__function__closures_I1_J,
% 208.03/28.79 fact_Divides_Otransfer__nat__int__function__closures_I2_J, fact_H_I1_J,
% 208.03/28.79 fact_H_I2_J, fact_H_I3_J, fact_H_I4_J, fact_H_I5_J, fact_Nat_Oadd__0__right,
% 208.03/28.79 fact_Nat_Odiff__diff__eq,
% 208.03/28.79 fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,
% 208.03/28.79 fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,
% 208.03/28.79 fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,
% 208.03/28.79 fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,
% 208.03/28.79 fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,
% 208.03/28.79 fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,
% 208.03/28.79 fact_One__nat__def, fact_Suc__diff__1, fact_Suc__diff__diff, fact_Suc__diff__le,
% 208.03/28.79 fact_Suc__eq__plus1, fact_Suc__eq__plus1__left, fact_Suc__inject, fact_Suc__leD,
% 208.03/28.79 fact_Suc__leI, fact_Suc__le__eq, fact_Suc__le__lessD, fact_Suc__le__mono,
% 208.03/28.79 fact_Suc__lessD, fact_Suc__lessI, fact_Suc__less__SucD, fact_Suc__less__eq,
% 208.03/28.79 fact_Suc__mono, fact_Suc__mult__cancel1, fact_Suc__mult__le__cancel1,
% 208.03/28.79 fact_Suc__mult__less__cancel1, fact_Suc__n__not__le__n, fact_Suc__n__not__n,
% 208.03/28.79 fact_Suc__neq__Zero, fact_Suc__not__Zero, fact_Suc__pred, fact_Suc__pred_H,
% 208.03/28.79 fact_Zero__neq__Suc, fact_Zero__not__Suc,
% 208.03/28.79 fact__096EX_Aea_0620_O_Aea_A_060_A1_A_G_Aea_A_060_Ae_A_P_Am_096,
% 208.03/28.79 fact__096EX_Am_0620_O_AALL_Az_O_Acmod_Az_A_060_061_A1_A_N_N_062_Acmod_A_Ipoly_Acs_Az_J_A_060_061_Am_096,
% 208.03/28.79 fact__096_B_Bthesis_O_A_I_B_Bd_O_A_091_124_A0_A_060_Ad_059_Ad_A_060_A1_059_Ad_A_060_Ae_A_P_Am_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,
% 208.03/28.79 fact__096_B_Bthesis_O_A_I_B_Bm_O_A_091_124_A0_A_060_Am_059_A_B_Bz_O_Acmod_Az_A_060_061_A1_A_061_061_062_Acmod_A_Ipoly_Acs_Az_J_A_060_061_Am_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,
% 208.03/28.79 fact__096_B_Bthesis_O_A_I_B_Bq_O_A_091_124_Adegree_Aq_A_061_Adegree_Ap_059_A_B_Bx_O_Apoly_Aq_Ax_A_061_Apoly_Ap_A_Iz_A_L_Ax_J_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,
% 208.03/28.79 fact__096_B_Bw_O_Apoly_Aq_A_Iw_A_N_Az_J_A_061_Apoly_Ap_Aw_096,
% 208.03/28.79 fact_ab__semigroup__add__class_Oadd__ac_I1_J,
% 208.03/28.79 fact_ab__semigroup__mult__class_Omult__ac_I1_J, fact_add1__zle__eq,
% 208.03/28.79 fact_add_Ocomm__neutral, fact_add__0, fact_add__0__iff, fact_add__0__left,
% 208.03/28.79 fact_add__0__right, fact_add__Suc, fact_add__Suc__right, fact_add__Suc__shift,
% 208.03/28.79 fact_add__diff__assoc, fact_add__diff__assoc2, fact_add__diff__cancel,
% 208.03/28.79 fact_add__diff__inverse, fact_add__divide__distrib, fact_add__divide__eq__iff,
% 208.03/28.79 fact_add__eq__if, fact_add__eq__self__zero, fact_add__frac__eq,
% 208.03/28.79 fact_add__frac__num, fact_add__gr__0, fact_add__imp__eq, fact_add__increasing,
% 208.03/28.79 fact_add__increasing2, fact_add__is__0, fact_add__is__1, fact_add__leD1,
% 208.03/28.79 fact_add__leD2, fact_add__leE, fact_add__le__cancel__left,
% 208.03/28.79 fact_add__le__cancel__right, fact_add__le__imp__le__left,
% 208.03/28.79 fact_add__le__imp__le__right, fact_add__le__less__mono, fact_add__le__mono,
% 208.03/28.79 fact_add__le__mono1, fact_add__left__cancel, fact_add__left__imp__eq,
% 208.03/28.79 fact_add__left__mono, fact_add__lessD1, fact_add__less__cancel__left,
% 208.03/28.79 fact_add__less__cancel__right, fact_add__less__imp__less__left,
% 208.03/28.79 fact_add__less__imp__less__right, fact_add__less__le__mono,
% 208.03/28.79 fact_add__less__mono, fact_add__less__mono1, fact_add__mono,
% 208.03/28.79 fact_add__mult__distrib, fact_add__mult__distrib2, fact_add__neg__neg,
% 208.03/28.79 fact_add__neg__nonpos, fact_add__nonneg__eq__0__iff, fact_add__nonneg__nonneg,
% 208.03/28.79 fact_add__nonneg__pos, fact_add__nonpos__neg, fact_add__nonpos__nonpos,
% 208.03/28.79 fact_add__num__frac, fact_add__poly__code_I1_J, fact_add__poly__code_I2_J,
% 208.03/28.79 fact_add__pos__nonneg, fact_add__pos__pos, fact_add__right__cancel,
% 208.03/28.79 fact_add__right__imp__eq, fact_add__right__mono, fact_add__scale__eq__noteq,
% 208.03/28.79 fact_add__strict__increasing, fact_add__strict__increasing2,
% 208.03/28.79 fact_add__strict__left__mono, fact_add__strict__mono,
% 208.03/28.79 fact_add__strict__right__mono, fact_assms, fact_combine__common__factor,
% 208.03/28.79 fact_comm__mult__left__mono, fact_comm__mult__strict__left__mono,
% 208.03/28.79 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,
% 208.03/28.79 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,
% 208.03/28.79 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,
% 208.03/28.79 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,
% 208.03/28.79 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,
% 208.03/28.79 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,
% 208.03/28.79 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,
% 208.03/28.79 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,
% 208.03/28.79 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,
% 208.03/28.79 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,
% 208.03/28.79 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,
% 208.03/28.79 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,
% 208.03/28.79 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,
% 208.03/28.79 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,
% 208.03/28.79 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,
% 208.03/28.79 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,
% 208.03/28.79 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,
% 208.03/28.79 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,
% 208.03/28.79 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,
% 208.03/28.79 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,
% 208.03/28.79 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,
% 208.03/28.79 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,
% 208.03/28.79 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,
% 208.03/28.79 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,
% 208.03/28.79 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,
% 208.03/28.79 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,
% 208.03/28.79 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,
% 208.03/28.79 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,
% 208.03/28.79 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,
% 208.03/28.79 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,
% 208.03/28.79 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,
% 208.03/28.79 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,
% 208.03/28.79 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,
% 208.03/28.79 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,
% 208.03/28.79 fact_comm__semiring__class_Odistrib, fact_complex__i__not__one,
% 208.03/28.79 fact_complex__i__not__zero, fact_complex__mod__triangle__ineq2,
% 208.03/28.79 fact_complex__mod__triangle__sub, fact_convex__bound__le,
% 208.03/28.79 fact_convex__bound__lt, fact_crossproduct__eq, fact_crossproduct__noteq,
% 208.03/28.79 fact_d1_I2_J, fact_d_I1_J, fact_d_I2_J, fact_d_I3_J, fact_decseq__def,
% 208.03/28.79 fact_degree__0, fact_degree__1, fact_degree__add__eq__left,
% 208.03/28.79 fact_degree__add__eq__right, fact_degree__add__le, fact_degree__add__less,
% 208.03/28.79 fact_degree__diff__le, fact_degree__diff__less, fact_degree__mult__eq,
% 208.03/28.79 fact_degree__mult__le, fact_degree__pcompose__le, fact_degree__power__le,
% 208.03/28.79 fact_degree__synthetic__div, fact_diff__0__eq__0, fact_diff__0__right,
% 208.03/28.79 fact_diff__Suc__1, fact_diff__Suc__Suc, fact_diff__Suc__diff__eq1,
% 208.03/28.79 fact_diff__Suc__diff__eq2, fact_diff__Suc__eq__diff__pred, fact_diff__Suc__less,
% 208.03/28.79 fact_diff__add__0, fact_diff__add__assoc, fact_diff__add__assoc2,
% 208.03/28.79 fact_diff__add__cancel, fact_diff__add__inverse, fact_diff__add__inverse2,
% 208.03/28.79 fact_diff__cancel, fact_diff__cancel2, fact_diff__commute,
% 208.03/28.79 fact_diff__diff__cancel, fact_diff__diff__left, fact_diff__diff__right,
% 208.03/28.79 fact_diff__divide__distrib, fact_diff__divide__eq__iff, fact_diff__eq__diff__eq,
% 208.03/28.79 fact_diff__eq__diff__less, fact_diff__eq__diff__less__eq, fact_diff__frac__eq,
% 208.03/28.79 fact_diff__is__0__eq, fact_diff__is__0__eq_H, fact_diff__le__mono,
% 208.03/28.79 fact_diff__le__mono2, fact_diff__le__self, fact_diff__less,
% 208.03/28.79 fact_diff__less__Suc, fact_diff__less__mono, fact_diff__less__mono2,
% 208.03/28.79 fact_diff__mult__distrib, fact_diff__mult__distrib2, fact_diff__poly__code_I2_J,
% 208.03/28.79 fact_diff__self, fact_diff__self__eq__0, fact_diffs0__imp__equal, fact_div__0,
% 208.03/28.79 fact_div__1, fact_div__add1__eq, fact_div__add__self1, fact_div__add__self2,
% 208.03/28.79 fact_div__by__0, fact_div__by__1, fact_div__geq, fact_div__if,
% 208.03/28.79 fact_div__le__dividend, fact_div__le__mono, fact_div__le__mono2, fact_div__less,
% 208.03/28.79 fact_div__less__dividend, fact_div__mult2__eq, fact_div__mult__mult1,
% 208.03/28.79 fact_div__mult__mult1__if, fact_div__mult__mult2, fact_div__mult__self1,
% 208.03/28.79 fact_div__mult__self1__is__id, fact_div__mult__self1__is__m,
% 208.03/28.79 fact_div__mult__self2, fact_div__mult__self2__is__id,
% 208.03/28.79 fact_div__mult__self__is__m, fact_div__neg__neg__trivial,
% 208.03/28.79 fact_div__neg__pos__less0, fact_div__nonneg__neg__le0,
% 208.03/28.79 fact_div__nonpos__pos__le0, fact_div__poly__eq, fact_div__poly__less,
% 208.03/28.79 fact_div__pos__pos__trivial, fact_div__self, fact_divide_Oadd,
% 208.03/28.79 fact_divide_Odiff, fact_divide_Ozero, fact_divide__1, fact_divide__add__eq__iff,
% 208.03/28.79 fact_divide__diff__eq__iff, fact_divide__eq__eq, fact_divide__eq__imp,
% 208.03/28.79 fact_divide__le__0__iff, fact_divide__le__eq, fact_divide__left__mono,
% 208.03/28.79 fact_divide__left__mono__neg, fact_divide__less__0__iff, fact_divide__less__eq,
% 208.03/28.79 fact_divide__neg__neg, fact_divide__neg__pos, fact_divide__nonneg__neg,
% 208.03/28.79 fact_divide__nonneg__pos, fact_divide__nonpos__neg, fact_divide__nonpos__pos,
% 208.03/28.79 fact_divide__pos__neg, fact_divide__pos__pos, fact_divide__right__mono,
% 208.03/28.79 fact_divide__right__mono__neg, fact_divide__self, fact_divide__self__if,
% 208.03/28.79 fact_divide__strict__left__mono, fact_divide__strict__left__mono__neg,
% 208.03/28.79 fact_divide__strict__right__mono, fact_divide__strict__right__mono__neg,
% 208.03/28.79 fact_divide__zero, fact_divide__zero__left, fact_divisors__zero,
% 208.03/28.79 fact_divmod__int__rel__div__eq, fact_dm_I1_J, fact_dm_I2_J,
% 208.03/28.79 fact_double__add__le__zero__iff__single__add__le__zero,
% 208.03/28.79 fact_double__add__less__zero__iff__single__add__less__zero,
% 208.03/28.79 fact_double__eq__0__iff, fact_double__zero__sym, fact_em0, fact_eq__add__iff1,
% 208.03/28.79 fact_eq__add__iff2, fact_eq__diff__iff, fact_eq__divide__eq,
% 208.03/28.79 fact_eq__divide__imp, fact_eq__iff__diff__eq__0, fact_eq__imp__le,
% 208.03/28.79 fact_even__less__0__iff, fact_ex__least__nat__less, fact_expi__add,
% 208.03/28.79 fact_expi__zero, fact_ext, fact_field__le__mult__one__interval,
% 208.03/28.79 fact_field__power__not__zero, fact_frac__eq__eq, fact_frac__le, fact_frac__less,
% 208.03/28.79 fact_frac__less2, fact_ge__natfloor__plus__one__imp__gt, fact_gr0I,
% 208.03/28.79 fact_gr0__conv__Suc, fact_gr__implies__not0, fact_gt__half__sum,
% 208.03/28.79 fact_int__0__less__1, fact_int__0__neq__1, fact_int__div__less__self,
% 208.03/28.79 fact_int__one__le__iff__zero__less, fact_int__power__div__base, fact_le0,
% 208.03/28.79 fact_leD, fact_leI, fact_le__0__eq, fact_le__SucE, fact_le__SucI,
% 208.03/28.79 fact_le__Suc__eq, fact_le__Suc__ex__iff, fact_le__add1, fact_le__add2,
% 208.03/28.79 fact_le__add__diff, fact_le__add__diff__inverse, fact_le__add__diff__inverse2,
% 208.03/28.79 fact_le__add__iff1, fact_le__add__iff2, fact_le__antisym, fact_le__cube,
% 208.03/28.79 fact_le__diff__conv, fact_le__diff__conv2, fact_le__diff__iff,
% 208.03/28.79 fact_le__div__geq, fact_le__divide__eq, fact_le__eq__less__or__eq,
% 208.03/28.79 fact_le__funD, fact_le__funE, fact_le__fun__def, fact_le__iff__add,
% 208.03/28.79 fact_le__iff__diff__le__0, fact_le__imp__0__less, fact_le__imp__diff__is__add,
% 208.03/28.79 fact_le__imp__less__Suc, fact_le__less__Suc__eq, fact_le__mod__geq,
% 208.03/28.79 fact_le__natfloor, fact_le__natfloor__eq, fact_le__natfloor__eq__one,
% 208.03/28.79 fact_le__neq__implies__less, fact_le__refl, fact_le__square, fact_le__trans,
% 208.03/28.79 fact_left__add__mult__distrib, fact_lemmaCauchy, fact_lemma__NBseq__def,
% 208.03/28.79 fact_lemma__NBseq__def2, fact_lemma__realpow__diff, fact_lessI,
% 208.03/28.79 fact_less__1__mult, fact_less__Suc0, fact_less__SucE, fact_less__SucI,
% 208.03/28.79 fact_less__Suc__eq, fact_less__Suc__eq__0__disj, fact_less__Suc__eq__le,
% 208.03/28.79 fact_less__add__Suc1, fact_less__add__Suc2, fact_less__add__eq__less,
% 208.03/28.79 fact_less__add__iff1, fact_less__add__iff2, fact_less__add__one,
% 208.03/28.79 fact_less__antisym, fact_less__bin__lemma, fact_less__diff__conv,
% 208.03/28.79 fact_less__diff__iff, fact_less__divide__eq, fact_less__eq__Suc__le,
% 208.03/28.79 fact_less__eq__nat_Osimps_I1_J, fact_less__eq__real__def, fact_less__fun__def,
% 208.03/28.79 fact_less__half__sum, fact_less__iff__Suc__add, fact_less__iff__diff__less__0,
% 208.03/28.79 fact_less__imp__diff__less, fact_less__imp__le__nat, fact_less__imp__neq,
% 208.03/28.79 fact_less__irrefl__nat, fact_less__le__not__le, fact_less__nat__zero__code,
% 208.03/28.79 fact_less__natfloor, fact_less__not__refl, fact_less__not__refl2,
% 208.03/28.79 fact_less__not__refl3, fact_less__or__eq__imp__le, fact_less__trans__Suc,
% 208.03/28.79 fact_less__zeroE, fact_linorder__antisym__conv1, fact_linorder__antisym__conv2,
% 208.03/28.79 fact_linorder__antisym__conv3, fact_linorder__cases, fact_linorder__le__cases,
% 208.03/28.79 fact_linorder__le__less__linear, fact_linorder__less__linear,
% 208.03/28.79 fact_linorder__linear, fact_linorder__neqE,
% 208.03/28.79 fact_linorder__neqE__linordered__idom, fact_linorder__neqE__nat,
% 208.03/28.79 fact_linorder__neq__iff, fact_linorder__not__le, fact_linorder__not__less,
% 208.03/28.79 fact_ln__add__one__self__le__self, fact_ln__div, fact_ln__eq__zero__iff,
% 208.03/28.79 fact_ln__ge__zero, fact_ln__ge__zero__iff, fact_ln__ge__zero__imp__ge__one,
% 208.03/28.79 fact_ln__gt__zero, fact_ln__gt__zero__iff, fact_ln__gt__zero__imp__gt__one,
% 208.03/28.79 fact_ln__inj__iff, fact_ln__le__cancel__iff, fact_ln__less__cancel__iff,
% 208.03/28.79 fact_ln__less__self, fact_ln__less__zero, fact_ln__less__zero__iff,
% 208.03/28.79 fact_ln__one, fact_m_I1_J, fact_minus__nat_Odiff__0, fact_mod__0, fact_mod__1,
% 208.03/28.79 fact_mod__Suc, fact_mod__Suc__eq__Suc__mod, fact_mod__add__cong,
% 208.03/28.79 fact_mod__add__eq, fact_mod__add__left__eq, fact_mod__add__right__eq,
% 208.03/28.79 fact_mod__add__self1, fact_mod__add__self2, fact_mod__by__0, fact_mod__by__1,
% 208.03/28.79 fact_mod__diff__cong, fact_mod__diff__eq, fact_mod__diff__left__eq,
% 208.03/28.79 fact_mod__diff__right__eq, fact_mod__div__trivial, fact_mod__eq__0__iff,
% 208.03/28.79 fact_mod__geq, fact_mod__if, fact_mod__less, fact_mod__less__divisor,
% 208.03/28.79 fact_mod__less__eq__dividend, fact_mod__mod__trivial, fact_mod__mult__cong,
% 208.03/28.79 fact_mod__mult__self1, fact_mod__mult__self1__is__0, fact_mod__mult__self2,
% 208.03/28.79 fact_mod__mult__self2__is__0, fact_mod__mult__self3, fact_mod__self,
% 208.03/28.79 fact_mult_Oadd__left, fact_mult_Oadd__right, fact_mult_Ocomm__neutral,
% 208.03/28.79 fact_mult_Odiff__left, fact_mult_Odiff__right, fact_mult_Oprod__diff__prod,
% 208.03/28.79 fact_mult_Ozero__left, fact_mult_Ozero__right, fact_mult__0,
% 208.03/28.79 fact_mult__0__right, fact_mult__1, fact_mult__1__left, fact_mult__1__right,
% 208.03/28.79 fact_mult__Suc, fact_mult__Suc__right, fact_mult__cancel1, fact_mult__cancel2,
% 208.03/28.79 fact_mult__diff__mult, fact_mult__divide__mult__cancel__left,
% 208.03/28.79 fact_mult__divide__mult__cancel__right, fact_mult__eq__0__iff,
% 208.03/28.79 fact_mult__eq__1__iff, fact_mult__eq__if, fact_mult__eq__self__implies__10,
% 208.03/28.79 fact_mult__imp__div__pos__le, fact_mult__imp__div__pos__less,
% 208.03/28.79 fact_mult__imp__le__div__pos, fact_mult__imp__less__div__pos, fact_mult__is__0,
% 208.03/28.79 fact_mult__le__0__iff, fact_mult__le__cancel1, fact_mult__le__cancel2,
% 208.03/28.79 fact_mult__le__cancel__left__neg, fact_mult__le__cancel__left__pos,
% 208.03/28.79 fact_mult__le__less__imp__less, fact_mult__le__mono, fact_mult__le__mono1,
% 208.03/28.79 fact_mult__le__mono2, fact_mult__left_Oadd, fact_mult__left_Odiff,
% 208.03/28.79 fact_mult__left_Ozero, fact_mult__left__le__imp__le,
% 208.03/28.79 fact_mult__left__le__one__le, fact_mult__left__less__imp__less,
% 208.03/28.79 fact_mult__left__mono, fact_mult__left__mono__neg, fact_mult__less__cancel1,
% 208.03/28.79 fact_mult__less__cancel2, fact_mult__less__cancel__left__disj,
% 208.03/28.79 fact_mult__less__cancel__left__neg, fact_mult__less__cancel__left__pos,
% 208.03/28.79 fact_mult__less__cancel__right__disj, fact_mult__less__imp__less__left,
% 208.03/28.79 fact_mult__less__imp__less__right, fact_mult__less__le__imp__less,
% 208.03/28.79 fact_mult__less__mono1, fact_mult__less__mono2, fact_mult__mono,
% 208.03/28.79 fact_mult__mono_H, fact_mult__neg__neg, fact_mult__neg__pos,
% 208.03/28.79 fact_mult__nonneg__nonneg, fact_mult__nonneg__nonpos,
% 208.03/28.79 fact_mult__nonneg__nonpos2, fact_mult__nonpos__nonneg,
% 208.03/28.79 fact_mult__nonpos__nonpos, fact_mult__poly__0__left, fact_mult__poly__0__right,
% 208.03/28.79 fact_mult__poly__add__left, fact_mult__pos__neg, fact_mult__pos__neg2,
% 208.03/28.79 fact_mult__pos__pos, fact_mult__right_Oadd, fact_mult__right_Odiff,
% 208.03/28.79 fact_mult__right_Ozero, fact_mult__right__le__imp__le,
% 208.03/28.79 fact_mult__right__le__one__le, fact_mult__right__less__imp__less,
% 208.03/28.79 fact_mult__right__mono, fact_mult__right__mono__neg,
% 208.03/28.79 fact_mult__strict__left__mono, fact_mult__strict__left__mono__neg,
% 208.03/28.79 fact_mult__strict__mono, fact_mult__strict__mono_H,
% 208.03/28.79 fact_mult__strict__right__mono, fact_mult__strict__right__mono__neg,
% 208.03/28.79 fact_mult__zero__left, fact_mult__zero__right, fact_n__less__m__mult__n,
% 208.03/28.79 fact_n__less__n__mult__m, fact_n__not__Suc__n, fact_nat_Oinject,
% 208.03/28.79 fact_nat_Osimps_I2_J, fact_nat_Osimps_I3_J, fact_nat__0__less__mult__iff,
% 208.03/28.79 fact_nat__1__eq__mult__iff, fact_nat__add__assoc, fact_nat__add__commute,
% 208.03/28.79 fact_nat__add__left__cancel, fact_nat__add__left__cancel__le,
% 208.03/28.79 fact_nat__add__left__cancel__less, fact_nat__add__left__commute,
% 208.03/28.79 fact_nat__add__right__cancel, fact_nat__diff__add__eq1,
% 208.03/28.79 fact_nat__diff__add__eq2, fact_nat__diff__split, fact_nat__diff__split__asm,
% 208.03/28.79 fact_nat__eq__add__iff1, fact_nat__eq__add__iff2, fact_nat__le__add__iff1,
% 208.03/28.79 fact_nat__le__add__iff2, fact_nat__le__linear, fact_nat__le__real__less,
% 208.03/28.79 fact_nat__less__add__iff1, fact_nat__less__add__iff2, fact_nat__less__cases,
% 208.03/28.79 fact_nat__less__le, fact_nat__less__real__le,
% 208.03/28.79 fact_nat__lt__two__imp__zero__or__one, fact_nat__mult__1,
% 208.03/28.79 fact_nat__mult__1__right, fact_nat__mult__assoc, fact_nat__mult__commute,
% 208.03/28.79 fact_nat__mult__div__cancel1, fact_nat__mult__div__cancel__disj,
% 208.03/28.79 fact_nat__mult__eq__1__iff, fact_nat__mult__eq__cancel1,
% 208.03/28.79 fact_nat__mult__eq__cancel__disj, fact_nat__mult__le__cancel1,
% 208.03/28.79 fact_nat__mult__less__cancel1, fact_nat__neq__iff, fact_nat__one__le__power,
% 208.03/28.79 fact_nat__power__eq__Suc__0__iff, fact_nat__power__less__imp__less,
% 208.03/28.79 fact_nat__zero__less__power__iff, fact_natceiling__add,
% 208.03/28.79 fact_natceiling__add__one, fact_natceiling__eq, fact_natceiling__le,
% 208.03/28.79 fact_natceiling__le__eq, fact_natceiling__le__eq__one, fact_natceiling__mono,
% 208.03/28.79 fact_natceiling__neg, fact_natceiling__one, fact_natceiling__real__of__nat,
% 208.03/28.79 fact_natceiling__subtract, fact_natceiling__zero, fact_natfloor__add,
% 208.03/28.79 fact_natfloor__add__one, fact_natfloor__div__nat, fact_natfloor__eq,
% 208.03/28.79 fact_natfloor__mono, fact_natfloor__neg, fact_natfloor__one,
% 208.03/28.79 fact_natfloor__power, fact_natfloor__real__of__nat, fact_natfloor__subtract,
% 208.03/28.79 fact_natfloor__zero, fact_neg__divide__le__eq, fact_neg__divide__less__eq,
% 208.03/28.79 fact_neg__imp__zdiv__neg__iff, fact_neg__imp__zdiv__nonneg__iff,
% 208.03/28.79 fact_neg__le__divide__eq, fact_neg__less__divide__eq, fact_neg__mod__bound,
% 208.03/28.79 fact_neq0__conv, fact_no__zero__divisors, fact_nonneg1__imp__zdiv__pos__iff,
% 208.03/28.79 fact_nonzero__divide__eq__eq, fact_nonzero__eq__divide__eq,
% 208.03/28.79 fact_nonzero__norm__divide, fact_nonzero__power__divide, fact_norm__add__less,
% 208.03/28.79 fact_norm__diff__ineq, fact_norm__diff__triangle__ineq, fact_norm__divide,
% 208.03/28.79 fact_norm__eq__zero, fact_norm__ge__zero, fact_norm__le__zero__iff,
% 208.03/28.79 fact_norm__minus__commute, fact_norm__not__less__zero, fact_norm__one,
% 208.03/28.79 fact_norm__power, fact_norm__power__ineq, fact_norm__triangle__ineq,
% 208.03/28.79 fact_norm__triangle__ineq2, fact_norm__triangle__ineq4, fact_norm__zero,
% 208.03/28.79 fact_not__add__less1, fact_not__add__less2, fact_not__leE, fact_not__less0,
% 208.03/28.79 fact_not__less__eq, fact_not__less__eq__eq, fact_not__less__iff__gr__or__eq,
% 208.03/28.79 fact_not__less__less__Suc__eq, fact_not__one__le__zero,
% 208.03/28.79 fact_not__one__less__zero, fact_not__real__of__nat__less__zero,
% 208.03/28.79 fact_not__square__less__zero, fact_not__sum__squares__lt__zero,
% 208.03/28.79 fact_odd__less__0, fact_odd__nonzero, fact_one0, fact_one__is__add,
% 208.03/28.79 fact_one__le__mult__iff, fact_one__le__power, fact_one__less__mult,
% 208.03/28.79 fact_one__less__power, fact_one__neq__zero, fact_one__reorient,
% 208.03/28.79 fact_ord__eq__le__trans, fact_ord__eq__less__trans, fact_ord__le__eq__trans,
% 208.03/28.79 fact_ord__less__eq__trans, fact_order__antisym, fact_order__antisym__conv,
% 208.03/28.79 fact_order__degree, fact_order__eq__iff, fact_order__eq__refl,
% 208.03/28.79 fact_order__le__imp__less__or__eq, fact_order__le__less,
% 208.03/28.79 fact_order__le__less__trans, fact_order__le__neq__trans, fact_order__less__asym,
% 208.03/28.79 fact_order__less__asym_H, fact_order__less__imp__le,
% 208.03/28.79 fact_order__less__imp__not__eq, fact_order__less__imp__not__eq2,
% 208.03/28.79 fact_order__less__imp__not__less, fact_order__less__irrefl,
% 208.03/28.79 fact_order__less__le, fact_order__less__le__trans, fact_order__less__not__sym,
% 208.03/28.79 fact_order__less__trans, fact_order__neq__le__trans, fact_order__refl,
% 208.03/28.79 fact_order__root, fact_order__trans, fact_pCons, fact_pcompose__0,
% 208.03/28.79 fact_pdivmod__rel__0, fact_pdivmod__rel__0__iff, fact_pdivmod__rel__by__0,
% 208.03/28.79 fact_pdivmod__rel__by__0__iff, fact_pdivmod__rel__def, fact_pdivmod__rel__mult,
% 208.03/28.79 fact_pdivmod__rel__unique, fact_pdivmod__rel__unique__div,
% 208.03/28.79 fact_pdivmod__rel__unique__mod, fact_plus__nat_Oadd__0, fact_poly__0,
% 208.03/28.79 fact_poly__1, fact_poly__add, fact_poly__bound__exists, fact_poly__diff,
% 208.03/28.79 fact_poly__div__mult__right, fact_poly__eq__iff, fact_poly__mult,
% 208.03/28.79 fact_poly__pcompose, fact_poly__power, fact_poly__zero, fact_pos__add__strict,
% 208.03/28.79 fact_pos__divide__le__eq, fact_pos__divide__less__eq,
% 208.03/28.79 fact_pos__imp__zdiv__neg__iff, fact_pos__imp__zdiv__nonneg__iff,
% 208.03/28.79 fact_pos__imp__zdiv__pos__iff, fact_pos__le__divide__eq,
% 208.03/28.79 fact_pos__less__divide__eq, fact_pos__mod__bound, fact_pos__zmult__eq__1__iff,
% 208.03/28.79 fact_power_Opower_Opower__0, fact_power_Opower_Opower__Suc, fact_power__0,
% 208.03/28.79 fact_power__0__Suc, fact_power__0__left, fact_power__Suc, fact_power__Suc2,
% 208.03/28.79 fact_power__Suc__0, fact_power__Suc__less, fact_power__Suc__less__one,
% 208.03/28.79 fact_power__add, fact_power__commutes, fact_power__decreasing, fact_power__diff,
% 208.03/28.79 fact_power__divide, fact_power__eq__0__iff, fact_power__eq__if,
% 208.03/28.79 fact_power__eq__imp__eq__base, fact_power__gt1, fact_power__gt1__lemma,
% 208.03/28.79 fact_power__increasing, fact_power__increasing__iff, fact_power__inject__base,
% 208.03/28.79 fact_power__inject__exp, fact_power__le__imp__le__base,
% 208.03/28.79 fact_power__le__imp__le__exp, fact_power__less__imp__less__base,
% 208.03/28.79 fact_power__less__imp__less__exp, fact_power__less__power__Suc,
% 208.03/28.79 fact_power__mono, fact_power__mult, fact_power__mult__distrib, fact_power__one,
% 208.03/28.79 fact_power__one__over, fact_power__one__right, fact_power__power__power,
% 208.03/28.79 fact_power__real__of__nat, fact_power__strict__decreasing,
% 208.03/28.79 fact_power__strict__increasing, fact_power__strict__increasing__iff,
% 208.03/28.79 fact_power__strict__mono, fact_psize__def, fact_psize__eq__0__iff, fact_q_I1_J,
% 208.03/28.79 fact_q_I2_J, fact_q__neg__lemma, fact_q__pos__lemma, fact_rcis__divide,
% 208.03/28.79 fact_rcis__zero__mod, fact_real__0__le__divide__iff, fact_real__add__left__mono,
% 208.03/28.79 fact_real__le__antisym, fact_real__le__eq__diff, fact_real__le__linear,
% 208.03/28.79 fact_real__le__refl, fact_real__le__trans, fact_real__less__def,
% 208.03/28.79 fact_real__natceiling__ge, fact_real__natfloor__add__one__gt,
% 208.03/28.79 fact_real__natfloor__gt__diff__one, fact_real__natfloor__le,
% 208.03/28.79 fact_real__of__nat__1, fact_real__of__nat__Suc,
% 208.03/28.79 fact_real__of__nat__Suc__gt__zero, fact_real__of__nat__add,
% 208.03/28.79 fact_real__of__nat__diff, fact_real__of__nat__div2, fact_real__of__nat__div3,
% 208.03/28.79 fact_real__of__nat__div4, fact_real__of__nat__div__aux,
% 208.03/28.79 fact_real__of__nat__ge__zero, fact_real__of__nat__gt__zero__cancel__iff,
% 208.03/28.79 fact_real__of__nat__inject, fact_real__of__nat__le__iff,
% 208.03/28.79 fact_real__of__nat__le__zero__cancel__iff, fact_real__of__nat__less__iff,
% 208.03/28.79 fact_real__of__nat__one, fact_real__of__nat__power, fact_real__of__nat__zero,
% 208.03/28.79 fact_real__of__nat__zero__iff, fact_real__squared__diff__one__factored,
% 208.03/28.79 fact_real__zero__not__eq__one, fact_realpow__Suc__le__self,
% 208.03/28.79 fact_realpow__minus__mult, fact_realpow__num__eq__if, fact_realpow__pos__nth,
% 208.03/28.79 fact_realpow__pos__nth__unique, fact_realpow__two__diff,
% 208.03/28.79 fact_reals__Archimedean6, fact_reals__Archimedean6a, fact_reduce__poly__simple,
% 208.03/28.79 fact_right__inverse__eq, fact_right__minus__eq, fact_self__quotient__aux1,
% 208.03/28.79 fact_self__quotient__aux2, fact_split__div, fact_split__div_H,
% 208.03/28.79 fact_split__div__lemma, fact_split__mult__neg__le, fact_split__mult__pos__le,
% 208.03/28.79 fact_split__neg__lemma, fact_split__zdiv, fact_sum__squares__eq__zero__iff,
% 208.03/28.79 fact_sum__squares__ge__zero, fact_sum__squares__gt__zero__iff,
% 208.03/28.79 fact_sum__squares__le__zero__iff, fact_synthetic__div__0,
% 208.03/28.79 fact_synthetic__div__eq__0__iff, fact_termination__basic__simps_I1_J,
% 208.03/28.79 fact_termination__basic__simps_I2_J, fact_termination__basic__simps_I3_J,
% 208.03/28.79 fact_termination__basic__simps_I4_J, fact_termination__basic__simps_I5_J,
% 208.03/28.79 fact_times__divide__eq__right, fact_times__divide__times__eq,
% 208.03/28.79 fact_trans__le__add1, fact_trans__le__add2, fact_trans__less__add1,
% 208.03/28.79 fact_trans__less__add2, fact_tsub__def, fact_tsub__eq,
% 208.03/28.79 fact_unimodular__reduce__norm, fact_unique__quotient__lemma,
% 208.03/28.79 fact_unique__quotient__lemma__neg, fact_xt1_I10_J, fact_xt1_I11_J,
% 208.03/28.79 fact_xt1_I12_J, fact_xt1_I1_J, fact_xt1_I2_J, fact_xt1_I3_J, fact_xt1_I4_J,
% 208.03/28.79 fact_xt1_I5_J, fact_xt1_I6_J, fact_xt1_I8_J, fact_xt1_I9_J, fact_zadd__0,
% 208.03/28.79 fact_zadd__0__right, fact_zadd__assoc, fact_zadd__commute,
% 208.03/28.79 fact_zadd__left__commute, fact_zadd__left__mono, fact_zadd__strict__right__mono,
% 208.03/28.79 fact_zadd__zless__mono, fact_zadd__zmult__distrib, fact_zadd__zmult__distrib2,
% 208.03/28.79 fact_zdiff__zmod__left, fact_zdiff__zmod__right, fact_zdiff__zmult__distrib,
% 208.03/28.79 fact_zdiff__zmult__distrib2, fact_zdiv__eq__0__iff, fact_zdiv__mono1,
% 208.03/28.79 fact_zdiv__mono1__neg, fact_zdiv__mono2, fact_zdiv__mono2__lemma,
% 208.03/28.79 fact_zdiv__mono2__neg, fact_zdiv__mono2__neg__lemma, fact_zdiv__self,
% 208.03/28.79 fact_zdiv__zadd1__eq, fact_zdiv__zero, fact_zdiv__zmult2__eq,
% 208.03/28.79 fact_zero__le__divide__iff,
% 208.03/28.79 fact_zero__le__double__add__iff__zero__le__single__add,
% 208.03/28.79 fact_zero__le__mult__iff, fact_zero__le__natceiling, fact_zero__le__natfloor,
% 208.03/28.79 fact_zero__le__one, fact_zero__le__power, fact_zero__le__square,
% 208.03/28.79 fact_zero__less__Suc, fact_zero__less__diff, fact_zero__less__divide__iff,
% 208.03/28.79 fact_zero__less__double__add__iff__zero__less__single__add,
% 208.03/28.79 fact_zero__less__mult__pos, fact_zero__less__mult__pos2,
% 208.03/28.79 fact_zero__less__norm__iff, fact_zero__less__one, fact_zero__less__power,
% 208.03/28.79 fact_zero__less__power__nat__eq, fact_zero__less__two, fact_zero__neq__one,
% 208.03/28.79 fact_zero__reorient, fact_zle__add1__eq__le, fact_zle__antisym,
% 208.03/28.79 fact_zle__diff1__eq, fact_zle__linear, fact_zle__refl, fact_zle__trans,
% 208.03/28.79 fact_zless__add1__eq, fact_zless__imp__add1__zle, fact_zless__le,
% 208.03/28.79 fact_zless__linear, fact_zmod__eq__0__iff, fact_zmod__le__nonneg__dividend,
% 208.03/28.79 fact_zmod__self, fact_zmod__simps_I1_J, fact_zmod__simps_I2_J,
% 208.03/28.79 fact_zmod__simps_I4_J, fact_zmod__zdiv__trivial, fact_zmod__zero, fact_zmult__1,
% 208.03/28.79 fact_zmult__1__right, fact_zmult__assoc, fact_zmult__commute,
% 208.03/28.79 fact_zmult__zless__mono2, fact_zpower__zadd__distrib, fact_zpower__zpower
% 208.03/28.79
% 208.03/28.79 Those formulas are unsatisfiable:
% 208.03/28.79 ---------------------------------
% 208.03/28.79
% 208.03/28.79 Begin of proof
% 208.03/28.80 |
% 208.03/28.80 | ALPHA: (fact_dme) implies:
% 208.03/28.80 | (1) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 208.03/28.80 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v0 & hAPP(v1,
% 208.03/28.80 | v_m____) = v2 & hAPP(v0, v_da____) = v1 & $i(v2) & $i(v1) & $i(v0)
% 208.03/28.80 | & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v_e))
% 208.03/28.80 |
% 208.03/28.80 | ALPHA: (fact_norm__mult__less) implies:
% 208.03/28.80 | (2) ? [v0: $i] : (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v0 &
% 208.03/28.80 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 208.03/28.80 | [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : !
% 208.03/28.80 | [v10: $i] : ! [v11: $i] : ( ~ (c_Groups_Otimes__class_Otimes(v5) =
% 208.03/28.80 | v6) | ~ (c_RealVector_Onorm__class_Onorm(v5, v8) = v9) | ~
% 208.03/28.80 | (hAPP(v10, v1) = v11) | ~ (hAPP(v7, v2) = v8) | ~ (hAPP(v6, v4) =
% 208.03/28.80 | v7) | ~ (hAPP(v0, v3) = v10) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3)
% 208.03/28.80 | | ~ $i(v2) | ~ $i(v1) | ~
% 208.03/28.80 | class_RealVector_Oreal__normed__algebra(v5) |
% 208.03/28.80 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v9, v11) | ? [v12:
% 208.03/28.80 | $i] : ? [v13: $i] : ((c_RealVector_Onorm__class_Onorm(v5, v4) =
% 208.03/28.80 | v12 & $i(v12) & ~
% 208.03/28.80 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v12, v3)) |
% 208.03/28.80 | (c_RealVector_Onorm__class_Onorm(v5, v2) = v13 & $i(v13) & ~
% 208.03/28.80 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v13, v1)))))
% 208.03/28.80 |
% 208.03/28.80 | ALPHA: (fact__096cmod_A_Iw_A_N_Az_J_A_K_Acmod_A_Ipoly_Acs_A_Iw_A_N_Az_J_J_A_060_061_Ad_A_K_Am_096)
% 208.03/28.80 | implies:
% 208.03/28.80 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 208.03/28.80 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 208.03/28.80 | (c_Polynomial_Opoly(tc_Complex_Ocomplex, v_cs____) = v4 &
% 208.03/28.80 | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v0 &
% 208.03/28.80 | c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_w____, v_z) = v1
% 208.03/28.80 | & c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v5) = v6 &
% 208.03/28.80 | c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v1) = v2 &
% 208.03/28.80 | hAPP(v8, v_m____) = v9 & hAPP(v4, v1) = v5 & hAPP(v3, v6) = v7 &
% 208.03/28.80 | hAPP(v0, v2) = v3 & hAPP(v0, v_da____) = v8 & $i(v9) & $i(v8) &
% 208.03/28.80 | $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)
% 208.03/28.80 | & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v7, v9))
% 208.03/28.80 |
% 208.03/28.80 | ALPHA: (fact_norm__mult) implies:
% 208.03/28.80 | (4) ? [v0: $i] : (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v0 &
% 208.03/28.80 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 208.03/28.80 | [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~
% 208.03/28.80 | (c_RealVector_Onorm__class_Onorm(v3, v2) = v4) | ~
% 208.03/28.80 | (c_RealVector_Onorm__class_Onorm(v3, v1) = v6) | ~ (hAPP(v5, v6) =
% 208.03/28.80 | v7) | ~ (hAPP(v0, v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1)
% 208.03/28.80 | | ~ class_RealVector_Oreal__normed__div__algebra(v3) | ? [v8: $i]
% 208.03/28.80 | : ? [v9: $i] : ? [v10: $i] : (c_Groups_Otimes__class_Otimes(v3) =
% 208.03/28.80 | v8 & c_RealVector_Onorm__class_Onorm(v3, v10) = v7 & hAPP(v9, v1)
% 208.03/28.80 | = v10 & hAPP(v8, v2) = v9 & $i(v10) & $i(v9) & $i(v8) & $i(v7))))
% 208.03/28.80 |
% 208.03/28.80 | ALPHA: (fact_th) implies:
% 208.03/28.80 | (5) ? [v0: $i] : ? [v1: $i] :
% 208.03/28.80 | (c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_w____, v_z) = v0
% 208.03/28.80 | & c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v0) = v1 &
% 208.03/28.80 | $i(v1) & $i(v0) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 208.03/28.80 | v1, v_da____))
% 208.03/28.80 |
% 208.03/28.80 | ALPHA: (fact_norm__mult__ineq) implies:
% 208.03/28.81 | (6) ? [v0: $i] : (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v0 &
% 208.03/28.81 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 208.03/28.81 | [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~
% 208.03/28.81 | (c_RealVector_Onorm__class_Onorm(v3, v2) = v4) | ~
% 208.03/28.81 | (c_RealVector_Onorm__class_Onorm(v3, v1) = v6) | ~ (hAPP(v5, v6) =
% 208.03/28.81 | v7) | ~ (hAPP(v0, v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1)
% 208.03/28.81 | | ~ class_RealVector_Oreal__normed__algebra(v3) | ? [v8: $i] : ?
% 208.03/28.81 | [v9: $i] : ? [v10: $i] : ? [v11: $i] :
% 208.03/28.81 | (c_Groups_Otimes__class_Otimes(v3) = v8 &
% 208.03/28.81 | c_RealVector_Onorm__class_Onorm(v3, v10) = v11 & hAPP(v9, v1) =
% 208.03/28.81 | v10 & hAPP(v8, v2) = v9 & $i(v11) & $i(v10) & $i(v9) & $i(v8) &
% 208.03/28.81 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v11, v7))))
% 208.03/28.81 |
% 208.03/28.81 | ALPHA: (fact_m_I2_J) implies:
% 208.03/28.81 | (7) ? [v0: $i] : ? [v1: $i] :
% 208.03/28.81 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 208.03/28.81 | c_Polynomial_Opoly(tc_Complex_Ocomplex, v_cs____) = v1 & $i(v1) &
% 208.03/28.81 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v1, v2) = v3) | ~
% 208.03/28.81 | $i(v2) | ? [v4: $i] : ? [v5: $i] :
% 208.03/28.81 | ((c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v3) = v5 &
% 208.03/28.81 | $i(v5) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 208.03/28.81 | v5, v_m____)) |
% 208.03/28.81 | (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v2) = v4 &
% 208.03/28.81 | $i(v4) & ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 208.03/28.81 | v4, v0)))))
% 208.03/28.81 |
% 208.03/28.81 | ALPHA: (fact_d1_I1_J) implies:
% 208.03/28.81 | (8) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 208.03/28.81 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v2 &
% 208.03/28.81 | c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_w____, v_z) = v0
% 208.03/28.81 | & c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v0) = v1 &
% 208.03/28.81 | $i(v2) & $i(v1) & $i(v0) &
% 208.03/28.81 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v2))
% 208.03/28.81 |
% 208.03/28.81 | ALPHA: (fact_norm__ratiotest__lemma) implies:
% 208.03/28.81 | (9) ? [v0: $i] : ? [v1: $i] :
% 208.03/28.81 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 208.03/28.81 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 208.03/28.81 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i]
% 208.03/28.81 | : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~
% 208.03/28.81 | (c_RealVector_Onorm__class_Onorm(v5, v3) = v6) | ~
% 208.03/28.81 | (c_RealVector_Onorm__class_Onorm(v5, v2) = v8) | ~ (hAPP(v7, v8) =
% 208.03/28.81 | v9) | ~ (hAPP(v1, v4) = v7) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3)
% 208.03/28.81 | | ~ $i(v2) | ~ class_RealVector_Oreal__normed__vector(v5) | ~
% 208.03/28.81 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v9) | ~
% 208.03/28.81 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v0) |
% 208.03/28.81 | c_Groups_Ozero__class_Ozero(v5) = v3))
% 208.03/28.81 |
% 208.03/28.81 | ALPHA: (fact_real__mult__le__cancel__iff2) implies:
% 208.03/28.81 | (10) ? [v0: $i] : ? [v1: $i] :
% 208.03/28.81 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 208.03/28.81 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 208.03/28.81 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 208.03/28.81 | $i] : ! [v7: $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) =
% 208.03/28.81 | v7) | ~ (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2)
% 208.03/28.81 | | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v7) |
% 208.03/28.81 | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) |
% 208.03/28.81 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v2)) & !
% 208.03/28.81 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] :
% 208.03/28.81 | ! [v7: $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~
% 208.03/28.81 | (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 208.03/28.81 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v2) | ~
% 208.03/28.81 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) |
% 208.03/28.81 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v7)))
% 208.03/28.81 |
% 208.03/28.81 | ALPHA: (fact_real__mult__le__cancel__iff1) implies:
% 208.03/28.81 | (11) ? [v0: $i] : ? [v1: $i] :
% 208.03/28.81 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 208.03/28.81 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 208.03/28.81 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 208.03/28.81 | $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (hAPP(v7, v4) = v8) | ~
% 208.03/28.81 | (hAPP(v5, v4) = v6) | ~ (hAPP(v1, v3) = v5) | ~ (hAPP(v1, v2) =
% 208.03/28.81 | v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 208.03/28.81 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v8) | ~
% 208.03/28.81 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) |
% 208.03/28.81 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v2)) & !
% 208.03/28.81 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] :
% 208.03/28.81 | ! [v7: $i] : ! [v8: $i] : ( ~ (hAPP(v7, v4) = v8) | ~ (hAPP(v5,
% 208.03/28.81 | v4) = v6) | ~ (hAPP(v1, v3) = v5) | ~ (hAPP(v1, v2) = v7) |
% 208.03/28.81 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 208.03/28.81 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v2) | ~
% 208.03/28.81 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) |
% 208.03/28.81 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6, v8)))
% 208.03/28.81 |
% 208.03/28.81 | ALPHA: (fact_real__mult__1) implies:
% 208.03/28.81 | (12) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 208.03/28.81 | (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 &
% 208.03/28.81 | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v0 & hAPP(v0, v1)
% 208.03/28.81 | = v2 & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : (v4 =
% 208.03/28.81 | v3 | ~ (hAPP(v2, v3) = v4) | ~ $i(v3)))
% 208.03/28.81 |
% 208.03/28.81 | ALPHA: (fact_real__mult__commute) implies:
% 208.03/28.81 | (13) ? [v0: $i] : (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v0 &
% 208.03/28.81 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 208.03/28.81 | (hAPP(v3, v2) = v4) | ~ (hAPP(v0, v1) = v3) | ~ $i(v2) | ~
% 208.03/28.81 | $i(v1) | ? [v5: $i] : (hAPP(v5, v1) = v4 & hAPP(v0, v2) = v5 &
% 208.03/28.81 | $i(v5) & $i(v4))))
% 208.03/28.81 |
% 208.03/28.81 | ALPHA: (fact_real__mult__assoc) implies:
% 208.03/28.81 | (14) ? [v0: $i] : (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v0 &
% 208.03/28.82 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 208.03/28.82 | [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (hAPP(v6, v1) = v7) | ~
% 208.03/28.82 | (hAPP(v4, v2) = v5) | ~ (hAPP(v0, v5) = v6) | ~ (hAPP(v0, v3) =
% 208.03/28.82 | v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ? [v8: $i] : ? [v9:
% 208.03/28.82 | $i] : (hAPP(v8, v1) = v9 & hAPP(v4, v9) = v7 & hAPP(v0, v2) = v8
% 208.03/28.82 | & $i(v9) & $i(v8) & $i(v7))))
% 208.03/28.82 |
% 208.03/28.82 | ALPHA: (fact_real__mult__right__cancel) implies:
% 208.03/28.82 | (15) ? [v0: $i] : ? [v1: $i] :
% 208.03/28.82 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 208.03/28.82 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 208.03/28.82 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 208.03/28.82 | $i] : ! [v7: $i] : (v4 = v0 | v3 = v2 | ~ (hAPP(v7, v4) = v6) |
% 208.03/28.82 | ~ (hAPP(v5, v4) = v6) | ~ (hAPP(v1, v3) = v5) | ~ (hAPP(v1, v2)
% 208.03/28.82 | = v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2)))
% 208.03/28.82 |
% 208.03/28.82 | ALPHA: (fact_real__mult__left__cancel) implies:
% 208.03/28.82 | (16) ? [v0: $i] : ? [v1: $i] :
% 208.52/28.82 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 208.52/28.82 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 208.52/28.82 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 208.52/28.82 | $i] : (v4 = v0 | v3 = v2 | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5,
% 208.52/28.82 | v2) = v6) | ~ (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) |
% 208.52/28.82 | ~ $i(v2)))
% 208.52/28.82 |
% 208.52/28.82 | ALPHA: (fact_real__mult__less__iff1) implies:
% 208.52/28.82 | (17) ? [v0: $i] : ? [v1: $i] :
% 208.52/28.82 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 208.52/28.82 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 208.52/28.82 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 208.52/28.82 | $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (hAPP(v7, v4) = v8) | ~
% 208.52/28.82 | (hAPP(v5, v4) = v6) | ~ (hAPP(v1, v3) = v5) | ~ (hAPP(v1, v2) =
% 208.52/28.82 | v7) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 208.52/28.82 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v6, v8) | ~
% 208.52/28.82 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) |
% 208.52/28.82 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v2)) & ! [v2:
% 208.52/28.82 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 208.52/28.82 | [v7: $i] : ! [v8: $i] : ( ~ (hAPP(v7, v4) = v8) | ~ (hAPP(v5, v4)
% 208.52/28.82 | = v6) | ~ (hAPP(v1, v3) = v5) | ~ (hAPP(v1, v2) = v7) | ~
% 208.52/28.82 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 208.52/28.82 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v2) | ~
% 208.52/28.82 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) |
% 208.52/28.82 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v6, v8)))
% 208.52/28.82 |
% 208.52/28.82 | ALPHA: (fact_real__mult__order) implies:
% 208.52/28.82 | (18) ? [v0: $i] : ? [v1: $i] :
% 208.52/28.82 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 208.52/28.82 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 208.52/28.82 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 208.52/28.82 | (hAPP(v4, v2) = v5) | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~
% 208.52/28.82 | $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0,
% 208.52/28.82 | v3) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2)
% 208.52/28.82 | | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v5)))
% 208.52/28.82 |
% 208.52/28.82 | ALPHA: (fact_real__mult__less__mono2) implies:
% 208.52/28.82 | (19) ? [v0: $i] : ? [v1: $i] :
% 208.52/28.82 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 208.52/28.82 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 208.52/28.82 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 208.52/28.82 | $i] : ! [v7: $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) =
% 208.52/28.82 | v7) | ~ (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2)
% 208.52/28.82 | | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v2) | ~
% 208.52/28.82 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) |
% 208.52/28.82 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v6, v7)))
% 208.52/28.82 |
% 208.52/28.82 | ALPHA: (fact_real__add__mult__distrib) implies:
% 208.52/28.82 | (20) ? [v0: $i] : (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v0 &
% 208.52/28.82 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 208.52/28.82 | [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~
% 208.52/28.82 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v5, v7) = v8) | ~
% 208.52/28.82 | (hAPP(v6, v1) = v7) | ~ (hAPP(v4, v1) = v5) | ~ (hAPP(v0, v3) =
% 208.52/28.82 | v4) | ~ (hAPP(v0, v2) = v6) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1)
% 208.52/28.82 | | ? [v9: $i] : ? [v10: $i] :
% 208.52/28.82 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v2) = v9 &
% 208.52/28.82 | hAPP(v10, v1) = v8 & hAPP(v0, v9) = v10 & $i(v10) & $i(v9) &
% 208.52/28.82 | $i(v8))))
% 208.52/28.82 |
% 208.52/28.82 | ALPHA: (fact_real__two__squares__add__zero__iff) implies:
% 208.52/28.82 | (21) ? [v0: $i] : ? [v1: $i] :
% 208.52/28.82 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v0 &
% 208.52/28.82 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0)
% 208.52/28.82 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 208.52/28.82 | $i] : ! [v7: $i] : (v3 = v1 | ~
% 208.52/28.82 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v5, v7) = v1) | ~
% 208.52/28.82 | (hAPP(v6, v2) = v7) | ~ (hAPP(v4, v3) = v5) | ~ (hAPP(v0, v3) =
% 208.52/28.82 | v4) | ~ (hAPP(v0, v2) = v6) | ~ $i(v3) | ~ $i(v2)) & ! [v2:
% 208.52/28.82 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 208.52/28.82 | [v7: $i] : (v2 = v1 | ~
% 208.52/28.82 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v5, v7) = v1) | ~
% 208.52/28.82 | (hAPP(v6, v2) = v7) | ~ (hAPP(v4, v3) = v5) | ~ (hAPP(v0, v3) =
% 208.52/28.82 | v4) | ~ (hAPP(v0, v2) = v6) | ~ $i(v3) | ~ $i(v2)) & ! [v2:
% 208.52/28.82 | $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v1 | ~
% 208.52/28.82 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v3) = v4) | ~
% 208.52/28.82 | (hAPP(v2, v1) = v3) | ~ (hAPP(v0, v1) = v2)))
% 208.52/28.82 |
% 208.52/28.82 | ALPHA: (fact_lemma__MVT) implies:
% 208.52/28.82 | (22) ? [v0: $i] : (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v0 &
% 208.52/28.82 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 208.52/28.82 | [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] :
% 208.52/28.82 | ! [v10: $i] : ! [v11: $i] : ( ~
% 208.52/28.82 | (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v6, v7) = v8) |
% 208.52/28.82 | ~ (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v5, v10) =
% 208.52/28.82 | v11) | ~ (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v5,
% 208.52/28.82 | v4) = v6) | ~
% 208.52/28.82 | (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v1, v2) = v7) |
% 208.52/28.82 | ~ (hAPP(v9, v1) = v10) | ~ (hAPP(v3, v2) = v4) | ~ (hAPP(v3, v1)
% 208.52/28.82 | = v5) | ~ (hAPP(v0, v8) = v9) | ~ $i(v3) | ~ $i(v2) | ~
% 208.52/28.82 | $i(v1) | ? [v12: $i] :
% 208.52/28.82 | (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v4, v12) = v11 &
% 208.52/28.82 | hAPP(v9, v2) = v12 & $i(v12) & $i(v11))))
% 208.52/28.82 |
% 208.52/28.82 | ALPHA: (fact_not__real__square__gt__zero) implies:
% 208.52/28.83 | (23) ? [v0: $i] : ? [v1: $i] :
% 208.52/28.83 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 208.52/28.83 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 208.52/28.83 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v0 | ~ (hAPP(v3,
% 208.52/28.83 | v2) = v4) | ~ (hAPP(v1, v2) = v3) | ~ $i(v2) |
% 208.52/28.83 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4)) & ! [v2:
% 208.52/28.83 | $i] : ! [v3: $i] : ( ~ (hAPP(v2, v0) = v3) | ~ (hAPP(v1, v0) =
% 208.52/28.83 | v2) | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0,
% 208.52/28.83 | v3)))
% 208.52/28.83 |
% 208.52/28.83 | ALPHA: (fact_real__divide__square__eq) implies:
% 208.52/28.83 | (24) ? [v0: $i] : (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v0 &
% 208.52/28.83 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 208.52/28.83 | [v5: $i] : ! [v6: $i] : ( ~
% 208.52/28.83 | (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v4, v5) = v6) |
% 208.52/28.83 | ~ (hAPP(v3, v2) = v5) | ~ (hAPP(v3, v1) = v4) | ~ (hAPP(v0, v2)
% 208.52/28.83 | = v3) | ~ $i(v2) | ~ $i(v1) |
% 208.52/28.83 | (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v1, v2) = v6 &
% 208.52/28.83 | $i(v6))))
% 208.52/28.83 |
% 208.52/28.83 | ALPHA: (fact_divide_Opos__bounded) implies:
% 208.52/28.83 | (25) ? [v0: $i] : ? [v1: $i] :
% 208.52/28.83 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 208.52/28.83 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 208.52/28.83 | & ? [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~
% 208.52/28.83 | class_RealVector_Oreal__normed__field(v3) | ? [v4: $i] : ($i(v4)
% 208.52/28.83 | & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) & !
% 208.52/28.83 | [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~
% 208.52/28.83 | (c_RealVector_Onorm__class_Onorm(v3, v5) = v6) | ~ (hAPP(v7,
% 208.52/28.83 | v4) = v8) | ~ (hAPP(v1, v6) = v7) | ~ $i(v5) | ? [v9:
% 208.52/28.83 | $i] : ? [v10: $i] : (c_Rings_Oinverse__class_Odivide(v3,
% 208.52/28.83 | v5, v2) = v9 & c_RealVector_Onorm__class_Onorm(v3, v9) =
% 208.52/28.83 | v10 & $i(v10) & $i(v9) &
% 208.52/28.83 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v10,
% 208.52/28.83 | v8))))))
% 208.52/28.83 |
% 208.52/28.83 | ALPHA: (fact_mult__left_Opos__bounded) implies:
% 208.52/28.83 | (26) ? [v0: $i] : ? [v1: $i] :
% 208.52/28.83 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 208.52/28.83 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 208.52/28.83 | & ? [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 208.52/28.83 | (c_Groups_Otimes__class_Otimes(v3) = v4) | ~ $i(v3) | ~ $i(v2) |
% 208.52/28.83 | ~ class_RealVector_Oreal__normed__algebra(v3) | ? [v5: $i] :
% 208.52/28.83 | ($i(v5) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v5)
% 208.52/28.83 | & ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~
% 208.52/28.83 | (c_RealVector_Onorm__class_Onorm(v3, v6) = v7) | ~ (hAPP(v8,
% 208.52/28.83 | v5) = v9) | ~ (hAPP(v1, v7) = v8) | ~ $i(v6) | ? [v10:
% 208.52/28.83 | $i] : ? [v11: $i] : ? [v12: $i] :
% 208.52/28.83 | (c_RealVector_Onorm__class_Onorm(v3, v11) = v12 & hAPP(v10,
% 208.52/28.83 | v2) = v11 & hAPP(v4, v6) = v10 & $i(v12) & $i(v11) &
% 208.52/28.83 | $i(v10) &
% 208.52/28.83 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v12,
% 208.52/28.83 | v9))))))
% 208.52/28.83 |
% 208.52/28.83 | ALPHA: (fact_mult_Opos__bounded) implies:
% 208.52/28.83 | (27) ? [v0: $i] : ? [v1: $i] :
% 208.52/28.83 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 208.52/28.83 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 208.52/28.83 | & ! [v2: $i] : ! [v3: $i] : ( ~ (c_Groups_Otimes__class_Otimes(v2)
% 208.52/28.83 | = v3) | ~ $i(v2) | ~
% 208.52/28.83 | class_RealVector_Oreal__normed__algebra(v2) | ? [v4: $i] :
% 208.52/28.83 | ($i(v4) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4)
% 208.52/28.83 | & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : !
% 208.52/28.83 | [v9: $i] : ! [v10: $i] : ! [v11: $i] : ! [v12: $i] : ( ~
% 208.52/28.83 | (c_RealVector_Onorm__class_Onorm(v2, v6) = v9) | ~
% 208.52/28.83 | (c_RealVector_Onorm__class_Onorm(v2, v5) = v7) | ~ (hAPP(v11,
% 208.52/28.83 | v4) = v12) | ~ (hAPP(v8, v9) = v10) | ~ (hAPP(v1, v10) =
% 208.52/28.83 | v11) | ~ (hAPP(v1, v7) = v8) | ~ $i(v6) | ~ $i(v5) | ?
% 208.52/28.83 | [v13: $i] : ? [v14: $i] : ? [v15: $i] :
% 208.52/28.83 | (c_RealVector_Onorm__class_Onorm(v2, v14) = v15 & hAPP(v13,
% 208.52/28.83 | v6) = v14 & hAPP(v3, v5) = v13 & $i(v15) & $i(v14) &
% 208.52/28.83 | $i(v13) &
% 208.52/28.83 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v15,
% 208.52/28.83 | v12))))))
% 208.52/28.83 |
% 208.52/28.83 | ALPHA: (fact_mult__right_Opos__bounded) implies:
% 208.52/28.83 | (28) ? [v0: $i] : ? [v1: $i] :
% 208.52/28.83 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 208.52/28.83 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 208.52/28.83 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 208.52/28.83 | (c_Groups_Otimes__class_Otimes(v3) = v4) | ~ (hAPP(v4, v2) = v5)
% 208.52/28.83 | | ~ $i(v3) | ~ $i(v2) | ~
% 208.52/28.83 | class_RealVector_Oreal__normed__algebra(v3) | ? [v6: $i] :
% 208.52/28.83 | ($i(v6) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v6)
% 208.52/28.83 | & ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ( ~
% 208.52/28.83 | (c_RealVector_Onorm__class_Onorm(v3, v7) = v8) | ~ (hAPP(v9,
% 208.52/28.83 | v6) = v10) | ~ (hAPP(v1, v8) = v9) | ~ $i(v7) | ? [v11:
% 208.52/28.83 | $i] : ? [v12: $i] : (c_RealVector_Onorm__class_Onorm(v3,
% 208.52/28.83 | v11) = v12 & hAPP(v5, v7) = v11 & $i(v12) & $i(v11) &
% 208.52/28.83 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v12,
% 208.52/28.83 | v10))))))
% 208.52/28.83 |
% 208.52/28.83 | ALPHA: (fact_divide_Ononneg__bounded) implies:
% 208.52/28.83 | (29) ? [v0: $i] : ? [v1: $i] :
% 208.52/28.83 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 208.52/28.83 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 208.52/28.83 | & ? [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~
% 208.52/28.83 | class_RealVector_Oreal__normed__field(v3) | ? [v4: $i] : ($i(v4)
% 208.52/28.83 | & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v4) &
% 208.52/28.83 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~
% 208.52/28.83 | (c_RealVector_Onorm__class_Onorm(v3, v5) = v6) | ~ (hAPP(v7,
% 208.52/28.83 | v4) = v8) | ~ (hAPP(v1, v6) = v7) | ~ $i(v5) | ? [v9:
% 208.52/28.83 | $i] : ? [v10: $i] : (c_Rings_Oinverse__class_Odivide(v3,
% 208.52/28.83 | v5, v2) = v9 & c_RealVector_Onorm__class_Onorm(v3, v9) =
% 208.52/28.83 | v10 & $i(v10) & $i(v9) &
% 208.52/28.83 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v10,
% 208.52/28.83 | v8))))))
% 208.52/28.83 |
% 208.52/28.83 | ALPHA: (fact_mult__left_Ononneg__bounded) implies:
% 208.52/28.83 | (30) ? [v0: $i] : ? [v1: $i] :
% 208.52/28.83 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 208.52/28.83 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 208.52/28.83 | & ? [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 208.52/28.83 | (c_Groups_Otimes__class_Otimes(v3) = v4) | ~ $i(v3) | ~ $i(v2) |
% 208.52/28.83 | ~ class_RealVector_Oreal__normed__algebra(v3) | ? [v5: $i] :
% 208.52/28.83 | ($i(v5) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0,
% 208.52/28.83 | v5) & ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] :
% 208.52/28.83 | ( ~ (c_RealVector_Onorm__class_Onorm(v3, v6) = v7) | ~
% 208.52/28.83 | (hAPP(v8, v5) = v9) | ~ (hAPP(v1, v7) = v8) | ~ $i(v6) | ?
% 208.52/28.83 | [v10: $i] : ? [v11: $i] : ? [v12: $i] :
% 208.52/28.83 | (c_RealVector_Onorm__class_Onorm(v3, v11) = v12 & hAPP(v10,
% 208.52/28.83 | v2) = v11 & hAPP(v4, v6) = v10 & $i(v12) & $i(v11) &
% 208.52/28.83 | $i(v10) &
% 208.52/28.84 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v12,
% 208.52/28.84 | v9))))))
% 208.52/28.84 |
% 208.52/28.84 | ALPHA: (fact_mult__right_Ononneg__bounded) implies:
% 208.52/28.84 | (31) ? [v0: $i] : ? [v1: $i] :
% 208.52/28.84 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 208.52/28.84 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 208.52/28.84 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 208.52/28.84 | (c_Groups_Otimes__class_Otimes(v3) = v4) | ~ (hAPP(v4, v2) = v5)
% 208.52/28.84 | | ~ $i(v3) | ~ $i(v2) | ~
% 208.52/28.84 | class_RealVector_Oreal__normed__algebra(v3) | ? [v6: $i] :
% 208.52/28.84 | ($i(v6) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0,
% 208.52/28.84 | v6) & ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] :
% 208.52/28.84 | ( ~ (c_RealVector_Onorm__class_Onorm(v3, v7) = v8) | ~
% 208.52/28.84 | (hAPP(v9, v6) = v10) | ~ (hAPP(v1, v8) = v9) | ~ $i(v7) | ?
% 208.52/28.84 | [v11: $i] : ? [v12: $i] :
% 208.52/28.84 | (c_RealVector_Onorm__class_Onorm(v3, v11) = v12 & hAPP(v5, v7)
% 208.52/28.84 | = v11 & $i(v12) & $i(v11) &
% 208.52/28.84 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v12,
% 208.52/28.84 | v10))))))
% 208.52/28.84 |
% 208.52/28.84 | ALPHA: (fact_mult_Ononneg__bounded) implies:
% 208.52/28.84 | (32) ? [v0: $i] : ? [v1: $i] :
% 208.52/28.84 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 208.52/28.84 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 208.52/28.84 | & ! [v2: $i] : ! [v3: $i] : ( ~ (c_Groups_Otimes__class_Otimes(v2)
% 208.52/28.84 | = v3) | ~ $i(v2) | ~
% 208.52/28.84 | class_RealVector_Oreal__normed__algebra(v2) | ? [v4: $i] :
% 208.52/28.84 | ($i(v4) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0,
% 208.52/28.84 | v4) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] :
% 208.52/28.84 | ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ! [v12: $i] : ( ~
% 208.52/28.84 | (c_RealVector_Onorm__class_Onorm(v2, v6) = v9) | ~
% 208.52/28.84 | (c_RealVector_Onorm__class_Onorm(v2, v5) = v7) | ~ (hAPP(v11,
% 208.52/28.84 | v4) = v12) | ~ (hAPP(v8, v9) = v10) | ~ (hAPP(v1, v10) =
% 208.52/28.84 | v11) | ~ (hAPP(v1, v7) = v8) | ~ $i(v6) | ~ $i(v5) | ?
% 208.52/28.84 | [v13: $i] : ? [v14: $i] : ? [v15: $i] :
% 208.52/28.84 | (c_RealVector_Onorm__class_Onorm(v2, v14) = v15 & hAPP(v13,
% 208.52/28.84 | v6) = v14 & hAPP(v3, v5) = v13 & $i(v15) & $i(v14) &
% 208.52/28.84 | $i(v13) &
% 208.52/28.84 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v15,
% 208.52/28.84 | v12))))))
% 208.52/28.84 |
% 208.52/28.84 | ALPHA: (fact_real__of__nat__mult) implies:
% 208.52/28.84 | (33) ? [v0: $i] : ? [v1: $i] :
% 208.52/28.84 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 208.52/28.84 | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 & $i(v1) &
% 208.52/28.84 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : !
% 208.52/28.84 | [v6: $i] : ! [v7: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v3) = v4)
% 208.52/28.84 | | ~ (c_RealDef_Oreal(tc_Nat_Onat, v2) = v6) | ~ (hAPP(v5, v6) =
% 208.52/28.84 | v7) | ~ (hAPP(v1, v4) = v5) | ~ $i(v3) | ~ $i(v2) | ? [v8:
% 208.52/28.84 | $i] : ? [v9: $i] : (c_RealDef_Oreal(tc_Nat_Onat, v9) = v7 &
% 208.52/28.84 | hAPP(v8, v2) = v9 & hAPP(v0, v3) = v8 & $i(v9) & $i(v8) &
% 208.52/28.84 | $i(v7))))
% 208.52/28.84 |
% 208.52/28.84 | ALPHA: (fact_le__mult__natfloor) implies:
% 208.52/28.84 | (34) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 208.52/28.84 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 208.52/28.84 | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v2 &
% 208.52/28.84 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v2) & $i(v1)
% 208.52/28.84 | & $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] :
% 208.52/28.84 | ! [v7: $i] : ! [v8: $i] : ( ~ (c_RComplete_Onatfloor(v4) = v5) | ~
% 208.52/28.84 | (c_RComplete_Onatfloor(v3) = v7) | ~ (hAPP(v6, v7) = v8) | ~
% 208.52/28.84 | (hAPP(v1, v5) = v6) | ~ $i(v4) | ~ $i(v3) | ~
% 208.52/28.84 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v4) | ~
% 208.52/28.84 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) | ?
% 208.52/28.84 | [v9: $i] : ? [v10: $i] : ? [v11: $i] :
% 208.52/28.84 | (c_RComplete_Onatfloor(v10) = v11 & hAPP(v9, v3) = v10 & hAPP(v2,
% 208.52/28.84 | v4) = v9 & $i(v11) & $i(v10) & $i(v9) &
% 208.52/28.84 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v8, v11))))
% 208.52/28.84 |
% 208.52/28.84 | ALPHA: (fact_LIMSEQ__inverse__realpow__zero__lemma) implies:
% 208.52/28.84 | (35) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 208.52/28.84 | (c_Power_Opower__class_Opower(tc_RealDef_Oreal) = v3 &
% 208.52/28.84 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v2 &
% 208.52/28.84 | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 208.52/28.84 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v3) & $i(v2)
% 208.52/28.84 | & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 208.52/28.84 | [v7: $i] : ! [v8: $i] : ( ~
% 208.52/28.84 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v5, v2) = v6) | ~
% 208.52/28.84 | (hAPP(v7, v4) = v8) | ~ (hAPP(v3, v6) = v7) | ~ $i(v5) | ~
% 208.52/28.84 | $i(v4) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 208.52/28.84 | v0, v5) | ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12:
% 208.52/28.84 | $i] : (c_RealDef_Oreal(tc_Nat_Onat, v4) = v9 &
% 208.52/28.84 | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v11, v2) = v12 &
% 208.52/28.84 | hAPP(v10, v5) = v11 & hAPP(v1, v9) = v10 & $i(v12) & $i(v11) &
% 208.52/28.84 | $i(v10) & $i(v9) &
% 208.52/28.84 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v12, v8))))
% 208.52/28.84 |
% 208.52/28.84 | ALPHA: (fact_DeMoivre2) implies:
% 208.52/28.84 | (36) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 208.52/28.84 | (c_Power_Opower__class_Opower(tc_Complex_Ocomplex) = v0 &
% 208.52/28.84 | c_Power_Opower__class_Opower(tc_RealDef_Oreal) = v1 &
% 208.52/28.84 | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v2 & $i(v2) &
% 208.52/28.84 | $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 208.52/28.84 | $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : !
% 208.52/28.84 | [v11: $i] : ( ~ (c_Complex_Orcis(v7, v10) = v11) | ~
% 208.52/28.84 | (c_RealDef_Oreal(tc_Nat_Onat, v3) = v8) | ~ (hAPP(v9, v4) = v10)
% 208.52/28.84 | | ~ (hAPP(v6, v3) = v7) | ~ (hAPP(v2, v8) = v9) | ~ (hAPP(v1,
% 208.52/28.84 | v5) = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ? [v12: $i] :
% 208.52/28.84 | ? [v13: $i] : (c_Complex_Orcis(v5, v4) = v12 & hAPP(v13, v3) =
% 208.52/28.84 | v11 & hAPP(v0, v12) = v13 & $i(v13) & $i(v12) & $i(v11))))
% 208.52/28.84 |
% 208.52/28.84 | ALPHA: (fact_rcis__mult) implies:
% 208.52/28.84 | (37) ? [v0: $i] : ? [v1: $i] :
% 208.52/28.84 | (c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex) = v0 &
% 208.52/28.84 | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 & $i(v1) &
% 208.52/28.84 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : !
% 208.52/28.84 | [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ( ~
% 208.52/28.84 | (c_Complex_Orcis(v7, v8) = v9) | ~
% 208.52/28.84 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v4, v2) = v8) | ~
% 208.52/28.84 | (hAPP(v6, v3) = v7) | ~ (hAPP(v1, v5) = v6) | ~ $i(v5) | ~
% 208.52/28.84 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v10: $i] : ? [v11: $i] : ?
% 208.52/28.84 | [v12: $i] : (c_Complex_Orcis(v5, v4) = v10 & c_Complex_Orcis(v3,
% 208.52/28.84 | v2) = v12 & hAPP(v11, v12) = v9 & hAPP(v0, v10) = v11 &
% 208.52/28.84 | $i(v12) & $i(v11) & $i(v10) & $i(v9))))
% 208.52/28.84 |
% 208.52/28.84 | ALPHA: (fact_reals__Archimedean4) implies:
% 208.52/28.85 | (38) ? [v0: $i] : ? [v1: $i] :
% 208.52/28.85 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 208.52/28.85 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 208.52/28.85 | & ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~
% 208.52/28.85 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) | ~
% 208.52/28.85 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | ? [v4:
% 208.52/28.85 | $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ?
% 208.52/28.85 | [v9: $i] : ? [v10: $i] : ? [v11: $i] : (c_Nat_OSuc(v4) = v8 &
% 208.52/28.85 | c_RealDef_Oreal(tc_Nat_Onat, v8) = v9 &
% 208.52/28.85 | c_RealDef_Oreal(tc_Nat_Onat, v4) = v5 & hAPP(v10, v3) = v11 &
% 208.52/28.85 | hAPP(v6, v3) = v7 & hAPP(v1, v9) = v10 & hAPP(v1, v5) = v6 &
% 208.52/28.85 | $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) &
% 208.52/28.85 | $i(v4) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v7,
% 208.52/28.85 | v2) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2,
% 208.52/28.85 | v11))))
% 208.52/28.85 |
% 208.52/28.85 | ALPHA: (fact_ln__realpow) implies:
% 208.52/28.85 | (39) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 208.52/28.85 | (c_Power_Opower__class_Opower(tc_RealDef_Oreal) = v1 &
% 208.52/28.85 | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v2 &
% 208.52/28.85 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v2) & $i(v1)
% 208.52/28.85 | & $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] :
% 208.52/28.85 | ! [v7: $i] : ! [v8: $i] : ( ~ (c_Transcendental_Oln(v4) = v7) | ~
% 208.52/28.85 | (c_RealDef_Oreal(tc_Nat_Onat, v3) = v5) | ~ (hAPP(v6, v7) = v8) |
% 208.52/28.85 | ~ (hAPP(v2, v5) = v6) | ~ $i(v4) | ~ $i(v3) | ~
% 208.52/28.85 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4) | ? [v9:
% 208.52/28.85 | $i] : ? [v10: $i] : (c_Transcendental_Oln(v10) = v8 & hAPP(v9,
% 208.52/28.85 | v3) = v10 & hAPP(v1, v4) = v9 & $i(v10) & $i(v9) & $i(v8))))
% 208.52/28.85 |
% 208.52/28.85 | ALPHA: (fact_ln__mult) implies:
% 208.52/28.85 | (40) ? [v0: $i] : ? [v1: $i] :
% 208.52/28.85 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 208.52/28.85 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0)
% 208.52/28.85 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 208.52/28.85 | $i] : ( ~ (c_Transcendental_Oln(v3) = v4) | ~
% 208.52/28.85 | (c_Transcendental_Oln(v2) = v5) | ~
% 208.52/28.85 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v4, v5) = v6) | ~
% 208.52/28.85 | $i(v3) | ~ $i(v2) | ~
% 208.52/28.85 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) | ~
% 208.52/28.85 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v2) | ? [v7:
% 208.52/28.85 | $i] : ? [v8: $i] : (c_Transcendental_Oln(v8) = v6 & hAPP(v7,
% 208.52/28.85 | v2) = v8 & hAPP(v1, v3) = v7 & $i(v8) & $i(v7) & $i(v6))))
% 208.52/28.85 |
% 208.52/28.85 | ALPHA: (arity_RealDef__Oreal__Orderings_Oorder) implies:
% 208.52/28.85 | (41) class_Orderings_Oorder(tc_RealDef_Oreal)
% 208.52/28.85 |
% 208.52/28.85 | ALPHA: (conj_0) implies:
% 208.52/28.85 | (42) $i(tc_RealDef_Oreal)
% 208.52/28.85 | (43) $i(v_e)
% 208.52/28.85 | (44) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 208.52/28.85 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] :
% 208.52/28.85 | (c_Polynomial_Opoly(tc_Complex_Ocomplex, v_cs____) = v4 &
% 208.52/28.85 | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v0 &
% 208.52/28.85 | c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_w____, v_z) =
% 208.52/28.85 | v1 & c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v5) = v6 &
% 208.52/28.85 | c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v1) = v2 &
% 208.52/28.85 | hAPP(v4, v1) = v5 & hAPP(v3, v6) = v7 & hAPP(v0, v2) = v3 & $i(v7) &
% 208.52/28.85 | $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ~
% 208.52/28.85 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v7, v_e))
% 208.52/28.85 |
% 208.52/28.85 | ALPHA: (function-axioms) implies:
% 208.52/28.85 | (45) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 208.52/28.85 | (c_Groups_Otimes__class_Otimes(v2) = v1) | ~
% 208.52/28.85 | (c_Groups_Otimes__class_Otimes(v2) = v0))
% 208.52/28.85 | (46) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 208.52/28.85 | (hAPP(v3, v2) = v1) | ~ (hAPP(v3, v2) = v0))
% 208.52/28.85 | (47) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 208.52/28.85 | (c_RealVector_Onorm__class_Onorm(v3, v2) = v1) | ~
% 208.52/28.85 | (c_RealVector_Onorm__class_Onorm(v3, v2) = v0))
% 208.52/28.85 | (48) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 208.52/28.85 | (c_Polynomial_Opoly(v3, v2) = v1) | ~ (c_Polynomial_Opoly(v3, v2) =
% 208.52/28.85 | v0))
% 208.52/28.85 | (49) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 208.52/28.85 | (v1 = v0 | ~ (c_Groups_Ominus__class_Ominus(v4, v3, v2) = v1) | ~
% 208.52/28.85 | (c_Groups_Ominus__class_Ominus(v4, v3, v2) = v0))
% 208.52/28.85 |
% 208.52/28.85 | DELTA: instantiating (5) with fresh symbols all_762_0, all_762_1 gives:
% 208.52/28.85 | (50) c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_w____, v_z) =
% 208.52/28.85 | all_762_1 & c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,
% 208.52/28.85 | all_762_1) = all_762_0 & $i(all_762_0) & $i(all_762_1) &
% 208.52/28.85 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_762_0,
% 208.52/28.85 | v_da____)
% 208.52/28.85 |
% 208.52/28.86 | ALPHA: (50) implies:
% 208.52/28.86 | (51) c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, all_762_1) =
% 208.52/28.86 | all_762_0
% 208.52/28.86 | (52) c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_w____, v_z) =
% 208.52/28.86 | all_762_1
% 208.52/28.86 |
% 208.52/28.86 | DELTA: instantiating (1) with fresh symbols all_868_0, all_868_1, all_868_2
% 208.52/28.86 | gives:
% 208.52/28.86 | (53) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_868_2 &
% 208.52/28.86 | hAPP(all_868_1, v_m____) = all_868_0 & hAPP(all_868_2, v_da____) =
% 208.52/28.86 | all_868_1 & $i(all_868_0) & $i(all_868_1) & $i(all_868_2) &
% 208.52/28.86 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_868_0, v_e)
% 208.52/28.86 |
% 208.52/28.86 | ALPHA: (53) implies:
% 208.52/28.86 | (54) c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_868_0, v_e)
% 208.52/28.86 | (55) hAPP(all_868_2, v_da____) = all_868_1
% 208.52/28.86 | (56) hAPP(all_868_1, v_m____) = all_868_0
% 208.52/28.86 | (57) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_868_2
% 208.52/28.86 |
% 208.52/28.86 | DELTA: instantiating (8) with fresh symbols all_926_0, all_926_1, all_926_2
% 208.52/28.86 | gives:
% 208.52/28.86 | (58) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_926_0 &
% 208.52/28.86 | c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_w____, v_z) =
% 208.52/28.86 | all_926_2 & c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,
% 208.52/28.86 | all_926_2) = all_926_1 & $i(all_926_0) & $i(all_926_1) &
% 208.52/28.86 | $i(all_926_2) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 208.52/28.86 | all_926_1, all_926_0)
% 208.52/28.86 |
% 208.52/28.86 | ALPHA: (58) implies:
% 208.52/28.86 | (59) c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, all_926_2) =
% 208.52/28.86 | all_926_1
% 208.52/28.86 | (60) c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_w____, v_z) =
% 208.52/28.86 | all_926_2
% 208.52/28.86 |
% 208.52/28.86 | DELTA: instantiating (12) with fresh symbols all_1043_0, all_1043_1,
% 208.52/28.86 | all_1043_2 gives:
% 208.52/28.86 | (61) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1043_1 &
% 208.52/28.86 | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1043_2 &
% 208.52/28.86 | hAPP(all_1043_2, all_1043_1) = all_1043_0 & $i(all_1043_0) &
% 208.52/28.86 | $i(all_1043_1) & $i(all_1043_2) & ! [v0: $i] : ! [v1: $i] : (v1 = v0
% 208.52/28.86 | | ~ (hAPP(all_1043_0, v0) = v1) | ~ $i(v0))
% 208.52/28.86 |
% 208.52/28.86 | ALPHA: (61) implies:
% 208.52/28.86 | (62) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1043_2
% 208.52/28.86 |
% 208.52/28.86 | DELTA: instantiating (24) with fresh symbol all_1085_0 gives:
% 208.52/28.86 | (63) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1085_0 &
% 208.52/28.86 | $i(all_1085_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 208.52/28.86 | : ! [v4: $i] : ! [v5: $i] : ( ~
% 208.52/28.86 | (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v3, v4) = v5) |
% 208.52/28.86 | ~ (hAPP(v2, v1) = v4) | ~ (hAPP(v2, v0) = v3) | ~
% 208.52/28.86 | (hAPP(all_1085_0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 208.52/28.86 | (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v0, v1) = v5 &
% 208.52/28.86 | $i(v5)))
% 208.52/28.86 |
% 208.52/28.86 | ALPHA: (63) implies:
% 208.52/28.86 | (64) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1085_0
% 208.52/28.86 |
% 208.52/28.86 | DELTA: instantiating (13) with fresh symbol all_1097_0 gives:
% 208.52/28.86 | (65) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1097_0 &
% 208.52/28.86 | $i(all_1097_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 208.52/28.86 | : ( ~ (hAPP(v2, v1) = v3) | ~ (hAPP(all_1097_0, v0) = v2) | ~ $i(v1)
% 208.52/28.86 | | ~ $i(v0) | ? [v4: $i] : (hAPP(v4, v0) = v3 & hAPP(all_1097_0,
% 208.52/28.86 | v1) = v4 & $i(v4) & $i(v3)))
% 208.52/28.86 |
% 208.52/28.86 | ALPHA: (65) implies:
% 208.52/28.86 | (66) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1097_0
% 208.52/28.86 |
% 208.52/28.86 | DELTA: instantiating (18) with fresh symbols all_1179_0, all_1179_1 gives:
% 208.52/28.86 | (67) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1179_0 &
% 208.52/28.86 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1179_1 &
% 208.52/28.86 | $i(all_1179_0) & $i(all_1179_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 208.52/28.86 | $i] : ! [v3: $i] : ( ~ (hAPP(v2, v0) = v3) | ~ (hAPP(all_1179_0,
% 208.52/28.86 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 208.52/28.86 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1179_1, v1) | ~
% 208.52/28.86 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1179_1, v0) |
% 208.52/28.86 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1179_1, v3))
% 208.52/28.86 |
% 208.52/28.86 | ALPHA: (67) implies:
% 208.52/28.86 | (68) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1179_0
% 208.52/28.86 |
% 208.52/28.86 | DELTA: instantiating (16) with fresh symbols all_1206_0, all_1206_1 gives:
% 208.52/28.86 | (69) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1206_0 &
% 208.52/28.86 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1206_1 &
% 208.52/28.86 | $i(all_1206_0) & $i(all_1206_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 208.52/28.86 | any] : ! [v3: $i] : ! [v4: $i] : (v2 = all_1206_1 | v1 = v0 | ~
% 208.52/28.86 | (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v4) | ~ (hAPP(all_1206_0,
% 208.52/28.86 | v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0))
% 208.52/28.86 |
% 208.52/28.86 | ALPHA: (69) implies:
% 208.52/28.86 | (70) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1206_0
% 208.52/28.86 |
% 208.52/28.86 | DELTA: instantiating (7) with fresh symbols all_1232_0, all_1232_1 gives:
% 208.52/28.86 | (71) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1232_1 &
% 208.52/28.86 | c_Polynomial_Opoly(tc_Complex_Ocomplex, v_cs____) = all_1232_0 &
% 208.52/28.86 | $i(all_1232_0) & $i(all_1232_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 208.52/28.86 | (hAPP(all_1232_0, v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i]
% 208.52/28.86 | : ((c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v1) = v3 &
% 208.52/28.86 | $i(v3) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3,
% 208.52/28.86 | v_m____)) |
% 208.52/28.86 | (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v0) = v2 &
% 208.52/28.86 | $i(v2) & ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 208.52/28.86 | v2, all_1232_1))))
% 208.52/28.86 |
% 208.52/28.86 | ALPHA: (71) implies:
% 208.52/28.86 | (72) c_Polynomial_Opoly(tc_Complex_Ocomplex, v_cs____) = all_1232_0
% 208.52/28.86 |
% 208.52/28.86 | DELTA: instantiating (23) with fresh symbols all_1244_0, all_1244_1 gives:
% 208.52/28.86 | (73) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1244_0 &
% 208.52/28.86 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1244_1 &
% 208.52/28.86 | $i(all_1244_0) & $i(all_1244_1) & ! [v0: any] : ! [v1: $i] : ! [v2:
% 208.52/28.86 | $i] : (v0 = all_1244_1 | ~ (hAPP(v1, v0) = v2) | ~
% 208.52/28.86 | (hAPP(all_1244_0, v0) = v1) | ~ $i(v0) |
% 208.52/28.86 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1244_1, v2)) &
% 208.52/28.86 | ! [v0: $i] : ! [v1: $i] : ( ~ (hAPP(v0, all_1244_1) = v1) | ~
% 208.52/28.86 | (hAPP(all_1244_0, all_1244_1) = v0) | ~
% 208.52/28.86 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1244_1, v1))
% 208.52/28.86 |
% 208.52/28.86 | ALPHA: (73) implies:
% 208.52/28.86 | (74) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1244_0
% 208.52/28.86 |
% 208.52/28.86 | DELTA: instantiating (15) with fresh symbols all_1262_0, all_1262_1 gives:
% 208.52/28.87 | (75) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1262_0 &
% 208.52/28.87 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1262_1 &
% 208.52/28.87 | $i(all_1262_0) & $i(all_1262_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 208.52/28.87 | any] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v2 = all_1262_1 |
% 208.52/28.87 | v1 = v0 | ~ (hAPP(v5, v2) = v4) | ~ (hAPP(v3, v2) = v4) | ~
% 208.52/28.87 | (hAPP(all_1262_0, v1) = v3) | ~ (hAPP(all_1262_0, v0) = v5) | ~
% 208.52/28.87 | $i(v2) | ~ $i(v1) | ~ $i(v0))
% 208.52/28.87 |
% 208.52/28.87 | ALPHA: (75) implies:
% 208.52/28.87 | (76) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1262_0
% 208.52/28.87 |
% 208.52/28.87 | DELTA: instantiating (19) with fresh symbols all_1274_0, all_1274_1 gives:
% 208.52/28.87 | (77) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1274_0 &
% 208.52/28.87 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1274_1 &
% 208.52/28.87 | $i(all_1274_0) & $i(all_1274_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 208.52/28.87 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v3, v1) =
% 208.52/28.87 | v4) | ~ (hAPP(v3, v0) = v5) | ~ (hAPP(all_1274_0, v2) = v3) | ~
% 208.52/28.87 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 208.52/28.87 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v0) | ~
% 208.52/28.87 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1274_1, v2) |
% 208.52/28.87 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v4, v5))
% 208.52/28.87 |
% 208.52/28.87 | ALPHA: (77) implies:
% 208.52/28.87 | (78) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1274_0
% 208.52/28.87 |
% 208.52/28.87 | DELTA: instantiating (14) with fresh symbol all_1392_0 gives:
% 208.52/28.87 | (79) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1392_0 &
% 208.52/28.87 | $i(all_1392_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 208.52/28.87 | : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5, v0) = v6) |
% 208.52/28.87 | ~ (hAPP(v3, v1) = v4) | ~ (hAPP(all_1392_0, v4) = v5) | ~
% 208.52/28.87 | (hAPP(all_1392_0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 208.52/28.87 | [v7: $i] : ? [v8: $i] : (hAPP(v7, v0) = v8 & hAPP(v3, v8) = v6 &
% 208.52/28.87 | hAPP(all_1392_0, v1) = v7 & $i(v8) & $i(v7) & $i(v6)))
% 208.52/28.87 |
% 208.52/28.87 | ALPHA: (79) implies:
% 208.52/28.87 | (80) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1392_0
% 208.52/28.87 |
% 208.52/28.87 | DELTA: instantiating (9) with fresh symbols all_1437_0, all_1437_1 gives:
% 208.52/28.87 | (81) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1437_0 &
% 208.52/28.87 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1437_1 &
% 208.52/28.87 | $i(all_1437_0) & $i(all_1437_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 208.52/28.87 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 208.52/28.87 | [v7: $i] : ( ~ (c_RealVector_Onorm__class_Onorm(v3, v1) = v4) | ~
% 208.52/28.87 | (c_RealVector_Onorm__class_Onorm(v3, v0) = v6) | ~ (hAPP(v5, v6) =
% 208.52/28.87 | v7) | ~ (hAPP(all_1437_0, v2) = v5) | ~ $i(v3) | ~ $i(v2) | ~
% 208.52/28.87 | $i(v1) | ~ $i(v0) | ~ class_RealVector_Oreal__normed__vector(v3) |
% 208.52/28.87 | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v7) | ~
% 208.52/28.87 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, all_1437_1)
% 208.52/28.87 | | c_Groups_Ozero__class_Ozero(v3) = v1)
% 208.52/28.87 |
% 208.52/28.87 | ALPHA: (81) implies:
% 208.52/28.87 | (82) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1437_0
% 208.52/28.87 |
% 208.52/28.87 | DELTA: instantiating (33) with fresh symbols all_1443_0, all_1443_1 gives:
% 208.52/28.87 | (83) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1443_1 &
% 208.52/28.87 | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1443_0 &
% 208.52/28.87 | $i(all_1443_0) & $i(all_1443_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 208.52/28.87 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 208.52/28.87 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) | ~
% 208.52/28.87 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v4) | ~ (hAPP(v3, v4) = v5) |
% 208.52/28.87 | ~ (hAPP(all_1443_0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i]
% 208.52/28.87 | : ? [v7: $i] : (c_RealDef_Oreal(tc_Nat_Onat, v7) = v5 & hAPP(v6,
% 208.52/28.87 | v0) = v7 & hAPP(all_1443_1, v1) = v6 & $i(v7) & $i(v6) &
% 208.52/28.87 | $i(v5)))
% 208.52/28.87 |
% 208.52/28.87 | ALPHA: (83) implies:
% 208.52/28.87 | (84) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1443_0
% 208.52/28.87 |
% 208.52/28.87 | DELTA: instantiating (20) with fresh symbol all_1470_0 gives:
% 208.52/28.87 | (85) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1470_0 &
% 208.52/28.87 | $i(all_1470_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 208.52/28.87 | : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~
% 208.52/28.87 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v4, v6) = v7) | ~
% 208.52/28.87 | (hAPP(v5, v0) = v6) | ~ (hAPP(v3, v0) = v4) | ~ (hAPP(all_1470_0,
% 208.52/28.87 | v2) = v3) | ~ (hAPP(all_1470_0, v1) = v5) | ~ $i(v2) | ~
% 208.52/28.87 | $i(v1) | ~ $i(v0) | ? [v8: $i] : ? [v9: $i] :
% 208.52/28.87 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v1) = v8 &
% 208.52/28.87 | hAPP(v9, v0) = v7 & hAPP(all_1470_0, v8) = v9 & $i(v9) & $i(v8) &
% 208.52/28.87 | $i(v7)))
% 208.52/28.87 |
% 208.52/28.87 | ALPHA: (85) implies:
% 208.52/28.87 | (86) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1470_0
% 208.52/28.87 |
% 208.52/28.87 | DELTA: instantiating (22) with fresh symbol all_1473_0 gives:
% 208.52/28.87 | (87) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1473_0 &
% 208.52/28.87 | $i(all_1473_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 208.52/28.87 | : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i]
% 208.52/28.87 | : ! [v9: $i] : ! [v10: $i] : ( ~
% 208.52/28.87 | (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v5, v6) = v7) |
% 208.52/28.87 | ~ (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v4, v9) = v10) |
% 208.52/28.87 | ~ (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v4, v3) = v5) |
% 208.52/28.87 | ~ (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v0, v1) = v6) |
% 208.52/28.87 | ~ (hAPP(v8, v0) = v9) | ~ (hAPP(v2, v1) = v3) | ~ (hAPP(v2, v0) =
% 208.52/28.87 | v4) | ~ (hAPP(all_1473_0, v7) = v8) | ~ $i(v2) | ~ $i(v1) | ~
% 208.52/28.87 | $i(v0) | ? [v11: $i] :
% 208.52/28.87 | (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v3, v11) = v10 &
% 208.52/28.87 | hAPP(v8, v1) = v11 & $i(v11) & $i(v10)))
% 208.52/28.87 |
% 208.52/28.87 | ALPHA: (87) implies:
% 208.52/28.87 | (88) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1473_0
% 208.52/28.87 |
% 208.52/28.87 | DELTA: instantiating (44) with fresh symbols all_1488_0, all_1488_1,
% 208.52/28.87 | all_1488_2, all_1488_3, all_1488_4, all_1488_5, all_1488_6, all_1488_7
% 208.52/28.87 | gives:
% 208.52/28.87 | (89) c_Polynomial_Opoly(tc_Complex_Ocomplex, v_cs____) = all_1488_3 &
% 208.52/28.87 | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1488_7 &
% 208.52/28.87 | c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_w____, v_z) =
% 208.52/28.87 | all_1488_6 & c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,
% 208.52/28.87 | all_1488_2) = all_1488_1 &
% 208.52/28.87 | c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, all_1488_6) =
% 208.52/28.87 | all_1488_5 & hAPP(all_1488_3, all_1488_6) = all_1488_2 &
% 208.52/28.87 | hAPP(all_1488_4, all_1488_1) = all_1488_0 & hAPP(all_1488_7,
% 208.52/28.87 | all_1488_5) = all_1488_4 & $i(all_1488_0) & $i(all_1488_1) &
% 208.52/28.87 | $i(all_1488_2) & $i(all_1488_3) & $i(all_1488_4) & $i(all_1488_5) &
% 208.52/28.87 | $i(all_1488_6) & $i(all_1488_7) & ~
% 208.52/28.87 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1488_0, v_e)
% 208.52/28.87 |
% 208.52/28.87 | ALPHA: (89) implies:
% 208.52/28.87 | (90) ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1488_0, v_e)
% 208.52/28.87 | (91) hAPP(all_1488_7, all_1488_5) = all_1488_4
% 208.52/28.87 | (92) hAPP(all_1488_4, all_1488_1) = all_1488_0
% 208.52/28.87 | (93) hAPP(all_1488_3, all_1488_6) = all_1488_2
% 208.52/28.87 | (94) c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, all_1488_6) =
% 208.52/28.87 | all_1488_5
% 208.52/28.87 | (95) c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, all_1488_2) =
% 208.52/28.87 | all_1488_1
% 208.52/28.87 | (96) c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_w____, v_z) =
% 208.52/28.87 | all_1488_6
% 208.52/28.87 | (97) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1488_7
% 208.52/28.87 | (98) c_Polynomial_Opoly(tc_Complex_Ocomplex, v_cs____) = all_1488_3
% 208.52/28.87 |
% 208.52/28.87 | DELTA: instantiating (40) with fresh symbols all_1490_0, all_1490_1 gives:
% 208.52/28.88 | (99) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1490_0 &
% 208.52/28.88 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1490_1 &
% 208.52/28.88 | $i(all_1490_0) & $i(all_1490_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 208.52/28.88 | $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_Transcendental_Oln(v1) =
% 208.52/28.88 | v2) | ~ (c_Transcendental_Oln(v0) = v3) | ~
% 208.52/28.88 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v3) = v4) | ~
% 208.52/28.88 | $i(v1) | ~ $i(v0) | ~
% 208.52/28.88 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1490_1, v1) | ~
% 208.52/28.88 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1490_1, v0) | ?
% 208.52/28.88 | [v5: $i] : ? [v6: $i] : (c_Transcendental_Oln(v6) = v4 & hAPP(v5,
% 208.52/28.88 | v0) = v6 & hAPP(all_1490_0, v1) = v5 & $i(v6) & $i(v5) &
% 208.52/28.88 | $i(v4)))
% 208.52/28.88 |
% 208.52/28.88 | ALPHA: (99) implies:
% 208.52/28.88 | (100) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1490_0
% 208.52/28.88 |
% 208.52/28.88 | DELTA: instantiating (25) with fresh symbols all_1496_0, all_1496_1 gives:
% 208.52/28.88 | (101) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1496_0 &
% 208.52/28.88 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1496_1 &
% 208.52/28.88 | $i(all_1496_0) & $i(all_1496_1) & ? [v0: $i] : ! [v1: $i] : ( ~
% 208.52/28.88 | $i(v1) | ~ $i(v0) | ~ class_RealVector_Oreal__normed__field(v1) |
% 208.52/28.88 | ? [v2: $i] : ($i(v2) &
% 208.52/28.88 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1496_1, v2) &
% 208.52/28.88 | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 208.52/28.88 | (c_RealVector_Onorm__class_Onorm(v1, v3) = v4) | ~ (hAPP(v5,
% 208.52/28.88 | v2) = v6) | ~ (hAPP(all_1496_0, v4) = v5) | ~ $i(v3) | ?
% 208.52/28.88 | [v7: $i] : ? [v8: $i] : (c_Rings_Oinverse__class_Odivide(v1,
% 208.52/28.88 | v3, v0) = v7 & c_RealVector_Onorm__class_Onorm(v1, v7) = v8
% 208.52/28.88 | & $i(v8) & $i(v7) &
% 208.52/28.88 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v8,
% 208.52/28.88 | v6)))))
% 208.52/28.88 |
% 208.52/28.88 | ALPHA: (101) implies:
% 208.52/28.88 | (102) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1496_0
% 208.52/28.88 |
% 208.52/28.88 | DELTA: instantiating (4) with fresh symbol all_1536_0 gives:
% 208.52/28.88 | (103) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1536_0 &
% 208.52/28.88 | $i(all_1536_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 208.52/28.88 | $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 208.52/28.88 | (c_RealVector_Onorm__class_Onorm(v2, v1) = v3) | ~
% 208.52/28.88 | (c_RealVector_Onorm__class_Onorm(v2, v0) = v5) | ~ (hAPP(v4, v5) =
% 208.52/28.88 | v6) | ~ (hAPP(all_1536_0, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~
% 208.52/28.88 | $i(v0) | ~ class_RealVector_Oreal__normed__div__algebra(v2) | ?
% 208.52/28.88 | [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 208.52/28.88 | (c_Groups_Otimes__class_Otimes(v2) = v7 &
% 208.52/28.88 | c_RealVector_Onorm__class_Onorm(v2, v9) = v6 & hAPP(v8, v0) = v9
% 208.52/28.88 | & hAPP(v7, v1) = v8 & $i(v9) & $i(v8) & $i(v7) & $i(v6)))
% 208.52/28.88 |
% 208.52/28.88 | ALPHA: (103) implies:
% 208.52/28.88 | (104) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1536_0
% 208.52/28.88 |
% 208.52/28.88 | DELTA: instantiating (29) with fresh symbols all_1539_0, all_1539_1 gives:
% 208.52/28.88 | (105) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1539_0 &
% 208.52/28.88 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1539_1 &
% 208.52/28.88 | $i(all_1539_0) & $i(all_1539_1) & ? [v0: $i] : ! [v1: $i] : ( ~
% 208.52/28.88 | $i(v1) | ~ $i(v0) | ~ class_RealVector_Oreal__normed__field(v1) |
% 208.52/28.88 | ? [v2: $i] : ($i(v2) &
% 208.52/28.88 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1539_1,
% 208.52/28.88 | v2) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (
% 208.52/28.88 | ~ (c_RealVector_Onorm__class_Onorm(v1, v3) = v4) | ~ (hAPP(v5,
% 208.52/28.88 | v2) = v6) | ~ (hAPP(all_1539_0, v4) = v5) | ~ $i(v3) | ?
% 208.52/28.88 | [v7: $i] : ? [v8: $i] : (c_Rings_Oinverse__class_Odivide(v1,
% 208.52/28.88 | v3, v0) = v7 & c_RealVector_Onorm__class_Onorm(v1, v7) = v8
% 208.52/28.88 | & $i(v8) & $i(v7) &
% 208.52/28.88 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v8,
% 208.52/28.88 | v6)))))
% 208.52/28.88 |
% 208.52/28.88 | ALPHA: (105) implies:
% 208.52/28.88 | (106) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1539_0
% 208.52/28.88 |
% 208.52/28.88 | DELTA: instantiating (39) with fresh symbols all_1553_0, all_1553_1,
% 208.52/28.88 | all_1553_2 gives:
% 208.52/28.88 | (107) c_Power_Opower__class_Opower(tc_RealDef_Oreal) = all_1553_1 &
% 208.52/28.88 | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1553_0 &
% 208.52/28.88 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1553_2 &
% 208.52/28.88 | $i(all_1553_0) & $i(all_1553_1) & $i(all_1553_2) & ! [v0: $i] : !
% 208.52/28.88 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (
% 208.52/28.88 | ~ (c_Transcendental_Oln(v1) = v4) | ~
% 208.52/28.88 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v2) | ~ (hAPP(v3, v4) = v5) |
% 208.52/28.88 | ~ (hAPP(all_1553_0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ~
% 208.52/28.88 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1553_2, v1) |
% 208.52/28.88 | ? [v6: $i] : ? [v7: $i] : (c_Transcendental_Oln(v7) = v5 &
% 208.52/28.88 | hAPP(v6, v0) = v7 & hAPP(all_1553_1, v1) = v6 & $i(v7) & $i(v6) &
% 208.52/28.88 | $i(v5)))
% 208.52/28.88 |
% 208.52/28.88 | ALPHA: (107) implies:
% 208.52/28.88 | (108) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1553_0
% 208.52/28.88 |
% 208.52/28.88 | DELTA: instantiating (6) with fresh symbol all_1562_0 gives:
% 208.52/28.88 | (109) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1562_0 &
% 208.52/28.88 | $i(all_1562_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 208.52/28.88 | $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 208.52/28.88 | (c_RealVector_Onorm__class_Onorm(v2, v1) = v3) | ~
% 208.52/28.88 | (c_RealVector_Onorm__class_Onorm(v2, v0) = v5) | ~ (hAPP(v4, v5) =
% 208.52/28.88 | v6) | ~ (hAPP(all_1562_0, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~
% 208.52/28.88 | $i(v0) | ~ class_RealVector_Oreal__normed__algebra(v2) | ? [v7:
% 208.52/28.88 | $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] :
% 208.52/28.88 | (c_Groups_Otimes__class_Otimes(v2) = v7 &
% 208.52/28.88 | c_RealVector_Onorm__class_Onorm(v2, v9) = v10 & hAPP(v8, v0) = v9
% 208.52/28.88 | & hAPP(v7, v1) = v8 & $i(v10) & $i(v9) & $i(v8) & $i(v7) &
% 208.52/28.88 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v10, v6)))
% 208.52/28.88 |
% 208.52/28.88 | ALPHA: (109) implies:
% 208.52/28.88 | (110) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1562_0
% 208.52/28.88 |
% 208.52/28.88 | DELTA: instantiating (37) with fresh symbols all_1577_0, all_1577_1 gives:
% 208.52/28.88 | (111) c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex) = all_1577_1 &
% 208.52/28.88 | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1577_0 &
% 208.52/28.88 | $i(all_1577_0) & $i(all_1577_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 208.52/28.88 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 208.52/28.88 | [v7: $i] : ( ~ (c_Complex_Orcis(v5, v6) = v7) | ~
% 208.52/28.88 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, v0) = v6) | ~
% 208.52/28.88 | (hAPP(v4, v1) = v5) | ~ (hAPP(all_1577_0, v3) = v4) | ~ $i(v3) |
% 208.52/28.88 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v8: $i] : ? [v9: $i] : ?
% 208.52/28.88 | [v10: $i] : (c_Complex_Orcis(v3, v2) = v8 & c_Complex_Orcis(v1, v0)
% 208.52/28.88 | = v10 & hAPP(v9, v10) = v7 & hAPP(all_1577_1, v8) = v9 & $i(v10)
% 208.52/28.88 | & $i(v9) & $i(v8) & $i(v7)))
% 208.52/28.88 |
% 208.52/28.88 | ALPHA: (111) implies:
% 208.52/28.88 | (112) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1577_0
% 208.52/28.88 |
% 208.52/28.88 | DELTA: instantiating (31) with fresh symbols all_1598_0, all_1598_1 gives:
% 208.52/28.89 | (113) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1598_0 &
% 208.52/28.89 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1598_1 &
% 208.52/28.89 | $i(all_1598_0) & $i(all_1598_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 208.52/28.89 | $i] : ! [v3: $i] : ( ~ (c_Groups_Otimes__class_Otimes(v1) = v2) |
% 208.52/28.89 | ~ (hAPP(v2, v0) = v3) | ~ $i(v1) | ~ $i(v0) | ~
% 208.52/28.89 | class_RealVector_Oreal__normed__algebra(v1) | ? [v4: $i] : ($i(v4)
% 208.52/28.89 | & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1598_1,
% 208.52/28.89 | v4) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : (
% 208.52/28.89 | ~ (c_RealVector_Onorm__class_Onorm(v1, v5) = v6) | ~ (hAPP(v7,
% 208.52/28.89 | v4) = v8) | ~ (hAPP(all_1598_0, v6) = v7) | ~ $i(v5) | ?
% 208.52/28.89 | [v9: $i] : ? [v10: $i] : (c_RealVector_Onorm__class_Onorm(v1,
% 208.52/28.89 | v9) = v10 & hAPP(v3, v5) = v9 & $i(v10) & $i(v9) &
% 208.52/28.89 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v10,
% 208.52/28.89 | v8)))))
% 208.52/28.89 |
% 208.52/28.89 | ALPHA: (113) implies:
% 208.52/28.89 | (114) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1598_0
% 208.52/28.89 |
% 208.52/28.89 | DELTA: instantiating (28) with fresh symbols all_1601_0, all_1601_1 gives:
% 208.52/28.89 | (115) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1601_0 &
% 208.52/28.89 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1601_1 &
% 208.52/28.89 | $i(all_1601_0) & $i(all_1601_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 208.52/28.89 | $i] : ! [v3: $i] : ( ~ (c_Groups_Otimes__class_Otimes(v1) = v2) |
% 208.52/28.89 | ~ (hAPP(v2, v0) = v3) | ~ $i(v1) | ~ $i(v0) | ~
% 208.52/28.89 | class_RealVector_Oreal__normed__algebra(v1) | ? [v4: $i] : ($i(v4)
% 208.52/28.89 | & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1601_1, v4)
% 208.52/28.89 | & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~
% 208.52/28.89 | (c_RealVector_Onorm__class_Onorm(v1, v5) = v6) | ~ (hAPP(v7,
% 208.52/28.89 | v4) = v8) | ~ (hAPP(all_1601_0, v6) = v7) | ~ $i(v5) | ?
% 208.52/28.89 | [v9: $i] : ? [v10: $i] : (c_RealVector_Onorm__class_Onorm(v1,
% 208.52/28.89 | v9) = v10 & hAPP(v3, v5) = v9 & $i(v10) & $i(v9) &
% 208.52/28.89 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v10,
% 208.52/28.89 | v8)))))
% 208.52/28.89 |
% 208.52/28.89 | ALPHA: (115) implies:
% 208.52/28.89 | (116) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1601_0
% 208.52/28.89 |
% 208.52/28.89 | DELTA: instantiating (2) with fresh symbol all_1616_0 gives:
% 208.52/28.89 | (117) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1616_0 &
% 208.52/28.89 | $i(all_1616_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 208.52/28.89 | $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : !
% 208.52/28.89 | [v8: $i] : ! [v9: $i] : ! [v10: $i] : ( ~
% 208.52/28.89 | (c_Groups_Otimes__class_Otimes(v4) = v5) | ~
% 208.52/28.89 | (c_RealVector_Onorm__class_Onorm(v4, v7) = v8) | ~ (hAPP(v9, v0) =
% 208.52/28.89 | v10) | ~ (hAPP(v6, v1) = v7) | ~ (hAPP(v5, v3) = v6) | ~
% 208.52/28.89 | (hAPP(all_1616_0, v2) = v9) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) |
% 208.52/28.89 | ~ $i(v1) | ~ $i(v0) | ~
% 208.52/28.89 | class_RealVector_Oreal__normed__algebra(v4) |
% 208.52/28.89 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v8, v10) | ? [v11:
% 208.52/28.89 | $i] : ? [v12: $i] : ((c_RealVector_Onorm__class_Onorm(v4, v3) =
% 208.52/28.89 | v11 & $i(v11) & ~
% 208.52/28.89 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v11, v2)) |
% 208.52/28.89 | (c_RealVector_Onorm__class_Onorm(v4, v1) = v12 & $i(v12) & ~
% 208.52/28.89 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v12, v0))))
% 208.52/28.89 |
% 208.52/28.89 | ALPHA: (117) implies:
% 208.52/28.89 | (118) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1616_0
% 208.52/28.89 |
% 208.52/28.89 | DELTA: instantiating (36) with fresh symbols all_1619_0, all_1619_1,
% 208.52/28.89 | all_1619_2 gives:
% 208.52/28.89 | (119) c_Power_Opower__class_Opower(tc_Complex_Ocomplex) = all_1619_2 &
% 208.52/28.89 | c_Power_Opower__class_Opower(tc_RealDef_Oreal) = all_1619_1 &
% 208.52/28.89 | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1619_0 &
% 208.52/28.89 | $i(all_1619_0) & $i(all_1619_1) & $i(all_1619_2) & ! [v0: $i] : !
% 208.52/28.89 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : !
% 208.52/28.89 | [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (c_Complex_Orcis(v4, v7) =
% 208.52/28.89 | v8) | ~ (c_RealDef_Oreal(tc_Nat_Onat, v0) = v5) | ~ (hAPP(v6,
% 208.52/28.89 | v1) = v7) | ~ (hAPP(v3, v0) = v4) | ~ (hAPP(all_1619_0, v5) =
% 208.52/28.89 | v6) | ~ (hAPP(all_1619_1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 208.52/28.89 | $i(v0) | ? [v9: $i] : ? [v10: $i] : (c_Complex_Orcis(v2, v1) = v9
% 208.52/28.89 | & hAPP(v10, v0) = v8 & hAPP(all_1619_2, v9) = v10 & $i(v10) &
% 208.52/28.89 | $i(v9) & $i(v8)))
% 208.52/28.89 |
% 208.52/28.89 | ALPHA: (119) implies:
% 208.52/28.89 | (120) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1619_0
% 208.52/28.89 |
% 208.52/28.89 | DELTA: instantiating (34) with fresh symbols all_1622_0, all_1622_1,
% 208.52/28.89 | all_1622_2 gives:
% 208.52/28.89 | (121) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1622_1 &
% 208.52/28.89 | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1622_0 &
% 208.52/28.89 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1622_2 &
% 208.52/28.89 | $i(all_1622_0) & $i(all_1622_1) & $i(all_1622_2) & ! [v0: $i] : !
% 208.52/28.89 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (
% 208.52/28.89 | ~ (c_RComplete_Onatfloor(v1) = v2) | ~ (c_RComplete_Onatfloor(v0)
% 208.52/28.89 | = v4) | ~ (hAPP(v3, v4) = v5) | ~ (hAPP(all_1622_1, v2) = v3) |
% 208.52/28.89 | ~ $i(v1) | ~ $i(v0) | ~
% 208.52/28.89 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1622_2, v1)
% 208.52/28.89 | | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 208.52/28.89 | all_1622_2, v0) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] :
% 208.52/28.89 | (c_RComplete_Onatfloor(v7) = v8 & hAPP(v6, v0) = v7 &
% 208.52/28.89 | hAPP(all_1622_0, v1) = v6 & $i(v8) & $i(v7) & $i(v6) &
% 208.52/28.89 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v5, v8)))
% 208.52/28.89 |
% 208.52/28.89 | ALPHA: (121) implies:
% 208.52/28.89 | (122) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1622_0
% 208.52/28.89 |
% 208.52/28.89 | DELTA: instantiating (3) with fresh symbols all_1631_0, all_1631_1,
% 208.52/28.89 | all_1631_2, all_1631_3, all_1631_4, all_1631_5, all_1631_6, all_1631_7,
% 208.52/28.89 | all_1631_8, all_1631_9 gives:
% 208.52/28.89 | (123) c_Polynomial_Opoly(tc_Complex_Ocomplex, v_cs____) = all_1631_5 &
% 208.52/28.89 | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1631_9 &
% 208.52/28.89 | c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_w____, v_z) =
% 208.52/28.89 | all_1631_8 & c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,
% 208.52/28.89 | all_1631_4) = all_1631_3 &
% 208.52/28.89 | c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, all_1631_8) =
% 208.52/28.89 | all_1631_7 & hAPP(all_1631_1, v_m____) = all_1631_0 &
% 208.52/28.89 | hAPP(all_1631_5, all_1631_8) = all_1631_4 & hAPP(all_1631_6,
% 208.52/28.89 | all_1631_3) = all_1631_2 & hAPP(all_1631_9, all_1631_7) =
% 208.52/28.89 | all_1631_6 & hAPP(all_1631_9, v_da____) = all_1631_1 & $i(all_1631_0)
% 208.52/28.89 | & $i(all_1631_1) & $i(all_1631_2) & $i(all_1631_3) & $i(all_1631_4) &
% 208.52/28.89 | $i(all_1631_5) & $i(all_1631_6) & $i(all_1631_7) & $i(all_1631_8) &
% 208.52/28.89 | $i(all_1631_9) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 208.52/28.89 | all_1631_2, all_1631_0)
% 208.52/28.89 |
% 208.52/28.89 | ALPHA: (123) implies:
% 208.52/28.89 | (124) c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1631_2,
% 208.52/28.89 | all_1631_0)
% 208.52/28.89 | (125) $i(all_1631_2)
% 208.52/28.89 | (126) $i(all_1631_0)
% 208.52/28.89 | (127) hAPP(all_1631_9, v_da____) = all_1631_1
% 208.52/28.89 | (128) hAPP(all_1631_9, all_1631_7) = all_1631_6
% 208.52/28.89 | (129) hAPP(all_1631_6, all_1631_3) = all_1631_2
% 208.52/28.89 | (130) hAPP(all_1631_5, all_1631_8) = all_1631_4
% 208.52/28.89 | (131) hAPP(all_1631_1, v_m____) = all_1631_0
% 208.52/28.89 | (132) c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, all_1631_8) =
% 208.52/28.89 | all_1631_7
% 208.52/28.89 | (133) c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, all_1631_4) =
% 208.52/28.89 | all_1631_3
% 208.84/28.89 | (134) c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_w____, v_z) =
% 208.84/28.89 | all_1631_8
% 208.84/28.89 | (135) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1631_9
% 208.84/28.89 | (136) c_Polynomial_Opoly(tc_Complex_Ocomplex, v_cs____) = all_1631_5
% 208.84/28.89 |
% 208.84/28.89 | DELTA: instantiating (30) with fresh symbols all_1639_0, all_1639_1 gives:
% 208.84/28.90 | (137) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1639_0 &
% 208.84/28.90 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1639_1 &
% 208.84/28.90 | $i(all_1639_0) & $i(all_1639_1) & ? [v0: $i] : ! [v1: $i] : ! [v2:
% 208.84/28.90 | $i] : ( ~ (c_Groups_Otimes__class_Otimes(v1) = v2) | ~ $i(v1) | ~
% 208.84/28.90 | $i(v0) | ~ class_RealVector_Oreal__normed__algebra(v1) | ? [v3:
% 208.84/28.90 | $i] : ($i(v3) &
% 208.84/28.90 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1639_1,
% 208.84/28.90 | v3) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (
% 208.84/28.90 | ~ (c_RealVector_Onorm__class_Onorm(v1, v4) = v5) | ~ (hAPP(v6,
% 208.84/28.90 | v3) = v7) | ~ (hAPP(all_1639_0, v5) = v6) | ~ $i(v4) | ?
% 208.84/28.90 | [v8: $i] : ? [v9: $i] : ? [v10: $i] :
% 208.84/28.90 | (c_RealVector_Onorm__class_Onorm(v1, v9) = v10 & hAPP(v8, v0) =
% 208.84/28.90 | v9 & hAPP(v2, v4) = v8 & $i(v10) & $i(v9) & $i(v8) &
% 208.84/28.90 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v10,
% 208.84/28.90 | v7)))))
% 208.84/28.90 |
% 208.84/28.90 | ALPHA: (137) implies:
% 208.84/28.90 | (138) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1639_0
% 208.84/28.90 |
% 208.84/28.90 | DELTA: instantiating (26) with fresh symbols all_1641_0, all_1641_1 gives:
% 208.84/28.90 | (139) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1641_0 &
% 208.84/28.90 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1641_1 &
% 208.84/28.90 | $i(all_1641_0) & $i(all_1641_1) & ? [v0: $i] : ! [v1: $i] : ! [v2:
% 208.84/28.90 | $i] : ( ~ (c_Groups_Otimes__class_Otimes(v1) = v2) | ~ $i(v1) | ~
% 208.84/28.90 | $i(v0) | ~ class_RealVector_Oreal__normed__algebra(v1) | ? [v3:
% 208.84/28.90 | $i] : ($i(v3) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 208.84/28.90 | all_1641_1, v3) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 208.84/28.90 | [v7: $i] : ( ~ (c_RealVector_Onorm__class_Onorm(v1, v4) = v5) |
% 208.84/28.90 | ~ (hAPP(v6, v3) = v7) | ~ (hAPP(all_1641_0, v5) = v6) | ~
% 208.84/28.90 | $i(v4) | ? [v8: $i] : ? [v9: $i] : ? [v10: $i] :
% 208.84/28.90 | (c_RealVector_Onorm__class_Onorm(v1, v9) = v10 & hAPP(v8, v0) =
% 208.84/28.90 | v9 & hAPP(v2, v4) = v8 & $i(v10) & $i(v9) & $i(v8) &
% 208.84/28.90 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v10,
% 208.84/28.90 | v7)))))
% 208.84/28.90 |
% 208.84/28.90 | ALPHA: (139) implies:
% 208.84/28.90 | (140) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1641_0
% 208.84/28.90 |
% 208.84/28.90 | DELTA: instantiating (10) with fresh symbols all_1673_0, all_1673_1 gives:
% 208.84/28.90 | (141) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1673_0 &
% 208.84/28.90 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1673_1 &
% 208.84/28.90 | $i(all_1673_0) & $i(all_1673_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 208.84/28.90 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v3, v1) =
% 208.84/28.90 | v4) | ~ (hAPP(v3, v0) = v5) | ~ (hAPP(all_1673_0, v2) = v3) |
% 208.84/28.90 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 208.84/28.90 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v5) | ~
% 208.84/28.90 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1673_1, v2) |
% 208.84/28.90 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v0)) & !
% 208.84/28.90 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 208.84/28.90 | [v5: $i] : ( ~ (hAPP(v3, v1) = v4) | ~ (hAPP(v3, v0) = v5) | ~
% 208.84/28.90 | (hAPP(all_1673_0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 208.84/28.90 | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v0) | ~
% 208.84/28.90 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1673_1, v2) |
% 208.84/28.90 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v5))
% 208.84/28.90 |
% 208.84/28.90 | ALPHA: (141) implies:
% 208.84/28.90 | (142) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1673_0
% 208.84/28.90 |
% 208.84/28.90 | DELTA: instantiating (35) with fresh symbols all_1685_0, all_1685_1,
% 208.84/28.90 | all_1685_2, all_1685_3 gives:
% 208.84/28.90 | (143) c_Power_Opower__class_Opower(tc_RealDef_Oreal) = all_1685_0 &
% 208.84/28.90 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1685_1 &
% 208.84/28.90 | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1685_2 &
% 208.84/28.90 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1685_3 &
% 208.84/28.90 | $i(all_1685_0) & $i(all_1685_1) & $i(all_1685_2) & $i(all_1685_3) &
% 208.84/28.90 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 208.84/28.90 | ( ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1, all_1685_1) =
% 208.84/28.90 | v2) | ~ (hAPP(v3, v0) = v4) | ~ (hAPP(all_1685_0, v2) = v3) |
% 208.84/28.90 | ~ $i(v1) | ~ $i(v0) | ~
% 208.84/28.90 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1685_3, v1)
% 208.84/28.90 | | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] :
% 208.84/28.90 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v5 &
% 208.84/28.90 | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v7, all_1685_1) =
% 208.84/28.90 | v8 & hAPP(v6, v1) = v7 & hAPP(all_1685_2, v5) = v6 & $i(v8) &
% 208.84/28.90 | $i(v7) & $i(v6) & $i(v5) &
% 208.84/28.90 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v8, v4)))
% 208.84/28.90 |
% 208.84/28.90 | ALPHA: (143) implies:
% 208.84/28.90 | (144) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1685_2
% 208.84/28.90 |
% 208.84/28.90 | DELTA: instantiating (17) with fresh symbols all_1688_0, all_1688_1 gives:
% 208.84/28.90 | (145) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1688_0 &
% 208.84/28.90 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1688_1 &
% 208.84/28.90 | $i(all_1688_0) & $i(all_1688_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 208.84/28.90 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 208.84/28.90 | (hAPP(v5, v2) = v6) | ~ (hAPP(v3, v2) = v4) | ~ (hAPP(all_1688_0,
% 208.84/28.90 | v1) = v3) | ~ (hAPP(all_1688_0, v0) = v5) | ~ $i(v2) | ~
% 208.84/28.90 | $i(v1) | ~ $i(v0) | ~
% 208.84/28.90 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v4, v6) | ~
% 208.84/28.90 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1688_1, v2) |
% 208.84/28.90 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v0)) & ! [v0:
% 208.84/28.90 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 208.84/28.90 | [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5, v2) = v6) | ~ (hAPP(v3, v2) =
% 208.84/28.90 | v4) | ~ (hAPP(all_1688_0, v1) = v3) | ~ (hAPP(all_1688_0, v0) =
% 208.84/28.90 | v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 208.84/28.90 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v0) | ~
% 208.84/28.90 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1688_1, v2) |
% 208.84/28.90 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v4, v6))
% 208.84/28.90 |
% 208.84/28.90 | ALPHA: (145) implies:
% 208.84/28.90 | (146) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1688_0
% 208.84/28.90 |
% 208.84/28.90 | DELTA: instantiating (11) with fresh symbols all_1691_0, all_1691_1 gives:
% 208.84/28.90 | (147) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1691_0 &
% 208.84/28.90 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1691_1 &
% 208.84/28.90 | $i(all_1691_0) & $i(all_1691_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 208.84/28.90 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 208.84/28.90 | (hAPP(v5, v2) = v6) | ~ (hAPP(v3, v2) = v4) | ~ (hAPP(all_1691_0,
% 208.84/28.90 | v1) = v3) | ~ (hAPP(all_1691_0, v0) = v5) | ~ $i(v2) | ~
% 208.84/28.90 | $i(v1) | ~ $i(v0) | ~
% 208.84/28.90 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v6) | ~
% 208.84/28.90 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1691_1, v2) |
% 208.84/28.90 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v0)) & !
% 208.84/28.90 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 208.84/28.90 | [v5: $i] : ! [v6: $i] : ( ~ (hAPP(v5, v2) = v6) | ~ (hAPP(v3, v2) =
% 208.84/28.90 | v4) | ~ (hAPP(all_1691_0, v1) = v3) | ~ (hAPP(all_1691_0, v0) =
% 208.84/28.90 | v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 208.84/28.90 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v0) | ~
% 208.84/28.90 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1691_1, v2) |
% 208.84/28.90 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v6))
% 208.84/28.90 |
% 208.84/28.90 | ALPHA: (147) implies:
% 208.84/28.90 | (148) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1691_0
% 208.84/28.90 |
% 208.84/28.90 | DELTA: instantiating (27) with fresh symbols all_1697_0, all_1697_1 gives:
% 208.84/28.91 | (149) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1697_0 &
% 208.84/28.91 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1697_1 &
% 208.84/28.91 | $i(all_1697_0) & $i(all_1697_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 208.84/28.91 | (c_Groups_Otimes__class_Otimes(v0) = v1) | ~ $i(v0) | ~
% 208.84/28.91 | class_RealVector_Oreal__normed__algebra(v0) | ? [v2: $i] : ($i(v2)
% 208.84/28.91 | & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1697_1, v2)
% 208.84/28.91 | & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 208.84/28.91 | $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ( ~
% 208.84/28.91 | (c_RealVector_Onorm__class_Onorm(v0, v4) = v7) | ~
% 208.84/28.91 | (c_RealVector_Onorm__class_Onorm(v0, v3) = v5) | ~ (hAPP(v9,
% 208.84/28.91 | v2) = v10) | ~ (hAPP(v6, v7) = v8) | ~ (hAPP(all_1697_0,
% 208.84/28.91 | v8) = v9) | ~ (hAPP(all_1697_0, v5) = v6) | ~ $i(v4) | ~
% 208.84/28.91 | $i(v3) | ? [v11: $i] : ? [v12: $i] : ? [v13: $i] :
% 208.84/28.91 | (c_RealVector_Onorm__class_Onorm(v0, v12) = v13 & hAPP(v11, v4)
% 208.84/28.91 | = v12 & hAPP(v1, v3) = v11 & $i(v13) & $i(v12) & $i(v11) &
% 208.84/28.91 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v13,
% 208.84/28.91 | v10)))))
% 208.84/28.91 |
% 208.84/28.91 | ALPHA: (149) implies:
% 208.84/28.91 | (150) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1697_0
% 208.84/28.91 |
% 208.84/28.91 | DELTA: instantiating (32) with fresh symbols all_1700_0, all_1700_1 gives:
% 208.84/28.91 | (151) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1700_0 &
% 208.84/28.91 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1700_1 &
% 208.84/28.91 | $i(all_1700_0) & $i(all_1700_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 208.84/28.91 | (c_Groups_Otimes__class_Otimes(v0) = v1) | ~ $i(v0) | ~
% 208.84/28.91 | class_RealVector_Oreal__normed__algebra(v0) | ? [v2: $i] : ($i(v2)
% 208.84/28.91 | & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1700_1,
% 208.84/28.91 | v2) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] :
% 208.84/28.91 | ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : ( ~
% 208.84/28.91 | (c_RealVector_Onorm__class_Onorm(v0, v4) = v7) | ~
% 208.84/28.91 | (c_RealVector_Onorm__class_Onorm(v0, v3) = v5) | ~ (hAPP(v9,
% 208.84/28.91 | v2) = v10) | ~ (hAPP(v6, v7) = v8) | ~ (hAPP(all_1700_0,
% 208.84/28.91 | v8) = v9) | ~ (hAPP(all_1700_0, v5) = v6) | ~ $i(v4) | ~
% 208.84/28.91 | $i(v3) | ? [v11: $i] : ? [v12: $i] : ? [v13: $i] :
% 208.84/28.91 | (c_RealVector_Onorm__class_Onorm(v0, v12) = v13 & hAPP(v11, v4)
% 208.84/28.91 | = v12 & hAPP(v1, v3) = v11 & $i(v13) & $i(v12) & $i(v11) &
% 208.84/28.91 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v13,
% 208.84/28.91 | v10)))))
% 208.84/28.91 |
% 208.84/28.91 | ALPHA: (151) implies:
% 208.84/28.91 | (152) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1700_0
% 208.84/28.91 |
% 208.84/28.91 | DELTA: instantiating (21) with fresh symbols all_1703_0, all_1703_1 gives:
% 208.84/28.91 | (153) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1703_1 &
% 208.84/28.91 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1703_0 &
% 208.84/28.91 | $i(all_1703_0) & $i(all_1703_1) & ! [v0: $i] : ! [v1: any] : !
% 208.84/28.91 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = all_1703_0
% 208.84/28.91 | | ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v5) =
% 208.84/28.91 | all_1703_0) | ~ (hAPP(v4, v0) = v5) | ~ (hAPP(v2, v1) = v3) |
% 208.84/28.91 | ~ (hAPP(all_1703_1, v1) = v2) | ~ (hAPP(all_1703_1, v0) = v4) | ~
% 208.84/28.91 | $i(v1) | ~ $i(v0)) & ! [v0: any] : ! [v1: $i] : ! [v2: $i] : !
% 208.84/28.91 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v0 = all_1703_0 | ~
% 208.84/28.91 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v5) =
% 208.84/28.91 | all_1703_0) | ~ (hAPP(v4, v0) = v5) | ~ (hAPP(v2, v1) = v3) |
% 208.84/28.91 | ~ (hAPP(all_1703_1, v1) = v2) | ~ (hAPP(all_1703_1, v0) = v4) | ~
% 208.84/28.91 | $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] :
% 208.84/28.91 | (v2 = all_1703_0 | ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,
% 208.84/28.91 | v1, v1) = v2) | ~ (hAPP(v0, all_1703_0) = v1) | ~
% 208.84/28.91 | (hAPP(all_1703_1, all_1703_0) = v0))
% 208.84/28.91 |
% 208.84/28.91 | ALPHA: (153) implies:
% 208.84/28.91 | (154) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1703_1
% 208.84/28.91 |
% 208.84/28.91 | DELTA: instantiating (38) with fresh symbols all_1709_0, all_1709_1 gives:
% 208.84/28.91 | (155) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1709_0 &
% 208.84/28.91 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1709_1 &
% 208.84/28.91 | $i(all_1709_0) & $i(all_1709_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 208.84/28.91 | $i(v1) | ~ $i(v0) | ~
% 208.84/28.91 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1709_1, v0)
% 208.84/28.91 | | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1709_1,
% 208.84/28.91 | v1) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ?
% 208.84/28.91 | [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 208.84/28.91 | (c_Nat_OSuc(v2) = v6 & c_RealDef_Oreal(tc_Nat_Onat, v6) = v7 &
% 208.84/28.91 | c_RealDef_Oreal(tc_Nat_Onat, v2) = v3 & hAPP(v8, v1) = v9 &
% 208.84/28.91 | hAPP(v4, v1) = v5 & hAPP(all_1709_0, v7) = v8 & hAPP(all_1709_0,
% 208.84/28.91 | v3) = v4 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4)
% 208.84/28.91 | & $i(v3) & $i(v2) &
% 208.84/28.91 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, v0) &
% 208.84/28.91 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v9)))
% 208.84/28.91 |
% 208.84/28.91 | ALPHA: (155) implies:
% 208.84/28.91 | (156) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1709_0
% 208.84/28.91 |
% 208.84/28.91 | GROUND_INST: instantiating (49) with all_926_2, all_1488_6, v_z, v_w____,
% 208.84/28.91 | tc_Complex_Ocomplex, simplifying with (60), (96) gives:
% 208.84/28.91 | (157) all_1488_6 = all_926_2
% 208.84/28.91 |
% 208.84/28.91 | GROUND_INST: instantiating (49) with all_1488_6, all_1631_8, v_z, v_w____,
% 208.84/28.91 | tc_Complex_Ocomplex, simplifying with (96), (134) gives:
% 208.84/28.91 | (158) all_1631_8 = all_1488_6
% 208.84/28.91 |
% 208.84/28.91 | GROUND_INST: instantiating (49) with all_762_1, all_1631_8, v_z, v_w____,
% 208.84/28.91 | tc_Complex_Ocomplex, simplifying with (52), (134) gives:
% 208.84/28.91 | (159) all_1631_8 = all_762_1
% 208.84/28.91 |
% 208.84/28.91 | GROUND_INST: instantiating (45) with all_1097_0, all_1179_0, tc_RealDef_Oreal,
% 208.84/28.91 | simplifying with (66), (68) gives:
% 208.84/28.91 | (160) all_1179_0 = all_1097_0
% 208.84/28.91 |
% 208.84/28.91 | GROUND_INST: instantiating (45) with all_1179_0, all_1206_0, tc_RealDef_Oreal,
% 208.84/28.91 | simplifying with (68), (70) gives:
% 208.84/28.91 | (161) all_1206_0 = all_1179_0
% 208.84/28.91 |
% 208.84/28.91 | GROUND_INST: instantiating (45) with all_1206_0, all_1244_0, tc_RealDef_Oreal,
% 208.84/28.91 | simplifying with (70), (74) gives:
% 208.84/28.91 | (162) all_1244_0 = all_1206_0
% 208.84/28.91 |
% 208.84/28.91 | GROUND_INST: instantiating (45) with all_1244_0, all_1262_0, tc_RealDef_Oreal,
% 208.84/28.91 | simplifying with (74), (76) gives:
% 208.84/28.91 | (163) all_1262_0 = all_1244_0
% 208.84/28.91 |
% 208.84/28.91 | GROUND_INST: instantiating (45) with all_1262_0, all_1274_0, tc_RealDef_Oreal,
% 208.84/28.91 | simplifying with (76), (78) gives:
% 208.84/28.92 | (164) all_1274_0 = all_1262_0
% 208.84/28.92 |
% 208.84/28.92 | GROUND_INST: instantiating (45) with all_1274_0, all_1392_0, tc_RealDef_Oreal,
% 208.84/28.92 | simplifying with (78), (80) gives:
% 208.84/28.92 | (165) all_1392_0 = all_1274_0
% 208.84/28.92 |
% 208.84/28.92 | GROUND_INST: instantiating (45) with all_1392_0, all_1437_0, tc_RealDef_Oreal,
% 208.84/28.92 | simplifying with (80), (82) gives:
% 208.84/28.92 | (166) all_1437_0 = all_1392_0
% 208.84/28.92 |
% 208.84/28.92 | GROUND_INST: instantiating (45) with all_1437_0, all_1443_0, tc_RealDef_Oreal,
% 208.84/28.92 | simplifying with (82), (84) gives:
% 208.84/28.92 | (167) all_1443_0 = all_1437_0
% 208.84/28.92 |
% 208.84/28.92 | GROUND_INST: instantiating (45) with all_1443_0, all_1470_0, tc_RealDef_Oreal,
% 208.84/28.92 | simplifying with (84), (86) gives:
% 208.84/28.92 | (168) all_1470_0 = all_1443_0
% 208.84/28.92 |
% 208.84/28.92 | GROUND_INST: instantiating (45) with all_1470_0, all_1473_0, tc_RealDef_Oreal,
% 208.84/28.92 | simplifying with (86), (88) gives:
% 208.84/28.92 | (169) all_1473_0 = all_1470_0
% 208.84/28.92 |
% 208.84/28.92 | GROUND_INST: instantiating (45) with all_1473_0, all_1488_7, tc_RealDef_Oreal,
% 208.84/28.92 | simplifying with (88), (97) gives:
% 208.84/28.92 | (170) all_1488_7 = all_1473_0
% 208.84/28.92 |
% 208.84/28.92 | GROUND_INST: instantiating (45) with all_1488_7, all_1490_0, tc_RealDef_Oreal,
% 208.84/28.92 | simplifying with (97), (100) gives:
% 208.84/28.92 | (171) all_1490_0 = all_1488_7
% 208.84/28.92 |
% 208.84/28.92 | GROUND_INST: instantiating (45) with all_1490_0, all_1496_0, tc_RealDef_Oreal,
% 208.84/28.92 | simplifying with (100), (102) gives:
% 208.84/28.92 | (172) all_1496_0 = all_1490_0
% 208.84/28.92 |
% 208.84/28.92 | GROUND_INST: instantiating (45) with all_1496_0, all_1536_0, tc_RealDef_Oreal,
% 208.84/28.92 | simplifying with (102), (104) gives:
% 208.84/28.92 | (173) all_1536_0 = all_1496_0
% 208.84/28.92 |
% 208.84/28.92 | GROUND_INST: instantiating (45) with all_1536_0, all_1539_0, tc_RealDef_Oreal,
% 208.84/28.92 | simplifying with (104), (106) gives:
% 208.84/28.92 | (174) all_1539_0 = all_1536_0
% 208.84/28.92 |
% 208.84/28.92 | GROUND_INST: instantiating (45) with all_1539_0, all_1553_0, tc_RealDef_Oreal,
% 208.84/28.92 | simplifying with (106), (108) gives:
% 208.84/28.92 | (175) all_1553_0 = all_1539_0
% 208.84/28.92 |
% 208.84/28.92 | GROUND_INST: instantiating (45) with all_1553_0, all_1562_0, tc_RealDef_Oreal,
% 208.84/28.92 | simplifying with (108), (110) gives:
% 208.84/28.92 | (176) all_1562_0 = all_1553_0
% 208.84/28.92 |
% 208.84/28.92 | GROUND_INST: instantiating (45) with all_1562_0, all_1577_0, tc_RealDef_Oreal,
% 208.84/28.92 | simplifying with (110), (112) gives:
% 208.84/28.92 | (177) all_1577_0 = all_1562_0
% 208.84/28.92 |
% 208.84/28.92 | GROUND_INST: instantiating (45) with all_1577_0, all_1598_0, tc_RealDef_Oreal,
% 208.84/28.92 | simplifying with (112), (114) gives:
% 208.84/28.92 | (178) all_1598_0 = all_1577_0
% 208.84/28.92 |
% 208.84/28.92 | GROUND_INST: instantiating (45) with all_1598_0, all_1601_0, tc_RealDef_Oreal,
% 208.84/28.92 | simplifying with (114), (116) gives:
% 208.84/28.92 | (179) all_1601_0 = all_1598_0
% 208.84/28.92 |
% 208.84/28.92 | GROUND_INST: instantiating (45) with all_1601_0, all_1616_0, tc_RealDef_Oreal,
% 208.84/28.92 | simplifying with (116), (118) gives:
% 208.84/28.92 | (180) all_1616_0 = all_1601_0
% 208.84/28.92 |
% 208.84/28.92 | GROUND_INST: instantiating (45) with all_1619_0, all_1639_0, tc_RealDef_Oreal,
% 208.84/28.92 | simplifying with (120), (138) gives:
% 208.84/28.92 | (181) all_1639_0 = all_1619_0
% 208.84/28.92 |
% 208.84/28.92 | GROUND_INST: instantiating (45) with all_1097_0, all_1639_0, tc_RealDef_Oreal,
% 208.84/28.92 | simplifying with (66), (138) gives:
% 208.84/28.92 | (182) all_1639_0 = all_1097_0
% 208.84/28.92 |
% 208.84/28.92 | GROUND_INST: instantiating (45) with all_1085_0, all_1639_0, tc_RealDef_Oreal,
% 208.84/28.92 | simplifying with (64), (138) gives:
% 208.84/28.92 | (183) all_1639_0 = all_1085_0
% 208.84/28.92 |
% 208.84/28.92 | GROUND_INST: instantiating (45) with all_1619_0, all_1641_0, tc_RealDef_Oreal,
% 208.84/28.92 | simplifying with (120), (140) gives:
% 208.84/28.92 | (184) all_1641_0 = all_1619_0
% 208.84/28.92 |
% 208.84/28.92 | GROUND_INST: instantiating (45) with all_1641_0, all_1685_2, tc_RealDef_Oreal,
% 208.84/28.92 | simplifying with (140), (144) gives:
% 208.84/28.92 | (185) all_1685_2 = all_1641_0
% 208.84/28.92 |
% 208.84/28.92 | GROUND_INST: instantiating (45) with all_1639_0, all_1688_0, tc_RealDef_Oreal,
% 208.84/28.92 | simplifying with (138), (146) gives:
% 208.84/28.92 | (186) all_1688_0 = all_1639_0
% 208.84/28.92 |
% 208.84/28.92 | GROUND_INST: instantiating (45) with all_1622_0, all_1688_0, tc_RealDef_Oreal,
% 208.84/28.92 | simplifying with (122), (146) gives:
% 208.84/28.92 | (187) all_1688_0 = all_1622_0
% 208.84/28.92 |
% 208.84/28.92 | GROUND_INST: instantiating (45) with all_1673_0, all_1691_0, tc_RealDef_Oreal,
% 208.84/28.92 | simplifying with (142), (148) gives:
% 208.84/28.92 | (188) all_1691_0 = all_1673_0
% 208.84/28.92 |
% 208.84/28.92 | GROUND_INST: instantiating (45) with all_1631_9, all_1691_0, tc_RealDef_Oreal,
% 208.84/28.92 | simplifying with (135), (148) gives:
% 208.84/28.92 | (189) all_1691_0 = all_1631_9
% 208.84/28.92 |
% 208.84/28.92 | GROUND_INST: instantiating (45) with all_1616_0, all_1691_0, tc_RealDef_Oreal,
% 208.84/28.92 | simplifying with (118), (148) gives:
% 208.84/28.92 | (190) all_1691_0 = all_1616_0
% 208.84/28.92 |
% 208.84/28.92 | GROUND_INST: instantiating (45) with all_1673_0, all_1697_0, tc_RealDef_Oreal,
% 208.84/28.92 | simplifying with (142), (150) gives:
% 208.84/28.92 | (191) all_1697_0 = all_1673_0
% 208.84/28.92 |
% 208.84/28.92 | GROUND_INST: instantiating (45) with all_1697_0, all_1700_0, tc_RealDef_Oreal,
% 208.84/28.92 | simplifying with (150), (152) gives:
% 208.84/28.92 | (192) all_1700_0 = all_1697_0
% 208.84/28.92 |
% 208.84/28.92 | GROUND_INST: instantiating (45) with all_1685_2, all_1703_1, tc_RealDef_Oreal,
% 208.84/28.92 | simplifying with (144), (154) gives:
% 208.84/28.92 | (193) all_1703_1 = all_1685_2
% 208.84/28.92 |
% 208.84/28.92 | GROUND_INST: instantiating (45) with all_868_2, all_1703_1, tc_RealDef_Oreal,
% 208.84/28.92 | simplifying with (57), (154) gives:
% 208.84/28.92 | (194) all_1703_1 = all_868_2
% 208.84/28.92 |
% 208.84/28.92 | GROUND_INST: instantiating (45) with all_1700_0, all_1709_0, tc_RealDef_Oreal,
% 208.84/28.92 | simplifying with (152), (156) gives:
% 208.84/28.92 | (195) all_1709_0 = all_1700_0
% 208.84/28.92 |
% 208.84/28.92 | GROUND_INST: instantiating (45) with all_1043_2, all_1709_0, tc_RealDef_Oreal,
% 208.84/28.92 | simplifying with (62), (156) gives:
% 208.84/28.92 | (196) all_1709_0 = all_1043_2
% 208.84/28.92 |
% 208.84/28.92 | GROUND_INST: instantiating (48) with all_1488_3, all_1631_5, v_cs____,
% 208.84/28.92 | tc_Complex_Ocomplex, simplifying with (98), (136) gives:
% 208.84/28.92 | (197) all_1631_5 = all_1488_3
% 208.84/28.92 |
% 208.84/28.92 | GROUND_INST: instantiating (48) with all_1232_0, all_1631_5, v_cs____,
% 208.84/28.92 | tc_Complex_Ocomplex, simplifying with (72), (136) gives:
% 208.84/28.92 | (198) all_1631_5 = all_1232_0
% 208.84/28.92 |
% 208.84/28.92 | COMBINE_EQS: (195), (196) imply:
% 208.84/28.92 | (199) all_1700_0 = all_1043_2
% 208.84/28.92 |
% 208.84/28.92 | SIMP: (199) implies:
% 208.84/28.92 | (200) all_1700_0 = all_1043_2
% 208.84/28.92 |
% 208.84/28.92 | COMBINE_EQS: (193), (194) imply:
% 208.84/28.92 | (201) all_1685_2 = all_868_2
% 208.84/28.92 |
% 208.84/28.92 | SIMP: (201) implies:
% 208.84/28.92 | (202) all_1685_2 = all_868_2
% 208.84/28.92 |
% 208.84/28.92 | COMBINE_EQS: (192), (200) imply:
% 208.84/28.92 | (203) all_1697_0 = all_1043_2
% 208.84/28.92 |
% 208.84/28.92 | SIMP: (203) implies:
% 208.84/28.92 | (204) all_1697_0 = all_1043_2
% 208.84/28.92 |
% 208.84/28.92 | COMBINE_EQS: (191), (204) imply:
% 208.84/28.92 | (205) all_1673_0 = all_1043_2
% 208.84/28.92 |
% 208.84/28.92 | SIMP: (205) implies:
% 208.84/28.92 | (206) all_1673_0 = all_1043_2
% 208.84/28.92 |
% 208.84/28.92 | COMBINE_EQS: (189), (190) imply:
% 208.84/28.92 | (207) all_1631_9 = all_1616_0
% 208.84/28.92 |
% 208.84/28.92 | COMBINE_EQS: (188), (189) imply:
% 208.84/28.92 | (208) all_1673_0 = all_1631_9
% 208.84/28.92 |
% 208.84/28.92 | SIMP: (208) implies:
% 208.84/28.92 | (209) all_1673_0 = all_1631_9
% 208.84/28.92 |
% 208.84/28.92 | COMBINE_EQS: (186), (187) imply:
% 208.84/28.92 | (210) all_1639_0 = all_1622_0
% 208.84/28.92 |
% 208.84/28.92 | SIMP: (210) implies:
% 208.84/28.92 | (211) all_1639_0 = all_1622_0
% 208.84/28.92 |
% 208.84/28.92 | COMBINE_EQS: (185), (202) imply:
% 208.84/28.92 | (212) all_1641_0 = all_868_2
% 208.84/28.92 |
% 208.84/28.92 | SIMP: (212) implies:
% 208.84/28.92 | (213) all_1641_0 = all_868_2
% 208.84/28.92 |
% 208.84/28.92 | COMBINE_EQS: (206), (209) imply:
% 208.84/28.92 | (214) all_1631_9 = all_1043_2
% 208.84/28.92 |
% 208.84/28.92 | SIMP: (214) implies:
% 208.84/28.92 | (215) all_1631_9 = all_1043_2
% 208.84/28.92 |
% 208.84/28.92 | COMBINE_EQS: (184), (213) imply:
% 208.84/28.92 | (216) all_1619_0 = all_868_2
% 208.84/28.92 |
% 208.84/28.92 | SIMP: (216) implies:
% 208.84/28.92 | (217) all_1619_0 = all_868_2
% 208.84/28.92 |
% 208.84/28.92 | COMBINE_EQS: (183), (211) imply:
% 208.84/28.92 | (218) all_1622_0 = all_1085_0
% 208.84/28.92 |
% 208.84/28.92 | COMBINE_EQS: (182), (211) imply:
% 208.84/28.92 | (219) all_1622_0 = all_1097_0
% 208.84/28.92 |
% 208.84/28.92 | COMBINE_EQS: (181), (211) imply:
% 208.84/28.92 | (220) all_1622_0 = all_1619_0
% 208.84/28.92 |
% 208.84/28.92 | COMBINE_EQS: (197), (198) imply:
% 208.84/28.92 | (221) all_1488_3 = all_1232_0
% 208.84/28.92 |
% 208.84/28.92 | SIMP: (221) implies:
% 208.84/28.92 | (222) all_1488_3 = all_1232_0
% 208.84/28.92 |
% 208.84/28.92 | COMBINE_EQS: (158), (159) imply:
% 208.84/28.92 | (223) all_1488_6 = all_762_1
% 208.84/28.92 |
% 208.84/28.92 | SIMP: (223) implies:
% 208.84/28.92 | (224) all_1488_6 = all_762_1
% 208.84/28.92 |
% 208.84/28.92 | COMBINE_EQS: (207), (215) imply:
% 208.84/28.92 | (225) all_1616_0 = all_1043_2
% 208.84/28.92 |
% 208.84/28.92 | SIMP: (225) implies:
% 208.84/28.92 | (226) all_1616_0 = all_1043_2
% 208.84/28.93 |
% 208.84/28.93 | COMBINE_EQS: (218), (220) imply:
% 208.84/28.93 | (227) all_1619_0 = all_1085_0
% 208.84/28.93 |
% 208.84/28.93 | SIMP: (227) implies:
% 208.84/28.93 | (228) all_1619_0 = all_1085_0
% 208.84/28.93 |
% 208.84/28.93 | COMBINE_EQS: (218), (219) imply:
% 208.84/28.93 | (229) all_1097_0 = all_1085_0
% 208.84/28.93 |
% 208.84/28.93 | SIMP: (229) implies:
% 208.84/28.93 | (230) all_1097_0 = all_1085_0
% 208.84/28.93 |
% 208.84/28.93 | COMBINE_EQS: (217), (228) imply:
% 208.84/28.93 | (231) all_1085_0 = all_868_2
% 208.84/28.93 |
% 208.84/28.93 | SIMP: (231) implies:
% 208.84/28.93 | (232) all_1085_0 = all_868_2
% 208.84/28.93 |
% 208.84/28.93 | COMBINE_EQS: (180), (226) imply:
% 208.84/28.93 | (233) all_1601_0 = all_1043_2
% 208.84/28.93 |
% 208.84/28.93 | SIMP: (233) implies:
% 208.84/28.93 | (234) all_1601_0 = all_1043_2
% 208.84/28.93 |
% 208.84/28.93 | COMBINE_EQS: (179), (234) imply:
% 208.84/28.93 | (235) all_1598_0 = all_1043_2
% 208.84/28.93 |
% 208.84/28.93 | SIMP: (235) implies:
% 208.84/28.93 | (236) all_1598_0 = all_1043_2
% 208.84/28.93 |
% 208.84/28.93 | COMBINE_EQS: (178), (236) imply:
% 208.84/28.93 | (237) all_1577_0 = all_1043_2
% 208.84/28.93 |
% 208.84/28.93 | SIMP: (237) implies:
% 208.84/28.93 | (238) all_1577_0 = all_1043_2
% 208.84/28.93 |
% 208.84/28.93 | COMBINE_EQS: (177), (238) imply:
% 208.84/28.93 | (239) all_1562_0 = all_1043_2
% 208.84/28.93 |
% 208.84/28.93 | SIMP: (239) implies:
% 208.84/28.93 | (240) all_1562_0 = all_1043_2
% 208.84/28.93 |
% 208.84/28.93 | COMBINE_EQS: (176), (240) imply:
% 208.84/28.93 | (241) all_1553_0 = all_1043_2
% 208.84/28.93 |
% 208.84/28.93 | SIMP: (241) implies:
% 208.84/28.93 | (242) all_1553_0 = all_1043_2
% 208.84/28.93 |
% 208.84/28.93 | COMBINE_EQS: (175), (242) imply:
% 208.84/28.93 | (243) all_1539_0 = all_1043_2
% 208.84/28.93 |
% 208.84/28.93 | SIMP: (243) implies:
% 208.84/28.93 | (244) all_1539_0 = all_1043_2
% 208.84/28.93 |
% 208.84/28.93 | COMBINE_EQS: (174), (244) imply:
% 208.84/28.93 | (245) all_1536_0 = all_1043_2
% 208.84/28.93 |
% 208.84/28.93 | SIMP: (245) implies:
% 208.84/28.93 | (246) all_1536_0 = all_1043_2
% 208.84/28.93 |
% 208.84/28.93 | COMBINE_EQS: (173), (246) imply:
% 208.84/28.93 | (247) all_1496_0 = all_1043_2
% 208.84/28.93 |
% 208.84/28.93 | SIMP: (247) implies:
% 208.84/28.93 | (248) all_1496_0 = all_1043_2
% 208.84/28.93 |
% 208.84/28.93 | COMBINE_EQS: (172), (248) imply:
% 208.84/28.93 | (249) all_1490_0 = all_1043_2
% 208.84/28.93 |
% 208.84/28.93 | SIMP: (249) implies:
% 208.84/28.93 | (250) all_1490_0 = all_1043_2
% 208.84/28.93 |
% 208.84/28.93 | COMBINE_EQS: (171), (250) imply:
% 208.84/28.93 | (251) all_1488_7 = all_1043_2
% 208.84/28.93 |
% 208.84/28.93 | SIMP: (251) implies:
% 208.84/28.93 | (252) all_1488_7 = all_1043_2
% 208.84/28.93 |
% 208.84/28.93 | COMBINE_EQS: (157), (224) imply:
% 208.84/28.93 | (253) all_926_2 = all_762_1
% 208.84/28.93 |
% 208.84/28.93 | SIMP: (253) implies:
% 208.84/28.93 | (254) all_926_2 = all_762_1
% 208.84/28.93 |
% 208.84/28.93 | COMBINE_EQS: (170), (252) imply:
% 208.84/28.93 | (255) all_1473_0 = all_1043_2
% 208.84/28.93 |
% 208.84/28.93 | SIMP: (255) implies:
% 208.84/28.93 | (256) all_1473_0 = all_1043_2
% 208.84/28.93 |
% 208.84/28.93 | COMBINE_EQS: (169), (256) imply:
% 208.84/28.93 | (257) all_1470_0 = all_1043_2
% 208.84/28.93 |
% 208.84/28.93 | SIMP: (257) implies:
% 208.84/28.93 | (258) all_1470_0 = all_1043_2
% 208.84/28.93 |
% 208.84/28.93 | COMBINE_EQS: (168), (258) imply:
% 208.84/28.93 | (259) all_1443_0 = all_1043_2
% 208.84/28.93 |
% 208.84/28.93 | SIMP: (259) implies:
% 208.84/28.93 | (260) all_1443_0 = all_1043_2
% 208.84/28.93 |
% 208.84/28.93 | COMBINE_EQS: (167), (260) imply:
% 208.84/28.93 | (261) all_1437_0 = all_1043_2
% 208.84/28.93 |
% 208.84/28.93 | SIMP: (261) implies:
% 208.84/28.93 | (262) all_1437_0 = all_1043_2
% 208.84/28.93 |
% 208.84/28.93 | COMBINE_EQS: (166), (262) imply:
% 208.84/28.93 | (263) all_1392_0 = all_1043_2
% 208.84/28.93 |
% 208.84/28.93 | SIMP: (263) implies:
% 208.84/28.93 | (264) all_1392_0 = all_1043_2
% 208.84/28.93 |
% 208.84/28.93 | COMBINE_EQS: (165), (264) imply:
% 208.84/28.93 | (265) all_1274_0 = all_1043_2
% 208.84/28.93 |
% 208.84/28.93 | SIMP: (265) implies:
% 208.84/28.93 | (266) all_1274_0 = all_1043_2
% 208.84/28.93 |
% 208.84/28.93 | COMBINE_EQS: (164), (266) imply:
% 208.84/28.93 | (267) all_1262_0 = all_1043_2
% 208.84/28.93 |
% 208.84/28.93 | SIMP: (267) implies:
% 208.84/28.93 | (268) all_1262_0 = all_1043_2
% 208.84/28.93 |
% 208.84/28.93 | COMBINE_EQS: (163), (268) imply:
% 208.84/28.93 | (269) all_1244_0 = all_1043_2
% 208.84/28.93 |
% 208.84/28.93 | SIMP: (269) implies:
% 208.84/28.93 | (270) all_1244_0 = all_1043_2
% 208.84/28.93 |
% 208.84/28.93 | COMBINE_EQS: (162), (270) imply:
% 208.84/28.93 | (271) all_1206_0 = all_1043_2
% 208.84/28.93 |
% 208.84/28.93 | SIMP: (271) implies:
% 208.84/28.93 | (272) all_1206_0 = all_1043_2
% 208.84/28.93 |
% 208.84/28.93 | COMBINE_EQS: (161), (272) imply:
% 208.84/28.93 | (273) all_1179_0 = all_1043_2
% 208.84/28.93 |
% 208.84/28.93 | SIMP: (273) implies:
% 208.84/28.93 | (274) all_1179_0 = all_1043_2
% 208.84/28.93 |
% 208.84/28.93 | COMBINE_EQS: (160), (274) imply:
% 208.84/28.93 | (275) all_1097_0 = all_1043_2
% 208.84/28.93 |
% 208.84/28.93 | SIMP: (275) implies:
% 208.84/28.93 | (276) all_1097_0 = all_1043_2
% 208.84/28.93 |
% 208.84/28.93 | COMBINE_EQS: (230), (276) imply:
% 208.84/28.93 | (277) all_1085_0 = all_1043_2
% 208.84/28.93 |
% 208.84/28.93 | SIMP: (277) implies:
% 208.84/28.93 | (278) all_1085_0 = all_1043_2
% 208.84/28.93 |
% 208.84/28.93 | COMBINE_EQS: (232), (278) imply:
% 208.84/28.93 | (279) all_1043_2 = all_868_2
% 208.84/28.93 |
% 208.84/28.93 | COMBINE_EQS: (252), (279) imply:
% 208.84/28.93 | (280) all_1488_7 = all_868_2
% 208.84/28.93 |
% 208.84/28.93 | COMBINE_EQS: (215), (279) imply:
% 208.84/28.93 | (281) all_1631_9 = all_868_2
% 208.84/28.93 |
% 208.84/28.93 | REDUCE: (132), (159) imply:
% 208.84/28.93 | (282) c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, all_762_1) =
% 208.84/28.93 | all_1631_7
% 208.84/28.93 |
% 208.84/28.93 | REDUCE: (94), (224) imply:
% 208.84/28.93 | (283) c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, all_762_1) =
% 208.84/28.93 | all_1488_5
% 208.84/28.93 |
% 208.84/28.93 | REDUCE: (59), (254) imply:
% 208.84/28.93 | (284) c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, all_762_1) =
% 208.84/28.93 | all_926_1
% 208.84/28.93 |
% 208.84/28.93 | REDUCE: (130), (159), (198) imply:
% 208.84/28.93 | (285) hAPP(all_1232_0, all_762_1) = all_1631_4
% 208.84/28.93 |
% 208.84/28.93 | REDUCE: (128), (281) imply:
% 208.84/28.93 | (286) hAPP(all_868_2, all_1631_7) = all_1631_6
% 208.84/28.93 |
% 208.84/28.93 | REDUCE: (127), (281) imply:
% 208.84/28.93 | (287) hAPP(all_868_2, v_da____) = all_1631_1
% 208.84/28.93 |
% 208.84/28.93 | REDUCE: (93), (222), (224) imply:
% 208.84/28.93 | (288) hAPP(all_1232_0, all_762_1) = all_1488_2
% 208.84/28.93 |
% 208.84/28.93 | REDUCE: (91), (280) imply:
% 208.84/28.93 | (289) hAPP(all_868_2, all_1488_5) = all_1488_4
% 208.84/28.93 |
% 208.84/28.93 | GROUND_INST: instantiating (46) with all_868_1, all_1631_1, v_da____,
% 208.84/28.93 | all_868_2, simplifying with (55), (287) gives:
% 208.84/28.93 | (290) all_1631_1 = all_868_1
% 208.84/28.93 |
% 208.84/28.93 | GROUND_INST: instantiating (46) with all_1488_2, all_1631_4, all_762_1,
% 208.84/28.93 | all_1232_0, simplifying with (285), (288) gives:
% 208.84/28.93 | (291) all_1631_4 = all_1488_2
% 208.84/28.93 |
% 208.84/28.93 | GROUND_INST: instantiating (47) with all_762_0, all_1488_5, all_762_1,
% 208.84/28.93 | tc_Complex_Ocomplex, simplifying with (51), (283) gives:
% 208.84/28.93 | (292) all_1488_5 = all_762_0
% 208.84/28.93 |
% 208.84/28.93 | GROUND_INST: instantiating (47) with all_1488_5, all_1631_7, all_762_1,
% 208.84/28.93 | tc_Complex_Ocomplex, simplifying with (282), (283) gives:
% 208.84/28.93 | (293) all_1631_7 = all_1488_5
% 208.84/28.93 |
% 208.84/28.93 | GROUND_INST: instantiating (47) with all_926_1, all_1631_7, all_762_1,
% 208.84/28.93 | tc_Complex_Ocomplex, simplifying with (282), (284) gives:
% 208.84/28.93 | (294) all_1631_7 = all_926_1
% 208.84/28.93 |
% 208.84/28.93 | COMBINE_EQS: (293), (294) imply:
% 208.84/28.93 | (295) all_1488_5 = all_926_1
% 208.84/28.93 |
% 208.84/28.93 | SIMP: (295) implies:
% 208.84/28.93 | (296) all_1488_5 = all_926_1
% 208.84/28.93 |
% 208.84/28.93 | COMBINE_EQS: (292), (296) imply:
% 208.84/28.93 | (297) all_926_1 = all_762_0
% 208.84/28.93 |
% 208.84/28.93 | SIMP: (297) implies:
% 208.84/28.93 | (298) all_926_1 = all_762_0
% 208.84/28.93 |
% 208.84/28.93 | COMBINE_EQS: (294), (298) imply:
% 208.84/28.93 | (299) all_1631_7 = all_762_0
% 208.84/28.93 |
% 208.84/28.93 | REDUCE: (133), (291) imply:
% 208.84/28.93 | (300) c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, all_1488_2) =
% 208.84/28.93 | all_1631_3
% 208.84/28.93 |
% 208.84/28.93 | REDUCE: (131), (290) imply:
% 208.84/28.93 | (301) hAPP(all_868_1, v_m____) = all_1631_0
% 208.84/28.93 |
% 208.84/28.93 | REDUCE: (286), (299) imply:
% 208.84/28.93 | (302) hAPP(all_868_2, all_762_0) = all_1631_6
% 208.84/28.93 |
% 208.84/28.93 | REDUCE: (289), (292) imply:
% 208.84/28.93 | (303) hAPP(all_868_2, all_762_0) = all_1488_4
% 208.84/28.93 |
% 208.84/28.93 | GROUND_INST: instantiating (46) with all_1488_4, all_1631_6, all_762_0,
% 208.84/28.93 | all_868_2, simplifying with (302), (303) gives:
% 208.84/28.93 | (304) all_1631_6 = all_1488_4
% 208.84/28.93 |
% 208.84/28.93 | GROUND_INST: instantiating (46) with all_868_0, all_1631_0, v_m____,
% 208.84/28.93 | all_868_1, simplifying with (56), (301) gives:
% 208.84/28.93 | (305) all_1631_0 = all_868_0
% 208.84/28.93 |
% 208.84/28.93 | GROUND_INST: instantiating (47) with all_1488_1, all_1631_3, all_1488_2,
% 208.84/28.93 | tc_Complex_Ocomplex, simplifying with (95), (300) gives:
% 208.84/28.93 | (306) all_1631_3 = all_1488_1
% 208.84/28.93 |
% 208.84/28.93 | REDUCE: (129), (304), (306) imply:
% 208.84/28.93 | (307) hAPP(all_1488_4, all_1488_1) = all_1631_2
% 208.84/28.93 |
% 208.84/28.93 | REDUCE: (126), (305) imply:
% 208.84/28.93 | (308) $i(all_868_0)
% 208.84/28.93 |
% 208.84/28.93 | REDUCE: (124), (305) imply:
% 208.84/28.93 | (309) c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1631_2,
% 208.84/28.93 | all_868_0)
% 208.84/28.93 |
% 208.84/28.93 | GROUND_INST: instantiating (46) with all_1488_0, all_1631_2, all_1488_1,
% 208.84/28.93 | all_1488_4, simplifying with (92), (307) gives:
% 208.84/28.94 | (310) all_1631_2 = all_1488_0
% 208.84/28.94 |
% 208.84/28.94 | REDUCE: (125), (310) imply:
% 208.84/28.94 | (311) $i(all_1488_0)
% 208.84/28.94 |
% 208.84/28.94 | REDUCE: (309), (310) imply:
% 208.84/28.94 | (312) c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1488_0,
% 208.84/28.94 | all_868_0)
% 208.84/28.94 |
% 208.84/28.94 | GROUND_INST: instantiating (fact_xt1_I7_J) with all_1488_0, v_e, all_868_0,
% 208.84/28.94 | tc_RealDef_Oreal, simplifying with (41), (42), (43), (54), (90),
% 208.84/28.94 | (308), (311), (312) gives:
% 208.84/28.94 | (313) $false
% 208.84/28.94 |
% 208.84/28.94 | CLOSE: (313) is inconsistent.
% 208.84/28.94 |
% 208.84/28.94 End of proof
% 208.84/28.94 % SZS output end Proof for theBenchmark
% 208.84/28.94
% 208.84/28.94 28332ms
%------------------------------------------------------------------------------