TSTP Solution File: SWW215+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWW215+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 00:49:27 EDT 2023
% Result : Theorem 107.03s 15.23s
% Output : Proof 253.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWW215+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.11/0.33 % Computer : n027.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Sun Aug 27 22:36:21 EDT 2023
% 0.17/0.33 % CPUTime :
% 0.17/0.61 ________ _____
% 0.17/0.61 ___ __ \_________(_)________________________________
% 0.17/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.17/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.17/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.17/0.61
% 0.17/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.17/0.61 (2023-06-19)
% 0.17/0.61
% 0.17/0.61 (c) Philipp Rümmer, 2009-2023
% 0.17/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.17/0.61 Amanda Stjerna.
% 0.17/0.61 Free software under BSD-3-Clause.
% 0.17/0.61
% 0.17/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.17/0.61
% 0.17/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.17/0.63 Running up to 7 provers in parallel.
% 0.17/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.17/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.17/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.17/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.17/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.17/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.17/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 24.95/4.25 Prover 4: Preprocessing ...
% 24.95/4.31 Prover 0: Preprocessing ...
% 25.62/4.32 Prover 6: Preprocessing ...
% 25.62/4.32 Prover 5: Preprocessing ...
% 26.18/4.41 Prover 1: Preprocessing ...
% 26.18/4.45 Prover 3: Preprocessing ...
% 26.18/4.51 Prover 2: Preprocessing ...
% 70.39/10.38 Prover 1: Warning: ignoring some quantifiers
% 74.21/10.84 Prover 3: Warning: ignoring some quantifiers
% 75.19/10.99 Prover 6: Proving ...
% 76.11/11.08 Prover 1: Constructing countermodel ...
% 76.77/11.16 Prover 3: Constructing countermodel ...
% 78.37/11.54 Prover 4: Warning: ignoring some quantifiers
% 86.98/12.59 Prover 4: Constructing countermodel ...
% 90.67/13.17 Prover 0: Proving ...
% 94.33/13.56 Prover 5: Proving ...
% 96.73/14.00 Prover 5: stopped
% 98.38/14.02 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 107.03/15.16 Prover 7: Preprocessing ...
% 107.03/15.23 Prover 3: proved (14580ms)
% 107.03/15.23
% 107.03/15.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 107.03/15.23
% 107.64/15.24 Prover 6: stopped
% 107.64/15.25 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 107.64/15.25 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 107.64/15.25 Prover 0: stopped
% 107.64/15.26 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 107.64/15.47 Prover 2: Proving ...
% 107.64/15.47 Prover 2: stopped
% 107.64/15.48 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 112.90/16.00 Prover 1: stopped
% 112.90/16.02 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 122.42/17.28 Prover 10: Preprocessing ...
% 123.09/17.32 Prover 11: Preprocessing ...
% 123.66/17.40 Prover 8: Preprocessing ...
% 126.75/17.89 Prover 16: Preprocessing ...
% 126.75/17.89 Prover 13: Preprocessing ...
% 133.66/18.84 Prover 7: Warning: ignoring some quantifiers
% 136.49/19.15 Prover 7: Constructing countermodel ...
% 136.91/19.39 Prover 13: stopped
% 136.91/19.40 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 141.90/19.86 Prover 10: Warning: ignoring some quantifiers
% 143.36/20.16 Prover 8: Warning: ignoring some quantifiers
% 143.36/20.22 Prover 10: Constructing countermodel ...
% 143.36/20.22 Prover 16: Warning: ignoring some quantifiers
% 146.29/20.44 Prover 16: Constructing countermodel ...
% 146.83/20.51 Prover 8: Constructing countermodel ...
% 148.64/20.77 Prover 16: stopped
% 149.42/20.89 Prover 19: Preprocessing ...
% 153.84/21.45 Prover 11: Warning: ignoring some quantifiers
% 155.12/21.80 Prover 11: Constructing countermodel ...
% 168.08/23.53 Prover 19: Warning: ignoring some quantifiers
% 170.92/23.79 Prover 19: Constructing countermodel ...
% 200.73/27.98 Prover 4: stopped
% 201.94/28.21 Prover 19: stopped
% 230.55/32.74 Prover 7: stopped
% 251.12/36.08 Prover 10: Found proof (size 378)
% 251.12/36.08 Prover 10: proved (20833ms)
% 251.12/36.08 Prover 11: stopped
% 251.12/36.09 Prover 8: stopped
% 251.12/36.09
% 251.12/36.09 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 251.12/36.09
% 252.02/36.17 % SZS output start Proof for theBenchmark
% 252.02/36.20 Assumptions after simplification:
% 252.02/36.20 ---------------------------------
% 252.02/36.20
% 252.02/36.20 (arity_Complex__Ocomplex__RealVector_Oreal__normed__vector)
% 252.02/36.20 $i(tc_Complex_Ocomplex) &
% 252.02/36.20 class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
% 252.02/36.20
% 252.02/36.20 (arity_RealDef__Oreal__Orderings_Oorder)
% 252.02/36.20 $i(tc_RealDef_Oreal) & class_Orderings_Oorder(tc_RealDef_Oreal)
% 252.02/36.20
% 252.02/36.20 (conj_0)
% 252.25/36.23 $i(tc_Complex_Ocomplex) & $i(tc_RealDef_Oreal) & $i(v_w____) & $i(v_z) & ?
% 252.25/36.23 [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 252.25/36.23 (c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_w____, v_z) = v0 &
% 252.25/36.23 c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v0) = v1 &
% 252.25/36.23 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v2 & $i(v2) & $i(v1) & $i(v0)
% 252.25/36.23 & ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v2))
% 252.25/36.23
% 252.25/36.23 (fact_H_I2_J)
% 252.25/36.23 $i(v_da____) & $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 252.25/36.23 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v0) &
% 252.25/36.23 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v_da____, v0))
% 252.25/36.23
% 252.25/36.23 (fact_H_I3_J)
% 252.25/36.23 $i(v_m____) & $i(v_e) & $i(v_da____) & $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 252.25/36.23 (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v_e, v_m____) = v0 & $i(v0)
% 252.25/36.23 & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v_da____, v0))
% 252.25/36.23
% 252.25/36.23 (fact_H_I5_J)
% 252.25/36.23 $i(tc_Complex_Ocomplex) & $i(v_da____) & $i(tc_RealDef_Oreal) & $i(v_w____) &
% 252.25/36.23 $i(v_z) & ? [v0: $i] : ? [v1: $i] :
% 252.25/36.23 (c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_w____, v_z) = v0 &
% 252.25/36.23 c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v0) = v1 & $i(v1) &
% 252.25/36.23 $i(v0) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v_da____))
% 252.25/36.23
% 252.25/36.23 (fact_LIMSEQ__inverse__realpow__zero__lemma)
% 252.25/36.23 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 252.25/36.23 $i] : ? [v3: $i] : (c_Power_Opower__class_Opower(tc_RealDef_Oreal) = v3 &
% 252.25/36.23 c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 252.25/36.23 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 252.25/36.23 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v2 & $i(v3) & $i(v2) & $i(v1)
% 252.25/36.23 & $i(v0) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8:
% 252.25/36.23 $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v5, v2) = v6) |
% 252.25/36.23 ~ (hAPP(v7, v4) = v8) | ~ (hAPP(v3, v6) = v7) | ~ $i(v5) | ~ $i(v4) |
% 252.25/36.23 ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v5) | ? [v9:
% 252.25/36.23 $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] :
% 252.25/36.23 (c_RealDef_Oreal(tc_Nat_Onat, v4) = v9 &
% 252.25/36.23 c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v11, v2) = v12 & hAPP(v10,
% 252.25/36.23 v5) = v11 & hAPP(v1, v9) = v10 & $i(v12) & $i(v11) & $i(v10) & $i(v9)
% 252.25/36.23 & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v12, v8))))
% 252.25/36.23
% 252.25/36.23 (fact__096EX_Aea_0620_O_Aea_A_060_A1_A_G_Aea_A_060_Ae_A_P_Am_096)
% 252.25/36.24 $i(v_m____) & $i(v_e) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : ?
% 252.25/36.24 [v2: $i] : ? [v3: $i] : (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,
% 252.25/36.24 v_e, v_m____) = v2 & c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 252.25/36.24 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & $i(v3) & $i(v2) & $i(v1)
% 252.25/36.24 & $i(v0) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v2) &
% 252.25/36.24 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v1) &
% 252.25/36.24 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3))
% 252.25/36.24
% 252.25/36.24 (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)
% 252.25/36.24 $i(v_cs____) & $i(tc_Complex_Ocomplex) & $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 252.25/36.24 ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 252.25/36.24 (c_Polynomial_Opoly(tc_Complex_Ocomplex, v_cs____) = v2 &
% 252.25/36.24 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 252.25/36.24 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & $i(v3) & $i(v2) & $i(v1)
% 252.25/36.24 & $i(v0) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) & ! [v4:
% 252.25/36.24 $i] : ! [v5: $i] : ( ~ (hAPP(v2, v4) = v5) | ~ $i(v4) | ? [v6: $i] : ?
% 252.25/36.24 [v7: $i] : ((c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v5) = v7
% 252.25/36.24 & $i(v7) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v7,
% 252.25/36.24 v3)) | (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v4) =
% 252.25/36.24 v6 & $i(v6) & ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 252.25/36.24 v6, v1)))))
% 252.25/36.24
% 252.25/36.24 (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)
% 252.25/36.24 $i(v_m____) & $i(v_e) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : ?
% 252.25/36.24 [v2: $i] : ? [v3: $i] : (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,
% 252.25/36.24 v_e, v_m____) = v2 & c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 252.25/36.24 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & $i(v3) & $i(v2) & $i(v1)
% 252.25/36.24 & $i(v0) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v2) &
% 252.25/36.24 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v1) &
% 252.25/36.24 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3))
% 252.25/36.24
% 252.25/36.24 (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)
% 252.25/36.25 $i(v_cs____) & $i(tc_Complex_Ocomplex) & $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 252.25/36.25 ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 252.25/36.25 (c_Polynomial_Opoly(tc_Complex_Ocomplex, v_cs____) = v2 &
% 252.25/36.25 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 252.25/36.25 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & $i(v3) & $i(v2) & $i(v1)
% 252.25/36.25 & $i(v0) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3) & ! [v4:
% 252.25/36.25 $i] : ! [v5: $i] : ( ~ (hAPP(v2, v4) = v5) | ~ $i(v4) | ? [v6: $i] : ?
% 252.25/36.25 [v7: $i] : ((c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v5) = v7
% 252.25/36.25 & $i(v7) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v7,
% 252.25/36.25 v3)) | (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v4) =
% 252.25/36.25 v6 & $i(v6) & ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 252.25/36.25 v6, v1)))))
% 252.25/36.25
% 252.25/36.25 (fact_abs__add__one__gt__zero)
% 252.25/36.25 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 252.25/36.25 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 252.25/36.25 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0) & ! [v2:
% 252.25/36.25 $i] : ! [v3: $i] : ( ~ (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v2) =
% 252.25/36.25 v3) | ~ $i(v2) | ? [v4: $i] :
% 252.25/36.25 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1, v3) = v4 & $i(v4) &
% 252.25/36.25 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4))))
% 252.25/36.25
% 252.25/36.25 (fact_abs__add__one__not__less__self)
% 252.25/36.25 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 252.25/36.25 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : !
% 252.25/36.25 [v2: $i] : ( ~ (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v1) = v2) | ~
% 252.25/36.25 $i(v1) | ? [v3: $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2,
% 252.25/36.25 v0) = v3 & $i(v3) & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 252.25/36.25 v3, v1))))
% 252.25/36.25
% 252.25/36.25 (fact_abs__real__of__nat__cancel)
% 252.25/36.25 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ! [v0: $i] : ! [v1: $i] : ( ~
% 252.25/36.25 (c_RealDef_Oreal(tc_Nat_Onat, v0) = v1) | ~ $i(v0) |
% 252.25/36.25 (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v1) = v1 & $i(v1)))
% 252.25/36.25
% 252.25/36.25 (fact_arctan__add)
% 252.41/36.26 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 252.41/36.26 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 252.41/36.26 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & ! [v2:
% 252.41/36.26 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 252.41/36.26 : ! [v8: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v2) =
% 252.41/36.26 v4) | ~ (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v4, v7) =
% 252.41/36.26 v8) | ~ (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v0, v6) = v7)
% 252.41/36.26 | ~ (hAPP(v5, v2) = v6) | ~ (hAPP(v1, v3) = v5) | ~ $i(v3) | ~ $i(v2)
% 252.41/36.26 | ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i]
% 252.41/36.26 : ? [v14: $i] : ((v14 = v13 & c_Transcendental_Oarctan(v8) = v13 &
% 252.41/36.26 c_Transcendental_Oarctan(v3) = v11 & c_Transcendental_Oarctan(v2) =
% 252.41/36.26 v12 & c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v11, v12) = v13 &
% 252.41/36.26 $i(v13) & $i(v12) & $i(v11)) |
% 252.41/36.26 (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v3) = v9 & $i(v9) & ~
% 252.41/36.26 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v9, v0)) |
% 252.41/36.26 (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v2) = v10 & $i(v10) & ~
% 252.41/36.26 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v10, v0)))))
% 252.41/36.26
% 252.41/36.26 (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J)
% 252.41/36.26 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 &
% 252.41/36.26 $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 252.41/36.26 (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v3, v1) = v4) | ~
% 252.41/36.26 $i(v2) | ~ $i(v1) | ~ class_Rings_Ocomm__semiring__1(v2) | hAPP(v4, v0)
% 252.41/36.26 = v1))
% 252.41/36.26
% 252.41/36.26 (fact_d_I2_J)
% 252.41/36.26 $i(v_d____) & $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 252.41/36.26 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v0) &
% 252.41/36.26 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v_d____, v0))
% 252.41/36.26
% 252.41/36.26 (fact_degree__synthetic__div)
% 252.41/36.26 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 &
% 252.41/36.26 $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i]
% 252.41/36.26 : ( ~ (c_Polynomial_Osynthetic__div(v3, v2, v1) = v4) | ~
% 252.41/36.26 (c_Polynomial_Odegree(v3, v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) |
% 252.41/36.26 ~ class_Rings_Ocomm__semiring__0(v3) | ? [v6: $i] :
% 252.41/36.26 (c_Polynomial_Odegree(v3, v2) = v6 &
% 252.41/36.26 c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v6, v0) = v5 & $i(v6) &
% 252.41/36.26 $i(v5))))
% 252.41/36.26
% 252.41/36.26 (fact_div__less__dividend)
% 252.41/36.26 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 252.41/36.26 (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 &
% 252.41/36.26 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: $i]
% 252.41/36.26 : ! [v3: $i] : ! [v4: $i] : ( ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat,
% 252.41/36.26 v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 252.41/36.26 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2) | ~
% 252.41/36.26 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) |
% 252.41/36.26 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v2)))
% 252.41/36.26
% 252.41/36.26 (fact_dvd__mult__cancel1)
% 252.41/36.27 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 252.41/36.27 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 252.41/36.27 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 &
% 252.41/36.27 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 & $i(v2) & $i(v1) & $i(v0) & !
% 252.41/36.27 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v3 = v2 | ~ (hAPP(v5,
% 252.41/36.27 v3) = v6) | ~ (hAPP(v1, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~
% 252.41/36.27 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v4) | ~
% 252.41/36.27 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4)) & ! [v3: $i] : !
% 252.41/36.27 [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, v2) = v5) | ~ (hAPP(v1, v3) = v4) |
% 252.41/36.27 ~ $i(v3) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) |
% 252.41/36.27 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v5, v3)))
% 252.41/36.27
% 252.41/36.27 (fact_dvd__mult__cancel2)
% 252.41/36.27 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 252.41/36.27 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 252.41/36.27 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 &
% 252.41/36.27 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 & $i(v2) & $i(v1) & $i(v0) & !
% 252.41/36.27 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v3 = v2 | ~ (hAPP(v5,
% 252.41/36.27 v4) = v6) | ~ (hAPP(v1, v3) = v5) | ~ $i(v4) | ~ $i(v3) | ~
% 252.41/36.27 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v4) | ~
% 252.41/36.27 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4)) & ! [v3: $i] : !
% 252.41/36.27 [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, v3) = v5) | ~ (hAPP(v1, v2) = v4) |
% 252.41/36.27 ~ $i(v3) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) |
% 252.41/36.27 c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v5, v3)))
% 252.41/36.27
% 252.41/36.27 (fact_ex__least__nat__less)
% 252.41/36.27 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 252.41/36.27 (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 &
% 252.41/36.27 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: $i]
% 252.41/36.27 : ! [v3: $i] : ! [v4: $i] : ( ~ (hAPP(v3, v2) = v4) | ~ $i(v3) | ~
% 252.41/36.27 $i(v2) | ~ hBOOL(v4) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8:
% 252.41/36.27 $i] : ($i(v6) & ((c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v6, v1) = v7
% 252.41/36.27 & hAPP(v3, v7) = v8 & $i(v8) & $i(v7) & hBOOL(v8) &
% 252.41/36.27 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v2) & ! [v9: $i] :
% 252.41/36.27 ! [v10: $i] : ( ~ (hAPP(v3, v9) = v10) | ~ $i(v9) | ~ hBOOL(v10) |
% 252.41/36.27 ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v9, v6))) |
% 252.41/36.27 (hAPP(v3, v0) = v5 & $i(v5) & hBOOL(v5))))))
% 252.41/36.27
% 252.41/36.27 (fact_gcd__lcm__complete__lattice__nat_Obot__least)
% 252.41/36.28 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 &
% 252.41/36.28 $i(v0) & ? [v1: $i] : ( ~ $i(v1) | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,
% 252.41/36.28 v0, v1)))
% 252.41/36.28
% 252.41/36.28 (fact_ge__natfloor__plus__one__imp__gt)
% 252.41/36.28 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 252.41/36.28 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v0) & ! [v1: $i] : ! [v2:
% 252.41/36.28 $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) =
% 252.41/36.28 v4) | ~ (c_RComplete_Onatfloor(v2) = v3) | ~ $i(v2) | ~ $i(v1) |
% 252.41/36.28 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v4) | ? [v5: $i] :
% 252.41/36.28 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v0) = v5 & $i(v5) & ~
% 252.41/36.28 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v5, v1))))
% 252.41/36.28
% 252.41/36.28 (fact_le__natfloor__eq__one)
% 252.41/36.28 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 252.41/36.28 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 &
% 252.41/36.28 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0) & ! [v2:
% 252.41/36.28 $i] : ! [v3: $i] : ( ~ (c_RComplete_Onatfloor(v2) = v3) | ~ $i(v2) | ~
% 252.41/36.28 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, v3) |
% 252.41/36.28 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v2)) & ! [v2: $i]
% 252.41/36.28 : ! [v3: $i] : ( ~ (c_RComplete_Onatfloor(v2) = v3) | ~ $i(v2) | ~
% 252.41/36.28 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v2) |
% 252.41/36.28 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, v3)))
% 252.41/36.28
% 252.41/36.28 (fact_lemmaCauchy)
% 252.41/36.28 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 252.41/36.28 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : !
% 252.41/36.28 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 252.41/36.28 (c_RealVector_Onorm__class_Onorm(v4, v5) = v6) | ~ (hAPP(v1, v2) = v5) |
% 252.41/36.28 ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ class_Orderings_Oord(v3)
% 252.41/36.28 | ~ class_RealVector_Oreal__normed__vector(v4) | ? [v7: $i] : ? [v8:
% 252.41/36.28 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ($i(v8) &
% 252.41/36.28 ((c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v0, v6) = v7 & $i(v7) &
% 252.41/36.28 ! [v12: $i] : ! [v13: $i] : ! [v14: $i] : ( ~
% 252.41/36.28 (c_RealVector_Onorm__class_Onorm(v4, v13) = v14) | ~ (hAPP(v1,
% 252.41/36.28 v12) = v13) | ~ $i(v12) | ~
% 252.41/36.28 c_Orderings_Oord__class_Oless__eq(v3, v2, v12) |
% 252.41/36.28 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v14, v7))) |
% 252.41/36.28 (c_Groups_Ominus__class_Ominus(v4, v5, v9) = v10 &
% 252.41/36.28 c_RealVector_Onorm__class_Onorm(v4, v10) = v11 & hAPP(v1, v8) = v9 &
% 252.41/36.28 $i(v11) & $i(v10) & $i(v9) & c_Orderings_Oord__class_Oless__eq(v3,
% 252.41/36.28 v2, v8) & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v11,
% 252.41/36.28 v0))))))
% 252.41/36.28
% 252.41/36.28 (fact_m_I2_J)
% 252.41/36.29 $i(v_cs____) & $i(v_m____) & $i(tc_Complex_Ocomplex) & $i(tc_RealDef_Oreal) &
% 252.41/36.29 ? [v0: $i] : ? [v1: $i] : (c_Polynomial_Opoly(tc_Complex_Ocomplex, v_cs____)
% 252.41/36.29 = v1 & c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) &
% 252.41/36.29 ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v1, v2) = v3) | ~ $i(v2) | ? [v4: $i]
% 252.41/36.29 : ? [v5: $i] : ((c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v3)
% 252.41/36.29 = v5 & $i(v5) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 252.41/36.29 v5, v_m____)) |
% 252.41/36.29 (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v2) = v4 & $i(v4)
% 252.41/36.29 & ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4, v0)))))
% 252.41/36.29
% 252.41/36.29 (fact_mult__eq__if)
% 252.41/36.29 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 252.41/36.29 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 252.41/36.29 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 &
% 252.41/36.29 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 & $i(v2) & $i(v1) & $i(v0) & !
% 252.41/36.29 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8:
% 252.41/36.29 $i] : (v4 = v0 | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v7) =
% 252.41/36.29 v8) | ~ (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v4, v2) = v5) | ~
% 252.41/36.29 (hAPP(v6, v3) = v7) | ~ (hAPP(v1, v5) = v6) | ~ $i(v4) | ~ $i(v3) | ?
% 252.41/36.29 [v9: $i] : (hAPP(v9, v3) = v8 & hAPP(v1, v4) = v9 & $i(v9) & $i(v8))) & !
% 252.41/36.29 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v0 | ~ (hAPP(v4, v3) = v5) |
% 252.41/36.29 ~ (hAPP(v1, v0) = v4) | ~ $i(v3)))
% 252.41/36.29
% 252.41/36.29 (fact_mult__eq__self__implies__10)
% 252.41/36.29 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 252.41/36.29 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 252.41/36.29 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v2 &
% 252.41/36.29 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & $i(v2) & $i(v1) & $i(v0) & !
% 252.41/36.29 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v2 | v3 = v1 | ~ (hAPP(v5, v3)
% 252.41/36.29 = v4) | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3)))
% 252.41/36.29
% 252.41/36.29 (fact_nat__1__eq__mult__iff)
% 252.41/36.29 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 252.41/36.29 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 252.41/36.29 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & ! [v2: $i]
% 252.41/36.29 : ! [v3: $i] : ! [v4: $i] : (v3 = v0 | ~ (hAPP(v4, v2) = v0) | ~
% 252.41/36.29 (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] :
% 252.41/36.29 ! [v4: $i] : (v2 = v0 | ~ (hAPP(v4, v2) = v0) | ~ (hAPP(v1, v3) = v4) |
% 252.41/36.29 ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~
% 252.41/36.29 (hAPP(v2, v0) = v3) | ~ (hAPP(v1, v0) = v2)))
% 252.41/36.29
% 252.41/36.29 (fact_nat__dvd__1__iff__1)
% 252.41/36.29 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 &
% 252.41/36.29 $i(v0) & c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v0, v0) & ! [v1: $i] : (v1 =
% 252.41/36.29 v0 | ~ $i(v1) | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1, v0)))
% 252.41/36.29
% 252.41/36.29 (fact_nat__le__real__less)
% 252.41/36.30 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 252.41/36.30 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : !
% 252.41/36.30 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v2)
% 252.41/36.30 = v3) | ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~ $i(v2) | ~
% 252.41/36.30 $i(v1) | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1) | ?
% 252.41/36.30 [v5: $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v4, v0) = v5 &
% 252.41/36.30 $i(v5) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v5))) & !
% 252.41/36.30 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 252.41/36.30 (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~ (c_RealDef_Oreal(tc_Nat_Onat,
% 252.41/36.30 v1) = v4) | ~ $i(v2) | ~ $i(v1) |
% 252.41/36.30 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1) | ? [v5: $i] :
% 252.41/36.30 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v4, v0) = v5 & $i(v5) & ~
% 252.41/36.30 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v5))))
% 252.41/36.30
% 252.41/36.30 (fact_nat__less__real__le)
% 252.41/36.30 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 252.41/36.30 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : !
% 252.41/36.30 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v2)
% 252.41/36.30 = v3) | ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~ $i(v2) | ~
% 252.41/36.30 $i(v1) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) | ? [v5:
% 252.41/36.30 $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v0) = v5 &
% 252.41/36.30 $i(v5) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, v4))) &
% 252.41/36.30 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 252.41/36.30 (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~ (c_RealDef_Oreal(tc_Nat_Onat,
% 252.41/36.30 v1) = v4) | ~ $i(v2) | ~ $i(v1) |
% 252.41/36.30 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) | ? [v5: $i] :
% 252.41/36.30 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v0) = v5 & $i(v5) & ~
% 252.41/36.30 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, v4))))
% 252.41/36.30
% 252.41/36.30 (fact_nat__mult__1)
% 252.41/36.30 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 252.41/36.30 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 252.41/36.30 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & hAPP(v0, v1) = v2 & $i(v2) &
% 252.41/36.30 $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : (v4 = v3 | ~ (hAPP(v2, v3) =
% 252.41/36.30 v4) | ~ $i(v3)))
% 252.41/36.30
% 252.41/36.30 (fact_nat__mult__1__right)
% 252.41/36.30 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 252.41/36.30 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 252.41/36.30 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: $i]
% 252.41/36.30 : ! [v3: $i] : ( ~ (hAPP(v0, v2) = v3) | ~ $i(v2) | hAPP(v3, v1) = v2))
% 252.41/36.30
% 252.41/36.30 (fact_nat__mult__eq__1__iff)
% 252.41/36.30 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 252.41/36.30 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 252.41/36.30 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: $i]
% 252.41/36.30 : ! [v3: $i] : ! [v4: $i] : (v3 = v1 | ~ (hAPP(v4, v2) = v1) | ~
% 252.41/36.30 (hAPP(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] :
% 252.41/36.30 ! [v4: $i] : (v2 = v1 | ~ (hAPP(v4, v2) = v1) | ~ (hAPP(v0, v3) = v4) |
% 252.41/36.30 ~ $i(v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~
% 252.41/36.30 (hAPP(v2, v1) = v3) | ~ (hAPP(v0, v1) = v2)))
% 252.41/36.30
% 252.41/36.30 (fact_natceiling__add__one)
% 252.41/36.30 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 252.41/36.30 $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 252.41/36.30 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 &
% 252.41/36.30 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & $i(v2) & $i(v1) & $i(v0)
% 252.41/36.30 & ! [v3: $i] : ! [v4: $i] : ( ~
% 252.41/36.30 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v1) = v4) | ~ $i(v3) |
% 252.41/36.30 ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) | ? [v5:
% 252.41/36.30 $i] : ? [v6: $i] : (c_RComplete_Onatceiling(v4) = v5 &
% 252.41/36.30 c_RComplete_Onatceiling(v3) = v6 &
% 252.41/36.31 c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v6, v2) = v5 & $i(v6) &
% 252.41/36.31 $i(v5))))
% 252.41/36.31
% 252.41/36.31 (fact_natceiling__eq)
% 252.41/36.31 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 252.41/36.31 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 &
% 252.41/36.31 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & ! [v2:
% 252.41/36.31 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v4 | ~
% 252.41/36.31 (c_RComplete_Onatceiling(v2) = v4) | ~
% 252.41/36.31 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v1) = v5) | ~ $i(v3) | ~
% 252.41/36.31 $i(v2) | ? [v6: $i] : ? [v7: $i] : (c_RealDef_Oreal(tc_Nat_Onat, v3) =
% 252.41/36.31 v6 & $i(v6) & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v6,
% 252.41/36.31 v2) | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v6, v0) = v7 &
% 252.41/36.31 $i(v7) & ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2,
% 252.41/36.31 v7))))))
% 252.41/36.31
% 252.41/36.31 (fact_natceiling__le__eq__one)
% 252.41/36.31 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 252.41/36.31 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 &
% 252.41/36.31 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0) & ! [v2:
% 252.41/36.31 $i] : ! [v3: $i] : ( ~ (c_RComplete_Onatceiling(v2) = v3) | ~ $i(v2) |
% 252.41/36.31 ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v0) |
% 252.41/36.31 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v1)) & ! [v2: $i]
% 252.41/36.31 : ! [v3: $i] : ( ~ (c_RComplete_Onatceiling(v2) = v3) | ~ $i(v2) | ~
% 252.41/36.31 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v1) |
% 252.41/36.31 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v0)))
% 252.41/36.31
% 252.41/36.31 (fact_natceiling__one)
% 252.41/36.31 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 252.41/36.31 (c_RComplete_Onatceiling(v0) = v1 & c_Groups_Oone__class_Oone(tc_Nat_Onat) =
% 252.41/36.31 v1 & c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0))
% 252.41/36.31
% 252.41/36.31 (fact_natfloor__add__one)
% 252.41/36.31 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : ? [v2:
% 252.41/36.31 $i] : (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 252.41/36.31 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 &
% 252.41/36.31 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & $i(v2) & $i(v1) & $i(v0)
% 252.41/36.31 & ! [v3: $i] : ! [v4: $i] : ( ~
% 252.41/36.31 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v1) = v4) | ~ $i(v3) |
% 252.41/36.31 ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) | ? [v5:
% 252.41/36.31 $i] : ? [v6: $i] : (c_RComplete_Onatfloor(v4) = v5 &
% 252.41/36.31 c_RComplete_Onatfloor(v3) = v6 &
% 252.41/36.31 c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v6, v2) = v5 & $i(v6) &
% 252.41/36.31 $i(v5))))
% 252.41/36.31
% 252.41/36.31 (fact_natfloor__div__nat)
% 252.41/36.31 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 252.41/36.31 (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 &
% 252.41/36.31 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & ! [v2:
% 252.41/36.31 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 252.41/36.31 (c_RealDef_Oreal(tc_Nat_Onat, v2) = v4) | ~
% 252.41/36.31 (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v3, v4) = v5) | ~
% 252.41/36.31 $i(v3) | ~ $i(v2) | ~
% 252.41/36.31 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) | ~
% 252.41/36.31 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2) | ? [v6: $i] : ? [v7:
% 252.41/36.31 $i] : (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v7, v2) = v6 &
% 252.41/36.31 c_RComplete_Onatfloor(v5) = v6 & c_RComplete_Onatfloor(v3) = v7 & $i(v7)
% 252.41/36.31 & $i(v6))))
% 252.41/36.31
% 252.41/36.31 (fact_natfloor__eq)
% 252.41/36.31 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 252.41/36.31 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : !
% 252.41/36.31 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v2 | ~
% 252.41/36.31 (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~ (c_RComplete_Onatfloor(v1) =
% 252.41/36.31 v4) | ~ $i(v2) | ~ $i(v1) | ~
% 252.41/36.31 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v1) | ? [v5: $i]
% 252.41/36.31 : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v0) = v5 & $i(v5) &
% 252.41/36.31 ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v5))))
% 252.41/36.31
% 252.41/36.31 (fact_natfloor__one)
% 252.41/36.31 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 252.41/36.31 (c_RComplete_Onatfloor(v0) = v1 & c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1
% 252.41/36.31 & c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0))
% 252.41/36.31
% 252.41/36.31 (fact_norm__minus__commute)
% 252.41/36.31 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 252.41/36.31 (c_Groups_Ominus__class_Ominus(v2, v0, v1) = v3) | ~
% 252.41/36.31 (c_RealVector_Onorm__class_Onorm(v2, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~
% 252.41/36.31 $i(v0) | ~ class_RealVector_Oreal__normed__vector(v2) | ? [v5: $i] :
% 252.41/36.31 (c_Groups_Ominus__class_Ominus(v2, v1, v0) = v5 &
% 252.41/36.31 c_RealVector_Onorm__class_Onorm(v2, v5) = v4 & $i(v5) & $i(v4)))
% 252.41/36.31
% 252.41/36.31 (fact_norm__one)
% 252.41/36.32 $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 252.41/36.32 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : !
% 252.41/36.32 [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ (c_RealVector_Onorm__class_Onorm(v1,
% 252.41/36.32 v2) = v3) | ~ (c_Groups_Oone__class_Oone(v1) = v2) | ~ $i(v1) | ~
% 252.41/36.32 class_RealVector_Oreal__normed__algebra__1(v1)))
% 252.41/36.32
% 252.41/36.32 (fact_one0)
% 252.41/36.32 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 252.41/36.32 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 252.41/36.32 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0) &
% 252.41/36.32 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v1))
% 252.41/36.32
% 252.41/36.32 (fact_order__less__le)
% 252.41/36.32 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ $i(v2) | ~ $i(v1) |
% 252.41/36.32 ~ $i(v0) | ~ class_Orderings_Oorder(v2) | ~
% 252.41/36.32 c_Orderings_Oord__class_Oless__eq(v2, v1, v0) |
% 252.41/36.32 c_Orderings_Oord__class_Oless(v2, v1, v0)) & ! [v0: $i] : ! [v1: $i] : !
% 252.41/36.32 [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ class_Orderings_Oorder(v2)
% 252.41/36.32 | ~ c_Orderings_Oord__class_Oless(v2, v1, v0) |
% 252.41/36.32 c_Orderings_Oord__class_Oless__eq(v2, v1, v0)) & ! [v0: $i] : ! [v1: $i] :
% 252.41/36.32 ( ~ $i(v1) | ~ $i(v0) | ~ class_Orderings_Oorder(v1) | ~
% 252.41/36.32 c_Orderings_Oord__class_Oless(v1, v0, v0))
% 252.41/36.32
% 252.41/36.32 (fact_power__dvd__imp__le)
% 252.41/36.32 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 252.41/36.32 (c_Power_Opower__class_Opower(tc_Nat_Onat) = v0 &
% 252.41/36.32 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: $i]
% 252.41/36.32 : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~
% 252.41/36.32 (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) = v7) | ~ (hAPP(v0, v4) = v5) | ~
% 252.41/36.32 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,
% 252.41/36.32 v6, v7) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) |
% 252.41/36.32 c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v2)))
% 252.41/36.32
% 252.41/36.32 (fact_power__eq__if)
% 252.41/36.32 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 252.41/36.32 (c_Power_Opower__class_Opower(tc_Nat_Onat) = v1 &
% 252.41/36.32 c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v3 &
% 252.41/36.32 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 &
% 252.41/36.32 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 & $i(v3) & $i(v2) & $i(v1) &
% 252.41/36.32 $i(v0) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i]
% 252.41/36.32 : ! [v9: $i] : ! [v10: $i] : (v5 = v0 | ~
% 252.41/36.32 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v5, v2) = v8) | ~ (hAPP(v7,
% 252.41/36.32 v9) = v10) | ~ (hAPP(v6, v8) = v9) | ~ (hAPP(v3, v4) = v7) | ~
% 252.41/36.32 (hAPP(v1, v4) = v6) | ~ $i(v5) | ~ $i(v4) | (hAPP(v6, v5) = v10 &
% 252.41/36.32 $i(v10))) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v6 = v2 | ~
% 252.41/36.32 (hAPP(v5, v0) = v6) | ~ (hAPP(v1, v4) = v5) | ~ $i(v4)))
% 252.41/36.32
% 252.41/36.32 (fact_power__one__right)
% 252.41/36.32 $i(tc_Nat_Onat) & ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 &
% 252.41/36.32 $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 252.41/36.32 (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v3, v1) = v4) | ~
% 252.41/36.32 $i(v2) | ~ $i(v1) | ~ class_Groups_Omonoid__mult(v2) | hAPP(v4, v0) =
% 252.41/36.32 v1))
% 252.41/36.32
% 252.41/36.32 (fact_real__le__trans)
% 252.41/36.32 $i(tc_RealDef_Oreal) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) |
% 252.41/36.32 ~ $i(v1) | ~ $i(v0) | ~
% 252.41/36.32 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v1) | ~
% 252.41/36.32 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v0) |
% 252.41/36.32 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v0))
% 252.41/36.32
% 252.41/36.32 (fact_real__mult__1)
% 252.41/36.32 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 252.41/36.32 (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v0 &
% 252.41/36.32 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & hAPP(v0, v1) = v2 &
% 252.41/36.32 $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : (v4 = v3 | ~
% 252.41/36.32 (hAPP(v2, v3) = v4) | ~ $i(v3)))
% 252.41/36.32
% 252.41/36.32 (fact_real__natfloor__add__one__gt)
% 252.41/36.32 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 252.41/36.32 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : !
% 252.41/36.32 [v2: $i] : ( ~ (c_RComplete_Onatfloor(v1) = v2) | ~ $i(v1) | ? [v3: $i] :
% 252.41/36.32 ? [v4: $i] : (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3 &
% 252.41/36.32 c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v0) = v4 & $i(v4) &
% 252.41/36.32 $i(v3) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v4))))
% 252.41/36.32
% 252.41/36.32 (fact_real__natfloor__gt__diff__one)
% 252.41/36.32 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 252.41/36.32 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : !
% 252.41/36.32 [v2: $i] : ( ~ (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v1, v0) =
% 252.41/36.32 v2) | ~ $i(v1) | ? [v3: $i] : ? [v4: $i] :
% 252.41/36.32 (c_RealDef_Oreal(tc_Nat_Onat, v3) = v4 & c_RComplete_Onatfloor(v1) = v3 &
% 252.41/36.32 $i(v4) & $i(v3) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2,
% 252.41/36.32 v4))))
% 252.41/36.32
% 252.41/36.32 (fact_real__of__nat__1)
% 252.41/36.32 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 252.41/36.32 (c_RealDef_Oreal(tc_Nat_Onat, v0) = v1 &
% 252.41/36.32 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 &
% 252.41/36.32 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0))
% 252.41/36.32
% 252.41/36.32 (fact_real__of__nat__div3)
% 252.41/36.33 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] :
% 252.41/36.33 (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v0) & ! [v1: $i] : !
% 252.41/36.33 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 252.41/36.33 $i] : ! [v8: $i] : ( ~ (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v2, v1) =
% 252.41/36.33 v6) | ~ (c_RealDef_Oreal(tc_Nat_Onat, v6) = v7) | ~
% 252.41/36.33 (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~ (c_RealDef_Oreal(tc_Nat_Onat,
% 252.41/36.33 v1) = v4) | ~ (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v3,
% 252.41/36.33 v4) = v5) | ~ (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v5,
% 252.41/36.33 v7) = v8) | ~ $i(v2) | ~ $i(v1) |
% 252.41/36.33 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v8, v0)))
% 252.41/36.33
% 252.41/36.33 (fact_real__zero__not__eq__one)
% 252.41/36.33 $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) &
% 252.41/36.33 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 252.41/36.33 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0))
% 252.41/36.33
% 252.41/36.33 (fact_realpow__minus__mult)
% 252.41/36.33 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 252.41/36.33 (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 &
% 252.41/36.33 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: $i]
% 252.41/36.33 : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : !
% 252.41/36.33 [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~
% 252.41/36.33 (c_Power_Opower__class_Opower(v4) = v6) | ~
% 252.41/36.33 (c_Groups_Otimes__class_Otimes(v4) = v5) | ~
% 252.41/36.33 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v3, v1) = v8) | ~ (hAPP(v10,
% 252.41/36.33 v2) = v11) | ~ (hAPP(v7, v8) = v9) | ~ (hAPP(v6, v2) = v7) | ~
% 252.41/36.33 (hAPP(v5, v9) = v10) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 252.41/36.33 class_Groups_Omonoid__mult(v4) | ~
% 252.41/36.33 c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) | (hAPP(v7, v3) = v11 &
% 252.41/36.33 $i(v11))))
% 252.41/36.33
% 252.41/36.33 (fact_realpow__num__eq__if)
% 252.41/36.33 $i(tc_Nat_Onat) & ? [v0: $i] : ? [v1: $i] :
% 252.41/36.33 (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 &
% 252.41/36.33 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: $i]
% 252.41/36.33 : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : !
% 252.41/36.33 [v8: $i] : ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ( ~
% 252.41/36.33 (c_Power_Opower__class_Opower(v4) = v5) | ~
% 252.41/36.33 (c_Groups_Otimes__class_Otimes(v4) = v7) | ~
% 252.41/36.33 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v3, v1) = v9) | ~ (hAPP(v8,
% 252.41/36.33 v10) = v11) | ~ (hAPP(v7, v2) = v8) | ~ (hAPP(v6, v9) = v10) | ~
% 252.41/36.33 (hAPP(v5, v2) = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 252.41/36.33 class_Power_Opower(v4) | ? [v12: $i] : ? [v13: $i] : (( ~ (v3 = v0) |
% 252.41/36.33 (v13 = v12 & c_Groups_Oone__class_Oone(v4) = v12 & hAPP(v6, v0) = v12
% 252.41/36.33 & $i(v12))) & (v3 = v0 | (v12 = v11 & hAPP(v6, v3) = v11 &
% 252.41/36.33 $i(v11))))))
% 252.41/36.33
% 252.41/36.33 (fact_reals__Archimedean6)
% 252.80/36.33 $i(tc_Nat_Onat) & $i(tc_RealDef_Oreal) & ? [v0: $i] : ? [v1: $i] :
% 252.80/36.33 (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 252.80/36.33 c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & ! [v2: $i]
% 252.80/36.33 : ( ~ $i(v2) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0,
% 252.80/36.33 v2) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] :
% 252.80/36.33 (c_RealDef_Oreal(tc_Nat_Onat, v4) = v5 & c_RealDef_Oreal(tc_Nat_Onat, v3)
% 252.80/36.33 = v6 & c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v3, v1) = v4 & $i(v6)
% 252.80/36.33 & $i(v5) & $i(v4) & $i(v3) &
% 252.80/36.33 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, v2) &
% 252.80/36.33 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v6))))
% 252.80/36.33
% 252.80/36.33 (fact_reduce__poly__simple)
% 252.80/36.33 $i(tc_Nat_Onat) & $i(tc_Complex_Ocomplex) & $i(tc_RealDef_Oreal) & ? [v0: $i]
% 252.80/36.33 : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] :
% 252.80/36.33 (c_Power_Opower__class_Opower(tc_Complex_Ocomplex) = v4 &
% 252.80/36.33 c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex) = v3 &
% 252.80/36.33 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 &
% 252.80/36.33 c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v0 &
% 252.80/36.33 c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = v2 &
% 252.80/36.33 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v5 & $i(v5) & $i(v4) & $i(v3)
% 252.80/36.33 & $i(v2) & $i(v1) & $i(v0) & ? [v6: $i] : ! [v7: $i] : ! [v8: $i] : (v7 =
% 252.80/36.33 v0 | v6 = v1 | ~ (hAPP(v3, v7) = v8) | ~ $i(v7) | ~ $i(v6) | ? [v9:
% 252.80/36.33 $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ?
% 252.80/36.33 [v14: $i] : (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v2, v12) =
% 252.80/36.33 v13 & c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v13) = v14 &
% 252.80/36.33 hAPP(v10, v6) = v11 & hAPP(v8, v11) = v12 & hAPP(v4, v9) = v10 & $i(v14)
% 252.80/36.33 & $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) &
% 252.80/36.33 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v14, v5))))
% 252.80/36.33
% 252.80/36.33 (fact_unimodular__reduce__norm)
% 252.80/36.34 $i(c_Complex_Oii) & $i(tc_Complex_Ocomplex) & $i(tc_RealDef_Oreal) & ? [v0:
% 252.80/36.34 $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = v1 &
% 252.80/36.34 c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) & ! [v2:
% 252.80/36.34 $i] : ! [v3: $i] : ( ~
% 252.80/36.34 (c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v2, v1) = v3) | ~
% 252.80/36.34 $i(v2) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8:
% 252.80/36.34 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : (( ~ (v4 = v0) &
% 252.80/36.34 c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v2) = v4 &
% 252.80/36.34 $i(v4)) | (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v2, v1) =
% 252.80/36.34 v5 & c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v5) = v6 &
% 252.80/36.34 $i(v6) & $i(v5) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v6,
% 252.80/36.34 v0)) | (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v2,
% 252.80/36.34 c_Complex_Oii) = v8 &
% 252.80/36.34 c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v8) = v9 & $i(v9)
% 252.80/36.34 & $i(v8) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v9, v0)) |
% 252.80/36.34 (c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v2, c_Complex_Oii) =
% 252.80/36.34 v10 & c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v10) = v11
% 252.80/36.34 & $i(v11) & $i(v10) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 252.80/36.34 v11, v0)) | (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,
% 252.80/36.34 v3) = v7 & $i(v7) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 252.80/36.34 v7, v0)))))
% 252.80/36.34
% 252.80/36.34 (function-axioms)
% 252.80/36.34 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 252.80/36.34 | ~ (c_Power_Opower_Opower(v4, v3, v2) = v1) | ~
% 252.80/36.34 (c_Power_Opower_Opower(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 252.80/36.34 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 252.80/36.34 (c_Polynomial_Osynthetic__div(v4, v3, v2) = v1) | ~
% 252.80/36.34 (c_Polynomial_Osynthetic__div(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 252.80/36.34 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 252.80/36.34 (c_Divides_Odiv__class_Omod(v4, v3, v2) = v1) | ~
% 252.80/36.34 (c_Divides_Odiv__class_Omod(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 252.80/36.34 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 252.80/36.34 (c_Divides_Odiv__class_Odiv(v4, v3, v2) = v1) | ~
% 252.80/36.34 (c_Divides_Odiv__class_Odiv(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 252.80/36.34 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 252.80/36.34 (c_Polynomial_Opcompose(v4, v3, v2) = v1) | ~ (c_Polynomial_Opcompose(v4,
% 252.80/36.34 v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 252.80/36.34 ! [v4: $i] : (v1 = v0 | ~ (c_Polynomial_Oorder(v4, v3, v2) = v1) | ~
% 252.80/36.34 (c_Polynomial_Oorder(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 252.80/36.34 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 252.80/36.34 (c_Groups_Oplus__class_Oplus(v4, v3, v2) = v1) | ~
% 252.80/36.34 (c_Groups_Oplus__class_Oplus(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 252.80/36.34 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 252.80/36.34 (c_Rings_Oinverse__class_Odivide(v4, v3, v2) = v1) | ~
% 252.80/36.34 (c_Rings_Oinverse__class_Odivide(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 252.80/36.34 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 252.80/36.34 (c_Groups_Ominus__class_Ominus(v4, v3, v2) = v1) | ~
% 252.80/36.34 (c_Groups_Ominus__class_Ominus(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 252.80/36.34 $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (c_RealDef_Oreal(v3, v2) =
% 252.80/36.34 v1) | ~ (c_RealDef_Oreal(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 252.80/36.34 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.80/36.34 (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v3, v2) = v1) | ~
% 252.80/36.34 (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v3, v2) = v0)) & ! [v0:
% 252.80/36.34 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.80/36.34 (c_Polynomial_Odegree(v3, v2) = v1) | ~ (c_Polynomial_Odegree(v3, v2) =
% 252.80/36.34 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 252.80/36.34 ~ (c_Polynomial_Opoly(v3, v2) = v1) | ~ (c_Polynomial_Opoly(v3, v2) = v0))
% 252.80/36.34 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.80/36.34 (c_Groups_Oabs__class_Oabs(v3, v2) = v1) | ~ (c_Groups_Oabs__class_Oabs(v3,
% 252.80/36.34 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 252.80/36.34 = v0 | ~ (tc_fun(v3, v2) = v1) | ~ (tc_fun(v3, v2) = v0)) & ! [v0: $i] :
% 252.80/36.34 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.80/36.34 (c_RealVector_Onorm__class_Onorm(v3, v2) = v1) | ~
% 252.80/36.34 (c_RealVector_Onorm__class_Onorm(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 252.80/36.34 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (hAPP(v3, v2) = v1) | ~ (hAPP(v3,
% 252.80/36.34 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 252.80/36.34 (c_Power_Opower__class_Opower(v2) = v1) | ~
% 252.80/36.34 (c_Power_Opower__class_Opower(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 252.80/36.34 [v2: $i] : (v1 = v0 | ~ (c_Complex_Oexpi(v2) = v1) | ~ (c_Complex_Oexpi(v2)
% 252.80/36.34 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 252.80/36.34 (c_RComplete_Onatfloor(v2) = v1) | ~ (c_RComplete_Onatfloor(v2) = v0)) & !
% 252.80/36.34 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 252.80/36.34 (c_RComplete_Onatceiling(v2) = v1) | ~ (c_RComplete_Onatceiling(v2) = v0))
% 252.80/36.34 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 252.80/36.34 (tc_Polynomial_Opoly(v2) = v1) | ~ (tc_Polynomial_Opoly(v2) = v0)) & !
% 252.80/36.34 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 252.80/36.34 (c_Transcendental_Oarctan(v2) = v1) | ~ (c_Transcendental_Oarctan(v2) =
% 252.80/36.34 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 252.80/36.34 (c_Groups_Otimes__class_Otimes(v2) = v1) | ~
% 252.80/36.34 (c_Groups_Otimes__class_Otimes(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 252.80/36.34 [v2: $i] : (v1 = v0 | ~ (c_Groups_Ozero__class_Ozero(v2) = v1) | ~
% 252.80/36.34 (c_Groups_Ozero__class_Ozero(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 252.80/36.34 [v2: $i] : (v1 = v0 | ~ (c_Groups_Oone__class_Oone(v2) = v1) | ~
% 252.80/36.34 (c_Groups_Oone__class_Oone(v2) = v0))
% 252.80/36.34
% 252.80/36.34 Further assumptions not needed in the proof:
% 252.80/36.34 --------------------------------------------
% 252.80/36.35 arity_Complex__Ocomplex__Fields_Ofield,
% 252.80/36.35 arity_Complex__Ocomplex__Fields_Ofield__inverse__zero,
% 252.80/36.35 arity_Complex__Ocomplex__Groups_Oab__group__add,
% 252.80/36.35 arity_Complex__Ocomplex__Groups_Oab__semigroup__add,
% 252.80/36.35 arity_Complex__Ocomplex__Groups_Oab__semigroup__mult,
% 252.80/36.35 arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add,
% 252.80/36.35 arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add,
% 252.80/36.35 arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add,
% 252.80/36.35 arity_Complex__Ocomplex__Groups_Ocomm__monoid__add,
% 252.80/36.35 arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult,
% 252.80/36.35 arity_Complex__Ocomplex__Groups_Ogroup__add,
% 252.80/36.35 arity_Complex__Ocomplex__Groups_Ominus,
% 252.80/36.35 arity_Complex__Ocomplex__Groups_Omonoid__add,
% 252.80/36.35 arity_Complex__Ocomplex__Groups_Omonoid__mult,
% 252.80/36.35 arity_Complex__Ocomplex__Groups_Oone, arity_Complex__Ocomplex__Groups_Ozero,
% 252.80/36.35 arity_Complex__Ocomplex__Int_Oring__char__0,
% 252.80/36.35 arity_Complex__Ocomplex__Power_Opower,
% 252.80/36.35 arity_Complex__Ocomplex__RealVector_Oreal__field,
% 252.80/36.35 arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra,
% 252.80/36.35 arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1,
% 252.80/36.35 arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra,
% 252.80/36.35 arity_Complex__Ocomplex__RealVector_Oreal__normed__field,
% 252.80/36.35 arity_Complex__Ocomplex__Rings_Ocomm__ring,
% 252.80/36.35 arity_Complex__Ocomplex__Rings_Ocomm__ring__1,
% 252.80/36.35 arity_Complex__Ocomplex__Rings_Ocomm__semiring,
% 252.80/36.35 arity_Complex__Ocomplex__Rings_Ocomm__semiring__0,
% 252.80/36.35 arity_Complex__Ocomplex__Rings_Ocomm__semiring__1,
% 252.80/36.35 arity_Complex__Ocomplex__Rings_Odivision__ring,
% 252.80/36.35 arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero,
% 252.80/36.35 arity_Complex__Ocomplex__Rings_Odvd, arity_Complex__Ocomplex__Rings_Oidom,
% 252.80/36.35 arity_Complex__Ocomplex__Rings_Omult__zero,
% 252.80/36.35 arity_Complex__Ocomplex__Rings_Ono__zero__divisors,
% 252.80/36.35 arity_Complex__Ocomplex__Rings_Oring, arity_Complex__Ocomplex__Rings_Oring__1,
% 252.80/36.35 arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors,
% 252.80/36.35 arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors,
% 252.80/36.35 arity_Complex__Ocomplex__Rings_Osemiring,
% 252.80/36.35 arity_Complex__Ocomplex__Rings_Osemiring__0,
% 252.80/36.35 arity_Complex__Ocomplex__Rings_Ozero__neq__one,
% 252.80/36.35 arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
% 252.80/36.35 arity_HOL__Obool__Groups_Ominus, arity_HOL__Obool__Orderings_Oord,
% 252.80/36.35 arity_HOL__Obool__Orderings_Oorder, arity_HOL__Obool__Orderings_Opreorder,
% 252.80/36.35 arity_Int__Oint__Divides_Oring__div, arity_Int__Oint__Divides_Osemiring__div,
% 252.80/36.35 arity_Int__Oint__Groups_Oab__group__add,
% 252.80/36.35 arity_Int__Oint__Groups_Oab__semigroup__add,
% 252.80/36.35 arity_Int__Oint__Groups_Oab__semigroup__mult,
% 252.80/36.35 arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,
% 252.80/36.35 arity_Int__Oint__Groups_Ocancel__comm__monoid__add,
% 252.80/36.35 arity_Int__Oint__Groups_Ocancel__semigroup__add,
% 252.80/36.35 arity_Int__Oint__Groups_Ocomm__monoid__add,
% 252.80/36.35 arity_Int__Oint__Groups_Ocomm__monoid__mult,
% 252.80/36.35 arity_Int__Oint__Groups_Ogroup__add,
% 252.80/36.35 arity_Int__Oint__Groups_Olinordered__ab__group__add,
% 252.80/36.35 arity_Int__Oint__Groups_Ominus, arity_Int__Oint__Groups_Omonoid__add,
% 252.80/36.35 arity_Int__Oint__Groups_Omonoid__mult, arity_Int__Oint__Groups_Oone,
% 252.80/36.35 arity_Int__Oint__Groups_Oordered__ab__group__add,
% 252.80/36.35 arity_Int__Oint__Groups_Oordered__ab__group__add__abs,
% 252.80/36.35 arity_Int__Oint__Groups_Oordered__ab__semigroup__add,
% 252.80/36.35 arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,
% 252.80/36.35 arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,
% 252.80/36.35 arity_Int__Oint__Groups_Oordered__comm__monoid__add,
% 252.80/36.35 arity_Int__Oint__Groups_Ozero, arity_Int__Oint__Int_Oring__char__0,
% 252.80/36.35 arity_Int__Oint__Orderings_Olinorder, arity_Int__Oint__Orderings_Oord,
% 252.80/36.35 arity_Int__Oint__Orderings_Oorder, arity_Int__Oint__Orderings_Opreorder,
% 252.80/36.35 arity_Int__Oint__Power_Opower, arity_Int__Oint__Rings_Ocomm__ring,
% 252.80/36.35 arity_Int__Oint__Rings_Ocomm__ring__1, arity_Int__Oint__Rings_Ocomm__semiring,
% 252.80/36.35 arity_Int__Oint__Rings_Ocomm__semiring__0,
% 252.80/36.35 arity_Int__Oint__Rings_Ocomm__semiring__1, arity_Int__Oint__Rings_Odvd,
% 252.80/36.35 arity_Int__Oint__Rings_Oidom,
% 252.80/36.35 arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,
% 252.80/36.35 arity_Int__Oint__Rings_Olinordered__idom,
% 252.80/36.35 arity_Int__Oint__Rings_Olinordered__ring,
% 252.80/36.35 arity_Int__Oint__Rings_Olinordered__ring__strict,
% 252.80/36.35 arity_Int__Oint__Rings_Olinordered__semidom,
% 252.80/36.35 arity_Int__Oint__Rings_Olinordered__semiring,
% 252.80/36.35 arity_Int__Oint__Rings_Olinordered__semiring__1,
% 252.80/36.35 arity_Int__Oint__Rings_Olinordered__semiring__1__strict,
% 252.80/36.35 arity_Int__Oint__Rings_Olinordered__semiring__strict,
% 252.80/36.35 arity_Int__Oint__Rings_Omult__zero, arity_Int__Oint__Rings_Ono__zero__divisors,
% 252.80/36.35 arity_Int__Oint__Rings_Oordered__cancel__semiring,
% 252.80/36.35 arity_Int__Oint__Rings_Oordered__comm__semiring,
% 252.80/36.35 arity_Int__Oint__Rings_Oordered__ring,
% 252.80/36.35 arity_Int__Oint__Rings_Oordered__ring__abs,
% 252.80/36.35 arity_Int__Oint__Rings_Oordered__semiring, arity_Int__Oint__Rings_Oring,
% 252.80/36.35 arity_Int__Oint__Rings_Oring__1,
% 252.80/36.35 arity_Int__Oint__Rings_Oring__1__no__zero__divisors,
% 252.80/36.35 arity_Int__Oint__Rings_Oring__no__zero__divisors,
% 252.80/36.35 arity_Int__Oint__Rings_Osemiring, arity_Int__Oint__Rings_Osemiring__0,
% 252.80/36.35 arity_Int__Oint__Rings_Ozero__neq__one,
% 252.80/36.35 arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
% 252.80/36.35 arity_Nat__Onat__Divides_Osemiring__div,
% 252.80/36.35 arity_Nat__Onat__Groups_Oab__semigroup__add,
% 252.80/36.35 arity_Nat__Onat__Groups_Oab__semigroup__mult,
% 252.80/36.35 arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,
% 252.80/36.35 arity_Nat__Onat__Groups_Ocancel__comm__monoid__add,
% 252.80/36.35 arity_Nat__Onat__Groups_Ocancel__semigroup__add,
% 252.80/36.35 arity_Nat__Onat__Groups_Ocomm__monoid__add,
% 252.80/36.35 arity_Nat__Onat__Groups_Ocomm__monoid__mult, arity_Nat__Onat__Groups_Ominus,
% 252.80/36.35 arity_Nat__Onat__Groups_Omonoid__add, arity_Nat__Onat__Groups_Omonoid__mult,
% 252.80/36.35 arity_Nat__Onat__Groups_Oone,
% 252.80/36.35 arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,
% 252.80/36.35 arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,
% 252.80/36.35 arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,
% 252.80/36.35 arity_Nat__Onat__Groups_Oordered__comm__monoid__add,
% 252.80/36.35 arity_Nat__Onat__Groups_Ozero, arity_Nat__Onat__Orderings_Olinorder,
% 252.80/36.35 arity_Nat__Onat__Orderings_Oord, arity_Nat__Onat__Orderings_Oorder,
% 252.80/36.35 arity_Nat__Onat__Orderings_Opreorder, arity_Nat__Onat__Power_Opower,
% 252.80/36.35 arity_Nat__Onat__Rings_Ocomm__semiring,
% 252.80/36.35 arity_Nat__Onat__Rings_Ocomm__semiring__0,
% 252.80/36.35 arity_Nat__Onat__Rings_Ocomm__semiring__1, arity_Nat__Onat__Rings_Odvd,
% 252.80/36.35 arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,
% 252.80/36.35 arity_Nat__Onat__Rings_Olinordered__semidom,
% 252.80/36.35 arity_Nat__Onat__Rings_Olinordered__semiring,
% 252.80/36.35 arity_Nat__Onat__Rings_Olinordered__semiring__strict,
% 252.80/36.35 arity_Nat__Onat__Rings_Omult__zero, arity_Nat__Onat__Rings_Ono__zero__divisors,
% 252.80/36.35 arity_Nat__Onat__Rings_Oordered__cancel__semiring,
% 252.80/36.35 arity_Nat__Onat__Rings_Oordered__comm__semiring,
% 252.80/36.35 arity_Nat__Onat__Rings_Oordered__semiring, arity_Nat__Onat__Rings_Osemiring,
% 252.80/36.35 arity_Nat__Onat__Rings_Osemiring__0, arity_Nat__Onat__Rings_Ozero__neq__one,
% 252.80/36.35 arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
% 252.80/36.35 arity_Polynomial__Opoly__Divides_Oring__div,
% 252.80/36.35 arity_Polynomial__Opoly__Divides_Osemiring__div,
% 252.80/36.35 arity_Polynomial__Opoly__Groups_Oab__group__add,
% 252.80/36.35 arity_Polynomial__Opoly__Groups_Oab__semigroup__add,
% 252.80/36.35 arity_Polynomial__Opoly__Groups_Oab__semigroup__mult,
% 252.80/36.35 arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add,
% 252.80/36.35 arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add,
% 252.80/36.35 arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add,
% 252.80/36.35 arity_Polynomial__Opoly__Groups_Ocomm__monoid__add,
% 252.80/36.35 arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult,
% 252.80/36.35 arity_Polynomial__Opoly__Groups_Ogroup__add,
% 252.80/36.35 arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add,
% 252.80/36.35 arity_Polynomial__Opoly__Groups_Ominus,
% 252.80/36.35 arity_Polynomial__Opoly__Groups_Omonoid__add,
% 252.80/36.35 arity_Polynomial__Opoly__Groups_Omonoid__mult,
% 252.80/36.35 arity_Polynomial__Opoly__Groups_Oone,
% 252.80/36.35 arity_Polynomial__Opoly__Groups_Oordered__ab__group__add,
% 252.80/36.35 arity_Polynomial__Opoly__Groups_Oordered__ab__group__add__abs,
% 252.80/36.35 arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add,
% 252.80/36.35 arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le,
% 252.80/36.35 arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add,
% 252.80/36.35 arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add,
% 252.80/36.35 arity_Polynomial__Opoly__Groups_Ozero,
% 252.80/36.35 arity_Polynomial__Opoly__Int_Oring__char__0,
% 252.80/36.35 arity_Polynomial__Opoly__Orderings_Olinorder,
% 252.80/36.35 arity_Polynomial__Opoly__Orderings_Oord,
% 252.80/36.35 arity_Polynomial__Opoly__Orderings_Oorder,
% 252.80/36.35 arity_Polynomial__Opoly__Orderings_Opreorder,
% 252.80/36.35 arity_Polynomial__Opoly__Power_Opower,
% 252.80/36.35 arity_Polynomial__Opoly__Rings_Ocomm__ring,
% 252.80/36.35 arity_Polynomial__Opoly__Rings_Ocomm__ring__1,
% 252.80/36.35 arity_Polynomial__Opoly__Rings_Ocomm__semiring,
% 252.80/36.35 arity_Polynomial__Opoly__Rings_Ocomm__semiring__0,
% 252.80/36.35 arity_Polynomial__Opoly__Rings_Ocomm__semiring__1,
% 252.80/36.35 arity_Polynomial__Opoly__Rings_Odvd, arity_Polynomial__Opoly__Rings_Oidom,
% 252.80/36.35 arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict,
% 252.80/36.35 arity_Polynomial__Opoly__Rings_Olinordered__idom,
% 252.80/36.35 arity_Polynomial__Opoly__Rings_Olinordered__ring,
% 252.80/36.35 arity_Polynomial__Opoly__Rings_Olinordered__ring__strict,
% 252.80/36.35 arity_Polynomial__Opoly__Rings_Olinordered__semidom,
% 252.80/36.35 arity_Polynomial__Opoly__Rings_Olinordered__semiring,
% 252.80/36.35 arity_Polynomial__Opoly__Rings_Olinordered__semiring__1,
% 252.80/36.35 arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict,
% 252.80/36.35 arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict,
% 252.80/36.35 arity_Polynomial__Opoly__Rings_Omult__zero,
% 252.80/36.35 arity_Polynomial__Opoly__Rings_Ono__zero__divisors,
% 252.80/36.35 arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring,
% 252.80/36.35 arity_Polynomial__Opoly__Rings_Oordered__comm__semiring,
% 252.80/36.35 arity_Polynomial__Opoly__Rings_Oordered__ring,
% 252.80/36.35 arity_Polynomial__Opoly__Rings_Oordered__ring__abs,
% 252.80/36.35 arity_Polynomial__Opoly__Rings_Oordered__semiring,
% 252.80/36.35 arity_Polynomial__Opoly__Rings_Oring, arity_Polynomial__Opoly__Rings_Oring__1,
% 252.80/36.35 arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors,
% 252.80/36.35 arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors,
% 252.80/36.35 arity_Polynomial__Opoly__Rings_Osemiring,
% 252.80/36.35 arity_Polynomial__Opoly__Rings_Osemiring__0,
% 252.80/36.35 arity_Polynomial__Opoly__Rings_Ozero__neq__one,
% 252.80/36.35 arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
% 252.80/36.35 arity_RealDef__Oreal__Fields_Ofield,
% 252.80/36.35 arity_RealDef__Oreal__Fields_Ofield__inverse__zero,
% 252.80/36.35 arity_RealDef__Oreal__Fields_Olinordered__field,
% 252.80/36.35 arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero,
% 252.80/36.35 arity_RealDef__Oreal__Groups_Oab__group__add,
% 252.80/36.35 arity_RealDef__Oreal__Groups_Oab__semigroup__add,
% 252.80/36.35 arity_RealDef__Oreal__Groups_Oab__semigroup__mult,
% 252.80/36.35 arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add,
% 252.80/36.35 arity_RealDef__Oreal__Groups_Ocancel__comm__monoid__add,
% 252.80/36.35 arity_RealDef__Oreal__Groups_Ocancel__semigroup__add,
% 252.80/36.35 arity_RealDef__Oreal__Groups_Ocomm__monoid__add,
% 252.80/36.35 arity_RealDef__Oreal__Groups_Ocomm__monoid__mult,
% 252.80/36.35 arity_RealDef__Oreal__Groups_Ogroup__add,
% 252.80/36.35 arity_RealDef__Oreal__Groups_Olinordered__ab__group__add,
% 252.80/36.35 arity_RealDef__Oreal__Groups_Ominus, arity_RealDef__Oreal__Groups_Omonoid__add,
% 252.80/36.35 arity_RealDef__Oreal__Groups_Omonoid__mult, arity_RealDef__Oreal__Groups_Oone,
% 252.80/36.35 arity_RealDef__Oreal__Groups_Oordered__ab__group__add,
% 252.80/36.35 arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs,
% 252.80/36.35 arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add,
% 252.80/36.35 arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le,
% 252.80/36.35 arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add,
% 252.80/36.35 arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add,
% 252.80/36.35 arity_RealDef__Oreal__Groups_Ozero, arity_RealDef__Oreal__Int_Oring__char__0,
% 252.80/36.35 arity_RealDef__Oreal__Orderings_Odense__linorder,
% 252.80/36.35 arity_RealDef__Oreal__Orderings_Olinorder, arity_RealDef__Oreal__Orderings_Oord,
% 252.80/36.35 arity_RealDef__Oreal__Orderings_Opreorder, arity_RealDef__Oreal__Power_Opower,
% 252.80/36.35 arity_RealDef__Oreal__RealVector_Oreal__field,
% 252.80/36.35 arity_RealDef__Oreal__RealVector_Oreal__normed__algebra,
% 252.80/36.35 arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1,
% 252.80/36.35 arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra,
% 252.80/36.35 arity_RealDef__Oreal__RealVector_Oreal__normed__field,
% 252.80/36.35 arity_RealDef__Oreal__RealVector_Oreal__normed__vector,
% 252.80/36.35 arity_RealDef__Oreal__Rings_Ocomm__ring,
% 252.80/36.35 arity_RealDef__Oreal__Rings_Ocomm__ring__1,
% 252.80/36.35 arity_RealDef__Oreal__Rings_Ocomm__semiring,
% 252.80/36.35 arity_RealDef__Oreal__Rings_Ocomm__semiring__0,
% 252.80/36.35 arity_RealDef__Oreal__Rings_Ocomm__semiring__1,
% 252.80/36.35 arity_RealDef__Oreal__Rings_Odivision__ring,
% 252.80/36.35 arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero,
% 252.80/36.35 arity_RealDef__Oreal__Rings_Odvd, arity_RealDef__Oreal__Rings_Oidom,
% 252.80/36.35 arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict,
% 252.80/36.35 arity_RealDef__Oreal__Rings_Olinordered__idom,
% 252.80/36.35 arity_RealDef__Oreal__Rings_Olinordered__ring,
% 252.80/36.35 arity_RealDef__Oreal__Rings_Olinordered__ring__strict,
% 252.80/36.35 arity_RealDef__Oreal__Rings_Olinordered__semidom,
% 252.80/36.35 arity_RealDef__Oreal__Rings_Olinordered__semiring,
% 252.80/36.35 arity_RealDef__Oreal__Rings_Olinordered__semiring__1,
% 252.80/36.35 arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict,
% 252.80/36.35 arity_RealDef__Oreal__Rings_Olinordered__semiring__strict,
% 252.80/36.35 arity_RealDef__Oreal__Rings_Omult__zero,
% 252.80/36.35 arity_RealDef__Oreal__Rings_Ono__zero__divisors,
% 252.80/36.35 arity_RealDef__Oreal__Rings_Oordered__cancel__semiring,
% 252.80/36.35 arity_RealDef__Oreal__Rings_Oordered__comm__semiring,
% 252.80/36.35 arity_RealDef__Oreal__Rings_Oordered__ring,
% 252.80/36.35 arity_RealDef__Oreal__Rings_Oordered__ring__abs,
% 252.80/36.35 arity_RealDef__Oreal__Rings_Oordered__semiring,
% 252.80/36.35 arity_RealDef__Oreal__Rings_Oring, arity_RealDef__Oreal__Rings_Oring__1,
% 252.80/36.35 arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors,
% 252.80/36.35 arity_RealDef__Oreal__Rings_Oring__no__zero__divisors,
% 252.80/36.35 arity_RealDef__Oreal__Rings_Osemiring, arity_RealDef__Oreal__Rings_Osemiring__0,
% 252.80/36.35 arity_RealDef__Oreal__Rings_Ozero__neq__one,
% 252.80/36.35 arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
% 252.80/36.35 arity_fun__Groups_Ominus, arity_fun__Orderings_Oord,
% 252.80/36.35 arity_fun__Orderings_Oorder, arity_fun__Orderings_Opreorder,
% 252.80/36.35 fact_DERIV__mult__lemma, fact_DIVISION__BY__ZERO, fact_Deriv_Oadd__diff__add,
% 252.80/36.35 fact_Divides_Omod__div__equality_H,
% 252.80/36.35 fact_Divides_Otransfer__nat__int__function__closures_I2_J, fact_H_I1_J,
% 252.80/36.35 fact_H_I4_J, fact_Nat_Oadd__0__right, fact_Nat_Odiff__diff__eq,
% 252.80/36.35 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,
% 252.80/36.35 fact_ab__semigroup__add__class_Oadd__ac_I1_J,
% 252.80/36.35 fact_ab__semigroup__mult__class_Omult__ac_I1_J, fact_abs__add__abs,
% 252.80/36.35 fact_abs__diff__less__iff, fact_abs__diff__triangle__ineq, fact_abs__div,
% 252.80/36.35 fact_abs__div__pos, fact_abs__divide, fact_abs__dvd__iff, fact_abs__eq__0,
% 252.80/36.35 fact_abs__eq__mult, fact_abs__ge__self, fact_abs__ge__zero,
% 252.80/36.35 fact_abs__idempotent, fact_abs__le__D1, fact_abs__le__zero__iff,
% 252.80/36.35 fact_abs__minus__commute, fact_abs__mult, fact_abs__mult__less,
% 252.80/36.35 fact_abs__mult__pos, fact_abs__mult__self, fact_abs__norm__cancel,
% 252.80/36.35 fact_abs__not__less__zero, fact_abs__of__nonneg, fact_abs__of__pos,
% 252.80/36.35 fact_abs__one, fact_abs__triangle__ineq, fact_abs__triangle__ineq2,
% 252.80/36.35 fact_abs__triangle__ineq2__sym, fact_abs__triangle__ineq3,
% 252.80/36.35 fact_abs__triangle__ineq4, fact_abs__zero, fact_add_Ocomm__neutral, fact_add__0,
% 252.80/36.35 fact_add__0__iff, fact_add__0__left, fact_add__0__right, fact_add__diff__assoc,
% 252.80/36.35 fact_add__diff__assoc2, fact_add__diff__cancel, fact_add__diff__inverse,
% 252.80/36.35 fact_add__divide__distrib, fact_add__divide__eq__iff, fact_add__eq__self__zero,
% 252.80/36.35 fact_add__frac__eq, fact_add__frac__num, fact_add__gr__0, fact_add__imp__eq,
% 252.80/36.35 fact_add__increasing, fact_add__increasing2, fact_add__is__0, fact_add__leD1,
% 252.80/36.35 fact_add__leD2, fact_add__leE, fact_add__le__cancel__left,
% 252.80/36.35 fact_add__le__cancel__right, fact_add__le__imp__le__left,
% 252.80/36.35 fact_add__le__imp__le__right, fact_add__le__less__mono, fact_add__le__mono,
% 252.80/36.35 fact_add__le__mono1, fact_add__left__cancel, fact_add__left__imp__eq,
% 252.80/36.35 fact_add__left__mono, fact_add__lessD1, fact_add__less__cancel__left,
% 252.80/36.35 fact_add__less__cancel__right, fact_add__less__imp__less__left,
% 252.80/36.35 fact_add__less__imp__less__right, fact_add__less__le__mono,
% 252.80/36.35 fact_add__less__mono, fact_add__less__mono1, fact_add__mono,
% 252.80/36.35 fact_add__mult__distrib, fact_add__mult__distrib2, fact_add__neg__neg,
% 252.80/36.35 fact_add__neg__nonpos, fact_add__nonneg__eq__0__iff, fact_add__nonneg__nonneg,
% 252.80/36.35 fact_add__nonneg__pos, fact_add__nonpos__neg, fact_add__nonpos__nonpos,
% 252.80/36.35 fact_add__num__frac, fact_add__poly__code_I1_J, fact_add__poly__code_I2_J,
% 252.80/36.35 fact_add__pos__nonneg, fact_add__pos__pos, fact_add__right__cancel,
% 252.80/36.35 fact_add__right__imp__eq, fact_add__right__mono, fact_add__scale__eq__noteq,
% 252.80/36.35 fact_add__strict__increasing, fact_add__strict__increasing2,
% 252.80/36.35 fact_add__strict__left__mono, fact_add__strict__mono,
% 252.80/36.35 fact_add__strict__right__mono, fact_arctan__monotone, fact_arctan__monotone_H,
% 252.80/36.35 fact_arctan__zero__zero, fact_assms, fact_combine__common__factor,
% 252.80/36.35 fact_comm__mult__left__mono, fact_comm__mult__strict__left__mono,
% 252.80/36.35 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,
% 252.80/36.35 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,
% 252.80/36.35 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,
% 252.80/36.35 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,
% 252.80/36.35 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,
% 252.80/36.35 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,
% 252.80/36.35 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,
% 252.80/36.35 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,
% 252.80/36.35 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,
% 252.80/36.35 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,
% 252.80/36.35 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,
% 252.80/36.35 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,
% 252.80/36.35 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,
% 252.80/36.35 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,
% 252.80/36.35 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,
% 252.80/36.35 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,
% 252.80/36.35 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,
% 252.80/36.35 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,
% 252.80/36.35 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,
% 252.80/36.35 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,
% 252.80/36.35 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,
% 252.80/36.35 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,
% 252.80/36.35 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,
% 252.80/36.35 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,
% 252.80/36.35 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,
% 252.80/36.35 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,
% 252.80/36.35 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,
% 252.80/36.35 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,
% 252.80/36.35 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,
% 252.80/36.35 fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,
% 252.80/36.35 fact_comm__semiring__class_Odistrib, fact_complex__i__not__one,
% 252.80/36.35 fact_complex__i__not__zero, fact_complex__mod__triangle__ineq2,
% 252.80/36.35 fact_complex__mod__triangle__sub, fact_convex__bound__le,
% 252.80/36.35 fact_convex__bound__lt, fact_crossproduct__eq, fact_crossproduct__noteq,
% 252.80/36.35 fact_d_I1_J, fact_d_I3_J, fact_decseq__def, fact_degree__0, fact_degree__1,
% 252.80/36.35 fact_degree__add__eq__left, fact_degree__add__eq__right, fact_degree__add__le,
% 252.80/36.35 fact_degree__add__less, fact_degree__diff__le, fact_degree__diff__less,
% 252.80/36.35 fact_degree__mod__less, fact_degree__mult__eq, fact_degree__mult__le,
% 252.80/36.35 fact_degree__pcompose__le, fact_degree__power__le, fact_dense__le,
% 252.80/36.35 fact_dense__le__bounded, fact_diff__0__eq__0, fact_diff__0__right,
% 252.80/36.35 fact_diff__add__0, fact_diff__add__assoc, fact_diff__add__assoc2,
% 252.80/36.35 fact_diff__add__cancel, fact_diff__add__inverse, fact_diff__add__inverse2,
% 252.80/36.35 fact_diff__cancel, fact_diff__cancel2, fact_diff__commute,
% 252.80/36.35 fact_diff__diff__cancel, fact_diff__diff__left, fact_diff__diff__right,
% 252.80/36.35 fact_diff__divide__distrib, fact_diff__divide__eq__iff, fact_diff__eq__diff__eq,
% 252.80/36.35 fact_diff__eq__diff__less, fact_diff__eq__diff__less__eq, fact_diff__frac__eq,
% 252.80/36.35 fact_diff__is__0__eq, fact_diff__is__0__eq_H, fact_diff__le__mono,
% 252.80/36.35 fact_diff__le__mono2, fact_diff__le__self, fact_diff__less,
% 252.80/36.35 fact_diff__less__mono, fact_diff__less__mono2, fact_diff__mult__distrib,
% 252.80/36.35 fact_diff__mult__distrib2, fact_diff__poly__code_I2_J, fact_diff__self,
% 252.80/36.35 fact_diff__self__eq__0, fact_diffs0__imp__equal, fact_div__0, fact_div__add,
% 252.80/36.35 fact_div__add1__eq, fact_div__add__self1, fact_div__add__self2, fact_div__by__0,
% 252.80/36.35 fact_div__by__1, fact_div__dvd__div, fact_div__le__dividend, fact_div__le__mono,
% 252.80/36.35 fact_div__le__mono2, fact_div__less, fact_div__mod__equality,
% 252.80/36.35 fact_div__mod__equality2, fact_div__mod__equality_H, fact_div__mult1__eq,
% 252.80/36.35 fact_div__mult2__eq, fact_div__mult__div__if__dvd, fact_div__mult__mult1,
% 252.80/36.35 fact_div__mult__mult1__if, fact_div__mult__mult2, fact_div__mult__self1,
% 252.80/36.35 fact_div__mult__self1__is__id, fact_div__mult__self1__is__m,
% 252.80/36.35 fact_div__mult__self2, fact_div__mult__self2__is__id,
% 252.80/36.35 fact_div__mult__self__is__m, fact_div__mult__swap, fact_div__poly__eq,
% 252.80/36.35 fact_div__poly__less, fact_div__power, fact_div__self, fact_divide_Oadd,
% 252.80/36.35 fact_divide_Odiff, fact_divide_Ononneg__bounded, fact_divide_Opos__bounded,
% 252.80/36.35 fact_divide_Ozero, fact_divide__1, fact_divide__add__eq__iff,
% 252.80/36.35 fact_divide__diff__eq__iff, fact_divide__eq__eq, fact_divide__eq__imp,
% 252.80/36.35 fact_divide__le__0__iff, fact_divide__le__eq, fact_divide__left__mono,
% 252.80/36.35 fact_divide__left__mono__neg, fact_divide__less__0__iff, fact_divide__less__eq,
% 252.80/36.35 fact_divide__neg__neg, fact_divide__neg__pos, fact_divide__nonneg__neg,
% 252.80/36.35 fact_divide__nonneg__pos, fact_divide__nonpos__neg, fact_divide__nonpos__pos,
% 252.80/36.35 fact_divide__pos__neg, fact_divide__pos__pos, fact_divide__right__mono,
% 252.80/36.35 fact_divide__right__mono__neg, fact_divide__self, fact_divide__self__if,
% 252.80/36.35 fact_divide__strict__left__mono, fact_divide__strict__left__mono__neg,
% 252.80/36.35 fact_divide__strict__right__mono, fact_divide__strict__right__mono__neg,
% 252.80/36.35 fact_divide__zero, fact_divide__zero__left, fact_divisors__zero,
% 252.80/36.35 fact_divmod__int__rel__div__eq, fact_divmod__int__rel__mod__eq, fact_dm_I1_J,
% 252.80/36.35 fact_dm_I2_J, fact_double__add__le__zero__iff__single__add__le__zero,
% 252.80/36.35 fact_double__add__less__zero__iff__single__add__less__zero,
% 252.80/36.35 fact_double__eq__0__iff, fact_double__zero__sym, fact_dvdI, fact_dvd_Oantisym,
% 252.80/36.35 fact_dvd_Oantisym__conv, fact_dvd_Oeq__iff, fact_dvd_Oeq__refl,
% 252.80/36.35 fact_dvd_Ole__imp__less__or__eq, fact_dvd_Ole__less, fact_dvd_Ole__less__trans,
% 252.80/36.35 fact_dvd_Ole__neq__trans, fact_dvd_Oless__asym, fact_dvd_Oless__asym_H,
% 252.80/36.35 fact_dvd_Oless__imp__le, fact_dvd_Oless__imp__neq, fact_dvd_Oless__imp__not__eq,
% 252.80/36.35 fact_dvd_Oless__imp__not__eq2, fact_dvd_Oless__imp__not__less,
% 252.80/36.35 fact_dvd_Oless__le, fact_dvd_Oless__le__trans, fact_dvd_Oless__not__sym,
% 252.80/36.35 fact_dvd_Oless__trans, fact_dvd_Oneq__le__trans, fact_dvd_Oord__eq__le__trans,
% 252.80/36.35 fact_dvd_Oord__eq__less__trans, fact_dvd_Oord__le__eq__trans,
% 252.80/36.35 fact_dvd_Oord__less__eq__trans, fact_dvd_Oorder__refl, fact_dvd_Oorder__trans,
% 252.80/36.35 fact_dvd__0__left, fact_dvd__0__right, fact_dvd__abs__iff, fact_dvd__add,
% 252.80/36.35 fact_dvd__antisym, fact_dvd__diff, fact_dvd__diffD, fact_dvd__diffD1,
% 252.80/36.35 fact_dvd__diff__nat, fact_dvd__div__div__eq__mult, fact_dvd__div__eq__mult,
% 252.80/36.35 fact_dvd__div__mult, fact_dvd__div__mult__self, fact_dvd__eq__mod__eq__0,
% 252.80/36.35 fact_dvd__if__abs__eq, fact_dvd__imp__degree__le, fact_dvd__imp__le,
% 252.80/36.35 fact_dvd__imp__le__int, fact_dvd__imp__mod__0, fact_dvd__mod,
% 252.80/36.35 fact_dvd__mod__iff, fact_dvd__mod__imp__dvd, fact_dvd__mult, fact_dvd__mult2,
% 252.80/36.35 fact_dvd__mult__cancel, fact_dvd__mult__cancel__left,
% 252.80/36.35 fact_dvd__mult__cancel__right, fact_dvd__mult__div__cancel,
% 252.80/36.35 fact_dvd__mult__left, fact_dvd__mult__right, fact_dvd__pos__nat,
% 252.80/36.35 fact_dvd__power, fact_dvd__power__le, fact_dvd__power__same, fact_dvd__reduce,
% 252.80/36.35 fact_dvd__refl, fact_dvd__trans, fact_dvd__triv__left, fact_dvd__triv__right,
% 252.80/36.35 fact_em0, fact_eq__add__iff1, fact_eq__add__iff2, fact_eq__diff__iff,
% 252.80/36.35 fact_eq__divide__eq, fact_eq__divide__imp, fact_eq__iff__diff__eq__0,
% 252.80/36.35 fact_eq__imp__le, fact_even__less__0__iff, fact_expi__add, fact_expi__zero,
% 252.80/36.35 fact_ext, fact_field__le__mult__one__interval, fact_field__power__not__zero,
% 252.80/36.35 fact_frac__eq__eq, fact_frac__le, fact_frac__less, fact_frac__less2,
% 252.80/36.35 fact_gcd__lcm__complete__lattice__nat_Otop__greatest, fact_gr0I,
% 252.80/36.35 fact_gr__implies__not0, fact_gt__half__sum, fact_inf__period_I3_J,
% 252.80/36.35 fact_inf__period_I4_J, fact_le0, fact_leD, fact_leI, fact_le__0__eq,
% 252.80/36.35 fact_le__Suc__ex__iff, fact_le__add1, fact_le__add2, fact_le__add__diff,
% 252.80/36.35 fact_le__add__diff__inverse, fact_le__add__diff__inverse2, fact_le__add__iff1,
% 252.80/36.35 fact_le__add__iff2, fact_le__antisym, fact_le__cube, fact_le__diff__conv,
% 252.80/36.35 fact_le__diff__conv2, fact_le__diff__iff, fact_le__divide__eq,
% 252.80/36.35 fact_le__eq__less__or__eq, fact_le__funD, fact_le__funE, fact_le__fun__def,
% 252.80/36.35 fact_le__iff__add, fact_le__iff__diff__le__0, fact_le__imp__diff__is__add,
% 252.80/36.35 fact_le__imp__power__dvd, fact_le__mod__geq, fact_le__mult__natfloor,
% 252.80/36.35 fact_le__natfloor, fact_le__natfloor__eq, fact_le__neq__implies__less,
% 252.80/36.35 fact_le__refl, fact_le__square, fact_le__trans, fact_left__add__mult__distrib,
% 252.80/36.35 fact_lemma__MVT, fact_lemma__interval, fact_lemma__interval__lt,
% 252.80/36.35 fact_less__1__mult, fact_less__add__eq__less, fact_less__add__iff1,
% 252.80/36.35 fact_less__add__iff2, fact_less__add__one, fact_less__diff__conv,
% 252.80/36.35 fact_less__diff__iff, fact_less__divide__eq, fact_less__eq__nat_Osimps_I1_J,
% 252.80/36.35 fact_less__eq__real__def, fact_less__fun__def, fact_less__half__sum,
% 252.80/36.35 fact_less__iff__diff__less__0, fact_less__imp__diff__less,
% 252.80/36.35 fact_less__imp__le__nat, fact_less__imp__neq, fact_less__irrefl__nat,
% 252.80/36.35 fact_less__le__not__le, fact_less__nat__zero__code, fact_less__natfloor,
% 252.80/36.35 fact_less__not__refl, fact_less__not__refl2, fact_less__not__refl3,
% 252.80/36.35 fact_less__or__eq__imp__le, fact_less__real__def, fact_less__zeroE,
% 252.80/36.35 fact_linorder__antisym__conv1, fact_linorder__antisym__conv2,
% 252.80/36.35 fact_linorder__antisym__conv3, fact_linorder__cases, fact_linorder__le__cases,
% 252.80/36.35 fact_linorder__le__less__linear, fact_linorder__less__linear,
% 252.80/36.35 fact_linorder__linear, fact_linorder__neqE,
% 252.80/36.35 fact_linorder__neqE__linordered__idom, fact_linorder__neqE__nat,
% 252.80/36.35 fact_linorder__neq__iff, fact_linorder__not__le, fact_linorder__not__less,
% 252.80/36.35 fact_m_I1_J, fact_minus__apply, fact_minus__nat_Odiff__0, fact_mod__0,
% 252.80/36.35 fact_mod__add__cong, fact_mod__add__eq, fact_mod__add__left__eq,
% 252.80/36.35 fact_mod__add__right__eq, fact_mod__add__self1, fact_mod__add__self2,
% 252.80/36.35 fact_mod__by__0, fact_mod__by__1, fact_mod__diff__cong, fact_mod__diff__eq,
% 252.80/36.35 fact_mod__diff__left__eq, fact_mod__diff__right__eq, fact_mod__div__equality,
% 252.80/36.35 fact_mod__div__equality2, fact_mod__div__trivial, fact_mod__eq__0__iff,
% 252.80/36.35 fact_mod__geq, fact_mod__if, fact_mod__le__divisor, fact_mod__lemma,
% 252.80/36.35 fact_mod__less, fact_mod__less__divisor, fact_mod__less__eq__dividend,
% 252.80/36.35 fact_mod__mod__cancel, fact_mod__mod__trivial, fact_mod__mult2__eq,
% 252.80/36.35 fact_mod__mult__cong, fact_mod__mult__distrib, fact_mod__mult__distrib2,
% 252.80/36.35 fact_mod__mult__eq, fact_mod__mult__left__eq, fact_mod__mult__mult1,
% 252.80/36.35 fact_mod__mult__mult2, fact_mod__mult__right__eq, fact_mod__mult__self1,
% 252.80/36.35 fact_mod__mult__self1__is__0, fact_mod__mult__self2,
% 252.80/36.35 fact_mod__mult__self2__is__0, fact_mod__mult__self3,
% 252.80/36.35 fact_mod__neg__neg__trivial, fact_mod__poly__eq, fact_mod__poly__less,
% 252.80/36.35 fact_mod__pos__pos__trivial, fact_mod__self, fact_mult_Oadd__left,
% 252.80/36.35 fact_mult_Oadd__right, fact_mult_Ocomm__neutral, fact_mult_Odiff__left,
% 252.80/36.35 fact_mult_Odiff__right, fact_mult_Ononneg__bounded, fact_mult_Opos__bounded,
% 252.80/36.35 fact_mult_Oprod__diff__prod, fact_mult_Ozero__left, fact_mult_Ozero__right,
% 252.80/36.35 fact_mult__0, fact_mult__0__right, fact_mult__1, fact_mult__1__left,
% 252.80/36.35 fact_mult__1__right, fact_mult__cancel1, fact_mult__cancel2,
% 252.80/36.35 fact_mult__diff__mult, fact_mult__div__cancel,
% 252.80/36.35 fact_mult__divide__mult__cancel__left, fact_mult__divide__mult__cancel__right,
% 252.80/36.35 fact_mult__dvd__mono, fact_mult__eq__0__iff, fact_mult__idem,
% 252.80/36.35 fact_mult__imp__div__pos__le, fact_mult__imp__div__pos__less,
% 252.80/36.35 fact_mult__imp__le__div__pos, fact_mult__imp__less__div__pos, fact_mult__is__0,
% 252.80/36.35 fact_mult__le__0__iff, fact_mult__le__cancel1, fact_mult__le__cancel2,
% 252.80/36.35 fact_mult__le__cancel__left__neg, fact_mult__le__cancel__left__pos,
% 252.80/36.35 fact_mult__le__less__imp__less, fact_mult__le__mono, fact_mult__le__mono1,
% 252.80/36.35 fact_mult__le__mono2, fact_mult__left_Oadd, fact_mult__left_Odiff,
% 252.80/36.35 fact_mult__left_Ononneg__bounded, fact_mult__left_Opos__bounded,
% 252.80/36.35 fact_mult__left_Ozero, fact_mult__left__idem, fact_mult__left__le__imp__le,
% 252.80/36.35 fact_mult__left__le__one__le, fact_mult__left__less__imp__less,
% 252.80/36.35 fact_mult__left__mono, fact_mult__left__mono__neg, fact_mult__less__cancel1,
% 252.80/36.35 fact_mult__less__cancel2, fact_mult__less__cancel__left__disj,
% 252.80/36.35 fact_mult__less__cancel__left__neg, fact_mult__less__cancel__left__pos,
% 252.80/36.35 fact_mult__less__cancel__right__disj, fact_mult__less__imp__less__left,
% 252.80/36.35 fact_mult__less__imp__less__right, fact_mult__less__le__imp__less,
% 252.80/36.35 fact_mult__less__mono1, fact_mult__less__mono2, fact_mult__mono,
% 252.80/36.35 fact_mult__mono_H, fact_mult__neg__neg, fact_mult__neg__pos,
% 252.80/36.35 fact_mult__nonneg__nonneg, fact_mult__nonneg__nonpos,
% 252.80/36.35 fact_mult__nonneg__nonpos2, fact_mult__nonpos__nonneg,
% 252.80/36.35 fact_mult__nonpos__nonpos, fact_mult__poly__0__left, fact_mult__poly__0__right,
% 252.80/36.35 fact_mult__poly__add__left, fact_mult__pos__neg, fact_mult__pos__neg2,
% 252.80/36.35 fact_mult__pos__pos, fact_mult__right_Oadd, fact_mult__right_Odiff,
% 252.80/36.35 fact_mult__right_Ononneg__bounded, fact_mult__right_Opos__bounded,
% 252.80/36.35 fact_mult__right_Ozero, fact_mult__right__le__imp__le,
% 252.80/36.35 fact_mult__right__le__one__le, fact_mult__right__less__imp__less,
% 252.80/36.35 fact_mult__right__mono, fact_mult__right__mono__neg,
% 252.80/36.35 fact_mult__strict__left__mono, fact_mult__strict__left__mono__neg,
% 252.80/36.35 fact_mult__strict__mono, fact_mult__strict__mono_H,
% 252.80/36.35 fact_mult__strict__right__mono, fact_mult__strict__right__mono__neg,
% 252.80/36.35 fact_mult__zero__left, fact_mult__zero__right, fact_nat__0__less__mult__iff,
% 252.80/36.35 fact_nat__add__assoc, fact_nat__add__commute, fact_nat__add__left__cancel,
% 252.80/36.35 fact_nat__add__left__cancel__le, fact_nat__add__left__cancel__less,
% 252.80/36.35 fact_nat__add__left__commute, fact_nat__add__right__cancel,
% 252.80/36.35 fact_nat__diff__add__eq1, fact_nat__diff__add__eq2, fact_nat__diff__split,
% 252.80/36.35 fact_nat__diff__split__asm, fact_nat__dvd__not__less, fact_nat__eq__add__iff1,
% 252.80/36.35 fact_nat__eq__add__iff2, fact_nat__le__add__iff1, fact_nat__le__add__iff2,
% 252.80/36.35 fact_nat__le__linear, fact_nat__less__add__iff1, fact_nat__less__add__iff2,
% 252.80/36.35 fact_nat__less__cases, fact_nat__less__le, fact_nat__mult__assoc,
% 252.80/36.35 fact_nat__mult__commute, fact_nat__mult__div__cancel1,
% 252.80/36.35 fact_nat__mult__div__cancel__disj, fact_nat__mult__dvd__cancel1,
% 252.80/36.35 fact_nat__mult__dvd__cancel__disj, fact_nat__mult__eq__cancel1,
% 252.80/36.35 fact_nat__mult__eq__cancel__disj, fact_nat__mult__le__cancel1,
% 252.80/36.35 fact_nat__mult__less__cancel1, fact_nat__neq__iff,
% 252.80/36.35 fact_nat__power__less__imp__less, fact_nat__zero__less__power__iff,
% 252.80/36.35 fact_natceiling__add, fact_natceiling__le, fact_natceiling__le__eq,
% 252.80/36.35 fact_natceiling__mono, fact_natceiling__neg, fact_natceiling__real__of__nat,
% 252.80/36.35 fact_natceiling__subtract, fact_natceiling__zero, fact_natfloor__add,
% 252.80/36.35 fact_natfloor__mono, fact_natfloor__neg, fact_natfloor__power,
% 252.80/36.35 fact_natfloor__real__of__nat, fact_natfloor__subtract, fact_natfloor__zero,
% 252.80/36.35 fact_neg__divide__le__eq, fact_neg__divide__less__eq, fact_neg__le__divide__eq,
% 252.80/36.35 fact_neg__less__divide__eq, fact_neg__mod__bound, fact_neg__mod__conj,
% 252.80/36.35 fact_neg__mod__sign, fact_neq0__conv, fact_no__zero__divisors,
% 252.80/36.35 fact_nonzero__abs__divide, fact_nonzero__divide__eq__eq,
% 252.80/36.35 fact_nonzero__eq__divide__eq, fact_nonzero__norm__divide,
% 252.80/36.35 fact_nonzero__power__divide, fact_norm__add__less, fact_norm__diff__ineq,
% 252.80/36.35 fact_norm__diff__triangle__ineq, fact_norm__divide, fact_norm__eq__zero,
% 252.80/36.35 fact_norm__ge__zero, fact_norm__le__zero__iff, fact_norm__mult,
% 252.80/36.35 fact_norm__mult__ineq, fact_norm__mult__less, fact_norm__not__less__zero,
% 252.80/36.35 fact_norm__power, fact_norm__power__ineq, fact_norm__ratiotest__lemma,
% 252.80/36.35 fact_norm__triangle__ineq, fact_norm__triangle__ineq2,
% 252.80/36.35 fact_norm__triangle__ineq3, fact_norm__triangle__ineq4, fact_norm__zero,
% 252.80/36.35 fact_not__add__less1, fact_not__add__less2, fact_not__leE, fact_not__less0,
% 252.80/36.35 fact_not__less__iff__gr__or__eq, fact_not__one__le__zero,
% 252.80/36.35 fact_not__one__less__zero, fact_not__real__of__nat__less__zero,
% 252.80/36.35 fact_not__real__square__gt__zero, fact_not__square__less__zero,
% 252.80/36.35 fact_not__sum__squares__lt__zero, fact_one__dvd, fact_one__le__power,
% 252.80/36.35 fact_one__less__power, fact_one__neq__zero, fact_one__reorient,
% 252.80/36.35 fact_ord__eq__le__trans, fact_ord__eq__less__trans, fact_ord__le__eq__trans,
% 252.80/36.35 fact_ord__less__eq__trans, fact_order__antisym, fact_order__antisym__conv,
% 252.80/36.35 fact_order__degree, fact_order__eq__iff, fact_order__eq__refl,
% 252.80/36.35 fact_order__le__imp__less__or__eq, fact_order__le__less,
% 252.80/36.35 fact_order__le__less__trans, fact_order__le__neq__trans, fact_order__less__asym,
% 252.80/36.35 fact_order__less__asym_H, fact_order__less__imp__le,
% 252.80/36.35 fact_order__less__imp__not__eq, fact_order__less__imp__not__eq2,
% 252.80/36.35 fact_order__less__imp__not__less, fact_order__less__irrefl,
% 252.80/36.35 fact_order__less__le__trans, fact_order__less__not__sym,
% 252.80/36.35 fact_order__less__trans, fact_order__neq__le__trans, fact_order__refl,
% 252.80/36.35 fact_order__root, fact_order__trans, fact_pCons, fact_pcompose__0,
% 252.80/36.35 fact_pdivmod__rel, fact_pdivmod__rel__0, fact_pdivmod__rel__0__iff,
% 252.80/36.35 fact_pdivmod__rel__by__0, fact_pdivmod__rel__by__0__iff, fact_pdivmod__rel__def,
% 252.80/36.35 fact_pdivmod__rel__mult, fact_pdivmod__rel__unique,
% 252.80/36.35 fact_pdivmod__rel__unique__div, fact_pdivmod__rel__unique__mod,
% 252.80/36.35 fact_plus__nat_Oadd__0, fact_poly__0, fact_poly__1, fact_poly__add,
% 252.80/36.35 fact_poly__bound__exists, fact_poly__diff, fact_poly__div__mult__right,
% 252.80/36.35 fact_poly__eq__iff, fact_poly__mod__mult__right, fact_poly__mult,
% 252.80/36.35 fact_poly__pcompose, fact_poly__power, fact_poly__zero, fact_pos__add__strict,
% 252.80/36.35 fact_pos__divide__le__eq, fact_pos__divide__less__eq, fact_pos__le__divide__eq,
% 252.80/36.35 fact_pos__less__divide__eq, fact_pos__mod__bound, fact_pos__mod__conj,
% 252.80/36.35 fact_pos__mod__sign, fact_positive__add, fact_positive__mult,
% 252.80/36.35 fact_positive__zero, fact_pow__divides__eq__int, fact_pow__divides__eq__nat,
% 252.80/36.35 fact_pow__divides__pow__int, fact_pow__divides__pow__nat, fact_power__0,
% 252.80/36.35 fact_power__0__left, fact_power__Suc__less, fact_power__abs, fact_power__add,
% 252.80/36.35 fact_power__commutes, fact_power__decreasing, fact_power__diff,
% 252.80/36.35 fact_power__divide, fact_power__eq__0__iff, fact_power__eq__imp__eq__base,
% 252.80/36.35 fact_power__gt1__lemma, fact_power__increasing, fact_power__increasing__iff,
% 252.80/36.35 fact_power__inject__exp, fact_power__le__dvd, fact_power__le__imp__le__exp,
% 252.80/36.35 fact_power__less__imp__less__base, fact_power__less__imp__less__exp,
% 252.80/36.35 fact_power__less__power__Suc, fact_power__mono, fact_power__mult,
% 252.80/36.35 fact_power__mult__distrib, fact_power__one, fact_power__one__over,
% 252.80/36.35 fact_power__power__power, fact_power__real__of__nat,
% 252.80/36.35 fact_power__strict__decreasing, fact_power__strict__increasing,
% 252.80/36.35 fact_power__strict__increasing__iff, fact_power__strict__mono,
% 252.80/36.35 fact_psize__eq__0__iff, fact_q_I1_J, fact_q_I2_J, fact_rabs__ratiotest__lemma,
% 252.80/36.35 fact_real__0__le__divide__iff, fact_real__add__left__mono,
% 252.80/36.35 fact_real__add__mult__distrib, fact_real__divide__square__eq,
% 252.80/36.35 fact_real__le__antisym, fact_real__le__eq__diff, fact_real__le__linear,
% 252.80/36.35 fact_real__le__refl, fact_real__less__def, fact_real__mult__assoc,
% 252.80/36.35 fact_real__mult__commute, fact_real__mult__le__cancel__iff1,
% 252.80/36.35 fact_real__mult__le__cancel__iff2, fact_real__mult__left__cancel,
% 252.80/36.35 fact_real__mult__less__iff1, fact_real__mult__less__mono2,
% 252.80/36.35 fact_real__mult__order, fact_real__mult__right__cancel,
% 252.80/36.35 fact_real__natceiling__ge, fact_real__natfloor__le, fact_real__norm__def,
% 252.80/36.35 fact_real__of__nat__add, fact_real__of__nat__diff, fact_real__of__nat__div,
% 252.80/36.35 fact_real__of__nat__div2, fact_real__of__nat__div4,
% 252.80/36.35 fact_real__of__nat__div__aux, fact_real__of__nat__ge__zero,
% 252.80/36.35 fact_real__of__nat__gt__zero__cancel__iff, fact_real__of__nat__inject,
% 252.80/36.35 fact_real__of__nat__le__iff, fact_real__of__nat__le__zero__cancel__iff,
% 252.80/36.35 fact_real__of__nat__less__iff, fact_real__of__nat__mult,
% 252.80/36.35 fact_real__of__nat__power, fact_real__of__nat__zero,
% 252.80/36.35 fact_real__of__nat__zero__iff, fact_real__squared__diff__one__factored,
% 252.80/36.35 fact_real__two__squares__add__zero__iff, fact_right__inverse__eq,
% 252.80/36.35 fact_right__minus__eq, fact_semiring__div__class_Omod__div__equality_H,
% 252.80/36.35 fact_split__div, fact_split__mod, fact_split__mult__neg__le,
% 252.80/36.35 fact_split__mult__pos__le, fact_split__neg__lemma, fact_split__pos__lemma,
% 252.80/36.35 fact_split__zdiv, fact_split__zmod, fact_sum__squares__eq__zero__iff,
% 252.80/36.35 fact_sum__squares__ge__zero, fact_sum__squares__gt__zero__iff,
% 252.80/36.35 fact_sum__squares__le__zero__iff, fact_synthetic__div__0,
% 252.80/36.35 fact_synthetic__div__eq__0__iff, fact_termination__basic__simps_I1_J,
% 252.80/36.35 fact_termination__basic__simps_I2_J, fact_termination__basic__simps_I3_J,
% 252.80/36.35 fact_termination__basic__simps_I4_J, fact_termination__basic__simps_I5_J,
% 252.80/36.35 fact_th, fact_times_Oidem, fact_times__divide__eq__right,
% 252.80/36.35 fact_times__divide__times__eq, fact_trans__le__add1, fact_trans__le__add2,
% 252.80/36.35 fact_trans__less__add1, fact_trans__less__add2, fact_unity__coeff__ex,
% 252.80/36.35 fact_xt1_I10_J, fact_xt1_I11_J, fact_xt1_I12_J, fact_xt1_I1_J, fact_xt1_I2_J,
% 252.80/36.35 fact_xt1_I3_J, fact_xt1_I4_J, fact_xt1_I5_J, fact_xt1_I6_J, fact_xt1_I7_J,
% 252.80/36.35 fact_xt1_I8_J, fact_xt1_I9_J, fact_xt5, fact_xt7, fact_zdiv__zmod__equality,
% 252.80/36.35 fact_zdiv__zmod__equality2, fact_zdiv__zmult1__eq, fact_zdiv__zmult2__eq,
% 252.80/36.35 fact_zdvd1__eq, fact_zdvd__antisym__abs, fact_zdvd__antisym__nonneg,
% 252.80/36.35 fact_zdvd__imp__le, fact_zdvd__mono, fact_zdvd__mult__cancel,
% 252.80/36.35 fact_zdvd__mult__cancel1, fact_zdvd__mult__div__cancel, fact_zdvd__not__zless,
% 252.80/36.35 fact_zdvd__period, fact_zdvd__reduce, fact_zdvd__zdiffD, fact_zdvd__zmod,
% 252.80/36.35 fact_zdvd__zmod__imp__zdvd, fact_zero__le__divide__iff,
% 252.80/36.35 fact_zero__le__double__add__iff__zero__le__single__add,
% 252.80/36.35 fact_zero__le__mult__iff, fact_zero__le__natceiling, fact_zero__le__natfloor,
% 252.80/36.35 fact_zero__le__one, fact_zero__le__power, fact_zero__le__power__abs,
% 252.80/36.35 fact_zero__le__square, fact_zero__le__zpower__abs, fact_zero__less__abs__iff,
% 252.80/36.35 fact_zero__less__diff, fact_zero__less__divide__iff,
% 252.80/36.35 fact_zero__less__double__add__iff__zero__less__single__add,
% 252.80/36.35 fact_zero__less__mult__pos, fact_zero__less__mult__pos2,
% 252.80/36.35 fact_zero__less__norm__iff, fact_zero__less__one, fact_zero__less__power,
% 252.80/36.35 fact_zero__less__two, fact_zero__less__zpower__abs__iff, fact_zero__neq__one,
% 252.80/36.35 fact_zero__reorient, fact_zmod__eq__0__iff, fact_zmod__eq__dvd__iff,
% 252.80/36.35 fact_zmod__le__nonneg__dividend, fact_zmod__self, fact_zmod__simps_I1_J,
% 252.80/36.35 fact_zmod__simps_I2_J, fact_zmod__simps_I3_J, fact_zmod__simps_I4_J,
% 252.80/36.35 fact_zmod__zdiv__equality, fact_zmod__zdiv__equality_H,
% 252.80/36.35 fact_zmod__zdiv__trivial, fact_zmod__zero, fact_zmod__zmult1__eq,
% 252.80/36.35 fact_zmod__zmult2__eq, fact_zmult2__lemma__aux1, fact_zmult2__lemma__aux2,
% 252.80/36.35 fact_zmult2__lemma__aux3, fact_zmult2__lemma__aux4, fact_zmult__div__cancel,
% 252.80/36.35 fact_zpower__zadd__distrib, fact_zpower__zmod, fact_zpower__zpower
% 252.80/36.35
% 252.80/36.35 Those formulas are unsatisfiable:
% 252.80/36.35 ---------------------------------
% 252.80/36.35
% 252.80/36.35 Begin of proof
% 252.80/36.36 |
% 252.80/36.36 | ALPHA: (fact_H_I2_J) implies:
% 252.80/36.36 | (1) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 252.80/36.36 | $i(v0) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v_da____,
% 252.80/36.36 | v0))
% 252.80/36.36 |
% 252.80/36.36 | ALPHA: (fact_H_I5_J) implies:
% 252.80/36.36 | (2) ? [v0: $i] : ? [v1: $i] :
% 252.80/36.36 | (c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_w____, v_z) = v0
% 252.80/36.36 | & c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v0) = v1 &
% 252.80/36.36 | $i(v1) & $i(v0) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1,
% 252.80/36.36 | v_da____))
% 252.80/36.36 |
% 252.80/36.36 | ALPHA: (fact_norm__one) implies:
% 252.80/36.36 | (3) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 252.80/36.36 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~
% 252.80/36.36 | (c_RealVector_Onorm__class_Onorm(v1, v2) = v3) | ~
% 252.80/36.36 | (c_Groups_Oone__class_Oone(v1) = v2) | ~ $i(v1) | ~
% 252.80/36.36 | class_RealVector_Oreal__normed__algebra__1(v1)))
% 252.80/36.36 |
% 252.80/36.36 | ALPHA: (fact_real__le__trans) implies:
% 252.80/36.36 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 252.80/36.36 | $i(v0) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2,
% 252.80/36.36 | v1) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1,
% 252.80/36.36 | v0) | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v0))
% 252.80/36.36 |
% 252.80/36.36 | ALPHA: (fact_d_I2_J) implies:
% 252.80/36.36 | (5) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 252.80/36.36 | $i(v0) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v_d____,
% 252.80/36.36 | v0))
% 252.80/36.36 |
% 252.80/36.36 | ALPHA: (fact_order__less__le) implies:
% 252.80/36.36 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 252.80/36.36 | $i(v0) | ~ class_Orderings_Oorder(v2) | ~
% 252.80/36.36 | c_Orderings_Oord__class_Oless(v2, v1, v0) |
% 252.80/36.36 | c_Orderings_Oord__class_Oless__eq(v2, v1, v0))
% 252.80/36.36 |
% 252.80/36.36 | ALPHA: (fact_one0) implies:
% 252.80/36.36 | (7) ? [v0: $i] : ? [v1: $i] :
% 252.80/36.36 | (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 252.80/36.36 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0) &
% 252.80/36.36 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v1))
% 252.80/36.36 |
% 252.80/36.36 | ALPHA: (fact_H_I3_J) implies:
% 252.80/36.36 | (8) $i(v_da____)
% 252.80/36.36 |
% 252.80/36.36 | ALPHA: (fact_abs__add__one__gt__zero) implies:
% 252.80/36.36 | (9) ? [v0: $i] : ? [v1: $i] :
% 252.80/36.36 | (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 252.80/36.36 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0) &
% 252.80/36.36 | ! [v2: $i] : ! [v3: $i] : ( ~
% 252.80/36.36 | (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v2) = v3) | ~ $i(v2)
% 252.80/36.36 | | ? [v4: $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1,
% 252.80/36.36 | v3) = v4 & $i(v4) &
% 252.80/36.36 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4))))
% 252.80/36.36 |
% 252.80/36.36 | ALPHA: (fact_abs__add__one__not__less__self) implies:
% 252.80/36.36 | (10) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 252.80/36.36 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~
% 252.80/36.36 | (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v1) = v2) | ~ $i(v1)
% 252.80/36.36 | | ? [v3: $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2,
% 252.80/36.36 | v0) = v3 & $i(v3) & ~
% 252.80/36.36 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v1))))
% 252.80/36.36 |
% 252.80/36.36 | ALPHA: (fact_real__zero__not__eq__one) implies:
% 252.80/36.36 | (11) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) &
% 252.80/36.36 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 252.80/36.36 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0))
% 252.80/36.36 |
% 252.80/36.36 | ALPHA: (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)
% 252.80/36.36 | implies:
% 252.80/36.36 | (12) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 252.80/36.36 | (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v_e, v_m____) = v2
% 252.80/36.36 | & c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 252.80/36.36 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & $i(v3) & $i(v2) &
% 252.80/36.36 | $i(v1) & $i(v0) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 252.80/36.36 | v3, v2) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v3, v1)
% 252.80/36.36 | & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3))
% 252.80/36.36 |
% 252.80/36.36 | ALPHA: (fact_real__mult__1) implies:
% 252.80/36.37 | (13) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 252.80/36.37 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v0 &
% 252.80/36.37 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & hAPP(v0, v1) = v2
% 252.80/36.37 | & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : (v4 = v3 |
% 252.80/36.37 | ~ (hAPP(v2, v3) = v4) | ~ $i(v3)))
% 252.80/36.37 |
% 252.80/36.37 | ALPHA: (fact_unimodular__reduce__norm) implies:
% 252.80/36.37 | (14) ? [v0: $i] : ? [v1: $i] :
% 252.80/36.37 | (c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = v1 &
% 252.80/36.37 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) &
% 252.80/36.37 | ! [v2: $i] : ! [v3: $i] : ( ~
% 252.80/36.37 | (c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v2, v1) = v3)
% 252.80/36.37 | | ~ $i(v2) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7:
% 252.80/36.37 | $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] :
% 252.80/36.37 | (( ~ (v4 = v0) &
% 252.80/36.37 | c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v2) = v4
% 252.80/36.37 | & $i(v4)) | (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,
% 252.80/36.37 | v2, v1) = v5 &
% 252.80/36.37 | c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v5) = v6
% 252.80/36.37 | & $i(v6) & $i(v5) &
% 252.80/36.37 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v6, v0)) |
% 252.80/36.37 | (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v2,
% 252.80/36.37 | c_Complex_Oii) = v8 &
% 252.80/36.37 | c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v8) = v9
% 252.80/36.37 | & $i(v9) & $i(v8) &
% 252.80/36.37 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v9, v0)) |
% 252.80/36.37 | (c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v2,
% 252.80/36.37 | c_Complex_Oii) = v10 &
% 252.80/36.37 | c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v10) =
% 252.80/36.37 | v11 & $i(v11) & $i(v10) &
% 252.80/36.37 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v11, v0)) |
% 252.80/36.37 | (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v3) = v7 &
% 252.80/36.37 | $i(v7) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v7,
% 252.80/36.37 | v0)))))
% 252.80/36.37 |
% 252.80/36.37 | ALPHA: (fact_arctan__add) implies:
% 252.80/36.37 | (15) ? [v0: $i] : ? [v1: $i] :
% 252.80/36.37 | (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 252.80/36.37 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0) &
% 252.80/36.37 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i]
% 252.80/36.37 | : ! [v7: $i] : ! [v8: $i] : ( ~
% 252.80/36.37 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v2) = v4) | ~
% 252.80/36.37 | (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v4, v7) = v8) |
% 252.80/36.37 | ~ (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v0, v6) = v7)
% 252.80/36.37 | | ~ (hAPP(v5, v2) = v6) | ~ (hAPP(v1, v3) = v5) | ~ $i(v3) | ~
% 252.80/36.37 | $i(v2) | ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i]
% 252.80/36.37 | : ? [v13: $i] : ? [v14: $i] : ((v14 = v13 &
% 252.80/36.37 | c_Transcendental_Oarctan(v8) = v13 &
% 252.80/36.37 | c_Transcendental_Oarctan(v3) = v11 &
% 252.80/36.37 | c_Transcendental_Oarctan(v2) = v12 &
% 252.80/36.37 | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v11, v12) = v13
% 252.80/36.37 | & $i(v13) & $i(v12) & $i(v11)) |
% 252.80/36.37 | (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v3) = v9 & $i(v9) &
% 252.80/36.37 | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v9,
% 252.80/36.37 | v0)) | (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v2) =
% 252.80/36.37 | v10 & $i(v10) & ~
% 252.80/36.37 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v10, v0)))))
% 252.80/36.37 |
% 252.80/36.37 | ALPHA: (fact_m_I2_J) implies:
% 252.80/36.37 | (16) ? [v0: $i] : ? [v1: $i] : (c_Polynomial_Opoly(tc_Complex_Ocomplex,
% 252.80/36.37 | v_cs____) = v1 & c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0
% 252.80/36.37 | & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v1, v2) =
% 252.80/36.37 | v3) | ~ $i(v2) | ? [v4: $i] : ? [v5: $i] :
% 252.80/36.37 | ((c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v3) = v5 &
% 252.80/36.37 | $i(v5) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 252.80/36.37 | v5, v_m____)) |
% 252.80/36.37 | (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v2) = v4 &
% 252.80/36.37 | $i(v4) & ~
% 252.80/36.37 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v4,
% 252.80/36.37 | v0)))))
% 252.80/36.37 |
% 252.80/36.37 | ALPHA: (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)
% 252.80/36.37 | implies:
% 252.80/36.37 | (17) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 252.80/36.37 | (c_Polynomial_Opoly(tc_Complex_Ocomplex, v_cs____) = v2 &
% 252.80/36.37 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 252.80/36.37 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & $i(v3) & $i(v2) &
% 252.80/36.37 | $i(v1) & $i(v0) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 252.80/36.37 | v0, v3) & ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v2, v4) = v5) | ~
% 252.80/36.37 | $i(v4) | ? [v6: $i] : ? [v7: $i] :
% 252.80/36.37 | ((c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v5) = v7 &
% 252.80/36.37 | $i(v7) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 252.80/36.37 | v7, v3)) |
% 252.80/36.37 | (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v4) = v6 &
% 252.80/36.37 | $i(v6) & ~
% 252.80/36.37 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v6,
% 252.80/36.37 | v1)))))
% 252.80/36.37 |
% 252.80/36.37 | ALPHA: (fact_mult__eq__if) implies:
% 253.02/36.38 | (18) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 253.02/36.38 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 253.02/36.38 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 &
% 253.02/36.38 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 & $i(v2) & $i(v1) &
% 253.02/36.38 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : !
% 253.02/36.38 | [v7: $i] : ! [v8: $i] : (v4 = v0 | ~
% 253.02/36.38 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v7) = v8) | ~
% 253.02/36.38 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v4, v2) = v5) | ~
% 253.02/36.38 | (hAPP(v6, v3) = v7) | ~ (hAPP(v1, v5) = v6) | ~ $i(v4) | ~
% 253.02/36.38 | $i(v3) | ? [v9: $i] : (hAPP(v9, v3) = v8 & hAPP(v1, v4) = v9 &
% 253.02/36.38 | $i(v9) & $i(v8))) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] :
% 253.02/36.38 | (v5 = v0 | ~ (hAPP(v4, v3) = v5) | ~ (hAPP(v1, v0) = v4) | ~
% 253.02/36.38 | $i(v3)))
% 253.02/36.38 |
% 253.02/36.38 | ALPHA: (fact_nat__mult__eq__1__iff) implies:
% 253.02/36.38 | (19) ? [v0: $i] : ? [v1: $i] :
% 253.02/36.38 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 253.02/36.38 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & !
% 253.02/36.38 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v3 = v1 | ~ (hAPP(v4, v2) =
% 253.02/36.38 | v1) | ~ (hAPP(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2)) & ! [v2:
% 253.02/36.38 | $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v1 | ~ (hAPP(v4, v2) =
% 253.02/36.38 | v1) | ~ (hAPP(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2)) & ! [v2:
% 253.02/36.38 | $i] : ! [v3: $i] : (v3 = v1 | ~ (hAPP(v2, v1) = v3) | ~
% 253.02/36.38 | (hAPP(v0, v1) = v2)))
% 253.02/36.38 |
% 253.02/36.38 | ALPHA: (fact_nat__mult__1__right) implies:
% 253.02/36.38 | (20) ? [v0: $i] : ? [v1: $i] :
% 253.02/36.38 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 253.02/36.38 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & !
% 253.02/36.38 | [v2: $i] : ! [v3: $i] : ( ~ (hAPP(v0, v2) = v3) | ~ $i(v2) |
% 253.02/36.38 | hAPP(v3, v1) = v2))
% 253.02/36.38 |
% 253.02/36.38 | ALPHA: (fact_nat__1__eq__mult__iff) implies:
% 253.02/36.38 | (21) ? [v0: $i] : ? [v1: $i] :
% 253.02/36.38 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 253.02/36.38 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v1) & $i(v0) & !
% 253.02/36.38 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v3 = v0 | ~ (hAPP(v4, v2) =
% 253.02/36.38 | v0) | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2)) & ! [v2:
% 253.02/36.38 | $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v0 | ~ (hAPP(v4, v2) =
% 253.02/36.38 | v0) | ~ (hAPP(v1, v3) = v4) | ~ $i(v3) | ~ $i(v2)) & ! [v2:
% 253.02/36.38 | $i] : ! [v3: $i] : (v3 = v0 | ~ (hAPP(v2, v0) = v3) | ~
% 253.02/36.38 | (hAPP(v1, v0) = v2)))
% 253.02/36.38 |
% 253.02/36.38 | ALPHA: (fact_nat__mult__1) implies:
% 253.02/36.38 | (22) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 253.02/36.38 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 253.02/36.38 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & hAPP(v0, v1) = v2 &
% 253.02/36.38 | $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : (v4 = v3 | ~
% 253.02/36.38 | (hAPP(v2, v3) = v4) | ~ $i(v3)))
% 253.02/36.38 |
% 253.02/36.38 | ALPHA: (fact_mult__eq__self__implies__10) implies:
% 253.02/36.38 | (23) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 253.02/36.38 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v0 &
% 253.02/36.38 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v2 &
% 253.02/36.38 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & $i(v2) & $i(v1) &
% 253.02/36.38 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v2 | v3 =
% 253.02/36.38 | v1 | ~ (hAPP(v5, v3) = v4) | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) |
% 253.02/36.38 | ~ $i(v3)))
% 253.02/36.38 |
% 253.02/36.38 | ALPHA: (fact_natceiling__add__one) implies:
% 253.02/36.38 | (24) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 253.02/36.38 | (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 253.02/36.38 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 &
% 253.02/36.38 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & $i(v2) & $i(v1) &
% 253.02/36.38 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ( ~
% 253.02/36.38 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v1) = v4) | ~
% 253.02/36.38 | $i(v3) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 253.02/36.38 | v0, v3) | ? [v5: $i] : ? [v6: $i] :
% 253.02/36.38 | (c_RComplete_Onatceiling(v4) = v5 & c_RComplete_Onatceiling(v3) =
% 253.02/36.38 | v6 & c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v6, v2) = v5 &
% 253.02/36.38 | $i(v6) & $i(v5))))
% 253.02/36.38 |
% 253.02/36.38 | ALPHA: (fact_natfloor__add__one) implies:
% 253.02/36.38 | (25) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 253.02/36.38 | (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 253.02/36.38 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 &
% 253.02/36.38 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & $i(v2) & $i(v1) &
% 253.02/36.38 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ( ~
% 253.02/36.38 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v1) = v4) | ~
% 253.02/36.38 | $i(v3) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 253.02/36.38 | v0, v3) | ? [v5: $i] : ? [v6: $i] : (c_RComplete_Onatfloor(v4)
% 253.02/36.38 | = v5 & c_RComplete_Onatfloor(v3) = v6 &
% 253.02/36.38 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v6, v2) = v5 & $i(v6) &
% 253.02/36.38 | $i(v5))))
% 253.02/36.38 |
% 253.02/36.38 | ALPHA: (fact_natfloor__one) implies:
% 253.02/36.38 | (26) ? [v0: $i] : ? [v1: $i] : (c_RComplete_Onatfloor(v0) = v1 &
% 253.02/36.38 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 &
% 253.02/36.38 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0))
% 253.02/36.38 |
% 253.02/36.38 | ALPHA: (fact_natceiling__one) implies:
% 253.02/36.38 | (27) ? [v0: $i] : ? [v1: $i] : (c_RComplete_Onatceiling(v0) = v1 &
% 253.02/36.38 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 &
% 253.02/36.38 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v1) & $i(v0))
% 253.02/36.38 |
% 253.02/36.38 | ALPHA: (fact_le__natfloor__eq__one) implies:
% 253.02/36.38 | (28) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) =
% 253.02/36.38 | v0 & c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & $i(v1) &
% 253.02/36.38 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (c_RComplete_Onatfloor(v2)
% 253.02/36.38 | = v3) | ~ $i(v2) | ~
% 253.02/36.38 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0, v3) |
% 253.02/36.38 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1, v2)) & !
% 253.02/36.38 | [v2: $i] : ! [v3: $i] : ( ~ (c_RComplete_Onatfloor(v2) = v3) | ~
% 253.02/36.38 | $i(v2) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 253.02/36.38 | v1, v2) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v0,
% 253.02/36.38 | v3)))
% 253.02/36.38 |
% 253.02/36.38 | ALPHA: (fact_natceiling__le__eq__one) implies:
% 253.02/36.38 | (29) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) =
% 253.02/36.38 | v0 & c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & $i(v1) &
% 253.02/36.38 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~
% 253.02/36.38 | (c_RComplete_Onatceiling(v2) = v3) | ~ $i(v2) | ~
% 253.02/36.38 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v0) |
% 253.02/36.38 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v1)) & !
% 253.02/36.38 | [v2: $i] : ! [v3: $i] : ( ~ (c_RComplete_Onatceiling(v2) = v3) | ~
% 253.02/36.38 | $i(v2) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 253.02/36.38 | v2, v1) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3,
% 253.02/36.38 | v0)))
% 253.02/36.38 |
% 253.02/36.38 | ALPHA: (fact_natceiling__eq) implies:
% 253.02/36.38 | (30) ? [v0: $i] : ? [v1: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) =
% 253.02/36.38 | v1 & c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v1) &
% 253.02/36.38 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5
% 253.02/36.38 | = v4 | ~ (c_RComplete_Onatceiling(v2) = v4) | ~
% 253.02/36.38 | (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v1) = v5) | ~
% 253.02/36.38 | $i(v3) | ~ $i(v2) | ? [v6: $i] : ? [v7: $i] :
% 253.02/36.39 | (c_RealDef_Oreal(tc_Nat_Onat, v3) = v6 & $i(v6) & ( ~
% 253.02/36.39 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v6, v2) |
% 253.02/36.39 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v6, v0) = v7 &
% 253.02/36.39 | $i(v7) & ~
% 253.02/36.39 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2,
% 253.02/36.39 | v7))))))
% 253.02/36.39 |
% 253.02/36.39 | ALPHA: (fact_ex__least__nat__less) implies:
% 253.02/36.39 | (31) ? [v0: $i] : ? [v1: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 253.02/36.39 | = v0 & c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & $i(v1) & $i(v0)
% 253.02/36.39 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (hAPP(v3, v2) = v4)
% 253.02/36.39 | | ~ $i(v3) | ~ $i(v2) | ~ hBOOL(v4) | ? [v5: $i] : ? [v6: $i]
% 253.02/36.39 | : ? [v7: $i] : ? [v8: $i] : ($i(v6) &
% 253.02/36.39 | ((c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v6, v1) = v7 &
% 253.02/36.39 | hAPP(v3, v7) = v8 & $i(v8) & $i(v7) & hBOOL(v8) &
% 253.02/36.39 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v6, v2) & ! [v9:
% 253.02/36.39 | $i] : ! [v10: $i] : ( ~ (hAPP(v3, v9) = v10) | ~ $i(v9)
% 253.02/36.39 | | ~ hBOOL(v10) | ~
% 253.02/36.39 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v9, v6))) |
% 253.02/36.39 | (hAPP(v3, v0) = v5 & $i(v5) & hBOOL(v5))))))
% 253.02/36.39 |
% 253.02/36.39 | ALPHA: (fact_abs__real__of__nat__cancel) implies:
% 253.02/36.39 | (32) ! [v0: $i] : ! [v1: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v0) =
% 253.02/36.39 | v1) | ~ $i(v0) | (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v1)
% 253.02/36.39 | = v1 & $i(v1)))
% 253.02/36.39 |
% 253.02/36.39 | ALPHA: (fact_real__of__nat__1) implies:
% 253.02/36.39 | (33) ? [v0: $i] : ? [v1: $i] : (c_RealDef_Oreal(tc_Nat_Onat, v0) = v1 &
% 253.02/36.39 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 &
% 253.02/36.39 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v1 & $i(v1) & $i(v0))
% 253.02/36.39 |
% 253.02/36.39 | ALPHA: (fact_nat__less__real__le) implies:
% 253.02/36.39 | (34) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 253.02/36.39 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 253.02/36.39 | (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~
% 253.02/36.39 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~ $i(v2) | ~ $i(v1) |
% 253.02/36.39 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) | ? [v5: $i]
% 253.02/36.39 | : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v0) = v5 &
% 253.02/36.39 | $i(v5) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5,
% 253.02/36.39 | v4))) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 253.02/36.39 | : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~
% 253.02/36.39 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~ $i(v2) | ~ $i(v1) |
% 253.02/36.39 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2, v1) | ? [v5: $i] :
% 253.02/36.39 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v0) = v5 &
% 253.02/36.39 | $i(v5) & ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 253.02/36.39 | v5, v4))))
% 253.02/36.39 |
% 253.02/36.39 | ALPHA: (fact_nat__le__real__less) implies:
% 253.02/36.39 | (35) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 253.02/36.39 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 253.02/36.39 | (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~
% 253.02/36.39 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~ $i(v2) | ~ $i(v1) |
% 253.02/36.39 | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1) | ? [v5:
% 253.02/36.39 | $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v4, v0) =
% 253.02/36.39 | v5 & $i(v5) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 253.02/36.39 | v3, v5))) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 253.02/36.39 | $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~
% 253.02/36.39 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~ $i(v2) | ~ $i(v1) |
% 253.02/36.39 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v2, v1) | ? [v5:
% 253.02/36.39 | $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v4, v0) =
% 253.02/36.39 | v5 & $i(v5) & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 253.02/36.39 | v3, v5))))
% 253.02/36.39 |
% 253.02/36.39 | ALPHA: (fact_real__natfloor__add__one__gt) implies:
% 253.02/36.39 | (36) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 253.02/36.39 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ (c_RComplete_Onatfloor(v1)
% 253.02/36.39 | = v2) | ~ $i(v1) | ? [v3: $i] : ? [v4: $i] :
% 253.02/36.39 | (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3 &
% 253.02/36.39 | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v0) = v4 &
% 253.02/36.39 | $i(v4) & $i(v3) &
% 253.02/36.39 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v4))))
% 253.02/36.39 |
% 253.02/36.39 | ALPHA: (fact_real__natfloor__gt__diff__one) implies:
% 253.02/36.39 | (37) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 253.02/36.39 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~
% 253.02/36.39 | (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v1, v0) = v2) |
% 253.02/36.39 | ~ $i(v1) | ? [v3: $i] : ? [v4: $i] :
% 253.02/36.39 | (c_RealDef_Oreal(tc_Nat_Onat, v3) = v4 & c_RComplete_Onatfloor(v1)
% 253.02/36.39 | = v3 & $i(v4) & $i(v3) &
% 253.02/36.39 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v4))))
% 253.02/36.39 |
% 253.02/36.39 | ALPHA: (fact_ge__natfloor__plus__one__imp__gt) implies:
% 253.02/36.39 | (38) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v0) &
% 253.02/36.39 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 253.02/36.39 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~
% 253.02/36.39 | (c_RComplete_Onatfloor(v2) = v3) | ~ $i(v2) | ~ $i(v1) |
% 253.02/36.39 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v4) | ? [v5:
% 253.02/36.39 | $i] : (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, v0) = v5 &
% 253.02/36.39 | $i(v5) & ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v5,
% 253.02/36.39 | v1))))
% 253.02/36.39 |
% 253.02/36.39 | ALPHA: (fact_natfloor__eq) implies:
% 253.02/36.39 | (39) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 253.02/36.39 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4
% 253.02/36.39 | = v2 | ~ (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~
% 253.02/36.39 | (c_RComplete_Onatfloor(v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~
% 253.02/36.39 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v1) | ?
% 253.02/36.39 | [v5: $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3, v0)
% 253.02/36.39 | = v5 & $i(v5) & ~
% 253.02/36.39 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v5))))
% 253.02/36.39 |
% 253.02/36.39 | ALPHA: (fact_reals__Archimedean6) implies:
% 253.02/36.39 | (40) ? [v0: $i] : ? [v1: $i] :
% 253.02/36.39 | (c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 253.02/36.39 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & $i(v1) & $i(v0) & !
% 253.02/36.39 | [v2: $i] : ( ~ $i(v2) | ~
% 253.02/36.39 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v2) | ?
% 253.02/36.39 | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] :
% 253.02/36.39 | (c_RealDef_Oreal(tc_Nat_Onat, v4) = v5 &
% 253.02/36.39 | c_RealDef_Oreal(tc_Nat_Onat, v3) = v6 &
% 253.02/36.39 | c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v3, v1) = v4 & $i(v6)
% 253.02/36.39 | & $i(v5) & $i(v4) & $i(v3) &
% 253.02/36.39 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v5, v2) &
% 253.02/36.39 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v6))))
% 253.02/36.39 |
% 253.02/36.39 | ALPHA: (fact_natfloor__div__nat) implies:
% 253.02/36.39 | (41) ? [v0: $i] : ? [v1: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 253.02/36.39 | = v1 & c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 & $i(v1) &
% 253.02/36.39 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 253.02/36.39 | (c_RealDef_Oreal(tc_Nat_Onat, v2) = v4) | ~
% 253.02/36.39 | (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v3, v4) = v5) |
% 253.02/36.39 | ~ $i(v3) | ~ $i(v2) | ~
% 253.02/36.39 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, v3) | ~
% 253.02/36.39 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v2) | ? [v6: $i] :
% 253.02/36.39 | ? [v7: $i] : (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v7, v2) =
% 253.02/36.39 | v6 & c_RComplete_Onatfloor(v5) = v6 & c_RComplete_Onatfloor(v3)
% 253.02/36.39 | = v7 & $i(v7) & $i(v6))))
% 253.02/36.39 |
% 253.02/36.39 | ALPHA: (fact_real__of__nat__div3) implies:
% 253.02/36.39 | (42) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 253.02/36.39 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 253.02/36.39 | [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~
% 253.02/36.39 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v2, v1) = v6) | ~
% 253.02/36.39 | (c_RealDef_Oreal(tc_Nat_Onat, v6) = v7) | ~
% 253.02/36.39 | (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3) | ~
% 253.02/36.39 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4) | ~
% 253.02/36.39 | (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v3, v4) = v5) |
% 253.02/36.39 | ~ (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v5, v7) = v8)
% 253.02/36.39 | | ~ $i(v2) | ~ $i(v1) |
% 253.02/36.39 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v8, v0)))
% 253.02/36.39 |
% 253.02/36.39 | ALPHA: (fact_div__less__dividend) implies:
% 253.02/36.40 | (43) ? [v0: $i] : ? [v1: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 253.02/36.40 | = v1 & c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v1) & $i(v0)
% 253.02/36.40 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 253.02/36.40 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v2, v3) = v4) | ~ $i(v3)
% 253.02/36.40 | | ~ $i(v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1,
% 253.02/36.40 | v2) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) |
% 253.02/36.40 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v2)))
% 253.02/36.40 |
% 253.02/36.40 | ALPHA: (fact_degree__synthetic__div) implies:
% 253.02/36.40 | (44) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v0) &
% 253.02/36.40 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] :
% 253.02/36.40 | ( ~ (c_Polynomial_Osynthetic__div(v3, v2, v1) = v4) | ~
% 253.02/36.40 | (c_Polynomial_Odegree(v3, v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~
% 253.02/36.40 | $i(v1) | ~ class_Rings_Ocomm__semiring__0(v3) | ? [v6: $i] :
% 253.02/36.40 | (c_Polynomial_Odegree(v3, v2) = v6 &
% 253.02/36.40 | c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v6, v0) = v5 & $i(v6)
% 253.02/36.40 | & $i(v5))))
% 253.02/36.40 |
% 253.02/36.40 | ALPHA: (fact_lemmaCauchy) implies:
% 253.02/36.40 | (45) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v0 &
% 253.02/36.40 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 253.02/36.40 | [v5: $i] : ! [v6: $i] : ( ~ (c_RealVector_Onorm__class_Onorm(v4,
% 253.02/36.40 | v5) = v6) | ~ (hAPP(v1, v2) = v5) | ~ $i(v4) | ~ $i(v3) |
% 253.02/36.40 | ~ $i(v2) | ~ $i(v1) | ~ class_Orderings_Oord(v3) | ~
% 253.02/36.40 | class_RealVector_Oreal__normed__vector(v4) | ? [v7: $i] : ? [v8:
% 253.02/36.40 | $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ($i(v8) &
% 253.02/36.40 | ((c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v0, v6) = v7 &
% 253.02/36.40 | $i(v7) & ! [v12: $i] : ! [v13: $i] : ! [v14: $i] : ( ~
% 253.02/36.40 | (c_RealVector_Onorm__class_Onorm(v4, v13) = v14) | ~
% 253.02/36.40 | (hAPP(v1, v12) = v13) | ~ $i(v12) | ~
% 253.02/36.40 | c_Orderings_Oord__class_Oless__eq(v3, v2, v12) |
% 253.02/36.40 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v14, v7)))
% 253.02/36.40 | | (c_Groups_Ominus__class_Ominus(v4, v5, v9) = v10 &
% 253.02/36.40 | c_RealVector_Onorm__class_Onorm(v4, v10) = v11 & hAPP(v1,
% 253.02/36.40 | v8) = v9 & $i(v11) & $i(v10) & $i(v9) &
% 253.02/36.40 | c_Orderings_Oord__class_Oless__eq(v3, v2, v8) & ~
% 253.02/36.40 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v11,
% 253.02/36.40 | v0))))))
% 253.02/36.40 |
% 253.02/36.40 | ALPHA: (fact_nat__dvd__1__iff__1) implies:
% 253.02/36.40 | (46) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v0) &
% 253.02/36.40 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v0, v0) & ! [v1: $i] : (v1 =
% 253.02/36.40 | v0 | ~ $i(v1) | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v1,
% 253.02/36.40 | v0)))
% 253.02/36.40 |
% 253.02/36.40 | ALPHA: (fact_dvd__mult__cancel1) implies:
% 253.02/36.40 | (47) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 253.02/36.40 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 253.02/36.40 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 &
% 253.02/36.40 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 & $i(v2) & $i(v1) &
% 253.02/36.40 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v3
% 253.02/36.40 | = v2 | ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v1, v4) = v5) | ~ $i(v4)
% 253.02/36.40 | | ~ $i(v3) | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v4) |
% 253.02/36.40 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4)) & ! [v3:
% 253.02/36.40 | $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, v2) = v5) | ~
% 253.02/36.40 | (hAPP(v1, v3) = v4) | ~ $i(v3) | ~
% 253.02/36.40 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) |
% 253.02/36.40 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v5, v3)))
% 253.02/36.40 |
% 253.02/36.40 | ALPHA: (fact_dvd__mult__cancel2) implies:
% 253.02/36.40 | (48) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 253.02/36.40 | (c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v1 &
% 253.02/36.40 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 &
% 253.02/36.40 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 & $i(v2) & $i(v1) &
% 253.02/36.40 | $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v3
% 253.02/36.40 | = v2 | ~ (hAPP(v5, v4) = v6) | ~ (hAPP(v1, v3) = v5) | ~ $i(v4)
% 253.02/36.40 | | ~ $i(v3) | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v4) |
% 253.02/36.40 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v4)) & ! [v3:
% 253.02/36.40 | $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v4, v3) = v5) | ~
% 253.02/36.40 | (hAPP(v1, v2) = v4) | ~ $i(v3) | ~
% 253.02/36.40 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) |
% 253.02/36.40 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v5, v3)))
% 253.02/36.40 |
% 253.02/36.40 | ALPHA: (fact_gcd__lcm__complete__lattice__nat_Obot__least) implies:
% 253.02/36.40 | (49) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v0) &
% 253.02/36.40 | ? [v1: $i] : ( ~ $i(v1) | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v0,
% 253.02/36.40 | v1)))
% 253.02/36.40 |
% 253.02/36.40 | ALPHA: (fact_LIMSEQ__inverse__realpow__zero__lemma) implies:
% 253.02/36.40 | (50) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 253.02/36.40 | (c_Power_Opower__class_Opower(tc_RealDef_Oreal) = v3 &
% 253.02/36.40 | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = v1 &
% 253.02/36.40 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v0 &
% 253.02/36.40 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v2 & $i(v3) & $i(v2) &
% 253.02/36.40 | $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 253.02/36.40 | $i] : ! [v8: $i] : ( ~
% 253.02/36.40 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v5, v2) = v6) | ~
% 253.02/36.40 | (hAPP(v7, v4) = v8) | ~ (hAPP(v3, v6) = v7) | ~ $i(v5) | ~
% 253.02/36.40 | $i(v4) | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 253.02/36.40 | v0, v5) | ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12:
% 253.02/36.40 | $i] : (c_RealDef_Oreal(tc_Nat_Onat, v4) = v9 &
% 253.02/36.40 | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v11, v2) = v12 &
% 253.02/36.40 | hAPP(v10, v5) = v11 & hAPP(v1, v9) = v10 & $i(v12) & $i(v11) &
% 253.02/36.40 | $i(v10) & $i(v9) &
% 253.02/36.40 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v12, v8))))
% 253.02/36.40 |
% 253.02/36.40 | ALPHA: (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J)
% 253.02/36.40 | implies:
% 253.02/36.40 | (51) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v0) &
% 253.02/36.40 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 253.02/36.40 | (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v3, v1) = v4) |
% 253.02/36.40 | ~ $i(v2) | ~ $i(v1) | ~ class_Rings_Ocomm__semiring__1(v2) |
% 253.02/36.40 | hAPP(v4, v0) = v1))
% 253.02/36.40 |
% 253.02/36.40 | ALPHA: (fact_realpow__num__eq__if) implies:
% 253.02/36.40 | (52) ? [v0: $i] : ? [v1: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 253.02/36.40 | = v0 & c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & $i(v1) & $i(v0)
% 253.02/36.40 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 253.02/36.40 | $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : !
% 253.02/36.40 | [v11: $i] : ( ~ (c_Power_Opower__class_Opower(v4) = v5) | ~
% 253.02/36.40 | (c_Groups_Otimes__class_Otimes(v4) = v7) | ~
% 253.02/36.40 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v3, v1) = v9) | ~
% 253.02/36.40 | (hAPP(v8, v10) = v11) | ~ (hAPP(v7, v2) = v8) | ~ (hAPP(v6, v9)
% 253.02/36.40 | = v10) | ~ (hAPP(v5, v2) = v6) | ~ $i(v4) | ~ $i(v3) | ~
% 253.02/36.40 | $i(v2) | ~ class_Power_Opower(v4) | ? [v12: $i] : ? [v13: $i] :
% 253.02/36.40 | (( ~ (v3 = v0) | (v13 = v12 & c_Groups_Oone__class_Oone(v4) = v12
% 253.02/36.40 | & hAPP(v6, v0) = v12 & $i(v12))) & (v3 = v0 | (v12 = v11 &
% 253.02/36.40 | hAPP(v6, v3) = v11 & $i(v11))))))
% 253.02/36.40 |
% 253.02/36.40 | ALPHA: (fact_realpow__minus__mult) implies:
% 253.02/36.40 | (53) ? [v0: $i] : ? [v1: $i] : (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 253.02/36.40 | = v0 & c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & $i(v1) & $i(v0)
% 253.02/36.40 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 253.02/36.40 | $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : !
% 253.02/36.40 | [v11: $i] : ( ~ (c_Power_Opower__class_Opower(v4) = v6) | ~
% 253.02/36.40 | (c_Groups_Otimes__class_Otimes(v4) = v5) | ~
% 253.02/36.40 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v3, v1) = v8) | ~
% 253.02/36.40 | (hAPP(v10, v2) = v11) | ~ (hAPP(v7, v8) = v9) | ~ (hAPP(v6, v2)
% 253.02/36.40 | = v7) | ~ (hAPP(v5, v9) = v10) | ~ $i(v4) | ~ $i(v3) | ~
% 253.02/36.40 | $i(v2) | ~ class_Groups_Omonoid__mult(v4) | ~
% 253.02/36.40 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v0, v3) | (hAPP(v7, v3)
% 253.02/36.40 | = v11 & $i(v11))))
% 253.02/36.40 |
% 253.02/36.40 | ALPHA: (fact_power__dvd__imp__le) implies:
% 253.02/36.40 | (54) ? [v0: $i] : ? [v1: $i] : (c_Power_Opower__class_Opower(tc_Nat_Onat)
% 253.02/36.40 | = v0 & c_Groups_Oone__class_Oone(tc_Nat_Onat) = v1 & $i(v1) & $i(v0)
% 253.02/36.40 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 253.02/36.40 | $i] : ! [v7: $i] : ( ~ (hAPP(v5, v3) = v6) | ~ (hAPP(v5, v2) =
% 253.02/36.40 | v7) | ~ (hAPP(v0, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2)
% 253.02/36.40 | | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v6, v7) | ~
% 253.02/36.40 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v4) |
% 253.02/36.40 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v3, v2)))
% 253.02/36.40 |
% 253.02/36.40 | ALPHA: (fact_power__eq__if) implies:
% 253.02/36.41 | (55) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 253.02/36.41 | (c_Power_Opower__class_Opower(tc_Nat_Onat) = v1 &
% 253.02/36.41 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = v3 &
% 253.02/36.41 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v0 &
% 253.02/36.41 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = v2 & $i(v3) & $i(v2) &
% 253.02/36.41 | $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 253.02/36.41 | $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] : (v5 = v0 | ~
% 253.02/36.41 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v5, v2) = v8) | ~
% 253.02/36.41 | (hAPP(v7, v9) = v10) | ~ (hAPP(v6, v8) = v9) | ~ (hAPP(v3, v4) =
% 253.02/36.41 | v7) | ~ (hAPP(v1, v4) = v6) | ~ $i(v5) | ~ $i(v4) | (hAPP(v6,
% 253.02/36.41 | v5) = v10 & $i(v10))) & ! [v4: $i] : ! [v5: $i] : ! [v6:
% 253.02/36.41 | $i] : (v6 = v2 | ~ (hAPP(v5, v0) = v6) | ~ (hAPP(v1, v4) = v5) |
% 253.02/36.41 | ~ $i(v4)))
% 253.02/36.41 |
% 253.02/36.41 | ALPHA: (fact_power__one__right) implies:
% 253.02/36.41 | (56) ? [v0: $i] : (c_Groups_Oone__class_Oone(tc_Nat_Onat) = v0 & $i(v0) &
% 253.02/36.41 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 253.02/36.41 | (c_Power_Opower__class_Opower(v2) = v3) | ~ (hAPP(v3, v1) = v4) |
% 253.02/36.41 | ~ $i(v2) | ~ $i(v1) | ~ class_Groups_Omonoid__mult(v2) |
% 253.02/36.41 | hAPP(v4, v0) = v1))
% 253.02/36.41 |
% 253.02/36.41 | ALPHA: (fact_reduce__poly__simple) implies:
% 253.02/36.41 | (57) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 253.02/36.41 | ? [v5: $i] : (c_Power_Opower__class_Opower(tc_Complex_Ocomplex) = v4 &
% 253.02/36.41 | c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex) = v3 &
% 253.02/36.41 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = v1 &
% 253.02/36.41 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v0 &
% 253.02/36.41 | c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = v2 &
% 253.02/36.41 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v5 & $i(v5) & $i(v4) &
% 253.02/36.41 | $i(v3) & $i(v2) & $i(v1) & $i(v0) & ? [v6: $i] : ! [v7: $i] : !
% 253.02/36.41 | [v8: $i] : (v7 = v0 | v6 = v1 | ~ (hAPP(v3, v7) = v8) | ~ $i(v7) |
% 253.02/36.41 | ~ $i(v6) | ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12:
% 253.02/36.41 | $i] : ? [v13: $i] : ? [v14: $i] :
% 253.02/36.41 | (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v2, v12) = v13 &
% 253.02/36.41 | c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v13) = v14
% 253.02/36.41 | & hAPP(v10, v6) = v11 & hAPP(v8, v11) = v12 & hAPP(v4, v9) = v10
% 253.02/36.41 | & $i(v14) & $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) &
% 253.02/36.41 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v14, v5))))
% 253.02/36.41 |
% 253.02/36.41 | ALPHA: (arity_RealDef__Oreal__Orderings_Oorder) implies:
% 253.02/36.41 | (58) class_Orderings_Oorder(tc_RealDef_Oreal)
% 253.02/36.41 |
% 253.02/36.41 | ALPHA: (arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) implies:
% 253.02/36.41 | (59) class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
% 253.02/36.41 |
% 253.02/36.41 | ALPHA: (conj_0) implies:
% 253.02/36.41 | (60) $i(v_z)
% 253.02/36.41 | (61) $i(v_w____)
% 253.02/36.41 | (62) $i(tc_RealDef_Oreal)
% 253.02/36.41 | (63) $i(tc_Complex_Ocomplex)
% 253.02/36.41 | (64) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 253.02/36.41 | (c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_w____, v_z) = v0
% 253.02/36.41 | & c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v0) = v1 &
% 253.02/36.41 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = v2 & $i(v2) & $i(v1) &
% 253.02/36.41 | $i(v0) & ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v1,
% 253.02/36.41 | v2))
% 253.02/36.41 |
% 253.02/36.41 | ALPHA: (function-axioms) implies:
% 253.02/36.41 | (65) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 253.02/36.41 | (c_Groups_Oone__class_Oone(v2) = v1) | ~
% 253.02/36.41 | (c_Groups_Oone__class_Oone(v2) = v0))
% 253.02/36.41 | (66) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 253.02/36.41 | (c_RealVector_Onorm__class_Onorm(v3, v2) = v1) | ~
% 253.02/36.41 | (c_RealVector_Onorm__class_Onorm(v3, v2) = v0))
% 253.02/36.41 | (67) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 253.02/36.41 | (v1 = v0 | ~ (c_Groups_Ominus__class_Ominus(v4, v3, v2) = v1) | ~
% 253.02/36.41 | (c_Groups_Ominus__class_Ominus(v4, v3, v2) = v0))
% 253.02/36.41 |
% 253.02/36.41 | DELTA: instantiating (1) with fresh symbol all_713_0 gives:
% 253.02/36.41 | (68) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_713_0 &
% 253.02/36.41 | $i(all_713_0) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 253.02/36.41 | v_da____, all_713_0)
% 253.02/36.41 |
% 253.02/36.41 | ALPHA: (68) implies:
% 253.02/36.41 | (69) c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v_da____, all_713_0)
% 253.02/36.41 | (70) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_713_0
% 253.02/36.41 |
% 253.02/36.41 | DELTA: instantiating (5) with fresh symbol all_729_0 gives:
% 253.02/36.41 | (71) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_729_0 &
% 253.02/36.41 | $i(all_729_0) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 253.02/36.41 | v_d____, all_729_0)
% 253.02/36.41 |
% 253.02/36.41 | ALPHA: (71) implies:
% 253.02/36.41 | (72) $i(all_729_0)
% 253.02/36.41 | (73) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_729_0
% 253.02/36.41 |
% 253.02/36.41 | DELTA: instantiating (49) with fresh symbol all_742_0 gives:
% 253.02/36.41 | (74) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_742_0 & $i(all_742_0) &
% 253.02/36.41 | ? [v0: $i] : ( ~ $i(v0) | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,
% 253.02/36.41 | all_742_0, v0))
% 253.02/36.41 |
% 253.02/36.41 | ALPHA: (74) implies:
% 253.02/36.41 | (75) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_742_0
% 253.02/36.41 |
% 253.02/36.41 | DELTA: instantiating (27) with fresh symbols all_773_0, all_773_1 gives:
% 253.02/36.41 | (76) c_RComplete_Onatceiling(all_773_1) = all_773_0 &
% 253.02/36.41 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_773_0 &
% 253.02/36.41 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_773_1 &
% 253.02/36.41 | $i(all_773_0) & $i(all_773_1)
% 253.02/36.41 |
% 253.02/36.41 | ALPHA: (76) implies:
% 253.02/36.41 | (77) $i(all_773_0)
% 253.02/36.41 | (78) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_773_1
% 253.02/36.41 | (79) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_773_0
% 253.02/36.41 |
% 253.02/36.41 | DELTA: instantiating (7) with fresh symbols all_797_0, all_797_1 gives:
% 253.02/36.41 | (80) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_797_1 &
% 253.02/36.41 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_797_0 &
% 253.02/36.41 | $i(all_797_0) & $i(all_797_1) &
% 253.02/36.41 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_797_1, all_797_0)
% 253.02/36.41 |
% 253.02/36.41 | ALPHA: (80) implies:
% 253.02/36.41 | (81) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_797_0
% 253.02/36.41 |
% 253.02/36.41 | DELTA: instantiating (26) with fresh symbols all_799_0, all_799_1 gives:
% 253.02/36.41 | (82) c_RComplete_Onatfloor(all_799_1) = all_799_0 &
% 253.02/36.41 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_799_0 &
% 253.02/36.41 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_799_1 &
% 253.02/36.41 | $i(all_799_0) & $i(all_799_1)
% 253.02/36.41 |
% 253.02/36.41 | ALPHA: (82) implies:
% 253.02/36.41 | (83) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_799_1
% 253.02/36.41 | (84) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_799_0
% 253.02/36.41 |
% 253.02/36.41 | DELTA: instantiating (2) with fresh symbols all_818_0, all_818_1 gives:
% 253.02/36.41 | (85) c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_w____, v_z) =
% 253.02/36.41 | all_818_1 & c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,
% 253.02/36.41 | all_818_1) = all_818_0 & $i(all_818_0) & $i(all_818_1) &
% 253.02/36.41 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_818_0, v_da____)
% 253.02/36.41 |
% 253.02/36.41 | ALPHA: (85) implies:
% 253.02/36.41 | (86) c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_818_0, v_da____)
% 253.02/36.41 | (87) c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, all_818_1) =
% 253.02/36.41 | all_818_0
% 253.02/36.41 | (88) c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_w____, v_z) =
% 253.02/36.41 | all_818_1
% 253.02/36.41 |
% 253.02/36.41 | DELTA: instantiating (11) with fresh symbols all_824_0, all_824_1 gives:
% 253.02/36.41 | (89) ~ (all_824_0 = all_824_1) &
% 253.02/36.41 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_824_1 &
% 253.02/36.41 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_824_0 &
% 253.02/36.41 | $i(all_824_0) & $i(all_824_1)
% 253.02/36.41 |
% 253.02/36.41 | ALPHA: (89) implies:
% 253.02/36.41 | (90) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_824_0
% 253.02/36.41 |
% 253.02/36.41 | DELTA: instantiating (33) with fresh symbols all_826_0, all_826_1 gives:
% 253.02/36.41 | (91) c_RealDef_Oreal(tc_Nat_Onat, all_826_1) = all_826_0 &
% 253.02/36.41 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_826_1 &
% 253.02/36.41 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_826_0 &
% 253.02/36.41 | $i(all_826_0) & $i(all_826_1)
% 253.02/36.41 |
% 253.02/36.41 | ALPHA: (91) implies:
% 253.02/36.41 | (92) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_826_0
% 253.02/36.41 | (93) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_826_1
% 253.02/36.42 | (94) c_RealDef_Oreal(tc_Nat_Onat, all_826_1) = all_826_0
% 253.02/36.42 |
% 253.02/36.42 | DELTA: instantiating (46) with fresh symbol all_855_0 gives:
% 253.02/36.42 | (95) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_855_0 & $i(all_855_0) &
% 253.02/36.42 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, all_855_0, all_855_0) & ! [v0:
% 253.02/36.42 | any] : (v0 = all_855_0 | ~ $i(v0) | ~
% 253.02/36.42 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v0, all_855_0))
% 253.02/36.42 |
% 253.02/36.42 | ALPHA: (95) implies:
% 253.02/36.42 | (96) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_855_0
% 253.02/36.42 |
% 253.02/36.42 | DELTA: instantiating (10) with fresh symbol all_912_0 gives:
% 253.02/36.42 | (97) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_912_0 &
% 253.02/36.42 | $i(all_912_0) & ! [v0: $i] : ! [v1: $i] : ( ~
% 253.02/36.42 | (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v0) = v1) | ~ $i(v0) |
% 253.02/36.42 | ? [v2: $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1,
% 253.02/36.42 | all_912_0) = v2 & $i(v2) & ~
% 253.02/36.42 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v0)))
% 253.02/36.42 |
% 253.02/36.42 | ALPHA: (97) implies:
% 253.02/36.42 | (98) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_912_0
% 253.02/36.42 |
% 253.02/36.42 | DELTA: instantiating (64) with fresh symbols all_915_0, all_915_1, all_915_2
% 253.02/36.42 | gives:
% 253.02/36.42 | (99) c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_w____, v_z) =
% 253.02/36.42 | all_915_2 & c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,
% 253.02/36.42 | all_915_2) = all_915_1 & c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
% 253.02/36.42 | = all_915_0 & $i(all_915_0) & $i(all_915_1) & $i(all_915_2) & ~
% 253.02/36.42 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_915_1,
% 253.02/36.42 | all_915_0)
% 253.02/36.42 |
% 253.02/36.42 | ALPHA: (99) implies:
% 253.02/36.42 | (100) ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_915_1,
% 253.02/36.42 | all_915_0)
% 253.02/36.42 | (101) $i(all_915_1)
% 253.02/36.42 | (102) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_915_0
% 253.02/36.42 | (103) c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, all_915_2) =
% 253.02/36.42 | all_915_1
% 253.02/36.42 | (104) c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_w____, v_z) =
% 253.02/36.42 | all_915_2
% 253.02/36.42 |
% 253.02/36.42 | DELTA: instantiating (3) with fresh symbol all_939_0 gives:
% 253.02/36.42 | (105) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_939_0 &
% 253.02/36.42 | $i(all_939_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 =
% 253.02/36.42 | all_939_0 | ~ (c_RealVector_Onorm__class_Onorm(v0, v1) = v2) | ~
% 253.02/36.42 | (c_Groups_Oone__class_Oone(v0) = v1) | ~ $i(v0) | ~
% 253.02/36.42 | class_RealVector_Oreal__normed__algebra__1(v0))
% 253.02/36.42 |
% 253.02/36.42 | ALPHA: (105) implies:
% 253.02/36.42 | (106) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_939_0
% 253.02/36.42 |
% 253.02/36.42 | DELTA: instantiating (20) with fresh symbols all_945_0, all_945_1 gives:
% 253.02/36.42 | (107) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_945_1 &
% 253.02/36.42 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_945_0 & $i(all_945_0) &
% 253.02/36.42 | $i(all_945_1) & ! [v0: $i] : ! [v1: $i] : ( ~ (hAPP(all_945_1, v0)
% 253.02/36.42 | = v1) | ~ $i(v0) | hAPP(v1, all_945_0) = v0)
% 253.02/36.42 |
% 253.02/36.42 | ALPHA: (107) implies:
% 253.02/36.42 | (108) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_945_0
% 253.02/36.42 |
% 253.02/36.42 | DELTA: instantiating (51) with fresh symbol all_957_0 gives:
% 253.02/36.42 | (109) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_957_0 & $i(all_957_0) &
% 253.02/36.42 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 253.02/36.42 | (c_Power_Opower__class_Opower(v1) = v2) | ~ (hAPP(v2, v0) = v3) |
% 253.02/36.42 | ~ $i(v1) | ~ $i(v0) | ~ class_Rings_Ocomm__semiring__1(v1) |
% 253.02/36.42 | hAPP(v3, all_957_0) = v0)
% 253.02/36.42 |
% 253.02/36.42 | ALPHA: (109) implies:
% 253.02/36.42 | (110) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_957_0
% 253.02/36.42 |
% 253.02/36.42 | DELTA: instantiating (56) with fresh symbol all_986_0 gives:
% 253.02/36.42 | (111) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_986_0 & $i(all_986_0) &
% 253.02/36.42 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 253.02/36.42 | (c_Power_Opower__class_Opower(v1) = v2) | ~ (hAPP(v2, v0) = v3) |
% 253.02/36.42 | ~ $i(v1) | ~ $i(v0) | ~ class_Groups_Omonoid__mult(v1) | hAPP(v3,
% 253.02/36.42 | all_986_0) = v0)
% 253.02/36.42 |
% 253.02/36.42 | ALPHA: (111) implies:
% 253.02/36.42 | (112) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_986_0
% 253.02/36.42 |
% 253.02/36.42 | DELTA: instantiating (9) with fresh symbols all_992_0, all_992_1 gives:
% 253.02/36.42 | (113) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_992_1 &
% 253.02/36.42 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_992_0 &
% 253.02/36.42 | $i(all_992_0) & $i(all_992_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 253.02/36.42 | (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v0) = v1) | ~ $i(v0)
% 253.02/36.42 | | ? [v2: $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,
% 253.02/36.42 | all_992_0, v1) = v2 & $i(v2) &
% 253.02/36.42 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_992_1, v2)))
% 253.02/36.42 |
% 253.02/36.42 | ALPHA: (113) implies:
% 253.02/36.42 | (114) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_992_0
% 253.02/36.42 |
% 253.02/36.42 | DELTA: instantiating (22) with fresh symbols all_1001_0, all_1001_1,
% 253.02/36.42 | all_1001_2 gives:
% 253.02/36.42 | (115) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1001_2 &
% 253.02/36.42 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1001_1 &
% 253.02/36.42 | hAPP(all_1001_2, all_1001_1) = all_1001_0 & $i(all_1001_0) &
% 253.02/36.42 | $i(all_1001_1) & $i(all_1001_2) & ! [v0: $i] : ! [v1: $i] : (v1 =
% 253.02/36.42 | v0 | ~ (hAPP(all_1001_0, v0) = v1) | ~ $i(v0))
% 253.02/36.42 |
% 253.02/36.42 | ALPHA: (115) implies:
% 253.02/36.42 | (116) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1001_1
% 253.02/36.42 |
% 253.02/36.42 | DELTA: instantiating (36) with fresh symbol all_1004_0 gives:
% 253.02/36.42 | (117) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1004_0 &
% 253.02/36.42 | $i(all_1004_0) & ! [v0: $i] : ! [v1: $i] : ( ~
% 253.02/36.42 | (c_RComplete_Onatfloor(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ?
% 253.02/36.42 | [v3: $i] : (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2 &
% 253.02/36.42 | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, all_1004_0) =
% 253.02/36.42 | v3 & $i(v3) & $i(v2) &
% 253.02/36.42 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v3)))
% 253.02/36.42 |
% 253.02/36.42 | ALPHA: (117) implies:
% 253.02/36.42 | (118) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1004_0
% 253.02/36.42 |
% 253.02/36.42 | DELTA: instantiating (37) with fresh symbol all_1021_0 gives:
% 253.02/36.42 | (119) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1021_0 &
% 253.02/36.42 | $i(all_1021_0) & ! [v0: $i] : ! [v1: $i] : ( ~
% 253.02/36.42 | (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v0, all_1021_0) =
% 253.02/36.42 | v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] :
% 253.02/36.42 | (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3 & c_RComplete_Onatfloor(v0)
% 253.02/36.42 | = v2 & $i(v3) & $i(v2) &
% 253.02/36.42 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v3)))
% 253.02/36.42 |
% 253.02/36.42 | ALPHA: (119) implies:
% 253.02/36.42 | (120) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1021_0
% 253.02/36.42 |
% 253.02/36.42 | DELTA: instantiating (13) with fresh symbols all_1027_0, all_1027_1,
% 253.02/36.42 | all_1027_2 gives:
% 253.02/36.42 | (121) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1027_2 &
% 253.02/36.42 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1027_1 &
% 253.02/36.42 | hAPP(all_1027_2, all_1027_1) = all_1027_0 & $i(all_1027_0) &
% 253.02/36.42 | $i(all_1027_1) & $i(all_1027_2) & ! [v0: $i] : ! [v1: $i] : (v1 =
% 253.02/36.42 | v0 | ~ (hAPP(all_1027_0, v0) = v1) | ~ $i(v0))
% 253.02/36.42 |
% 253.02/36.42 | ALPHA: (121) implies:
% 253.02/36.42 | (122) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1027_1
% 253.02/36.42 |
% 253.02/36.42 | DELTA: instantiating (12) with fresh symbols all_1043_0, all_1043_1,
% 253.02/36.42 | all_1043_2, all_1043_3 gives:
% 253.02/36.42 | (123) c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v_e, v_m____) =
% 253.02/36.42 | all_1043_1 & c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) =
% 253.02/36.42 | all_1043_3 & c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1043_2
% 253.02/36.42 | & $i(all_1043_0) & $i(all_1043_1) & $i(all_1043_2) & $i(all_1043_3) &
% 253.02/36.42 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1043_0,
% 253.02/36.42 | all_1043_1) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 253.02/36.42 | all_1043_0, all_1043_2) &
% 253.02/36.42 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1043_3,
% 253.02/36.42 | all_1043_0)
% 253.02/36.42 |
% 253.02/36.42 | ALPHA: (123) implies:
% 253.02/36.42 | (124) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1043_2
% 253.02/36.42 |
% 253.02/36.42 | DELTA: instantiating (38) with fresh symbol all_1057_0 gives:
% 253.02/36.42 | (125) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1057_0 & $i(all_1057_0)
% 253.02/36.42 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 253.02/36.42 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v3) | ~
% 253.02/36.42 | (c_RComplete_Onatfloor(v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 253.02/36.42 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v1, v3) | ? [v4:
% 253.02/36.42 | $i] : (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v2, all_1057_0) =
% 253.02/36.42 | v4 & $i(v4) & ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,
% 253.02/36.42 | v4, v0)))
% 253.02/36.42 |
% 253.02/36.42 | ALPHA: (125) implies:
% 253.02/36.42 | (126) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1057_0
% 253.02/36.42 |
% 253.02/36.42 | DELTA: instantiating (12) with fresh symbols all_1081_0, all_1081_1,
% 253.02/36.42 | all_1081_2, all_1081_3 gives:
% 253.02/36.42 | (127) c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v_e, v_m____) =
% 253.02/36.42 | all_1081_1 & c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) =
% 253.02/36.42 | all_1081_3 & c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1081_2
% 253.02/36.42 | & $i(all_1081_0) & $i(all_1081_1) & $i(all_1081_2) & $i(all_1081_3) &
% 253.02/36.42 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1081_0,
% 253.02/36.42 | all_1081_1) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,
% 253.02/36.42 | all_1081_0, all_1081_2) &
% 253.02/36.42 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1081_3,
% 253.02/36.42 | all_1081_0)
% 253.02/36.42 |
% 253.02/36.42 | ALPHA: (127) implies:
% 253.02/36.42 | (128) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1081_2
% 253.02/36.42 |
% 253.02/36.42 | DELTA: instantiating (43) with fresh symbols all_1083_0, all_1083_1 gives:
% 253.02/36.42 | (129) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1083_0 &
% 253.02/36.42 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1083_1 & $i(all_1083_0)
% 253.02/36.42 | & $i(all_1083_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 253.02/36.42 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v0, v1) = v2) | ~ $i(v1)
% 253.02/36.42 | | ~ $i(v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 253.02/36.42 | all_1083_0, v0) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,
% 253.02/36.42 | all_1083_1, v1) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v2,
% 253.02/36.42 | v0))
% 253.02/36.42 |
% 253.02/36.42 | ALPHA: (129) implies:
% 253.02/36.42 | (130) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1083_1
% 253.02/36.43 |
% 253.02/36.43 | DELTA: instantiating (42) with fresh symbol all_1092_0 gives:
% 253.02/36.43 | (131) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1092_0 &
% 253.02/36.43 | $i(all_1092_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 253.02/36.43 | $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~
% 253.02/36.43 | (c_Divides_Odiv__class_Odiv(tc_Nat_Onat, v1, v0) = v5) | ~
% 253.02/36.43 | (c_RealDef_Oreal(tc_Nat_Onat, v5) = v6) | ~
% 253.02/36.43 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) | ~
% 253.02/36.43 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v3) | ~
% 253.02/36.43 | (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v2, v3) = v4) |
% 253.02/36.43 | ~ (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, v4, v6) = v7) |
% 253.02/36.43 | ~ $i(v1) | ~ $i(v0) |
% 253.02/36.43 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v7,
% 253.02/36.43 | all_1092_0))
% 253.02/36.43 |
% 253.02/36.43 | ALPHA: (131) implies:
% 253.02/36.43 | (132) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1092_0
% 253.02/36.43 |
% 253.02/36.43 | DELTA: instantiating (39) with fresh symbol all_1104_0 gives:
% 253.02/36.43 | (133) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1104_0 &
% 253.02/36.43 | $i(all_1104_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 253.02/36.43 | $i] : (v3 = v1 | ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) | ~
% 253.02/36.43 | (c_RComplete_Onatfloor(v0) = v3) | ~ $i(v1) | ~ $i(v0) | ~
% 253.02/36.43 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v2, v0) | ?
% 253.02/36.43 | [v4: $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2,
% 253.02/36.43 | all_1104_0) = v4 & $i(v4) & ~
% 253.02/36.43 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4)))
% 253.02/36.43 |
% 253.02/36.43 | ALPHA: (133) implies:
% 253.02/36.43 | (134) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1104_0
% 253.02/36.43 |
% 253.02/36.43 | DELTA: instantiating (23) with fresh symbols all_1145_0, all_1145_1,
% 253.02/36.43 | all_1145_2 gives:
% 253.02/36.43 | (135) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1145_2 &
% 253.02/36.43 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1145_0 &
% 253.02/36.43 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1145_1 & $i(all_1145_0)
% 253.02/36.43 | & $i(all_1145_1) & $i(all_1145_2) & ! [v0: any] : ! [v1: any] : !
% 253.02/36.43 | [v2: $i] : (v1 = all_1145_0 | v0 = all_1145_1 | ~ (hAPP(v2, v0) =
% 253.02/36.43 | v1) | ~ (hAPP(all_1145_2, v1) = v2) | ~ $i(v1) | ~ $i(v0))
% 253.02/36.43 |
% 253.02/36.43 | ALPHA: (135) implies:
% 253.02/36.43 | (136) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1145_1
% 253.02/36.43 |
% 253.02/36.43 | DELTA: instantiating (28) with fresh symbols all_1148_0, all_1148_1 gives:
% 253.02/36.43 | (137) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1148_1 &
% 253.02/36.43 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1148_0 &
% 253.02/36.43 | $i(all_1148_0) & $i(all_1148_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 253.02/36.43 | (c_RComplete_Onatfloor(v0) = v1) | ~ $i(v0) | ~
% 253.02/36.43 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_1148_1, v1) |
% 253.02/36.43 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1148_0,
% 253.02/36.43 | v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ (c_RComplete_Onatfloor(v0)
% 253.02/36.43 | = v1) | ~ $i(v0) | ~
% 253.02/36.43 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1148_0, v0)
% 253.02/36.43 | | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, all_1148_1, v1))
% 253.02/36.43 |
% 253.02/36.43 | ALPHA: (137) implies:
% 253.02/36.43 | (138) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1148_0
% 253.02/36.43 | (139) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1148_1
% 253.02/36.43 |
% 253.02/36.43 | DELTA: instantiating (44) with fresh symbol all_1156_0 gives:
% 253.02/36.43 | (140) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1156_0 & $i(all_1156_0)
% 253.02/36.43 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 253.02/36.43 | : ( ~ (c_Polynomial_Osynthetic__div(v2, v1, v0) = v3) | ~
% 253.02/36.43 | (c_Polynomial_Odegree(v2, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~
% 253.02/36.43 | $i(v0) | ~ class_Rings_Ocomm__semiring__0(v2) | ? [v5: $i] :
% 253.02/36.43 | (c_Polynomial_Odegree(v2, v1) = v5 &
% 253.02/36.43 | c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v5, all_1156_0) = v4 &
% 253.02/36.43 | $i(v5) & $i(v4)))
% 253.02/36.43 |
% 253.02/36.43 | ALPHA: (140) implies:
% 253.02/36.43 | (141) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1156_0
% 253.02/36.43 |
% 253.02/36.43 | DELTA: instantiating (16) with fresh symbols all_1168_0, all_1168_1 gives:
% 253.02/36.43 | (142) c_Polynomial_Opoly(tc_Complex_Ocomplex, v_cs____) = all_1168_0 &
% 253.02/36.43 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1168_1 &
% 253.02/36.43 | $i(all_1168_0) & $i(all_1168_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 253.02/36.43 | (hAPP(all_1168_0, v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i]
% 253.02/36.43 | : ((c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v1) = v3 &
% 253.02/36.43 | $i(v3) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 253.02/36.43 | v3, v_m____)) |
% 253.02/36.43 | (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v0) = v2 &
% 253.02/36.43 | $i(v2) & ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 253.02/36.43 | v2, all_1168_1))))
% 253.02/36.43 |
% 253.02/36.43 | ALPHA: (142) implies:
% 253.02/36.43 | (143) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1168_1
% 253.02/36.43 |
% 253.02/36.43 | DELTA: instantiating (29) with fresh symbols all_1171_0, all_1171_1 gives:
% 253.02/36.43 | (144) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1171_1 &
% 253.02/36.43 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1171_0 &
% 253.02/36.43 | $i(all_1171_0) & $i(all_1171_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 253.02/36.43 | (c_RComplete_Onatceiling(v0) = v1) | ~ $i(v0) | ~
% 253.02/36.43 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, all_1171_1) |
% 253.02/36.43 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0,
% 253.02/36.43 | all_1171_0)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 253.02/36.43 | (c_RComplete_Onatceiling(v0) = v1) | ~ $i(v0) | ~
% 253.02/36.43 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0, all_1171_0)
% 253.02/36.43 | | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, all_1171_1))
% 253.02/36.43 |
% 253.02/36.43 | ALPHA: (144) implies:
% 253.02/36.43 | (145) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1171_0
% 253.02/36.43 | (146) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1171_1
% 253.02/36.43 |
% 253.02/36.43 | DELTA: instantiating (54) with fresh symbols all_1240_0, all_1240_1 gives:
% 253.02/36.43 | (147) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1240_1 &
% 253.02/36.43 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1240_0 & $i(all_1240_0)
% 253.02/36.43 | & $i(all_1240_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 253.02/36.43 | $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (hAPP(v3, v1) = v4) | ~
% 253.02/36.43 | (hAPP(v3, v0) = v5) | ~ (hAPP(all_1240_1, v2) = v3) | ~ $i(v2) |
% 253.02/36.43 | ~ $i(v1) | ~ $i(v0) | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v4,
% 253.02/36.43 | v5) | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1240_0,
% 253.02/36.43 | v2) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0))
% 253.02/36.43 |
% 253.02/36.43 | ALPHA: (147) implies:
% 253.02/36.43 | (148) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1240_0
% 253.02/36.43 |
% 253.02/36.43 | DELTA: instantiating (25) with fresh symbols all_1263_0, all_1263_1,
% 253.02/36.43 | all_1263_2 gives:
% 253.02/36.43 | (149) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1263_2 &
% 253.02/36.43 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1263_0 &
% 253.02/36.43 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1263_1 &
% 253.02/36.43 | $i(all_1263_0) & $i(all_1263_1) & $i(all_1263_2) & ! [v0: $i] : !
% 253.02/36.43 | [v1: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v0,
% 253.02/36.43 | all_1263_1) = v1) | ~ $i(v0) | ~
% 253.02/36.43 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1263_2, v0)
% 253.02/36.43 | | ? [v2: $i] : ? [v3: $i] : (c_RComplete_Onatfloor(v1) = v2 &
% 253.02/36.43 | c_RComplete_Onatfloor(v0) = v3 &
% 253.02/36.43 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, all_1263_0) = v2 &
% 253.02/36.43 | $i(v3) & $i(v2)))
% 253.02/36.43 |
% 253.02/36.43 | ALPHA: (149) implies:
% 253.02/36.43 | (150) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1263_1
% 253.02/36.43 | (151) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1263_0
% 253.02/36.43 |
% 253.02/36.43 | DELTA: instantiating (24) with fresh symbols all_1266_0, all_1266_1,
% 253.02/36.43 | all_1266_2 gives:
% 253.02/36.43 | (152) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1266_2 &
% 253.02/36.43 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1266_0 &
% 253.02/36.43 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1266_1 &
% 253.02/36.43 | $i(all_1266_0) & $i(all_1266_1) & $i(all_1266_2) & ! [v0: $i] : !
% 253.02/36.43 | [v1: $i] : ( ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v0,
% 253.02/36.43 | all_1266_1) = v1) | ~ $i(v0) | ~
% 253.02/36.43 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1266_2, v0)
% 253.02/36.43 | | ? [v2: $i] : ? [v3: $i] : (c_RComplete_Onatceiling(v1) = v2 &
% 253.02/36.43 | c_RComplete_Onatceiling(v0) = v3 &
% 253.02/36.43 | c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v3, all_1266_0) = v2 &
% 253.02/36.43 | $i(v3) & $i(v2)))
% 253.02/36.43 |
% 253.02/36.43 | ALPHA: (152) implies:
% 253.02/36.43 | (153) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1266_1
% 253.02/36.43 | (154) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1266_0
% 253.02/36.43 |
% 253.02/36.43 | DELTA: instantiating (30) with fresh symbols all_1285_0, all_1285_1 gives:
% 253.02/36.43 | (155) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1285_0 &
% 253.02/36.43 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1285_1 &
% 253.02/36.43 | $i(all_1285_0) & $i(all_1285_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 253.02/36.43 | $i] : ! [v3: $i] : (v3 = v2 | ~ (c_RComplete_Onatceiling(v0) =
% 253.02/36.43 | v2) | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v1,
% 253.02/36.43 | all_1285_0) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ?
% 253.02/36.43 | [v5: $i] : (c_RealDef_Oreal(tc_Nat_Onat, v1) = v4 & $i(v4) & ( ~
% 253.02/36.43 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v4, v0) |
% 253.02/36.43 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v4, all_1285_1)
% 253.02/36.43 | = v5 & $i(v5) & ~
% 253.02/36.43 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v0,
% 253.02/36.43 | v5)))))
% 253.02/36.43 |
% 253.02/36.43 | ALPHA: (155) implies:
% 253.02/36.43 | (156) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1285_1
% 253.02/36.43 | (157) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1285_0
% 253.02/36.43 |
% 253.02/36.43 | DELTA: instantiating (41) with fresh symbols all_1288_0, all_1288_1 gives:
% 253.02/36.43 | (158) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1288_0 &
% 253.02/36.43 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1288_1 &
% 253.02/36.43 | $i(all_1288_0) & $i(all_1288_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 253.02/36.43 | $i] : ! [v3: $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v0) = v2) |
% 253.02/36.43 | ~ (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v1, v2) = v3)
% 253.02/36.43 | | ~ $i(v1) | ~ $i(v0) | ~
% 253.02/36.43 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1288_1, v1)
% 253.02/36.43 | | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1288_0, v0) |
% 253.02/36.43 | ? [v4: $i] : ? [v5: $i] : (c_Divides_Odiv__class_Odiv(tc_Nat_Onat,
% 253.02/36.43 | v5, v0) = v4 & c_RComplete_Onatfloor(v3) = v4 &
% 253.02/36.43 | c_RComplete_Onatfloor(v1) = v5 & $i(v5) & $i(v4)))
% 253.02/36.43 |
% 253.02/36.43 | ALPHA: (158) implies:
% 253.02/36.43 | (159) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1288_1
% 253.02/36.43 |
% 253.02/36.43 | DELTA: instantiating (40) with fresh symbols all_1306_0, all_1306_1 gives:
% 253.02/36.43 | (160) c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1306_1 &
% 253.02/36.43 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1306_0 & $i(all_1306_0)
% 253.02/36.43 | & $i(all_1306_1) & ! [v0: $i] : ( ~ $i(v0) | ~
% 253.02/36.44 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1306_1, v0)
% 253.02/36.44 | | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 253.02/36.44 | (c_RealDef_Oreal(tc_Nat_Onat, v2) = v3 &
% 253.02/36.44 | c_RealDef_Oreal(tc_Nat_Onat, v1) = v4 &
% 253.02/36.44 | c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, all_1306_0) = v2 &
% 253.02/36.44 | $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 253.02/36.44 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v3, v0) &
% 253.02/36.44 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v0, v4)))
% 253.02/36.44 |
% 253.02/36.44 | ALPHA: (160) implies:
% 253.02/36.44 | (161) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1306_0
% 253.02/36.44 |
% 253.02/36.44 | DELTA: instantiating (17) with fresh symbols all_1331_0, all_1331_1,
% 253.02/36.44 | all_1331_2, all_1331_3 gives:
% 253.02/36.44 | (162) c_Polynomial_Opoly(tc_Complex_Ocomplex, v_cs____) = all_1331_1 &
% 253.02/36.44 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1331_3 &
% 253.02/36.44 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1331_2 &
% 253.02/36.44 | $i(all_1331_0) & $i(all_1331_1) & $i(all_1331_2) & $i(all_1331_3) &
% 253.02/36.44 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1331_3,
% 253.02/36.44 | all_1331_0) & ! [v0: $i] : ! [v1: $i] : ( ~ (hAPP(all_1331_1, v0)
% 253.02/36.44 | = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] :
% 253.02/36.44 | ((c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v1) = v3 &
% 253.02/36.44 | $i(v3) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 253.02/36.44 | v3, all_1331_0)) |
% 253.02/36.44 | (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v0) = v2 &
% 253.02/36.44 | $i(v2) & ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 253.02/36.44 | v2, all_1331_2))))
% 253.02/36.44 |
% 253.02/36.44 | ALPHA: (162) implies:
% 253.02/36.44 | (163) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1331_2
% 253.02/36.44 |
% 253.02/36.44 | DELTA: instantiating (17) with fresh symbols all_1343_0, all_1343_1,
% 253.02/36.44 | all_1343_2, all_1343_3 gives:
% 253.02/36.44 | (164) c_Polynomial_Opoly(tc_Complex_Ocomplex, v_cs____) = all_1343_1 &
% 253.02/36.44 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1343_3 &
% 253.02/36.44 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1343_2 &
% 253.02/36.44 | $i(all_1343_0) & $i(all_1343_1) & $i(all_1343_2) & $i(all_1343_3) &
% 253.02/36.44 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, all_1343_3,
% 253.02/36.44 | all_1343_0) & ! [v0: $i] : ! [v1: $i] : ( ~ (hAPP(all_1343_1, v0)
% 253.02/36.44 | = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] :
% 253.02/36.44 | ((c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v1) = v3 &
% 253.02/36.44 | $i(v3) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 253.02/36.44 | v3, all_1343_0)) |
% 253.02/36.44 | (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v0) = v2 &
% 253.02/36.44 | $i(v2) & ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 253.02/36.44 | v2, all_1343_2))))
% 253.02/36.44 |
% 253.02/36.44 | ALPHA: (164) implies:
% 253.02/36.44 | (165) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1343_2
% 253.02/36.44 |
% 253.02/36.44 | DELTA: instantiating (19) with fresh symbols all_1370_0, all_1370_1 gives:
% 253.02/36.44 | (166) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1370_1 &
% 253.02/36.44 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1370_0 & $i(all_1370_0)
% 253.02/36.44 | & $i(all_1370_1) & ! [v0: $i] : ! [v1: any] : ! [v2: $i] : (v1 =
% 253.02/36.44 | all_1370_0 | ~ (hAPP(v2, v0) = all_1370_0) | ~ (hAPP(all_1370_1,
% 253.02/36.44 | v1) = v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: any] : ! [v1: $i]
% 253.02/36.44 | : ! [v2: $i] : (v0 = all_1370_0 | ~ (hAPP(v2, v0) = all_1370_0) |
% 253.02/36.44 | ~ (hAPP(all_1370_1, v1) = v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0:
% 253.02/36.44 | $i] : ! [v1: int] : (v1 = all_1370_0 | ~ (hAPP(v0, all_1370_0) =
% 253.02/36.44 | v1) | ~ (hAPP(all_1370_1, all_1370_0) = v0))
% 253.02/36.44 |
% 253.02/36.44 | ALPHA: (166) implies:
% 253.02/36.44 | (167) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1370_0
% 253.02/36.44 |
% 253.02/36.44 | DELTA: instantiating (21) with fresh symbols all_1376_0, all_1376_1 gives:
% 253.02/36.44 | (168) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1376_0 &
% 253.02/36.44 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1376_1 & $i(all_1376_0)
% 253.02/36.44 | & $i(all_1376_1) & ! [v0: $i] : ! [v1: any] : ! [v2: $i] : (v1 =
% 253.02/36.44 | all_1376_1 | ~ (hAPP(v2, v0) = all_1376_1) | ~ (hAPP(all_1376_0,
% 253.02/36.44 | v1) = v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: any] : ! [v1: $i]
% 253.02/36.44 | : ! [v2: $i] : (v0 = all_1376_1 | ~ (hAPP(v2, v0) = all_1376_1) |
% 253.02/36.44 | ~ (hAPP(all_1376_0, v1) = v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0:
% 253.02/36.44 | $i] : ! [v1: int] : (v1 = all_1376_1 | ~ (hAPP(v0, all_1376_1) =
% 253.02/36.44 | v1) | ~ (hAPP(all_1376_0, all_1376_1) = v0))
% 253.02/36.44 |
% 253.02/36.44 | ALPHA: (168) implies:
% 253.02/36.44 | (169) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1376_1
% 253.02/36.44 |
% 253.02/36.44 | DELTA: instantiating (48) with fresh symbols all_1400_0, all_1400_1,
% 253.02/36.44 | all_1400_2 gives:
% 253.02/36.44 | (170) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1400_1 &
% 253.02/36.44 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1400_2 &
% 253.02/36.44 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1400_0 & $i(all_1400_0)
% 253.02/36.44 | & $i(all_1400_1) & $i(all_1400_2) & ! [v0: any] : ! [v1: $i] : !
% 253.02/36.44 | [v2: $i] : ! [v3: $i] : (v0 = all_1400_0 | ~ (hAPP(v2, v1) = v3) |
% 253.02/36.44 | ~ (hAPP(all_1400_1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 253.02/36.44 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v3, v1) | ~
% 253.02/36.44 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1400_2, v1)) & !
% 253.02/36.44 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (hAPP(v1, v0) = v2) | ~
% 253.02/36.44 | (hAPP(all_1400_1, all_1400_0) = v1) | ~ $i(v0) | ~
% 253.02/36.44 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1400_2, v0) |
% 253.02/36.44 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v2, v0))
% 253.02/36.44 |
% 253.02/36.44 | ALPHA: (170) implies:
% 253.02/36.44 | (171) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1400_0
% 253.02/36.44 |
% 253.02/36.44 | DELTA: instantiating (47) with fresh symbols all_1426_0, all_1426_1,
% 253.02/36.44 | all_1426_2 gives:
% 253.02/36.44 | (172) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1426_1 &
% 253.02/36.44 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1426_2 &
% 253.02/36.44 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1426_0 & $i(all_1426_0)
% 253.02/36.44 | & $i(all_1426_1) & $i(all_1426_2) & ! [v0: any] : ! [v1: $i] : !
% 253.02/36.44 | [v2: $i] : ! [v3: $i] : (v0 = all_1426_0 | ~ (hAPP(v2, v0) = v3) |
% 253.02/36.44 | ~ (hAPP(all_1426_1, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 253.02/36.44 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v3, v1) | ~
% 253.02/36.44 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1426_2, v1)) & !
% 253.02/36.44 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (hAPP(v1, all_1426_0) =
% 253.02/36.44 | v2) | ~ (hAPP(all_1426_1, v0) = v1) | ~ $i(v0) | ~
% 253.02/36.44 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1426_2, v0) |
% 253.02/36.44 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat, v2, v0))
% 253.02/36.44 |
% 253.02/36.44 | ALPHA: (172) implies:
% 253.02/36.44 | (173) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1426_0
% 253.02/36.44 |
% 253.02/36.44 | DELTA: instantiating (34) with fresh symbol all_1445_0 gives:
% 253.33/36.44 | (174) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1445_0 &
% 253.33/36.44 | $i(all_1445_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 253.33/36.44 | $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) | ~
% 253.33/36.44 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v3) | ~ $i(v1) | ~ $i(v0) |
% 253.33/36.44 | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0) | ? [v4: $i]
% 253.33/36.44 | : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, all_1445_0) =
% 253.33/36.44 | v4 & $i(v4) & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 253.33/36.44 | v4, v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 253.33/36.44 | $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) | ~
% 253.33/36.44 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v3) | ~ $i(v1) | ~ $i(v0) |
% 253.33/36.44 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v1, v0) | ? [v4: $i] :
% 253.33/36.44 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v2, all_1445_0) = v4
% 253.33/36.44 | & $i(v4) & ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,
% 253.33/36.44 | v4, v3)))
% 253.33/36.44 |
% 253.33/36.44 | ALPHA: (174) implies:
% 253.33/36.44 | (175) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1445_0
% 253.33/36.44 |
% 253.33/36.44 | DELTA: instantiating (35) with fresh symbol all_1448_0 gives:
% 253.33/36.44 | (176) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1448_0 &
% 253.33/36.44 | $i(all_1448_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 253.33/36.44 | $i] : ( ~ (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) | ~
% 253.33/36.44 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v3) | ~ $i(v1) | ~ $i(v0) |
% 253.33/36.44 | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0) | ? [v4:
% 253.33/36.44 | $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3,
% 253.33/36.44 | all_1448_0) = v4 & $i(v4) &
% 253.33/36.44 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v4))) & !
% 253.33/36.44 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 253.33/36.44 | (c_RealDef_Oreal(tc_Nat_Onat, v1) = v2) | ~
% 253.33/36.44 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v3) | ~ $i(v1) | ~ $i(v0) |
% 253.33/36.44 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v1, v0) | ? [v4:
% 253.33/36.44 | $i] : (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v3,
% 253.33/36.44 | all_1448_0) = v4 & $i(v4) & ~
% 253.33/36.44 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v2, v4)))
% 253.33/36.44 |
% 253.33/36.44 | ALPHA: (176) implies:
% 253.33/36.44 | (177) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1448_0
% 253.33/36.44 |
% 253.33/36.44 | DELTA: instantiating (53) with fresh symbols all_1451_0, all_1451_1 gives:
% 253.33/36.44 | (178) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1451_1 &
% 253.33/36.44 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1451_0 & $i(all_1451_0)
% 253.33/36.44 | & $i(all_1451_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 253.33/36.44 | $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : !
% 253.33/36.44 | [v8: $i] : ! [v9: $i] : ( ~ (c_Power_Opower__class_Opower(v2) = v4)
% 253.33/36.44 | | ~ (c_Groups_Otimes__class_Otimes(v2) = v3) | ~
% 253.33/36.44 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, all_1451_0) = v6) |
% 253.33/36.44 | ~ (hAPP(v8, v0) = v9) | ~ (hAPP(v5, v6) = v7) | ~ (hAPP(v4, v0)
% 253.33/36.44 | = v5) | ~ (hAPP(v3, v7) = v8) | ~ $i(v2) | ~ $i(v1) | ~
% 253.33/36.44 | $i(v0) | ~ class_Groups_Omonoid__mult(v2) | ~
% 253.33/36.44 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, all_1451_1, v1) |
% 253.33/36.44 | (hAPP(v5, v1) = v9 & $i(v9)))
% 253.33/36.44 |
% 253.33/36.44 | ALPHA: (178) implies:
% 253.33/36.44 | (179) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1451_0
% 253.33/36.44 |
% 253.33/36.44 | DELTA: instantiating (18) with fresh symbols all_1503_0, all_1503_1,
% 253.33/36.44 | all_1503_2 gives:
% 253.33/36.44 | (180) c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1503_1 &
% 253.33/36.44 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1503_2 &
% 253.33/36.44 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1503_0 & $i(all_1503_0)
% 253.33/36.44 | & $i(all_1503_1) & $i(all_1503_2) & ! [v0: $i] : ! [v1: any] : !
% 253.33/36.44 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = all_1503_2
% 253.33/36.44 | | ~ (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v0, v4) = v5) | ~
% 253.33/36.44 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, all_1503_0) = v2) |
% 253.33/36.44 | ~ (hAPP(v3, v0) = v4) | ~ (hAPP(all_1503_1, v2) = v3) | ~ $i(v1)
% 253.33/36.44 | | ~ $i(v0) | ? [v6: $i] : (hAPP(v6, v0) = v5 & hAPP(all_1503_1,
% 253.33/36.44 | v1) = v6 & $i(v6) & $i(v5))) & ! [v0: $i] : ! [v1: $i] : !
% 253.33/36.44 | [v2: int] : (v2 = all_1503_2 | ~ (hAPP(v1, v0) = v2) | ~
% 253.33/36.44 | (hAPP(all_1503_1, all_1503_2) = v1) | ~ $i(v0))
% 253.33/36.44 |
% 253.33/36.44 | ALPHA: (180) implies:
% 253.33/36.44 | (181) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1503_0
% 253.33/36.44 |
% 253.33/36.44 | DELTA: instantiating (55) with fresh symbols all_1518_0, all_1518_1,
% 253.33/36.44 | all_1518_2, all_1518_3 gives:
% 253.33/36.45 | (182) c_Power_Opower__class_Opower(tc_Nat_Onat) = all_1518_2 &
% 253.33/36.45 | c_Groups_Otimes__class_Otimes(tc_Nat_Onat) = all_1518_0 &
% 253.33/36.45 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1518_3 &
% 253.33/36.45 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1518_1 & $i(all_1518_0)
% 253.33/36.45 | & $i(all_1518_1) & $i(all_1518_2) & $i(all_1518_3) & ! [v0: $i] : !
% 253.33/36.45 | [v1: any] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] :
% 253.33/36.45 | ! [v6: $i] : (v1 = all_1518_3 | ~
% 253.33/36.45 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, all_1518_1) = v4) |
% 253.33/36.45 | ~ (hAPP(v3, v5) = v6) | ~ (hAPP(v2, v4) = v5) | ~
% 253.33/36.45 | (hAPP(all_1518_0, v0) = v3) | ~ (hAPP(all_1518_2, v0) = v2) | ~
% 253.33/36.45 | $i(v1) | ~ $i(v0) | (hAPP(v2, v1) = v6 & $i(v6))) & ! [v0: $i] :
% 253.33/36.45 | ! [v1: $i] : ! [v2: int] : (v2 = all_1518_1 | ~ (hAPP(v1,
% 253.33/36.45 | all_1518_3) = v2) | ~ (hAPP(all_1518_2, v0) = v1) | ~ $i(v0))
% 253.33/36.45 |
% 253.33/36.45 | ALPHA: (182) implies:
% 253.33/36.45 | (183) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1518_1
% 253.33/36.45 |
% 253.33/36.45 | DELTA: instantiating (31) with fresh symbols all_1527_0, all_1527_1 gives:
% 253.33/36.45 | (184) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1527_1 &
% 253.33/36.45 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1527_0 & $i(all_1527_0)
% 253.33/36.45 | & $i(all_1527_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 253.33/36.45 | (hAPP(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ hBOOL(v2) | ?
% 253.33/36.45 | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ($i(v4) &
% 253.33/36.45 | ((c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v4, all_1527_0) = v5 &
% 253.33/36.45 | hAPP(v1, v5) = v6 & $i(v6) & $i(v5) & hBOOL(v6) &
% 253.33/36.45 | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v4, v0) & ! [v7:
% 253.33/36.45 | $i] : ! [v8: $i] : ( ~ (hAPP(v1, v7) = v8) | ~ $i(v7) |
% 253.33/36.45 | ~ hBOOL(v8) | ~
% 253.33/36.45 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v7, v4))) |
% 253.33/36.45 | (hAPP(v1, all_1527_1) = v3 & $i(v3) & hBOOL(v3)))))
% 253.33/36.45 |
% 253.33/36.45 | ALPHA: (184) implies:
% 253.33/36.45 | (185) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1527_0
% 253.33/36.45 |
% 253.33/36.45 | DELTA: instantiating (50) with fresh symbols all_1542_0, all_1542_1,
% 253.33/36.45 | all_1542_2, all_1542_3 gives:
% 253.33/36.45 | (186) c_Power_Opower__class_Opower(tc_RealDef_Oreal) = all_1542_0 &
% 253.33/36.45 | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1542_2 &
% 253.33/36.45 | c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = all_1542_3 &
% 253.33/36.45 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1542_1 &
% 253.33/36.45 | $i(all_1542_0) & $i(all_1542_1) & $i(all_1542_2) & $i(all_1542_3) &
% 253.33/36.45 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 253.33/36.45 | ( ~ (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1, all_1542_1) =
% 253.33/36.45 | v2) | ~ (hAPP(v3, v0) = v4) | ~ (hAPP(all_1542_0, v2) = v3) |
% 253.33/36.45 | ~ $i(v1) | ~ $i(v0) | ~
% 253.33/36.45 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_1542_3, v1)
% 253.33/36.45 | | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] :
% 253.33/36.45 | (c_RealDef_Oreal(tc_Nat_Onat, v0) = v5 &
% 253.33/36.45 | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v7, all_1542_1) =
% 253.33/36.45 | v8 & hAPP(v6, v1) = v7 & hAPP(all_1542_2, v5) = v6 & $i(v8) &
% 253.33/36.45 | $i(v7) & $i(v6) & $i(v5) &
% 253.33/36.45 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v8, v4)))
% 253.33/36.45 |
% 253.33/36.45 | ALPHA: (186) implies:
% 253.33/36.45 | (187) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1542_1
% 253.33/36.45 |
% 253.33/36.45 | DELTA: instantiating (52) with fresh symbols all_1557_0, all_1557_1 gives:
% 253.33/36.45 | (188) c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1557_1 &
% 253.33/36.45 | c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1557_0 & $i(all_1557_0)
% 253.33/36.45 | & $i(all_1557_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 253.33/36.45 | $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : !
% 253.33/36.45 | [v8: $i] : ! [v9: $i] : ( ~ (c_Power_Opower__class_Opower(v2) = v3)
% 253.33/36.45 | | ~ (c_Groups_Otimes__class_Otimes(v2) = v5) | ~
% 253.33/36.45 | (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v1, all_1557_0) = v7) |
% 253.33/36.45 | ~ (hAPP(v6, v8) = v9) | ~ (hAPP(v5, v0) = v6) | ~ (hAPP(v4, v7)
% 253.33/36.45 | = v8) | ~ (hAPP(v3, v0) = v4) | ~ $i(v2) | ~ $i(v1) | ~
% 253.33/36.45 | $i(v0) | ~ class_Power_Opower(v2) | ? [v10: $i] : ? [v11: $i] :
% 253.33/36.45 | (( ~ (v1 = all_1557_1) | (v11 = v10 & c_Groups_Oone__class_Oone(v2)
% 253.33/36.45 | = v10 & hAPP(v4, all_1557_1) = v10 & $i(v10))) & (v1 =
% 253.33/36.45 | all_1557_1 | (v10 = v9 & hAPP(v4, v1) = v9 & $i(v9)))))
% 253.33/36.45 |
% 253.33/36.45 | ALPHA: (188) implies:
% 253.33/36.45 | (189) c_Groups_Oone__class_Oone(tc_Nat_Onat) = all_1557_0
% 253.33/36.45 |
% 253.33/36.45 | DELTA: instantiating (15) with fresh symbols all_1578_0, all_1578_1 gives:
% 253.33/36.45 | (190) c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal) = all_1578_0 &
% 253.33/36.45 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1578_1 &
% 253.33/36.45 | $i(all_1578_0) & $i(all_1578_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 253.33/36.45 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 253.33/36.45 | (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v1, v0) = v2) | ~
% 253.33/36.45 | (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, v2, v5) = v6) |
% 253.33/36.45 | ~ (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, all_1578_1, v4)
% 253.33/36.45 | = v5) | ~ (hAPP(v3, v0) = v4) | ~ (hAPP(all_1578_0, v1) = v3) |
% 253.33/36.45 | ~ $i(v1) | ~ $i(v0) | ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 253.33/36.45 | ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ((v12 = v11 &
% 253.33/36.45 | c_Transcendental_Oarctan(v6) = v11 &
% 253.33/36.45 | c_Transcendental_Oarctan(v1) = v9 &
% 253.33/36.45 | c_Transcendental_Oarctan(v0) = v10 &
% 253.33/36.45 | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v9, v10) = v11 &
% 253.33/36.45 | $i(v11) & $i(v10) & $i(v9)) |
% 253.33/36.45 | (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v1) = v7 & $i(v7) &
% 253.33/36.45 | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v7,
% 253.33/36.45 | all_1578_1)) | (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,
% 253.33/36.45 | v0) = v8 & $i(v8) & ~
% 253.33/36.45 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v8,
% 253.33/36.45 | all_1578_1))))
% 253.33/36.45 |
% 253.33/36.45 | ALPHA: (190) implies:
% 253.33/36.45 | (191) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1578_1
% 253.33/36.45 |
% 253.33/36.45 | DELTA: instantiating (45) with fresh symbol all_1584_0 gives:
% 253.33/36.45 | (192) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1584_0 &
% 253.33/36.45 | $i(all_1584_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 253.33/36.45 | $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 253.33/36.45 | (c_RealVector_Onorm__class_Onorm(v3, v4) = v5) | ~ (hAPP(v0, v1) =
% 253.33/36.45 | v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 253.33/36.45 | class_Orderings_Oord(v2) | ~
% 253.33/36.45 | class_RealVector_Oreal__normed__vector(v3) | ? [v6: $i] : ? [v7:
% 253.33/36.45 | $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ($i(v7) &
% 253.33/36.45 | ((c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, all_1584_0, v5) =
% 253.33/36.45 | v6 & $i(v6) & ! [v11: $i] : ! [v12: $i] : ! [v13: $i] : (
% 253.33/36.45 | ~ (c_RealVector_Onorm__class_Onorm(v3, v12) = v13) | ~
% 253.33/36.45 | (hAPP(v0, v11) = v12) | ~ $i(v11) | ~
% 253.33/36.45 | c_Orderings_Oord__class_Oless__eq(v2, v1, v11) |
% 253.33/36.45 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v13, v6)))
% 253.33/36.45 | | (c_Groups_Ominus__class_Ominus(v3, v4, v8) = v9 &
% 253.33/36.45 | c_RealVector_Onorm__class_Onorm(v3, v9) = v10 & hAPP(v0, v7)
% 253.33/36.45 | = v8 & $i(v10) & $i(v9) & $i(v8) &
% 253.33/36.45 | c_Orderings_Oord__class_Oless__eq(v2, v1, v7) & ~
% 253.33/36.45 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v10,
% 253.33/36.45 | all_1584_0)))))
% 253.33/36.45 |
% 253.33/36.45 | ALPHA: (192) implies:
% 253.33/36.45 | (193) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1584_0
% 253.33/36.45 |
% 253.33/36.45 | DELTA: instantiating (14) with fresh symbols all_1587_0, all_1587_1 gives:
% 253.33/36.45 | (194) c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = all_1587_0 &
% 253.33/36.45 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1587_1 &
% 253.33/36.45 | $i(all_1587_0) & $i(all_1587_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 253.33/36.45 | (c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v0, all_1587_0)
% 253.33/36.45 | = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: $i] : ?
% 253.33/36.45 | [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 253.33/36.45 | (( ~ (v2 = all_1587_1) &
% 253.33/36.45 | c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v0) = v2 &
% 253.33/36.45 | $i(v2)) | (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v0,
% 253.33/36.45 | all_1587_0) = v3 &
% 253.33/36.45 | c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v3) = v4 &
% 253.33/36.45 | $i(v4) & $i(v3) &
% 253.33/36.45 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v4,
% 253.33/36.45 | all_1587_1)) |
% 253.33/36.45 | (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v0,
% 253.33/36.45 | c_Complex_Oii) = v6 &
% 253.33/36.45 | c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v6) = v7 &
% 253.33/36.45 | $i(v7) & $i(v6) &
% 253.33/36.45 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v7,
% 253.33/36.45 | all_1587_1)) |
% 253.33/36.45 | (c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v0,
% 253.33/36.45 | c_Complex_Oii) = v8 &
% 253.33/36.45 | c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v8) = v9 &
% 253.33/36.45 | $i(v9) & $i(v8) &
% 253.33/36.45 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v9,
% 253.33/36.45 | all_1587_1)) |
% 253.33/36.45 | (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v1) = v5 &
% 253.33/36.45 | $i(v5) & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v5,
% 253.33/36.45 | all_1587_1))))
% 253.33/36.45 |
% 253.33/36.45 | ALPHA: (194) implies:
% 253.33/36.45 | (195) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1587_1
% 253.33/36.45 |
% 253.33/36.45 | DELTA: instantiating (57) with fresh symbols all_1602_0, all_1602_1,
% 253.33/36.45 | all_1602_2, all_1602_3, all_1602_4, all_1602_5 gives:
% 253.33/36.45 | (196) c_Power_Opower__class_Opower(tc_Complex_Ocomplex) = all_1602_1 &
% 253.33/36.45 | c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex) = all_1602_2 &
% 253.33/36.45 | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = all_1602_4 &
% 253.33/36.45 | c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = all_1602_5 &
% 253.33/36.45 | c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = all_1602_3 &
% 253.33/36.45 | c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1602_0 &
% 253.33/36.45 | $i(all_1602_0) & $i(all_1602_1) & $i(all_1602_2) & $i(all_1602_3) &
% 253.33/36.45 | $i(all_1602_4) & $i(all_1602_5) & ? [v0: any] : ! [v1: any] : !
% 253.33/36.45 | [v2: $i] : (v1 = all_1602_5 | v0 = all_1602_4 | ~ (hAPP(all_1602_2,
% 253.33/36.45 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] :
% 253.33/36.45 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] :
% 253.33/36.45 | (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, all_1602_3, v6) =
% 253.33/36.45 | v7 & c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v7) =
% 253.33/36.45 | v8 & hAPP(v4, v0) = v5 & hAPP(v2, v5) = v6 & hAPP(all_1602_1, v3)
% 253.33/36.45 | = v4 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) &
% 253.33/36.45 | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v8, all_1602_0)))
% 253.33/36.45 |
% 253.33/36.45 | ALPHA: (196) implies:
% 253.33/36.45 | (197) c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = all_1602_0
% 253.33/36.45 |
% 253.33/36.45 | GROUND_INST: instantiating (65) with all_773_1, all_797_0, tc_RealDef_Oreal,
% 253.33/36.45 | simplifying with (78), (81) gives:
% 253.33/36.45 | (198) all_797_0 = all_773_1
% 253.33/36.45 |
% 253.33/36.45 | GROUND_INST: instantiating (65) with all_773_1, all_799_1, tc_RealDef_Oreal,
% 253.33/36.45 | simplifying with (78), (83) gives:
% 253.33/36.45 | (199) all_799_1 = all_773_1
% 253.33/36.45 |
% 253.33/36.45 | GROUND_INST: instantiating (65) with all_799_1, all_824_0, tc_RealDef_Oreal,
% 253.33/36.45 | simplifying with (83), (90) gives:
% 253.33/36.45 | (200) all_824_0 = all_799_1
% 253.33/36.45 |
% 253.33/36.45 | GROUND_INST: instantiating (65) with all_797_0, all_826_0, tc_RealDef_Oreal,
% 253.33/36.45 | simplifying with (81), (92) gives:
% 253.33/36.45 | (201) all_826_0 = all_797_0
% 253.33/36.45 |
% 253.33/36.45 | GROUND_INST: instantiating (65) with all_826_0, all_912_0, tc_RealDef_Oreal,
% 253.33/36.45 | simplifying with (92), (98) gives:
% 253.33/36.46 | (202) all_912_0 = all_826_0
% 253.33/36.46 |
% 253.33/36.46 | GROUND_INST: instantiating (65) with all_912_0, all_915_0, tc_RealDef_Oreal,
% 253.33/36.46 | simplifying with (98), (102) gives:
% 253.33/36.46 | (203) all_915_0 = all_912_0
% 253.33/36.46 |
% 253.33/36.46 | GROUND_INST: instantiating (65) with all_824_0, all_939_0, tc_RealDef_Oreal,
% 253.33/36.46 | simplifying with (90), (106) gives:
% 253.33/36.46 | (204) all_939_0 = all_824_0
% 253.33/36.46 |
% 253.33/36.46 | GROUND_INST: instantiating (65) with all_939_0, all_992_0, tc_RealDef_Oreal,
% 253.33/36.46 | simplifying with (106), (114) gives:
% 253.33/36.46 | (205) all_992_0 = all_939_0
% 253.33/36.46 |
% 253.33/36.46 | GROUND_INST: instantiating (65) with all_992_0, all_1004_0, tc_RealDef_Oreal,
% 253.33/36.46 | simplifying with (114), (118) gives:
% 253.33/36.46 | (206) all_1004_0 = all_992_0
% 253.33/36.46 |
% 253.33/36.46 | GROUND_INST: instantiating (65) with all_1004_0, all_1021_0, tc_RealDef_Oreal,
% 253.33/36.46 | simplifying with (118), (120) gives:
% 253.33/36.46 | (207) all_1021_0 = all_1004_0
% 253.33/36.46 |
% 253.33/36.46 | GROUND_INST: instantiating (65) with all_1021_0, all_1027_1, tc_RealDef_Oreal,
% 253.33/36.46 | simplifying with (120), (122) gives:
% 253.33/36.46 | (208) all_1027_1 = all_1021_0
% 253.33/36.46 |
% 253.33/36.46 | GROUND_INST: instantiating (65) with all_1027_1, all_1043_2, tc_RealDef_Oreal,
% 253.33/36.46 | simplifying with (122), (124) gives:
% 253.33/36.46 | (209) all_1043_2 = all_1027_1
% 253.33/36.46 |
% 253.33/36.46 | GROUND_INST: instantiating (65) with all_915_0, all_1081_2, tc_RealDef_Oreal,
% 253.33/36.46 | simplifying with (102), (128) gives:
% 253.33/36.46 | (210) all_1081_2 = all_915_0
% 253.33/36.46 |
% 253.33/36.46 | GROUND_INST: instantiating (65) with all_1043_2, all_1148_0, tc_RealDef_Oreal,
% 253.33/36.46 | simplifying with (124), (138) gives:
% 253.33/36.46 | (211) all_1148_0 = all_1043_2
% 253.33/36.46 |
% 253.33/36.46 | GROUND_INST: instantiating (65) with all_729_0, all_1148_0, tc_RealDef_Oreal,
% 253.33/36.46 | simplifying with (73), (138) gives:
% 253.33/36.46 | (212) all_1148_0 = all_729_0
% 253.33/36.46 |
% 253.33/36.46 | GROUND_INST: instantiating (65) with all_1148_0, all_1171_0, tc_RealDef_Oreal,
% 253.33/36.46 | simplifying with (138), (145) gives:
% 253.33/36.46 | (213) all_1171_0 = all_1148_0
% 253.33/36.46 |
% 253.33/36.46 | GROUND_INST: instantiating (65) with all_1171_0, all_1263_1, tc_RealDef_Oreal,
% 253.33/36.46 | simplifying with (145), (150) gives:
% 253.33/36.46 | (214) all_1263_1 = all_1171_0
% 253.33/36.46 |
% 253.33/36.46 | GROUND_INST: instantiating (65) with all_1263_1, all_1266_1, tc_RealDef_Oreal,
% 253.33/36.46 | simplifying with (150), (153) gives:
% 253.33/36.46 | (215) all_1266_1 = all_1263_1
% 253.33/36.46 |
% 253.33/36.46 | GROUND_INST: instantiating (65) with all_1266_1, all_1285_1, tc_RealDef_Oreal,
% 253.33/36.46 | simplifying with (153), (156) gives:
% 253.33/36.46 | (216) all_1285_1 = all_1266_1
% 253.33/36.46 |
% 253.33/36.46 | GROUND_INST: instantiating (65) with all_1288_1, all_1331_2, tc_RealDef_Oreal,
% 253.33/36.46 | simplifying with (159), (163) gives:
% 253.33/36.46 | (217) all_1331_2 = all_1288_1
% 253.33/36.46 |
% 253.33/36.46 | GROUND_INST: instantiating (65) with all_1081_2, all_1331_2, tc_RealDef_Oreal,
% 253.33/36.46 | simplifying with (128), (163) gives:
% 253.33/36.46 | (218) all_1331_2 = all_1081_2
% 253.33/36.46 |
% 253.33/36.46 | GROUND_INST: instantiating (65) with all_1288_1, all_1343_2, tc_RealDef_Oreal,
% 253.33/36.46 | simplifying with (159), (165) gives:
% 253.33/36.46 | (219) all_1343_2 = all_1288_1
% 253.33/36.46 |
% 253.33/36.46 | GROUND_INST: instantiating (65) with all_1285_1, all_1445_0, tc_RealDef_Oreal,
% 253.33/36.46 | simplifying with (156), (175) gives:
% 253.33/36.46 | (220) all_1445_0 = all_1285_1
% 253.33/36.46 |
% 253.33/36.46 | GROUND_INST: instantiating (65) with all_1445_0, all_1448_0, tc_RealDef_Oreal,
% 253.33/36.46 | simplifying with (175), (177) gives:
% 253.33/36.46 | (221) all_1448_0 = all_1445_0
% 253.33/36.46 |
% 253.33/36.46 | GROUND_INST: instantiating (65) with all_1331_2, all_1542_1, tc_RealDef_Oreal,
% 253.33/36.46 | simplifying with (163), (187) gives:
% 253.33/36.46 | (222) all_1542_1 = all_1331_2
% 253.33/36.46 |
% 253.33/36.46 | GROUND_INST: instantiating (65) with all_1168_1, all_1542_1, tc_RealDef_Oreal,
% 253.33/36.46 | simplifying with (143), (187) gives:
% 253.33/36.46 | (223) all_1542_1 = all_1168_1
% 253.33/36.46 |
% 253.33/36.46 | GROUND_INST: instantiating (65) with all_1448_0, all_1578_1, tc_RealDef_Oreal,
% 253.33/36.46 | simplifying with (177), (191) gives:
% 253.33/36.46 | (224) all_1578_1 = all_1448_0
% 253.33/36.46 |
% 253.33/36.46 | GROUND_INST: instantiating (65) with all_1331_2, all_1584_0, tc_RealDef_Oreal,
% 253.33/36.46 | simplifying with (163), (193) gives:
% 253.33/36.46 | (225) all_1584_0 = all_1331_2
% 253.33/36.46 |
% 253.33/36.46 | GROUND_INST: instantiating (65) with all_1092_0, all_1584_0, tc_RealDef_Oreal,
% 253.33/36.46 | simplifying with (132), (193) gives:
% 253.33/36.46 | (226) all_1584_0 = all_1092_0
% 253.33/36.46 |
% 253.33/36.46 | GROUND_INST: instantiating (65) with all_1343_2, all_1587_1, tc_RealDef_Oreal,
% 253.33/36.46 | simplifying with (165), (195) gives:
% 253.33/36.46 | (227) all_1587_1 = all_1343_2
% 253.33/36.46 |
% 253.33/36.46 | GROUND_INST: instantiating (65) with all_713_0, all_1587_1, tc_RealDef_Oreal,
% 253.33/36.46 | simplifying with (70), (195) gives:
% 253.33/36.46 | (228) all_1587_1 = all_713_0
% 253.33/36.46 |
% 253.33/36.46 | GROUND_INST: instantiating (65) with all_1578_1, all_1602_0, tc_RealDef_Oreal,
% 253.33/36.46 | simplifying with (191), (197) gives:
% 253.33/36.46 | (229) all_1602_0 = all_1578_1
% 253.33/36.46 |
% 253.33/36.46 | GROUND_INST: instantiating (65) with all_1104_0, all_1602_0, tc_RealDef_Oreal,
% 253.33/36.46 | simplifying with (134), (197) gives:
% 253.33/36.46 | (230) all_1602_0 = all_1104_0
% 253.33/36.46 |
% 253.33/36.46 | GROUND_INST: instantiating (65) with all_742_0, all_799_0, tc_Nat_Onat,
% 253.33/36.46 | simplifying with (75), (84) gives:
% 253.33/36.46 | (231) all_799_0 = all_742_0
% 253.33/36.46 |
% 253.33/36.46 | GROUND_INST: instantiating (65) with all_957_0, all_1001_1, tc_Nat_Onat,
% 253.33/36.46 | simplifying with (110), (116) gives:
% 253.33/36.46 | (232) all_1001_1 = all_957_0
% 253.33/36.46 |
% 253.33/36.46 | GROUND_INST: instantiating (65) with all_1001_1, all_1083_1, tc_Nat_Onat,
% 253.33/36.46 | simplifying with (116), (130) gives:
% 253.33/36.46 | (233) all_1083_1 = all_1001_1
% 253.33/36.46 |
% 253.33/36.46 | GROUND_INST: instantiating (65) with all_1083_1, all_1145_1, tc_Nat_Onat,
% 253.33/36.46 | simplifying with (130), (136) gives:
% 253.33/36.46 | (234) all_1145_1 = all_1083_1
% 253.33/36.46 |
% 253.33/36.46 | GROUND_INST: instantiating (65) with all_1083_1, all_1148_1, tc_Nat_Onat,
% 253.33/36.46 | simplifying with (130), (139) gives:
% 253.33/36.46 | (235) all_1148_1 = all_1083_1
% 253.33/36.46 |
% 253.33/36.46 | GROUND_INST: instantiating (65) with all_1145_1, all_1171_1, tc_Nat_Onat,
% 253.33/36.46 | simplifying with (136), (146) gives:
% 253.33/36.46 | (236) all_1171_1 = all_1145_1
% 253.33/36.46 |
% 253.33/36.46 | GROUND_INST: instantiating (65) with all_1171_1, all_1240_0, tc_Nat_Onat,
% 253.33/36.46 | simplifying with (146), (148) gives:
% 253.33/36.46 | (237) all_1240_0 = all_1171_1
% 253.33/36.46 |
% 253.33/36.46 | GROUND_INST: instantiating (65) with all_1240_0, all_1263_0, tc_Nat_Onat,
% 253.33/36.46 | simplifying with (148), (151) gives:
% 253.33/36.46 | (238) all_1263_0 = all_1240_0
% 253.33/36.46 |
% 253.33/36.46 | GROUND_INST: instantiating (65) with all_1148_1, all_1266_0, tc_Nat_Onat,
% 253.33/36.46 | simplifying with (139), (154) gives:
% 253.33/36.46 | (239) all_1266_0 = all_1148_1
% 253.33/36.46 |
% 253.33/36.46 | GROUND_INST: instantiating (65) with all_1001_1, all_1306_0, tc_Nat_Onat,
% 253.33/36.46 | simplifying with (116), (161) gives:
% 253.33/36.46 | (240) all_1306_0 = all_1001_1
% 253.33/36.46 |
% 253.33/36.46 | GROUND_INST: instantiating (65) with all_945_0, all_1306_0, tc_Nat_Onat,
% 253.33/36.46 | simplifying with (108), (161) gives:
% 253.33/36.46 | (241) all_1306_0 = all_945_0
% 253.33/36.46 |
% 253.33/36.46 | GROUND_INST: instantiating (65) with all_855_0, all_1306_0, tc_Nat_Onat,
% 253.33/36.46 | simplifying with (96), (161) gives:
% 253.33/36.46 | (242) all_1306_0 = all_855_0
% 253.33/36.46 |
% 253.33/36.46 | GROUND_INST: instantiating (65) with all_1001_1, all_1376_1, tc_Nat_Onat,
% 253.33/36.46 | simplifying with (116), (169) gives:
% 253.33/36.46 | (243) all_1376_1 = all_1001_1
% 253.33/36.46 |
% 253.33/36.46 | GROUND_INST: instantiating (65) with all_986_0, all_1376_1, tc_Nat_Onat,
% 253.33/36.46 | simplifying with (112), (169) gives:
% 253.33/36.46 | (244) all_1376_1 = all_986_0
% 253.33/36.46 |
% 253.33/36.46 | GROUND_INST: instantiating (65) with all_1370_0, all_1400_0, tc_Nat_Onat,
% 253.42/36.46 | simplifying with (167), (171) gives:
% 253.42/36.46 | (245) all_1400_0 = all_1370_0
% 253.42/36.46 |
% 253.42/36.46 | GROUND_INST: instantiating (65) with all_1285_0, all_1400_0, tc_Nat_Onat,
% 253.42/36.46 | simplifying with (157), (171) gives:
% 253.42/36.46 | (246) all_1400_0 = all_1285_0
% 253.42/36.46 |
% 253.42/36.46 | GROUND_INST: instantiating (65) with all_1266_0, all_1400_0, tc_Nat_Onat,
% 253.42/36.46 | simplifying with (154), (171) gives:
% 253.42/36.46 | (247) all_1400_0 = all_1266_0
% 253.42/36.46 |
% 253.42/36.46 | GROUND_INST: instantiating (65) with all_1057_0, all_1400_0, tc_Nat_Onat,
% 253.42/36.46 | simplifying with (126), (171) gives:
% 253.42/36.46 | (248) all_1400_0 = all_1057_0
% 253.42/36.46 |
% 253.42/36.46 | GROUND_INST: instantiating (65) with all_1376_1, all_1426_0, tc_Nat_Onat,
% 253.42/36.46 | simplifying with (169), (173) gives:
% 253.42/36.46 | (249) all_1426_0 = all_1376_1
% 253.42/36.46 |
% 253.42/36.46 | GROUND_INST: instantiating (65) with all_855_0, all_1451_0, tc_Nat_Onat,
% 253.42/36.46 | simplifying with (96), (179) gives:
% 253.42/36.46 | (250) all_1451_0 = all_855_0
% 253.42/36.46 |
% 253.42/36.46 | GROUND_INST: instantiating (65) with all_826_1, all_1451_0, tc_Nat_Onat,
% 253.42/36.46 | simplifying with (93), (179) gives:
% 253.42/36.46 | (251) all_1451_0 = all_826_1
% 253.42/36.46 |
% 253.42/36.46 | GROUND_INST: instantiating (65) with all_799_0, all_1451_0, tc_Nat_Onat,
% 253.42/36.46 | simplifying with (84), (179) gives:
% 253.42/36.46 | (252) all_1451_0 = all_799_0
% 253.42/36.46 |
% 253.42/36.46 | GROUND_INST: instantiating (65) with all_1426_0, all_1503_0, tc_Nat_Onat,
% 253.42/36.46 | simplifying with (173), (181) gives:
% 253.42/36.46 | (253) all_1503_0 = all_1426_0
% 253.42/36.46 |
% 253.42/36.46 | GROUND_INST: instantiating (65) with all_1503_0, all_1518_1, tc_Nat_Onat,
% 253.42/36.46 | simplifying with (181), (183) gives:
% 253.42/36.46 | (254) all_1518_1 = all_1503_0
% 253.42/36.46 |
% 253.42/36.46 | GROUND_INST: instantiating (65) with all_1263_0, all_1527_0, tc_Nat_Onat,
% 253.42/36.46 | simplifying with (151), (185) gives:
% 253.42/36.47 | (255) all_1527_0 = all_1263_0
% 253.42/36.47 |
% 253.42/36.47 | GROUND_INST: instantiating (65) with all_773_0, all_1527_0, tc_Nat_Onat,
% 253.42/36.47 | simplifying with (79), (185) gives:
% 253.42/36.47 | (256) all_1527_0 = all_773_0
% 253.42/36.47 |
% 253.42/36.47 | GROUND_INST: instantiating (65) with all_1518_1, all_1557_0, tc_Nat_Onat,
% 253.42/36.47 | simplifying with (183), (189) gives:
% 253.42/36.47 | (257) all_1557_0 = all_1518_1
% 253.42/36.47 |
% 253.42/36.47 | GROUND_INST: instantiating (65) with all_1156_0, all_1557_0, tc_Nat_Onat,
% 253.42/36.47 | simplifying with (141), (189) gives:
% 253.42/36.47 | (258) all_1557_0 = all_1156_0
% 253.42/36.47 |
% 253.42/36.47 | GROUND_INST: instantiating (67) with all_818_1, all_915_2, v_z, v_w____,
% 253.42/36.47 | tc_Complex_Ocomplex, simplifying with (88), (104) gives:
% 253.42/36.47 | (259) all_915_2 = all_818_1
% 253.42/36.47 |
% 253.42/36.47 | COMBINE_EQS: (229), (230) imply:
% 253.42/36.47 | (260) all_1578_1 = all_1104_0
% 253.42/36.47 |
% 253.42/36.47 | SIMP: (260) implies:
% 253.42/36.47 | (261) all_1578_1 = all_1104_0
% 253.42/36.47 |
% 253.42/36.47 | COMBINE_EQS: (227), (228) imply:
% 253.42/36.47 | (262) all_1343_2 = all_713_0
% 253.42/36.47 |
% 253.42/36.47 | SIMP: (262) implies:
% 253.42/36.47 | (263) all_1343_2 = all_713_0
% 253.42/36.47 |
% 253.42/36.47 | COMBINE_EQS: (225), (226) imply:
% 253.42/36.47 | (264) all_1331_2 = all_1092_0
% 253.42/36.47 |
% 253.42/36.47 | SIMP: (264) implies:
% 253.42/36.47 | (265) all_1331_2 = all_1092_0
% 253.42/36.47 |
% 253.42/36.47 | COMBINE_EQS: (224), (261) imply:
% 253.42/36.47 | (266) all_1448_0 = all_1104_0
% 253.42/36.47 |
% 253.42/36.47 | SIMP: (266) implies:
% 253.42/36.47 | (267) all_1448_0 = all_1104_0
% 253.42/36.47 |
% 253.42/36.47 | COMBINE_EQS: (257), (258) imply:
% 253.42/36.47 | (268) all_1518_1 = all_1156_0
% 253.42/36.47 |
% 253.42/36.47 | SIMP: (268) implies:
% 253.42/36.47 | (269) all_1518_1 = all_1156_0
% 253.42/36.47 |
% 253.42/36.47 | COMBINE_EQS: (222), (223) imply:
% 253.42/36.47 | (270) all_1331_2 = all_1168_1
% 253.42/36.47 |
% 253.42/36.47 | SIMP: (270) implies:
% 253.42/36.47 | (271) all_1331_2 = all_1168_1
% 253.42/36.47 |
% 253.42/36.47 | COMBINE_EQS: (255), (256) imply:
% 253.42/36.47 | (272) all_1263_0 = all_773_0
% 253.42/36.47 |
% 253.42/36.47 | SIMP: (272) implies:
% 253.42/36.47 | (273) all_1263_0 = all_773_0
% 253.42/36.47 |
% 253.42/36.47 | COMBINE_EQS: (254), (269) imply:
% 253.42/36.47 | (274) all_1503_0 = all_1156_0
% 253.42/36.47 |
% 253.42/36.47 | SIMP: (274) implies:
% 253.42/36.47 | (275) all_1503_0 = all_1156_0
% 253.42/36.47 |
% 253.42/36.47 | COMBINE_EQS: (253), (275) imply:
% 253.42/36.47 | (276) all_1426_0 = all_1156_0
% 253.42/36.47 |
% 253.42/36.47 | SIMP: (276) implies:
% 253.42/36.47 | (277) all_1426_0 = all_1156_0
% 253.42/36.47 |
% 253.42/36.47 | COMBINE_EQS: (250), (251) imply:
% 253.42/36.47 | (278) all_855_0 = all_826_1
% 253.42/36.47 |
% 253.42/36.47 | SIMP: (278) implies:
% 253.42/36.47 | (279) all_855_0 = all_826_1
% 253.42/36.47 |
% 253.42/36.47 | COMBINE_EQS: (251), (252) imply:
% 253.42/36.47 | (280) all_826_1 = all_799_0
% 253.42/36.47 |
% 253.42/36.47 | COMBINE_EQS: (221), (267) imply:
% 253.42/36.47 | (281) all_1445_0 = all_1104_0
% 253.42/36.47 |
% 253.42/36.47 | SIMP: (281) implies:
% 253.42/36.47 | (282) all_1445_0 = all_1104_0
% 253.42/36.47 |
% 253.42/36.47 | COMBINE_EQS: (220), (282) imply:
% 253.42/36.47 | (283) all_1285_1 = all_1104_0
% 253.42/36.47 |
% 253.42/36.47 | SIMP: (283) implies:
% 253.42/36.47 | (284) all_1285_1 = all_1104_0
% 253.42/36.47 |
% 253.42/36.47 | COMBINE_EQS: (249), (277) imply:
% 253.42/36.47 | (285) all_1376_1 = all_1156_0
% 253.42/36.47 |
% 253.42/36.47 | SIMP: (285) implies:
% 253.42/36.47 | (286) all_1376_1 = all_1156_0
% 253.42/36.47 |
% 253.42/36.47 | COMBINE_EQS: (245), (248) imply:
% 253.42/36.47 | (287) all_1370_0 = all_1057_0
% 253.42/36.47 |
% 253.42/36.47 | COMBINE_EQS: (245), (246) imply:
% 253.42/36.47 | (288) all_1370_0 = all_1285_0
% 253.42/36.47 |
% 253.42/36.47 | COMBINE_EQS: (245), (247) imply:
% 253.42/36.47 | (289) all_1370_0 = all_1266_0
% 253.42/36.47 |
% 253.42/36.47 | COMBINE_EQS: (244), (286) imply:
% 253.42/36.47 | (290) all_1156_0 = all_986_0
% 253.42/36.47 |
% 253.42/36.47 | COMBINE_EQS: (243), (286) imply:
% 253.42/36.47 | (291) all_1156_0 = all_1001_1
% 253.42/36.47 |
% 253.42/36.47 | COMBINE_EQS: (288), (289) imply:
% 253.42/36.47 | (292) all_1285_0 = all_1266_0
% 253.42/36.47 |
% 253.42/36.47 | COMBINE_EQS: (287), (288) imply:
% 253.42/36.47 | (293) all_1285_0 = all_1057_0
% 253.42/36.47 |
% 253.42/36.47 | COMBINE_EQS: (219), (263) imply:
% 253.42/36.47 | (294) all_1288_1 = all_713_0
% 253.42/36.47 |
% 253.42/36.47 | SIMP: (294) implies:
% 253.42/36.47 | (295) all_1288_1 = all_713_0
% 253.42/36.47 |
% 253.42/36.47 | COMBINE_EQS: (218), (271) imply:
% 253.42/36.47 | (296) all_1168_1 = all_1081_2
% 253.42/36.47 |
% 253.42/36.47 | COMBINE_EQS: (217), (271) imply:
% 253.42/36.47 | (297) all_1288_1 = all_1168_1
% 253.42/36.47 |
% 253.42/36.47 | SIMP: (297) implies:
% 253.42/36.47 | (298) all_1288_1 = all_1168_1
% 253.42/36.47 |
% 253.42/36.47 | COMBINE_EQS: (265), (271) imply:
% 253.42/36.47 | (299) all_1168_1 = all_1092_0
% 253.42/36.47 |
% 253.42/36.47 | COMBINE_EQS: (240), (241) imply:
% 253.42/36.47 | (300) all_1001_1 = all_945_0
% 253.42/36.47 |
% 253.42/36.47 | SIMP: (300) implies:
% 253.42/36.47 | (301) all_1001_1 = all_945_0
% 253.42/36.47 |
% 253.42/36.47 | COMBINE_EQS: (241), (242) imply:
% 253.42/36.47 | (302) all_945_0 = all_855_0
% 253.42/36.47 |
% 253.42/36.47 | COMBINE_EQS: (295), (298) imply:
% 253.42/36.47 | (303) all_1168_1 = all_713_0
% 253.42/36.47 |
% 253.42/36.47 | SIMP: (303) implies:
% 253.42/36.47 | (304) all_1168_1 = all_713_0
% 253.42/36.47 |
% 253.42/36.47 | COMBINE_EQS: (292), (293) imply:
% 253.42/36.47 | (305) all_1266_0 = all_1057_0
% 253.42/36.47 |
% 253.42/36.47 | SIMP: (305) implies:
% 253.42/36.47 | (306) all_1266_0 = all_1057_0
% 253.42/36.47 |
% 253.42/36.47 | COMBINE_EQS: (216), (284) imply:
% 253.42/36.47 | (307) all_1266_1 = all_1104_0
% 253.42/36.47 |
% 253.42/36.47 | SIMP: (307) implies:
% 253.42/36.47 | (308) all_1266_1 = all_1104_0
% 253.42/36.47 |
% 253.42/36.47 | COMBINE_EQS: (239), (306) imply:
% 253.42/36.47 | (309) all_1148_1 = all_1057_0
% 253.42/36.47 |
% 253.42/36.47 | SIMP: (309) implies:
% 253.42/36.47 | (310) all_1148_1 = all_1057_0
% 253.42/36.47 |
% 253.42/36.47 | COMBINE_EQS: (215), (308) imply:
% 253.42/36.47 | (311) all_1263_1 = all_1104_0
% 253.42/36.47 |
% 253.42/36.47 | SIMP: (311) implies:
% 253.42/36.47 | (312) all_1263_1 = all_1104_0
% 253.42/36.47 |
% 253.42/36.47 | COMBINE_EQS: (238), (273) imply:
% 253.42/36.47 | (313) all_1240_0 = all_773_0
% 253.42/36.47 |
% 253.42/36.47 | SIMP: (313) implies:
% 253.42/36.47 | (314) all_1240_0 = all_773_0
% 253.42/36.47 |
% 253.42/36.47 | COMBINE_EQS: (214), (312) imply:
% 253.42/36.47 | (315) all_1171_0 = all_1104_0
% 253.42/36.47 |
% 253.42/36.47 | SIMP: (315) implies:
% 253.42/36.47 | (316) all_1171_0 = all_1104_0
% 253.42/36.47 |
% 253.42/36.47 | COMBINE_EQS: (237), (314) imply:
% 253.42/36.47 | (317) all_1171_1 = all_773_0
% 253.42/36.47 |
% 253.42/36.47 | SIMP: (317) implies:
% 253.42/36.47 | (318) all_1171_1 = all_773_0
% 253.42/36.47 |
% 253.42/36.47 | COMBINE_EQS: (213), (316) imply:
% 253.42/36.47 | (319) all_1148_0 = all_1104_0
% 253.42/36.47 |
% 253.42/36.47 | SIMP: (319) implies:
% 253.42/36.47 | (320) all_1148_0 = all_1104_0
% 253.42/36.47 |
% 253.42/36.47 | COMBINE_EQS: (236), (318) imply:
% 253.42/36.47 | (321) all_1145_1 = all_773_0
% 253.42/36.47 |
% 253.42/36.47 | SIMP: (321) implies:
% 253.42/36.47 | (322) all_1145_1 = all_773_0
% 253.42/36.47 |
% 253.42/36.47 | COMBINE_EQS: (299), (304) imply:
% 253.42/36.47 | (323) all_1092_0 = all_713_0
% 253.42/36.47 |
% 253.42/36.47 | COMBINE_EQS: (296), (299) imply:
% 253.42/36.47 | (324) all_1092_0 = all_1081_2
% 253.42/36.47 |
% 253.42/36.47 | COMBINE_EQS: (290), (291) imply:
% 253.42/36.47 | (325) all_1001_1 = all_986_0
% 253.42/36.47 |
% 253.42/36.47 | SIMP: (325) implies:
% 253.42/36.47 | (326) all_1001_1 = all_986_0
% 253.42/36.47 |
% 253.42/36.47 | COMBINE_EQS: (211), (320) imply:
% 253.42/36.47 | (327) all_1104_0 = all_1043_2
% 253.42/36.47 |
% 253.42/36.47 | COMBINE_EQS: (212), (320) imply:
% 253.42/36.47 | (328) all_1104_0 = all_729_0
% 253.42/36.47 |
% 253.42/36.47 | COMBINE_EQS: (235), (310) imply:
% 253.42/36.47 | (329) all_1083_1 = all_1057_0
% 253.42/36.47 |
% 253.42/36.47 | SIMP: (329) implies:
% 253.42/36.47 | (330) all_1083_1 = all_1057_0
% 253.42/36.47 |
% 253.42/36.47 | COMBINE_EQS: (234), (322) imply:
% 253.42/36.47 | (331) all_1083_1 = all_773_0
% 253.42/36.47 |
% 253.42/36.47 | SIMP: (331) implies:
% 253.42/36.47 | (332) all_1083_1 = all_773_0
% 253.42/36.47 |
% 253.42/36.47 | COMBINE_EQS: (327), (328) imply:
% 253.42/36.47 | (333) all_1043_2 = all_729_0
% 253.42/36.47 |
% 253.42/36.47 | SIMP: (333) implies:
% 253.42/36.47 | (334) all_1043_2 = all_729_0
% 253.42/36.47 |
% 253.42/36.47 | COMBINE_EQS: (323), (324) imply:
% 253.42/36.47 | (335) all_1081_2 = all_713_0
% 253.42/36.47 |
% 253.42/36.47 | SIMP: (335) implies:
% 253.42/36.47 | (336) all_1081_2 = all_713_0
% 253.42/36.47 |
% 253.42/36.47 | COMBINE_EQS: (233), (330) imply:
% 253.42/36.47 | (337) all_1057_0 = all_1001_1
% 253.42/36.47 |
% 253.42/36.47 | COMBINE_EQS: (330), (332) imply:
% 253.42/36.47 | (338) all_1057_0 = all_773_0
% 253.42/36.47 |
% 253.42/36.47 | COMBINE_EQS: (210), (336) imply:
% 253.42/36.47 | (339) all_915_0 = all_713_0
% 253.42/36.47 |
% 253.42/36.47 | SIMP: (339) implies:
% 253.42/36.47 | (340) all_915_0 = all_713_0
% 253.42/36.47 |
% 253.42/36.47 | COMBINE_EQS: (337), (338) imply:
% 253.42/36.47 | (341) all_1001_1 = all_773_0
% 253.42/36.47 |
% 253.42/36.47 | SIMP: (341) implies:
% 253.42/36.47 | (342) all_1001_1 = all_773_0
% 253.42/36.47 |
% 253.42/36.47 | COMBINE_EQS: (209), (334) imply:
% 253.42/36.47 | (343) all_1027_1 = all_729_0
% 253.42/36.47 |
% 253.42/36.47 | SIMP: (343) implies:
% 253.42/36.47 | (344) all_1027_1 = all_729_0
% 253.42/36.47 |
% 253.42/36.47 | COMBINE_EQS: (208), (344) imply:
% 253.42/36.47 | (345) all_1021_0 = all_729_0
% 253.42/36.47 |
% 253.42/36.47 | SIMP: (345) implies:
% 253.42/36.47 | (346) all_1021_0 = all_729_0
% 253.42/36.47 |
% 253.42/36.47 | COMBINE_EQS: (207), (346) imply:
% 253.42/36.47 | (347) all_1004_0 = all_729_0
% 253.42/36.47 |
% 253.42/36.47 | SIMP: (347) implies:
% 253.42/36.47 | (348) all_1004_0 = all_729_0
% 253.42/36.47 |
% 253.42/36.47 | COMBINE_EQS: (206), (348) imply:
% 253.42/36.47 | (349) all_992_0 = all_729_0
% 253.42/36.47 |
% 253.42/36.47 | SIMP: (349) implies:
% 253.42/36.47 | (350) all_992_0 = all_729_0
% 253.42/36.47 |
% 253.42/36.47 | COMBINE_EQS: (232), (326) imply:
% 253.42/36.47 | (351) all_986_0 = all_957_0
% 253.42/36.47 |
% 253.42/36.47 | COMBINE_EQS: (301), (326) imply:
% 253.42/36.47 | (352) all_986_0 = all_945_0
% 253.42/36.47 |
% 253.42/36.47 | COMBINE_EQS: (326), (342) imply:
% 253.42/36.47 | (353) all_986_0 = all_773_0
% 253.42/36.47 |
% 253.42/36.47 | COMBINE_EQS: (205), (350) imply:
% 253.42/36.47 | (354) all_939_0 = all_729_0
% 253.42/36.47 |
% 253.42/36.47 | SIMP: (354) implies:
% 253.42/36.48 | (355) all_939_0 = all_729_0
% 253.42/36.48 |
% 253.42/36.48 | COMBINE_EQS: (351), (352) imply:
% 253.42/36.48 | (356) all_957_0 = all_945_0
% 253.42/36.48 |
% 253.42/36.48 | COMBINE_EQS: (351), (353) imply:
% 253.42/36.48 | (357) all_957_0 = all_773_0
% 253.42/36.48 |
% 253.42/36.48 | COMBINE_EQS: (356), (357) imply:
% 253.42/36.48 | (358) all_945_0 = all_773_0
% 253.42/36.48 |
% 253.42/36.48 | SIMP: (358) implies:
% 253.42/36.48 | (359) all_945_0 = all_773_0
% 253.42/36.48 |
% 253.42/36.48 | COMBINE_EQS: (302), (359) imply:
% 253.42/36.48 | (360) all_855_0 = all_773_0
% 253.42/36.48 |
% 253.42/36.48 | SIMP: (360) implies:
% 253.42/36.48 | (361) all_855_0 = all_773_0
% 253.42/36.48 |
% 253.42/36.48 | COMBINE_EQS: (204), (355) imply:
% 253.42/36.48 | (362) all_824_0 = all_729_0
% 253.42/36.48 |
% 253.42/36.48 | SIMP: (362) implies:
% 253.42/36.48 | (363) all_824_0 = all_729_0
% 253.42/36.48 |
% 253.42/36.48 | COMBINE_EQS: (203), (340) imply:
% 253.42/36.48 | (364) all_912_0 = all_713_0
% 253.42/36.48 |
% 253.42/36.48 | SIMP: (364) implies:
% 253.42/36.48 | (365) all_912_0 = all_713_0
% 253.42/36.48 |
% 253.42/36.48 | COMBINE_EQS: (202), (365) imply:
% 253.42/36.48 | (366) all_826_0 = all_713_0
% 253.42/36.48 |
% 253.42/36.48 | SIMP: (366) implies:
% 253.42/36.48 | (367) all_826_0 = all_713_0
% 253.42/36.48 |
% 253.42/36.48 | COMBINE_EQS: (279), (361) imply:
% 253.42/36.48 | (368) all_826_1 = all_773_0
% 253.42/36.48 |
% 253.42/36.48 | SIMP: (368) implies:
% 253.42/36.48 | (369) all_826_1 = all_773_0
% 253.42/36.48 |
% 253.42/36.48 | COMBINE_EQS: (201), (367) imply:
% 253.42/36.48 | (370) all_797_0 = all_713_0
% 253.42/36.48 |
% 253.42/36.48 | SIMP: (370) implies:
% 253.42/36.48 | (371) all_797_0 = all_713_0
% 253.42/36.48 |
% 253.42/36.48 | COMBINE_EQS: (280), (369) imply:
% 253.42/36.48 | (372) all_799_0 = all_773_0
% 253.42/36.48 |
% 253.42/36.48 | SIMP: (372) implies:
% 253.42/36.48 | (373) all_799_0 = all_773_0
% 253.42/36.48 |
% 253.42/36.48 | COMBINE_EQS: (200), (363) imply:
% 253.42/36.48 | (374) all_799_1 = all_729_0
% 253.42/36.48 |
% 253.42/36.48 | SIMP: (374) implies:
% 253.42/36.48 | (375) all_799_1 = all_729_0
% 253.42/36.48 |
% 253.42/36.48 | COMBINE_EQS: (231), (373) imply:
% 253.42/36.48 | (376) all_773_0 = all_742_0
% 253.42/36.48 |
% 253.42/36.48 | COMBINE_EQS: (199), (375) imply:
% 253.42/36.48 | (377) all_773_1 = all_729_0
% 253.42/36.48 |
% 253.42/36.48 | SIMP: (377) implies:
% 253.42/36.48 | (378) all_773_1 = all_729_0
% 253.42/36.48 |
% 253.42/36.48 | COMBINE_EQS: (198), (371) imply:
% 253.42/36.48 | (379) all_773_1 = all_713_0
% 253.42/36.48 |
% 253.42/36.48 | SIMP: (379) implies:
% 253.42/36.48 | (380) all_773_1 = all_713_0
% 253.42/36.48 |
% 253.42/36.48 | COMBINE_EQS: (378), (380) imply:
% 253.42/36.48 | (381) all_729_0 = all_713_0
% 253.42/36.48 |
% 253.42/36.48 | COMBINE_EQS: (369), (376) imply:
% 253.42/36.48 | (382) all_826_1 = all_742_0
% 253.42/36.48 |
% 253.42/36.48 | REDUCE: (94), (367), (382) imply:
% 253.42/36.48 | (383) c_RealDef_Oreal(tc_Nat_Onat, all_742_0) = all_713_0
% 253.42/36.48 |
% 253.42/36.48 | REDUCE: (103), (259) imply:
% 253.42/36.48 | (384) c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, all_818_1) =
% 253.42/36.48 | all_915_1
% 253.42/36.48 |
% 253.42/36.48 | REDUCE: (77), (376) imply:
% 253.42/36.48 | (385) $i(all_742_0)
% 253.42/36.48 |
% 253.42/36.48 | REDUCE: (72), (381) imply:
% 253.42/36.48 | (386) $i(all_713_0)
% 253.42/36.48 |
% 253.42/36.48 | REDUCE: (100), (340) imply:
% 253.42/36.48 | (387) ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_915_1,
% 253.42/36.48 | all_713_0)
% 253.42/36.48 |
% 253.42/36.48 | GROUND_INST: instantiating (66) with all_818_0, all_915_1, all_818_1,
% 253.42/36.48 | tc_Complex_Ocomplex, simplifying with (87), (384) gives:
% 253.42/36.48 | (388) all_915_1 = all_818_0
% 253.42/36.48 |
% 253.42/36.48 | REDUCE: (101), (388) imply:
% 253.42/36.48 | (389) $i(all_818_0)
% 253.42/36.48 |
% 253.42/36.48 | REDUCE: (387), (388) imply:
% 253.42/36.48 | (390) ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_818_0,
% 253.42/36.48 | all_713_0)
% 253.42/36.48 |
% 253.42/36.48 | GROUND_INST: instantiating (6) with v_da____, all_818_0, tc_RealDef_Oreal,
% 253.42/36.48 | simplifying with (8), (58), (62), (86), (389) gives:
% 253.42/36.48 | (391) c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, all_818_0,
% 253.42/36.48 | v_da____)
% 253.42/36.48 |
% 253.42/36.48 | GROUND_INST: instantiating (6) with all_713_0, v_da____, tc_RealDef_Oreal,
% 253.42/36.48 | simplifying with (8), (58), (62), (69), (386) gives:
% 253.42/36.48 | (392) c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v_da____,
% 253.42/36.48 | all_713_0)
% 253.42/36.48 |
% 253.42/36.48 | GROUND_INST: instantiating (fact_norm__minus__commute) with v_w____, v_z,
% 253.42/36.48 | tc_Complex_Ocomplex, all_818_1, all_818_0, simplifying with (59),
% 253.42/36.48 | (60), (61), (63), (87), (88) gives:
% 253.42/36.48 | (393) ? [v0: $i] : (c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,
% 253.42/36.48 | v_z, v_w____) = v0 &
% 253.42/36.48 | c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v0) =
% 253.42/36.48 | all_818_0 & $i(v0) & $i(all_818_0))
% 253.42/36.48 |
% 253.42/36.48 | GROUND_INST: instantiating (32) with all_742_0, all_713_0, simplifying with
% 253.42/36.48 | (383), (385) gives:
% 253.42/36.48 | (394) c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, all_713_0) = all_713_0 &
% 253.42/36.48 | $i(all_713_0)
% 253.42/36.48 |
% 253.42/36.48 | DELTA: instantiating (393) with fresh symbol all_1739_0 gives:
% 253.42/36.48 | (395) c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_z, v_w____) =
% 253.42/36.48 | all_1739_0 & c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,
% 253.42/36.48 | all_1739_0) = all_818_0 & $i(all_1739_0) & $i(all_818_0)
% 253.42/36.48 |
% 253.42/36.48 | GROUND_INST: instantiating (4) with all_713_0, v_da____, all_818_0,
% 253.42/36.48 | simplifying with (8), (386), (389), (390), (391), (392) gives:
% 253.42/36.48 | (396) $false
% 253.42/36.48 |
% 253.42/36.48 | CLOSE: (396) is inconsistent.
% 253.42/36.48 |
% 253.42/36.48 End of proof
% 253.42/36.48 % SZS output end Proof for theBenchmark
% 253.42/36.48
% 253.42/36.48 35864ms
%------------------------------------------------------------------------------